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Physical flow modelling of a kraft recovery boiler Ketler, Stephen Paul 1993

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PHYSICAL FLOW MODELLING OF A KRAFT RECOVERY BOILER  by STEPHEN PAUL KETLER B.A.Sc., The University of British Columbia, 1988  A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF APPLIED SCIENCE in THE FACULTY OF GRADUATE STUDIES Department of Mechanical Engineering  We accept this thesis as conforming to the required standard  THE UNIVERSITY OF BRITISH COLUMBIA November 1993  © Stephen Paul Ketler, 1993  ________  In presenting this thesis in  partial fulfilment of the requirements for an advanced degree at the University of British Columbia, I agree that the Library shall make it freely available for reference and study. I further agree that permission for extensive copying of this thesis for scholarly purposes may be granted by the head of my department or by his or her representatives. It is understood that copying or publication of this thesis for financial gain shall not be allowed without my written permission.  (Signature)  Department of Mechanical Engineering The University of British Columbia Vancouver, Canada  Date December 15, 1993  DE-6 (2/88)  11  ABSTRACT Measurements of the vertical, and one horizontal, components of velocity have been made in an isothermal scale model of a kraft black liquor recovery boiler. The model used water as the working fluid, and was a 1:28 scale representation of an operating recovery boiler in Plymouth, North Carolina. All of the air ports were represented in the model; however, the char bed shape, mass flow from the bed, and liquor flow were not. Laser-Doppler velocimetry was used to measure velocities and power spectral densities in the model on a 6x6 grid of points on three horizontal planes. Quantitative flow visualization was performed using laser sheet illumination of particles in the flow, with subsequent analysis of the particle images. Flow conditions simulating industrial arrangements and special configurations were run in the model. Industrial configurations employed flows from primary, starting burner, secondary, and either concentric load-burner or interlaced tertiary ports. Special configurations using only primary and secondary port flows were tested to investigate the sensitivity of the flowfield to variations in the lower furnace port flows. Orifice-plate flowmeters and valves were used to set the flowrates through manifolds connected to groups of ports. The error between the set and actual model total flowrate was shown to be dependent on the choice of flowmeters, and on the drift of valve settings with time. Considering both sources of error, for a typical model flowrate of 150 US gallons per minute, the expected difference between the set and actual total flowrate was —6.5 percent. Differences between the set mass flows, and the values calculated from the vertical velocities measured by the laser Doppler velocimeter, were less than ten percent on average. Larger variances between measured and predicted mass flows were explained on the basis of observed low frequency oscillations. Computer software was created for the computation of velocity power spectral densities using the output of the laser-Doppler velocimeter. A system of digital particle image velocimetry was also created for quantitative two-dimensional flow visualization. Laser light was spread into a planar sheet, and the motion of small polystyrene particles added to the flow was recorded on videotape at 30 frames per second. The information on the videotape was digitized, and cross-correlation analysis  111  of successive image pairs yielded a grid of velocity vectors for each 1/30 second interval which could be animated. It was found that the flow in the model was extremely sensitive to any asymmetries in the secondary level port flows. An increase in secondary flow velocity of 10% on one wall, and a corresponding decrease on the opposite wall, caused the core region of vertical upflow at the liquor gun level to occupy half of the model cross section near the wali with the lower velocity. It was very difficult to balance the flows accurately enough to have the core region of vertical upflow in the model centre. In the upper regions of the furnace, the majority of the upflow was near the walls, with down or stagnant flow in the model centre. The flow exhibited low frequency unsteadiness in addition to a high level of turbulence throughout. Periods on an order of 10-20 seconds were observed in the velocity power spectral densities, and in the particle image velocimetry results. The use of concentric load-burner port flows on the tertiary level, as opposed to a 2x2 interlaced arrangement of high velocity tertiary ports, was found to provide a somewhat more uniform distribution of turbulence kinetic energy in the upper furnace. Implications for design and operation of industrial recovery boilers are discussed.  iv  TABLE OF CONTENTS  ABSTRACT  ii  TABLE OF CONTENTS  iv  LIST OF TABLES  vi  LIST OF FIGURES  vii  LIST OF SYMBOLS  ix  ACKNOWLEDGMENTS  xii  INTRODUCTION  1  1. MODELLING OF KRAFT RECOVERY BOILER FLOW FIELDS 1.1 Review of Methods 1.2 Non-Dimensional Parameters for Isothermal Modelling 1.2.1 Velocities 1.2.2 Frequencies  3 3  5 5 7  2. APPARATUS 2.1 Plymouth Recovery Boiler Model 2.2 Water Flow Systems 2.3 Argon-Ion Laser 2.4 Laser-Doppler Velocimeter 2.5 Particle Image Velocimetry  8 8 13 13 14 18  3. EXPERIMENTAL PROCEDURES 3.1 Water Flow System Calibration 3.1.1 Meter Error 3.1.2 Drift Error 3.1.3 Error Calculation for Typical Experimental Run 3.2 Laser Doppler Velocimetry 3.2.1 Experimental Arrangements 3.3 Laser Sheet Illumination 3.3.1 Experimental Arrangements 3.3.2 Recording Methods 3.4 Particle Tracking Accuracy  19 19 21 24 26 29 29 32 32 33 33  4. ANALYSIS METHODS 4.1 Laser Doppler Velocimetry 4.1.1 Velocities 4.1.2 Turbulence Kinetic Energy 4.2 Power Spectral Density 4.2.1 Direct Transform Method 4.2.2 Computational Implementation  35 35 35 36 37 37 39  V  4.2.3 Validation Simulated Data Fan Blade Experiment 4.3 Particle Image Velocimetry 4.3.1 Review of Techniques 4.3.2 Digital Particle Image Velocimetry 4.3.3 Computational Implementation 4.3.4 Temporal Smoothing 4.3.5 Animation 4.3.6 Validation  .39 39 39 41 41 43 43 46 46 46  5. RESULTS 5.1 Laser Doppler Velocimetry 5.1.1 EarlyRuns 5.1.2 Load Burner Port Flow Case 5.1.3 Tertiary Port Flow Case 5.1.4 Balanced Primary and Secondary Port Flow Case 5.1.5 Balanced Primaries; Biased Secondaries Port Flow Case 5.2 Power Spectral Densities 5.3 Particle Image Velocimetry 5.3.1 Builnose Side View 5.3.2 Lower Boiler Side View  50 50 54 58 62 66 70 79 82 82 85  6. DISCUSSION OF RESULTS 6.1 Velocities 6.1.1 Air System Objectives 6.1.2 Velocity Effects in Full-Scale Furnaces 6.1.3 Upper Furnace Flow Configurations 6.2 Transient Behaviour 6.2.1 Data Qualification 6.2.2 Turbulence 6.2.3 Mixing 6.3 Experimental Limitations 6.3.1 Physical Variation 6.3.2 Input Information 6.3.3 Two-Phase Flow 6.3.4 Buoyancy Force Effects  87 87 87 88 89 90 90 93 94 95 95 96 97 97  7. CONCLUSIONS AND RECOMMENDATIONS  99  REFERENCES  101  APPENDIX A ORIFICE-PLATE CALIBRATION STATISTICS  104  APPENDIX B POWER SPECTRAL DENSITY CALCULATIONS  110  APPENDIX C SUMMARY OF COMPUTER PROGRAMS DEVELOPED  116  vi  LIST OF TABLES  Table 1.2.1  Typical Port Velocities in Plymouth Recovery Boiler Model  Table 2.1.1  Plymouth Recovery Boiler Model Ports  11  Table 2.1.2  Plymouth Recovery Boiler Feature Locations  12  Table 2.2.1  Water Flow System Apparatus  13  Table 2.3.1  Argon-Ion Laser Apparatus  14  Table 2.4.1  Laser-Doppler Velocimeter Apparatus  15  Table 2.4.2  Measurement Volume Parameters  16  Table 2.5.1  Particle Image Velocimetry Apparatus  18  Table 3.1.1  Example Flow Condition  20  6  Table Orifice-Plate Meter Error B9  23  Table Orifice-Plate Meter Error D7  23  Table Orifice-Plate Drift Error B9 (3.5 US gpm Set)  25  Table Orifice-Plate Drift Error D7 (2.5 US gpm Set)  26  Table Meter Errors for Typical Run No Drift  26  Table Meter Errors for Typical Run After Drift  27  Table Summary of Flowrates for Typical Run (150 US gpm)  28  Table 5.1.1  Plymouth Model Laser-Doppler Velocimetry Conditions  50  Table 5.1.2  Plymouth Model Laser-Doppler Velocimetry Results  52  Table 5.1.3  Measured Flowrate Errors  53  Table 5.1.4  Mean Non-Dimensionalized Vertical Velocities  55  -  -  -  -  -  -  vii  LIST OF FIGURES  Figure 2.1.1  Recovery Boiler Water Model Experimental Facility  Figure 2.1.2  Plymouth Recovery Boiler Arrangement  10  Figure 2.1.3  Plymouth Recovery Boiler Ports  12  Figure 2.4.1  Beam Focal Point Location  16  Figure  Measured versus Set Flowrates B9 Orifice—Plates  21  Figure  Measured versus Set Flowrates D7 Orifice-Plates  22  Figure  Flowmeter Reading versus Time B9 Orifice-Plates  24  Figure  Flowmeter Reading versus Time D7 Orifice-Plates  25  Figure  Laser Doppler Velocimetry Experimental Arrangement  29  Figure  Tertiary Port Arrangement  31  Figure  Particle Image Velocimetry Experimental Arrangement  32  9  -  -  -  -  Figure Power Spectral Density versus Frequency Fan Experiment  40  Figure  Digital Particle Image Velocimetry Analysis Procedure  44  Figure  Simulated Vortex Flow Images  47  Figure  Results of Cross-Correlation Analysis for Simulated Data  48  Figure  Velocity Error for Simulated Data  49  Figure  Two Components of Mean and RMS Velocities Run 3  56  Figure  Two Components of Mean and RMS Velocities Run 4  57  Figure  Two Components of Mean and RMS Velocities Run 21  59  Figure  Contours of Non-dimensionalized Vertical Velocity Run 21  60  Figure  Contours of Non-dimensionalized K½ Run 21  61  Figure  Two Components of Mean and RMS Velocities Run 26  63  Figure  Contours of Non-dimensionalized Vertical Velocity Run 26  64  Figure  Contours of Non-dimensionalized K½ Run 26  65  Figure  Two Components of Mean and RMS Velocities Run 25  -  -  -  -  -  -  -  -  -  -  67  viii  Figure  Contours of Non-dimensionalized Vertical Velocity Run 25  68  Figure  Contours of Non-dimensionalized K½ Run 25  69  Figure  Two Components of Mean and RMS Velocities Run 23  71  Figure  Contours of Non-dimensionalized Vertical Velocity Run 23  72  Figure  Contours of Non-dimensionalized K½ Run 23  73  Figure  Flow Schematic Front View Run 23  74  Figure  Two Components of Mean and RMS Velocities Run 24  76  Figure  Contours of Non-dimensionalized Vertical Velocity Run 24  77  Figure  Contours of Non-dimensionalized K½ Run 24  78  Figure 5.2.1  Velocity Trace Run 25, Level 1, u Component  80  Figure 5.2.2  Velocity Trace Run 25, Level 1, w Component  80  Figure 5.2.3  Power Spectral Density Run 25, Level 1, a Component  81  Figure 5.2.4  Power Spectral Density Run 25, Level 1, w Component  81  Figure  Builnose Side View 30 Second Average  83  Figure  Bulinose Side View Consecutive 5 Second Averages  84  Figure  Lower Boiler Side View 30 Second Average  85  Figure  Lower Boiler Side View Consecutive 5 Second Averages  86  Figure  Sequence of Mean Square Measurements, Level 1, w Component  92  Figure  Extended Power Spectral Density, Run 25, Level 1, w Component  93  -  -  -  -  -  -  -  -  -  -  -  -  -  ix  LIST OF SYMBOLS A  area, or amplitude  C  degrees Celsius  d  horizontal distance, or particle diameter  de-2  Gaussian beam width focal length in air  4  fringe spacing  dm  measurement volume diameter  D  smoothing window function  E  expectation operator  f  frequency  Fr  Froude number  g  gray-scale function, or acceleration due to gravity  h  vertical distance  hf  ½ beam separation distance  k  wavenumber  K  turbulence kinetic energy  L  length measurement volume length  m  metre  n  index of refraction, or general integer  N  number of samples  fr  maximum number of fringes  q  flowrate rate of heat transfer per unit mass  r  radius  R  correlation coefficient  x Re  Reynolds number  s  second  s  vector displacement  S  power spectral density  S,  sample standard deviation of quantity x  St  Strouhal number  t  time  T  general dependent variable, or record duration  At  residence time of particle in LDV measurement volume  u  instantaneous velocity in x, or general, direction  U  mean velocity in x, or general, direction  u’  fluctuating component of velocity in x, or general, direction  Au  velocity difference between particles and fluid  v  instantaneous velocity in y direction  V  mean velocity in y direction fluctuating component of velocity in y direction  w  instantaneous velocity in z direction  W  mean velocity in z direction  w’  fluctuating component of velocity in z direction  x  random variable  x  vector coordinates  z  standard normal random variable  z  standard normal quantile of order a  a  significance level, probability of type I error weighting value  6  error  •  phase angle  y  coefficient of dispersion  xi K  half angle between laser beams of same frequency  A  wavelength, or shape parameter location parameter  p  density  Ap  density difference between particles and fluid standard deviation, or scale parameter  O  general independent variable  V  kinematic viscosity, or mean sampling rate angular velocity, or frequency  XII  ACKNOWLEDGMENTS I would like to thank Dr. I.S. Gartshore for his encouragement and advice throughout the course of this research. The assistance of Mr. Michael Savage with the construction of the water model facility, and in performing countless hours of experimental runs, was greatly appreciated. Gerry Rohling developed image digitization software crucial to the particle image velocimetry technique developed in this work. Financial assistance was provided to myself by the Natural Sciences and Engineering Research Council and the British Columbia Science Council. Financial assistance and equipment were provided to this project by the Weyerhaeuser Paper Company, the Natural Sciences and Engineering Research Council, Energy Mines and Resources, the United States Department of Energy, and H.A. Simons through the GREAT program. Finally, I would like to acknowledge the contribution of Dr.  J. Peter Gorog to the genesis of  recovery boiler physical modelling at the University of British Columbia.  1 INTRODUCTION An integral process in the manufacture of kraft pulp involves recovery of the inorganic chemicals used during pulping in the digester. Pulp mills use a complex system called a black liquor kraft recovery boiler for this chemical recovery, and for additional power generation. The black liquor is a liquid containing the cooking chemkals along with the lignin from the wood, which has been concentrated to approximately 70% solids prior to firing. The capital cost of such a boiler is on the order of 100 million dollars. A typical recovery boiler will process approximately 1-3 million kilograms of dry liquor solids per day. Any improvement in the combustion rate, reduction efficiency, and reduction in fouling or shutdown times of such a boiler would provide a substantial economic benefit to the industry. Such economic arguments form the rationak for the present experimental investigations into the fluid mechanics of recovery boilers since these units are very complex and difficult to model analytically or computationally. Such experiments also provide data for validation of computational methods currently under development. A kraft recovery boiler is a tube-wall cavity typically 10 metres square by 40 metres high. Black liquor is fired into the boiler though liquor guns placed on either two or all four walls, approximately 10 metres above the boiler floor. These guns use either a conical spray nozzle or a splash plate design. Combustion air is provided through various combinations of ports on the boiler walls both below and above the liquor gun level. The lowest level of air, typically referred to as primary, uses many small ports of low velocity on all four walls, and controls and shapes the bed of smelt and char which forms on the boiler floor. The secondary level consists of fewer, higher velocity ports on all four walls, just above the primaries. Secondary air limits the height of the bed, and is used to burn gases coming off of the bed. Tertiary level ports are placed above the liquor guns, either on two or four walls. They are the largest ports in the boiler, and may be configured to provide an interlaced, directly opposed, or tangentially oriented flow pattern. The tertiary ports provide the excess air used to complete the combustion and mixing of the gases. Spouts placed on the rear wall of the boiler near the base allow molten smelt to flow out of the boiler to be causticized  2 and re-used in the pulping process. The floor of the boiler may either be flat, or sloped down towards the smelt spouts. Mass flow ratios between the three levels of combustion air vary according to boiler manufacturer, owner, and operator preferences and objectives. A typical arrangement might have a split between primaries,, secondaries, and tertiaries of 30, 45, and 25 percent respectively. Combustion air is usually heated to approximately 150°C prior to introduction into the boiler. Temperatures in the boiler centre can reach 1100°C, and the flow is full of entrained smelt, fume, and particulate, creating an extremely inhospitable environment for velocity measurements. The Weyerhaeuser Technical Center (WTC) in Tacoma, Washington originally constructed a Plexiglas water model of a company boiler located in Plymouth, North Carolina. After the termination of their experimental program with the model, it was donated, along with associated plumbing hardware, to the University of British Columbia (UBC). Subsequently, a water model of the Weyerhaeuser boiler in Kamloops, British Columbia, was also constructed by WTC and donated to UBC. An argon-ion laser and laser-Doppler velocimetry system were acquired, and installed along with the models into a new experimental laboratory located at the UBC Pulp and Paper Centre. The objectives of this research are to develop experimental methods for quantitative velocity measurement in water models, and to apply these methods in investigating the flow patterns in the Plymouth recovery boiler model.  3 1.  