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Development of the tolerant wind tunnel for bluff body testing Hameury, Michel 1987

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DEVELOPMENT OF THE TOLERANT WIND TUNNEL FOR BLUFF BODY TESTING by M I C H E L H A M E U R Y M . A . S c , E C O L E P O L Y T E C H N I Q U E , 1982 A THESIS S U B M I T T E D I N P A R T I A L F U L F I L M E N T O F T H E R E Q U I R E M E N T S F O R T H E D E G R E E OF DOCTOR O F P H I L O S O P H Y in T H E F A C U L T Y OF G R A D U A T E STUDIES Department of Mechanical Engineering We accept this thesis as conforming to the required standard T H E U N I V E R S I T Y O F BRITISH C O L U M B I A February 1987 • M I C H E L H A M E U R Y , 1987 ln presenting this thesis in partial fulfilment of the requirements for an advanced degree at the THE UNIVERSITY OF BRITISH COLUMBIA, I agree that the Library shall make it freely available for reference and study. I further agree that permission for extensive copying of this thesis for scholarly purposes may be granted by the Head of my Department or by his or her representatives. It is understood that copying or publication of this thesis for financial gain shall not be allowed without my written permission. Department of Mechanical Engineering THE UNIVERSITY OF BRITISH COLUMBIA 2075 Wesbrook Place Vancouver, Canada V6T 1W5 Date: FEBRUARY 1987 Abstract In conventional wind tunnels the solid-wall or open-jet test section imposes on the flow field around the test model new boundary conditions absent in free air. Unless a small model is used, the solid-wall test section generally increases the loadings on the model while the open-jet boundary decreases the loadings compared to the unconfined case. However, the development of a low wall-interference test section and its successful demonstration would allow the testing of relatively large models without the application of often uncertain correction formulae. The Tolerant wind tunnel, which makes use of the opposite effects of solid and open boundaries, is a transversely slatted-wall test section designed to produce at an optimal wall open-area ratio (OAR) low-correction data for a wide variety of model shapes and sizes. Initially intended for low-speed airfoil testing, its use is theoretically and experimentally investigated here in connection with bluff body testing. A simple mathematical model based on two-dimensional potential flow theory and solved with the help of a vortex surface-singularity technique is used to estimate the best wall configuration. The theory predicts an optimum OAR of about 0.45 at which pressure distributions on flat plate and circular cylinder models of blockage ratios up to 33.3 % would differ from the free-air values by not more than 1 %. On the other hand, experiments performed with flat plate, circular cylinder and circular-cylinder-with-splitter-plate models indicate the existence of an optimum configuration around OAR = 0.6. The experiments also show a maximum allowable blockage in the Tolerant wind tunnel to be equivalent to the blockage created by a 33.3 %-blockage-ratio flat plate model. Table of Contents Abstract « List of Figures vi Nomenclature xii Acknowledgements xv 1. INTRODUCTION 1 1.1 Generalities 1 1.2 An Overview of the Related Literature 4 2. THE TOLERANT TEST SECTION 7 2.1 General Description 7 2.2 Degrees of Freedom 8 3. MODELLING OF BLUFF BODIES IN THE TOLERANT WIND TUNNEL 10 3.1 Bluff Bodies 10 3.1.1 Definitions and Descriptions 10 3.1.2 Wall Effects on Bluff Bodies 11 3.1.3 Bluff Body Models 12 3.2 Numerical Model of the Tolerant Wind Tunnel 14 3.2.1 Wake Source Model in the Tolerant Wind Tunnel 14 3.2.2 Mathematical Representation 18 4. NUMERICAL RESULTS 25 4.1 Free Air Results 25 4.1.1 Computation in the Transform Plane 25 4.1.2 Computation in the Physical Plane 26 4.2 Solid-Wall Confined Flow Results 27 4.2.1 Flat Plate Model 27 4.2.2 Circular Cylinder Model 28 4.3 Tolerant Wind Tunnel Results 29 4.3.1 Flat Plate Model 29 iii 4.3.2 Circular Cylinder Model 31 5. EXPERIMENTAL ARRANGEMENT 34 5.1 Apparatus and Equipment 34 5.2 Test Procedure 37 5.3 Error Analysis 37 5.4 Flow Visualization 38 6. EXPERIMENTAL RESULTS 40 6.1 Flat Plate Model 40 6.1.1 Model Pressure Distribution 40 6.1.2 Floor Pressure Distribution 41 6.1.3 Variation with OAR , 43 6.1.4 Effect of Model Position 44 6.2 Circular Cylinder Model 45 6.2.1 Model Pressure Distribution 45 6.2.2 Variation with OAR 47 6.2.3 Effect of Non-evenly Spaced Slats, 49 6.3 Effect of Splitter Plate 50 6.3.1 Model Pressure Distribution '. 51 6.3.2 Variation With OAR 52 6.4 Plenum Flow 53 7. CLOSING COMMENTS 56 7.1 Concluding Remarks 56 7:2 Recommendations for Future Work 58 LIST OF REFERENCES 60 APPENDIX 1...WIND TUNNEL CALIBRATION 64 APPENDIX 2...EVALUATION OF THE INFLUENCE COEFFICIENTS 66 APPENDIX 3...DETERMINATION OF VELOCITY FIELD .67 iv APPENDIX 4...REGRESSION METHOD FOR COMPARING TWO DATA SETS 69 APPENDIX 5...GRADED OPEN AREA RATIO 71 APPENDIX 6...INSTRUMENTATION 74 APPENDIX 7...ERROR ANALYSIS 76 v List of Figures Figure 2.1 : Single-slatted-wall tunnel configuration for airfoil testing. Figure 2.2 : Double-slatted-wall tunnel configuration for bluff body testing. Figure 3.1 (a): Physical and basic transform planes for a flat plate model. Figure 3.1 (b): Physical and basic transform planes for a circular cylinder model. Figure 3.2 : Theoretical representation of the Tolerant wind tunnel. Figure 4.1 : Pressure distribution over a normal flat plate in unconfined flow : comparison of numerical calculation in transform plane with analytical solution. Given C pfc = - 1.38, N = 70 Figure 4.2 : Pressure distribution over a circular cylinder in unconfined flow : comparison of numerical calculation in transform plane with analytical solution. Given C pfc = - 0.96, @ s = 80° , N = 70 Figure 4.3 : Variation of source strength with number of panels in transform plane, for flat plate and circular cylinder in unconfined flow. Figure 4.4: Pressure distribution over a normal flat plate in unconfined flow : comparison of numerical calculation in physical plane with analytical solution. Given C pfc = - 1.38, N = 60 Figure 4.5 : Pressure distribution over a circular cylinder in unconfined flow : comparison of numerical calculation in physical plane with analytical solution. Civen Cpfc = - 0.96, p\. = 80° , N = 60 Figure 4.6 (a) : Variation of source strength with number of panels in physical plane, for flat plate and circular cylinder in unconfined flow. Figure 4.6 (b): Variation of base pressure coefficient with number of panels in physical plane, for flat plate and circular cylinder in unconfined flow. Figure 4.7 : Pressure distribution over a normal flat plate in solid-wall confined flow : comparison of numerical calculation in physical plane with analytical solution. Given C p 5 - - 1.0, h/H = 1/3 , N(model) = 80, N(wall) = 20 Figure 4.8 : Corrected pressure distribution over a normal flat plate in solid-wall confined flow : comparison of corrected numerical calculation in physical plane with free-air analytical solution. Given C pfc = - 1.0 , h/H = 1/3 , CF = 0.6749 Figure 4.9 : Variation of base pressure coefficient with number of panels on solid walls, for a normal flat plate model in confined flow. Given C p 6 = - 1.0 , h/H = 1/3 , Wall Length = 12 vi Figure 4.10 : Variation of base pressure coefficient with wall length, for a normal flat plate in confined flow. Given C p o = - 1.0 , h/H = 1/3 , N(model) = 80, N(wall) = 20 Figure 4.11 : Variation of base pressure coefficient with blockage ratio, for a normal flat plate in confined flow. Given C p o = - 1.0 , N(model) = 80 , N(wall) = 20 Figure 4.12 : Variation of blockage-correction factor with blockage ratio, for a normal flat plate in confined flow. Given C p o = - 1.0, N(model) = 80 , N(wall) = 20 Figure 4.13 : Pressure distribution over a circular cylinder in solid-wall confined flow : comparison of numerical calculation in physical plane with free-air analytical solution. Given C p o = - 0.96 , 0S = 80° , h/H = 1/3 , N(model) = 80 , N(wall) = 20 Figure 4.14 : Corrected pressure distribution over a circular cylinder in solid-wall confined flow : comparison of corrected numerical calculation in physical plane with free-air analytical solution. Given C p o = - 0.96 , 0 S = 80° , h/H = 1/3 , CF = 0.7827 Figure 4.15 : Variation of base pressure coefficient with number of panels on solid walls, for a circular cylinder model in confined flow. Given C p o = - 1.0 , p\. = 80° , h/H = 1/3 , Wall Length = 12 Figure 4.16 : Variation of base pressure coefficient with wall length, for a circular cylinder in confined flow. Given C pfc = - 0.96, Ps = 80° , h/H = 1/3 , N(model) = 80, N(wall) = 20 Figure 4.17: Variation of base pressure coefficient with blockage ratio, for a circular cylinder in confined flow. Given C pfc = - 1.0, p\. = 80° , N(model) = 80, N(wall) = 20 Figure 4.18 : Variation of blockage-correction factor with blockage ratio, for a circular cylinder in confined flow. Given C p o = - 1.0, p\. = 80° , N(model) = 80 , N(wall) = 20 Figure 4.19 : Theoretical variation of base pressure coefficient as a function of OAR for 4 sizes of flat plate model positioned at the center of the test section. Figure 4.20 : Theoretical variation of blockage correction factor as a function of OAR for 4 sizes of flat plate model positioned at the center of the test section. Figure 4.21 : Theoretical variation of standard deviation as a function of OAR for 4 sizes of flat plate model positioned at the center of the test section. Figure 4.22 : Theoretical variation of pressure coefficient at /3 = 30° as a function of OAR for 4 sizes of circular cylinder model positioned at the center of the test section. Given C p o = - 0.96 , /3«. = 80° vii Figure 4.23 : Theoretical variation of pressure coefficient at 0 = 60° as a function of OAR for 4 sizes of circular cylinder model positioned at the center of the test section. Given C p 5 = - 0.96 , /3S = 80° Figure 4.24 : Theoretical variation of pressure coefficient at 0 = 70° as a function of OAR for 4 sizes of circular cylinder model positioned at the center of the test section. Given C p o = - 0.96, /3S = 80° Figure 4.25 : Theoretical variation of base pressure coefficient ( /? = 80° ) as a function of OAR for 4 sizes of circular cylinder model positioned at the center of the test section. Given C p fc = - 0.96 , /3S = 80° Figure 4.26 : Theoretical variation of blockage correction factor as a function of OAR for 4 sizes of circular cylinder model positioned at the center of the test section. Given C pfc = - 0.96 , /3S = 80° Figure 4.27 : Theoretical variation of standard deviation as a function of OAR for 4 sizes of circular cylinder model positioned at the center of the test section. Given C p £, = - 0.96 , 0S = 80° Figure 5.1 : The closed-circuit "Green" wind tunnel. Figure 5.2 : Pressure tap positions on the floor and in the plenum. Figure 5.3 : Pressure tap positions on models. Figure 5.4 : Tuft positions in the plenum. Figure 5.5 : Modified "Green" wind tunnel for smoke flow visualization. Figure 6.1 (a) to (m): Pressure distributions over 3 different sizes of flat plate model. Re = 10 s Figure 6.2 (a) to (d): Floor static pressure distributions for 3 different sizes of flat plate model positioned at center (dimensionalized plot). Figure 6.3 (a) to (d): Floor static pressure distributions for 3 different sizes of flat plate model positioned at center (non-dimensionalized plot). Figure 6.4 : Variation of base pressure coefficient as a function of OAR for 3 sizes of flat plate model positioned at center. Figure 6.5 : Variation of front drag coefficient as a,function of OAR for 3 sizes of flat plate model positioned at center. Figure 6.6 : Variation of drag coefficient as a function of OAR for 3 sizes of flat plate model positioned at center. Figure 6.7 : Variation of Strouhal number as a function of OAR for 3 sizes.of flat plate model positioned at center. viii Figure 6.8 : Variation of blockage-correction factor as a function of OAR for 3 sizes of flat plate model positioned at center. Figure 6.9 : Variation of standard deviation as a function of OAR for 3 sizes of flat plate model positioned at center. Figure 6.10 (a) to (d) : Floor static pressure distributions for 3 different sizes of flat plate model positioned at 22 inches upstream of the center (dimensionalized plot). Figure 6.11 (a) to (d) : Floor static pressure distributions for 3 different sizes of flat plate model positioned at 22 inches upstream of the center (non-dimensionalized plot). Figure 6.12 : Variation of base pressure coefficient as a function of OAR for 3 sizes of flat plate model positioned at 22 inches upstream of the center. Figure 6.13 : Variation of front drag coefficient as a function of OAR for 3 sizes of flat plate model positioned at 22 inches upstream of the center. Figure 6.14 : Variation of drag coefficient as a function of OAR for 3 sizes of flat plate model positioned at 22 inches upstream of the center. Figure 6.15 : Variation of Strouhal number as a function of OAR for 3 sizes of flat plate model positioned at 22 inches upstream of the center. Figure 6.16 : Variation of blockage-correction factor as a function of OAR for 3 sizes of flat plate model positioned at 22 inches upstream of the center. Figure 6.17 : Variation of standard deviation as a function of OAR for 3 sizes of flat plate model positioned at 22 inches upstream of the center. Figure 6.18 (a) to (m): Pressure distributions over 4 sizes of circular cylinder model. Re = 10 5 Figure 6.19 : Variation of pressure coefficient at 0 = 50° as a function of OAR for 4 sizes of circular cylinder model positioned at the center of the test section. Figure 6.20 : Variation of pressure coefficient at j3 = 100° as a function of OAR for 4 sizes of circular cylinder model positioned at the center of the test section. Figure 6.21 : Variation of pressure coefficient at 0 = 180° as a function of OAR for 4 sizes of circular cylinder model positioned at the center of the test section. Figure 6.22 : Variation of front drag coefficient as a function of OAR for 4 sizes of circular cylinder model positioned at the center of the test section. Figure 6.23 : Variation of rear drag coefficient as a function of OAR for 4 sizes of circular cylinder model positioned at the center of the test section. Figure 6.24 : Variation of drag coefficient as a function of OAR for 4 sizes of circular cylinder model positioned at the center of the test section. ix Figure 6.25 : Variation of Strouhal number as a function of OAR for 4 sizes of circular cylinder model positioned at the center of the test section. Figure 6.26 : Variation of blockage-correction factor as a function of OAR for 4 sizes of circular cylinder model positioned at the center of the test section. Figure 6.27 : Variation of standard deviation as a function of OAR for 4 sizes of circular cylinder model positioned at the center of the test section. Figure 6.28 : Pressure distributions over 4 sizes of circular cylinder model tested between non-evenly spaced slatted-wall. Re = 10 5 , OAR = 0.453 , AORT = 1.5 Figure 6.29 : Pressure distributions over 4 sizes of circular cylinder model tested between non-evenly spaced slatted-wall. Re = 10 s , OAR = 0.453 , AORT = 3.0 Figure 6.30 (a) to (m) : Pressure distributions over 4 sizes of circular-cylinder-splitter-plate model. Re = 10 s Figure 6.31 : Variation of pressure coefficient at j3 = 50° as a function of OAR for 4 sizes of circular-cylinder-with-splitter-plate model positioned at the center of the test section. Figure 6.32 : Variation of pressure coefficient at 0 = 100° as a function of OAR for 4 sizes of circular-cylinder-with-splitter-plate model positioned at the center of the test section. Figure 6.33 : Variation of pressure coefficient at /? = 180° as a function of OAR for 4 sizes of circular-cylinder-with-splitter-plate model positioned at the center of the test section. Figure 6.34 : Variation of front drag coefficient as a function of OAR for 4 sizes of circular-cylinder-with-splitter-plate model positioned at the center of the test section. Figure 6.35 : Variation of rear drag coefficient as a function of OAR for 4 sizes of circuiar-cylinder-with-splitter-plate model positioned at the center of the test section. Figure 6.36 : Variation of drag coefficient as a function of OAR for 4 sizes of circular-cylinder-with-splitter-plate model positioned at the center of the test section. Figure 6.37 : Variation of blockage-correction factor as a function of OAR for 4 sizes of circular-cylinder-with-splitter-plate model positioned at the center of the test section. Figure 6.38 : Variation of standard deviation as a function of OAR for 4 sizes of circular-cylinder-with-splitter-plate model positioned at the center of the test section. Figure 6.39 : General flow pattern in the plenums for normal operation. x Figure 6.40 (a) to (I) : Plenum pressure distributions for 4 sizes of circular-cylinder-with-splitter-plate model positioned at the center of the test section. Figure 6.41 : General flow pattern in the plenums for extreme conditions. Figure 6.42 : Plenum pressure distributions corresponding to testing of normal flat plates at 22 inches upstream of the test section center. OAR = 0.563 xi Nomenclature A Test section height. AORT Graded OAR parameter. A , , A 2 Constants. a Radius of the circle in the $ -plane. a;- Open areas. C Constant. C Model boundary in the Z-plane. Crf Drag coefficient. CF Blockage correction factor. Cp Pressure coefficient. C p 0 Base pressure coefficient. ^pmin Minimum pressure coefficient. C p 0 Empty-test-section pressure coefficient. c / H Normalized chord length of airfoil slats. D Plenum depth. f Vortex-shedding frequency. H Test section width. H Total Head. h Model width. K!, K 2 Calibration constants. L Test section length. N Number of panels. n Number of slats. OAR Open area ratio. xii Poo Free-stream static pressure. Q Source strength. q Dynamic pressure. Re Reynolds number. SD Standard deviation. St Strouhal number. s,,s2 Separation positions. s Boundary surfaces. t / H Normalized thickness of airfoil slats. U Velocity of uniform flow. V Normalized velocity. V Velocity, * ,y Cartesian coordinates. z Physical plane. a Separation angle in the ([-plane. a Free stream angle to the x-axis. •P Angular position on C in the Z-plane. Panel angle to the x-axis. 0S Separation angles in the Z-plane. 7 Circle boundary in the $-plane. 7(s) Vortex strength per unit length of perimeter. 6 Source angular positions. ex. Uncertainty in x , . Transform plane. 0 Angular position on y in the $-plane. K Normalized separation velocity. V Fluid kinematic viscosity. xiii p Fluid density. }pu Stream function due to uniform flow. Stream function due to vortex sheets. \bs Stream function due to source flow. Subscripts c Corrected. n Wind tunnel nozzle. r Wind tunnel test section. r Reference. xiv Acknowledgements The author would like to thank Dr. C. V. Parkinson, not only for his guidance throughout this project, but also for his enjoyable and inspiring lectures. I wish also to express my sincere appreciation to Dr. I. S. Cartshore for his helpful discussions, constant interest and encouragement without which this work would have been impossible. Thanks to Dr. V. J. Modi who kindly provided most of the test models used in this work. Special thanks are due to Ed Abell, senior technician in the Mechanical Engineering Workshop, for his fine technical assistance. xv 1. INTRODUCTION 1.1 GENERALITIES Wind tunnel testing of scale models is a practice almost as old as designing aircraft. Even today, where fast and cost-effective digital computers combined to efficient algorithms make computational aerodynamics the primary tool for airplane design, the wind tunnel, because of its general reliability and accuracy, remains an essential instrument for obtaining aerodynamic data. It is also one of the few means for verification and validation before the first flight test of a prototype. Moreover, in the case of industrial aerodynamics the construction of a prototype is frequently an impossible task. For example the wind loadings on buildings and bridges which are always unique as a result of their architecture and location, can only be predicted from wind tunnel tests. Unfortunately, the virtues of this essential tool are tarnished by a vice inherently present in its construction: boundaries. The presence of solid walls in conventional wind tunnels imposes to the flow boundary conditions not existing in real unbounded flow. The basic effects of these boundary conditions are twofold: firstly, they prevent any lateral expansion of the streamtube blocked by the model, and secondly they force the limiting streamlines to be parallel to the walls. The result, known as solid and wake blockage, is to increase the velocity around the model and its wake due to a reduction in area through which the air must flow. Consequently, a model being tested in a solid-wall test section experiences loadings generally higher than the ones measured in an unconstrained flow. On the other hand, the open-jet test section for which the streamtube is free to expand under blockage effect causes the loadings to be slightly lower than the ones obtained in free-air conditions. Other types of blockage such as horizontal buoyancy, which implies a variation of static pressure along the test section, and lift interference, which is due to an alteration of stream direction and streamline curvature, are also the direct results of boundary interferences. 1 2 The extent to which the boundaries ( solid-wall or open-jet) affect the flow field in the test section and therefore the loadings on the test model is primarily a function of the blockage ratio, i.e., the model to tunnel cross-section area ratio. A minimum wall interference condition would therefore require the testing of the smallest possible model. The use of large models, on the other hand, is often needed for similarity purposes to achieve large enough Reynolds number, for greater accuracy or simply because they are easier to work with. Although the problem of wall constraint was recognized early in the existence of wind tunnels, there still is no final solution to it. There is, however, a multitude of mathematical formulae derived to correct measured aerodynamic characteristics such as drag and lift coefficients. Unfortunately, these formulae are often empirical and their utilization is always limited to certain configurations. Also, the interpretation of large corrections, especially the ones larger than the quantities to be corrected, becomes questionable unless the mathematical model used calculates the flow field with great accuracy (but this would then render the tunnel testing unnecessary!). An alternate way to deal with the problem of wall confinement is to create a test environment in which boundary corrections are kept small and maybe negligible. Basically, two techniques which can be adapted to an existing small wind tunnel can be used: the active and passive wall concepts. The former consists in dynamically adjusting, through a feedback control system, the boundary conditions at the wall so that the test section streamline-tube is made to approach the free-air pattern. Practically, this is achieved by either deflecting solid flexible walls or using suctjon and blowing through porous walls. This system, however, requires costly equipment and is therefore not suitable for modest facilities most often found in university laboratories. The passive method is a less expensive system which uses the principle of ventilated walls. This type of wall makes use of the opposing effects associated with closed and open boundaries which, correctly combined, can simulate free-air conditions resulting in negligible interference for a wide range of blockage ratios. 3 Boundaries of this type, using longitudinal slots or patterns of holes, have been used successfully in transonic wind tunnel testing to prevent the working section from choking at high Mach number. Their adaptation to low speed testing with larger models has been considered, but the separated flows from the edges of the slots or holes introduce additional empiricism severely limiting the usefulness of the configuration. Consequently, a new low-correction design of test section for low speed wind tunnel testing has been devised and is under development in the aerodynamics laboratory of the Department of Mechanical Engineering at U.B.C. Designed on the basis of potential flow theory and known as the Tolerant wind tunnel, it was first intended for two-dimensional airfoil testing. Three of the four walls of this novel ventilated test section are solid flat panels, while the fourth one, opposite the suction side of the test airfoil, consists of an array of transverse symmetrical airfoil-shaped slats at zero incidence. These are spaced so that the outer streamline of the test section flow can pass into an outer plenum and return to the test section downstream in such a way that the overall streamline pattern closely approximates the corresponding free-air pattern. The ever growing area of industrial aerodynamics becomes a natural extension of the use for the Tolerant wind tunnel. Symmetrical bluff bodies could then be tested in a working section modified so that both walls opposite the test body have arrays of airfoil slats in a symmetrical configuration. The purpose of this work is to rate the possibilities and limitations of the Tolerant wind tunnel when used for bluff body testing. The study of the effect of different wall configurations (i.e. porosity) on the flow surrounding the model is done through numerical modelling, flow visualization and measurements of aerodynamic data such as pressure distribution, drag and vortex shedding frequency. 