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Evaluation of wind load on large telescope structure based on performance-based design Wang, Ryan Po Chao 2012

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Evaluation of Wind Load on Large Telescope Structure based on Performance-based Design by Ryan Po Chao Wang B.A.Sc., The University of British Columbia, 2012 A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF APPLIED SCIENCE in THE FACULTY OF GRADUATE STUDIES (Civil Engineering) THE UNIVERSITY OF BRITISH COLUMBIA (Vancouver)  October 2012 © Ryan Po Chao Wang, 2012  Abstract Wind loads have been the governing factor that influences structural stability in overwhelmingly large structures. This is particularly of major concern when the analyzed structure in this study is merely a conceptual design. Previous studies have shown reduced pressure on structures due to application of windscreens, and a proposal had been made with preliminary structural analysis performed and proven to be feasible. Therefore, this research aims to analyze the extent of the functionality of the proposed windscreen by utilizing computational fluid dynamics and taking a performance-based design approach with performance objectives determined based on historical environmental data. In addition, different scenarios and boundary conditions are applied to provide a pressure envelope that generalizes the range of pressure experienced by the telescope.  Simulation of air flow is performed with CFDesign, and the results obtained supported the previously-made hypothesis suggesting that implementation of windscreen enables pressure reduction. Although in some cases pressure increase is observed, the general trend of decrease dominates the trend of increase. Pressure envelopes for all structural elements are also provided for engineers as a performance-based design guideline based on different impact levels of wind loading. However, further analyses are needed to investigate the possibility of a windscreen of greater height, to emphasize on the simulation of finer details, and to validate the results from this analysis in an actual scaled-model wind tunnel testing if possible.  ii  Table of Contents  Abstract .................................................................................................................................... ii Table of Contents ................................................................................................................... iii List of Tables ......................................................................................................................... vii List of Figures ......................................................................................................................... ix List of Abbreviations ............................................................................................................ xii Acknowledgements .............................................................................................................. xiii Dedication ............................................................................................................................. xiv Chapter 1:  Introduction ..................................................................................................... 1  1.1  Background ........................................................................................................................... 1  1.2  Telescope Structure ............................................................................................................... 2  1.3  Objectives ............................................................................................................................. 4  Chapter 2: 2.1  Literature Review ........................................................................................... 5  Past Wind Studies ................................................................................................................. 5  2.1.1  Water Tunnel Tests ........................................................................................................... 5  2.1.2  Wind Tunnel Tests............................................................................................................ 6  2.1.3  Numerical Simulation ....................................................................................................... 6  2.1.4  Computational Fluid Dynamics ........................................................................................ 7  2.2  Computational Fluid Dynamics ............................................................................................ 9  2.3  CFDesign ............................................................................................................................ 11  Chapter 3:  Design Approach ........................................................................................... 13  3.1  Allowable Stress Design ..................................................................................................... 13  3.2  Limit States Design ............................................................................................................. 16  3.2.1  Ultimate Limit States ...................................................................................................... 18  3.2.2  Serviceability Limit States .............................................................................................. 20  3.2.3  Fatigue Limit State ......................................................................................................... 21  3.3  Performance-Based Design ................................................................................................. 22  3.3.1  Literature Reviews .......................................................................................................... 22  3.3.1.1  Performance-based Engineering ............................................................................ 22 iii  3.3.1.2 3.3.2  Performance Guideline ................................................................................................... 29  Chapter 4: 4.1  Performance-based Wind Engineering .................................................................. 25  Analysis Procedures ...................................................................................... 33  Model Generation ............................................................................................................... 33  4.1.1  Optic Model .................................................................................................................... 33  4.1.2  Plate Model ..................................................................................................................... 33  4.1.3  Permeable Model ............................................................................................................ 34  4.1.3.1  Literature Review................................................................................................... 34  4.1.3.2  Procedure ............................................................................................................... 37  4.1.3.2.1 Free Area Ratio ................................................................................................. 37 4.1.3.2.2 Permeability ...................................................................................................... 38 4.1.3.3  Methodology .......................................................................................................... 38  4.1.3.4  Analysis Results ..................................................................................................... 40  4.1.4  Windscreen model .......................................................................................................... 41  4.1.5  Enclosure Model ............................................................................................................. 43  4.1.6  Geometric Orientation .................................................................................................... 44  4.1.7  Wind Directions (Angle of Attack) ................................................................................ 44  4.2  CFDesign Wind Load Simulation ....................................................................................... 46  4.3  Boundary conditions of CFDesign Simulation ................................................................... 48  4.4  Result Validation................................................................................................................. 49  4.4.1  Convergence ................................................................................................................... 49  4.4.2  Iteration Steps ................................................................................................................. 49  4.4.3  Automatic and Manual Mesh.......................................................................................... 50  4.4.4  Bernoulli’s Constant ....................................................................................................... 51  Chapter 5: 5.1  Analysis Results............................................................................................. 53  Pressure Variation in Structural Elements .......................................................................... 55  5.1.1  Optic Top surfaces .......................................................................................................... 55  5.1.1.1  0 Degree Orientation .............................................................................................. 55  5.1.1.2  45 Degree Orientation ............................................................................................ 57  5.1.1.3  Pressure Variation .................................................................................................. 59  5.1.2  Optic Bottom Surface ..................................................................................................... 61  5.1.2.1  0 Degree Orientation .............................................................................................. 61  5.1.2.2  45 Degree Orientation ............................................................................................ 63  iv  5.1.2.3 5.1.3  Pressure Variation .................................................................................................. 65  Optic Frame .................................................................................................................... 67  5.1.3.1  0 Degree Orientation .............................................................................................. 67  5.1.3.2  45 Degree Orientation ............................................................................................ 69  5.1.3.3  Pressure Variation .................................................................................................. 71  5.1.4  Support Girders............................................................................................................... 73  5.1.4.1  0 Degree Orientation .............................................................................................. 73  5.1.4.2  45 Degree Orientation ............................................................................................ 75  5.1.4.3  Pressure Variation .................................................................................................. 77  5.1.5  Optic Tube ...................................................................................................................... 79  5.1.5.1  0 Degree Orientation .............................................................................................. 79  5.1.5.2  45 Degree Orientation ............................................................................................ 81  5.1.5.3  Pressure Variation .................................................................................................. 83  5.1.6  Bottom Frames ............................................................................................................... 85  5.1.6.1  0 Degree Orientation .............................................................................................. 85  5.1.6.2  45 Degree Orientation ............................................................................................ 87  5.1.6.3  Pressure Variation .................................................................................................. 89  5.1.7  Top Frames ..................................................................................................................... 91  5.1.7.1  0 Degree Orientation .............................................................................................. 91  5.1.7.2  45 degree orientation.............................................................................................. 93  5.1.7.3  Pressure Variation .................................................................................................. 95  5.1.8  Summary of Individual Structural Element Analysis ..................................................... 96  5.2  Comparison of Model Types............................................................................................... 98  5.3  Pressure Envelope ............................................................................................................. 100  5.4  Validation .......................................................................................................................... 101  5.4.1  Convergence ................................................................................................................. 101  5.4.2  Iteration Steps ............................................................................................................... 105  5.4.3  Mesh Generation........................................................................................................... 109  5.4.4  Bernoulli’s Constant ..................................................................................................... 111  Chapter 6:  Conclusion ................................................................................................... 115  Bibliography ........................................................................................................................ 117 Appendices ........................................................................................................................... 121 Appendix A : Pressure on Structural Elements .............................................................................. 121 v  A.1  Pressure Envelope of Optic Top Surface ...................................................................... 121  A.2  Pressure Envelope of Optic Bottom Surface ................................................................ 122  A.3  Pressure Envelope of Optic Frames .............................................................................. 125  A.4  Pressure Envelope of Support Girders .......................................................................... 127  A.5  Pressure Envelope of Optic Tube ................................................................................. 129  A.6  Pressure Range of Bottom Frames ............................................................................... 131  A.7  Pressure Envelope of Top Frames ................................................................................ 133  Appendix B : Pressure on Structural Elements .............................................................................. 135 B.1  Bernoulli Constants for Telescope Models ................................................................... 135  B.2  Bernoulli Constants for Telescope with Windscreen Models....................................... 136  vi  List of Tables Table 3.1 Performance guideline of impact loads on concrete beams ................................. 24 Table 3.2 Probability analysis of wind data ......................................................................... 25 Table 3.3 Performance levels of wind loads ........................................................................ 26 Table 3.4 Performance groups of structural requirements ................................................... 27 Table 3.5 Performance-based design guideline ................................................................... 32 Table 4.1 Pressure Variation between different methods .................................................... 40 Table 4.2  List of models ...................................................................................................... 46  Table 4.3 Boundary conditions in CFDesign ....................................................................... 48 Table 4.4 Bernoulli’s Principle ............................................................................................ 51 Table 5.2 Summary of pressure for optic top surfaces with 0° orientation ......................... 55 Table 5.3 Summary of pressure for optic top surfaces with 45° orientation ....................... 57 Table 5.4 Pressure variation in percentage of optic top surfaces ......................................... 59 Table 5.5 Pressure variation in magnitude of optic top surfaces ......................................... 59 Table 5.6 Summary of pressure for optic bottom surfaces with 0° orientation ................... 61 Table 5.7 Summary of pressure for optic bottom surfaces with 45° orientation ................. 63 Table 5.8 Pressure variation in percentage of optic bottom surfaces .................................. 65 Table 5.9 Pressure variation in magnitude of optic bottom surfaces ................................... 66 Table 5.10 Summary of pressure for optic frames with 0° orientation ................................ 67 Table 5.11 Summary of pressure for optic frames with 45° orientation ............................... 69 Table 5.12 Pressure variation in percentage of optic frames ............................................... 71 Table 5.13 Percentage variation in magnitude of optic frames ........................................... 71 Table 5.14 Summary of pressure for support girders with 0° orientation ........................... 73 Table 5.15 Summary of pressure for support girders with 45° orientation ......................... 75 Table 5.16 Pressure variation in percentage of support girders ........................................... 77 Table 5.17 Pressure variation in magnitude of support girders ........................................... 77 Table 5.18 Summary of pressure for optic tube with 0° orientation .................................... 79 Table 5.19 Summary of pressure for optic tube with 45° orientation.................................. 81 Table 5.20 Pressure variation in percentage of optic tube ................................................... 83 Table 5.21 Pressure variation in magnitude of optic tube ................................................... 83 vii  Table 5.22 Summary of pressure for bottom frames with 0° orientation ............................ 85 Table 5.23 Summary of pressure for bottom frames with 45° orientation .......................... 87 Table 5.24 Pressure variation in percentage of bottom frames ............................................ 89 Table 5.25 Pressure variation in magnitude of bottom frames ............................................ 89 Table 5.26  Summary of pressure for top frames with 0° orientation .................................. 91  Table 5.27  Summary of pressure for top frames with 45° orientation ................................ 93  Table 5.28  Pressure variation in percentage of top frames .................................................. 95  Table 5.29  Pressure variation in magnitude of top frames .................................................. 95  Table 5.30 Pressure envelope of structural elements .......................................................... 100 Table 5.31 Velocity and pressure values from 100 and 200 iteration steps ...................... 105 Table 5.32 Percentage different between different iteration results .................................. 107 Table 5.33 Pressure values of different iterations .............................................................. 108 Table 5.34 Pressure variations between different mesh generation methods .................... 110 Table 5.35  Coordinates for telescope models .................................................................... 111  Table 5.36  Coordinates for telescope with windscreen models ......................................... 112  viii  List of Figures Figure 3.1  Allowable Stress Design..................................................................................... 14  Figure 3.2  Probability of ultimate limit states design .......................................................... 18  Figure 3.3  Relationship between load and displacement ..................................................... 19  Figure 3.4  Deflection requirement ....................................................................................... 20  Figure 3.5  Performance-based earthquake engineering procedures .................................... 23  Figure 3.6  Historical wind data ............................................................................................ 30  Figure 3.7  Annual recorded data of weather conditions ...................................................... 30  Figure 4.1  Telescope Structure ............................................................................................ 34  Figure 4.2  Relationship between drag coefficient and angle of attack ................................ 35  Figure 4.3  Relationship between resistance coefficient and permeability ........................... 36  Figure 4.4  90 degree Angle of Attack .................................................................................. 39  Figure 4.5  0 Degree Angle of Attack ................................................................................... 39  Figure 4.6  Reading Locations of 90 Degree Angle of Attack ............................................. 40  Figure 4.7  Reading Locations of 0 Degree Angle of Attack ............................................... 