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

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D E V E L O P M E N T OF T H E  T O L E R A N T WIND T U N N E L FOR  B L U F F BODY  TESTING by MICHEL  HAMEURY  M.A.Sc, ECOLE POLYTECHNIQUE, A THESIS SUBMITTED  1982  IN PARTIAL FULFILMENT  THE REQUIREMENTS DOCTOR  FOR  OF  THE DEGREE  OF  PHILOSOPHY  in THE  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 to the  required standard  THE UNIVERSITY  OF BRITISH  February •  conforming  COLUMBIA  1987  MICHEL HAMEURY,  1987  OF  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.  2.  3.  INTRODUCTION  1  1.1  Generalities  1  1.2  An Overview of the Related Literature  4  THE TOLERANT TEST SECTION  7  2.1  General Description  7  2.2  Degrees of Freedom  8  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  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  3.2  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  Solid-Wall Confined Flow Results  27  4.2.1 Flat Plate Model  27  4.2.2 Circular Cylinder Model  28  Tolerant Wind Tunnel Results  29  4.3.1 Flat Plate Model  29  4.2  4.3  iii  4.3.2 Circular Cylinder Model 5.  6.  31  EXPERIMENTAL ARRANGEMENT  34  5.1  34  Apparatus and Equipment  5.2 Test Procedure  37  5.3  Error Analysis  37  5.4  Flow Visualization  38  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  6.2  6.3  ,  6.1.4 Effect of Model Position  44  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  Effect of Splitter Plate  50  6.3.1 Model Pressure Distribution  '.  51  6.3.2 Variation With OAR  52  Plenum Flow  53  CLOSING COMMENTS  56  7.1  Concluding Remarks  56  7:2  Recommendations for Future Work  58  6.4 7.  43  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 : numerical calculation in transform plane with analytical solution. Given C fc = - 1.38, N = 70  comparison of  Pressure distribution over a circular cylinder in unconfined flow : numerical calculation in transform plane with analytical solution. Given C fc = - 0.96, @ = 80° , N = 70  comparison of  p  Figure  4.2 :  p  s  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 : numerical calculation in physical plane with analytical solution. Given C fc = - 1.38, N = 60  comparison of  Pressure distribution over a circular cylinder in unconfined flow : numerical calculation in physical plane with analytical solution. Civen Cpfc = - 0.96, p\. = 80° , N = 60  comparison of  p  Figure  4.5 :  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 5 - - 1.0, h/H = 1/3 , N(model) = 80, N(wall) = 20 p  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 fc = - 1.0 , h/H = 1/3 , CF = 0.6749 p  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 6 = - 1.0 , h/H = 1/3 , Wall Length = 12 p  vi  Figure  4.10 :  Variation of base pressure coefficient with wall length, for a normal flat plate in confined flow. Given C = - 1.0 , h/H = 1/3 , N(model) = 80, N(wall) = 20 p  Figure  4.11 :  Variation of base pressure coefficient with blockage ratio, for a normal flat plate in confined flow. Given C = - 1.0 , N(model) = 80 , N(wall) = 20 p  Figure  4.12 :  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 = - 0.96 , 0 = 80° , h/H = 1/3 , N(model) = 80 , N(wall) = 20  4.14 :  4.15 :  S  o  S  Variation of base pressure coefficient with number of panels on solid walls, for a circular cylinder model in confined flow. Given C = - 1.0 , p\. = 80° , h/H = 1/3 , Wall Length = 12 p  Figure  o  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 = - 0.96 , 0 = 80° , h/H = 1/3 , CF = 0.7827 p  Figure  o  4.13 :  p  Figure  o  Variation of blockage-correction factor with blockage ratio, for a normal flat plate in confined flow. Given C = - 1.0, N(model) = 80 , N(wall) = 20 p  Figure  o  4.16 :  o  Variation of base pressure coefficient with wall length, for a circular cylinder in confined flow. Given C fc = - 0.96, P p  Figure  4.17:  s  = 80° , h/H = 1/3 , N(model) = 80, N(wall) = 20  Variation of base pressure coefficient with blockage ratio, for a circular cylinder in confined flow. Given C fc = - 1.0, p\. = 80° , N(model) = 80, N(wall) = 20 p  Figure  4.18  : Variation of blockage-correction factor with blockage ratio, for a circular cylinder in confined flow. Given C = - 1.0, p\. = 80° , N(model) = 80 , N(wall) = 20 p  o  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 = - 0.96 , /3«. = 80° p  o  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 5 = - 0.96 , /3 = 80° p  Figure  4.24 :  S  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 = - 0.96, /3 = 80° p  Figure  4.25 :  o  S  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 fc = - 0.96 , /3 = 80° p  Figure  4.26 :  S  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 fc = - 0.96 , /3 = 80° p  Figure  4.27 :  S  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 £ , = - 0.96 , 0 = 80° p  S  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 = 1 0 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): Re = 1 0  Pressure distributions over 4 sizes of circular cylinder model. 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 = 1 0 , OAR = 0.453 , AORT = 1.5 5  Figure  6.29 :  Pressure distributions over 4 sizes of circular cylinder model tested between non-evenly spaced slatted-wall. Re = 10 , OAR = 0.453 , AORT = 3.0 s  Figure  6.30 (a) to (m) : Pressure distributions over 4 sizes of circular-cylinder-splitter-plate model. Re = 1 0 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  Figure  6.41 :  Figure  6.42 :  (a) to (I) : Plenum pressure distributions for 4 sizes of circular-cylinder-with-splitter-plate model positioned at the center of the test section. General flow pattern in the plenums for extreme conditions. 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.  ;  Cp  Base pressure coefficient.  0  ^pmin  Minimum pressure coefficient.  Cp  Empty-test-section pressure coefficient.  0  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,,s  2  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.  0  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 , .  S  Transform plane. 0  Angular position on y in the $-plane.  K  Normalized separation velocity.  V  Fluid kinematic viscosity.  xiii  p  Fluid density.  }p  u  Stream function due to uniform flow. Stream function due to vortex sheets.  \b  s  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 . The unsteadiness of the flow is also D  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 O N 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 wake,bounded  2  . The  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 C p ^ , which also determines the separation velocity *cU through Bernoulli's equation:  K  = (  1  ~ pfa >*  (3-D  c  The angular position 5 and strength Q of the sources are determined by the requirements of separation positions at S , , S , zero velocity (stagnation points) at S ^, S 2  $-plane and a separation velocity equivalent to KU at S,, S  2  2  in the  in the Z-plane. The conformal  mapping transformation, Z = f($), is chosen so as to make the two stagnation points S ^ ,S  2  ,  critical points in the $-plane in order to insure tangential separation in the physical Z-plane. In the particular case where the model is a flat plate, the separation positions are well defined and the well known Joukowski transformation is chosen to map the vertical slit onto a circle :  a Z = f($)=  2  $  (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  sec5 = K and the source strength is  (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 0 2  Cftd) = 1  (cos6 - cosfl)  (3.6) 2  y = *hsin0  (3.7)  For the circular cylinder model the mapping transformation is  1  Z = f($) = $ - cota  ($ - cota)  (3.8)  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 /3 , assumed known empirically, in the S  Z-plane by  a = i(7r-/3 ) s  (3.10)  The diameter of the circular cylinder is given by  h = 4cscp\. The source positions are  (3.11)  17  sin a 3  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 c o s 0 + c o s a ) 2  Cp{6) = 1 - [  cos6 - cos©  ]  2  (3.14)  The angular position (i on C, in the Z-plane, corresponding to 6 in the $-plane is given by  sin/3 = cosa [  seca - cos0 J(seca+cosa) - cos0  ] sin0  (3.15)  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-surfacesingularity 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// from the vortex sheets and source v  19 flows  from the wake sources. Hence  *k  * u  =  +  +v  +  *s  (  3  1  6  )  for which  \\/ = lm[ U Z e  ] = U (y cosa - x sina)  ia  u  where  U  is the uniform flow velocity ( U = 1);  y, x a  (3.17)  are the boundary coordinates; is the flow angle (a = 0) ;  or after simplification  * = y  (3.18)  u  and 1 4>v = ~  2-n  f  7<s) r<x,y;s) ds ln  (3.19)  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^) + X (x,y)] 2;r 2  (3.20)  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  ^k~~  Q S 7<s) i n r(x,y;s) d s - - [X,(x,y) + X (x,y)] = y 27T 2TT 2  (3.21)  T h e v o r t i c i t y d i s t r i b u t i o n ( 7(s) ) a n d t h e s o u r c e s t r e n g t h Q are t h e p r i n c i p a l u n k n o w n s f r o m w h i c h t h e v e l o c i t y d i s t r i b u t i o n a n d t h e r e f o r e t h e p r e s s u r e d i s t r i b u t i o n c a n b e o b t a i n e d . In t h e s p e c i a l c a s e w h e r e t h e b o u n d a r y o f t h e m o d e l is a c l o s e d c o n t o u r , t h e v e l o c i t y d i s t r i b u t i o n is e x a c t l y i d e n t i c a l t o t h e v o r t i c i t y d i s t r i b u t i o n ( s e e K e n n e d y [32]). H o w e v e r , w h e n t h e m o d e l is a n o p e n c o n t o u r , as i n t h e c a s e h e r e , t h e v e l o c i t y d i s t r i b u t i o n m u s t b e c a l c u l a t e d f r o m t h e d i f f e r e n t c o n t r i b u t i o n s : u n i f o r m f l o w , v o r t i c e s a n d s o u r c e s ( s e e A p p e n d i x 3). T h e i n t e g r a l e q u a t i o n (3.21) is e x a c t ; n o a p p r o x i m a t i o n h a s b e e n m a d e y e t . H o w e v e r , s o l v i n g f o r 7(s), Q , a n d ^  c a n o n l y b e d o n e t h r o u g h a n a p p r o x i m a t i o n . A n u m e r i c a l s o l u t i o n is  o b t a i n e d b y d i s c r e t i z i n g t h e s u r f a c e s s i n t o N s t r a i g h t - l i n e p a n e l s Sy, o n t h e 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,-, y -), t h e e q u a t i o n (3.21) is a p p l i e d . T h e result is a s y s t e m o f N ;  7  linear e q u a t i o n s :  " tj ij " K  Q  s  i  =  i=1,2,...,N  ' i R  (3.22)  where  1 K :1 = -  lit  /ln[r(x ,y;s:)]ds /  /  ' ' l l  (3.23)  are c a l l e d i n f l u e n c e c o e f f i c i e n t s . K^- is t h e r e f o r e t h e i n f l u e n c e o f p a n e 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 o n l y . T h u s , . t h e s u m m a t i o n o f all  K y , f o r / = 1,...,N, is t h e e f f e c t o f ;  all t h e v o r t e x p a n e l s o n t h e c o n t r o l p o i n t C -. T h e result o f i n t e g r a l (3.23) is g i v e n in A p p e n d i x 2. ;  Also,  1  S- = ;  2TT  [ X, ( x - , y ) + X ( x , y,-) ] ;  2  ;  (3.25)  21  and R; = y -  (3.26)  ;  W h e n this d i s c r e t i z a t i o n is a p p l i e d t o t h e airfoil-slats, a n e x t r a e q u a t i o n p e r airfoil is r e q u i r e d t o fix t h e a m o u n t o f c i r c u l a t i o n a r o u n d t h e airfoil-slat; t h u s s a t i s f y i n g w h a t is k n o w n as t h e K u t t a 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 a n a d d i t i o n a l c o n t r o l p o i n t  s i t u a t e d at  t h e trailing e d g e o f e a c h airfoil.  W h e n t h e d i s c r e t i z a t i o n is a p p l i e d t o s o l i d w a l l s , e i t h e r a full s o l i d w a l l o r t h e s o l i d s e c t i o n s at t h e e n t r a n c e a n d e x i t , t h e v a l u e o f ty^ o n t h e s e s u r f a c e s are s p e c i f i e d a n d e q u a t i o n  (3.22)  becomes  -  7  y K;/ ~ Q S,- = R, = y - - ^  w h e n ; belongs to c o m p o n e n t k . A n d since  (3.28)  #  ^  =  y;  o n the  ( solid wall )  c o m p o n e n t w e h a v e R,- = 0. W h e n t h e d i s c r e t i z a t i o n is a p p l i e d t o t h e b l u f f b o d y , in e i t h e r t h e p h y s i c a l o r  the  t r a n s f o r m p l a n e , t h e s t r e a m f u n c t i o n i//^ is arbitrarily s e t at z e r o a n d a n e x t r a e q u a t i o n is r e q u i r e d t o s o l v e f o r Q . A n a d d i t i o n a l e q u a t i o n c a n b e o b t a i n e d w h e n e q u a t i o n ( 3 . 2 1 ) is a p p l i e d t o a control point c h o s e n c l o s e to t h e separation point in o r d e r t o force the streamline to leave the s u r f a c e of t h e b o d y at a f i x e d g i v e n p o i n t . B u t , n u m e r i c a l e x p e r i m e n t s h a v e s h o w n t h e r e s u l t s t o b e v e r y s e n s i t i v e t o t h e e x t r a - c o n t r o l p o i n t p o s i t i o n as w e l l as t h e s i z e o f t h e p a n e l s s u r r o u n d i n g it. T h e m e t h o d a d o p t e d h e r e u s e s t h e c o n d i t i o n that v o r t i c i t y 7 ( s ) s h o u l d v a n i s h at t h e s e p a r a t i o n p o i n t . T h i s is n o t a real f l o w c o n d i t i o n b u t it arises in t h e p o t e n t i a l f l o w m o d e l in  22  o r d e r t o h a v e t h e s e p a r a t i n g s t r e a m l i n e s t a n g e n t t o t h e e d g e s o f t h e m o d e l . T h i s t e c h n i q u e has also the advantage of r e m o v i n g o n e equation. Finally, t h e d i s c r e t i z a t i o n o f t h e b o u n d a r y s h o u l d b e s u c h t h a t t h e s o u r c e s are p l a c e d b e t w e e n t w o p a n e l s in o r d e r t o r e d u c e t h e s i n g u l a r i n f l u e n c e o f t h e s o u r c e s at t h e c o n t r o l p o i n t of adjacent panels. N o w , u s i n g matrix n o t a t i o n , e q u a t i o n (3.21) c a n b e w r i t t e n f o r t h e k'^ c o m p o n e n t as  +  where  [K*.]  k {Sj}  k  k  { 1 } + [ KJfy. ] { 7y } + Q {  = [-^L_  V/'  i = {—}  {*/} =  ]  }= { }  (3.29)  ;  S  V  ;  i  R  [—}  i n c l u d e t h e a d d i t i o n a l e q u a t i o n c a l c u l a t e d at t h e e x t r a - c o n t r o l p o i n t . A s s e m b l i n g all t h e u n k n o w n s in o n e v e c t o r , w e g e t  A*. 