4 1.2 AN OVERVIEW OF THE RELATED LITERATURE The literature concerning both theoretical and experimental wall effects on wind tunnel models is quite abundant. A brief sketch of the available relevant literature is given in this section. An entire chapter of Low-Speed Wind Tunnel Testing [1 ] describes briefly but clearly the different constraint effects such as solid and wake blockage, and streamline curvature on two and three-dimensional models. It also explains the classical method of images used in connection with fundamental solutions (i.e., vortex,source, and doublet) and thus derives basic formulae for correcting wind tunnel data. A more detailed account of wall interferences can be found in ACARDograph 109 [2]. This NATO publication discusses carefully the problem of solid, wake and lift interferences for airfoils, bodies of revolution, wings and wing body configurations tested in various wind tunnels such as closed rectangular and non-rectangular test sections as well as open and ventilated jet tunnels. Since most of the formulae are derived from linearized theory it is not surprising that they are valid only for blockage ratios less than ten percent. More relevant to this work is the important paper published by Maskell [31 on the blockage effects on bluff bodies in closed wind tunnels. Maskell used an approximate relation describing the momentum balance in the flow outside the mean structure of the wake and two empirical auxiliary relations to derive expressions for the correction of force and pressure coefficients measured in closed tunnels on bluff models. He then demonstrated the validity of his correction on thin, flat rectangular plates set normal to the flow, for which the blockage ratios ranged from 1.9 % to 4.51 %. He concluded that the theory was sound as long as the correction it calculates remains small. Could [4] showed that MaskelPs wake blockage corrections for rectangular plates normal to the flow remain valid whether the plates are mounted on the tunnel axis or adjacent to a wall. He also showed that for the model investigated only small non-linear effects were found even when the corrections approached 100 %. For higher blockage ratios, up to 15 % , Could empirically derived quadratic expressions which take into consideration the little 5 non-linearity. Finally, he developed in his paper some blockage correction formulae to use when two models, with non interfering wakes, are present in the working section at the same time. Works on adaptive walls (active concept) and ventilated test sections (passive concept) for streamlined-model testing are reviewed in a number of ACARD publications [5,6,7,8,9]. The concept of the Tolerant wind tunnel (although not bearing this name), for two-dimensional airfoil testing, was introduced in a paper published by Williams and Parkinson [5]. It briefly summarized a doctoral thesis by Williams [10] and showed that uncorrected lift coefficients and pressure distributions, accurate to within one percent, could be obtained for a wide range of airfoil shapes, sizes, and lift coefficients, using a transversely slotted wall of open-area ratio between 60 and 70 percent. In subsequent papers [11,12] they concluded that although uncorrected lift coefficients are close to unconstrained flow, pitching moment coefficients seemed to require an open-area ratio varying along the longitudinal axis. The use of slotted-wall wind tunnels for bluff body testing does not seem to have attracted investigators until very recently. Raimondo and Clark [13] experimentally investigated the use of longitudinally-slotted-wall test sections for automotive facilities. Their results showed that accurate model pressure distribution data which does not require blockage correction could be achieved in two test section sizes corresponding to blockage ratios of 16.4 and 21.4 %. In addition, other results [14,15] also showed good agreement for car and truck models of about 15 % blockage ratio, even at extreme yaw angles (less than 20 degrees). Finally, an experimentally-derived blockage correction factor was found to be the same for 3 vehicle configurations, for all yaw angles from 0 to 30 degrees, and was only weakly dependent on the slot open-area ratio (OAR) over the range tested (20 % to 40 %). Parkinson, in reference [16], introduced the concept of the Tolerant wind tunnel for industrial aerodynamics. He proposed a symmetrical configuration with both walls,opposite the test model, formed by arrays of airfoil slats surrounded by plenum chambers. He rationalized that the low cost and simplicity of a passive system such as this one would be most desirable to improve the capability of small wind tunnels found in university laboratories. 6 This proposal led to the theoretical and experimental investigation reported in this thesis. The theoretical flow modelling is merely to provide at least a qualitative, perhaps a quantitative, guide to the choice of a suitable wall configuration, for which the experimental study is the determining factor. The immediate objective is a low- or negligible-wall-correction test section for two-dimensional bluff body testing. The long term objective is such a test section for general wind engineering testing. 2. THE TOLERANT TEST SECTION The purpose of this chapter is to explain the principle and describe the physical aspects of the Tolerant test section. 2.1 GENERAL DESCRIPTION As mentioned by Williams [10], conventional ventilated test sections have slots or holes which lead to undesirable flow separations, thus limiting the applicability of existing theories. The Tolerant test section was therefore introduced first in the configuration of Figure 2.1 as an alternate means for two-dimensional airfoil testing. In its configuration for two-dimensional bluff body testing, the Tolerant wind tunnel has two solid panels as ceiling and floor while the walls, parallel to the model, consist of arrays of transverse symmetrical airfoil-shaped slats at zero incidence (Figure 2.2). The local angle of attack of these slats should remain small, within their unstalled incidence range, thus preventing any flow separations from them. The slats are spaced so that the outer streamlines of the test section flow can pass into the plenums and return to the test section downstream in such a way that the overall streamline pattern closely approximates the corresponding free-air pattern. The shear layer so formed and its associated turbulent mixing should remain, for most of the wall length, in the plenum separated from the model by the arrays of slats, thus reducing the adverse effects on the test section flow. Only downstream, where the diverted flow re-enters the working section will the test section flow be affected. However, this effect should be minimal since the flow there will already be very turbulent due to the separated wake from the model. This design is a passive one in that a fixed optimal slatted wall configuration is used for all test models. For most sizes and shapes of test model, an optimized configuration should reduce boundary corrections on the test data to less than 2 %. The premise that at least one solution exists is based on the fact that closed and open jet boundaries have opposite effects on a test model. Consequently, in an infinitely long test section a correct combination of partly-solid and partly-open boundaries would lead to an 7 8 interference-free test section. In a finite working section, however, the existence of a solution is not assured unless the upstream and downstream ends of the test section are far enough from the model to have negligible effects. An optimal configuration yielding low boundary corrections will be the result of an overall proper geometric arrangement which, because of the number of possible variables, is probably not unique. The next section identifies the possible variables: the degrees of freedom. 2.2 DECREES OF FREEDOM In general, any of the test section dimensions, non-dimensionalized with respect to a characteristic length, say the width of the test section H, can be considered as a degree of freedom. This great number of variables makes the problem difficult to handle and must therefore be reduced. Even if the test model is not necessarily symmetrical, for simplicity, the test section is chosen to be symmetric with respect to the longitudinal center line of the tunnel. Another reason for this choice is the near symmetrical time-averaged shape of the large wake behind a two-dimensional bluff body. The Tolerant-test-section overall dimensions, such as width H, length L, and height A, will generally be fixed by the existing tunnel it is being adapted to. The plenum depth D, should be as large as possible; however, its size will generally be dictated by practicability and available room. In addition, all airfoil slats are chosen, again for simplicity, to be symmetrical and of the same shape. The degrees of freedom are thus reduced as far as the slats are concerned, to the chord length, c/H, the shape or thickness function, t/c, and the slat angle of attack. In this particular case the shape of the airfoil was chosen to be the NACA 0015 profile with a chord size c/H = 0.0972 (3.5 inches). The angle of incidence is kept at zero, i.e., parallel to the longitudinal axis of the tunnel. The number of slats and the distribution of open areas (or slats) are also important variables. It seems possible to eliminate one variable by combining the slat size (chord) and the 9 number of slats in order to form a new variable: the open-area ratio, OAR = 1 - [(N * c/H)/(L/H)]. However, a given slat size will fix the increment in OAR and therefore limits the available OAR. Furthermore,since the test section length is finite, the position of the test model can vary along the center line of the tunnel. Finally, the wind tunnel airspeed can also be varied through the non-dimensional Reynolds number. In summary, the Tolerant wind tunnel is, in this study, of fixed overall geometry and only the open-area ratio, OAR, is varied for a variety of bluff body shapes of different blockage ratios. The question is therefore : is there a single OAR which permits the testing of different bluff bodies at high blockage ratios? 3. MODELLING OF BLUFF BODIES IN THE TOLERANT WIND TUNNEL Because of the great number of possible variables, as shown in the previous chapter,a complete experimental investigation of the Tolerant wind tunnel would be rather tedious and time-consuming. A simple mathematical model representing the most important features of the flow and capable of estimating the effects of different variables or boundary conditions would not only be of great help in the investigation but could also become a useful design tool as well as a means of evaluating some of the residual wall interferences. This chapter, before describing such a model, will provide the reader with some background information on bluff body flows [17,18], wall effects on them and some of the existing models. 3.1 BLUFF BODIES 3.1.1 DEFINITIONS AND DESCRIPTIONS The flow past bluff bodies, as opposed to streamlined bodies, is generally characterized by well-separated turbulent wakes originating from the detaching of the flow from the body surface. In addition to the geometry of the body itself, the angle at which the flow encounters the body is also of decisive importance. For instance, a normally streamlined body such as an airfoil behaves as a bluff body when exposed to a flow at an incidence exceeding the stall angle of attack. The separation-point positions, on either side of a two-dimensional bluff body, from which the boundary layers leave the surface to create the wake, are fixed and independent of the Reynolds number when salient points or sharp edges are responsible for flow separation, as for a flat plate normal to the flow. On the other hand, when boundary layers detach from the surface of a well-rounded body, the separation-point positions will move according to the kinetic-energy level in the boundary layer, surface roughness and Reynolds number. 10 11 At small Reynolds numbers the separated shear layers come together downstream creating a "bubble" in which a pair of vortices remains stationary behind the body. Past a critical Reynolds number the shear layers become unstable at some distance downstream, break up and roll up into discrete vortices that move downstream at a velocity somewhat less than that of the main flow. The vortex layers break up closer to the body as the Reynolds number increases. At the back of the solid body, the vortices are shed alternatively from each side with a remarkable regularity resulting downstream in a double row of vortices in which each vortex is opposite the mid-point of the interval between two vortices in the opposite row. A more detailed description of the real wake is given by Roshko [19]. The fluctuating surface- pressure distribution around the body is a direct result of the periodicity of the wake. Important measurements on bluff bodies usually include the Strouhal number, St, which is the dimensionless frequency at which the vortices are shed, the time-averaged drag coefficient, C^, and the base pressure coefficient , C p D . The unsteadiness of the flow is also directly responsible for the creation of an oscillatory force (lift or side force) normal to the wind axis. This force is however difficult to measure and usually requires special equipment. 3.1.2 WALL EFFECTS ON BLUFF BODIES The qualitative effects of wall confinement on bluff bodies have been experimentally observed for many years. In general, as the flow goes around a confined bluff obstacle, the walls restrict the lateral expansion of the streamtube. Mass continuity will accordingly imply an increase in the velocities around the model. This effect is called solid blockage. A similar phenomenon will arise downstream around the wake where a region of lower total pressure (or energy) displaces the free stream. This is called wake blockage. Another effect, not much investigated yet, is the interaction between the walls and the vortices themselves; some authors [20,21] have demonstrated that base pressure, drag coefficient and Strouhal number can be strongly affected by elements, such as a splitter plate or a nearby plane surface, interfering with the vortex formation. 12 Consequently, due to wall confinement local velocities and therefore pressure values are greatly modified usually resulting in lower base pressure, higher drag coefficient, and higher vortex-shedding frequency (Strouhal number) than in unconfined flow. In addition, the separation-point positions on well-rounded bodies are, as mentioned before, a function of the Reynolds number and will therefore be affected by wall confinement. 3.1.3 BLUFF BODY MODELS No mathematical theory has ever been derived to model and predict all aspects of the high-Reynolds number separated flow past bluff bodies. A complete detailed description of such a flow could only be achieved through the yet impossible task of solving the full Navier-Stokes equations. However, as Thwaites [18] notes "... resort may be made to another model, which, while seemingly remote from the physical reality, not only is simple enough for the analysis to be completed, but also gives results which have a clear and valid physical interpretation ". Despite the fact that high levels of turbulence and significant three-dimensional effects are always observed in well separated flows, two-dimensional potential flow theory remains the most widely used method for modelling two-dimensional bluff body flows. There are two main types of model, both requiring some empirical inputs. The first type, a steady flow model, known as the free-streamline model and often treated in the complex plane, describes the time-averaged flow. In this model the thin separating shear layers are replaced by free streamlines and the irrotational flow external to the wake is evaluated. The base pressure and separation-point positions are determined experimentally and used as empirical inputs. This method which uses the hodograph technique was pioneered by Helmholtz and later improved by Kirchhoff [22]. Although they obtained for the first time a non-zero value for the drag of a two-dimensional flat plate, their drag coefficients seriously underestimated the experimental results. Their assumption of. making the separation velocity equal to the free stream velocity is likely to be too low. 13 This problem was recognized by Roshko [23] who used a new method, the notched hodograph, in which a constant low pressure region behind the body was introduced. His results are in good agreement with experiments. A simpler model, by Parkinson and Jandali [24], was shown to produce the same good agreement as Roshko's model. It uses a conformal mapping technique in which a circle is mapped onto a slit with the shape of the bluff body surface upstream of the separation points. The wake, bounded by free streamlines, is created by two surface sources symmetrically placed on the downstream part of the circle. This model is used in this work and is described in detail in the next section. Parkinson and ]andali's wake source model became widely used by many other authors: El-Sherbiny [25] used it for an analytical study of wall effects on the aerodynamics of bluff bodies. Christopher and Wolton [26] adapted the wake-source model for non-symmetric flow. Kiya and Arie [27] have modified it to include the effect of the far-wake displacement. Bearman and Fackrell [28] demonstrated the possibilities of using the wake source model with body shapes that cannot be treated easily by conformal mapping. The second type of model uses potential flow theory to model the unsteady separated flow behind a bluff body. The method consists of replacing the separating free shear layers by arrays of discrete vortices introduced into the flow field at appropriate time intervals at some points near the separation positions which are usually empirically known. The results, which are of course more expensive to calculate than steady flow, are reported to predict the form of the vortex shedding, the Strouhal number and the time-varying loadings on the model. The accuracy of the predictions is, however, an area where more work is needed. Some examples of this method can be found in references 29, 30, and 31. 14 3.2 NUMERICAL MODEL OF THE TOLERANT WIND TUNNEL Because of the unusual configuration of the Tolerant test section and ignoring, for now, the thin boundary layers on solid surfaces, the wake behind the model and the shear layers lying inside the plenums, the entire viscosity effect is restricted to the "production of circulation" at the airfoil slats, thus making irrotationality of the flow a logical assumption. And, since only low wind speed is envisaged, the flow can be considered as being incompressible. Consequently, with the replacement of plenum and wake shear layers by streamlines in order to isolate the irrotational flow from the turbulent region, one can then use potential flow theory to model the regions of interest. The displacement thickness effect of the wake is controlled by the distance between the bounding free streamlines. The present two-dimensional model combines Parkinson's wake source model, devised for bluff bodies in unconstrained flows, and two arrays of airfoils immersed in an infinite uniform flow. Pairs of upstream and downstream solid walls insure mass conservation between the entrance and exit of the test section. Because of the complexity of the boundaries the solution has to be evaluated numerically; a vortex surface-singularity technique on discretized boundaries lends itself to an efficient solution. The next three sub-sections give a more detailed description of how the wake source model is used in the Tolerant test section. 3.2.1 WAKE SOURCE MODEL IN THE TOLERANT WIND TUNNEL Parkinson's wake source model is a semi-empirical model using a conformal mapping technique (Figure 3.1), in which a circle 7 in the $-plane is mapped onto a slit C in the Z-plane with the shape of the bluff body surface upstream of the separation points S, and S 2 . The wake,bounded by free streamlines, is created by two surface sources of strength Q, symmetrically located at angle i 6 on the downstream part of the circle. In the analytically-solved model, image sources and sinks, which will not be necessary in this numerical adaptation, must be added to preserve the circle as a streamline in the transform $-plane. As 15 these wake-sources are meant only to reproduce the displacement thickness observed in real flow, the portion of the body inside the wake and the wake flow itself are not modelled. In fact, it is assumed that the body surface exposed to the wake is at the constant base pressure coefficient Cp^, which also determines the separation velocity *cU through Bernoulli's equation: K = ( 1 ~ cpfa >* (3-D The angular position 5 and strength Q of the sources are determined by the requirements of separation positions at S , , S 2 , zero velocity (stagnation points) at S ^, S 2 in the $-plane and a separation velocity equivalent to KU at S,, S 2 in the Z-plane. The conformal mapping transformation, Z = f($), is chosen so as to make the two stagnation points S ^  ,S 2 , critical points in the $-plane in order to insure tangential separation in the physical Z-plane. In the particular case where the model is a flat plate, the separation positions are well defined and the well known Joukowski transformation is chosen to map the vertical slit onto a circle : a 2 Z = f($)= $ (3.2) $ where a, the radius of the circle, is given by a = }h (3.3) and h is the breadth of the plate. The source positions were found to be and the source strength is sec5 = K (3.4) 16 Q = iirU h cos6 (3.5) The pressure distribution on the front part of the plate in free air is given by sin 2 0 Cftd) = 1 (3.6) (cos6 - cosfl) 2 y = *hsin0 (3.7) For the circular cylinder model the mapping transformation is 1 Z = f($) = $ - cota (3.8) ($ - cota) where the radius of the circle in $-plane is taken to be a = csca (3.9) and a in the 5 -plane is related to the separation angle /3S, assumed known empirically, in the Z-plane by a = i(7r - / 3 s ) (3.10) The diameter of the circular cylinder is given by h = 4cscp\. (3.11) The source positions are 17 sin 3 a cos5 = cosa -I (3.12) K and their strength is Q = 2ir U csca ( cos6 - cosa ) (3.13) Finally, the pressure distribution over the circular cylinder in unconfined flow can then be obtained by sin0(1 - 2cosa cos0+cos 2 a) Cp{6) = 1 - [ ] 2 (3.14) cos6 - cos© The angular position (i on C, in the Z-plane, corresponding to 6 in the $-plane is given by seca - cos0 sin/3 = cosa [ ] sin0 (3.15) J(seca+cosa) - cos0 In the modelling of the Tolerant wind tunnel the bluff model is placed on the centerline of the test section which is represented, as shown in Figure 3.2, by arrays of airfoils of NACA 0015 section between a pair of entrance and exit solid walls. The normalized dimensions of the real test section ( see Chapter 5 ) are used for the computations. The test section length is L/H = 2.666; the airfoil-slat chord length is c/H = 0.09722. Also, the length of the inlet and outlet solid walls are 4 times the width ( H ) of the test section. The width ( or diameter), h, of the model is kept constant equal to unity while the dimension H, the width of the tunnel, is calculated according to the desired blockage ratio ( h/H ). The combination model-walls is then immersed in an infinite uniform flow of unit velocity. Even if the plenums and the plenum flow are not modelled, the plenum shear layers are approximated by streamlines leaving the entrance walls to expand outside the tunnel and finally reattach downstream at the exit walls. These boundary streamlines are allowing the test-section 18 airstream to expand to an extent controlled by the open-area ratio (OAR) of the slotted walls, under the effects of solid and wake blockage. However, as mentioned earlier, this only approximates the behaviour of a shear layer since the required boundary condition which is constant pressure along the shear layer, is not satisfied. Now, because of the presence of the walls, the normalized separation velocity, K , and possibly the separation positions are no longer specified and therefore become unknowns. However, El-Sherbiny [25], in an adaptation of the wake source model to solid-wall confined flows, has shown that the calculated base pressure coefficient correlates well with the experimental results if the source position 8, determined from the free-air condition, is kept fixed. This assumption, empirically verified, along with fixed separation positions are adopted for the ventilated-wall wind tunnel model. This is also justified by the fact that the ideal airfoil-slatted boundary condition would produce the unconstrained flow pattern around the test body, and that this would correspond to the free-air positions of the wake sources. Unfortunately, while the model is designed to predict the ideal OAR, it is not expected to correlate well with the experiments, especially far away from the optimal configuration where some assumptions (constant 5, floating pressure value on separated streamlines) are not realistic. 