41  Figure 4.8  Windscreen model in 3D .................................................................................... 42  Figure 4.9  Enclosure model in 3D ....................................................................................... 43  Figure 4.10  Telescope orientation of 45 degree and 0 degree ............................................. 44  Figure 4.11  Angle of attack ................................................................................................. 45  Figure 5.1  Components of telescopes .................................................................................. 54  Figure 5.2  Optic top surfaces ............................................................................................... 55  Figure 5.3  Pressure variation of optic top surfaces at 0° attack angle and 0° orientation ... 56  Figure 5.4  Pressure variation of optic top surfaces at 90° attack angle and 0° orientation . 56  Figure 5.5  Pressure variation of optic top surfaces at 0° attack angle and 45° orientation . 57  Figure 5.6  Pressure variation of optic top surfaces at 90° attack angle and 45° orientation 58  Figure 5.7  Pressure variation of optic top surfaces at 180° attack angle and 45° orientation  ................................................................................................................................................. 58 Figure 5.8  Optic bottom surfaces ......................................................................................... 61  Figure 5.9  Pressure variation of optic bottom surfaces at 0° attack angle and 0° orientation  ................................................................................................................................................. 62 ix  Figure 5.10  Pressure variation of optic bottom surfaces at 90° attack angle and 0°  orientation ............................................................................................................................... 62 Figure 5.11  First contacting surfaces of different orientations ............................................ 63  Figure 5.12  Pressure variation of optic bottom surfaces at 0° attack angle and 45°  orientation ............................................................................................................................... 64 Figure 5.13  Pressure variation of optic bottom surfaces at 90° attack angle and 45°  orientation ............................................................................................................................... 64 Figure 5.14  Pressure variation of optic bottom surfaces at 180° attack angle and 45°  orientation ............................................................................................................................... 64 Figure 5.15  Optic frames ..................................................................................................... 67  Figure 5.16  Pressure variation of optic frames at 0° attack angle and 0° orientation .......... 68  Figure 5.17  Pressure variation of optic frames at 90° attack angle and 0° orientation ........ 68  Figure 5.18  Pressure variation of optic frames at 0° attack angle and 45° orientation ........ 69  Figure 5.19  Pressure variation of optic frames at 90° attack angle and 45° orientation ...... 70  Figure 5.20  Pressure variation of optic frames at 180° attack angle and 45° orientation .... 70  Figure 5.21  Support girders ................................................................................................. 73  Figure 5.22  Pressure variation of support girders at 0° attack angle and 0° orientation ..... 74  Figure 5.23  Pressure variation of support girders at 90° attack angle and 0° orientation ... 74  Figure 5.24  Pressure variation of support girders at 0° attack angle and 45° orientation ... 75  Figure 5.25  Pressure variation of support girders at 90° attack angle and 45° orientation . 76  Figure 5.26  Pressure variation of support girders at 180° attack angle and 45° orientation 76  Figure 5.27  Optic tube ......................................................................................................... 79  Figure 5.28  Pressure variation of optic tube at 0° attack angle and 0° orientation .............. 80  Figure 5.29  Pressure variation of optic tube at 90° attack angle and 0° orientation ............ 80  Figure 5.30  Pressure variation of optic tube at 0° attack angle and 45° orientation ............ 81  Figure 5.31  Pressure variation of optic tube at 90° attack angle and 45° orientation .......... 82  Figure 5.32  Pressure variation of optic tube at 180° attack angle and 45° orientation ........ 82  Figure 5.33  Bottom frames .................................................................................................. 85  Figure 5.34  Pressure variation of bottom frames at 0° attack angle and 0° orientation ...... 86  Figure 5.35  Pressure variation of bottom frames at 90° attack angle and 0° orientation .... 86  Figure 5.36  Pressure variation of bottom frames at 0° attack angle and 45° orientation .... 87  x  Figure 5.37  Pressure variation of bottom frames at 90° attack angle and 45° orientation .. 88  Figure 5.38  Pressure variation of bottom frames at 180° attack angle and 45° orientation 88  Figure 5.39  Top frames ........................................................................................................ 91  Figure 5.40  Pressure variation of top frames at 0° attack angle and 0° orientation ............. 92  Figure 5.41  Pressure variation of top frames at 90° attack angle and 0° orientation ........... 92  Figure 5.42  Pressure variation of top frames at 0° attack angle and 45° orientation ........... 93  Figure 5.43  Pressure variation of top frames at 90° attack angle and 45° orientation ......... 94  Figure 5.44  Pressure variation of top frames at 180° attack angle and 45° orientation ....... 94  Figure 5.45  Pressure variation between types of model ...................................................... 98  Figure 5.46  Velocity convergence plot of plate models .................................................... 101  Figure 5.47  Pressure convergence plot of plate models .................................................... 102  Figure 5.48  Velocity convergence plot of permeable models .......................................... 103  Figure 5.49  Pressure convergence plot of permeable models............................................ 103  Figure 5.50  Velocity convergence plot of optic models .................................................... 104  Figure 5.51  Pressure convergence plot of optic models .................................................... 104  Figure 5.52  Iteration validation of velocity ....................................................................... 106  Figure 5.53  Iteration validation of pressure ....................................................................... 106  Figure 5.54  Pressure values of different iterations ............................................................ 108  Figure 5.55  Pressure variations between different mesh generation methods ................... 110  Figure 5.56  Bernoulli’s constants for telescope models .................................................... 112  Figure 5.57  Bernoulli’s constants for telescope and windscreen models .......................... 113  xi  List of Abbreviations CFD – Computational Fluid Dynamics PBWE – Performance-based Wind Engineering DM – Damage Measures EDP – Engineering Demand Parameters  xii  Acknowledgements I offer my sincere gratitude to Dr. Siegfried. F. Stiemer as my valuable instructor who broadens my vision of engineering and provides his own time and effort to accompany me in the pursuit of knowledge. I thank the employees at Dynamic Structure Ltd who patiently respond to my seemingly endless questions and provide valuable answers of significance to my research, especially Mr. David J. Halliday, Dr. Ye Zhou, and Dr. Nathan Loewen, who happened to show unconditional encouragement when needed the most. Special thanks to Dr. Wudi and Christopher Man, who have shown great support throughout my years of education, both physically and morally.  xiii  Dedication  This thesis is dedicated to the old me from last year who was vastly reluctant in continuing my professional education in Masters of Applied Science, as well as my supporting family who is enthusiastically supporting and encouraging in my final decision.  xiv  Chapter 1: Introduction 1.1  Background  One of the major concerns for operating an extremely large telescope is the reduction of operation efficiency due to excessive wind loads. It has been proven that larger wetted surfaces experience more dynamic wind forces due to their geometry (Vogiatzis et al.). Although past researches and analyses have been conducted to evaluate the turbulence profile and resulting loading on telescope structures, the telescope involved in this study with such large dimensions is merely a conceptual design. It should also be noted that difficulties involved in a large structure with unproven feasibility are rather obvious when accounting for the square-cube law, which depicts that direct scaling up of existing designs may lead to failure due to the mass increase by the cube of the scale factor when its surface area increases only by the square (Stiemer, 2010). Consequently, previous guidelines and approaches with proven feasibility should serve as references only.  Pressure variation around the telescope is created as wind flows through structures. Fluctuation in pressure can also be generated by turbulence that is capable of significant damages such as excessive vibrations. Turbulence may exist due to several factors including, but not limited to, local topography characteristics and airflow through openings in telescope structures and ventilation openings. Cho et al. (2002) performed a study on the South Gemini Observatory and analyzed the source of pressure variation. The results indicated the maximum variability of pressure tends to be on the right and left sides of mirrors relative to the wind direction. It was also shown that the dynamic pressure differences are mainly caused by the interaction between airflow and telescope structure rather than the turbulence  1  in the incoming wind (Cho et al., 2002). As a result, this study will heavily emphasize on the pressure distribution due to airflow on surfaces of structural elements.  Former research conducted by Upnere et al. (2012) had shown the severe impacts of wind loading on telescope performance and operation, whether or not the damage is significant or insignificant, using computational fluid dynamics. Thus, the importance of mitigating wind loads lead to a proposal of windscreen from Dr. Siegfried. F. Stiemer from University of British Columbia (2011). In the proposal, an adjustable windscreen is recommended; however, no evidence was provided to prove its extent of efficiency because it was presented as a preliminary design concept (Stiemer, 2011). In addition, other studies had indicated the relevant turbulence caused by the interaction between enclosure systems and telescope structures (MacMynowski et al. 2006). Although typical enclosure systems are in smaller scale than windscreens, they can still be related as they both serve the purpose of protecting telescopes. Therefore, this study will study the effect of windscreen on reducing wind loads.  1.2  Telescope Structure  The telescope structure to be analyzed in this study is a conceptual design without previous construction records close to its scale. Therefore, it presents itself as a major advancement forward beyond the current standards (Dynamic Structures Ltd. 2011). The proposed concept consists of an 80 meter height telescope that weights 6500 tones and contains typical components such as optics, mirror modules, support frames, base structures, and mechanical components, and an enclosure system that will house the telescope during operation downtime to prevent prolonged exposure to wind loads and dusting.  2  The telescope is an idealization and a conceptual design of the final product; however, structural elements have undergone finite element analysis and sensitivity analysis to meet the performance requirements. The enclosure system is a box-shaped structure with a door that can slide open to allow sufficient room for the telescope to exit for wider astronomically observational angles. In addition, an independent windscreen is proposed to locate around the telescope for enhancing structural stability, reducing resultant wind speed, and alleviating wind-induced pressure. The windscreen is currently designed to be 31 meters in height with minimum opening on one side to allow linear retractable movement of the enclosure system.  The structural and mechanical concept is previously developed with precise engineering techniques and thorough numerical computations and simulations to establish strong feasibility. It was concluded that such proposal is possible with aids of technical knowledge and professional experiences from the past.  3  1.3  Objectives  One of the purposes of this study is to estimate and evaluate the potential pressure distribution on the telescope structure under specified weather conditions based on historical weather records retrieved from Atacama Large Millimeter/submillimeter Array and based on the performance objectives determined through a probabilistic approach. Also, it aims to review the static pressures induced by wind loads on the telescope and investigate the differences between models with or without windscreen applied as a validation to the previously proposed theory. Furthermore, by summarizing the data from simulations involved in this research, it is hoped to establish a systematic envelope of pressure profile to generalize the wind-induced loading such that it can serve as a reference for future designs based on the performance-based impact levels. By accomplishing these goals, it will enable the audience a more thorough understanding of wind load effects on the proposed telescope structure as a feasibility study for possible future analysis.  4  Chapter 2: Literature Review  2.1  Past Wind Studies  To achieve the goals mentioned above, the methodology utilized in this study needs to be determined as priority based on past approaches with proven validity. Over the years extensive studies have been performed to evaluate airflow around large telescopes and their protecting structures. These studies also focused on the distributed wind loads and are published through reports and papers. Some of the common techniques used include water tunnel tests, wind tunnel tests, numerical modeling, and computational fluid dynamics.  2.1.1  Water Tunnel Tests  Water tunnel testing, although less commonly applied, have been used on several telescope projects. For instance, this technique was implemented on the design of enclosures of Apache Point Observatory, Sloan Digital Sky Survey telescope, and Gemini Observatory (Cho et al. 2002).  As an effective approach to estimate efficiency of enclosure and an economical method to profile flow path, water tunnel testing does show its advantages in wind studies; however, disadvantages do exist. Due to the considerable variations in Reynolds number, water tunnel tests are incapable of capturing precise turbulence profile and of presenting numerical data regarding wind loading. (Cho et al. 2002)  5  2.1.2  Wind Tunnel Tests  Wind tunnel tests, as a another reliable and credible wind study method, have been widely implemented into a large number of telescope and enclosure designs to determine distributed forces and applied pressures on surfaces of structures (Cho et al. 2002). For example, extensive wind tunnel tests were conducted for the Giant Magellan Telescope, a 25-meter optical/infrared extremely large telescope built by multiple universities and research institutions, to investigate the wind flow around and through the enclosure and the distributed wind loads on the structure (Johns et al, 2012).  It is beneficial to implement wind tunnel tests as data can be used to map out flow profiles accurately even with different wind orientations (Johns et al. 2012). Also, static pressures on tested structures or scaled-models can be recorded to gain a better understanding of the distributed loads. Nevertheless, due to the lack of continuity when recording data, mapping of simultaneous pressure values experienced by structures cannot be accomplished. Also, the Reynolds number must be accurately matched to the expected operating conditions to have credible outcomes to represent reality (Cho et al, 2002).  2.1.3  Numerical Simulation  Numerical strategy for analyzing fluid dynamics or aerodynamics is more of a purely mathematical approach in which models and equations are selected first to obtain a qualitative and quantitative outcome. For instance, Codina et al. (1999) implemented incompressible Navier-Stokes equations with Smagorinsky’s turbulence model, followed by discretizing these equations according to the standard trapezoidal rule in a finite element  6  formulation. As a result, the flow assessment could be applied on the design of a large telescope building based on the same aerodynamic methodology to prove its reliability. Another analysis using numerical simulation is conducted by Pescador et al. (1999) who used Reynolds Stress Method to solve differential transport equations while considering non-local effects to analyze enclosure degradation for Roque de los Muchachos Observatory.  2.1.4  Computational Fluid Dynamics  As a branch of fluid mechanics that gradually becomes extensively utilized to analyze fluid flow patterns with numerical methods and algorithms, computational fluid dynamics, usually abbreviated as CFD, has been applied commonly on several telescope and enclosure projects (Cho et al, 2012). For instance, this methodology is applied to the design of the Thirty Meter Telescope (TMT) in the United States as an evolutionary approach of modeling for performance estimation (Vogiatzis, 2008). CFD simulation for TMT included wind loading on the telescope structure and the housing enclosure, general topology and configuration, flow profiles, and steady and unsteady simulation. Also, CFD modeling is applied to study the wind flow around and through the structure of the Giant Magellan Telescope (Johns et al. 2012). Additionally, MacMynowski et al. (2006) applied CFD to summarize wind characteristics and turbulence to enable dynamic modeling.  Although past CFD analysis have shown significant data variation to conclude that qualitative results can only be achieved if CFD models capture sufficient geometric details to represent actual structures (Cho et la, 2012). Nevertheless, due to the lack of scaled models  7  and funding for wind or water tunnel testing, it was determined that the most efficient and inexpensive approach is simulation using computational fluid dynamic models.  8  2.2  Computational Fluid Dynamics  The fundamental principles of computational fluid dynamics are the Navier-Stokes equations that are the differential form of linear momentum principle by considering forces acting on small elements (Finnemore and Franzini, 2002). The forces accounted for consist of gravitational, viscous, and pressure forces. The equations are particularly of interest because they are able to determine the behavior of fluids in multiple fields such as environmental science and aerodynamics. Combining with various numerical computation methods, computational fluid dynamics divide the flow region of interest into multiple small elements and solve the resultant flow fields iteratively to obtain final visualization of flow profiles Finnemore and Franzini, 2002). Since each element is divided into fine mesh, the discretization methods used should be addressed carefully to handle discontinuity accurately. Typical discretization methods include finite volume method, finite element method, and spectral element method.  Another valuable aspect of computational fluid dynamics is the convergence issue that is typically involved in all CFD analyses. CFD analyses are intended to solve non-linear and unsteady phenomena such as turbulent flows; therefore, an exact and converged solution is normally not guaranteed to be reached since the numerical simulation is prone to experience the identical problems like the actual processes in reality (Nafems, 2012). In mathematics, convergence is defined as the limiting behavior of an infinite sequence or series while the existence of a limit may be uncertain or unknown (CFD Online, 2012). As the solutions are continuously improved by iterative processes to be more precise, they are usually recognized as “converged” when they are sufficiently close to a particular constant where changes of  9  final values are relatively insignificant compared to the previously obtained result. In other words, the number of unsatisfied residual equations that are discretized is kept within a desirable limit to reach an acceptable outcome (Nafems, 2012).  10  2.3  CFDesign  CFDesign is a simulation program that iterates possible flow and thermal patterns based on user-defined boundary conditions and material properties. It can be viewed as a development process that eliminates the needs of prototype lab testing (CFD Online, 20120). Ranges of functions include simulation of fluid flow, heat transfer, electronics design, and mechanical motions. As a well-known industry application, CFDesign is highly flexible at generating multiple working environment and design approaches for the users to determine the most suitable design. Typically, CFDesign can import CAD models directly to facilitate tooling options and simulation analysis. It can also detect challenging features in imported models that may result in computational difficulties present the options of eliminating them automatically or manually.  