MODELLING OF KRAFT RECOVERY BOILER FLOW FIELDS 1.1  Review of Methods Modelling of physical phenomena may be undertaken using one or more of three  approaches: analytical, computational, or experimental. Due to the complexity of the flow in a kraft recovery boiler, analytical solutions of the complete or simplified Navier-Stokes equations of fluid flow are not possible. Computation of the flow inside such a boiler may be attempted, providing certain assumptions are made in order to model the turbulent properties of the flow. This work does not concern itself with computational flow simulations, although the results found here may be used for validation of computational algorithms. Experimental studies of boiler flows may be conducted either on real boilers or on some form of scale model. Flow studies are extremely difficult to conduct on operating boilers firing black liquor. The inhospitable thermal environment of up to 1100°C, the fume and char present in the flow, and the necessity of co-existing with operational requirements such as soot-blowing, make the taking of flow-field measurements extremely difficult. Some qualitative studies of flow patterns using infra-red cameras tracking char particles, or added materials such as coke, have been attempted. Some researchers are attempting to develop velocity probes which will tolerate the thermal environment of a recovery boiler, but none are past the prototype stage. The use of acoustic Doppler techniques has been attempted by some researchers, but this has been applied to mapping the thermal field rather than the more difficult task of velocity field estimation in the presence of such thermal gradients. Measurements may be made in a full-scale recovery boiler which is operating isothermally without combustion. ‘While such measurements neglect the effects of buoyancy, liquor and smelt flow, and the gas flow off of the bed, they can provide insight into flow patterns and characteristics. Such studies are typically conducted using hot-wire or hot-film velocity probes which are cantilevered into the furnace cavity through maintenance or liquor-gun openings. These  4 investigations are hampered by the lack of conclusive velocity direction information, and the lowfrequency sampling rates usually employed, and so provide results of limited use (Blackwell 1992). A full-scale boiler is usually only available for isothermal flow studies a few days a year during shutdowns, and the effort required to conduct even a minor velocity study in such a facility is significant in terms of both personnel and expense. It would be advantageous to conduct isothermal studies of the velocity flow field inside a small-scale representation of a kraft recovery boiler. Such experimental studies have been conducted in the past using a model with air as the working fluid, and a five-hole pitot tube or hot-wire anemometer for velocity measurements (Chapman and Jones 1990, Jones, Grace, and Monacelli 1989). Due to the expected high turbulence level of the flow, a non-intrusive measurement technique capable of recording the instantaneous velocity direction and magnitude in multiple components would be preferable. Multihole pitot-static tubes cannot resolve highly turbulent flows, are disruptive to the flow, and have low temporal resolution (Pankhurst and Holder 1968). Measurement devices such as the pulsed hot-wire anemometer (Lomas 1986) are capable of distinguishing instantaneous velocity vectors, but are still disruptive to a highly turbulent flow of this nature and are rather fragile. A method capable of accurate measurement of unsteady velocities, while not physically altering the flow, is the laser-Doppler velocimeter (LDV) (Fingerson et al. 1991). The LDV is able to simultaneously measure multiple components of velocity at a single point, with both high temporal and spatial resolutions. The technique requires that light be scattered from small particles which accurately follow the flow. ‘While an air model is economical in terms of construction and operation, it is not conducive to accurate flow visualization or LDV measurements in turbulent flow, due to the difficulty in generating small particles with a specific gravity very close to that of the fluid. For this reason the working fluid in the model was chosen to be water, as opposed to air. The use of a water analog to simulate a gaseous internal flow has been shown to be a valid representation for a wide range of applications (Sacher 1987).  5  1.2  Non-Dimensional Parameters for Isothermal Modelling The use of a scale model of a boiler for experiments requires that the parameters measured in  the model may be scaled, via some method, to equivalent values in the full-scale boiler. The parameters considered here will be velocity and frequency. 1.2.1  Velocities  For experimental modelling of fluid flows, a customary dimensionless parameter used is the Reynolds number UL Re=— V  -  (  -  which is a measure of the ratio of inertial to viscous forces. At high enough Reynolds number, provided wall shear is not an important parameter, the large scale motions become independent of viscosity, and therefore of Reynolds number. There is no possibility of equating the Reynolds number of a small water model to that of an operating furnace: the model will have a Reynolds number, defined in any convenient way, at least an order of magnitude smaller than that of an actual furnace. However, provided that both flows are fully turbulent, and viscous effects at walls are not important, the Reynolds number should not be a significant parameter, and the velocity at which the model is run can be set for the convenience of the test apparatus and not to satisfy any similarity requirement. Jets become turbulent at quite iow Reynolds numbers so there is no concern over the initial state of the jets entering the cavity of the model. Round, simple turbulent jets have an effective turbulent viscosity which decreases in the streamwise direction so that the ratio of effective to molecular viscosity decreases along the length of the jet, and reverse transition to laminar flow will ultimately occur. For a jet in a surrounding stream which is itself turbulent, the point at which molecular viscosity, and hence Reynolds number, becomes important, is difficult to estimate. At  6  some point in the boiler flow near the outlet, the flow may re-laminarize, but there have been no indications in this experimental study that the flow is anything but turbulent for locations at or below the builnose. Tests were completed with identical flow percentages between port levels, but different Reynolds numbers. Results of the test, which will be discussed in §5.1.1, showed comparable non-dimensional velocities, within experimental accuracy, for the two Reynolds numbers. In the actual furnace, the combustion air enters at a temperature of approximately 15OC, while the temperature in the furnace is about 1OOOC. The density change which the combustion air in the full-scale furnace undergoes cannot be simulated in an isothermal water model. The model ports in the Plymouth model are scaled using the same size ratio as the boiler itselE With subscripts “p” and  1 “v’  denoting port flow and vertical cross-flow respectively, if the mass flux ratio between  vertical and port flow is maintained between the full-scale and model, the ratio of velocities between model and full-scale is: (UI’  i .  i vJ full-scale  p) full-scale  v  model  Because this relationship uses ratios rather than absolute velocities, at least one velocity in the  full-scale boiler must be known before the model results may be scaled. For a typical experimental run in the model, the expected bulk vertical velocity is approximately 5 cm/s. Typical port velocities in the experimental model are shown in Table 1.2.1. Table 1.2.1 Typical Port Velocities in Plymouth Recovery Boiler Model Port Name Typical Velocity [mis] Primary 2.2 Starting Burner 0.8 Secondary 3.4 Tertiary 6.8 Load Burner 2.0  7  This scaling arrangement used does not permit the ratio of momentum between port and vertical flows to be preserved between model and full-scale. When momentum flux is preserved by appropriate enlargement of the ports, jet trajectories should scale between model and full-scale. Experiments have been successfully conducted using such scaling criteria (Perchanok, Bruce, and Gartshore 1991); however, the present geometric port scaling arrangement was a legacy from the construction of the Plymouth model and could not be changed. 1.2.2  Frequencies  The velocity frequencies observed in the model may also be translated to full-scale equivalents. The non-dimensional frequency may be defined as the Strouhal number fL (  Preserving this non-dimensional number between model and full-scale 1JfulIscaJe  .ñ,ll-scale Jmodel  =  11  “model  Lmodel  (  r Lfullsca1e  Equations and may be combined to form .ñxll-sc l 2 e model  Lmodel ull-scale  1 (UfUllSCe”  model }p  1’”1 pvJ  full-scale  For a typical total flowrate in the Plymouth boiler model of 150 Us gallons per minute, assuming flu-scale boiler air temperatures of 1000°C and 150°C for interior and port flows respectively, fullscale total air flow of 1012 pounds per hour, and secondary port velocities, this ratio may be estimated as hsi 1 scaie  odel  (68.2(0.837 i28)3.4 )1\O.277,) 2.16 (1  (  8 APPARATUS  2.  2.1  Plymouth Recovery Boiler Model An experimental flow facility has been constructed at the UBC Pulp and Paper Centre in  which water models of kraft recovery boilers may be tested. Up to two models may be tested in the facility at a given time. The focus of the present experimental study is a 1:28 scale model of a boiler located in Plymouth, North Carolina, originally commissioned by Combustion Engineering (flow Asea Brown Boveri). The second model is of a recovery boiler in Kamloops, British Columbia which will not be considered here. A centrifugal pump draws water from a 5600 litre reservoir, sending it vertically into three header pipes feeding the primary, secondary, and load-burner or tertiary model ports respectively. Gross flow control is achieved by adjusting four gate valves which control the bypass line and the flow into each of the three headers. A total of 59 lines of 1.6 cm diameter flexible hose each transport water from the header pipes through a valve and an orifice-plate flowmeter. The hoses then lead to manifolds feeding between four and nine ports each, with the exception of the load burner ports which are connected direcdy to the headers. To set a given flow condition, a portable differential pressure meter is ‘attached to each orifice-plate in turn and the corresponding valve adjusted to achieve the desired flowrates. A plan view of the experimental facility is shown in Figure 2.1.1.  9  Figure 2.1.1 Recovery Boiler Water Model Experimental Facility The arrangement of the Plymouth recovery boiler model is shown in Figure 2.1.2, which is drawn to scale. The full-scale boiler is approximately 43 metres high, has a square cross-section of 11 metres per side, and employs one liquor gun at the centre of each wall. The model is constructed of 4.8 mm thick Plexiglas, and all ports present in the full-scale boiler are modelled. The floor of the model is flat, as in the full-scale furnace. Liquor flow into, and smelt flow out of, the boiler are not modelled. It is assumed that the mass flux of each is approximately equal, and any influence of the liquor droplets or their combustion products on the flow patterns or velocities is neglected. A representation of the char bed is not included in the model. The three horizontal levels shown designate the planes on which laser velocimetry measurements are made.  10  Figure 2.1.2 Plymouth Recovery Boiler Arrangement The arrangement of the Plymouth recovery boiler model is shown in Figure 2.1.2, which is drawn to scale. The full—scale boiler is approximately 43 metres high, has a square cross-section of 11 metres per side, and employs one liquor gun at the centre of each wall. The model is constructed of 4.8 mm thick Plexiglas, and all ports present in the full-scale boiler are modelled. The floor of the model is flat, as in the full-scale furnace. Liquor flow into, and smelt flow out of, the boiler are not modelled. It is assumed that the mass flux of each is approximately equal, and any influence of the liquor droplets or their combustion products on the flow patterns or velocities is neglected. A  11 representation of the smelt bed is not included in the model. The three horizontal levels shown designate the planes on which laser velocimetry measurements are made. A total of four starting burners are located at the corners of the front and rear faces at the primary air port level, angled in a horizontal plane towards the centre at 25° from the perpendicular. Primary air ports on all four walls are angled down  100  from the horizontal while secondary air ports  on all four walls are directed straight into the boiler. The third level of flow may use one of two port sets: load-burner (sometimes referred to as high-secondary) air ports which are directed along the tangent of an imaginary horizontal circle located above the liquor gun level, or directly opposed tertiary air ports on the front and rear walls. The model ports are summarized in Table 2.1.1, and illustrated in Figure 2.1.3. The model primary ports were constructed larger than required for the overall scale, so two strips of 1/32” stainless steel was bolted to the inner wall of the model, symmetrically above and below the primary ports. The plates were separated by a vertical gap of 0.23” inch, changing the primary port shape to a rectangle, and maintaining the proper scale. Table 2.1.1 Plymouth Recovery Boiler Model Ports Port Name Number Area (in2) Comments 144* Primary 156 0.0 Vertical rectangle angled down 10° Starting Burner 4 0.066 1 Vertical oval angled to centre at 25° Secondary 66 0.0262 Vertical oval Tertiary 28 0.0262 Vertical oval Load Burner 10 0.3526 Circular * After accounting for adjustable plate opening -  12 •O.O78 ± O.005  CR5  LOAD BURNER PORTS  SECONDARY & TERTIARY PORTS  H  25  (TYP) ± O.OO5 CR5  .—l  ± O.005  CR5  0 SIDE VIEW  FRONT VIEW  PRIMARY PORTS  PLAN VIEW  FRONT VIEW  STARTING BURNER PORtS  Figure 2.1.3 Plymouth Recovery Boiler Ports Heights above the boiler floor of the measurement levels, port centres, and liquor guns are shown in Table 2.1.2 for both model and flu-scale. Table 2.1.2 Plymouth Recovery Boiler Feature Elevations Height Above Boiler Floor [ml Feature Model Full-Scale Primaries 0.042 1.19 Starting Burners 0.051 1.43 Secondaries 0.108 3.02 Liquor Guns 0.242 6.78 Tertiaries 0.316 8.86 Load Burners* 0.383 10.72 Level 1 0.256 7.16 Level 2 0.546 15.29 Level 3 0.705 19.74 * -  N.B. Top load-burner; for each lower port subtract O.0295m (model scale)  13 2.2  Water Flow Systems Equipment necessary for running, and measuring the flowrates into, the model flow system  are summarized in Table 2.2.1. The measurement range of the D7 orifice-pLate is from 1.0 to 7.5 US gallons per minute, while the B9 models are capable of measuring from 2.0 to 12.5 US gallons  per minute.  Quant. 1 1 22 23 1  2.3  Name Motor Pump Orifice-Plate Orifice-Plate Meter  Table 2.2.1 Water Flow System Apparatus Description Manufacturer kW AC Electric Motor 30 U.S. Electrical Motors Centrifugal Pump Bingham Orifice-plate flowmeter Gerand Orifice-plate flowmeter Gerand Differential pressure meter Gerand calibrated for B9 and D7 orifice-plates  Model RC-1  D7 B9 M- 125  Argon-Ion Laser The apparatus used in the operation of the argon-ion laser, either for laser-Doppler or  particle image velocimetry measurements, is detailed in Table 2.3.1 The laser is configured for multiline operation, and is rated for five watts total output, but has typically produced up to 6.8 watts. With the laser at full power, the three wavelengths available for LDV use are respectively rated at: 476.5 nm  -  0.60 W, 488.0 nm  mm with a divergence of 0.5 mrad.  -  1.5 W, 514.5 nm  -  2.0 W. Beam diameter is specified as 1.5  14  Quant. 1  Name Laser  1  Power Meter  2  Mirror  2 2 2 2 1  Mirror Holder Mounting Post Post Holder Base Optical Table  1 1  Collimator Water Filter  2.4  Table 2.3.1 Argon-Ion Laser Apparatus Description Manufacturer Coherent 5-Watt Argon-Ion Continuous-Wave Laser Broadband Power/Energy Melles Griot Meter 4)25mm mirror wI Maxbrite Melles Griot coating Melles Griot 4)25mm kinematic type Melles Griot 4)12 mm, L=6Omm Melles Griot 4)12 mm, L=5Omm square, ¼-20 thds Melles Griot 2’x6½’ optical mounting Newport bench 1.1:1 Collimator TSI Inc. Envirogard Prod. 5-tim Water filter  Model Innova 70-5 1 3PEMOO 1 02-MPG007/001 07-MHT-001 07-RMH-002 07-PHS-013 07-RPC-012 CS-26-4 9108 FC-100  Laser-Doppler Velocimeter The main pieces of equipment needed for acquisition of velocity measurements using laser-  Doppler velocimetry, in addition to the laser apparatus listed in Table 2.3.1, are shown in Table 2.4.1. The LDV is capable of measuring two components of velocity simultaneously, and is capable of being expanded to measure three components with the addition of a second probe. The beam from the laser enters the Colorburst and is split into two laser lines of 514.5 and 488.0 nm. Each line is split again, and one is shifted by a user-selected frequency. The four beams then are directed into single-mode polarization-preserving optical fibres via appropriate fibre-optic couplers. The fibre-optic cable is connected to the portable barrel probe. This probe focuses the beams to a waist at the measurement volume, and receives light scattered by the particles passing though the measurement volume. The separation of the beams and focal length of the probe are 50 and 350 mm respectively.  15  Quant. 1 4  Name Colorburst Coupler  1  FIND  2 1 1  Processor Computer Probe  1  Colorlink  Table 2.4.1 Laser-Doppler Velocimeter Apparatus Description Manufacturer Multicolour beam separator TSI Inc. Polarization-preserving fibre TSI Inc. optic coupler Software for controlling TSI Inc. processors and Colorlink Burst-correlator processor TSI Inc. Intel 486DX compatible V-Com 2-component backscatter TSI Inc. transmitting & receiving probe Photomultiplier tubes & TSI Inc. bandpass filters  Model 9201 9271 Ver. 3.5.3 IFA 550 486-33 9832  9230  The back-scattered light received by the probe is transmitted by another fibre-optic cable to the Colorlink device. Here each laser line is separated and sent to a high voltage photomultiplier tube for amplification. The signal is bandpass filtered and the shift frequency removed, leaving the Doppler signal. The signal from each channel is sent to a separate processor unit. An autocorrelation is performed on the signal, and if 8 successive zero-crossings of the signal correlate, it is considered a true Doppler frequency. If not, no measurement is considered to have been made. The Doppler frequency, and the time between measurements points, are sent to the computer via the FIND software program. The measurement volume of a laser-Doppler velocimeter is ellipsoidal in shape, the dimensions of which may be found as (Fingerson et al 1991)  4f) dmd dm m  4 2 sinsc  (2.4.1)  (2.4.2)  (2.4.3)  d (2.4.4)  16 where d_ 2  4  =  laser beam diameter fringe spacing  dm = measurement volume diameter  f  = frequency = measurement volume length = maximum number of fringes  Ic  = half angle between laser beams of same frequency  A  = wavelength  For the two laser velocimeter components used, parameters of the measurement volume are summarized in Table 2.4.2, which assumes that the collimator is not in use. Table 2.4.2 Measurement Volume Parameters 488.0 nm dm  4 fr  514.5 nm  145.0 pm  152.9 pm  2.03mm  2.14mm  3. 3 4 pm  3.61 pm  42  42  n3  n2  ni  Id  Figure 2.4.1 Beam Focal Point Location  17 The measurement location of the focused laser beams within the water model is shown in Figure 2.4.1. Only one beam is shown; the probe is located to the right with the beam pointing towards the left. The dotted line shows where the beam would cross the probe centre-Line if measurements were made in air only. The location of the measurement volume depends on the probe focal length in air, the separation of the beams, the indices of refraction of the mediums the beams pass through, the wall thickness of the model, and the distance the probe is placed from the model outside wall. The distance the probe should be located from the model wall, as a function of the measurement volume distance inside the model may calculated by application of SnelUs law as h=€4 tan 1 IC  I  =  —  so  €4  where  4 4  1 3 K +t4tanK 2 +4tanK  —  I  2 K  tan K 2  —  3 d  -1  =  Sifl  (n  I  —  1 Sin K  )  K3  .  =  Sin  =  horizontal distance beam travels in medium i  =  probe focal length in air  =  ½ beam separation distance  =  vertical distance beam travels in medium i  =  refractive index for medium i beam half-angle in medium i  The following values apply to the apparatus used in the measurements: 1 n  —  Sin K2  (2.4.5)  tan ic  =  I  3 tafl K  =  hf  -1  =  1.00 (air)  4  =  1.50 (Plexiglas)  hf= 25 mm  =  1.33 (water)  4= 350 mm  9.525 mm (3/8”)  For example, if €4 is to be 60 mm,€4 should be made equal to 298.6 mm.  18 Particle Image Velocimetry  2.5  Velocity measurements made by particle image velocimetry require the apparatus listed in Table 2.5.1, in addition to the laser equipment shown in Table 2.3.1. The core diameter of the fibre-optic cable is 4 2O0 m , and the doped silica cladding has a diameter of 25Ojim. The glass/glass construction makes this fibre more suitable for high-power handling than plastic-clad silica fibres. At argon-ion laser wavelengths, the attenuation of the fibre is approximately 18 dB per kilometre. The microscope objectives focus the beams to a waist of size roughly equal to the transmitting fibre diameter. Using a higher magnification objective could cause the laser beam to exceed the energy density limitation of the fibre. A concave cylindrical lens was used to eliminate the hazard caused by the focal point created by a similar convex lens. The fibre-optic positioner used has only two translational degrees of freedom, limiting the practical coupling efficiency to about 40 percent. This might be improved through the addition of a tilt-stage to the positioner, adding two angular degrees of freedom.  