3.2.2 MATHEMATICAL REPRESENTATION The complex geometry of the wind tunnel boundaries requires the flow field to be solved numerically. The technique used here, based on reference [32], is a vortex-surface-singularity method (also known as boundary element method or simply panel method) in which the solid boundaries, airfoil-slats and model are replaced by vortex sheets. The solid-surface boundary condition of zero normal velocity is satisfied by using the stream function formulation and requiring that the surface of each solid-boundary component (solid walls, airfoil-slats and model) should be a streamline of the flow. The stream function ^ of the k^ component is the result of combining 3 fundamental flows: uniform flow \j/ of unit velocity, line-vortex flows i//v from the vortex sheets and source 19 flows from the wake sources. Hence * k = * u + +v + *s ( 3 1 6 ) for which \\/u = lm[ U Z eia ] = U (y cosa - x sina) (3.17) where U is the uniform flow velocity ( U = 1); y, x are the boundary coordinates; a is the flow angle (a = 0) ; or after simplification * u = y (3.18) and 1 4>v = ~ f 7<s)ln r<x,y;s) ds (3.19) 2-n where s represents all the surfaces in the flow over which the unknown vorticity y(s) is distributed, and r(x,y;s) is the distance from a point on s to (x,y). Also, Q </  =- [X^x^) + X2(x,y)] (3.20) 2;r where Q is the unknown source strength and Xy (x,y) is the angle of the line joining the point source i to the point (x,y). The source positions ( 6 ) are calculated for the free-air case from equations (3.4) or (3.12) given by Parkinson & Jandali. Equation (3.16) can then be re-written as 20 1 Q ^k~~ S 7<s) in r(x,y;s) ds - - [X,(x,y) + X 2(x,y)] = y (3.21) 27T 2TT T h e vor t ic i ty d i s t r i bu t ion ( 7(s) ) a n d the s o u r c e s t reng th Q are the p r inc ipa l u n k n o w n s f r o m w h i c h t he v e l o c i t y d i s t r i bu t i on a n d the re fo re t he p ressu re d i s t r i bu t ion c a n b e o b t a i n e d . In the spec ia l case w h e r e t h e b o u n d a r y o f t he m o d e l is a c l o s e d c o n t o u r , t he ve loc i t y d i s t r i bu t ion is exac t l y iden t i ca l t o t he vor t ic i ty d i s t r i bu t ion (see K e n n e d y [32]). H o w e v e r , w h e n the m o d e l is an o p e n c o n t o u r , as in t h e case he re , t he ve loc i t y d i s t r i bu t i on mus t b e ca l cu la ted f r o m the d i f ferent c o n t r i b u t i o n s : u n i f o r m f l o w , vo r t i ces a n d s o u r c e s (see A p p e n d i x 3). T h e in tegra l e q u a t i o n (3.21) is exac t ; n o a p p r o x i m a t i o n has b e e n m a d e yet . H o w e v e r , s o l v i n g fo r 7(s), Q , a n d ^  can o n l y b e d o n e t h r o u g h an a p p r o x i m a t i o n . A numer i ca l s o l u t i o n is o b t a i n e d by d i sc re t i z i ng t h e sur faces s in to N st ra ight - l ine pane ls Sy, o n the m i d d l e o f w h i c h , at a c o n t r o l p o i n t C ; - o f c o o r d i n a t e (x,-, y7-), the e q u a t i o n (3.21) is a p p l i e d . T h e resul t is a s y s t e m o f N l inear e q u a t i o n s : " tj Kij " Q s i = ' R i i=1 ,2, . . . ,N (3.22) w h e r e 1 K : = - / l n [ r ( x / , y ; s : ) ] d s / (3.23) 1 lit ' ' l l are ca l l ed i n f l u e n c e coe f f i c i en ts . K^- is the re fo re t he i n f l uence of pane l /' o n t h e c o n t r o l p o i n t C f - ; it is g e o m e t r y d e p e n d e n t on ly . Thus , . t he s u m m a t i o n of al l K ;y , f o r / = 1 , . . . ,N, is t he e f fec t o f all t he vo r tex pane l s o n t h e c o n t r o l p o i n t C ;-. T h e resul t o f in tegra l (3.23) is g i ven in A p p e n d i x 2. A l s o , 1 S ;- = - [ X, ( x - , y ; ) + X 2 ( x ; , y,-) ] 2TT (3.25) 21 and R; = y;- (3.26) W h e n this d i sc re t i za t i on is a p p l i e d t o t he air foi l -s lats, an ex t ra e q u a t i o n pe r ai r fo i l is r equ i red to f ix t he a m o u n t of c i r cu la t ion a r o u n d the air foi l -s lat; thus sat is fy ing w h a t is k n o w n as the Kut ta c o n d i t i o n . E q u a t i o n (3.21) is t h e n a p p l i e d at an add i t i ona l c o n t r o l p o i n t s i tua ted at t he trai l ing e d g e o f e a c h air fo i l . W h e n the d i sc re t i za t i on is a p p l i e d t o so l i d wa l ls , e i ther a ful l so l i d wa l l o r the s o l i d s e c t i o n s at t he en t rance a n d ex i t , t he va lue o f ty^ o n t hese sur faces are s p e c i f i e d and e q u a t i o n (3.22) b e c o m e s - 7 y K;/ ~ Q S,- = R, = y#- - ^ (3.28) w h e n ; b e l o n g s t o c o m p o n e n t k . A n d s i nce ^ = y;- o n t h e ( s o l i d wa l l ) c o m p o n e n t w e have R,- = 0. W h e n the d i sc re t i za t i on is a p p l i e d to t he bluf f b o d y , in e i the r the phys ica l o r t he t rans fo rm p l a n e , the s t ream f u n c t i o n i//^ is arbitrari ly se t at z e r o a n d an ex t ra e q u a t i o n is r equ i r ed to so l ve fo r Q . A n add i t i ona l e q u a t i o n can b e o b t a i n e d w h e n e q u a t i o n (3.21) is a p p l i e d t o a c o n t r o l p o i n t c h o s e n c l o s e t o t h e sepa ra t i on p o i n t in o r d e r t o f o r c e the s t reaml ine t o leave the sur face of t h e b o d y at a f i xed g i ven p o i n t . Bu t , n u m e r i c a l e x p e r i m e n t s have s h o w n the resul ts t o b e very sens i t i ve t o t h e ex t ra -con t ro l p o i n t p o s i t i o n as w e l l as the s ize of the pane ls s u r r o u n d i n g it. The m e t h o d a d o p t e d he re uses the c o n d i t i o n that vor t ic i ty 7(s) s h o u l d van ish at t he separa t ion p o i n t . This is n o t a real f l o w c o n d i t i o n bu t it ar ises in t he po ten t ia l f l o w m o d e l in 22 o r d e r t o have the separa t ing s t reaml ines tangen t t o t h e e d g e s of t h e m o d e l . Th is t e c h n i q u e has a lso the advan tage o f r e m o v i n g o n e e q u a t i o n . Final ly, t he d i sc re t i za t i on o f t he b o u n d a r y s h o u l d be s u c h that the s o u r c e s are p l a c e d b e t w e e n t w o pane ls in o r d e r t o r e d u c e the s ingular i n f l u e n c e o f t h e s o u r c e s at t he c o n t r o l p o i n t o f ad jacen t pane l s . N o w , us ing matr ix n o t a t i o n , e q u a t i o n (3.21) c a n b e wr i t ten fo r t he k'^ c o m p o n e n t as + k { 1 } + [ KJfy. ] { 7y } + Q { } = { } (3.29) w h e r e [ K * . ] = [-^L_ ] ; V/' k Si {Sj} = {—} ; V k Ri {*/} = [ — } i n c l u d e the add i t i ona l e q u a t i o n ca l cu la ted at t he ex t ra -con t ro l p o i n t . A s s e m b l i n g all t he u n k n o w n s in o n e vec to r , w e ge t A*. 1 S? f k } < I Q in w h i c h w e sti l l have t o app ly t h e z e r o - v e l o c i t y c o n d i t i o n at e a c h sepa ra t i on po in t . Th is is d o n e b y r e m o v i n g o n e c o l u m n in t he matr ix [ K^- ] a n d o n e e l e m e n t in the vec to rs { 7y } and { Ry } c o r r e s p o n d i n g t o the t e rm in w h i c h 7^ = 0. In this par t icu lar case w h e r e there is o n l y o n e c o m p o n e n t in the u n i f o r m f l o w f ie ld ( i .e., the bluff b o d y m o d e l ; flat p la te o r c i rcu lar cy l inder ) , 23 [ Kyy ] is a N x N sub-mat r i x w h i l e { }, { Ry } a n d { 7 y } are v e c t o r c o l u m n s of d i m e n s i o n N c o r r e s p o n d i n g t o the n u m b e r o f pane l s (and c o n t r o l po in t s ) in the d i sc re t i za t ion . \ ^ and Q are scalar va lues . W h e n the re are t w o c o m p o n e n t s in the f l o w f i e ld , e . g . a test m o d e l w i th N c o n t r o l po in t s a n d a wa l l c o m p o n e n t hav ing M d i s c r e t i z e d c o n t r o l po in t s o n its sur face, t he g l o b a l matr ix b e c o m e s 1 o s? 0 1 Sk+1 f 7> ] < I Q ) If the wal l c o m p o n e n t is an airfoi l-slat w i t h M c o n t r o l po in t s C ; - , the airfoi l-slat has the re fo re ( M - 1) d i sc re te pane ls a n d an extra e q u a t i o n s is p r o v i d e d by the Kut ta c o n d i t i o n . T h e sub-mat r i x [ K^- ] has a d i m e n s i o n of N x ( N + M ) w h i l e [ K^J 1 ] is a M x ( N + M ) sub-mat r i x . T h e s u b - v e c t o r s { }, { R^ } a n d { 7 y } have N e l e m e n t s w h i l e the sub -vec to r s { S ^ * 1 { R / * 1 } and { 7 ^ + 1 } have M e l emen ts . T h e g l o b a l matr ix is d e s i g n e d t o g r o w au tomat i ca l l y t o a c c e p t u p t o 15 wal l c o m p o n e n t s , i.e., sub -ma t r i ces . A t yp ica l d i sc re t i za t i on of t he b o u n d a r i e s c o m p r i s e s 80 pane ls fo r t he bluff b o d y (flat p la te o r c i rcu la r cy l inder ) , 2 0 pane ls p e r airfoi l-slats a n d 10 pane ls fo r e a c h o f the inlet a n d ou t l e t so l i d wa l ls . In t he c o m p u t e r i m p l e m e n t a t i o n the p r o g r a m m a k e s use o f t he s y m m e t r y t o r e d u c e the s ize o f the mat r i ces . T h e s o l u t i o n o f a m o d e l - w a l l c o n f i g u r a t i o n m a d e o f a (100 x 100) matr ix takes a b o u t 1 C P U - m i n u t e o n a V A X - 1 1 / 7 5 0 c o m p u t e r wh i l e it takes a b o u t 2 C P U - h o u r s t o s o l v e fo r a 24 (400 x 400 ) matr ix . Thus , the s o l u t i o n of m a n y wa l l con f i gu ra t i ons ( for d i f fe rent O A R ) requ i res severa l h o u r s of c o m p u t a t i o n . 4. NUMERICAL RESULTS This chapter presents the results obtained from the mathematical model. It is divided in 3 sections, each of these containing results about the modelling of a flat plate and circular cylinder test body. The results calculated in unconfined and solid-wall confined flow and presented in the first two sections are used to evaluate and validate the mathematical model.The third section analyses the results obtained in the Tolerant wind tunnel. 4.1 FREE AIR RESULTS 4.1.1 COMPUTATION IN THE TRANSFORM PLANE Figure 4.1 shows a comparison between analytically and numerically calculated pressure distributions on a normal flat plate in an unconfined airstream. In order to save on computational time, the numerical calculations were performed on only half of the symmetrical domain. The numerical results show little loss of accuracy compared to the analytical method. The base pressure value which is the pressure coefficient at x/h = 0.5 was not obtained through the inverse transformation like the other pressure values, but through the source strength value. This is a special case which is only valid in unconfined flow. The use of the inverse conformal mapping transformation to obtain the base pressure leads to a singularity at the separation point which becomes more severe for a circular cylinder, as demonstrated by Figure 4.2. This graph shows the free air pressure distribution over a circular cylinder calculated analytically and numerically in the transform plane. For this case where the given empirical base pressure value is C p D = - 0.96 and separation position is 0S = 80 degrees, the numerical results agree well with the analytical calculations but only on a 45 degree arc starting from the stagnation point. On the remaining part of the cylinder, the two curves diverge as they approach the separation point where the numerical results eventually explode. The reason for this behaviour becomes obvious when one realizes that both the velocity in the 25 26 t rans fo rm p lane and the der iva t ive of t he m a p p i n g t rans fo rmat ion van i sh , as t hey s h o u l d , at t h e sepa ra t i on p o i n t , a n d that the v e l o c i t y in t he phys ica l p l a n e is o b t a i n e d b y d i v i d i ng the f o r m e r b y the latter. This s ingular i ty d o e s n o t o c c u r w h e n the p r o b l e m is s o l v e d analyt ical ly s i nce t h e L ' H o p i t a l ru le c a n b e u s e d . T h e e f fec t o f the d i sc re t i za t i on o n t h e n u m e r i c a l ca lcu la t ion is s h o w n in F igure 4 .3 w h e r e the s o u r c e s t reng th va lue is p l o t t e d against t he n u m b e r o f pane ls u s e d t o d e s c r i b e t h e c i r c l e - m o d e l in the t rans fo rm p l a n e . N o t e that t he d i sc re t i za t ion t e c h n i q u e is c o m p l i c a t e d b y s o m e cons t ra in ts s u c h as the s o u r c e a n d the sepa ra t i on pos i t i ons w h i c h n e e d to b e p l a c e d b e t w e e n t w o pane ls fo r m o r e c o n s i s t e n t resul ts . T h e t rans fo rm-p lane d i sc re t i za t i on leads t o g o o d b e h a v i o u r f o r t he flat p la te fo r w h i c h the s o u r c e s t rength reaches a va lue we l l w i t h i n 0.08 % of t h e analyt ical va lue ( Q = 1 .01819 ) fo r 70 pane l s o n the c i rc le ( that is 34 pane ls o n the f ron t part o f t h e c i rc le c o r r e s p o n d i n g t o the f ron t part o f the flat p la te) . H o w e v e r , t h e d i sc re t i za t i on m e t h o d u s e d he re g ives p o o r resul ts in t h e case o f t he c i rcu lar cy l i nde r fo r w h i c h t h e s o u r c e s t reng th va lue osc i l la tes i r regular ly w h i l e s tay ing away, b y as m u c h as 2.5 %, f r o m t h e analyt ica l s o u r c e s t reng th va lue o f Q = 0 .64842 , e v e n w h e n the n u m b e r o f pane ls u s e d is o v e r 150 . 4 .1 .2 C O M P U T A T I O N IN T H E P H Y S I C A L P L A N E T h e s a m e n u m e r i c a l m e t h o d can a lso be a p p l i e d to d isc re t i ze the actua l m o d e l in t h e phys i ca l p l ane . A n e x a m p l e o f p ressu re d i s t r i bu t i on o v e r a flat p la te a n d a c i rcu lar cy l i nde r m o d e l , c o m p u t e d in the phys i ca l p l ane , are s h o w n in F igures 4 .4 a n d 4 .5 , respec t i ve ly . T h e s e f igu res s h o w g o o d a g r e e m e n t w i t h the analyt ical ca lcu la t ions o v e r m o s t o f t he d o m a i n , i n c l u d i n g t h e base p ressure at t he sepa ra t i on po in t . H o w e v e r , t he re is in b o t h cases a p o i n t w h e r e n u m e r i c a l ca lcu la t ions e n c o u n t e r a s ingular i ty . Th is ef fect c o m e s f r o m t h e s o u r c e p o i n t p l a c e d o n the slit t o create the d i s p l a c e m e n t t h i c kness o b s e r v e d in the w a k e o f bluff b o d i e s . For tuna te ly , t he s ingular i ty af fects o n l y a smal l part o f t h e p ressure d i s t r i bu t ion w h i c h can o f t en be o m i t t e d w i t h o u t l os i ng any essen t ia l i n f o rma t i on . 27 F igures 4 .6 (a) and (b) s h o w the var ia t ion o f s o u r c e s t rength a n d base p ressure coe f f i c i en t , respec t i ve ly , w i t h the n u m b e r of pane ls fo r b o t h the flat p la te a n d t h e c i rcu lar cy l i nde r m o d e l . B o t h f igures s h o w an ident ica l s m o o t h b e h a v i o u r w i t h an inc rease in t h e n u m b e r of pane ls u s e d to d e s c r i b e t h e m o d e l . T h e numer i ca l s o l u t i o n of t he flat p la te m o d e l , in par t icu lar , d e m o n s t r a t e s h igh a c c u r a c y by o b t a i n i n g the s o u r c e s t rength va lue and base p ressure coe f f i c ien t w i t h i n 0.05 % o f t he analyt ical va lue , fo r a d i sc re t i za t ion o f 60 pane ls . T h e numer i ca l s o l u t i o n o f the c i rcu lar c y l i nde r s h o w s , h o w e v e r , an a c c u r a c y w i t h i n a b o u t 1% fo r a d i sc re t i za t i on o f 100 pane l s . In o r d e r t o a v o i d a s ingular i ty c l o s e t o a sepa ra t i on po in t w h e r e the p ressu re va lue is o f cr i t ical i m p o r t a n c e , as w e l l as b e c a u s e the p r o c e d u r e is s imp le r , the n u m e r i c a l ca l cu la t i on w i l l , f r o m here o n , b e p e r f o r m e d in t he phys ica l p l ane on l y . 4 .2 S O L I D - W A L L C O N F I N E D F L O W RESULTS 4.2.1 FLAT PLATE M O D E L A n e x a m p l e o f a c o m p u t e d p ressu re d i s t r i bu t i on o v e r a no rma l flat p la te e x p e r i e n c i n g a b l o c k a g e rat io o f h /H = 1/3 in a s o l i d - w a l l e d w i n d t unne l is c o m p a r e d in F igure 4 .7 t o E l -Sherb iny 's [25] analyt ical s o l u t i o n . T h e part of t he cu r ve a f fec ted by the s o u r c e s ingular i ty is o m i t t e d fo r clari ty. A b l o c k a g e c o r r e c t i o n fac to r ,eva lua ted as d e s c r i b e d in A p p e n d i x 4 , w a s a p p l i e d t o th is e x a m p l e a n d f o u n d t o b e C F = 0 .6749 . This f ac to r w h e n d i v i d e d by the s o l i d wa l l f rees t ream s p e e d g ives the bes t a g r e e m e n t in a leas t -square s e n s e w i th the re fe rence f ree-air p ressure d i s t r i bu t i on . F igure 4 .8 s h o w s this a g r e e m e n t a n d d e m o n s t r a t e s the poss ib i l i t y of u s i n g a s i m p l e c o r r e c t i o n fac to r t o eva luate wa l l e f fec ts o n a m o d e l . B e c a u s e the C F m e a s u r e s , relat ive to a set of re fe rence - tes t da ta , t h e overa l l e f fec t of wa l l i n te r fe rences o n a m o d e l p ressure d i s t r i bu t i on , it can t he re fo re b e u s e d fo r c o m p a r i n g the e f fec ts o f d i f ferent wal l ( i nc lud ing s lo t ted-wa l l ) con f i gu ra t i ons . 28 T h e n u m b e r o f pane ls u s e d t o d e s c r i b e the s o l i d wal l can have a s ign i f i cant i n f l uence o n the p ressu re d i s t r i bu t ion a n d in part icular o n the base p ressure w h i c h wi l l b e an impor tan t charac ter is t i c f o r c o m p a r i n g the ef fects o f d i f fe rent wa l l con f i gu ra t i ons ( i nc l ud ing s lo t ted-wa l l ) . F igure 4.9 s h o w s , f o r e x a m p l e , that f o r a flat p la te m o d e l e x p e r i e n c i n g a b l o c k a g e rat io (h /H) o f 1/3 b e t w e e n s o l i d wa l l s e x t e n d i n g u p s t r e a m and d o w n s t r e a m by 6 p la te w i d t h s , t h e base p ressu re coe f f i c i en t r eaches a p la teau w h e n the n u m b e r of pane ls is g rea te r t han 12. T h e e n d ( inlet and out le t ) e f fec t is a lso an impo r tan t pa ramete r w h i c h c a n m o d i f y t he p ressu re va lues . Thus , F igure 4.10 s h o w s that t h e wa l l l eng th s h o u l d b e at least 7 t imes the w i d t h o f t he flat p la te t o have base p ressu re va lues i n d e p e n d e n t o f wa l l l e n g t h . T h e var ia t ion o f base p ressure coe f f i c i en t w i t h b l o c k a g e rat io is p l o t t e d in F igure 4 .11. It c o m p a r e s the n u m e r i c a l ca lcu la t ions to E l -Sherb iny ' s analyt ical s o l u t i o n ; t he a g r e e m e n t is very g o o d . Final ly, F igure 4.12 p resen ts t he var ia t ion o f t h e b l o c k a g e c o r r e c t i o n factor , C F , w i t h b l o c k a g e rat io. Th is re la t ion s h o w s a remarkab le l inear i ty and thus just i f ies , for smal l b l o c k a g e rat ios, t he use o f l i near i zed c o r r e c t i o n f o rmu lae w h e n avai lable. 4.2.2 C I R C U L A R C Y L I N D E R M O D E L Th is s e c t i o n s u m m a r i z e s the numer i ca l l y c a l c u l a t e d wal l i n te r fe rence e f fec ts o n a c i rcu lar cy l i nde r m o d e l fo r w h i c h the emp i r i ca l f ree-a i r base pressure is C p = - 0 .96 w i t h f l o w sepa ra t i on o c c u r r i n g at an ang le of / 3 S = 80 d e g r e e s f r o m the f ront s tagna t i on po in t . T h e p ressu re d i s t r i bu t ion o v e r a m o d e l e x p e r i e n c i n g a b l o c k a g e rat io (h /H) o f 1/3 is c o m p a r e d in F igure 4.13 w i t h the free-air analy t ica l s o l u t i o n . It is n o t c o m p a r e d , as in the p r e v i o u s s e c t i o n , t o E l -Sherb iny ' s s o l u t i o n f o r c o n f i n e d f l o w b e c a u s e his resul ts l o o k m o r e l ike the n u m e r i c a l ca lcu la t ions of F igure 4.2 f o r w h i c h d iv is ions by very smal l n u m b e r s (and even tua l l y z e r o ) was the cause of i naccu rac ies nea r t he separa t ion po in t . T h e cu rve o f F igure 4.13 is m o r e real is t ic s i nce it s h o w s a fast d e c r e a s e in p ressure f o l l o w e d b y a p ressure recove ry w h i c h r ises t o base p ressu re at sepa ra t i on . T h e resu l ts s h o w , a l so , that t he p ressure recove ry 29 ( C p 0 - C p m i n ) s e e m s t o b e i n d e p e n d e n t o f b l o c k a g e rat io, w h i c h is in a g r e e m e n t w i t h s o m e e x p e r i m e n t a l obse rva t i ons [25,35]. F igure 4 .14 c o m p a r e s the c o r r e c t e d numer i ca l p ressure d i s t r i bu t ion w i t h the f ree-air analyt ical s o l u t i o n . T h e c o m p a r i s o n s h o w s g o o d a g r e e m e n t , a l t h o u g h ove res t ima t i ng the resul ts espec ia l l y be fo re the p o i n t o f m i n i m u m p ressu re . H o w e v e r , f r o m )3 = 6 0 ° u p t o t h e separa t i on p o i n t , t h e p ressu re is l o w e r t han the f ree-a i r da ta by as m u c h as 1 6 % . N e v e r t h e l e s s , t h e c o r r e c t i o n fac to r rema ins a s i m p l e and use fu l t o o l for c o m p a r i n g the e f fec ts of d i f ferent wa l l con f i gu ra t i ons . F igures 4 .15 a n d 4 .16 s h o w that t h e d isc re t i za t ion o f the wa l l a n d wa l l l eng th , respec t i ve ly , i n f l uence the resul ts in a s a m e m a n n e r as in t he p rev ious s e c t i o n fo r t he .flat p la te m o d e l . Th is sugges ts the re fo re that wa l l d i sc re t i za t i on a n d wal l l eng th are i n d e p e n d e n t of m o d e l s h a p e . T h e var ia t ion o f base p ressure w i t h b l o c k a g e rat io again agrees w e l l w i t h E l -Sherb iny ' s s o l u t i o n , as s h o w n in F igure 4 .17 . Final ly, F igure 4 .18 s h o w s the c o r r e c t i o n factor , C F , p l o t t e d against t he b l o c k a g e rat io. A g a i n , t h e re la t ion is a lmos t pe r fec t l y l inear. 4 .3 T O L E R A N T W I N D T U N N E L RESULTS 4.3.1 FLAT PLATE M O D E L T h e theo re t i ca l e f fect o f d i f ferent o p e n - a r e a rat ios o n the sur face p ressu re d is t r ibu t ion o f va r ious s izes o f f lat p late m o d e l is s u m m a r i z e d in F igures 4 .19 and 4 .20 . T h e s e ca lcu la t ions w e r e p e r f o r m e d fo r m o d e l s p l a c e d at t he c e n t e r o f t he test s e c t i o n and an emp i r i ca l f ree-air base p ressu re coe f f i c i en t o f C p D = - 1.38. T h e var ia t ion of base p ressure coe f f i c i en t as a f u n c t i o n of O A R is p l o t t e d in F igure 4 .19 . Star t ing w i t h a l o w O A R va lue w h e r e the so l i d -wa l l t ype o f i n te r fe rence ef fect is felt by the d i f ferent m o d e l s in a m a n n e r i nc reas ing w i t h b l o c k a g e rat ios, t he base p ressu re va lues inc rease , 30 w i t h i nc reas ing O A R , at rates vary ing w i t h the s i ze o f the m o d e l ; t he larger the m o d e l t h e faster t he p ressu re rises w i t h O A R . Eventual ly , the base p ressure coe f f i c ien t o v e r s h o o t s the g i v e n f ree-a i r va lue ( C p 0 = - 1.38 ) and t h e n reaches a m a x i m u m f o l l o w e d , at h i g h OAR, by a p ressu re d e c r e a s e o f errat ic behav iou r . T h e fact that t h e s e cu rves reach a m a x i m u m f o l l o w e d b y a rap id d e c r e a s e c a n n o t b e c o n s i d e r e d as real is t ic s ince it is k n o w n f r o m e x p e r i m e n t that open - j e t b o u n d a r i e s t e n d t o g ive h ighe r base p ressu re than the free-air va lue . T h e impo r t an t p o i n t o f this g r a p h , h o w e v e r , is t he near b l o c k a g e i n d e p e n d e n c y of t he base p ressure va lue s h o w n at OAR = 0 .49 fo r at least th ree of t he f ou r b l o c k a g e rat ios. For t he t h ree b l o c k a g e rat ios ( 8.3 % , 19 .4 % and 25 % ) t he base p ressure coe f f i c ien ts are app rox ima te l y - 1.40, l o w e r than the f ree-a i r va lue by less than 2 %, w h i l e t he fou r th m o d e l (33.3 %) at C p D = - 1.35 is h i ghe r than the f ree-a i r va lue by a b o u t 2 %. It is in te res t ing t o n o t e , a l so , that F igure 4 .19 s h o w s a n o t h e r p o i n t w h e r e b l o c k a g e i n d e p e n d e n c y is p r e d i c t e d ; at OAR = 0 .38 , t he th ree h i ghe r b l o c k a g e rat ios have a C p 0 o f a b o u t - 1.50. H o w e v e r , t hese resul ts , b e i n g far f r o m the f ree-a i r c o n d i t i o n , are n o t c o n s i d e r e d as l ikely as the va lues at OAR = 0 .49. B e c a u s e o f t he p rev ious l y m e n t i o n e d emp i r i ca l a s s u m p t i o n ( sou rce p o s i t i o n s are o b t a i n e d fo r f ree-a i r Cp£, a n d k e p t cons tan t f o r d i f ferent wa l l con f igu ra t i ons ) the ma thema t i ca l m o d e l is t h o u g h t t o b e m o s t accura te w h e n the f l o w f ie ld a r o u n d the flat p la te r e s e m b l e s t h e f ree-a i r c o n d i t i o n s fo r w h i c h the base p ressu re is t he g i ven C p o = - 1 - 3 8 . T h e errat ic b e h a v i o u r e n c o u n t e r e d at h i g h OAR w h e r e the n u m b e r o f slats is less than 5 s e e m s t o b e d u e t o the ind iv idua l e f fec t o f e a c h slat; in o t h e r w o r d s the s la t ted-wa l l b o u n d a r y c o n d i t i o n is n o l o n g e r fel t as a h o m o g e n e o u s c o n d i t i o n . A l s o , m o s t l ike ly b e c a u s e of t h e f ree-s t reaml ine m o d e l u s e d fo r t he p l e n u m shear layer, t he f l ows c a l c u l a t e d at O A R = 1.0 are far f r o m b e i n g the an t i c ipa ted open - j e t resul ts f o r w h i c h the base p ressu re coe f f i c i en t s s h o u l d b e h i ghe r than the f ree-air va lue . F igure 4 . 2 0 s h o w s , t h r o u g h the var ia t ion o f t h e b l o c k a g e c o r r e c t i o n fac to r w i t h O A R , the e f fec t of d i f fe ren t s lo t t ed -wa l l con f i gu ra t i ons o n the overa l l sur face p ressure d is t r ibu t ions . T h e 31 fact that t h e g raph of F igure 4 .20 c l ose l y r e s s e m b l e s the o n e o f F igure 4 .19 c o n f i r m s the p o i n t that t he base p ressu re var ia t ion is a represen ta t i ve m e a s u r e o f t he g loba l p ressure c h a n g e o n the sur face o f t h e m o d e l . N o t e , h o w e v e r , that t h e bes t O A R va lue ( t h e O A R at w h i c h m o d e l s o f d i f ferent s ize e x p e r i e n c e the s a m e f l o w c o n d i t i o n s ) is sh i f ted t o a b o u t 0.41 fo r w h i c h the b l o c k a g e c o r r e c t i o n fac tor , C F , is a b o u t 0.99 fo r t he t h ree smal le r flat p la tes w h i l e the largest m o d e l ( 33 .3 % ) has a C F just a b o v e 1.0 . This p o t e n t i a l f l o w m o d e l , t he re fo re , p red i c t s that a flat p late m o d e l of b l o c k a g e rat io less than 25 .0 % t e s t e d in t he To le ran t w i n d t u n n e l w i t h an O A R = 0.41 wi l l e x p e r i e n c e a res idua l i n te r fe rence ef fect equ iva len t t o very l o w b l o c k a g e in a so l i d -wa l l ed w i n d t unne l f o r w h i c h a c o r r e c t i o n fac to r o f on l y 1 % wi l l b e necessa ry t o ob ta i n f ree-air p ressu re d i s t r i bu t i on . The s tandard dev ia t i on , assoc ia ted w i t h the eva lua t i on o f the b l o c k a g e c o r r e c t i o n fac tor , is p l o t t e d in F igure 4.21 as a f u n c t i o n o f O A R . In g e n e r a l , the va lues are qu i te l o w ( less than 0.02 ); th is p l o t a lso s h o w s that the error , after c o r r e c t i o n of t he p ressure d i s t r i bu t ion , d e c r e a s e s m o r e o r less l inear ly w i t h inc reas ing O A R to reach a m i n i m u m va lue at O A R = 1.0 . Th is m e a n s that e v e n in the case w h e r e the b l o c k a g e c o r r e c t i o n fac to r is equa l t o uni ty, t h e p ressu re d is t r ibu t ion is no t , in all po i n t s of t h e b o d y su r face , equ iva len t t o the f ree-a i r p ressu re d i s t r i bu t i on ; o n average , h o w e v e r , it is t h e bes t fit. T h e fact that the m i n i m u m ( a f te r - co r rec t i on ) e r ror o c c u r s at O A R = 1.0 t e n d s t o i nd ica te that t he p r e s e n c e o f air foi l -slats, a l t h o u g h c a p a b l e o f r e d u c i n g the b l o c k a g e ef fect , w i l l a l so b e r e s p o n s i b l e f o r d i s to r t i ng the p ressure d i s t r i bu t i on at t he sur face of t h e b o d y . 4 .3 .2 C I R C U L A R C Y L I N D E R M O D E L Pressure d i s t r i bu t ions o v e r c i rcu lar cy l inders are great ly a f fec ted by wa l l i n te r fe rences . H o w e v e r , b e c a u s e o f t he nature o f this ma thema t i ca l m o d e l f o r w h i c h the sepa ra t i on p o s i t i o n s are g i ven emp i r i ca l va lues and kep t f i xed fo r all con f i gu ra t i ons , it c a n n o t s h o w any c h a n g e s in p ressure d i s t r i bu t i on d u e t o var ia t ion in sepa ra t i on p o s i t i o n s . A g a i n , m o r e s o than t h e flat p la te m o d e l case , o n l y a r o u n d the s imu la ted f ree-air c o n d i t i o n s , w h e r e the separa t i on po in t s , 32 /3 S = 8 0 ° , a n d base p ressure va lue , C p £ = - 0 .96 , are va l i d , is the m o d e l e x p e c t e d t o g ive re l iab le i n f o r m a t i o n . P ressu re va lues ca lcu la ted at f ou r d i f ferent p o s i t i o n s ( 3 0 ° , 6 0 ° , 7 0 ° a n d 8 0 ° f r o m s tagna t i on po in t ) o n the c i rc le a n d p l o t t e d in F igures 4 .22 t o 4 .25 d e s c r i b e the s lo t ted -wa l l e f fec t o n d i f fe ren t s i zes o f c i rcu lar cy l i nde r m o d e l s . Qua l i ta t i ve ly , t h e p lo t s of F igures 4 .22 t o 4 .25 r e s s e m b l e the g raph of F igure 4 .19 s h o w i n g the flat p la te resul ts. T h e ma jo r d i f f e rence , h o w e v e r , is t he relat ive p o s i t i o n o f t he d i f ferent b l o c k a g e - r a t i o curves w h i c h vary w i t h the l o c a t i o n w h e r e the p ressu re is ca l cu l a ted . For i ns tance , in F igure 4 .22 w h e r e the p ressu re coe f f i c i en t s are ca l cu la ted at 3 0 ° f r o m t h e s tagna t i on po in t , t h e m a x i m u m va lues o f e a c h b l ockage - ra t i o cu rve are relat ively far apart f r o m e a c h o t h e r thus p r e s e n t i n g a c r iss -c ross o f t he cu rves at a r o u n d O A R = 0 .35. But as t h e l o c a t i o n at w h i c h the p ressu re coe f f i c i en ts are ca l cu la ted m o v e s t o w a r d s the separa t ion po in t , the b l ockage - ra t i o curves m o v e d o w n w a r d w i t h respec t t o t he smal les t m o d e l . Th is ef fect resul ts in a c o n t i n u o u s sh i f t ing o f t h e i n te rsec t i on p o i n t t o w a r d s a m o r e o p e n s lo t ted -wa l l w i n d t u n n e l . T h u s at 6 0 ° t he o p t i m u m O A R va lue is 0.45 w h i l e it shifts t o 0 .49 w h e n the C p ' s are eva lua ted at 7 0 ° . A t sepa ra t i on p o s i t i o n ( 8 0 ° ) t he d i f ferent b l ockage - ra t i o cu rves have m o v e d d o w n w a r d s o m u c h w i t h r e s p e c t t o t he smal l m o d e l that n o i n te r sec t i on ex is ts a n y m o r e . F igure 4 .25 s h o w s a base p ressu re a lways l o w e r than t h e f ree-a i r va lue a n d , t he re fo re , neve r e f fec t ive ly e x p e r i e n c i n g the ef fect o f an open - j e t b o u n d a r y . T h e b a s e p ressu re va lues c l oses t t o f ree-air va lue can t h e n b e o b t a i n e d at O A R c o r r e s p o n d i n g t o t he m a x i m u m of the b l ockage - ra t i o cu rves w h i c h is a b o u t O A R = 0 .68. D e s p i t e this d i s to r t i on o f t h e cy l i nde r p ressu re d i s t r i bu t ion by the s lo t ted -wa l l , it is r emarkab le that the bes t overa l l fit t o the f ree-a i r c o n d i t i o n s , as s h o w n by the var ia t ion o f b l o c k a g e c o r r e c t i o n fac to r w i t h O A R in Figure 4 . 