As mesh generates the discretized elements in complex 3D simulation, its importance is undoubtedly well-recognized. CFDesign automatically creates the suitable mesh size and distributes them in accordance with the model surface geometry to ensure iteration accuracy. The enhancement function also provides a further tuning adjustment to the automatic mesh as it adds element counts and layers along interfaces between different materials to closely analyze the contacting surfaces (CFDesign Online, 2012). It also produces a smooth distribution along challenging features such as walls and sharp corners to avoid simulation that may result in inaccurate flow prediction. In addition, layer enhancement enables sufficient mesh along small gaps and edges such that these complex feature can be analyzed thoroughly and precisely.  11  Although AIAA’s Meshing, Visualization, and Computational Environment Technical Committee admits that no evident conclusion has shown the direct correlation between mesh and solution accuracy, a mesh is still an important intermediate product to facilitate the simulation of flow patterns (Another Fine Mesh, 2012). A mesh has no characteristic requirement but to be sufficient to capture details around features such that desired analysis can perform (Nafems, 2012). Therefore, the accuracy of the result of this analysis will be heavily dependent on the convergence.  12  Chapter 3: Design Approach In this section, three different design methods are reviewed and evaluated based on their extent of capabilities to determine the optimal solution for this research. The methods discussed are Allowable Stress Design, Limit States Design, and Performance-based Design.  3.1  Allowable Stress Design  Allowable stress design is a design philosophy emphasizing on elastic limits that are not to be exceeded by service loads applied on structures as the ultimate guideline. Factors of safety are thus applied to ensure such limitation is satisfied. Allowable stress design compares the allowable stress level, which is computed by dividing the nominal strength by a factor of safety to limit the capacity below material yielding point, to the actual stress level. The concept in illustrated below in the figure. This methodology has been implemented by engineers into structural design for more than 150 years (Yang, 2009).  13  Figure 3.1  Allowable Stress Design  Source: Quimby, 2008 The fundamental concept of this methodology is limiting the sum of individual loads using load combination equations that take the probability of loads occurring simultaneously into account (Civil Engineering Terms, 2012). Load factors are applied to individual loads in the load combination equations. Afterwards, the outcomes are checked with the actual stress levels to ensure capacities are not exceeded.  As a conservative approach that yields safe results, elastic analysis of applied loads are compatible for the design, and it is acceptable to assume the structural elements to act in a perfectly elastic behavior. There are also other available references as a major benefit of employing this design philosophy since this method has been acknowledged for a long period of time; nevertheless, disadvantages surely are inevitable (Civil Engineering Terms, 2012). For instance, since this method has gradually been replaced by limit states design 14  internationally in recent years, latest researches and literature reviews are rather limited to have a thorough validation against updated standards. In addition, it is almost impossible to predict or even observe the failure modes because structural capacity is kept within the elastic range. Due to the same reason, preliminary structural failure warnings cannot be observed and investigated precisely as a safety study in contrast to Limit States Design method, which allows elements to fail in specified modes for particular structural purposes such as seismic energy dissipation (Civil Engineering Terms, 2012).  15  3.2  Limit States Design  Limit States Design is a design philosophy that has gradually replaced Allowable Stress Design as a more sophisticated approach to represent actual material behaviour due to its consideration of inelastic behaviour, ultimate failure, and redistribution of applied loads after elastic range (Civil Engineering Terms, 2012). Multiple structural theories are employed into this methodology, including elastic theory that accounts for serviceability limit states, fatigue limit state, and ultimate limit states of linearly elastic systems, and plastic theory that considers ultimate limit states of ductile systems (Metten, 2011). The limit states that are most commonly applied can be categorized into two groups based on whether or not the load factors are applied: ultimate limit states are examined with factors applied to the loads while serviceability limit states are analyzed using unfactored loads.  Ultimate Limit State:   Exceeding load carrying capacity    Overturning    Sliding    Fracture    Fatigue (crack propagation)  Serviceability Limit State:   Deflection    Vibration    Permanent deformation  16  The limit states design process typically begins with determining the loads experienced by structural elements and follows by applying load factors that are provided by building codes to generate factored loads. Similarly, factored resistance is obtained through the same steps. After member resistance is calculated, it is multiplied by a reduction factor to give the factored resistance. The factored resistance must be greater than the factored loads to satisfy the limit states and guarantee structural integrity and safety as the ultimate goal of implementing this design methodology. The factors involved account for the uncertainty and probabilistic nature of loads that may come from statistical errors when producing load and resistance factors and human errors (Metten, 2011).  As a relatively newer design philosophy compared to Allowable Stress Design, limit states design lacks some of the old references to validate results with; however, plastic design concept takes the material behavior after yielding into account as one of the benefits that makes limit states design well recognized (Civil Engineering Terms, 2012). In addition, limit states design utilizes different load factors for different load types to account for uncertainty in design parameters such as probability of overload, number of occurrences, and change of loading locations as opposed to allowable stress design that applies constant safety factor for every loading scenario (Civil Engineering Terms, 2012). Furthermore, as discussed in earlier sections, limit states design monitors and considers behavior at collapse. Nevertheless, this design approach does have its disadvantage of incompatibility between analyzed elastic behaviour and actual plastic material behavior.  17  3.2.1  Ultimate Limit States  The fundamental objective of limit states analysis is to guarantee safety and functionality by ensuring factored loads are not greater than factored resistance (Metten, 2011). The desired relationship is illustrated in the figure below to show the bell curves with a mean value where L stands for loads and R stands for resistance. The shaded area indicates that failure zone where load carrying capacity is lower than the applied loads and thus should be avoided during design at all times. Therefore, implementing this design method is to confirm that the capacity of factored resistance exceeds the demand of factored loading to have a sufficiently structurally stable structure.  Figure 3.2  Probability of ultimate limit states design  Source: Marshal, 1983  18  In order to estimate the load carrying capacity to account for both elastic behavior and plastic strength, it is common to refer to the estimates of buckling strength of structural components that is shown as point A below in the figure and typically computed by applying an adjustment factor to the elastic limit (ULS Design of Steel-plated Structures).  Figure 3.3  Relationship between load and displacement  Source: ULS Design of Steel-plated Structures  As structures reach beyond the elastic threshold, there is residual strength that can still be utilized due to plastic behavior. Therefore, the ultimate strength may be desired sometimes to be considered as a safety margin for an economic solution when utilizing the remaining plastic strength (ULS Design of Steel-plated Structures). Another advantage of such action is to access the degree of survivability and residual tolerance level for structures that are already damaged. 19  The figure above also indicates the design load level to be slightly higher than the elastic strength limit. This aims to purposely direct the failure mechanism to ideally occur in ductile instead of brittle failure as ductile behavior is capable of redistributing internal stresses and absorb significant energy before failure mechanism occurs in contrast to brittle behavior that allows sudden collapse without preceding warnings (ULS Design of Steel-plated Structures).  3.2.2  Serviceability Limit States  Serviceability limit states consider deflections, vibrations, and permanent deformations that are evaluated using variable loads such as live load, snow load, and wind load, instead of permanent loads like dead load (Metten, 2011).  Figure 3.4  Deflection requirement  Source: ULS Design of Steel-plated Structures  The figure provided above illustrates the typical deflection criteria examined in limit states design (reference). The maximum deflection is represented by is the camber value,  , where  is the immediate deflection due to permanent loading applied after  structures are completed, and  is the deflection over time due to any variable load and any  20  succeeding deformation due to permanent loads (ULS Design of Steel-plated Structures). There are no assigned load combinations for serviceability computations; however, the final calculation results should be verified with standards published in the Steel Handbook of Construction (CISC, 2009).  3.2.3  Fatigue Limit State  Fatigue limit state evaluates crack propagation due to stress concentration under repeated loading and is usually a function of magnitude and range of stress values on structures during its serviceable lifespan (Metten, 2011). This limit state typically does not govern for residential buildings because variable live loads are relatively much smaller than permanent dead loads that constitute the majority of loading. As a result, the stress range fluctuation is rather limited to a small degree to present itself as a minor safety concern. Nevertheless, for structures undergo dramatic stress fluctuations on a regular basis, such as bridges and roads, this requirement should definitely be evaluated and inspected carefully and thoroughly (Metten, 2011).  21  3.3  Performance-Based Design  Performance based design approach has become widely recognized as the ideal solution when it comes to assessing risk analysis and uncertainties in regards to natural or man-made hazards. It serves as the combination between form and function of any structure to be a guideline with multi-criteria, multi-disciplinary evaluation of behavior functions (Kalay, 1999). Coverage of this methodology ranges from designing new buildings to rehabilitation of existing ones. Performance based design evaluates risk and uncertainties induced by sitespecific characteristics on a probabilistic basis and relates performance goals to structural solutions according to the needs of structures to develop target objectives, as well as grouping them into different levels of requirements. Furthermore, this design approach is capable of extending throughout the building life cycle, from the beginning of the project to the end, including preliminary design, construction stage, post operation, and demolition procedures (Jain et al, 2001). Consequently, after comparison between the three distinctive methods discussed in this report, performance based design approach will be implemented in this study to achieve the goal of optimal design solution of the proposed telescope structure.  3.3.1 3.3.1.1  Literature Reviews Performance-based Engineering  Performance based design was first introduced as a structural analytical application to the seismic division of civil engineering as performance-based seismic design (PBSD) by the researchers of the Pacific Earthquake Engineering Research Center (Pertrini and Ciampoli, 2010). It was employed to quantify performance objectives without the restraints that conventional design philosophy is usually accompanied with. This method also aims to  22  establish bridging connection between demands and performance, thus enabling engineers to predict outcomes within a reasonable amount of certainty after natural hazards or unexpected emergencies (Murphy, 2011).  Dr. Yang and associates at the University of Berkley have developed Performance Based Earthquake Engineering that is appropriate for measuring building damages and quantifying repair costs after seismic excitations (Yang et al, 2009). This approach is further utilized to design innovative seismic resisting systems and develop associated damage states (Yang et al, 2011). The design process is separated into four steps: seismic hazard analysis that defines the magnitude and frequency of potential earthquake excitation, response analysis that determines the engineering design parameters including inter-story drift and story acceleration, damage analysis that evaluates the different performance groups involved in the study, and loss analysis that estimates the possible costs of repair based on the results from damage analysis and the arbitrarily chosen repair methods (Yang et al, 2011).  Figure 3.5  Performance-based earthquake engineering procedures  Source: Yang et al, 2011  23  Performance-based design approach is also applied to study the effect of perpendicular impact loads on concrete structures and develop performance guideline of quantified objectives (Tachibana et al, 2010). This study examines the behavior of concrete beams under accidental rock falls, which is, however, treated as a certain scenario of identified variable parameter, through physical experiments. Developed level of impact actions and performance criterions are shown in the table below. This performance guideline shows direct relations between designed impact action levels and expected structure performance, and it is based on these relations that engineers can refer to as target requirements depending on structure importance and functionality constraints.  Table 3.1  Performance guideline of impact loads on concrete beams  Source: Tachibana et al, 2010  The performance objectives proposed by Tachibana et al. to study the vertical impact loads on concrete beams can serve as a reference to the analysis of wind loads for this study. Although due to the difference in requirements of structural performance and building purposes, some of the objectives presented in the later section of the report may vary considerably. However, the structural demand parameters of damage, safety, serviceability, and repair addressed can be applied. 24  3.3.1.2  Performance-based Wind Engineering  Another branch of performance-based design that has been extensively researched on and applied in industries over the years based on derivation of the previous methods developed for seismic engineering is wind engineering (Ciampoli et al, 2011). This was first introduced by an Italian research project (Ciampoli et al, 2011).  Table 3.2  Probability analysis of wind data  Source: Jain et al, 2001  A study on performance-based wind design of tall buildings under extreme wind loads was carried out by Jain et al (2001). In this study, a probabilistic analysis comprised of mixed distribution and Monte Carlo simulation is combined with probability distribution of historical records to generate performance range of different wind speeds. The table provided above shows the wind hazard levels that were investigated in a statistical approach to relate probability of exceedance directly with mean return periods. The same probabilistic method will be applied on the telescope structure involved in this study to establish levels of wind loading. In light to study regarding the climatology at the building site and the topographic effects, Jain et al (2001) created the performance-based design hazard levels as indicated in the table below and inspected the resultant pressure distribution along the height of the proposed building to assist engineers in achieving target objectives.  25  Table 3.3  Performance levels of wind loads  Source: Jain et al, 2001  Another study regarding performance-based wind engineering was performed by Ciampoli et al. (2011) to generalize a framework of procedures of PBWE and to further apply the proposed methodology on a case study of assessment of the serviceability of a suspension bridge. Decision variables were implemented in the research as particular performance requirements of, for example, building safety during disastrous events, damage tolerance and survivability, and repair time and costs. The probability of exceeding a relevant value of the corresponding decision variables was stated to be directly related to the evaluation of risks. Ciampolo et al. (2011) also employed complementary cumulative distribution function to express probability of exceedance of decision variables that accounted for site-specific hazards, structural response, and the connection between damage and the associated decision variable. Consequently, the subsequent steps are presented by Ciampoli et al. (2011) as general procedures of PBWE.  As the first step, site hazard analysis is performed to consider the characteristics of wind intensity and relevant turbulence profile, as well as the interaction relationship between structural properties and wind field. These are referred to as the intensity measure vector, IM, which are highly susceptible to environmental factors. The following step is structural analysis that involves selection of engineering demand parameter, EDP, to identify important 26  structural performance requirement such as inter-storey drifts, displacements, stress, etc. This step also involves identifying damage parameter measure, DM, which is used to quantify expected damages due to wind loads regarding performance objectives. The third step is to quantify performance objectives by characterizing decision variables in relation to the resultant damages of structures, followed by evaluating risks based on a probabilistic approach for each decision variable. At last, the final step of the procedure is the optimization of design structures by minimizing possible risks. During this stage, economical losses as well as casualties and losses of lives should be taken into account; nevertheless, Ciampoli et al. (2011) also pointed out that rather than determining the optimal design in the proposed method, in reality it is more common to compare the associated risks of each design solution. A design case study of a suspension bridge is also implemented in the research as a validation of the proposed procedure. The considered performances and failure criteria is provided in the table below in which performance objectives consist of different levels of serviceability in relation to the engineering design parameters of rotational velocities and their relevant threshold limitations.  Table 3.4  Performance groups of structural requirements  Source: Ciampoli et al, 2011  27  The generalized procedure discussed in the preceding paragraph is applied to the telescope structure of this study as it can greatly benefit from the similarities in performance-based design approach. A detailed discussion regarding the relevance will be provided in later section of the report.  Another research of great relevance and correlation to this study is done by Petrini and Ciampoli (2012) to investigate the performance-based design of tall buildings. Petrini and Ciampoli (2011) studied the performance-based wind design procedures of tall buildings to accounts for both functionality and comfort. A set of decision variables, DV, is introduced as measurable attributes that represents target performance requirements (Petrini and Ciampoli, 2012). The authors applied the procedures that are previously developed by Ciampoli et al. (2011) First of all, site-specific and structure design parameters are identified before commence of analysis of dynamic structural response, followed by characterizing and evaluating the decision variables, which determines and quantifies the different levels of performance objective in terms of consequential damages. Afterwards, risk assessments were performed on the basis of uncertainty and probabilistic nature of the design variables, and the optimal designs were decided to minimizing risks and maximizing desired functionality of buildings. In short, this is the direct application of the previously discussed design procedure to further enhance the validity.  28  3.3.2  Performance Guideline  For the proposed telescope under significantly high performance requirements as calibration of optics needs to be sufficiently accurate to the nanometers in order to maximize the visibilities and image resolution, structure is extremely sensitive to any kind of hazards. Therefore, it is essential to study the wind data of the selected site carefully based on historical records as the first step in the procedure proposed by Ciampoli et al. (2011).  The proposed site to allocate the telescope structure is Chajnantor that is on a high (5000m) plateau southwest of Cerro Chajnator, Chile. The meteorological conditions of the area around have been monitored since 1995 to be a highly suitable location for astronomical observation at millimeter and submillimeter due to the extraordinary atmospheric conditions (ALMA, 2011). There has been statistical weather data recorded over the years. As a typical weather condition in the southern hemisphere, summer is characterized by higher temperature, higher humidity, low wind speeds, and slightly higher pressures in comparison to winter.  