1  S?  f  k }  I  Q  <  in w h i c h w e still h a v e t o a p p l y 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 s e p a r a t i o n p o i n t . T h i s 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 h e m a t r i x [ K^- ] a n d o n e e l e m e n t in t h e v e c t o r s { 7y } a n d { Ry } c o r r e s p o n d i n g t o t h e t e r m in w h i c h 7^  =  0. In this p a r t i c u l a r c a s e w h e r e t h e r e is o n l y o n e  c o m p o n e n t in t h e u n i f o r m f l o w f i e l d (i.e., t h e bluff b o d y m o d e l ; flat p l a t e o r c i r c u l a r c y l i n d e r ) ,  23  [ Kyy ] is a N x N s u b - m a t 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 o f 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 t h e n u m b e r o f p a n e l s ( a n d c o n t r o l p o i n t s ) in t h e d i s c r e t i z a t i o n . \ ^ a n d Q are scalar v a l u e s . W h e n t h e r e are t w o c o m p o n e n t s in t h e f l o w f i e l d , e . g . a t e s t m o d e l w i t h N  control  p o i n t s a n d a w a l l c o m p o n e n t h a v i n g M d i s c r e t i z e d c o n t r o l p o i n t s o n its s u r f a c e , t h e  global  matrix b e c o m e s  1  o  s?  0  1  S  f >  ]  I Q  )  7  <  k+1  If t h e w a l l c o m p o n e n t is a n airfoil-slat w i t h M c o n t r o l p o i n t s C -, t h e airfoil-slat ;  has  t h e r e f o r e ( M - 1) d i s c r e t e p a n e l s a n d a n e x t r a e q u a t i o n s is p r o v i d e d b y t h e K u t t a c o n d i t i o n . T h e s u b - m a t r i x [ K^- ] has a d i m e n s i o n o f N x ( N + M ) w h i l e [ K ^ J sub-matrix. The sub-vectors { {S^*  1  { /* R  The  1  } and { 7 ^  global  +  matrix  1  1  ] is a M x ( N + M )  }, { R^ } a n d { 7 y } h a v e N e l e m e n t s w h i l e t h e s u b - v e c t o r s  } have M elements. is  designed  to  grow  automatically  to  accept  up  to  15  wall  c o m p o n e n t s , i.e., s u b - m a t r i c e s . A t y p i c a l d i s c r e t i z a t i o n of t h e b o u n d a r i e s c o m p r i s e s 8 0 p a n e l s f o r t h e bluff b o d y (flat p l a t e o r c i r c u l a r c y l i n d e r ) , 2 0 p a n e l s p e r airfoil-slats a n d 1 0 p a n e l s f o r e a c h o f t h e inlet a n d o u t l e t solid walls. In t h e c o m p u t e r i m p l e m e n t a t i o n t h e p r o g r a m m a k e s u s e o f t h e s y m m e t r y t o r e d u c e t h e size of the matrices. 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 ( 1 0 0 x 1 0 0 ) matrix t a k e s a b o u t 1 C P U - m i n u t e o n a VAX-11/750 computer while  it t a k e s a b o u t  2 C P U - h o u r s to solve for a  24  ( 4 0 0 x 4 0 0 ) m a t r i x . T h u s , t h e s o l u t i o n o f m a n y w a l l c o n f i g u r a t i o n s (for d i f f e r e n t O A R ) r e q u i r e s several 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 0  S  = 80  degrees, the numerical results agree well with the analytical calculations but only on a 45 degree arc starting from the stagnation point. O n 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 r a n s f o r m p l a n e a n d t h e d e r i v a t i v e o f t h e m a p p i n g t r a n s f o r m a t i o n v a n i s h , as t h e y s h o u l d , at t h e s e p a r a t i o n p o i n t , a n d that t h e v e l o c i t y in t h e p h y s i c a l p l a n e is o b t a i n e d b y d i v i d i n g t h e f o r m e r b y t h e latter. T h i s s i n g u l a r i t y d o e s n o t o c c u r w h e n t h e p r o b l e m is s o l v e d analytically s i n c e t h e L'Hopital rule can be used. T h e e f f e c t o f t h e d i s c r e t i z a t i o n o n t h e n u m e r i c a l c a l c u l a t i o n is s h o w n in F i g u r e 4 . 3 w h e r e the  source strength  v a l u e is p l o t t e d  against the  number  of  panels u s e d to  describe  the  c i r c l e - m o d e l in t h e t r a n s f o r m p l a n e . N o t e t h a t t h e d i s c r e t i z a t i o n 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 c o n s t r a i n t s s u c h as t h e s o u r c e a n d t h e s e p a r a t i o n p o s i t i o n s w h i c h n e e d t o b e p l a c e d b e t w e e n t w o panels for m o r e c o n s i s t e n t results. T h e transform-plane discretization leads t o g o o d b e h a v i o u r f o r t h e flat p l a t e f o r w h i c h t h e s o u r c e s t r e n g t h r e a c h e s a v a l u e w e l l w i t h i n 0 . 0 8 % o f t h e a n a l y t i c a l v a l u e ( Q = 1 . 0 1 8 1 9 ) f o r 7 0 p a n e l s o n t h e c i r c l e ( that is 34 p a n e l s o n t h e f r o n t part o f t h e c i r c l e c o r r e s p o n d i n g t o t h e f r o n t part o f t h e flat p l a t e ) . H o w e v e r , t h e d i s c r e t i z a t i o n m e t h o d u s e d h e r e g i v e s p o o r results in t h e c a s e o f t h e c i r c u l a r c y l i n d e r f o r w h i c h t h e s o u r c e s t r e n g t h v a l u e o s c i l l a t e s i r r e g u l a r l y w h i l e s t a y i n g a w a y , b y as m u c h as 2 . 5 %, f r o m t h e a n a l y t i c a l s o u r c e s t r e n g t h v a l u e o f Q = 0 . 6 4 8 4 2 , e v e n w h e n t h e n u m b e r o f p a n e l s 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 c a n a l s o b e a p p l i e d t o d i s c r e t i z e t h e a c t u a l m o d e l in t h e physical plane. A n example of pressure distribution  o v e r a flat p l a t e a n d a c i r c u l a r c y l i n d e r  m o d e l , c o m p u t e d in t h e p h y s i c a l p l a n e , are s h o w n in F i g u r e s 4 . 4 a n d 4 . 5 , r e s p e c t i v e l y . T h e s e figures  show good  agreement  with the  analytical calculations o v e r m o s t  of  the  domain,  i n c l u d i n g t h e b a s e p r e s s u r e at t h e s e p a r a t i o n p o i n t . H o w e v e r , t h e r e is i n b o t h c a s e s a p o i n t w h e r e n u m e r i c a l calculations e n c o u n t e r a singularity. This effect 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 t h e slit t o c r e a t e t h e d i s p l a c e m e n t t h i c k n e s s o b s e r v e d in t h e w a k e o f bluff b o d i e s . F o r t u n a t e l y , t h e s i n g u l a r i t y a f f e c t s o n l y a s m a l l part o f t h e p r e s s u r e d i s t r i b u t i o n w h i c h c a n o f t e n be o m i t t e d w i t h o u t l o s i n g any essential i n f o r m a t i o n .  27  F i g u r e s 4 . 6 (a) a n d (b)  s h o w the variation  of  source strength  and base pressure  c o e f f i c i e n t , r e s p e c t i v e l y , w i t h t h e n u m b e r o f p a n e l s f o r b o t h t h e flat p l a t e a n d t h e  circular  c y l i n d e r m o d e l . B o t h f i g u r e s s h o w an i d e n t i c a l s m o o t h b e h a v i o u r w i t h a n i n c r e a s e in t h e n u m b e r o f p a n e l s u s e d t o d e s c r i b e t h e m o d e l . T h e n u m e r i c a l s o l u t i o n o f t h e flat p l a t e m o d e l , i n particular, d e m o n s t r a t e s high 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 strength value a n d base pressure c o e f f i c i e n t w i t h i n 0.05 % o f t h e a n a l y t i c a l v a l u e , f o r a d i s c r e t i z a t i o n o f 6 0 p a n e l s . T h e numerical s o l u t i o n of the circular cylinder s h o w s , h o w e v e r , an accuracy w i t h i n a b o u t 1% f o r a d i s c r e t i z a t i o n o f 1 0 0 p a n e l s . In o r d e r t o a v o i d a s i n g u l a r i t y c l o s e t o a s e p a r a t i o n p o i n t w h e r e t h e p r e s s u r e v a l u e is o f critical i m p o r t a n c e , as w e l l as b e c a u s e t h e p r o c e d u r e is s i m p l e r , t h e n u m e r i c a l c a l c u l a t i o n w i l l , f r o m h e r e o n , b e p e r f o r m e d in t h e p h y s i c a l p l a n e o n 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 F L A T P L A T E 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 r e s s u r e d i s t r i b u t i o n o v e r a n o r m a l flat p l a t e e x p e r i e n c i n g a b l o c k a g e ratio of  h/H  =  1/3  in a s o l i d - w a l l e d w i n d t u n n e l  is c o m p a r e d in F i g u r e 4 . 7  to  E l - S h e r b i n y ' s [25] a n a l y t i c a l s o l u t i o n . T h e part o f t h e c u r v e a f f e c t e d b y t h e s o u r c e s i n g u l a r i t y is o m i t t e d f o r clarity. A b l o c k a g e c o r r e c t i o n f a c t o r , e v a l u a t e d 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 t h i s example and found to be C F =  0.6749. This factor w h e n divided by the s o l i d wall freestream  s p e e d g i v e s t h e b e s t a g r e e m e n t in a l e a s t - s q u a r e s e n s e w i t h t h e r e f e r e n c e f r e e - a i r p r e s s u r e d i s t r i b u t i o n . F i g u r e 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 t h e p o s s i b i l i t y o f u s i n g a s i m p l e c o r r e c t i o n f a c t o r t o e v a l u a t e w a l l e f f e c t s o n a m o d e l . B e c a u s e t h e C F m e a s u r e s , relative t o a s e t of r e f e r e n c e - t e s t d a t a , t h e o v e r a l l e f f e c t o f w a l l i n t e r f e r e n c e s o n a 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 , it can therefore configurations.  be used for  comparing the  effects  of  different wall (including  slotted-wall)  28  T h e n u m b e r of panels u s e d t o d e s c r i b e the s o l i d wall can have a significant influence o n the pressure distribution a n d in particular o n the b a s e pressure w h i c h will b e an i m p o r t a n t characteristic for c o m p a r i n g the effects of different wall configurations ( i n c l u d i n g slotted-wall). F i g u r e 4.9 s h o w s , f o r e x a m p l e , t h a t f o r a flat p l a t e 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 ratio ( h / H ) o f 1/3 b e t w e e n s o l i d w a l l s e x t e n d i n g u p s t r e a m a n d d o w n s t r e a m b y 6 p l a t e w i d t h s , t h e b a s e p r e s s u r e c o e f f i c i e n t r e a c h e s a p l a t e a u w h e n t h e n u m b e r o f p a n e l s is g r e a t e r t h a n 1 2 . T h e e n d (inlet a n d o u t l e t ) e f f e c t is a l s o a n i m p o r t a n t p a r a m e t e r w h i c h c a n m o d i f y t h e p r e s s u r e v a l u e s . T h u s , F i g u r e 4.10 s h o w s that t h e w a l l l e n g t h s h o u l d b e at least 7 t i m e s t h e w i d t h o f t h e flat p l a t e t o h a v e b a s e p r e s s u r e v a l u e s i n d e p e n d e n t o f w a l l l e n g t h . T h e v a r i a t i o n o f b a s e p r e s s u r e c o e f f i c i e n t w i t h b l o c k a g e ratio is p l o t t e d in F i g u r e 4.11. It c o m p a r e s t h e n u m e r i c a l c a l c u l a t i o n s t o E l - S h e r b i n y ' s analytical s o l u t i o n ; t h e a g r e e m e n t is v e r y good. Finally, F i g u r e 4.12 p r e s e n t s t h e v a r i a t i o n o f t h e b l o c k a g e c o r r e c t i o n f a c t o r , C F , w i t h b l o c k a g e ratio. This relation s h o w s a r e m a r k a b l e linearity a n d thus justifies,for small b l o c k a g e ratios, the use of linearized c o r r e c t i o n f o r m u l a e w h e n available.  4.2.2 C I R C U L A R C Y L I N D E R M O D E L This s e c t i o n s u m m a r i z e s the numerically calculated wall interference effects o n a circular cylinder m o d e l for w h i c h the  e m p i r i c a l f r e e - a i r b a s e p r e s s u r e is C p  =  -  0.96 w i t h  flow  s e p a r a t i o n o c c u r r i n g at a n a n g l e o f / 3 = 8 0 d e g r e e s f r o m t h e f r o n t s t a g n a t i o n p o i n t . S  T h e p r e s s u r e d i s t r i b u t i o n 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 r a t i o ( h / H ) o f 1/3 is c o m p a r e d in F i g u r e 4.13 w i t h t h e free-air a n a l y t i c a l s o l u t i o n . It is n o t c o m p a r e d , as in t h e p r e v i o u s s e c t i o n , t o E l - S h e r b i n y ' 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 r e s u l t s l o o k m o r e like the  n u m e r i c a l c a l c u l a t i o n s of  F i g u r e 4.2  for w h i c h  divisions by very small n u m b e r s  (and  eventually z e r o ) was the cause of inaccuracies n e a r the separation p o i n t . T h e curve of Figure 4.13 is m o r e r e a l i s t i c s i n c e it s h o w s a fast d e c r e a s e in p r e s s u r e f o l l o w e d b y a p r e s s u r e r e c o v e r y w h i c h rises t o b a s e p r e s s u r e at s e p a r a t i o n . T h e r e s u l t s s h o w , a l s o , that t h e p r e s s u r e r e c o v e r y  29  (Cp  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 r a t i o , w h i c h is i n 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 o b s e r v a t i o n s [25,35]. Figure 4.14 c o m p a r e s the c o r r e c t e d numerical pressure distribution w i t h the  free-air  analytical 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 o v e r e s t i m a t i n g the results e s p e c i a l l y b e f o r e t h e p o i n t o f m i n i m u m p r e s s u r e . H o w e v e r , f r o m )3 = 6 0 ° u p t o t h e s e p a r a t i o n p o i n t , t h e p r e s s u r e is l o w e r t h a n t h e f r e e - a i r d a t a b y 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 factor remains a s i m p l e a n d useful t o o l for c o m p a r i n g the effects of different wall configurations. Figures 4.15  and 4.16 s h o w  that t h e  discretization  of  the  wall  and wall  length,  r e s p e c t i v e l y , i n f l u e n c e t h e results in a s a m e m a n n e r as in t h e p r e v i o u s s e c t i o n f o r t h e .flat p l a t e m o d e l . T h i s s u g g e s t s t h e r e f o r e t h a t w a l l d i s c r e t i z a t i o n a n d w a l l l e n g t h are i n d e p e n d e n t o f m o d e l shape. T h e v a r i a t i o n o f b a s e p r e s s u r e w i t h b l o c k a g e ratio a g a i n a g r e e s w e l l w i t h E l - S h e r b i n y ' s s o l u t i o n , as s h o w n in F i g u r e 4 . 1 7 . Finally, F i g u r e 4 . 1 8 s h o w s t h e c o r r e c t i o n f a c t o r , C F , p l o t t e d a g a i n s t t h e b l o c k a g e ratio. A g a i n , t h e r e l a t i o n is a l m o s t p e r f e c t l y l i n e a r .  4.3 T O L E R A N T W I N D T U N N E L RESULTS  4.3.1 F L A T P L A T E M O D E L T h e t h e o r e t i c a l e f f e c t o f d i f f e r e n t o p e n - a r e a ratios o n t h e s u r f a c e p r e s s u r e d i s t r i b u t i o n o f v a r i o u s s i z e s o f flat p l a t e m o d e l is s u m m a r i z e d i n F i g u r e s 4 . 1 9 a n d 4 . 2 0 . T h e s e c a l c u l a t i o n s w e r e p e r f o r m e d f o r m o d e l s p l a c e d at t h e c e n t e r o f t h e t e s t s e c t i o n a n d a n e m p i r i c a l free-air b a s e pressure coefficient of C p  D  = -  1.38.  T h e v a r i a t i o n o f b a s e p r e s s u r e 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 is p l o t t e d in F i g u r e 4 . 1 9 . S t a r t i n g w i t h a l o w O A R v a l u e w h e r e t h e s o l i d - w a l l t y p e o f i n t e r f e r e n c e e f f e c t is felt b y t h e different m o d e l s in a m a n n e r increasing w i t h b l o c k a g e ratios, the base pressure values increase,  30  w i t h i n c r e a s i n g O A R , at rates v a r y i n g w i t h t h e s i z e o f t h e m o d e l ; t h e l a r g e r t h e m o d e l t h e f a s t e r t h e p r e s s u r e rises w i t h O A R . E v e n t u a l l y , t h e b a s e p r e s s u r e c o e f f i c i e n t o v e r s h o o t s t h e g i v e n free-air value ( C p  0  =  -  1.38 ) a n d t h e n r e a c h e s 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 r e s s u r e d e c r e a s e o f erratic b e h a v i o u r . T h e fact t h a t t h e s e c u r v e s r e a c h a m a x i m u m f o l l o w e d b y a r a p i d 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 r e a l i s t i c s i n c e it is k n o w n f r o m e x p e r i m e n t t h a t o p e n - j e t b o u n d a r i e s t e n d t o g i v e h i g h e r b a s e p r e s s u r e t h a n t h e free-air v a l u e . T h e i m p o r t a n t p o i n t o f this g r a p h , h o w e v e r , is t h e n e a r b l o c k a g e i n d e p e n d e n c y o f t h e b a s e p r e s s u r e v a l u e s h o w n at OAR = 0 . 