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Investigation of the acoustical and airflow performance of interior natural ventilation openings Bibby, Chris 2011

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INVESTIGATION OF THE ACOUSTIC AND AIRFLOW PERFORMANCE OF INTERIOR NATURAL VENTILATION OPENINGS  by Chris Bibby  B.A.Sc., The University of British Columbia, 2009  A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF  MASTER OF APPLIED SCIENCE in THE FACULTY OF GRADUATE STUDIES (MECHANICAL ENGINEERING)  THE UNIVERSITY OF BRITISH COLUMBIA (VANCOUVER)  December 2011  © Chris Bibby, 2011  Abstract Natural ventilation is being adopted in building design to reduce building operational energy usage and increasing building occupant comfort. Unfortunately, ventilation openings in interior partitions of naturally ventilated buildings also reduce the noise isolation across the partition, resulting in a poor acoustical environment – for example, insufficient privacy and excessive annoyance. This work moves toward an understanding of, and design methodology for, interior natural ventilation opening silencers which will allow design optimization for both airflow and noise isolation. An optimization parameter is defined in terms of both airflow and acoustical transmission performance. Using a simple diffuse-field model, factors that affect acoustical privacy between two spaces separated by a partition are investigated, showing the relationship between ventilation opening acoustical performance and acoustical privacy. In order to maintain the privacy provided by a partition it is shown that the sound energy transmitted through the ventilation opening should not exceed 10% of that transmitted through the remainder of the partition. Ventilation openings and ventilation opening silencers in naturally ventilated buildings are studied experimentally to gain an understanding of current design practices. Airflow and acoustical performance of 19 ventilation opening and ventilation opening silencer types were measured in a purpose-built lab facility. Cross talk silencers are shown to have the highest performance of all silencer types tested. Lining the ceiling above a slot ventilation opening was measured to increase the transmission loss by 3 to 6 dB. A novel “acoustical baffle” silencer type is proposed for application when the silencer length is limited; measured performance is superior to that of an acoustical louver. Numerical acoustical and airflow modeling techniques are developed for ventilation opening silencer performance optimization and analysis work. Airflow modeling indicates that the errors associated with using a high-Reynolds number discharge coefficient are not of practical concern. By way of result synthesis, best-practice guidelines for silencer design in the context of speech privacy are provided. Select conclusions for cross talk silencers are: flow-path shape does not affect acoustical performance; straight sections before the silencer termination increase airflow performance by up to 30%; elbows in the silencer flow path reduce overall silencer performance.  ii  Table of Contents Abstract.................................................................................................................................... ii Table of Contents ................................................................................................................... iii List of Tables .......................................................................................................................... ix List of Figures.......................................................................................................................... x List of Symbols and Abbreviations ................................................................................... xvii Acknowledgements .............................................................................................................. xix Chapter 1: Introduction ........................................................................................................ 1 1.1  Literature Review...................................................................................................... 4  1.2  Research Objectives.................................................................................................. 8  1.3  Thesis Outline ........................................................................................................... 8  Chapter 2: Optimization Metric: Open Area Ratio ......................................................... 10 2.1  Calculating Equivalent Open Areas........................................................................ 10  2.1.1  Equivalent Open Area for Sound.................................................................... 10  2.1.2  Equivalent Open Area for Flow...................................................................... 14  2.2  Summary Discussion on the Optimization Parameter ............................................ 15  2.3  Diffuse Field Theory and Ventilation Opening Characterization........................... 17  Chapter 3: Investigating the Factors in Speech Privacy .................................................. 20 3.1  Speech Intelligibility Index..................................................................................... 20  3.2  Model Description .................................................................................................. 21  3.2.1  Model Inputs ................................................................................................... 22  3.2.2  Calculating the Source Room Sound Pressure Levels.................................... 24  3.2.3  Calculating the Transmission Loss of the Partition ........................................ 24  3.2.4  Calculating the Receiver Room Sound Pressure Levels................................. 25  3.2.5  Cautionary Note .............................................................................................. 25  3.3  Results..................................................................................................................... 26  3.3.1  Vocal Effort and SII........................................................................................ 26  3.3.2  Room Size, Furnishings and SII ..................................................................... 27  3.3.3  Background Noise and SII .............................................................................. 28  3.3.4  TL and SII ....................................................................................................... 29  3.3.4.1  Partitions without Ventilation Openings..................................................... 30 iii  3.3.4.2 3.4  Partitions with Ventilation Openings.......................................................... 31  Factors Affecting Speech Privacy: Summary ......................................................... 34  Chapter 4: Describing Flow Performance of Ventilation Openings ............................... 35 4.1  Navier-Stokes Equation .......................................................................................... 35  4.2  Bernoulli’s Equation ............................................................................................... 36  4.3  Empirical Prediction of Flow Behavior .................................................................. 38  4.4  Determining Viscous Losses in Ducts .................................................................... 39  4.4.1  Discharge and Loss Coefficients .................................................................... 39  4.4.2  Dependence on the Reynolds Number............................................................ 41  Chapter 5: Measurement of Natural Ventilation Openings ............................................ 46 5.1  Ventilator Measurement Method ............................................................................ 46  5.1.1  Ventilator Transmission Loss ......................................................................... 46  5.1.1.1  Theory ......................................................................................................... 46  5.1.1.2  Measurement Method – In Field................................................................. 49  5.1.1.3  Measurement Method – In Lab................................................................... 49  5.1.2  Ventilator Flow Rate....................................................................................... 49  5.1.2.1  Theory ......................................................................................................... 50  5.1.2.2  Measurement Method – In-Situ and Laboratory......................................... 52  5.2  Design and Performance of the Lab Facility .......................................................... 52  5.2.1  Room Dimensions and Construction .............................................................. 53  5.2.2  Acoustic Performance of Lab Facility ............................................................ 54  5.2.3  Air Flow Performance of Laboratory Test Facility ........................................ 55  5.3  Report on Field Measurements of Natural Ventilation Openings .......................... 59  5.3.1  Regent College Library................................................................................... 60  5.3.1.1  Regent College L020 .................................................................................. 60  5.3.1.1.1  L020 Results: Grille On ........................................................................ 61  5.3.1.1.2  L020 Results: Grille Removed.............................................................. 61  5.3.2  Fred Kaiser Building....................................................................................... 63  5.3.2.1  Fred Kaiser 4036......................................................................................... 63  5.3.2.1.1 5.3.3  4036 Results.......................................................................................... 63  Liu Institute..................................................................................................... 65  iv  5.3.3.1  Liu 216C ..................................................................................................... 65  5.3.3.1.1 5.3.3.2  Liu 308 ........................................................................................................ 66  5.3.3.2.1 5.3.3.3  216C Results ......................................................................................... 66  308 Results............................................................................................ 66  Liu 313 ........................................................................................................ 67  5.3.3.3.1  313 Results: Grilles On......................................................................... 67  5.3.3.3.2  313 Results: Grilles Off ........................................................................ 67  5.3.4  C. K. Choi Building ........................................................................................ 69  5.3.4.1  C. K. Choi 167 ............................................................................................ 70  5.3.4.1.1 5.3.4.2  C.K. Choi 321 ............................................................................................. 70  5.3.4.2.1 5.3.4.3  326 Results............................................................................................ 72  C.K. Choi 327 ............................................................................................. 72  5.3.4.4.1 5.3.5  321 Results............................................................................................ 71  C.K. Choi 326 ............................................................................................. 71  5.3.4.3.1 5.3.4.4  167 Results............................................................................................ 70  327 Results............................................................................................ 73  Langara College Library ................................................................................. 74  5.3.5.1  Langara L104 .............................................................................................. 75  5.3.5.1.1  L104 Results: Grille On ........................................................................ 75  5.3.5.1.2  L104 Results: Grille Off ....................................................................... 76  5.3.5.2  Langara L112 .............................................................................................. 76  5.3.5.2.1 5.3.5.3  L112 Results ......................................................................................... 76  Langara L208 .............................................................................................. 77  5.3.5.3.1  L208 Results: Grille On ........................................................................ 77  5.3.5.3.2  L208 Results: Grille Off ....................................................................... 77  5.3.6  Operational Ventilator Flow Conditions......................................................... 80  5.3.7  In-Situ Results Summary ................................................................................ 84  5.4  Analysis of BRE Ventilator Measurements............................................................ 86  5.4.1  Ventilator Configurations ............................................................................... 86  5.4.1.1  Straight Ventilator....................................................................................... 86  5.4.1.2  L-shaped Ventilator .................................................................................... 87  v  5.4.2  Results............................................................................................................. 87  5.4.2.1  Effect of Acoustic Foam ............................................................................. 87  5.4.2.2  Effect of Elbow (L-shaped silencer) ........................................................... 88  5.4.2.3  Effect of Grilles........................................................................................... 88  5.4.2.4  Effect of PVC Lining .................................................................................. 88  5.4.2.5  Effect of Angled Baffles ............................................................................. 89  5.4.2.6  Effect of Wave-Shaped Absorptive Liner................................................... 89  5.4.3 5.5  Summary of BRE Ventilator Test Results ...................................................... 89 Laboratory Measurements of Ventilation Openings and Silencers ........................ 99  5.5.1  Slot Ventilation Opening ................................................................................ 99  5.5.2  Acoustical Louver......................................................................................... 103  5.5.3  Acoustical Baffle .......................................................................................... 108  5.5.4  Acoustical Air Filter?.................................................................................... 111  5.5.5  Cross Talk Silencer ....................................................................................... 114  5.5.6  Lab Measurement Results Summary ............................................................ 119  Chapter 6: Ventilation Silencer Performance Prediction .............................................. 122 6.1  Fundamental Mode Attenuation ........................................................................... 122  6.1.1  General Cartesian Solution for Sound in a Duct........................................... 122  6.1.2  Solution for a Rigid Walled Duct ................................................................. 124  6.1.3  Non-rigid Walled Duct ................................................................................. 125  6.1.3.1  Defining the Surface Impedance............................................................... 128  6.1.3.1.1  Transfer Function Method .................................................................. 128  6.1.3.1.2  Characterizing Porous Absorptive Materials ...................................... 130  6.1.4  Attenuation of the Fundamental Mode Results ............................................ 131  6.1.4.1  Duct Liner Properties................................................................................ 131  6.1.4.2  Cross Sectional Dimensions ..................................................................... 134  6.1.5 6.2 6.2.1  6.1.4.2.1  Flow Path Height ................................................................................ 134  6.1.4.2.2  Flow Path Aspect Ratio ...................................................................... 136  Attenuation of the Fundamental Mode Summary......................................... 139 Acoustical FEM Predictions of Ventilation Opening Transmission Loss ............ 139 Acoustical FEM Design................................................................................ 140  vi  6.2.1.1  Domains and Boundary Conditions .......................................................... 141  6.2.1.2  Calculation of Model Results.................................................................... 144  6.2.1.2.1  Frequency Averaging.......................................................................... 145  6.2.1.2.2  Lp (x, f)................................................................................................ 146  6.2.1.2.3  Lp (f).................................................................................................... 146  6.2.1.2.4  Lp (x)................................................................................................... 146  6.2.1.2.5  σLp ....................................................................................................... 147  6.2.1.2.6  Ii(x, f)................................................................................................... 147  6.2.1.2.7  Win(f), Wout(f)....................................................................................... 148  6.2.1.2.8  WLp(f).................................................................................................. 148  6.2.1.2.9  TL_Win(f) ............................................................................................ 149  6.2.1.2.10  TL_WLp(f).......................................................................................... 150  6.2.1.2.11  TL_Win and TL_WLp ......................................................................... 150  6.2.1.3  Designing for Convergence of Transmission Loss FEM.......................... 150  6.2.1.3.1  Mesh Convergence.............................................................................. 151  6.2.1.3.2  Frequency Convergence...................................................................... 152  6.2.1.3.3  Diffuse Field Convergence ................................................................. 155  6.2.2  Transmission Loss FEM Validation ............................................................. 166  6.2.2.1  Analytical Validation ................................................................................ 166  6.2.2.1.1  Plane Wave Attenuation ..................................................................... 167  6.2.2.1.2  Calculating the Inlet Power through Sound Pressure Level  or Intensity ............................................................................................................ 170 6.2.2.2  Comparing Measured Results to FEM Prediction .................................... 173  6.2.2.2.1  Slot Ventilation Opening .................................................................... 173  6.2.2.2.2  CT Silencers........................................................................................ 174  6.2.3  Acoustic FEM Design Summary .................................................................. 177  6.2.4  Acoustic FEM CT Silencer Results .............................................................. 179  6.2.4.1 6.3  Frequency Dependence of CT Silencer Transmission Loss ..................... 181  CFD Predictions of Ventilation Opening Discharge Coefficients ........................ 187  6.3.1  Flow Domain Geometry ............................................................................... 187  6.3.2  Flow-Equation Model ................................................................................... 190  vii  6.3.2.1  Reynolds Averaging (RANS) ................................................................... 190  6.3.3  Boundary Conditions .................................................................................... 191  6.3.4  Mesh.............................................................................................................. 191  6.3.5  Processing Flow Model Results.................................................................... 192  6.3.6  Model Validation .......................................................................................... 192  6.3.6.1  Validation by Comparison to Published Results ...................................... 192  6.3.6.2  Validation by Comparison to Measured Results ...................................... 194  6.3.7  CFD Prediction Results for CT Silencers ..................................................... 194  6.3.7.1  Effect of Length on the Straight Silencer’s Cd.......................................... 195  6.3.7.2  Effect of CT-Silencer Type on Cd ............................................................. 196  6.3.7.3  Effect of Reynolds Number on Cd ............................................................ 197  6.4  CT Silencer Modeling Summary .......................................................................... 202  Chapter 7: Conclusions ..................................................................................................... 205 7.1  Summary ............................................................................................................... 205  7.2  Future Work .......................................................................................................... 211  7.2.1  Set Optimization Objectives ......................................................................... 211  7.2.2  Improve Physical and Numerical Performance Prediction Methods............ 211  7.2.3  Optimize Natural Ventilation Openings ....................................................... 212  References ............................................................................................................................ 214 Appendices........................................................................................................................... 221 Appendix A: Manufacturer Data Sheets ........................................................................... 222 A.1  CertainTeed OEM Acoustic Fiberglass Absorber ............................................ 222  A.2  Kinetics Noise Control Acoustical Louver ....................................................... 224  A.3  Filter Data Sheets.............................................................................................. 226  Appendix B: MATLAB Code........................................................................................... 229 B.1  Diffuse Field Sound Transmission Model ........................................................ 229  B.2  Attenuation in a Lined Duct.............................................................................. 236  B.3  Processing COMSOL Results........................................................................... 241  Appendix C: Numerical Prediction Appendices............................................................... 244 C.1  Predicted CT Silencer Transmission Loss ........................................................ 245  C.2  Velocity- and Pressure-Field Figures for CT Silencers at High-Re ................. 246  viii  List of Tables Table 1: Background noise level L90 [dB]. ............................................................................. 22 Table 2: Speech power levels [dB] [23]. ................................................................................ 23 Table 3: Absorption coefficients of room surfaces [41]. ........................................................ 23 Table 4: Room surface configuration types. ........................................................................... 23 Table 5: Room volumes. ......................................................................................................... 23 Table 6: Transmission loss and STC of various partitions [36].............................................. 23 Table 7: Equivalent open area of the partitions. ..................................................................... 32 Table 8: Flow-rate coefficients. .............................................................................................. 50 Table 9: Performance measures for Regent College, L020. ................................................... 62 Table 10: Performance measures for the ventilator in Fred Kaiser 4036. .............................. 65 Table 11: Performance measures for ventilation openings in the Liu Institute. ..................... 67 Table 12: Performance measures for ventilation openings in the C. K. Choi building. ......... 73 Table 13: Performance measures for ventilation openings in the Langara College Library. . 78 Table 14: Selected minimum required air exchange rates [59]. ............................................. 81 Table 15: Assumed ventilation opening operating conditions................................................ 83 Table 16: In-situ measurement results summary. ................................................................... 85 Table 17: BRE ventilator measurement results summary, (xxx) – estimated values. ............ 90 Table 18: Performance measures for the slot ventilation opening........................................ 102 Table 19: Performance measures for the acoustical louver. ................................................. 105 Table 20: Performance measures for the acoustical baffle. .................................................. 109 Table 21: Performance measures for the acoustical air filters. ............................................. 112 Table 22: Performance measures for the 0.3 m CT silencers. .............................................. 118 Table 23: Laboratory measurements results summary. ........................................................ 121 Table 24: Modes in each third-octave band.......................................................................... 157 Table 25: Number of modes in each third octave band, 2D geometry (1 x 1.26 m). ........... 160 Table 26: CT silencer dimensions......................................................................................... 180 Table 27: CT silencer performance....................................................................................... 180 Table 28: Measured and predicted silencer discharge coefficients – high Re...................... 194 Table 29: Predicted flow performance of CT silencers at high Re....................................... 197 Table 30: CT silencer performance prediction summary. .................................................... 202 ix  List of Figures Figure 1: Typical natural ventilation configuration. ................................................................. 2 Figure 2: Acoustic characterization of ventilation openings. ................................................... 4 Figure 3: Air flow characterization of ventilation openings. .................................................... 4 Figure 4: Variation of SII vocal effort for various room sizes. .............................................. 27 Figure 5: Variation of SII with surface absorption in various room sizes .............................. 28 Figure 6: Variation of SII with increasing surface absorption for various BGN.................... 29 Figure 7: Variation of SII with STC for various vocal efforts (Large Office, Surface Configuration 4)...................................................................................................................... 30 Figure 8: Variation in SII with EOAs for different wall types................................................ 32 Figure 9: Variation in the normalized SII as a function of EOAs for different wall types. .... 33 Figure 10: Variation in the normalized SII as a function of EOAA_V /EOAA_W, for different wall types. ............................................................................................................................... 33 Figure 11: Flow meter types ................................................................................................... 43 Figure 12: Flow meter error resulting from using turbulent discharge coefficient................. 44 Figure 13: Discharge coefficient of orifice plates with various geometries ........................... 44 Figure 14: Measured reverberation time with 95% confidence intervals for source and receiver rooms......................................................................................................................... 56 Figure 15: Measured receiver room total absorption and the maximum permissible value according to ASTM E90. ........................................................................................................ 57 Figure 16: Uncertainty in measured Lp - 95% confidence values.......................................... 57 Figure 17: Measured transmission loss of laboratory partition - 95% confidence values. ..... 58 Figure 18: Measured equivalent open area of high pressure room (leakage). ........................ 58 Figure 19: Measured SEOAf of 0.6 x 0.6 m opening.............................................................. 59 Figure 20: Regent College L020............................................................................................. 62 Figure 21: Regent College L020 grille. .................................................................................. 62 Figure 22: Fred Kaiser 4036. .................................................................................................. 64 Figure 23: Fred Kaiser 4036 ventilator cross section ............................................................. 64 Figure 24: Liu 216C (showing ventilation openings blocked). .............................................. 68 Figure 25: Liu 308. ................................................................................................................. 68 Figure 26: Liu Institute 308 ventilator cross section .............................................................. 68 x  Figure 27: Liu 313 (showing ventilation openings blocked). ................................................. 69 Figure 28: Liu 313 grille. ........................................................................................................ 69 Figure 29: C. K. Choi 167....................................................................................................... 73 Figure 30: C. K. Choi 321....................................................................................................... 73 Figure 31: C. K. Choi 326....................................................................................................... 74 Figure 32: C. K. Choi 327....................................................................................................... 74 Figure 33: Langara L104. ....................................................................................................... 78 Figure 34: Langara L208. ....................................................................................................... 78 Figure 35: Langara L104 ventilator cross section................................................................... 79 Figure 36: Langara L104 and L208 ventilator grilles............................................................. 79 Figure 37: Langara L208 ventilator cross Section.................................................................. 79 Figure 38: Langara L112 (ventilation opening at top left). .................................................... 80 Figure 39: BRE ventilator Configuration 1. ........................................................................... 91 Figure 40: BRE ventilator Configuration 5. ........................................................................... 92 Figure 41: BRE ventilator Configuration 2. ........................................................................... 93 Figure 42: BRE ventilator Configuration 3. ........................................................................... 94 Figure 43: BRE ventilator Configuration 4. ........................................................................... 95 Figure 44: BRE ventilator Configuration 8. ........................................................................... 96 Figure 45: BRE ventilator Configuration 6. ........................................................................... 97 Figure 46: BRE ventilator Configuration 7. ........................................................................... 98 Figure 47: Slot ventilation opening, no fiberglass. ............................................................... 100 Figure 48: Slot ventilation opening, 1 m x 1 m x 25 mm fiberglass..................................... 100 Figure 49: Slot ventilation opening, 1 m x 1 m x 50 mm fiberglass..................................... 100 Figure 50: Slot ventilation opening, away from floor/ceiling............................................... 100 Figure 51: Measured transmission loss of slot ventilation openings. ................................... 102 Figure 52: Measured transmitted speech spectrum of slot ventilation openings. ................. 103 Figure 53: Louver configuration 1, view from receiver room (perforations not visible). .... 104 Figure 54: Louver configuration 2, view from receiver room (perforations not visible). .... 104 Figure 55: Louver configuration 3, view from receiver room (perforations visible). .......... 104 Figure 56: Louver configuration 4, view from receiver room (perforations visible) ........... 104 Figure 57: Louver configuration 5, view from receiver room (perforations not visible) ..... 104  xi  Figure 58: Measured transmission loss of acoustical louver. ............................................... 106 Figure 59: Measured transmitted speech spectrum of acoustical louver. ............................. 106 Figure 60: Measured (diffuse field receiver) and published (free field receiver) louver insertion loss. ........................................................................................................................ 107 Figure 61: Measured and published SEOAf of louver. ......................................................... 108 Figure 62: Acoustical baffle.................................................................................................. 109 Figure 63: Measured acoustical baffle transmission loss. .................................................... 110 Figure 64: Measured acoustical baffle transmitted speech spectrum ................................... 110 Figure 65: Acoustic fiberglass .............................................................................................. 111 Figure 66: Pink air filter........................................................................................................ 111 Figure 67: White air filter ..................................................................................................... 111 Figure 68: Measured acoustical air filter transmission loss.................................................. 112 Figure 69: Measured acoustical air filter transmitted speech spectrum................................ 113 Figure 70: Measured acoustical air filter insertion loss. ....................................................... 113 Figure 71: 0.3 m Straight CT silencer diagram..................................................................... 114 Figure 72: 0.3 m Straight CT silencer................................................................................... 115 Figure 73: 0.3 m L-shaped CT silencer diagram .................................................................. 115 Figure 74: 0.3 m L-shaped CT silencer. ............................................................................... 115 Figure 75: 0.3 m Z-shaped CT silencer diagram .................................................................. 116 Figure 76: 0.3 m Z-shaped CT silencer. ............................................................................... 116 Figure 77: 0.3 m Straight CT silencer diagram – fiberglass removed. ................................. 116 Figure 78: 0.3 m Straight CT silencer – fiberglass removed. ............................................... 117 Figure 79: Measured transmission loss of 0.3 m CT silencers. ............................................ 118 Figure 80: Measured transmitted speech spectrum of 0.3 m CT silencers. .......................... 119 Figure 81: Absorption coefficient of OEM fiberglass measured and predicted by the DelaneyBazley model for different flow resistivities. σ – [MKS Rayl/m] ....................................... 133 Figure 82: Variation of normal incidence absorption coefficient for various liner thicknesses as predicted by Delaney-Bazley, σ = 60,000 MKS Rayl/m. ................................................ 133 Figure 83: Silencer dimensions............................................................................................. 134 Figure 84: Predicted transmission loss for various duct heights and liner thicknesses ........ 135  xii  Figure 85: Predicted transmission loss for various duct heights and liner thicknesses with transmission loss plotted on a log scale ................................................................................ 136 Figure 86: Predicted transmission loss for various aspect ratios: dy=dx=25 mm................. 137 Figure 87: Predicted transmission loss for various aspect ratios: dy=dx=50 mm................. 138 Figure 88: Predicted transmission loss for various aspect ratios: dy=dx=100 mm............... 138 Figure 89: 3D acoustic domain. ............................................................................................ 143 Figure 90: Source volume sub-domain. ................................................................................ 143 Figure 91: Source volume sampling sub-domain. ................................................................ 143 Figure 92: Ventilator flow path sub-domain......................................................................... 143 Figure 93: Ventilator liner sub-domain................................................................................. 144 Figure 94: Receiver volume sub-domain.............................................................................. 144 Figure 95: PML sub-domain................................................................................................. 144 Figure 96: Point sound power source.................................................................................... 144 Figure 97: Variation of the predicted sound power with mesh resolution............................ 152 Figure 98: Error in average Lp as a function of frequency sampling resolution for various source volume dimensions and reflection coefficients. ........................................................ 154 Figure 99: Lp Standard deviation as a function of frequency sampling resolution for various source volume dimensions and reflection coefficients. ........................................................ 155 Figure 100: Standard deviation of Lp vs minimum order of axial mode.............................. 159 Figure 101: External view of source volume with diffusing surfaces. ................................. 159 Figure 102: Standard deviation of sound pressure in an empty office sized room, with and without diffusers ................................................................................................................... 160 Figure 103: Third-octave source volume surface Lp distribution. N=6, color scale in dB... 162 Figure 104: Sample area on source volume surface area...................................................... 162 Figure 105: Standard deviation of sample Lp averages vs. to sample side-length to wavelength ratio for various source volume dimensions. Square sample surface, away from source volume corner. ........................................................................................................... 164 Figure 106: Standard deviation of sample Lp averages vs. sample width to wavelength ratio for various sample height to wavelength ratios. N=6, sample surface away from source volume corner. ...................................................................................................................... 164  xiii  Figure 107: Standard deviation of average sample Lp vs. sample width to wavelength ratio (w/l) for various sample height to wavelength ratios (h/l). Sample surface at source volume edge. ...................................................................................................................................... 166 Figure 108: 3 m lined duct geometry for analytical validation with 503 Hz Lp solution..... 167 Figure 109: Transmission loss in center section of duct – discrete data points.................... 169 Figure 110: Analytical solution and 2D FEM solution with locally reacting liner – discrete data points. ............................................................................................................................ 169 Figure 111: Predicted transmission loss calculated using source sound pressure level and inlet intensity................................................................................................................................. 172 Figure 112: Difference in transmission loss result when calculated using source sound pressure level and inlet intensity. 95% confidence intervals provided................................. 172 Figure 113: Measured and predicted TL of a 50 mm slot. 95% confidence intervals.......... 174 Figure 114: Measured and predicted TL of 0.3 m straight CT silencer. 95% confidence intervals................................................................................................................................. 175 Figure 115: Measured and predicted TL of 0.3 m L-shaped CT silencer. 95% confidence intervals................................................................................................................................. 176 Figure 116: Measured and predicted TL of 0.3 m Z-shaped CT silencer. 95% confidence intervals................................................................................................................................. 176 Figure 117: Shapes and dimensions of CT silencers. Clockwise from top left: Straight, L, Z, and U..................................................................................................................................... 180 Figure 118: Predicted transmission loss of 1 m CT silencers. 95% confidence intervals shown. ................................................................................................................................... 183 Figure 119: Predicted transmitted speech spectrum, 1 m CT silencers. 95% confidence intervals given....................................................................................................................... 183 Figure 120: Predicted Lp (left) and sound pressure (right) at 500 Hz, 1 m Straight silencer. ............................................................................................................................................... 184 Figure 121: Predicted Lp (left) and sound pressure (right) at 500 Hz, 1 m L-shaped silencer. ............................................................................................................................................... 184 Figure 122: Predicted Lp (left) and sound pressure (right) at 2500 Hz, 1 m Straight silencer. ............................................................................................................................................... 185  xiv  Figure 123: Predicted Lp (left) and sound pressure (right) at 2500 Hz, 1 m L-shaped silencer. ............................................................................................................................................... 185 Figure 124: Predicted Lp (left) and sound pressure (right) at 8000 Hz, 1 m Straight silencer. ............................................................................................................................................... 186 Figure 125: Predicted Lp (left) and sound pressure (right) at 8000 Hz, 1 m L-shaped silencer. ............................................................................................................................................... 186 Figure 126: Flow domain of ventilator model (sample velocity contours shown). .............. 189 Figure 127: Published experimental results for the orifice plate discharge coefficient........ 193 Figure 128: Predicted results for the orifice plate discharge coefficient. ............................. 193 Figure 129: Predicted Straight CT silencer discharge coefficients as a function of Re. ...... 198 Figure 130: Predicted flow velocity in 1 m Straight CT silencer – Re = 27,000. ................ 198 Figure 131: Predicted flow pressure in 1 m Straight CT silencer – Re = 27,000. ................ 198 Figure 132: Predicted flow velocity in 0.05 m Straight CT silencer – Re = 22,000. ........... 199 Figure 133: Predicted flow pressure in 0.05 m Straight CT silencer – Re = 22,000. ........... 199 Figure 134: Predicted discharge coefficients of 0.3 m CT silencers as a function of Re. .... 199 Figure 135: Predicted discharge coefficients of 0.5 m CT silencers as a function of Re. .... 200 Figure 136: Predicted discharge coefficients of 1 m CT silencers as a function of Re. ....... 200 Figure 137: Predicted discharge coefficients as a function of pressure loss for all silencer configurations. ...................................................................................................................... 201 Figure 138: Predicted open area ratio as a function of pressure loss for all silencer configurations. ...................................................................................................................... 203 Figure 139: Predicted open area ratio as a function of Reynolds number for all silencer configurations. ...................................................................................................................... 204 Figure 140: Predicted transmission loss of 0.3 m CT silencers. 95% confidence intervals shown. ................................................................................................................................... 245 Figure 141: Predicted transmission loss of 0.5 m CT silencers. 95% confidence intervals shown. ................................................................................................................................... 245 Figure 142: Predicted transmission loss of 1 m CT silencers. 95% confidence intervals shown. ................................................................................................................................... 246 Figure 143: Predicted flow velocity in 0.05 m Straight CT silencer – Re = 22,000. ........... 246 Figure 144: Predicted flow velocity in 0.3 m Straight CT silencer – Re = 25,000. ............. 246  xv  Figure 145: Predicted flow velocity in 0.5 m Straight CT silencer – Re = 25,000. ............. 247 Figure 146: Predicted flow velocity in 1 m Straight CT silencer – Re = 27,000. ................ 