Temperature fluctuation may result in element shrinkage and expansion, which is capable of significant displacement considering the effect of error accumulation. However, because only wind disturbance is at concern in this research, issues regarding temperature variation are therefore neglected. Since the flow patterns and the resultant wind speed around the telescope structure are at concern in this study, yearly wind data is used to generate the performance guideline for CFD analysis. According to the online data provided by ALMA, there’s sustained wind for more than one hour of up to 32 m/s and wind gusts of up to 46 m/s  29  (ALMA, 2011). Also, the average wind speed within the 3rd quartile is 7 m/s and 9 m/s in winter and summer respectively, as indicated by the figure below.  Figure 3.6  Historical wind data  Source: ALMA, 2011  Figure 3.7  Annual recorded data of weather conditions  Source: Dynamic Structures Ltd. 2012  30  A probabilistic approach is taken to address the uncertainties in wind loading according to the recorded site conditions. The weather statistics are shown in the figure provided above, and it should be noted that yellow indicates the full moon period during which no observation was made and no data was recorded. Out of the observed nights with a total number of 309, strong wind velocities are only observed and recorded in 5 nights. That gives us a percentage of 1.6 percent of occurring as the worst case scenario, assuming cloudy and partially cloudy periods generate wind velocities lower than maximum wind gusts. These data are combined with average wind speeds provided in the statistical data plot, as well as recorded sustained wind of 32 m/s for more than one hour that is neglected during the process of smoothing median filter, to serve as intensity measure IM.  The next step is to provide structural analysis and identify engineering demand parameters. Previous structural analysis had satisfied code-specified requirements, but will not be discussed in this report due to confidentiality issues. Nevertheless, computational fluid dynamic simulation is applied to this study as another analytical approach to study the induced pressure on structural elements. Through distributed pressure on element surfaces, engineering demand parameters such as maximum stresses, cyclic loading, and differential displacements can be derived. In addition, damage parameter measure, DM, are reviewed to quantify damages in relation to the considered performance objectives. In reference to the performance guideline discussed in the literature review, the telescope structure is to be designed to experience no damage under yearly average wind speed, slight damage under higher recorded wind speed, in which case regular maintenance would suffice, and higher damage due to sustained wind gusts such that immediate attention is necessary. It should be  31  noted that damage addressed here is not necessarily limited to physical damages of structures but also include readjustment or recalibration of equipment or operation downtime.  After the damage parameters are properly defined, the following step consists of quantifying performance objectives in terms of consequences of damage. Since the decision variables must be distinguished between low performance level, which concerns structural and personal safety such as permanent damages and displacements as well as losses of lives, and high performance level, which affect only serviceability and occupant discomfort, the objectives are set as full serviceability without operation downtime, full serviceability with slight operation downtime due to regular scheduled maintenance, and partial serviceability with immediate attention required. However, this by adopting this method it is impossible to quantify intangible losses that cannot be defined in monetary terms (Ciampoli et al. 2011). Consequently, the performance guideline for this research is listed as below.  Table 3.5  Impact Action  Performance-based design guideline  Wind Speed  Occurrence frequency Average wind speed  Level 1  9 m/s  corresponding to very frequent occurrence  Performance  Full Serviceability  Damage and Repair  No damage  Possible sustained high Level 2  32 m/s  wind speed corresponding to wind occurrence during  Full serviceability  Regular maintenance needed  cloudy periods  Level 3  46 m/s  Maximum wind gusts  Serviceability  corresponding to 1.6  affected slightly  Readjustment of  percent of occurrence  due to wind  equipment required  annually  disturbance  32  Chapter 4: Analysis Procedures  4.1  4.1.1  Model Generation  Optic Model  The optic model is used to represent the actual telescope as a reasonable simplification with valuable and necessary components presented in sufficient details while eliminating the minor elements that are less significant and would not interfere considerably with analytical outcomes when absent. Due to confidentiality issues no figures can be shown in this report. The material assigned for the structure is steel with a wall roughness value of zero. The optics is modeled as glass with the same wall roughness value of zero.  4.1.2  Plate Model  The plate model is a further simplification of the optic model discussed above. It is created to generate more diverse results for pressure envelope as a solid plate model shares less similarities with the actual telescope. Subsequently, differences are expected between results generated by these two models, and a detailed comparison for validity and compatibility will be addressed and discussed in the result section. Although having a completely solid plate to replace the optics in simulation will certainly introduce inaccuracies into the analysis process, it is hoped to still be capable of serving as a reference for pressure assessment due to more compression resulted from solid plates.  33  Figure 4.1  Telescope Structure  Source: Generated by AutoCAD Inventor Professional \ 4.1.3 4.1.3.1  Permeable Model Literature Review  Due to the incapability of the solid plate model to optimally represent the geometric features of actual optics such that different patterns of wind disturbance and fluctuations of applied pressure will be resulted, adopting permeable layers to replace the solid plates with distributed resistance is proposed and aims to function as an another approach to represent the optics in the telescope. It is an intermediate solution between the plate model and the optic model. As void spaces are present between optics in the telescope, it is necessary to take those into account as they serve as potential sources of turbulence.  34  Past academic research regarding possible influence of permeable materials on wind loads had been conducted to show the effect on resultant resistance. Cohen et al. studied the relationship between drag coefficient, in other words, flow resistance of porous reflectors and the angle of attack using practical experiments.  Figure 4.2  Relationship between drag coefficient and angle of attack  Source: Cohen et al.  The results indicated minimum resistance at the lowest angle of attack; as a result, flow passes through porous reflectors at a parallel orientation is subjected to the least disturbance with the highest wind separation effect.  35  Figure 4.3  Relationship between resistance coefficient and permeability  Source: Miguel, 1998  Another experiment performed by Antonio F. Miguel (1998) also yielded in credible results that can serve as a reference for the permeability study in this analysis. The principles of fluid mechanics with mathematical equations were applied on experiments to examine the flow characteristics around porous screens based on the relationship between permeability and resistance coefficient as shown above in the figure. The effect of different Reynolds’ number is also included in the study, and it was found that the influence is apparent on the magnitude of resistance coefficient and follows similar trend shown in the graph above. Conclusion was made to state that as permeability of the studied material increases, the wind velocity across the material rises.  36  4.1.3.2  Procedure  A computational fluid dynamic program named CFDesign is utilized to perform flow analysis. CFDesign has preinstalled functions to simulate distributed resistance to represent obstructions. The mesh elements in the region of interest are assigned a resistance parameter to model the potential effect of having obstacles in the flow path. The available approaches include constant loss coefficients, free area ratio, friction factor, pressure-flow rate curve, and permeability coefficient (Darcy equation). Due to the scope of this project and the limited existing data, free area ratio and permeability coefficient are utilized to perform simple experiments and to be validated against the academic research findings to determine the ideal approach that is most suitably applicable to this analysis.  4.1.3.2.1  Free Area Ratio  As a comparatively simpler method to represent obstructions, this method utilizes the equation listed below.  Source: CFDesign, 2012 By monitoring prescribed void spaces within the region with assigned resistance to allow fluid flow, it aims to capture the flow pattern within and around the structure within a certain extent of similarities as that would happen with the actual telescope optics. Based on the details provided by a third party in the industry, the ratio is calculated according to the model geometry and results in a number of 0.38.  37  4.1.3.2.2  Permeability  Using Darcy equation to generate the permeability value to implement in the analysis, the resultant resistance remains constant in all directions based on the formula provided below. The permeability constant, k, comes in the unit of m2.  Source: CFDesign, 2012 Difficulties were experienced during application of this method due to the lack of existing data. The permeability value was estimated under the assumption that it is half of the solid plate, which is determined using CFDesign according to the pressure drop with a presumed wind velocity of 46 m/s. The actual numerical value employed in the analysis shall not affect the result significantly as long as the key objective is to compare the differential patterns.  4.1.3.3  Methodology  The telescope models are run in CFDesign with angle of attack of both 0 degree and 90 degrees with an arbitrarily selected incoming wind velocity of 46 m/s as shown in the pictures provided below. These two extreme cases are chosen due to their most evident variations in results as expected that will facilitate the comparison processes. In order to verify the validity of the two methods discussed above, the resultant applied pressures on model faces and edges will be examined and reviewed for applicability after comparison with the academic research findings. In addition, to further increase the credibility of this analysis, solid plate models are also implemented to gain more comparison data to reach a reliable conclusion. In addition, bother simulated cases are illustrated with figures below to explain  38  the flow pattern around structures to provide a fundamental understanding of how streamlines are separated due to various geometric features.  Figure 4.4  90 degree Angle of Attack  Source: Generated by CFDesign Figure 4.5  0 Degree Angle of Attack  Source: Generated by CFDesign  39  4.1.3.4  Analysis Results  Distributed pressure readings are taken directly from CFDeisgn to investigate the maximum normal pressure and suction pressure. Provided Below are a summary table of the pressure from all methods and figures indicating the locations of maximum pressure on the system.  Table 4.1  Pressure Variation between different methods  Static Pressure (Pa) Location Free Area Ratio Permeability Solid Plate  Figure 4.6  90 Degree Angle of Attack Exterior Frame Edge 139.6 121.134 5420.8  Optic Face 85 79.3 5538.9  0 Degree Angle of Attack Exterior Frame Edge 48.7 160.1 1526.3  Optic Face 38.8 127.5 274.5  Reading Locations of 90 Degree Angle of Attack  Source: Generated by CFDesign  40  Figure 4.7  Reading Locations of 0 Degree Angle of Attack  Source: Generated by CFDesign  The numerical data obtained show consistency in the free area ratio method and the solid plate model where resultant wind pressure from 90 degree angle of attack is higher than the readings from 0 degree angle of attack. However, the permeability coefficient approach produced the completely opposite results with pressure from 0 degree angle of attack higher than the 90 degree angle of attack. Consequently, after verifying these numerical outcomes with the academic research findings discussed earlier, the free area ratio method is implemented into this telescope study as a simpler approach yet with higher academic validity. By using this method, it is hoped to generate a suitable representation of optics that captures the geometric features without jeopardizing data accuracy.  4.1.4  Windscreen model  A windscreen model, proposed by Dr. Stiemer of the University of British Columbia, is applied to all of the previously discussed telescope models to study the efficiency of reducing pressure. As mentioned before, a massive structure this size with a large gravitational dead  41  weight is highly susceptible to wind disturbance due to its low structure frequency caused by high stiffness value. In addition, structures with strict demands for functionality and performance requirement such as astronomical telescopes typically fine-tune its positioning to the nearest nanometers. Consequently, one of the key objectives of this study is to investigate the effectiveness of employing windscreen on reducing pressure on the structure.  The proposed windscreen is 31 meters high with an opening for exist to allow the enclosure structure to slide out along preinstalled rails. The picture below shows the design preview of such model (Stiemer, 2011). The material assigned to monitor windscreen in CFDesign is polystyrene as the available option that has the closest material properties to common windscreens.  Figure 4.8  Windscreen model in 3D  Source: Stiemer, 2011  42  4.1.5  Enclosure Model  The enclosure model is to mainly house the telescope while it is off operation to avoid excessive exposure to wind load and equipment worn-off. It is a cube-shaped box structure that is located on 2 rail tracks as a mean of linear movement of the enclosure system. When the telescope is in use, the sliding door will open and roll away to allow sufficient room for rotation around the telescope to perform astronomical observation.  Before the model was proposed, a series of requirements were evaluated to generate the optimized outcome. For example, the telescope must be protected from potential hazardous elements from the exterior while providing sufficient interior spaces for instruments, personnel, facilities, and operation and being able to move freely at a reasonable cost. As a result, the final preferred outcome particularly emphasizes on a light weight design that extracts in a linear motion with minimum space needed. The proposed mechanism also conserves energy due to its simplicity.  Figure 4.9  Enclosure model in 3D  Source: Stiemer, 2011 43  4.1.6  Geometric Orientation  It is inevitable for the proposed telescope to rotate around in all angles to monitor any desired astronomical bodies; thus, orientations are divided into 2 separate cases to gain a more thorough understanding of how the possible outcomes may be: 0 degree and 45 degree orientations. Due to the support mechanism of the base structure, the telescope cannot rotate further down than 45 degrees where the optic frames are in contact with the top edge of the bottom girders. Implementation of these 2 separate models aims to achieve an envelope by generating the most extreme variations in induced pressures.  Figure 4.10  Telescope orientation of 45 degree and 0 degree  Source: Generated by CFDesign  4.1.7  Wind Directions (Angle of Attack)  In light to the asymmetric nature of the telescope and the possible changes of wind directions, it is of best interest to study the effect of wind coming from all directions. Therefore, a total of 2 separate cases are applied to the 0 degree orientation: 0 degree and 90  44  degree attack angle, and a total of 3 are applied to the 45 degree orientation: 0 degree, 90 degree, and 180 degree attack angle.  Figure 4.11  Angle of attack  Due to hardware limitations, it is impossible to analyze the models including telescope, windscreen, and enclosure all at once because of the significant number of mesh accounts and the relatively fine elements compared to the entire scale such that external volume cannot be generated. Therefore, they are excluded from this study.  45  4.2  CFDesign Wind Load Simulation  The models listed above are created in AutoCAD Professional 2013, including plate model, permeability plate model using free area ratio method, and optics model and exported into CFDesign with boundary conditions of 46 m/s, 32 m/s, and 9 m/s from an incoming attack angle of 0 degree, 90 degree, and 180 degree.  Table 4.2  List of models  Model Types No Windscreen Orientation  Attack Angle 0  Windscreen  Plate  Permeable  Optics  Plate  Permeable  Optics  Model  Model  Model  Model  Model  Model  0  0  0  0  0  0  Wind Speed  45  45  45  45  45  45  (m/s) 46 32 9  90  46 32 9  180  46 32 9  Cases with different inbound wind velocities will be studied separately according to the performance guideline mentioned earlier. In addition, the fluid is assumed to be incompressible as an application of the Bernoulli’s principle.  46  It is the purpose of this study to investigate the applied pressures on structures coming from simulated flows. However, due to the large amount of elements in these models, it is more efficient to summarize average pressure readings on structural elements in accordance to their performance functions. As a result, the element categories are divided into 7 major groups: optic top surface, optic bottom surface, optic frame, support girders, optic tube, bottom frames, and top frames. Although the simplification process might result in reduction of accuracy as taking average values causes overlooking of particular components, it is the purpose of this study to provide a more generalized range.  Moreover, the efficiency of windscreen on reducing resultant pressure is examined by comparing the differences in pressure values. Detailed discussion will be provided with the assistance of tables and figures for better understanding. At last, pressure range containing maximum and minimum values obtained from both cases involving telescope and windscreen will be made as an envelope to provide a fundamental knowledge of the loads that the structure might experience.  47  4.3  Boundary conditions of CFDesign Simulation  Table 4.3  Boundary conditions in CFDesign  Source: Generated by CFDesign  The figure above shows the setup of boundary conditions in CFDesign. In the picture, black represents incoming fluid velocity, blue represents slip/symmetry that causes fluid to flow along a wall instead of stopping at a wall, and yellow represents pressure that is typically set as zero to be a flow outlet. The fluid velocity is set as normal magnitude to flow in perpendicularly to the plane.  48  4.4  Result Validation  The subsequent validation methods are implemented to verify the reliability of the analytical results.  4.4.1  Convergence  As mentioned in the introduction of this report, computational fluid dynamic analyses do not guarantee a precisely accurate solution due to the nature of iterative process such that unsatisfied residual equations may still exist when analysis stops, whether automatically or manually. In addition, CFDesign Online Help also points out that in some aerodynamic and hydrodynamic analyses in which induced forces are investigated, the solution may have had not been reached before it is stopped (CFDesign Online Help, 2011). Thus, it is necessary to review the convergence graph of the models in this study and check for indication of acceptable accuracy.  Convergence plot of each model will be exported into excel from CFDesign and emphasized on velocity and static pressure as these two parameters are the most relevant in this study.  4.4.2  Iteration Steps  The amount of iteration for models involved in this study is arbitrarily chosen as 100 steps. Although more iteration may lead to more accurate results if the converged limit moves closer towards the actual solution, due to hardware limitations, an amount of 100 was selected as the default number selected by the CFDesign and believed to be sufficiently appropriate to produce credible output. Nevertheless, it is necessary to review the possible variation that may occur from having a different number of iteration. As a result, one of the  49  models is selected to run analysis with 200 iterations, and the output values will be compared for consistency, as well as their associated convergence plots. This validation aims to emphasize closely on the effect of iteration amount on the accuracy of flow simulation.  The model selected is a plate model with zero degree orientation, an attack angle of zero degree, and an incoming wind speed of 46 m/s. It is selected arbitrarily because the result with 100 iterations seems to converge.  4.4.3  Automatic and Manual Mesh  Automatic mesh generation is applied to all models as the first attempt to assign mesh elements, and this approach functions perfectly well on the plate and permeable plate models to produce data for detailed investigation; however, this does not apply to optic models. It is impossible to run optic models with automatic mesh generation as the element count typically exceeds 2 million, and it is definitely beyond the limitation of available hardware capability. Therefore, an alternative of manual mesh generation was resulted to provide a smaller mesh element count for the analysis to be able to perform successfully. However, the accuracy may be at risk as the automatically determined meshes are the optimal setting to include sufficient features and exclude excessive details. As a result, the plate model with 0 degree orientation and 0 degree angle of attack is run with manual mesh setting to examine the differences comparing to automatic mesh generation.  50  4.4.4  Bernoulli’s Constant  Bernoulli’s principle is applied in this study to assume incompressible fluid for every model; thus, an applicable validation method is using the Bernoulli’s constant to check for consistency along a streamline.  