Quant. 2 2 1 1  1 1 1 1 1 1 1 1  Table 2.5.1 Particle Image Velocimetry Apparatus Description Manufacturer Fibre-optic positioner with Newport Delrin jaws 5:1 Microscopic objective Newport for fibre-optic coupler Multi-mode enhanced Newport transmission fibre [lOm] Cylindrical Lens Piano-concave optical glass Newport with anti-reflection coating F.L. =—6 mm, L=25 mm Lens Mount Cylindrical lens mounting Newport ring 900 angle bracket Bracket Newport Video Recorder S-VHS Video Recorder Sony Digitizer Imaging Board Sharp Video Camera S-VHS Movie Camera Panasonic Tripod Heavy-duty tripod & head Hercules Optical Rail Newport lOOxSOOmm Rail Carrier Newport lOOx65mm Name Fibre-Optic Positioner Microscopic Objective Optical Fibre  Model F9 1 5T-DJ M-5X FC-2UV-10 CKVOO6AR. 14  LM-1 360-90 SVO-9500MD GPB-1 AG-455P 5302/522 1 07-ORP-003 07-OCP-003  19  EXPERIMENTAL PROCEDURES  3.  3.1  Water Flow System Calibration Early experimental results recorded in the Plymouth boiler model displayed a tendency for  the core region of vertical flow to be near the front-left corner of the boiler (Ketler, Savage, and Gartshore 1993), and will be discussed further in 5.l.1. A manifold feeding secondary ports in the rear-right corner was subsequently found to be permitting an additional 10% of the total secondary mass flow into the boiler due to a faulty orifice-plate flowmeter. This finding emphasized the sensitivity of the model to any secondary flow imbalance, and the importance of being able to set the port flowrates accurately. A statistical test of the flow errors was therefore initiated for each of the 59 orifice-plate/valve packages used in the facility. During an experimental run, flowrates are measured by connecting a portable differential pressure meter across each orifice-plate in turn. The meter measures pressure differential, but has a dial calibrated by the manufacturer which reads in US gallons per minute. The error in a port flowrate is  =fi ( where  8 m eter  or  time)  t8 oral  fi2  (  6 m eter’  6 d rift)  (3.1.1)  refers to the error between the meter reading and the true flowrate, which may be a  function of time, and  8 d rjft  measures the change in the meter reading, which may be a function of  time and the flowrate set. The expected values and variances of each error may be separately determined through experimentation and statistical analysis. Where E is the expectation operator, the variance of a function Tof k random variables var(T) i=i  If k= 2, then  or  k 0 °l••’  may be found as (Bury 1986, 159)  or  }  oE{O oE{O  }  (3.1.2)  20  ]  (aT  var(T){  2  (OT”2  + 2 var0  1 var0  oE{o}J  I or ( or 2{ 2 }JoE{o  }].  COV(o, O)  (3.1.3)  To demonstrate the effects of the two types of orifice-plate error, an example scenario is shown in Table 3.1.1. Table 3.1.1 Example Flow Condition Meter Reading [US gpm] True Flowrate [US gpmj 5.00 4.85 =  Time 0  18jftlO%  11  4.50  =  4.40  —2.22%  In this example, the flowrate is set at five gallons per minute at time 0, when the meter error is —3%. After some interval, time 1 is reached, when the drift error is —10%. However, the meter error has now changed to —2.22%. The overall error at time index 1 (1  —  .10)(1  —  .0222)  —  1  =  is therefore  —0.12. Note that the errors cannot be simply added; rather the two  sources of error compound. Therefore E{8total  }=E{emeter  If we assume that var 0 (e a l)  where  and  Emeter  8 d rjft  (i  }+E{smeter }E{c. drift }+E{8. drift  coy  meter )2  +  drifr 6  .  var  drift  j  =  }  (3.1.4)  0, from Equation 3.1.2  ()  +  (i  )2 + 8 meter  .  var (Sd f)  (3.1.5)  is taken at the meter reading to which the flow has drifted to after the specified time,  is taken at the original meter reading. The total error may increase or decrease as time  progresses following the setting of the flow. Assuming that the absolute value of the drift error increases with time, and assuming nothing about the sign of the error  21  tot 8  Lax  =  £meter  meter + EmererEdrift + 8  (3.1.6)  Ejf  where liii indicates that the maximum of the contents should be taken. 3.1.1  Meter Error  The meter error of each orifice-plate used with the Plymouth boiler model was measured in the experimental facility. The model was modified so that the model flow oudet to the reservoir was removed and replaced with a hose emptying into a closed cylindrical column which had been accurately calibrated to a capacity of 12.0 US gallons. All valves except for the bypass were fully closed, the pump was turned on, and the system was purged of air. After confirming that the flowrate into the calibrated column was zero, one valve was turned on. The differential pressure meter was attached across the orifice-plate meter connected to the opened valve. The valve was then set to a number of flowrates as measured by the meter, and the times to fill the column were recorded and converted to flowrates. Figures and show the mean values, and the means plus or minus 3 standard deviations, of the measured flowrates for each set value. 11 10  .  :z:.. z.:::z  9  E  .  8  C)  0 D  .:2  7 6  0 LL 0  a)  4  0 a)  a)  3 2  0 0  z 1  2  II  3  4  5  6  7  Set Flowrate [US gpm]  8  9  10  11  22 9 8 7  ....  E Co D  :z:zzzzz::.  6  -  E  I  4 3 2 1  EEfE  0 0  1  2  3  4  5  6  7  8  9  Set Flowrate [US gpml  Figure Measured versus Set Flowrates D7 Orifice-Plates -  A number of statistical distributions were postulated to model the data, and preliminary probability analysis revealed that the Weibull distribution would be a suitable choice. The B9 orifice-plate flowmeters were well represented by the two-parameter model, while the threeparameter model was required to adequately represent the data from the D7 flowmeters. The threeparameter model employs a location parameter which gives a lower bound to the model. This may be required due to the fact that many measurements on the D7 scale were very close to the minimum measurable flowrate of the orifice-plate. Weibull parameters were estimated using maximum likelihood equations, and are detailed in Appendix A. Expected values and standard errors (square root of the variance of the expected value) of the Weibull models, for each set flowrate, are shown in Tables and Values have been converted to percentages of the set flowrates.  23  Table Orifice-Plate Meter Error B9 Set Flow [US gpm] E{Meter Error} [%] SE(Meter Error) [%] 4.732 2.5 —4.608 4.205 3.5 —1.676 2.130 4.5 3.216 2.442 6.0 5.033 2.211 6.164 7.5 2.413 9.0 7.125 -  Table Orifice-Plate Meter Error D7 Set Flow [US gpm] E{Meter Error} [%] SE(Meter Error) 1.5 2.117 —0.962 2.0 0.404 2.048 4.881 2.5 2.072 3.0 1.814 6.076 8.972 4.5 2.147 6.0 9.613 2.273 10.435 2.096 7.5 -  [%]  Expected values and standard errors of the meter error for any set flowrate may be interpolated from the above tables. For the meter error of an entire boiler model flowrate, the expected value may be geometrically averaged. The standard error of the meter error of the entire flow may found through geometric averaging of the variances, again assuming that the covariances are zero. From the expected error values and the measured versus predicted figures, it is seen that the meter error is negative for low flowrates, and positive for higher flows. It appears that the factory calibration as shown on the meter scale is incorrect in both intercept and slope. This deviation between the manufacturer’s calibration and the data presented here may be related to the particular installation in the experimental facility.  24  3.1.2  Drift Error  The drift error was measured using the same experimental arrangement as described in §3.1.1. A flowrate typical used in a LDV run of the Plymouth model was chosen for each orificeplate type. All of the valves connected to B9 orifice-plates were set to 3.5 US gpm as read by the differential pressure meter, while those valves attached to D7 orifice-plates were set to 2.5 US gpm. This arrangement provided a uniform starting point for each flowmeter, at approximately the same percentage of the full-scale reading. However, any dependence of the drift error on the set flowrate was assumed to be insignificant. The flowrate as displayed on the differential pressure meter, for each orifice-plate, was recorded at discrete time intervals over approximately 7.5 hours, which approximated the length of an experimental run. Flowmeter readings as a functions of time for the B9 and D7 orifice-plates are shown in Figures and 5  4 E U) D  3 0  a) a) E  2  0 U-  1  0 0  60  120  180  240  300  360  420  Time Since Flowrate Set [mm.]  Figure Flowmeter Reading versus Time B9 Orifice-Plates -  480  25 4  E  3  (I)  D  D) C  a)  2  a) E LL  I  Ill,.  0. 0  llli  60  120  ll  180  Ill  l  il• trill  240  300  li• Ill  360  illl  420  480  Time Since Flowrate Set [mm.]  Figure Flowmeter Reading versus Time D7 Orifice-Plates -  Probability analysis revealed that the Weibull distribution would adequately represent the drift error. Weibull model parameters for the drift error data were estimated using maximum likelihood equations, a scale parameter again being necessary for the D7 data. Expected values and standard errors of the drift error for the B9 and D7 orifice-plates are shown as percentages in Tables and Table Orifice-Plate Drift Error B9 (3.5 US gpm Set) Time Since Set [mm] E{Drift Error) [%] SE(Drift Error) [%] 73.0 6.077 —5.538 147.5 6.566 —6.377 221.5 —6.834 6.589 299.0 —8.062 8.386 372.5 8.203 —9.528 447.5 7.711 —8.867 -  26 Table Orifice-Plate Drift Error D7 (2.5 US gpm Set) Time Since Set [mini E{Drift Error} [%] SE(Drift Error) [%J 73.0 8.900 —12.258 147.5 9.188 —14.253 221.5 9.922 —14.712 299.0 12.118 —17.511 372.5 16.604 —21.690 447.5 19.855 —24.703 -  It is seen that the drift error increases with time, and that the D7 drift errors are substantially higher than those for the B9 orifice-plates. The expected values are all negative, and increase the most shortly after the flows are set, reaching an approximately asymptotic value as time increases. The variance of the drift error increases with time, particularly for the D7 orifice-plates.  3.1.3  Error Calculation for Typical Experimental Run  To estimate the total meter flowrate error in a real experimental run, consider Table The number and type of orifice-plates set to each flowrate are shown, along with the expected value and standard errors of the flowrates assuming only meter error to be present. This corresponds to the  case immediately after setting the flows for an experimental run, before enough time has passed for any of the valves to drift from their set values.  Table Meter Errors for Typical Run No Drift Orifice Number of Set Flowrate E{Flowrate} SE(Flowrate) Type Orifices-Plates [US gpm] [US gpmj [US gpm] 6 2.73 2.628 0.1249 B9 12 3.64 3.603 0.1468 1 6.00 6.302 0.1465 4 8.62 9.216 0.2042 10 1.82 1.820 0.03764 4 D7 2.12 2.155 0.04356 4 2.65 2.790 0.05259 4 3.05 3.240 0.05582 -  27 The tabulated data corresponds to the flow condition of Run 21, which had a total flowrate set to 150 US gallons per minute, and used primary, starting burner, secondary, and load burner ports. Considering meter error only, the expected value of the total flowrate is 153.11 US gallons per minute, or 2.07%. From Equation 3.1.2, the standard error of the total flowrate is then 2.15 US gallons per minute, or 1.43%. Table Meter Errors for Typical Run After Drift Number of Set Flowrate Meter Reading E{Flowrate} Orifice-Plates after 73 mm [US gpml [US gpm] [US gpm] 6 2.73 2.469 2.58 12 3.44 3.64 3.378 1 6.00 5.67 5.927 4 8.62 8.14 8.679 10 1.82 1.60 1.590 4 1.86 2.12 1.862 4 2.413 2.33 2.65 4 2.68 2.824 3.05 -  Orifice Type  B9  D7  SE(Flowrate) [US gpm] 0.1206 0.1454 -0.1461 0.1877 0.03360 0.03838 0.04812 0.05275  The addition of drift error to the equation requires that the meter errors be calculated at the meter reading drifted to, not the value set to. Assuming that the flow was reset at least every 73 minutes, the values in Table show the resulting flowrates from meter error only, but after having drifted. Percentages are based on the meter reading at the given time. After the valves have been allowed to drift for 73 minutes, the cumulative meter readings total to 138.47 US gpm, or —7.69%, with standard error of 2.81%. The expected value and standard error of the true total flowrate are 140.29 and 2.09 US gpm respectively. This translates to expected value and standard deviation of the meter error after drift, based on the “drifted” meter readings, of 1.3 14% and 1.5 10% respectively. Using the above total meter and total drift errors along with Equation 3.1.4, the expected value of the total error is —6.48%. From Equation 3.1.5, the standard error of the combination is 3.17%. This is a larger error than the meter error alone before drift is accounted for, and should be  28 taken as an upper bound on the port flowrate error during an experimental run. Meter and drift  errors for the typical run of 150 US gpm set total flowrate are summarized in Table Table Summary of Flowrates for Typical Run (150 US gpm) Errors Expected Value Standard Error Considered [US gpm] [US gpm] [%] [%] Meter Only 153.1 1.43 2.07 2.15 Meter & Drift 140.2 4.75 3.17 —j48 Using the central limit theorem for large samples, confidence bounds my be found on the total error using the standard normal distribution z = (x  —  u)Icr where the parameters p and a are  given by Efe } and \Jvar(ç,) respectively. Considering meter error only, for a typical run of 150 0 US gpm set total flowrate, a 95% confidence interval for the expected value of the total flowrate is given by (148.9, 157.3) US gpm or (—0.9%, +4.9%) error. If both meter and drift error are considered, for a typical run of 150 US gpm set total flowrate, a 95% confidence interval for the expected value of the total flowrate is given by (130.9, 149.5) US gpm or (—12.7%, —0.3%) error.  29 3.2  Laser Doppler Velocimetry  3.2.1  Experimental Arrangements  The laser-Doppler velocimeter used for making measurements was a two-component differential beam system using a burst-correlator processor as detailed in 2.4. A continuous-wave argon-ion laser was used as the coherent light source. Vertical and horizontal velocities, including negative and near-zero velocities, may be measured simultaneously at any point within the model. The experimental arrangement is shown in Figure Argon-Ion Laser Fibre Optic Couplers  Colorlink IFA 550 #1 1FA550#2  Fibres  IBM Compatible 486 Computer Transmitting and  Recovery Boiler  Receiving Probe  Water Model  Figure Laser Doppler Velocimetry Experimental Arrangement  30  The flow was not seeded with artificial particles to enhance data rates. It was found that unfiltered tap water possessed suitable scattering particles of approximately 10-50 jim in diameter. With natural seeding, data rates of between 50 and 5000 samples per second were attained, depending on the laser power, optical efficiency, and measurement location within the model. To maintain adequate laser power at the model, it was necessary to realign the fibre-optic couplers using the laser power meter prior to, and during, every run. The software which controlled the processors did not permit selection of measurement times, but only the total number of Doppler bursts between the two processors. This required that the approximate data rate be observed at each location, and the sample size adjusted to approximate the desired record length. The measurement duration was desired to be approximately two and one-half minutes, which was chosen to obtain a suitable mean value in the presence of very low frequency oscillations in the velocity. However, as the software was written for the DOS operating system, the maximum number of data points per measurement was limited to about 30,000. In order to stay within this limit, the laser power often had to be reduced, sometimes to minimum levels, to lower the data rates. Data rates could also be modified by selecting different bandpass filters in the Colorlink processor of varying gains, but which still bracketed the expected Doppler frequencies. This procedure did not affect the actual velocities measured but only the signal to noise ratio of the Doppler signal. Simultaneous measurements were made of the instantaneous velocity components in the x and z directions, as defined in Figure 2.1.1. Mean and root-mean-square velocities were found by averaging the data over the entire length of the data record. Nominal port exit velocities were approximately 0.8 mIs for the starting burners, 2.2 m/s for the primaries, and 3.4 m/s for the secondaries. ‘When in use, nominal port velocities were 2.0 m/s for the load burners, and 6.8 m/s for the tertiaries. To permit comparison of results to those from computational fluid dynamics, all runs following Run 6 were made with the Plexiglas plates which model the screen tubes and boiler tube banks removed.  31 Two-dimensional velocity information was obtained on three different horizontal planes of 36 points each, as shown in Figure 2.1.1. Horizontal planes were divided into 6x6 grids of equal area, the centre of each being the measurement location. These levels are seen to be near the liquor guns, above the load burners, and below the builnose. It was necessary to interrogate the model from  two sides in order to obtain sufficient data rates at all points. Cleaning the model walls and tuning the optics was helpful in increasing data rates, but measuring 6 rows deep into the model from one side was never possible in the Plymouth boiler.  x000Xxx0000Xxx For those runs in which the tertiary  ports  arrangement  were shown  used, in  the  Figure was used. This grouping of ports effectively generates a 2x2 interlaced arrangement, with a slight  X O  —  —  PORT CLOSED PORT OPEN  clockwise .  swirl  viewed from above.  xx  xxooo  ox  xooox  FRONT Figure Tertiary Port Arrangement  component,  as  32 3.3  Laser Sheet Illumination  3.3.1  Experimental Arrangements  Using the same laser as for the LDV, a separate fibre-optic cable brought laser power to the boiler model to be spread into a sheet of approximately 3 mm thickness by a cylindrical lens, as shown in Figure This laser sheet was used to illuminate sections of the model to permit observation and recording of the flow patterns. For this purpose, the water was seeded with polystyrene latex spheres of approximately 300 jim diameter, and specific gravity of 1.05. The sheet could either be oriented to enter the boiler model though one of the side walls, or through the clear model bottom. The coupling efficiency between the laser itself and the output of the cylindrical lens  was approximately 40 percent, so nearly three watts of laser light could be presented to the model with this system. Recovery Boiler Water Model Fibre Optic Coupler Argon-Ion Laser  Cylindrical Lens Collimator  Optical Fibre  S-VHS Video Camera  Light Sheet  Figure Particle Image Velocimetry Experimental Arrangement  33 3.3.2  Recording Methods  The movement of the polystyrene spheres in the flow was recorded using a Super-VHS (S VHS) camcorder which had a lens system optimized for low-light situations. A tripod was required to stabilize the camera at slow shutter speeds. Through trial and error, the optimum shutter speed was found to be either 1/00 or 1/60 second, with the aperture fully open. Laser powers of 0.5, 1.0, and 3.0 watts were used. The entire system was checked for distortion error by photographing a square 8.5” on a side with the camera, and then digitized. The number of pixels in the x and y direction were 353 and 361 pixels respectively, for a distortion error of 2.22 percent. This distortion error was considered small enough to neglect when calculating the  u and v velocities.  