4 9 f o r at least t h r e e o f t h e f o u r b l o c k a g e ratios. F o r t h e three  b l o c k a g e ratios  approximately ( 3 3 . 3 %) at C p  D  ( 8.3 % , 1 9 . 4  %  and  25  % ) the  base pressure coefficients  are  1.40, l o w e r t h a n t h e f r e e - a i r v a l u e b y less t h a n 2 %, w h i l e t h e f o u r t h m o d e l = - 1.35 is h i g h e r t h a n t h e f r e e - a i r v a l u e b y a b o u t 2 %.  It is i n t e r e s t i n g t o n o t e , a l s o , t h a t F i g u r e 4 . 1 9 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 about -  =  0 . 3 8 , t h e t h r e e h i g h e r b l o c k a g e ratios h a v e a C p  0  of  1.50. H o w e v e r , t h e s e r e s u l t s , b e i n g far f r o m t h e f r e e - 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 likely as t h e v a l u e s at OAR = 0 . 4 9 . B e c a u s e o f t h e p r e v i o u s l y m e n t i o n e d e m p i r i c a l a s s u m p t i o n (source  positions  are  obtained  for  free-air  Cp£,  and  kept  constant  for  different  wall  c o n f i g u r a t i o n s ) t h e m a t h e m a t i c a l m o d e l is t h o u g h t t o b e m o s t a c c u r a t e w h e n t h e f l o w f i e l d a r o u n d t h e flat p l a t e r e s e m b l e s t h e f r e e - a i r c o n d i t i o n s f o r w h i c h t h e b a s e p r e s s u r e is t h e g i v e n Cpo =  -1-38. T h e e r r a t i c 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 t h e n u m b e r o f slats is less t h a n 5  s e e m s t o b e d u e t o t h e i n d i v i d u a l e f f e c t o f e a c h slat; in o t h e r w o r d s t h e s l a t t e d - w a 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 felt 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 i k e l y b e c a u s e o f t h e f r e e - s t r e a m l i n e m o d e l u s e d f o r t h e p l e n u m s h e a r layer, t h e f l o w s 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 t h e a n t i c i p a t e d o p e n - j e t r e s u l t s f o r w h i c h the base p r e s s u r e coefficients s h o u l d b e h i g h e r than the free-air value. Figure 4.20 s h o w s , t h r o u g h the variation of the b l o c k a g e correction factor with O A R , the e f f e c t of d i f f e r e n t s l o t t e d - w a l l c o n f i g u r a t i o n s o n t h e o v e r a l l s u r f a c e p r e s s u r e d i s t r i b u t i o n s . T h e  31  fact t h a t t h e g r a p h o f F i g u r e 4 . 2 0 c l o s e l y r e s s e m b l e s t h e o n e o f F i g u r e 4 . 1 9 c o n f i r m s t h e p o i n t t h a t t h e b a s e p r e s s u r e v a r i a t i o n is a r e p r e s e n t a t i v e m e a s u r e o f t h e g l o b a l p r e s s u r e c h a n g e o n t h e s u r f a c e o f t h e m o d e l . N o t e , h o w e v e r , t h a t t h e b e s t O A R v a l u e ( t h e O A R at w h i c h m o d e l s o f different  s i z e e x p e r i e n c e t h e s a m e f l o w c o n d i t i o n s ) is s h i f t e d t o a b o u t 0.41 f o 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 f a c t o r , C F , is a b o u t 0 . 9 9 f o r t h e t h r e e s m a l l e r flat p l a t e s w h i l e t h e largest m o d e l ( 3 3 . 3 % ) h a s a C F just a b o v e 1.0 . T h i s p o t e n t i a l f l o w m o d e l , t h e r e f o r e , p r e d i c t s t h a t a flat p l a t e m o d e l o f b l o c k a g e r a t i o less t h a n 2 5 . 0 % t e s t e d in t h e T o l e r a n t w i n d t u n n e l w i t h a n O A R =  0.41 w i l l e x p e r i e n c e a  r e s i d u a l i n t e r f e r e n c e e f f e c t e q u i v a l e n t t o v e r y l o w b l o c k a g e in a s o l i d - w a l l e d w i n d t u n n e l  for  w h i c h a c o r r e c t i o n factor of o n l y 1 % will b e necessary t o o b t a i n free-air pressure distribution. The standard deviation, associated w i t h the evaluation of the b l o c k a g e correction factor, is p l o t t e d in F i g u r e 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 , t h e v a l u e s are q u i t e l o w ( less t h a n 0 . 0 2 ); t h i s p l o t a l s o s h o w s t h a t t h e e r r o r , after c o r r e c t i o n o f t h e p r e s s u r e d i s t r i b u t i o n , d e c r e a s e s m o r e o r less l i n e a r l y w i t h i n c r e a s i n g O A R t o r e a c h a m i n i m u m v a l u e at O A R = 1.0 . T h i s m e a n s t h a t e v e n in t h e c a s e w h e r e t h e b l o c k a g e c o r r e c t i o n f a c t o r is e q u a l t o unity, t h e p r e s s u r e distribution  is n o t ,  in all p o i n t s  of  the  body  surface, equivalent to  the  free-air  pressure  d i s t r i b u t i o n ; o n a v e r a g e , h o w e v e r , it is t h e b e s t fit. T h e fact that t h e m i n i m u m ( a f t e r - c o r r e c t i o n ) e r r o r o c c u r s at O A R = 1.0 t e n d s t o i n d i c a t e t h a t t h e p r e s e n c e o f airfoil-slats, a l t h o u g h c a p a b l e of r e d u c i n g the b l o c k a g e effect, will also b e r e s p o n s i b l e f o r distorting the pressure distribution at t h e s u r f a c e o f 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 P r e s s u r e d i s t r i b u t i o n s o v e r c i r c u l a r c y l i n d e r s are g r e a t l y a f f e c t e d b y w a l l i n t e r f e r e n c e s . H o w e v e r , b e c a u s e o f t h e n a t u r e o f this m a t h e m a t i c a l m o d e l f o r w h i c h t h e s e p a r a t i o n p o s i t i o n s are g i v e n e m p i r i c a l v a l u e s a n d k e p t f i x e d f o r all c o n f i g u r a t i o n s , it c a n n o t s h o w a n y c h a n g e s in p r e s s u r e d i s t r i b u t i o n d u e t o v a r i a t i o n in s e p a r a t i o n p o s i t i o n s . A g a i n , m o r e s o t h a n t h e flat p l a t e model  case,  only  around  the  s i m u l a t e d free-air c o n d i t i o n s , w h e r e  the  separation  points,  32  /3  S  =  8 0 ° , and base pressure value, C p £ =  -  0 . 9 6 , are v a l i d , is t h e m o d e l e x p e c t e d t o g i v e  reliable i n f o r m a t i o n . P r e s s u r e v a l u e s c a l c u l a t e d at f o u r  different  positions (30°, 60°,70°  and 80°  from  s t a g n a t i o n p o i n t ) o n t h e c i r c l e a n d p l o t t e d in F i g u r e s 4 . 2 2 t o 4 . 2 5 d e s c r i b e t h e s l o t t e d - w a l l e f f e c t o n different sizes of circular cylinder m o d e l s . Q u a l i t a t i v e l y , t h e p l o t s o f F i g u r e s 4 . 2 2 t o 4 . 2 5 r e s s e m b l e t h e g r a p h of F i g u r e 4 . 1 9 s h o w i n g t h e flat p l a t e r e s u l t s . T h e m a j o r d i f f e r e n c e , h o w e v e r , is t h e r e l a t i v e p o s i t i o n o f  the  d i f f e r e n t b l o c k a g e - r a t i o c u r v e s w h i c h vary w i t h t h e l o c a t i o n w h e r e t h e p r e s s u r e is c a l c u l a t e d . F o r i n s t a n c e , in F i g u r e 4 . 2 2 w h e r e t h e p r e s s u r e c o e f f i c i e n t s are c a l c u l a t e d at 3 0 ° f r o m t h e s t a g n a t i o n p o i n t , t h e m a x i m u m v a l u e s o f e a c h b l o c k a g e - r a t i o c u r v e are relatively far apart f r o m e a c h o t h e r t h u s p r e s e n t i n g a c r i s s - c r o s s o f t h e c u r v e s at a r o u n d O A R = 0 . 3 5 . B u t as t h e l o c a t i o n at w h i c h t h e p r e s s u r e c o e f f i c i e n t s are c a l c u l a t e d m o v e s t o w a r d s t h e s e p a r a t i o n p o i n t , t h e b l o c k a g e - r a t i o c u r v e s m o v e d o w n w a r d w i t h r e s p e c t t o t h e s m a l l e s t m o d e l . T h i s e f f e c t r e s u l t s in a c o n t i n u o u s s h i f t i n g o f t h e i n t e r s e c t i o n p o i n t t o w a r d s a m o r e o p e n s l o t t e d - w a l l w i n d t u n n e l . T h u s at 6 0 ° t h e optimum  O A R v a l u e is 0.45 w h i l e it shifts t o 0 . 4 9 w h e n t h e C p ' s are e v a l u a t e d at 7 0 ° . A t  separation p o s i t i o n ( 8 0 ° ) the different blockage-ratio curves 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 the small m o d e l that n o intersection exists a n y m o r e . Figure 4.25 s h o w s a base pressure always l o w e r than the free-air value a n d , therefore, never effectively e x p e r i e n c i n g the effect of an o p e n - j e t b o u n d a r y . T h e b a s e pressure values c l o s e s t t o free-air value 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 h e m a x i m u m o f t h e b l o c k a g e - r a t i o c u r v e s w h i c h is a b o u t OAR =  0.68. D e s p i t e this d i s t o r t i o n o f t h e c y l i n d e r p r e s s u r e d i s t r i b u t i o n  b y t h e s l o t t e d - w a l l , it is  r e m a r k a b l e t h a t t h e b e s t o v e r a l l fit t o t h e f r e e - a i r c o n d i t i o n s , as s h o w n b y t h e v a r i a t i o n o f b l o c k a g e c o r r e c t i o n f a c t o r w i t h O A R in F i g u r e 4 . 2 6 , is s i m i l a r t o t h e flat p l a t e r e s u l t s . T h e optimum  O A R is a g a i n a b o u t  0.42 w h e r e  the  correction to  be applied to  the  pressure  d i s t r i b u t i o n is less t h a n 1 %. T h e s h a p e o f t h e m o d e l u n d e r test, t h e r e f o r e , d o e s n o t s e e m t o greatly a f f e c t t h e o p t i m u m O A R v a l u e .  33  Finally, F i g u r e 4 . 2 7 s h o w s t h e s t a n d a r d d e v i a t i o n t o b e h a v e m u c h t h e s a m e as in t h e flat p l a t e m o d e l c a s e . T h e m a g n i t u d e s o f t h e e r r o r , h o w e v e r , are a b o u t t w i c e as h i g h as t h e v a l u e s o b t a i n e d f o r t h e flat p l a t e 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 m a i n p u r p o s e s o f this 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 t u d y t h e real f l o w in t h e T o l e r a n t w i n d t u n n e 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 d a t a f o r t h e t h e o r e t i c a l m o d e l . T h e first s e c t i o n o f t h i s c h a p t e r , t i t l e d A p p a r a t u s a n d E q u i p m e n t , d e s c r i b e s t h e w i n d tunnel  a n d the  m o d e l s u s e d in t h e  e x p e r i m e n t s . It  also provides information  about  the  i n s t r u m e n t a t i o n u s e d a n d t h e d a t a m e a s u r e d d u r i n g a t y p i c a l test. T h e s e c o n d section d e s c r i b e s the p r o c e d u r e for testing a m o d e l while the third o n e s u m m a r i z e s t h e e r r o r analysis. T h e f o u r t h a n d final s e c t i o n o f c h a p t e r five d e s c r i b e s t h e f l o w v i s u a l i z a t i o n t e c h n i q u e s a p p l i e d t o s t u d y 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 e s t - s e c t i o n insert d e s i g n e d a n d b u i l t b y W i l l i a m s [10] f o r a n e x i s t i n g l o w - s p e e d c l o s e d c i r c u i t w i n d t u n n e l ( F i g u r e 5.1). T h i s insert is 9 1 5 m m w i d e b y 3 8 8 m m d e e p in c r o s s - s e c t i o n , a n d 2 . 5 9 m l o n g . T h e c o n t r a c t i o n ratio t h u s changes from  7 to  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  v e r t i c a l l y in  the  c e n t e r - p l a n e of the w o r k i n g s e c t i o n b e t w e e n s o l i d ceiling a n d floor. B o t h s i d e walls consist of vertical uniformly  s p a c e d ( e x c e p t w h e r e m e n t i o n e d ) a i r f o i l - s h a p e d w o o d e n slats o f s e c t i o n  N A C A 0 0 1 5 a n d c h o r d o f 8 9 m m , at z e r o i n c i d e n c e . T h e s e s l a t t e d w a l l s w e r e s u r r o u n d e d b y 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 d e wall of o n e of the p l e n u m s was m a d e of t r a n s p a r e n t a c r y l i c f o r b e t t e r o b s e r v a t i o n o f t h e f l o w . A f u l l r a n g e o f o p e n - a r e a ratio ( O A R ) c o u l d b e t e s t e d b y v a r y i n g t h e n u m b e r o f slats in t h e w a l l s . T h e t u n n e l w i n d s p e e d r a n g e s f r o m 0 t o a b o u t 4 0 m / s e c a n d is r e g u l a t e d t h r o u g h a f e e d b a c k c o n t r o l s y s t e m . T h e f r e e s t r e a m t u r b u l e n c e l e v e l is c o n s i d e r e d t o b e b e t t e r t h a n 0.1 %. T h e s o l i d f l o o r h a d a t o t a l o f 16 p r e s s u r e t a p s p o s i t i o n e d o n t h e c e n t e r l i n e u p s t r e a m a n d d o w n s t r e a m of the m o d e l . T h e s i d e wall of o n e p l e n u m was also e q u i p p e d w i t h 7 pressure t a p s a l o n g t h e h a l f - h e i g h t l i n e . F i g u r e 5.2 g i v e s t h e e x a c t p o s i t i o n o f all t h e p r e s s u r e t a p s in t h e  34  35  wind tunnel. T h r e e t y p e s o f bluff b o d y m o d e l w e r e t e s t e d ; flat p l a t e s , c i r c u l a r c y l i n d e r s a n d c i r c u l a r cylinder w i t h splitter plate o n the w a k e center line. T h e s h a r p e d g e d flat p l a t e s w e r e o f t h r e e d i f f e r e n t s i z e s ; 3 (7.6), 7 ( 1 7 . 8 ) a n d 1 2 (30.5) i n c h e s ( c m ) 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 r a t i o s o f 8.3 %, 1 9 . 4 % a n d 3 3 . 3 % , r e s p e c t i v e l y . A 4 5 d e g r e e b e v e l w a s c u t a l o n g t h e rear e d g e s s o t h a t t h e b o u n d a r y layer o n t h e f r o n t f a c e w o u l d separate cleanly f r o m the sharp lip. T h e s e m o d e l s w e r e built of steel, a l u m i n u m , o r acrylic d e p e n d i n g o n t h e required section strength, and e q u i p p e d w i t h pressure taps ( b e t w e e n 9 a n d 15 d e p e n d i n g o n t h e s i z e ) d i s t r i b u t e d at t h e m i d - s p a n s e c t i o n o n t h e f r o n t a n d rear f a c e s , as s h o w n in Figure 5.3. F o u r s i z e s of c i r c u l a r c y l i n d e r s 3 (7.6), 5 ( 1 3 . 7 ) , 9 (22.8). a n d 1 2 (30.5) i n c h e s ( c m ) 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 r a t i o s o f 8.3 % , 1 3 . 8 % , 2 5 . 0 %, a n d 3 3 . 