Table 4.4  Bernoulli’s Principle  Source: Jack and Lewis, 2012  Bernoulli’s principle states that an increase in the speed of the fluid is always accompanied by a decrease in pressure or a decrease in the fluid’s potential energy. This concept can be verified by the figure provided above, which illustrates that along a streamline with consistent potential energy, the pressure value (P1) at the location with larger cross sectional area and lower flow velocity will be greater than the pressure value (P2) at the location with smaller cross sectional area and higher velocity. Consequently, the equation below is derived and utilized in this study to justify the analytical results.  Source: Finnemore and Franzini, 2002  51  Using the formula provided above, two arbitrary points are selected along a streamline in the model with 0 degree orientation and 0 degree of wind attack angle, and the constant value along that streamline is computed for comparison. The outcomes are shown in the next chapter.  52  Chapter 5: Analysis Results In this section of the report, each structural element groups will be discussed individually to closely investigate the applied pressure due to wind loads in different models with different boundary values and geometric orientations. Comparison will also be made between telescope structures and the addition of windscreens to examine the efficiency in possible reduction and produce a generalized pressure variation in both magnitude and percentage differences. In addition, discussion will be made regarding the differences or similarities in different models and the data they generate. At last, pressure range containing the maximum and minimum pressure experienced by all structural elements will be summarized in a table to provide an approximate envelope.  The element groups addressed include optic top surfaces, optic bottom surfaces, optic support frames, optic tube, support girders, bottom frames, top frames.  53  Figure 5.1 Components of telescopes  Source: Generated by AutoCAD Inventor Professional  54  5.1  Pressure Variation in Structural Elements  5.1.1  Optic Top surfaces  Figure 5.2  Optic top surfaces  Source: Generated by CFDesign 5.1.1.1  0 Degree Orientation  The table below lists the difference in resultant pressures due to wind loads between pure telescope and the addition of windscreen for 0 degree orientation.  Table 5.1  Summary of pressure for optic top surfaces with 0° orientation  Optic Top Surface Wind Attack Speed Angle (m/s) 46 0 32 9 46 90 32 9  0 Degree Orientation Plate Model 485.6 232.0 17.6 732.7 357.5 29.5  No Windscreen Permeable Model 618.2 293.3 21.9 518.5 249.8 19.0  Optics Model 368.9 173.2 12.5 425.3 205.1 15.9  Plate Model 223.7 105.8 9.0 666.4 318.2 24.8  Windscreen Permeable Model 353.5 149.9 10.7 479.4 227.8 17.0  Optics Model 95.7 50.1 4.4 413.0 209.8 16.3  55  Before commence of detailed analysis, it should be noted that there is an evident pattern of pressure trend that decreases as wind speed drops from 46 m/s to 9 m/s. This is observed in every single model utilized in this study; therefore, to simplify and facilitate the reading process for the benefits of audience, only cases with 46 m/s wind speed will be graphed in this section. Please refer to Appendix for the rest of the graphs.  Pressure variation of optic top surfaces at 0° attack angle and 0° orientation  Figure 5.3  Pressure Variation - 0 degree attack angle @ 46m/s  Pressure (Pa)  700.0 600.0 500.0 400.0 300.0 200.0 100.0 0.0  No Windscreen Windscreen  Plate Model  Permeable Model  Optics Model  Model Type  Pressure variation of optic top surfaces at 90° attack angle and 0° orientation  Pressure Variation - 90 degree attack angle @ 46m/s 800.0 700.0 600.0 Pressure (Pa)  Figure 5.4  500.0 400.0  No Windscreen  300.0  Windscreen  200.0 100.0 0.0 Plate Model  Permeable Model  Optics Model  Model Type  56  For all three telescope models, there is an obvious trend of pressure reduction shown by the analytical results such that windscreen is capable of reducing wind load when the geometric orientation is 0 degree, whether or not the angle of attack is 0 or 90, as the figures show above; however, different results are observed in models with a 45 degree orientation.  5.1.1.2  45 Degree Orientation  Table 5.2  Summary of pressure for optic top surfaces with 45° orientation  Optic Top Surface Wind Attack Speed Angle (m/s) 46 0 32 9 46 90 32 9 46 180 32 9  Plate Model 3588.5 1742.8 138.4 294.5 143.2 12.2 373.3 177.6 13.4  No Windscreen Permeable Model 1324.8 639.7 57.6 425.7 204.5 15.6 829.7 399.5 32.6  Optics Model 1950.0 928.3 69.9 306.0 160.9 14.9 492.1 250.7 22.2  Plate Model 803.1 392.9 31.8 318.4 155.0 12.6 626.0 303.0 23.3  Windscreen Permeable Model 320.8 153.2 11.6 609.1 291.6 21.9 398.1 190.6 14.8  Optics Model 822.9 414.3 34.0 327.0 153.8 13.3 910.0 436.0 34.0  Pressure variation of optic top surfaces at 0° attack angle and 45° orientation  Pressure Variation - 0 degree attack angle @ 46m/s 4000.0 Pressure (Pa)  Figure 5.5  45 Degree Orientation  3000.0 2000.0  No Windscreen  1000.0  Windscreen  0.0 Plate Model  Permeable Model  Optics Model  Model Type  57  Pressure variation of optic top surfaces at 90° attack angle and 45° orientation  Figure 5.6  Pressure Variation - 90 degree attack angle @ 46m/s Pressure (Pa)  800.0 600.0 400.0  No Windscreen  200.0  Windscreen  0.0 Plate Model  Permeable Model  Optics Model  Model Type  Figure 5.7  Pressure variation of optic top surfaces at 180° attack angle and 45° orientation  Pressure Variation - 180 degree attack angle @ 46m/s Pressure (Pa)  1000.0 800.0 600.0 400.0  No Windscreen  200.0  Windscreen  0.0 Plate Model  Permeable Model  Optics Model  Model Type  Based on the comparison made in the graphs shown above, having windscreen can occasionally result in higher wind load for the optic surfaces. This scenario is particularly dominant when wind is coming at a 180 degree angle from the back of the structure that results in almost 200% increase of the original value.  58  5.1.1.3  Pressure Variation  Table 5.3  Pressure variation in percentage of optic top surfaces  Optic Frames Attack Angle  0°  90°  180°  Table 5.4  Wind Speed 46 m/s 32 m/s 9 m/s 46 m/s 32 m/s 9 m/s 46 m/s 32 m/s 9 m/s  0°  90°  180°  53.9  42.8  74.1  77.6  75.8  57.8  54.4  48.9  71.1  77.5  76.1  55.4  48.6  51.0  65.2  77.0  79.9  51.4  9.0  7.5  2.9  -8.1  -43.1  -6.9  11.0  8.8  -2.3  -8.2  -42.6  4.4  15.9  10.5  -2.5  -3.4  -40.5  10.5  -67.7  52.0  -84.9  -70.6  52.3  -73.9  -74.4  54.6  -53.4  N/A  Pressure variation in magnitude of optic top surfaces  Optic Frames Attack Angle  Percentage Variation (%) 0 Degree Orientation 45 Degree Orientation Plate Permeable Optics Plate Permeable Optics Model Model Model Model Model Model  Wind Speed 46 m/s 32 m/s 9 m/s 46 m/s 32 m/s 9 m/s 46 m/s 32 m/s 9 m/s  Magnitude Variation (Pa) 0 Degree Orientation 45 Degree Orientation Plate Permeable Optics Plate Permeable Optics Model Model Model Model Model Model 261.8  264.7  273.2  2785.4  1004.0  1127.1  126.2  143.4  123.1  1349.9  486.5  514.0  8.5  11.2  8.2  106.6  46.0  35.9  66.3  39.1  12.3  -23.9  -183.4  -21.0  39.3  22.0  -4.7  -11.8  -87.1  7.1  4.7  2.0  -0.4  -0.4  -6.3  1.6  -252.7  431.6  -417.9  -125.4  208.9  -185.3  -9.9  17.8  -11.8  N/A  59  The tables above show pressure difference in percentage and magnitude, respectively. A positive number indicates reduction and a negative number indicates pressure increase after implementing windscreen, and this is applicable for the remaining tables provided in this section. Based on the percentage variation, the maximum increase in pressure in 85%, which is slightly higher than the maximum reduction of 78%; however, the maximum reduction in terms of magnitude is much higher than the maximum increase. There is a decrease of almost 3000 Pascal and an increase of 430 Pascal. As a result, the windscreen is determined to be capable of functioning as it is intended to originally to reduce pressure due to wind load.  60  5.1.2  Optic Bottom Surface  The figure below illustrates the surfaces where the pressure reading is taken from.  Figure 5.8  Optic bottom surfaces  Source: Generated by CFDesign 5.1.2.1  0 Degree Orientation  Table 5.5  Summary of pressure for optic bottom surfaces with 0° orientation  Optic Bottom Surfaces Wind Attack Speed Angle (m/s) 46 32 0.00 9 46 90.00 32 9  0 Degree Orientation Plate Model 1284.3 615.5 45.9 1323.1 641.2 51.2  No Windscreen Permeable Model 656.9 313.8 23.5 626.5 302.1 23.2  Optics Model 1334.8 631.2 45.8 1605.6 774.2 59.5  Plate Model 375.3 177.3 12.8 675.7 325.4 25.4  Windscreen Permeable Model 331.6 158.9 11.5 522.6 248.7 18.7  Optics Model 420.5 218.0 16.3 798.5 384.1 31.0  61  Pressure variation of optic bottom surfaces at 0 ° attack angle and 0° orientation  Figure 5.9  Pressure Variation - 0 degree attack angle @ 46m/s 1600.0 1400.0 Pressure (Pa)  1200.0 1000.0 800.0  No Windscreen  600.0  Windscreen  400.0 200.0 0.0 Plate Model  Permeable Model  Optics Model  Model Type  Figure 5.10  Pressure variation of optic bottom surfaces at 90° attack angle and 0° orientation  Pressure (Pa)  Pressure Variation - 90 degree attack angle @ 46m/s 1800.0 1600.0 1400.0 1200.0 1000.0 800.0 600.0 400.0 200.0 0.0  No Windscreen Windscreen  Plate Model  Permeable Model  Optics Model  Model Type  The optic bottom surfaces experience lower pressure as data exhibits evident decrease in the figures provided above. Although numbers from 3 different model types differ, results from plate models and optics model are somewhat similar. In addition, the numbers from 0 degree and 90 degree orientations show slight differences. This might be caused by the different  62  positioning of geometric features in first contact, shown in figure below, between the two orientation models; thus, flow patterns possibly change and result in different applied pressures. Figure 5.11  First contacting surfaces of different orientations  Source: Generated by CFDesign 5.1.2.2  45 Degree Orientation  Table 5.6  Summary of pressure for optic bottom surfaces with 45° orientation  Optic Bottom  45 Degree Orientation  Surface Attack Angle  0.00  90.00  180.00  No Windscreen  Wind  Windscreen  Speed  Plate  Permeable  Optics  Plate  Permeable  Optics  (m/s)  Model  Model  Model  Model  Model  Model  46  615.6  1189.8  -520.7  -788.0  279.7  -706.8  32  310.6  574.6  -234.1  -385.0  132.5  -339.0  9  24.3  42.4  -25.1  -27.2  9.9  -27.7  46  800.6  521.9  1344.1  438.4  680.0  833.9  32  385.6  251.1  636.6  232.0  326.2  401.9  9  29.6  19.3  49.2  18.0  24.6  31.7  46  3345.3  1579.0  2454.9  1946.0  771.2  1772.0  32  1616.9  761.2  1180.1  942.0  371.4  836.0  9  127.0  57.9  91.1  74.6  29.2  66.5  63  Figure 5.12  Pressure variation of optic bottom surfaces at 0° attack angle and 45° orientation  Pressure Variation - 0 degree attack angle @ 46m/s 1500.0  Pressure (Pa)  1000.0 500.0 No Windscreen  0.0  Windscreen  Plate Model  Permeable Model  Optics Model  -500.0 -1000.0  Figure 5.13  Model Type  Pressure variation of optic bottom surfaces at 90 ° attack angle and 45° orientation  Pressure (Pa)  Pressure Variation - 90 degree attack angle @ 46m/s 1600.0 1400.0 1200.0 1000.0 800.0 600.0 400.0 200.0 0.0  No Windscreen Windscreen  Plate Model  Permeable Model  Optics Model  Model Type  Figure 5.14  Pressure variation of optic bottom surfaces at 180° attack angle and 45° orientation  Pressure Variation - 180 degree attack angle @ 46m/s  Pressure (Pa)  4000.0 3000.0 2000.0 No Windscreen  1000.0  Windscreen  0.0 Plate Model  Permeable Model  Optics Model  Model Type  64  For models with 45 degree orientations, inconsistency becomes dominant in the data obtained in which no clear patterns are observed. Different wind attack angles result in both increase and decrease of pressure in all three models implemented. In addition, some cases display suction pressure in models with windscreen as opposed to normal pressure in models without windscreen. A possible explanation is that the flow profile might have experienced an alteration due to the existence of windscreen to disrupt or change the original path. Another observation of importance made is that different telescope models can sometimes generate completely different results. This will be addressed in later sections of the report when discussions are made regarding the differences between simulated geometric features.  5.1.2.3  Pressure Variation  Table 5.7  Pressure variation in percentage of optic bottom surfaces  Optic Bottom Surfaces 0 Degree Attack Angle 90 Degree Attack Angle 180 Degree Attack Angle  46 m/s 32 m/s 9 m/s 46 m/s 32 m/s 9 m/s 46 m/s 32 m/s 9 m/s  Percentage Variation (%) 0 Degree Orientation 45 Degree Orientation Plate Permeable Optics Plate Permeable Optics Model Model Model Model Model Model 70.8  49.5  68.5  -28.0  76.5  -35.7  71.2  49.4  65.5  -24.0  76.9  -44.8  72.1  51.0  64.4  -12.2  76.6  -10.5  48.9  16.6  50.3  45.2  -30.3  38.0  49.3  17.7  50.4  39.8  -29.9  36.9  50.3  19.4  47.9  39.1  -27.6  35.6  41.8  51.2  27.8  41.7  51.2  29.2  41.3  49.6  27.0  N/A  65  Table 5.8  Pressure variation in magnitude of optic bottom surfaces  Optic Top Surface  0 Degree Attack Angle 90 Degree Attack Angle 180 Degree Attack Angle  46 m/s 32 m/s 9 m/s 46 m/s 32 m/s 9 m/s 46 m/s 32 m/s 9 m/s  Magnitude Variation (Pa) 0 Degree Orientation 45 Degree Orientation Plate Permeable Optics Plate Permeable Optics Model Model Model Model Model Model 908.9  325.3  914.3  -172.4  910.1  -186.1  438.2  154.9  413.2  -74.4  442.1  -104.9  33.1  12.0  29.5  -3.0  32.5  -2.6  647.4  103.9  807.1  362.2  -158.1  510.2  315.8  53.4  390.1  153.6  -75.1  234.7  25.8  4.5  28.5  11.6  -5.3  17.5  1399.3  807.8  682.9  674.9  389.8  344.1  52.4  28.7  24.6  N/A  The optic bottom surfaces experience slight increase of pressure in both plate and optic models when windscreen is added; however, the amount of growth is comparatively less significant than the reduction undergone in most cases. Judging by the computational values provided in the tables above, the maximum pressure variation is 70% and 1400 Pascal decrease and 40% and 200 Pascal increase in percentage and magnitude, respectively; as a result, adding windscreen to the proposed telescope structure is proven to be able to alleviate the applied pressure on the optic surfaces.  66  5.1.3  Optic Frame  The figure below illustrates the surfaces where the pressure reading is taken from.  Figure 5.15  Optic frames  Source: Generated by CFDesign 5.1.3.1  0 Degree Orientation  Table 5.9  Summary of pressure for optic frames with 0° orientation  Optic Frames Attack Angle 0.00  90.00  Wind Speed (m/s) 46 32 9 46 32 9  0 Degree Orientation Plate Model 2010.0 968.0 74.0 1998.6 966.5 76.3  No Windscreen Permeable Model 681.0 305.4 24.4 1339.5 648.6 50.6  Optics Model 2177.5 1040.4 78.3 1767.9 848.1 64.4  Plate Model 1303.1 627.2 48.5 1367.3 657.9 50.3  Windscreen Permeable Model 361.3 174.0 12.6 881.3 422.2 32.4  Optics Model 877.0 434.6 33.6 1042.0 505.7 38.9  67  Figure 5.16  Pressure variation of optic frames at 0° attack angle and 0° orientation  Pressure Variation - 0 degree attack angle @ 46m/s  Pressure (Pa)  2500.0 2000.0 1500.0 No Windscreen  1000.0  Windscreen  500.0 0.0 Plate Model  Permeable Model  Optics Model  Model Type  Figure 5.17  Pressure variation of optic frames at 90° attack angle and 0° orientation  Pressure Variation - 90 degree attack angle @ 46m/s Pressure (Pa)  2500.0 2000.0 1500.0  No Windscreen  1000.0  Windscreen  500.0 0.0  Plate Model  Permeable Model  Optics Model  Model Type  Pressure along the support frames typically reaches the highest point at the face that is directly facing the incoming wind as observed in CFDesign simulated models; nevertheless, it is successfully lessened when telescopes are oriented in an angle of 0 degree, as proven by the comparison provided above. Incoming wind is slowed by the screen that is approximately at the same height of the frame elevation; therefore, the resultant pressure on frame surfaces is decreased.  68  5.1.3.2  45 Degree Orientation  Table 5.10 Summary of pressure for optic frames with 45° orientation  Optic Frames Attack Angle  No Windscreen  Wind  Windscreen  Speed  Plate  Permeable  Optics  Plate  Permeable  Optics  (m/s)  Model  Model  Model  Model  Model  Model  46  -1391.9  2032.1  1421.2  -1333.0  522.2  -838.0  32  -666.0  982.1  679.1  -615.9  250.2  -406.0  9  -51.5  88.5  51.6  -51.0  19.2  -32.8  46  1507.8  1218.2  1585.7  1521.0  1178.0  1182.0  32  727.0  588.1  757.5  736.0  567.4  557.0  9  56.2  45.9  57.6  58.9  43.8  21.9  46  -449.3  1493.4  668.5  -1378.0  778.0  -921.0  32  -215.8  720.4  318.6  -670.8  375.2  -446.0  9  -17.1  55.3  23.7  -52.7  29.4  -36.3  0.00  90.00  180.00  Figure 5.18  45 Degree Orientation  Pressure variation of optic frames at 0° attack angle and 45° orientation  Pressure (Pa)  Pressure Variation - 0 degree attack angle @ 46m/s 2500.0 2000.0 1500.0 1000.0 500.0 0.0 -500.0 -1000.0 -1500.0 -2000.0  No Windscreen  Plate Model  Permeable Model  Optics Model  Windscreen  Model Type  69  Figure 5.19  Pressure variation of optic frames at 90° attack angle and 45° orientation  Pressure (Pa)  Pressure Variation - 90 degree attack angle @ 46m/s 1800.0 1600.0 1400.0 1200.0 1000.0 800.0 600.0 400.0 200.0 0.0  No Windscreen Windscreen  Plate Model  Permeable Model  Optics Model  Model Type  Figure 5.20  Pressure variation of optic frames at 180° attack angle and 45° orientation  Pressure Variation - 180 degree attack angle @ 46m/s 2000.0  Pressure (Pa)  1500.0 1000.0 500.0 No Windscreen  0.0 -500.0  Plate Model  Permeable Model  Optics Model  Windscreen  -1000.0 -1500.0 -2000.0  Model Type  Similar to the inconsistent data obtained from the optic surfaces in models oriented at a 45 degree angle, data of optic support frames also lack of regularities. There exist indications of pressure decrease and increase in all three models when windscreen is implemented. Similar to what had been discussed before, normal pressure is changed to suction in some cases as well. Also, at 90 degree attack angle, there is almost no relevant effect of windscreen on changing the applied pressure in both plate and permeable plate models. Therefore, percentage and magnitude differences of pressure need to be reviewed prior to determining 70  the performance efficiency of windscreen. However, it should be noted that high pressure readings are mostly recorded on the locations with higher elevation than that of windscreen. As a result, the limitation on performance caused by screen height might be the dominant factor here to prevent pressure reduction.  5.1.3.3 Table 5.11  Pressure Variation Pressure variation in percentage of optic frames  Optic Frames Attack Angle  0°  90°  180°  Table 5.12  Wind Speed 46 m/s 32 m/s 9 m/s 46 m/s 32 m/s 9 m/s 46 m/s 32 m/s 9 m/s  Percentage Variation (%) 0 Degree Orientation 45 Degree Orientation Plate Permeable Optics Plate Permeable Optics Model Model Model Model Model Model 35.2  46.9  59.7  4.2  74.3  41.0  35.2  43.0  58.2  7.5  74.5  40.2  34.5  48.4  57.1  0.9  78.3  36.5  31.6  34.2  41.1  -0.9  3.3  25.5  31.9  34.9  40.4  -1.2  3.5  26.5  34.1  36.0  39.6  -4.7  4.6  62.0  -206.7  47.9  -37.8  -210.8  47.9  -40.0  -208.9  46.8  -53.2  N/A  Percentage variation in magnitude of optic frames  Optic Frames Attack Angle  Wind Speed  0°  46 m/s 32 m/s 9 m/s  Magnitude Variation (Pa) 0 Degree Orientation 45 Degree Orientation Plate Permeable Optics Plate Permeable Optics Model Model Model Model Model Model 706.9  319.7  1300.5  58.9  1509.9  583.2  340.8  131.4  605.8  50.1  731.9  273.1  25.5  11.8  44.7  0.5  69.3  18.8 71  Optic Frames Attack Angle  90°  180°  Wind Speed 46 m/s 32 m/s 9 m/s 46 m/s 32 m/s 9 m/s  Magnitude Variation (Pa) 0 Degree Orientation 45 Degree Orientation Plate Permeable Optics Plate Permeable Optics Model Model Model Model Model Model 631.3  458.2  725.9  -13.3  40.2  403.7  308.6  226.4  342.4  -9.0  20.7  200.5  26.0  18.2  25.5  -2.7  2.1  35.7  -928.7  715.4  -252.5  -455.0  345.2  -127.4  -35.6  25.9  -12.6  N/A  If the efficiency and functionality of windscreen is determined solely based on percentage variation of pressure, its applicability is questionable and in need of further analysis due to the 200% increase at 180 degree attack angle in comparison with 74% decrease at a 0 degree attack angle. However, judging from the maximum differences in terms of magnitudes, having a windscreen proves to be cost-effective as it is capable of more reduction than of increase in resultant pressure measured in Pascal.  72  5.1.4  Support Girders  The figure shown below illustrate where the pressure reading is take from.  Figure 5.21  Support girders  Source: Generated by CFDesign 5.1.4.1 Table 5.13  0 Degree Orientation Summary of pressure for support girders with 0° orientation  Support Girders Wind Attack Speed Angle (m/s) 46 32 0.00 9 46 90.00 32 9  0 Degree Orientation  Plate Model 2019.4 968.6 73.8 2293.6 1109.0 87.4  No Windscreen Permeable Model 1720.6 827.0 63.7 2162.7 1044.0 81.2  Optics Model 2019.6 956.9 70.7 2114.3 1017.2 77.8  Plate Model 1091.3 530.0 40.5 1146.5 728.0 57.0  Windscreen Permeable Model 1088.7 526.9 40.3 1353.0 650.4 50.3  Optics Model 801.3 389.2 33.8 1218.6 586.1 47.7  73  Figure 5.22  Pressure variation of support girders at 0° attack angle and 0° orientation  Pressure Variation - 0 degree attack angle @ 46m/s Pressure (Pa)  2500.0 2000.0 1500.0 No Windscreen  1000.0 500.0  Windscreen  0.0 Plate Model  Permeable Model  Optics Model  Model Type  Figure 5.23  Pressure variation of support girders at 90° attack angle and 0° orientation  Pressure Variation - 90 degree attack angle @ 46m/s Pressure (Pa)  2500.0 2000.0 1500.0 No Windscreen  1000.0 500.0  Windscreen  0.0 Plate Model  Permeable Model  Optics Model  Model Type  The data from CFD simulation for support girders that are located at the bottom of the telescope displays high resemblance in all three models indicating the coherent reduction of pressure when implemented with windscreen. It is also observed that numerical values achieved between different attack angles are fairly close to each other such that it serves as a clear indication of the efficiency in windscreen when telescopes are oriented horizontally.  