Particle Tracking Accuracy  3.4  The accuracy of both laser-Doppler and particle-image velocimetry depend on the ability of particles to accurately follow the motion of the fluid. Ideally this means that they should be as small as possible and neutrally buoyant. As the detectability of a particle is proportional to its size, extremely small particles are not practical. If the motion of the fluid near a particle is expressed as a superposition of harmonics, AguI and Jimenez (1987) have shown that  Lu) where  p) 56v  u tXu  =  instantaneous fluid velocity  =  velocity difference between particles and fluid  p  =  fluid density  iXp  =  density difference between particles and fluid  d  =  particle diameter  =  typical fluctuation frequency  =  kinematic viscosity  V  341 (..)  34 In LDV experiments, the sediment in the water is estimated to have diameters of up to 5Opm, and specific gravity of approximately 4. Assuming an arbitrary maximum frequency of 10  Hz, the error in the velocity would be 0.4 percent. In PIV experiments, the polystyrene latex spheres used have diameters of approximately 300pm, and specific gravity of 1.05. Again assuming a typical frequency of 10 Hz, the particle tracking error would be 0.6 percent. This analysis shows that the particle tracking error may be neglected unless regions of high frequency flow motion are encountered.  35  4.  ANALYSIS METHODS 4.1  Laser Doppler Velocimetry Data taken using the laser-Doppler velocimeter was stored as binary data files (TSI FIND  Version 3.5.3) containing the times required for eight Doppler cycles, and the times between successive data points. Each raw data file corresponding to one measurement location was analyzed using the FIND software to create an ASCII file of statistics and a binary file of velocities. The program CONCAT13 was written to perform concatenation of the ASCII statistics files from all of the measurement locations from one run into a single file, and is summarize in Appendix C. 4.1.1  Velocities  The FIND program was run to estimate velocity moments such as the mean, standard deviation, skewness, and flatness coefficients, excluding data points lying outside U± 3 .S from all velocity statistics. Bias in the estimates of velocity moments arises due to faster particles having higher probabilities of traversing the measurement volume than do slower particles. Methods have been proposed for correction of bias in the measured u 1 values, using various weighting functions as uin  i 13  (  where u j 3 ‘  =  estimator of the n-th  =  weighting value for the i-th measurement  statistical moment of  the flow  For cases of low data rates, such as in the experimental facility used in this research, the most appropriate choice for the weighting function j3. is the residence time of the i-th particle in the measurement volume (Edwards 1987). While the IFA 550 processors used are unable to record residence times, they do record multiple measurements per particle as a result of the use of frequency shifting. The number of measurements recorded per particle is inversely correlated with velocity,  36 reducing somewhat the effects of velocity bias. Ensemble averaging, where j3.  =  1 for all i, was used  for estimation of all velocity statistics in this work. This approach was felt to be acceptable in light of the agreement shown in §5.1 between bulk flowrates measured by the orifice-plate flowmeters and the laser-Doppler velocimeter. For plotting velocity vectors, the program BOILER1 3 was written in the AutoLisp language for use with Autodesk Autocad Version 11 or higher. This program takes the concatenated data files as input, and plots vectors of length proportional to velocity inside a three-dimensional wireframe drawing of the Plymouth boiler. This wireframe drawing is used as a template on which the results of each run are plotted. The standard deviation of each velocity component is represented by a cross emanating from the root of each velocity vector. Contour plots of the vertical velocity component, non-dimensionalized by the expected bulk upwards velocity at level three, were generated using standard surface-plotting programs, missing points being interpolated from the neighbours. The measured bulk upward velocity was calculated as the geometric mean of all recorded vertical velocities on each plane. This could be compared to the expected bulk velocity of (  uIkA  where q accounts only for the flowrate contributed by ports located below the measurement level. Full-scale velocities may be found from model measurements through Equation 4.1.2  Turbulence Kinetic Energy  The kinetic energy in all fluctuating components of velocity may be used as a tool for evaluating the potential for mixing and combustion at a particular location. Although only two components of velocity were recorded at each location, the turbulence kinetic energy may be estimated by assuming that the fluctuating velocity in the y direction is approximately equal to that in the x direction. With superscript  ““  denoting an estimator of the quantity underneath, the  standard representation (White 1991, 405) of turbulence kinetic energy may be modified as  37 K=(2.uu’+ w’)  (  which was calculated by the program CONCAT13 from the individual statistics files. Contour plots of K½ were generated, again non-dimensionalized by the expected vertical velocity at level three, for each horizontal measurement plane. 4.2  Power Spectral Density Oscillations in the flow field may be roughly noted by examining velocity traces. However, a  quantitative method of determining the relative energy in the velocity fluctuations as a function of frequency would be preferable. Traditional methods of determining power spectral density require that the data be equi-spaced in time, a requirement not met by laser-Doppler velocimetry. Particles arrive at the measurement volume randomly, and data approximates a continuous signal only in cases of extremely high seeding, a condition not possible in the boiler flow apparatus. A number of methods have been advocated for the generation of spectral estimates from randomly sampled signals. These include the discretized lag product (Gaster and Roberts 1975), the direct transform (Gaster and Roberts 1977, Srikantaiah and Coleman 1985), correlation (Mayo 1978, Roberts and Ajmani 1986), and fractal reconstruction methods (Chao and Leu 1991). One review (Bell 198 1.) of some of these techniques indicates that a variation of the correlation technique which resolves the random times into equidistant time intervals shows the best compromise between speed and accuracy. 4.2.1  Direct Transform Method  The method chosen for computation of power spectral densities for these experiments was the direct transform method. ‘While the correlation method may be faster, the direct transform is more easily implemented computationally, does not suffer from aliasing, and is robust with respect to data dropouts.. With the superscript  ““  indicating an estimator of the quantity underneath, the  power spectral density function S(f) of the process is given by Gaster and Roberts (1977)  38 )D(  )ej22  )D2()].  =  where S  =  power spectral density  f  =  frequency  V  =  mean sampling rate  T  =  record duration  =  fluctuating component of velocity  =  time at index j  =  smoothing window function  D  i=J  (  The Hanning function was used as a smoothing window D() =1  —  cosjJ  (  As the record length increases, the variance of the spectral estimate becomes (Gaster and Roberts 1977) as T  (  The coefficient of dispersion of the spectral estimate is therefore of order unity, which is fairly high. Because the laser velocimeter measures the flow velocity at random intervals corresponding to the arrival of particles, the Nyquist criteria is not applicable. Power spectral densities may be computed at frequencies above the mean sampling rate. The minimum frequency at which spectra may be computed should be related to the length of the record. Generating simulated data records of a Poisson-sampled normal process, and using the direct transform method, power spectral densities computed at frequencies greater than SIT were found to represent both the height and width of peaks accurately. Calculations on the minimum frequency for computation of power spectral density using the direct transform method are shown in Appendix B.  39 4.2.2  Computational Implementation  The computer program SPECTRA21 was written by this author to evaluate the spectral estimator of Equation, and is described in the summary of programs given in Appendix C. The program computes power spectral densities at a user-specified number of frequencies between an upper and lower frequency bound. The user inputs the frequency range of interest, number of spectral estimates, choice of data window (Hanning or none), and the axis style (linear or log for both abscissa and ordinate). A coarse smoothing algorithm was included which calculates average power spectra over a number of frequencies which increase by one for each subsequent log frequency decade. Computations typically take ten to fifteen minutes to determine the spectral densities at 500 frequencies from a record of about 20,000 data points from each of two processors. 4.2.3  Validation  While investigators have reported validation of the direct transform method using simulated and experimental data, some brief validation of the technique as implemented in the water model facility was desired. Two methods were devised for validation; the first being a computational simulation of a data record, and the second a physical test using a known frequency. Simulated Data Simulated data records were created in order to test the algorithm as implemented. These were generated by adding three out of phase sine waves and random noise. The resulting function was randomly sampled according to a Poisson waiting interval, simulating a real LDV data record. Results of power spectral density analysis of simulated data records are shown in Appendix B. Fan Blade Experiment To test the spectral estimate using the actual laser velocimetry apparatus in the laboratory, some sort of reference frequency was needed. A small, alternating-current cooling fan was chosen. ‘While not an ideal constant-frequency source, it is a source of a relatively constant velocity which can be observed intermittently. This ‘square-wav& signal of zero and non-zero velocity should  40 provide a frequency close to that of the blade. One shortcoming of this approach is that the signal is not randomly sampled. A small square of reflective tape was placed on one of the fan blades where there was zero twist and the radius was 7.0 cm. The fan speed was measured with a digital stroboscope, and found to be 1800 revolutions per minute, or 30 Hertz. The laser velocimeter apparatus was set up for one velocity component, the measurement volume being oriented parallel to the blade path. The resulting data file was analyzed using the FIND and SPECTRA21 programs for velocity statistics and power spectral density respectively. The plot of computed power spectral density versus logarithmic frequency is shown in Figure The data record used spanned 6.25 seconds with a mean sampling rate of 648 samples per second. Power spectral densities were computed for a total of 500 frequencies using a Hanning spectral window, and the resulting data was then smoothed. The 30 Hertz frequency is clearly visible above the background noise. Harmonics of the main frequency are also seen at 60 and 90 Hertz, but this may be due to the quasi even-time sampling, rather than the power spectral density estimator itself. 0.010 0.009 0.008 0.007 0.006 0.005 0.004 0.003 0.002 0.001 0.000 10  100  1000  f [Hz]  Figure Power Spectral Density versus Frequency Fan Experiment -  41 4.3  Particle Image Velocimetry A limitation of studies made using laser-Doppler velocimetry is that velocities may only be  resolved at single point in time. If the flow is steady, averaging over some appropriate duration allows measurements to be made at different places at different times. The flow must also be ergodic if experiments are stopped and then resumed. A method capable of resolving velocities on a grid of points in a plane or volume at an instant of time would be a valuable tool as an addition to LDV. Such a method has been developed for planar velocity measurements by analysis of video recordings  made using the apparatus described in §2.5 and the arrangements of §3.3. 4.3.1  Review of Techniques  -  Many methods and variations of are described in the literature (Adrian 1986) for quantitative measurement of planar fluid flow velocities using optical means. These methods include laser speckle, streak photography, marker image tracking using photography or holography, and particle image velocimetry. In general, four things are needed for quantitative flow visualization: illumination, markers, recording, and analysis. Light illumination is typically provided by some sort of laser source. Incandescent sources can be used, but suffer disadvantages in their incoherence, large power consumption, and heat generation. Very fast pulsed Nd:Yag (Nyodium:Yttrium-garnet) lasers can provide extremely high powers over short durations (i.e. 13MW over 15 ns). Pulsed lasers may also be made from adding Q-switching apparatus to standard continuous-wave lasers, or by using mechanical beam chopping. Regardless of the laser source used, some form of cylindrical lens is used to turn the laser beam into a two-dimensional sheet. A spherical lens used downstream of the cylindrical lens may be used to halt the spreading induced by the angle of the cylindrical lens. Power may be transferred from the laser source to the measurement volume either through free-air beams via mirrors, or by fibre-optic means capable of handling high power levels.  42  Recording methods may use either film or electronic means to capture the particle motions. Standard reflex cameras are limited to the frame rates capable of high-speed winders. Rotating mirror or other film motion picture cameras offer high temporal and spatial resolution (>3000 lines per inch), but suffer from drawbacks such as film shrinkage, expense, and the need to transfer the information to an electronic media for analysis. Digital video camera recording of the flow is generally a preferable alternative. Video camera-recorders such as the Kodak Ektapro system offer limited resolution (230x 192) but high frame rates of up to 10,000 per second. Low light levels can be a problem for some charge-coupled-device (CCD) digital cameras, unless they are equipped with an intensifier lens. Cameras which record on S-VHS format tape offer a fairly high resolution (>400 lines) but are limited to 30 frames per second. Analog cameras employ interlacing where first the even, and then the odd, horizontal lines are eachrecorded at 60 frames per second, for an overall rate of 30 frames per second. Combining data from such cameras into a digital format is difficult. The exposure time of any camera must be carefully selected to ensure that blurring of the particles is not significant, unless the streak method is being employed. Some form of particles must typically be added to the flow in order to reflect light from the illumination source onto the recording media. These particles must have a density which permits them to follow the flow with sufficient accuracy and still generate a high signal to noise ratio. In water, titanium dioxide and other heavy particles offer good optical properties, but tend to come out of suspension and cover surfaces, undesirable in a complex Plexiglas apparatus. Polystyrene latex (PSL) beads having a specific gravity of 1.05 are often used in water experimental apparatus. The optimum seeding density of particles in the fluid is usually determined empirically. As the particle density is increased, the light attenuated by the water between the camera and the light plane also increases, indicating that an optimum seeding density may exist. Analysis methods must first deal with any directional ambiguity present on the images. Double exposure images offer no indication of the particle direction, and some form of image shifting may have to be employed between frames. Laser pulses or encoding may be used to show  43 direction of particle streaks. Analysis methods are typically based on some sort of particle tracking or correlation method. The particle tracking method becomes complicated when the particle density, and amount of out of plane movement, increases. The correlation process may be performed through optical interrogation of double-exposure images to create Young’s fringes, or computationally using digitized single or double-exposure images. The optical Fourier transform requires the least analysis time per vector, but requires a second laser to generate the fringe pattern from the film, and an automatic traversing mechanism to make the method practical. 4.3.2  Digital Particle Image Velocimetry  Digital particle image velocimetry uses sequential, single-exposure images that are captured using a digital video camera (Cho and Park 1990). Some of the advantages of this technique include the lack of any directional ambiguity, and the ability to dispense with particle identification and tracking algorithms. Such images may be analyzed using the digital Fourier transform or crosscorrelation method, which are equivalent in principle. On a digital video tape, the brightness of each element, or pixel, is recorded as an integer between 0 and 255. If the gray-scale functions of two successive images are represented by g 1 (x and g 2 x) then  )  (  s)=f ( 2 ( 1 fg x).g x+ s)dx  (  An identical grid of cells are superimposed on each image, and the integration is carried out for the local area enclosed by each sampling cell, in which the velocity is assumed to be uniform. This uniform velocity in the cell is defined by the vector s, divided by the image separation time, at which the cross-correlation function R is maximized. 