247 Figure 147: Predicted flow pressure in 0.05 m Straight CT silencer – Re = 22,000. ........... 247 Figure 148: Predicted flow pressure in 0.3 m Straight CT silencer – Re = 25,000. ............. 247 Figure 149: Predicted flow pressure in 0.5 m Straight CT silencer – Re = 25,000. ............. 248 Figure 150: Predicted flow pressure in 0.5 m Straight CT silencer – Re = 27,000. ............. 248 Figure 151: Predicted flow velocity in 0.3 m L-shaped CT silencer – Re = 15,000. ........... 249 Figure 152: Predicted flow velocity in 0.5 m L-shaped CT silencer – Re = 15,000. ........... 249 Figure 153: Predicted flow velocity in 1 m L-shaped CT silencer – Re = 18,000. .............. 249 Figure 154: Predicted flow pressure in 0.3 m L-shaped CT silencer – Re = 15,000............ 250 Figure 155: Predicted flow pressure in 0.5 m L-shaped CT silencer – Re = 15,000............ 250 Figure 156: Predicted flow pressure in 1 m L-shaped CT silencer – Re = 18,000............... 250 Figure 157: Predicted flow velocity in 0.5 m U-shaped CT silencer – Re = 20,000............ 251 Figure 158: Predicted flow velocity in 1 m U-shaped CT silencer – Re = 21,000............... 251 Figure 159: Predicted flow pressure in 0.5 m U-shaped CT silencer – Re = 20,000. .......... 252 Figure 160: Predicted flow pressure in 1 m U-shaped CT silencer – Re = 21,000. ............. 252 Figure 161: Predicted flow velocity in 0.3 m Z-shaped CT silencer – Re = 15,000. ........... 253 Figure 162: Predicted flow velocity in 0.5 m Z-shaped CT silencer – Re = 12,000. ........... 253 Figure 163: Predicted flow velocity in 1 m Z-shaped CT silencer – Re = 14,000. .............. 253 Figure 164: Predicted flow pressure in 0.3 m Z-shaped CT silencer – Re = 15,000............ 254 Figure 165: Predicted flow pressure in 0.5 m Z-shaped CT silencer – Re = 12,000............ 254 Figure 166: Predicted flow velocity in 1 m Z-shaped CT silencer – Re = 14,000. .............. 254  xvi  List of Symbols and Abbreviations α  Random incidence absorption coefficient  c  Speed of sound in air  c0  Speed of sound in air at STP  ε  Porosity  f  Frequency [Hz]  k  Wavenumber, or flow-pressure loss coefficient  µ  Dynamic viscosity  ν  Kinematic viscosity  p  Pressure (acoustic, or flow)  ρ  Density of air  ρ0  Density of air at STP  σ  Flow resistivity MKS Rayl/m  u  Particle velocity (acoustic, or flow)  ω  Frequency [rad/s]  Z0  Characteristic impedance of air  A  Surface area  Aα  Total absorptive area  AR  Aspect ratio  Cd  Discharge coefficient  Dh  Hydraulic diameter  EOAf  Equivalent open area for air flow  EOAs  Equivalent open area for sound  I  Sound intensity  IL  Insertion Loss  Leq  Equivalent sound pressure level  Lp  Sound pressure level xvii  Lw  Sound power level  NR  Noise reduction  OAR  Open area ratio  Q  Air flow rate  R  Room constant  Re  Reynolds number  Retr  Transitional Reynolds number – the Reynolds number above which the discharge coefficient is constant with respect to Reynolds number. This may not correspond to transition to turbulence.  SEOAf  Specific equivalent open area for air flow  SEOAs  Specific equivalent open area for sound  SII  Speech intelligibility index  STC  Sound transmission class  T60  Reverberation time  TL  Transmission loss  U  Average flow velocity  V  Room volume  W  Sound power  Z  Propagation impedance  Zs  Surface impedance  xviii  Acknowledgements There are many people to whom I owe my gratitude for their contribution to this work.  Thank you to my supervisor, Dr. Murray Hodgson, who has helped guide this research, provided technical support, and assisted with measurements throughout all stages of this project and my M.A.Sc. program. I am very grateful to have had such a knowledgeable, caring, and engaged supervisor.  Thank you to the Natural Sciences and Engineering Research Council of Canada for the financial support by way of a NSERC CGS-M scholarship and a NSERC CREATE grant.  Thank you to Fitsum Tariku, Steve Rogak, Sheldon Green, Max Richter, Andrea Frisque, Greg Johnson, Albert Bicol, Alireza Khaleghi, and many other people for your technical guidance and advice. Additionally, thank you to Fitsum Tariku and BCIT for loaning us their blower door which was essential for all of our airflow measurements, and to Sheldon Green for providing us with ANSYS Fluent which was essential for airflow modeling.  Thank you to Richard Anthony and Mehrzad Salkhordeh of Kinetics Noise Control Inc. for your interest and support toward this project. It is unfortunate that we were not able to collaborate further.  Thank you to the many building managers who spent time to show and discuss their buildings, and provided us with assess to complete our measurements.  Thank you to my wife, family and friends for the financial and emotional support, as well as the late nights helping with my measurements.  xix  Chapter 1: Introduction In developed nations buildings are responsible for 20-40% of all energy consumption; in Canada this number is 30% [1]. In order to reduce our national energy consumption, building scientists and engineers must develop methods to reduce the energy used by buildings. The use of natural ventilation, as opposed to mechanical ventilation, is one such method. In addition to a reduction in energy consumption, natural ventilation can provide a host of other occupant health and satisfaction benefits, including reduced mechanical noise and sick building syndrome, if implemented properly [2].  Natural ventilation works by using wind or buoyancy (stack effect) induced pressure differentials to drive the ventilation air through a building [3]. Typically these pressures are small compared to those available in a mechanically ventilated building, often not exceeding 10 Pa [3]. In order for the small pressure to drive a sufficient volume of air it is necessary to have low resistance to air flow throughout the building [4, 5]; to achieve this, large openings are often created in partitions, allowing air to flow from one room to the adjacent space. The large openings prove detrimental to the noise isolation between the spaces [3-8]. Figure 1 shows a typical configuration for a naturally ventilated building. In this example, the natural ventilation openings between the offices and corridors could result in reduced privacy of conversations inside an otherwise private office, as well as increased annoyance for the occupants of the office due to noise generated in the corridor.  1  Corridor  Office  Figure 1: Typical natural ventilation configuration.  The UBC Acoustics and Noise Research Group at UBC has had previous involvement with ventilation openings in naturally ventilated buildings, which came about due to occupant complaints in then-new buildings on UBC campus; the Liu Institute for Global Studies [5], the C.K. Choi building, the AERL building[9], and Regent College. The complaints surrounded a lack of noise isolation, causing either a lack of privacy or increased distraction, between the offices and the corridor. In the Liu Institute for Global Studies project the UBC Noise and Research Group, in combination with Stantec Architecture Inc., designed silencing devices to increase the noise isolation to an acceptable level without overly effecting airflow; the devices proved successful and the building occupants claim to be satisfied with the resulting noise isolation.  It was clear that there is a great need for further understanding of ventilation openings in naturally ventilated buildings to provide engineers and architects with design techniques which allow sufficient air flow while providing adequate noise isolation. Under the direction and supervision of Murray Hodgson, I have continued this work.  2  In order to provide a vocabulary for discussing ventilation openings, the general descriptors of the acoustic and airflow performance of a ventilation opening are provided here. Further discussion about this characterization method appears in many areas throughout this thesis.  Acoustic performance of a ventilation opening is defined by its transmission loss (TL). Transmission loss is transmission coefficient (τ ) expressed in decibels, where the transmission coefficient is the ratio of the sound energy emitted from the outlet (Wout) to the sound energy incident on the inlet (Win):  W TL = 10 log(τ ) = 10 log out  Win      (1)  The transmission loss of a ventilation opening affects the difference in sound levels between the two rooms that it separates – the noise reduction (NR). Assuming the sound fields in both rooms are diffuse, a concept which will be discussed in detail later (sections 2.3, 3.2, 5.1.1, and 6.2.1.3), the difference in sound levels is found to be:  A  NR = Lp s − Lp r = TL − 10 log  v   Aα , r   (2)  With reference to Figure 2, Lps is the sound pressure level in the source room containing the sound source, Lpr is the sound pressure level in the receiver room, Aα, r is the total receiver room acoustic absorption, Av is the cross sectional area of the ventilator, and TL is the transmission loss of the ventilator. Sound generated in the source room enters, propagates through, and is emitted from, the ventilation opening resulting in a reverberant sound field with some sound pressure level in the receiver room. Here it is assumed that the ventilation opening is the only path for sound to propagate from the source to the receiver room. Eq. (2) shows that the ventilator’s transmission loss is a key factor in the noise isolation between the two rooms, but not the only factor. The reverberant conditions in the receiver room and other noise propagation paths are examples of other factors.  3  Source Room Lps  Receiver Room Lpr, Aα, r Ventilator Av, TL  Figure 2: Acoustic characterization of ventilation openings.  Airflow performance of a ventilation opening is typically given by Cd, its discharge coefficient [10]:   2(Ps − Pr )  Q = Av C d   ρ    0.5  (3)  The form of Eq. (3) is a result of its empirical derivation from conservation of energy in a flow along a streamline. It states that the flow rate through the ventilator (Q) is directly proportional to the ventilator area (Av) and the pressure differential squared, and inversely proportional to the fluid density (ρ). Ps and Pr are the static pressures in the source and receiver rooms. The discharge coefficient is determined experimentally and is constant over suitable flows; for a thin orifice it takes a value of around 0.61. There will be discussion later in the thesis about the suitability and implications of using a constant value for Cd (sections 4.4.2, 5.3.6, and 6.3.7.3).  Source Room Ps  Receiver Room Pr Ventilator A v, C d , Q  Figure 3: Air flow characterization of ventilation openings.  1.1 Literature Review The intent of this literature review is to give the reader an understanding of the work completed to date on interior natural ventilation opening silencers. It is not the intent to 4  provide a theoretical discussion of the physics of acoustics and airflow through openings – that will come later.  Oldham and de Salis [3, 4] provide a discussion of concerns associated with placing natural ventilation openings in a façade, based on the theoretical framework implied by Eq. (2) and Eq. (3). This discussion is also relevant to interior partitions. They discuss the effect of an aperture on the transmission loss of a partition, by finding the effective transmission loss of a partition from the area-weighted average of the wall and aperture transmission coefficients:   τ ⋅ A + τ a ⋅ Aa TL w+ a = 10 log w w Aw + Aa       Subscripts w and a indicate the wall and aperture. Their theoretical analysis concluded that the creation of a ventilation aperture in a typical façade that is large enough to provide effective ventilation rates would be detrimental to the noise isolation provided by the façade. Conclusions are made that natural ventilation openings must be treated acoustically; that is to say, τ a , the transmission coefficient of the ventilation opening must be reduced. Oldham and de Salis go on to discuss the applicability of various noise control solutions in the context of traffic noise and apertures in a façade [3, 4]. It is suggested that, to acoustically silence ventilation apertures:  •  active noise control can be effective at very low frequencies; however, it has poor performance at higher frequencies and for non-steady sound  •  resonator absorber devices can be effective at mid frequencies  •  porous, absorptive linings can be effective at higher frequencies  •  hybrid solutions may be most effective  Oldham completed an investigation of the performance of lined ventilation apertures using numerical modeling [11]. The Finite Element Method (FEM) was used to determine the insertion loss of an absorptive lining, and CFD was used to determine the effective free area of an aperture. Insertion loss (IL) is the change in transmission loss due to the addition of the absorptive liner; effective free area is the cross sectional area of a thin orifice that provides the same flow rate as the aperture in question. The modeling investigated the effect of height, width, and length on the insertion loss and free area of a rectangular aperture. In all cases the 5  width was much larger than the height. Results concluded that the insertion loss increased with aperture length and decreased with aperture height; aperture width had nearly no effect. The effective free area of the apertures was very nearly equal to the actual aperture area in all cases, provided the height remained above 40 mm; for heights less than 40 mm the free area is reduced – no explanations are given. Very few details were given on the FEM and CFD modeling techniques used in this work.  Hopkins [12] completed an experimental investigation into the performance of lined-duct type ventilation openings for application in cross-ventilated schools. Acoustic performance was measured using a standardized acoustic transmission suite, and flow performance was measured by driving the air through the ventilation opening at a known rate and measuring the pressure drop across it. The results from this work are analyzed in detail in section 5.4 of this thesis. For now, it will suffice to state that the lined duct type ventilation openings, with a length of 2 – 3 m, and a 50 mm thick absorptive liner, provided sufficient noise isolation for application in interior partitions in a school, and did not result in flow restrictions significantly greater than an aperture in a wall with equivalent cross-sectional area.  Previous work completed by the UBC Acoustics and Noise Research Group, in collaboration with Stantec Architecture Inc., [5] investigated complaints of poor noise isolation in a naturally ventilated building, identified the transmission issues, designed and installed silencing devices, and completed follow-up measurements. The noise isolation problems were determined to be associated with natural ventilation openings; one type was in the partition between offices and a corridor; the other type comprised a vertical shaft between floors, with inlets on each floor. A ray-tracing acoustical model was implemented to design a silencer for the vertical shafts consisting of either a lining, or vertical splitter-type baffles. It is not known what methods were used to specify the design criteria for flow performance; however, guidelines were given for minimum flow path dimensions. A Z-shaped cross-talk silencer was installed in a partition between an office and the corridor. Post-installation measurements confirmed that the vertical shaft silencer increased the noise isolation of the spaces to an acceptable level. The addition of the Z-shaped cross-talk silencer to the partition between the office and corridor did not sufficiently increase noise isolation.  6  Nunes of MACH Acoustics has designed a unique silencer that is essentially a porous absorber material in the shape of an extruded lattice [13, 14]. It is claimed to have excellent acoustic performance; unfortunately no design details are provided. A methodology is also proposed for measuring ventilation openings in situ, recognizing the problems associated with differentiating the acoustic transmission through the ventilation opening and the transmission through the remainder of the partition [14]. The approach taken is to characterize the acoustic performance of the partition when the ventilator is in its normal state, and when it is blocked acoustically. The difference between the two states can be used to determine the transmission through the ventilation opening alone1. Nunes stated that CFD simulations should be used to determine the flow performance of the ventilation silencers; however, no methodology or results are given [13, 14].  A great amount of literature exists on the airflow performance of natural ventilation systems; however, the bulk of it focuses on either buoyancy or wind driven flows through external building surfaces. Research that considers interior cross-ventilation flows commonly describes the flow, according to Eq. (3), by stating a discharge coefficient and opening area, or equivalents such as the effective free area [3, 4, 10-12, 15-17]. In practice, as well as in research, ventilation openings in naturally ventilated buildings are specified using either the discharge coefficient and area, or effective free area [18-20].  Very little work, from either the natural ventilation research or design communities, focuses on designing interior ventilation openings for a large discharge coefficient (i.e. low pressure drop given a fixed opening dimension). It is the author’s opinion that this lack of attention is because, when designing an entire natural ventilation system, interior ventilation openings are relatively well understood and predictably behaved. Ventilation system design factors such as wind and buoyancy based driving mechanisms are much more variable, less wellunderstood and more challenging to research. As a result they are generally a larger concern in the design process. To address the noise transmission through ventilation openings,  1  This work was published after the research presented in this thesis was conducted; however, a similar approach was used for the in-situ measurements presented here.  7  however, it is very important to have a strong understanding of, and optimize for, airflow behavior through these openings because the design of an optimal ventilation silencer will require compromise between acoustic and airflow performance.  1.2 Research Objectives Ideally the objectives of this work would be to develop specifications for optimal ventilation opening silencers for naturally ventilated buildings. Unfortunately, a single “optimal” design is not possible for interior natural ventilations openings, as the optimal design will be dependent on factors that vary on a case-by-case basis. Such factors may be the level of acoustical isolation required, flow performance required, geometrical constraints, aesthetic constraints or material selection constraints.  Recognizing the inability to provide a single optimized design, this work is based on the following objectives: 1. Propose an optimization metric for the performance of an interior natural ventilation opening that considers both acoustics and airflow. 2. Provide an understanding of the factors that affect speech privacy in a naturally ventilated building. 3. Develop methods for measuring natural ventilation opening performance. 4. Develop methods for predicting natural ventilation opening performance. 5. Provide performance results for natural ventilation opening silencers. 6. Provide best practice guidelines for designing successful interior natural ventilation openings.  1.3 Thesis Outline Using common theories of acoustics and airflow in the context of interior ventilation openings in naturally ventilated buildings, this thesis begins, in Chapter 2 by proposing an optimization metric. The optimization metric is a single number that describes the combined acoustic and airflow performance of the ventilation opening.  8  Chapter 3 investigates how relevant factors, including the natural ventilation opening, affect speech privacy between two spaces separated by a partition containing a natural ventilation opening.  Chapter 4 examines discusses how air flow is analyzed and develops known flow performance metrics. A discussion of the validity of using a single number discharge coefficient to specify flow performance, as described by Eq. 3, is provided.  Chapter 5 presents a preliminary study of ventilation silencers, both in-situ, and in a custombuilt lab facility. The intent is to gain an understanding of the general performance characteristics of various types of ventilation silencers. These measurements allow us to establish which of the current silencer designs have the best performance, which of the current silencer designs have the worst performance, as well as the common constraints or motivating factors that would lead to the final selection of a silencer design.  In order to move towards improving the design of natural ventilation openings, computational methods are outlined in Chapter 6 for predicting the acoustical and airflow performance of ventilation openings. Performance predictions are presented for a number of ventilation opening silencers and comparisons are made to laboratory measurements.  This work is summarized in Chapter 7 by directly addressing the research objectives, as stated above.  9  Chapter 2: Optimization Metric: Open Area Ratio In order to optimize the performance of a silencer a metric must exist to optimize over. Typically a silencer’s acoustic performance would be characterized by its transmission loss, a frequency dependent value, and its flow performance characterized by the flow rate through it as a function of pressure. Here it is proposed to use “equivalent open areas” for the acoustic transmission and air flow to characterize the performance of the ventilator at a specific operating condition. The ratio of the equivalent open areas – the open area ratio (OAR) – provides a single number metric to optimize over by maximizing: OAR =  EOA f  (4)  EOA s  EOAf is the equivalent flow area and EOAs is the equivalent acoustic area. OAR is independent of the size of the opening to the extent that the sound energy transmission and ventilation flow rate are directly related to the size of the opening. The reader and/or user should keep in mind that this is a performance optimization. Other factors such as cost, dimensions, and aesthetics will be crucial in the final design and selection of a silencer, and are not considered here. Once the OAR is defined, this section provides a discussion of the implications of using diffuse field room-acoustic theory to describe ventilation opening performance.  2.1 Calculating Equivalent Open Areas The equivalent open area for flow and for sound must address the fact that flow characterization is flow-rate dependent and that acoustic characterization is frequency dependent.  2.1.1  Equivalent Open Area for Sound  It is common practice to assume that the sound field in most rooms is diffuse, which implies that the reverberant sound intensity is uniform in terms of location and direction throughout the room. In this case, the sound intensity in one direction through a plane can be related to the sound pressure in the room, which is also uniform in a diffuse field [21]:  10  2  p Is = s 4ρ 0 c  (5)  The sound power transmitted through a ventilation opening in the wall of a room ( Wt ) is equivalent to the sound intensity travelling in one direction through a plane in the room, multiplied by the area of the ventilation opening ( Av ): Wt = I s Av  (6)  If the sound energy transmitted through the opening is radiated into a receiver room with a diffuse sound field, and the steady-state sound pressure in the receiver room is measured along with the reverberation time in the room, it is possible to calculate the sound power being transmitted into it ( Wt ): 2  A p Wt = r r 4 ρ 0c  (7)  Ar , the total acoustic absorption in the receiver room can be determined from the measured reverberation time ( T60 ) and receiver room volume ( Vr ):  Ar =  0.161Vr T60  (8)  From the sound pressure level in the source and receiver rooms, and the receiver room reverberation time, work backwards and deduce how large the opening must be.  Av =  Wt I1  Now, assume that there is a treatment applied to the opening such that some of the sound energy transmitted into the opening is dissipated prior to being emitted into the receiver room. Based on the difference in sound pressure levels between the source and receiver rooms, and the reverberation time, again calculate how big the opening between the rooms must be; however, this time the area will be smaller than the actual size of the opening. The area that is calculated is the size of an untreated opening that would transmit an equivalent amount of sound energy. This is called the equivalent open area for sound ( EOA s ).  11  The equivalent open area of the ventilator is simply the product of the ventilator’s power transmission coefficient ( τ v ) and the corresponding ventilator area (Av). This can be shown through an equivalence of power transmission: W2 = I 1τ v Av = I 1EOA s EOA s = τ v Av  (9)  In reality, acoustic fields in rooms are not generally diffuse and, certainly, sound through small openings cannot be predicted accurately using diffuse field theory (see section 2.3). The equivalent acoustic open area is the equivalent open area based on a diffuse field sound transmission model and therefore will not necessarily be physically meaningful. That being said, it is a useful measure, can be easily visualized, and can be contrasted to equivalent flow area.  Unfortunately, because the transmission coefficient of a silencer will be strongly frequency dependent, an equivalent open area would be required at each frequency to describe the silencer. It is common practice in acoustics to convert frequency dependent values into single number values; in order to do so the relative importance of each frequency band must be understood for weighting purposes then, by summing weighted values or some other method, a single number value may be produced. The EOA s will be converted into a single number through frequency averaging the weighted EOA s at each frequency band. Weighting is done by considering the spectral shape of the source sound power and the spectral shape of the receiver sensitivity. In essence, the weighting makes the EOA s particularly sensitive to frequencies that are likely to be produced at a high level by the source as well as frequencies that receiver is sensitive to.  To choose a source spectrum weighting scheme, it is first assumed that the silencer will be mounted in an office partition to another interior space. Noises such as computer fans are constant and contain no information, so they are not considered as important in terms of privacy (sounds exiting the room) or annoyance (sounds entering the room). The most significant source of annoying noises to be controlled to acceptable levels is speech;  12  therefore speech levels have been used to generate the source spectra. Supporting this conclusion, previous work has shown that irrelevant speech is more annoying than broadband noise [22]. Third octave band speech pressure level spectrum, combined with the directivity of a human speaker, at a normal speaking level were averaged to create the source power level spectrum. Speech levels are generated by converting the ‘Normal’ Speech Spectrum Level given by ANSI S3.5 into third octave band values using the band width ∆f [23]:  Speech Level = Speech Spectrum Level + 10 log(∆f ) This conversion corrects for the increasing band width, and therefore increasing band power, with increasing frequency. The receiver spectrum is most simply the common A-weighting which approximates the auditory sensitivity of an average adult with normal hearing. However, A-weighting is only one approach. If it were desirable to find a metric specifically to correlate with a lack of speech privacy, then a weighting scheme based on the importance of each band for understanding speech would need to be determined and used (SII/STI methods incorporate such a weighting but it is not readily applicable). If it were desired to produce a metric related to distraction, which is not necessarily related to intelligibility, then a different frequency weighting scheme would need to be developed. Research has shown that distraction may be related to temporal variability, making it hard to correlate it with a frequency spectrum alone [24]. A listener’s auditory sensitivity is related to both intelligibility and distraction; therefore, the A-weighting was used as a good general weighting scheme.  A-weighting is applied to the speech source levels (decibel addition) to give the A-weighted speech source levels. Prior to using the A-weighted speech source levels as a weighting spectrum they must first be normalized so that its sum is equal to zero dB. Subtracting the ventilators transmission loss spectrum from the, normalized, A-weighted speech levels produces a spectral shape that represents the levels that a human would hear on the receiver side of the partition, due to transmission of speech sounds through the ventilator, reverberant field not included. The normalized A-weighted speech levels minus the silencer transmission loss will be referred to in this work as simply the Transmitted Speech Spectrum ( − TL A_Speech ). Peaks in this transmitted speech spectrum represent the most audible sounds,  13  and thus they are the frequencies that should be targeted for silencer improvement. Summing all of the levels produces an effective, single value, transmission coefficient for an Aweighted speech source. It is now possible to convert the effective transmission loss into a single number equivalent open area to characterize the silencer: − TL A _ speech  EOA s = Avτ A _ speech = Av 10  10  In North America, the most common method for assessing the capability of a partition to provide speech privacy is the Sound Transmission Class (STC) [25]. Research has shown the STC not to correlate well with intelligibility [26]; therefore, there was little motivation to use it in this method. Additionally, the STC is not, by definition, the decibel representation of a transmission coefficient; therefore, it can’t be used to directly calculate an equivalent open area.  2.1.2  Equivalent Open Area for Flow To characterize ventilation openings, flow rate and pressure differential are measured  at a number of different applied pressures. Following ASTM E779-10 [27], a log-linear regression is applied to the result such that the data is fit to a curve of the form: Q = C∆p n  (10)  Conservation of energy for lossless, horizontal, streamline flow through a constriction can be written, according to Bernoulli’s equation (conservation of energy), as:  p1 +  1 1 ρ u1 2 = p 2 + ρ u 2 2 2 2  If the velocity in the constriction is much larger than the velocity upstream of it ( u 2 >> u1 ), then we can deduce:  2∆p  Q = A   ρ   0.5  (11)  The orifice area is A, and ∆p is the difference in pressure. Combining Eq. 3 and 11, assuming identical flow rates and pressures, an effective flow area can be solved for. This is identical to the ‘effective leakage area’ (Af) defined by ASTM E779-10 [27].  14  A f (∆p ) = C  ρ 2  ∆p n −0.5  (12)  The effective leakage area can be normalized by the discharge coefficient of an opening in a flat plate (Cd = 0.61) [12], giving the equivalent open area in a flat plate required to produce the same flow rate as the ventilation opening in question: EOA f (∆p ) =  A f (∆p )  (13)  0.61  Provided n = 0.5, there is a simple relationship between the equivalent open area for flow and the discharge coefficient. EOA f = Av  Cd 0.61  (14)  Note that, for n ≠ 0.5 , the equivalent open area is dependent on the applied pressure. For this reason, the equivalent open area should be measured and calculated at a pressure that is typical of the ventilator’s operating conditions. Unfortunately, typical operating pressures for interior natural ventilation openings are small compared to the pressures during testing as described by ASTM E779-10 [27]. Additionally, it is not possible to accurately extrapolate below the measured data points because the data measured at high flow rates is not necessarily an accurate predictor of the ventilator’s performance at low flow rates. Section 4.4.2 of this thesis discusses the implication of flow conditions on ventilator performance characterization; section 5.3.6 discusses what the actual flow conditions are in natural ventilation openings. In this work the lowest measurement pressure was used as the reference pressure in calculating EOAf.  2.2 Summary Discussion on the Optimization Parameter The OAR has been presented as an optimization parameter for ventilation openings. It is very promising, as it is simple to use and based on common standardized measurement and analysis techniques. A simple aperture takes on a value of one, and higher values indicate better performance, lower values worse.  15  It is useful to introduce specific equivalent open areas for sound and flow to get nondimensional performance metrics that are nominally independent of the ventilator size. The specific equivalent open area for sound is akin to the transmission coefficient, and the specific equivalent open area for flow is akin to the discharge coefficient.  SEOA s =  SEOA f =  EOA s Av EOA f  15  16  Av  When using these performance metrics care needs to be taken regarding the assumptions being made, the most significant of which are that the sound fields are diffuse, and the equivalent open area for flow is independent of flow rate.  The OAR optimization parameter recognizes that the airflow and acoustic performance can not be optimized independently; however, it also assumes that their physics are not coupled. In fact, the acoustic and airflow behavior must be coupled as they are both the response to pressure and particle velocity fluctuations in air. The two ways that acoustic-flow coupling can be significant in ducts are flow-generated noise, and changes in the speed of sound; however, it can be argued that in natural ventilation openings these effects are insignificant.  Flow-generated noise is caused by turbulent flow interacting with duct surfaces [28]. It has been demonstrated analytically and experimentally that below the cut-off frequency the sound power level generated by flow in a duct is proportional to the flow velocity to the fourth power, and above the cut-off frequency the sound power level generated is proportional to the flow velocity to the sixth power [28]. Because the flow velocities in naturally ventilated buildings are much lower than in a mechanically ventilated building, the flow noise will be much less. Even if the ventilation opening did generate flow noise, it is not necessarily a problem. Many of the speech privacy related problems in naturally ventilated buildings are understood to be a result of low background masking noise due to the lack of a mechanical ventilation system [29, 30]; this is exemplified in section 3.3.3.  16  Variations in sound speed are typically due to temperature gradients or flow; in a duct temperature can be assumed uniform. Mean flow changes the speed of sound relative to the duct, and flow gradients in the duct cross section cause refraction; mean flow and refraction can result in either higher or lower attenuation depending on the direction of sound propagation with respect to flow. In outdoor sound propagation, where sound travels great distances and slight variations in speed result in a large displacement of the wave front, refraction and mean flow effects are significant, even for low Mach number (M) flows. In ducts however, because the distances travelled are much smaller, refraction effects are small provided M<0.05 [21, 31].  2.3 Diffuse Field Theory and Ventilation Opening Characterization In order to calculate the sound transmission properties of a ventilation opening, be it the TL, EOAs, or STC, the sound power incident on the ventilator is calculated, based on measurements of the sound pressure level in the room, using diffuse field theory. Sound fields in real rooms are rarely a good approximation of a diffuse sound field; even in the best of cases, sound fields are never diffuse near the room surfaces. This section will provide a brief discussion of the assumptions and implications of using diffuse field theory for measuring the transmission loss of a ventilation opening.  A diffuse sound field is one that is uniform in magnitude and direction at all locations; additionally, the temporal and spatial relationships of the pressure modes in the room must be random [32]. When rooms are very large, very small, have uneven absorption distributions, large amounts of acoustically absorbing material, or large interior dimension aspect ratios, the sound field will not be diffuse. Measurements must be made in all types of spaces, so acousticians measure the standard deviation of sound pressure levels in the sound field which, because a highly diffuse sound field will have a low standard deviation, is used to imply a level of confidence in the result. Sound pressure levels are unable to give directional information about the sound field; therefore the sound pressure level standard deviation is only an indicator of the diffuseness, it does not tell the complete story. Diffuse field theory is used exclusively in practice; experience is required to judge the diffuseness of a field and its significance to the calculated result. 17  In the case of natural ventilation openings, even if the room supports an excellent approximation of a diffuse field, diffuse field theory is incomplete and wave effects become important. To determine the sound power entering a ventilation opening, two wave effects that warrant discussion here are constructive interference and diffraction.  In a diffuse field, the phases of various modes are random; therefore, the time-average pressure at any location can be found through energy addition of the modes. At room boundaries, due to the boundary condition of zero particle velocity normal to the wall, the spatial phase relationship of the modes is not random; they all have pressure maximums at the surface and will interfere constructively [33]. At a wall the sound pressure level is 2.2 dB higher than in the diffuse field; in double and triple corners the pressure level is further increased [34]. The sound pressure level is within 1 dB of the room average value if measured more than a quarter of the acoustic wavelength from the wall. This shows that the sound field at the wall is, by definition, never diffuse. The implication is that the sound pressure level that the ventilation opening is exposed to is higher if it is on a room boundary, especially if it is at a double or triple corner.  Diffraction will cause additional energy to enter the duct. The surface adjacent to the duct is typically hard and will therefore be the location of a pressure maximum (anti-node). At the duct inlet surface there is, to a first approximation, no impedance change and no pressure mode. Air adjacent to the duct will follow the pressure gradient and progress toward the duct. The effect of diffraction will increase as the ratio of the wavelength to ventilator inlet dimension increases.  Even if the room containing a ventilator has a highly diffuse sound field, it should not be expected that diffuse field theory will accurately predict the sound energy entering the ventilation opening. If the ventilation opening is near a room surface, or corner, it will be exposed to an elevated sound level caused by the constructive sound field. If the ventilation opening is not large compared to the wavelength, significantly more energy than predicted will diffract into the duct inlet. As a result, even in a room with a diffuse sound field, the location of the ventilation opening will affect the sound transmitted through it (and thus its  18  transmission loss). Additionally, because more energy may enter the ventilation opening than predicted by diffuse field theory, we must allow measures of TL and STC to be negative, and the SEOAs to take a value greater than one.  19  Chapter 3: Investigating the Factors in Speech Privacy In order to understand how ventilation openings affect speech privacy between two interior spaces a simple model has been created. This model considers two adjacent rooms with a separating wall containing a ventilation opening. One of the rooms, the source room, contains a talker, and the privacy is assessed for a listener in the other room, the receiver room. Speech privacy is determined by the lack of speech intelligibility, as quantified by the speech intelligibility index (SII). Using this model the effects that ventilation openings, partition transmission loss, room size, room furnishings, background noise levels, and speech power levels have on privacy can be predicted.  3.1 Speech Intelligibility Index The speech intelligibility index (SII) is a parameter that varies from 0 to 1 and is intended to correlate with intelligibility [23, 35, 36]. It is calculated using a signal to noise approach, where the signal is the speech and the noise is background noise. The effect of noise is determined through how it masks a signal of speech frequency that is being modulated at various subsonic frequencies which correspond to the temporal modulation of sound levels in speech. Early reverberation will enhance the signal, as it does not mask the signal modulation. Late reverberation will contribute to noise, as it exists later in time and will mask the modulation. Diffuse field theory is used to model the presence of reverberation in the SII calculation [36]. A low value of SII has been used to imply speech privacy [26, 3739]. Previous work has suggested that, for open plan offices, SII less than 0.2 is acceptable [38]. Other work has suggested that if the articulation index (AI), which has subsequently been replaced by SII, is greater 0.05 there will be some level of dissatisfaction with the level of privacy [37]. Therefore, for this work, it will be assumed that for SII less than 0.2 there is Moderate privacy, and than for less than 0.05 there is a High level of privacy. It is important to note that the SII has been shown to be an ineffective predictor of speech security, largely because total speech security does not exist even for SII = 0 [40].  20  3.2 Model Description In order to determine the SII at the receiver it is necessary to know the sound levels, as well as the reverberation time and background noise levels, at the receiver.  Speech levels at the receiver are calculated starting in the source room with the speech source sound power level. Knowing the source room’s dimensions and surface materials, the sound pressure level in the source room can be determined. The transmission loss of the composite partition can be calculated and used to determine the sound power transmitted into the receiver room based on the source pressure level if the area and transmission loss of both the wall and the ventilation opening are known. Using the sound power transmitted into the receiver room, and also knowing its size and surface materials, the sound pressure level at the receiver can finally be determined.  The reverberation time in the receiver room can be determined based on its dimensions and surface materials.  When calculating the SII, typically one would want to use the background level most representative of a typical office scenario; as such it is sensible to use mean, time averaged, background levels. Here, however, the SII is being calculated for a non-typical application; that is, to measure levels of distraction or speech privacy (the presence of unwanted intelligibility). In an environment where one is talking on the phone, or even typing with confidence, the background noise levels will be at an elevated level as compared to when involved in a quieter activity such as thinking. If mean sound pressure levels were determined in a room where the noise levels were fluctuating, the dB scale naturally biases the durations of high levels, and the durations of low background noise levels are concealed. By concealing the durations of low noise levels, the most likely periods of distraction or unwanted speech intelligibility are also concealed. In order to provide a background level that is representative of the quieter periods in the receiving room, statistical pressure levels can be used. L90 is the level of sound that is exceeded 90% of the time, making it more appropriate than Leq as a background level for SII measurements intended to infer privacy or distraction. In this work, the L90 has been measured in a typical office scenario. 21  3.2.1  Model Inputs  To investigate how room and partition design effect the SII, appropriate speech levels, background noise levels, partition types, room surface materials and room dimensions must be specified.  The background noise level, L90 in a quiet office, is given in Table 1; the speech power levels in dB for several vocal efforts are given in Table 2 [23]. Unless otherwise noted, the background noise levels as stated in Table 1 will be used; however, elevated background noise levels are created by adding a constant decibel value to each third octave band pressure level shown in Table 2. The levels in Table 2 correspond to NC20; however, the room’s actual NC, as calculated from Leq instead of L90, would be higher.  Table 3 shows the surface materials used and their random incidence absorption coefficients [41]. These materials are combined to create five different room configurations, as shown in Table 4, named 1 through 5 and increasing in average absorption.  Dimensions representative of a typical small office, large office, classroom and small gymnasium are given in Table 5.  The transmission loss and associated STC of four different partition types are shown in Table 6 [36]. The partition types are: •  10 mm glass  •  Two layers of drywall separated by a wooden stud  •  Two double layers of drywall separated by a wooden stud  •  Two double layers of drywall on resilient hangars separated by a wooden stud  Quiet office (NC 20)  Table 1: Background noise level L90 [dB]. Frequency [Hz] 125 250 500 1000 2000 35.6 22.0 20.4 18.1 16.0  4000 11.6  8000 12.3  22  Table 2: Speech power levels [dB] [23]. Frequency [Hz] 125 250 500 1000 2000 50 59 61 55 50 58 67 69 61 56 62 71 75 70 64 65 74 79 79 73 76 75 84 88 83  4000 45 50 57 66 75  8000 40 44 48 54 63  Table 3: Absorption coefficients of room surfaces [41]. Frequency [Hz] Material 125 250 500 1000 2000 Concrete 0.01 0.01 0.02 0.02 0.02 Drywall 0.08 0.11 0.05 0.03 0.02 Carpet 0.02 0.04 0.08 0.20 0.35 Carpet with underlay 0.03 0.09 0.20 0.54 0.70 Acoustic Tile 0.09 0.28 0.78 0.84 0.73  4000 0.05 0.03 0.40 0.72 0.64  8000 0.05 0.03 0.40 0.72 0.64  Speech effort Casual Normal Raised Loud Shout  Configuration # 1 2 3 4 5  Type Small Office Large Office Classroom Gymnasium  Partition 1 2 3 4  Table 4: Room surface configuration types. Floor Wall Concrete Concrete Concrete Drywall Carpet Drywall Concrete Drywall Carpet with underlay Drywall Table 5: Room volumes. Length [m] Width [m] 3 3 5 5 10 10 20 20  Height [m] 3 3 4 10  Ceiling Concrete Drywall Drywall Acoustic Tile Acoustic Tile  3  Volume [m ] 27 45 400 4000  Table 6: Transmission loss and STC of various partitions [36]. Frequency [Hz] STC 125 250 500 1000 2000 4000 16 10 12 14.5 15 18 18.5 34 15 24 32 41 37 43 39 15 35 43 48 53 50 52 28 43 51 56 61 57  8000 20 43 50 57  23  3.2.2  Calculating the Source Room Sound Pressure Levels  The source room sound pressure level ( Lp s ) can be calculated, using Sabine diffuse field theory, from the source power level ( Lws ) and the room’s dimensions and materials [21]:   4 Lp s = Lws + 10 log  Rs      (17)  Rs , the room constant, is calculated from the room’s area-weighted average absorption coefficient ( α s ) and the room’s surface area S s (Sabine version):  Rs =  α s Ss 1−αs  (18)  Knowing the source room volume ( Vs ), the reverberation time of the source room can also be estimated:  T60 s =  3.2.3  0.16Vs α sSs  (19)  Calculating the Transmission Loss of the Partition  A single transmission loss value ( TL p ) is required for the partition. The single, equivalent, transmission loss is the combined effect of the transmission loss of the wall and ventilation opening. It is calculated, based on average energy transmission, by finding the area-weighted average transmission coefficient (τ p ) . Here subscripts w and v represent the original wall and the ventilation opening: TL p = −10 log(τ p )  τp =  τ w Aw + τ v Av Aw + Av  τ w = 10  −  (20)  TL w 10  24  τ v = 10  3.2.4  −  TL v 10  Calculating the Receiver Room Sound Pressure Levels  The receiver room sound pressure level ( Lp r ) is calculated from the source room sound pressure level, the transmission loss of the partition, and the room’s dimensions and materials:   Ap Lp r = Lp s − TL p + 10 log  α r Ar      (21)  S p is the total partition area, and α r and S r are the area-weighted average absorption  coefficient and the total receiver room surface area. As in the source room, the reverberation time can be calculated in the receiver room:  T60 r =  3.2.5  0.16Vr α s Ar  (22)  Cautionary Note  The model just described is excellent because of its simplicity; however, it relies on a number of assumptions that must be respected.  