74  5.1.4.2  45 Degree Orientation Summary of pressure for support girders with 45° orientation  Table 5.14  Support Girders Wind Attack Speed Angle (m/s) 46 32 0.00 9 46 90.00 32 9 46 180.00 32 9  Figure 5.24  45 Degree Orientation  Plate Model 1016.2 503.3 40.4 -1842.8 -899.3 -74.6 3151.1 1521.6 119.0  No Windscreen Permeable Model 1226.4 571.1 50.4 1982.4 957.0 74.6 2322.4 1121.2 87.5  Optics Model 576.9 272.6 19.5 1783.8 853.2 65.3 2440.8 1168.4 89.0  Plate Model -861.0 -419.5 -34.0 970.0 474.1 36.7 1400.0 683.0 53.6  Windscreen Permeable Model -590.0 -286.0 -22.3 1486.0 719.0 53.6 1485.0 715.3 56.1  Optics Model -466.0 -221.8 -17.9 1093.0 535.4 42.5 1592.0 729.0 58.7  Pressure variation of support girders at 0° attack angle and 45° orientation  Pressure Variation - 0 degree attack angle @ 46m/s 1500.0  Pressure (Pa)  1000.0 500.0 No Windscreen 0.0 Plate Model  Permeable Model  Optics Model  Windscreen  -500.0 -1000.0  Model Type  75  Figure 5.25  Pressure variation of support girders at 90° attack angle and 45° orientation  Pressure Variation - 90 degree attack angle @ 46m/s 3000.0  Pressure (Pa)  2000.0 1000.0 No Windscreen  0.0 -1000.0  Plate Model  Permeable Model  Optics Model  Windscreen  -2000.0 -3000.0  Figure 5.26  Model Type  Pressure variation of support girders at 180° attack angle and 45° orientation  Pressure (Pa)  Pressure Variation - 180 degree attack angle @ 46m/s 3500.0 3000.0 2500.0 2000.0 1500.0 1000.0 500.0 0.0  No Windscreen Windscreen Plate Model  Permeable Model  Optics Model  Model Type  Although suction is developed in the case with 0 degree attack angle, the numerical differences between windscreens present and absent in absolute values are rather recognizable based on the figures shown above. In addition, consistent reduction pattern is also present for the simulation with wind coming at 180 degree. This conclusion is further reinforced by the percentage and magnitude variation provided in the tables below.  76  5.1.4.3 Table 5.15  Pressure Variation Pressure variation in percentage of support girders  Support Girders Attack Angle  0°  90°  180°  Table 5.16  Wind Speed 46 m/s 32 m/s 9 m/s 46 m/s 32 m/s 9 m/s 46 m/s 32 m/s 9 m/s  Percentage Variation (%) 0 Degree Orientation Plate Permeable Optics Model Model Model 46.0  36.7  60.3  15.3  51.9  19.2  45.3  36.3  59.3  16.7  49.9  18.6  45.1  36.8  52.2  15.8  55.8  8.0  50.0  37.4  42.4  47.4  25.0  38.7  34.4  37.7  42.4  47.3  24.9  37.2  34.8  38.1  38.7  50.8  28.1  34.9  55.6  36.1  34.8  55.1  36.2  37.6  54.9  35.9  34.0  N/A  Pressure variation in magnitude of support girders  Support Girders Attack Angle  0°  90°  180°  45 Degree Orientation Plate Permeable Optics Model Model Model  Wind Speed 46 m/s 32 m/s 9 m/s 46 m/s 32 m/s 9 m/s 46 m/s 32 m/s 9 m/s  Magnitude Variation (Pa) 0 Degree Orientation Plate Permeable Optics Model Model Model  45 Degree Orientation Plate Permeable Optics Model Model Model  928.2  631.9  1218.3  155.2  636.4  110.9  438.6  300.1  567.7  83.8  285.1  50.8  33.3  23.4  36.9  6.4  28.1  1.6  1147.1  809.7  895.7  872.8  496.4  690.8  381.0  393.6  431.1  425.2  238.0  317.8  30.4  30.9  30.1  37.9  21.0  22.8  1751.1  837.4  848.8  838.6  405.9  439.4  65.4  31.4  30.3  N/A  77  The computation provided above show consistency of pressure reduction in all models under all scenarios and boundary conditions; as a result, a desirable outcome is achieved to conclude that application of windscreen can successfully reduce wind pressure on the girders supporting telescope structure.  78  5.1.5  Optic Tube  The figure below shows where the pressure reading is taken from.  Figure 5.27  Optic tube  Source: Generated by CFDesign  5.1.5.1  0 Degree Orientation  Table 5.17  Summary of pressure for optic tube with 0° orientation  Optic Tube Attack Angle  0.00  90.00  Wind Speed (m/s) 46 32 9 46 32 9  0 Degree Orientation Plate Model 292.5 137.5 8.9 477.4 230.2 18.0  No Windscreen Permeable Optics Model Model -84.7 218.4 -44.4 94.1 -4.6 4.0 85.3 239.0 40.3 105.9 2.1 5.8  Plate Model 139.9 65.6 4.5 595.0 282.0 20.8  Windscreen Permeable Model -39.0 -26.0 -3.6 300.0 137.9 9.5  Optics Model 2.2 1.6 0.6 301.0 148.8 10.6  79  Figure 5.28  Pressure variation of optic tube at 0° attack angle and 0° orientation  Pressure Variation - 0 degree attack angle @ 46m/s 400.0  Pressure (Pa)  300.0 200.0 No Windscreen  100.0  Windscreen  0.0 -100.0  Plate Model  -200.0  Figure 5.29  Permeable Model  Optics Model  Model Type  Pressure variation of optic tube at 90° attack angle and 0° orientation  Pressure (Pa)  Pressure Variation - 90 degree attack angle @ 46m/s 700.0 600.0 500.0 400.0 300.0 200.0 100.0 0.0  No Windscreen Windscreen  Plate Model  Permeable Model  Optics Model  Model Type  The support tube around the center optic is analyzed to monitor the average pressure on all surfaces; however, there are major differences between 0 and 90 degree attack angle when the telescope orients horizontally. Variation goes as high as 500 Pascal according to the data provided above. In addition, the effect of windscreen on resultant pressure also highly varies. Pressure increase and decrease are both observed in all three models. Therefore, if possible, enhanced detail analysis might be necessary to elaborate on this structural component to verify the results obtained in this study.  80  5.1.5.2  45 Degree Orientation Summary of pressure for optic tube with 45° orientation  Table 5.18  Optic Tube Attack Angle  0.00  90.00  180.00  Figure 5.30  Wind Speed (m/s) 46 32 9 46 32 9 46 32 9  45 Degree Orientation Plate Model 2731.2 1327.9 105.7 139.4 64.3 3.8 226.6 109.3 8.1  No Windscreen Permeable Model 1017.8 490.2 48.2 5.8 1.5 -0.6 16.0 6.8 0.6  Optics Model 1084.1 508.2 36.8 67.9 20.1 -0.8 183.8 82.3 4.9  Plate Model 609.0 294.6 23.2 290.0 145.4 10.6 -595.0 -287.0 -22.2  Windscreen Permeable Model 82.7 36.0 1.9 442.0 208.2 15.0 -11.5 -7.5 -0.8  Optics Model 299.6 150.7 12.3 235.5 111.5 9.0 -430.0 -215.0 -17.2  Pressure variation of optic tube at 0° attack angle and 45° orientation  Pressure Variation - 0 degree attack angle @ 46m/s 3000.0  Pressure (Pa)  2500.0 2000.0 1500.0  No Windscreen  1000.0  Windscreen  500.0 0.0 Plate Model  Permeable Model  Optics Model  Model Type  81  Figure 5.31  Pressure variation of optic tube at 90° attack angle and 45° orientation  Pressure Variation - 90 degree attack angle @ 46m/s 500.0 Pressure (Pa)  400.0 300.0 No Windscreen  200.0  Windscreen  100.0 0.0 Plate Model  Permeable Model  Optics Model  Model Type  Figure 5.32  Pressure variation of optic tube at 180° attack angle and 45° orientation  Pressure (Pa)  Pressure Variation - 180 degree attack angle @ 46m/s 300.0 200.0 100.0 0.0 -100.0 -200.0 -300.0 -400.0 -500.0 -600.0 -700.0  Plate Model  Permeable Model  Optics Model No Windscreen Windscreen  Model Type  Similarly, inconsistent patterns are also observed in the models oriented at 45 degree in which increasing and decreasing pressure reading, as well as suction and normal pressure are observed. A possible explanation is that since the optic tube consists of multiple distinctive geometric features including round surfaces, flat surfaces, and, hollow sections, taking the average value out of them when it is being modeled as one solid component might be disadvantageous to achieve an optimal number. Additionally, the void spaces between the  82  tube and the optic might be the source of turbulence as flow passes through, which causes incapability of CFDesign to successfully and accurately capture the actual subsequent flow profile to generate reliable results. Consequently, a proposal for better results is to further divide the optic tube into smaller and finer elements for better analytical outcomes. 5.1.5.3 Table 5.19  Pressure Variation Pressure variation in percentage of optic tube  Optic Tube Attack Angle  0°  90°  180°  Table 5.20  Wind Speed 46 m/s 32 m/s 9 m/s 46 m/s 32 m/s 9 m/s 46 m/s 32 m/s 9 m/s  0°  90°  180°  52.2  54.0  99.0  77.7  91.9  72.4  52.3  41.4  98.3  77.8  92.7  70.3  48.9  21.4  85.9  78.1  96.1  66.6  -24.6  -251.7  -25.9  -108.0  -7494.5  -246.9  -22.5  -242.2  -40.6  -126.3  -14258.6  -453.9  -15.8  -352.4  -83.2  -178.9  -2627.3  -979.5  -162.5  28.5  -134.0  -162.7  -10.9  -161.4  -175.8  -24.6  -248.9  N/A  Pressure variation in magnitude of optic tube  Optic Tube Attack Angle  Percentage Variation (%) 0 Degree Orientation 45 Degree Orientation Plate Permeable Optics Plate Permeable Optics Model Model Model Model Model Model  Wind Speed 46 m/s 32 m/s 9 m/s 46 m/s 32 m/s 9 m/s 46  Magnitude Variation (Pa) 0 Degree Orientation 45 Degree Orientation Plate Permeable Optics Plate Permeable Optics Model Model Model Model Model Model 152.6  45.7  216.3  2122.2  935.1  784.4  71.9  18.4  92.5  1033.3  454.2  357.5  4.3  1.0  3.4  82.5  46.3  24.5  -117.6  -214.7  -62.0  -150.6  -436.2  -167.6  -51.8  -97.6  -42.9  -81.1  -206.8  -91.4  -2.8  -7.4 N/A  -4.8  -6.8 -368.4  -14.5 4.6  -8.1 -246.2 83  Optic Tube Attack Angle  Wind Speed m/s 32 m/s 9 m/s  Magnitude Variation (Pa) 0 Degree Orientation 45 Degree Orientation Plate Permeable Optics Plate Permeable Optics Model Model Model Model Model Model -177.7  -0.7  -132.8  -14.2  -0.2  -12.3  The percentage variation show significant pressure increase in some of the performed analyses, and on the contrary of what it is hoped to achieve, most data show pressure growth instead of reduction. Nonetheless, the reduction in magnitude goes as high as 2000 Pascal while growth in magnitude merely goes up to 450 Pascal. This result shows that the overall efficiency of windscreen on reducing the pressure experienced by optic tube is somewhat reliable to a certain extent; however, due to the specific reasons discussed in the previous paragraph, more analyses should be conducted and the actual efficiency of windscreen can greatly benefit from those analyses to generate accurate data.  84  5.1.6  Bottom Frames  The figure shown below illustrates the surfaces of bottom frames where pressure reading is taken from.  Figure 5.33  Bottom frames  Source: Generated by CFDesign 5.1.6.1 Table 5.21  0 Degree Orientation Summary of pressure for bottom frames with 0° orientation  Bottom Frames Wind Attack Speed Angle (m/s) 46 32 0.00 9 46 90.00 32 9  0 Degree Orientation  Plate Model 981.1 468.6 34.3 1872.8 905.6 71.7  No Windscreen Permeable Optics Model Model 756.9 834.5 362.2 386.8 27.3 25.9 1302.2 1254.3 629.1 596.9 48.9 43.9  Plate Model 297.5 142.6 -11.6 945.2 455.2 35.6  Windscreen Permeable Model 382.1 183.9 13.6 805.1 384.8 29.4  Optics Model 275.9 135.2 9.9 743.4 354.7 28.4  85  Figure 5.34  Pressure variation of bottom frames at 0° attack angle and 0° orientation  Pressure Variation - 0 degree attack angle @ 46m/s Pressure (Pa)  1200.0 1000.0 800.0 600.0  No Windscreen  400.0  Windscreen  200.0 0.0 Plate Model  Permeable Model  Optics Model  Model Type  Figure 5.35  Pressure variation of bottom frames at 90° attack angle and 0° orientation  Pressure Variation - 90 degree attack angle @ 46m/s  Pressure (Pa)  2000.0 1500.0 1000.0  No Windscreen Windscreen  500.0 0.0 Plate Model  Permeable Model  Optics Model  Model Type  The comparison charts provided above illustrate evident reduction in pressure magnitude for both attack angles. The reduced amount in plate models is the largest compared to that of other two models in which similar decrease is observed. This phenomenon is observed consistently in all three types of model implemented in the study as a positive reinforcement to the hypothesis suggesting that implementing windscreen enables pressure drop.  86  5.1.6.2  45 Degree Orientation Summary of pressure for bottom frames with 45° orientation  Table 5.22  Bottom Frames Attack Angle  0.00  90.00  180.00  Figure 5.36  Wind Speed (m/s) 46 32 9 46 32 9 46 32 9  45 Degree Orientation Plate Model 431.8 218.3 17.6 1288.4 621.2 46.0 2918.4 1409.3 110.5  No Windscreen Permeable Model 900.4 435.3 37.0 1153.2 556.8 43.5 1879.2 906.3 69.9  Optics Model 377.5 175.5 12.8 1010.4 474.5 34.8 1624.2 773.1 57.5  Plate Model -633.0 -307.9 -25.2 612.0 298.8 23.1 1503.0 728.8 57.4  Windscreen Permeable Model -291.0 -140.0 -10.8 937.0 450.6 34.5 1001.0 481.6 37.9  Optics Model -404.0 -191.4 -15.5 734.0 354.3 27.9 913.0 411.5 33.2  Pressure variation of bottom frames at 0° attack angle and 45° orientation  Pressure Variation - 0 degree attack angle @ 46m/s  Pressure (Pa)  1000.0 500.0 No Windscreen  0.0 Plate Model  Permeable Model  Optics Model  Windscreen  -500.0 -1000.0  Model Type  87  Figure 5.37  Pressure variation of bottom frames at 90° attack angle and 45° orientation  Pressure (Pa)  Pressure Variation - 90 degree attack angle @ 46m/s 1400.0 1200.0 1000.0 800.0 600.0 400.0 200.0 0.0  No Windscreen Windscreen  Plate Model  Permeable Model  Optics Model  Model Type  Figure 5.38  Pressure variation of bottom frames at 180° attack angle and 45° orientation  Pressure (Pa)  Pressure Variation - 180 degree attack angle @ 46m/s 3500.0 3000.0 2500.0 2000.0 1500.0 1000.0 500.0 0.0  No Windscreen Windscreen  Plate Model  Permeable Model  Optics Model  Model Type  The data from 45 degree orientation show similar trend as the 0 degree orientation except when wind is coming at 0 degree attack angle in which consequential pressure is suction instead of normally applied. Reduction appears to occur in most cases other than the plate and optic models with 0 degree attack angle. Considering the geometric orientation that positions the bottom frame directly away from the incoming wind in this case, adding windscreen might cause the flow path to divert and approach the bottom frames from different directions than ones without windscreen implemented. Therefore, suction is  88  generated as an alteration due to the changes in flow filed. However, the general reduction pattern provides acceptable evidence to additionally validate the desired outcome. 5.1.6.3 Table 5.23  Pressure Variation Pressure variation in percentage of bottom frames  Bottom Frames Attack Angle  0°  90°  180°  Table 5.24  Wind Speed 46 m/s 32 m/s 9 m/s 46 m/s 32 m/s 9 m/s 46 m/s 32 m/s 9 m/s  0°  90°  180°  69.7  49.5  66.9  -46.6  67.7  -7.0  69.6  49.2  65.0  -41.0  67.8  -9.1  66.1  50.1  61.8  -43.3  70.8  -21.3  49.5  38.2  40.7  52.5  18.7  27.4  49.7  38.8  40.6  51.9  19.1  25.3  50.4  39.9  35.3  49.9  20.8  19.7  92.3  7.2  46.8  92.3  50.2  23.7  96.6  40.5  8.4  N/A  Pressure variation in magnitude of bottom frames  Bottom Frames Attack Angle  Percentage Variation (%) 0 Degree Orientation 45 Degree Orientation Plate Permeable Optics Plate Permeable Optics Model Model Model Model Model Model  Wind Speed 46 m/s 32 m/s 9 m/s 46 m/s 32 m/s 9 m/s 46 m/s 32 m/s 9 m/s  Magnitude Variation (Pa) 0 Degree Orientation 45 Degree Orientation Plate Permeable Optics Plate Permeable Optics Model Model Model Model Model Model 683.6  374.8  558.6  -201.2  609.4  -26.5  326.0  178.3  251.5  -89.6  295.3  -15.9  22.7  13.7  16.0  -7.6  26.2  -2.7  927.6  497.1  510.9  676.4  216.2  276.4  450.4  244.3  242.2  322.4  106.2  120.2  36.1  19.5  15.5  23.0  9.0  6.9  658.1  12.5  133.9  319.6  44.3  27.9  26.5  2.7  0.5  N/A  89  In terms of the discrepancy in both percentage and magnitude, pressure decrease in all models surpasses pressure increase when windscreen is employed. Maximum reduction values are calculated to be 90% and 700 Pascal in terms of percentage and magnitude, respectively, which are considerably higher than 50% and 200 Pascal for pressure increase. In conclusion, the bottom frame elements are subjected to pressure reduction with windscreen installed.  90  5.1.7  Top Frames  Surfaces shown below in the figure represents the location of pressure reading.  Figure 5.39  Top frames  Source: Generated by CFDesign 5.1.7.1  0 Degree Orientation  Table 5.25  Summary of pressure for top frames with 0° orientation  Top Frames Attack Angle  0.00  90.00  Wind Speed (m/s) 46 32 9 46 32 9  0 Degree Orientation Plate Model 531.0 252.3 18.0 727.9 350.3 27.6  No Windscreen Permeable Optics Model Model 637.0 496.4 305.4 229.5 22.9 -18.9 902.7 577.3 435.8 271.7 33.8 19.2  Plate Model 465.5 223.1 16.6 833.4 396.4 29.5  Windscreen Permeable Model 453.8 224.6 16.9 797.4 380.8 29.0  Optics Model -330.8 -162.7 -14.4 545.5 268.3 20.1  91  Figure 5.40  Pressure variation of top frames at 0° attack angle and 0° orientation  Pressure Variation - 0 degree attack angle @ 46m/s 800.0  Pressure (Pa)  600.0 400.0 No Windscreen  200.0  Windscreen  0.0 Plate Model  Permeable Model  Optics Model  -200.0 -400.0  Figure 5.41  Model Type  Pressure variation of top frames at 90° attack angle and 0° orientation  Pressure Variation - 90 degree attack angle @ 46m/s 1000.0 Pressure (Pa)  800.0 600.0 No Windscreen  400.0  Windscreen  200.0 0.0 Plate Model  Permeable Model  Optics Model  Model Type  The top frames supporting the optic tube undergo higher pressure in the 90 degree orientation than in the 0 degree orientation in all of the 3 type of models implemented. Out of those 3 types, permeable plate models generate the highest results, followed by plate models and optic models, consecutively. In addition, reducing pressure is generally observed except the plate model with a 90 degree attack angle in which increased pressure is, on the contrary,  92  shown. The general comparison between models with different orientations and model types will be addressed in later parts of this section. 5.1.7.2  45 degree orientation Summary of pressure for top frames with 45° orientation  Table 5.26  Top Frames Attack Angle  0.00  90.00  180.00  Figure 5.42  Wind Speed (m/s) 46 32 9 46 32 9 46 32 9  45 Degree Orientation Plate Model 3222.8 1566.4 124.6 347.6 164.6 11.5 339.0 163.1 12.2  No Windscreen Permeable Model 1810.4 874.8 78.5 784.8 378.4 29.4 289.5 139.8 11.4  Optics Model 1400.8 601.0 48.7 370.1 168.5 -15.0 240.9 109.7 7.5  Plate Model 715.0 346.0 27.3 515.4 248.3 18.3 -665.0 -320.5 -24.6  Windscreen Permeable Model 563.0 274.0 21.2 888.2 426.0 32.5 159.0 75.9 6.1  Optics Model 443.3 225.4 18.1 423.0 200.6 15.7 -534.0 -268.6 -21.2  Pressure variation of top frames at 0° attack angle and 45° orientation  Pressure Variation - 0 degree attack angle @ 46m/s 3500.0  Pressure (Pa)  3000.0 2500.0 2000.0 1500.0  No Windscreen  1000.0  Windscreen  500.0 0.0 Plate Model  Permeable Model  Optics Model  Model Type  93  Figure 5.43  Pressure variation of top frames at 90° attack angle and 45° orientation  Pressure Variation - 90 degree attack angle @ 46m/s 1000.0  Pressure (Pa)  800.0 600.0 No Windscreen  400.0  Windscreen  200.0 0.0 Plate Model  Permeable Model  Optics Model  Model Type  Figure 5.44  Pressure variation of top frames at 180° attack angle and 45° orientation  Pressure Variation - 180 degree attack angle @ 46m/s 400.0  Pressure (Pa)  200.0 0.0 Plate Model  Permeable Model  Optics Model No Windscreen  -200.0  Windscreen  -400.0 -600.0 -800.0  Model Type  In the case analysis involving 45 degree orientation, top frame elements experience rather irregular pressure type and magnitude between scenarios with different wind attack angles. At 0 degree attack angle, consistent results are seen to validate the efficiency of windscreen on reducing pressure in all models, even though values from each model vary significantly; however, at 90 degree attack angle, adding windscreen contrarily increase the applied pressure as opposed to what it is hoped to be. Taken into account that these models are  94  oriented at 45 degree such that optics are positioned behind the top frames when wind is coming at 0 degree attack angle and in front of the top frames when at 180 degree attack angle, the effect of positioning on flow profile should be studied in future analyses if possible. 5.1.7.3 Table 5.27  Pressure Variation Pressure variation in percentage of top frames  Top Frames Attack Angle  0°  90°  180°  Table 5.28  Wind Speed 46 m/s 32 m/s 9 m/s 46 m/s 32 m/s 9 m/s 46 m/s 32 m/s 9 m/s  0°  90°  12.3  28.8  33.4  77.8  68.9  68.4  11.6  26.5  29.1  77.9  68.7  62.5  8.3  26.2  24.0  78.1  73.0  62.8  -14.5  11.7  5.5  -48.3  -13.2  -14.3  -13.1  12.6  1.2  -50.8  -12.6  -19.1  -7.1  14.2  -4.5  -59.2  -10.6  -4.8  -96.1  45.1  -121.7  -96.4  45.7  -145.0  -100.8  46.6  -181.9  N/A  Pressure variation in magnitude of top frames  Top Frames Attack Angle  Percentage Variation (%) 0 Degree Orientation 45 Degree Orientation Plate Permeable Optics Plate Permeable Optics Model Model Model Model Model Model  Wind Speed 46 m/s 32 m/s 9 m/s 46 m/s 32 m/s 9 m/s  Magnitude Variation (Pa) 0 Degree Orientation 45 Degree Orientation Plate Permeable Optics Plate Permeable Optics Model Model Model Model Model Model 65.5  183.2  165.6  2507.8  1247.4  957.5  29.2  80.8  66.8  1220.4  600.8  375.6  1.5  6.0  4.5  97.3  57.3  30.6  -105.5  105.3  31.7  -167.8  -103.4  -52.9  -46.1  55.0  3.4  -83.7  -47.6  -32.1  -2.0  4.8  -0.9  -6.8  -3.1  -0.7  95  Top Frames Attack Angle  Wind Speed  180°  46 m/s 32 m/s 9 m/s  Magnitude Variation (Pa) 0 Degree Orientation 45 Degree Orientation Plate Permeable Optics Plate Permeable Optics Model Model Model Model Model Model  N/A  -326.0  130.5  -293.1  -157.4  63.9  -159.0  -12.4  5.3  -13.7  The maximum pressure reduction is close to 2500 Pascal representing a 78% in percentage value, and the maximum increase is approximately 330 Pascal indicating a 96% in percentage. Since the actual amount of increase measured in Pascal seems to be of importance as a representation of the structural requirement for performance and functionality, top frame elements are likely to experience higher reduction in pressure than increase based on the magnitude difference shown above.  5.1.8  Summary of Individual Structural Element Analysis  Different structural elements implemented in telescopes experience different pressure changes, whether increase or decrease, based on the scenarios and boundary conditions applied. Some of them appear to have completely different pressure profiles with the addition of windscreen structure as normally applied pressure switches to suction pressure. However, it is observed that these cases commonly occurred in elements with higher elevations than that of the windscreen. For instance, the optic tube and the top frame elements, as well as the optic surfaces, exhibit data with the widest range when comparing with support girders and bottom frames. It should also be noted that highest pressure readings from optic surfaces are mostly recorded on the locations exceeding the height of windscreen. Therefore, one of the  96  proposed future researches could elaborate on a windscreen with higher elevation and its associated feasibility study including both structural and economical aspects.  