4.3.3  Computational Implementation  A series of programs have been written by the present author to compute cross-correlations for successive image pairs, all of which are summarized in Appendix C. The steps involved in the  digital particle image velocimetry analysis procedure are shown in Figure  44  Figure Digital Particle Image Velocimetry Analysis Procedure After images have been recorded on a S-VHS tape, sections of interest are digitized using a video frame grabber unit. The program BUBBLE was developed specifically for this hardware, and aliows the user to define a region of interest on the tape of the fluid motion. The program requests the number of successive frames that are to be digitized, and the threshold integer gray-scale value. Within the region of interest on each frame, those pixels with a brightness value greater than the threshold value are noted, and the coordinates of each pixel are written to a file. The software is able to automatically advance the tape and scan each frame until the total number is reached. The maximum resolution of the digitizer is 51 2x5 12 pixels in any frame. The actual pixel gray-scale values returned were not used for simplicity of analysis, but could be added in order to increase the sophistication of the technique. This would require the addition of a routine to eliminate bias  45  towards the cross-correlation of bright over dim points. Geometric overlapping of cells could also be employed to increase the number of vector points, at the expense of computational time. The program CCR17 was written to compute the velocity values on a grid of points for successive images, using the binary data file returned by BUBBLE as input. The user supplies the name of the input data file, the recording rate in frames per second, the window width in metres, and the desired number of cells in the x and y directions, which may differ. The program reads into memory the coordinates of the pixels which are ‘on’ for the first two images. The information from each frame is then subdivided into an appropriate grid of cells, and the cross-correlation function R is computed for each cell. To limit computational times, the maximum displacements within each cell must be less than half the width or height of the cell. The maximum value of R is then searched for within each cell. The displacement in the x and y directions corresponding to the maximum value of R within each cell s and  Sy,  the frame rate, and the window width in metres, are used to find  the actual velocities in metres per second. When the function R has two or more equal peaks within a cell, the maximum is found through linear interpolation. Accuracy of the calculated velocity is limited by the physical size recorded on each pixel, and could be improved through the use of curve-fitting functions applied to the R function, which is not done at this time. The number of cells that the measurement window may be subdivided into is limited by the search algorithm for the R maxima. The maximum x and y distance covered by a moving particle between frames must not be more than half the cell width and height respectively. Computational time is proportional to the number of ‘on’ pixels in an image, the number of cells, and the area of each cell. A large number of small cells requires less computation time than do few very large cells. For a typical digitization of the full 51 2x5 12 pixel window size, the time to compute velocity vectors on a lOxlO grid is approximately 10 minutes on an Intel-based 486 computer. The CCR17 program then outputs an ASCII file which contains the location of the centre of each cell, and the velocity for each cell for each image pair. Measures of the cross-correlation signal-to-noise ratio, R value, and the number of peaks are also contained. The entire R function may be included in the output if requested.  46  4.3.4  Temporal Smoothing  The resulting velocity data computed at every 1/30 of a second may be quite turbulent, and may need temporal smoothing prior to plotting or animation. The program IMGAVG was written to average output files from CCR1 7 using a sliding window format of variable length and stepsize. The length of the averaging window is the number of consecutive image pairs to include in the average. The stepsize is the number of image pairs to advance before creating a new average. The entire record of analyzed images may be averaged to find a grid of mean velocity vectors over that time.  4.3.5  Animation  The averaging program, IMGAVG, provides output for each averaged image frame in an ASCII format compatible with the TECPLOT program. Each frame may be viewed on the screen, or plotted on the printer, as vectors of length proportional to velocity. A macro file has been written which will, running under TECPLOT, automatically create a raster metafile containing information on each frame. The raster metafile may then be animated with the program FRAMER The frame rate at which the raster metafile may be played back depends on the hardware, an R4000 based Silicon Graphics workstation being capable of approximately 6 frames per second.  4.3.6  Validation  In order to gain confidence in the ability of the cross-correlation technique to provide accurate velocities, a validation method was devised. A program was written which generated a simulated image of pixels at random locations, corresponding to a given seeding density. The program then generated a second image, which shifted the pixels in the first image as if they were in a forced vortex U= cor. The simulated images of a forced vortex flow are shown in Figure Such a flow case is a non-trivial test of the analysis algorithm, due to the large range of velocities contained in the images.  47  Image 0  Image 1  Figure Simulated Vortex Flow Images  The rotational speed of the simulated vortex was chosen as 617 revolutions per minute with an image separation time of 1/30 second. This was calculated to the be the limiting speed to permit analysis on a lOxlO grid of cells, keeping the maximum particle displacement between images within the limit of ½ the cell width or height. The window size was 512x512 pixels, and the number of illuminated pixels was two percent of the total. Results of the cross-correlation analysis of the two simulated images are shown in Figure  48  7/ -r -  / / t I,  —  t  I  ,_r  IL  t  —  —  \  -  \  i  /  \ \  -.  -  /  e/  /  I / /  Figure Results of Cross Correlation Analysis for Simulated Data It is seen that the velocities calculated by cross-correlation represent the real flow with reasonable accuracy. This is the case even in the image corners, where many of the simulated particles in the first image are not present in the second. In this example, each cell is a square 52 pixels wide, so the maximum allowable displacement in the x or y directions would be 26 pixels, or 37 pixels on a cell diagonal. Therefore the limit on the precision to which the maximum R may be found is 2.7% for this example. Figure shows the error in the calculated mean cell velocity as a function of the predicted velocity for the sample data file. The predicted velocity has been non dimensionalized by the maximum velocity that can be resolved. A least-squares fit line is superimposed on the data, and shows that the mean error decreases as the cell velocity approaches  the maximum allowable by the cell size. The high error for low-velocity situations is due to the mean displacement between images being only two to three pixels, and the large velocity variation across the cell area, as a fraction of the mean velocity. Accuracy at resolving near-zero velocities could be improved by incorporating a smoothing algorithm into the resulting cross-correlation function so  49 the location of the maximum could be resolved with sub-pixel resolution. Other sources of error include the random location of the particles in an image, and any noise induced by the digitization process.  0.2 0.1 0.0 -0.1 -0.2 .  -0.3 -0.4  C)  -0.5 -0.6 -0.7 -0.8 -0.9 0.0  0.1  0.2  0.3  0.4  0.5  0.6  0.7  0.8  0.9  1.0  Vte I Vm  Figure Velocity Error for Simulated Data It was also intended to find a steady, laminar flow with which to test the actual velocities obtained from the cross-correlation method. Unfortunately, a suitable flowfield was not found, and so the flow near the model bullnose was used instead. The flowfield there was found to be still unsteady and turbulent, so its use for validation is limited. The results of this experiment are discussed in §5.3.1.  50  5.  RESULTS 5.1  Laser Doppler Velocimetry A total of 26 experimental runs were conducted using the Plymouth recovery boiler model  and the laser-Doppler velocimetry measurement system. Each run took approximately ten hours for data acquisition during which time the model was run continuously. The configurations of the model during the runs are summarized in Table 5.1.1.  Run No. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26  Table 5.1.1 Plymouth Model Laser-Doppler Velocimetry Conditions Set Flowrate Set Mass Flow Ratios [%] Comments S.B. [US gpm] Pri. L.B. Ter. Sec. 150.0 40 23 L.B. -2 ports/wall 37 150.0 40 L.B. -2 ports/wall 37 23 40 75.0 L.B. 2 ports/wall 37 23 150.0 40 37 23 L.B. -2 ports/wall new primary plates from now on 40 150.0 L.B. 1 port/wall now on 37 23 40 4 150.0 33 23 4 150.0 40 screen tubes removed from now on 33 23 4 150.0 40 23 33 4 150.0 40 boiler banks removed from now on 23 33 4 150.0 32 49 15 2x2 interlaced grouping 150.0 4 32 49 15 2x2 interlaced grouping 11 89 55.5 100 60.0 Four wall secondaries 29.0 100 Front & rear secondaries only 62.0 100 Left & right secondaries only 43 115.5 52 5 Secondaries: L+10%, R—10% 115.5 43 52 5 Secondaries: L+10%, R—10% 115.5 43 52 5 Secondaries: L+10%, R—10% 115.5 43 52 5 Secondaries: L+10%, R—10% 115.5 43 52 5 Secondaries: L—10%, R+10% 4 150.0 40 33 Orifice-plates O.K. from now on 23 115.5 43 52 Secondaries: balanced 5 115.5 43 52 5 Secondaries: L+10%, R—10% 115.5 43 52 5 Secondaries: L—10%, R+10% 115.5 43 52 Secondaries: balanced 5 139.0 4 43 36 17 2x2 interlaced grouping -  -  -  -  -  -  -  -  -  -  -  -  -  -  -  -  -  -  -  -  -  -  -  -  -  -  -  -  -  -  -  -  -  -  -  -  -  -  -  -  -  -  -  -  -  -  51 Early runs in the load-burner configuration used two load-burner ports per wall, which was later changed to one port per wall in order to more closely match the full-scale boiler. Primary plates were re-constructed and adjusted prior to Run 4 in order to minimize differences between the four walls. Plexiglas plates which modelled the screen tubes and boiler banks were removed prior to Runs 7 and 9 respectively to permit comparison of computational fluid dynamics results with the experiments: The removal of the plates caused a slight increase in the swirl component on level three as compared to the flow with the plates. For each of the runs noted above, bulk average vertical velocities were calculated from the means of the 36 measured vertical velocities on each plane. This comparison between measured and predicted vertical velocities is given in Table 5.1.2. Runs 1, 14, and 18 were aborted due to malfunctions with the laser. During the test program, it was decided to calibrate each and every orifice-plate flowmeter used in conjunction with the Plymouth model, and in the course of this work, one orifice-plate flowmeter was found to be incorrectly labelled as to its size. This orifice-plate was attached to a secondary level port at the rear-right of the model. For runs 1 through 20, an additional 10% of the total predicted secondary flow was passing through this port. While this does not invalidate the results from these runs, the asymmetric port flow must be taken into account. The results from these runs clearly show that the upflow is predominantly near the front-left corner. From Run 21 on, the offending orifice-plate was replaced. Following the completion of Run 22, one secondary port was found to be plugged with teflon tape, and so the run was repeated.  52  Table 5.1.2 Plymouth Model Laser-Doppler Velocimetry Results Run No.  Predicted w [mis] 1  Level 2  3  1  .0483 .0483 .0241 .0483 .0483 .0483 .0483 .0483 .0483 .0530 .0530 .0232 .0251 .0121 .0259 .0483 .0483 .0483 .0483 .0483 .0483 .0483 .0483 .0483 .0483 .0483  .0627 .0627 .0313 .0627 .0627 .0627 .0627 .0627 .0627 .0627 .0627 .0232 .0251 .0121 .0259 .0483 .0483 .0483 .0483 .0483 .0627 .0483 .0483 .0483 .0483 .0483  .0627 .0627 .0313 .0627 .0627 .0627 .0627 .0627 .0627 .0627 .0627 .0232 .0251 .0121 .0259 .0483 .0483 .0483 .0483 .0483 .0627 .0483 .0483 .0483 .0483 .0579  .0541 .0279 .0393 .0529 .0482 .0627 .0601 .0498 .0778 .0889 .0354 .0267 .0268 .0163 .02 13 .009 1 .0212 .0398 .0528 .0266 .0523 .0432 .0600 .0346 .0653  (  1 2 3 4  5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26  Comments  Measured w [mis] >  <  Level 2  3  Laser malfunctioning .0464 .0292 .0711 .0571 .0593 .0545 .0664 .0633 .0707 .0599 .0250 .0349 —.0071 —.0050 .0258 .0294 -  .0520 .0534 .067 1 .0838 .0592 .0490 .0682 .0499  .0617 .0319 .0774 .0594 .0589 .0512 .0672 .0607 .0693 .0675 .0269 .0318 -  —.0121 .0 107 .0342 -  .0416 .0534 .0623 .0478 .0496 .0488 .0636 .0598  -  Laser & processor problems Processors malfunctioning Processors malfunctioning Laser malfunctioning  Orifice-plates O.K. now on One secondary port plugged  Results from laser-Doppler velocimetry investigations of particular flow arrangements in the Plymouth recovery boiler model will be presented in three formats. The two components of mean velocity (averaged over  2½ minutes) recorded using the LDV system will be shown in vector form  superimposed on a three-dimensional wireframe representation of the boiler model interior walls. The length, and arrowhead size, of each vector is proportional to the magnitude of the velocity at that location. These plots also show horizontal projections of the velocity vectors on each level separately. Because each arrowhead is drawn as a three-dimensional object, the horizontal projection may appear as an odd shape depending on the vector angle. A cross emanates from the base of each  53 vector, the length of each branch being proportional to the root-mean-square velocity in that direction. Vertical velocities on each level were also non-dimensionalized by the predicted bulk velocity for level three, and used to generate contour plots. Using the same non-dimensionalization value for each level permits comparisons between contour plots of the three levels. The square root of the turbulence kinetic energies, as defined by equation, measured at each point have been non dimensionalized using the same predicted bulk velocity for level three, and used to generate contour plots.  Run No. 2 3 4 5 6 7 8 9 10 11 12 13 17 19 20 21 23 24 25 26  Table 5.1.3 Measured Flowrate Errors Flowrate Errors [%] < Level 1 2 3 12.01 —26.00 —1.59 15.77 1.92 —6.71 13.40 23.44 —18.63 9.52 —8.93 —5.26 —0.21 —6.06 —5.42 29.81 13.08 —18.34 24.43 5.90 7.18 3.11 0.96 —3.19 46.79 12.76 10.53 67.74 7.66 —4.47 52.59 7.76 15.95 6.37 39.04 26.69 —81.16 —39.13 —29.19 7.66 —17.60 —13.87 9.32 10.56 10.56 7.02 —44.93 —0.64 22.57 2.69 —10.56 24.22 1.04 1.45 41.20 31.68 —28.36 35.20 3.31 3.28  Bulk vertical velocity (or flowrate) errors are shown in Table 5.1.3 for all runs where data  was obtained on all levels, and during which there were no equipment malfunctions. The mean errors for each level are 6.8, 4.8, and 3.2 percent for levels one, two, and three respectively. It is  54  evident that the variance of this error is substantial. Both the mean and variance of the error decrease as the level increases. Seldom is the error in the bulk vertical velocity less than ten percent on all three levels for the same run. Run 25 is an example of how poor Ilowrate agreement can occur on all three levels even when data is taken for over 2½ minutes at every point. The unsteadiness of this configuration probably contributes to this difficulty in obtaining a good average velocity in the plane, and will be discussed further in §5.2 and §5.3. The large velocity gradients present, especially on level one, also increase the difficulty in obtaining a good average on a grid of only 36 points. Port flow arrangements were originally chosen based on consultations with the Weyerhaeuser Paper Company, the operator of the full-scale boiler. Two basic configurations have been used in the real boiler: primaries, secondaries, and load-burners; and primaries, secondaries, and interlaced trtiaries. ‘When it became clear that the resulting flow pattern was sensitive to secondary port flows, various configurations of two-level flows without any load-burner or tertiary flow. This allowed the effect of variations in secondary level flows to be examined without any complicating effects from higher level flows. In the following sections, LDV results will be presented for a select number of runs which are representative of each major port flow arrangement, and for which the flow conditions are not in question. Results from other runs listed in Table 5.1.1 may be requested from the Department of Mechanical Engineering, U.B.C. It may not be possible to provide every data plot from every run. 5.1.1  Early Runs  Vector plots of velocity from two early runs are presented in Figures and These are both for the load-burner upper flow configuration, and are shown to illustrate the effects of the secondary flow imbalance, and the mass flowrate independence. Figure shows the results from Run 3, which was conducted at 75 US gallons per minute, half the standard value. Results from Run 4, which was performed at 150 US gallons per minute, are shown in Figure Run 4 also had re-manufactured primary port plates, as described in §2.1. Reynolds  55 numbers, based on predicted bulk average vertical velocities and the model width, were 12,200 and 24,400 for Runs 3 and 4 respectively. It can be seen that both Run 3 and 4 show similar velocity patterns, accounting for the difference in total flowrates. The tendency for the region of maximum vertical upflow to be near the front-left corner of the boiler is apparent. A comparison of the mean non-dimensionalized vertical velocities from the LDV results on each level are shown for the two runs in Table 5.1.4. Table 5.1.4 Mean Non-Dimensionalized Vertical Velocities Level Run 3 Run 4 1 1.0664 0.8986 2 1.0639 1.1850 1.0064 1.2344 3  56  a  C4  z ZD  0 U-)  U-’  0  C,’  a’ I  F— t  ft  ,  ‘  ft  *  I  ‘  4  4  4  4  I  I  4  .  .  .  .  FRONT  .  .  4  6  .  ‘  .  FRONT  .  .  .  ‘  •  t  0  U >-  t It  I, 4  I  t  4  U  •  4  1 I  C)’ 420  —J  C”  0:: -J F  0 w I’-)  0 0  a > U -J  z o  o  FRONT  I  0  0 C  0  a  I?  A U > U,  0 42 U,  Li )1 0 0  ‘V V V  57  It)  z  0  —  D  0  H  0 CN  0  ow  C)I. — Q  •  I  I I  I  I .  I  I  •  .  FRONT  7  j  I  II  I  0  (‘4 -J bi -J  •  FRONT  ?  It)  -J  (.1  It •  U >ci z  H  I  I ‘4  0  C  FRONT  > b4  0 ID Li  I:-J U 0 0  58  5.1.2  Load Burner Port Flow Case  For the configuration using starting burners, four-wall primaries and secondaries, and the tangentially-firing load burners in Run 21, a plot of two components of velocity is shown in Figure, and contours of vertical velocity, non-dimensionalized by the expected bulk velocity, are shown in Figure Non-dimensionalized contours of the square root of the turbulence kinetic energy K½ are shown in Figure On level one, most of the upflow is near the centre of the cross-section, with downflow near the corners. Level two shows upflow in the centre and near the right wall, while on level three, the majority of the upflow is near the back and rear wall, with stagnant flow in the centre. The swirl component imparted by the load burner ports is clearly seen on levels two and three, both above the load burner port level. Some evidence of swirl in the opposite direction is seen on level one. On levels one and two, the regions of maximum K ½ correspond to the regions of maximum vertical upflow. On level three, the turbulence kinetic energy distribution is quite even. Upflow covers approximately 75% of level one, 90% of level two, and all of level three.  59  (-)  z  C)  I  4 I  I  I  ii  I  I I  FRONT  I  I  I  I  I In  ii itt  I  I  ‘  I  •  U  I  w 1  I  I  II it  I  In  D  0  H  I.,  0  In 0  >-  0  0) bJ -J I—  r’4  •  I  U  •  ,  I  U  I  I I  j  FRONT  U  ‘  I  -J  w  U,  -J  • FRONT  N 0  z  0 E In  60  z 0 LI  Level  3  Level  2  Level  I  I  z  0 lI  (  I  z  0 IY U-  Figure Contours of Non-dimensionalized Vertical Velocity Run 21 -  61  H  z  0  Level  3  Level  2  Level  1  H  z  0 Li  H  z  0 li  Figure Contours of Non-dimensionalized K½ Run 21 -  62 5.1.3  Tertiary Port Flow Case  The configuration using starting burners, four-wall primaries and secondaries, and interlaced tertiaries was tested in Run 26. The banks of 14 tertialy level ports on the front and rear wall were each ganged into four groups, alternating on and off as shown in Figure This provided an effective 2x2 interlaced arrangement, which induced some clockwise swirl, as viewed from above. Two components of velocity are shown in vector form in Figure, contours of non dimensionalized vertical velocity in Figure, and contours of non-dimensionalized K ½ in Figure The plots show that the upflow is in the centre of the furnace at level one, with two roughly symmetric, distinct peaks apparent. This may be due to oscillations of the core flow region from front to rear, as has been seen in flows with balanced primaries and secondaries, and will be discussed in 5.3. Such separate peaks of upflow could not be noted when the flow was observed qualitatively during the course of the run. On levels two and three, the upflow is fairly uniformly distributed about the four walls, with stagnant flow in the central region. The maximum turbulence kinetic energy is seen to be between the two vertical velocity peaks on level one, with secondary peaks offset clockwise from the velocity peaks. Level two shows the peak K½ at the rear wall, while the turbulence is maximum along the front and rear walls on level three. Vertical upflow covers approximately 60% of level one, 90% of level two, and all of level three.  