The speech levels in the receiver room have been influenced by the reverberation in the source room and the receiver room. As such, in reality, the associated reverberation time will be longer and have a double-sloped decay. The SII method assumes that the reverberation time in the receiver room is the only reverberation and will therefore underestimate the masking due to reverberation. Especially if the source room has a longer reverberation time than the receiver room, the model will under-estimate masking due to late reverberation and over-estimate the intelligibility.  This work will not consider the reality that a talker will change their vocal effort based on the presence of speech masking noise or the dimensions of the room. Masking noise, from either  25  background noise or late reverberation, can increase vocal effort as explained by the Lombard effect [42]. Room dimensions are related to the source-receiver separation distance; vocal effort is also known to increase with this separation distance [43].  Additionally, note that the background noise levels in the source room are not considered. If the background levels in the source room are not small compared to the speech pressure levels, the background noise may provide some masking that is neglected in this model.  Finally, and most importantly, this model is only accurate if the sound fields are diffuse. In very large, very small or very absorptive rooms, sound fields are not diffuse. If the aspect ratio of the rooms is large, the sound field is not diffuse. If the speech source, or the receiver, is near the partition, the direct sound level will not be small compared to the reverberant sound level and diffuse field sound transmission will not be applicable.  3.3 Results The model, as described above, was implemented in MATLAB. A copy of the code is provided in Appendix B.1. Prior to observing the effect of transmission loss on SII, the effect of other factors such as vocal effort, room size, room furnishings and background noise is investigated. The effect of ventilation opening size and wall performance on SII is then investigated. Ventilation opening size is discussed in terms of equivalent open area making the results valid for any silencer with the specified equivalent open area regardless of the silencer’s actual dimensions.  3.3.1  Vocal Effort and SII  Figure 4 shows the effect of vocal effort on the speech intelligibility between two identical rooms. Results are plotted for each of the room sizes; in each case the room surfaces are in Configuration 4 and separated by Partition 2. In the Small Office reverberant levels are high and the reverberation time is low leading to high levels of intelligibility. Even for a Casual voice level there is insignificant privacy between the two rooms. As the room sizes increase, the reverberant level decreases and the reverberation time increases, increasing the masking noise and decreasing the speech level. As a result there is a High level of speech privacy in 26  the gymnasium provided the vocal effort is not greater than Normal. In the gymnasium the vocal effort must be increased to Shout before speech privacy is deemed Moderate (SII<0.2). 0.8 0.7 0.6  Small Office Large Office Classroom Gymnasium  SII  0.5 0.4 0.3 0.2 0.1 0 Casual  Normal  Raised Vocal Effort  Loud  Shout  Figure 4: Variation of SII vocal effort for various room sizes.  3.3.2  Room Size, Furnishings and SII  Figure 5 shows how speech intelligibility varies with the surface materials (surface absorption). Results are plotted for all of the room sizes. The vocal effort is at a Normal level and the sound is transmitted through Partition 2. Increasing the reverberation time (via decreased absorption) leads to both increased signal levels from the early reverberation, and increased masking noise due to the late reverberation; the resultant effect on the SII is complicated. For all rooms it appears that speech intelligibility is maximized (privacy is minimized) for rooms with moderate absorption. This implies that for optimal privacy the rooms should be highly absorptive or highly reflective; unfortunately this is in direct contradiction to the typical requirement for high intelligibility within each individual room. As the rooms become larger the amount of absorption leading to the lowest privacy decreases. This is likely because, as the room becomes larger, the speech sound levels decrease while the background noise remains fixed; as a result, increased reverberant levels  27  are required to bring the signal out of the background noise. As observed in Figure 4, for a fixed vocal effort, SII is highly dependent on room size. 0.5 Small Office Large Office Classroom Gymnasium  0.45 0.4 0.35  SII  0.3 0.25 0.2 0.15 0.1 0.05 0  1  2  3 Surface Configuration  4  5  Figure 5: Variation of SII with surface absorption in various room sizes – successive surface configurations have increasing absorption.  3.3.3  Background Noise and SII  Figure 6 shows the dependence of SII on background noise and room-surface absorption. The vocal effort at a Normal level and the sound is transmitted through Partition 2. For a given room configuration, SII is highly dependent on background noise level. At the baseline noise level, poor privacy exists for all but the most absorptive rooms. Raise the level by 10 dB and the privacy becomes Moderate for all room-absorption cases. If the background levels are raised by 30 dB, then there is High speech privacy for all room-surface configurations. This provides a strong argument for the application of noise masking systems.  As in Figure 5, it can be observed that there is a worst case scenario for room absorption. As background noise levels increase, the more reverberant rooms have higher intelligibility, likely because the early reverberant energy is required to bring the signal out of the background noise. For the smaller rooms, the speech levels are much higher and high levels  28  of reverberation can cause increased masking of the signal. Previous work by Hodgson and Nosal at the UBC Acoustics and Noise Research Group has concluded, similarly, that reverberation time is beneficial for intelligibility if background noise is present [44]. Hodgson and Nosal also note that these dependencies are not so simple. The reverberant field due to the noise source, and thereby the noise levels for a fixed noise-source power level, will increase with reverberation time. Additionally, the proximity of the noise source to the receiver can be a critical factor [44]. 0.35 BGN0+0dB BGN0+10dB  0.3  BGN0+20dB 0.25  BGN0+30dB  SII  0.2 0.15  0.1  0.05  0  1  2  3 Suface Configuration  4  5  Figure 6: Variation of SII with increasing surface absorption for various BGN.  3.3.4  TL and SII  The partition, with its performance quantified by transmission loss, is typically the primary design element intended to create speech privacy between two locations. This next section will attempt to quantify the effect of a partition’s transmission loss on SII, as well as the effect of a reduction in the partition’s transmission loss due to the addition of a ventilation opening.  29  3.3.4.1  Partitions without Ventilation Openings  Figure 7 shows the relationship between SII and the partition type, plotted with respect to their STC value. Here the vocal effort is Normal and the partition is separating two large offices with the surfaces in Configuration 4. As expected, the SII is highly correlated with the partition’s STC. For the lowest STC partition – a 10mm glass sheet (STC 16) – the speech intelligibility is high, implying no privacy for any vocal effort. Improving the partition to a typical stud separating two layers of drywall (STC 32) provides Moderate privacy at Casual speech levels, but not at higher ones. A wall with two double layers of drywall separated by a stud and connected with resilient hangars (STC 52) provides a High level of privacy for Casual and Normal vocal efforts, Moderate privacy for Raised and Loud vocal efforts, but insignificant privacy if the vocal effort is Shout. Pleasingly, the ANSI Standard S12.60 Acoustical Performance Criteria, Design Requirements, and Guidelines for Schools, requires that the minimum STC of a partitions between offices is 45 dB [45]. As can be seen in Figure 7, 45 dB this agrees quite well with the 0.05 SII criterion, at a Normal vocal effort, for High speech privacy. 0.8 Casual Normal Raised Loud Shout  0.7 0.6  SII  0.5 0.4 0.3 0.2 0.1 0 15  20  25  30  35 STC [dB]  40  45  50  55  Figure 7: Variation of SII with STC for various vocal efforts (Large Office, Surface Configuration 4).  30  3.3.4.2  Partitions with Ventilation Openings  When ventilation openings exist, without a silencing device, in a partition, building occupants often complain about poor speech privacy (see Introduction). To examine the effect of ventilation openings in partitions, they will be included and considered in terms of their equivalent open area. Figure 8 shows the results, with the ventilator’s EOAs expressed as a percentage of the total partition area (Aw =15 m2). Considered here are two Large Offices with Surface Configuration 4; the vocal effort is a Normal level. Partition 1, even without an opening, does not provide privacy; further reductions in transmission loss do not make the problem much worse, as it is already nearly as bad as it can be. Partitions 2, 3 and 4, which do provide privacy as complete partitions, have essentially lost all ability to provide privacy if the ventilator’s EOAs reaches 0.1% of the partition area (0.12 x 0.12 m opening). With 1% EOAs (0.39 x 0.39 m opening) they provide similar attenuation to the glass partition (Partition 1). This figure clearly shows that, if a ventilation opening is included in a partition with out being silenced, it is of no benefit to provide a high performance wall for the remainder of the partition.  Figure 9 is similar to Figure 8; however, the SII for each partition has been normalized to the SII with a complete partition. This allows examination of the relative effect of the ventilation opening on privacy. Once again, for Partition 1, the intelligibility is not increased by an EOAs up 1% the size of the partition. Partition 2, however, will allow the SII to double if the ventilator’s EOAs is 0.1% of the total wall area (0.12 x 0.12 m). Partitions 3 and 4 are even more restrictive, allowing the SII to double with the ventilator’s EOAs only 0.01% and 0.001% (4x4cm, and 1.2x1.2cm) respectively. This is sufficient to conclude that un-treated ventilation openings can not be included in higher performance partitions without greatly reducing the privacy that the partition would otherwise provide.  Figure 10 shows another approach to describing the effect of ventilation openings on the privacy that a partition provides. As in Figure 9, in Figure 10 the SII is normalized to its value with a complete partition so that the relative effect is observed. The ventilator’s EOAs, instead of being expressed as a percentage of the wall’s area, is normalized to the equivalent open area of the wall (EOAs_w). For reference, the EOAs_w values of the partitions are given  31  in Table 7. For Partition 1, it is observed that the privacy cannot be reduced when there is none to begin with. For Partitions 2, 3 and 4, however, if the EOAs_v (subscript v refers to the ventilator) is less than one tenth of the EOAs_w the reduction in privacy is small. Moreover, if the EOAs_v reaches or exceeds 50-100% of the EOAs_w, then there is a large reduction in the privacy provided. As a rule of thumb, it can be concluded that the EOA of the ventilator should optimally be less than 10% of the original partition’s EOA, and it should never exceed 50%, to avoid a major loss in performance. 1 Partition 1 Partition 2 Partition 3 Partition 4  0.9 0.8 0.7  SII  0.6 0.5 0.4 0.3 0.2 0.1 0 0.0001  0.001  0.01 EOA s /Aw [%]  0.1  1  5  Figure 8: Variation in SII with EOAs for different wall types.  Partition 1 2 3 4  Table 7: Equivalent open area of the partitions. 2 2 STC Aw [m ] EOAs_w [m ] SEOA s_w 16 15 0.56 0.037 34 15 0.016 0.0011 39 15 0.0032 0.00021 52 15 0.00025 16E-06  32  5 Partition 1 Partition 2 Partition 3 Partition 4  4.5 4  SII/SII0  3.5 3 2.5 2 1.5 1 0.001  0.01 EOA s /Aw [%]  0.1  1  Figure 9: Variation in the normalized SII as a function of EOAs for different wall types.  5 4.5 4  Partition 1 Partition 2 Partition 3 Partition 4  SII/SII0  3.5 3 2.5 2 1.5 1 0.01  0.1  1 10 EOA s v /EOA s w Figure 10: Variation in the normalized SII as a function of EOAA_V /EOAA_W, for different wall types.  33  3.4 Factors Affecting Speech Privacy: Summary As observed in Figure 7, SII is highly dependent on the transmission loss of the partition. Unfortunately, as shown in Figures 4, 5 and 6, it can also be greatly affected by changes in vocal effort, room size, room furnishings and background noise. As such, when designing a partition to achieve a required level of privacy, it is insufficient to consider the partition’s transmission loss alone.  The transmission loss of a partition, and the privacy it provides, can be greatly reduced if ventilation openings without adequate silencing are included. As shown in Figure 8 for a typical office, no significant level of privacy can be obtained, regardless of the wall construction type, if an untreated opening one tenth of a percent of the total wall area exists (0.12 x 0.12 m opening in a 5 x 3 m wall). It is doubtful that a successful ventilation system can be designed with an opening restricted to these dimensions. As a result, to achieve significant privacy, natural ventilation openings must be treated acoustically. Figure 10 shows that, in a typical office, the SII is significantly increased (privacy reduced) if the ventilator’s EOAs exceeds 10% of the wall’s EOAs. Additionally, the SII approximately doubles (for low values of initial SII) if the ventilator’s EOAs exceeds 50% of the wall’s EOAs.  34  Chapter 4: Describing Flow Performance of Ventilation Openings In this section a derivation is provided for the discharge coefficient, as well as other similar metrics, in order to assess the applicability of these metrics for describing the flow performance of interior natural ventilation openings. A number of texts were used to develop this discussion [46-48].  The general solution for fluid flow is represented by the Navier-Stokes equation. It can be developed through a general consideration of the forces and accelerations on a fluid element. The Navier-Stokes equation can be simplified to form a more user-friendly solution known as Bernoulli’s equation. Bernoulli’s equation is the mathematical basis for the design of duct systems. Empirically derived energy losses must be added to Bernoulli’s equation in order to sufficiently describe the flow; these losses are what concern us in the design of ventilators.  4.1 Navier-Stokes Equation The Navier-Stokes equation is created by setting up a force balance on the flow element: v v v  ∂u v v  (23) ρ  + u ⋅ ∇u  = −∇p + µ∇ 2 u + ρg ∂ t   v Variables are the density ( ρ ), particle velocity vector( u ), time (t), pressure (p), dynamic v viscosity ( µ ), and the body force vector ( g , often gravity). Insight into the behavior of the  flow can be gained by introducing non-dimensional parameters [46]. Each variable is replaced by the product of a characteristic value and a dimensionless quantity identified by a caret:  v v u = Uuˆ , t = τ tˆ ,  1 ˆ 1 ˆ2 v v p = Ppˆ , g = Fgˆ , ∇ = ∇ , ∇2 = 2 ∇ L L  U is the characteristic velocity, τ is a characteristic time period, P is a characteristic pressure, F is a characteristic body force and L is a characteristic dimension. Inserting these into the Navier Stokes equation and rearranging can produce:   ρL2   µτ  2  ∂uˆ ˆ 2 uˆ −  ρL F  gˆ = − PL ∇ ˆ pˆ  + Re uˆ ⋅ ∇uˆ − ∇     ˆ  µU   ∂t  µU   35  in which Re is the Reynolds number, the well-known non-dimensional number that describes the ratio of inertial forces to viscous forces: Re =  ρUL µ  For incompressible (constant density) flows, in the absence of elevation change, gravity can be neglected. If the flow is steady, derivatives with respect to time are zero – using these assumptions the Navier-Stokes equation can be written as:   PL  ˆ v v ˆ 2 vˆ Re uˆ ⋅ ∇uˆ − ∇ u = − ∇pˆ µ U    The pressure’s dependence on velocity is clearly dependent on the Reynolds number; general conclusions can be drawn: 1. If Re is large, indicating relatively large inertial forces, then the forces due to convective acceleration will dominate the shear forces; as a result, the pressure fluctuations will be proportional to fluctuations in the velocity squared. 2. If Re is small then the viscous forces dominate the inertial forces and the pressure fluctuations will be proportional to the velocity fluctuations.  Understanding what constitutes ‘large’ and ‘small’ Reynolds numbers is not trivial; however, it becomes very important when using empirical, engineering analysis methods for determining flow behavior. As shown below, the value of Re often describes the limits of the method’s validity.  4.2 Bernoulli’s Equation The Navier-Stokes solution can be used to develop another result commonly known as Bernoulli’s equation. If we believe shear forces to be relatively small, either due to the low viscosity of the fluid, or small velocity gradients, then we can remove them from the force balance. Bernoulli’s equation is said to be a high Reynolds number approximation along a streamline [46] because, at high Reynolds numbers, viscous forces are small compared to the inertial forces. Removing the viscous stresses, the Navier-Stokes equation can be written as:  36  v ∂u v v ∇p v + u ⋅ ∇u = − +g ρ ∂t  v u2  v v v v Next, substitute the vector identity u ⋅ ∇u = ∇  − u × (∇ × u ) to obtain:  2  v v  u 2  ∇p v v ∂u v + ∇  + − g = u × (∇ × u ) ∂t  2  ρ  (24)  If we integrate the second term of Eq. 24 between points 1 and 2 along a streamline s: v v v 2 u2  u2 u2 ∫1 ∇ 2  ds = 2 − 2 2 1 Integrating the third term of Eq. (24), assuming constant fluid density: 2  ∫ 1  ∇p  ρ  ds =  p 2 − p1  ρ  Integrating the fourth term of Eq. (24): 2  v  ∫ g ds = g (h  2  − h1 )  1  v Because we are integrating along a streamline, u × ds = 0 ; thus the right hand side of Eq.  (24) becomes zero:  v v u × (∇ × u ) = 0 Combining all of these terms gives a spatially discrete form of Eq. (24):  ρ  (  )  ∂u ρ 2 2 + u 2 − u1 + p 2 − p1 + ρg (h2 − h1 ) = 0 ∂t 2  (25)  For steady flow, the change in velocity with respect to time is zero. Also, we can take the conditions at 1 and call them constant ‘c’; i.e. a reference total pressure (Eq. (26)). These considerations give us a common form of Bernoulli’s Equation, concisely and eloquently describing conservation of energy in a flow along a streamline:  ρ 2  u 2 + p + ρgh = c  (26)  37  The first term of Eq. (26) is the dynamic pressure (kinetic energy), the second term is the static pressure (potential energy). If there is no elevation change, the total pressure is the sum of the dynamic and static pressure.  4.3 Empirical Prediction of Flow Behavior The analytical review of fluid dynamics and flow in ducts has given us the Navier-Stokes equation and Bernoulli’s equation. While the forms of these equations provide great insight into the nature of fluid flow and the factors that govern its behavior, they are generally not directly useful for finding solutions to engineering problems. The Navier-Stokes equation is too difficult to solve in a general system, especially without numerical methods (CFD). Even with CFD, simplifications to the Navier-Stokes equation are generally required to solve a turbulent flow problem. Bernoulli’s equation is simple to solve; however, it does not account for any viscous losses in the system. To make Bernoulli’s equation practically useful, engineers modify its form and make additions. Bernoulli’s equation can be modified as:   ρ1u1 2 − ρ 2 u 2 2   2     + ( p s1 − p s 2 ) + (ρ1 h1 − ρ 2 h2 )g = ∆p t ,1− 2    Equivalently:  ρ 1 u1 2 2  + p s1 + ρ1 gh1 =  ρ 2u2 2 2  + p s 2 + ρ 2 gh2 + ∆p t ,1− 2  (27)  ∆pt ,1− 2 is a total pressure loss between 1 and 2. This is a loss that was not available in the original lossless representation of Bernoulli’s equation, but has been added to allow changes in energy to the system. ps1 and p s 2 are the static pressures. Eq. (26) can be simplified to:  ∆p t ,1− 2 = ∆pt + ∆p se ; where,   ρ 1 u1 2   ρ 2u2 2   ∆p t =  + p s1  −  + p s 2   2   2  ∆p se = g (ρ a − ρ )(h1 − h2 ) ∆pt is the total pressure change in the fluid, and ∆pse is the change in pressure due to the thermal-gravity effect (buoyancy). Changes in total pressure are conventionally separated 38  into friction losses over lengths of duct, friction losses at fittings, and buoyancy. The change in total pressure over section i is expressed as [47]: m  n  j =1  k =1  ∆p ti = ∆p f i + ∑ ∆p ij − ∑ ∆p seik where ∆p f i = loss due to friction in section i, ∆pij = loss due to jth fitting in section i, and  ∆pseik = stack effect due to kth stack in section i. The friction and fitting losses, commonly known as major and minor losses, respectively, are both viscous energy dissipations. The concept of adding the losses of each distinct section of duct together is applied successfully in designing conventional HVAC ducting systems, where each fitting or section is separated from the previous one by a section of straight duct. This way, the flow at the entrance of each section is fully developed (not changing along the length of the duct) and independent of the upstream geometry. In the case of short silencer sections, where the flow at the entrance of one section of the silencer is not fully developed and affected by the upstream section, losses at each section cannot be considered independent of each other. There is, however, a strong motivation to use this formulation of discrete and independent pressure losses, as it is very common, well understood, and because results exist for many geometries.  4.4 Determining Viscous Losses in Ducts Two coefficients are commonly used to describe the losses in a duct section. One, the discharge coefficient, describes the flow rate as a function of the difference in static pressure between two points. The other, the loss coefficient, describes the change in total pressure as a function of flow rate. With these two coefficients defined, their dependence on Reynolds number will be discussed.  4.4.1  Discharge and Loss Coefficients  At high Reynolds numbers, conservation of energy between two points for lossless, horizontal, streamline flow through a constriction can be written, according to Bernoulli’s equation, as:  p1 +  1 1 ρ u1 2 = p 2 + ρ u 2 2 2 2  (28)  39  Here, p is the pressure, u is the velocity, and the subscripts refer to locations 1 and 2 on a streamline. Assuming incompressible flow, conservation of mass results in:  u1 =  A2 u2 A1  (29)  where A is the cross sectional area. Eq. (28) and Eq. (29) can be combined to produce: 2  A2  u 2 1 − 2 A1  2   2∆p =  ρ   If the orifice is small compared to the inlet area ( A2 << A1 ), we can approximate:  u2 = 2  2∆p  ρ  (30)  What follows is an expression for the flow rate through a constriction, dependent on only the opening area, and the pressure differential. It assumes that no energy is lost, and the area ratios are large:   2∆p  Q = A2    ρ   0.5  In reality, to account for phenomena such as the vena-contracta at the orifice, as well as losses, an experimentally determined factor called the discharge coefficient ( Cd ) is introduced:   2∆p  Q = AC d    ρ   0.5  (31)  The discharge coefficient is calculated as:  Q ρ   C d =  A  2∆p   0.5   ρ   = U   2∆p   0.5  (32)  The discharge coefficient is useful for calculating the flow rate given a geometry and pressure; however, another coefficient, the loss coefficient (k), is introduced into Eq. (30) to define the pressure loss given a flow rate.  40  ∆p = k  k=  1 ρU 2 2  (33)  ∆p 1 ρU 2 2  (34)  The loss coefficient can succinctly be defined as the ratio of the loss in total pressure to the dynamic pressure. An important distinction is that the pressure difference used to calculate the discharge coefficient is the difference in static pressures between two locations; the pressure difference used to calculate the loss coefficient is the difference in total pressures between two locations. For ventilation openings, because the ventilation opening area is very small compared to the upstream and downstream areas, the static pressure will dominate the total pressures up and down stream; therefore, the pressures used to calculate the discharge coefficient and the loss coefficient are effectively identical. Both the discharge coefficient ( Cd ) and the loss coefficient (k) are used regularly in engineering application. Typically the discharge coefficient is used for flow meters, and the loss coefficient is used for determining the pressure head required in pipe and duct systems to achieve a desired flow. One must be careful when selecting coefficients from the literature, the use of symbols Cd and k for the discharge and loss coefficients are not universal.  4.4.2  Dependence on the Reynolds Number  As stated in section 4.1, at high Reynolds numbers, the pressure is proportional to the velocity squared. As such, the discharge and loss coefficients are assumed independent of flow rate:  ρ   C d (High Re ) = U   2∆p   0.5   1  ∝ U 2  U   0.5  =1  C d (High Re ) ∝ 1 At low Reynolds numbers, however, the pressure becomes proportional to the velocity. Therefore the discharge coefficient behaves as:  ρ   C d (Low Re ) = U  2 ∆ p    0.5  1 ∝U  U   0.5  = U  41  It follows that, at low Reynolds numbers, the discharge coefficient is directly related to the square root of the Reynolds number:  C d (Low Re ) ∝ Re In the case of flow through ducts, the characteristic length is the hydraulic diameter (Dh), which can be found from the cross section al area (A) and the perimeter length (P). Dh =  4A P  The Reynolds number can be conveniently written as: Re =  UDh  ν  At low Reynolds numbers the discharge coefficient decreases with decreasing flow rate. If a high Re discharge coefficient is used to predict pressure loss at low Re, the pressure loss will be under-predicted. The system will be under-designed. It is therefore necessary to understand what constitutes low and high Reynolds numbers, as it will define the lower bound for the region of validity for the discharge or loss coefficient of a flow element. As flow in conventional HVAC systems is, for engineering purposes, assumed turbulent, little information exists on the low Reynolds number behavior of duct elements. In hydraulic flow applications, however, because the viscosity is much higher and characteristic dimensions are much smaller than in air flow applications, low Reynolds number behavior is much better understood. As the same assumptions made for ventilation air flow are made for hydraulic flow (incompressible and Newtonian), the same non-dimensional analysis will apply; discharge coefficients are interchangeable.  From hydraulic flow metering, a good understanding of the discharge coefficient of various constrictions has been developed; this information is very useful for understanding natural ventilation openings, as they are typically both short constrictions in the flow path. Numerical simulations have produced the discharge coefficient results for venturi, orifice, vcone and wedge-type flow meters [49]. Flow meter types can be identified by the cross sections shown in Figure 11. The V-cone is more of an obstruction than a constriction so it will not be discussed. The percentage errors in the calculated flow rate based on the turbulent discharge coefficient are shown in Figure 12.  42  Here the transitional Reynolds number (Retr) is defined as the Reynolds number below which errors in the calculated flow rate greater then 10% will result from using the high Re characterization. The transitional Reynolds number (Retr) for flow through the venturi and wedge constrictions are around 1000 and 100, respectively. Interestingly, flow through the orifice is under-predicted near the transitional regime. From other published results this effect can be partially attributed to the small beta value, the ratio of the orifice diameter to the pipe diameter [50]. Figure 13 shows the discharge coefficient of various orifice plates for different diameter ratios. As the orifice diameter becomes relatively small the discharge coefficient over-prediction near transitional Reynolds numbers is reduced. It is safe to conclude that the flow calculated from the turbulent discharge coefficient of an orifice constriction is accurate for Re>100 provided the orifice diameter is small relative to the upstream and downstream diameters. Johansen is also able to conclude that the regime where the pressure relates linearly with flow rate is only for Re<10 [50].  Interestingly, the behavior of orifices changes dramatically if it is elongated to form a short tube. In addition to an increase in the discharge coefficient, the transitional Reynolds number increases [51]. If the ratio of the length to diameter (l/d) is 0.5 or less, Retr is still around 100; however if l/d increases to 1, then Retr increases to 500, if to 4 then Retr increases to 2000. Lichtarowicz draws a general conclusion that, for all short tubes, the discharge coefficient is only completely independent of Reynolds number for Re > 20,000. A visual inspection of Lichtarowicz’s results suggests that his conclusion is quite conservative. For the purposes of this work it will be sufficient to say that the losses in short tubes are characterized well by the turbulent discharge coefficient if the Reynolds number is greater than 4000, which corresponds to turbulent flow in a long section of duct [48].  Venturi  Orifice  Wedge  Figure 11: Flow meter types (ref Figure 12).  43  Figure 12: Flow meter error resulting from using turbulent discharge coefficient [49].  Figure 13: Discharge coefficient of orifice plates with various geometries [50].  Another issue is that often grilles are added to the ventilation openings. The grille will have little effect on the average flow velocity; however, the hydraulic diameter will be greatly reduced. As a result, grilles will have a much lower Re than the duct cross section, and may 44  result in a “low” Re condition when the Reynolds number based on the ventilation opening cross section is “high”.  Work in hydraulic flow has proposed unifying the high and low Reynolds number regions by creating a single discharge coefficient model that describes the pressure loss in both high and low Re regions [51-53]. This idea may be quite useful for designing composite systems where each element is understood beforehand; however, it is less useful for the design of individual elements, as it is required to know the transient Reynolds number of the element (Retr) beforehand. In summary, the loss in a flow element, be it an orifice or uniform length of duct, can only be described by a single-number coefficient if the Reynolds number is high. Unfortunately, there is no single guideline for what constitutes a high Reynolds number; it is dependent on the geometry. For sudden constrictions in the flow, similar to the orifice or wedge shown in Figure 11, and where the flow element’s length is less than one half of its diameter, a single discharge coefficient may be valid for all Re > 100. If the constriction is gradual, as it is with a venture flow meter (Figure 11), or if the constriction has some length, a single discharge coefficient may only be valid for all Re > 4000.  In the end we are compelled to use a high Re characterization of the pressure loss because it is both convenient and the industry standard. Unfortunately, in natural ventilation openings, flow velocities are often very small and the typical HVAC assumption of high Re may no longer be a safe one. In certain instances ventilation openings are best described as thin orifices and a “high” Re may be as low as 100; however, this is not always be the case. In some designs, the flow rate may be small, and the ventilation opening may be designed in a way that the resultant Re is not large enough to be considered “high”. Regardless of this, previous work on flow in naturally ventilated buildings uses the high Re characterization of losses for interior ventilation openings [3, 4, 10-12, 15-20]. Reynolds number dependent loss is mentioned at times, but not treated seriously [54]. In the following sections of this report the Reynolds number will be discussed on a case-by-case basis to judge the accuracy of the loss or flow rate characterization.  45  Chapter 5: Measurement of Natural Ventilation Openings The current state of natural ventilation openings has been assessed through measurement and analysis; in-situ measurement and laboratory measurements have been taken, and results from a previous published work have been analyzed. A new measurement method was developed for the in-situ measurements, and a facility was constructed and commissioned for the lab measurements. This section will outline the measurement methods and lab performance, and then present the results from in situ measurements, laboratory measurements, and the analysis of results published by the UK Building Research Establishment (BRE) [12].  5.1 Ventilator Measurement Method The method used to determine the acoustic and air flow performance of existing interior natural ventilation openings is presented in this section. The general acoustic performance of a ventilator is described by its transmission loss (TL), which can be converted into a sound transmission class (STC) and the equivalent open area for sound (EOAS). The method used to calculate transmission loss in the field is motivated by ASTM E336-10 [55]. ASTM E9009 [56] motivates the transmission loss measurements in the laboratory. It is not possible to follow ASTM E90-09 completely due to size limitations of the facility. STC is calculated following ASTM 413-10 [25]. Flow performance is described by the flow rate as a function of pressure differential, from which the discharge coefficient (Cd), loss coefficient (k), and the equivalent open area for flow (EOAf) can be calculated. The method of measurement and calculation is motivated by ASTM E779-10 [27].  5.1.1  Ventilator Transmission Loss  The theory for calculating transmission loss is given here briefly, followed by the measurement method.  5.1.1.1  Theory  In section 2.1.1, the background theory to the measurement of transmission loss was provided. Eq. 5 and Eq. 6 show that the sound power entering the ventilator can be determined by calculating the average sound pressure level in the source room: 46  2  p Win = Av s 4ρ 0 c Additionally, Eq. 7 and Eq. 8 show that the sound power exiting the ventilator can be determined from the average sound pressure level and reverberation time in the receiver room: 2  Wout =  Ar p r ; 4 ρ0c  Ar =  0.161Vr T60  The transmission coefficient of the ventilator is equal to the ratio of the power entering to the power exiting the ventilator: 2  A p τv = v s2 Ar p r The transmission performance is typically stated in decibel form as the transmission loss:  A TL v = Leq s − Leq r + 10 log v  Ar      The standard deviation of the transmission loss ( σ TL v ) is calculated from the standard deviation of the source and receiver sound pressure levels ( σ Leq s and σ Leq r ), and the reverberation time ( σ T60 ):  σ TL = σ Leq + σ Leq 2  v  s  2 r  σT + 18.9 60  T60       2  The ventilator’s transmission loss cannot generally be measured directly because the sound transmitted through the ventilator cannot be measured independently of the sound transmitted through the rest of the partition (unless the rest of the partition has a very high transmission loss). To estimate the contribution of the transmission due to the ventilator alone, the transmission will be measured once with the ventilator open and once with it blocked off. Blocking the ventilator gives an approximation of the partition’s transmission loss without the ventilator. As stated in section 3.2.3, the total transmission coefficient of the composite partition ( τ p ) is equal to the area-weighted sum of the transmission through the ventilator  47  ( τ v ) and the transmission through the rest of the wall ( τ w ). The ventilator area, unless otherwise noted, is taken as the area of partition that it displaces:  τp =  τ wA w +τ vA v Ap  Rearranging gives the ventilator transmission coefficient:  τv =  τ p A p − τ w Aw Av  If the transmission loss of the wall (partition without the ventilation opening) is much higher than the transmission loss of the partition with the ventilation opening, then the transmission through the wall is negligible compared to that through the ventilation opening and need not be considered in the calculation. If, however, the wall has a low TL, or the ventilator a high TL, there will be very little measureable effect due to blocking the ventilation opening. To control error, the transmission loss of the ventilation opening will be limited to the transmission loss of the wall. As a result, the calculated transmission loss of the ventilation opening will represent a lower bound for its actual performance.  The difference in sound levels across the partition is called the noise reduction ( NR = Leq s − Leq r ). If the NR increases by 10 dB due to blocking the ventilator, the ventilator TL result is independent of the wall TL. If there is not at least a 3 dB increase in NR, the TL measurement should be treated with a large degree of uncertainty.  All of these calculations rely on the assumption that the sound field is diffuse; often, even generally, this is not the case. In order for a room to promote a diffuse sound field it needs to be large (but not too large), have small (but not identical or rational) aspect ratios, and reflective surfaces. Additionally measurements must be made more than one half wavelength from any reflective surface because, near surfaces, the sound field is never diffuse. Large uncertainties exist in these measurements and we attempt to describe the uncertainties through the spatial variation of the measurements; however, spatial variation alone is not sufficient to completely recognize all uncertainties. Whenever conditions exist that are suspected to introduce significant uncertainty they will be noted. 48  5.1.1.2  Measurement Method – In Field  To calculate the transmission loss of the ventilation openings it is necessary to have measurements of the source room sound pressure level, receiver room sound pressure level, and receiver room reverberation time, both with and without the ventilator blocked off. The method provided by ASTM E336 for measuring apparent transmission loss (ATL) is followed as closely as possible for these measurements. Corresponding to ASTM E336, the average sound pressure levels are measured using a 1 min average, manual scan. The reverberation time, calculated from the room impulse response, is the spatial average of six measurements. The ventilation openings are blocked off using one half-inch thick sheet of plywood attached to either end of the opening.  5.1.1.3  Measurement Method – In Lab  In the laboratory we follow the guidelines outlined by ASTM E90-09 which is very similar to that given by ASTM E336. Initially a full partition is constructed in the lab to determine the transmission loss and flanking limits, characterizing the maximum acoustic isolation between the two spaces. Provided this transmission loss is at least 10 dB greater than the transmission loss of all ventilator measurements at all frequencies, the energy transmitted via all paths besides the ventilator can be neglected. Average sound pressure levels are made by averaging nine sound pressure levels measured at different locations in the room. Each measurement is a 10 s average. Spot measurements are made instead of scanning measurements, because the operator is required not to be in the room. The lab facility has low absorption; thus, the presence of an absorptive operator would have a significant effect on the reverberant field and sound pressure levels in the room. Nine measurements of reverberation time are made in the receiver room to average spatial variations.  5.1.2  Ventilator Flow Rate  Here the theory of calculating the flow pressure loss as a function of flow rate will be given briefly, followed by the measurement method. Many methods of measuring airflow exist [57]; the blower door fan pressurization technique has been adopted and modified for these measurements because it is well known, standardized [27], accessible, and readily produces the desired results.  49  5.1.2.1  Theory  The volume flow rate being driven into the room, and the corresponding pressure differential across the partition, are measured with the ventilation opening sealed and open. The difference between the two flow rates, at a common pressure, gives the flow rate through the ventilation opening at that pressure.  Flow rate is measured using a blower door, a calibrated fan unit designed for testing airtightness of buildings. It provides a method of calculating the flow rate based on the difference between the ambient pressure and the pressure at a tap in the fan ( ∆p tap ), as well as the pressure differential across the fan ( ∆p fan ). The equation and associated table shown below are used:  Q=  (∆p  Range 22 A B C8 C4 C2 C1  − ∆p fan ⋅ K 1 ) ⋅ (K + K 3 * ∆ptap ) N  tap  2118.882 Table 8: Flow-rate coefficients. N K K1 0.5214 486.99 -0.07 0.503 259.04 -0.075 0.50075 159.84 -0.035 0.5025 77.418 -0.03 0.495 42.448 0.045 0.4655 24.864 0.4 0.473 13.349 0.32  m3 s  K3 -0.12 0 0 0.004 0.011 0.008 0.004  The “Range” values in Table 8 correspond to the fan setting, which can be adjusted to give different flow rate ranges. 22 is the range that provides the largest flow rate and C1 provides the smallest. After selecting an appropriate range, Table 8 is used to select the coefficients N, K, K1, and K3 to determine the flow rate.  The flow rate is measured at a number of different pressures, from which a log linear regression is used to define the flow rate as a function of pressure, plus provide confidence intervals for the curve fit. The desired expression is: Q = C∆p n  m3 s  50  C and n are the flow coefficient and flow exponent. Letting x = ln(∆p ) and y = ln (Q ) the linear regression can be used to determine C and n from the variance and covariance of x and y [27]:  y = ln(C ) + n ⋅ x 2  Sx =  1 N ( x i − x )2 ; ∑ N − 1 i =1 S xy =  2  Sy =  1 N ( y i − y )2 ∑ N − 1 i =1  1 N ∑ (xi − x )( yi − y ) N − 1 i =1 n=  S xy Sx  2  C = e y − nx  It is not possible to directly subtract the flow with the ventilator sealed from the flow with the ventilator open because the flow rates cannot be readily measured at identical pressures. To allow the subtraction, a linear regression for the flow with the ventilator sealed is first found. Using the linear regression, the leakage rates at the pressures corresponding to the pressures of the open ventilator measurement are calculated and subtracted from the open ventilator results. The corrected open ventilator measurement results are then used in a linear regression to find an equation that describes the flow through the ventilator.  Finally, the standard deviation of n and ln(C) can be found as [27]: 1 2 1  S y − n ⋅ S xy Sn = S x  N − 2  S ln (C )   N 2  ∑ xi = S n  i =1  N    2     1  2       51  5.1.2.2  Measurement Method – In-Situ and Laboratory  In order to calculate the flow characteristics of the ventilator the pressure differential across the ventilator, and the corresponding flow rate through the room, must be measured with the ventilator sealed and open.  To improve the accuracy of the results, any obvious flow paths exiting the room, besides the ventilator, are sealed off. The fan unit is fitted into the door, and pressure taps are inserted in the rooms on either side of the fan, and on either side of the ventilator2. The fan pressure is measured as the difference between the fan tap pressure and the ambient pressure in the room on the inlet (low pressure) side of the fan. The room to be pressurized (i.e. downstream of the fan) is chosen as the one that offers the least obstruction to the flow of high velocity air exiting the fan. A similar work has concluded that the flow characteristics of the ventilator are not significantly dependent on the flow direction [12].  The ventilator is sealed off for the first set of measurements to allow calculation of the flow rate exiting the room through paths other than the ventilator. Measurements are then repeated with the ventilator open to allow calculation of the airflow through all flow paths. If the flow rate with the ventilator sealed off is not small compared to that when it is open, additional uncertainties will exist. Additionally, the pressure differential across the ventilator should be measured with the fan off, to confirm a zero reading. A non-zero pressure would typically indicate that the ventilation system is influencing the measurement.  5.2 Design and Performance of the Lab Facility Using an empty office space that had become available, a small laboratory for testing ventilator air flow and acoustical performance was constructed. The lab comprises two adjacent rooms separated by a partition in which ventilation openings and silencers can be installed. In this section, the facility’s construction and performance in terms of acoustics and airflow will be described. It is important to note that, while the laboratory measurements  2  For the in-situ measurements, the fan and ventilator were generally installed in the same partition; therefore, the pressure differential across the fan and ventilator were the same.  52  were motivated by ASTM E90 [56], due to facility size limitations, no attempt was made to meet its requirements.  5.2.1  Room Dimensions and Construction  The office space obtained for conversion into the lab was 4.88 m in length, 2.62 m in width, and 2.70 m in height. The floor was linoleum on concrete, the walls were gypsum boards on steel studs, and the ceiling was suspended acoustic tile. A ventilation air inlet and exhaust were located in the ceiling.  To create two rooms, a 115 mm partition was built to nominally divide the space in two, leaving ‘source’ and ‘receiver’ rooms with floor dimensions of 2.33 x 2.62 and 2.42 x 2.62 m respectively. The partition was created using two sheets of ½” (12.7 mm) gypsum boards separated by ‘2x4’ (38.1 x 88.9 mm) studs on 520 mm centers. The cavity was filled with fiberglass batt to improve the noise isolation. All joints in the partition were caulked. This partition is not one of high acoustical performance; however, creating a partition with a high performance was not necessary, as the transmission loss was limited by flanking through the walls and ceiling. To achieve a high degree of isolation, a room within a room would need to be constructed; this was not deemed necessary.  