2 6 , is s imi lar t o t he flat p la te resul ts . T h e o p t i m u m O A R is aga in a b o u t 0 .42 w h e r e the c o r r e c t i o n t o b e a p p l i e d t o t he p ressu re d i s t r i bu t i on is less than 1 %. T h e s h a p e o f t he m o d e l u n d e r test , t he re fo re , d o e s no t s e e m to great ly a f fect t he o p t i m u m O A R va lue . 33 Final ly, F igure 4 . 2 7 s h o w s the s tandard d e v i a t i o n t o b e h a v e m u c h the s a m e as in the flat p la te m o d e l case . T h e m a g n i t u d e s of t he error , h o w e v e r , are a b o u t t w i c e as h i g h as the va lues o b t a i n e d fo r t he flat p la te m o d e l . 5. E X P E R I M E N T A L A R R A N G E M E N T T h e ma in p u r p o s e s o f th is e x p e r i m e n t a l p r o g r a m m e are t o s tudy the real f l o w in the To le ran t w i n d t unne l as w e l l as p r o v i d i n g c o m p a r a t i v e data f o r t he theo re t i ca l m o d e l . T h e first s e c t i o n of th is chap te r , t i t led A p p a r a t u s and E q u i p m e n t , desc r i bes the w i n d t u n n e l a n d the m o d e l s u s e d in t he e x p e r i m e n t s . It a l so p r o v i d e s i n fo rma t i on a b o u t t he i ns t rumen ta t i on u s e d and the data m e a s u r e d du r i ng a typ ica l test . T h e s e c o n d s e c t i o n d e s c r i b e s t h e p r o c e d u r e f o r t es t i ng a m o d e l w h i l e t he th i rd o n e s u m m a r i z e s the e r ro r analysis. T h e fou r th and f inal s e c t i o n o f chap te r f ive d e s c r i b e s the f l o w v isua l i za t ion t e c h n i q u e s a p p l i e d t o s tudy t h e f l o w in t h e p l e n u m . 5.1 A P P A R A T U S A N D E Q U I P M E N T T h e e x p e r i m e n t s w e r e p e r f o r m e d in a t w o - d i m e n s i o n a l t es t - sec t i on insert d e s i g n e d and bu i l t by W i l l i a m s [10] fo r an ex i s t i ng l o w - s p e e d c l o s e d c i rcu i t w i n d t unne l (F igure 5.1). This insert is 915 m m w i d e by 388 m m d e e p in c r o s s - s e c t i o n , a n d 2 .59 m l o n g . T h e c o n t r a c t i o n rat io thus c h a n g e s f r o m 7 t o 11 .8 . T h e t w o - d i m e n s i o n a l test m o d e l was m o u n t e d ver t ica l ly in the c e n t e r - p l a n e of t he w o r k i n g s e c t i o n b e t w e e n so l i d ce i l i ng a n d f loo r . B o t h s i de wa l ls cons is t of ver t ica l un i f o rm ly s p a c e d (excep t w h e r e m e n t i o n e d ) a i r fo i l - shaped w o o d e n slats of s e c t i o n N A C A 0 0 1 5 and c h o r d o f 89 m m , at z e r o i n c i d e n c e . T h e s e s la t ted wal ls w e r e s u r r o u n d e d by 0.39 by 0 .30 by 2.44 m w o o d e n p l e n u m s . T h e s i de wa l l o f o n e o f the p l e n u m s was m a d e of t ransparent acry l ic f o r bet ter o b s e r v a t i o n o f the f l ow . A ful l range of o p e n - a r e a rat io ( O A R ) c o u l d b e t e s t e d b y vary ing the n u m b e r o f slats in the wal ls . T h e t unne l w i n d s p e e d ranges f r o m 0 t o a b o u t 4 0 m/sec and is r egu la ted t h r o u g h a f e e d b a c k c o n t r o l s ys tem. T h e f ree s t ream t u r b u l e n c e leve l is c o n s i d e r e d t o b e be t te r than 0.1 %. T h e so l i d f l o o r had a to ta l of 16 p ressu re taps p o s i t i o n e d o n t h e cen te r l ine ups t ream a n d d o w n s t r e a m o f t he m o d e l . T h e s i de wa l l of o n e p l e n u m was a lso e q u i p p e d w i t h 7 p ressure taps a l o n g the ha l f -he ight l ine. F igure 5.2 g ives the exac t p o s i t i o n o f all t he p ressure taps in the 34 35 w i n d t u n n e l . T h r e e t ypes o f bluff b o d y m o d e l w e r e t e s t e d ; flat p la tes , c i rcu lar cy l i nde rs a n d c i rcu lar c y l i nde r w i t h sp l i t te r p la te o n the w a k e c e n t e r l ine . T h e sharp e d g e d flat p la tes w e r e of t h ree d i f ferent s i zes ; 3 (7.6), 7 (17.8) and 12 (30.5) i n c h e s ( cm) w i d e , c o r r e s p o n d i n g t o b l o c k a g e rat ios o f 8.3 %, 19.4 % a n d 3 3 . 3 % , respec t i ve ly . A 4 5 d e g r e e b e v e l was cu t a l o n g the rear e d g e s s o that t h e b o u n d a r y layer o n the f ron t face w o u l d separa te c lean ly f r o m the sharp l ip . T h e s e m o d e l s w e r e bu i l t of s tee l , a l u m i n u m , o r acry l ic d e p e n d i n g o n t h e r equ i r ed s e c t i o n s t reng th , and e q u i p p e d w i t h p ressure taps ( b e t w e e n 9 a n d 15 d e p e n d i n g o n the s ize) d i s t r i bu ted at the m i d - s p a n s e c t i o n o n the f ron t a n d rear faces , as s h o w n in F igure 5 .3 . F o u r s i zes of c i rcu lar cy l inders 3 (7.6), 5 (13.7) , 9 (22.8). and 12 (30.5) i n c h e s ( cm) in d i a m e t e r c o r r e s p o n d i n g t o b l o c k a g e rat ios of 8.3 %, 13 .8 %, 25 .0 %, and 33.3 %, respec t i ve ly , w e r e a lso u s e d . T h e y w e r e all bu i l t o f acry l ic and h a d very s m o o t h sur faces . Each cy l i nde r w a s e q u i p p e d w i t h p ressu re taps l o c a t e d every 10 d e g r e e s o v e r a quar te r o f the c i r c u m f e r e n c e at t he m i d d l e s e c t i o n . In a d d i t i o n , o n e p ressure or i f i ce w a s i nse r t ed at 180 d e g r e e s f r o m the first tap w i t h a n o t h e r o n e d i rec t ly b e l o w at 5 (13.7) i n c h e s (cm) f r o m m i d s p a n . T h e cy l i nde rs c o u l d b e ro ta ted in s u c h w a y that p ressure d i s t r i bu t i on o v e r half o f t h e c i r c u m f e r e n c e was m e a s u r e d . S y m m e t r y o f the t ime -ave raged f l o w was a s s u m e d a n d m o n i t o r e d t h r o u g h the ex t ra p ressu re taps. T h e c i rcu lar cy l i nde r m o d e l s c o u l d a lso be f i t ted w i t h a spl i t ter p la te o f 4 cy l i nde r d iamete rs in l eng th . T h e s e p la tes w e r e m a d e o f a l u m i n u m shee t o f abou t 1 m m th ick ; they w e r e s e c u r e d t o t h e t u n n e l f l o o r a n d ce i l i ng w i t h the h e l p o f 90 d e g r e e ang le b racke ts . T h e g a p b e t w e e n t h e p la te a n d the cy l i nde r was a lways carefu l ly s e a l e d . A l l t he m o d e l s w e r e m o u n t e d o n a tu rn tab le in t he cen te r o f t he w i n d t u n n e l test s e c t i o n . In a d d i t i o n , the flat p la te m o d e l c o u l d a lso b e m o u n t e d o n a f i xed s u p p o r t 22 i n c h e s u p s t r e a m of t h e c e n t e r p lane . 36 B e c a u s e the m o d e l s w e r e 27 (68.6) i n c h e s (cm) l o n g , and t he re fo re e x t e n d e d o u t s i d e the test s e c t i o n , t he h o l e s a l l o w i n g the m o d e l t o p i e r c e the f l o o r a n d ce i l i ng w e r e carefu l ly s e a l e d b e f o r e e a c h test . In o r d e r t o i m p r o v e the t w o d imens iona l i t y o f t he f l o w ove r the m o d e l , large end-p la tes w e r e t r i ed but d i f f icu l t ies o f insta l la t ion a n d i ncons i s ten t results m a d e the i r use unre l iab le . C e i l i n g a n d f l o o r b o u n d a r y layer s u c t i o n c o u l d a l so b e u s e d bu t was n o t t r i ed he re . T h e e x p e r i m e n t s w e r e car r ied ou t at a R e y n o l d s n u m b e r of 1 0 5 , b a s e d o n t h e w i d t h of the flat p la tes o r t h e d i a m e t e r of t he c i rcu lar cy l i nders . T h e tunne l w i n d s p e e d was c o n t i n u o u s l y m o n i t o r e d t h r o u g h a ca l ib ra ted Pi tot-stat ic t u b e , m o u n t e d o f f - cen te r l i ne in t he n o z z l e s e c t i o n b e t w e e n the s e t t l i n g - c h a m b e r ex i t and test s e c t i o n en t rance , a n d c o n n e c t e d t o a B e t z m a n o m e t e r . This t u b e w a s ca l ib ra ted against a s e c o n d Pi tot -s tat ic t u b e m o u n t e d in t he s l o t t ed wa l l e m p t y test s e c t i o n , o n the f l o w cen te r l i ne , w h e r e t h e test m o d e l w o u l d b e l o c a t e d . Deta i ls c o n c e r n i n g ca l ib ra t ion are g i v e n in A p p e n d i x 1. A l s o the to ta l a n d stat ic p ressu re por ts o f t he P i to t t u b e as w e l l as all t he p ressu re taps w e r e h o o k e d u p , w i t h p las t ic t u b e o f 1.6 m m ins ide d i a m e t e r a n d app rox ima te l y a m e t e r in l eng th , to a 4 8 - p o r t " s c a n i v a l v e " . Ind iv idual p ressure or i f i ces c o u l d t h e n b e manua l l y s e l e c t e d a n d f e d t o a " B a r o c e l " p ressu re t r ansduce r w h i c h t rans fo rms t h e inpu t p ressure i n to an a n a l o g e lect r ica l s igna l . T h e t ime -ave raged sur face p ressure c o u l d t h e n b e read , as a v o l t a g e , of f an averag ing digi ta l v o l m e t e r . T h e t ime-vary ing e lec t r ica l s igna l was a lso f e d t o an s p e c t r u m ana lyser t o ob ta in the v o r t e x - s h e d d i n g f r e q u e n c i e s . B e c a u s e the m o d e l s w e r e t o u c h i n g f l o o r a n d ce i l i ng t h r o u g h the sea led g a p , d i rect d rag f o r c e m e a s u r e m e n t s w e r e n o t a t t e m p t e d , h o w e v e r d rag coe f f i c i en t c o u l d be es t ima ted f r o m in teg ra t ion of sur face p ressure d i s t r i bu t ion . 37 5.2 TEST P R O C E D U R E A typ ica l ser ies o f tests starts, after hav ing m o d i f i e d t h e ex is t i ng w i n d t unne l by a d d i n g n o z z l e , test s e c t i o n and d i f fuser inser ts (see W i l l i ams [10]), by a care fu l ca l ib ra t ion o f t he n o z z l e P i to t t u b e u s e d fo r w i n d s p e e d m o n i t o r i n g . O n c e the ca l ib ra t ion is c o m p l e t e d the bluff m o d e l is ins ta l led in t he test s e c t i o n a n d the p ressu re taps are c o n n e c t e d t o the " s c a n i v a l v e " . T h e n , a first wa l l c o n f i g u r a t i o n is m o u n t e d , usual ly so l i d wa l l c o r r e s p o n d i n g t o z e r o o p e n - a r e a rat io, a n d the w i n d s p e e d is ad jus ted a c c o r d i n g t o t h e d e s i r e d R e y n o l d s n u m b e r of 10 5 . Final ly, p ressure taps are ind iv idua l ly s e l e c t e d a n d p ressu re is m e a s u r e d w h i l e a spec t ra l p l o t is a lso o b t a i n e d . A n averag ing - t ime of abou t 3 t o 5 m i n u t e s , d e p e n d i n g o n t h e uns tead iness , w a s a l l oca ted t o e a c h p ressu re tap in o r d e r t o o b t a i n r e p r o d u c i b l e p ressure coe f f i c i en ts a n d spec t ra . T h e c y c l e r e s u m e s b y m o d i f y i n g the wa l l c o n f i g u r a t i o n t o o b t a i n a n e w o p e n - a r e a rat io. A f te r hav ing t e s t e d a ful l r ange of o p e n - a r e a rat io, the m o d e l is r e p l a c e d b y a n o t h e r o n e o f d i f fe rent s i ze c o r r e s p o n d i n g t o a d i f ferent b l o c k a g e rat io, and the s a m e m e a s u r e m e n t s are d o n e aga in fo r a c o m p l e t e se t o f wa l l con f i gu ra t i ons . T h e da ta are t hen t y p e d in a c o m p u t e r t o ca lcu la te p ressure a n d d rag coe f f i c i en ts , S t rouha l n u m b e r s , b l o c k a g e c o r r e c t i o n factors a n d s tanda rd dev ia t i ons . 5.3 E R R O R A N A L Y S I S C a l c u l a t i o n s o f the uncer ta in t ies are d e s c r i b e d in deta i l in A p p e n d i x 3. T h e tab le b e l o w s u m m a r i z e s the es t ima t i on of m a x i m u m uncer ta in t ies o n the impor tan t var iab les . The er ror o n the sur face p ressure coe f f i c i en t C p is es t ima ted t o b e m a x i m u m at the rear o f t he m o d e l w h e r e the m e a s u r e m e n t s are h igh ly osc i l la to ry . T h e uncer ta in ty w i l l t he re fo re d e c r e a s e as C p is m e a s u r e d f r o m rear t o f ron t of t he m o d e l (or f r o m base p ressu re t o s tagna t i on po in t ) . A l s o , t he m a x i m u m uncer ta in ty w i l l ar ise at t he l o w e s t s p e e d w h e n tes t i ng the largest m o d e l . Re ± 4 . 0 % q ± 2 . 0 % Cp ± 2.0 t o 3.0 % 38 St ± 2.5 % C(j ± 5.0 % 5.4 F L O W V I S U A L I Z A T I O N T w o f l o w v isua l i za t ion t e c h n i q u e s , tufts a n d s m o k e , w e r e u s e d t o h e l p acqu i re s o m e i n f o r m a t i o n a b o u t t he To le ran t w i n d t u n n e l f l o w m e c h a n i s m . B e c a u s e o f the test s e c t i o n g e o m e t r y n o p h o t o g r a p h y was a t t e m p t e d . T h e f l o w pat terns w e r e o b s e r v e d a n d r e c o r d e d t h r o u g h s k e t c h e s . T h e tufts f l o w v isua l iza t ion t e c h n i q u e uses w o o l th read app rox ima te l y ha l f - inch l o n g a t t ached t o s o l i d sur faces w i t h mask ing tape . By a l i gn ing t h e m s e l v e s w i t h the sur face f l o w , t he tufts i nd ica te t h e l oca l d i r ec t i on of t he f l ow . R o w s of tufts w e r e ins ta l led o n the f l o o r and wal ls of o n e o f t he p l e n u m s , as s h o w n in F igure 5.4. ln a d d i t i o n , s o m e tuf ts w e r e a t t ached t o e a c h a i r fo i l - shaped slat in o r d e r t o de tec t any o c c u r r e n c e o f s ta l led f l o w o n t h e m . A l l tufts w e r e p e r m a n e n t l y m o u n t e d a n d c o n t i n u o u s l y o b s e r v e d d u r i n g e a c h test. A l s o , s m o k e f l o w v isua l iza t ion was p e r f o r m e d in t he c l o s e d c i rcu i t w i n d t unne l spec ia l l y m o d i f i e d fo r t h e o c c a s i o n . B e c a u s e of p o s s i b l e b u i l d u p o f s m o k e in t h e t u n n e l a n d c l o g g i n g o f the s e t t l i n g - c h a m b e r sc reens , s m o k e is no rma l l y n o t u s e d in c l o s e d c i rcu i t w i n d t unne l s . C o n s e q u e n t l y , U B C ' s G r e e n w i n d tunne l w a s m o d i f i e d in s u c h a w a y that it e f fec t ive ly b e c a m e an o p e n - c i r c u i t w i n d t unne l . Th is was easi ly a c c o m p l i s h e d , as s h o w n in F igure 5.5, by c l o s i n g the first c o m e r w i t h c a r d b o a r d and o p e n i n g t w o i n s p e c t i o n s ide d o o r s : o n e just b e f o r e the o b s t r u c t e d c o m e r by w h i c h the f l o w e x i t e d ; a n d a s e c o n d o n e i m m e d i a t e l y after the c o m e r w h i c h b e c a m e the air en t rance . Even t h o u g h t h e en t r ance a n d exit w e r e no t far apart f r o m e a c h o the r , n o r e - i n g e s t i o n p r o b l e m was e n c o u n t e r e d . D e c r e a s e in p o w e r e f f i c iency a n d , poss ib l y , f l o w qua l i ty are e x p e c t e d c o n s e q u e n c e s of s u c h a t unne l m o d i f i c a t i o n . H o w e v e r , this n e w t u n n e l c o n f i g u r a t i o n w o u l d on l y b e u s e d fo r f l o w v isua l i za t ion a n d usual ly at very l o w s p e e d , a r o u n d 5 m / s e c in this case , in o r d e r t o ge t a c o h e r e n t streak of s m o k e . A s m o k e gene ra to r ( C O N C E P T G E N I E M K V f r o m C O N C E P T E N G . L td . o f Eng land) was u s e d t o p r o d u c e b u r n e d - o i l 39 s m o k e at a t m o s p h e r i c p ressu re w h i c h w a s f e d t o a f i ve -ga l lon capac i t y tank. A streak o f s m o k e w a s t h e n o b t a i n e d by p u m p i n g the s m o k e w i t h a smal l e lec t r i c fan in to a 5 c m d i a m e t e r t u b e t e r m i n a t e d by a n o z z l e o f f inal d i a m e t e r o f 6 m m . V isua l i za t i on was d o n e by in jec t ing s m o k e at d i f ferent po in t s in t h e t unne l s u c h as at the base o f t he m o d e l , a h e a d o f t he m o d e l a n d t h r o u g h d i f ferent o r i f i ces i n t h e p l e n u m . 6 . E X P E R I M E N T A L RESULTS Th is c h a p t e r p resen ts and d i s c u s s e s t h e e x p e r i m e n t a l resu l ts o b t a i n e d in t he w i n d t u n n e l . The first th ree s e c t i o n s of t h e c h a p t e r re late d i rec t ly t o t h e tes t ing of th ree bluff b o d y m o d e l s ; flat p la te and c i rcu lar cy l i nde r w i t h and w i t h o u t spl i t ter p la te . In gene ra l , e a c h of t h e s e s e c t i o n s s h o w s the e f fec ts o f d i f fe rent wa l l con f i gu ra t i ons o n p ressu re d i s t r i bu t ion , base p ressu re coe f f i c i en t , d rag coe f f i c i en t , S t rouha l n u m b e r a n d overa l l b l o c k a g e c o r r e c t i o n fac to r f o r o n e m o d e l . In a d d i t i o n , the first s e c t i o n s h o w s s o m e f l o o r p ressu re d is t r ibu t ions and d i scusses the resul ts f o r a d i f fe rent m o d e l p o s i t i o n . The f ou r t h s e c t i o n of th is c h a p t e r is c o n c e r n e d w i t h the f l o w ins ide the p l e n u m ; wa l l p ressu re d i s t r i bu t ions a n d f l o w v isua l i za t ion f o r m t h e bas is fo r t h e d i s c u s s i o n . 6.1 FLAT PLATE M O D E L 6 .1 .1 M O D E L P R E S S U R E D I S T R I B U T I O N Effects o f d i f ferent wa l l o p e n - a r e a rat ios o n the t i m e - a v e r a g e d p ressure d i s t r i bu t ion o n a flat p la te m o d e l are s h o w n in F igures 6.1 (a) t o (m). Each o f t h e s e 1 3 f igures c o m p a r e s , fo r a g i ven o p e n - a r e a rat io, 3 m o d e l p ressu re d is t r ibu t ions c o r r e s p o n d i n g t o 3 b l o c k a g e rat ios ( 8 . 3 %, 1 9 . 4 % and 3 3 . 3 %), w i t h an analyt ical cu r ve fo r w h i c h t h e f ree-air base p ressu re is c o n s i d e r e d t o b e C p D = - 1 . 1 3 [33 ] . Figure 6.1 (a), f o r w h i c h the O A R = 0 , s h o w s c lear ly t he " s q u e e z i n g " i n f l uence o f s o l i d wal ls o n the p ressure m e a s u r e m e n t s ; t he h ighe r t he b l o c k a g e rat io is, the faster the p ressu re d r o p s d o w n f r o m the s tagna t ion p o i n t a n d the l o w e r is t he base p ressu re . T h e genera l s h a p e o f the var ia t ion , h o w e v e r , stays the s a m e w h i l e at t he rear o f the p la te t h e t ime -ave raged p ressu re rema ins re lat ively cons tan t in sp i te of h igh ly tu rbu len t f l ows . S i n c e the rear s u c t i o n b e h i n d the flat p la te d o m i n a t e s the d rag , its inc rease in c o n v e n t i o n a l w i n d t unne l s can great ly inc rease the d r a g ; here , m o r e than d o u b l e the f ree-air d rag ( C Q 1 = 1 . 9 8 ) at a b l o c k a g e rat io o f 3 3 . 3 % (C(j = 4 . 6 6 ) , a b o u t 5 0 % t o o h igh fo r a b l o c k a g e rat io o f 1 9 . 4 % a n d sti l l a r o u n d 1 5 % t o o h igh 4 0 41 for a re lat ively sma l l b l o c k a g e rat io o f 8.3 %. T h e nex t f igures , 6.1 (b) t o (m), s h o w the e f fec t o f " o p e n i n g " the wal ls . First, o n e c a n clear ly o b s e r v e that the wa l l b o u n d a r y c o n d i t i o n has a large i n f l uence o n h igh b l o c k a g e rat io m o d e l s w h i l e t h e sma l l m o d e l is l i t t le a f fec ted o v e r the en t i re range of O A R . A l s o , t he p ressu re d i s t r i bu t ion o n the f ron t face of t h e p la te , b e i n g l i t t le sens i t ive t o wa l l cons t ra in t , r ema ins c l o s e t o t he a c c e p t e d f ree-air va lues w h i l e s h o w i n g s o m e c o n f i n e d f l o w character is t ics at l o w o p e n - a r e a rat ios ( O A R less than 0.5). O n the o t h e r h a n d , t he base p ressu re coe f f i c i en t s h o w s a relat ively large var ia t ion w i t h i nc reas ing O A R . In par t icu lar , the l a r g e - m o d e l (h /H = 33.3 %) base p ressure increases rap id ly w i t h O A R to reach the s m a l l - m o d e l (h /H = 8.3 %) va lue at O A R •=. 0 .526 a n d t h e n k e e p s o n inc reas ing t o o v e r s h o o t t h e re fe rence base p ressu re o f C p D = - 1.13. M o r e detai ls o n the var ia t ion of base p ressure w i t h O A R wi l l b e g i ven in s e c t i o n 6 .1 .3 . It is i m p o r t a n t t o n o t e , he re , that s ta l led f l ows w e r e o b s e r v e d o n s o m e slats u p s t r e a m of the 12 - i nch (h /H = 33.3 %) flat p la te m o d e l . Th is is sure ly an i nd i ca t i on of t he m a x i m u m s ize flat p la te w h i c h can be t es ted w i t h o u t f l o w sepa ra t i on as r e q u i r e d by the cr i ter ia fo r d e s i g n i n g the To le ran t w i n d t u n n e l . T h e p ressu re d is t r ibu t ions a n d in par t icu lar the base p ressure coe f f i c i en t s m e a s u r e d at a wa l l o p e n - a r e a rat io of z e r o c o r r e s p o n d i n g t o an open - j e t tes t s e c t i o n are p r e s e n t e d he re o n l y as ind ica t i ve va lues a n d s h o u l d n o t b e c o n s i d e r e d as re l iable s i n c e g o o d t w o - d i m e n s i o n a l open - j e t f l o w c o n d i t i o n s in t he p resen t test s e c t i o n c o u l d n o t be a c h i e v e d . 6.1.2 F L O O R P R E S S U R E D I S T R I B U T I O N C e n t e r l i n e f l o o r p ressure d is t r ibu t ions w e r e sys temat ica l l y o b t a i n e d fo r all flat p la te m o d e l s a n d wa l l con f i gu ra t i ons . H o w e v e r , o n l y a f e w sets of resul ts are p r e s e n t e d he re , in F igures 6.2 a n d 6 .3 , fo r they s u m m a r i z e c lear ly e n o u g h the u p s t r e a m a n d d o w n s t r e a m cen te r l i ne f l o w b e h a v i o u r o v e r the ful l range of b l o c k a g e rat ios a n d O A R . F igures 6.2 s h o w , fo r 3 b l o c k a g e rat ios, t he p ressu re var ia t ion a l o n g the actual cen te r l i ne o f t he t unne l , w h i l e F igures 6.3 p resen t 42 the p ressu re var ia t ion c o m p e n s a t e d fo r the e m p t y so l i d -wa l l p ressure g rad ien t a l o n g a n o n - d i m e n s i o n a l i z e d axis. T h e m o d e l p o s i t i o n is at z e r o o n the absc issa , fo r e i ther sca le , a n d the f l o w is g o i n g f r o m r ight (ups t ream) t o left ( downs t ream) . A n impo r t an t p o i n t c o n f i r m e d by the u p s t r e a m f l o o r p ressure d i s t r i bu t ion is that in all cases the n o z z l e Pi tot -s tat ic t u b e , u s e d t o m o n i t o r the t u n n e l w i n d s p e e d , is s i t ua ted far e n o u g h u p s t r e a m (1 .68 m away f r o m the m o d e l ) a n d is n e v e r a f fec ted b y the m o d e l p ressu re f i e ld . O n e c a n a lso n o t e that the " o p e n i n g " o f t he wal ls s t imula tes ear ly ups t ream t ransverse ve loc i t i es a l l o w i n g the pe r t u rba t i on , part icular ly at h igh b l o c k a g e rat io, t o reach far ther ups t ream than in so l i d -wa l l c o n f i n e d f l ow . M o r e o v e r , the u p s t r e a m f l o o r p ressure d i s t r i bu t ion s e e m s to be i n d e p e n d e n t o f O A R in ven t i la ted wa l ls in add i t i on t o s h o w i n g co l l aps ib l e cu rves i nd i ca t i ng s imi lar f l o w fo r d i f ferent b l o c k a g e rat ios. O n t h e d o w n s t r e a m part, t he t i m e - a v e r a g e d stat ic f l o o r p ressure d i s t r i bu t ion r e a c h e s a m i n i m u m n o t o n the rear face o f the flat p la te m o d e l bu t at s o m e d i s tance d o w n s t r e a m c o r r e s p o n d i n g t o a b o u t o n e w i d t h o f t he m o d e l . This is f o l l o w e d by a p ressure recove ry , w h i c h l ike the rest o f t he w a k e , is sens i t i ve t o wa l l e f fects as s h o w n in F igure 6.2 (a). T h e n o n - d i m e n s i o n a l i z e d p l o t o f t he s a m e da ta , s h o w n in F igure 6.3 (a), fails t o s u p e r i m p o s e the b l o c k a g e - r a t i o cu rves ind ica t ing that the non - l i nea r e f fects of wa l l i n te r fe rence l ead t o non -s im i l a r f l o w . Part ly b e c a u s e o f h ighe r base p ressures , t he p ressu re recove r ies in t he To le ran t test s e c t i o n are m o r e c o m p l e t e than in c o n v e n t i o n a l w i n d t unne l s ; t h e b l ockage - ra t i o cu rves are a lso m o r e al ike s u g g e s t i n g m o r e s imi lar f l ows . In g e n e r a l , t he test s e c t i o n s e e m s t o b e l o n g e n o u g h t o ob ta i n r easonab le p ressu re recove ry , e x c e p t pe rhaps fo r t he large m o d e l w h i c h appea rs t o " f e e l " s o m e e n d ef fec ts . T h e d ramat i c air re-ent ry c a u s e d by the s u d d e n e n d of t he p l e n u m s , o b v i o u s l y m o r e impo r tan t at h i ghe r b l o c k a g e rat io fo r w h i c h m o r e air is d e f l e c t e d in to the p l e n u m s , is a lso r e s p o n s i b l e fo r an art i f icial s h o r t e n i n g of t he s lo t ted -wa l l s . C o n s e q u e n t l y , t h e avai lable t es t - sec t i on l eng th can b e c o m e a l im i t i ng fac to r w h e n assess ing the m a x i m u m p e r m i s s i b l e b l o c k a g e rat io. 4 3 6.1.3 V A R I A T I O N W I T H O A R T h e nex t ser ies of p l o t s , F igures 6.4 t o 6.8, s u m m a r i z e the sensi t iv i ty of s o m e a e r o d y n a m i c character is t ics t o wa l l s o f vary ing o p e n - a r e a rat ios, f o r flat p la te m o d e l s o f d i f ferent b l o c k a g e rat ios. F igure 6.4 s h o w s the var ia t ion o f base p ressu re coe f f i c ien t , ave raged o v e r t he back o f t he flat p la te , as a f u n c t i o n o f O A R . Star t ing w i t h a c l o s e d - w a l l tes t s e c t i o n , the base p ressure coe f f i c i en t s a u g m e n t s teadi ly w i t h o p e n i n g of t he wa l l ; at a rate i nc reas ing w i t h b l o c k a g e rat io. T w o b l ockage - ra t i o cu rves , 8.3 % a n d 19.4 %, c r i ssc ross at O A R « 0.63 w h e r e C p D = - 1.20, w h i l e t he th i rd cu rve c o r r e s p o n d i n g t o the largest m o d e l inc reases m o r e rap id ly t o c ross the l o w e s t b l ockage - ra t i o cu rve at O A R = 0.53 w h e r e C p D = - 1.23. Var ia t ion o f d rag coe f f i c i en ts as a f u n c t i o n o f O A R is p r e s e n t e d in F igure 6.6. It is n o surpr ise t o s e e he re the s a m e b e h a v i o u r as in F igure 6.4 s ince d rag coe f f i c ien ts are o b t a i n e d b y in tegra t ing t h e sur face p ressure d i s t r i bu t i on in w h i c h the c o n t r i b u t i o n f r o m the f ront face o f t he p la te , F igure 6.5, is l itt le a f f ec ted by wa l l c o n f i n e m e n t . T h e d rag coe f f i c i en t o b t a i n e d at O A R = 0 .63 , f o r t he i n te rsec t ing cu rves , is a b o u t 1.96 wh i l e at O A R = 0.53 the va lue is C(j = 2 .00 , a d i f f e rence o f a b o u t 2 %. T h e e f fec t of d i f ferent wa l l con f i gu ra t i ons o n t h e S t rouha l n u m b e r , t he d i m e n s i o n l e s s v o r t e x - s h e d d i n g f r equency , is p l o t t e d in F igure 6.7. Th is g raph s h o w s the 8.3 % a n d 19.4 % b l o c k a g e - r a t i o cu rves d e c r e a s i n g l inear ly w i t h an inc rease o f O A R a n d in te rcep t t he s a m e S t r o u h a l - n u m b e r va lue (St = 0.142) at O A R = 0.67. T h e o t h e r b l ockage - ra t i o cu r ve (33.3 %), d e c r e a s i n g l inear ly on l y f o r O A R less than 0.6, c rosses the S t r o u h a l - n u m b e r va lue of 0.141 at a s l ight ly h i g h e r O A R of 0.74. T h e b l o c k a g e c o r r e c t i o n fac tors ca l cu la ted by the m e t h o d e x p l a i n e d in a p p e n d i x 4 are p l o t t e d against o p e n - a r e a rat io in F igure 6.8. T h e gene ra l aspec t o f th is g raph is s imi lar t o t he base p ressu re resul ts s h o w i n g an i n te r sec t i on p o i n t at an O A R of a b o u t 0.6, b e t w e e n t h e 8.3 a n d 19.4 % b l ockage - ra t i o cu rves , a n d a n o t h e r o n e at a r o u n d 0 .49 fo r the 8.3 and 33.3 % b l o c k a g e - r a t i o cu rves . The va lues o f t he b l o c k a g e c o r r e c t i o n fac to r are, at t h o s e p o i n t s , a b o u t 4 4 0 .980 and 0 .974 , respec t i ve ly , c o r r e s p o n d i n g t o l o w b l o c k a g e rat ios, pe rhaps 2 t o 3 %, in a c o n v e n t i o n a l w i n d t u n n e l . F igure 6.9 s h o w s the e f fec t of o p e n i n g the wal ls o n the s tandard dev ia t i on w h i c h c a n b e i n te rp re ted as a m e a s u r e o f t he qua l i ty of the overa l l fit o f t he T o l e r a n t - w i n d - t u n n e l da ta t o t he r e f e rence p ressure d i s t r i bu t i on . Th is g raph d o e s n o t s h o w any par t icu lar pat tern e x c e p t pe rhaps that t he s tandard d e v i a t i o n osc i l l a tes a r o u n d a cons tan t va lue w h i c h inc reases as t h e b l o c k a g e rat io inc reases . A l s o , the re is in genera l a be t te r fit w h e n the tests are p e r f o r m e d in the s lo t ted -wa l l w i n d t unne l . 