3 % , r e s p e c t i v e l y , w e r e a l s o u s e d . T h e y w e r e all b u i l t o f a c r y l i c a n d h a d v e r y s m o o t h s u r f a c e s . E a c h c y l i n d e r w a s e q u i p p e d w i t h p r e s s u r e t a p s l o c a t e d e v e r y 1 0 d e g r e e s o v e r a q u a r t e r o f t h e c i r c u m f e r e n c e at t h e 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 r e s s u r e o r i f i c e w a s i n s e r t e d at 1 8 0 d e g r e e s f r o m t h e first t a p w i t h a n o t h e r o n e d i r e c t l y b e l o w at 5 (13.7) i n c h e s ( c m ) f r o m m i d s p a n . T h e c y l i n d e r s c o u l d b e r o t a t e d i n s u c h w a y that p r e s s u r e d i s t r i b u t i o n o v e r half o f t h e c i r c u m f e r e n c e w a s m e a s u r e d . Symmetry of the time-averaged flow was a s s u m e d a n d m o n i t o r e d through the extra pressure taps. T h e circular c y l i n d e r m o d e l s c o u l d also b e fitted w i t h a splitter plate of 4 c y l i n d e r d i a m e t e r s in l e n g t h . T h e s e p l a t e s w e r e m a d e o f a l u m i n u m s h e e t o f a b o u t 1 m m t h i c k ; t h e y w e r e secured to the tunnel floor and ceiling with the h e l p of 90 degree angle brackets. The gap b e t w e e n the plate a n d the cylinder was always carefully sealed. A l l t h e m o d e l s w e r e m o u n t e d o n a t u r n t a b l e in t h e c e n t e r o f t h e 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 , t h e flat p l a t e m o d e l c o u l d a l s o b e m o u n t e d o n a f i x e d s u p p o r t 2 2 i n c h e s upstream of the center plane.  36  B e c a u s e t h e m o d e l s w e r e 2 7 (68.6) i n c h e s ( c m ) l o n g , a n d t h e r e f o r e e x t e n d e d o u t s i d e the test s e c t i o n , the 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 ceiling w e r e carefully 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 t h e t w o d i m e n s i o n a l i t y o f t h e f l o w o v e r t h e m o d e l , l a r g e e n d - p l a t e s w e r e t r i e d b u t d i f f i c u l t i e s o f i n s t a l l a t i o n a n d i n c o n s i s t e n t results m a d e t h e i r u s e u n r e l i a b l e . 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 s o b e u s e d b u t w a s n o t t r i e d h e r e . T h e e x p e r i m e n t s w e r e c a r r i e d o u t at a R e y n o l d s n u m b e r o f 1 0 , b a s e d o n t h e w i d t h o f 5  t h e flat p l a t e s o r t h e d i a m e t e r o f t h e c i r c u l a r c y l i n d e r s . T h e t u n n e 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 calibrated Pitot-static t u b e , m o u n t e d o f f - c e n t e r l i n e in t h e n o z z l e s e c t i o n b e t w e e n t h e s e t t l i n g - c h a m b e r e x i t a n d test s e c t i o n e n t r a n c e , 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 calibrated against a s e c o n d P i t o t - s t a t i c t u b e m o u n t e d in t h e s l o t t e d w a l l e m p t y t e s t s e c t i o n , o n t h e f l o w c e n t e r l i n e , 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 . D e t a i l s c o n c e r n i n g c a l i b r a t i o n are g i v e n in A p p e n d i x 1. A l s o t h e t o t a l a n d static p r e s s u r e p o r t s o f t h e P i t o t t u b e as w e l l as all t h e p r e s s u r e t a p s w e r e h o o k e d u p , w i t h p l a s t i c t u b e o f 1.6 m m i n s i d e d i a m e t e r a n d a p p r o x i m a t e l y a m e t e r i n l e n g t h , t o a 4 8 - p o r t " s c a n i v a l v e " . Individual pressure orifices c o u l d t h e n b e manually s e l e c t e d a n d f e d t o a " B a r o c e l " pressure transducer w h i c h transforms the input pressure into an a n a l o g electrical s i g n a l . T h e t i m e - a v e r a g e d s u r f a c e p r e s s u r e c o u l d t h e n b e r e a d , as a v o l t a g e , off a n a v e r a g i n g digital v o l m e t e r . T h e t i m e - v a r y i n g e l e c t r i c a l s i g n a l w a s a l s o f e d t o an s p e c t r u m a n a l y s e r t o o b t a i n the vortex-shedding frequencies. Because the m o d e l s w e r e t o u c h i n g floor a n d ceiling t h r o u g h the sealed g a p , direct drag force measurements were not attempted, however drag coefficient c o u l d be estimated from integration of surface pressure distribution.  37  5.2 T E S T P R O C E D U R E A t y p i c a l s e r i e s o f t e s t s starts, after h a v i n g m o d i f i e d t h e e x i s t i n g w i n d t u n n e l b y a d d i n g n o z z l e , test s e c t i o n a n d d i f f u s e r i n s e r t s ( s e e W i l l i a m s [10]), b y a c a r e f u l c a l i b r a t i o n o f t h e n o z z l e P i t o t t u b e u s e d f o r w i n d s p e e d m o n i t o r i n g . O n c e t h e c a l i b r a t i o n is c o m p l e t e d t h e bluff m o d e l is i n s t a l l e d in t h e test s e c t i o n a n d t h e p r e s s u r e t a p s are c o n n e c t e d t o t h e " s c a n i v a l v e " . T h e n , a first w a l l c o n f i g u r a t i o n is m o u n t e d , u s u a l l y s o l i d w a 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 r a t i o , a n d t h e w i n d s p e e d is a d j u s t e d 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 o f 1 0 . Finally, p r e s s u r e t a p s 5  are i n d i v i d u a l l y s e l e c t e d a n d p r e s s u r e is m e a s u r e d w h i l e a s p e c t r a l p l o t is a l s o o b t a i n e d . A n averaging-time of a b o u 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 u n s t e a d i n e s s , w a s allocated t o e a c h p r e s s u r e t a p 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 r e s s u r e c o e f f i c i e n t s a n d s p e c t r a . 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 wall 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 ratio. A f t e r h a v i n g t e s t e d a f u l l r a n g e of o p e n - a r e a r a t i o , t h e 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 f e r e n t s i z e c o r r e s p o n d i n g t o a d i f f e r e n t b l o c k a g e r a t i o , a n d t h e s a m e m e a s u r e m e n t s are d o n e again for a c o m p l e t e set of wall configurations. T h e d a t a are t h e n t y p e d in a c o m p u t e r t o c a l c u l a t e p r e s s u r e a n d d r a g c o e f f i c i e n t s , Strouhal 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 standard deviations.  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 t h e u n c e r t a i n t i e s are d e s c r i b e d in d e t a i l in A p p e n d i x 3. T h e t a b l e b e l o w s u m m a r i z e s the estimation of m a x i m u m uncertainties o n the i m p o r t a n t variables. T h e error o n t h e s u r f a c e p r e s s u r e c o e f f i c i e n t C p is e s t i m a t e d t o b e m a x i m u m at t h e rear o f t h e 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 i g h l y o s c i l l a t o r y . T h e u n c e r t a i n t y w i l l t h e r e f o r e  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 r o n t o f t h e m o d e l (or f r o m b a s e p r e s s u r e t o s t a g n a t i o n p o i n t ) . A l s o , t h e m a x i m u m u n c e r t a i n t y w i l l arise at t h e l o w e s t s p e e d w h e n t e s t i n g t h e l a r g e s t m o d e l . Re q  Cp  ±4.0 % ±2.0 % ± 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 i s u a l i z a t i o n 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 a c q u i r e s o m e information  about the Tolerant w i n d tunnel flow  m e c h a n i s m . B e c a u s e of the test  section  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 patterns w e r e o b s e r v e d a n d r e c o r d e d through sketches. T h e tufts f l o w v i s u a l i z a t i o n t e c h n i q u e u s e s w o o l t h r e a d a p p r o x i m a t e l y h a l f - i n c h l o n g attached to solid surfaces with masking tape. By aligning themselves with the surface flow, the tufts i n d i c a t e t h e l o c a l d i r e c t i o n of t h e f l o w . R o w s of tufts w e r e i n s t a l l e d o n t h e f l o o r a n d w a l l s o f o n e o f t h e p l e n u m s , as s h o w n i n F i g u r e 5.4. l n a d d i t i o n , s o m e t u f t s w e r e a t t a c h e d t o e a c h a i r f o i l - s h a p e d slat in o r d e r t o d e t e c t a n y o c c u r r e n c e o f s t a l l e d 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 i s u a l i z a t i o n w a s p e r f o r m e d in t h e c l o s e d c i r c u i t w i n d t u n n e l s p e c i a l l y m o d i f i e d f o r t h e o c c a s i o n . B e c a u s e o f 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  settling-chamber  s c r e e n s , s m o k e is n o r m a l l y  not  u s e d in c l o s e d c i r c u i t w i n d  tunnels.  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 t u n n e l w a s m o d i f i e d in s u c h a w a y t h a t it e f f e c t i v e l y b e c a m e a n o p e n - c i r c u i t w i n d t u n n e l . T h i s w a s easily a c c o m p l i s h e d , as s h o w n in F i g u r e 5 . 5 , b y c l o s i n g t h e first c o m e r w i t h c a r d b o a r d a n d o p e n i n g t w o  i n s p e c t i o n s i d e 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 b y w h i c h t h e 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 t h e c o m e r w h i c h b e c a m e t h e air e n t r a n c e . E v e n t h o u g h t h e e n t r a n c e a n d exit w e r e n o t far apart f r o m e a c h other, n o re-ingestion 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 efficiency a n d , possibly, f l o w q u a l i t y are e x p e c t e d c o n s e q u e n c e s o f s u c h a t u n n e l m o d i f i c a t i o n . H o w e v e r , this  new  t u n n e l c o n f i g u r a t i o n w o u l d o n l y b e u s e d f o r f l o w v i s u a l i z a t i o n a n d u s u a l l y at v e r y l o w s p e e d , a r o u n d 5 m / s e c in this c a s e , in o r d e r t o g e t a c o h e r e n t streak o f s m o k e . A s m o k e g e n e r a t o r ( C O N C E P T GENIE M K V from C O N C E P T E N G . Ltd. of England) was u s e d to p r o d u c e burned-oil  39  s m o k e at a t m o s p h e r i c p r e s s u r e w h i c h w a s f e d t o a f i v e - g a l l o n c a p a c i t y t a n k . A streak o f s m o k e w a s t h e n o b t a i n e d b y p u m p i n g the s m o k e w i t h a small electric fan into 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 b y a n o z z l e o f final d i a m e t e r o f 6 m m . V i s u a l i z a t i o n w a s d o n e b y i n j e c t i n g s m o k e at d i f f e r e n t p o i n t s in t h e t u n n e l s u c h as at t h e base of the m o d e l , a h e a d of the m o d e l a n d t h r o u g h different orifices in the p l e n u m .  6. EXPERIMENTAL RESULTS T h i s c h a p t e r p r e s e n t s a n d d i s c u s s e s t h e e x p e r i m e n t a l r e s u l t s o b t a i n e d in t h e  wind  t u n n e l . T h e first t h r e e s e c t i o n s o f t h e c h a p t e r r e l a t e d i r e c t l y t o t h e t e s t i n g of t h r e e bluff b o d y m o d e l s ; flat p l a t e a n d c i r c u l a r c y l i n d e r w i t h a n d w i t h o u t s p l i t t e r p l a t e . In g e n e r a l , e a c h o f t h e s e sections shows the  effects of  different  wall configurations  on  pressure distribution,  base  pressure coefficient, drag coefficient, Strouhal n u m b e r a n d overall b l o c k a g e correction factor for o n e m o d e l . In a d d i t i o n , t h e first s e c t i o n s h o w s s o m e 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 s a n d d i s c u s s e s t h e results f o r a d i f f e r e n t m o d e l p o s i t i o n . T h e f o u r t h s e c t i o n o f this c h a p t e r is c o n c e r n e d w i t h t h e f l o w i n s i d e t h e p l e n u m ; w a l l pressure distributions a n d f l o w visualization f o r m the basis for the d i s c u s s i o n .  6.1 F L A T P L A T E M O D E L  6.1.1 M O D E L PRESSURE DISTRIBUTION Effects o f d i f f e r e n t w a l l o p e n - a r e a r a t i o s o n t h e t i m e - a v e r a g e d p r e s s u r e d i s t r i b u t i o n o n a flat p l a t e m o d e l are s h o w n in F i g u r e s 6.1 (a) t o ( m ) . E a c h o f t h e s e 1 3 f i g u r e s c o m p a r e s , f o r a g i v e n o p e n - a r e a r a t i o , 3 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 s c o r r e s p o n d i n g t o 3 b l o c k a g e ratios ( 8 . 3 % , 1 9 . 4 % a n d 3 3 . 3 %), w i t h a n analytical c u r v e f o r w h i c h t h e f r e e - a i r b a s e p r e s s u r e is c o n s i d e r e d t o be C p  D  =  -  1.13  [33].  F i g u r e 6 . 1 (a), f o r w h i c h t h e O A R = 0 , s h o w s c l e a r l y t h e " s q u e e z i n g " i n f l u e n c e o f s o l i d w a l l s o n t h e p r e s s u r e m e a s u r e m e n t s ; t h e h i g h e r t h e b l o c k a g e r a t i o is, t h e faster t h e p r e s s u r e d r o p s d o w n f r o m t h e s t a g n a t i o n p o i n t a n d t h e l o w e r is t h e b a s e p r e s s u r e . T h e g e n e r a l s h a p e o f t h e v a r i a t i o n , h o w e v e r , stays t h e s a m e w h i l e at t h e rear o f t h e p l a t e t h e t i m e - a v e r a g e d p r e s s u r e r e m a i n s r e l a t i v e l y c o n s t a n t in s p i t e o f h i g h l y t u r b u l e n t f l o w s . S i n c e t h e rear s u c t i o n b e h i n d t h e flat p l a t e d o m i n a t e s t h e d r a g , its i n c r e a s e in c o n v e n t i o n a l w i n d t u n n e l s c a n g r e a t l y i n c r e a s e t h e d r a g ; here , m o r e than d o u b l e the free-air drag ( C Q = 1  (C(j  =  4.66),  about  50  % t o o h i g h f o r a b l o c k a g e ratio o f  40  1 . 9 8 ) at a b l o c k a g e ratio o f 3 3 . 3 % 19.4  % a n d still a r o u n d  15  % t o o high  41  f o r a r e l a t i v e l y s m a l l b l o c k a g e ratio o f 8.3 %. T h e n e x t f i g u r e s , 6.1 (b) t o (m), s h o w t h e e f f e c t o f " o p e n i n g " t h e w a l l s . First, o n e c a n clearly o b s e r v e t h a t t h e w a l l b o u n d a r y c o n d i t i o n has a l a r g e i n f l u e n c e o n h i g h b l o c k a g e r a t i o m o d e l s w h i l e t h e s m a l l m o d e l is little a f f e c t e d o v e r t h e e n t i r e r a n g e of O A R . A l s o , t h e p r e s s u r e d i s t r i b u t i o n o n t h e f r o n t f a c e o f t h e p l a t e , b e i n g little s e n s i t i v e t o w a l l constraint, r e m a i n s c l o s e t o the a c c e p t e d free-air v a l u e s 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 c h a r a c t e r i s t i c s at l o w o p e n - a r e a r a t i o s ( O A R less t h a n 0.5). O n t h e o t h e r h a n d , t h e b a s e p r e s s u r e c o e f f i c i e n t s h o w s a relatively l a r g e v a r i a t i o n w i t h i n c r e a s i n g O A R . In p a r t i c u l a r , t h e l a r g e - m o d e l (h/H  =  33.3  %)  base  pressure  increases  rapidly  with  O A R to  reach  the  small-model  ( h / H = 8.3 %) v a l u e at O A R •=. 0 . 5 2 6 a n d t h e n k e e p s o n i n c r e a s i n g t o o v e r s h o o t t h e r e f e r e n c e base pressure of C p  D  = - 1.13. M o r e d e t a i l s o n t h e v a r i a t i o n o f b a s e p r e s s u r e w i t h O A R w i l l b e  g i v e n 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 , h e r e , t h a t s t a l l e d f l o w s 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 t h e 1 2 - i n c h ( h / H = 3 3 . 