Openings for a ventilator, and a “door” to access the source room were included in the partition. The section for ventilators is a removable portion of the partition, bordering the floor, 2m wide and 1m high. If necessary, it was partially filled in, with construction similar to the rest of the partition, to accept various ventilators. To test the partition’s nominal transmission loss, the ventilator opening was completely filled in. A door to the source room was created by making a ‘2x4’ framed plug. The plug was covered with gypsum on one side and 1” MDF on the other; it fits tightly into the framed opening created in the partition. The MDF is larger than the plug, to provide an exposed lip to seal against the partition frame. The door-partition mating surfaces were treated with gasket foam.  A second ceiling, constructed of ½” (12.7 mm) gypsum board, suspended by ‘2x4’ (38.1 x 88.9 mm) studs, was added just below the acoustic tile of the source room to reduce  53  absorption and increase transmission loss; the final source room height is 2.58 m. A 1.5 m2 trap door, constructed of one ½” ply layer and one ½” gypsum board layer, was added to the ceiling; it can be opened to allow air to exit the room through the ceiling and into the adjacent corridor, and closed to provide acoustic isolation. In the receiver room, the ceiling was modified by adding a layer of gypsum to the acoustic tile such that the gypsum faced toward the room and the acoustic tile faced toward the ceiling. The ventilation supply was disconnected and allowed to discharge into the ceiling. A fan was placed at the door of the room for ventilation during use.  5.2.2  Acoustic Performance of Lab Facility  The acoustic performance of the facility was assessed in terms of the diffuseness of the sound fields in the rooms and the acoustic isolation between them.  A diffuse sound field requires a long reverberation time to create a strong reverberant field. The reverberation time, calculated from an average of nine measurements at different locations, is shown for the source and receiver rooms in Figure 14. At low frequencies the reverberation time is low due to membrane absorption from the gypsum board; at high frequencies it is low due to air absorption. In the mid-frequency range, especially considering the small volume of the spaces, the reverberation time is fairly high, around 1.5 s. To maintain a reverberant field, instead of specifying a minimum reverberation time, ASTM E90 specifies a maximum total absorption area (A): A≤  V23 = 2.21 m2 3  for  2000 ≤ f ≤ 2000 Hz V13  The author suspects that the low frequency limit, which equals 776 Hz for the receiver room, is specified because below this frequency there is not a high enough modal density for the field to be diffuse. Increasing absorption can reduce the modal behavior of the room response and result in a more uniform pressure field. The high frequency limit exists because, at frequencies above 2000 Hz, the reverberation is controlled by air absorption and not by the surfaces of the room. The total absorption area and the ASTM absorption area maximum, in its region of validity, are shown in Figure 15. The facility meets the requirements of ASTM E90 for maximum total absorption.  54  The uniformity of the sound field can be assessed by the standard deviation of the sound pressure level over the room’s volume. Measurement positions in the volumes are chosen randomly while keeping the microphone at least 1 m from any surface as required by ASTM E90; near the surfaces the various modes are spatially in phase with each other, causing a non-diffuse field and an elevated sound pressure level. The uncertainties in sound pressure level associated with a 95% confidence in the mean are shown in Figure 16 for the source and receiver rooms. The uncertainty at 125 Hz is high, around 4 dB, at 250 it drops to around 1.5 dB, and above the 500 Hz band the uncertainty is below 1 dB. Uncertainties in the average sound pressure levels dominate the uncertainties in reverberation time when calculating the transmission loss uncertainty.  Figure 17 shows the partition transmission loss with 95% confidence error bars. The transmission loss is 25 dB at 125 Hz, increasing to over 35 dB between 500 and 2000 Hz. Above 2000Hz there is a reduction in transmission loss due to coincidence; it then increases with frequency from 31 dB at 2500 Hz to 47 dB at 10 kHz.  5.2.3  Air Flow Performance of Laboratory Test Facility  To commission the facility for air flow measurements it was necessary to show that the air entering the upstream room, as provided by the fan, flows through the ventilator. To do this, the air-tightness of the room was tested with a complete and sealed partition. An acceptable condition is when the equivalent open area of the upstream room due to leakage is much less than that of any ventilator tested. Additionally, the SEOAf was measured for a known orifice size to confirm that the result is close to unity.  The equivalent open area of the high pressure (upstream) room is shown in Figure 18. The equivalent open area increases slightly with applied pressure, possibly because gaps are being forced open by increasing force; however, the equivalent open area never exceeds 0.005 m2. If the EOAf of any ventilator is not significantly greater that this, the results should be used with caution.  55  Measurement results, shown in Figure 19, for a thin, square opening with a 0.6 m edge length, give an average SEOAf of 1.024 with 95% confidence interval of 0.026. In this work, uncertainties and errors on the order of 3% are quite small. Measurement tests were completed at Reynolds numbers above 200k; the flow was highly turbulent. 2 Source Room Receiver Room  1.8 1.6 1.4  T30 [s]  1.2 1 0.8 0.6 0.4 0.2 0  125  250  500  1000 Frequency [Hz]  2000  4000  8000  Figure 14: Measured reverberation time with 95% confidence intervals for source and receiver rooms.  56  7 Receiver Room Max Permissible (ASTM E90)  6  A [m2]  5  4 3  2  1  0  125  250  500  1000 Frequency [Hz]  2000  4000  8000  Figure 15: Measured receiver room total absorption and the maximum permissible value according to ASTM E90. 4  Lp Uncertainty (95% confidence)  3.5  Source Room Receiver Room  3 2.5 2 1.5 1 0.5 0  125  250  500  1000 2000 Frequency [Hz]  4000  8000  Figure 16: Uncertainty in measured Lp - 95% confidence values.  57  50 45 40  TL [dB]  35 30 25 20 15 10  125  250  500  1000 2000 Frequency [Hz]  4000  8000  Figure 17: Measured transmission loss of laboratory partition - 95% confidence values. -3  5  x 10  4.5 4  EOAf [m2]  3.5 3 2.5 2 1.5 1 0.5 0  0.5  1  2  5 Pressure [Pa]  10  20  50  Figure 18: Measured equivalent open area of high pressure room (leakage).  58  1  SEOAf  0.8  0.6  0.4  0.2  0 Re=200k 10  15  20  25 30 35 Pressure [Pa]  40  45  50 Re=800k  Figure 19: Measured SEOAf of 0.6 x 0.6 m opening.  5.3 Report on Field Measurements of Natural Ventilation Openings In this section the in-situ measurements and their results are presented. In order to appreciate the results, room geometry, ventilator geometry, and noteworthy measurement method variations for each test are discussed. Results are given for both acoustic and airflow performance. Various calculated results are presented to inform the reader of both the ventilation opening’s performance, as well as the accuracy of the result. Apparent sound transmission class (ASTC) [25], and the specific equivalent open area for sound (SEOAs), are both measures which indicate the acoustic performance of the ventilation opening independent of its environment. ASTC is provided in addition to SEOAs as it is the North American standard performance metric. The noise isolation class (NIC), a single number rating defined by ASTM E413 [25] to indicate the difference in sound levels on the source and receiver sides of a partition, is used to indicate the effect of blocking the ventilation opening. A large decibel reduction in the NIC due to blocking the ventilation opening will allow accurate calculation of the ventilation opening’s transmission loss. The difference between the NIC and the ASTC is that the NIC is dependent on the reverberant environment of the receiver room; ASTC uses the reverberation time and diffuse field theory to 59  compensate for the reverberant field in the receiver room. The specific equivalent open area for flow (SEOAf) is provided to evaluate the flow performance of the ventilation opening. The change in equivalent open area for flow (%∆EOAf), is used to indicate the reduction in flow caused by blocking the ventilator. A large difference indicates a high confidence measure of the ventilator flow rate. Finally, the open area ratio (OAR) is given to rate the total combined performance of the NVO.  It is necessary to understand the normal operating conditions of these ventilation openings, as the validity of using a single number EOAf is dependent on a high Re flow (see section 4.4.2). In order to assess the normal operating conditions, the rough assumption will be made that the ventilation systems are designed to provide the exchange rates required by the relevant standard for mechanically ventilated spaces. The air exchange rate – combined with room dimensions, ventilator dimensions, and measured flow performance – can be used to determine the operational Reynolds number and pressure loss.  In this work, due to limitations of the measurement equipment, the lowest flow rate was measured at a pressure differential between rooms of 5 Pa. As such, the EOAf will be calculated at 5 Pa (see section 2.1.2).  5.3.1  Regent College Library  In the Regent College Library, small rooms around the periphery of the building are supplied with ventilation air through grates in the floor. This air then flows out of the room through ventilation openings which are grilles in the wall above the door.  5.3.1.1  Regent College L020  Room L020, shown in Figure 20, has a volume of 98 m3 with carpet floors and concrete ceiling. It shares a 21.5 m2 partition with the main library, mostly composed of double pane glass. One single pane glass door exists in the partition with a 12 mm gap between the door and the carpet. The grille (Figure 21) had 10 mm thick blades spaced on 30 mm centers.  60  Transmission loss tests were completed using the main library as the source room and L020 as the receiver. Airflow test were completed by pressurizing L020 with the operator outside. Measurements were completed with the grille on, and again with the grille off.  5.3.1.1.1  L020 Results: Grille On (see Table 9)  An 8 dB increase in NIC and 82% reduction in the EOAf are observed between open and closed vent conditions; therefore, it is confirmed that the resultant OAR is reliable. A 0 dB ASTC, and 0.89 SEOAs indicate that the grille provides insignificant sound attenuation. A SEOAf of 0.64 indicates that the opening with the grille permits 36% less airflow than a thin opening of the same dimensions. The resultant OAR of 0.73 shows that this opening is more restrictive to airflow than it is to noise.  5.3.1.1.2  L020 Results: Grille Removed (See Table 9)  An 8 dB decrease in NIC and 90% reduction in the EOAf are observed between open and closed conditions, confirming that the OAR is again reliable. Removing the grille, surprisingly, causes a slight increase in acoustic transmission loss (1 dB ASTC, and 0.8 SEOAs); however, the difference is well within the limits of uncertainty. The grille has no significant effect on acoustic transmission. The removal of the grille caused an increase of 84% in SEOAf. An OAR of 1.41 indicates this opening without the grill is of slightly higher performance than a thin orifice.  61  Figure 20: Regent College L020.  Figure 21: Regent College L020 grille. Table 9: Performance measures for Regent College, L020. Vent Condition Grille On Grille Off ∆NIC [dB] 8 8 ASTC [dB] 0 1 SEOAs 0.89 0.83 %∆EOAf -82 90 SEOAf 0.64 1.18 OAR 0.73 1.41  62  5.3.2  Fred Kaiser Building  Offices and meeting rooms on the third and fourth floor of the Fred Kaiser building are naturally ventilated. Air is let in through vents in the window and is drawn out of the room through ventilators at the top of a partition common to an atrium. The ventilators are acoustically treated using a Z-shaped crosstalk silencer built into the partition.  5.3.2.1  Fred Kaiser 4036  Room 4036 (Figure 22) has a volume of 42 m3 with and concrete floor and ceiling. It shares an 8.5 m2, double drywall construction partition with the atrium. One solid wood door exists in the partition. The ventilator cross section, which runs the entire 3.05 m width of the partition above the door, is shown in Figure 23.  Transmission loss tests were completed using the atrium as the source room and 4036 as the receiver. Airflow test were completed by pressurizing 4036 with the operator outside.  5.3.2.1.1  4036 Results (see Table 10)  As there is only a 1 dB change in NIC due to blocking the ventilator, the transmission loss results for the ventilator can only provide a lower bound on its performance, and a large degree of uncertainty must be acknowledged. The EOAf was reduced by 78% by blocking the ventilator; therefore the flow results are accurate. Keeping in mind the uncertainties, the ventilator is shown to greatly reduce acoustic transmission (16 dB ASTC, 0.046 SEOAs). The equivalent open area for flow is about one tenth of the ventilator area. A OAR of 2.48 results; however, this should be considered a lower bound because the ventilator’s measured TL was limited by the rest of the partition.  63  Figure 22: Fred Kaiser 4036.  130mm  570mm 90mm  250mm  120mm  Figure 23: Fred Kaiser 4036 ventilator cross section– 25mm fiberglass shown as crosshatched.  64  Table 10: Performance measures for the ventilator in Fred Kaiser 4036. ∆NIC [dB] 1 ASTC [dB] 16 SEOAs 0.046 %∆EOAf -78 SEOAf 0.11 OAR 2.48  5.3.3  Liu Institute  UBC’s Liu Institute is a three story naturally ventilated building. Ventilation air enters the offices on the second and third floor through trickle vents and operable windows, after which it is drawn out of the room through ventilators at the top of the partition common to a corridor. Originally the ventilators were 0.4 m high rectangular openings at the top of the partition; however, following previous work [5], all but one (room 216C) of these ventilators have been acoustically treated using a Z-shaped crosstalk silencer built into the partition. One additional room was created with, instead of rectangular ventilators at the top of the partition, two smaller openings covered with pairs of grilles, one grille mounted to each side of the partition. Tests were carried out on the room with a long ventilation opening (216C), a room with a z-shaped cross-talk silencer (308), and a room with grille-covered ventilation openings (313). Room 313 was tested with all grilles installed and with all grilles removed.  5.3.3.1  Liu 216C  Room 216C has a volume of 49 m3 with and concrete floor and ceiling. It shares an 8.1 m2, double drywall construction, partition with the 27 m3 room 216. One solid wood door exists in the partition. The ventilator is a rectangular opening near the top of the partition 0.4 m high and 2.63 m long.  Transmission loss tests were completed using 216 as the source room and 216C as the receiver room. Airflow test were completed by pressurizing 216C, with the operator in 216. Error may have been induced in the flow measurement, as the fan was partially obstructed by a desk 1.5 m away. This could lead to pressure loss not attributable to the ventilator, thus a lower flow rate measurement.  65  5.3.3.1.1  216C Results (see Table 11)  A 13 dB change in NIC is observed between open and closed vent conditions providing a reliable ASTC. EOAf is reduced 95% by blocking the ventilator, indicating that the air flow results are accurate. A -1 dB ASTC and 1.04 SEOAs indicate that the ventilation opening provides insignificant attenuation. A SEOAf of 0.74 indicates that the opening is moderately more restrictive to airflow than a thin aperture; however, the flow performance is likely under-estimated due to measurement conditions. This ventilator is very large, causing high flow rates and large velocities in the rooms. The high velocities away from the ventilator would cause increased dissipation of energy and thereby increased flow restriction. The resultant OAR of 0.71 shows that this opening is slightly more restrictive to airflow than it is to noise.  5.3.3.2  Liu 308  Room 308 (Figure 25) has a volume of 34 m3. It shares an 8.1 m2, double drywall construction partition with the corridor. One solid wood door exists in the partition. The Zshaped ventilator cross section, which runs the 2.9 m length of the partition above the door, is shown in Figure 26.  Transmission loss tests were completed using the corridor as the source room and 308 as the receiver. Airflow tests were completed by pressurizing 308 with the operator in the corridor.  5.3.3.2.1  308 Results (see Table 11)  Due to the high transmission loss of the ventilator, there is no measured change in NIC due to closing the ventilator; therefore, a large degree of uncertainty must be acknowledged. The transmission loss results for the ventilator only provide a lower bound on its performance. The ventilator appears to reduce acoustic transmission to a large degree (16 dB ASTC, 0.030 SEOAs). SEOAf is reduced by 75% by blocking the ventilation opening; therefore, the air flow results should be accurate. The equivalent open area for flow is one tenth of the ventilator area. An OAR of 3.42 results; however, this should be considered a lower bound because the ventilator’s measured TL was limited by the rest of the partition.  66  5.3.3.3  Liu 313  Room 313 (Figure 27) has a volume of 46 m3 and shares a 7.7 m2, double drywall construction partition with the corridor. One solid wood door exists in the partition. The partition has two 250 x 350 mm ventilation openings, each with two grilles – one on either side. The grilles (Figure 28) are made of 1 mm thick steel fins on 20 mm centers.  Transmission loss tests were completed using the corridor as the source room and 313 as the receiver. Airflow test were completed by pressurizing 313 with the operator in the corridor.  5.3.3.3.1  313 Results: Grilles On (see Table 11)  A 3 dB change in NIC is observed between open and closed vent conditions, which should allow for moderately accurate transmission loss calculation. A 0 dB ASTC, and 0.85 SEOAs indicate that the grille provides insignificant sound attenuation. Blocking the ventilation opening reduced the EOAf by 68% allowing for accurate flow calculations. A SEOAf of 0.65 indicates that the opening permits significantly less airflow than a thin opening of the same dimensions. The resultant OAR of 0.76 indicates that the performance of this opening is worse than a thin aperture.  5.3.3.3.2  313 Results: Grilles Off (see Table 11)  With the grilles removed, the acoustic transmission remains essentially unchanged (-1dB ASTC, and 0.88 SEOAs). The grille appears to have no significant effect on acoustic transmission. The removal of the grille resulted in an 84% increase in flow, increasing the SEOAf to 0.88. An OAR of 1.38 indicates that this opening without the grill has slightly superior performance to a thin aperture.  Table 11: Performance measures for ventilation openings in the Liu Institute. 313 313 Vent Condition 216C 308 Grille On Grille Off ∆NIC [dB] -1 0 3 4 ASTC [dB] 1.04 16 0 -1 SEOAs -95 0.030 0.85 0.88 %∆EOAf 0.74 -75 -68 -81 SEOAf 0.71 0.10 0.65 1.22 OAR -1 3.42 0.76 1.38  67  Figure 24: Liu 216C (showing ventilation openings blocked).  130mm  480mm 130mm  130mm  Figure 25: Liu 308.  Figure 26: Liu Institute 308 ventilator cross section– 50mm fiberglass shown as crosshatched.  68  Figure 27: Liu 313 (showing ventilation openings blocked).  Figure 28: Liu 313 grille.  5.3.4  C. K. Choi Building  UBC’s C. K. Choi Building is a three story naturally ventilated building. Ventilation air enters the office trickle vents and operable windows, after which it is drawn out of the room through ventilators at the top of the partition common to a corridor. The ventilators are typically rectangular openings at the top of the partition. The top of the ventilators originally terminated at a steel deck ceiling (room 167); however, some of the ventilators have since 69  been acoustically treated by covering the steel deck with acoustic tile (rooms 321 and 326). One additional room was modified for high acoustical privacy. The ventilation opening was replaced with a transfer duct silencer in which a fan is mounted to assist the natural ventilation airflow mechanisms (room 327).  5.3.4.1  C. K. Choi 167  Room 167, shown in Figure 29, has a volume of 30 m3, with a steel deck ceiling. It shares an 8.9 m2, glass and double drywall construction partition with the corridor. One wood door exists in the partition. The ventilator runs the length of the partition and has an average height of 0.2 m.  Transmission loss tests were completed using the corridor as the source room and 167 as the receiver. Due to the ventilation opening geometry, at the time of testing it was not possible to block it acoustically and measure the partition’s transmission loss. A conservative assumption is made that the energy transmitted through the partition is insignificant compared to that transmitted through the ventilator. Thus, the true acoustic performance of the ventilator will be higher than that measured. Airflow tests were completed by depressurizing 167 with the operator in the corridor. The ventilator flow was blocked using poly sheeting.  5.3.4.1.1  167 Results (see Table 12)  A 1 dB ASTC and 0.92 SEOAs indicate that the opening provides no significant sound attenuation. Blocking the ventilator reduced the EOAf by 77% allowing accurate calculation of the ventilator air flow. A SEOAf of 0.98 indicates that the opening is not restrictive to airflow. The resultant OAR of 1.06 shows that this opening is equally restrictive to airflow and noise.  5.3.4.2  C.K. Choi 321  Room 321 (Figure 30) has a volume of 32 m3 with an acoustic tile ceiling. It shares an 8.5 m2 double drywall partition with the corridor. One wood door exists in the partition. The ventilator runs the 2.4 m length of the partition and has an average height of 0.13 m. The top  70  surface of the ventilation opening is acoustic tile. The bottom surface is a structural wooden beam 0.1 m wide; as a result, the ventilation opening has a non-zero length; the ventilators length is comparable to its height.  Transmission loss tests were completed using the corridor as the source room and 321 as the receiver. Due to the ventilation opening geometry, at the time of testing it was not possible to block it acoustically and measure the partition’s transmission loss. A conservative assumption is made that the energy transmitted through the partition is insignificant compared to that transmitted through the ventilator. The true acoustic performance of the ventilator will be higher than that measured. Airflow test were completed by pressurizing 321 with the operator in the corridor. The ventilator flow was blocked using poly sheeting.  5.3.4.2.1  321 Results (see Table 12)  A 4 dB ASTC and 0.51 SEOAs indicate that the lined slot opening provides acoustic attenuation; additionally, the SEOAf of 1.46 indicates that the opening provides efficient airflow. As the reduction in EOAf after blocking the ventilator was 76%, the flow results are accurate. The resultant OAR of 3.42 shows that this opening is more restrictive to noise than it is to airflow.  5.3.4.3  C.K. Choi 326  Room 326, shown in Figure 31, has a volume of 18 m3 with an acoustic tile ceiling. It shares a 7.1 m2 glass partition with the corridor. One wood door exists in the partition. The ventilator is a 2.47 x 0.52 m opening at the top of the partition. The top surface of the ventilation opening is acoustic tile.  Transmission loss tests were completed using the corridor as the source room and 326 as the receiver. Due to the ventilation opening geometry, at the time of testing it was not possible to block it acoustically and measure the partition’s transmission loss. A conservative assumption is made that the energy transmitted through the partition is insignificant compared to that transmitted through the ventilator. The true acoustic performance of the ventilator will be higher than it is measured to be. Airflow test were completed by  71  pressurizing 326 with the operator in the corridor. In this case the ventilation opening area is not very small compared to the corridor or room 326 cross-sectional areas. As a result the air velocities in this room remained high, and a fully recovered static pressure was not measured. In addition, due to high air velocities in the room, significant pressure losses occurred away from the ventilator. Due to the size of the opening, and fan limitations, the maximum room pressure reached was 15 Pa.  5.3.4.3.1  326 Results (see Table 12)  A 6 dB ASTC and 0.22 SEOAs indicates that the opening provides significant acoustic attenuation – surprisingly large given the ventilator’s geometry; as a result the author is not confident in the validity of this result. A 94% decrease in the EOAf due to blocking the ventilator confirms that the ventilator flow results are accurate. A SEOAf of 0.83 indicates that the opening provides some restriction to airflow; however, as mentioned previously, the ventilator is very large, causing high flow rates and large velocities in the rooms. The high velocities away from the ventilator dissipate energy and increase flow restriction. A resultant OAR of 3.82 shows that this opening is more restrictive to noise than it is to airflow.  5.3.4.4  C.K. Choi 327  Room 327, shown in Figure 32, has a volume of 33 m3 with an acoustic tile ceiling. It shares an 8.6 m2 glass partition with the corridor. One wood door exists in the partition. The ventilator is a 2.5 m long, Z-shaped section of lined duct with interior dimensions approximately 100 x 200 mm and grilles on the inlet and outlet. Its outlet grille is visible at the top left of the partition in Figure 32. A fan, which was turned off, is installed in the ventilator and could not be removed for testing. As the airflow is driven be a fan, this room should not be considered as an example of typical ventilation openings for naturally ventilated buildings.  Transmission loss tests were completed using the corridor as the source room and 327 as the receiver. Airflow test were completed by pressurizing 327 with the operator in the corridor. The ventilator flow area was significantly impeded by the fan.  72  5.3.4.4.1  327 Results (see Table 12)  As there is only a 1 dB change in NIC due to closing the ventilator, the transmission loss results for the ventilator only provide a lower bound on its performance, and a large degree of uncertainty must be acknowledged. In addition, blocking the ventilator caused only a 6% reduction in leakage area, causing great uncertainties in the flow result. Keeping the uncertainties in mind, the ventilator is shown to greatly reduce acoustic transmission (18 dB ASTC, 0.0073 SEOAs); however, the SEOAf is very low at 0.0033. A OAR of 0.87 results; however, this should be considered a lower bound because the ventilator’s measured TL was limited by that of the rest of the partition. Additionally, as the flow was obstructed by a stationary blower, the SEOAf is likely much lower than it would be with the duct alone. Table 12: Performance measures for ventilation openings in the C. K. Choi building. Vent Condition 167 321 326 327 ∆NIC [dB] N/A N/A N/A 1 ASTC [dB] 1 4 6 18 SEOAs 0.92 0.51 0.22 0.0073 %∆EOAf -77 -76 -94 -6 SEOAf 0.98 1.46 0.83 0.0033 OAR 1.06 3.42 3.82 0.87  Figure 29: C. K. Choi 167.  Figure 30: C. K. Choi 321.  73  Figure 31: C. K. Choi 326.  5.3.5  Figure 32: C. K. Choi 327  Langara College Library  Langara College’s library is a hybrid naturally and mechanically ventilated building. It is equipped with environmental sensors and a control system to determine if the outdoor and indoor conditions are suitable for the natural ventilation system to ventilate the building. If they are, electrical actuators open windows and louvers on the building façade and on the towers at the top of the building. If weather conditions are not appropriate for natural ventilation, the windows and louvers are closed and a mechanical ventilation system is used. The natural ventilation system functions by drawing air in through the façade, through the building and out the towers.  While the majority of the library is open-plan, there were three interior partitions with unique ventilation openings suitable for this study. The spaces are a computer lab (L104), a printer room (L112), and a classroom (L208).  74  5.3.5.1  Langara L104  Room L104 (Figure 33) has a volume of 360 m3 and shares a 55 m2, 0.3 m thick, concrete partition with a large atrium. Besides the ventilator, the door is the only other apparent sound transmission path. The ventilator (Figure 35) is an L-shaped crosstalk silencer with a mean length of 1.8 m and has both inlet and outlet covered with grilles (Figure 36). The outlet grille has a chevron cross section, is 20 mm thick, with 1 mm thick fins and 4 mm spacing between the fins. The inlet ventilator is a 10 mm grid of 1 mm thick, 10 mm long fins aligned with the flow. From a visual inspection, the outlet grille appears as if it would offer a high restriction to airflow. Tests were completed with the grilles installed and removed.  Transmission loss tests were completed using the L104 as the source room and the atrium as the receiver. L104 could not be used as the receiver because it was not possible to turn off the computers in the room which produced high background noise levels.  Airflow tests were completed by pressurizing L104 with the operator in the atrium. The mechanical ventilation system was running; however, the flow during testing was eliminated by covering the inlet with sheet plastic and tape.  5.3.5.1.1  L104 Results: Grille On (see Table 13)  There was no significant difference in noise isolation when the ventilation opening was open or closed - in fact, a 1 dB reduction was measured when the opening was blocked off. This reduction must be attributed to measurement uncertainty. Unfortunately, because the atrium was so large, it did not provide the diffuse field required to measure the apparent sound transmission class accurately. As a result of the non-diffuse field, and a lack of noise transmission through the ventilator, no meaningful results can be given for ASTC or EOAs (and therefore OAR)  The EOAf was reduced 62% by blocking the ventilator; the airflow results are therefore significant. The SEOAf was calculated to be 0.25.  75  5.3.5.1.2  L104 Results: Grille Off (See Table 13)  As was the case in L104 with the grille on, no significant results can be given for ASTC, EOAs, or OAR. Blocking the ventilator reduced the EOAf by 78%, allowing accurate flow calculation for the ventilator. The SEOAf was calculated to be 0.48, corresponding to nearly twice the value measured with the grille on.  5.3.5.2  Langara L112  Room L112 (Figure 38) has a volume of 51 m3 and shares a 15 m2, 0.3 m thick, concrete partition with a large atrium. The ventilator is a rectangular hole, 0.33 x 0.13 m through the 0.3 m concrete partition. As a result, the ventilator opening is not thin; its length is more than twice its smallest cross sectional dimension. The interior surfaces of the ventilator are rough concrete. L112 is not naturally ventilated; a small ventilation fan drives air from the adjacent commuter lab, through the room, and out the ventilator; however, it was still of interest to measure the ventilator’s performance. The ventilation fan was turned off and sealed for testing.  Transmission loss tests were completed using L112 as the source room and the atrium as the receiver. L112 could not be used as the receiver as there was a fan in operation, resulting in high background noise levels. The fan could not be accessed; however, it is suspected that it was providing cooling for the printer. Airflow test were completed by pressurizing L112 with the operator in the atrium.  5.3.5.2.1  L112 Results (see Table 13)  A 2 dB increase in noise isolation was measured due to blocking the ventilator; however, as in L104, the transmission loss could not be accurately determined due to the non-diffuse field in the atrium. No significant results can be given for ATL, EOAs, of OAR. The equivalent leakage area of the room was reduced 95% by blocking the ventilator, allowing accurate ventilator airflow calculation. The equivalent open area for flow was measured to be 160% of the actual ventilator area.  76  5.3.5.3  Langara L208  Room L208 (Figure 34) has a volume of 285 m3 and shares a 26 m2, 0.3 m thick, concrete partition with a corridor. The ventilator (Figure 37) is an L-shaped crosstalk silencer with a mean length of 1.2 m and has both inlet and outlet covered with grilles. Grilles are identical to those installed in L102 (Figure 36). Tests were completed with the grilles installed and removed.  Transmission loss tests were completed using the corridor as the source and L208 as the receiver. Airflow test were completed by pressurizing L208 with the operator in the atrium. The mechanical ventilation system was running; however, the flow was eliminated during testing by covering the ventilation supply with plastic sheet and tape.  5.3.5.3.1  L208 Results: Grille On (see Table 13)  Blocking the ventilation opening reduced the noise isolation by only 1 dB. As a result, the apparent transmission loss values provide only a lower limit of the ventilator’s actual performance. With that in mind, the ventilator was measured to be ASTC 14 and have a SEOAs of only 2%. The equivalent leakage are of the room was reduced by only 30% by blocking the ventilator; as such the airflow results should be considered with caution. It appears that, unfortunately, attempts made to seal all other openings in the room were not completely successful. The SEOAf was calculated to be 32%, and the OAR is calculated to be 4.47.  5.3.5.3.2  L208 Results: Grille Off (see Table 13)  Unfortunately the acoustic measurements were not repeated with the grille removed. Based on the results from previous measurements in the Regent College and Liu building, it is understood that the grilles would have negligible effect on sound transmission. It is assumed that the measurements made with the grilles on also apply in this case with the grilles off.  Blocking the ventilator reduced the flow rate by 50% allowing the ventilator flow to be calculated with moderate accuracy. The SEOAf was measured to be 0.72, corresponding to over twice the value measured with the grille on. The result is an OAR of 9.89.  77  Table 13: Performance measures for ventilation openings in the Langara College Library. L104 L104 L208 L208 Vent Condition Grille On Grille Off L112 Grille On Grille Off ∆NIC [dB] -1 -1 2 1 1 ASTC [dB] 14 14 SEOAs 0.02 0.02 %∆EOAf -62 -78 95 -30 -50 SEOAf 0.25 0.48 1.61 0.32 0.72 OAR 4.47 9.89  Figure 33: Langara L104.  Figure 34: Langara L208.  78  Side View  Top View 870 mm  250 mm 500 mm  450 mm  870 mm  Figure 35: Langara L104 ventilator cross section– 50 mm fiberglass shown as crosshatched.  Exterior Grille Face  Interior Grille  Cross Section  Face  Cross Section  Figure 36: Langara L104 and L208 ventilator grilles.  Top View  Side View  460mm 460mm 380mm  350mm  520mm  Figure 37: Langara L208 ventilator cross Section– 50 mm fiberglass shown as crosshatched.  79  Figure 38: Langara L112 (ventilation opening at top left).  5.3.6  Operational Ventilator Flow Conditions  The National Building Code of Canada [58] states that outdoor air must be supplied to buildings at rates not less than that required by ANSI/ASHRAE 62 “Ventilation for Acceptable Indoor Air Quality” [59]. ASHRAE 62 ha a clause for natural ventilation requirements; however, they are stated as a required open area to the outdoors per unit of occupiable floor space. A requirement, stated in this way, is not useful for directly determining air exchange rates. The required exchange rates for mechanically ventilated spaces will therefore be used as an estimate of the flow rate for each space. Table 14 shows the required air exchange rates for the relevant spaces. Each required air exchange rate is calculated as the sum of the exchange rates required for people and for occupiable floor area3.  3  Assumes the “Zone Air Distribution Effectiveness” is 1.0 {{708 Standard, A. 2007}}.  80  Table 14: Selected minimum required air exchange rates [59].  Space type Office Meeting room Class room Computer room  Air exchange rate [L/s/m2] 0.3 0.3 0.6 0.6  Air exchange rate [L/s/person] 5 5 5 5  Standard ventilation rate information will be used, in combination with the measurements taken, to estimate the pressure drop across the ventilator and the Reynolds number of the flow. The Reynolds number is calculated as: Re Dh =  QDh νA  Q is the standard flow rate. At room temperature (300K) the kinematic viscosity (ν ) of air is 15.7x10-6 m2/s. The pressure required to achieve the standard air flow rate can be calculated as:  ρ   Q ∆p = 2  0.61EOA f       2  Note that, because EOAf is measured and calculated at 5 Pa, error is introduced if the calculated pressure is very different than 5 Pa. At any rate, this analysis provides a good first approximation of the operational conditions.  The assumed ventilator operating conditions are shown in Table 15. Langara L112, and C.K. Choi 327 ventilator results are not shown, as the ventilators were not designed for natural ventilation. Table 15 provides the ventilator’s EOAf, the flow rate (calculated based on Table 14), average flow velocity (Q/A), hydraulic diameter, Reynolds number, and pressure drop. The hydraulic diameter of a ventilator with a grille is given as the hydraulic diameter of the path between the grille fins.  The most striking result in Table 15 may be the complete lack of consistency in operational conditions of the various designs. For adequate ventilation, the ventilators in C.K Choi 326 and Liu 216C, both very large rectangular openings with approximately 1 m2 equivalent open area, would only need average flow velocities on the order of 0.01 m/s. This low flow rate  81  corresponds to a sub-micro Pascal pressure drop, four orders of magnitude less than the total pressure available in a typical natural ventilation system. The ventilators in Langara are at the other end of the spectrum. While having an EOAf that is an order of magnitude less than the C.K Choi 326 and Liu 216C ventilators, the required flow rate is at least an order of magnitude more. As a result, the velocities in the Langara ventilators are over 1 m/s, and the pressure loss is tens of Pascals, which exceeds the 10 Pa value (see Chapter 1) commonly assumed available to an entire natural ventilation system. The rest of the ventilators have operating conditions in between these two extremes.  The operational Reynolds number of the ventilator flow also varies greatly; however, it can be firmly concluded that the flow in these ventilation openings is not generally dominated by inertial forces alone (Re>4000), and is certainly not dominated by viscous forces (Re<10). Addition of grilles, besides reducing the equivalent open area, greatly reduces the hydraulic diameter, thereby reducing Re. Unfortunately, because there is little known information on the Re dependence of openings geometrically similar to the natural ventilation openings, it is not possible to conclude how much error is induced by using a single high-Re characterization for the design of these ventilators. Further study in this field, possibly through scale modeling or CFD, is warranted.  While the operational Re may not be high for some of these ventilators, the errors associated with using a high Re characterization may be not be of great practical consequence. Excluding ventilation openings with grilles, any ventilator that operates at Re < 4000 has an associated pressure loss that two to four orders of magnitude smaller than the total pressure available to a typical naturally ventilated building. The pressure loss across such a ventilator will be insignificant compared to pressure losses elsewhere in the system. Grilles, however, are an exception as their very small hydraulic diameter leads to a small Re at flow rates that result in significant pressure loss. This issue is revisited with CFD predictions in section 6.3.  82  Table 15: Assumed ventilation opening operating conditions.  Ventilator Location Regent L020 – Grille On Regent L020 – Grille Off Kaiser 4036 Liu 216C Liu 308 Liu 313 – Grille On Liu 313 – Grille Off C.K. Choi 167 C.K. Choi 321 C.K. Choi 326 Langara L104 – Grille On Langara L104– Grille Off Langara L208 – Grille On Langara L208– Grille Off  EOAf 0.26 0.49 0.19 0.78 0.18 0.027 0.050 0.54 0.46 1.07 0.05 0.10 0.068 0.15  Q [m3/s] 0.048 0.048 0.044 0.013 0.014 0.0075 0.0075 0.013 0.013 0.014 0.295 0.295 0.247 0.247  U (m/s) 0.12 0.11 0.16 0.012 0.037 0.18 0.18 0.024 0.041 0.011 1.37 1.36 1.17 1.17  Dh 0.026 0.60 0.17 0.69 0.25 0.028 0.20 0.37 0.25 0.86 0.008 0.39 0.008 0.46  Re 190 4500 1800 550 590 330 2300 560 650 600 690 34000 590 34000  ∆p 0.053 0.016 0.086 0.00045 0.0098 0.13 0.037 0.00094 0.0013 0.00028 47 13 21 4.2  83  5.3.7  In-Situ Results Summary (see Table 16)  Based on the results of the in situ measurements, a number of conclusions can be made about the effect of grilles, acoustic absorption on the ceiling above openings, and cross-talk silencers.  Rectangular ventilation openings (Regent L020 Grille Off, and Liu 313 Grille Off) have very little acoustic attenuation, with their SEOAs being around 0.9. Additionally, the SEOAf, is nearly 1.2 in both cases. When grilles are installed there is almost no change in EOAs; however, EOAf approximately halves. These results indicate that the OAR of a plain rectangular opening will typically halve if it is covered with a non-acoustical grille. The practical implication is that, if one intends to cover an opening with a grille, the opening will have to be twice as large to not induce additional pressure loss at the same flow rate; moreover, as a result of doubling the ventilator size, roughly twice the sound power will be transmitted. The effect of grilles on airflow was also noted in Langara library’s L104 and L208 where the EOAf was halved by installing grilles on the L-shaped cross talk silencers. Ventilation openings that are essentially rectangular openings but have a significant length compared to their cross sectional dimension, such as in Langara L112 and C.K. Choi 321, have an interesting behavior. Their EOAf is around 50% greater than the result expected for a thin orifice of the same cross section. This suggests it is possible to reduce pressure losses by creating a short length of duct instead of a thin orifice, and effect which is also observed in the laboratory measurements (section 5.5.5), and CFD predictions (section 6.3.7).  Measurements were made on slot openings between the top of a partition and an acoustically reflective ceiling (Liu 216C and C.K. Choi 167), as well as an acoustically absorptive ceiling (C.K. Choi 321 and 326). The presence of absorptive material appears to reduce the SEOAs from around 1 down to 0.5 or less, while causing no notable reduction in SEOAf. Adding acoustically absorptive material to the ceiling above a slot ventilation opening doubles the OAR of the ventilation opening.  84  Z-shaped cross talk silencers (Kaiser 4036 and Liu 308) provide a large reduction in sound transmission – around 16 dB over that of a rectangular opening; the SEOAs is around 3-5%. This is also associated with a small SEOAf of around 10%. In this case, the acoustic benefits outweigh the airflow disadvantages, resulting in an OAR of 2.5-3.5. Note that the acoustic transmission may be smaller than the stated result as its performance in both cases was largely limited by that of the partition in which it was installed.  By observing the change in noise isolation due to blocking the ventilation opening one is able to determine if a significant portion of the sound energy passing through the partition can be contributed to energy passing through the ventilation opening. For every CT silencer measured (Kaiser 4036, Liu 308 and Langara L208), blocking the ventilation opening resulted in no more than a 1 dB NIC increase. This indicates that, in all case where a designer has made a serious attempt to silence the ventilation opening, the silencer is effective in that the ventilation opening does not detrimentally affect the acoustic performance of the partition.  Table 16: In-situ measurement results summary.  # 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16  Room Regent L020 – Grille On Regent L020 – Grille Off Kaiser 4036 Liu 216C Liu 308 Liu 313 – Grille On Liu 313 – Grille Off C.K. Choi 167 C.K. Choi 321 C.K. Choi 326 C.K. Choi 327 Langara L104 – Grille On Langara L104– Grille Off Langara L112 Langara L208 – Grille On Langara L208– Grille Off  ASTC 0 1 16 -1 16 0 -1 1 4 6 18 14 14  SEOAs 0.89 0.83 0.046 1.04 0.030 0.85 0.88 0.92 0.51 0.22 0.0073 0.02 0.02  SEOAf 0.64 1.18 0.11 0.74 0.10 0.65 1.22 0.98 1.46 0.83 0.0033 0.25 0.48 1.61 0.32 0.72  OAR 0.73 1.41 2.48 0.71 3.42 0.76 1.38 1.06 3.42 3.82 0.87 4.47 9.89  85  5.4 Analysis of BRE Ventilator Measurements In an attempt to produce ventilators for naturally ventilated schools, Hopkins of the BRE proposed and tested the transmission loss and air flow characteristics of a number of crosstalk silencer type ventilation openings. The purpose of the ventilators is to allow cross ventilation between classrooms and corridors or cafeterias. Results and testing information were published [12].  The acoustics and airflow performance were tested using a method effectively identical to the laboratory experimental procedure implemented in this report. Ventilators were inserted into the common wall of a sound transmission suite. Transmission loss was measured by standard techniques, and airflow was measured by driving air at a known flow rate from one room, through the ventilator, and into the other room, while measuring the pressure difference between the two rooms. All measured values required to calculate the OAR were published, allowing discussion of these results in the same terms as the original work presented in this thesis.  5.4.1  Ventilator Configurations  All ventilators tested were based on a 2.264 m wide by 0.2 m tall cross section. Using this cross section, the effect of different configurations of absorber, the addition of a 90 degree bend to make an L-shaped ventilator, the addition of grilles, and the addition of a PVC film lined absorber, were tested. Addition of the absorber reduced the internal dimensions of the ventilators. The PVC lining was included to make it possible to wipe the absorber surfaces clean. For naming convention, ‘g’ is added to indicate the use of grilles; ‘PVC’ is added to indicate a PVC film lining.  5.4.1.1  Straight Ventilator  The straight ventilator, with a cross section of 2.264 x 0.2 m, was 1.9 m in length. It was tested without a lining (Figure 39) and with 50 mm thick acoustic foam on both top and bottom (Figure 40). Foam reduces the cross section height to 0.1 m. Following Hopkins’ naming convention, these are Configurations 1 and 5, respectively.  86  5.4.1.2  L-shaped Ventilator  The L-shaped ventilator was composed of the straight ventilator, with a 0.782 m long elbow added to the end. It was tested with no lining (Figure 41), with 50 mm thick acoustic foam on the bottom surface (Figure 42), with 50 mm thick acoustic foam on both top and bottom surfaces (Figure 43), with additional foam baffles inserted at an angle to the flow (Figures 44 and 45), and with smaller waves of acoustic foam (Figure 46).  