6.1.4 EFFECT O F M O D E L P O S I T I O N In o r d e r t o s t u d y the e f fec t o f l o n g e r s l o t t e d wa l ls e x t e n d i n g d o w n s t r e a m of t h e m o d e l , a ser ies o f tests was c o n d u c t e d w i t h the s a m e m o d e l s bu t at a n e w p o s i t i o n 22 (55.8) i nches (cm) u p s t r e a m of t he c e n t e r (p rev ious pos i t i on ) o f t h e test s e c t i o n . Un fo r t una te l y , th is c h a n g e in p o s i t i o n a lso resul ts in a r e d u c t i o n o f s lo t ted -wa l l su r faces (and the re fo re o p e n areas) u p s t r e a m of the m o d e l thus m a k i n g the in te rp re ta t ion o f t he resul ts m o r e di f f icul t . N e v e r t h e l e s s , t h e f l oo r p ressure d i s t r i bu t ions o f F igures 6.10 a n d 6.11 t e n d t o ind ica te n o ma jo r c h a n g e in f inal p ressure r ecove ry w i t h the n e w l o n g a f t e r - m o d e l wal ls . T h e n e w m o d e l p o s i t i o n s i m p l y a l l ows t h e rear p ressu re d i s t r i bu t i on t o rema in c o n s t a n t ove r a l o n g e r d i s tance after r e c o v e r i n g f r o m the l o w p ressure peak e x p e r i e n c e d in t he separa t ion " b u b b l e " , just b e h i n d t h e m o d e l . T h e larger the m o d e l is, t h e sho r te r is the d i s t ance o n w h i c h the p ressu re remains cons tan t b e f o r e b e i n g a f fec ted b y e n d ef fects (b rea ther a n d s u d d e n e n d i n g o f t h e p l e n u m s ) . T h e f l o o r p ressu re d is t r i bu t ions o b t a i n e d a h e a d o f the m o d e l s i nd ica te the p r e s e n c e of d i s t u r b e d f l o w at t h e in le t o f the tes t s e c t i o n . A s a resu l t , t he P i to t t u b e u s e d t o m o n i t o r t he t u n n e l w i n d s p e e d h a d to b e m o v e d farther u p s t r e a m in o r d e r to insure s u r r o u n d i n g u n d i s t u r b e d stat ic p ressu re . Th is n e w p o s i t i o n , at a s o m e w h a t larger c r o s s - s e c t i o n area o f t he n o z z l e , resul ts in a l o w e r i nd i ca ted w i n d s p e e d thus d e g r a d i n g the accu racy o f the ca l ib ra t ion ( the h i g h e r t he w i n d s p e e d is in t h e n o z z l e , the m o r e accura te ly it c a n b e m e a s u r e d ) . 4 5 Figures 6 .12 t o 6 .17 s u m m a r i z e the ef fect o f vary ing o p e n - a r e a rat io o n cer ta in a e r o d y n a m i c character is t ics w h e n the m o d e l s are t es ted at t he ups t ream p o s i t i o n . Excep t f o r t h e m o d e l o f 33 .3 % b l o c k a g e rat io, t he resul ts are, w i t h i n t h e expe r imen ta l error , s imi la r to t h e data o b t a i n e d w h e n the m o d e l s w e r e t es ted at t h e cen te r o f t he test s e c t i o n . H o w e v e r , t he c h a n g e in test p o s i t i o n b e c a m e s ign i f icant ly impor tan t f o r t he 12 - i nch flat p la te m o d e l ; o v e r m o s t of t he t e s t e d range of O A R (0.4 - 0.8), base p ressure coe f f i c i en t s w e r e h ighe r and d rag coe f f i c ien ts w e r e t he re fo re l o w e r than fo r t he s a m e m o d e l t es ted at m i d - s e c t i o n . A l s o , the S t rouha l n u m b e r va lues w e r e l o w e r e d b e c o m i n g c o m p a r a b l e t o the o t h e r m o d e l s izes at O A R = 0.6. T h e fact that t h e l eng th u p s t r e a m of t he m o d e l is r e d u c e d b y the n e w p o s i t i o n l imi ts t he d i s t ance ove r w h i c h the f l o w can m o v e t h r o u g h the s lo t ted -wa l l i n to the p l e n u m s thus c a u s i n g larger ve loc i t y g rad ien ts a r o u n d the m o d e l . C o n s e q u e n t l y , m o s t of the air foi l -slats ups t ream of t he 33 .3 % b l o c k a g e - r a t i o m o d e l w e r e hit by h igh i n c i d e n c e f l o w resu l t ing in w e l l separa ted f l o w s in the p l e n u m s . Th is is o b v i o u s l y a fac to r c o n t r i b u t i n g t o t he d i f fe rences e n c o u n t e r e d b e t w e e n the t w o test p o s i t i o n s . 6.2 C I R C U L A R C Y L I N D E R M O D E L 6.2.1 M O D E L P R E S S U R E D I S T R I B U T I O N The t i m e - a v e r a g e d p ressu re d is t r ibu t ions m e a s u r e d o n d i f ferent s izes o f c i rcu lar cy l i nde r p o s i t i o n e d at t h e c e n t e r of the test s e c t i o n are s h o w n in F igures 6.18 (a) t o (m), f o r var ious wa l l con f i gu ra t i ons . T h e s e f igures p resen t , sys temat ica l ly , t he resul ts fo r 3 b l o c k a g e rat ios (33.3 %, 25 % a n d 13.8 %) o v e r t he inves t iga ted range of O A R as w e l l as l o w b lockage - ra t i o (8.3 %) data at 4 O A R ' s : 0 , 0 .563 , 0635 a n d 0 .708 . In a d d i t i o n , e a c h g raph s h o w s , fo r c o m p a r i s o n p u r p o s e s , a re fe rence p ressu re cu rve m e a s u r e d by R o s h k o [20] at a R e y n o l d s n u m b e r o f 14 ,500 and a b l o c k a g e rat io o f 4 .4 % fo r w h i c h the c o r r e s p o n d i n g d r a g coe f f i c ien t is C ^ = 1.15. A l t h o u g h d i f ferent than t h e t rue u n c o n f i n e d va lue , th is r e fe rence cu rve a p p r o x i m a t e s , w e l l e n o u g h and p r o b a b l y w i th in the e x p e r i m e n t a l er ror , t he d e s i r e d f ree-a i r p ressu re d is t r ibu t ion o v e r a c i rcu lar 46 cy l i nde r at a R e y n o l d s n u m b e r o f a h u n d r e d t h o u s a n d . ( I ndeed , R o s h k o ' s resul ts w o u l d n e e d on l y , after A l l e n a n d V i n c e n t i ' s f o rmu lae (as r e p o r t e d by R o s h k o [38] ), a ve l oc i t y c o r r e c t i o n of less than 1.5 % a n d a d r a g coe f f i c ien t c o r r e c t i o n o f a b o u t 3 %). T h e first p l o t (F igure 6.18 (a) ) s h o w s the resul ts o b t a i n e d in a c o n v e n t i o n a l test s e c t i o n ( O A R = 0); the usua l p ressu re pat terns o v e r t w o - d i m e n s i o n a l c i rcu lar cy l inders of d i f ferent b l o c k a g e rat ios are o b s e r v e d : s tar t ing f r o m the s tagna t i on po in t , t he m o s t ups t ream p o i n t o n the cy l i nde r , and m o v i n g c i rcumferen t ia l l y t o w a r d s the back o f the m o d e l , t he p ressure d e c r e a s e s rap id ly t o r e a c h a m i n i m u m va lue a r o u n d 70 d e g r e e s , be fo re u n d e r t a k i n g a p ressure r ecove ry w h i c h is ab rup t l y s t o p p e d by f l o w sepa ra t i on at a b o u t 80 d e g r e e s . Un fo r tuna te l y , the exac t p o i n t o f s e p a r a t i o n w h i c h osc i l la tes w i t h t h e v o r t e x - s h e d d i n g f r e q u e n c y c a n n o t be accura te ly d e t e r m i n e d f r o m the p ressure p lo t . A f t e r sepa ra t i on , the p ressu re stays relat ively cons tan t o v e r abou t 60 d e g r e e s (up t o 0 = 120 d e g r e e s ) b e f o r e d r o p p i n g o n t h e rest of the cy l i nde r at a rate w h i c h inc reases w i t h i nc reas ing b l o c k a g e rat ios. A l t h o u g h t h e m i n i m u m pressure a n d the p ressu re at separa t i on s h o w large var iat ions (dec rease ) w i t h i nc reas ing b l o c k a g e ra t ios , the d i f f e rence b e t w e e n t h o s e t w o va lues rema ins re lat ively i n d e p e n d e n t of the s i ze of t h e m o d e l . T h e use o f t h e To le ran t w i n d t unne l f o r t h e tes t ing of c i rcu lar cy l inders resul ts in a t r e m e n d o u s i m p r o v e m e n t of t h e p ressu re d i s t r i bu t i on e v e n fo r a large m o d e l w i t h 33.3 % b l o c k a g e rat ios and a l o w O A R s u c h as 0 .344 . A t th is O A R (Figure 6.18 (b)) the 13.8 % b l o c k a g e - r a t i o curve f o l l o w s the re fe rence l ine u p t o t h e m i n i m u m p ressu re p o i n t w h e r e the p resen t resul ts b e c o m e s l ight ly h igher ; the p ressu re d i s t r i bu t ion at the b a c k of t h e cy l i nde r is h o w e v e r t o o nega t i ve . O n e c a n a lso n o t e that t he 25 % b lockage - ra t i o cu rve stays s l ight ly h igher than the r e f e rence cu rve o n the part o f the cy l i nde r p r e c e d i n g the m i n i m u m p ressu re po in t . Past this p o i n t t h e p ressu re d i s t r i bu t ion rema ins t o o nega t i ve by a b o u t 13 %. T h e largest m o d e l s h o w s a s l ight ly t o o nega t i ve p ressure b e f o r e s e p a r a t i o n w h i l e the p ressu re o n the rear part of the cy l i nde r is b e l o w R o s h k o ' s cu rve by a b o u t 25 %. 47 As the open-area ratio increases (Figure 6.18 (b) to (m)) all the curves move upward at a rate which increases with increasing blockage ratio. Unfortunately, a complete collapse of all the blockage ratio curves never occurs. It is however possible, as shown in Figure 6.18 (f) where OAR = 0.526, to obtain for the separated-flow region a good collapse of all curves. It appears that the part of the cylinder preceding the separation point experiences the effects of an open-jet type of boundary while the rear of the cylinder feels the desired effects of unconfined flow. These results suggest two possible ways for obtaining better collapsible data: a non evenly-spaced slat distribution along the longitudinal axis resulting in a varying-OAR along the wall or, maybe, a simple shift in the angular position of the pressure taps would be enough to correct a possible misalignment of the cylinder. 6.2.2 VARIATION WITH OAR The effects of various wall open-area ratios on the aerodynamics of circular cylinders are presented in the next 9 figures. Figures 6.19, 6.20 and 6.21 summarize the pressure distributions presented in the previous section by showing the influence of OAR on 3 different parts of the circular cylinder, namely: before the separation point, immediately after separation and directly behind the cylinder. The pressure data measured at 50 degrees from the stagnation point and which are considered to be representative of the pressure variation encountered in the unseparaled flow region of the cylinder, are plotted in Figure 6.19. Three main features can be observed. This graph shows, firstly, very little difference between the 8.3 and 13.8 % blockage-ratio curves. In addition, they are only weakly dependent upon OAR over the studied range. Secondly, the two other cylinder-size curves not only are distinctively different from each other through their slope and initial value but also remain higher than Cp = - 0.75 , Roshko's value at 0 — 50°, over the considered range of OAR. Lastly, no optimum OAR point, at which the pressure at 50 degrees becomes independent of the blockage ratio, can be determined. 4 8 F igure 6.20 repor ts t he e f fec ts of O A R u p o n the p ressu re coe f f i c i en t m e a s u r e d at 100 d e g r e e s f r o m t h e s tagna t ion p o i n t ; th is is a s e c t o r o f t he cy l i nde r ear l ier d e f i n e d t o b e the r e g i o n o f cons tan t p ressu re f o l l o w i n g t h e sepa ra t i on o f t he b o u n d a r y layer. T h e i m p o r t a n c e of th is p ressu re coe f f i c i en t res ides in t h e fact that it is , in t he eva lua t ion o f t h e d r a g , o f t en c o n s i d e r e d t o b e the base p ressure coe f f i c ien t a n d taken cons tan t o v e r the w h o l e sepa ra ted f l o w r e g i o n . Th is g raph exh ib i ts a w e l l d e f i n e d c r iss -c ross o f all t he b l ockage - ra t i o cu rves at a s ing le O A R of a b o u t 0 .53 w h e r e t h e p ressure coe f f i c ien t c o r r e s p o n d s t o C p = - 0 .96 . This is a d e s i r e d b e h a v i o u r of t he To le ran t w i n d t u n n e l w h i c h is t o p r o v i d e a s ing le O A R fo r a w i d e range o f b l o c k a g e rat ios. T h e p ressu re va lues m e a s u r e d at 180 d e g r e e s f r o m the s tagna t i on po in t a n d p l o t t e d in F igure 6 .21 , charac te r i ze the m a x i m u m p ressu re var ia t ion o n the rear part o f the cy l i nde r w h e r e the s h a p e of t h e p ressu re d is t r ibu t ion cu rve is i n f l u e n c e d by wa l l c o n f i n e m e n t (as s e e n in F igures 6.18) . A n art i f icial u n c o n f i n e d e n v i r o n m e n t , n o mat te r h o w it is r ea l i zed , s h o u l d b e ab le t o e l im ina te this e f fec t w h i c h c o u l d b e r e s p o n s i b l e fo r large d rag d i s c r e p a n c i e s . A l t h o u g h i ncapab le o f c o m p l e t e l y e l im ina t ing the rear p ressu re d i f f e rences the To le ran t w i n d t unne l can c o n s i d e r a b l y r e d u c e this p r o b l e m t o a m a x i m u m d i f f e rence , in t e rms o f p ressu re coe f f i c ien ts , of a b o u t 10 %. T h e r e a s o n for th is res idua l e r ro r is no t to ta l ly c lear bu t s i n c e the p r e s e n c e of p e r i o d i c vo r t i ces is part ly r e s p o n s i b l e fo r t he l o w p ressu re r e g i o n b e h i n d the cy l inder , it is t h o u g h t that t he in te r fe rence e f fec t of t he s la t ted-wa l l , e v e n at large O A R , c o u l d alter t he d y n a m i c s of t h e vo r t i ces thus caus ing a d i f ferent - than- f ree-a i r p ressure pa t te rn in the back of the cy l inder . T h e cy l i nde r d rag character is t ics , o b t a i n e d f r o m in teg ra t ion o f t he p ressure d is t r i bu t ions , are p l o t t e d in F igures 6.22, 6.23 a n d 6.24 (no te that the drag is d e f i n e d as pos i t i ve in t he d i r e c t i o n o f t he f l ow) . T h e g raph o f F igure 6 .22 s h o w s t h e var ia t ion of t he f ron t d rag coe f f i c ien ts as b e i n g a l m o s t i den t i ca l to F igure 6 .18, the p ressu re coe f f i c i en ts at 50 d e g r e e s , thus c o n f i r m i n g an overa l l b e h a v i o u r in t he unsepa ra ted f l o w r e g i o n o f t h e cy l inder . 49 T h e n o n - e x i s t e n c e o f an op t ima l O A R fo r the d rag coe f f i c ien t (F igure 6.24) s e e m s ma in ly d u e t o t h e f ronta l b e h a v i o u r , s i nce the var ia t ion o f t he rear d rag coe f f i c i en t , a l t h o u g h n o t d is t inc t ive ly c lear, b e c o m e s i n d e p e n d e n t of the b l o c k a g e rat io at an o p e n - a r e a rat io of a b o u t 0.56 . T h e S t rouha l n u m b e r (F igure 6.25) w h i c h charac te r i zes the uns tead iness o f the f l o w d u e t o vo r tex s h e d d i n g , b e c o m e s a lso i n d e p e n d e n t o f t h e m o d e l s i ze at an O A R of a b o u t 0.56 w i t h a va lue o f St = 0 .185 c o m p a r e d t o 0.18 g i ven in t he l i terature [35] f o r a R e y n o l d s n u m b e r o f 1 0 5 . N o t e a lso that t he 8.3 % b l ockage - ra t i o resul ts r ema in s l ight ly h i g h e r than t h o s e f o r t he o t h e r cy l i nde r s i zes ; the diff e r e n c e , h o w e v e r , i s less t han 3 % at the c r i ss -c ross po in t . Final ly, the var ia t ion of b l o c k a g e c o r r e c t i o n fac to r a n d its assoc ia ted s tandard dev ia t i on w i th O A R are g i ven in F igures 6.26 and 6 .27 . It is in te res t ing t o n o t e that all the b lockage - ra t i o cu rves c ross at O A R = 0.53 w h e r e the b l o c k a g e c o r r e c t i o n fac to r is C F = 1.0. H e n c e , o n average at O A R = 0 .53 , t h e p ressu re d i s t r i bu t i on cu rves o f any b l o c k a g e rat io (in the range c o n s i d e r e d ) can b e a p p r o x i m a t e d by the re fe rence cu rve . T h e er ror o r s tandard dev ia t i on , o n the o t h e r h a n d , i nc reases w i t h i nc reas ing b l o c k a g e rat io, as s h o w n in F igure 6 .27 . 6.2.3 EFFECT O F N O N - E V E N L Y S P A C E D S L A T S It has b e e n s h o w n in t he p r e v i o u s s e c t i o n s that a c i rcu lar cy l i nde r m o d e l t es ted at l o w O A R o f t en p resen ts a spl i t b e h a v i o u r cha rac te r i zed by a so l id -wa l l " s q u e e z i n g " ef fect in t he back o f the cy l i nde r w h i l e t he f ront part fee ls t h e e f fec t o f an open - j e t b o u n d a r y . It is the re fo re log ica l t o a s s u m e , if n o sys temat i c e r ro r d u e t o se t -up m isa l i gnmen t is i n v o l v e d , that a non -even l y - spaced^s la t s lo t ted-wa l l w i t h o p e n areas inc reas ing in t he d i r e c t i o n of t he f l o w c o u l d lead t o a s i m p l e s o l u t i o n . Th is s e c t i o n p r o v i d e s m e r e l y a s tar t ing p o i n t to a p o s s i b l e fu ture inves t iga t ion o f this t ype o f s l o t t ed -wa l l by s h o w i n g the resul ts o f f ou r s izes of c i rcu lar cy l i nde r m o d e l t es ted at a s ing le O A R of 0 .453 bu t w i t h 2 d i f ferent slat d i s t r i bu t ions . B o t h o p e n - a r e a d is t r ibu t ions are c h o s e n t o i nc rease l inear ly w i t h the slat n u m b e r bu t w i t h d i f ferent s l o p e s w h i c h , as e x p l a i n e d in 50 deta i l in A p p e n d i x 5 , are d e t e r m i n e d t h r o u g h a g i ven f ac to r (AORT). This fac to r is d e f i n e d fo r the first s lo t o p e n - a r e a as the rat io o f t h e even l y - spaced -s la t s lo t s ize t o t h e actual ( n o n - e v e n l y - s p a c e d ) s lo t s ize . A fac to r of AORT = 2 , f o r e x a m p l e , m e a n s that the first s lo t is half t he s ize of t he e v e n l y - s p a c e d case and that t h e s l o p e w o u l d b e ca l cu la ted a c c o r d i n g l y t o ob ta i n a l inear inc rease o f o p e n areas. T h e resul ts o b t a i n e d f o r va lues o f AORT o f 1.5 a n d 3 are p l o t t e d , respec t i ve ly , in Figures 6.28 a n d 6 .29. T h e s e can be c o m p a r e d t o F igure 6 .18 (d) w h i c h s h o w s a s imi lar tes t in an e v e n l y - s p a c e d s lo t t ed -wa l l (AORT = 1) test s e c t i o n . T h e resu l t ing p ressu re d is t r i bu t ions are genera l l y l o w e r than the h o m o g e n e o u s - O A R case w h i l e b r i ng ing the p ressure in the unsepa ra ted f l o w r e g i o n c l o s e t o o r l o w e r t han the re fe rence cu rve . W h e n c o m p a r i n g the n e w p ressu re d i s t r i bu t i ons to each o the r , o n e c a n o b s e r v e n o t i c e a b l e c h a n g e be fo re the separa t i on p o i n t b u t a l m o s t n o n e o n the rear part of t h e cy l inder . C o n s e q u e n t l y , t h e l o a d d is t r ibu t ions of F igure 6 .29, w h e r e AORT = 3, a p p e a r t o b e m o r e c o n s i s t e n t all a r o u n d . Th is s i m p l e test , a l t h o u g h pre l im inary , d e m o n s t r a t e s the poss ib i l i t y of us ing g r a d e d O A R to o b t a i n c o n s i s t e n t b o u n d a r y c o n d i t i o n s . 6.3 EFFECT O F SPLITTER PLATE T h e s u g g e s t i o n that i n te rac t ions b e t w e e n the vo r t i ces s h e d f r o m the cy l i nde r and the slats of the s l o t t e d wa l l c o u l d b e r e s p o n s i b l e fo r a l ter ing the sur face p ressure d i s t r i bu t ion o f large m o d e l s p r o m p t e d this i nves t iga t ion . A s s h o w n b y R o s h k o [20], t he i n t r o d u c t i o n of a l o n g e n o u g h (abou t 4 d iameters ) spl i t ter p la te a l o n g t h e cen te r l i ne of t he w a k e is suf f ic ient t o p r o v o k e rea t t achmen t o f the shear layers o n e i t he r s ide o f t he p la te thus resu l t ing in a s u p p r e s s i o n o f t h e vo r tex s h e d d i n g , a n d a c o n s i d e r a b l e inc rease o f the base p ressure . T h e use of th is t y p e o f m o d e l a l l ows us t o test a bluff b o d y m o d e l w i t h o u t vo r t i ces in terac t ing w i t h the s l o t t ed wa l ls . In a d d i t i o n t o e l im ina t i ng t h e uns tead iness o f the f l o w this t ype of m o d e l w i l l a lso i n t r o d u c e t w o rec i r cu la t ing r e g i o n s , o n e i ther s i de of t h e spl i t ter p la te , w h i c h e f fec t ive ly b e c o m e part of t he m o d e l a f te r -body a n d the re fo re have t o b e r e p r o d u c e d co r rec t l y in the To le ran t w i n d 51 t unne l in o r d e r t o ge t t he co r rec t f ree-a i r c o n d i t i o n . 6.3.1 M O D E L P R E S S U R E D I S T R I B U T I O N Sur face p ressu re d is t r ibu t ions o n 4 s izes o f c i rcu lar cy l i nde r w i t h sp l i t ter p la te o b t a i n e d w i t h 13 d i f ferent wa l l con f i gu ra t i ons are c o m p a r e d t o a re fe rence l o a d i n g d is t r i bu t ion in F igures 6.30 (a) t o (m). A s in t he p rev ious s e c t i o n the re fe rence cu rve was m e a s u r e d by R o s h k o [20] in a c o n v e n t i o n a l w i n d t u n n e l w i th a b l o c k a g e rat io o f 4 .4 % at a R e y n o l d s n u m b e r o f 14 ,500 ; t he c o r r e s p o n d i n g d r a g coe f f i c i en t is Crf = 0 .72. T h e p la in -wa l l sur face l o a d i n g d is t r ibu t ions , p l o t t e d in F igure 6 .30 (a), s h o w clear ly t he i n f l uence o f wa l l i n te r fe rence . Even at t he l o w e s t b l o c k a g e rat io of 8.3 %, t he base p ressure coe f f i c ien ts d i f fer f r o m the re fe rence va lues by as m u c h as 38 % resu l t ing in a d rag d i f f e rence of a b o u t 12 %. O n e c a n n o t e , h o w e v e r , that f o r all b l ockage - ra t i o cu rves the p ressure d is t r i bu t ions after sepa ra t i on (o r in t he separa t i on b u b b l e ) r ema in relat ively cons tan t . A n o p e n i n g of t he wal ls resul ts o n c e again in an impo r tan t inc rease in sur face p ressure . T h e bes t c o l l a p s e o f all t he data w i t h t h e re fe rence cu rve o c c u r s at an O A R va lue o f a b o u t 0 .563 o r 0 .599. B u t , aga in , w h i l e the base p ressu re d is t r i bu t ions are w e l l r e p r o d u c e d , t he f ron t l o a d i n g d is t r ibu t ions c o r r e s p o n d i n g to t he b l o c k a g e rat ios of 13 .8 % a n d 25 % are h i ghe r than the re fe rence cu rve . T h e s e d i f fe rences c a n n o t be e x p l a i n e d , n o w , b y f l o w uns tead iness o r vo r tex -wa l l i n te rac t ions . It is h o w e v e r easy t o pos tu la te that a m i sa l i gned m o d e l w o u l d resul t in s u c h d i f f e rences . A n e r ro r of a b o u t 2 d e g r e e s w o u l d , i n a r e g i o n o f h i g h g rad ien t s u c h as the f ront part o f t he cy l i nde r , b e suf f ic ient t o cause the d i s c repanc ies o b s e r v e d in Figure 6.30. O n the w h o l e , c o n s i d e r i n g a sys temat i c e r ro r in se t t ing u p 2 o f t he m o d e l s , t h e O A R va lue of a b o u t 0 .563 can b e c o n s i d e r e d as b e i n g c l o s e t o the o p t i m u m va lue . By r e p r o d u c i n g the p ressure d i s t r i bu t i ons of the c i rcu la r -cy l inder -w i th -sp i t te r -p la te m o d e l , w h i c h p o s s e s s e d l o n g separa t ion b u b b l e s , t he To le ran t w i n d t unne l t ends t o d e m o n s t r a t e its capabi l i ty t o s imu la te u n c o n f i n e d f l o w c o n d i t i o n s a r o u n d m o d e l s w i th a f te r -body . It is a s s u m e d here that the base p ressure , i n d e e d the w h o l e cy l i nde r p ressure d i s t r i bu t i on , is a f fec ted by the shape of t he 52 s e p a r a t i o n - b u b b l e w h i c h in turn is qu i te sens i t ive t o wa l l i n te r fe rence . A m o r e c o m p l e t e s tudy s h o u l d , h o w e v e r , i n c l u d e g e o m e t r i c a l m e a s u r e m e n t s s u c h as rea t tachment l eng th and he igh t o f t he b u b b l e . 