63  (0  I.,  m  CN  0  z  F D 0  4 t 4  4  f  I  I  I  I •  4  ..  FRONT  .1  -J  I  1  It  ‘ft  It  .  •  4  4  I  1  I.,  Li  I  •  ‘  •  .  ,  C-)  ttt  I  -  I  I  Li  Li  I  -J  •4  P  04 I1 w  -J I— 4,-) uJ In  >-  -J  -  0  0  0 U  I  z 2.4  •  FRONT  4  E  1  4  4  •  I  I  -  FRONT  Li > Li  0 Li -J  0  0 C-)  64  I—  z  0 IL  Lovol  3  Level  2  Lvol  1  /  I  z 0 IL  Figure Contours of Non-dimensionalized Vertical Velocity Run 26 -  0  N  0  C.’,  z 0  -  0  -I C.’,  0 C  0  C.)  3  a  F a  FRONT  F  FRONT  C  1.)  C  F  FRONT  66 5.1.4  Balanced Primary and Secondary Port Flow Case  Run 25 was conducted using starting burners, primaries and secondaries with equal flow on each wall. The flow showed a tendency to quickly drift away from the balanced condition, and for the core to move towards one wall or another. Ports were continuously monitored during the run to ensure that the flows on each of the walls remained balanced, and that none became plugged. A vector plot of two components of velocity is shown in Figure, non-dimensionalized contours of vertical velocity in Figure, and contours of K½ in Figure  The figures show a symmetric core of upflow on level one, with downflow on the perimeter. On level two, the most upflow is near the left wall and the central region, with no downflow. Level  three shows a fairly even vertical velocity distribution, with slightly more flow on the left wall. Peaks in the turbulence kinetic energy occur slightly to the left and right and right of the central core on level one. Levels two and three have clear maximums of K½ very nearly in the boiler centre, where  their is no correspondingly pronounced velocity maxima. Vertical upflow covers approximately 50% of the horizontal cross-section on level one, 95% of level two, and all of level three.  67  •  .  .  •  .  I  •  .  ::  ¶ I  .  I  I I  I  I  •  I  I  •_  I  I  I  0  rz  0  0  z  0  0  C) 0  F  FRONT  l’)  0  0  0  F  FRONT  0  F  FRONT  Co  C’  t)  N  0  C.,  z 0  0  fr C’,  n 0  c)3  F 0  0  C  FRONT  F  0  FRONT  V  0  F  FRONT  70  5.1.5  Balanced Primaries; Biased Secondaries Port Flow Case  Run 23 was performed using starting burners, four-wall primaries and secondaries. Primary port flows on each wall are identical, as in Run 25. The mass flow, and hence velocity, of the leftwall secondaries are 10% higher than nominal, while the right-wall secondary mass flows are 10% lower than nominal. Two components of velocity are shown in Figure, and non dimensionalized contours of vertical velocity in Figure Contours of non-dimensionalized K½ are shown in Figure  The majority of the upflow is near the right side wall of the boiler on level one, symmetric from front to rear. Higher in the boiler on levels two and three, the upflow is still predominantly up on the right side, and stagnant on the left. The peak of the turbulence kinetic energy distribution is also on the right side of boiler on levels one and two. Level three shows K ½ to be higher near the perimeter of the model, as opposed to the right wall. Vertical upflow occurs for about 60%, 75%, and 80% of the cross-sectional areas at levels one, two, and three respectively.  71  t  4  4 4  1 •  4  :  1  .  •  .  .  I  o  F  0  z  0  8  0  r1  r K 0  C  FRONT  r  FRONT  ()  C 0  r 0  FRONT  CD  N  0  (D  0  z  0  C  8  C-) 0  ri FRONT  C  F  FRONT  I,  C  F  FRONT  74 BULLNOSE  LEVEL3  f  +  A  A LEVEL 2  —  LEVEL1  SECONDARY +10 %  w4  PRIMARY  / 4  I  -10 %  :  Figure Flow Schematic Front View Run 23 -  Figure shows qualitatively the flow pattern as viewed from the front of the boiler model. A large recirculation region is noted at level one, slightly to the left of the model centreline. Flow beneath the secondary port level was too turbulent to be sketched accurately. The configuration used in Run 24 is the mirror image of that in Run 23. The mass flow of  the left-wall secondaries are 10% lower than nominal, while the right-wall secondary mass flows are 10% higher than nominal. Two components of velocity are shown in Figure, non dimensionalized contours of vertical velocity in Figure Contours of non-dimensionalized are shown in Figure The region of upflow is now towards the left side wall of the boiler on level one, fairly symmetric from front to rear, with downflow on the right wall. Higher in the boiler on levels two  V  75  and three, the upflow is still predominantly up on the left side. The zero velocity line is somewhat angled from front to rear on level two. The contours of turbulence kinetic energy on level one are steep, coming to a maximum near the centre, where the vertical velocity is near zero. The maximum of the K½ distributions on levels two and three are near the cross-section centre. Upflow occurs on approximately 60%, 75%, and 90% of the areas on levels one, two, and three respectively. Thus the change of flow of 10% has effectively switched the flow pattern from side to side on the three planes of measurement.  76  m  z  H . .  .  t  4  -.  ,  I  I ,  ,  •  ,  U  1 1  I  I  -J 4  o  OI  In 0  Lfl  0:: bJ -J I IiJ  U  Cr;  -J I-i  t  I *  ‘  • 0  I  I  I  .  FRONT  -J  I. 4  I  .  FRONT  >-  -J  Li  .  I-)  0  4  I  I  In a  •  III. (N  QII,  FRONT 8  Li > Li  0 LI -J  0 I-,  CD  0  C.,  0  z  -  0  0  0  0  F  FRONT  0  ( 0  r\)  F 0  0  FRONT  F  FRONT  —1  L%J  0-  0  C-,  CD  S  0-  0  t)  0  0)  0  n 0  CD  C  rj  0 1-)  0  N  0  F  F  FRONT  0  0  FRONT  F 0  FRONT  00  —.4  79 5.2  Power Spectral Densities Low frequency oscillations in the velocities were noted on the plots of power spectral density  for all of the cases run. This unsteadiness could sometimes be observed in the velocity time trace itself, and also from qualitative and quantitative visualization. For flow cases in which the mass flows from each wall of primaries and secondaries were balanced, the distribution of the unsteadiness seemed somewhat more uniform throughout the boiler volume. The observed unsteadiness should not be confused with turbulence, for which the frequencies are at least an order of magnitude higher. For a single measurement location on level one for Run 25 (starting burners, balanced primaries and secondaries), plots of velocity are shown in Figures 5.2.1 and 5.2.2, and plots of power spectral density are shown in Figures 5.2.3 and 5.2.4.  -  The data record displayed had a length of 155.2 seconds, and mean sampling rates of 42.3 and 56.6 samples per second for u and w components respectively. The PSD values computed at frequencies lower than the 5/ T boundary described in §4.2.1 are shown as a dotted line. Peaks of power spectral density are seen at 0.049 Hertz in the u component and 0.088 Hertz in the w component, corresponding to periods of 20 and 11 seconds respectively. Such plots as those shown are representative of the power spectral density in other runs also. Results varied with the geometric location within the boiler, but low frequency peaks in the range of 0.05 and 0.1 Hertz were dominant in all locations and configurations tested.  80 0.4 0.3 0.2 0.1 0.0  FI11E  E -0.1 -0.2 -0.3 -0.4 -0.5  I 0  ‘  20  40  60  80  100  120  140  160  time [s]  Figure 5.2.1 Velocity Trace Run 25, Level 1, u Component -  0.7  :Lh I L1  0.6 0.5 0.4  h  i1  Ifi I.”’  ••••i  i  J  IIII  0.3 E 0.2 0.1  :  0.0 -0.1  :::....  I  1•  9i  I  -0.2 0  20  40  60  80  100  120  time [s]  Figure 5.2.2 Velocity Trace Run 25, Level 1, w Component -  140  160  81 0.040  0.035  0.030  0.025  U, 0.020  0.015  0.010  0.005  N-.__1’  0.000 0.01  . —  .  0.1  1  10  f [Hz]  Figure 5.2.3 Power Spectral Density Run 25, Level 1, u Component -  0.07  0.06  0.05 N I  0.04 U)  0.03 (0  0.02  0.01  Th, V  0.00 0.01  V V 0.1  j  VV  v.  *W4VW 1  f [Hz]  Figure 5.2.4 Power Spectral Density Run 25, Level 1, w Component -  10  82 5.3  Particle Image Velocimetry For the case of balanced flow from only the primary and secondary ports, equivalent to Run  25, two different views of the flow were analyzed using particle image velocimetry. The boiler was  illuminated using the laser sheet system, and the flow pattern recorded using the video technique as described in §3.3. The laser sheet was introduced through the clear bottom of the model to illuminate an x-z plane, using the coordinate system of Figure 2.1.1. The flow was viewed from the side of the model at two levels; near the bulinose, and between the secondary and tertiary levels. About thirty minutes of the flow were recorded at each location, but storage and time requirements limited the maximum analysis segment to thirty seconds of data. Filming was also conducted from the front of the model, using a laser sheet oriented in the y plane. Unfortunately, the threaded bolt holes holding the model together are in the front and rear walls. These glowed with an intensity greater than that of most of the particles, reducing the possible analysis area to a small region in the centre of the model. To effectively film the flow from the front, the rear and side interior walls of the model would have to be coated with a flat black paint or coating to eliminate any glow other than that from particles. If laser velocimetry was also to be performed through these walls, the coating would have to be easily removable.  5.3.1  Bullnose Side View  The region near the builnose was photographed through the right side wall, and analyzed using particle image velocimetry, originally for validation of the experimental method. It was thought that this region of the boiler would have a reasonably steady, uniform upflow which would lend itself well to validation of the absolute velocities returned by the particle image velocimetry. However, it was found that, even near the bullnose, the flow was neither uniform nor steady. The results are of more use in describing the boiler characteristics than validating the approach. The laser light sheet was placed below the model and aligned vertically in a plane running from the front to rear walls, in the centre of the model. The unsteady characteristics of the flow are  83 not adequately described by static vector plots, but can be observed using the animation procedure described previously. An average of the velocity vectors over the entire 30 second length of the data record is shown in Figure Flow is generally up near the front wall and down off the top of the builnose.  ft  ft  \  t tt  t t t f f  \  I  ‘  \  \  \  \  \  \‘-\  nose  O.lrn/s ,  \ t\\,  -  ‘I \  t  .  / •  Figure Bullnose Side View 30 Second Average For the same 30 seconds of data, averages over six consecutive five second intervals are -  shown in Figures (a) through  (0.  It is clearly evident that the flow pattern is not static  during the 30 second record duration, rather changing continually over time. The flow pattern does not appear to re-occur during the 30 second interval, indicating that any period of the flow may be longer than this. The 30 second average is therefore probably not long enough to provide a stationary average. A vortex which appears in (d) is seen to convect up and to the right in (e).  84 1  -  \  \  \\\ t\  /\  \  I  \  \ t  I’  /  f  t  ft t  \ /\ 0.1 rn/S  ‘.  \  I  \\\  \ 1  -  /  I  \  7  \ t  /  1  buliriose  —  /  .  \ \\ \ \  I  t  I I  \  N  /  I  -  -  (b)  \  I  ‘I  I  /  “j  I  \  \  ,  /  I  /  I 7 / I \ I /7 /\\ t \\ \ \ / /  \  t f  \  7-  \  \  /  I  \  S-S-S  -  -  t._ S  71  I  1  /  t  I  t// / 7 / —  -  /  I  ‘  / S  t I  I  -.  /N builnose  ‘.5  /  I.-  ‘  /  \  —S  /  I  /  -  S  .  -  /  7,  /  I  t  ‘S  \ 1  /  /  (d)  /  /  /  /  /  /  /  ‘  /  /  /  ti .‘  \  -  —  -  *1  \-S.S  ,,  I’  -.  I  S  -S.  0.1 rn/S  \ (I)  / N bulinose  III  /  (e)  /  -  it  (C)  I  /  ,  0.1 ni/S  \  0.1 rn/S  \  —  \ \ \  \‘S.5  S  /  0.1 rn/s  t \  ‘  I  //,,____  t  —  \  itt, / j / / 1 / /1_I  (a)  S  \-.-.  -.5  7  -  \  \ ,  -  tN_  /  Figure Builnose Side View Consecutive 5 Second Averages  \  I  85  5.3.2  Lower Boiler Side View  A 30 second average of the flow pattern for balanced primaries and secondaries only, as viewed from the left side of the model between the secondary and tertiary levels, is shown in Figure The laser sheet was introduced from the model bottom, illuminating a x-z plane located halftvay between the side walls. A load burner port which blocked the view of all particles behind  it  is shown in the lower right region of the frame. The 30 second average of the flow shows a central core region of upflow near the secondary level, which shifts towards the boiler front as the tertiary level is approached. For the same 30 seconds of data shown in Figure, consecutive five second averages of the flow are shown in Figure (a) through (f). Large vortices approximately one third the model width in size may be seen in (b) and (c). Downflow near the rear wall appears, disappears, and reappears with a period of about ten seconds. This is similar to the low frequency oscillations seen in the power spectral densities discussed in §5.2.  f  t  I  t  t  f REAR  II  /  FRONT  I  t  I’  t  t  t  Load  /  t  ii”  I  I ,  0.lm/s  4’  I  Burner  t  Port  \  \\  t  Figure Lower Boiler Side View 30 Second Average  86 /  _._-  7  71  t  Ac  t REAR  FRONT  ‘7 t  \  ‘\  \  ‘  /  I  Load  \  -_  t  —  /  ,  t  ._  \  \  \  ‘S.  ‘IS..  I  ‘I  •/  1 FRONT  /ILoad  REAR  /  I I  i  ,.n  t  /  t  REAR  /  -\  It  I  (e)  \\ —  I  S  Burner  I I’ P 01  -  /  01 rn/s  I  1  —  REAR  ‘  Load  ?I I  Load  0.1  I  I  Ron  I I  \  / “  -  ?.  f\  I ‘Ac / / / 1 I  /  r--  /I  —  I  —  Load  ‘  I  -  PonI I  (I)  Figure Lower Boiler Side View Consecutive 5 Second Averages  FRONT  It  0_I rn/s  I  /\t  ‘  Ifl/S  Burner  I  t  It  /  Ac  FRONT  I  T  /1  \\  ,  r-’-----  /4  I  ‘r--  t  Ac  (d)  I ‘i / / It  \  I  1\ i//Ac  I  \l  f  Port  I  7/I I  /  ‘  ‘  FRONT  /  ,i\  ‘5  \/P Ott  ft  (c)  Burner  Burner  /  It  \t  I,’  Load  /T  -_  /  / ‘  —_-  I  /  /%7  0.1 tn/S ‘5  /  —FIt  ‘5  /  \  ‘5t  (0)  /  FRONT  r—-----’  1’’  / /t /  /  0.1 ntIs  —  / /  I  \  ‘\  \  -  f//II  1-i  \  \  t  ‘,  ,)_  REAR  ‘5  I  Burner  I  I  -  /  0.1 mIs  P On  ‘  /  /  REAR  t  r---  I  ‘—___  t  —  /IH (a)  I t  \  I  87  6.  DISCUSSION OF RESULTS One of the difficulties in modelling a recovery boiler is that an optimum flow condition or  goal is difficult to define. The isothermal flowfield resulting from a particular physical port arrangement and mass flow ratio may be determined with adequate precision, but the implication for real boilers is somewhat more subjective. Some of the relationships between the experimental results and the full-scale boiler condition will be examined in the following sections. The two main findings of the experimental results have been that the core of central upflow does not persist much higher than the liquor gun level, and that low frequency unsteadiness is a dominant feature. 6.1  Velocities  6.1.1  Air System Objectives  The optimal air system must maximize the recovery of both chemicals and energy as measured by the chemical efficiency ( 2 S/(Na + 4 Na S S), 2 Na ) O and the thermal efficiency (Isteaml2liiquor)’ and these two requirements may conflict with each other (Lefebure and Burelle 1989).  For efficient chemical recovery, the lower part of the furnace must be oxygen deficient to obtain maximum reduction efficiency defined as the percentage of Na S which is obtained in the smelt. 2 However, for thermal efficiency and maximum heat release, the combustion of the organics must be completed higher in the furnace in an oxygen-rich environment. The high temperatures necessary in the bottom of the boiler are maintained by partial combustion of the organics. The simultaneous optimization of all of these processes is the goal of a recovery boiler air system. For maximum thermal efficiency, the heat release rates must be maximized with minimum entrainment, or carryover, of liquor droplets and char particles. It has been suggested that one of the functions of the tertiaries is to break up the “high velocity central core” which can cause carryover. Adams and Frederick (1988, 160) suggest that a typical flow will have a central core of upflow covering about 18% of the cross-section. Typical results for level one in Figure show an upflow area of about 50% with downflow elsewhere in the cross-section, and a maximum velocity of  88 approximately five times the bulk average. Results shown in Figure for arrangements with only primary and secondary port flows indicate that the high velocity central core dissipates on its own by the time it reaches the tertiary level. This leaves the main function of the tertiaries to be provision of oxygen for combustion, hopefully without promotion of carryover.  6.1.2  Velocity Effects in Full-Scale Furnaces  The realization that a central core of upflow does not necessarily persist at all levels in a recovery boiler may have consequences for other researchers. Those who model liquor droplet flight, drying, and pyrolysis often use a symmetric core flow profile as an input to their models (Adams and Horton 1992). The effects of using a flowfield without an upper furnace core of vertical upflow should be used to examine its effects on any model of other phenomena in recovery boilers. Chapman and Jones (1990) have argued that secondary level flows are a critical aspect of the overall air delivery, affecting the intensity of the flow channel and recirculation zones. Their experiments and calculations led to the conclusion that at a plane just above the secondaries, the central upward velocities and perimeter recirculation zones can be attenuated by interlacing or the use of a strong-weak flow arrangement, but not eliminated. This finding is not incompatible with the results presented in this work. One problem in full-scale boiler operation is entrainment, or carryover, of black liquor and char particles which can cause plugging of the tubes in the convective heat transfer section. It may be impossible to eliminate carryover completely, unless the regions of liquor injection, and upflow of organics into the burning zone, can be separated. A more uniform distribution of liquor droplets may be achieved if the flow is weakly up near the walls, permitting the droplets to fall slowly and allowing time for drying and pyrolysis to occur. A fairly even flow distribution is needed at the superheater entrance for uniform heat transfer and mechanical and thermal loading. The particle image velocimetry results show that, at least for an arrangement without tertiary or load-burner flows, oscillating downflow may occur at the builnose. Although the plates representing the  89 convective heat transfer were not present for these runs, such results indicate that a uniform flow distribution may not exist in all situations at the superheater entrance. Regions of higher velocity in the upper furnace may be related to zones of increased tube wear or fouling due to the high mechanical and thermal stresses. Regions of oscillation between high and low velocity may indicate zones of increased tube-wall cracking due to the high cyclic loading of both thermal and mechanical stresses. 