3 %) flat p l a t e m o d e l . T h i s is s u r e l y a n i n d i c a t i o n o f t h e m a x i m u m s i z e flat p l a t e w h i c h c a n b e t e s t e d w i t h o u t f l o w s e p a r a t i o n as r e q u i r e d b y t h e c r i t e r i a f o r d e s i g n i n g t h e Tolerant w i n d tunnel. T h e p r e s s u r e d i s t r i b u t i o n s a n d in p a r t i c u l a r t h e b a s e p r e s s u r e c o e f f i c i e n t s m e a s u r e d at a w a l l o p e n - a r e a r a t i o o f z e r o c o r r e s p o n d i n g t o a n o p e n - j e t t e s t s e c t i o n are p r e s e n t e d h e r e o n l y as i n d i c a t i v e v a l u e s 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 r e l i a b l e s i n c e g o o d  two-dimensional  o p e n - j e t f l o w c o n d i t i o n s in t h e p r e s e n t t e s t s e c t i o n c o u l d n o t b e 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 r e s s u r e d i s t r i b u t i o n s w e r e s y s t e m a t i c a l l y o b t a i n e d f o r all flat p l a t e m o d e l s a n d w a l l c o n f i g u r a t i o n s . H o w e v e r , o n l y a f e w s e t s o f r e s u l t s are p r e s e n t e d h e r e , in F i g u r e s 6.2 a n d 6 . 3 , f o r t h e y s u m m a r i z e c l e a r l y e n o u g h t h e u p s t r e a m a n d d o w n s t r e a m c e n t e r l i n e f l o w b e h a v i o u r o v e r t h e full r a n g e o f b l o c k a g e ratios a n d O A R . F i g u r e s 6.2 s h o w , f o r 3 b l o c k a g e ratios, t h e p r e s s u r e v a r i a t i o n a l o n g t h e a c t u a l c e n t e r l i n e o f t h e t u n n e l , w h i l e F i g u r e s 6.3 p r e s e n t  42  the  pressure variation  c o m p e n s a t e d for  the  empty  solid-wall  pressure  gradient  along  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 t h e a b s c i s s a , f o r e i t h e r s c a l e , a n d t h e f l o w is g o i n g f r o m r i g h t ( u p s t r e a m ) t o left ( d o w n s t r e a m ) . A n i m p o r t a n t p o i n t c o n f i r m e d b y t h e u p s t r e a m 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 is t h a t i n all c a s e s t h e n o z z l e P i t o t - s t a t i c t u b e , u s e d t o m o n i t o r t h e t u n n e l w i n d s p e e d , is s i t u a t e d far e n o u g h u p s t r e a m ( 1 . 6 8 m a w a y f r o m t h e m o d e l ) a n d is n e v e r a f f e c t e d b y t h e m o d e l p r e s s u r e f i e l d . O n e c a n also n o t e that the " o p e n i n g " of the walls stimulates early upstream transverse v e l o c i t i e s a l l o w i n g t h e p e r t u r b a t i o n , p a r t i c u l a r l y at h i g h b l o c k a g e r a t i o , t o r e a c h f a r t h e r u p s t r e a m t h a n in solid-wall confined flow.  M o r e o v e r , the upstream floor  pressure distribution  seems to  be  i n d e p e n d e n t o f O A R in v e n t i l a t e d w a l l s in a d d i t i o n t o s h o w i n g c o l l a p s i b l e c u r v e s i n d i c a t i n g similar f l o w for different b l o c k a g e ratios. O n t h e d o w n s t r e a m part, t h e t i m e - a v e r a g e d s t a t i c 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 r e a c h e s a minimum  not  o n t h e rear f a c e o f t h e flat p l a t e m o d e l b u t at s o m e d i s t a n c e  downstream  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 h e m o d e l . T h i s is f o l l o w e d b y a p r e s s u r e r e c o v e r y , w h i c h like  the  rest  of  the  wake,  is s e n s i t i v e t o  wall  effects  as s h o w n  in  Figure  6.2  (a).  The  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 h e s a m e d a t a , s h o w n i n F i g u r e 6.3 (a), fails t o s u p e r i m p o s e t h e blockage-ratio  curves indicating  that  the  non-linear  effects  of  wall  interference  lead  to  non-similar flow. Partly b e c a u s e o f h i g h e r b a s e p r e s s u r e s , t h e p r e s s u r e r e c o v e r i e s in t h e T o l e r a n t  test  s e c t i o n are m o r e c o m p l e t e t h a n in c o n v e n t i o n a l w i n d t u n n e l s ; t h e b l o c k a g e - r a t i o c u r v e s are a l s o m o r e alike s u g g e s t i n g m o r e s i m i l a r f l o w s . In g e n e r a l , t h e t e s t 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 o b t a i n r e a s o n a b l e p r e s s u r e r e c o v e r y , e x c e p t p e r h a p s for t h e large m o d e l w h i c h a p p e a r s t o " f e e l " s o m e e n d effects. T h e d r a m a t i c air r e - e n t r y c a u s e d b y t h e s u d d e n e n d o f t h e p l e n u m s , o b v i o u s l y m o r e i m p o r t a n t at h i g h e r b l o c k a g e r a t i o f o r w h i c h m o r e air is d e f l e c t e d i n t o t h e p l e n u m s , is a l s o r e s p o n s i b l e f o r an artificial s h o r t e n i n g o f t h e s l o t t e d - w a l l s . C o n s e q u e n t l y , t h e a v a i l a b l e t e s t - s e c t i o n l e n g t h b e c o m e a l i m i t i n g f a c t o r w h e n a s s e s s i n g t h e 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 ratio.  can  43  6.1.3 V A R I A T I O N W I T H O A R The  next  series of  plots,  F i g u r e s 6.4  to  6.8, s u m m a r i z e the  sensitivity  of  some  a e r o d y n a m i c c h a r a c t e r i s t i c s t o w a l l s o f v a r y i n g o p e n - a r e a ratios, f o r flat p l a t e m o d e l s o f d i f f e r e n t b l o c k a g e ratios. F i g u r e 6.4 s h o w s t h e v a r i a t i o n o f b a s e p r e s s u r e c o e f f i c i e n t , a v e r a g e d o v e r t h e b a c k o f t h e flat p l a t e , as a f u n c t i o n o f O A R . S t a r t i n g w i t h a c l o s e d - w a l l t e s t s e c t i o n , t h e b a s e p r e s s u r e c o e f f i c i e n t s a u g m e n t s t e a d i l y w i t h o p e n i n g o f t h e w a l l ; at a rate i n c r e a s i n g w i t h b l o c k a g e ratio. T w o b l o c k a g e - r a t i o c u r v e s , 8.3 % a n d 1 9 . 4 %, c r i s s c r o s s at O A R « 0 . 6 3 w h e r e C p  D  =  -  1.20,  w h i l e the third curve c o r r e s p o n d i n g t o the largest m o d e l increases m o r e rapidly t o c r o s s the l o w e s t b l o c k a g e - r a t i o c u r v e at O A R = 0 . 5 3 w h e r e C p  D  = -  1.23.  V a r i a t i o n o f d r a g c o e f f i c i e n t s 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 i g u r e 6.6. It is n o s u r p r i s e t o s e e h e r e t h e s a m e b e h a v i o u r as in F i g u r e 6.4 s i n c e d r a g c o e f f i c i e n t s are o b t a i n e d b y integrating the surface pressure distribution in w h i c h the contribution f r o m the front face of the plate, OAR  F i g u r e 6 . 5 , is little a f f e c t e d =  by wall c o n f i n e m e n t . The drag coefficient  0 . 6 3 , f o r t h e i n t e r s e c t i n g c u r v e s , is a b o u t 1.96 w h i l e at O A R =  obtained  at  0 . 5 3 t h e v a l u e is  C(j = 2 . 0 0 , a d i f f e r e n c e o f a b o u t 2 %. T h e effect of different wall c o n f i g u r a t i o n s o n t h e Strouhal n u m b e r , the 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 e q u e n c y , is p l o t t e d in F i g u r e 6.7. T h i s g r a p h s h o w s t h e 8.3 % a n d 1 9 . 4 % b l o c k a g e - r a t i o curves d e c r e a s i n g linearly w i t h an increase of O A R a n d intercept S t r o u h a l - n u m b e r v a l u e (St =  0 . 1 4 2 ) at O A R =  the  same  0.67. T h e o t h e r b l o c k a g e - r a t i o c u r v e (33.3 %),  d e c r e a s i n g l i n e a r l y o n l y f o r O A R less t h a n 0.6, c r o s s e s t h e S t r o u h a l - n u m b e r v a l u e of 0.141 at a slightly 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 f a c t o r s c a l c u l a t e d b y t h e 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 a g a i n s t o p e n - a r e a r a t i o in F i g u r e 6.8. T h e g e n e r a l a s p e c t o f this g r a p h is s i m i l a r t o t h e b a s e p r e s s u r e r e s u l t s s h o w i n g a n i n t e r s e c t i o n p o i n t at a n O A R o f a b o u t 0 . 6 , b e t w e e n t h e 8.3 a n d 19.4  %  blockage-ratio curves, and another  one  at a r o u n d  0.49 for  the  8.3  and 33.3  %  b l o c k a g e - r a t i o c u r v e s . T h e v a l u e s o f t h e b l o c k a g e c o r r e c t i o n f a c t o r are, at t h o s e p o i n t s , a b o u t  44  0 . 9 8 0 a n d 0 . 9 7 4 , r e s p e c t i v e l y , 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 ratios, p e r h a p s 2 t o 3 %, in a conventional wind tunnel. F i g u r e 6.9 s h o w s t h e e f f e c t o f o p e n i n g t h e w a l l s o n t h e s t a n d a r d d e v i a t i o n w h i c h c a n b e i n t e r p r e t e d as a m e a s u r e o f t h e q u a l i t y o f t h e o v e r a l l fit o f t h e T o l e r a n t - w i n d - t u n n e l d a t a t o t h e reference pressure distribution. This graph d o e s n o t s h o w any particular pattern e x c e p t perhaps t h a t t h e s t a n d a r d d e v i a t i o n o s c i l l a t e s a r o u n d a c o n s t a n t v a l u e w h i c h i n c r e a s e s as t h e b l o c k a g e r a t i o i n c r e a s e s . A l s o , t h e r e is in g e n e r a l a b e t t e r fit w h e n t h e t e s t s are p e r f o r m e d  in  the  slotted-wall w i n d tunnel.  6.1.4 E F F E C T 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 t h e e f f e c t o f l o n g e r s l o t t e d w a l l s e x t e n d i n g d o w n s t r e a m o f t h e m o d e l , a s e r i e s o f t e s t s w a s c o n d u c t e d w i t h t h e s a m e m o d e l s b u t at a n e w p o s i t i o n 2 2 (55.8) i n c h e s ( c m ) u p s t r e a m o f t h e c e n t e r ( p r e v i o u s p o s i t i o n ) o f t h e t e s t s e c t i o n . U n f o r t u n a t e l y , this c h a n g e in p o s i t i o n a l s o r e s u l t s in a r e d u c t i o n o f s l o t t e d - w a l l s u r f a c e s ( a n d t h e r e f o r e 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 interpretation of the results m o r e difficult. N e v e r t h e l e s s , t h e floor p r e s s u r e d i s t r i b u t i o n s o f F i g u r e s 6 . 1 0 a n d 6.11 t e n d t o i n d i c a t e n o m a j o r c h a n g e in final p r e s s u r e r e c o v e r y w i t h t h e n e w l o n g a f t e r - m o d e l w a l l s . 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 o w s t h e rear p r e s s u r e d i s t r i b u t i o n t o r e m a i n c o n s t a n t o v e r a l o n g e r d i s t a n c e after r e c o v e r i n g f r o m t h e l o w p r e s s u r e p e a k e x p e r i e n c e d in t h e s e p a r a t i o n " b u b b l e " , just b e h i n d t h e m o d e l . T h e l a r g e r t h e m o d e l is, t h e s h o r t e r is t h e d i s t a n c e o n w h i c h t h e p r e s s u r e r e m a i n s c o n s t a n t b e f o r e  being  affected b y e n d effects (breather a n d s u d d e n e n d i n g of the p l e n u m s ) . T h e f l o o r pressure distributions o b t a i n e d a h e a d of the m o d e l s indicate 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 i n l e t o f t h e t e s t s e c t i o n . A s a r e s u l t , t h e P i t o t t u b e u s e d t o m o n i t o r t h e tunnel  wind  speed  had  to  be  moved  farther  upstream  in  order  to  insure  surrounding  u n d i s t u r b e d s t a t i c p r e s s u r e . T h i s n e w p o s i t i o n , at a s o m e w h a t l a r g e r c r o s s - s e c t i o n a r e a o f t h e n o z z l e , r e s u l t s in a l o w e r i n d i c a t e d w i n d s p e e d t h u s d e g r a d i n g t h e a c c u r a c y o f t h e c a l i b r a t i o n (the h i g h e r t h e w i n d s p e e d is in t h e n o z z l e , t h e m o r e a c c u r a t e l y it c a n b e m e a s u r e d ) .  45  Figures  6.12  to  6.17 s u m m a r i z e the  effect  of  varying o p e n - a r e a ratio o n  certain  a e r o d y n a m i c c h a r a c t e r i s t i c s w h e n t h e m o d e l s are t e s t e d at t h e u p s t r e a m p o s i t i o n . E x c e p t f o r t h e m o d e l o f 3 3 . 3 % b l o c k a g e r a t i o , t h e r e s u l t s are, w i t h i n t h e e x p e r i m e n t a l e r r o r , s i m i l a r t o t h e d a t a o b t a i n e d w h e n t h e m o d e l s w e r e t e s t 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 . H o w e v e r , t h e c h a n g e in t e s t p o s i t i o n b e c a m e s i g n i f i c a n t l y i m p o r t a n t f o r t h e 1 2 - i n c h flat p l a t e m o d e l ; o v e r m o s t o f t h e t e s t e d r a n g e o f O A R (0.4 - 0.8), b a s e p r e s s u r e c o e f f i c i e n t s w e r e h i g h e r a n d d r a g c o e f f i c i e n t s w e r e t h e r e f o r e l o w e r t h a n f o r t h e s a m e m o d e l t e s t e d at m i d - s e c t i o n . A l s o , t h e S t r o u h a l n u m b e r v a l u e s 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 t h e o t h e r m o d e l s i z e s at O A R = 0 . 6 . T h e f a c t t h a t t h e l e n g t h u p s t r e a m o f t h e m o d e l is r e d u c e d b y t h e n e w p o s i t i o n l i m i t s t h e distance over w h i c h the f l o w can m o v e t h r o u g h the slotted-wall into the p l e n u m s thus causing l a r g e r v e l o c i t y g r a d i e n t s a r o u n d t h e m o d e l . C o n s e q u e n t l y , m o s t o f t h e airfoil-slats u p s t r e a m o f t h e 3 3 . 3 % b l o c k a g e - r a t i o m o d e l w e r e hit b y h i g h i n c i d e n c e f l o w r e s u l t i n g i n w e l l s e p a r a t e d f l o w s in t h e p l e n u m s . T h i s is o b v i o u s l y a f a c t o r c o n t r i b u t i n g t o t h e d i f f e r e n c e s 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 pressure distributions m e a s u r e d o n different sizes of circular cylinder 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 t e s t s e c t i o n are s h o w n i n F i g u r e s 6 . 1 8 (a) t o (m), f o r v a r i o u s w a l l c o n f i g u r a t i o n s . T h e s e f i g u r e s p r e s e n t , s y s t e m a t i c a l l y , t h e results f o r 3 b l o c k a g e ratios ( 3 3 . 3 %, 2 5 % a n d 1 3 . 8 %) o v e r t h e i n v e s t i g a t e d r a n g e o f O A R as w e l l as l o w b l o c k a g e - r a t i o (8.3 %) d a t a at 4 O A R ' s : 0 , 0 . 5 6 3 , 0 6 3 5 a n d 0 . 7 0 8 . In a d d i t i o n , e a c h g r a p h s h o w s , f o r c o m p a r i s o n p u r p o s e s , a r e f e r e n c e p r e s s u r e c u r v e m e a s u r e d b y 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 1 4 , 5 0 0 a n d a  b l o c k a g e ratio o f 4 . 4 % f o r w h i c h t h e c o r r e s p o n d i n g d r a g c o e f f i c i e n t is C ^ =  1.15. A l t h o u g h  d i f f e r e n t t h a n t h e t r u e u n c o n f i n e d v a l u e , this r e f e r e n c e c u r v e a p p r o x i m a t e s , w e l l e n o u g h a n d p r o b a b l y within the e x p e r i m e n t a l error, the d e s i r e d free-air pressure distribution o v e r a circular  46  c y l i n d e 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 n d e e d , R o s h k o ' s r e s u l t s w o u l d n e e d o n l y , after A l l e n a n d V i n c e n t i ' s f o r m u l a e (as r e p o r t e d b y R o s h k o [38] ), a v e l o c i t y c o r r e c t i o n o f l e s s t h a n 1.5 % a n d a d r a g c o e f f i c i e n 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 i g u r e 6 . 