Nevertheless, it was established that in all structural elements studied, the extent of pressure reduction in terms of magnitude exceeds the increase as solid evidence supporting the previously proposed hypothesis that predicts pressure diminution due to windscreen. Although in some scenarios the increase is significantly high to be of concern and should be investigated more thoroughly for better structural performance, the effect of pressure lessening is generally observed in all models. Consequently, the implementation of windscreen on the proposed telescope structures is capable of decreasing the applied pressure caused by heavy wind loads.  97  5.2  Comparison of Model Types  An average calculation of the pressure values obtained in 3 distinctive models is carried out to gain a fundamental understanding of the differences between them. The optic model follows the geometry closest to the original design concept, and the other two methods are implemented to achieve a broader range of data and analytical results. It is of interest and of significance to compare these results and establish a reasonable generalization between these 3 models with different geometric features.  Figure 5.45  Pressure variation between types of model  Pressure Variation - Model Types 1800 1600  Pressure (Pa)  1400 1200 1000 800  Plate Model  600  Permeable Model  400  Optics Model  200 0 Optic Top Optic Surface Bottom Surface  Optic Frames  Support Girders  Optic Tube  Bottom Frames  Top Frames  Elements  According to the chart provided, it is evidently shown that plate models typically yield the highest subsequent pressures, while optics models and permeable plate models take turns generating the second largest values. This is within expectation as solid plates restrict fluid flow from passing through and completely divert it to other directions; therefore, solid surfaces directly experience the impact from incoming wind flow that results in typically higher pressure readings. However, this is not the most accurate representation of the 98  physical features of optic surfaces to produce the most precise numbers. On the other hand, permeable plate model uses free area ratio as a resistance method to allow flow to pass through evenly distributed spaces without simulation of sharp edges and corners like the actual structure. As a result, it is possible that such modeling approach causes lower pressure values compared to ones from solid plate models due to the inability to correctly capture all those features mentioned. In addition, optic models yield results that are generally lower than the plate models. A reasonable explanation is that spaces between optics provide possible flow paths instead of causing disruption and disturbance to a certain extent. Furthermore, interactions with other physical features involved in the models could make a difference as well as their modeled properties will affect the flow profile and thus possibly change the pressures.  However, it is not of interest in this study to determine which model yields the most accurate answer as all of them are reliable yet hold sources of error to a certain extent. Both of the plate and permeable plate models are unable to capture the exact geometric features to accurately simulate the flow profiles, and the optic models had to be run at a reduced mesh element than optimized to lack some credibility. Therefore, all three models are considered for evaluation in this study to gain a broader range of data for analysis and comparison. Nonetheless, further work can be done to emphasize on details and elaborate on the optic models, assuming the hardware limitation can be tackled successfully.  99  5.3  Pressure Envelope  Table 5.29 Pressure envelope of structural elements  Level of Wind Speed  Pressure Envelope (Pa)  Optic Top Surface  Optic Bottom Surface  Optic Frame  Support Girders  Optic Tube  Bottom Frame  Top Frame  46 m/s  Max  3589  3345  2178  3151  2731  2918  3223  Min  -910  -788  -1392  -1843  -595  -633  -540  32 m/s  Max  1743  1617  1040  1522  1328  1409  1566  Min  -436  -339  -671  -899  -287  -259  -269  Max  138  127  89  119  106  111  125  Min  -34  -28  -53  -75  -22  -25  -21  9 m/s  The table above shows the pressure envelope experienced by each structural element based on the performance levels of requirement discussed earlier. Both the maximum pressures and minimum pressures are presented, and the negative value represents suction. By organizing these numbers, it is hoped to serve as a performance-based design guideline as it indicates approximately the extent of loading that the structure might undergo. As the values show, the maximum pressure occurs to optic surfaces under the highest wind loading, 46 m/s, as expected, and the lowest pressure is shared between the top frame elements and optic tube under the lowest wind speed, 9 m/s. Although the highest wind load on the historical records occur with a very limited possibility, it is still of importance to design the structure to withstand such loading since this is a structure with significantly high demands of performance and functionality. Consequently, the pressure envelope generated from the data obtained in this study aims to provide an appropriate guideline and serve as a reliable source for engineers.  100  5.4  5.4.1  Validation  Convergence  The convergence plots provided in this section are separated into two categories in terms of relationships with velocity and pressure. Since the velocity values obtained from CFDesign are individual values in all x, y, and z directions, the SRSS method is applied to compute the square root of the sum of the squares as shown by the formula below to get the resultant velocity vector.  The figures below show the plots for plate models.  Figure 5.46  Velocity convergence plot of plate models  Convergence Plot - Plate Model - Velocity 7 0 degree 32 m/s  6 Scalar Value  0 Degree 46 m/s  5  0 degree 9 m/s  4  90 degree 46 m/s 90 degree 32 m/s  3  90 degree 9 m/s 180 degree 46 m/s  2  180 degree 32 m/s  1  180 degree 9 m/s  0 0  20  40  60  80  100  Iteration Number  101  Figure 5.47  Pressure convergence plot of plate models  Convergence Plot - Plate Model - Presure 2500 0 degree 32 m/s  2000  Scalar Value  0 Degree 46 m/s 0 degree 9 m/s  1500  90 degree 46 m/s  1000  90 degree 32 m/s 90 degree 9 m/s  500  180 degree 46 m/s 180 degree 32 m/s  0 0 -500  20  40  60  80  100  Iteration Number  On the y-scale of the figures provided, the units in measure are in scalar quantities; as a result, the end values are not relevant. Based on the figures above, both of them show the trending towards a constant value as the evident indication of convergence reached since the slopes are getting closer and closer to zero when trend lines turn flat. However, for the models with 90 degree orientation, it seems that more iteration steps would have contributed to a more converged result as the slope at the end is not quite constant.  102  Figure 5.48  Velocity convergence plot of permeable models  Convergence Plot - Permeable Model Velocity Scalar Value  35  0 degree 46 m/s  30  0 degree 32 m/s  25  0 degree 9 m/s  20  90 degree 46 m/s 90 degree 32 m/s  15  90 degree 9 m/s  10  180 degree 46 m/s  5  180 degree 32 m/s 180 degree 9 m/s  0 0  20  40  60  80  100  Iteration Number  Figure 5.49  Pressure convergence plot of permeable models  Convergence Plot - Permeable Model Pressure 3000 0 degree 46 m/s  Scalar Value  2500  0 degree 32 m/s  2000  0 degree 9 m/s  1500  90 degree 46 m/s 90 degree 32 m/s  1000  90 degree 9 m/s  500  180 degree 46 m/s  0  180 degree 32 m/s  0  20  40  60  80  100  180 degree 9 m/s  Iteration Number  The figures shown above summarize the convergence values from permeable plate models in velocities and pressure, respectively. There are clear indication of fluctuations in the data obtained for models with 180 degree orientations and wind speed of 46 m/s and 32 m/s; nevertheless, the overall trend lines still move towards constant values as a proof of achieved valid analysis results.  103  Figure 5.50  Velocity convergence plot of optic models  Scalar Value  Convergence Plot - Optic Model Velocity 7 6 5 4 3 2 1 0  0 degree 46 m/s 0 degree 32m/s 0 degree 9 m/s 90 degree 46 m/s 90 degree 32m/s 0  20  40  60  80  100  180 degree 46 m/s  Iteration Number  Figure 5.51  90 degree 9 m/s  Pressure convergence plot of optic models  Convergence Plot - Optic Model - Pressure 2500  0 degree 46 m/s  Scalar Value  2000  0 degree 32m/s  1500  0 degree 9 m/s  1000  90 degree 46 m/s 90 degree 32m/s  500  90 degree 9 m/s  0 -500  0  20  40  60  Iteration Number  80  100  180 degree 46 m/s 180 degree 32 m/s  The convergence graphs for optics models do not appear as promising as the ones for plate models and permeability models as it can be observed that slopes are still changing when the iteration stops at 100 for the velocity plot even though they cease to change in the pressure plot. As a result, the values for optics models might lack a certain degree of credibility to be exactly accurate and reliable.  104  The overall results were satisfactory as convergence is obtained in most of the models to obtain reliable output; nevertheless, some of the optic models were less convincing with their changing slopes when iteration stopped and thus cannot be concluded as precisely accurate. Therefore, it should be kept in mind that in the future, more iteration should be implemented when complex models are modeled.  5.4.2  Iteration Steps  The pressure reading and velocity values are taken off along an arbitrarily selected line in the plate model with 0 degree orientation and 0 wind attack angle to compare for consistency. It is expected to see some variations, but whether or not if it is dominant to be a major concern is the fundamental purpose of this validation method. The table below provides the velocities and pressures from both cases with 100 and 200 iterations.  Table 5.30  Velocity and pressure values from 100 and 200 iteration steps  Length Units 1 2 3 4 5 6 7 8 9 10 11 12 13 14  200 Iterations Velocity (m/s) Pressure (Pa) 44.7 470.4 44.1 511.3 43.7 559.1 47.3 463.0 51.1 -96.5 47.8 -247.4 45.5 -228.1 44.1 -132.2 43.8 -29.0 42.3 149.7 38.1 67.2 0.0 798.3 32.7 217.1 32.7 292.4  100 Iterations Velocity (m/s) Pressure (Pa) 44.7 802.9 44.2 842.1 44.0 884.1 48.3 754.7 51.6 108.0 46.8 -31.3 43.8 29.6 42.1 146.2 41.6 265.2 40.0 457.2 34.0 312.3 0.0 994.2 28.4 339.1 28.8 377.5  105  200 Iterations Velocity (m/s) Pressure (Pa) 32.1 312.8 31.7 305.2 31.9 269.0 34.5 131.5 33.9 -46.8 29.9 -61.2 26.9 -46.5  Length Units 15 16 17 18 19 20 21  Figure 5.52  100 Iterations Velocity (m/s) Pressure (Pa) 28.3 363.1 27.8 342.0 27.7 295.0 30.0 168.9 27.4 -11.6 22.1 -59.4 17.0 -57.0  Iteration validation of velocity  Iteration Validation - Velocity 60 Velocity (ms)  50 40 30  200 Iteration  20  100 Iteration  10 0 0  5  10  15  20  Parametric Distance  Iteration validation of pressure  Iteration Validation - Pressure 1200 1000 800 Pressure (Pa)  Figure 5.53  600 400  200 Iteration  200  100 Iteration  0 -200 0 -400  5  10  15  20  Parametric Distance  106  Both figures show the same pattern of data trending in both velocity and pressure although the actual values rather vary. Analysis with 200 iterations reaches a higher velocity value at the end but with a much lower pressure at the beginning of the arbitrary line from the model. The table below shows the calculated percentage difference. As observed, the pressure difference is larger with 200 iterations with a maximum percentage difference of almost 700% increase.  Table 5.31  Percentage different between different iteration results  Length Units 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21  Percentage Difference (%) Velocity Pressure 0.0 41.4 0.2 39.3 0.7 36.8 2.0 38.7 1.0 189.4 2.1 689.8 3.8 871.1 4.7 190.4 5.3 110.9 5.8 67.2 11.9 78.5 0.0 19.7 15.1 36.0 13.7 22.6 13.5 13.9 14.1 10.7 15.2 8.8 14.8 22.1 23.7 304.8 35.2 3.0 57.8 18.4  107  Differences are further verified with average pressures from surfaces of structure elements in the same model utilized for this section, and the readings are summarized below with a percentage difference in comparison attached.  Table 5.32  Pressure values of different iterations  Pressure (Pa)  Optic Top Surface  Optic Frame  Optic Bottom Surface  Support  Optic Tube  Bottom Frame  Top Frame  100 Iteration (Pa)  486  2010  1284  2019  292  981  531  200 Iteration (Pa)  428.7  1703  844.7  1654  139.43  746  273  Percentage Difference (%)  11.7  15.3  34.2  18.1  52.3  24.0  48.6  Figure 5.54  Pressure values of different iterations  Validation - Iteration Steps Pressure (Pa)  2500 2000 1500 1000 100 Iteration  500  200 Iteration  0 Optic Top Surface  Optic Frame  Optic Support Bottom Surface  Optic Tube  Bottom Frame  Top Frame  Elements  The maximum difference expressed in percentage between 2 iteration cases appears to be almost 50%. Also, figure 71 above show the general pattern of reduction in pressure in 200 iterations as compared to 100 iterations in all elements considered. In addition, it had been  108  pointed out in analyses involving aerodynamic- or hydrodynamic-induced forces that fully accurate computation can only be acquired when hundreds of iterations are involved (CFDesign Online Help, 2011). Consequently, combining the results from previous validation with convergence plots, future analyses regarding induced-forces or applied pressures should implement higher iteration numbers to achieve a more credible and reliable result. It is recommended to start with at least 200 steps, assuming sufficient hardware capability is provided.  5.4.3  Mesh Generation  Some of the models applied in this study generate a substantial amount of mesh counts that are close to 2 million under automatic mesh generation; thus, they cannot be successfully modeled in CFDesign due to hardware limitations that restrict analysis from even starting. Hence, manual mesh generation had to be applied even though mesh counts varied significantly from an average of 1.5 million to four hundred thousand.  A plate model with the same boundary conditions and geometry setup is run with both automatic mesh and manual mesh generation with a comparison to verify for consistency as listed below in the table and figure. They show the numerical data obtained and the trending pattern.  109  Table 5.33  Pressure variations between different mesh generation methods  Pressure (Pa) Automatic Mesh Manual Mesh Percentage Difference (%)  Figure 5.55  Optic Top Surface  Optic Frame  Optic Bottom Surface  Support  Optic Tube  Bottom Frame  Top Frame  486 498  2010 1991  1284 1176  2019 1930  292 256  981 880  531 443  2.6  1.0  8.4  4.4  12.4  10.3  16.6  Pressure variations between different mesh generation methods  Pressure (Pa)  Validation - Mesh Generation 2500 2000 1500 1000 500 0 Optic Top Surface  Optic Frame Optic Bottom Surface  Support  Optic Tube Bottom Frame Top Frame  Elements  Automatic Mesh Manual Mesh  The results with manual mesh generation indicate overall smaller pressures on all structure elements when comparing to the ones with automatic mesh generation. Although differences do exist, they seem to be not of major concern as percentage variation only goes as high as approximately 17%. Nevertheless, this is solely based on the plate model where complex geometric features are kept at a minimum in comparison with other models. It is possible that consistent results like these data might not have been achieved when the exact validation process is applied t models with complex features. Consequently, more elaboration should be addressed on sophisticated models to determine if severe problems do exist when employing manual mesh generation to replace automatic mesh generation.  110  5.4.4  Bernoulli’s Constant  During derivation of the Bernoulli’s equation, the following assumptions must be satisfied. They include:   Viscous effects are negligible    Steady flow    Equations are applied along a streamline    Fluid is incompressible    No energy addition or removal from the fluid along the streamline  These assumptions are meant to be strictly complied with to produce accurate output, and critical errors may occur if otherwise (Finnemore & Franzini, 2002).  To verify the analytical outcomes of both telescope models and telescope with windscreen models, separate studies are made with computation using Bernoulli’s equations discussed in Chapter 3. Both pressure values and velocities values are read off along a plane that is arbitrarily chosen, and the same coordinates are implemented in every other model to ensure values are obtained from the same locations. The coordinates for the telescope models and telescope with windscreen models are:  Table 5.34  Coordinates for telescope models  Coordinates  x  y  z  Start  30.28  55.66  15.48  End  136.7  55.66  15.48  111  Table 5.35  Coordinates for telescope with windscreen models  Coordinates  x  y  z  Start  152.7  -2.78  4.706  End  -177.1  -2.78  4.706  The figures below provide the data for telescope models and telescope with windscreen models and the relative comparison.  Figure 5.56  Bernoulli’s constants for telescope models  Validation (Telescope) - Bernoulli Constant 2000 1800 Constant Value  1600 1400 1200 1000  Bernoulli's Constant  800  Permeable Model  600  Plate Model  400 200 0 0.0  50.0  100.0  150.0  Parametric Distance  112  Figure 5.57  Bernoulli’s constants for telescope and windscreen models  Validation (Telescope+Windscreen - Bernoulli Constant 2500 2000 Constant Value  1500  -200  1000  Plate Model Permeable Model  500  Optics Model  0 -100  -500  0  100  200  -1000 Parametric Distance  For both cases analyzing consistency of telescope models and telescope with windscreen models, there is considerable inconsistency observed in the obtained data. The constant value that is supposed to remain identical throughout the entire selected streamline does not remain the same. The variation can be as great as 200%. In addition, there are huge drops in values between the beginning and the end of the streamline in all three models studied. Furthermore, even for some cases, which have identical initial and end values, the computational results along the streamline fluctuate notably without existing patterns. This can be observed in all three models as well. As a result, this verification approach does not provide any solid evidence suggesting valid results established.  Nevertheless, this does not necessarily indicate that the analytical results are completely unreliable and shall be discarded. Several explanations are possible to appropriately clarify these outcomes based on the assumptions of Bernoulli’s principle utilized during the  113  analysis. Referring back to the discussion made at the beginning of this section, Bernoulli’s constant is only applicable along a streamline such that if not complied with, errors may occur. Since the coordinates are arbitrarily selected from a plane that is also arbitrarily chosen, it might not precisely represent a streamline across the simulation flow profile. Therefore, sizable errors are observed in the data as shown in the figures above. Additionally, unsteady flow might be resulted by the interaction between simulated flows and modeled structural features such that violation of the steady flow assumption is made and thus fallacious output is produced. Moreover, if unsteady flow is present, energy could be added or removed from the streamline to further reduce the applicability of Bernoulli’s Principle to this validation method. Hence, no credible output is generated to verify the analytical results in this case.  Although the attempt of applying Bernoulli’s Principle and the associated constant equations to justify the pressure output was not successfully carried out to reach a positive solution, it can still serve as a reference for upcoming studies to ensure that all assumptions are strictly conform to before commence of experimental analysis.  114  Chapter 6: Conclusion In this research, flow simulation is run using computational fluid dynamics to determine the applied pressure on the previously structurally analyzed telescope based on performancebased objectives and impact levels that are established according to statistical wind data from historical records. As the primary goal of this study is to prove the validity of the proposed windscreen around the telescope, analytical results obtained from modeling verified the hypothesis of that implementation of windscreen enables pressure reduction as past researches had shown; however, in some cases pressure increase was observed. Although the increased amount was less significant compared to the decreased one, further validation shall be required to elaborate on fine details of cases involving increase in pressure. In addition, a pressure envelope for all structural elements of the telescope is drafted from the simulation and aims to serve as a reference guideline for design engineers based on the performance impact levels and objectives.  During the analysis, it was found that some of the issues were not addressed fully. There were certain components whose geometric features were not captured accurately in the simulation process due to hardware limitations. As a result, the reliability of this research is partially reduced. In addition, simulation was run at a reasonably justified iteration number as a default value recommended by the CFD program; however, it was found that in some cases that involve a considerable amount of elements to be captured and modeled, analytical results could benefit from more iterations to generate more converged values. Furthermore, the simulation was modeled under the assumption of incompressible fluid and steady flow throughout the entire process. Nonetheless, it might be possible that turbulent flow did occur  115  to create energy adding or removal, as suggested by the validation method using Bernoulli’s equations. Therefore, these limitations shall be addressed to verify the findings in this study.  