5.4.2  Results  STC, SEOAs, SEOAf, and OAR were calculated for each of these configurations from the published measurement data. Results are shown in Table 17. These results can be used to determine the effect of the absorptive lining, the elbow, grilles, PVC film lining, angled baffles, and wave-shaped absorptive liner.  5.4.2.1  Effect of Acoustic Foam  Both the straight and L-shaped silencers were tested with and without acoustic foam. The straight and L-shaped silencers without foam are Configurations 1 and 2. Acoustic attenuation from both configurations is small or negligible; likewise, the equivalent area for flow is similar to the silencer’s actual cross sectional area. As a result, the OARs of these two configurations are both near one.  Adding 50 mm thick acoustic foam to both top and bottom surfaces of the straight and Lshaped silencers creates Configurations 5 and 4. The open area for flow in both cases is reduced to half of what it was without the foam; however, this is expected as the duct height was reduced from 20 to 10 cm by adding the foam. Equivalent acoustic open area is reduced greatly, by a factor of 1/310 in the straight duct, and by 1/970 the L-shaped duct. As the acoustic open area was reduced much more than the flow open area, the resulting OAR is 177 for the straight duct and 885 for the L-shaped duct.  Configuration 3 is the L-shaped silencer with foam on the bottom side only. The SEOAs is 18 times the value of the same silencer with foam on both surfaces, but less than that of the  87  unlined duct by a factor of 1/55. Airflow results are not given; however, we can assume a value of 0.75 by interpolating between Configurations 2 and 4. The result is an OAR of 63.  As expected, these results show that an acoustic lining is a critical component of a passive silencer. Much improved performance was observed by lining both the top and bottom surfaces.  5.4.2.2  Effect of Elbow (L-shaped silencer)  The L-shaped silencer was created by appending an elbow section to the straight duct. As a result, the L-shaped silencer is 1.5 times the length of the straight silencer. This must be considered in the comparison. Configuration 5 and 4 are the straight and L-shaped silencers with lining on both surfaces.  The L-shaped silencer has very slightly higher restriction to airflow than the straight silencer; however, it offers much higher noise reduction. As a result the OAR of the L-shaped silencer is 5 times that of the straight silencer. Unfortunately, as the L-shaped silencer is 1.5 times the length of the straight silencer, this is not a fair comparison.  5.4.2.3  Effect of Grilles  Nearly all of the configurations were tested with and without a 48% open area grille on one end of the ventilator. Adding the grille resulted in almost no effect on the sound transmission; less than one dB variation was observed in all cases. For airflow however, adding the grilles to the un-lined ventilators reduced the equivalent open area by nearly 50%. This result agrees with our own measurements (see section 5.3). For lined configurations, the SEOAf was already reduced by around 50%; adding the grille caused further reduction of only 10-20%.  5.4.2.4  Effect of PVC Lining  A PVC film liner was applied to the surface of the acoustic foam on both the straight and Lshaped silencers. In the straight silencer it was measured to increase noise transmission by 30% and reduce airflow by 4%; in the L-shaped silencer it was shown it reduce noise transmission by 35% and reduce airflow by 17%. These results are contradictory, but lead to  88  the general conclusion that the performance is not greatly affected by the addition of a PVC film validating its use to facilitate cleaning. The reduction in airflow is surprising, in that it is suspected to reduce the surface roughness. A possible explanation is that, without a lining in place, some of the air passes through the foam, increasing the total flow rate.  5.4.2.5  Effect of Angled Baffles  Baffles were inserted into the silencer as shown in Figures 44 and 45; these create Configurations 8 and 6, respectively. Unfortunately airflow results were not published.  Configuration 8, which includes baffles without a liner on the top or bottom surfaces, reduces the EOAs to about half that of the un-lined configuration. Adding the baffles to the lined Lshaped ventilator, as in Configuration 6, reduces the EOAs by around 30%. It is likely that, if the airflow was measured, the EOAf would be reduced by at least 30%, showing that the angled baffles are not beneficial to the ventilator’s performance.  5.4.2.6  Effect of Wave-Shaped Absorptive Liner  The wave-shaped liner, shown in Figure 46, creates Configuration 7. Airflow of this configuration was only tested with the grille on. The EOAf was 25% higher than for the lined L-shaped duct; however, the EOAs was 38 times greater. As a result, the OAR with the waveshaped liner is only 3% of the fully lined silencer.  5.4.3  Summary of BRE Ventilator Test Results  The BRE has produced a very good and very useful set of experimental results on interior natural ventilation opening silencers. The results have been analyzed using the open area ratio metric and a number of conclusions can be drawn: 1. Cross-talk type silencers must have acoustic absorption to attenuate noise. In addition, it is much more effective to line the top and bottom surfaces than the bottom surface alone. 2. The addition of a 90° bend (elbow) slightly reduces the airflow and may not cause a large increase in transmission loss. It can not be concluded that elbows increase the OAR of a silencer.  89  3. Provided the SEOAf is greater than 0.5, adding a grille significantly reduces the airflow. If the SEOAf is nearly 1, adding a grille may reduce the airflow by 50%. Grilles do not increase transmission loss. 4. Covering the acoustic foam liner with a PVC film to facilitate cleaning did not have strong adverse effects on the silencer’s performance (sound transmission or airflow). 5. Initial attempts at creative acoustic foam placement (angled baffles and wave-shaped liner) did not have superior performance to the basic lined duct.  Table 17: BRE ventilator measurement results summary, (xxx) – estimated values. Configuration STC SEOAs SEOAf OAR 1 0 1.19 1.12 0.95 1g 0 1.24 0.68 0.55 2 4 0.66 0.95 1.44 2g 4 0.65 0.62 0.96 3 24 0.012 (0.75) (63) 3g 25 0.012 4 36 0.00068 0.60 885 4g 37 0.00058 0.50 860 4 PVC 31 0.00046 0.55 1180 4g PVC 31 0.00045 0.51 1140 5 28 0.0038 0.68 177 5g 29 0.0034 0.57 166 5g PVC 17 0.0048 0.55 113 6 38 0.00048 6g 38 0.00050 7 20 0.026 7g 20 0.025 0.62 24.8 8 8 0.32 8g 9 0.30 -  90  Figure 39: BRE ventilator Configuration 1.  91  Figure 40: BRE ventilator Configuration 5.  92  Figure 41: BRE ventilator Configuration 2.  93  Figure 42: BRE ventilator Configuration 3.  94  Figure 43: BRE ventilator Configuration 4.  95  Figure 44: BRE ventilator Configuration 8.  96  Figure 45: BRE ventilator Configuration 6.  97  Figure 46: BRE ventilator Configuration 7.  98  5.5 Laboratory Measurements of Ventilation Openings and Silencers Measurements were carried out in the purpose-built ventilator test suite to measure the performance of a number of distinct ventilation opening and silencer types. The intent of these measurements was three-fold. First, they were made to satisfy our curiosity about the relative performance of some of the very different ventilator types that are currently being used in practice. Second, they were intended to assess the performance of novel ventilators. Finally, the results provide insight into which ventilator types should be prototyped for further optimization and which should not be pursued.  Five different types of ventilation openings were tested, each in a variety of configurations. These ventilation opening types are the slot, acoustical louver, baffle, air filter, and crosstalk (CT) silencer.  The performance characteristics of the ventilation openings are stated in terms of their SEOAs, SEOAf and OAR. Additionally, the STC rating is given, as it is a standard metric and can be used to compare the performance of these silencers to other published acoustical data. Plots of the third octave band transmission loss are given to show the frequency dependence. Also the transmitted speech spectrum, defined as the transmission loss subtracted from a normalized A-weighted speech spectrum, are given as they show the relative importance of each frequency band on the resultant SEOAs.  5.5.1  Slot Ventilation Opening  The slot ventilation opening is often created, in practice by leaving a gap between the top of the partition and the ceiling. To study this design a 50 mm high, 1 m wide, and 0.11 m long slot has been created between the bottom of the wall and the floor; the results should be the same as if the slot was at the ceiling.  The effect of acoustic absorption on the ceiling above the slot was measured. This is of interest because, as observed in the C.K. Choi building (see section 5.3.4) ceilings are often constructed of acoustic tiles. In order to maintain a constant ventilation opening geometry, the absorptive tiles, when removed, were replaced with gypsum board of the same geometry. 99  Various configurations of the absorption were tested to see the effect of absorber dimensions. With the absorber width equal to the width of the slot (1 m), and a 1 m length (the absorber extends 0.5 m on either side of the partition), absorber thicknesses of 0, 25 and 50 mm were tested (see Figures 47 through 50). An additional test was made to test the effect of absorber length by having the 50 mm thick absorber only 0.5 m long, extending 0.25 m either side of the partition (no image shown). Manufacturer data for the fiberglass absorber is provided in Appendix A.1  It was also of interest to see the effect of the ventilation opening being located away from, as opposed to adjacent to, the floor (or ceiling). A 1 m x 50 mm opening was created 1m away from the corner as shown in Figure 50.  Figure 47: Slot ventilation opening, no fiberglass.  Figure 49: Slot ventilation opening, 1 m x 1 m x 50 mm fiberglass.  Figure 48: Slot ventilation opening, 1 m x 1 m x 25 mm fiberglass.  Figure 50: Slot ventilation opening, away from floor/ceiling.  A summary of the slot ventilation opening measurement results are given in Table 18. Frequency dependent transmission loss and transmitted speech spectrum are given in Figures 100  51 and 52. All of the slot openings were geometrically similar; therefore, no significant differences in the SEOAf exist; the fiberglass does not affect airflow. A SEOAf of 1.09 indicates that, as expected, the flow performance of the slot ventilation opening is slightly better than that of an open hole.  The slot opening without any fiberglass has a SEOAS of 2.38 resulting in an OAR of 0.46. This is quite poor performance. Figure 51 shows that the negative transmission loss (equivalent to SEOAS greater than one) is dominant at low frequencies; two physical explanations for this exist, and have been previously discussed in section 2.3. Firstly, if the wavelength is greater than the opening dimension, as it is below about 6 kHz for the 50 mm slot, then diffraction will be significant and more energy than is predicted by diffuse field theory will enter the ventilation opening. Secondly, diffuse field theory does not apply at walls or corners because the phase relationship of different modes is not random. In a reverberant environment with a diffuse sound field, the sound pressure level at a wall is 2.2 dB higher than the mean value in the room’s volume. The effect is significant within one quarter of the wavelength of the wall; therefore, at frequencies below 2000 Hz, coherence will occur over the majority of the 50 mm high opening, and its effect should be observed. In double and triple corners the sound field coherence is further increased.  Adding a 25 mm thick piece of fiberglass greatly increases the transmission loss above the 400 Hz third octave band, and increases it by up to 8 dB at and above 2 kHz. The SEOAs is reduced to 1.43. The benefits of the great increases in TL at high frequencies are not realized in the SEOAs; as is shown in Figure 52, the SEOAs is governed by transmission in the 250 and 500 Hz octave bands.  To further reduce the SEOAs, more absorption is required in the 250 and 500 Hz bands. Increasing the fiberglass thickness to 50 mm, as shown in Figure 51, increases the transmission loss in these bands. As a result, the SEOAS is further reduced to 0.94, providing an OAR of 1.15.  101  Reducing the length of the absorber from 1 m to 0.5 m has only a small negative effect on the sound transmission, which reduces the OAR from 1.15 to 1.06.  As explained above, moving the ventilator away from the corner was expected to reduce the sound transmission at 2000 Hz and below as the ventilation opening is exposed to a lower sound field (see Figure 51). Indeed, the transmission loss is reduced by 1-2dB in this range. Above 2000 Hz coherence becomes insignificant for the opening in the corner; correspondingly, the measured TL above 2000Hz is identical for the opening near and away from the corner. In effect, the SEOAf was reduced by 15%, and the STC was increased by 1.3dB. Surprisingly, moving the slot away from the corner increased the SEOAf by 10%, resulting in a 54% increase in OAR.  Table 18: Performance measures for the slot ventilation opening. Configuration STC SEOAs SEOAf OAR No FG -3 2.38 1.09 0.46 1m x 1m x 2.5cm FG 3 1.43 1.09 0.76 1m x 1m x 5cm FG 4 0.94 1.09 1.15 1m x 0.5m x 5cm FG 3 1.03 1.09 1.06 Away from corner -2 2.03 1.27 0.71 10 No FG 1m x 1m x 2.5cm FG 1m x 1m x 5cm FG 1m x 10.5m x 5cm FG Away from corner  8  Transmisson Loss [dB]  6 4 2 0 -2 -4 -6 -8 -10  125  250  500  1000 2000 Frequency [Hz]  4000  8000  Figure 51: Measured transmission loss of slot ventilation openings.  102  0  Transmitted Speech Spectrum [dB]  -5 -10 -15 -20 -25 -30  No FG 1m x 1m x 2.5cm FG 1m x 1m x 5cm FG 1m x 0.5m x 5cm FG Away from corner  -35 -40 -45  125  250  500  1000 2000 Frequency [Hz]  4000  8000  Figure 52: Measured transmitted speech spectrum of slot ventilation openings.  5.5.2  Acoustical Louver  An acoustical louver was obtained from Kinetics Noise Control (see Appendix A.2). It is 0.6 m tall, 0.6 m wide and 0.15 m thick. The sheet metal was perforated to expose the fiberglass packing on only one side of the louver. The louver is not geometrically symmetric, so it was tested in a number of different orientations to observe the dependence. In addition, the transmission loss was tested with fiberglass on the adjacent floor surface. The configurations, numbered 1 through 5, were: 1. Perforations facing the source room, louvers facing down toward receiver room (Figure 53) 2. Perforations facing the source room, louvers facing up toward receiver room (Figure 54) 3. Perforations facing the receiver room, louvers facing down toward receiver room (Figure 55) 4. Perforations facing the receiver room, louvers facing up toward receiver room (Figure 56)  103  5. As configuration 1, but with a 50 mm thick, 1 m x 1 m piece of fiberglass on the floor at base of louver (Figure 57)  Figure 53: Louver configuration 1, view from receiver room (perforations not visible).  Figure 55: Louver configuration 3, view from receiver room (perforations visible).  Figure 54: Louver configuration 2, view from receiver room (perforations not visible).  Figure 56: Louver configuration 4, view from receiver room (perforations visible)  Figure 57: Louver configuration 5, view from receiver room (perforations not visible)  104  Table 19 shows the results summary for all acoustical louver configurations. All configurations have similar airflow performance and, with the exception of configuration 5, similar transmission loss performance. Intuitively, one might expect the transmission loss to be greater with the perforations facing the source; however, according to the theory of reciprocity for linear systems, switching the location of source and receiver should produce identical results [60]. In this case, as the source and receiver rooms are effectively identical, flipping the louver front to back is the same as switching source and receiver; reciprocity predicts that identical results are measured. The louver has a SEOAs of 0.12 to 0.14 and a STC of 12 dB in all orientations.  Airflow is not a linear system that should obey reciprocity; however, the airflow performance is nearly identical for any orientation. The SEOAf is 0.21-0.22 in all configurations. Adding the fiberglass to the floor in configuration 1, as in configuration 5, reduced the SEOAs to 0.076 and increased the STC to 15 dB. The OAR of the acoustical louver varied from 1.5 to 1.8 depending on orientation, and increased to 2.9 by adding fiberglass adjacent to the inlet.  Table 19: Performance measures for the acoustical louver. Configuration STC SEOAs SEOAf OAR 1 12 0.13 0.22 1.68 2 12 0.14 0.21 1.51 3 12 0.12 0.22 1.79 4 12 0.12 0.21 1.71 5 15 0.076 0.21 2.79  105  25 1 2 3 4 5  Transmission Loss [dB]  20  15  10  5  0  -5  125  250  500  1,000 2,000 Frequency [dB]  4,000  8,000  Figure 58: Measured transmission loss of acoustical louver.  -10  Transmitted Speech Spectrum [dB]  -15 -20 -25 -30 -35  1 2 3 4 5  -40 -45 -50 -55  125  250  500  1000 2000 Frequency [Hz]  4000  8000  Figure 59: Measured transmitted speech spectrum of acoustical louver.  106  Performance data for this louver has been published by Kinetics Noise Control, allowing comparison. Figure 60 shows the insertion loss from the measured and published data; Figure 61 shows the SEOAf results. The measured insertion loss was calculated by subtracting the transmission loss of an empty opening the size of the louver from the transmission loss of the louver. Ideally the transmission loss of an empty hole is 0 dB; in reality this is not necessarily the case. Subtracting the transmission loss of the empty opening from the transmission loss of the louver makes the result less dependent on the room. The published insertion loss was measured with a free field receiver. Substantial disagreement between the results exists.  Excellent agreement exists between measured and published air flow results. 16 Measured (Diffuse Field) Published (Free Field)  14  Insertion Loss [dB]  12 10 8 6 4 2 0  125  250  500  1,000 2,000 Frequency [dB]  4,000  8,000  Figure 60: Measured (diffuse field receiver) and published (free field receiver) louver insertion loss.  107  0.25  0.2  SEOA f  0.15  0.1  0.05  0  Measured Published  5  10  20 Pressure [Pa]  50  Figure 61: Measured and published SEOAf of louver.  5.5.3  Acoustical Baffle  The acoustical baffle, a novel idea for a natural ventilation opening silencer, is shown in Figure 62. The acoustical baffle constructed for these tests consists of a 0.6 m wide, 0.3 m tall opening in the partition which is then covered on either side by a 1m wide, 0.65 m tall, 12 mm thick gypsum panel lined with 25 mm thick fiberglass (see Appendix A.1). This results in the baffle overlapping the partition by 0.175 m at the top and bottom and 0.2 m at the sides. Measurements have been made with the baffles offset 20 mm and 40 mm from the wall.  108  1m  0.3 m  0.65 m  0.6 m  Figure 62: Acoustical baffle – 25mm fiberglass shown as crosshatched.  The performances from these two configurations of acoustical baffle are encouraging. With the 20 mm offset the SEOAs is 0.054, and is moderately worse (0.090) with the 40 mm offset; however, the 20 mm offset is more restrictive to airflow, with an SEOAf of 0.20 as opposed to 0.49 with a 40 mm offset. As a result, the 40 mm offset is superior, with the OAR being 5.43 as compared to 3.70 in the case of the 20 mm offset.  The transmission loss plots of these two configurations, shown in Figure 63, indicate that the baffle with a 20 mm offset has a higher transmission loss than the 40 mm offset below 1000 Hz; however, interestingly, above 1000 Hz it is lower. From Figure 64 we see that it is the lower frequencies of 250 to 500 Hz that limit the acoustic performance of this silencer, which results in the baffle with a 20 mm offset having superior acoustic performance.  Many variables, such as baffle size, absorber thickness and location, and aperture size remain un-explored. It may be possible to optimize this design to obtain much higher performance.  Table 20: Performance measures for the acoustical baffle. Configuration STC SEOAs SEOAf OAR 2 cm 15 0.054 0.20 3.70 4 cm 14 0.090 0.49 5.43  109  35 20 mm offset 40 mm offset  30  Transmission Loss [dB]  25 20 15 10 5 0 -5  125  250  500  1000 2000 Frequency [Hz]  4000  8000  Figure 63: Measured acoustical baffle transmission loss. -15  Transmitted Speech Spectrum [dB]  -20 -25 -30 -35 -40 -45 -50 20 mm offset 4 mm offset  -55 -60 -65  125  250  500  1000 2000 Frequency [Hz]  4000  8000  Figure 64: Measured acoustical baffle transmitted speech spectrum  110  5.5.4  Acoustical Air Filter?  In naturally ventilated buildings, air filtration poses a problem in the very same way as ventilation silencing: conventional methods (fibrous filters) create flow restriction, thereby greatly reducing the ventilation flow rates. An idea was proposed to make a device that acted as both a silencer and a filter to reduce the total load on the system. Combining the two systems seems possible because fibrous filters appear visually similar to fibrous absorbers, and electrostatic precipitator filters appear similar to splitter silencers. This work represents a preliminary investigation into combining fibrous filters and absorbers. The acoustic transmission and air flow of one type of fiberglass acoustic absorber (Figure 65) and two types of air filters (Figures 66 and 67) have been measured. Manufacturer data for the filters is provided in Appendix A.3.  Figure 65: Acoustic fiberglass (see Appendix A.1).  Figure 66: Pink air filter (see Appendix A.3).  Figure 67: White air filter (see Appendix A.3).  111  The acoustical fiberglass is able to reduce the SEOAs to 0.14; however, it reduces the SEOAf to 0.005, resulting in a very poor OAR of 0.014. The air filters do not attenuate sound effectively, with SEOAs of 0.65 and 0.73; however, are less (but still significantly) restrictive to airflow with SEOAf of 0.20 and 0.29. The highest OAR of the filters, 0.39, is the filter that causes the least restriction to air flow – the white air filter.  In order to see the effect of the filter alone on acoustic transmission, it is better to look at the insertion loss – the difference in transmission loss between the empty opening and the opening with the filter installed. Insertion loss results are shown in Figure 70. At low frequencies the two air filters have no effect. Their insertion loss increases with frequency, but never exceeds 5 dB at frequencies below 10 kHz. The pink air filter has slightly higher transmission loss over mid and high frequencies. As expected, the acoustic fiberglass provides better transmission loss; however, it is less than 5 dB at all but high frequencies.  Table 21: Performance measures for the acoustical air filters. Configuration STC SEOAs SEOAf OAR Acoustic Fiberglass 6 0.14 0.0051 0.014 Pink Air Filter 2 0.65 0.20 0.31 White Air Filter 1 0.73 0.29 0.39 20 Acoustic Fiberglass Pink Filter White Filter  Transmission Loss [dB]  15  10  5  0  -5  125  250  500  1000 2000 Frequency [Hz]  4000  8000  Figure 68: Measured acoustical air filter transmission loss.  112  -5  Transmitted Speech Spectrum [dB]  -10 -15 -20 -25 -30 -35 Acioustic Fiberglass Pink Air Filter White Air Filter  -40 -45 -50  125  250  500  1000 2000 Frequency [Hz]  4000  8000  Figure 69: Measured acoustical air filter transmitted speech spectrum.  16 Acoustic Fiberglass Pink Air Filter White Air Filter  14 12  Insertion Loss [dB]  10 8 6 4 2 0 -2 -4  125  250  500  1000 2000 Frequency [Hz]  4000  8000  Figure 70: Measured acoustical air filter insertion loss.  113  5.5.5  Cross Talk Silencer  Cross talk (CT) silencers are short lengths of lined duct. Z-shaped CT silencers were measured in the Fred Kaiser building, and in the Liu Institute for Global Studies. L-shaped CT silencers were measured in Langara College library. Here the performance of straight, Lshaped, and Z-shaped CT silencers are measured. Additionally, to observe the acoustic effect of the fiberglass liner, the straight silencer was also tested with the fiberglass removed.  To allow a comparison of the different shapes, all three of the silencers were constructed so that the length of the flow path through the center of the silencer was 0.3 m. Unfortunately it was not possible to accurately test CT silencers with longer lengths due to transmission loss limitations of the lab facility. Highly accurate transmission loss measurements were required so that they could be used to validate the numerical model presented in section 6.2.2. Diagrams and photographs of the straight, L and Z-shaped CT silencers, as tested, are shown in Figures 71 through 76. Figures 77 and 78 show the straight silencer with the fiberglass removed. All of the CT silencers were constructed out of 25 mm thick plywood, and lined with 50 mm of fiberglass on either side (fiberglass details in Appendix A.1). The height of the flow path was 0.1 m, and the width 2 m. The fiberglass surfaces exposed to the source and receiver rooms have been covered by a layer of 12 mm gypsum board, indicated in the drawings by a heavy black line. All of the silencers were sealed to the floor using plasticine. The brick section shown in the figure represents the mounting with respect to the partition. In all cases the acoustic transmission was tested with the flow travelling from right to left, and the acoustic transmission from left to right.  100 mm  300 mm Figure 71: 0.3 m Straight CT silencer diagram – 50 mm fiberglass shown as crosshatched.  114  Figure 72: 0.3 m Straight CT silencer.  200 mm 100 mm  200 mm Figure 73: 0.3 m L-shaped CT silencer diagram– 50 mm fiberglass shown as crosshatched.  Figure 74: 0.3 m L-shaped CT silencer.  115  200 mm 100 mm  150 mm Figure 75: 0.3 m Z-shaped CT silencer diagram – 50 mm fiberglass shown as crosshatched.  Figure 76: 0.3 m Z-shaped CT silencer.  50 mm 100 mm  300 mm Figure 77: 0.3 m Straight CT silencer diagram – fiberglass removed.  116  Figure 78: 0.3 m Straight CT silencer – fiberglass removed.  A summary of the 0.3m CT silencer measurement results is given in Table 22. Frequency dependent transmission loss and transmitted speech spectrum are given in Figures 79 and 80. The acoustic performance of the Straight, L and Z-shaped silencers are quite similar, with STC 9 (Straight and L) or 10 (Z) and a SEOAs near 0.3. The Z-shaped silencer has slightly superior performance. Without fiberglass the CT silencer looses essentially all acoustical value. For airflow, the straight CT silencer has a SEOAf greater than unity, at 1.29. This effect of enhanced airflow through, in essence, elongated orifices has also been observed and discussed in the in situ and numerical modeling sections of this thesis (sections 5.3 and 6.3 respectively). The L-shaped CT silencer is more restrictive than an orifice (SEOAf of 0.8); the Z-shape (SEOAf of 0.68) is more restrictive than the L-shape CT Silencer. As shown in Figure 79, except for local variations, the transmission losses of the three silencers are very similar below 4 kHz, increasing from -5 dB at low frequencies up to 15 dB at 4 kHz. Above 4 kHz the performance of the L-shaped silencer is superior. This can be explained by the geometry of the silencers; the L-shaped silencer is the only one of the three that had no unobstructed line-of sight path through it. High frequencies are directional will “beam” through any unobstructed path. As is characteristic of absorptive liners, the attenuation is very small at low frequencies and increases with frequency. Regardless of high frequency variation in the performance, the SEOAs is essentially identical for all three silencers because, as shown in Figure 80, the critical bands are at low and mid frequencies. Negative transmission loss at very low frequencies can be explained by wave effects (see section 2.3). 117  Comparing the straight silencer with and without an absorptive liner we see that they have essentially identical performance below 250 Hz, at which point the liner becomes effective. While the duct alone does have a small effect, above 500 Hz the vast majority of attenuation is due to the presence of the liner.  Table 22: Performance measures for the 0.3 m CT silencers. SEOAf OAR Configuration STC SEOAs Straight 9 0.32 1.29 4.07 L 9 0.34 0.80 2.32 Z 10 0.28 0.68 2.44 Straight w/o fiberglass 2 1.12 -  25 Straight L Z Straight w/o liner  Transmission Loss [dB]  20  15  10 5  0  -5  -10  125  250  500  1000 2000 Frequency [Hz]  4000  8000  Figure 79: Measured transmission loss of 0.3 m CT silencers.  118  0  Transmitted Speech Spectrum [dB]  -5 -10 -15 -20 -25 -30 -35  Straight L Z Straight w/o liner  -40 -45 -50 -55  125  250  500  1000 2000 Frequency [Hz]  4000  8000  Figure 80: Measured transmitted speech spectrum of 0.3 m CT silencers.  5.5.6  Lab Measurement Results Summary  Three known classes of silencers – the lined slot, the acoustic louver, and the crosstalk (CT) silencer – as well as two unknown silencer prototypes – the acoustic baffle, and the acoustic air filter – have been tested for acoustics and airflow. The performance results are summarized in Table 23.  The silencer with the best performance in terms of OAR is the baffle with a 40 mm offset. It caused some restriction in airflow, with a SEOAf of 0.49; however, the SEOAs is reduced to 0.09, resulting in an OAR of 5.43.  Following the baffle in performance are the CT silencers with OARs of 4.07, 2.44, and 2.32 for the Straight, Z, and L-shapes. The CT silencers all have similar acoustic performance, with SEOAs around 0.3 which is limited by low frequency transmission. CT silencers, especially the straight silencer, have good performance due to low airflow resistance. The SEOAf of the straight silencer is 1.29, and reduces to 0.8 and 0.68 for the more obstructive L and Z-shaped silencers. 119  Next in performance is the Louver. Its SEOAs of 0.12 is nearly as low as the baffle; however, its SEOAf is much worse at 0.22, resulting in a maximum OAR of 1.79. Adding fiberglass to the floor below the louver reduced the SEOAs to 0.075 resulting in an improved OAR of 2.79.  The slot opening, lined with 50 mm of fiberglass follows the louver in terms of performance. It has great airflow properties, with a SEOAf of 1.1; however, it does little to attenuate noise, with a SEOAs of 0.94. As a result the OAR is only 1.15. It is important to realize that, while the SEOAf is near unity, the fiberglass lining has a positive effect. Because of diffraction and sound field coherence in the corner (see section 2.3) the acoustic performance of the slot opening without any lining is much worse, with the SEOAs increasing to 2.38. Using acoustical fiberglass or fibrous air filters as a combined silencer and filter did not provide good performance. The acoustical fiberglass attenuates noise, but is detrimental to the airflow; the fibrous filters allow better airflow, but provide very little attenuation of sound. The best performance was from the white air filter, providing an OAR of 0.39.  An interesting observation from all ventilation opening types is that the acoustic performance in terms of the SEOAs is limited by the 500 Hz octave band. Any improvements on these silencers must therefore seek to improve the transmission loss around this frequency.  120  Table 23: Laboratory measurements results summary.  Class CT Silencer  Slot  Louver  Baffle Filter  Configuration Straight L Z Straight w/o fiberglass No FG 1m x 1m x 2.5cm FG 1m x 1m x 5cm FG 1m x 0.5m x 5cm FG Away from corner 1 2 3 4 5 2 cm 4 cm Acoustic Fiberglass Pink Air Filter White Air Filter  STC 9 9 10 2 -3 3 4 3 -2 12 12 12 12 15 15 14 6 2 1  SEOAs 0.32 0.34 0.28 1.12 2.38 1.43 0.94 1.03 2.03 0.13 0.14 0.12 0.12 0.076 0.054 0.090 0.14 0.65 0.73  SEOAf 1.29 0.80 0.68 1.09 1.09 1.09 1.09 1.27 0.22 0.21 0.22 0.21 0.21 0.20 0.49 0.0051 0.20 0.29  OAR 4.07 2.32 2.44 0.46 0.76 1.15 1.06 0.71 1.68 1.51 1.79 1.71 2.79 3.70 5.43 0.014 0.31 0.39  121  Chapter 6: Ventilation Silencer Performance Prediction Numerical methods exist, and are commonly used, for solving problems involving both sound propagation and air flow. Using these methods for performance prediction can be highly useful in two ways: 1. Time, facilities, and cost required to do optimization and validation through physical experiments can be greatly reduced 2. Numerical methods can provide the entire pressure or flow field solution, which allows valuable insight into factors that govern the ventilation openings’ performance. This chapter will present methods for modeling the attenuation of the fundamental mode in a lined duct, diffuse field transmission loss using COMSOL FEM, and airflow using ANSYS Fluent CFD.  6.1 Fundamental Mode Attenuation Analytical solutions for the random incidence transmission loss attenuation of ventilation openings do not exist; as a result, FEM must be implemented to obtain a numerical solution. Unfortunately, FEM predictions are time consuming, computationally expensive, and prone to error. There is, however, an analytical solution for the attenuation of the fundamental model in a lined duct [31, 61] and it is understood that, in straight sections of lined silencers, the attenuation of the fundamental mode largely governs the performance because it is the least-attenuated [61]. This section will explain the analytical solution and investigate the effect of silencer geometry on attenuation performance.  6.1.1  General Cartesian Solution for Sound in a Duct  In rectangular ducts, as the geometries are made of planes defined by simple Cartesian coordinates, it is useful to use the wave equation in Cartesian coordinates. The linear wave equation can be written as: ∇2 p =  1 ∂2 p c 2 ∂t 2  122  Using separation of variables to find solutions, the pressure can be solved as the product of three location-dependent functions and a time dependent function. p(r , t ) = Px (x )Py ( y )Py ( z )T (t ) By inserting this assumption into the wave equation, spatially dependent variables can be separated from the time dependent variable, creating multiple ordinary differential equations from the single partial differential equation.  p x (x )  ″  p x (x ) − s x c 2 = 0  py (y)  ″ =0  p y (t ) − s y c2 ODEs :   ″ p z (z ) =0  p z (z ) − s z c2   p ″ (t ) − sp (t ) = 0 t  t where s x + s y + s z = s . Differential equations of this form can hold the following solutions: sx s  x − x2 x 2  A1e c + A2 e c if s x > 0  p x , y or z ( x, y or z ) =  A1 + A2 x if s x = 0  −sx −sx j x x −j  c2 c2 A e + A e if s x < 0 2  1   A1e st + A2 e − st if s t > 0  pt (t ) =  A1 + A2 t if st = 0  j − st + A2 e − j − st if s t < 0  A1e  Our interest is in the harmonic solution where sx, t<0. It is convenient and informative to introduce the wave number, k, and angular frequency, ω at this point. The wave number is the number of radians per unit distance in the direction of the associated coordinate; the frequency is the number of radians per unit time at one location. Letting − s x = k x c 2 and 2  − s = ω 2 , the general Cartesian solution can be written as:  123  p = p x ( x ) p y ( y ) p z ( z ) pt (t )  − jk x jk x  p x ( x ) = A1e x + A2 e x  − jk y jk y y + A4 e y  p y ( y ) = A3 e  where :  p z ( z ) = A5 e jk z z + A6 e − jk z z  − jωt jωt  pt (t ) = A7 e + A8 e  2 ω2 2 2 2 k x + k y + k z = k = 2 c  This solution form represents waves, with some amplitude and wave number, propagating in the positive and negative directions on each axis, and propagating in both directions with respect to time.  6.1.2  Solution for a Rigid Walled Duct  In an infinite-length duct, or equivalently in a duct with an anechoic termination, waves will not be considered to propagate in the –z direction. Waves travel forward with unit amplitude as time increases. With these restrictions the general solution can modified to:  p z ( z ) = A5 e − jk z z pt (t ) = e jωt Taking the cross section of the duct to extend from 0 to Lx in x, and 0 to Ly in y, the Neumann condition is applied to the duct walls: dp x ( x ) = 0 at x = 0 and x = L x dx dp y ( y ) = 0 at y = 0 and y = L y dy Using the boundary condition and the general solution, a modal solution can be presented as: p = A cos(kl x ) cos(k m y )e j (ωt − k z z ) kl + k m + k z = 2  2  2  ω2 c2  lπ   k l = L l = 0,1, 2, 3K  x where   k m = mπ m = 0,1, 2, 3K  Ly  124  By letting kl + k m = klm and solving for the wave number in z some properties of the 2  2  2  system become apparent: kz =  ω2 c  2  − k lm  2  35  For relatively high frequencies or ducts of large cross section with respect to a given mode, the pressure fluctuates sinusoidally with z:  ω2 c  2  − klm > 0 2  p = A cos(kl x ) cos(k m y )e e jωt  −j  ω2 c2  − klm 2 z  When the frequency becomes low, or the duct is small with respect to a given mode, the wave number becomes complex resulting in a pressure that decays exponentially with increasing z. This is known as the cut-off frequency for a mode in a duct. The only mode that does not have a cut-off frequency is the plane wave mode (l=0, m=0).  ω2 c  2  − k lm < 0 2  p = A cos(k l x ) cos(k m y )e jωt e  6.1.3  − k lm 2 −  ω2 c2  z  Non-rigid Walled Duct  If a duct does not have rigid walls the Neumann boundary condition becomes invalid. If the normal incidence surface impedance is known then the boundary condition can be replaced with: Zs =  p u  Using Newton’s second law on an element of fluid, the particle velocity can be related to pressure: F = m&x& ∂p x ∂u = −ρ0 x ∂x ∂t ∂p y ∂u y = −ρ0 ∂y ∂t 125  Assuming that ux and uy have solutions that vary sinusoidally with time, it follows that: ux =  − kx − 1 dp x A1e jk x x − A2 e − jk x x = jρ 0ω dx ρ0k c  uy =  − ky − 1 dp y jk y − jk y = A3 e y − A4 e y jρ 0ω dy ρ0k c  (  (  )  )  Solving for the impedance at the duct walls (hx, -hx, hy, -hy) gives:  Z s , x (hx ) =  A1e jk x hx + A2 e − jhx − kx A1e jhx − A2 e − jhx ρ0k c  (  Z s , x (− hx ) =  Z s , y (h y ) =  )  A1e − jk x hx + A2 e jhx − kx A1e − jhx − A2 e jhx ρ0k c  (  A3 e  jk y h y  − ky  (A e ρ kc  + A4 e  − jk y h y  jk y h y  − A4 e  − jk y h y  − jk y h y  + A4 e  jk y h y  3  )  )  0  Z s , y (− h y ) =  A3 e − ky  (A e ρ kc  − jk y h y  3  − A4 e  jk y h y  )  0  If the impedances of opposite walls are equal, the simplifying assumption can be made that the propagating modes will be either symmetric or antisymmetric [31]. For symmetric mode propagation:  A1 = A2 A3 = A4 Z s , x (hx ) Z0 Z s , y (h y ) Z0  = =  − Z s , x (− hx ) Z0 − Z s , y (− h y ) Z0  =  −k cot (k x hx ) jk x  =  −k cot (k y h y ) jk y  For antisymmetric mode propagation:  − A1 = A2 − A3 = A4  126  Z s , x (hx ) Z0 Z s , y (h y ) Z0  = =  − Z s , x (− hx ) Z0 − Z s , y (− h y ) Z0  =  k tan (k x hx ) jk x  =  k tan (k y h y ) jk y  Re-written, the system of equations for a duct in which opposite walls have equal impedance is:  jkZ 0  Z s,x   jkZ 0   k y tan (k y h y ) = Z s, y   2 2 2 k x + k y + k z = k 2  k x tan (k x hx ) =  Symmetric  36  − jkZ 0  Z s,x   − jkZ 0   k y cot (k y h y ) = Z s, y   2 2 2 k x + k y + k z = k 2  k x cot (k x h x ) =  Antisymmetric  These two sets of equations can be solved numerically to find k z as a function of k (k is directly related to frequency). A numerical iteration scheme, such as the Newton-Raphson method, can be used to find the roots of and solution to these equations.  One important observation from this analysis is that, if the wall impedance is not infinite, the wavenumbers will be complex. If the wavenumber in z is complex, p3, the pressure variation with respect to the ducts length, can be written:  p3 ( z ) = A5 e j Re (k z )z e − Im (k z ) z This result shows that the modal pressure decays exponentially along the length of the duct. The attenuation can be conveniently expressed in dB as: Attenuation = 20 Im(k z )z log(e ) = 8.686 Im(k z )z dB  127  6.1.3.1  Defining the Surface Impedance  A solution for the plane wave attenuation in a lined duct has been presented; however, it is required to know the surface impedance of the absorptive liner. The transfer function method is presented here as a simple method for converting an absorptive material’s propagation impedance and wave number into a surface impedance. A brief background will also be given on absorptive materials to describe how the propagation impedance and wavenumber are determined.  6.1.3.1.1  Transfer Function Method  In order to use the propagation impedance and wavenumber for design in typical applications it must be converted into an equivalent surface impedance [41, 62]. The transfer function method is convenient for this purpose. The transfer function method starts by defining the pressure and velocity at position x=0 and x=d as a function of the forward and backward propagating waves. These four equations are then rearranged to relate the pressure and velocity at x=d to the pressure and velocity at x=0 by a general ‘transfer function’:  p x (0 ) = A1 + A2 u x (0 ) =  ( A1 − A2 ) ρω  p x (d x ) = A1e − jk x d x + A2 e jk x d x  u x (d x ) =  (  k x A1e − jk x d x − A2 e jk x d x  )  ρω  Subscript x indicates the component of the variable in the x direction. Combining these equations gives:  p x (0 ) = p (d x ) cos(k x d x ) + ju (d x ) u x (0 ) =  jk x p (d x )  ρω  ρω kx  sin (k x d x )  sin (k x d x ) + u (d x ) cos(k x d x )  which can be equivalently expressed in matrix form as:   p (d x )  p (0 )  u (0 ) = [T ] u (d )   x    128  ρω   cos(k x d x ) + j k sin (k x d x ) x [T ] =  jk  x  sin (k x d x ) + cos(k x d x )   ρω  [T] is the transfer matrix for a finite thickness layer. Transfer matrices can be defined for many different simple geometries, and multiplied together to find the total transfer function for compound layers and geometries. Here, we see that if we let the surface impedance at x = d be Z s , x (d x ) , we can solve for the surface impedance at x = 0, Zs(0):  Z s , x (d x ) cot(k x d x ) + jZ 0 Z s , x ( 0) = j  k kx  Z s , x(d x )k x + cot(k x d x ) Z0k  If the layer is backed by a rigid surface then Z s , x (d x ) is effectively infinite and the surface impedance can be simplified to:  Z s , x (0) = − jZ 0  k cot(k x d x ) kx  37  This result can be used, in combination with Eq. 36, to define the surface impedance of a duct, provided the propagation impedance and wavenumber, Z 0 and k respectively, are known for the porous absorber. For clarity, from here on the impedance and wavenumber of the porous absorber will be identified as Z w and kw. The symmetric equations are:  kw jkZ 0  cot(k w, x d x ) = j cot (k x hx ) k w, x kx   kw jkZ 0   − jZ w cot(k w, y d y ) = j cot (k y h y ) k w, y ky   2 2 2 kx + k y + kz = k 2  − jZ w  Symmetric  38  This formulation allows for arbitrary incidence angle; however, kw,x must be found using Snell’s law, as refraction occurs due to the difference in wave speed in air and a porous absorber. With ψ and φ being the incident and transmitted angles, kw,x is [41]:  k x , w = k w 1 − sin (φ ) = k w − k 2 sin (ψ ) 2  129  In practice, the wave speed in many porous materials is much smaller than it is in air; thus the waves propagate nearly normal to the surface [63]. Considering this effect, k w, x ≈ k w . Materials in which sound will only propagate normal to the surface are referred to as ‘locally reacting’. The surface impedance of a rigidly backed, locally reacting absorber is:  Z s , x = − jZ w cot(k w d x ) The local reaction assumption can be expected to produce accurate results provided R<4 [63], where R is the normalized flow resistance given by:  R=  σd ρ 0c  where σ is the flow resistivity in MKS Rayl/m.  6.1.3.1.2  Characterizing Porous Absorptive Materials  Porous acoustic absorbers are materials that absorb sound energy passively by means of thermal dissipation. As sound waves propagate through the porous material, the shear forces due to no-slip conditions on the absorber surface convert the kinetic energy into heat. In addition, the great amount of surface area in the porous material makes the compression process non-adiabatic.  Porous absorbers are, as shown above, most usefully described in terms of their acoustic propagation impedance and wavenumber. Many methods have been developed, both empirical and analytical, to determine the acoustic impedance based on material properties [41, 63]. Analytical methods based on models of the microscopic fluid domain have proven successful; however, they are quite complicated as compared to the empirical methods. Empirical methods, such as the long-popular and well-known Delaney-Bazley model [41], provide a simple method of calculating the impedance from easily measured properties.  The Delaney-Bazley model is based on a data curve-fit of many samples of fibrous acoustic absorbers with different flow resistivities; therefore, it should not be expected to give accurate results for non-fibrous absorbers such as open-cell foams. The acoustic impedance and wavenumber of a fibrous porous absorber are given as [41]:  130  Zw = 1 + 0.0571X −0.754 − j 0.087 X − 0.732 Z0 kw =  ω c0  (1 + 0.0978 X  − 0.700  − j 0.189 X −0..595  )  X is a function of the flow resistivity ( σ ) and frequency: X =  ρ0 f σ  The Delaney-Bazley model is a single log-linear curve fit of the impedance and wavenumber’s real and imaginary components to represent all fibrous absorbers. Its validity is held when [41]:  •  ε (porosity) ≈ 1  •  0.01 < X < 1.0  •  1000 < σ < 50,000 MKS Rayl/m  6.1.4  Attenuation of the Fundamental Mode Results  To investigation plane wave attenuation in a lined duct it is necessary to define realistic liner properties. For this analysis, a liner will be defined to have properties similar to the material used in the laboratory-measured CT silencers, as presented in section 5.5.5 of this thesis. Once a lining material is established the effect of geometry on attenuation will be investigated. The MATLAB script used to calculate results is provided in Appendix B.2.  6.1.4.1  Duct Liner Properties  To use the Delaney-Bazley method of describing the porous material it is necessary to define the material’s flow resistivity. This has been done by selecting a flow resistivity that, by using the Delaney-Bazley and transfer function methods, defines a material with a similar normal incidence absorption coefficient (a) to the liner used in the laboratory measurements. Using the pressure reflection coefficient (r) the normal incidence pressure coefficient can be calculated from the surface impedance. a = 1− r  r=  2  Z s − ρ0c Z s + ρ0c 131  The normal incidence absorption coefficient of a 1” thick fiberglass sample has been measured using an impedance tube and a standardized measurement procedure [64]; the fiberglass is the same material that was used in the CT silencers in section 5.5.5. A comparison between the measured fiberglass material (called OEM, see Appendix A.1) and the Delaney-Bazley prediction for different flow resistivities is shown in Figure 81. Absorption data above 2000 Hz does not exist due to impedance tube limitations. Above 500 Hz the predicted absorption agrees best with the measurement when the flow resistivity is 60,000 MKS Rayl/m; however, below 500 Hz Delaney-Bazley under-predicts the measured absorption. Using a flow resistivity higher than 60k would slightly increase the low frequency absorption; however, it would step outside of the range of validity of the local reaction assumption (see section 6.1.3.1). Direct measurements of the OEM fiberglass by UBC Mechanical Engineering student Michael Gosselin showed the flow resistivity to be 46,000 MKS Rayl/m [65]. In conclusion, reasonable normal incidence absorption agreement exists for σ = 60k MKS Rayl/m.  