1 8 (a) ) s h o w s t h e r e s u l t s o b t a i n e d in a c o n v e n t i o n a l t e s t s e c t i o n (OAR  =  0); t h e u s u a l p r e s s u r e p a t t e r n s o v e r t w o - d i m e n s i o n a l c i r c u l a r c y l i n d e r s of d i f f e r e n t  b l o c k a g e ratios are o b s e r v e d : starting f r o m the stagnation point, the m o s t upstream p o i n t o n the  cylinder,  and moving  circumferentially  towards  the  back of  the  m o d e l , the  pressure  decreases rapidly to reach a m i n i m u m value a r o u n d 70 degrees, before undertaking a pressure r e c o v e r y w h i c h is a b r u p t l y s t o p p e d b y f l o w s e p a r a t i o n at a b o u t 8 0 d e g r e e s . U n f o r t u n a t e l y , t h e exact point  of separation w h i c h oscillates with the vortex-shedding f r e q u e n c y  cannot  be  a c c u r a t e l y d e t e r m i n e d f r o m t h e p r e s s u r e p l o t . A f t e r s e p a r a t i o n , t h e p r e s s u r e stays relatively constant o v e r about 60 d e g r e e s (up to 0 =  1 2 0 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 o f t h e  c y l i n d e r at a rate w h i c h i n c r e a s e s w i t h i n c r e a s i n g b l o c k a g e ratios. A l t h o u g h t h e pressure and the  p r e s s u r e at s e p a r a t i o n s h o w  large variations  (decrease) with  minimum increasing  b l o c k a g e ratios,the d i f f e r e n c e b e t w e e n t h o s e t w o values remains relatively i n d e p e n d e n t of the size of t h e m o d e l . T h e u s e o f t h e T o l e r a n t w i n d t u n n e l f o r t h e t e s t i n g o f c i r c u l a r c y l i n d e r s results 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 pressure distribution  e v e n for a large m o d e l w i t h 33.3 %  b l o c k a g e r a t i o s a n d a l o w O A R s u c h as 0 . 3 4 4 . A t t h i s O A R ( F i g u r e 6 . 1 8 (b)) t h e  13.8 %  b l o c k a g e - r a t i o curve f o l l o w s the reference line u p t o t h e m i n i m u m pressure p o i n t w h e r e the p r e s e n t r e s u l t s b e c o m e s l i g h t l y h i g h e r ; t h e p r e s s u r e d i s t r i b u t i o n at t h e b a c k o f t h e c y l i n d e r is h o w e v e r t o o n e g a t i v e . O n e c a n a l s o n o t e t h a t t h e 2 5 % b l o c k a g e - r a t i o c u r v e stays s l i g h t l y h i g h e r t h a n t h e r e f e r e n c e c u r v e o n t h e part o f t h e c y l i n d e r p r e c e d i n g t h e m i n i m u m p r e s s u r e p o i n t . Past this p o i n t t h e p r e s s u r e d i s t r i b u t i o n r e m a i n s t o o n e g a t i v e b y a b o u t 13 %. T h e l a r g e s t m o d e l s h o w s a s l i g h t l y t o o n e g a t i v e p r e s s u r e b e f o r e s e p a r a t i o n w h i l e t h e p r e s s u r e o n t h e rear part o f t h e c y l i n d e r is b e l o w R o s h k o ' s c u r v e b y a b o u t 2 5 %.  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 — 5 0 ° , 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.  48  F i g u r e 6 . 2 0 r e p o r t s t h e e f f e c t s o f O A R u p o n t h e p r e s s u r e c o e f f i c i e n t m e a s u r e d at 1 0 0 d e g r e e s f r o m t h e s t a g n a t i o n p o i n t ; this is a s e c t o r o f t h e c y l i n d e r e a r l i e r d e f i n e d t o b e t h e r e g i o n o f c o n s t a n t p r e s s u r e f o l l o w i n g t h e s e p a r a t i o n o f t h e b o u n d a r y layer. T h e i m p o r t a n c e o f this p r e s s u r e c o e f f i c i e n t r e s i d e s in t h e fact t h a t it i s , in t h e e v a l u a t i o n o f t h e d r a g , o f t e n c o n s i d e r e d to be the base pressure coefficient and taken constant over the w h o l e separated flow region. T h i s g r a p h e x h i b i t s a w e l l d e f i n e d c r i s s - c r o s s o f all t h e b l o c k a g e - r a t i o c u r v e s at a s i n g l e O A R o f a b o u t 0.53 w h e r e the pressure coefficient c o r r e s p o n d s t o C p =  -  0 . 9 6 . This is a d e s i r e d  b e h a v i o u r o f t h e T o l e r a n 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 i n g l e O A R f o r a w i d e r a n g e o f b l o c k a g e ratios. T h e p r e s s u r e v a l u e s m e a s u r e d at 1 8 0 d e g r e e s f r o m t h e s t a g n a t i o n p o i n t a n d p l o t t e d in F i g u r e 6 . 2 1 , c h a r a c t e r i z e t h e m a x i m u m p r e s s u r e v a r i a t i o n o n t h e rear p a r t o f t h e c y l i n d e r w h e r e t h e s h a p e o f t h e p r e s s u r e d i s t r i b u t i o n c u r v e is i n f l u e n c e d b y w a l l c o n f i n e m e n t (as s e e n in F i g u r e s 6 . 1 8 ) . A n artificial u n c o n f i n e d e n v i r o n m e n t , n o m a t t e r h o w it is r e a l i z e d , s h o u l d b e a b l e t o e l i m i n a t e this e f f e c t w h i c h c o u l d b e r e s p o n s i b l e f o r l a r g e d r a g d i s c r e p a n c i e s . A l t h o u g h i n c a p a b l e of  completely  eliminating  the  rear  pressure  differences  the  Tolerant  wind  tunnel  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 r e n c e , i n t e r m s o f p r e s s u r e c o e f f i c i e n t s , o f a b o u t 1 0 %. T h e r e a s o n f o r this r e s i d u a l e r r o r is n o t t o t a l l y c l e a r b u t s i n c e t h e p r e s e n c e o f p e r i o d i c v o r t i c e s is p a r t l y r e s p o n s i b l e f o r t h e l o w p r e s s u r e r e g i o n b e h i n d t h e c y l i n d e r , it is t h o u g h t t h a t t h e i n t e r f e r e n c e e f f e c t o f t h e s l a t t e d - w a l l , e v e n at l a r g e O A R , c o u l d alter  the  d y n a m i c s o f t h e v o r t i c e s t h u s c a u s i n g a d i f f e r e n t - t h a n - f r e e - a i r p r e s s u r e p a t t e r n in t h e b a c k of t h e cylinder. The cylinder drag characteristics, o b t a i n e d f r o m integration of the pressure distributions, are p l o t t e d in F i g u r e s 6 . 2 2 , 6 . 2 3 a n d 6.24 ( n o t e that t h e d r a g is d e f i n e d as p o s i t i v e in t h e d i r e c t i o n of the flow). T h e graph of Figure 6.22 s h o w s t h e variation of the front drag coefficients as b e i n g a l m o s t i d e n t i c a l t o F i g u r e 6 . 1 8 , t h e p r e s s u r e c o e f f i c i e n t s at 5 0 d e g r e e s , t h u s c o n f i r m i n g a n o v e r a l l b e h a v i o u r in t h e u n s e p a r a t e d f l o w r e g i o n o f t h e c y l i n d e r .  49  T h e n o n - e x i s t e n c e o f a n o p t i m a l O A R f o r t h e d r a g c o e f f i c i e n t ( F i g u r e 6.24) s e e m s m a i n l y d u e t o t h e f r o n t a l b e h a v i o u r , s i n c e t h e v a r i a t i o n o f t h e rear d r a g c o e f f i c i e n t , a l t h o u g h  not  d i s t i n c t i v e l y c l e a r , b e c o m e s i n d e p e n d e n t o f t h e b l o c k a g e ratio at a n o p e n - a r e a ratio o f a b o u t 0.56 . T h e S t r o u h a l n u m b e r ( F i g u r e 6.25) w h i c h c h a r a c t e r i z e s t h e u n s t e a d i n e s s o f t h e f l o w d u e t o v o r t e x s h e d d i n g , b e c o m e s a l s o i n d e p e n d e n t o f t h e m o d e l s i z e at a n O A R o f a b o u t 0 . 5 6 w i t h a v a l u e o f St =  0 . 1 8 5 c o m p a r e d t o 0 . 1 8 g i v e n in t h e literature [35] f o r a R e y n o l d s n u m b e r o f  1 0 . N o t e a l s o t h a t t h e 8.3 % b l o c k a g e - r a t i o r e s u l t s r e m a i n s l i g h t l y h i g h e r t h a n t h o s e f o r t h e 5  o t h e r c y l i n d e r s i z e s ; t h e diff e r e n c e , h o w e v e r , i s less t h a n 3 % at t h e c r i s s - c r o s s p o i n t . Finally, t h e v a r i a t i o n o f b l o c k a g e c o r r e c t i o n f a c t o r a n d its a s s o c i a t e d s t a n d a r d d e v i a t i o n w i t h O A R are g i v e n in F i g u r e s 6 . 2 6 a n d 6 . 2 7 . It is i n t e r e s t i n g t o n o t e t h a t all t h e b l o c k a g e - r a t i o c u r v e s c r o s s at O A R = a v e r a g e at O A R =  0 . 5 3 w h e r e t h e b l o c k a g e c o r r e c t i o n f a c t o r is C F =  1.0. H e n c e ,  on  0 . 5 3 , t h e p r e s s u r e d i s t r i b u t i o n c u r v e s o f a n y b l o c k a g e ratio (in t h e r a n g e  considered) can be a p p r o x i m a t e d by the reference curve. The error or standard deviation, o n t h e o t h e r h a n d , i n c r e a s e s w i t h i n c r e a s i n g b l o c k a g e r a t i o , as s h o w n i n F i g u r e 6 . 2 7 .  6.2.3 EFFECT O F N O N - E V E N L Y S P A C E D SLATS It has b e e n s h o w n in t h e p r e v i o u s s e c t i o n s t h a t a c i r c u l a r c y l i n d e r m o d e l t e s t e d at l o w O A R o f t e n p r e s e n t s a s p l i t b e h a v i o u r c h a r a c t e r i z e d b y a s o l i d - w a l l " s q u e e z i n g " e f f e c t in t h e b a c k o f t h e c y l i n d e r w h i l e t h e f r o n t p a r t f e e l s t h e e f f e c t o f a n o p e n - j e t b o u n d a r y . It is t h e r e f o r e l o g i c a l to  assume,  if  no  systematic  error  due  to  set-up  misalignment  is  involved,  that  a  n o n - e v e n l y - s p a c e d ^ s l a t s l o t t e d - w a l l w i t h o p e n areas i n c r e a s i n g in t h e d i r e c t i o n o f t h e f l o w c o u l d lead t o a simple solution. T h i s s e c t i o n p r o v i d e s m e r e l y a s t a r t i n g p o i n t t o a p o s s i b l e f u t u r e i n v e s t i g a t i o n o f this t y p e o f s l o t t e d - w a l l b y s h o w i n g t h e results o f f o u r s i z e s o f c i r c u l a r c y l i n d e r m o d e l t e s t e d at a s i n g l e O A R o f 0 . 4 5 3 b u t w i t h 2 d i f f e r e n t slat d i s t r i b u t i o n s . B o t h o p e n - a r e a d i s t r i b u t i o n s  are  c h o s e n t o i n c r e a s e linearly w i t h t h e slat n u m b e r b u t w i t h d i f f e r e n t s l o p e s w h i c h , as e x p l a i n e d in  50  d e t a i l i n 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 v e n f a c t o r (AORT). T h i s f a c t o r is d e f i n e d f o r t h e first  slot  open-area  as  the  ratio  of  the  evenly-spaced-slat  slot  size  to  the  actual  ( n o n - e v e n l y - s p a c e d ) s l o t s i z e . A f a c t o r of A O R T = 2 , f o r e x a m p l e , m e a n s t h a t t h e first s l o t is half t h e s i z e of t h e e v e n l y - s p a c e d c a s e a n d t h a t t h e s l o p e w o u l d b e c a l c u l a t e d a c c o r d i n g l y t o o b t a i n a l i n e a r i n c r e a s e o f o p e n areas. T h e r e s u l t s o b t a i n e d f o r v a l u e s o f A O R T o f 1.5 a n d 3 are p l o t t e d , r e s p e c t i v e l y , in F i g u r e s 6 . 2 8 a n d 6 . 2 9 . T h e s e c a n b e c o m p a r e d t o F i g u r e 6 . 1 8 (d) w h i c h s h o w s a s i m i l a r t e s t in an e v e n l y - s p a c e d s l o t t e d - w a l l (AORT = generally  lower  than  the  1) t e s t s e c t i o n . T h e r e s u l t i n g p r e s s u r e d i s t r i b u t i o n s  h o m o g e n e o u s - O A R case  while  bringing  the  pressure  in  are the  unseparated flow region close to or lower than the reference curve. W h e n comparing the n e w pressure distributions to each other, o n e can observe noticeable change before the separation p o i n t b u t a l m o s t n o n e o n t h e rear part o f t h e c y l i n d e r . C o n s e q u e n t l y , t h e l o a d d i s t r i b u t i o n s of F i g u r e 6 . 2 9 , w h e r e A O R T = 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 . T h i s s i m p l e test, a l t h o u g h p r e l i m i n a r y , d e m o n s t r a t e s t h e p o s s i b i l i t y o f u s i n g g r a d e d O A R to obtain consistent boundary conditions.  6.3 E F F E C T O F SPLITTER P L A T E T h e s u g g e s t i o n that interactions b e t w e e n the vortices s h e d f r o m the c y l i n d e r a n d the slats o f t h e s l o t t e d w a l l c o u l d b e r e s p o n s i b l e f o r a l t e r i n g t h e s u r f a c e p r e s s u r e d i s t r i b u t i o n  of  l a r g e m o d e l s p r o m p t e d this i n v e s t i g a t i o n . A s s h o w n b y R o s h k o [20], t h e i n t r o d u c t i o n o f a l o n g e n o u g h ( a b o u t 4 d i a m e t e r s ) s p l i t t e r p l a t e a l o n g t h e c e n t e r l i n e o f t h e w a k e is s u f f i c i e n t provoke reattachment  of the  s h e a r layers o n e i t h e r s i d e o f t h e  to  p l a t e t h u s r e s u l t i n g in a  s u p p r e s s i o n of t h e vortex s h e d d i n g , a n d a c o n s i d e r a b l e increase of the b a s e pressure. T h e use of t h i s t y p e o f m o d e l a l l o w s us t o test a bluff b o d y m o d e l w i t h o u t v o r t i c e s i n t e r a c t i n g w i t h t h e s l o t t e d w a l l s . In a d d i t i o n t o e l i m i n a t i n g t h e u n s t e a d i n e s s o f t h e f l o w this t y p e o f m o d e l w i l l a l s o i n t r o d u c e t w o recirculating r e g i o n s , o n either s i d e of t h e splitter plate, w h i c h effectively b e c o m e p a r t o f t h e m o d e l a f t e r - b o d y a n d t h e r e f o r e h a v e t o b e r e p r o d u c e d c o r r e c t l y in t h e T o l e r a n t w i n d  51  t u n n e l in o r d e r t o get the correct free-air 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 Surface pressure distributions o n 4 sizes of circular cylinder w i t h splitter plate o b t a i n e d w i t h 1 3 d i f f e r e n t w a l l c o n f i g u r a t i o n s are c o m p a r e d t o a r e f e r e n c e l o a d i n g d i s t r i b u t i o n in F i g u r e s 6 . 3 0 (a) t o ( m ) . A s in t h e p r e v i o u s s e c t i o n t h e r e f e r e n c e c u r v e w a s m e a s u r e d b y R o s h k o [20] i n 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 t h a b l o c k a g e ratio o f 4 . 4 % at a R e y n o l d s n u m b e r o f 1 4 , 5 0 0 ; t h e c o r r e s p o n d i n g d r a g c o e f f i c i e n t is Crf =  0.72.  T h e p l a i n - w a l l s u r f a c e l o a d i n g d i s t r i b u t i o n s , p l o t t e d in F i g u r e 6 . 3 0 (a), s h o w c l e a r l y t h e i n f l u e n c e o f w a l l i n t e r f e r e n c e . E v e n at t h e l o w e s t b l o c k a g e r a t i o o f 8.3 %, t h e b a s e p r e s s u r e c o e f f i c i e n t s d i f f e r f r o m t h e r e f e r e n c e v a l u e s b y as m u c h as 3 8 % r e s u l t i n g in a d r a g d i f f e r e n c e o f a b o u t 1 2 % . O n e c a n n o t e , h o w e v e r , that f o r all b l o c k a g e - r a t i o c u r v e s t h e p r e s s u r e d i s t r i b u t i o n s after s e p a r a t i o n ( o r in t h e s e p a r a t i o n b u b b l e ) r e m a i n relatively c o n s t a n t . A n o p e n i n g o f t h e w a l l s r e s u l t s o n c e a g a i n in a n i m p o r t a n t i n c r e a s e i n s u r f a c e p r e s s u r e . T h e b e s t c o l l a p s e o f all t h e d a t a w i t h t h e r e f e r e n c e c u r v e o c c u r s at a n O A R v a l u e o f a b o u t 0 . 