6.1.3  Upper Furnace Flow Configurations  One of the reasons the Weyerhaeuser Paper Company began a research program into recovery boiler fluid mechanics was to investigate differences between load burner and tertiary upper furnace arrangements in the Plymouth boiler. Examining Figures and, it may be seen that there are only subtle differences between the measured velocities in the two cases. At level one, two distinct velocity peaks exist when tertiaries are used, indicating the possibility of oscillation of the core between these two places. On level two, there is a more uniform velocity distribution using tertiaries (Figure By the time level three is reached, the velocities in the load burner case (Figure are more evenly distributed about the cross-section, while the maximum velocities using tertiaries (Figure are on the front and rear walls. Measured turbulence kinetic energies are slightly higher on Level 1 using tertiaries (Figure, while the regions of maximum K½ are near the front and rear walls (as opposed to being evenly distributed) using load-burners (Figure The swirl component of velocity is of course much stronger using tangentially firing load burners than the interlaced tertiaries. Compared to the case of a 2x2 interlaced tertiary flow, the swirl component induced by the load-burner upper flow arrangement may be more effective at diffusion and mixing, and providing an even velocity distribution in the upper furnace region.  90  6.2  Transient Behaviour 6.2.1  Data Qualification  The low frequency oscillations observed in the course of this work have not been reported previously for recovery boilers, although similar phenomena has been noted in an isothermal model of a hog-fuel boiler (Perchanok, Bruce, and Gartshore 1989). To help understand the processes occurring in recover boiler flow, some classification of the observed “unsteadiness” is warranted. Bendat and Piersol (1986) provide a good starting point for analysis of random data. Theoretically, the fluid velocity inside a kraft recovery boiler is a deterministic process in that mean values could be described by the Reynolds averaged Navier-Stokes equations. The impracticality of specif,ring initial conditions and solving these equations means that the instantaneous fluid velocity at a point inside a kraft recovery boiler must be considered a partly random, as opposed to a completely deterministic, process. The goal of any experimental modelling is to obtain statistical moments of parameters which represent the data from a very large number of realizations, or ensemble, of a particular experiment. To avoid having to perform many identical experiments, the assumption is .typically made that the process is stationary and ergodic, which implies the equality of ensemble and time averages. ‘While such an assumption is convenient, and has been implicitly made in this work, its validity should be examined in light of the transient velocity behaviour observed. A stationary random process is defined as one in which the ensemble, (infinite collection of identical experiments) statistical moments are not a function of the instant in time at which they are calculated. An individual time history record may also be considered stationary if statistical moments computed over short time intervals do not vary with more than “normal statistical variation” from interval to interval. Thus the velocity at a particular location in a turbulent, time-dependent flow such as a recovery boiler is stationary only if an appropriate averaging time interval is chosen.  91  A stationary random process is considered ergodic if statistical moments do not vary when computed for different realizations of identical experiments. Note that a non-stationary random process cannot be ergodic, and a stationary process need not be ergodic. Statistical properties of a stationary, ergodic, random process may be computed from either ensemble or time averages. The similar results shown for two different runs at two different flowrates in Figures and suggest that, for one configuration at least, the flow was both ergodic and stationary in general. However, the transient velocity behaviour documented in §5.2 and §5.3, and the difficulty in obtaining accurate bulk vertical velocities suggest that recovery boiler flow may not be a stationary process, at all locations, at all times. Bendat and Piersol (1986, 437) have shown that the bias error of a time-averaged mean value estimate of a non-stationary random process is proportional to the square of the averaging time T Random error in the estimate should decrease as T becomes larger, so the choice of averaging time T for a non-stationary process must be a compromise between random and bias errors. The demonstrated difficulty in estimating bulk velocities may result from the fact that for a constant averaging time 7 the random and bias errors vary with location in the boiler. If the flow is non-stationary, the only practical way of measuring parameters in a plane is to use simultaneous measurements, as is done in the particle image velocimetry technique. A test for stationarity has been performed using the method describedby Bendat and Piersol (1986, 342-345). The boiler model was configured for the balanced primary and secondary port flow case, and a velocity record was made using the laser-Doppler apparatus. This record was then divided into 25 equal time intervals of 2½ minutes duration each. This time was chosen as representative of measurement intervals during actual runs, over which the data is considered independent. A mean square value was computed for each interval, and the sequence of values is shown in Figure The data were tested for the presence of underlying trends using the run test, and for stationarity using the reverse arrangements test.  92 0.024  0.022 c’1 U)  E  0.020  >  0.018  0.016  0.014  0.012 0  5  10  15  20  25  Measurement  Figure Sequence of Mean Square Measurements, Level 1, w Component Let  it  be hypothesized that the observations are independent, and there are no underlying  trends. At the a=0.02 level of significance, from run distribution tables, the acceptance region for this hypothesis is [7, 19] runs. This hypothesis is accepted, as the number of runs are 13 and 15 for u and w components respectively. Now let it be hypothesized that the data are stationary. From  tables of the reverse arrangements distribution, at the a=0.02 level of significance, the acceptance region is [106, 206] reverse arrangements. The number of reverse arrangements is 131 and 126 for the u and w components respectively, and so the hypothesis of stationarity is accepted at the 2% level of significance. Such a statistical test cannot establish truth, but only states whether the data supports the hypothesis or not, and the term “accepted” should stricdy be replaced by the term “not rejected”. The possibility remains that the flow may still be non-stationary at some locations for some flow configurations.  93 6.2.2  Turbulence  For the configuration of balanced primary and secondary flows only, Figure shows computed power spectral densities (PSD) for the vertical flow component measured on level one. Values were computed for frequencies from the minimum value of 5/7 up to a frequency where the first unrealistic negative value was obtained. The data are plotted against the wavenumber,  k  =  22rf/ U, which has been non-dimensionalized by the boiler half-width, L /2. The results of  Lawn (1971) for the power spectral density of the axial component of turbulent pipe flow are shown for reference. Both the pipe flow data of Lawn and the present spectrum have been non dimensionalized such that  _I_ JS(.k)dk)= 1  (  w  as required by the definition of the power spectral density function. 100  -  —  rI!P now ua  10  Qj Lawn  /  10.2  ..  .::::::.  U)  :  1’  1  *!!HH E /  C”  io 4  LI  io  6 w  1 01  100  101  102  (L12)k  Figure Extended Power Spectral Density, Run 25, Level 1,  1  w Component  94 Below nondimensional wavenumbers of approximately 1O, a noise type spectrum is seen, where computed PSD values are much below those for pipe flow, and which decay only slightly with increasing wavenumber. At higher wavenumbers, evidence is seen of a —5/3 region (inertial subrange), where energy production and viscous dissipation are in balance (Tennekes and Lumley 1972, 248-287). The boiler flow power spectra is seen to approach the —5/3 slope at approximately one log decade higher wavenumber than does the power spectra of fully developed turbulent pipe flow. The use of the boiler width as the non-dimensionalizing value L may be inappropriate due to the greater influence from small scales of turbulence than in pipe flow. The scales of turbulence in the boiler flow may be related to the port sizes, which are nearly two orders of magnitude less than the boiler width. The computed PSD values also do not show a clear separation between frequencies corresponding to unsteadiness and turbulence respectively. Similar results were also seen in computed spectra from velocities measured on level three.  6.2.3  Mixing  Gas mixing dictates the combustion rate and final combustion efficiency. Reaction rates at furnace temperatures are often fast enough that mixing between fuel and oxidizer becomes the limiting step in combustion (Adams and Frederick 1988, 150). Incomplete mixing results in high carbon monoxide and total reduced sulfur (TRS) in the exhaust gases. “While intimate mixing is dependent on very small scale turbulence, gross diffusion of species across the boiler cross section requires regions of fluid shear stress. Such action occurs on the edges of a high velocity jet where the shear stress entrains the surrounding fluid. Large scales of motion provide the power source for the turbulence energy cascade from large to small scales. Low frequency oscillations may be beneficial in the oxidation zone, from approximately above the liquor guns to below the bulinose level. If such low frequency oscillations exist in operating recovery boilers, they probably persist with varying strength throughout the entire volume. Figures and indicate that large vortices approximately half the boiler width in diameter may be slowly convected up the furnace. Unsteady behaviour has also been reported in  95  computations of turbulent flow of symmetrical arrays of opposed rectangular jets in a weak cross flow (Quick, Gartshore, and Salcudean 1993). Oscillations which persist down near the bed will bring oxygen down with them, reducing  the reduction efficiency, and possibly disrupting the bed shape or causing plugging of low velocity primary ports. Should strong oscillations continue up above the bulinose, temperature and flow distributions may be uneven at the superheater entrance, and flow could go backwards through the superheater. However, weak, low frequency oscillations without direction reversals occurring at the superheater entrance might be beneficial in distributing mechanical and thermal loading through the  tube banks. 6.3  Experimental Limitations Modelling, whether mathematical, computational, or physical, is limited as to the accuracy  with which any problem may be represented. Certainly modelling a recovery boiler requires a number of simplifications as to the flow conditions.  6.3.1  Physical Variation  Geometrically, the only significant divergence between model and full-scale is the absence of a char bed shape. Effects on the flowfield resulting from the lack of a bed shape are difficult to ascertain further without experimental testing. Primary jets which would be deflected upward by the bed in the frill-scale are permitted to oppose each other in the model. However, the low velocity primary jets probably cannot penetrate far enough across the cross-section to interact with each other, and may attach to the floor. The higher velocity secondary jets are able to be deflected downward in the model, while they would be constrained by the bed in the full-scale. The effects of gas flow off of the bed are not known. The examination of bed effects is complicated by the fact that bed shape is not constant in an operating furnace. For comparison with computational results, a constant shape would be the simplest addition. However, a shape that is initially deformable by the flow to a constant shape could  96 be used. This could be accomplished by placing a layer of ball-bearings on the furnace floor, of appropriate density so that the forces on the bed scale from model to full-scale. Another method would be to place a plastic bladder on the model floor, connected to the drain hose on the model bottom. Water would be pumped in through the drain line, and the bladder pressurized to maintain a relatively constant shape against the pressure of the primary jets. The shape of the bed during the test would be noted and input to the computational model. Alternatively, a physical bed shape could be machined from Plexiglas or stainless steel and placed in the model. Holes could be placed in the top surface through which water could be pumped to simulate the gas flow off of the bed. The limited accuracy with which port flows may be set in the model affects the accuracy of bulk average vertical velocities calculated from laser-Doppler measurements taken at different locations and time. Flow setting accuracy could be improved through the use of an electronic flow monitoring and controlling system. Ideally, the orifice-plates would be replaced with flowmeters which output a voltage proportional to flowrate. Possible choices include vortex, paddlewheel, rotameter, and turbine flowmeters as well as differential pressure transducers. The present gate-type valves could be replaced with a different type such as globe or butterfly valves, which may be more stable over time. The replacement of the centrifugal pump with one of lower capacity may reduce the tendency of the valves to drift from their set values over time. 6.3.2  Input Information  One of the real problems associated with physical and CFD modelling of recovery boilers is the lack of knowledge of the appropriate full-scale input conditions, even for a purely isothermal case. In a real recovery boiler, air is typically delivered to the air ports at a given level by a windbox wrapping around the boiler perimeter. Air enters on one side, splits in two directions and travels around the boiler to respective sides. The distribution of air to the individual ports is not known, as it  is difficult to accurately measure the port velocities in an operating recovery boiler. Generally, this  is attempted by trying to measure static pressure in the windbox around the boiler at different locations. Through application of Bernoulli’s equation and some empirical corrections, the average  97 port velocity is estimated. No attempt is made to find the distribution of velocity within a port. Unfortunately, static pressure cannot be accurately measured without a priori knowledge of the flow direction. While such windbox measurements can be used by an experienced operator to balance a furnace, it cannot provide accurate input information for a model. In addition, the air ports, particularly the primaries, tend to plug and so vary their effective shape with time. When modelling, one typically assumes equal flows around the model perimeter, and these are applied separately by different hoses, or to great precision by CFD modelling. Monte Carlo simulation may be necessary if small differences in the inputs cause seemingly random variation in the computed flowfields. One other variation in flows between model and full-scale is the lack of air infiltration in the model. Approximately 8.5 percent of the total fan air flow may typically be drawn into by the furnace draft through port and liquor gun openings (Adams and Frederick 1988, 27).  6.3.3  Two-Phase Flow  The effect of the liquor droplets on the flow was neglected in this work. Adams and Horton (1992) have shown that the impact of the liquor sprays on the flowfield is modest due to the relative momentum of the flows and the large droplet size. Any effects should be confined to regions near the liquor guns where jet velocities are the highest and the jet is most concentrated.  6.3.4  Buoyancy Force Effects  An isothermal model cannot represent effects on the flowfield from buoyancy forces. This limitation was accepted at the start of this study as isothermal results are still valid for comparisons with full-scale cold flow tests and isothermal computations. Such computation of the isothermal flowfield is generally carried out before attempting to calculate the coupled energy and momentum equations. A brief examination of expected effects of buoyancy forces is in order. The ratio of inertial to buoyant forces is given by the Froude number for a jet in a crossflow (Schetz 1980)  98 Fr= r g[( P  2 U jet  (  1  —  Pjet) “PiJ  ‘4et  Assuming typical values from §1.22, full-scale Froude numbers vary from 152,000 to 1019 for the tertiary and starting-burner port flows respectively. This indicates that buoyancy forces on  the jets are not significant, although they may become important elsewhere in the flow depending on the local velocity and thermal environment.  99  7.  CONCLUSIONS AND RECOMMENDATIONS Isothermal modelling of a recovery boiler using water as the working fluid has been  accomplished. Principal sources of experimental error will be summarized prior to discussion of major conclusions and recommendations. The error in the actual model flowrate with respect to the set value was shown to be dependent on the orifice-plate flowmeters, and the tendency of the valves to drift. Considering meter error oniy, for a typical run of 150 US gpm total set flowrate, a 95% confidence interval for the expected value of the total flowrate is given by (148.9, 157.3) US gpm. If both meter and drift error are considered, for the same typical run, a 95% confidence interval for the expected value of the total flowrate is given by (130.9, 149.5) US gpm. The major source of error in setting the model flowrate is due to the drifting of valves from the set values. Bulk vertical velocities at the three measurement planes, found by integration of measured vertical velocities, erred from the set values by mean errors of 6.8, 4.8, and 3.2 percent for levels one, two, and three respectively. The error in the measured bulk velocities may be affected by a sampling grid which is too coarse in light of the large velocity gradients, or by non-stationary behaviour of the flow. The central core of vertical upflow thought to dominate boiler flow was, at least for the -  physical boiler and flow configurations examined here, found to represent only a portion of the flow. A central core of upflow was observed near the liquor gun level, but disappeared above the tertiary port level for all flow configurations examined. In the upper regions of the boiler below the bullnose, the upflow was concentrated near the boiler walls, with down or stagnant flow in the central region. It was not possible to balance the port flows so that a stable, central core upflow was present at all levels. The model was found, in the absence of any tertiary level flow, to be extremely sensitive to asymmetries in secondary level port flows. An increase in secondary port flow velocity of 10% on one wall, and a corresponding decrease by 10% in the velocity of the port flows on the opposite wall, caused the region of maximum vertical upflow to occupy the half of the boiler cross-section near the  100 wall with the Lower velocity. The port flow setting apparatus was not accurate enough to test imbalances of less than 10%. Strong iow frequency unsteadiness with periods on an order of 10 to 20 seconds was observed in the velocity power spectral densities. For the case of balanced flows from primary and secondary ports, particle image velocimetry analysis of central, vertical planes, showed gross motions of similar frequencies. At the bulinose level, the location of the region of maximum upflow was seen to oscillate between the boiler front and rear. Such oscillation was also seen at the tertiary level, as was the passage of large vortices on the order of one half the boiler width. The use of concentric load-burner port flows, as opposed to a 2x2 interlaced arrangement of high velocity tertiary ports, was found to provide a more uniform distribution of turbulence kinetic energy in the upper furnace. Configurations employing opposed, high velocity port flows appeared to generate large vortices and regions of unsteadiness. The region of maximum vertical upflow tended to move towards the wall or walls with the lowest port flowrate. This effect has been shown to occur with the secondary ports, and may also occur with high velocity opposed tertiary ports. Swirling or interlaced flow arrangements may be superior for establishing a stable flow condition which is not affected by port plugging or minor changes in port flowrates. The marked tendency for the flow in the upper levels of the boiler to be up near the walls, and the possibility of downflow, should be accounted for in the design of the convective heat transfer section. Methods for reduction of the errors in setting port flowrates in the model by installation of higher quality valves, or a pump of lower capacity, or an electronic flow control system should be investigated. The particle image velocimetry technique should be applied to other flow configurations and boiler models. Possible sources of the observed unsteadiness should be investigated through the testing of other flow configurations and port geometries, and the addition of a char bed shape. Results should be compared against future computational fluid dynamics calculations of flows in the Plymouth boiler. The applicability of particle image velocimetry methods for velocity measurements in cold or hot flows in full-scale boilers should be examined. Finally, to enable an increase in sophistication of recovery boiler modelling, more velocity data on the port flows in full-scale operating recovery boilers should be obtained.  