Absorption is also strongly dependent on the liner thickness. Using a material with a flow resistivity of 60,000 MKS Rayl/m, the Delaney-Bazley model was used to calculate the absorption coefficient of a layer of fiberglass with varying thickness. Results are shown in Figure 82. All liner thicknesses generally increase in absorption with increasing frequency. Above 1 kHz all three liners have high absorption. Decreasing thickness results in decreased absorption at low frequency. The 25 mm liner is effectively incapable of absorbing in the 125 Hz octave band; only modest absorption is achieved in the 125 Hz band with a 100 mm liner.  132  1  Normal Incidence Absorption Coefficient  0.9  OEM  σ σ σ σ  0.8 0.7 0.6  =80k, R=4.8 =60k, R=3.6 =40k, R=2.4 = 20k, R=1.2  0.5 0.4 0.3 0.2 0.1 0  125  250  500 Frequency [Hz]  1000  2000  Figure 81: Absorption coefficient of OEM fiberglass measured and predicted by the Delaney-Bazley model for different flow resistivities. σ – [MKS Rayl/m]  1  Normal Incidence Absorption Coefficient  0.9 0.8 dy = 25 mm  0.7  dy = 50 mm  0.6  dy = 100 mm  0.5 0.4 0.3 0.2 0.1 0  125  250  500  1000 2000 Frequency [Hz]  4000  8000  Figure 82: Variation of normal incidence absorption coefficient for various liner thicknesses as predicted by Delaney-Bazley, σ = 60,000 MKS Rayl/m.  133  6.1.4.2  Cross Sectional Dimensions  To optimize the performance of a straight section of lined duct one must consider the effect of the silencer flow path dimensions, lining thickness, and the acoustic properties of the liner. The height and width of the flow cavity in the silencer will have a great effect on both the acoustic attenuation; the cross section geometry was examined by looking into the effect of flow path height and aspect ratio, and how the behaviour is dependent on liner thickness. As required for Eq. 38, the silencer height is equal to 2h, and the liner thickness is d (Figure 83). The plane wave attenuation is determined by solving Eq. 36 and Eq. 37 using the NewtonRaphson numerical iteration scheme.  d 2h  Figure 83: Silencer dimensions.  6.1.4.2.1  Flow Path Height  To examine the effect of flow path height a 2D silencer will be examined. Attenuation of the fundamental mode in a 2D silencer is identical to the attenuation of the fundamental mode in a 3D silencer with the same height, and with a width much larger than the height. Figure 84 shows the attenuation of the first order mode in a duct with varying height and absorber thickness. Transmission loss is plotted against frequency. If the Transmission loss (already a logarithm of power) is plotted on a log scale with respect to frequency the relationships are better illustrated (see Figure 85).  It is apparent that at low frequencies the absorption is governed by the absorber thickness. Below 1000 Hz the performance of the silencer with a 25 mm liner falls off relative to that of the 50 and 100 mm liners. Likewise, below 250 Hz the attenuation with 50 mm liner falls off with respect to the 100 mm thick liner. This result corresponds to the normal incidence absorption coefficient results shown in Figure 82.  134  Above 250 Hz for the 50 mm liner, and 1000 Hz for the 25 mm liner, the transmission loss is not governed by the thickness of the liner (although it may yet be affected by the flow resistivity). In this region the transmission loss is limited by the rate at which energy in the fundamental mode can diffract into the absorptive material. In all cases, the frequency at which the rate of attenuation is maximized is very close to the frequency at which the wavelength is equal to the duct height (2h). 200 180  Transmission Loss [dB/m]  160 140 120 100 80 60 40 20 0  125  250  500  1000 2000 Frequency [Hz]  4000  8000  Figure 84: Predicted transmission loss for various duct heights and liner thicknesses: Blue – d=25 mm, green – d=50 mm, red – d=100 mm, solid – h=20 mm, dash – h=50 mm, dot – h=100 mm.  135  Transmission Loss [dB/m]  100  10  1  0.1  125  250  500  1000 2000 Frequency [Hz]  4000  8000  Figure 85: Predicted transmission loss for various duct heights and liner thicknesses with transmission loss plotted on a log scale: Blue – d=25 mm, green – d=50 mm, red – d=100 mm, solid – h=20 mm, dash – h=50 mm, dot – h=100 mm.  6.1.4.2.2  Flow Path Aspect Ratio  In the previous section the relationship between duct height and attenuation was investigated. The duct was 2D, equivalent to an infinite aspect ratio for calculating the fundamental mode attenuation. This section investigates the effect of varying aspect ratio on the attenuation of the fundamental mode of a duct with all four walls acoustically lined. Figure 86 shows the effect of varying the aspect ratio in a lined duct with a 0.1 m total internal height and all four walls lined with 25 mm thick absorptive material. As expected, if the aspect ratio is large (AR>10), the result is effectively identical to that of the 2D solution. As the aspect ratio decreases there is an increase in attenuation. The increase in attenuation due to a reduction in AR appears to be directly related to the original attenuation – this is to say, if the 2D silencer has negligible attenuation, reducing the AR will not result in significant attenuation. If a 2D silencer has significant attenuation at a given frequency, a silencer with the same height but AR = 1 will have greatly increased attenuation. Figures 87 and 88 show the same result for ducts with 50 and 100 mm thick absorptive liners. The same results are observed for all liner 136  thicknesses; however, as before, the transmission losses are more pronounced at lower frequencies for thicker liners.  The increase in the absorption of a lined duct with a small aspect ratio should be expected. With a 2D duct the wave front will form a 2D arc as it diffracts into the liner. Because the length of an arc increases proportionally to the arc radius, the maximum energy attenuation rate is inversely proportional to the radius. In a 3D duct with AR = 1, the wavefront will approximate the spherical end of a 3D cone as it diffracts into the liner. The area of a sphere increases proportionally to the radius squared; therefore the maximum attenuation rate is inversely proportional to the radius squared. As transmission loss is energy attenuation on a log scale, this suggest that the transmission in a duct with an aspect ratio of 1 loss will be twice as large as in a 2D duct (or equivalently AR>10) with the same height. Figures 86, 87, and 88 suggest that the transmission loss with AR = 1 is indeed nearly twice the 2D value for any duct configuration and frequency. 140 2D AR=10 AR=5 AR=2 AR=1  Transmission Loss [dB/m]  120  100  80 60  40  20  0  125  250  500  1000 2000 Frequency [Hz]  4000  8000  Figure 86: Predicted transmission loss for various aspect ratios: hy=50 mm, hx=hy*AR, dy=dx=25 mm.  137  140 2D  Transmission Loss [dB/m]  120  AR=10 AR=5  100  AR=2 80  AR=1  60  40  20  0  125  250  500  1000 2000 Frequency [Hz]  4000  8000  Figure 87: Predicted transmission loss for various aspect ratios: hy=50 mm, hx=hy*AR, dy=dx=50 mm.  140 2D AR=10 AR=5 AR=2 AR=1  Transmission Loss [dB/m]  120  100  80 60  40  20  0  125  250  500  1000 2000 Frequency [Hz]  4000  8000  Figure 88: Predicted transmission loss for various aspect ratios: hy=50 mm, hx=hy*AR, dy=dx=100 mm.  138  6.1.5  Attenuation of the Fundamental Mode Summary  Through comparison of the absorption coefficients, it was determined that a fibrous material with a flow resistivity of 60,000 MKS Rayl/m, as defined by the Delaney-Bazley model, has similar acoustical performance to the fiberglass liner used in the laboratory measurements of this thesis. Using this material with an analytical solution for plane wave attenuation in a lined duct, the effect of varying the duct’s cross sectional dimensions has been analyzed, providing information about how the liner thickness, duct height, and duct aspect ratio affect attenuation.  Duct liner thickness does not affect high-frequency performance; however, it limits lowfrequency performance. The performance of a 25 mm liner falls off below 1000 Hz, and a 50 mm liner falls off below 250 Hz. From the ventilation opening laboratory measurements (section 5.5) it was observed that the ventilation opening silencer’s performance is often limited by the 500 Hz frequency band; as a result, the 25 mm liner is likely not thick enough to be effective; however, the 100 mm liner may be excessive. Increasing the duct height will reduce attenuation at all frequencies; however, if the frequency is high enough, or the duct is large enough, so that the wavelength is shorter than the duct height, the attenuation will decrease rapidly. In order to provide effective attenuation through the 4000 Hz band, the duct height should not exceed 100 mm.  If the aspect ratio of a duct is greater than 10, the attenuation of its fundamental mode is in effect identical to that of a 2D duct. Provided the duct liner and dimensions are such that the 2D silencer is effective at absorbing sound at a given frequency, reducing the aspect ratio will result in large attenuation gains. The TL of a lined duct with AR=1 is approximately twice the transmission loss of a 2D lined duct.  6.2 Acoustical FEM Predictions of Ventilation Opening Transmission Loss FEM provides an opportunity for the numerical prediction of a ventilation opening’s diffusefield transmission loss; however, to the author’s knowledge, this has never before been done. In this section the development of a FEM technique for diffuse field transmission loss is presented. Validation of the modeling technique is completed through comparison to 139  analytical and experimental results. The performance of various CT silencers is predicted and discussed.  6.2.1  Acoustical FEM Design  Modeling ventilation openings provides a significant challenge. The ventilation opening’s dimensions are small compared to the sound wavelengths of interest, which results in waveeffects such as diffraction being dominant in the propagation and transmission of sound energy. Traditional geometric acoustic prediction methods such as image source and ray tracing are therefore not suitable, because they are not fundamentally wave-based4. In ducts, wave effects are critical. Finite element modeling (FEM), which solves the wave equation, is well suited to predicting acoustic transmission in ducts. The difficulty in using FEM for ventilation openings is that, by convention, the ventilation opening inlet needs to be exposed to a diffuse sound field. In a laboratory the diffuse sound field is created by providing a large volume at the inlet side of the ventilation opening such that the smallest dimension of the volume is large compared to the largest wavelength of interest [56, 66]; modeling this large volume by FEM is problematic at high frequencies. As the finite element model must discretize space with some number of elements per wavelength, large volumes involve a large number of elements and quickly become computationally expensive at high frequencies.  To reduce the FEM computational expense at high frequencies, a new source volume was defined for each third-octave band, maintaining a diffuse sound field but not solving an excessively large domain. One must be aware that, in using this approach, the dimension-towavelength ratios are identical for each third octave band. This will cause the error due to imperfections in the diffuse field to be correlated between each third octave band, thereby reducing the apparent variation between successive third octave band predictions.  4  Geometric models that model wave effects such as interference, diffraction, and scattering [87] may have potential in this area. Further study is required.  140  Reducing the source volume with increasing frequency allows calculation of the transmission loss until one of two high frequency conditions is reached. The first high frequency limit that may be reached is when the silencer’s volume alone is too large for the computer to discretize and store in memory. Secondly, if the source volume is continually reduced with increasing frequency, at some limiting frequency, the silencer will no longer fit on its surface. To extend the solution to higher frequencies it may be possible, depending on the geometry of the silencer, to use a 2D model without excessive loss in accuracy.  Previous work has proven FEM to be effective at predicting the steady-state sound field in rooms at low frequencies [67-69], and the transmission loss in ventilation duct silencers and mufflers [70-73]. The present work has made the additional step of combine the FEM for rooms and silencers. COMSOL 4.1 is used for the simulations. COMSOL and MATLAB were used for post processing. A computer with an Intel i7 processor and 24 GB of memory was purpose-built for these simulations. Run times are typically under 24 hours; however, they are highly dependent on geometry, mesh, and frequency resolution.  6.2.1.1  Domains and Boundary Conditions  The model, built in COMSOL, is composed of a number of different domains and has a number of surfaces with different boundary conditions. The full acoustic domain is shown in Figure 89. As detailed below, the sub-domains are the source volume, source volume sampling volume, ventilator cavity, ventilator liner, receiver volume, and the perfectly matched layer (Figures 90 through 95). The boundary conditions are the hard boundary (infinite impedance), normal impedance boundary, hard internal boundary, and point power source. Specific properties of the sub-domains are discussed later.  Source Volume Sub-domain The source volume, highlighted in Figure 90, is responsible for generating a diffuse field. Its boundaries have either a hard, or a normal impedance boundary condition. For all predictions in this work, the ventilator is modeled flush with the surface of the source volume.  141  Source Volume Sampling Sub-domain A sub-domain within the source volume, shown in Figure 91, is created to define the region that is sampled in order to determine the average sound pressure level in the source volume. This is the sub-volume in which the sound field is diffuse.  Ventilator Flow Path Sub-domain The ventilator flow path, connecting the source and receiver volumes, is shown in Figure 92.  Ventilator Liner Sub-domain The ventilator liner, shown in Figure 93, is a dissipative acoustic domain. Dissipative propagation is modeled using a complex wavenumber and propagation impedance, as defined by the Delaney-Bazley model for fibrous materials (see section 6.1.3.1). This model requires the flow resistivity of the material to be specified; to allow comparison of modeled results to measured results, the flow resistivity was selected so that the normal incidence absorption of the modeled material was similar to that of the actual absorber used in the experiment in section 5.5.5. The boundary conditions on all surfaces of the liner, beside the ones adjacent to the ventilator flow path, are hard.  Receiver Volume Sub-domain The ventilator terminates into the receiver volume. It is defined such that its boundary with the perfectly matched layer is always greater than one wavelength from any part of the ventilator. All surfaces of the receiver volume, aside from the ones adjacent to the ventilator cavity and the perfectly matched layer, are hard.  Perfectly Matched Layer Sub-domain An anechoic termination to the receiver volume is modeled with a perfectly matched layer (PML) as shown in Figure 95. This arrangement allows the ventilator outlet to see an impedance equivalent to a free field. The PML thickness is equal to the longest wavelength. Care must be taken in defining the PML geometry and how it relates to the type of PML specified. According to COMSOL documentation, PMLs are a very good approximation to  142  an anechoic termination. All surfaces of the PLM, besides the one adjacent to the receiver volume, are hard.  Point Sound Power Source A point is defined, in the corner farthest from the ventilation opening, as shown in Figure 96, as a sound power source. As all results of interest are transfer functions of a linear system, the magnitude of the power output is irrelevant and was set arbitrarily. It is not beneficial to use multiple sources in the same model, as would be recommended in a physical measurement, because it is not possible to model them with random phase relations in a timeindependent solution.  Figure 89: 3D acoustic domain.  Figure 91: Source volume sampling sub-domain.  Figure 90: Source volume sub-domain.  Figure 92: Ventilator flow path sub-domain.  143  Figure 93: Ventilator liner sub-domain.  Figure 95: PML sub-domain.  Figure 94: Receiver volume sub-domain.  Figure 96: Point sound power source.  6.2.1.2  Calculation of Model Results  At each frequency of interest COMSOL solves the Helmholtz equation providing the acoustic pressure solution for the entire acoustic domain. The Helmholtz equation is the wave equation assuming a harmonic solution and the time dependency removed. From the pressure field solution, and the fact that the solution is harmonic, all of the quantities of interest are calculated. The MATLAB script used to calculate the third-octave band transmission loss is provided in Appendix B.3. The quantities calculated for each third-octave band are:  Lp(x, f)  Average sound pressure level as a function of frequency and position  Lp(f)  Average sound pressure level as a function of frequency  Lp(x)  Band average sound pressure level as a function of position  σ Lp  Standard deviation of band average sound pressure level 144  Ii(x, f)  Acoustic intensity in direction i as a function of frequency and position  Win(f)  Sound power through inlet as a function of frequency  Wout(f)  Sound power through outlet as a function of frequency  WLp(f)  Apparent sound power through inlet as estimated from Lp(f) as a function of frequency  TL_Win(f)  Transmission loss calculated from the inlet and outlet sound powers as a function of frequency  TL_WLp(f)  Transmission loss calculated from WLp(f) and the outlet sound power as a function of frequency  TL_Win  Band average transmission loss calculated from TL_Win(f)  TL_WLp  Band average transmission loss calculated from TL_WLp(f)  6.2.1.2.1  Frequency Averaging  Third octave-band results, as presented in this work, are the average of a frequency dependent property over a corresponding range of frequencies. Frequency dependent values are considered on a logarithmic scale; therefore, the third-octave band result should be centered at the midpoint of the band on a logarithmic scale. Our predictions give results on a linear frequency scale; by linearly averaging the results over the octave band the result would be more heavily representative of the high frequency component of the band. If P, a set of n data points, is linearly distributed over the frequency range f i → f i +1 , then the logarithmic average of the data over that frequency band can be found as:  Plog =  1 f log n  f1  n   f i +1    fi   ∑ P log  i     i =1  39  By comparison, the linear average is: Plin =  1 n ∑ P(i ) n i =1  This expression makes the assumption that the data point at the i th frequency is representative of the frequency range f i → f i +1 . In reality, they are not representative of the range, but of one individual frequency. Unless there are very few samples of data and they 145  vary rapidly with frequency, Eq. 39 is accurate; however, a more accurate representation may be:  Plog =  1 f log n  f1  n  ∑     i =1  P(i ) + P(i + 1)  f i +1   log 2  fi   The average given by Eq. 39 is used in this work. From experience, the correction in using a logarithmic average results in a small, but significant, difference of up to 0.5 dB in thirdoctave bands. This correction in octave band averages, or for averages of spectrum that vary more rapidly with frequency, will result in larger differences.  6.2.1.2.2  Lp (x, f)  The sound pressure level is calculated in the conventional way as:  p rms 2 Lp ( x, f ) = 10 * log10   2e −5 Pa   (  6.2.1.2.3    2    )  Lp (f)  To average the sound pressure level over a volume, the solution points defined by the mesh are connected by a 4th-order fit, and an integral is calculated to determine the average. Before integrating, the log scale is removed so that the result is the average squared sound pressure, corresponding to sound power, instead of the average sound pressure level.  1 Lp ( f ) = 10* log10 V  ∫∫∫10  Lp ( x,f 10  )  ∂x∂y∂z  V  An analogous calculation is made to average the sound pressure level over a surface or line.  6.2.1.2.4  Lp (x)  Band average sound pressure level as a function of position is calculated by finding the average of the squared pressures, corresponding to an energy average. With respect to Eq. 39, the energy average is found by:  Pi = 10  Lp ( x,f i ) 10  Lp ( x ) = 10* log 10 (Plog ) 146  Energy averaging is appropriate because it is representative of a random phase relationship between the various frequencies [34]. It is not physically possible to have a fixed phase relationship at different frequencies, as would be implied by summing sound pressures instead of energy.  6.2.1.2.5  σLp  The sound pressure level standard deviation, in this work and context, is calculated from the band average sound pressure level to describe the variation of a band average sound pressure level over the volume, surface or line:  σ Lp =  [  1 n ∑ Lp ( xi ) − Lp n − 1 i =1 Lp =  ]  2  1 n ∑ Lp( xi ) n i =1  Note that Lp is a decibel average, not an energy average. Additionally, the standard deviation is calculated from discrete points instead of from a continuous integral, as done for  Lp(f) because the data needs to be exported from COMSOL into MATLAB to calculate band average values. Apparently it is possible to purchase a ‘livelink’ between MATLAB and COMSOL, allowing the user to drive COMSOL from MATLAB and increase its post processing computational flexibility. For now, because the mesh is so spatially uniform, using a discrete representation without area weighting should give a very good approximation to the continuous representation.  6.2.1.2.6  Ii(x, f)  The acoustic intensity is the acoustic power per unit area. From a frequency domain solution it can be calculated from the product of the acoustic pressure and the complex conjugate of the particle velocity in direction i:  I i ( x, f ) = pu i  *  An equation is required to determine the particle velocity as a function of the pressure solution. Equivalent to Newton’s F = ma :  147  ∂u ∂p = ρ0 i ∂i ∂t Because the velocity varies harmonically with time, ∂u i = − jkc u i ∂t Therefore the particle velocity is:  ui =  6.2.1.2.7  ∂p kρ 0 c ∂i  j  Win(f), Wout(f)  The sound power through the inlet or outlet surface is calculated by integrating the intensity normal to the surface over the surface:  W ( f ) = ∫∫ I i ( x, f )ds S  Direction i is normal to surface s.  6.2.1.2.8  WLp(f)  In order to calculate the predicted transmission loss for comparison to measured results, it is necessary to calculate the predicted sound power entering the ventilation opening in the same way as in experiment. The standard method is to measure the average sound pressure level in the source room, assume that the sound field is diffuse, and use the sound pressure level to determine the intensity on the duct inlet.  Calculating the inlet sound power in a 2D model can be achieved with the standard method used in the 3D experiment method; however, an adjustment needs to be made. The inlet sound power is calculated by assuming the sound field is composed of plane waves travelling in all directions with equal intensity. The intensity of a plane wave is related to its pressure by:  I=  p2 ρ 0c  The intensity passing through a plane, in one direction, is equal to the integration of the intensity, normal to the plane, over all angles of incidence (hemisphere): 148  π  I n ,3 D  1 p2 1 2 = 2π cos(φ )sin (φ )dφ 2 ρ 0 c 2π ∫0  Here the 1 2π term is the area of a hemisphere with unity radius, and φ is the azimuthal angle. The p 2 term is multiplied by one half because only the contribution of the pressure waves travelling in the positive direction through the plane is desired. A 90 degree azimuthal angle corresponds to normal incidence: π  I n ,3 D  1 p 2 2 sin (2φ ) = dφ 2 ρ 0 c ∫0 2 I n ,3 D =  p2 4ρ 0 c  In the 2D model the angles of incidence, and thus the integration, take place over a semicircle instead of a hemisphere: π  I n,2 D  1 p2 1 = sin (φ )dφ 2 ρ 0 c π ∫0 I n,2 D  1 p2 = π ρ0c  Note that the intensity through the plane with respect to the pressure is higher in the 2D model. This makes sense as, in the 3D case, the area weighting for high azimuthal angles is small compared to low azimuthal angles, approaching zero at 90 degrees (normal incidence). In the 2D case, all azimuthal angles have the same weight. This illuminates a significant difference in the models. In a 2D model, a greater portion of the energy will strike the ventilation opening (and any other surface) at large angles of incidence.  6.2.1.2.9  TL_Win(f)  The transmission loss calculated directly from the sound power entering the ventilator is calculated as:  W ( f )  TL _ Win ( f ) = −10 * log10  out  Win ( f )   149  6.2.1.2.10  TL_WLp(f)  The transmission loss calculated indirectly from the sound power entering the ventilator is estimated from the source volume sound pressure level and the actual sound power exiting the ventilator: W ( f )  TL _ WLp ( f ) = −10 * log10  out W (f )  Lp   6.2.1.2.11  TL_Win and TL_WLp  The band average values of transmission loss are calculated in the same manner as Lp. With respect to Eq. 39, and using P as a temporary variable, the third-octave-band energy-average TL_Win is found as:  Pi = 10  Tl_Win ( f i ) 10  TL_Win = 10 * log10 (Plog ) Likewise, TL_WLp is found as: Tl_WLp ( f i )  Pi = 10  10  TL_WLp = 10 * log10 (Plog )  6.2.1.3  Designing for Convergence of Transmission Loss FEM  The objective of this work is to determine the transmission loss of a silencer exposed to a diffuse sound field. To achieve this we need a model that will achieve convergence with respect to a number of different criteria as shown below. All modeling in this section, unless otherwise noted, is done for the 500 Hz third octave band only; however, the results can be scaled and applied to any frequency band.  1. Mesh convergence For a finite element model to be physically correct it is necessary to use small enough elements so that the spatially discrete model creates a sufficiently accurate reproduction of the spatially continuous model.  150  2. Frequency Convergence The frequency domain must also be sampled with a sufficient resolution so that, when averaged over third octave bands, the result is representative of the result for continuous frequency sampling.  3. Diffuse Field Convergence The transmission loss metric used to evaluate the silencer performance assumes that the silencer inlet is exposed to a diffuse sound field. This requires that the sound field in the source volume is uniform at any location and in any direction.  6.2.1.3.1  Mesh Convergence  A model was built, similar to that shown in Figure 89. The source volume was small (dimensions approximately one wavelength at 500 Hz) so that the mesh could be resolved to a high degree without being computationally prohibitive. Win, Wout, and WLp are calculated and shown in Figure 97 to display their convergence as the number of elements per wavelength is increased from 0.5 to 15. The mesh is comprised of tetrahedral elements with quadratic discretization. COMSOL recommends tetrahedral elements for diffuse sound fields due to their anisotropic form. All power level results are normalized to the result with 15 elements per wavelength at which point it is assumed that the solution is independent of the mesh. According to Figure 97, given 3.5 elements per wavelength, all parameters have converged within 10%, or 0.4 dB, of their final value. To err on the conservative side, five elements per wavelength were used for all subsequent predictions. Higher accuracy could be achieved by using 10-15 elements per wavelength; however, the increased computational effort cannot be justified. In addition, increasing the resolution reduces the maximum possible source volume (memory limitation), reducing the modal density and diffuseness of the field, thereby reducing the accuracy of the model. Five elements per wavelength represent a good compromise in this work.  151  4 W in  3.5  W out  Sound Power [dB]  3  W Lp  2.5 2 1.5 1 0.5 0  0  5 10 Elements per wavelength  15  Figure 97: Variation of the predicted sound power with mesh resolution.  There is an additional complication, in that we know the speed of sound is slower in a porous absorber; therefore, the wavelength in the porous absorber will be relatively short. A separate size condition was set for the absorber domain so that the condition of at least 5 elements per wavelength is respected. Based on the Delaney-Bazley model (section 6.1.3.1) the absorber wavelength ( λw ) can be written as a function of its wavenumber ( k w ):  λw = kw =  6.2.1.3.2  ω c0  (1 + 0.0978 X  2π kw  − 0.700  − j 0.189 X −0..595  )  Frequency Convergence  To provide a result that is representative of a third-octave band it is necessary to produce results at multiple frequencies in the band. Multiple results can be used to find an average value, and provide statistical information about how well the sample average represents the actual average. The frequency resolution required may be dependent on the modal density and absorption in the space. Larger source volume will lead to a higher modal density, and 152  more modal overlap, possibly leading to a smaller standard deviation of the sound field with respect to frequency. More absorption will provide more damping, thus lower quality factor of the modes, and again more modal overlap. Excessive absorption will lead to a greater rate of decrease of levels away from the source, thereby increasing the standard deviation of levels in the sound field. Examined here is the number of equally-spaced frequency samples required to accurately represent a continuous third-octave band.  Figures 98 and 99 show, respectively, the error in the average source volume sound pressure level, and the spatial standard deviation in sound pressure level, as a function of the number of frequency samples in one third-octave band. The reference sound pressure level for Figure 98 is taken from the result for 200 frequency samples. Curves are shown for different values of r, the source volume surface reflection coefficient (0.98, 0.95, 0.9), and different values of  N, twice the ratio of the minimum source volume dimension to the maximum wavelength in the third octave band (4 and 6). The source volume size is described in terms of N for convenience, and is explained below. Source volume absorption is implemented by defining the source volume surface boundary condition as ‘finite impedance’. The impedance is written as [41]:  Z = ρ0c  1+ r 1− r  Figure 98 shows that the calculated average source pressure level has converged to within 0.1 dB of the true value when averaged over 10 or more frequencies in the third octave band, in all cases.  As shown in Figure 99, the sound field standard deviation is strongly dependent on the frequency resolution below a sampling rate of 10 frequencies per third octave. Above this sampling rate, the standard deviation is nearly constant, indicating that 10 samples are sufficient to calculate the sound field standard deviation. For low absorption surfaces, increasing the source volume dimensions from N=4 to N=6 makes little difference; however, for high absorption (r = 0.9) the standard deviation decreases approximately 0.5 dB. Decreasing the absorption from r = 0.90 to r = 0.98 is responsible for approximately 1 dB decreases in standard deviation. Erratic, highly varying results are obtained if the source  153  volume is entirely, reflective (r =1). As a result, the source volume should be highly, but not completely, reflective. If a ventilator opening represents a large absorptive area, the sound field standard deviation may increase.  Sampling the frequency domain 20 times in each third octave band is sufficient to provide an accurate prediction of the sound pressure level’s average and standard deviation values. This result holds for the source volume; however, a ventilator domain may have a more frequency-dependent response. If the behaviour of a ventilator appears to be highly frequency dependent it may be of interest to increase the frequency sampling resolution and check if the third octave solution has changed.  Due to its energy-absorptive behaviour, the presence of a ventilator may increase the standard deviation of sound pressure level with respect to frequency. As a result, the standard deviation corresponding to each calculated average should be determined in order to assess the significance of the result. 0.15 r=0.98, r=0.98, r=0.95, r=0.95, r=0.90, r=0.90,  Average Lp error [dB]  0.1  0.05  N=4 N=6 N=4 N=6 N=4 N=4  0  -0.05  -0.1  0  20  40  60 80 100 120 140 Frequencies per third octave band  160  180  200  Figure 98: Error in average Lp as a function of frequency sampling resolution for various source volume dimensions and reflection coefficients.  154  4 r=0.98, r=0.98, r=0.95, r=0.95, r=0.90, r=0.90,  Lp Standard Deviation [dB]  3.5  3  N=4 N=6 N=4 N=6 N=4 N=6  2.5  2  1.5  1  5  10 20 50 Frequencies per third octave band  100  Figure 99: Lp Standard deviation as a function of frequency sampling resolution for various source volume dimensions and reflection coefficients.  6.2.1.3.3  Diffuse Field Convergence  Away from the walls, a diffuse sound field can be approximated if the room’s dimensions and surfaces are such that they support an even distribution of modes with respect to frequency and space, and a high enough density of modes with respect to frequency and space.  Source Volume Dimensions To achieve an even spectral distribution of modes it is necessary that the room dimensions not be multiples of each other. Modes occur when the wavelength is related to the dimensions of the room; therefore, if the dimensions of the room are equal to, or multiples of, each other the room will be expected to have a strong response at that frequency. The room dimensions should also be similar to each other; if they are not, it can result in large spatial variations. Various dimension ratios have been proposed based on different criteria, such as even modal spacing, or low standard deviation of modal spacing [74]. In the present work,  155  the ratio 1:21/3:41/3 [74, 75], a well-known and often-implemented ratio for even modal spacing, was used.  A high modal density is required so that the sound field is uniform with respect to frequency and location. Modes in a room with three sets of parallel walls, all at right angles to each other, occur at frequencies described by [60]:  c f = 2   nx   Lx  2  2    n y   nz   +   +       L y   Lz   2  for all integer values of nx , n y and n z . The room dimensions are Lx , L y and Lz . This equation shows that the frequency separation of modes becomes larger at lower frequencies. In addition, because results are averaged over frequency bands (octave or third octave) that decrease in width with decreasing frequency, lower frequency results will include much smaller numbers of room modes. Sufficient modal density for a diffuse sound field will therefore be limited at low frequencies. The low frequency limit for a diffuse field has been proposed by Schroeder [76]:  f > 2000  T60 V  This relationship provides a criterion for which the response at a single frequency is composed of at least three modes. In other words, there are at least three modes within the width of the frequency response of any single mode.  Schroeder’s limit has been shown to be unnecessarily stringent when results are taken from band-averaged values instead of single frequencies [77]. Another approach that is more commonly taken for band averaged values is to specify a minimum number of modes in each band; 20 modes is common [77-79]. For a cubic volume, 20 modes per octave is achieved when the volume is equal to the wavelength cubed [77], and 20 modes per third octave is achieved when the volume is equal to four times the wavelength cubed [78, 79]. The corresponding frequency limits can be written as:  f (octave ) >  c 3  V  156  f (third octave ) >  c 3  V 4  Here N, which is related to the minimum order of axial mode observed, is introduced as a method of specifying the source-volume dimensions relative to the wavelength. N is calculated as twice the ratio of the smallest dimension to the largest wavelength. In equation form:  N =2  Lmin  λ max  N can take any value; however, the smallest order of axial mode, if one exists in the band, will be N rounded up to an integer value.  The relationship between the number of modes and parameter N has been investigated for rooms of the chosen aspect ratio. Given a room in which the smallest dimension is 1 m and the aspect ratio is 1:21/3:41/3, the numbers of modes in each third-octave band are shown in Table 24. Band Modes  100 1  125 1  160 2  Table 24: Modes in each third-octave band. 200 250 315 400 500 630 3 4 8 14 28 47  800 97  1000 180  1250 342  Over 20 modes are observed at and above the 500 Hz third-octave band. The ratio of the room’s smallest dimension (1 m) to the largest wavelength in the 500 Hz third-octave band (0.77 m at 445.5 Hz) is 1.3. This can be scaled to imply that, for any third-octave band, the room’s smallest dimension should not be less than 1.3 times the smallest wavelength; thus, N should be greater than 2.6, and there should not be an axial mode of order less than 3.  It is of interest to test this “diffuse field convergence” with the finite element model. ‘Diffuseness’ of the source volume sound field is assessed by the standard deviation of the sound pressure level in the source volume. The source volume near the walls is not sampled, as it cannot be diffuse. Near the walls it is not possible to have a diffuse sound field because all modes have a pressure maximum at the wall, a result of the zero particle velocity boundary condition normal to the wall [33]. If, at one frequency, there is equal energy incident from all directions, then the sound field at the wall will be 2.2 dB higher than its  157  constant value away from the wall. This error is further increased in double and triple corners. In order to avoid errors of more than 1 dB, the source volume sound field must not be sampled less than 0.25 λ from the walls and 0.7 λ from the corners [34].  Figure 100 shows the standard deviation of the sound pressure level in the source volume as it varies with source volume size. At N=4 the standard deviation falls below 2 dB. Above N=4 there are diminishing returns on increased dimensions; at N=8 the standard deviation is just under 1.5 dB. Quadratic residue diffusers, tuned to the bottom of the frequency band being predicted, were added to the surfaces in an attempt to reduce the sound field variation. The diffuser is a single 2D sequence with 17 elements in each direction [41, 80]. Its well width is less than one quarter wavelength and it has no periodicity; therefore it should be an excellent diffuser [80, 81]. An external view of the source volume with diffusely reflecting surfaces is shown in Figure 101. As shown in Figure 100, very slight reduction in the standard deviation of Lp was observed by implementing the diffusers, regardless of source volume size. This result agrees with previous measurement results by the author in an empty office sized room, shown in Figure 102, where the standard deviation in sound pressure was not affected by the addition of a diffusely reflecting surface [82]. The diffuser used in this measurement was known to scatter sound well above 500 Hz; however, no reduction in sound pressure standard deviation was measured in this range. Due to the increased model complexity, the addition of diffusers is not deemed to be beneficial; the increased computational cost to model the diffusers can be more effectively spent on increased room dimensions. It has been demonstrated, however, that if the source position is changed a room without parallel walls the sound pressure level standard deviation is less likely to increase [69]. This may imply that the diffuseness of rooms is more robust to source location if the surfaces are diffusely reflecting.  158  3.5 Flat surfaces Scattering surfaces  Lp Standard Deviation [dB]  3  2.5  2  1.5  1  1  2  3  4  5  6  7  8  N  Figure 100: Standard deviation of Lp vs minimum order of axial mode. Blue – flat surfaces, Red – diffuser surfaces.  Figure 101: External view of source volume with diffusing surfaces.  159  0.016 With Scattering Surface Empty Room  Sound Pressure St. Dev. [Pa]  0.014 0.012 0.01 0.008 0.006 0.004 0.002 0  63  125  250  500 1000 Frequency [Hz]  2000  4000  8000  Figure 102: Standard deviation of sound pressure in an empty office sized room, with and without diffusers [82].  A 2D source volume will have many less modes than a similar geometry in 3D. As such, its dimensions must be increased relative to the wavelength in order to maintain the modal density. A 2D source volume with dimension ratios 1:21/3 and a minimum dimension of 1m, has third octave band modes as shown in Table 25. This can be compared to the results for the 3D source volume in Table 24. In order to achieve 200 modes in the source volume for each third octave band the smallest dimension must be approximately 10 times the largest wavelength (i.e. N=20).  Band Modes  Band Modes  Table 25: Number of modes in each third octave band, 2D geometry (1 x 1.26 m). 100 125 160 200 250 315 400 500 0 1 1 1 1 2 2 4  800 12  1000 17  1250 28  1600 41  2000 64  2500 104  3150 165  4000 253  630 6  5000 406  160  Source Surface Sample Area (Ventilation Opening Size and Location) The ventilator, located on a section of the source-volume surface, must also be exposed to a diffuse sound field. If we acknowledge that the sound pressure level must be uniform for a sound field to be diffuse, Figure 100 shows that it is not possible to create a perfectly diffuse sound field; some variation will exist. Figure 103 shows the predicted third-octave Lp distribution on the source-volume surface (this is the pressure distribution on the actual source-volume surface (see Figure 90), not the source-volume-sampling surface (see Figure 91)). Solutions from 60 frequencies have been averaged to produce the third octave result. The ventilation opening will, however, occupy a non-zero surface area. As a result, the average sound pressure level on the ventilator will have less variability than the sound pressure level at any single point on the source-volume surface. This section investigates the relationship between the ventilation opening dimensions and the uncertainty in the average ventilation opening sound pressure level. The investigation has been completed, using a Monte Carlo simulation, by calculating the average sound pressure level on randomly sampled sub-sections of the source volume surface to determine the standard deviation of the sample averages. The standard deviation of the sample averages can be used to indicate the uncertainty in measured transmission loss due to the chosen ventilator location. With reference to Figure 104, the Monte Carlo process is as follows: 1. Define sample area size (corresponds to the ventilator inlet area) 2. Position the sample area randomly on the source volume surface 3. Knowing the source volume surface sound pressure distribution, calculate the average sound pressure level on the sample area 4. Repeat steps 2 and 3 many times until an accurate measure of the standard deviation of the samples’ average sound pressure levels is found.  The standard deviation of the sound pressure level for different sample area sizes provides a measure of the uncertainty due to the location of the ventilator on the source volume surface given the dimensions of the ventilator inlet. Initially, the source volume surface used for sampling was chosen as the largest surface on the source volume; however, the edges of the surface were not included, in order to avoid the increased sound pressure level at those locations due to constructive interference (spatial coherence) of the room modes in the  161  double corners. Elevated sound levels near the edge of the surface are clearly shown in Figure 103. Subsequently the sound field near the edge of the source volume surface is investigated. As ventilation openings are typically installed adjacent to the ceiling in the partition, it was of interest to predict their performance in a corner.  Note that, because the sound field was predicted without any ventilation opening, this analysis assumes that the sound pressure level on the source volume surface is either not affected by the presence of the ventilator, or equally affected at each location sampled, so that the relative comparison remains valid. 6 2.5  y location [m]  4 2  2  1.5  0  -2  1  -4 0.5 -6 0  0  0.5  1  1.5 2 x location [m]  2.5  3  3.5  Figure 103: Third-octave source volume surface Lp distribution. N=6, color scale in dB.  Sample area h Source volume  w  surface area  Figure 104: Sample area on source volume surface area.  162  Figure 105 shows the standard deviation of the sample sound pressure level averages. It is tested for square sample areas for which the sample’s side length to wavelength ratio is varied from 0 to 2, for source volume sizes N=4, N=6 and N=8. The standard deviation is well explained by the sample side length and not greatly dependent on the source volume size (in the range tested). For very small samples the standard deviation is limited to around 1.5 dB; this is very similar to the standard deviation observed in the center of the source volume (Figure 100). Increasing the edge length of a square sample above one half of the longest wavelength reduces the standard deviation to less than 0.5 dB; however, many ventilation openings are rectangular instead of square. Figure 106 shows the standard deviation results for a rectangular samples; it is clear that both dimensions of the ventilator do not need to be large. If either the width or the height of the sample area (ventilation opening) is greater than one half of the longest wavelength the standard deviation will be less than 0.5 dB. From this it can be concluded that, in order to be 95% confident (2 standard deviations) that the sample average is within 1 dB of the total source volume surface average, the dimensions of a square ventilator should not be less than 0.5 times the longest wavelength of sound. This result also has implications for silencers in real rooms – if they are small compared to the longest wavelengths of sound, the noise isolation they are able to provide will be dependent on where they are located on the partition.  163  1.5 N=4 N=6 N=8  σ Lp [dB]  1  0.5  0  0  0.2  0.4  0.6  0.8  1 w/ λ  1.2  1.4  1.6  1.8  2  Figure 105: Standard deviation of sample Lp averages vs. to sample side-length to wavelength ratio for various source volume dimensions. Square sample surface, away from source volume corner.  1.5 h/ λ = 0.1 h/ λ = 0.5 Lp Standard Deviation [dB]  h/ λ = 1 h/ λ = 2 1  0.5  0  0  0.2  0.4  0.6  0.8  1 w/ λ  1.2  1.4  1.6  1.8  2  Figure 106: Standard deviation of sample Lp averages vs. sample width to wavelength ratio for various sample height to wavelength ratios. N=6, sample surface away from source volume corner.  164  If a ventilation opening’s dimensions are smaller than one half of the largest acoustic wavelength it is still possible to obtain an accurate diffuse-field transmission loss prediction by modeling it numerous times in different locations until an estimate of the mean performance can be obtained. The numerous ventilation opening models could be obtained through either multiple predictions with a ventilator in different locations, or a single prediction with multiple ventilators positioned on the source volume surface.  