5 6 3 o r 0 . 5 9 9 . B u t , a g a i n , w h i l e t h e b a s e p r e s s u r e d i s t r i b u t i o n s are w e l l r e p r o d u c e d , t h e f r o n t l o a d i n g d i s t r i b u t i o n s c o r r e s p o n d i n g t o t h e b l o c k a g e ratios o f 1 3 . 8 % a n d 2 5 % are h i g h e r t h a n t h e reference  curve. These differences  cannot  be  explained, now,  by  flow  unsteadiness  or  v o r t e x - w a l l i n t e r a c t i o n s . It is h o w e v e r e a s y t o p o s t u l a t e t h a t a m i s a l i g n e d m o d e l w o u l d result in s u c h d i f f e r e n c e s . A n e r r o r o f 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 r a d i e n t s u c h as t h e f r o n t part o f t h e c y l i n d e r , b e s u f f i c i e n t t o c a u s e t h e d i s c r e p a n c i e s o b s e r v e d in F i g u r e 6 . 3 0 . O n t h e w h o l e , c o n s i d e r i n g a s y s t e m a t i c e r r o r in s e t t i n g u p 2 o f t h e m o d e l s , t h e O A R v a l u e o f a b o u t 0 . 5 6 3 c a n 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 t h e o p t i m u m v a l u e . B y r e p r o d u c i n g the pressure distributions of the circular-cylinder-with-spitter-plate m o d e l , w h i c h p o s s e s s e d l o n g s e p a r a t i o n b u b b l e s , t h e T o l e r a n t w i n d t u n n e l t e n d s t o d e m o n s t r a t e its c a p a b i l i t y t o s i m u l a t e 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 t h a f t e r - b o d y . It is a s s u m e d h e r e t h a t t h e b a s e pressure, i n d e e d the w h o l e cylinder pressure distribution,  is a f f e c t e d b y t h e s h a p e o f  the  52  s e p a r a t i o n - b u b b l e w h i c h in t u r n is q u i t e s e n s i t i v e t o w a l l i n t e r f e r e n c e . A m o r e c o m p l e t e s t u d y 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 r e a t t a c h m e n t l e n g t h a n d h e i g h t o f the bubble.  6.3.2 V A R I A T I O N W I T H O A R Figures  6.31  to  6.38  summarize  the  effects  of  wall-OAR on  the  aerodynamic  characteristics of the circular cylinder e q u i p p e d w i t h splitter plate. Effects o f d i f f e r e n t o p e n - a r e a r a t i o s o n t h e u n s e p a r a t e d f l o w r e g i o n o f t h e m o d e l , a n d r e p o r t e d in F i g u r e 6 . 3 1 , are w e l l c h a r a c t e r i z e d b y t h e v a r i a t i o n o f p r e s s u r e c o e f f i c i e n t at 0 = d e g r e e s . E v e n if t h e  e x i s t e n c e of  an o p t i m u m  O A R v a l u e is n o t  apparent,  the  50  different  b l o c k a g e - r a t i o c u r v e s s h o w t h e d e s i r a b l e i n c r e a s e in s l o p e w i t h i n c r e a s i n g b l o c k a g e ratios. A s r e p o r t e d in t h e p r e v i o u s s e c t i o n , a m i s a l i g n m e n t of t h e m o d e l b y a b o u t 2 d e g r e e s is s u f f i c i e n t t o shift t w o o f t h e b l o c k a g e - r a t i o c u r v e s ( 1 3 . 8 % a n d 2 5 %) h i g h e n o u g h u p w a r d t o e l i m i n a t e t h e s i n g l e - O A R c r i s s - c r o s s . N o t e , h o w e v e r , t h a t t h e i n t e r s e c t i o n b e t w e e n t h e 3 3 . 3 % a n d 8.3 % c u r v e s a n d t h e i n t e r s e c t i o n b e t w e e n t h e 2 5 % a n d 1 3 . 8 % c u r v e s o c c u r at t h e s a m e O A R o f 0.563. The  next  two  figures,  6.32  and  6 . 3 3 , are  almost  identical  and  therefore  show  h o m o g e n e i t y o f p r e s s u r e in t h e 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 l o t s a l s o s h o w t h e p r e s e n c e o f a n O A R v a l u e o f a b o u t 0 . 5 6 3 at w h i c h t h e p r e s s u r e c o e f f i c i e n t s are i n d e p e n d e n t o f t h e b l o c k a g e ratio. T h e v a r i a t i o n s of d r a g c o e f f i c i e n t s w i t h O A R are p l o t t e d in F i g u r e s 6 . 3 4 , 6 . 3 5 a n d 6 . 3 6 . A s c a n b e a n t i c i p a t e d f r o m p r e v i o u s r e s u l t s , t h e v a r i a t i o n o f d r a g o n t h e f r o n t part o f t h e 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 t h e d r a g v a l u e o n t h e rear part o f t h e c y l i n d e r b e c o m e s i n d e p e n d e n t o f t h e m o d e l s i z e at an O A R o f a b o u t 0 . 5 6 3 . S i n c e t h e 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 . 2 7 5 o n t h e rear a n d 0.5 o n t h e f r o n t , t o t h e t o t a l d r a g v a l u e is o f t h e s a m e o r d e r o f m a g n i t u d e , the variation of  d r a g as a w h o l e  is s u b s t a n t i a l l y a f f e c t e d  by the  (speculative)  m i s a l i g n m e n t o f t h e m o d e l s . E v e n if F i g u r e 6 . 3 6 s h o w s a c r i s s - c r o s s o f 3 b l o c k a g e - r a t i o c u r v e s at  53  a n O A R o f a b o u t 0 . 6 3 5 , it is b e l i e v e d t h a t a b e t t e r a l i g n m e n t o f t h e m o d e l s w o u l d b r i n g t h e 2 5 % a n d 13.8 % blockage-ratio curves 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 f o r a  of 0 . 7 5 .  Finally, v a r i a t i o n o f t h e b l o c k a g e c o r r e c t i o n f a c t o r , F i g u r e 6 . 3 7 , t e n d s t o i n d i c a t e t h a t pressure values m e a s u r e d in the Tolerant w i n d tunnel with an O A R of 0.563 w o u l d n o t require a n y c o r r e c t i o n w h e r e t h e m a x i m u m v a l u e o f t h e s t a n d a r d d e v i a t i o n , as s h o w n i n F i g u r e 6 . 3 8 , w o u l d b e as l o w as 0 . 0 4 .  6.4 P L E N U M F L O W T h e u s e o f a p r o p e r s l a t t e d - w a l l c o n f i g u r a t i o n in t h e T o l e r a n 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 of 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 h e simulation of u n c o n f i n e d a r o u n d m o d e l s o f relatively l a r g e b l o c k a g e r a t i o s . T o a c c o m p l i s h t h i s , t h e s i d e w a l l  flows  limiting  s t r e a m l i n e s are a l l o w t o s e p a r a t e as f r e e s h e a r 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 t o p l e n u m b o x e s in w h i c h t h e y t a k e a s h a p e w h i c h in t u r n i n f l u e n c e s t h e n a t u r e o f t h e 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 assessment of the capabilities a n d limitations o f t h e T o l e r a n t w i n d t u n n e l d o e s n o t s e e m p o s s i b l e w i t h o u t a full u n d e r s t a n d i n g o f t h e f l o w i n s i d e t h e p l e n u m s . T h i s s e c t i o n m a k e s a first a t t e m p t t o r e a c h s u c h a g o a l b y p r o v i d i n g b a s i c i n f o r m a t i o n s u c h as p r e s s u r e d i s t r i b u t i o n s i n t h e c a v i t y a n d f l o w p a t t e r n s 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 i s u a l i z a t i o n s . ( C h a p t e r 5 s h o w s t h e p r e s s u r e t a p a n d tuft p o s i t i o n s in t h e plenum) D e p e n d i n g mainly o n the b l o c k a g e , t w o general pictures of p l e n u m f l o w have b e e n observed. 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 r a t i o s u p t o o n e t h i r d ( e x c e p t f o r t h e flat p l a t e ) at a l m o s t a n y o p e n - a r e a r a t i o s e x c e p t u n i t y ( o p e n - j e t ) , t h e o b s e r v e d f l o w s h o w e d a single e l o n g a t e d recirculation with an e d d y center located d o w n s t r e a m of t h e geometric c e n t e r o f t h e p l e n u m ( F i g u r e 6 . 3 9 ). S t r o n g p r e s e n c e o f e n t r a i n m e n t a l o n g t h e s h e a r layer w a s always e v i d e n t . A l s o , t h e s h e a r l a y e r h a s b e e n o b s e r v e d t o i m p i n g e o n t h e d o w n s t r e a m e n d w a l l o f t h e p l e n u m at a p o s i t i o n o s c i l l a t i n g w i t h a f r e q u e n c y c o r r e l a t i n g w i t h t h e v o r t e x s h e d d i n g  54  frequency. Unfortunately,  n o s m o k e f l o w visualization was d o n e w h i l e testing the circular  c y l i n d e r s e q u i p p e d w i t h s p l i t t e r p l a t e s f o r w h i c h n o v o r t e x 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 visualization s h o w e d a m u c h m o r e steady recirculation b u b b l e than a p l e n u m subjected to the u n s t e a d i n e s s o r i g i n a t i n g 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 i s u a l i z a t i o n has revealed a strong interaction b e t w e e n the oscillatory free shear-layer springing f r o m the m o d e l a n d t h e p l e n u m f l o w . T h i s i n t e r a c t i o n w a s m o s t l y e v i d e n t at h i g h b l o c k a g e r a t i o s w h e r e t h e m o d e l f r e e s h e a r l a y e r w a s o b s e r v e d t o o s c i l l a t e far e n o u g h s i d e w a y s t o p a s s t h r o u g h t h e s l a t t e d wall into the  p l e n u m p r o v o k i n g large transverse f l o w s t h r o u g h  t h e d o w n s t r e a m slats. T h e  p l e n u m free shear layer w o u l d t h e n m o v e a c c o r d i n g l y . A s s h o w n in F i g u r e s 6 . 4 0 , t h e m e a n static p r e s s u r e d i s t r i b u t i o n s 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 f e c t e d b y O A R in a n i n c r e a s i n g m a n n e r w i t h i n c r e a s i n g b l o c k a g e ratios. A t l o w b l o c k a g e v a l u e s ( a r o u n d 8 %) t h e p r e s s u r e d i s t r i b u t i o n is p r a c t i c a l l y c o n s t a n t a n d v a r i e s little w i t h O A R : it is s l i g h t l y p o s i t i v e 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 t h i n c r e a s i n g O A R . A t h i g h e r b l o c k a g e ratios t h e p r e s s u r e d i s t r i b u t i o n o v e r t h e u p s t r e a m part o f t h e p l e n u m s h o w s a negative pressure w h i c h decreases w i t h increasing O A R . This negative pressure r e g i o n is a l w a y s f o l l o w e d b y a p r e s s u r e r e c o v e r y w h i c h c o u l d b r i n g t h e p r e s s u r e v a l u e i n t h e d o w n s t r e a m e n d o f t h e p l e n u m s i g n i f i c a n t l y h i g h e r t h a n z e r o at h i g h O A R . T h e s e c o n d t y p e o f f l o w p a t t e r n 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 c a v i t y f l o w (as o p p o s e d t o o p e n c a v i t y f l o w i n t h e first c a s e ) b y S i n h a et al. [36]. It is c h a r a c t e r i z e d b y t w o separation b u b b l e s , o n e attached o n the upstream face a n d the o t h e r o n the d o w n s t r e a m f a c e o f t h e p l e n u m ( F i g u r e 6.41 ). T h i s t y p e o f f l o w w a s m a i n l y e n c o u n t e r e d in t h e (OAR =  open-jet  1) c o n f i g u r a t i o n w h e r e t h e slats w e r e n o t t h e r e t o p r e v e n t t h e b r e a k u p o f t h e f r e e  s h e a r - l a y e r ; a n d w h i l e t e s t i n g h i g h b l o c k a g e - r a t i o m o d e l s s u c h as t h e 1 2 - i n c h n o r m a l flat p l a t e . In this latter c a s e , t h e l a r g e 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 s h e a r - l a y e r far e n o u g h s i d e w a y s t o i m p i n g e o n t h e p l e n u m s i d e - w a l l w h e r e it w o u l d r e a t t a c h . A l s o , t h e t e s t i n g o f t h e l a r g e flat p l a t e at t h e 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 o f large b l o c k a g e w i t h little u p s t r e a m s l a t t e d - w a l l o p e n a r e a c a n result in a j e t - l i k e f l o w t h r o u g h t h e s l o t s o f t h e w a l l t o c r e a t e 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, " t o 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  section. S i m i l a r l y , t h e e x p e r i m e n t a l i n v e s t i g a t i o n h a s s h o w n a c o n v e r g e n c e , a l b e i t n o t at a s i n g l e o p t i m u m O A R v a l u e , o f all t h e b l o c k a g e - r a t i o c u r v e s . T h e r a n g e o f o p t i m u m O A R v a l u e s lies b e t w e e n 0.55 a n d 0 . 6 5 . B e c a u s e o f t h e l a r g e s l o p e o f c e r t a i n b l o c k a g e - r a t i o c u r v e s , a s m a l l s y s t e m a t i c e x p e r i m e n t a l e r r o r c a n translate i n t o a s i g n i f i c a n t shift in w h a t is c o n s i d e r e d t h e o p t i m u m O A R . T h e r e f o r e , g r e a t c a r e s h o u l d b e t a k e n in a c q u i r i n g t h e d a t a , e s p e c i a l l y at l a r g e b l o c k a g e ratios. T h e e x p e r i m e n t s h a v e a l s o 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 e q u i v a l e n t t o a n o r m a l flat p l a t e o f 3 3 . 3 % b l o c k a g e ratio w o u l d b e e x c e e d i n g t h e c a p a b i l i t y o f t h e T o l e r a n t w i n d t u n n e l . A l t h o u g h f r e e - a i r c o n d i t i o n s c a n still b e o b t a i n e d f o r t h i s h i g h b l o c k a g e v a l u e , 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 t h e s a m e o p t i m u m O A R v a l u e o f s m a l l e r m o d e l s . It s h o u l d b e p o i n t e d o u t that d u e t o t h e relative s i z e o f its w a k e t h e n o r m a l flat p l a t e is t h e " b l u f f e s t " m o d e l ; a n d t h a t t h e u s e o f o t h e r t y p e s o f bluff b o d y s u c h as t h e c i r c u l a r c y l i n d e r ( w i t h o r w i t h o u t s p l i t t e r p l a t e ) w i l l s u f f e r less w a k e b l o c k a g e t h a n t h e flat p l a t e o f t h e s a m e b l o c k a g e ratio. T h e u s e o f tufts in t h e p l e n u m a n d o n t h e airfoil-slats m a k e s t h e T o l e r a n 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  put u p with. This s i m p l e f l o w visualization  p r o v i d e s a n e a s y m e a n s f o r d e t e c t i n g t h e 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 t h e s e p a r a t i n g s h e a r - l a y e r in t h e p l e n u m . W h e n d e t e r m i n i n g t h e s i z e s o f t h e T o l e r a n t test s e c t i o n , t h e d e p t h o f t h e s h o u l d b e great e n o u g h to  e n s u r e t h a t slat stall a n g l e r e m a i n s t h e l i m i t i n g  plenum  condition  for  present study, based  on  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 ratio. Although  power  consumption was not  m e a s u r e d in t h e  m e a s u r e m e n t s m a d e in a n e a r l i e r s t u d y o f t h e T o l e r a n t w i n d t u n n e l b y M a l e k [12], it s e e m s l i k e l y that t h e p o w e r w o u l d b e a b o u t 5 t o 1 0 % h i g h e r f o r t h e T o l e r a n t t u n n e l t h a n f o r a s o l i d - w a l l t u n n e l , largely b e c a u s e of t h e effects of the p l e n u m flow.  58  Finally, it is i m p o r t a n t t o n o t e t h a t t h e w a k e o f a m o d e l t e s t e d in t h e T o l e r a n t w i n d t u n n e l c a n b e a l t e r e d i n t w o w a y s . Firstly, t h e i n t e r a c t i o n b e t w e e n t h e s h e d v o r t i c e s a n d t h e s l o t t e d w a l l is l i k e l y t o m o d i f y t h e d y n a m i c s o f t h e v o r t e x f l o w ( a n d p e r h a p s t h e s e p a r a t i o n p o s i t i o n ) b e h i n d the m o d e l . S e c o n d l y , the oscillatory f l o w re-entry, the f l o w rushing out of t h e p l e n u m t o r e - e n t e r t h e test s e c t i o n , w i l l i n c r e a s i n g l y affect t h e w a k e f l o w as t h e  distance  d o w n s t r e a m of the m o d e l increases.  