6.3.2 V A R I A T I O N W I T H O A R F igures 6.31 t o 6 .38 s u m m a r i z e the e f fec ts o f w a l l - O A R o n the a e r o d y n a m i c character is t ics o f the c i rcular cy l i nde r e q u i p p e d w i th sp l i t ter p la te . Effects o f d i f ferent o p e n - a r e a rat ios o n the unsepa ra ted f l o w r e g i o n o f t he m o d e l , a n d r e p o r t e d in F igure 6 .31 , are w e l l cha rac te r i zed by t h e var ia t ion o f p ressure coe f f i c i en t at 0 = 50 d e g r e e s . Even if t he ex i s tence of an o p t i m u m O A R va lue is n o t apparen t , the d i f ferent b l ockage - ra t i o cu rves s h o w the des i rab le inc rease in s l o p e w i th inc reas ing b l o c k a g e rat ios. A s r e p o r t e d in t h e p rev ious s e c t i o n , a m i sa l i gnmen t of t he m o d e l by a b o u t 2 d e g r e e s is suf f ic ient t o shift t w o o f t h e b lockage - ra t i o curves (13.8 % and 25 %) h i g h e n o u g h u p w a r d t o e l im ina te the s i n g l e - O A R c r i ss -c ross . N o t e , h o w e v e r , that t he i n t e r sec t i on b e t w e e n the 33 .3 % a n d 8.3 % curves a n d t h e in te rsec t ion b e t w e e n the 25 % a n d 13 .8 % curves o c c u r at t h e s a m e O A R of 0 .563. T h e nex t t w o f igures , 6.32 a n d 6 .33, are a lmos t iden t ica l a n d the re fo re s h o w h o m o g e n e i t y o f p ressure in t he s e p a r a t e d - f l o w r e g i o n . T h e s e p lo ts a lso s h o w the p r e s e n c e o f an O A R va lue o f a b o u t 0.563 at w h i c h the p ressure coe f f i c i en t s are i n d e p e n d e n t o f the b l o c k a g e rat io. T h e var ia t ions of d rag coe f f i c ien ts w i t h O A R are p l o t t e d in F igures 6 .34 , 6 .35 and 6 .36. A s can b e an t i c i pa ted f r o m p r e v i o u s resul ts , the var ia t ion of d rag o n the f ron t part o f t he m o d e l s s h o w s i n c o n c l u s i v e results w h i l e the d rag va lue o n the rear part of t h e cy l i nde r b e c o m e s i n d e p e n d e n t o f t he m o d e l s i ze at an O A R of a b o u t 0 .563 . S ince the c o n t r i b u t i o n o f e a c h part , a b o u t 0 .275 o n the rear a n d 0.5 o n t h e f ron t , to t h e to ta l d rag va lue is of t h e s a m e o r d e r of m a g n i t u d e , t h e var ia t ion o f d rag as a w h o l e is substant ia l ly a f fec ted by the (specu la t ive) m i sa l i gnmen t o f the m o d e l s . Even if F igure 6.36 s h o w s a c r i ss -c ross of 3 b l ockage - ra t i o curves at 53 an O A R of a b o u t 0 .635 , it is b e l i e v e d that a be t te r a l i g n m e n t of t he m o d e l s w o u l d b r i n g the 25 % a n d 13.8 % b lockage - ra t i o cu rves d o w n e n o u g h t o c o i n c i d e w i t h 0.563 fo r a of 0 .75 . Final ly, var ia t ion of the b l o c k a g e c o r r e c t i o n fac tor , F igure 6 .37, t e n d s t o ind ica te that p ressure va lues m e a s u r e d in t he To le ran t w i n d t unne l w i t h an O A R of 0 .563 w o u l d n o t requ i re any c o r r e c t i o n w h e r e the m a x i m u m va lue o f t he s tandard dev ia t i on , as s h o w n in F igure 6 .38, w o u l d b e as l o w as 0.04. 6.4 P L E N U M F L O W T h e use o f a p r o p e r s la t ted-wa l l c o n f i g u r a t i o n in t h e To le ran t w i n d t u n n e l i n t r o d u c e s n e w sets o f b o u n d a r y c o n d i t i o n s w h i c h m a k e p o s s i b l e t he s imu la t i on of u n c o n f i n e d f l ows a r o u n d m o d e l s of relat ively large b l o c k a g e rat ios. T o a c c o m p l i s h th is , t he s ide wa l l l im i t ing s t reaml ines are a l l o w t o separa te as f ree shear layers a n d f l o w d o w n s t r e a m , b e h i n d arrays o f slats, i n to p l e n u m b o x e s in w h i c h they take a s h a p e w h i c h in turn i n f l uences the na tu re of t he f l o w a r o u n d the m o d e l . C o n s e q u e n t l y , a c o m p l e t e assessmen t o f t he capabi l i t ies a n d l imi ta t ions of the To le ran t w i n d t unne l d o e s no t s e e m p o s s i b l e w i t h o u t a ful l u n d e r s t a n d i n g of t he f l o w ins ide t h e p l e n u m s . Th is s e c t i o n m a k e s a first a t t emp t t o reach s u c h a g o a l b y p r o v i d i n g bas ic i n fo rma t i on s u c h as p ressure d is t r i bu t ions in t he cav i ty a n d f l o w pat terns as o b s e r v e d f r o m tuft a n d s m o k e f l o w v isua l i za t ions . ( C h a p t e r 5 s h o w s t h e p ressu re tap a n d tuft p o s i t i o n s in t he p l e n u m ) D e p e n d i n g main ly o n the b l o c k a g e , t w o genera l p i c tu res o f p l e n u m f l o w have b e e n o b s e r v e d . First, in n o r m a l c o n d i t i o n s c o r r e s p o n d i n g t o b l o c k a g e rat ios u p t o o n e th i rd ( e x c e p t for the flat p la te) at a l m o s t any o p e n - a r e a rat ios e x c e p t un i ty (open- je t ) , the o b s e r v e d f l o w s h o w e d a s ing le e l o n g a t e d rec i rcu la t ion w i t h an e d d y c e n t e r l o c a t e d d o w n s t r e a m o f t h e g e o m e t r i c cen te r o f t he p l e n u m ( F igure 6 .39 ). S t r ong p r e s e n c e o f en t ra inmen t a l o n g the shear layer was always ev iden t . A l s o , t h e shear layer has b e e n o b s e r v e d t o i m p i n g e o n the d o w n s t r e a m e n d wal l of the p l e n u m at a p o s i t i o n osc i l l a t ing w i t h a f r e q u e n c y co r re la t ing w i t h t he vo r tex s h e d d i n g 54 f r e q u e n c y . Un fo r tuna te l y , n o s m o k e f l o w v isua l i za t ion was d o n e w h i l e tes t ing the c i rcu lar cy l i nde rs e q u i p p e d w i t h sp l i t ter p la tes fo r w h i c h n o vo r tex s h e d d i n g e x i s t e d . H o w e v e r , tuft f l o w v i sua l i za t ion s h o w e d a m u c h m o r e s teady rec i r cu la t ion b u b b l e than a p l e n u m s u b j e c t e d t o t he u n s t e a d i n e s s o r ig ina t ing f r o m a v o r t e x - s h e d d i n g m o d e l . I n d e e d , s m o k e f l o w v isua l iza t ion has r e v e a l e d a s t r o n g in te rac t ion b e t w e e n the osc i l l a to ry f ree shear- layer s p r i n g i n g f r o m the m o d e l a n d the p l e n u m f l o w . Th is in te rac t ion was mos t l y e v i d e n t at h igh b l o c k a g e rat ios w h e r e the m o d e l f ree shear layer was o b s e r v e d t o osc i l la te far e n o u g h s ideways t o pass t h r o u g h the s la t ted wa l l i n to the p l e n u m p r o v o k i n g large t ransverse f l ows t h r o u g h t h e d o w n s t r e a m slats. The p l e n u m f ree shear layer w o u l d t h e n m o v e acco rd i ng l y . A s s h o w n in F igures 6.40, the m e a n stat ic p ressu re d is t r ibu t ions m e a s u r e d in this first t y p e o f p l e n u m f l o w are a f fec ted by O A R in an i nc reas ing m a n n e r w i t h inc reas ing b l o c k a g e rat ios. A t l o w b l o c k a g e va lues (a round 8 %) the p ressu re d is t r ibu t ion is pract ica l ly cons tan t and var ies l i tt le w i t h O A R : it is s l ight ly pos i t i ve at l o w O A R a n d d e c r e a s e s t o w a r d s z e r o w i th i nc reas ing O A R . A t h i g h e r b l o c k a g e rat ios the p ressu re d i s t r i bu t i on o v e r t he ups t ream part o f the p l e n u m s h o w s a nega t i ve p ressu re w h i c h d e c r e a s e s w i t h i nc reas ing O A R . Th is nega t i ve p ressure r e g i o n is a lways f o l l o w e d b y a p ressure r ecove ry w h i c h c o u l d b r i ng the p ressure va lue in the d o w n s t r e a m e n d of t h e p l e n u m s ign i f icant ly h ighe r t h a n z e r o at h igh O A R . T h e s e c o n d t y p e o f f l o w pat tern o b s e r v e d in t h e p l e n u m is t e r m e d s h a l l o w - c l o s e d cavi ty f l o w (as o p p o s e d t o o p e n cavi ty f l o w in t h e first case) by S i n h a et al . [36]. It is charac te r i zed by t w o sepa ra t i on b u b b l e s , o n e a t tached o n the u p s t r e a m face a n d the o t h e r o n the d o w n s t r e a m face o f the p l e n u m ( F igure 6.41 ). This t y p e of f l o w was main ly e n c o u n t e r e d in the open- je t ( O A R = 1) c o n f i g u r a t i o n w h e r e the slats w e r e n o t t he re t o p reven t the b reak u p o f the f ree shear - layer ; a n d w h i l e tes t ing h igh b l ockage - ra t i o m o d e l s s u c h as the 12 - inch n o r m a l flat p la te . In this latter case , t h e large b l o c k a g e w o u l d p u s h t h e p l e n u m shear- layer far e n o u g h s ideways t o i m p i n g e o n the p l e n u m s ide-wa l l w h e r e it w o u l d rea t tach. A l s o , t he tes t ing o f t he large flat p late at the u p s t r e a m p o s i t i o n s h o w e d that a c o m b i n a t i o n of large b l o c k a g e w i t h l i tt le ups t ream s la t ted-wal l o p e n area can resul t in a jet- l ike f l o w t h r o u g h the s lo ts of the wa l l t o c reate an e v e n 55 more obvious shallow-closed-cavity type of flow in the plenum. Moreover, this kind of large flow deflection caused most of the upstream slats to operate at high angles of attack resulting in stalled flows. These facts have definite implications in establishing the limitations of the Tolerant wind tunnel. Figure 6.42 shows pressure distributions in the plenum for testing of flat plate models at 22 inches upstream of the test-section center in a wall OAR of 0.563. Note the pressure distribution of the 33.3 % blockage-ratio model corresponding to the shallow-closed-cavity flow in the plenum. A large negative pressure in the plenum upstream comer is quickly followed by a rapid pressure recovery which stabilises at a value slightly below zero on the portion of the wall where the shear layer has reattached; this is then followed by yet another small pressure recovery to finally end up at a pressure value slightly above zero. This curve will also move upward as the wall OAR increases. Figure 6.40 (I) is an example of plenum pressure distributions obtained in an open-jet (OAR = 1) test section configuration in which no airfoil slats were present. It is interesting to note the near collapse of the data in the upstream half of the plenum; this was observed for all models except in the case of the flat plate tested at the upstream position. These types of pressure distribution are typically a combination of pressure distribution on a backstep followed by one due to a forward-facing step [36]. These results therefore indicate the important effect of the slats on the free shear layer. The high vorticity originating from the trailing edges of the slats feeds in turbulence to the free shear layers inside the plenums thus preventing them from breaking. Although this effect is not entirely understood, " it is likely ", as suggested by Bearman and Morel [37] in the case of free stream turbulence effect, " to reduce the spanwise coherence of the structures and this may in some way enhance the shear layer growth ". 7. CLOSING COMMENTS The Tolerant wind tunnel was originally devised to produce a low-correction data environment for airfoil testing. The possibility of extending its use for the testing of symmetrical bluff bodies was investigated here, theoretically and experimentally. Also, the fluid mechanics leading to the desired characteristics of blockage-ratio independency was examined in order to establish the capabilities and limitations of the Tolerant test section. Based on this investigation, this chapter presents the conclusions related to the use and aerodynamics of the Tolerant wind tunnel as well as making some recommendations for future work. 7.1 CONCLUDING REMARKS Due to the particular nature of the mathematical model, accurate prediction of the base pressure coefficient, the principal unknown, was not anticipated. Numerical results, however, have shown a variation of the base pressure coefficient with OAR similar in trend to the experimental results, at least over a limited range of QAR less than 0.7. Also, the theoretical results do not indicate a definite optimum OAR, but identify a range of OAR between 0.4 and 0.5 suitable for the testing of different blockage-ratio models. The slopes of the blockage-ratio curves, e.g. Figure 4.20, suggest the magnitude of the error occurring in case of wrong OAR choice. The numerical model also predicts, around optimum OAR, a residual slotted-wall effect equivalent to very low blockage effect in solid-wall wind tunnels. The corresponding blockage correction factor is of the order of 1 %. Unfortunately, the mathematical modelling of the Tolerant wind tunnel cannot, in terms of maximum allowable blockage ratio, predict the limitation of the test section. However, the theoretical results show an optimum OAR shared by only 3 of the 4 model sizes, thus suggesting a maximum blockage ratio close to 33.3 %. Another possible way to do this would be to compare the calculated airfoil-slat angle of attack with the stall angle of the NACA 0015 airfoil 56 57 s e c t i o n . Simi lar ly , t he e x p e r i m e n t a l i nves t iga t ion has s h o w n a c o n v e r g e n c e , a lbe i t no t at a s i ng le o p t i m u m O A R va lue , of all t he b lockage - ra t i o c u r v e s . T h e range o f o p t i m u m O A R va lues l ies b e t w e e n 0.55 a n d 0.65. B e c a u s e o f t h e large s l o p e o f cer ta in b l ockage - ra t i o cu rves , a sma l l sys temat i c e x p e r i m e n t a l e r ro r can translate in to a s ign i f icant shift in w h a t is c o n s i d e r e d the o p t i m u m O A R . T h e r e f o r e , great care s h o u l d b e t aken in acqu i r ing the da ta , espec ia l l y at large b l o c k a g e rat ios. T h e e x p e r i m e n t s have a lso s h o w n that a m o d e l w h o s e b l o c k a g e is equ iva len t t o a n o r m a l flat p la te o f 33 .3 % b l o c k a g e rat io w o u l d b e e x c e e d i n g the capab i l i t y o f t he To le ran t w i n d t u n n e l . A l t h o u g h f ree-air c o n d i t i o n s c a n st i l l b e o b t a i n e d for th is h i g h b l o c k a g e va lue , it c a n n o t b e e x p e c t e d t o o c c u r at the s a m e o p t i m u m O A R va lue o f sma l le r m o d e l s . It s h o u l d b e p o i n t e d ou t that d u e t o the relat ive s i ze of its w a k e the n o r m a l f lat p la te is t he " b luf fest " m o d e l ; a n d that the use o f o t h e r t ypes o f bluff b o d y s u c h as t h e c i rcu la r c y l i nde r (wi th o r w i t h o u t sp l i t ter p late) wi l l suf fer less w a k e b l o c k a g e than the flat p la te o f the s a m e b l o c k a g e rat io. T h e u s e o f tufts in t he p l e n u m and o n t h e air foi l -slats makes the To le ran t w i n d t u n n e l " s e l f - c o m p l a i n i n g " a b o u t t h e b l o c k a g e it has t o pu t u p w i t h . This s i m p l e f l o w v isua l i za t ion p r o v i d e s an easy m e a n s f o r d e t e c t i n g the p r e s e n c e o f stall f l o w o r t h e d i s a p p e a r a n c e o f the separa t i ng shear - layer in t he p l e n u m . W h e n d e t e r m i n i n g the s izes o f t he To le ran t test s e c t i o n , t he d e p t h o f t he p l e n u m s h o u l d b e great e n o u g h t o ensu re that slat stall ang le remains the l im i t ing c o n d i t i o n fo r m a x i m u m p e r m i s s i b l e b l o c k a g e rat io. A l t h o u g h p o w e r c o n s u m p t i o n was n o t m e a s u r e d in t he p resen t s tudy , b a s e d o n m e a s u r e m e n t s m a d e in an ear l ier s tudy o f t h e To le ran t w i n d tunne l b y M a l e k [12], it s e e m s l ike ly that t he p o w e r w o u l d b e a b o u t 5 t o 10 % h i g h e r fo r t he To lerant t unne l than fo r a so l i d -wa l l t u n n e l , largely b e c a u s e o f t h e ef fects of t he p l e n u m f l ow . 58 Final ly, it is impor tan t t o n o t e that t he w a k e o f a m o d e l t e s t e d in the To le ran t w i n d t unne l c a n b e a l te red in t w o w a y s . First ly, the in te rac t ion b e t w e e n t h e s h e d vo r t i ces a n d t h e s l o t t ed wa l l is l ikely t o m o d i f y t he d y n a m i c s of t he vo r tex f l o w (and pe rhaps the separa t i on pos i t i on ) b e h i n d the m o d e l . S e c o n d l y , t he osc i l l a to ry f l o w re-entry, t he f l o w rush ing ou t o f t h e p l e n u m to re -en te r t he test s e c t i o n , w i l l i nc reas ing ly af fect t he w a k e f l o w as the d i s tance d o w n s t r e a m of t he m o d e l inc reases . 7.2 R E C O M M E N D A T I O N S F O R F U T U R E W O R K D e p e n d i n g o n the goa ls s o u g h t fo r the theore t i ca l m o d e l l i n g o f the To le ran t test s e c t i o n , th is m o d e l can be i m p r o v e d in m a n y ways ; bu t m o s t i m p r o v e m e n t s are l ikely t o se r ious ly c o m p l i c a t e the ma thema t i cs o f t he m o d e l and l e n g t h e n c o n s i d e r a b l y the c o m p u t a t i o n o f the s o l u t i o n . For e x a m p l e , t h e m o d e l l i n g o f t he p l e n u m free shea r layer by i m p o s i n g a cons tan t p ressure d is t r ibu t ion a l o n g the separa t ing s t reaml ine s h o u l d b r i n g the s o l u t i o n c l o s e r t o real i ty. T h e p r o b l e m , h o w e v e r , w o u l d b e c o m e non- l i nea r ; that is , t he g e o m e t r y of the shear layer has t o b e k n o w n to b e ab le t o i m p o s e t h e requ i red c o n d i t i o n a n d the app l i ca t i on o f t he c o n s t a n t p ressure d is t r ibu t ion w i l l m o d i f y t he g e o m e t r y o f t he separa t i ng s t reaml ine . C lear ly , t he s o l u t i o n requ i res an i terat ive p r o c e d u r e . T h e adap ta t i on o f the ma thema t i ca l m o d e l f o r t he tes t ing o f n o n - s y m m e t r i c bluff b o d i e s s u c h as an i n c l i n e d flat p late w o u l d b e a use fu l a d d i t i o n . C h r i s t o p h e r a n d W o l t o n [26] have d e v e l o p e d s u c h a m o d e l fo r u n c o n f i n e d c o n d i t i o n s . A n e x p e r i m e n t a l coun te rpa r t w o u l d t h e n b e r e q u i r e d t o assess the real f l o w a n d eva luate the theory . In o r d e r t o d e t e r m i n e t h e m a x i m u m a l l owab le bluff b o d y l e n g t h , t h e tes t ing o f m o d e l s w i t h l o n g after b o d i e s s u c h as the half Rahk ine b o d y and l o n g rec tangu la r cy l i nde r s h o u l d b e c o n s i d e r e d . T h e y wi l l p r o v i d e f i xed " w a k e " d i m e n s i o n s . In t he case o f t he half Rank ine b o d y an equ i va len t n u m e r i c a l s o l u t i o n w o u l d a lso be easy t o o b t a i n . S h o u l d a l o n g e r test s e c t i o n (or s lo t ted-wa l l ) b e c o m e necessary , the o p e n i n g o f t he p l e n u m d o w n s t r e a m end -wa l l t o a t m o s p h e r i c p ressure s h o u l d de lay s o m e of the re -en te r ing 59 f l o w r e s p o n s i b l e fo r a s h o r t e n i n g o f t h e u s e a b l e test s e c t i o n . T h e b rea the r w o u l d t h e n take care o f mass c o n s e r v a t i o n in the t unne l . Final ly, t he To le ran t w i n d t unne l s h o u l d n o w b e c o n s i d e r e d f o r t h r e e - d i m e n s i o n a l bluf f b o d y tes t ing ; i n c l u d i n g bounda ry - l aye r w i n d tunne ls w i t h l o n g test s e c t i o n s . For e x a m p l e , the use o f 3 s l o t t e d pane l s (wal ls a n d ce i l i ng ) w i t h an O A R of a b o u t 0.6 a n d a s o l i d - w a l l e d f l o o r c o u l d be u s e d fo r t he tes t i ng of m o d e l s s u c h as aircraft in take-of f o r l a n d i n g con f i gu ra t i on , cars, a n d bu i l d ings . LIST O F R E F E R E N C E S 1. Rae Jr., W . H . a n d P o p e , A . Low-Speed Wind Tunnel Testing. J o h n W i l e y & S o n s , S e c o n d Ed i t i on , 1984 . 2. Ga rne r , H . C , R o g e r s , E .W.E . , A c u m , W . E . A . a n d M a s k e l l , E .C . Subsonic Wind Tunnel Wall Corrections. A G A R D o g r a p h 1 0 9 , 1 9 6 6 3. M a s k e l l , E . C . A Theory of the Blockage Effects on Bluff Bodies and Stalled Wings in a Closed Wind Tunnel. A R C R. & M . N o . 3 4 0 0 , N o v e m b e r 1 9 6 3 . 4 . G o u l d , R .W.F . Wake Blockage Corrections in a Closed Wind Tunnel for One or Two Wall-Mounted Models Subject to Separated Flows. N P L A E R O R E P O R T 1 2 9 0 , February 1969 . 5. W i l l i a m s , C D . a n d Pa rk inson , C V . A Low-Correction Wall Configuration for Airfoil Testing. P r o c . A G A R D C o n f . 174 o n Wind Tunnel Design and Testing Techniques. L o n d o n , p p . 21.1 - 2 1 . 7 , M a r c h 1976 . 6. A G A R D P u b l i c a t i o n Numerical Methods and Wind Tunnel Testing. A G A R D - C P - 2 1 0 , O c t o b e r 1976 . 7. A G A R D P u b l i c a t i o n Wind Tunnel Corrections for High Angle of Attack models. A G A R D - R - 6 9 2 , February 1 9 8 1 . 8. A G A R D P u b l i c a t i o n Wall Interference in Wind Tunnels. A G A R D - C P - 3 3 5, S e p t e m b e r 1982 . 9. M o k r y , M . , C h a n , Y . Y . , Jones , D .J . and O h m a n , L H . Two-Dimensional Wind Tunnel Wall Interference. A G A R D - A C - 2 8 1 , N o v e m b e r 1983 10. W i l l i a m s , C D . A New Slotted-Wall Method for Producing Low Boundary Corrections in Two-Dimensional Airfoil Testing. P h . D. Thes is , D e p t . of M e c h a n i c a l Eng inee r i ng , T h e Un ive rs i t y of Br i t ish C o l u m b i a , O c t o b e r 1975 . 60 61 11 . P a r k i n s o n , C . V . , W i l l i a m s , C D . a n d M a l e k , A . Development of a low-Correction Wind Tunnel Wall Configuration for Testing High Lift Airfoils. I C A S P r o c e e d i n g s 1978 , V o l . 1, S e p t e m b e r 1978 , p p . 355 -360 . 12. M a l e k , A . F . A n Investigation of the Theoretical and Experimental Aerodynamic Characteristics of a Low-Correction Wind Tunnel Wall Configuration for Airfoil Testing. P h . D . Thes is , D e p t . o f M e c h a n i c a l Eng inee r i ng , T h e Un ive rs i t y of Br i t ish C o l u m b i a , Ap r i l 1983 . 13 . R a i m o n d o , S. a n d C la rk , P.J.F. Slotted Wall Test Section for Automotive Aerodynamic Facilities. A I A A 12 th A e r o d y n a m i c Tes t i ng C o n f e r e n c e , M a r c h 22 -24 , 1 9 8 2 , W i l l i a m s b u r g , V i rg in ia , U . S . A . , Paper A I A A - 8 2 - 0 5 8 5 - C P . 14 . Flay, R . C . J . , E l f s t rom, C M . a n d C la rk , P.J.F. Slotted-Wall Test Section for Automotive Aerodynamic Tests at Yaw. S A E Internat ional C o n g r e s s , February 28 t o M a r c h 4, 1 9 8 3 , M i c h i g a n , U . S . A . , P a p e r 830302 . 15 . E l f s t rom, C M . , Flay, R .G.J . a n d C la rk , P.J.F. Slotted Wall Test Section for Car and Truck Aerodynamic Testing. P r o c e e d i n g s o f the A S M E C o n f e r e n c e o n A e r o d y n a m i c s of T ranspo r ta t i on , B o s t o n , N o v e m b e r 1 4 - 1 8 , 1 9 8 3 . 16. P a r k i n s o n , C V . A Tolerant Wind Tunnel for Industrial Aerodynamics. Jour . W i n d Eng . a n d Ind. A e r o . , 1 6 , 1 9 8 4 , p p . 2 9 3 - 3 0 0 . 17 . G o l d s t e i n , S. Modern developments in Fluid Dynamics. V o l . 1 & 2, D o v e r P u b . , 1 9 6 5 . 18. Thwa i tes , B. Incompressible Aerodynamics. O x f o r d at the C l a r e n d o n Press , 1960 . 19 . R o s h k o , A . On the Development of Turbulent Wakes from Vortex Streets. N A C A repor t 1 1 9 1 , 1958 . 20 . R o s h k o , A . On the Drag and Shedding Frequency of Two-Dimensional Bluff bodies. N A C A T e c h n i c a l N o t e 3 1 6 9 , 1 9 5 4 . 2 1 . K a m e m o t o , K., O d a , Y . a n d A i z a w a , M . Characteristics of the Flow Around a Bluff Body near a Plane Surface. Bul le t in of J S M E , V o l . 2 7 , N o . 2 3 0 , A u g u s t 1984. 62 22 . L a m b , H . Hydrodynamics. Six th Ed i t i on , D o v e r P u b . , 1 9 4 5 . 2 3 . R o s h k o , A . A New Hodograph for Free-Streamline Theory. N A C A Techn i ca l N o t e 3 1 6 8 , 1954. 24 . P a r k i n s o n , C V . and Jandal i , T. A Wake Source Model for Bluff Body Potential Flow. J. F lu id M e c h . , V o l . 4 0 , part 3, p p . 577 -594 , 1970 . 25 . E l -Sherb iny , S.EI-S. Effect of Wall Confinement on the Aerodynamics of Bluff Bodies. P h . D . Thes i s , D e p t . o f M e c h a n i c a l E n g i n e e r i n g , T h e Un ive rs i t y of Br i t ish C o l u m b i a , 1 9 7 2 . 26 . C h r i s t o p h e r , P.A.T. a n d W o l t o n I. A Wake Source Model for Non-Symmetric Flow Past Bluff Bodies in Two-Dimensional Flow. C - o f - A - M E M O 8 1 0 9 , C o l l e g e of A e r o n a u t i c s , C r a n f i e l d , E n g l a n d , S e p t e m b e r 1 9 8 1 . 27 . K iya, M . a n d A r i e , M . An inviscid Bluff-Body Wake Model Which Includes the Far-Wake Displacement Effect. J. F lu id M e c h . , V o l . 8 1 , part 3, p p . 5 9 3 - 6 0 7 , 1 9 7 7 . 28 . B e a r m a n , P . W . a n d Fackre l l , J.E. Calculation of Two-Dimensional and Axisymmetric Bluff-Body Potential Flow. J. F lu id M e c h . , V o l . 72 , part 2, p p . 2 2 9 - 2 4 1 , 1975 . 2 9 . S tansby , P.K. A Generalized Discrete-Vortex Method for Sharp-Edged Cylinders. A I A A Journa l , V o l . 23 , N o . 6, p p . 8 5 6 - 8 6 1 , June 1985 . 30 . Inamuro , T. , A d a c h i , T. a n d Sakata , H . A Numerical Analysis of Unsteady Separated Flow by Vortex Shedding Model. Bul le t in o f J S M E , V o l . 2 6 , N o . 2 2 2 , D e c e m b e r 1 9 8 3 . 31 . K iya , M . and A r i e , M . A Contribution to an Inviscid Vortex-Shedding Model for an Inclined Flat Plate in Uniform Flow. J. F lu id M e c h . , V o l . 82 , part 2 , p p . 2 2 3 - 2 4 0 , 1977 . 32 . K e n n e d y , S.F. The Design and Analysis of Airfoil Sections. P h . D. Thes is , T h e Un ive rs i t y o f A lbe r t a , 1977 . 33 . H o e r n e r , S.F. Fluid-Dynamic Drag. H o e m e r Flu id D y n a m i c s , 1965 . 63 34. B lev ins , R .D . Applied Fluid Dynamics Handbook. V a n N o s t r a n d R e i n h o l d C o . , 1984. 35 . Farrel , C , C a r r a s q u e l , S. , C u v e n , D . and Pate l , V . C . Effect of Wind-Tunnel Walls on the Flow Past Circular Cylinders and Cooling Tower Models. A S M E Journa l of F lu ids Eng inee r i ng , p p . 4 7 0 - 4 7 9 , S e p t e m b e r 1977 . 36 . S inha , S . N . , G u p t a , A . K . a n d O b e i r a , M . M . Laminar Separating Flow Over Backsteps and Cavities, Part II: Cavities. A I A A Journa l , V o l . 20 , N o . 3, p p . 3 7 0 - 3 7 5 , M a r c h 1982 . 37 . B e a r m a n , P . W . a n d M o r e l , T. Effect of Free Stream Turbulence on the Flow Around Bluff Bodies. P r o g . A e r o s p a c e S c i . V o l . 20 , p p . 9 7 - 1 2 3 , 1 9 8 3 . 38. R o s h k o , A . Experiments on the Flow Past a Circular Cylinder at Very High Reynolds Number. J. F lu id M e c h . , V o l . 