Ventilation openings are often located in the edge formed by a partition and the ceiling; therefore, it is of practical interest to model them at a corner of the source volume, knowing the sound field there is not diffuse, because it is a better approximation of how the silencer is used in the field. The Monte Carlo sampling process was used again to determine the uncertainty in the average ventilation opening sound pressure level, based on its cross sectional dimensions, given that its edge is coincident with the source volume surface. Results are shown in Figure 107. It appears that the sound field variation is higher in the corner than it is in the central area of the surface; however, provided the ventilator dimension parallel to the edge (length) is greater than one wavelength, the standard deviation is less than 0.5 dB. If the ventilator width is small compared to the wavelength, the standard deviation will be greater than 0.5 dB, even if the ventilator’s height is large.  165  1.5 h/ λ = 0.1 h/ λ = 0.5 h/ λ = 1 h/ λ = 2  σ Lp [dB]  1  0.5  0  0  0.2  0.4  0.6  0.8  1 w/ λ  1.2  1.4  1.6  1.8  2  Figure 107: Standard deviation of average sample Lp vs. sample width to wavelength ratio (w/l) for various sample height to wavelength ratios (h/l). Sample surface at source volume edge.  6.2.2  Transmission Loss FEM Validation  A method for determining the transmission loss of ventilation opening silencers that are exposed to a diffuse incident sound field has been proposed. In order to validate this method, a model was created using a geometry that can be verified in comparison with an analytical solution and measured data.  6.2.2.1  Analytical Validation  The silencer for validation is a 0.10 m tall, 3 m long duct. Its width is let to be equal to the source volume width less 0.7λmax on either side to avoid the non-diffuse sound field in the corners. A 50 mm thick fiberglass liner is applied to the top and bottom surfaces. The modeled geometry with the sound pressure level solution at 503 Hz is shown in Figure 108.  The 3D model is solved for the 100 to 2500 Hz third octave bands, after which the duct mesh becomes too fine for the computer to hold in memory. A 2D model is constructed and solved for the 1600 to 10000 Hz third-octave bands.  166  Figure 108: 3 m lined duct geometry for analytical validation with 503 Hz Lp solution.  Two results from this solution are examined. First, in order to see that the attenuation and liner performance agree with theory, the transmission loss between the duct cross sections at 1 m, and at 2 m was compared to the analytical solution for plane wave attenuation (section 6.1). The center section (1-2 m) was used because near the entrance there will be higher order modes (which are rapidly attenuated), and near the outlet the sound field will be affected by reflections caused by the outlet impedance change (radiation impedance). Secondly, the transmission loss calculated directly from the sound intensity was compared to the transmission loss determined from the source volume sound pressure level.  6.2.2.1.1  Plane Wave Attenuation  The attenuation in the middle third of the 3 m long duct should be very similar to the analytical solution for the attenuation of the fundamental mode in a duct, as non-fundamental modes should be largely attenuated in the first third of the duct, and reflections from the end of the duct are should be largely attenuated in the last third. Results for the analytical solution, the 3D low frequency FEM solution and the 2D high frequency solution are shown in Figure 109. Up to 2000 Hz the analytical, 3D, and 2D solutions are in near perfect agreement. In the range of overlap, 1400 to 2800 Hz, the 3D and 2D solutions are in good  167  agreement, with the 3D case only slightly over-predicting the 2D TL solution. Above 5000 Hz the analytical and 2D solutions are in good agreement. Disagreement exists between 2000 and 5000 Hz, where the 3D and 2D FEM results under-predict the analytical result by up to 12 dB/m. One way in which the analytical model is dissimilar to the FEM is that the porous layer is modeled as a surface impedance rather than a dissipative acoustic domain. Simply put, the analytical model assumes local reaction [62] and the FEM does not.  To investigate the effect of assuming local reaction, the 2D FEM model was re-created with the liner implemented as a complex finite impedance boundary condition instead of as an acoustic domain. This is, in effect, identical to the boundary condition treatment in the analytical solution (section 6.1). Figure 110 shows the result – perfect agreement between the analytical and FEM solutions. This confirms that the disagreement between the analytical result and the FEM results in Figure 109 can be attributed to the local reaction assumption made in the analytical solution. The FEM solution, through modeling the absorber as a dissipative acoustic domain (bulk absorption), should be considered the more accurate result. This is in agreement with previous research on numerical modeling of silencers, which has concluded that boundary element methods are inferior to FEM due to their inability to model dissipative domains [71, 72].  168  70 3D FEM 2D FEM Analytical  Transmission Loss [dB/m]  60  50  40 30  20  10  0  125  250  500  1000 2000 Frequency [Hz]  4000  8000  Figure 109: Transmission loss in center section of duct – discrete data points.  70 Analytical 2D FEM, Locally Reacting Liner  Transmission Loss [dB/m]  60  50  40 30  20  10  0  125  250  500  1000 2000 Frequency [Hz]  4000  8000  Figure 110: Analytical solution and 2D FEM solution with locally reacting liner – discrete data points.  169  6.2.2.1.2  Calculating the Inlet Power through Sound Pressure Level or Intensity  It is interesting to compare the transmission loss results based on calculating the inlet power indirectly from sound pressure levels to that calculated directly from sound field intensity. Figure 111 shows the third-octave band transmission losses calculated through both measures of inlet sound power. At high frequencies there is good agreement between the two results; however, at low frequencies the solutions diverge by up to 11 dB.  Two reasons exist for why the transmission loss solutions diverge at low frequencies, both having to do with the sound pressure level, and diffuse field acoustic theory, not being a good predictors of inlet intensity. These two reasons also explain why it is inadequate to study insertion loss instead of transmission loss, as has been done in previous work [11]. 1. As the ventilation opening is situated in the corner, the opening will see around 2 dB higher sound levels, provided it is less than one quarter wavelength from the corner [34] (see section 2.3). In the present case, where the duct is 0.1 m tall and in the corner, elevated sound pressure levels should be expected until around 1000 Hz. Above 1000 Hz only a fraction of the ventilation opening will be exposed to the elevated sound field and the effect will be diminished. 2. Diffraction will also cause the sound pressure level to provide an erroneous measure of intensity. If the wavelength is not much smaller than the dimensions of the opening, increased sound energy will diffract into the duct due to the high impedance adjacent walls [60, 62]. Diffraction will continue to increase with increasing wavelength. The wavelength is smaller than the 0.1 m duct, and diffraction should be reduced, above 3500 Hz.  The difference in the transmission loss results when the inlet power is calculated directly, as compared to indirectly from the sound pressure level, is shown in Figure 112; 95% confidence intervals are provided. As the outlet power is calculated in the same way in both cases, the difference is entirely due to the inlet sound power calculation method. At 125 Hz the inlet power is under-predicted by over 11 dB using the sound pressure level. Above 1000 Hz, and moving towards 3500 Hz, the sound pressure level is able to effectively predict the inlet intensity.  170  There are two reasons why it is appropriate to use the sound pressure level for calculating inlet power, even though it is not an accurate measure of actual inlet power. First, the standardized transmission loss measurements are done this way [55, 56]; the design community is used to interpreting and designing with them. Secondly, the transmission loss, calculated based on the ratio of squared source sound pressure level to receiver sound pressure level, instead of its actual definition of inlet sound power to outlet sound power, is a more appropriate measure of its ability to isolate spaces.  Figure 111 also shows that the 2D model tends to under-predict the 3D transmission loss by around 5 dB in the range of solution overlap. A likely cause is that the 2D model does not include the higher order duct modes that exist in three dimensions. As higher order modes decay more rapidly, the 2D model would under-predict the transmission loss. In addition, because the angles of incidence are on a hemisphere in the 3D model, but on a semicircle in the 2D case, lower angles of incidence are more heavily represented in the 3D model. Lower angles of incidence will more easily couple with higher order and more rapidly attenuated modes. The 3D solution will be considered as the more accurate result, and the 2D solution will be used with caution, especially if the silencer’s performance is limited by high frequency transmission.  171  180 160  3D TLWin  140  3D TLLp  120  2D TLWin 2D TLLp  TL [dB]  100 80 60 40 20 0 -20  125  250  500  1000 2000 Frequency [Hz]  4000  8000  Figure 111: Predicted transmission loss calculated using source sound pressure level and inlet intensity.  14 3D Prediction 2D Prediction  12  TLLp - TLWin [dB]  10 8 6 4 2 0 -2 -4  125  250  500  1000 2000 Frequency [Hz]  4000  8000  Figure 112: Difference in transmission loss result when calculated using source sound pressure level and inlet intensity. 95% confidence intervals provided.  172  6.2.2.2  Comparing Measured Results to FEM Prediction  FEM predictions were compared to measurements made in a lab facility (ref section) for validation purposes. Comparisons were made for a simple unlined slot opening and 0.3 m CT silencers. 95% confidence intervals were plotted with the transmission loss results; for the measured performance the uncertainty is associated with spatial variation – for the modeled performance the uncertainty is associated with spectral variation. FEM predictions, as plotted, are composed of the 3D solution up to and including the 2500 Hz third octave band, and the 2D solution at and above the 3150 Hz octave band.  An important difference to note between the measurements and the predictions is that the prediction results determine the transmission loss at each frequency, and then average those values, reducing the effect of non-flat sound-source and source-volume frequency responses. Physical measurements find the frequency-band sound pressure levels, and then calculate the transmission loss from them. As such, the frequency-band transmission loss will be affected by the frequency response of the source and source-volume within the frequency band. The transmission loss will be more representative of any specific frequency which was relatively loud within the frequency band.  6.2.2.2.1  Slot Ventilation Opening  Measured and predicted transmission loss results, with 95% confidence intervals, for sound transmission through a 50 mm tall, and 25 mm long slot opening are shown in Figure 113. See section 5.5.1 for further information on the measurements. In general the agreement is quite good, within 1 or 2 dB and the confidence intervals at most frequencies. At low frequencies the measured results are erratic due to the non-diffuse sound field; of course, the FEM prediction’s accuracy is not limited at low frequencies. The discrepancy between the predicted and measured performance does not appear to be completely random; predicted results are often slightly lower than the measured results. This suggests that there is some slight difference between the prediction and model which is not explained by random sampling error.  173  6 4  Transmission Loss [dB]  2 0 -2 -4 -6 -8 -10  Measured Predicted  -12 -14  125  250  500  1000 2000 Frequency [Hz]  4000  8000  Figure 113: Measured and predicted TL of a 50 mm slot. 95% confidence intervals.  6.2.2.2.2  CT Silencers  FEM predictions were made for comparison to experimental results for the CT silencers measured in the lab facility (section 5.5.5). Below are the measured and predicted results for the 0.3 m straight CT silencer (Figure 114), 0.3 m L-shaped CT silencer (Figure 115), and the 0.3 m Z-shaped CT silencer (Figure 116). Below the 250 Hz third octave band and above the 1000 Hz third octave band the agreement between measured and predicted results appears quite good; note however that disagreement cannot always be explained by the random sampling error. Between 250 and 1000 Hz the predicted results are consistently around 5 dB lower than the measured results for all three CT silencer types. In an attempt to identify the cause of the discrepancy, predictions have been made for these silencers using a characteristic impedance ( ρ 0 c ) free field termination in place of the PML, and a different point source location. Additionally, the lab measurements were repeated for the 0.3 m straight CT silencer. All of these attempts produced effectively identical results to those shown below. A statistically significant difference between the measurement and prediction results exists. The difference was consistent over all CT silencers but not over the entire  174  frequency spectrum, suggesting that calculation error is not the problem, but a frequencydependent dissimilarity between the physical and modeled acoustic domain may be. This dissimilarity may be due to: •  non-diffuse laboratory sound field  •  reactive (complex impedance) boundary condition due to stud-mounted gypsum wall board in the lab  •  inaccurate modeling of fiberglass liner absorption.  A number of variations have been modeled in an attempt to determine the source of this measurement-prediction discrepancy, all of which had no significant effect on the predicted result. These variations were: •  reverberant receiver volume in-place of anechoic termination  •  characteristic impedance anechoic termination in-place of the perfectly matched layer  •  sound source located away from corner to change source volume sound field  •  increased resolution of mesh near ventilator. 20 Measured Predicted  Transmission Loss [dB]  15  10  5  0  -5  -10  125  250  500  1000 2000 Frequency [Hz]  4000  8000  Figure 114: Measured and predicted TL of 0.3 m straight CT silencer. 95% confidence intervals.  175  25 Measured Predicted  Transmission Loss [dB]  20  15  10 5  0  -5  -10  125  250  500  1000 2000 Frequency [Hz]  4000  8000  Figure 115: Measured and predicted TL of 0.3 m L-shaped CT silencer. 95% confidence intervals.  20 Measured Predicted  Transmission Loss [dB]  15  10  5 0  -5  -10  -15  125  250  500  1000 2000 Frequency [Hz]  4000  8000  Figure 116: Measured and predicted TL of 0.3 m Z-shaped CT silencer. 95% confidence intervals.  176  6.2.3  Acoustic FEM Design Summary  A FEM modeling process has been developed to predict the diffuse-field transmission loss performance of a ventilation opening. The diffuse field is created on the inlet side of the ventilation opening by modeling a source volume containing a point source. The ventilator outlet is a free field termination created using a perfectly matched layer. Sound power through the inlet of the ventilation opening can be calculated directly from the pressure field solution, or inferred using diffuse field theory from the average source volume sound pressure level. Outlet sound power is calculated directly from the pressure field solution.  The model is sufficiently mesh-independent if the volume is resolved to at least five tetrahedral elements per wavelength with quadratic discretization. Acoustic waves in porous materials have a slower speed and shorter wavelength relative to air; as a result, porous materials require a finer mesh.  In order to provide an accurate estimation of the source volume sound pressure level, average and standard deviation twenty frequencies should be sampled in each third-octave band. The frequency samples are energy-averaged on a logarithmic scale. Ventilation openings may have very different frequency dependences; the uncertainty in band-average values should be determined and the number of averages increased as necessary.  In order to provide a diffuse sound field, as characterized by a low sound pressure level standard deviation, the minimum source volume dimension must be three times the longest wavelength (N=6). It is be possible to use a smaller source volume with a modest increase in uncertainty, or a larger source volume for a decrease in uncertainty, but at a computational cost. Source volume aspect ratios are chosen to be 1:21/3:41/3.  In order to be 95% confident that the sound pressure level at the ventilator inlet is independent of its position on the source volume surface within a 1 dB uncertainty, one of the following two conditions should be met:  177  1. One dimension of the ventilator cross section is greater than one half of the longest wavelength, and no part of the ventilator is within one quarter wavelength of a corner. 2. The ventilator is adjacent to a corner and its dimension parallel to the corner is greater than the longest wavelength.  A 2D model is described in the same way as the 3D model, with the exception of its shortest dimension needing to be ten times the longest wavelength to provide equivalent modal density (N=20).  FEM predictions agree very well with an analytical model for dissipation of the fundamental mode in a lined duct. Any disagreement was shown to be due to the assumption in the analytical model of a locally reacting liner. FEM predictions were also compared to lab measurements. Good agreement was observed between predictions and measurement for a slot-type ventilation opening. Disagreements of around 5 dB existed between predicted and measured results for 0.3 m lined CT silencers between 250 and 1000 Hz. Comparing predictions to measured results indicates how much uncertainty is associated with diffuse field modeling and how difficult this uncertainty is to control. Further predictions should be compared to carefully-conducted measurements. Physical scale modeling could be beneficial to provide a better diffuse-field approximation in the measurements. Additionally, comparisons should be made with silencers measured away from the corners to maximize the sound field diffuseness.  A significant remaining concern is that, since the dimension-to-wavelength ratios are identical for each third octave band, any statistical bias will appear identical in each third octave band, reducing the apparent uncertainties in the prediction.  This modeling and performance prediction method provides an excellent new tool for developing and optimizing silencers for diffuse field application. It is a vast improvement over the previously-used insertion loss modeling because it accounts for random incidence, diffraction into the ventilation opening, and radiation impedance at the outlet.  178  6.2.4  Acoustic FEM CT Silencer Results  The Acoustic FEM model has been used to predict the transmission loss performance of four types of CT silencers, each with three different total lengths (the path length along the center of the flow path). The CT silencer types were Straight, L-shaped, U-shaped, and Z-shaped as shown in Figure 117; the total lengths were 0.3, 0.5, and 1 m. The dimensions labeled in Figure 117 correspond to the values shown in Table 26. Note that there is no 0.3 m U shape. Based on results from the analytical study of plane wave attenuation in a lined duct (Section 6.1.5), the duct liner was chosen to be 50 mm thick with a flow resistivity of 60,000 Rayl/m, and the flow path was chosen to be 0.1 m high.  Performance results for silencer predictions are summarized in terms of the STC and SEOAs in Table 27. A complete set of frequency-dependent transmission loss plots is given in Appendix C.1. Transmission loss performance increases with increasing length for each silencer type. Of the silencers modeled, silencers with the same total length have very similar predicted transmission loss performance: •  0.3 m CT silencers have a STC of 5 to 6 dB and a SEOAs of 0.9 to 1.1  •  0.5 m CT silencers have a STC of 8 to 9 dB and a SEOAs of 0.5 to 0.6  •  0.5 m CT silencers have a STC of 8 to 9 dB and a SEOAs of 0.15 to 0.16  In the FEM validation, predicted mid frequency transmission loss was less than the measured transmission loss by up to 5 dB. The cause of the disagreement could not be identified; as a result, the actual transmission loss of these silencers might be up to 5 dB higher than these predictions.  179  L1  100 mm  100 mm L1  S1  U2  Z1  100 mm U1  100 mm  150 mm Figure 117: Shapes and dimensions of CT silencers. Clockwise from top left: Straight, L, Z, and U. 50 mm fiberglass shown as crosshatched. Heavy black lines are sound-hard boundaries. Table 26: CT silencer dimensions.  Total Length [m] 0.3 0.5 1  S1 [m] 0.3 0.5 1  L1 [m] 0.2 0.3 0.55  U1 [m] N/A 0.2 0.4  U2 [m] N/A 0.3 0.4  Z1 [m] 0.2 0.4 0.9  Table 27: CT silencer performance.  Type Straight  L-shaped U-shaped Z-shaped  Length [m] 0.3 0.5 1 0.3 0.5 1 0.5 1 0.3 0.5 1  STC [dB] 5 8 13 6 8 13 9 13 6 8 13  SEOAs 1.06 0.58 0.16 0.89 0.50 0.15 0.42 0.14 0.95 0.51 0.16 180  6.2.4.1  Frequency Dependence of CT Silencer Transmission Loss  Table 27 suggests that, in the range of geometries tested, silencers of similar length have nearly identical performance regardless of the silencer type (i.e. shape). Observing the frequency-dependent transmission loss of the 1 m silencers in Figure 118, it is clear that the transmission loss at high frequencies actually varies greatly between silencer types. The reason the SEOAs is identical for each shape, regardless of high frequency variation, is shown in Figure 119 by the transmitted speech spectrum, as introduced in 2.1.1. The performance of all silencers is limited by low frequency transmission loss; therefore, any variability in the high frequency transmission loss will have negligible effect on the SEOAs. STC ratings are similarly limited by low and mid frequency transmission.  It is not necessarily the case that all silencers will be limited by low frequency transmission loss; therefore, it is beneficial to understand the cause of the variation in high frequency transmission loss between the various silencer shapes. The frequency dependent transmission loss can be discussed in terms of attenuation due to the liner, and attenuation at the elbows.  Figures 120 and 121 show the sound pressure level and sound pressure at 500 Hz, a relatively low frequency at which all silencer shapes have very similar performance. The rate of attenuation is low throughout the silencers due to the relatively ineffective liner, and there is no notable attenuation at the elbow. The 0.69 m wavelength at 500 Hz is long with respect to the 0.1 m duct width, so the fundamental mode in the duct section before the elbow couples well with the fundamental mode in the section past the elbow.  At a mid-to-high frequency of 2500 Hz the 0.14 m wavelength is comparable to the duct width. As shown in Figure 123, there is some attenuation at the elbow; however, the duct liner is very effective and most of the attenuation occurs in the straight section. As the attenuation is dominant in the straight sections, the total attenuation in the straight (Figure 122) and L-shaped (Figure 123) silencers is very similar at 2500 Hz.  At the high frequency of 8000 Hz, the 0.04 m wavelength is much smaller than the duct width. As concluded in section 6.1.4, if the wavelength is smaller than the duct width, the  181  fundamental mode will propagate with little attenuation, as the rate of diffraction into the liner is small. This conclusion is confirmed visually in Figure 124. At these high frequencies, however, because the wavelength is small compared to the duct width, the fundamental mode upstream of the elbow couples very weakly with the fundamental mode downstream of the elbow. Figure 125 shows that the elbow causes a large attenuation, and the attenuation at the elbow dominates the attenuation in the straight sections.  In summary, elbows become effective at providing attenuation as the wavelength of sound becomes smaller than the duct height. Attenuation in straight sections of lined duct is reduced when the wavelength is much smaller than the duct height. It is therefore beneficial to incorporate elbows into a silencer when it is desired to attenuate high frequencies at which the wavelength is much smaller than the duct height.  182  90 80  1m 1m 1m 1m  Transmission Loss [dB]  70 60  Straight L U Z  50 40 30 20 10 0 -10 -20  125  250  500  1000 2000 Frequency [Hz]  4000  8000  Figure 118: Predicted transmission loss of 1 m CT silencers. 95% confidence intervals shown.  Transmitted Speech Spectrum [dB]  0 1m 1m 1m 1m  -20  Straight L U Z  -40  -60  -80  -100  -120  125  250  500  1000 2000 Frequency [Hz]  4000  8000  Figure 119: Predicted transmitted speech spectrum, 1 m CT silencers. 95% confidence intervals given.  183  Figure 120: Predicted Lp (left) and sound pressure (right) at 500 Hz, 1 m Straight silencer. Lp color scale 0 to 100 dB. Sound pressure color scale -0.5 to 0.5 Pa. Axis dimensions in meters.  Figure 121: Predicted Lp (left) and sound pressure (right) at 500 Hz, 1 m L-shaped silencer. Lp color scale 0 to 100 dB. Sound pressure color scale -0.5 to 0.5 Pa. Axis dimensions in meters.  184  Figure 122: Predicted Lp (left) and sound pressure (right) at 2500 Hz, 1 m Straight silencer. Lp color scale 0 to 100 dB. Sound pressure color scale -0.5 to 0.5 Pa. Axis dimensions in meters.  Figure 123: Predicted Lp (left) and sound pressure (right) at 2500 Hz, 1 m L-shaped silencer. Lp color scale 0 to 100 dB. Sound pressure color scale -0.5 to 0.5 Pa. Axis dimensions in meters.  185  Figure 124: Predicted Lp (left) and sound pressure (right) at 8000 Hz, 1 m Straight silencer. Lp color scale 0 to 100 dB. Sound pressure color scale -0.5 to 0.5 Pa. Axis dimensions in meters.  Figure 125: Predicted Lp (left) and sound pressure (right) at 8000 Hz, 1 m L-shaped silencer. Lp color scale 0 to 100 dB. Sound pressure color scale -0.5 to 0.5 Pa. Axis dimensions in meters.  186  6.3 CFD Predictions of Ventilation Opening Discharge Coefficients Duct fitting loss coefficients have been investigated numerically many times and the results have shown that, using CFD, it is possible to reliably obtain discharge coefficient results for the duct fitting within 15% of the experimental result [83]. While similar in many ways, ventilation openings are unique from duct fittings in that the dynamic pressures upstream and downstream from the opening are small. Only one study has predicted the performance of a ventilation opening, and very few details are provided as to how the modeling was carried out [11]. The following section will present the methods and results from the flow performance predictions carried out in the present work. These results are intended to be used in combination with the acoustic FEA results to provide a complete performance prediction method for ventilation openings.  In this next section, the ventilation opening flow model used in this work is described in terms of flow domain geometry, flow-equation model, boundary conditions, and mesh. The flow domain solution provides the flow rate through, and pressure loss across, the ventilation opening. Finite volume based CFD software ANSYS FLUENT is used for all simulations. The model was validated by comparison with published results for an orifice, and by comparison with measured results for CT silencers. Results are predicted for the same silencer geometries that have been modeled using the acoustic FEM technique described in section 6.2.4.  6.3.1  Flow Domain Geometry  To model the flow performance in terms of discharge coefficient or, more generally, in terms of flow rate as a function of pressure loss, the ventilator is inserted in a partition between two volumes as shown in Figure 126. Fluid flow progresses from left to right. Only ventilators with 2D geometries will be modeled in this work; the results are therefore only a valid prediction for ventilators with a large aspect ratio.  The discharge coefficient, in the case of natural ventilation openings, can be interpreted as a measure of how efficiently energy is converted from potential energy (pressure on the upstream side of the opening) to kinetic energy (velocity through the ventilation opening), 187  and back to potential energy (pressure on the downstream side). The conversion from kinetic to potential is also known as pressure recovery [84]. In order to observe this process in the model the flow domain must include a relatively large volume on either side of the ventilation opening. The upstream volume must be large enough that the dynamic pressure associated with the inlet velocity is negligible as compared to the dynamic pressure associated with the ventilator velocity. The downstream volume must be large enough to allow the high velocity flow in the opening to slow down and recover or dissipate its dynamic pressure; i.e. the downstream volume must have low air velocity so that the dynamic pressure is negligible.  The flow in the upstream volume will be relatively uniform normal to the flow direction; therefore, its entire leading surface will be set as the inlet. For the downstream volume this will not be sufficient as the domain would need to be very long to allow for significant dissipation or recovery of the kinetic energy. Instead, an outlet is created in one corner of the downstream volume so that the flow is encouraged to convert its kinetic energy in a smaller region.  It is possible to determine the required inlet area analytically. The flow at the inlet is expected to be nearly uniform; therefore, the velocity, at a given flow rate, is inversely proportional to the area of the inlet. Likewise, the ratio of the average velocity in the inlet to the average velocity in the ventilator is directly related to the ratio of the ventilator cross sectional area to the inlet area:  U inlet A = vent U vent Ainlet To assure that the dynamic pressure in the inlet is negligible, the ratio of the dynamic pressures in the inlet and ventilator should be 1 to 100:  ρ  U inlet  2  1 = 2 100 ρ 2 U vent 2  U vent = 10 U inlet  It follows that,  Ainlet = 10 Avent 188  Provided the inlet area is ten times the ventilator area, the dynamic pressure in the inlet will be negligible in the inlet compared to the dynamic pressure in the ventilator.  The above analysis is actually conservative, as the flow will generally not be uniform in the ventilator. Using average velocity to calculate dynamic pressures will under-estimate the actual value in the ventilator.  U=  1 u dA A ∫A  U2 ≤  1 2 u dA A ∫A  This same result, unfortunately, also precludes the ability to use area ratios to determine the dynamic pressure and domain size required in the volume downstream of the ventilation opening. Average velocity will greatly under-predict the dynamic pressure downstream of the ventilator.  3  1  1: Upstream Volume 2: Downstream Volume  4  3: Ventilator 4: Inlet  2  5: Outlet 5  Figure 126: Flow domain of ventilator model (sample velocity contours shown).  189  6.3.2  Flow-Equation Model  Unless otherwise noted, the information and theory presented in this section were taken from the ANSYS Fluent 12 documentation [85].  As described in section 4.1 of this thesis, the Navier-Stokes equation (Eq. (23)), derived from conservation of momentum and mass, provides a solution for Newtonian flow. If constant density is not assumed, an additional equation that relates the change in density to mass flux must be included for conservation of mass: Conservation of mass  ∂ρ ∂ρu i + =0 ∂t ∂xi  If the flow is turbulent, fluctuations in the flow field variables will occur over very small distances in space and time. In order to accurately model these properties, spatial and temporal discretization must be extremely small. For most applications the implied computational requirements to solve the flow field in this way, known as direct numerical simulation (DNS), are not feasible. In order to reduce the required spatial and temporal resolution so that the computation is possible, methods have been devised to filter out, or average out, small-scale fluctuations. One of these methods of averaging is called Reynolds averaging, with the class of resultant models being called RANS (Reynolds average of Navier Stokes).  6.3.2.1  Reynolds Averaging (RANS)  RANS is based on the idea of representing all flow field variables ( φ ) as a mean value ( φ ) plus a fluctuation from the mean ( φ ′ ):  φ = φ + φ′ With the variables represented in this way, the Navier-Stokes equation for steady incompressible flow can be presented as [48]:  ρu j  ∂pδ ij ∂u i ∂ =− +µ ∂x j ∂x j ∂x j   ∂u i ∂u j  +  ∂x  j ∂xi   ∂ + − ρu i′u ′j  ∂x i   (  )  The result is a set of equations containing only average results, save one additional term, named the Reynolds stresses, which represents the turbulent fluctuations:  190  − ρui′u ′j The Reynolds stresses must be modeled, and many methods exist to do so. A very popular method is the k − ε model, where k is the turbulent kinetic energy and ε is the dissipation rate of turbulent kinetic energy. The turbulent viscosity ( µt ) is defined to relate the turbulent kinetic energy to its dissipation rate. The standard k − ε model assumes turbulent flow and is therefore only valid for fully turbulent flows. Variations of the k − ε model have been developed to make it more applicable to special classes of flow. One of those variations is the Renormalized Group theory (RNG k − ε ). It is similar to the standard k − ε ; however, it includes a number of improvements. One of the improvements is that the turbulent viscosity is calculated using a differential equation, providing an improvement in accuracy for low Reynolds number flows. The RNG k − ε RANS method has been identified as the most appropriate model for indoor airflow [86]. For this work, the flow has been modeled using both laminar and RNG k − ε RANS methods. Following the method used in a previous work modeling hydraulic flow meters [49], the laminar model was used to predict the behaviour of flows below Re = 2000, and the RNG k − ε model was used for flows above Re = 2000.  6.3.3  Boundary Conditions  The inlet and outlet boundary conditions will be set as Pressure Inlet and Pressure Outlet. All interior surfaces are set to be no-slip walls.  6.3.4  Mesh  The mapped mesh feature in ANSYS is used for mesh generation. Resolution of the mesh is set by specifying the grid spacing at boundaries. Intuition and iteration were used to specify a fine mesh near regions with high gradients in the flow. Mesh-independence of the flow solution was confirmed by doubling the mesh resolution and confirming that the discharge coefficient result did not change by more than 1%. Typically, at Re ≈ 25000 , convergence was achieved with 0.1 mm mesh spacing at the ventilator wall. The maximum mesh spacing anywhere in the flow domain was 50 mm. In a number of the predictions in this work, doubling the mesh resolution resulted in as much as a 3% change in Cd; however, further increases in mesh resolution would cause the numerical solver to become unstable and the  191  solution would diverge. Future work should use a structured mesh in order to produce better solver-stability and mesh-independence. Unstructured meshes were used in this work due to time constraints.  6.3.5  Processing Flow Model Results  To characterize the ventilator performance in terms of the discharge coefficient, loss coefficient, or equivalent open area, the flow rate through the ventilator and the pressure loss across the ventilator are required. The flow rate was calculated from the solution by integrating the velocity, normal to the inlet, over the inlet area. Pressure differential was calculated as the difference in static pressure between the upstream and downstream volumes. Each pressure was calculated from an area-weighted average of a region in a corner away from the ventilator, the inlet, and the outlet, where the flow velocity is low.  6.3.6  Model Validation  The modeling technique outlined above was validated by comparison with published results for an orifice plate, and in comparison to measured results for CT silencers.  6.3.6.1  Validation by Comparison to Published Results  The discharge coefficient of a 50 mm diameter orifice plate was predicted in both laminar and turbulent regimes for comparison to published measurement results. A 2D axisymmetric model was used; the diameter and length of the upstream volume was 0.5 m, and the downstream volume was 1.5 m.  Published results [50] define the orifice plate, and provide the discharge coefficient as a function of orifice-to-pipe diameter ratio; however, in our model the ‘pipe’ diameter is not defined, only specified to be much larger than the orifice diameter. Predicted results should therefore be compared to published results with very small diameter ratios. Published results for the discharge coefficient are shown in Figure 127, the predicted results in Figure 128. Predictions up to Re = 2000 (Re0.5= 43) were performed using the laminar flow model; predictions beyond Re = 2000 used the RNG k − ε . The discharge coefficient is plotted against Re0.5 because their relationship is linear at very low Re (see section 4.4.2).  192  Comparison of predicted and published results at small diameter ratios shows excellent agreement for all Reynolds numbers.  Figure 127: Published experimental results for the orifice plate discharge coefficient [50]. 0.8 0.7 0.6 0.8  0.5  0.7  Cd  0.6  0.4  Cd  0.5  0.3  0.4 0.3  0.2  0.2  0.1 0.1 0  0 0 1 2 3 4 5 6 7  0  20  40  60  80  100  120  140  160  Re0.5 Re Figure 128: Predicted results for the orifice plate discharge coefficient. 0.5  193  6.3.6.2  Validation by Comparison to Measured Results  Laboratory measurements of the discharge coefficient of Straight, L-shaped, and Z-shaped CT silencers, and a slot ventilator, were conducted at high Re, and the results were presented in section 5.5.5. Predictions were made for these same geometries. The upstream volume height (1 m) was ten times the silencer height (0.1 m). The downstream volume height (3 m) was 30 times the silencer height; increasing the downstream volume height further resulted in no change to the predicted discharge coefficient. All measured and predicted results correspond to Re>15,000; therefore, as shown in Table 28, all results are independent of Re and directly comparable to each other (see section 4.4.2).  As seen in Table 28, there is modest agreement between the predicted and measured results, with disagreements of up to 20%. The predictions and measurements do, however, show better agreement with respect to the relative performance of the different silencers types. Predictions show the L-shaped and Z-shaped silencers to be 38% more restrictive to airflow than the Straight silencer; measurements show the L and Z shapes to be 38 and 47% more restrictive, respectively. It is possible that a major source of the disagreement between measurement and prediction is because the silencers were measured with a porous liner. Some amount of flow could pass through the liner, increasing the flow rate. Further work should implement a porous liner in the flow model to increase prediction accuracy.  Table 28: Measured and predicted silencer discharge coefficients – high Re.  Cd - Predicted Cd - Measured  6.3.7  Straight 0.64 0.79  L 0.39 0.49  Z 0.40 0.42  Slot 0.64 0.66  CFD Prediction Results for CT Silencers  Predictions were made for the flow performance of the CT silencers shown in Figure 117 and Table 26; these are the same geometries for which the acoustic performance was predicted. Additionally, the performance of a 50 mm long Straight CT silencer – essentially a slot ventilator – was predicted to better observe the effect of ventilator cavity length. Discussion of the results will start by investigating the effect of length on the discharge coefficient of the straight silencer, and then move on to a comparison between the different silencer types. The  194  results will conclude with general comments on the Re dependence of the discharge coefficient. Figures showing the velocity and pressure fields in each CT silencer at high-Re are provided in Appendix C.2.  6.3.7.1  Effect of Length on the Straight Silencer’s Cd  Results for the discharge coefficient of different lengths of the Straight silencers as a function of Re are shown in Figure 129. At very low Re the discharge coefficient approaches zero, as expected, for all silencer lengths. With increasing Re, the discharge coefficient of shorter silencers increases at a higher rate; as a result, the shorter silencers can be characterized by a constant, high-Re, discharge coefficient at a relatively low Re. In other words, the transitional Reynolds number (Retr) is lower for shorter silencers. For flow rates above Retr, however, the longer silencers have a greater discharge coefficient than shorter ones. These conclusions mirror the results by Lichtarowicz [51], which provides the Re-dependent discharge coefficients for hydraulic flow in elongated orifices.  Through observation of the velocity and static pressure profiles in the flow it is possible to hypothesize the cause of the increase in Cd with increasing silencer length at high Re. In Figure 130, showing the flow velocity in the 1 m Straight silencer at high Re, a venacontracta is present immediately following the entrance to the silencer, which results in high velocity flow near the top of the duct, and recirculating flow near the bottom. The high velocity flow is associated with a high dynamic pressure and, as predicted by Bernoulli’s equation (see section 4.2), the corresponding static pressure in the flow must decrease. Figure 131 shows that the static pressure does indeed decrease in the region of the vena-contracta. Moving beyond the vena-contracta, where the bottom boundary layer attaches and the velocity profile becomes more uniform, there is a recovery in static pressure which corresponds to the reduction in dynamic pressure. One might expect the length of the region of pressure recovery to be associated with the duct entrance length ( l e = Dh ⋅ 4.4 Re1 6 [46]); however, the recovery actually occurs much more rapidly. At Re = 27000, the entrance length ( le ) is 24 times the hydraulic diameter; however, in Figure 131, and in results published by Lichtarowicz [51], the pressure recovery is does not extend beyond two or three times the hydraulic diameter. Additionally, beyond the silencer outlet there is effectively no 195  recovery of the dynamic pressure. In Figure 132 and Figure 133, the velocity profile in a 0.05 m long Straight silencer, there is a vena-contracta which will cause an increase in the dynamic pressure near the inlet, like the 1 m Straight silencer; however, as there is no length of duct in which the dynamic pressure can recover, there is no pressure recovery, which directly explains the lower discharge coefficient for very short Straight silencers.  Recovery of dynamic pressure, beyond the dynamic pressure associated with the venacontracta, can be obtained using diffusers [47]. The use of diffusers to optimize ventilation openings silencers should be considered for future optimization work.  6.3.7.2  Effect of CT-Silencer Type on Cd  The discharge coefficients for the 0.3, 0.5, and 1 m CT silencers as a function of pressure are shown in Figures 134, 135 and 136; the high Re flow performance is summarized in Table 29 in terms of Cd and SEOAf. SEOAf results are provided for convenience; however, as they are proportional to Cd, they are not discussed directly. From these result a number of observations can be made: •  For Re<100 there is only slight variation of Cd with silencer shape; for Re<10 the discharge coefficient and silencer shape appear to be independent.  •  With the exception of the 0.3 m Z-shaped silencer, the discharge coefficient increases with increasing silencer length.  •  Straight silencers are the least restrictive to airflow, having a Cd 34 to 46% less than the L-shaped silencer, 30% less than the U-shaped silencer, and 38 to 58% less than the Z-shaped silencer.  •  Z-shaped silencers are the most restrictive to airflow; a likely explanation is that they terminate at an elbow where there will be high dynamic pressure. As shown above for the Straight silencers, energy will be lost if the increased dynamic pressure does not recover before the silencer terminates into the downstream volume.  •  Surprisingly, the U-shaped silencer is less restrictive than the L-shaped silencer, even though it has two elbows instead of one. The 1 m U-shaped silencer, which geometry can be very nearly created from the addition of two 0.5 m L-shaped silencers end-to-  196  end, has a smaller discharge coefficient than either the 0.5 or 1 m L-shaped silencer alone. Clearly it is not possible to consider the effect of elbows as additive.  Table 29: Predicted flow performance of CT silencers at high Re.  Type Straight  L-shaped U-shaped Z-shaped  6.3.7.3  Length [m] 0.05 0.3 0.5 1 0.3 0.5 1 0.5 1 0.3 0.5 1  Cd 0.65 0.73 0.77 0.80 0.39 0.40 0.51 0.53 0.54 0.40 0.31 0.36  SEOAf 1.06 1.20 1.26 1.31 0.64 0.65 0.84 0.87 0.89 0.65 0.50 0.60  Effect of Reynolds Number on Cd  Previous discussion of analytical and experimental results has concluded that Cd is linearly related to Re if Re is low, and independent of Re if Re is high (see section 4.4.2). The predictions show the same result. It is valuable to discuss what is meant by ‘high’, and how that relates to interior natural ventilation openings. To put the results into perspective, Figure 137 shows the discharge coefficient for all silencers as a function of the pressure loss. It is apparent that, for these geometries, the discharge coefficient is largely independent of flow rate for any pressure differential above about 0.01 Pa – this is three orders of magnitude less than the total pressure typically available for the ventilation system in a naturally ventilated building (see Chapter 1). Ventilation openings that operate at pressures well below 0.01 Pa do indeed exist (see section 5.3.6); however, it may not be of great importance to accurately define the losses through them, because they are likely negligible in comparison to losses elsewhere in the system. If, however, the ventilation opening silencer is highly restrictive to flow, or if the hydraulic diameter of the flow path is very small, the pressure loss will increase with respect to the Reynolds number, and low Re behaviour may become critical. The addition of grilles is common in natural ventilation openings; by reducing the hydraulic diameter, they may cause a significant pressure drop at flow rates that are not well characterized by a high Re discharge coefficient. 197  0.9 0.05 m 0.3 m 0.5 m 1m  0.8 0.7 0.6  Cd  0.5 0.4 0.3 0.2 0.1 0  1  10  100 Re  1,000  10,000  Figure 129: Predicted Straight CT silencer discharge coefficients as a function of Re.  Figure 130: Predicted flow velocity in 1 m Straight CT silencer – Re = 27,000.  Figure 131: Predicted flow pressure in 1 m Straight CT silencer – Re = 27,000.  198  Figure 132: Predicted flow velocity in 0.05 m Straight CT silencer – Re = 22,000.  Figure 133: Predicted flow pressure in 0.05 m Straight CT silencer – Re = 22,000.  