Possible future research in the related field shall be conducted to elaborate on the accuracy and reliability of the data obtained in this study. 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University of Berkley:  120  Appendices Appendix A : Pressure on Structural Elements  A.1  Pressure Envelope of Optic Top Surface  Optic Top Surface  0 Degree Orientation Plate Model  No Windscreen Permeable Model  Plate Model  Windscreen Permeable Model  Optics Model  Optics Model  -----------485.553 -120.214 -----------232.0 -63.2 -----------17.6 -7.0  -----------618.2 -75.2 -----------293.3 -37.1 -----------21.9 -3.2  -----------368.889 287.574 -----------173.2 137.1 -----------12.5 8.3  -----------223.728 51.5 -----------105.8 22.0 -----------9.0 0.2  -----------353.535 2 -----------149.9 -41.1 -----------10.7 -2.6  -----------95.7 -77.1 -----------50.1 -36.2 -----------4.4 -3.8  46 m/s  ------------  ------------  ------------  ------------  ------------  ------------  Max Pressure  732.7  518.5  425.3  666.4  479.4  413.0  Min Pressure  71.9  17.4  169.4  488.1  285.0  151.2  32 m/s Max Pressure Min Pressure 9 m/s Max Pressure  -----------357.5 33.1 -----------29.5  -----------249.8 9.0 -----------19.0  -----------205.1 -84.6 -----------15.9  -----------318.2 225.9 -----------24.8  -----------227.8 136.7 -----------17.0  -----------209.8 77.5 -----------16.3  Min Pressure  2.4  0.7  -9.8  15.1  10.5  4.6  Wind Speed (m/s) 0 degree angle of attack 46 m/s Max Pressure Min Pressure 32 m/s Max Pressure Min Pressure 9 m/s Max Pressure Min Pressure 90 degree angle of attack  121  Optic Top Surface  45 Degree Orientation Plate Model  No Windscreen Permeable Model  Plate Model  Windscreen Permeable Model  Optics Model  Optics Model  -----------3588.5 2717.2 -----------1742.8 1328.7 -----------138.4 108.1  -----------1324.82 734.466 -----------639.7 356.2 -----------57.6 38.3  -----------1950 1178.72 -----------928.3 581.5 -----------69.9 46.3  -----------803.1 639.8 -----------392.9 312.0 -----------31.8 25.0  -----------320.8 223.6 -----------153.2 19.8 -----------11.6 2.4  -----------822.9 220.2 -----------414.3 -105.0 -----------34.0 11.7  46 m/s  ------------  ------------  ------------  ------------  ------------  ------------  Max Pressure  294.5  425.7  200.0  318.4  609.1  327.0  Min Pressure  -272.9  -50.2  -306.0  132.8  390.0  -21.2  32 m/s Max Pressure Min Pressure 9 m/s Max Pressure Min Pressure 180 degree angle of attack 46 m/s Max Pressure Min Pressure 32 m/s Max Pressure Min Pressure 9 m/s Max Pressure Min Pressure  -----------143.2 -135.4 -----------11.6 -12.2  -----------204.5 -24.2 -----------15.6 -1.8  -----------94.6 -160.9 -----------8.0 -14.9  -----------155.0 61.0 -----------12.6 3.2  -----------291.6 190.1 -----------21.9 14.4  -----------153.8 -15.7 -----------13.3 -1.2  -----------373.3 235.9 -----------177.6 114.8 -----------13.4 8.7  -----------829.7 -39.0 -----------399.5 -19.4 -----------32.6 -0.9  -----------165.3 -492.1 -----------101.2 -250.7 -----------4.7 -22.2  ------------626.0 -577.0 ------------303.0 -277.0 ------------23.3 -21.3  -----------398.1 -16.6 -----------190.6 -6.8 -----------14.8 -0.2  ------------580.0 -910.0 ------------284.0 -436.0 ------------18.0 -34.0  Wind Speed (m/s) 0 degree angle of attack 46 m/s Max Pressure Min Pressure 32 m/s Max Pressure Min Pressure 9 m/s Max Pressure Min Pressure 90 degree angle of attack  A.2  Pressure Envelope of Optic Bottom Surface 122  0 Degree Orientation Optic Bottom Surface  Plate Model  No Windscreen Permeable Model  Plate Model  Windscreen Permeable Model  Optics Model  Optics Model  0 degree angle of attack 46 m/s  ------------  ------------  ------------  ------------  ------------  ------------  Max Pressure  1284.3  656.9  1334.8  375.3  331.6  420.5  Min Pressure  -169.2  -91.5  -109.6  -305.7  -98.5  -283.1  32 m/s Max Pressure Min Pressure  -----------615.5 -86.1  -----------313.8 -45.0  -----------631.2 -57.2  -----------177.3 -144.9  -----------158.9 -22.0  -----------218.0 -136.4  9 m/s Max Pressure  -----------45.9  -----------23.5  -----------45.8  -----------12.8  -----------11.5  -----------16.3  Min Pressure 90 degree angle of attack 46 m/s  -8.8  -3.8  -6.0  -11.4  -2.9  -10.7  ------------  ------------  ------------  ------------  ------------  ------------  Max Pressure Min Pressure 32 m/s  1323.1 119.1 ------------  626.5 2.1 ------------  1605.6 -107.7 ------------  675.7 207.1 ------------  522.6 261.8 ------------  798.5 44.2 ------------  Max Pressure Min Pressure  641.2 60.6  302.1 1.9  774.2 -56.1  325.4 102.1  248.7 125.8  384.1 26.2  9 m/s  ------------  ------------  ------------  ------------  ------------  ------------  Max Pressure  51.2  23.2  59.5  25.4  18.7  31.0  Min Pressure  5.9  0.2  -4.6  7.8  9.7  1.2  123  45 Degree Orientation Optic Bottom Surface 0 degree angle of attack 46 m/s Max Pressure Min Pressure 32 m/s Max Pressure Min Pressure 9 m/s Max Pressure Min Pressure 90 degree angle of attack 46 m/s Max Pressure Min Pressure 32 m/s Max Pressure Min Pressure 9 m/s Max Pressure Min Pressure 180 degree angle of attack 46 m/s Max Pressure Min Pressure 32 m/s Max Pressure Min Pressure 9 m/s Max Pressure Min Pressure  Plate Model  No Windscreen Permeable Model  Optics Model  Plate Model  Windscreen Permeable Model  -----------615.6 -325.1 -----------310.6 -148.3 -----------24.3 -11.0  -----------1189.8 127.1 -----------574.6 62.2 -----------42.4 5.0  -----------61.3 -520.7 -----------57.0 -234.1 -----------2.6 -25.1  ------------481.0 -788.0 ------------385.0 -234.0 ------------27.2 -19.2  -----------279.7 -150.6 -----------132.5 -73.2 -----------9.9 -5.5  ------------82.0 -706.8 ------------30.0 -339.0 ------------2.3 -27.7  -----------800.6 -374.6 -----------385.6 -181.8 -----------29.6 -14.6  -----------521.9 -72.1 -----------251.1 -34.8 -----------19.3 -2.6  -----------1344.1 -275.8 -----------636.6 -136.3 -----------49.2 -11.2  -----------438.4 1.7 -----------232.0 6.5 -----------18.0 1.4  -----------680.0 372.0 -----------326.2 180.0 -----------24.6 13.8  -----------833.9 -24.0 -----------401.9 -13.9 -----------31.7 -1.2  -----------3345.3 598.1 -----------1616.9 288.7 -----------127.0 23.2  -----------1579.0 61.3 -----------761.2 29.4 -----------57.9 2.5  -----------2454.9 212.7 -----------1180.1 109.0 -----------91.1 10.0  -----------1946.0 -50.0 -----------942.0 -23.0 -----------74.6 -1.0  -----------771.2 13.6 -----------371.4 8.1 -----------29.2 1.2  -----------1772.0 -550.0 -----------836.0 -128.0 -----------66.5 -10.4  Optics Model  124  A.3  Pressure Envelope of Optic Frames 0 Degree Orientation  Optic Frames 0 degree angle of attack 46 m/s Max Pressure Min Pressure 32 m/s Max Pressure Min Pressure 9 m/s Max Pressure Min Pressure 90 degree angle of attack 46 m/s Max Pressure Min Pressure 32 m/s Max Pressure Min Pressure 9 m/s Max Pressure Min Pressure  Plate Model  No Windscreen Permeable Model  Optics Model  Plate Model  Windscreen Permeable Model  Optics Model  -----------2010.0 -276.0 -----------968.0 -134.8 -----------74.0 -11.5  -----------681.0 -116.9 -----------305.4 -31.6 -----------24.4 -4.3  -----------2177.5 -213.7 -----------1040.4 -106.9 -----------78.3 -9.1  -----------1303.1 -476.0 -----------627.2 -223.7 -----------48.5 -16.8  -----------361.3 -125.1 -----------174.0 -56.4 -----------12.6 -3.3  -----------877.0 -338.1 -----------434.6 -156.9 -----------33.6 -12.6  -----------1998.6 -150.2 -----------966.5 -70.5 -----------76.3 -4.2  -----------1339.5 -94.6 -----------648.6 -44.2 -----------50.6 -3.2  -----------1767.9 -120.6 -----------848.1 -59.3 -----------64.4 -5.1  -----------1367.3 109.1 -----------657.9 52.0 -----------50.3 4.1  -----------881.3 180.0 -----------422.2 87.1 -----------32.4 7.0  -----------1042.0 24.7 -----------505.7 17.5 -----------38.9 0.6  125  45 Degree Orientation Plate Model  No Windscreen Permeable Model  Optics Model  -----------1006.5 -1391.9 -----------490.8 -666.0 -----------38.9 -51.5  -----------2032.1 127.7 -----------982.1 64.4 -----------88.5 7.4  46 m/s Max Pressure Min Pressure 32 m/s Max Pressure Min Pressure 9 m/s Max Pressure Min Pressure  -----------1507.8 -562.5 -----------727.0 -271.3 -----------56.2 0.0  180 degree angle of attack 46 m/s Max Pressure Min Pressure 32 m/s Max Pressure Min Pressure 9 m/s Max Pressure Min Pressure  -----------365.7 -449.3 -----------179.6 -215.8 -----------14.1 -17.1  Optic Frames  Plate Model  Windscreen Permeable Model  Optics Model  -----------1421.2 -971.3 -----------679.1 -486.0 -----------51.6 -41.3  ------------263.0 -1333.0 ------------133.8 -615.9 ------------12.0 -51.0  -----------522.2 -233.6 -----------250.2 -112.0 -----------19.2 -8.2  -----------793.0 -838.0 -----------396.0 -406.0 -----------31.4 -32.8  -----------1218.2 -174.7 -----------588.1 -83.8 -----------45.9 -6.3  -----------1585.7 -279.6 -----------757.5 -139.8 -----------57.6 -11.3  -----------1521.0 -13.7 -----------736.0 -7.0 -----------58.9 -1.5  -----------1178.0 273.0 -----------567.4 132.0 -----------43.8 10.2  -----------1182.0 31.0 -----------557.0 0.6 -----------21.9 0.7  -----------1493.4 -246.6 -----------720.4 -118.7 -----------55.3 -8.4  -----------668.5 -417.0 -----------318.6 -211.0 -----------23.7 -18.3  -----------179.0 -1378.0 -----------88.7 -670.8 -----------6.9 -52.7  -----------778.0 -76.0 -----------375.2 -59.7 -----------29.4 -4.4  -----------906.0 -921.0 -----------434.0 -446.0 -----------33.5 -36.3  0 degree angle of attack 46 m/s Max Pressure Min Pressure 32 m/s Max Pressure Min Pressure 9 m/s Max Pressure Min Pressure 90 degree angle of attack  126  A.4  Pressure Envelope of Support Girders 0 Degree Orientation  Support Girders 0 degree angle of attack 46 m/s Max Pressure Min Pressure 32 m/s Max Pressure Min Pressure 9 m/s Max Pressure Min Pressure 90 degree angle of attack 46 m/s Max Pressure Min Pressure 32 m/s Max Pressure Min Pressure 9 m/s Max Pressure Min Pressure  Plate Model  No Windscreen Permeable Model  Optics Model  Plate Model  Windscreen Permeable Model  Optics Model  -----------2019.4 1045.0 -----------968.6 432.0 -----------73.8 35.2  -----------1720.6 -1097.0 -----------827.0 -533.3 -----------63.7 -41.0  -----------2019.6 928.0 -----------956.9 510.0 -----------70.7 40.1  -----------1091.3 -651.5 -----------530.0 -310.7 -----------40.5 -24.2  -----------1088.7 -408.0 -----------526.9 -193.4 -----------40.3 -14.0  -----------801.3 -410.7 -----------389.2 -198.4 -----------33.8 -15.6  -----------2293.6 1203.0 -----------1109.0 560.0 -----------87.4 45.2  -----------2162.7 -1109.6 -----------1044.0 -537.8 -----------81.2 -42.9  -----------2114.3  -----------1146.5 -314.6 -----------728.0 -158.0 -----------57.0 -13.5  -----------1353.0 -159.5 -----------650.4 -86.4 -----------50.3 -8.5  -----------1218.6 -209.1 -----------586.1 -103.0 -----------47.7 -9.2  -----------1017.2 -----------77.8  127  45 Degree Orientation Support Girders  Plate Model  No Windscreen Permeable Model  Plate Model  Windscreen Permeable Model  Optics Model  Optics Model  -----------1016.2 -194.0 -----------503.3 -86.3 -----------40.4 -7.1  -----------1226.4 -362.0 -----------571.1 -173.0 -----------50.4 -16.4  -----------576.9 -187.2 -----------272.6 -105.0 -----------19.5 -10.5  ------------291.0 -861.0 ------------161.1 -419.5 ------------34.0 -11.0  ------------590.0 394.6 -----------190.0 -286.0 -----------13.9 -22.3  ------------17.0 -466.0 -----------13.0 -221.8 -----------0.6 -17.9  46 m/s Max Pressure Min Pressure 32 m/s Max Pressure Min Pressure 9 m/s Max Pressure Min Pressure  -----------1662.2 -1842.8 -----------801.9 -899.3 -----------62.0 -74.6  -----------1982.4 -940.2 -----------957.0 -530.1 -----------74.6 -42.6  -----------1783.8 -1055.4 -----------853.2 -552.1 -----------65.3 -46.4  -----------970.0 -514.0 -----------474.1 -248.2 -----------36.7 -6.1  -----------1486.0 -7.2 -----------719.0 -3.8 -----------53.6 -2.9  -----------1093.0 -141.0 -----------535.4 -57.6 -----------42.5 -5.4  180 degree angle of attack 46 m/s Max Pressure Min Pressure 32 m/s Max Pressure Min Pressure 9 m/s Max Pressure Min Pressure  -----------3151.1 282.5 -----------1521.6 137.6 -----------119.0 10.9  -----------2322.4 -308.5 -----------1121.2 -152.7 -----------87.5 -12.7  -----------2440.8 108.3 -----------1168.4 50.7 -----------89.0 3.1  -----------1400.0 -468.0 -----------683.0 -228.0 -----------53.6 -17.8  -----------1485.0 -158.0 -----------715.3 -73.0 -----------56.1 -5.6  -----------1592.0 -322.0 -----------729.0 -163.0 -----------58.7 -13.0  0 degree angle of attack 46 m/s Max Pressure Min Pressure 32 m/s Max Pressure Min Pressure 9 m/s Max Pressure Min Pressure 90 degree angle of attack  128  A.5  Pressure Envelope of Optic Tube 0 Degree Orientation  Optic Tube 0 degree angle of attack 46 m/s Max Pressure 32 m/s Max Pressure 9 m/s Max Pressure 90 degree angle of attack 46 m/s Max Pressure 32 m/s Max Pressure 9 m/s Max Pressure  Plate Model  No Windscreen Permeable Model  Optics Model  Plate Model  Windscreen Permeable Model  Optics Model  -----------292.5 -----------137.5 -----------8.9  ------------84.7 ------------44.4 ------------4.6  -----------218.4 -----------94.1 -----------4.0  -----------139.9 -----------65.6 -----------4.5  ------------39.0 ------------26.0 ------------3.6  -----------2.2 -----------1.6 -----------0.6  -----------477.4 -----------230.2 -----------18.0  -----------85.3 -----------40.3 -----------2.1  -----------239.0 -----------105.9 -----------5.8  -----------595.0 -----------282.0 -----------20.8  -----------300.0 -----------137.9 -----------9.5  -----------301.0 -----------148.8 -----------10.6  129  45 Degree Orientation Optic Tube 0 degree angle of attack 46 m/s Max Pressure 32 m/s Max Pressure 9 m/s Max Pressure 90 degree angle of attack 46 m/s Max Pressure 32 m/s Max Pressure 9 m/s Max Pressure 180 degree angle of attack 46 m/s Max Pressure 32 m/s Max Pressure 9 m/s Max Pressure  No Windscreen Permeable Plate Model Model  Optics Model  Plate Model  Windscreen Permeable Model  Optics Model  -----------2731.2 -----------1327.9 -----------105.7  -----------1017.8 -----------490.2 -----------48.2  -----------1084.1 -----------508.2 -----------36.8  -----------609.0 -----------294.6 -----------23.2  -----------82.7 -----------36.0 -----------1.9  -----------299.6 -----------150.7 -----------12.3  -----------139.4 -----------64.3 -----------3.8  -----------5.8 -----------1.5 ------------0.6  -----------67.9 -----------20.1 ------------0.8  -----------290.0 -----------145.4 -----------10.6  -----------442.0 -----------208.2 -----------15.0  -----------235.5 -----------111.5 -----------9.0  -----------226.6 -----------109.3 -----------8.1  -----------16.0 -----------6.8 -----------0.6  -----------183.8 -----------82.3 -----------4.9  ------------595.0 ------------287.0 ------------22.2  ------------11.5 ------------7.5 ------------0.8  ------------430.0 ------------215.0 ------------17.2  130  A.6  Pressure Range of Bottom Frames 0 Degree Orientation  Bottom Frames 0 degree angle of attack 46 m/s Max Pressure Min Pressure 32 m/s Max Pressure Min Pressure 9 m/s Max Pressure Min Pressure 90 degree angle of attack 46 m/s Max Pressure Min Pressure 32 m/s Max Pressure Min Pressure 9 m/s Max Pressure Min Pressure  Plate Model  No Windscreen Permeable Model  Optics Model  Plate Model  Windscreen Permeable Model  Optics Model  -----------981.1 -213.7 -----------468.6 -108.0 -----------34.3 -10.4  -----------756.9 -228.9 -----------362.2 -113.5 -----------27.3 -10.1  -----------834.5 -127.1 -----------386.8 -76.4 -----------25.9 -10.4  -----------297.5 -294.2 -----------142.6 -140.7 -----------10.1 -11.6  -----------382.1 -107.0 -----------183.9 -48.7 -----------13.6 -3.9  -----------275.9 -248.7 -----------135.2 -119.0 -----------9.9 -9.3  -----------1872.8 134.6 -----------905.6 50.4 -----------71.7 5.2  -----------1302.2 -69.9 -----------629.1 -35.4 -----------48.9 -1.5  -----------1254.3 -98.9 -----------596.9 -73.9 -----------43.9 -12.4  -----------945.2 198.2 -----------455.2 96.3 -----------35.6 7.2  -----------805.1 221.8 -----------384.8 108.3 -----------29.4 8.4  -----------743.4 96.8 -----------354.7 53.2 -----------28.4 3.5  131  45 Degree Orientation Bottom Frames 0 degree angle of attack 46 m/s Max Pressure Min Pressure 32 m/s Max Pressure Min Pressure 9 m/s Max Pressure Min Pressure 90 degree angle of attack 46 m/s Max Pressure Min Pressure 32 m/s Max Pressure Min Pressure 9 m/s Max Pressure Min Pressure 180 degree angle of attack 46 m/s Max Pressure Min Pressure 32 m/s Max Pressure Min Pressure 9 m/s Max Pressure Min Pressure  Plate Model  No Windscreen Permeable Model  Optics Model  Plate Model  Windscreen Permeable Model  Optics Model  -----------431.8 -45.7 -----------218.3 -13.6 -----------17.6 -0.8  -----------900.4 -69.2 -----------435.3 -33.3 -----------37.0 -6.0  -----------377.5 -51.0 -----------175.5 -20.7 -----------12.8 -6.9  ------------532.0 -633.0 ------------307.9 -259.0 ------------20.5 -25.2  ------------291.0 178.0 -----------88.0 -140.0 -----------6.9 -10.8  ------------88.0 -404.0 ------------35.8 -191.4 ------------15.5 -4.6  -----------1288.4 -421.5 -----------621.2 -206.6 -----------46.0 -17.0  -----------1153.2 -108.9 -----------556.8 -52.2 -----------43.5 -3.9  -----------1010.4 -169.0 -----------474.5 -102.8 -----------34.8 -14.8  -----------612.0 -69.0 -----------298.8 -26.7 -----------23.1 -2.2  -----------937.0 339.0 -----------450.6 170.1 -----------34.5 13.3  -----------734.0 109.0 -----------354.3 36.2 -----------27.9 3.3  -----------2918.4 713.1 -----------1409.3 346.1 -----------110.5 27.4  -----------1879.2 174.5 -----------906.3 88.3 -----------69.9 6.7  -----------1624.2 285.9 -----------773.1 117.9 -----------57.5 6.2  -----------1503.0 -55.0 -----------728.8 -26.5 -----------57.4 -0.9  -----------1001.0 162.0 -----------481.6 44.0 -----------37.9 4.0  -----------913.0 -152.0 -----------411.5 -90.0 -----------33.2 -5.7  132  A.7  Pressure Envelope of Top Frames 0 Degree Orientation  Top Frames 0 degree angle of attack 46 m/s Max Pressure Min Pressure 32 m/s Max Pressure Min Pressure 9 m/s Max Pressure Min Pressure 90 degree angle of attack 46 m/s Max Pressure Min Pressure 32 m/s Max Pressure Min Pressure 9 m/s Max Pressure Min Pressure  Plate Model  No Windscreen Permeable Model  Optics Model  Plate Model  Windscreen Permeable Model  Optics Model  -----------531.0 217.8 -----------252.3 103.3 -----------18.0 7.4  -----------637.0 -62.0 -----------305.4 -31.8 -----------22.9 -3.1  -----------496.4 -295.4 -----------229.5 -160.2 -----------14.8 -18.9  -----------465.5 -50.5 -----------223.1 -18.5 -----------16.6 -0.5  -----------453.8 -130.0 -----------224.6 -61.4 -----------16.9 -4.6  -----------132.4 -330.8 ------------162.7 62.1 -----------4.4 -14.4  -----------727.9 357.0 -----------350.3 175.0 -----------27.6 14.8  -----------902.7 -38.7 -----------435.8 -17.7 -----------33.8 -1.3  -----------577.3 -201.4 -----------271.7 -107.2 -----------19.2 -11.2  -----------833.4 386.6 -----------396.4 187.8 -----------29.5 15.1  -----------797.4 169.8 -----------380.8 82.1 -----------29.0 6.4  -----------545.5 55.6 -----------268.3 28.6 -----------20.1 0.5  133  45 Degree Orientation Top Frames 0 degree angle of attack 46 m/s Max Pressure Min Pressure 32 m/s Max Pressure Min Pressure 9 m/s Max Pressure Min Pressure 90 degree angle of attack 46 m/s Max Pressure Min Pressure 32 m/s Max Pressure Min Pressure 9 m/s Max Pressure Min Pressure 180 degree angle of attack 46 m/s Max Pressure Min Pressure 32 m/s Max Pressure Min Pressure 9 m/s Max Pressure Min Pressure  Plate Model  No Windscreen Permeable Model  Optics Model  Plate Model  Windscreen Permeable Model  Optics Model  -----------3222.8 2371.9 -----------1566.4 1156.7 -----------124.6 93.3  -----------1810.4 1089.0 -----------874.8 525.0 -----------78.5 50.6  -----------1400.8 929.0 -----------601.0 440.1 -----------48.7 31.2  -----------715.0 518.0 -----------346.0 252.0 -----------27.3 20.2  -----------563.0 142.0 -----------274.0 68.0 -----------21.2 5.5  -----------443.3 266.1 -----------225.4 135.4 -----------18.1 11.1  -----------347.6 -17.4 -----------164.6 -7.6 -----------11.5 -0.6  -----------784.8 -101.7 -----------378.4 -49.0 -----------29.4 -3.8  -----------370.1 -281.2 -----------168.5 -149.2 -----------11.3 -15.0  -----------515.4 137.4 -----------248.3 75.2 -----------18.3 7.1  -----------888.2 315.3 -----------426.0 166.0 -----------32.5 13.0  -----------423.0 -3.5 -----------200.6 -1.8 -----------15.7 -1.4  -----------339.0 216.0 -----------163.1 105.0 -----------12.2 8.0  -----------289.5 -105.8 -----------139.8 -50.5 -----------11.4 -3.6  -----------240.9 87.6 -----------109.7 33.7 -----------7.5 0.6  ------------665.0 -540.0 ------------320.5 -261.0 ------------24.6 -20.1  -----------159.0 -79.0 -----------75.9 -36.0 -----------6.1 -2.3  ------------340.0 -534.0 ------------172.0 -268.6 ------------14.2 -21.2  134  Appendix B : Pressure on Structural Elements  B.1  Bernoulli Constants for Telescope Models  Bernoulli's Constant Parametric Distance 30.3 35.6 40.9 46.2 51.6 56.9 62.2 67.5 72.8 78.2 94.1 99.5 104.8 110.1 115.4 120.7 126.1 131.4 136.7  Optics Model Constant 1655 1659 1629 1161 598 638 968 938 907 972 1088 757 998 859 618 738 1390 1645 1658  Permeable Model Constant 1455 1447 1444 1441 1410 1392 1378 1368 1343 1331 628 633 601 561 540 499 470 463 459  Plate Model Constant 1644 1650 1677 1768 1417 1072 985 1004 1079 1164 676 716 676 716 692 660 619 586 366  135  B.2  Bernoulli Constants for Telescope with Windscreen Models  Bernoulli's Constant Parametric Distance 157 140 124 107 90 74 57 40 23 7 -10 -27 -43 -60 -77 -94 -110 -127 -144 -160 -177  Plate Model Constant 1727 1368 -402 67 429 696 756 749 711 598 -249 -141 -87 61 204 327 499 603 662 687 721  Permeable Model Constant 1737 1515 -257 472 745 817 773 693 678 614 -30 147 234 386 618 769 849 933 991 1018 1040  Optics Model Constant 469 425 396 289 165 39 -23 -45 -98 -202 744 831 856 873 808 749 289 174 1815 1699 1666  136  

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