10 , p. 3 4 5 , 1 9 6 1 . A P P E N D I X 1 WIND TUNNEL CALIBRATION The p u r p o s e o f t he e m p t y w i n d t unne l ca l ib ra t ion is t o re late the ve loc i t y o b t a i n e d w i t h a P i to t t u b e in t he n o z z l e t o the ve loc i t y in the test r e g i o n . This m e t h o d f o l l o w s c l o s e l y the t e c h n i q u e u s e d b y W i l l i a m s f10] . T h e ma in d i f f e rences are the use o f a sma l le r P i to t t u b e (0.25 i nch in d iamete r ) in o r d e r t o r e d u c e its w a k e in te r fe rence w i t h the m o d e l , a n d its p o s i t i o n of 22 inches ups t ream of t he t es t - sec t i on en t rance . Th is n e w t u b e p o s i t i o n was c h o s e n t o i m p r o v e accu racy by p r o d u c i n g larger n u m e r i c a l o u t p u t o n b o t h t h e B e t z m a n o m e t e r a n d the B a r o c e l p ressure t ransducer . T h e m e t h o d is b a s e d o n the a s s u m p t i o n that the re is n o a p p r e c i a b l e d i f f e rence in to ta l h e a d , H , b e t w e e n the test s e c t i o n and the n o z z l e . T h u s H f = P e o f + q , = H n = P e o n + q n (A1.1) w h e r e H is the to ta l h e a d , the stat ic p ressure a n d q the d y n a m i c p ressu re . T h e subsc r ip ts t and n re fer t o the test s e c t i o n and n o z z l e P i to t - t ubes , respec t i ve ly . T h e ca l ib ra t ion was p e r f o r m e d by r unn ing the w i n d t u n n e l o v e r a range o f s p e e d s c o v e r i n g the n o m i n a l test s p e e d s , and measu r i ng q f a n d q n . T h e n , t he rat io qt I q n leads t o a cons tan t of p ropo r t i ona l i t y , o r q f = K 2 q n (A1.2) The p ressu re coe f f i c i en t Cp d e f i n e d as P/" P»f CPi = - (A1.3) 64 65 w h e r e p ;- is a sur face p ressure m e a s u r e d at a p o i n t /*, c a n b e rewr i t ten u s i n g e q u a t i o n s (A1.1) a n d (A1.2) t o o b t a i n C p , = o r K 2 q n r _ P / - ( H n - « 2 q „ ) C p -o r f inal ly C p . = 1 + J. " (A1.4) N o t e that all t he quant i t ies p y , H n a n d q n are m e a s u r e d in vo l ts a n d d o n o t n e e d t o b e c o n v e r t e d t o p ressure un i ts . T h e va lue of t he ca l ib ra t ion cons tan t K , is typ ica l ly 0.95 fo r fo r the so l i d -wa l l test s e c t i o n a n d 0.98 fo r t he s lo t ted -wa l l test s e c t i o n ( i n d e p e n d e n t o f O A R ) . H o w e v e r , f o r cer ta in app l i ca t i ons l ike the eva lua t i on of the S t rouha l n u m b e r , the c o n v e r s i o n f r o m vo l t age t o p ressu re uni ts b e c o m e s necessa ry a n d is o b t a i n e d t h r o u g h a ca l ib ra t ion c o n s t a n t K , , s u c h that q n ( m m H 2 0 ) = K , ( m m H 2 0 / v o l t ) q n ( v o l t ) (A1.5) T h e q n va lues are s i m u l t a n e o u s l y m e a s u r e d in vo l ts w i t h the B a r o c e l p ressu re t r ansduce r and in m m H 2 O o n the B e t z w a t e r m i c r o m a n o m e t e r . A P P E N D I X 2 EVALUATION OF THE INFLUENCE COEFFICIENT T h e de ta i l ed s o l u t i o n o f t h e in tegra l e q u a t i o n l ead ing t o t he i n f l u e n c e coe f f i c i en t is g i v e n in r e f e rence [32]. Th is a p p e n d i x s u m m a r i z e s t h e necessary e x p r e s s i o n s fo r the eva lua t ion o f K^- f o r t he case w h e r e a straight p a n e l w i t h cons tan t vor t ic i ty 7- is u s e d . 1 2 a A K ; / = - { ( b + A ) l n ( r 2 ) - ( b - A . ) l n ( r | ) + 2 a t a n " 1 ( - 4 A } w h e r e r 2 = a 2 + (b + A)2 r§ = a 2 + (b - A ) 2 2 A is the s i ze of t h e p a n e l . a n d a = (y,- - yj) cosdj - (x;- - xy) sinf ly b = (y;- - y-) sindj + (x;- - \j) cosdj 6: is t he ang le b e t w e e n the pane l / a n d the w i n d axis (usual ly ho r i zon ta l ) . 66 A P P E N D I X 3 DETERMINATION OF VELOCITY FIELD A v e l o c i t y v e c t o r ca l cu la ted e i ther at a c o n t r o l p o i n t C 7- o r any p o i n t (xy-,y;-) in the d o m a i n is t he resul t o f th ree c o n t r i b u t i o n s : U n i f o r m (onset ) f l o w V s Po in t s o u r c e s V v Vor t i c i t y d i s t r i bu t ion o n the b o u n d a r i e s Each o n e o f t h e s e c o n t r i b u t i o n s can b e d i v i d e d in t w o ve loc i t y c o m p o n e n t s a l o n g t he x a n d y axes , as f o l l o w s : Uniform flow F r o m t h e ve loc i t y po ten t i a l o f t h e u n i f o r m f l o w the ve loc i t y c o m p o n e n t s are f o u n d t o b e V = 1 Point sources The x a n d y ve loc i t y c o m p o n e n t s resu l t ing f r o m t w o po in t s o u r c e s o f c o m m o n s t reng th Q a n d s i tua ted at ( x „ , y . ) and ( x c , y c ) can b e wr i t t en as Q c o s X , c o s A 2  V s x = - < + } Q s i n X , s i n X 2 V = - { + } 2TT r. rQ w h e r e 67 68 rS l =t(*/-x S l ) 2 + <y,-ySl>8]* rs 2 = t ^ / - x s 2 ) 2 + (y/-'ys 2) 2^ a n d X! ,X 2 are t he ang les b e t w e e n a h o r i z o n t a l l ine a n d r ,r ( N o t e that fo r s y m m e t r y X ^  is d e f i n e d pos i t i ve in t he c o u n t e r c l o c k w i s e d i r e c t i o n w h i l e X 2 is pos i t i ve in t he c l o c k w i s e d i rec t i on ) . Vortex sheets T h e n o r m a l a n d tangent ia l ve loc i t i es i n d u c e d by a straight pane l w i t h d i s t r i bu ted vor t i c i t y 7 are g i ven b y v_ = — In — " 27T r 2 7 v = - - ( 0 , - 0 2 ) w h e r e 5 \, 6 2 are the ang les b e t w e e n the p a n e l a n d r , , r 2 . A l s o r, = { tx; - (xy+A)]2 + [yr (yy- - A)] 2 }* r 2 = {fr/ - (xy- A)] 2 + [y,-- (yy+A)]2 }* T h e x a n d y ve loc i t y c o m p o n e n t s c a n t h e n b e ca l cu la ted by V vx = v t c o s 0 + v n s i n 0 w h e r e )3 is t h e ang le b e t w e e n the p a n e l and t he x-ax is . A P P E N D I X 4 REGRESSION METHOD USED FOR COMPARING TWO PRESSURE COEFFICIENT DATA SETS This reg ress ion m e t h o d w a s u s e d b y Flay, E l fs t rom a n d C la rk [14] f o r c o m p a r i n g car p ressu re d is t r ibu t ions m e a s u r e d in d i f ferent w i n d t u n n e l con f i gu ra t i ons t o an equ iva len t re fe rence p ressure d i s t r i bu t i on . A l inear r e g r e s s i o n analysis, u s i n g a leas t -squares t e c h n i q u e , is p e r f o r m e d o n a re fe rence- tes t and ac tua l da ta set , o n a ve loc i t y bas is , t o ob ta i n t w o coe f f i c ien ts : a b l o c k a g e c o r r e c t i o n fac tor , C F , a n d an a s s o c i a t e d s tandard d e v i a t i o n , S D . T h e b l o c k a g e c o r r e c t i o n fac to r is t he va lue b y w h i c h the s lo t ted -wa l l f rees t ream s p e e d mus t b e d i v i d e d t o g ive the bes t a g r e e m e n t w i t h the equ i va len t re fe rence- tes t p ressure d i s t r i bu t ion . T h e s tandard dev ia t i on c a n b e r e g a r d e d as the res idua l e r ro r a s s o c i a t e d w i t h t h e c o r r e c t e d p ressu re d i s t r i bu t ion . Fo r p ressu re - tap n u m b e r / , the n o r m a l i z e d v e l o c i t y is ca l cu la ted us ing fo r b o t h p ressure da ta sets . T h e coe f f i c i en ts C F and S D o f t he l inear reg ress ion are o b t a i n e d t h r o u g h a leas t -squares fit. ( I" Cp;)* (A4.1) Let V r ; , / = 1,.. . ,N b e the set o f n o r m a l i z e d re fe rence ve loc i t i es and V ; t h e actual v e l o c i t y set . T h e c o r r e c t e d va lues , V c - , are o b t a i n e d t h r o u g h t h e l inear reg ress ion V C / = A , + A 2 V ; . (A4.2) fo r w h i c h the coe f f i c i en ts A , a n d A 2 are ca l cu la ted t o m i n i m i z e the s u m of the d i f fe rences b e t w e e n Vc f - a n d t h e r e f e rence va lues Vr7-. 69 70 That is N Z ( v r ; - ( A , + A 2 V - ) ) 2 is m i n i m i z e d . (A4.3) / s i A , is set t o z e r o o n t h e a s s u m p t i o n that at t he s tagna t i on p o i n t t he ve loc i t y is necessar i l y z e r o in b o t h the re fe rence a n d s lo t ted-wa l l da ta sets . The re fo re d N I ( V r ; - ( A 2 Vj))2 = 0 (A4.4) d A 2 P i A 2 is n o w ca l l ed C F ( b l o c k a g e - c o r r e c t i o n fac tor ) a n d is u s e d t o o b t a i n e d the c o r r e c t e d p ressu re coe f f i c ien ts C p c ; - as f o l l o w s (1 - Cpcj) = C F 2 (1 - C P / ) (A4.5) T h e qual i ty o f t h e overa l l fit of the s lo t ted -wa l l d a t a t o t h e re fe rence- tes t da ta is j u d g e d o n the va lue o f t he s tandard dev ia t i on : 1 N S D = [ - Z ( C P f / - C p c / ) 2 P (A4.6) N /i i T o s u m m a r i z e , t h e b l o c k a g e c o r r e c t i o n f ac to r C F is a measu re of t he co r re la t i on b e t w e e n a s lo t ted -wa l l a n d a re fe rence- tes t d a t a se t ; A va lue o f C F = 1 resul ts in n o b l o c k a g e c o r r e c t i o n . C o n s e q u e n t l y , the idea l con f i gu ra t i on o f t h e To le ran t w i n d t unne l s h o u l d p r o d u c e C F ' s c l o s e t o uni ty. A n d , the s tandard dev ia t i on S D ind ica tes the er ror b e t w e e n the c o r r e c t e d and re fe rence p ressu re d i s t r i bu t i on ; o r h o w w e l l C F w o u l d c o r r e c t a set o f s lo t ted -wa l l da ta . A P P E N D I X 5 GRADED OPEN AREA RATIO This a p p e n d i x der ives t he e x p r e s s i o n s u s e d t o ob ta i n vary ing o p e n areas a l o n g the w i n d axis. A c o m p l e t e l y d e f i n e d s lo t ted -wa l l c o n f i g u r a t i o n requ i res , in a d d i t i o n t o wa l l l eng th a n d slat s i ze , th ree parameters : t he O A R w h i c h f ixes t he n u m b e r of g i ven -s i ze slats t o b e u s e d , the o p e n - a r e a d i s t r i bu t i on a n d f inal ly an init ial c o n d i t i o n w h i c h c a n , fo r e x a m p l e , b e the s i ze o f t h e first s lo t . Let a 0 , a 1 , . . . , a n be the s ize o f t he s lo ts w h e r e the subscr ip ts i nd ica te t he s lo t n u m b e r i nc reas ing in t h e d o w n s t r e a m d i r e c t i o n . Fo r a s lo t ted -wa l l c o n t a i n i n g n slats, t he re wi l l b e (n + 1) s lo ts . A l s o , let L b e the leng th o f the wal l a n d c t he c h o r d of the a i r fo i l - shaped slats. T h e o p e n area rat io is t h e n d e f i n e d as 1 n n » c O A R = - { Z a ; } = 1 - — L /=o L (A5.1) Fo r a d is t r i bu t ion o f o p e n areas vary ing l inear ly w i t h t h e s lo t n u m b e r , w e have a,- = a 0 + b « i i = 1,2,...,n (A5.2) w h e r e b is t h e s l o p e of t he l inear var ia t ion . T h e o p e n - a r e a rat io can n o w b e wr i t t en as 1 n O A R = - { Z ( a 0 + b « i ) } L /'=o (A5.3) o r 71 72 1 n O A R = — { (n + 1) a 0 + b 2 i } (A5.4) L /=o A n d s i n c e n Z i = i n (n + 1) (A5.5) /:0 t he e x p r e s s i o n fo r O A R b e c o m e s 1 O A R = - { ( n + 1 ) [ a 0 + i n b ] } (A5 .6 ) a n d t h e s l o p e b can t h e n b e e x p r e s s e d as O A R * L - (n + 1 ) a 0 b = (A5.7) i n ( n + 1) If w e requ i re t h e o p e n areas t o i nc rease in t h e d o w n s t r e a m d i r e c t i o n , w e the re fo re have o r Thus w e have b £ 0 O A R * L - ( n + 1 ) a 0 £ 0 (A5.8) O A R * L 0 < a 0 * (A5.9) n + 1 or , us ing e q u a t i o n (A5.1) 73 L - n « c 0 £ a 0 * (A5 .10) n + 1 w h e r e the u p p e r b o u n d c o r r e s p o n d s t o t h e e v e n l y - s p a c e d slat d i s t r i bu t i on . O n e c a n n o w de f i ne a pa ramete r , AORT, w h i c h re lates t h e s ize of t h e 0tn s lo t ( a 0 ) t o t he e v e n l y - s p a c e d s lot s i ze , s u c h that T h e va lue of AORT is t he re fo re a lways grea ter o r e q u a l t o 1. C o n s e q u e n t l y , f o r a g i v e n (l inear) var ia t ion o f o p e n areas on l y o n e pa rame te r n e e d t o b e g i ven : AORT. T h e n , f o r a g i ven AORT, the s lo t s ize a 0 a n d the s l o p e b o f t he l inear d i s t r i bu t i on is ca l cu la ted . For the spec ia l case w h e r e AORT = 1 w e have b = 0 w h i c h is t he e v e n l y - s p a c e d slat case . Slat Position T h e slat p o s i t i o n x S / . m e a s u r e d f r o m t h e n o z z l e exi t t o the l ead ing e d g e of t he slat n u m b e r i , can t h e n b e ca l cu la ted as f o l l o w s L - n « c AORT = (A5.11) n + 1 (A5 .12) i-i x s . = a 0 + 2 (a.- + c) i = 2,3, . . . ,n (A5.13) A f te r s imp l i f i ca t i on , w e ge t x = i . a 0 + ( i - 1 ) c + * i ( i - 1 ) b i = 1,2,...,n (A5.14) A P P E N D I X 6 INSTRUMENTATION Pressure Transducer B a r o c e l Pressure S e n s o r ( D A T A M E T R I C S inc. ) T y p e 511J-10 range : 10 m m H g . S igna l C o n d i t i o n e r ( D A T A M E T R I C S inc.) T y p e 1015 P o w e r S u p p l y ( D A T A M E T R I C S inc. ) T y p e 7 0 0 Mechanical Pressure Scanner Scan iva lve 4 8 - p o r t s ( S C A N I V A L V E C o r p . ) M o d e l 48J9 -2273 Pressure Lines P o l y e t h y l e n e t u b i n g ( I N T R A M E T R I C ) Ins ide d i a m e t e r : 1.67 m m (0 .066 in.) O u t s i d e d i a m e t e r : 2 .42 m m (0.095 in.) L e n g t h : m o d e l t o Scan iva lve ="1 m (3 ft.) Scan iva lve t o p ressu re t r a n s d u c e r » 2 m (6.5 ft.) Manometer B e t z W a t e r M i c r o m a n o m e t e r ( M a x - P L A N C K - I N S T I T U T f u r S t r o m u n g s f o r s c h u n g C o t t i n g e n ) Smal les t d i v i s ion : 0.1 m m H a O Averaging Voltmeter T i m e D o m a i n A n a l y s e r (So la t ron , S C H L U M B E R C E R ) Smal les t d iv i s ion : 1 m V 74 Real Time Analyser S p e c t r a s c o p e II ( S P E C T R A L D Y N A M I C S C o r p . ) M o d e l S D 3 3 5 Smal les t D i v i s i o n : 0.2 % o f range (20 ,100 ,200 ,500 H z ) Smoke Generator C o n c e p t G e n i e M K V ( C O N C E P T E N G . L td . , Eng land) A P P E N D I X 7 ERROR ANALYSIS This s e c t i o n d e s c r i b e s in deta i l t h e eva lua t i on o f expe r imen ta l er rors o n r e d u c e d da ta s u c h as d y n a m i c p ressu re , ve loc i t y , R e y n o l d s n u m b e r , p ressu re coe f f i c i en t a n d S t rouha l n u m b e r . T h e m e t h o d u s e d he re is t e r m e d uncer ta in ty analysis a n d p r o v i d e s relat ive w e i g h t i n g f o r the errors. For a d e p e n d e n t var iab le , Y , re la ted t o s o m e i n d e p e n d e n t var iab les, x , , x 2 , . . . , x n , by the f u n c t i o n Y = f ( x , , x 2 , . . . , x n ) , the uncer ta in ty of t h e resul ts is 9f 3f , e Y = [ ( — e x , ) 2 +...•+(— e x n ) 2 ] * (A7.1) 9x, 3x n w h e r e e x , , e x 2 , . . . , e x n are t h e uncer ta in t ies o r p r o b a b l e er rors o f the var iab les x , , x 2 , . . . , x n , respec t i ve ly . T o u s e uncer ta in ty analysis it is necessa ry t o o b t a i n the e r ro r assoc ia ted w i t h e a c h i n d e p e n d e n t var iab le . S u c h uncer ta in t ies are d e t e r m i n e d s o m e t i m e s f r o m the p r e c i s i o n of an ins t rument , o r f r o m t h e e x p e r i e n c e o f the e x p e r i m e n t e r . T h e f o l l o w i n g tab le s u m m a r i z e s the uncer ta in t ies in the bas ic var iab les, and f o rms t h e basis fo r t he s u b s e q u e n t ca lcu la t ions . e K , e K 2 e H „ ± 1 % ± 1 % ± 0 .002 vo l ts ± 0 .003 vo l ts ± 0 .003 vo l t s Tab le A7.1 : Unce r ta i n t i es in bas i c va lues . 76 77 Uncertainty in Pressure Coefficients, Cp A p p l y i n g e q u a t i o n (A7.1) o n the e x p r e s s i o n u s e d t o ca lcu la te t he p ressu re coe f f i c i en t s , P i " H n C p . = i + J. " (A7.2) K »q„ t he uncer ta in ty in Cpy b e c o m e s 1 -1 P;_ H n P;_ H n e C P / = [ ( — e P / > » + ( — e H „ > » + (- -^—neK2)* + (- ^-feo,n)2 F (A7.3) K 2 % K 2 % K l q n K 2 This re la t ion s h o w s that m a x i m u m er ror w i l l o c c u r w h e n q n is the l owes t , w h e n tes t ing t he largest m o d e l (12 i n c h e s in d iameter ) and w h e n (py - H n ) is largest, genera l l y c o r r e s p o n d i n g t o the base p ressu re . T h e uncer ta in ty at the s tagna t i on p o i n t ( C p = 1), w h e n (py - H n ) = 0 and fo r K 2 = 0 .985 a n d q n = 0 .179 vo l t s c o r r e s p o n d i n g t o a typ ica l test fo r a 12 - i nch d i a m e t e r cy l i nde r , leads t o e C p = ± 0.02 o r a b o u t ± 2 % . T h e s a m e ca l cu la t i on but i n c l u d i n g a base p ressu re py = - 0 .377 vo l t a n d a to ta l h e a d H n = 0 .308 vo l t c o r r e s p o n d i n g t o a tes t i ng o f the s a m e 12 - i nch cy l i nde r b e t w e e n s o l i d wal ls g ives e C p = ± 0 . 0 8 . For t h e s e c o n d i t i o n s t h e base p ressu re is C p D = - 3.0 w h i c h t ranslates t o p e r c e n t a g e er ro r o f a b o u t 3 %. Uncertainty in Dynamic Pressure, q T h e re la t ion b e t w e e n q n , the d y n a m i c p ressu re o b t a i n e d in the n o z z l e a n d e x p r e s s e d in vo l ts , a n d q , the t rue d y n a m i c p ressure o f the tes t s e c t i o n in ps i un i ts , is g i v e n by q (psi) = K , ( m m H 2 0 / vo l t ) q n (vol ts) C (psi / m m H 2 0 ) (A7.4) w h e r e K , is a ca l ib ra t ion va lue a n d C is u s e d t o c o n v e r t t he un i ts . A g a i n u s i n g e q u a t i o n (A7.1) to 78 ob ta i n a m e a s u r e o f t he u n c e r t a i n t y , w e ge t e q = [ ( q n C e K , ) 2 + ( K 1 C e q n ) 2 ] ^ (A7.5) o r in te rms of p e r c e n t a g e - = [( ) 2 + ( — ) 2 F q K , • q „ w h i c h g ives f o r the l o w e s t w i n d s p e e d an er ror of a b o u t ± 2 %. Uncertainty in Reynolds Number, Re T h e gene ra l e x p r e s s i o n fo r Re is w h e r e t h e v e l o c i t y U is o b t a i n e d f r o m the d y n a m i c p ressure thus , (A7.6) U h Re (A7.7) V U = V - (A7.8) h / q Re = (A7.9) In ca lcu la t ing t he e r ro r in Re w e neg lec t t h e uncer ta in ty in t he m o d e l s i ze h bu t i n c l u d e an er ro r in the k i nema t i c v i scos i t y v a n d dens i t y p d u e t o tempera tu re var ia t ions. A p p l y i n g (A7.1) o n (A7.9) w e ge t 79 e R e e q e p -ev , — = [(i - ) 2 ) 2 + ( — ) 2 F (A7.10) Re q p v a n d t he error in v a n d p is e s t i m a t e d fo r a var ia t ion of 1 0 ° F a b o u t t h e s tandard t e m p e r a t u r e 7 0 ° F. T h u s , f o r p = 0 .07492 ± 0 .0014 l b / f t 3 v = 1.64 ± 0.06 x 1 0 " * f t 2 / s e c w e o b t a i n an er ro r in Re o f a b o u t ± 4 .0 %. Uncertainty in Strouhal numbers, St T h e e x p r e s s i o n f o r the S t rouha l n u m b e r is g i ven b y f h St = — (A7.11) U w h e r e f is the v o r t e x - s h e d d i n g f r e q u e n c y . T h e ve loc i t y U is o b t a i n e d f r o m (A7.8) . H e n c e , f h / i p St = (A7 .12) and the er ro r in St b e c o m e s eSt ef e q e p . — = [ ( - ) 2 + - ) 2 + — ) 2 P (A7.13) St f q p For an er ror in f r e q u e n c y es t ima ted t o b e n o m o r e than ± 2 %, t h e resu l t ing er ror o n the St is ± 2 . 5 %. 80 Uncertainty in Drag Coefficients, B e c a u s e t he d rag coe f f i c i en ts are o b t a i n e d f r o m in tegra t ion o f the sur face p ressu re d i s t r i bu t ion and the re fo re d e p e n d o n t h e i n te rpo la t i on m e t h o d u s e d , it is di f f icul t t o ca lcu la te its error . H o w e v e r , it is es t ima ted , b a s e d ma in ly o n t h e e r ro r in Cp, t o b e a b o u t 5 % . 81 Figure 2.1 : Single-slatted-wall tunnel configuration for airfoil testing. r D T h h/H = Blockaqe r a t i o VS////////, V, /, Figure 2.2 Double-slatted-wall tunnel configuration for bluff body testing. 82 Figure 3.1 ( b ) : Phys ica l a n d bas ic t r ans fo rm p l a n e s f o r a c i rcu lar c y l i n d e r m o d e l . (a) 1n the physical plane (b) 1n the transform plane Figure 3.2 : Theoretical representation of the Tolerant wind tunnel. X/h Figure 4.1 : P ressure d is t r ibu t ion o v e r a n o r m a l flat p la te in u n c o n f i n e d f l o w c o m p a r i s o n o f n u m e r i c a l ca lcu la t ion in t rans fo rm p lane w i th analyt ica l so l u t i on . G i v e n C p b = - 1.38, N = 70 0.0 30.0 60.0 90.0 120.0 150.0 180 BETA 4.2 : P ressure d i s t r i bu t i on o v e r a c i rcu la r cy l i nde r in u n c o n f i n e d f l o w : c o m p a r i s o n of n u m e r i c a l ca l cu la t i on in t r ans fo rm p l a n e w i t h analyt ica l s o l u t i o n . G i v e n C p o = - 0 .96, 0S = 8 0 ° , N = 70 Figure 4.3 : Va r ia t i on o f s o u r c e s t r eng th w i t h n u m b e r o f pane l s in t r ans fo rm p l a n e , f o r flat p la te a n d c i rcu la r c y l i nde r in u n c o n f i n e d f l o w . ii 8 - Tr— Air (Analytical) a Numerical Cofculotlsn -0.5 -0.3 —I r— -o.i o.i X/h —1— 0.3 0.5 Figure 4.4 : Pressure distribution over a normal flat plate in unconfined flow : comparison of numerical calculation in physical plane with analytical solution. Given Cpo = - 1.38, N = 60 - Frtw Air (AiNtrttoal) O Numerical Calculation 0.0 Figure 4.5 - 1 — 30.0 —I 60.0 —I 90.0 -1 120.0 150.0 180.0 BETA Pressure distribution over a circular cylinder in unconfined flow comparison of numerical calculation in physical plane with analytical solution. Given C p D = - 0.96, p*s = 80° , N = 60 CO Q, FLAT PLATE era c 3 Q. O .. 71 — a> <• 9> 3 W I*s" a 3. g g -o fl> °- o °S a 3" o -5 < * I-<o | g-Q.5 Q, CIRCULAR CYLINDER Cpb, FLAT PLATE era c 3 13 3 .. sr c £§.< n 2.5" ^ = = § 9, S{ 2.CT 2 "° Q.T3 2 ^ •< to 3 = C 2 3 2 ~ n Q T3 O If * fO (B Cpb, CIRCULAR CYLINDER Figure 4.7 : Pressure d is t r ibu t ion ove r a n o r m a l flat p la te in so l id -wa l l c o n f i n e d f l o w : c o m p a r i s o n of numer i ca l ca lcu la t ion in phys ica l p l ane w i t h analyt ical so l u t i on . ?-G i v e n C p D = C F = 0 .6749 -0.3 —I— -0.3 -I 1 --0.1 0.1 X/h - I — 0.3 0.S Figure 4 .8 : C o r r e c t e d p ressu re d i s t r i bu t i on o v e r a n o r m a l flat p la te in so l i d -wa l l c o n f i n e d f l o w : c o m p a r i s o n o f c o r r e c t e d numer i ca l ca l cu la t i on in phys i ca l p l ane w i t h free-air analyt ical s o l u t i o n . co co - 3 . 5 7 5 - 3 . 5 7 0 -- 3 . 5 6 5 -- 3 . 5 6 0 -- 3 . 5 5 5 -- 3 . 5 5 0 - 3 . 5 4 5 10 20 i 3 0 N 4 0 5 0 Figure 4 .9 : Var ia t ion of base p ressure coe f f i c ien t w i t h n u m b e r o f pane ls o n so l i d wal ls , f o r a no rma l flat plate m o d e l in c o n f i n e d f l ow . G i v e n C p o = - 1.0 , h /H = 1/3 , W a l l Leng th = 12 - 3 . 6 5 XI D_ a - 3 . 6 0 - 3 . 5 5 -- 3 . 5 0 - 3 . 4 5 - 3 . 4 0 - 3 . 3 5 - 3 . 3 0 10 15 Wall Length Figure 4 .10 : Va r ia t i on o f base p ressu re coe f f i c i en t w i t h wa l l l e n g t h , f o r a n o r m a l f lat plate in c o n f i n e d f l o w . G i v e n CpD - - 1.0 , h /H = 1/3 , N ( m o d e l ) = 8 0 , N(wa l l ) = 20 co U3 z o f £ •hP © II I OT C § o < Correction Factor 2 oo I s • o o O 7T -1 Qi on 3 o 3 o Q. 00 O n O 3/ _ o ^ ST 3 3" O b p In p p CD O o Q CD p o A. p In' p 06 7-j 1 1 1 1 1 1 0.0 30.0 80.0 90.0 120.0 150.0 160.0 BETA Figure 4 . 1 3 : Pressure d is t r ibu t ion ove r a c i rcu lar cy l i nde r in so l i d -wa l l c o n f i n e d f l o w : c o m p a r i s o n o f n u m e r i c a l ca l cu la t i on in phys ica l p l a n e w i t h f ree-a i r analyt ical s o l u t i o n . G i v e n Cpb ~ - 0 .96 , 0 S = 8 0 ° , h / H = 1/3 , C F = 0 . 7 8 2 7 i i 1 1 1 1 1 0.0 30.0 60.0 90.0 120.0 150.0 160 BETA ure 4 .14 : C o r r e c t e d p ressu re d i s t r i bu t i on o v e r a c i rcu la r c y l i n d e r in so l i d -wa l l c o n f i n e d f l o w : c o m p a r i s o n o f c o r r e c t e d n u m e r i c a l ca l cu l a t i on in phys i ca l p l ane w i t h f ree-a i r ana ly t ica l s o l u t i o n . -2.51 X) o_ a - 2 . 5 0 --2.49 - 2 . 4 8 -- 2 . 4 7 - 2 . 4 6 --2.45 -2 .44 -r 0 T " 10 I 20 3 0 4 0 50 N Figure 4 . 1 5 : Var ia t ion o f base p ressure coe f f i c ien t w i t h n u m b e r o f pane ls o n s o l i d wal ls , fo r a c i rcu lar cy l i nde r m o d e l in c o n f i n e d f l ow . G i v e n C p o = - 1.0 , 0 = 80 ° , h /H = 1/3 , W a l l Leng th = 12 Wall Length Figure 4 .16 : Va r ia t i on o f base p ressu re coe f f i c i en t w i t h wa l l l e n g t h , f o r a c i rcu la r c y l i nde r in c o n f i n e d f l o w . G i v e n C p o = - 0 .96 , 0$ = 8 0 " , h / H = 1/3 , N ( m o d e l ) = 80 , N(wal l ) = 20 era c —T Base Pressure, Cpb z a f ™ 0 3 Q. l l O -ao ° II 1 ' 2 Z 3 O -=• *T 3. 3 w w 2 era a; d (t Q o "OS 03 O | 3 o ' Per" cu _^ i/i O » - "O cu n in _ <n 0. C —* O CD i -o - S 9- 2-3 3" Correction Factor o o o o o o •vi 00 09 (O (O o cn o in o in £6 94 c Q> o <D O O Q> D tn V) 0) 0) o m 0.3 0.4 0.5 0.6 0.7 Open Area Ratio Figure 4 . 1 9 : T h e o r e t i c a l var ia t ion o f base p ressu re c o e f f i c i e n t as a f u n c t i o n o f O A R fo r 4 s i zes o f flat p la te m o d e l p o s i t i o n e d at t h e c e n t e r o f t he tes t s e c t i o n . 1.04 1.02-1.00 0.98 0.96-0.94 0.92 f Blockage Ratios f o 83% (Sin.) 19.4 X Cftn.) + 23.0 X OK) X 33.3 X Win.) 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Open Area Ratio Figure 4 . 2 0 : Theo re t i ca l var ia t ion o f b l o c k a g e c o r r e c t i o n fac to r as a f u n c t i o n o f O A R fo r 4 Sizes o f flat p la te m o d e l p o s i t i o n e d at the c e n t e r o f the test s e c t i o n . 0.020 0.015-0.010-0.005 0.000 c c c c d c C l 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 Open Area Ratio Figure 4.21 : T h e o r e t i c a l var ia t ion o f s tandard dev ia t i on as a f u n c t i o n o f O A R fo r 4 s izes o f flat p la te m o d e l p o s i t i o n e d at t he c e n t e r o f t he test s e c t i o n . o c *o Q) O O CD V. V) V) <D \-CL 0.30 0.28-° 0.26-0.24 0.22 0.20-0.18 r f i H c 7 / :.++++ . : X Blockage Ratios: O 6.3 % (i In.) A 13.8 X O K ) + 25.0 X (9 K) X 33 J X (ttln.) 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 Open Area Ratio Figure 4.22 : Theo re t i ca l var iat ion o f p ressure coe f f i c ien t a t 0 = 3 O ° a s a f u n c t i o n o f OAR fo r 4 s i zes o f c i rcu lar cy l i nder m o d e l p o s i t i o n e d at the c e n t e r of t he test s e c t i o n . G i v e n Cpo = - 0 . 9 6 , 0S = 8 0 ° -0.95 -1.00--1.10 -1.15--1.20 0 Blockage Ratios O 8.3 X (3 In.) A 13.8 X (3 In.) -f 23.0 X (9 In.) X 33.3 X (12 In.) 0.1 I I I I I 0.5 0.6 0.7 0.8 0.9 Figure 4.23 0.2 0.3 0.4 Open Area Ratio T h e o r e t i c a l var ia t ion o f p ressu re coe f f i c i en t at (3 = 6 0 ° as a f u n c t i o n o f OAR f o r 4 s i zes o f c i r cu la r c y l i nde r m o d e l p o s i t i o n e d at t he c e n t e r o f the test s e c t i o n . G i v e n C p o = - 0 . 9 6 , p*s = 8 0 ° Pressure Coefficient at 70 era c 3 3 ro cr j II « i 5 o S •ca 5' cn 3 II oo 2. •a o o 3 ro CL 2 o o> =: 52. ° a N 3" o 2. 2J-n -ca 3 1 2 " 3 5T 3. ~" <= o = £ < 3 W Q. W 3. "* c S1 3 | § 8.02 ~ > a jo ro O « o p § p. <D cn Q o - j - o O ^ O ba o ( 0 cn i u M u U w b a M * M M CO a 3" p p co o o a X-w Q O CM O I cn i IS) o I o—=— Base Pressure Coefficient ao c 3 ho U I 9"8 2 cr a. pj-ii a 2 1 5- _ o « 2. S 5 o ii oo 3* -1/1 i ~ Q. in 2 fO ~" n 3 g. ro %:1 n ro ro2 3 ro a •O Si-ll < a» 09 3. 0 cu o C. 81 3 tu O 1 o-as 5 " 3 2,3 ro ?o ro O O O O P j TJ CM o 3 p (D cn Q o 5-2 p p M o i cn o o cn i o o I x + t>o 00 o o 33.3 2S.0 13.8 a X* Id M * X M * JO M a o? a p 3 3 rX^>+^....>,CL. x - x N , ^ I p cn Z6 1.02 o»96 f j j j j i i i i i • | 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Open Area Ratio Figure 4 .26 : Theore t i ca l var ia t ion of b l o c k a g e c o r r e c t i o n fac to r as a f u n c t i o n of O A R for 4 s izes of c i rcu lar cy l i nde r m o d e l p o s i t i o n e d at the c e n t e r of the test s e c t i o n . G i v e n C p o = - 0.96 , 0S = 8 0 ° 0.06 0.05-0.04-0.03-£ 0.02-0.01-0 . 0 0 l r 0.1 0. c c N c c c c ^ ^ t I I \ 2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 Open Area Ratio Figure 4 .27 : T h e o r e t i c a l var ia t ion o f s tanda rd dev ia t i on as a f u n c t i o n o f O A R fo r 4 s i zes of c i rcular cy l i nde r m o d e l p o s i t i o n e d at the c e n t e r of t he test s e c t i o n . G i v e n CpD = - 0 .96 , Bg = 8 0 ° Figure 5.1 : T h e c l osed -c i r cu i t " G r e e n " w i n d t u n n e l . —• 6M. |<— -I 1 1-§ i i i i i rn '/777777777777777777777777777777777777777f/' 77777? Figure 5.2 : P ressu re tap p o s i t i o n s o n the f l o o r a n d in the p l e n u m . TOO *>• - f t * ! -a I ' l l P I ' l 7 Pressure tops 20' 12" 13 , 1 I • ' 2 14- •H —I—14—-U - L i { - — L - H - L i i 12 d i a . = 3,5,9,12 IN. Figure 5.3 P ressure tap p o s i t i o n s o n m o d e l s . 101 r r r r r/. + ^ ^ ^ ^ ^ ^- -t- + j,—y •» +. - H — K 4 •> 4 4 t - » •++•-)• 4T/ V i- + + * + +4- + -»-4.t-»--*-t-+-»- + +-»- + + -f + + -t--t--t 4- + + + V + + + + + + + 4 + + + 4 + +.