0.9 0.8  0.3 m Straight 0.3 m L 0.3 m Z  0.7 0.6  Cd  0.5 0.4 0.3 0.2 0.1 0  1  10  100  1,000  10,000  Re  Figure 134: Predicted discharge coefficients of 0.3 m CT silencers as a function of Re.  199  0.9 0.5 m 0.5 m 0.5 m 0.5 m  0.8 0.7  Straight L U Z  0.6  Cd  0.5 0.4 0.3 0.2 0.1 0  1  10  100  1,000  10,000  Re  Figure 135: Predicted discharge coefficients of 0.5 m CT silencers as a function of Re.  0.9 1m 1m 1m 1m  0.8 0.7  Straight L U Z  0.6  Cd  0.5 0.4 0.3 0.2 0.1 0  1  10  100  1,000  10,000  Re  Figure 136: Predicted discharge coefficients of 1 m CT silencers as a function of Re.  200  1  0.9  0.8  0.7  Cd  0.6  0.5  0.4  0.3  0.2  0.1  0 -6 10  -5  10  -4  10  -3  -2  10  10  -1  10  0  10  1  10  ∆p [Pa] Figure 137: Predicted discharge coefficients as a function of pressure loss for all silencer configurations. Black – 0.05 m, blue – 0.3 m, green – 0.5 m, red – 1 m. ––––– Straight, – – – – – L-shaped, ········· U-shaped, – · – · – · Z-shaped.  201  6.4 CT Silencer Modeling Summary Methods have been developed for predicting the diffuse-field transmission coefficient and the Re-dependent flow performance of ventilation openings. Only 2D geometries have been modeled; however, nothing in the proposed method prevents the modeling of 3D geometries. In this section the OAR of the CT silencers, for which acoustic and flow performance predictions have been made, are presented. Because attempts to validate the transmission loss predictions in comparison to experimental results were inconclusive, the OAR results should not be considered conclusive. This summary discussion therefore only compares the relative performance of various CT silencer types. Table 30 presents the specific equivalent open area and open area ratio results from all CT silencer predictions, assuming high Re. Figures 138 and 139 show the OAR as it varies with pressure loss and Reynolds number for all CT silencer types. General conclusions about the silencer OAR performance are: •  Silencer length is dominant in determining the OAR, as it is highly related the acoustic performance; interestingly, over the range of silencer shapes and lengths predicted, increasing the length also tends to improve airflow performance.  •  The Straight silencer has the highest OAR of any silencer shape, because it has the best airflow performance; acoustic performance is largely independent of silencer shape.  •  The Z-shaped silencer has the lowest OAR due to high airflow restriction.  Table 30: CT silencer performance prediction summary.  Type Straight  L-shaped U-shaped Z-shaped  Length [m] 0.3 0.5 1 0.3 0.5 1 0.5 1 0.3 0.5 1  SEOAs 1.06 0.58 0.16 0.89 0.50 0.15 0.42 0.14 0.95 0.51 0.16  SEOAf 1.20 1.26 1.31 0.64 0.65 0.84 0.87 0.89 0.65 0.50 0.60  OAR 1.13 2.17 8.19 0.72 1.30 5.60 2.07 6.36 0.68 0.98 3.75  202  10  5  OAR  2  1  0.5  0.2  0.1  -6  10  -5  10  -4  10  -3  -2  10  10  -1  10  0  10  1  10  ∆ p [Pa]  Figure 138: Predicted open area ratio as a function of pressure loss for all silencer configurations. Blue – 0.3 m, green – 0.5 m, red – 1 m. ––––– Straight, – – – – – L-shaped, ········· U-shaped, – · – · – · Z-shaped.  203  10  5  OAR  2  1  0.5  0.2  0.1  0  10  1  10  2  10 Re  3  10  4  10  Figure 139: Predicted open area ratio as a function of Reynolds number for all silencer configurations. Blue – 0.3 m, green – 0.5 m, red – 1 m. ––––– Straight, – – – – – L-shaped, ········· U-shaped, – · – · – · Z-shaped.  204  Chapter 7: Conclusions To conclude, the results are summarized and recommendations for future work are presented.  7.1 Summary The work presented in this thesis is now summarized by directly addressing the research objectives stated in section 1.2.  Objective 1: Propose an optimization metric for the performance of an interior natural ventilation opening that considers both acoustics and airflow.  Ventilation opening silencer design for acoustical performance cannot be done independently of the design for airflow performance, as many of the possible modifications to improve the acoustic performance are to the detriment of airflow performance. To address this, an optimization parameter, the open area ratio (OAR), has been developed as a single number performance metric (see Chapter 2). OAR is the ratio of the equivalent open area for airflow (EOAf) to the equivalent open area for sound transmission (EOAs). Normalizing the equivalent open areas to the ventilator area gives the specific equivalent open areas for airflow (SEOAf) and sound transmission (SEOAs). Both SEOAf and SEOAs approach unity for a plain, large aperture; OAR is also unity for any ventilation opening with a combined performance equivalent to a large aperture.  The SEOAf is directly related to the discharge coefficient (Cd), and the effective leakage area defined by ASTM E779-10 [27] assuming a high Reynolds number.  The frequency-dependent SEOAs is calculated from the frequency-dependent diffuse field transmission loss. Frequency averaging is completed using an A-weighted speech-spectrum frequency weighting to produce a value that correlates best with levels of speech privacy. The SEOAs is equivalent to an effective sound energy transmission coefficient.  205  Objective 2: Provide an understanding of the factors that affect speech privacy in a naturally ventilated building.  A diffuse field model was developed to predict the speech privacy, in terms of SII, between two rooms separated by a common partition (see Chapter 3).  Independent of the partition construction, privacy was shown to increase with room volume and background noise. The effect of surface material acoustic absorption, which alters the reverberation time, is complicated. If background noise is very low, increasing reverberation reduces privacy; however, if the background noise is not low compared to the speech signal, then a moderate reverberation time corresponds to the lowest level of privacy. Previous work by Hodgson and Nosal has addressed this issue more completely for speech intelligibility in a single room and drawn similar conclusions [44].  When a ventilation opening is included in a partition, its effect on privacy is dependent on the transmission loss of the original partition. If the ventilation opening does not increase the EOAs of the original partition by more than 10%, it will have negligible effect on privacy. If, however, the ventilator increases the EOAs of the original partition by more than 50%, there will be a significant reduction in privacy.  Objective 3: Develop methods for measuring natural ventilation opening performance.  For this work it was necessary to measure the acoustic and airflow performance of ventilation openings in naturally ventilated buildings in a laboratory environment and in real buildings.  Standardized methods exist for measuring acoustic transmission loss of building elements in laboratory environments [56], and in buildings [55]. Measuring ventilation openings buildings, however, is challenging because the ventilation opening represents only a small portion of the partition between two spaces – the energy transmitted through the ventilation opening must be distinguished from that transmitted through the rest of the partition and by other flanking paths. The standard method requires the elimination of all flanking paths, to  206  overcome this challenge [55]; this approach is not realistic here. An alternative method was developed for this work. The transmission loss was measured with the ventilator open and again with the ventilator acoustically blocked (see section 5.1.1.2); the difference between the open and closed transmission is the transmission through the ventilator alone. This approach is effective; however, it is only able to provide a lower bound for the performance of the ventilation opening.  A standardized method [27] was also adopted and modified to measure the airflow performance of the ventilation openings (see section 5.1.2). A blower door – typically used to measure building envelope air tightness – was used to introduce a known flow rate into the room containing the ventilation opening. The corresponding pressure differential across the ventilation opening, due to the air exiting the room through it, was measured. In order to isolate the flow rate through the ventilation opening from other exit flow paths, the flow rate and pressure differential were measured with the ventilator open and again blocked in a similar fashion to the transmission loss measurements. Subtracting the two measurements provided the flow through the ventilator alone. This method has been used successfully for both laboratory and building measurements. A limitation of this method was that it is not able to test the ventilation opening flow at low pressures – as a result, only high Re results can be obtained.  Objective 4: Develop methods for predicting natural ventilation opening performance.  Analytical prediction techniques, such as the one implemented in section 6.1, exist for determining the transmission loss of propagating modes of silencers; additionally, finite element and boundary element methods have been used to predict the transmission loss of duct silencers. While these methods are useful in investigating the attenuation mechanisms within the silencer, they are unable to predict the effect of diffraction into the ventilator, diffuse sound field incidence on the ventilator, or the effect of mounting location on the partition. These factors have been discussed theoretically in section 2.3, and investigated using FEM prediction in section 6.2.2.1.2. Prior to this work, no methods existed for predicting the diffuse field transmission loss of a ventilation opening. A FEM based  207  technique, motivated by standardized measurement methods [56, 66], has been developed and implemented using COMSOL to predict the diffuse field transmission loss of ventilation openings and silencers (see section 6.2). Validation of the model was inconclusive and needs further work; however, the FEM prediction technique was able to provide valuable insights into the mechanisms of acoustic transmission through silencers (see section 6.2.4).  ANSYS Fluent CFD has been used to model airflow through ventilation openings (see section 6.3). As with the FEM acoustic model, validation of the model proved inconclusive and needs further work; however, the CFD predictions are able to provide valuable insights into the mechanisms of airflow through, and pressure loss across, ventilation openings and silencers (see section 6.3.7). Limitations of the flow modeling were that the porous domain was not modeled, and the surfaces were all modeled as smooth.  The techniques developed for predicting the acoustic transmission loss and airflow properties of ventilation openings are of great value for optimization and characterization work, as laboratory measurements are time consuming and facilities are often not available. Additionally, FEM and CFD techniques, as compared to conventional physical measurements, can provide greater detail and insights into the mechanisms that govern silencer performance by providing a solution for the entire acoustic and flow domain.  Objective 5: Provide performance results for natural ventilation opening silencers.  Four different sections of this thesis provide measurement or prediction results for the acoustical and airflow performance of ventilation openings, along with exact descriptions of their geometry, to inform designers of configurations available for use: •  In situ measurements of the acoustic and airflow performance of ventilation openings in naturally ventilated buildings were performed for 15 ventilation opening configurations in five different buildings; the results have been presented in section 5.3.  208  •  Laboratory measurements have been completed, in a purpose-built testing facility, for 19 different ventilation opening configurations; the results are presented in section 5.5.  •  Results from a BRE research project on interior natural ventilation opening silencers [12] have been analyzed using the techniques developed in this work. Acoustic and airflow performance results for 12 different cross-talk silencers, measured by the BRE, are presented in section 5.4.  •  Numerical techniques have been used to predict the performance of 11 different cross-talk silencers, as presented in section 6.2.4.  Objective 6: Provide best practice guidelines for designing successful interior natural ventilation openings.  Throughout this thesis, a number of best practices for successful ventilation opening silencer design have been identified: •  Non-acoustical grilles should be avoided. In situ measurements (section 5.3), and a review of measurements by the BRE (section 5.4), show that adding grilles to a ventilation opening halves the flow rate for a given pressure loss. All measurements showed that grilles have negligible effect on acoustic transmission.  •  The addition of a fiberglass absorptive liner to the ceiling above a slot ventilation opening has been shown, in laboratory (section 5.5.1) and in situ (section 5.3) measurements, to increase the opening’s STC by 3 to 6 dB.  •  The acoustic baffle, a novel silencer concept presented in section 5.5.3, was shown to be an effective silencer for situations where the depth of the silencer is restricted.  •  Cross-talk silencers, as studied in situ (section 5.3), in the BRE measurements (section 5.4), in the laboratory measurements (section 5.5.5), and in the numerical modeling section (sections 6.2.4 and 6.3.7), are capable of the highest combined acoustical and airflow performance when compared to any other type of silencer tested. Their acoustical performance can be improved by increasing the length of the acoustically-lined flow path; within reasonable limits, this increase in length does not further restrict, and can actually increase, air flow. 209  •  Reducing the aspect ratio of a CT silencer to one, if the silencer is lined on all four sides, can increase the attenuation of the fundamental acoustic mode by up to twice that of an otherwise identical silencer with an aspect ratio greater than 10. This conclusion is based on an analytical investigation presented in section 6.1.  •  Elbows in the L-, U-, and Z-shaped CT silencers increase the transmission loss at high frequencies; however, the overall acoustic performance in these silencers (STC or SEOAs) is limited by low frequency transmission. Elbows will increase the transmission loss if the wavelength is shorter than the duct height. As elbows increase the flow losses but do not increase the overall acoustic performance (EOAs, or STC), the Straight CT silencer has the best performance of any CT silencer shape tested. This result was observed in laboratory measurements, (section 5.5.5), and in modeling predictions (sections 6.2.4 and 6.3.7).  •  In order to be effective at attenuating speech frequencies, the acoustic liner in a silencer liner should be at least 50 mm thick (see sections 6.1 and 5.5.1).  •  The attenuation rate in straight sections of lined duct is maximized when the wavelength is equal to the duct height (see sections 6.1 and 6.2.4). As the wavelength becomes smaller than the duct height the attenuation rate decreases. For this reason, it is best to use a duct height no greater than the wavelength of the highest critical frequency; a 0.1 m tall duct provides good attenuation for A-weighted speech sounds.  •  EOAf and Cd are both generally dependent on Reynolds number; however, they are constant if the Reynolds number is sufficiently high. In mechanical ventilation systems, high Re flow is a good assumption, and Cd is considered constant with respect to flow rate for duct fittings. To investigate the Reynolds number dependence in the context of natural ventilation openings an analytical discussion has been provided in section 4.4.2, and a discussion of in situ measurement and modeling results is given in sections 5.3.6 and 6.3.7.3. It was shown that the EOAf and Cd become independent of Re when the Reynolds number is above some ‘transitional’ Reynolds number. The transitional Reynolds number is geometry-dependent and exists in the range of 100 – 4000. As shown in section 5.3.6, ventilation openings in naturally ventilated buildings cannot be assumed to operate at high Re. Also, because  Cd decreases with decreasing Re below the transitional Reynolds number, using the 210  high Reynolds number discharge coefficient to design a ventilation opening for low Reynolds number flow could result in an underestimation of the flow losses and an undersized system (section 4.4.2). In most cases, however, if the flow rates are low enough such that Re<4000, the pressure loss through the ventilation opening is at least two or three orders of magnitude less than the 10 Pa often assumed available in a naturally ventilated building (sections 5.3.6 and 6.3.7.3). As a result, the errors associated with using a high Re discharge coefficient to determine the losses through a ventilation opening at low Re may not be of practical concern. These same errors, however, will be of concern if either the silencer is very restrictive (i.e. small Cd), or if the hydraulic diameter is very small (low Re at high flow rate), as significant pressure losses would be observed at low Reynolds numbers. Grilles are likely the most common example of low Re flow leading to significant errors in predicted pressure loss because they are often implemented and, due to small fin spacing, have a small hydraulic diameter.  7.2 Future Work Many areas of this research leave room for further work. In order to attempt any optimization work, the performance requirements of the silencers must be better understood. In order to complete the optimization work, laboratory measurements and numerical predictions must be improved and/or further validated. Optimization must look into variations in silencer design with parameters which have not been investigated in this work.  7.2.1  Set Optimization Objectives  The optimal design of a ventilation opening silencer is dependent on its performance requirements. Design targets for different applications should be set so that applicationspecific optimization can take place.  7.2.2  Improve Physical and Numerical Performance Prediction Methods  The laboratory measurements and numerical predictions in this work can be improved upon and expanded.  211  Laboratory measurements were limited due to the low partition transmission loss, small room size, and inability to measure at low-Re flow rates. Physical scale modeling may be a useful method to improve the measurements while making use of the present facilities. Scale modeling can: •  increase the noise-isolation effectiveness of the partition  •  provide a diffuse sound field at lower frequencies  •  increase the ventilator pressure drop with respect to Re, allowing measurements of airflow performance at relatively low Re.  Calculation of the airflow measurement results should also be modified. Because the assumption of high Re flow is used, it is also assumed that n from Eq. (10), section 2.1.2, is equal to 0.5. Allowing n to take any value is inappropriate and will result in an underestimation of the actual uncertainties in the measured result.  Numerical predictions in this work were limited primarily by a lack of confidence in the validation results. Before the proposed numerical models are used for optimization work, their accuracy, or regions of validity, must be established. In the acoustical model the porous absorber is modeled empirically; in the airflow model, it is not modeled at all. The porous absorber should be investigated as a possible cause of disagreement between measurement and prediction for both acoustical and airflow results. Additionally, to provide improved mesh independence and solver stability, a structured mesh should be implemented in the airflow model.  With validated models, it would be interesting to implement 3D silencer geometries. There are no indications from the work presented in this thesis that 3D geometries will be problematic to model.  7.2.3  Optimize Natural Ventilation Openings  This thesis has identified CT silencers as the most effective silencing devices for interior natural ventilation openings. Additionally, the 125-500 Hz octave bands have been identified as generally responsible for limiting the performance of a silencer in attenuating A-weighted 212  speech sounds. Modifications for increased acoustic performance should target these frequencies. 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JASA, vol. 125, 2009, pp. 2494.  220  Appendices Appendix A: Manufacturer Data Sheets .......................................................................... 222 A.1  CertainTeed OEM Acoustic Fiberglass Absorber ................................................ 222  A.2  Kinetics Noise Control Acoustical Louver (2’x2’, 6” Val/1) ............................... 224  A.3  Filter Data Sheets.................................................................................................. 226  Appendix B: MATLAB Code ............................................................................................ 229 B.1  Diffuse Field Sound Transmission Model ............................................................ 229  B.2  Attenuation in a Lined Duct.................................................................................. 236  B.3  Processing COMSOL Results............................................................................... 241  Appendix C: Numerical Prediction Appendices .............................................................. 244 C.1  Predicted CT Silencer Transmission Loss ............................................................ 245  C.2  Velocity- and Pressure-Field Figures for CT Silencers at High-Re ..................... 246  221  Appendix A: Manufacturer Data Sheets Manufacturer data sheets are provided for further information on the fiberglass absorber, acoustical louver, and air filters used in the laboratory measurements.  A.1  CertainTeed OEM Acoustic Fiberglass Absorber  222  223  A.2  Kinetics Noise Control Acoustical Louver (2’x2’, 6” Val/1)  224  225  A.3  Filter Data Sheets  Pink air filter: “Red Excel” by B.G.E.  226  White air filter: Series 400 Pleated air filter by Aerostar (2” Std. Cap)  227  228  Appendix B: MATLAB Code Code is provided for the diffuse field model, the analytical model for attenuation in a lined duct, and the code used to process typical FEA results.  B.1  Diffuse Field Sound Transmission Model  This model consists of four scripts. The first script must be run to load data for defining the room. Script 2 is then modified to define the room, partition, and source conditions. Script 3 is the main program which calculates all parameters. The STC calculation is written as a separate function and presented here as Script 4.  Script 1: Data for Diffuse Field Sound Transmission Model %Define octave and third octave frequencies f_1 = [125, 250, 500, 1000, 2000, 4000, 8000]; f_1_3 = [125, 160, 200, 250, 315, 400, 500, 630, 800, 1000, 1250, 1600,... 2000, 2500, 3150, 4000, 5000, 6300, 8000]; STC_curve = [-16, -13, -10, -7, -4, -1, 0, 1, 2, 3, 4, 4, 4, 4, 4, 4]; %STC_SII_curve taken from log(SII_weights) %STC_SII_curve = [-62, -42, -23, -4, -3, -1, 0, 1, 1, 2, 2, 2, 2, 2, 1, 1]; %% Absorption coefficients %Ref: Acoustic Abs. and Diff., Cox, pg 441 carpetWithUnderlay = [0.03, 0.09, 0.2, 0.54, 0.7, 0.72, 0.72]; %Thin(6mm) carpet on underlay carpetNoUnderlay = [0.02, 0.04, 0.08, 0.2, 0.35, 0.4, 0.4]; %Thin carpet cemented to concrete concrete = [0.01, 0.01, 0.02, 0.02, 0.02, 0.05, 0.05]; %Smooth, unpainted concrete acousticTile = [0.09, 0.28, 0.78, 0.84, 0.73, 0.64, 0.64]; %Acoustic tile, 1.9cm thick drywall = [0.08, 0.11, 0.05, 0.03, 0.02, 0.03, 0.03]; %Plasterboard on frame, 13mm boards, 10cm empty cavity %% Speech source levels %(SII standard) casual = [50, 59, 61, 55, 50, 45, 40]; normal = [58, 67, 69, 61, 56, 50, 44]; raised = [62, 71, 75, 70, 64, 57, 48]; loud = [65, 74, 79, 79, 73, 66, 54]; shout= [76, 75, 84, 88, 83, 75, 63]; %Olsen normal_F = [26, 37, 48, 47, 42, 49, 50, 48, 46, 42, 43, 42, 38, 36, 38, 40, 36, 36, 34]; normal_M = [48, 43, 48, 52, 51, 53, 54, 52, 46, 45, 47, 44, 40, 41, 41, 38, 24, 35, 32]; normal_C = [24, 29, 42, 51, 47, 47, 53, 52, 49, 44, 43, 43, 41, 38, 39, 40, 38, 36, 37];  229  speech_A_norm = [-26.7, -22.7, -17.4, -14, -11.9, -8.8, -7.1, -7.3, 9.4,... -11.2, -12, -13.6, -15.6, -19, -19.9, -21.6, -25.5, -28.2, -30.1]; %% Transmission Loss data %Ref: Architectural Acoustics, Long, pg 358 glass = [10, 12, 14.5, 15, 18, 18.5, 20]; glass_1_3 = [10, 11, 11, 12, 12.5, 13, 14.5, 15, 15, 15, 16, 17, 18, 18, 18.5, 18.5, 19, 19.5, 20]; drywall_1W1 = [15, 24, 32, 41, 37, 43, 43]; drywall_1W1_1_3 = [15, 15, 20, 24, 27, 29, 32, 36, 39, 41, 41, 40, 37, 36, 39, 43, 43, 43, 43]; drywall_1W2 = [19, 26, 34, 38, 43, 52, 52]; drywall_1W2_1_3 = [19, 19, 23, 26, 28, 28, 34, 36, 39, 38, 38, 41, 43, 44, 49, 52, 52, 52, 52]; drywall_2W2 = [15, 35, 43, 48, 53, 50, 50]; drywall_2W2_1_3 = [15, 19, 35, 35, 34, 42, 43, 43, 47, 48, 50, 52, 53, 48, 46, 50, 50, 50, 50]; drywall_1WR2 = [27, 33, 40, 45, 49, 54, 54]; drywall_1WR2_1_3 = [27, 28, 34, 33, 34, 37, 40, 42, 44, 45, 46, 49, 49, 49, 53, 54, 54, 54, 54]; drywall_2WR2 = [28, 43, 51, 56, 61, 57, 57]; drywall_2WR2_1_3 = [28, 33, 41, 43, 44, 51, 51, 53, 56, 56, 60, 60, 61, 55, 52, 57, 57, 57, 57];  Script 2: Model Inputs %% Model Input - Room descriptions %Room L_1 = W_1 = H_1 = L_2 = W_2 = H_2 =  1 (source) and 2 (reciever) length, width and height in meters 5; 5; 3; 5; 5; 3;  %Flag_reverbCalc: 0 for description of room by materials, 1 for %description of room by reverberation time Flag_reverbCalc = 0; %Room 1 and 2 surface materials (concrete, carpetNoUnderlay, carpetWithUnderlay, %drywall, acousticTile) % % % % % % %  % 1 floorAbs_1 = wallsAbs_1 = ceilingAbs_1 floorAbs_2 = wallsAbs_2 = ceilingAbs_2  concrete; concrete; = concrete; concrete; concrete; = concrete;  230  % % % % % % %  %2 floorAbs_1 = wallsAbs_1 = ceilingAbs_1 floorAbs_2 = wallsAbs_2 = ceilingAbs_2  concrete; drywall; = drywall; concrete; drywall; = drywall;  % % % % % % %  % 3 floorAbs_1 = wallsAbs_1 = ceilingAbs_1 floorAbs_2 = wallsAbs_2 = ceilingAbs_2  carpetNoUnderlay; drywall; = drywall; carpetNoUnderlay; drywall; = drywall;  % 4 floorAbs_1 = carpetNoUnderlay; wallsAbs_1 = drywall; ceilingAbs_1 = acousticTile; floorAbs_2 = carpetNoUnderlay; wallsAbs_2 = drywall; ceilingAbs_2 = acousticTile; % % %5 % floorAbs_1 = carpetWithUnderlay; % wallsAbs_1 = drywall; % ceilingAbs_1 = acousticTile; % floorAbs_2 = carpetWithUnderlay; % wallsAbs_2 = drywall; % ceilingAbs_2 = acousticTile; %T60 in onctave bands, 125 Hz to 8 kHz RT_1 = [0.5, 0.5, 0.5, 0.4, 0.3, 0.2, 0.2]; RT_2 = [0.5, 0.5, 0.5, 0.4, 0.3, 0.2, 0.2]; %% Partition description %Common wall area, s_P [m^2] s_P = L_1*H_1; %Ventilation openeing area, s_V, in m^2 s_V = 0.75; %Flag_TL_P: 0 for description of partition by type, 1 for description of %partition by STC, 2 for descrition of partition by transmission loss Flag_TL_P = 0; %Flag_TL_P = 0, Partition type (glass, drywall_1W1, drywall_1W2, drywall_2W2, %drywall_1WR2, drywall_2WR2) W:wood stud, R:resiliant channel Partition_1 = glass; Partition_1_3 = glass_1_3; %Flag_TL_P = 1, Partition STC  231  %PartitionSTC = 30; %Flag_TL_P = 2, Partition transmission loss, TL_P [dB], in octave bands %from 125 Hz to 8 kHz %TL_P = [15, 20, 25, 30, 30, 35, 45]; %Scilencer Insertion Loss, IL_S [dB], in octave bands from 125 Hz to 8 kHz IL_S = [0, 0, 0, 0, 0, 0, 0]; IL_S_1_3 = [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]; %% Source and background levels %Flag_source: 0 for speech source acording to SII levels, 1 for %custom defined levels Flag_source = 0; %Speech Source level, speechLevel, according to SII levels (casual, normal, %raised, loud, shout) % speechLevel = casual; speechLevel = normal; % speechLevel = raised; % speechLevel = loud; % speechLevel = shout; %Source power level, Lw_1 [dB], in octave bands from 125 Hz to 8 kHz Lw_1 = [60, 60, 60, 60, 60, 60, 60]; % % % % % %  %Flag_backGround: 0 for reciever room background level according to NC %level, 1 for custom defined levels Flag_backGround = 1; %NC background level, backGround_NC backGroud_NC = 30;  %Background pressure Levels, backGround [dB], in octave bands from 125 Hz %to 8 kHz Lp_BG = [35.6, 22, 20.4, 18.1, 16, 11.6, 12.3]; %L90 from lab Lp_BG = Lp_BG+0;  Script 3: Diffuse Field Model Main Program %% Load data and inputs %% Calculate room parameters %Room Volumes vol_1 = L_1*W_1*H_1; vol_2 = L_2*W_2*H_2; %Surface floorS_1 floorS_2 wallsS_1 wallsS_2  areas = L_1*W_1; = L_2*W_2; = 2*L_1*H_1+2*W_1*H_1; = 2*L_2*H_2+2*W_2*H_2;  232  ceilingS_1 = floorS_1; ceilingS_2 = floorS_2; Stot_1 = floorS_1+wallsS_1+ceilingS_1; Stot_2 = floorS_2+wallsS_2+ceilingS_2; %% Calculate reverberation times if (Flag_reverbCalc == 0) Atot_1 = floorS_1*floorAbs_1+wallsS_1*wallsAbs_1+ceilingS_1*ceilingAbs_1; Atot_2 = floorS_2*floorAbs_2+wallsS_2*wallsAbs_2+ceilingS_2*ceilingAbs_2; RT_1 = 0.16*vol_1./Atot_1; RT_2 = 0.16*vol_2./Atot_2; end if (Flag_reverbCalc == 1) Atot_1 = 0.16*vol_1./RT_1; Atot_2 = 0.16*vol_2./RT_2; end Aavg_1 = Atot_1/Stot_1; Aavg_2 = Atot_2/Stot_2; R_1 = Atot_1./(1-Aavg_1); R_2 = Atot_2./(1-Aavg_2); %% Calculate equivalent transmission loss, TL_E [dB], of partition if (Flag_TL_P == 0) TL_P = Partition_1; TL_P_1_3 = Partition_1_3; end if (Flag_TL_P == 1) TL_P = PartitionSTC+[-16, -7, 0, 3, 4, 4, 4]; end TL_E = -10.*log10((10.^(-TL_P./10).*(s_P-s_V)+10.^(IL_S./10).*s_V)./(s_P)); TL_E_1_3 = -10.*log10((10.^(-TL_P_1_3./10).*(s_P-s_V)+10.^(IL_S_1_3./10).*s_V)./(s_P)); %% Calculate sound levels if (Flag_source == 0) Lw_1 = speechLevel; end Lp_1 = Lw_1+10*log10(4./R_1); Lp_2 = Lp_1-TL_E+10*log10(s_P./Atot_2); SNL = Lp_2-Lp_BG; NI = Lp_1-Lp_2; %% Calculate Articulation Index AI_weight = [0, 0.0024, 0.0048, 0.0074, 0.0109, 0.0078, 0]; SNL_AI = SNL; for i=1:length(SNL)  233  if(SNL_AI(1, i)<0) SNL_AI(1, i)=0; disp('SNL_AI increased to 0dB'); end if(SNL_AI(1, i)>30) SNL_AI(1, i)=30; disp('SNL_AI decreased to 30dB'); end end AI = SNL_AI*AI_weight'; %% Calculate Speech Inteligibility Index %f_mod: modulation frequencies f_mod = [0.63, 0.8, 1, 1.25, 1.6, 2, 2.5, 3.15, 4, 5, 6.3, 8, 10, 12.5]; %m_SN: modulation trnasferfunction for signal to background noises m_SN = 1./(1+10.^(-SNL/10)); %m_RT: modulaiton transfer function for signal to reverberant noise m_RT = zeros(length(f_mod), length(f_1)); for i=1:length(f_1) m_RT(:, i)=(1+(2*pi()*f_mod'*RT_2(1, i)/13.82).^2).^(-1/2); end %mod: modulation transfer function, m_SN*m_RT mod = zeros(length(f_mod), length(f_1)); for i=1:length(f_1) mod(:, i)=m_RT(:, i)*m_SN(1, i); end %SN_app_noLim: apparent signal to noise, not level-limited SN_app_noLim = 10*log10(mod./(1-mod)); %SN_app: apparent signal to noise, level-limited SN_app = SN_app_noLim; for i=1:length(f_mod) for t=1:length(f_1) if(SN_app(i, t) > 15) SN_app(i, t) = 15; disp ('STI SN_app decreased to 15'); end if(SN_app(i, t) <= -15) SN_app(i, t) = -15; disp ('STI SN_app increased to -15'); end end end %SN_eff: effective signal to noise - averaged over modulation bands SN_eff = zeros(1, length(f_1)); for i=1:length(f_1) SN_eff(1, i)=mean(SN_app(:, i)); end %K_inx: adjust from SNL to index level K_inx = (SN_eff+15)/30; %frequency weighting SII_bandWeight = [0, 0.0617, 0.1671, 0.2373, 0.2648, 0.2142, 0.0549]; %BAF: band audiablility factors after frequency weighting BAF = SII_bandWeight.*K_inx;  234  %SII = sum(BAF); sum seems to not want to work SII = 0; for i=1:length(BAF) SII = SII+BAF(1, i); end %% Calculate Sound Transmission Class %STC_P: STC of partition w/o ventilation opening STC_P = Calc_STC(TL_P_1_3(1:16)); %STC_E: STC of partition with ventilation opening STC_E = Calc_STC(TL_E_1_3(1:16)); %% Calculate Noise Isolation Class %NIC: NIC of partition with ventilation opening NI_round = round(NI); NIC = Calc_STC(NI_round(1:16)); %% Calculate SRI (based on transmitted speech spectrum) SRI_E_weighted_spA = -TL_E_1_3+speech_A_norm; SRI_P_weighted_spA = -TL_P_1_3+speech_A_norm; SRI_S_weighted_spA = -IL_S_1_3+speech_A_norm; SRI_E_speech = -10*log10(sum(10.^(SRI_E_weighted_spA/10))); SRI_P_speech = -10*log10(sum(10.^(SRI_P_weighted_spA/10))); SRI_S_speech = -10*log10(sum(10.^(SRI_S_weighted_spA/10))); %% Calculate Equivalent Open Area %partition EOA EOA_p = s_P*10^(-SRI_E_speech/10); %wall EOA EOA_w = (s_P-s_V)*10^(-SRI_P_speech/10); %ventilator EOA EOA_v = s_V*10^(-SRI_S_speech/10);  Script 4: Function to Calculate STC function STC = Calc_STC(TL) %This function takes in 1/3rd octave TL data from 125-4kHz and returns the %STC value STC_curve = [-16, -13, -10, -7, -4, -1, 0, 1, 2, 3, 4, 4, 4, 4, 4, 4]; STC_curve = STC_curve - 20; %lower the curve to allow for negative STC result TL_round = round(TL); cont = 1; while cont == 1 total = 0; STC_curve = STC_curve+1; %raise STC curve %Check if deficiency exceeds 8dB for i=1:16 temp = STC_curve(1, i)-TL_round(1, i);  235  if(temp == 9) cont = 0; disp(['STC limited by 8: Temp = end %sum deficiencies if(temp >= 0) total = total+temp; end  ', num2str(temp)]);  end %check if sum of deficiencies exceed 32 if total > 32 cont = 0; disp(['STC limited by 32: Total = ', num2str(total-16)]); end end STC_curve = STC_curve -1; STC = STC_curve(1, 7); disp(['STC = ', num2str(STC)]);  B.2  Attenuation in a Lined Duct  This program works by running the main script in which the duct geometry and absorber flow resistivity is defined. The main scrip calls either the “Delaney-Bazley”, or “Mechel and Grundmann” scripts for defining the absorber properties.  Script 1: Main Program %% % This program calculates the attenuation of the funamental mode in a % lined duct. It uses Delany-Bazley or Mechel and Grundmann emperical % models to calculate the wavenumber and impedance of the liner (see Cox, Acoustic Absorbers and Diffusers). These % models are defined in seperate functions. Solution for the first mode of % the trancidental equations are found using Newton-Raphson iteration. %% clear all %% Inputs T = 20; c = 331.3*(1+(T+273.15)/273.15)^1/2; rho = 1.204; %Density of air Z0 = c*rho; %Characteristic Impedance f = 90:5:11310; %Frequencies k=2*pi*f/c; %Wavenumber dx = 0.0254; dy = 0.0254;  %Speed of sound  %Absorber thickness  sigmay = 40000; sigmax = 20000;  236  Ry = sigmay*dy/Z0; %Normalized flow resistance (flow resistance *d/Z0) Rx = sigmax*dx/Z0; %Rx = 5; %Normalized flow resistance (flow resistance *d/Z0) %Ry = 5; hx = 0.02; hy = 0.05;  %Half height of channel  %%Select Model (Uses R, d, f, k, Z0. Creates Zw and kw (absorber impedance %%and wavenumber)). Open file to adjust model. Delany_Bazley; %Mechel_Grundmann; %% Calculate absorber properites Zsx=-j*Zwx.*cot(kwx*dx); Zsy=-j*Zwy.*cot(kwy*dy); rx = (Zsx/Z0-1)./(Zsx/Z0+1); ry = (Zsy/Z0-1)./(Zsy/Z0+1); ax=1-abs(rx.^2); ay=1-abs(ry.^2);  %Surface impedance of absorber  %Normal incidence reflection coefficient  %Normal incidence absorption coefficient  %Plot normal incidence absorption figure (1) semilogx(f, ax); title('Liner Absorption (liner on x)') ylabel('Normal Incidence Absorption') xlabel('Frequency Hz') xlim([90 11310]) %% Calculate initial guess for iteration (ref Munjal Acoustics of ducts and % mufflers, 1987, pg 235) Qx=j*k.*hx*Z0./Zsx; Qy=j*k.*hy*Z0./Zsy; ikxa=1/hx*((2.47+Qx+((2.47+Qx).^2-1.87*Qx).^0.5)/0.38).^0.5; ikxb=1/hx*((2.47+Qx-((2.47+Qx).^2-1.87*Qx).^0.5)/0.38).^0.5; ikya=1/hy*((2.47+Qy+((2.47+Qy).^2-1.87*Qy).^0.5)/0.38).^0.5; ikyb=1/hy*((2.47+Qy-((2.47+Qy).^2-1.87*Qy).^0.5)/0.38).^0.5; kxa = zeros(2, length(f)); kya = zeros(2, length(f));  %Wavenumber in x  kxb = zeros(2, length(f)); kyb = zeros(2, length(f));  %Wavenumber in x  %% Calculate for initial ikxa, ikya  237  for i=1:length(f) syms kxi kyi %Define variables (symbols) %Define functions gx=j*Zwx(1, i)*cot(kwx(1, i)*dx)+j*Z0*k(1, i)/kxi*cot(kxi*hx); gy=j*Zwy(1, i)*cot(kwy(1, i)*dy)+j*Z0*k(1, i)/kyi*cot(kyi*hy); d1gx = diff(gx); d1gy = diff(gy);  %Differentiate functions  % Initial guess oldx = ikxa(1, i); oldy = ikya(1, i); % Initial error parameter Exa = 1; Eya = 1; iteration = 0; %Begin Newton-Raphson Iteration while (((Exa>0.1)||(Eya>0.1))&& iteration<10) newx = oldx-subs(gx,kxi,oldx)/subs(d1gx,kxi,oldx); newy = oldy-subs(gy,kyi,oldy)/subs(d1gy,kyi,oldy); oldx = newx; oldy = newy; Exa = 100*abs((oldx-newx)/oldx); Eya = 100*abs((oldy-newy)/oldy); iteration = iteration+1; end %Define k kxa(1, i) kxa(2, i) kya(1, i) kya(2, i)  and E @ f = newx; = Exa; = newy; = Eya;  end %% Calculate for initial ikxb, ikyb for i=1:length(f) syms kxi kyi %Define varriables (symbols) %Define functions gx=j*Zwx(1, i)*cot(kwx(1, i)*dx)+j*Z0*k(1, i)/kxi*cot(kxi*hx); gy=j*Zwy(1, i)*cot(kwy(1, i)*dy)+j*Z0*k(1, i)/kyi*cot(kyi*hy); d1gx = diff(gx); d1gy = diff(gy);  %Differentiate functions  % Initial guess  238  oldx = ikxb(1, i); oldy = ikyb(1, i); % Initial error parameter Exb = 1; Eyb = 1; iteration = 0; %Begin Newton-Raphson Iteration while (((Exb>0.1)||(Eyb>0.1))&& iteration<10) newx = oldx-subs(gx,kxi,oldx)/subs(d1gx,kxi,oldx); newy = oldy-subs(gy,kyi,oldy)/subs(d1gy,kyi,oldy); oldx = newx; oldy = newy; Exb = 100*abs((oldx-newx)/oldx); Eyb = 100*abs((oldy-newy)/oldy); iteration = iteration+1; end %Define k kxb(1, i) kxb(2, i) kyb(1, i) kyb(2, i)  and E @ f = newx; = Exb; = newy; = Eyb;  end %% Check to confirm convergence if ((max(Exa)>0.1)||(max(Eya)>0.1)||(max(Eya)>0.1)||(max(Eya)>0.1)) disp('Solution did not converge within 0.1%') end %% Calculate wavenumber in z kzi = zeros(1, length(f)); %Determine which of the initial guesses provided the appropriate answer %(minimum transmissionloss, or smallest imaginairy component of kz) for i=1:length(f) kzaai=((2*pi*f(1, i)/c)^2-kxa(1, i)^2-kya(1, i)^2)^(1/2); kzabi=((2*pi*f(1, i)/c)^2-kxa(1, i)^2-kyb(1, i)^2)^(1/2); kzbai=((2*pi*f(1, i)/c)^2-kxb(1, i)^2-kya(1, i)^2)^(1/2); kzbbi=((2*pi*f(1, i)/c)^2-kxb(1, i)^2-kyb(1, i)^2)^(1/2); temp = [(kzaai), (kzabi), (kzbai), (kzbbi)]; [C, I]=min(abs(imag(temp))); kzi(1, i)=temp(1, I); end %% Calculate and plot TL results TL = -8.686*imag(kzi);  %Transmission loss per meter  239  Lh = -8.686*imag(kzi)*hy; %Normalized attenuation coefficient eta=2*hy*f/c; %Ratio of channel height to wavelength figure (2) semilogx(f, TL) title('Transmission Loss') ylabel('TL dB/m') xlabel('f Hz') xlim([90 11310]) %ylim([0 10]) figure (3) loglog(eta, Lh); title('Normalized Attenuation') ylabel('Lh dB') xlabel('2hf/c (Channel depth / Wavelength)') %xlim([0.01 5]) %ylim([0.1 10])  Script 2: Delaney-Bazley %% Delany-Bazley model (ref Cox, Acoustic absorbers and diffusers, 2009, %% pg 173) % Define dy and Ry arbitrarily if they dont exist if (~exist('dx')) dx = 1; end if (~exist('Rx')) Rx = 1; end sigmax = Rx*Z0/dx; sigmay = Ry*Z0/dy; Xx = rho*f./sigmax; Xy = rho*f./sigmay; Zwx = rho*c*(1+0.0571*Xx.^(-0.754)-j*0.087*Xx.^(-0.732)); Zwy = rho*c*(1+0.0571*Xy.^(-0.754)-j*0.087*Xy.^(-0.732)); kwx = 2*pi*f./c.*(1+0.0978*Xx.^(-0.700)-j*0.189*Xx.^(-0.595)); kwy = 2*pi*f./c.*(1+0.0978*Xy.^(-0.700)-j*0.189*Xy.^(-0.595));  Script 3: Mechel and Grundmann %% Mechel and Grundmann model (ref Cox, Acoustic absorbers and diffusers, %% 2009, pg 175) % Define dy and Ry arbitrarily if they dont exist if (~exist('dx')) dx = 1; end if (~exist('Rx')) Rx = 1; end sigmax = Rx*Z0./dx;  240  sigmay = Ry*Z0./dy; Xx = rho*f./sigmax; Xy = rho*f./sigmay; %% Select glass or mineral fibre %Glass Fibre B = [-0.00451836+j*0.000541333, -0.00171387+j*0.00119489;... 0.421987+j*0.376270, 0.283876-j*0.292168;... -0.383809-j*0.353780, -0.463860+j*0.188081;... -0.610867+j*2.59922, 3.12763+j*0.914600;... 1.13341-j*1.74819, -2.10920-j*1.32398;... 0, 0]; % %Mineral Fibre % B = [-0.00355757-j*.0000164897, 0.0026786+j*0.00385761;... % 0.421329+j*0.342011, 0.135298-j*0.394160;... % -0.507733+j*0.086655, 0.946702+j*1.47653;... % -0.142339+j*1.25986, -1.45202-j*4.56233;... % 1.29048-j*0.0820811, 4.03171+j*7.56031;... % -0.771857-j*0.668050, -2.86993-j*4.90437]; kwx = -j*k.*(Xx.^(-1)*B(1, 1)+Xx.^(-1/2)*B(2, 1)+B(3, 1)+Xx.^(1/2)*B(4, 1)+Xx*B(5, 1)+Xx.^(3/2)*B(6, 1)); kwy = -j*k.*(Xy.^(-1)*B(1, 1)+Xy.^(-1/2)*B(2, 1)+B(3, 1)+Xy.^(1/2)*B(4, 1)+Xy*B(5, 1)+Xy.^(3/2)*B(6, 1)); Zwx = Z0*(Xx.^(-1)*B(1, 2)+Xx.^(-1/2)*B(2, 2)+B(3, 2)+Xx.^(1/2)*B(4, 2)+Xx*B(5, 2)+Xx.^(3/2)*B(6, 2)); Zwy = Z0*(Xy.^(-1)*B(1, 2)+Xy.^(-1/2)*B(2, 2)+B(3, 2)+Xy.^(1/2)*B(4, 2)+Xy*B(5, 2)+Xy.^(3/2)*B(6, 2));  B.3  Processing COMSOL Results  FEM results are processed by copying results for the average source-volume sound pressure level, inlet sound intensity, and outlet sound intensity from COMSOL into MATLAB. The third octave band transmission loss is calculated based on sound pressure level and intensity. Because the relationship between sound pressure level and sound intensity is different in 2D and 3D models, the 2D and 3D results are processed by separated scripts.  Script 1: 3D COMSOL Results %% Takes in 3D data Lp_Sv, W_in, W_out. % W_in and W_out must be in peak values. % Vertical columns are octave bands No_bands=length(Lp_Sv(1, :)); No_frequencies=length(Lp_Sv(:, 1)); tao_Sv_third=zeros(1, No_bands); tao_Win_third=zeros(1, No_bands); TL_Sv_third=zeros(1, No_bands); TL_Win_third=zeros(1, No_bands);  241  %Generate sampled frequencies frequencies=zeros(No_frequencies, No_bands); frequencies(1, :)=[88.39, 111.36, 140.31, 176.78, 222.72,... 280.62, 353.55, 445.45, 561.23, 707.11, 890.9,... 1122.46, 1414.21, 1781.8, 2244.92]; for i=1:No_bands for s=2:No_frequencies frequencies(s, i)=frequencies(1, i)+(frequencies(1, i)*2^(1/3)frequencies(1, i))... /(No_frequencies-1)*(s-1); end end %duct area Vc_h=0.05; A=343./frequencies(1, :)*(3*4^(1/3)-1.4)*Vc_h;  %Calculate Win from Lp_Sv Win_Lp=zeros(No_frequencies, No_bands); for i=1:No_bands Win_Lp(:, i)=A(1, i)*(10.^(Lp_Sv(:, i)./10)*(2*10^(5))^2)/(4*1.2044*343.2); end %Calcaulte transmission coefficients tau_Sv=real(W_out/2)./Win_Lp; %devided by to to convert from peak to RMS tau_Win=real(W_out)./real(W_in); TL_Sv=-10.*log10(tau_Sv); TL_Win=-10.*log10(tau_Win); %Calculate stdev and confidence intervals (normal, 95% confidence in %mean) StDev_Sv=zeros(1, No_bands); StDev_Win=zeros(1, No_bands); for i=1:No_bands StDev_Sv(1, i)=std(TL_Sv(:, i)); StDev_Win(1, i)=std(TL_Win(:, i)); end con_int_Sv=StDev_Sv.*1.96./(No_frequencies.^0.5); con_int_Win=StDev_Win.*1.96./(No_frequencies.^0.5);  % Third octaves for TL_Sv for i=1:No_bands temp = 0; %Loop through each data point in the band, multiplying eachpoint by a %weighting factor and summing for s=1:No_frequencies temp = temp+log10(((frequencies(s, i)+(frequencies(2, i)frequencies(1, i)))/frequencies(s, i)))*tau_Sv(s, i); end %divide through by the frequency range  242  tao_Sv_third(1, i)=temp/(log10(frequencies(end, i)/frequencies(1, i))); TL_Sv_third(1, i)=-10*log10(tao_Sv_third(1, i)); end % Third octaves for TL_Win for i=1:No_bands temp = 0; %Loop through each data point in the band, multiplying eachpoint by a %weighting factor and summing for s=1:No_frequencies temp = temp+log10(((frequencies(s, i)+(frequencies(2, i)frequencies(1, i)))/frequencies(s, i)))*tau_Win(s, i); end %divide through by the frequency range tao_Win_third(1, i)=temp/(log10(frequencies(end, i)/frequencies(1, i))); TL_Win_third(1, i)=-10*log10(tao_Win_third(1, i)); end  Script 2: 2D COMSOL Results %% Takes in 2D data Lp_Sv, W_in, W_out. % W_in and W_out must be in peak values. % Vertical columns are octave bands No_bands=length(Lp_Sv(1, :)); No_frequencies=length(Lp_Sv(:, 1)); tao_Sv_third=zeros(1, No_bands); tao_Win_third=zeros(1, No_bands); TL_Sv_third=zeros(1, No_bands); TL_Win_third=zeros(1, No_bands); A=0.1; %duct height %Calculate Win from Lp_Sv Win_Lp=A*(10.^(Lp_Sv./10)*(2*10^(-5))^2)/(pi*1.2044*343.2); %Calcaulte transmission coefficients tau_Sv=real(W_out/2)./Win_Lp; %devided by to to convert from peak to RMS tau_Win=real(W_out)./real(W_in); TL_Sv=-10.*log10(tau_Sv); TL_Win=-10.*log10(tau_Win); %Calculate stdev and confidence intervals (normal, 95% confidence in %mean) StDev_Sv=zeros(1, No_bands); StDev_Win=zeros(1, No_bands); for i=1:No_bands StDev_Sv(1, i)=std(TL_Sv(:, i)); StDev_Win(1, i)=std(TL_Win(:, i)); end con_int_Sv=StDev_Sv.*1.96./(No_frequencies.^0.5); con_int_Win=StDev_Win.*1.96./(No_frequencies.^0.5);  243  %Generate sampled frequencies frequencies=zeros(No_frequencies, No_bands); frequencies(1, :)=[1414.21, 1781.8, 2244.92, 2828.43, 3563.59, 4489.85, 5656.85, 7127.19, 8979.7]; for i=1:No_bands for s=2:No_frequencies frequencies(s, i)=frequencies(1, i)+(frequencies(1, i)*2^(1/3)frequencies(1, i))... /(No_frequencies-1)*(s-1); end end % Third octaves for TL_Sv for i=1:No_bands temp = 0; %Loop through each data point in the band, multiplying eachpoint by a %weighting factor and summing for s=1:No_frequencies temp = temp+log10(((frequencies(s, i)+(frequencies(2, i)frequencies(1, i)))/frequencies(s, i)))*tau_Sv(s, i); end %divide through by the frequency range tao_Sv_third(1, i)=temp/(log10(frequencies(end, i)/frequencies(1, i))); TL_Sv_third(1, i)=-10*log10(tao_Sv_third(1, i)); end % Third octaves for TL_Win for i=1:No_bands temp = 0; %Loop through each data point in the band, multiplying eachpoint by a %weighting factor and summing for s=1:No_frequencies temp = temp+log10(((frequencies(s, i)+(frequencies(2, i)frequencies(1, i)))/frequencies(s, i)))*tau_Win(s, i); end %divide through by the frequency range tao_Win_third(1, i)=temp/(log10(frequencies(end, i)/frequencies(1, i))); TL_Win_third(1, i)=-10*log10(tao_Win_third(1, i)); end  Appendix C: Numerical Prediction Appendices Figures are provided here for the predicted acoustic transmission loss of all CT silencers, as well as the airflow velocity and pressure field for all CT silencers at high-Re.  244  Predicted CT Silencer Transmission Loss 25 0.3 m Straight 0.3 m L 0.3 m Z  Transmission Loss [dB]  20  15  10 5  0  -5  -10  125  250  500  1000 2000 Frequency [Hz]  4000  8000  Figure 140: Predicted transmission loss of 0.3 m CT silencers. 95% confidence intervals shown.  40 0.5 m 0.5 m 0.5 m 0.5 m  35 30 Transmission Loss [dB]  C.1  25  Straight L U Z  20 15 10 5 0 -5 -10  125  250  500  1000 2000 Frequency [Hz]  4000  8000  Figure 141: Predicted transmission loss of 0.5 m CT silencers. 95% confidence intervals shown.  245  90 80  1m 1m 1m 1m  Transmission Loss [dB]  70 60  Straight L U Z  50 40 30 20 10 0 -10 -20  125  250  500  1000 2000 Frequency [Hz]  4000  8000  Figure 142: Predicted transmission loss of 1 m CT silencers. 95% confidence intervals shown.  C.2  Velocity- and Pressure-Field Figures for CT Silencers at High-Re  Figure 143: Predicted flow velocity in 0.05 m Straight CT silencer – Re = 22,000.  Figure 144: Predicted flow velocity in 0.3 m Straight CT silencer – Re = 25,000.  246  Figure 145: Predicted flow velocity in 0.5 m Straight CT silencer – Re = 25,000.  Figure 146: Predicted flow velocity in 1 m Straight CT silencer – Re = 27,000.  Figure 147: Predicted flow pressure in 0.05 m Straight CT silencer – Re = 22,000.  Figure 148: Predicted flow pressure in 0.3 m Straight CT silencer – Re = 25,000.  247  Figure 149: Predicted flow pressure in 0.5 m Straight CT silencer – Re = 25,000.  Figure 150: Predicted flow pressure in 0.5 m Straight CT silencer – Re = 27,000.  248  Figure 151: Predicted flow velocity in 0.3 m L-shaped CT silencer – Re = 15,000.  Figure 152: Predicted flow velocity in 0.5 m L-shaped CT silencer – Re = 15,000.  Figure 153: Predicted flow velocity in 1 m Lshaped CT silencer – Re = 18,000.  249  Figure 154: Predicted flow pressure in 0.3 m L-shaped CT silencer – Re = 15,000.  Figure 155: Predicted flow pressure in 0.5 m L-shaped CT silencer – Re = 15,000.  Figure 156: Predicted flow pressure in 1 m L-shaped CT silencer – Re = 18,000.  250  Figure 157: Predicted flow velocity in 0.5 m U-shaped CT silencer – Re = 20,000.  Figure 158: Predicted flow velocity in 1 m U-shaped CT silencer – Re = 21,000.  251  Figure 159: Predicted flow pressure in 0.5 m U-shaped CT silencer – Re = 20,000.  Figure 160: Predicted flow pressure in 1 m U-shaped CT silencer – Re = 21,000.  252  Figure 161: Predicted flow velocity in 0.3 m Z-shaped CT silencer – Re = 15,000.  Figure 162: Predicted flow velocity in 0.5 m Z-shaped CT silencer – Re = 12,000.  Figure 163: Predicted flow velocity in 1 m Zshaped CT silencer – Re = 14,000.  253  Figure 164: Predicted flow pressure in 0.3 m Z-shaped CT silencer – Re = 15,000.  Figure 165: Predicted flow pressure in 0.5 m Z-shaped CT silencer – Re = 12,000.  Figure 166: Predicted flow velocity in 1 m Zshaped CT silencer – Re = 14,000.  254  

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