101  REFERENCES Adams, Terry N., and Wm. James Frederick. 1988. Kraft Recovery Boiler Physical and Chemical Processes. New York: The American Paper Institute. Adams, Terry N., and Robert R Horton. 1992. The Effects of Black Liquor Sprays on Gas Phase Flows in a Recovery Boiler, 1992 Engineering Conftrence Proceedings, 81-101. Atlanta: TAPPI Press. Adrian, R.J. 1986. Multi-Point Optical Measurements of Simultaneous Vectors in Unsteady Flow A Review, InternationalJournal ofHeat d Fluid Flow, 7: 127-145.  -  AguI, Juan C., and J. Jimenez. 1987. On the performance of particle tracking, Journal of Fluid Mechanics, 185: 447-468. Bell, W.A. 1981. Spectral Analysis Algorithms for the Laser Velocimeter: A Comparative Study, AJAAJourna42l:714-719.  Bendat, Julius S., and Allan G. Piersol. 1986. Random Data: Analysis and Measurement Procedures, 2nd ed., 1-36. New York: John Wiley & Sons, Inc. Blackwell, Brian. 1992. Validity of physical flow modeling of kraft recovery boilers, Tappi Journai 75(9): 122-128. Bury, Karl V. 1986. Statistical Models in Applied Science. New York: John Wiley & Sons, 1975; reprint, Malabar, Florida: Robert E. Kreiger (page references are to reprint edition). Chao, Y.C., and J.H. Leu. 1992. A fractal reconstruction method for LDV spectral analysis. Experiments in Fluids, 13: 9 1-97. Chapman, P.J, and A.K. Jones. 1990. Recovery Boiler Secondary Air System Development Using Experiments and Computational Fluid Dynamics, 1990 Engineering Conference Proceedings, 193-203. Atlanta: TAPPI Press. Cho Y.C., and H. Park. 1990. Instantaneous Velocity Field Measurement of Objects in Coaxial Rotation Using Digital Image Velocimetry, SPIE Ultrahih and High-Speed Photography, Videography, Photonics, and Velocimetry, (1346): 160-171. Edwards, R.V., ed. 1987. Report of the Special Panel on Statistical Particle Bias Problems in Laser Anemometry, Journal ofFluids Engineering, 109: 89-93. FIND Manual Ver. 3.5.3. 1991. St. Paul: TSI Inc. Fingerson, L.M., R.J. Adrian, R.K. Menon, and S.L. Kaufman. 1991. Data Analysis, Laser Doppler Velocimetry and Particle Image Velocimetry, TSI Short Course Text, 1-16. St. Paul: TSI Inc. Gaster, M., and J.B. Roberts. 1975. Spectrum analysis of randomly sampled signals, Journal of the Institute ofMathematics and its Applications, 15: 195-216.  102 1977. The spectral analysis of randomly sampled records by a direct transform, Proceedings ofthe Royal Society, London, A.354: 27-5 8. Jones, A.K., T.M. Grace, and T.E. Monacelli. 1989. A comparison of computational and experimental methods for determining the gas-flow patterns in the kraft recovery boiler, TappiJournah 72(5): 193-198. Ketler, S.P., M.C. Savage, and I.S. Gartshore. 1993. Physical modeling of flows in black liquor recovery boilers, Tappi journaL 76(9): 97-106. Lawn, C.J. 1971. The determination of the rate of dissipation in turbulent pipe flow, Journal of Fluid Mechanics, 48: 477-505. Lefebvre, B.E., R Burelle. 1989. The Chemical Recovery Boiler Optimized Air System, 1989 Kraft Recovery Operations Seminar Proceedings, 239-246. Adanta: TAPPI Press. Lomas, C.G. 1986. Fundamentals of Hot Wire Anemometry, 190-195. Cambridge: Cambridge University Press. -  Mayo, W.T. 1978. Spectrum measurements with laser velocimeters, Proceedings of Dynamic Flow Conference, Skoolunder, Denmark, 851-868. Denmark: DISA Electronik S/A. Pankhurst, RC., and D.W. Holder. 1968. Wind Tunnel Technique, 2nd ed., 204-211. London: Sir Isaac Pitman & Sons. Perchanok, M.S., D.M. Bruce, and I.S. Gartshore. 1989. Velocity Measurements in an Isothermal Scale Model of a Hog Fuel Boiler Furnace, Journal of Pulp and Paper Science, 15(6): 212219. Quick, J.W., I.S. Gartshore, and M. Salcudean. 1993. The interaction of opposing jets. In Proceedings ofthe Ninth Symposium on “Turbulent Shear Flows” held in Kyoto, Japan, August 16-18, 1993, 64 1-646. Roberts, J.B., and D.B.S. Ajmani, 1986. Spectral analysis of randomly sampled signals using a correlation-based slotting technique, lEE Proceedings, F. 133 (April): 153-162. Sacher, P.W. ed. 1987. Aerodynamic and Related Hydrodynamic Studies Using Water Facilities: AGARD Confrence Proceedings No. 413. Neuilly sur Seine, France: North Atlantic Treaty Organization, Advisory Group for Aerospace Research and Development. Schetz, J.A. 1980. Injection and Mixing in Turbulent Flow. New York: American Institute of Aeronautics and Astronautics. Srikantaiah, D.V., and H.W. Coleman. 1985. Turbulence spectra from individual realization laser velocimetry data, Experiments in Fluids, 3: 3 5-44. Tennekes, H., and J.L. Lumley. 1972. A First Course in Turbulence. Cambridge, Massachusetts: The MIT Press.  103 White, Frank M. 1991. Viscous Fluid Flow. New York: McGraw.-Hill, Inc.  104 APPENDIX A ORIFICE-PLATE CALIBRATION STATISTICS The suitability of a number of distributions for representing the data was explored using probability plotting (Bury 1986, 208). In this technique, the cumulative distribution function of the proposed model is linearized to develop plotting positions. The ordered sample data is plotted against these plotting positions; if a relatively linear relationship is observed, the postulated model cannot be rejected. This technique cannot be used for parameter estimation, but rather for preliminary examination of the suitability of different models. The Weibull model was chosen to represent the data from meter and drift errors from both B9 and D7 orifice-plates. A. 1 Weibull Analysis  -  An example of a Weibull probability plot using meter error from B9 orifice-plates is shown in Figure A. 1.1. Each curve represents one set flowrate tested; the relatively linear relationships between the data and the plotting positions indicate that the hypothesis that the data is modelled by the Weibull distribution cannot be rejected. 1.5  1.0 0.5 0.0  it/f III  0.6  0.8  1.0  1.2  1.4  1.6  1.8  2.0  2.2  Set Flowrate [US —B-— 2.5  3.5 —v--— 4.5 6 —±-— 7.5 —s—— 9 —z——  —-—  2.4  In(measured flowrate) [US gpm]  Figure A. 1.1 Weibull Probability Plot B9 Meter Error Data -  gpml  105 The probability distribution function of the three-parameter Weibull model is =X_lexp{_X_iLJ} ))  fw(x;  where ji<x, —<p<, 0<cr,A  (A.1.1)  The three-parameter Weibull cumulative distribution function is Fw(x; p,  where x  A  ,  A)  =  1  —  exp{_  =  random variable  =  location parameter  =  scale parameter  =  shape parameter  x_}  (A.1.2)  -  The two-parameter Weibull model is a special case of the above when the location parameter j.i  is equal to zero. The Weibull distribution requires that realizations of the random variable x  always be greater than the value of the location parameter. Methods for maximum likelihood estimation and unbiasing of the Weibull parameters by iterative methods are described by Bury (1986, 405 439). The first two moments of the measured data were calculated separately from the -  data for each set flowrate (meter error) or time after flowrate setting (drift error). (A.1.3)  Sq=qIn1l(q;_)2 V  where n  =  (A.1.4)  number of orifice-plates of each respective type.  The sample coefficient of dispersion is a non-dimensional measure of the variance of the measured data  106 S (A.1.5) q  During calibration of the orifice-plates in the recovery boiler water model facility, the back pressure on the orifice-plates was determined by the difference in height of the water free surface and the orifice-plates. This back pressure was kept constant at 1.49 metres of water throughout the trials. When measuring meter errors, times to fill the calibrated cylinder were recorded, and converted to flowrates q=  (A.1.6)  While data must be kept in actual units when calculating statistical quantities, the results may be converted to fractional meter errors as represented by s q_qset  —  8  (A.1.7)  =  S (A.1.8)  Using the Weibull parameters calculated from maximum likelihood methods, the expected value and standard error (square root of the model variance) of the model may be calculated. As the sample size is greater than 15 for both error types and orifice-plate models, large sample methods may be used to calculate confidence intervals and perform hypothesis tests using the calculated expected values and standard errors. Confidence intervals are found as CIonE’ . 2 (z SE+EVzi SE+EV)  where z 41 = a quantile of standardized normal distribution -  107 A.2 Meter Error For testing the meter error, a number of flowrates were chosen to test each type of orificeplate at. These completely covered the range of flows set during all experimental runs, and are shown in Table A.2.1. Table A.2.1 Set Flowrates for Meter Error B9 q, [US gpmj D7 1.5 No Yes 2.0 No Yes 2.5 Yes Yes 3.0 No Yes 3.5 Yes No 4.5 Yes Yes 6.0 Yes Yes 7.5 Yes Yes 9.0 Yes No Statistics of the sampled data from the meter error test for both types of orifice-plate flowmeters are summarized in Table A.2.2. Table A.2.2 Meter Error Means, Standard Deviations, and Coefficients of Dispersion q, B9 6 D7 6meer meter [USgpmJ 8 S 8 S y 1.5 2.0 2.5 3.0 3.5 4.5 6.0 7.5 9.0  -  -  -  -  —0.04346 -  —0.01428 0.02309 0.05174 0.06266 0.07228  0.03833 -  0.03446 0.02636 0.02034 0.01966 0.02103  -  -  —0.8821 -  —2.4134 1.1419 0.3932 0.3138 0.2909  —0.00900 —0.00398 0.04900 0.06075  0.01954 0.02002 0.01960 0.01763  0.01972 0.01994 0.01869 0.01662  -  -  -  0.08967 0.09636 0.10445  0.02086 0.02154 0.01995  0.01915 0.01964 0.01806  -  -  -  Unbiased parameters, expected values, and standard errors of the Weibull random variable representing meter error are shown in Tables A.2.3 and A.2.4. Because the Weibull model requires the use of actual flowrate values, as opposed to errors which may be negative, values shown in the tables are dimensional as opposed to fractional values.  108 Table A.2.3 Meter Error Weibull Model Parameters and Moments B9 Orifice-Plates Model Moments [US gpm] Model Parameters set [USgpm] SE(q) E{q} A 0.1183 0.0 2.437 2.5 2.385 25.16 0.0 0.1472 3.441 29.29 3.507 3.5 4.660 0.0 40.02 4.5 0. 1447 4.596 6.0 0.0 6.302 6.367 0. 1465 54.45 0.0 60.86 7.962 8.036 0.1658 7.5 0.0 9.0 9.641 0.2172 9.738 56.22 -  Table A.2.4 Meter Error Weibull Model Parameters and Moments D7 Orifice-Plates Model Moments [US gpm] q Model Parameters SE(q) [US gpm] E{q} A 1.232 1.486 0.2676 0.03174 1.5 9.611 2.0 2.280 2.008 1.920 0.0995 0.04095 0.1408 2.497 2.622 2.5 0.05183 2.590 3.072 0.1251 3.0 3.182 0.05440 2.145 2.160 0.2237 4.904 4.706 4.5 0.09666 6.0 6.203 0.4191 0.13638 2.991 6.577 2.664 7.894 8.283 0.15720 0.4375 7.5 -  A.3 Drift Error The drift error was measured for the orifice-plates at six different times following the setting of the entire suite of orifice-plates, simulating a real experimental run. The B9 orifice-plates were all set to a flowrate of 3.5 US gallon per minute, while the D7 models were set to 2.5 US gpm. The maximum time for checking the meter error roughly corresponded to the duration of a boiler run. Means and standard deviations of the drift error for B9 and D7 orifice-plates in Table A.3. 1. Table A.3. 1 Drift Error Means, Standard Deviations, and Coefficients of Dispersion B9 Emeter tsjnce set D7 Emeter [mm.] 5 S y y 73.0 147.5 221.5 299.0 372.5 447.5  —0.05280 —0.06250 —0.06522 —0.07702 —0.09130 —0.08634  0.05353 0.05498 0.05646 0.07230 0.07139 0.07136  —1.0138 —0.8797 —0.8657 —0.9387 —0.7819 —0.8265  —0.1217 —0.1439 —0.1483 —0.1767 —0.2178 —0.2472  0.09263 0.10072 0.10694 0.13910 0.18472 0.21520  —0.7613 —0.6700 —0.7210 —0.7874 —0.8482 —0.8705  109 Parameters and moments of the Weibi.ill model for drift error for the B9 and D7 orificeplate flowmeters are shown in Tables A.3.2 and A.3.3 respectively. Table A.3.2 q [USgpm] 73.0 147.5 221.5 299.0 372.5 447.5  Drift Error Weibull Model Parameters and Moments B9 Orifice-Plates Model Moments [US gpm] Model Parameters E{q} SE(q) u A 11 0.0 19.243 3.399 3.306 0.2127 0.0 17.665 3.377 3.277 0.2290 0.0 3.362 17.445 3.261 0.2306 0.0 13.388 3.346 3.219 0.2935 0.0 3.291 13.468 3.167 0.2871 0.0 14.476 3.307 3.190 0.2699  Table A.3.3 q, [US gpm] 73.0 147.5 221.5 299.0 372.5. 447.5  Drift Error Weibull Model Parameters and Moments D7 Orifice-Plates Model Moments [US gpm] Model Parameters E{q } SE(q) A 0.0 2.289 11.972 2.1936 0.2225 0.0 2.242 11.301 2.1437 0.2297 0.0 2.238 10.362 0.2480 2.1322 0.0 2.189 2.0622 8.085 0.3030 0.0 2.122 5.440 1.9578 0.4151 0.0 2.069 1.8824 4.283 0.4964  -  -  110  APPENDIX B POWER SPECTRAL DENSITY CALCULATIONS A simulated laser-Doppler velocimetry signal was generated and used for validation of the direct transform method of power spectral density calculations, and for exploration of the minimum frequency detectable using the method. For thçse purposes, consider a function made up of three sinusoidal components of differing frequency and phase. y (t) where A 1  =  1 A  Sifl( W 1 t+  1  =1 2 A  +  2 Sifl( °2 A  =1 3 A  2)  +  3 Sifl( A  =0.6.27r 1 0)  0)23.0  Jr =  •12  and  A  =  =  time  0)  frequency =  2ir  0)320.  22r  3,r 2  amplitude  t  •  (B.1)  0)3 t+ 3)  phase angle  The simulated signal is shown as a continuous function in Figure B. 1. 3.0  2.0  1.0 C,  a)  >  0.0  C) 0  a)  >  -1.0  -2.0  -3.0 0.0  0.5  1.0  1.5  2.0  time [sec.]  Figure B. 1 Simulated Signal as a Continuous Function  2.5  111 Now the continuous function of Equation B. 1, with a random noise component added, will be sampled at random time intervals corresponding to the arrival of particles in the laser-Doppler velocimeter measurement volume. A total of N random numbers between 0 and 1 will be generated from a larger set of 10*N random numbers, where v  =  mean sampling rate  N  =  number of samples from the continuous signal  It is known that the inter-arrival times of particles in a measurement volume is a Poisson process, and the waiting times to given arrivals may be modelled by the Erlang distribution. The final set of random numbers is thereby used to generate an equal number of realizations of waiting times from the Erlang cumulative distribution function (Bury 1986, 323-326) x F(x; o, A) =  where x  =  =  fj j  exp(_  9  (B.2)  waiting time to -th particle (1 mean inter-arrival-time I =  V  A  =  particle number (integer)  Having chosen a mean sampling rate, the continuous signal of Equation B. 1 is sampled at N= 100 random times as determined by Equation B.2. A random noise component is added to the simulated signal, where the amplitude signal to noise ratio was arbitrarily set equal to 5, a relatively low value. The final randomly sampled random signal is shown in Figure B.2.  112 3.0  2.0  1.0 C,  a)  >  0.0  0  0 ‘1) >  -1.0  -2.0  -3.0 0.0  0.5  1.0  1.5  2.0  2.5  time [sec.]  Figure B.2 Randomly-Sampled Simulated Laser-Doppler Velocity Signal The power spectral density of the simulated signal may now be computed using the methods of §4.2. Holding the number of measurements constant at 100, the mean sampling rate v and total record length Tmay be varied to observe the effects on the output spectra. Plots of computed power spectral density are shown in Figures B3 through B6. It can be seen that a record of longer duration is required to adequately capture the information in the lowest frequencies. The resolution with which each frequency component of the signal is detected could be quantified by peak location and width, but would still somewhat subjective. Note that in Figure B.6 the 20 Hertz component is not visible because the limited number of frequencies at which spectra were computed happen to overlap the narrow bandwidth of the spectral peak.  •  ci  I)  0  ii  -‘  —  p 0 0) 0  p —  t3  0  p  -  p —  o  C  0 0  0 0  0 4.  p  0 0  t’)  o  p  0  o  0  p  o o  S(f) [(mis) 2 /Hz]  T1  p o o p 0  0 -.  o 0 (.  o .  0  o  S(f) [(m/s) 2 /Hz] 0 0)  p  o  0  -I  0 0 0 C)  [(mis)  /2 Hz] 0 0  I>z  o  •  S(f)  N  r * I  I.  0  (P  Ti  0 0)  C,j  c—i  (p  C.,  4  0  N  -h  0 0  0  0  ..  o o C,) 0  -  •  C  0  z  zN:.c  0 0  p  o o  S(f) [(m/s) /2 Hz] p C.) 0  p I’3 (71  o C.) 0)  115 Table B.1 Number of Periods of Each Frequency in Simulated Signal Figure T v f.T [samples/sec.] No. [sec.] 0.6 Hz 20 Hz 3.0 Hz B.3 500 0.259 0.78 0.155 5.18 B.4 250 0.517 1.80 0.310 10.3 100 B.5 1.292 0.775 3.88 25.8 B.6 50 2.584 1.550 7.75 51.7 The number of periods of each of the three frequencies in the simulated signals which are captured on each figure are shown in Table B.1. It was concluded that frequencies greater than approximately 5/ 7 where T is the record length, could be detected with reasonable resolution using  the direct transform method of power spectral density estimation.  116  APPENDIX C SUMMARY OF COMPUTER PROGRAMS DEVELOPED A number of computer programs were developed in the course of this work to accomplish analysis not possible using commercial software. The name and description of each piece of software is shown in Table C.1. With the exception of BOILER13, all programs were written in the ANSI standard C language, and compiled using a Borland compiler for either DOSIWindows or OS/2. They are executable on any personal computer which uses an Intel-compatible 386 or higher processor. An i387 math coprocessor is required for execution using an i386 machine. Unless stated otherwise, all programs were developed and written by the present author. A copy of any of these computer codes may be requested from the Department of Mechanical Engineering, U.B.C.  117  Tide CONCAT13  Table C. 1 Summary of Computer Programs Developed Required Description Comments Operating System Concatenation of multiple DOS Ver. statistics files generated from 5.0 TSI FIND software into format usable by BOILER13 for plotting  BOILER1 3  Plotting three-dimensional velocity vectors onto a wireframe boiler representation  Autocad Ver. 11 under DOS Ver. 5.0  Written in AutoLisp language (provided with AutoCad)  SPECTRA2 1  Computation of power spectral densities from velocity data files generated by TSI FIND software, including graphical display and plotting  OS/2 Ver. ix  Flat memory model and 32-bit speed of OS/2 essential  BUBBLE  Binarization of particle data recorded on a S-VHS tape, including VCR control  Windows Ver. 3.x with DOS Ver. 5.0  Written by G. Rohling, Dept. of Mech. Eng., U.B.C. specifically for SFIARP GPB digitizer  CCR17  Cross-correlation analysis of successive single-exposure images using input files from BUBBLE  OS/2 Ver. 2.x  Flat memory model and 32-bit speed of OS/2 essential  IMGAVG  Temporal averaging of cross-correlation results, and generation of Tecplot format files for plotting and animation  DOS Ver. 5.0  


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