-t-4- + 4 + + + +- f4+-f + ++ + + 07777777777777777777777777777777777777777^ + + + + + + • •+--f + +- + +• + + + + ++ + + + -»• + 4 + Figure 5.4 : Tuf t p o s i t i o n s in t h e p l e n u m . -Turning Figure 5.5 M o d i f i e d " G r e e n " w i n d t u n n e l f o r s m o k e f l o w v i sua l i za t i on . 5 ; 4 b f • r innn to l R M U V S 4 / A e wk Kkagt M b t S.S t A \ 1 4 A m •ckaoa M b 1 10.4 I 4 \ 4 Ok ickapi Mh> t SS.S I — An a V « e 4 0*- -to • • >J|IWt b i * 1 L I M I T S ' •b . ml B o b 1 W Opan i • T M M b 10.000 Mob 1 W b i 1 O.t o e 0 e e A A * A A A A A * A A • • • • • 4 • 4 + + + • • (a) - « . 9 - « .S R.I I.I x / h o.s n o.s • n m i M i l b , H . O O i B * l b . •< SW* 1 18 0*wn A r w M b I0.S44 Ptab faalbfi t 0.0 S O O O O A A A A A A A A A A A ( b ) -4.3 - 1 -O.S I .1 0.1 x / h —r— o.s Egparlmonlal RnuHs \ O Obckag* Ik h i l l 1 A A Sbckog* Ik «o 1 10.4 f \ 4 Sbckogt tk fie 1 SS.S » \ *b> - t o \ • I . O S i D * lob. ojf Stata 1 10 Opm Area Rail 1 10.417 1 0.0 O O O e e A A A A A A A A A A • 4 4 • • • • • 4 4 + 4 4 (c) 1.9 -O.S -O.S x / h 0.1 O.S O.S Figure 6.1 (a) t o (m) : Pressure d i s t r i bu t ion ove r 3 d i f ferent s i zes o f flat p la te m o d e l . Re = I O 5 — o ro 1 *• feynoMi i*. tl.M>»> Mb. o» SWt i 13 Opwi V M Mto I0.4S3 I 0.0 Expert men ol Rtiudt \ O HeehOM ft •Do t B.S 1 A A •teckooa Ratio l 18.4 1 \ iH» I 93.9 1 \ — AnayHc* Cpt» -ia I RtynoWi rfe* > l.00«»» Iti. of SWl < M Optn Arvo Hal) > 10.480 i 0.0 • * + + +° + • A * A A A A A * A + A (e) o.s -0.9 -0.9 -0.1 0.1 x/ri 1 * i d Id 0.9 0.9 KqmeMi f*. il.00«»» Mb, ef SWi i 19 OpwiAraaMlo lO.SM • 0.0 .0+ + + t» ft -O + + +<S. * A A * * A * A + (f) -0.9 -fl.3 T r— -0.1 0.1 x/h —r— 0.9 0.9 Figure 6.1 (a) t o ( m ) : Pressure d is t r ibu t ions o v e r 3 d i f fe ren t s i zes o f f lat p la te m o d e l . Re = 1 0 s o co Mb. of Vjti t » Open ATM Ml* 10.563 Mi PMUhn i 0.0 3 =J - * — . » + • • — > * • » » . — * -A ° A A .Uf. A ° A ( g ) -0.8 -0.9 -0.1 «/h —I— 0.1 — I — 0.9 1 ? 3 + • Mb. of Stall i II Opon Arw Mto i0.9 - • - • i o.O + + 4 4 4 + + t • A t a I o i A A 9 (h) 0.8 -0.9 -0.9 - I -0.1 x/h —1— 0.9 J 3 - i 0.9 Experimental Resutrt O Ibckosi Ratio i 6.9 I A Btodcoa* Ro)k> i 10.4 t 4 Mode opt 1Mb i 93.9 I — Anahffkol Cpb- -IO RvynoMj nb. • 1.00 if)* Mb. ef Stall i 10 Open Arie RaHo iO.B99 i 0.0 • 4 + + • 4 4 + 4 + + (& A A # B *3 A D -0.9 -0.9 -0.1 x/h —r— o.i — i — 0.9 0.9 Figure 6.1 (a) t o ( m ) : P ressure d is t r ibu t ions o v e r 3 d i f fe ren t s izes o f f lat p la te m o d e l . Re = 10 5 o p in o ' Expcclrmrrld Rttulti \ O tfactlOBJ* Ro •No I 8.9 I A A Btockoou Ri nto I 18.4 I \ *4* Btodtofljt Ri Mo t 33.9 « \ o o" "™~ AnoiyiloQlf ( Ipba - tO \ Rvynolds nb* 1 1.80 »»» Mb. of State 1 9 Op*Mi Arvo RoH ) 10.872 ?- PW*) PotiftOfl 1 0.0 T" + • • + • • + • • + + + + A a * * c? 6 T" o 7-i-e 7-( j ) -O.S -0.9 -0.1 x/h o.i 0.3 ?H 3 d 0.5 I LOOKS' Mb. al StaN I 0 Open Ano Mh> 10.708 I 8.8 • + • + -A + + + + •A—A 8 + + (K) -8.9 -0.1 x/h 8.1 —1— 8.9 i nb. rl.00i«>» Nb. ef SW* I 7 Open Ana Rotto t0.74S • 0.8 + + + + + * + ++ + + (1) 8.9 D.9 -0.9 T -8.1 x/h —r— e.i -1— 8.9 e.s Figure 6.1 (a) t o ( m ) : P ressure d is t r ibu t ions o v e r 3 d i f fe ren t s i zes o f flat p la te m o d e l . Re = 1 0 s o Figure 6.1 (a) t o ( m ) : P ressu re d is t r ibu t ions o v e r 3 d i f fe ren t s izes of f lat p la te m o d e l . Re = 1 0 s i o CTl - | O Btockogo Katie i 8.3 I *•>. of Stato t 89 A Blockage Ratio t 18.4 I Opm Area Ratio 10.000 + Blockage Ratio t 33.3 I Petition t 0.0 S t * - * . O O O O O g A A A A A O O (a) -s.o -3.0 -1.0 y (feet) T 1.0 3.0 S.O 1- p. O. N . O Btoekag* Ratio i 8.3 I A Btockoge Ratio t 19.4 I + Blockage Ratio i 33.3 I Mb. of State t 18 Open Area Rotto 10.344 Plato Position i 0.0 Q O O O O O * * * * * * . + + + ° ° o I J $ * o A + (b) -3.0 -3.0 T -1.0 y (feet) i— 1.0 -1— 3.0 S.O Figure 6.2 (a) t o (d) : F loo r stat ic p ressu re d is t r ibu t ions fo r 3 d i f fe rent s i zes o f flat p la te m o d e l p o s i t i o n e d at c e n t e r ( d i m e n s i o n a l i z e d p lo t ) . O Btoekoy* Ratio s 8.3 I A Btockag* Ratio : 18.4 I + Btockag* Ratio I 33.3 I * o-o I 3 a. N . m O O 0 0 o Nb. of Stahj i 13 Opm Area Raho :0.526 < 0.0 ° o o H i * * J + + 2 (c) -3.0 -3.0 -1.0 y (feet) T— 1.0 I— 3.0 5.0 o I O <=! U k. 0L 7-O Btocfcago Ratio i 8.3 I A Btockag* Ratio « 19.4 I 4 Bbckog* Ratio I 33.3 1 Nb. of Stall i 8 Opm Ar*a Ratio 10.708 Pkit* Position i 0.0 t _ 6 o o o + X is* + -5.0 -3.0 I 1— 1.0 1.0 y (feet) — l — 3.0 5.0 Figure 6.2 (a) t o ( d ) : F l oo r stat ic p ressure d is t r ibu t ions fo r 3 d i f ferent s i zes o f flat p la te m o d e l p o s i t i o n e d at cen te r ( d i m e n s i o n a l i z e d p lo t ) . —• CO e m* O Blockage Rone t 8.3 A Btockog* Ratio I 19.4 + Btockog* Ratio s 33.3 + A 4 . 8. 7 u a. e o 7-o o o A O A A3 O + + A + A e T-Nb. of Stall i 99 Opm Area Ratio 10.000 s 0.0 o o o o (a) -20.0 -12.0 .0 4.0 V h ~T 12.0 20.0 8. u a e u ti. T i O Blockage Ratio i 0.3 I A Blockage Ratio i 19.4 I + Blockage Ratio t 33.3 I Nb. of SM* t IB Opm Aroa Ratio : 0.344 Plate Position i n.O + A. KA. ° O O O +4 4 b) •20.0 -12.0 y/h T— 4.0 I 12.0 20.0 Figure 6.3 (a) to (d) : Floor static pressure distributions for 3 different sizes of flat plate model positioned at center (non-dimensionalized plot). - . o VD Ii o a e o r O Blockage RaHo t 8.3 I A Blockage Ratio i 19.4 I + Btockog* Rone t 33.3 I Nb. of Stat. i 13 Open Area Ratio :0.326 Plato Peottton t 0.0 * Is ix ^Af f l O © O <D B •H-A (c) -20.0 -12.0 -4.0 4.0 y/h 12.0 20.0 11 ' U a p O re. T i O Blockage Ratio i 8.3 f Nb. of Stato t 8 A Blockage Ratio I 19.4 I Open Area Ratio 10.708 + Blockage Ratio i 33.3 I P*** PooRlon i 0.0 © O "^AB o o o 6 S o ++ A (d) -20.0 I -12.0 ~1 -4.0 y/h 4.0 12.0 20.0 Figure 6.3 (a) to (d): Floor static pressure distributions for 3 different sizes of flat plate model positioned at center (non-dimensionalized plot). ni 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Open Area Ratio Figure 6.4 Var ia t i on o f base p ressu re c o e f f i c i e n t as a f u n c t i o n of O A R f o r 3 s i zes o f flat p la te m o d e l p o s i t i o n e d at c e n t e r . 0.85 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 Open Area Ratio Figure 6.5 : Var ia t ion o f f ron t d rag coe f f i c ien t as a f u n c t i o n o f O A R fo r 3 s i zes of flat p la te m o d e l p o s i t i o n e d at cen te r . 5.0 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Open Area Ratio Figure 6.6 : Va r ia t i on o f d rag coe f f i c i en t as a f u n c t i o n o f O A R f o r 3 s i zes o f f lat p la te m o d e l p o s i t i o n e d at cen te r . _ , ro 113 0.28 o.io 4 i i i i i i i i i I 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Open Area Ratio Figure 6.7 : Va r ia t i on o f S t r o u h a l n u m b e r as a f u n c t i o n o f O A R f o r 3 s i zes o f flat p la te m o d e l p o s i t i o n e d at cen te r . 1.10 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Open Area Ratio Figure 6.8 : Var ia t ion o f b l o c k a g e - c o r r e c t i o n fac to r as a f unc t i on o f O A R fo r 3 s i zes o f flat p late m o d e l p o s i t i o n e d at cen te r . 0.10 C o o *> <D Q "2 O TJ C CJ to 0.09-0.08-0.07 0.06 0.05 0 . 0 4 ^ 0.03-0.02 0.01 I o-Blockage Ratios : O 8.3 X (3 In.) A 19.4 » (7 In.) -f 33.3 % (12 In.) + . . . Y . A . + . . / . \ i . . / . . V . -a 0.00 + 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Open Area Ratio Figure 6.9 : Va r ia t i on o f s tandard dev ia t i on as a f u n c t i o n o f O A R fo r 3 s i zes o f flat p la te m o d e l p o s i t i o n e d at cen te r . Ratio i 8.3 * »*• °< Slot* t 99 Ratio t 19.4 I Opon Aroo RaMo :0.000 Position t 22.0 Pockogo Ratio t 33.3 I 4 A • Q Q O O O O Q Q A J A A A A A A A O o + + + + (a) -3.0 -3.0 y (*•«*) + —f— 3.0 5.0 "E o l 1 . 3 k. a. T-O Blockage Ratio ! 8.3 I A Btockog* Ratio t 19.4 I 4 Block age Ratio : 33.3 I Nb. of SWo > 18 Opon Aroa Ratio 10.344 i 22.0 o o 0 0 0 o o o o 0  A A * A A A * * A 4 + + + + . 4 A 4 A 4 O A + a A o + i (b) -s.o i — -3.0 y (*••*) 3.0 3.0 Figure 6.10 (a) to (d) : Floor static pressure distributions for 3 different sizes of flat plate model positioned at 22 inches upstream of the center (dimensionalized plot). O Btocfcog* Roflo i 8.9 I A Btockog* Ratio l 19.4 I + Wochop*> rtoHo t 33.3 t "E 3 § D . o o o O O O O Nb. of Start i 13 Open Ar*o RoHo t0.526 PW* PoslHon i 22.0 + A + O A + •St M M o A A O + + A O A T-( c ) -S.O -3.0 .0 .xI.O i 3.0 S.O S o O - . i 3 n « o. a. N . T-O Btockaoa Ratio t 8.3 I A Btoekog* Ratio i 19.4 I 4 Btockag* Ratio I 33.3 I Nb. of Stat* i t Opon Aroo Ratio :0.708 i 22.0 ° A A * * + + A O i + a A + ° o 0 A + + + + % + A O (d) -S.O -3.0 -1.0 y (feet)' ~i— 3.0 5.0 Figure 6 .10 (a) t o (d) : F l o o r stat ic p ressure d is t r ibu t ions fo r 3 d i f fe rent s izes of flat p la te m o d e l p o s i t i o n e d at 22 i nches ups t ream o f the c e n t e r ( d i m e n s i o n a l i z e d p lo t ) . CTi Ratio i 8.3 t Hotle i 19.4 I Ratio i 33.3 f I*, of State i 99 Open Area Ratio 10.000 l 22.0 + A •f'B b o ° o o o o o o & A S A A AA V (a) -30.0 -22.0 -14.0 -6.0 2.0 8. a e o ~ 10.0 O Blockage Ratio i 8.3 J A Blockage Ratio I 19.4 I + Blockage Ratio I 33.3 I Nb. of Stall i 18 Open Area Ratio :0.344 Plate Position t 22.0 + A + O o o o o o o o A 9 (b) -30.0 I -22.0 I 1 -14.0 , L - 6 . 0 i— 2.0 10.0 Figure 6.11 (a) t o (d) : F loo r stat ic p ressure d is t r ibu t ions fo r 3 d i f fe rent s i zes o f flat p la te m o d e l p o s i t i o n e d at 22 inches ups t ream o f the c e n t e r ( n o n - d i m e n s i o n a l i z e d p lo t ) . O Btockog* Ratio i 6.3 J A Btockog* Ratio I 19.4 I 4 Btockog* Ratio i 33.3 I s. T-Nb. of Stall I 13 Opon Aroa Ratio 10.326 Plato PMStton : 22.0 4 A 4 0» O o (c) -30.0 O O o o o o o -22.0 4I-A O A -14.0 -6.0 y/h —\— 2.0 10.0 u a °. T-O Btockog* Ratio t 8.3 % A Btockog* Ratio t 19.4 I 4 Btockog* Ratio i 33.3 I Nb. of Stall j 8 Optn Aroa Ratio 10.708 Plat* Pocltton t 22.0 4 Of o o ( d ) o o o o o o o -30.0 -22.0 4 4 4 -14.0 / . -6.0 yA 2.0 10.0 Figure 6.11 (a) t o (d) : F l o o r stat ic pressure d i s t r i bu t i ons fo r 3 d i f fe ren t s i zes o f flat p la te m o d e l p o s i t i o n e d at 22 inches u p s t r e a m o f t he c e n t e r ( n o n - d i m e n s i o n a l i z e d p lo t ) . CO 119 c O 0> o o © »_ 3 f/> CO d> CO o 00 -1.0--1.5-0.3 0.4 0.5 0.6 0.7 Open Area Ratio Figure 6 .12 : Va r ia t i on o f base p ressu re c o e f f i c i e n t as a f u n c t i o n o f O A R f o r 3 s i zes o f flat p la te m o d e l p o s i t i o n e d at 22 i n c h e s u p s t r e a m of the cen te r . 0.85 0.45 I j i | j j j j j j I 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Open Area Ratio Figure 6.13 : Var ia t ion of f ron t d rag coe f f i c ien t as a f u n c t i o n of O A R fo r 3 s i zes of flat p late m o d e l p o s i t i o n e d at 22 i nches ups t ream of t he cen te r . i 1 1 1 1 1 i 1 i i r 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Open Area Ratio Figure 6.14 : Va r ia t i on o f d rag c o e f f i c i e n t as a f u n c t i o n o f O A R fo r 3 s izes of flat p la te m o d e l p o s i t i o n e d at 22 i n c h e s u p s t r e a m o f t he cen te r . 121 0.28 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Open Area Ratio Figure 6.15 : Va r ia t i on o f S t rouha l n u m b e r as a f u n c t i o n o f O A R f o r 3 s i zes o f flat p la te m o d e l p o s i t i o n e d at 22 i n c h e s u p s t r e a m of t h e cen te r . v.uv n 1 1 1 1 1 1 1 1 1 r 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Open Area Ratio Figure 6.16 : Var ia t ion o f b l o c k a g e - c o r r e c t i o n fac to r as a f u n c t i o n of O A R fo r 3 s izes of flat p late m o d e l p o s i t i o n e d at 22 i nches ups t ream of the cen te r . 0.10 C .o ~o *> Q) Q "S O TJ C D in i i i i i i i i i 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Open Area Ratio Figure 6 . 1 7 : Var ia t i on o f s tanda rd dev ia t i on as a f u n c t i o n o f O A R fo r 3 s i zes o f flat p la te m o d e l p o s i t i o n e d at 2 2 i n c h e s ups t ream o f the cen te r . Experimental Results O Blockage Ratio : 8.3 X A Blockogt Ratio : 13.8 % + Blockog* Ratio : 25.0 * X Btockaga Ratio : 33.3 X — Roshko, Raf. 20 A Reynolds nb« Nb. of Skill Opon Arta Ratio 1.00 xK>» 99 0.000 O O O © o A A A A A A + + + O O A A X X 60.0 90.0 120.0 150.0 180.0 Beta Experimental Results A Btockaga Ratio : 13.8 I + Blockage Ratio : 25.0 I X Blockog*) Ratio : 33.3 I — Roshko, Rof. 20 Reynolds nb* Nb. of Slati t Opon Aria Ratio 1.00 x t t ' 18 0.344 Figure 6.18 (a) to (m) : Pressure d is t r ibu t ions o v e r d i f fe rent s izes o f c i r cu la r c y l i n d e r m o d e l . Re = 1 0 5 Experimental Results A Btockog* Ratio : + Btockog* Ratio : X Btockog* Ratio : — Roshko, R*f. 20 Reynolds nb. Nb. of Slats Open Aroa Ratio 13.8 X 25.0 X 33.3 X 1.00 x»» 16 0.417 90.0 Bota 120.0 150.0 160.0 Experimental Results A Blockage Ratio : + Btockog* Ratio : X Btockog* Ratio : — Roshko, Rof. 20 Reynolds nb. Nb. of Stats : Opart Aroa Ratio 13.8 X 25.0 X 33.3 X 1.00 x»» IS 0.453 Figure 6 .18 (a) t o ( m ) : Pressure d i s t r i bu t i ons o v e r 4 s i zes o f c i rcu lar c y l i nde r m o d e l . Re = 1 0 5 Experimental Results A Btockog* Ratio : + Btockog* Ratio : X Btockog* Ratio : — Roshko, R*f. 20 Reynolds nb. Nb. of Slats Open Area Ratio : 13.8 X 2S.0 X 33.3 X 1.00 xlO* 14 0.490 90.0 Beta - i — 120.0 Experimental Results A Btockog* Ratio : + Btockog* Ratio : X Btockog* Ratio : — Roshko, Ret. 20 Reynolds nb. Nb. of Slats Open Area Ratio 13.8 X 2S.0 X 33.3 X 1.00 xlO* 13 0.526 150.0 180.0 0.0 90 Figure 6 .18 (a) t o ( m ) : Pressure d i s t r i bu t i ons o v e r 4 s izes o f c i rcu la r c y l i n d e r m o d e l . Re = 1 0 s 180.0 Figure 6.18 (a) t o ( m ) : Pressure d is t r ibu t ions o v e r 4 s i zes o f c i rcu lar c y l i n d e r m o d e l . Re = 1 0 s Experimental Results Blockage Ratio : 8lockog« Ratio : Blockage Ratio : Blockage Ratio : Roshko, Rof. 20 Reynolds nb. Nb. of Slats Opon Aroa Ratio i 6.3 X 13.8 I 2S.0 I 33.3 X 1.00 xW» 10 0.635 X X X 90.0 Beta 120.0 150.0 160.0 Beta Figure 6 .18 (a) t o ( m ) : Pressure d i s t r i bu t i ons o v e r 4 s izes o f c i rcu lar c y l i n d e r m o d e l . Re = 1 0 * 180.0 Figure 6.18 (a) t o ( m ) : Pressure d is t r ibu t ions o v e r 4 s izes o f c i rcu la r c y l i n d e r m o d e l . Re = 1 0 * £ 00 120.0 150.0 180.0 Figure 6.18 (a) t o ( m ) : Pressure d is t r ibu t ions o v e r 4 s izes o f c i rcu lar c y l i n d e r m o d e l . Re = 1 0 * ro 130 0.3 0.4 0.5 0.6 0.7 Open Area Ratio Figure 6 .19 : Va r ia t i on o f p ressu re coe f f i c i en t at ft = 5 0 ° a s a f u n c t i o n o f O A R for 4 s i zes o f c i rcu la r cy l i nde r m o d e l p o s i t i o n e d at t he c e n t e r o f t he test s e c t i o n . Pressure Coefficient at 100 Pressure Coefficient at 180 era c o o ro — U S 5 ST CD tt» t 3' ? ST Q -S 3 3-. 2 § 1 : TJ O o ro 3 8 o <= ro O n > 2 T : ro 5" o Q. S - a ro .U s. Q. » N " f a II CD cn Q O ? b> Q o O V O CO o x + >o s o o u M m ? f 2" u o - "<o X M M * a) 10 3 3 ? ? ? Le L c .92 a> o O CD o o c .2 - 0 . 1 --0.4 -0.5 ..4-+$' ; .^AKAAQASAQA Blockage Ratios O « (s '"•) A u.e K (S In.) + 2 3 . 0 * ( t in . ) X 33.3 X (12 In.) Figure 0.1 0.2 0.3 OA 0.5 0.6 0.7 0.8 ti!9 Open Area Ratio 6.22 : Var ia t ion o f f ron t d rag coe f f i c ien t as a f u n c t i o n of O A R fo r 4 s izes o f c i rcu lar cy l i nde r m o d e l p o s i t i o n e d at the c e n t e r of the test s e c t i o n . 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Open Area Ratio Figure 6 .23 : Var ia t ion o f rear d rag coe f f i c i en t as a f u n c t i o n o f O A R f o r 4 s i zes o f c i rcu lar cy l i nde r m o d e l p o s i t i o n e d at t he c e n t e r o f the test s e c t i o n . 2.4 i i i i r i i i r 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Open Area Ratio Figure 6.24 : Var ia t ion o f d rag coe f f i c i en t as a f unc t i on o f O A R for 4 s izes o f c i rcu lar cy l inder m o d e l p o s i t i o n e d at t h e cen te r of t he test s e c t i o n . 0.24 0.23-0.18-0.17-0.16-0.15-0.14-0.13 Blockage Ratios : O 8-5 * (3 '"•) A 13.8 X (5 In.) + 25.0 % (9 In.) X 33.3 X (12 In.) I I I I I i i I 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Open Area Ratio Figure 6.25 : Va r ia t i on o f S t r ouha l n u m b e r as a f u n c t i o n o f O A R fo r 4 s izes o f c i rcu la r cy l i nde r m o d e l p o s i t i o n e d at the c e n t e r o f t he test s e c t i o n . 1.10 0.75-1-—I I I I i I I I I 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Open Area Ratio Figure 6 .26 : Var ia t ion o f b l o c k a g e - c o r r e c t i o n fac to r as a f u n c t i o n of O A R fo r 4 s izes o f c i rcu lar cy l i nde r m o d e l p o s i t i o n e d at the c e n t e r of t he test s e c t i o n . 0.04 O 0.02-0.00 Blockage Ratios : O 8.3 X (3 In.) A 13.8 X (3 In.) + 2 3 . 0 * (9 In.) X 33.3 X (12 In.) 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 Open Area Ratio Figure 6 .27 : Va r ia t i on o f s tandard d e v i a t i o n as a f u n c t i o n o f O A R f o r 4 s izes o f c i rcu la r c y l i nde r m o d e l p o s i t i o n e d at t he c e n t e r o f the test s e c t i o n . co Experimental Results © Blockoge Folio : A Blockoo* Ratio : + Blockage Ratio : X Blockage Ratio : — Roshko, Ref. 20 Reynolds nb. Nb. of Slots : Open Area Ratio : 8.3 S 13.8 I 25.0 X 33.3 % 1.00 xlO' 99 0.000 O Q O O O O O O O O I I ° A A A A A A A A A A A A + * + + + + + + + + x M x x X X x x X X 90.0 Beta 120.0 150.0 I80.0 180.0 Figure 6.30 (a) t o (rh) : Pressure d i s t r i bu t ions o v e r d i f ferent s i zes of c i rcu lar-cy l i r ider-spl i t ter -p late m o d e l . Re = 1 0 5 ^ Pnaxurm Coefficient -2.3 -2.0 -1.5 -1.0 cm c u> o 3 S o — S- 0 ro II o 3 ui (/> t/i C - i ro a. 3 . O" C o 3 V I O < n N O c 3 a. ro i in •a row ro 8 -S--Ss--8 ' S' x + 1.3 - 4 , I 3 (a 3 a A n a ^ 3 0 O D O D O D O D 8 ?cT?? I m i a a a a o apis? t l l O S3 ft) to rVessurev Coefficient -2.3 -2.0 -1.5 . a. o ; 8" X + 0> G (* "8 • u i • ut a « • x 3 3 D O D C P O D O D i i i i ! M i l l ? 3 0 X 3 ) 3 ) ^ a a a a K> 5" 5" 5" 5" o ai tn ui CU O CO M >* M * • *» p Jo 00 1.5 -4, Experimental Results O Btockog* Ratio : 8.3 X A Blockog* Ratio : 13.8 X + Btockog* Ratio : 25.0 X X Btockog* Ratio : 33.3 X \ — Roshko, R*f. 20 Reynolds nb. i .00 xtO* Nb. of Slats : 14 'A Open Ar*a Ratio : 0.490 » * * * * x x x ) 1 ! X x '(e) ' r-— ' h — 1 1 ' 1 ' 1 <-0.0 90.0 60.0 90.0 120.0 150.0 180.0 Beta Experimental Results O Blockage Ratio : 8.3 X A Blockoge Ratio : 13.8 X + Btockog* Ratio : 25.0 X X Blockage Ratio : 33.3 X — Roshko, Ref. 20 Reynolds nb. 1.00 « » ' Nb. of Slats : 13 Open Area Ratio : 0.S26 ' ( f ) 0.0 30.0 60.0 90.0 120.0 150.0 180.0 Beta Figure 6 .30 (a) t o (m) : Pressure d is t r ibu t ions o v e r 4 s i zes o f c i r cu la r -cy l inder -sp l i t te r -p la te m o d e l . Re = 1 0 5 Lo CO Experimental Results J (g) H ' I——' 1 1 1 ' 1 1 1 • 0-0 30.0 60.0 90.0 120.0 150.0 160.0 M a 0 1.3 Experimental Results —1 O Btockaga Ratio : 8.3 I A Btockoge Ratio : 13.8 I + Btockogt Ratio : 25.0 * X Btockaga Ratio : 33.3 % e>" — Roshko, Ref. 20 Reynolds nb. : 1.00 xtO8 Nb. of Slats : 11 o o~ ^ Open Area Ratio : 0.599 -0.5 \ — i 8 8 i 8—1—I—8—8—< e — • i-wt 1 ' (h) — 1 — I — —< 1 1 H — i 1 1 1 1 I I I I ' 1 1  1 1 ' 1 0-0 30.0 60.0 90.0 120.0 150.0 180.0 Beta Figure 6 .30 (a) t o (m) : Pressure d i s t r i bu t ions o v e r 4 s i zes o f c i r cu la r -cy l inder -sp l i t te r -p la te m o d e l . Re = 1 0 s co Experimental Results Blockage Rollo Blockoge Ratio Blockoga Ratio Btockaga Ratio O A + X —• Roshko, Raf. Ray no kit nb. Nb. of Skits t Opan Area Ratio 6.3 X 13.8 X 2S.0 X 33.3 X 1.00 K10* 9 0.672 I 4 4 I 4 X L 1BO.0 Figure 6.30 (a) t o (m) : Pressure d is t r ibu t ions o v e r 4 s i zes o f c i r cu la r -cy l inder -sp l i t te r -p la te m o d e l . Re = 1 0 5 Experimental Results Btockog* Ratio : Btockog* Ratio : Btockog* Ratio : Btockog* Ratio : Roshko, R*f. 20 Reynolds nb. Nb. of Slats Op*n Area Ratio 8.3 X 13.8 X 25.0 X 33.3 X 1.00 x«» 8 0.708 IXLOJJLl B I H B C I B B G S -B*fa Figure 6 .30 (a) t o (m) : Pressure d is t r ibu t ions o v e r 4 s i zes o f c i r cu la r -cy l inder -sp l i t t e r -p la te m o d e l . Re = 10 s m 150.0 180.0 Figure 6 .30 (a) t o (m) : Pressure d is t r ibu t ions o v e r 4 s i zes o f c i r cu la r -cy l inder -sp l i t te r -p la te m o d e l . Re = 10 s ro 143 0.0 X 1.6 1 i i i i i i i i | 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Open Area Ratio Figure 6.31 : Va r ia t i on of p ressu re coe f f i c i en t at B = 5 0 ° as a f u n c t i o n o f O A R fo r 4 s izes o f c i rcu la r -cy l inder -w i th -sp l i t te r -p la te m o d e ! p o s i t i o n e d at t h e c e n t e r o f t h e test s e c t i o n . - 2 . 0 - 1 — 1 1 1 I I 1 l l l 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Open Area Ratio Figure 6 .32 : Var ia t ion o f p ressure coe f f i c ien t at B = 1 0 0 ° as a f unc t i on of O A R fo r 4 s izes o f c i rcu lar -cy l inder-wi th-sp l i t te r -p la te m o d e l p o s i t i o n e d at t he cen te r of the test s e c t i o n . o « A : : : • : . : : : : : -2.0 i i I I 1 1 — r — — i 1 r— 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Open Area Ratio Figure 6 .33 : Va r ia t i on o f p ressu re coe f f i c i en t at 0 — 1 8 0 ° as a f u n c t i o n o f O A R f o r 4 s i zes o f c i rcu la r -cy l inder -w i th -sp l i t te r -p la te m o d e l —• p o s i t i o n e d at t h e c e n t e r o f t h e tes t s e c t i o n . - P » - 0 . 4 — t — i — i — i i i — r — i — I 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Open Area Ratio Figure 6.34 : Variation of front drag coefficient as a function of OAR for 4 sizes of circular-cylinder-with-splitter-plate model positioned at the center of the test section. 2 . 0 X i 1 1 1 1 1 i i i i r 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Open Area Ratio Figure 6.35 : Variation of rear drag coefficient as a function of OAR for 4 sizes of circular-cylinder-with-splitter-plate model positioned at the center of the test section. 146 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 Open Area Ratio Figure 6 .36 : Var ia t ion o f d r a g coe f f i c i en t as a f u n c t i o n o f O A R f o r 4 s izes o f c i rcu la r -cy l inder -w i th -sp l i t te r -p la te m o d e ! p o s i t i o n e d at t he c e n t e r o f t h e tes t s e c t i o n . -I—I 1 I I 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 Open Area Ratio Figure 6 .37 : Va r ia t i on of b l o c k a g e - c o r r e c t i o n fac to r as a f u n c t i o n o f O A R fo r 4 s i zes o f c i rcu lar -cy l inder-wi th-sp l i t te r -p la te m o d e l p o s i t i o n e d at t he cen te r o f the test s e c t i o n . 0.10 ~i 1 1 I I I I I 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 Open Area Ratio Figure 6 .38 : Va r ia t i on o f s tanda rd d e v i a t i o n as a f u n c t i o n o f O A R fo r 4 s i zes o f c i rcu la r -cy l inder -w i th -sp l i t te r -p la te m o d e l p o s i t i o n e d at t he c e n t e r o f t he test s e c t i o n . Figure 6.39 : G e n e r a l f l o w pat tern in t he p l e n u m s fo r n o r m a l o p e r a t i o n . -Pa CD 3! era c 3 en o ifi <"> 2 " —» n n «a ? S. w § W 5' CL _ ro ~ i . . 3 " IA 3 -g_ r o 5" S 9 3 T J . OJ _ j-» T J rB 3 r o 1 s 3 g, 2- ft S* 3 -2 c ro a. o. 5 3 " _ * rT o •> ro 3 ro * 5- ro ro » ro _ ui o -0 .8 -0.4 —I Pressure Co«yfflclWit 0.0 -0 .2 -4— 0.2 -I— 0.4 -4— O.S x + » o fill an 5* 5*6" 5* uoo> X+ SB X 4- 09 X + DO X + X • X 4-X • at s* I Prtmufti Coofflcktnt -0 .8 -0.4 -0 .2 -I— 0.0 -4— 0.2 -4— 0.4 -4— 0.8 . X + B - 3 Bock Block Block Block X-0B ° •s-s-s-s X4-09 1 _ ,ff 6-5* 6" X + DO •? • apito 0' X + 0>O 1 uibia z- X + D> Q X +• P> 8 X + ><3 f 5 ft I" 5* . CT •0 .8 -0.4 -I -0.2 -I 0.0 —I— 0.2 0.4 O.S 1 III! an » 1 m 'tm ,6-5-6-6-x* 00 I 8.3 13.8 25.0 33.3 x 4- t»a X X 4- e>8 + ra tm_ o X + ra o* Nb. of Soli : 14 Opon Aroo Ratio : 0.490 I * 8 2 2 2 8 X • + * * X X -s.o O Btockog* Ratio t 6.3 f A Btockog* Ratio : I3.B I 4 Btockog* Ratio : 25.0 I X Btockog* Ratio : 33.3 I i — ' r ( d ) -3.0 -'y CM)1 ° s.o s.o Nb. of Skjti : 13 Opon Ar*o Ratio : 0.526 fi 8 s 8 4 X + 4 4 X X X 9.0 O Btockog* Ratio : 8.3 I A Btockog* Ratio t 13.8 I 4 Btockog* Ratio : 25.0 I X Btockog* Ratio : 33.3 f -1 ' r (e) -s.o ?-s.o s.o Nb. of Slat* : 12 Open Ar*a Ratio : 0.563. 4 A O 4 6 a g fi fi * 4 4 4 * X X -S .O O Btockog* Ratio : 8.3 I A Btockog* Ratio : 13.B J 4 Btockog* Ratio : 25.0 < X Btockog* Ratio : 33.3 I -I ' r (f) -s.o s.o s.o Figure 6.40 (a) t o (I) : P l e n u m p ressu re d i s t r i bu t i ons fo r 4 s i z e s o f c i rcu lar -cy l inder -wi th-sp l i t te r -p la te m o d e l p o s i t i o n e d at t h e c e n t e r o f t h e test s e c t i o n . Nb. of SMI : 11 Open A S M Ratio t 0.599 A O A O X s O Btockog* Ratio : A Blockag* Ratio : 4 Btockago Ratio s x Btockog* Ratio : a a • x a a + • x * 8.9 I 13.8 1 25.0 I 33.31 ( g ) -5.0 -t--9.0 -t- -1-- 0 r (W° 9.0 5.0 Nb. of Stall Op*n Ar*o Ratio + A O A e 10 0.635 O Btockog* Ratio t A Btockog* Ratio : + Btockog* Ratio : X Blockag* Ratio : if 4 a • + + x x a + x 8.3 J 13.8 I 25.0 I 33.3 I (h) 9.0 - r --9.0 •+- -I-9.0 s.o Nb. of Stat* i 9 Open Aroa Ratio i 0.672 A e A e O Blockag* Ratio : A Blockag* Ratio : 4 Btockog* Ratio : X Blockag* Ratio I e 4 a 4 X 8.3 I 13.8 I 25.0 I 33.3 1 a 4 x a 4 x ( D -s.o -s.o -+- -t-9.0 9.0 Figure 6.40 (a) t o (I) : P l e n u m p ressu re d i s t r i bu t i ons fo r 4 s i zes o f c i rcu lar -cy l inder -wi th-sp l i t te r -p la te m o d e l p o s i t i o n e d at t h e c e n t e r o f t h e tes t s e c t i o n . Nb. of Stall : 8 Opto Ar*a Ratio i 0.708 A o A O O Bloekago Ratio : Btockog* Ratio : Blockag* Ratio Blockag* Ratio : X 6 4 X 8.3 I 13.81 25.0 J 33.3 I e e 4 4 X * (j) -5.0 -1--s .o ?-5.0 S.O X 4 A 6 Nb. of Stall : 7 Op*n Ar*a Ratio i 0.745 X 4 A O A O O Blockag* Ratio A Btockog* Ratio 4 Btockog* Ratio X Blockag* Ratio X i 8.3 j 13.8 I 25.0 I 33.3 I 4 X (k) 9.0 -r--3.0 et 7-9.0 S.O 4 X A Nb. of Stats : Opsn Aroa Ratio : 0 1.000 a Btockog* Ratio t A Btockog* Ratio : 4 Btockog* Ratio : X Btockog* Ratio : A 9 I « I 8.3 f 13.8 I 25.0 X 33.3 I (1) 9.0 -t--9.0 -r- •+-- i o 1.0 r ('••») 9.0 5.0 Figure 6 .40 (a) t o (I) P l e n u m p ressu re d i s t r i bu t i ons fo r 4 s i zes o f d rcu la r -cy l inder -w i th -sp l i t te r -p la te m o d e l p o s i t i o n e d at t h e c e n t e r o f t h e test s e c t i o n . Figure 6.41 : G e n e r a l f l o w pat tern i n the p l e n u m s fo r e x t r e m e c o n d i t i o n s . 154 C D O c 75 9 O u 3 to CM + O o Nb. of Slots : 12 Open Area Ratio : 0.563 Plate Position : 22.0 O O © © O + a. o _ O Blockage Ratio : 8.3 J A Blockage Ratio : 19.4 X + Blockage Ratio : 33.3 Z -5.0 —I— -3.0 -1.0 y (feet) T— 1.0 I— 3.0 S.O Figure 6 .42 P l e n u m p ressu re d is t r i bu t ions c o r r e s p o n d i n g t o tes t i ng o f n o r m a l flat p la tes at 22 i n c h e s u p s t r e a m o f t h e test s e c t i o n c e n t e r . O A R = 0 .563 

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