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 goals s o u g h t for the theoretical m o d e l l i n g of the Tolerant  test  s e c t i o n , this m o d e l c a n b e i m p r o v e d in m a n y w a y s ; b u t m o s t i m p r o v e m e n t s are l i k e l y  to  seriously complicate the mathematics of the m o d e l and lengthen considerably the c o m p u t a t i o n o f t h e s o l u t i o n . F o r e x a m p l e , t h e m o d e l l i n g o f t h e p l e n u m f r e e s h e a r layer b y i m p o s i n g a constant pressure distribution a l o n g the separating streamline s h o u l d bring the solution closer t o reality. 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 n o n - l i n e a r ; t h a t i s , t h e g e o m e t r y o f t h e s h e a r layer has t o b e k n o w n t o b e able t o i m p o s e t h e r e q u i r e d c o n d i t i o n a n d the application of the constant pressure distribution will modify the g e o m e t r y of the separating streamline. Clearly, the s o l u t i o n r e q u i r e s a n iterative p r o c e d u r e . T h e a d a p t a t i o n o f t h e m a t h e m a t i c a l m o d e l f o r t h e t e s t i n g 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 a n i n c l i n e d flat p l a t e w o u l d b e a u s e f u 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 such a m o d e l for u n c o n f i n e d conditions. A n experimental counterpart w o u l d then b e r e q u i r e d t o a s s e s s t h e real f l o w a n d e v a l u a t e t h e t h e o r y . 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 o w a b l e bluff b o d y l e n g t h , t h e t e s t i n g 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 t h e half R a h k i n e b o d y a n d l o n g r e c t a n g u l a r c y l i n d e r s h o u l d b e c o n s i d e r e d . T h e y w i l l p r o v i d e f i x e d " w a k e " d i m e n s i o n s . In t h e c a s e o f t h e half R a n k i n e b o d y a n equivalent numerical solution w o u l d also be easy to obtain. S h o u l d a l o n g e r test s e c t i o n ( o r s l o t t e d - w a l l ) b e c o m e n e c e s s a r y , t h e o p e n i n g o f t h e p l e n u m d o w n s t r e a m end-wall t o a t m o s p h e r i c pressure s h o u l d delay s o m e of the  re-entering  59 f l o w r e s p o n s i b l e for a s h o r t e n i n g of t h e u s e a b l e test s e c t i o n . T h e breather w o u l d t h e n take care o f m a s s c o n s e r v a t i o n in t h e t u n n e l . Finally, t h e T o l e r a n t w i n d t u n n e 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 b l u f f b o d y testing; i n c l u d i n g boundary-layer w i n d tunnels 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 u s e o f 3 s l o t t e d p a n e l s (walls a n d c e i l i n g ) w i t h a n O A R o f 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 b e u s e d f o r t h e t e s t i n g o f m o d e l s s u c h as aircraft i n t a k e - o f f o r l a n d i n g c o n f i g u r a t i o n , c a r s , and buildings.  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. John Wiley & S o n s , S e c o n d Edition, 1984. 2. G a r n e 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. AGARDograph 109,1966 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 Wall-Mounted Models Subject to Separated Flows.  or  Two  N P L A E R O REPORT 1290, February 1969. 5. W i l l i a m s , C D . a n d P a r k i n s o n , C V .  A Low-Correction Wall Configuration for Airfoil Testing. P r o c . A G A R D C o n f . 1 7 4 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 1 9 7 6 . 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 1981. 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 1 9 8 2 . 9. M o k r y , M . , C h a n , Y . Y . , J o n e s , D . J . a n d 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. Williams, C D .  A New Slotted-Wall Method for Producing Low Boundary Corrections in Two-Dimensional Airfoil Testing. Ph.  D.  Thesis,  Dept.  of  Mechanical  C o l u m b i a , O c t o b e r 1975.  60  Engineering,  The  University  of  British  61  11. Parkinson, C . V . , Williams, C D . and Malek, 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 1 9 7 8 , V o l . 1, S e p t e m b e r 1 9 7 8 , p p . 3 5 5 - 3 6 0 . 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. Ph. D. Thesis, Dept. C o l u m b i a , April 1983.  of  Mechanical  Engineering,  The  University  of  British  1 3 . R a i m o n d o , S. a n d C l a r k , P.J.F.  Slotted Wall Test Section for Automotive Aerodynamic Facilities. A I A A 12th A e r o d y n a m i c Testing C o n f e r e n c e , M a r c h 22-24, 1982, Williamsburg, Virginia, U.S.A., Paper A I A A - 8 2 - 0 5 8 5 - C P . 1 4 . Flay, R . C . J . , E l f s t r o m , C M . a n d C l a r k , P.J.F.  Slotted-Wall Test Section for Automotive Aerodynamic Tests at Yaw. SAE International C o n g r e s s , February 28 t o M a r c h 4, 1983, M i c h i g a n , Paper 830302.  U.S.A.,  1 5 . E l f s t r o m , C M . , Flay, R . G . J . a n d C l a r k , P.J.F.  Slotted Wall Test Section for Car and Truck Aerodynamic Testing. Proceedings of the A S M E C o n f e r e n c e Boston, November 14-18,1983.  on  Aerodynamics  of  Transportation,  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 . 1 7 . 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. T h w a i t e s , B.  Incompressible Aerodynamics. O x f o r d at t h e C l a r e n d o n P r e s s , 1 9 6 0 . 19. R o s h k o , A .  On the Development of Turbulent Wakes from Vortex Streets. N A C A report 1191, 1958. 20. R o s h k o , A .  On the Drag and Shedding Frequency of Two-Dimensional Bluff bodies. N A C A Technical Note 3169,1954. 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. B u l l e t i n of J S M E , V o l . 2 7 , N o . 2 3 0 , A u g u s t 1 9 8 4 .  62  22. Lamb, H .  Hydrodynamics. Sixth Edition, D o v e r P u b . , 1945. 23. Roshko, A .  A New Hodograph for Free-Streamline Theory. N A C A Technical N o t e 3168, 1954. 2 4 . P a r k i n s o n , C V . a n d Jandali, T .  A Wake Source Model for Bluff Body Potential Flow. J. F l u i d M e c h . , V o l . 4 0 , p a r t 3, p p . 5 7 7 - 5 9 4 , 1 9 7 0 . 2 5 . E l - S h e r b i n y , S.EI-S.  Effect of Wall Confinement on the Aerodynamics of Bluff Bodies. Ph.D. Thesis, Dept. Columbia, 1972.  of  Mechanical  Engineering,  T h e University  of  British  2 6 . 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 Two-Dimensional Flow. C-of-A-MEMO 1981.  8109, C o l l e g e of Aeronautics,  Flow Past Bluff Bodies in  Cranfield,  England,  September  27. Kiya, M . a n d Arie, M .  An inviscid Bluff-Body Wake Model Which Includes the Far-Wake Displacement Effect. J. F l u i d M e c h . , V o l . 8 1 , part 3 , p p . 5 9 3 - 6 0 7 , 1 9 7 7 . 2 8 . B e a r m a n , P . W . a n d F a c k r e l l , J.E.  Calculation of Two-Dimensional and Axisymmetric Bluff-Body Potential Flow. J. F l u i d M e c h . , V o l . 7 2 , part 2, p p . 2 2 9 - 2 4 1 , 1 9 7 5 . 2 9 . S t a n s b y , P.K.  A Generalized Discrete-Vortex Method for Sharp-Edged Cylinders. A I A A Journal, V o l . 23, N o . 6, pp. 856-861, June 1985. 3 0 . I n a m u r o , T., A d a c h i , T. a n d S a k a t a , H .  A Numerical Analysis of Unsteady Separated Flow by Vortex Shedding Model. Bulletin of JSME, V o l . 26, N o . 222, D e c e m b e r 1983. 31. Kiya, M . and Arie, M .  A Contribution to an Inviscid Vortex-Shedding Model for an Inclined Flat Plate in Uniform Flow. J. F l u i d M e c h . , V o l . 8 2 , p a r t 2 , p p . 2 2 3 - 2 4 0 , 1 9 7 7 . 32. K e n n e d y , S.F.  The Design and Analysis of Airfoil Sections. Ph. D. Thesis, The University of Alberta, 1977. 33. H o e r n e r , S.F.  Fluid-Dynamic Drag. H o e m e r Fluid D y n a m i c s , 1 9 6 5 .  63  34. Blevins, R.D.  Applied Fluid Dynamics Handbook. V a n Nostrand Reinhold C o . , 1984. 3 5 . Farrel, C , C a r r a s q u e l , S . , C u v e n , D . a n d P a t e l , V . C .  Effect of Wind-Tunnel Walls on the Flow Past Circular Cylinders and Cooling Tower Models. A S M E J o u r n a l of F l u i d s E n g i n e e r i n g , p p . 4 7 0 - 4 7 9 , S e p t e m b e r 1 9 7 7 . 36. Sinha, S . N . , G u p t a , A . K . and O b e i r a , M . M .  Laminar Separating Flow Over Backsteps and Cavities, Part II: Cavities. A I A A J o u r n a l , V o l . 2 0 , N o . 3, p p . 3 7 0 - 3 7 5 , M a r c h 1 9 8 2 . 3 7 . 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. Prog. A e r o s p a c e Sci. V o l . 20, pp.  97-123,1983.  38. R o s h k o , A .  Experiments on the Flow Past a Circular Cylinder at Very High Reynolds Number. J. F l u i d M e c h . , V o l . 1 0 , p. 3 4 5 , 1 9 6 1 .  APPENDIX 1  WIND TUNNEL CALIBRATION  T h e p u r p o s e o f t h e e m p t y w i n d t u n n e l c a l i b r a t i o n is t o r e l a t e t h e v e l o c i t y o b t a i n e d w i t h a P i t o t t u b e in t h e n o z z l e t o t h e v e l o c i t y in t h e 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 t h e t e c h n i q u e u s e d b y W i l l i a m s f 1 0 ] . T h e m a i n d i f f e r e n c e s are t h e u s e o f a s m a l l e r P i t o t t u b e ( 0 . 2 5 i n c h in d i a m e t e r ) in o r d e r t o r e d u c e its w a k e i n t e r f e r e n c e w i t h t h e m o d e l , a n d its p o s i t i o n o f 2 2 inches u p s t r e a m of the test-section entrance. This n e w t u b e p o s i t i o n was c h o s e n t o  improve  accuracy 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 pressure transducer. T h e m e t h o d is b a s e d o n t h e a s s u m p t i o n that t h e r e is n o a p p r e c i a b l e d i f f e r e n c e i n t o t a l h e a d , H , b e t w e e n the test s e c t i o n a n d the n o z z l e . T h u s  H  f  w h e r e H is t h e t o t a l h e a d , and  n  =  P e o f  + q,  =  H  n  =  P  e  o  n  + q  (A1.1)  n  the static pressure a n d q the d y n a m i c pressure. T h e subscripts  t  refer to the test s e c t i o n a n d n o z z l e Pitot-tubes, respectively. The calibration was p e r f o r m e d by running the w i n d tunnel over a range of 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 , a n d m e a s u r i n g q  f  and q  n  . T h e n , t h e ratio q  t  I q  n  leads to a  constant of proportionality, o r  q  f  = K  2  q  n  (A1.2)  T h e p r e s s u r e c o e f f i c i e n t Cp d e f i n e d as  P / " P»f C  Pi  =  -  64  (A1.3)  65  w h e r e p - is a s u r f a c e p r e s s u r e m e a s u r e d at a p o i n t  /*, c a n b e r e w r i t t e n u s i n g e q u a t i o n s ( A 1 . 1 )  ;  a n d (A1.2) t o o b t a i n  Cp,= K  2  q  n  or r  _ P / - ( H  n  - «  2  q„)  Cp-  o r finally  Cp. = 1 +  N o t e t h a t all t h e q u a n t i t i e s p y , H  n  and q  "  J.  n  (A1.4)  are m e a s u r e d in v o l t s 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 r e s s u r e u n i t s . T h e v a l u e of t h e c a l i b r a t i o n c o n s t a n t K , is t y p i c a l l y 0 . 9 5 f o r f o r t h e s o l i d - w a l l t e s t s e c t i o n a n d 0 . 9 8 f o r t h e s l o t t e d - w a 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 ) . However, for conversion from  c e r t a i n a p p l i c a t i o n s l i k e t h e e v a l u a t i o n of  voltage to  pressure units  the  Strouhal number,  b e c o m e s n e c e s s a r y a n d is o b t a i n e d t h r o u g h  the a  calibration c o n s t a n t K , , s u c h that  q  The q  n  n  ( m m H  2  0 )  = K, ( m m H 0 / v o l t ) q ( volt) n  (A1.5)  v a l u e s are s i m u l t a n e o u s l y m e a s u r e d in v o l t s w i t h t h e B a r o c e l p r e s s u r e t r a n s d u c e r a n d in  m m H O o n the Betz water micromanometer. 2  2  APPENDIX 2  EVALUATION OF THE INFLUENCE  COEFFICIENT  T h e d e t a i l e d s o l u t i o n o f t h e i n t e g r a l e q u a t i o n l e a d i n g t o t h e i n f l u e n c e c o e f f i c i e n t is g i v e n in r e f e r e n c e [32]. T h i s a p p e n d i x s u m m a r i z e s t h e n e c e s s a r y e x p r e s s i o n s f o r t h e e v a l u a t i o n o f K^- f o r t h e c a s e w h e r e a straight p a n e l w i t h c o n s t a n t v o r t i c i t y 7- is u s e d .  1 K  ; /  = -  2 a A {(b + A ) l n ( r ) - ( b - A . ) l n ( r | ) + 2 a t a n " 2  1  (  where r  2  = a  r§ =  a  2  2  + (b +  A)2  + (b -  A)  2  2 A is t h e s i z e o f t h e p a n e l . and  a = (y,- - yj) cosdj - (x - - xy) sinfly ;  b = (y - - y-) sindj + (x - - \j) cosdj ;  ;  6: is t h e a n g l e b e t w e e n t h e p a n e l / a n d t h e w i n d axis ( u s u a l l y h o r i z o n t a l ) .  66  - 4 A}  APPENDIX 3  DETERMINATION OF VELOCITY FIELD  A v e l o c i t y v e c t o r c a l c u l a t e d e i t h e r at a c o n t r o l p o i n t C - o r a n y p o i n t (x -,y -) i n t h e d o m a i n 7  y  ;  is t h e r e s u l t o f t h r e e 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  Point sources  V  v  Vorticity distribution o n the boundaries  Each o n e o f t h e s e contributions can b e d i v i d e d in t w o velocity c o m p o n e n t s a l o n g t h e x a n d y a x e s , as f o l l o w s :  Uniform flow F r o m t h e v e l o c i t y p o t e n t i a l o f t h e u n i f o r m f l o w t h e v e l o c 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 velocity c o m p o n e n t s resulting from t w o point sources of c o m m o n strength Q a n d s i t u a t e d at ( x „  , y . ) and ( x  c  ,y  c  ) c a n b e w r i t t e n as  Q V  sx = -  V  cosX, <  cosA  2  +  Q sinX, = - { 2TT r.  where  67  }  sinX +  2  } r  Q  68 r S l  r  and X! ,X defined  2  s  =t(*/-x )  + <y,-y > ]*  2  8  Sl  t^/- s )  =  x  2  Sl  2  (y/-'ys ) ^  +  2  2  2  are t h e a n g l e s b e t w e e n a h o r i z o n t a l l i n e a n d r  positive  in t h e c o u n t e r c l o c k w i s e direction  ,r  while  X  ( N o t e t h a t f o r s y m m e t r y X ^ is is p o s i t i v e  2  in t h e clockwise  direction).  Vortex sheets T h e n o r m a l a n d t a n g e n t i a l v e l o c i t i e s i n d u c e d b y a straight p a n e l w i t h d i s t r i b u t e d v o r t i c i t y 7 are g i v e n b y v_ = "  — In — 27T r  2  7  v  w h e r e 5 \, 6  2  = -  -  ( 0 , - 0 2 )  are t h e a n g l e s b e t w e e n t h e p a n e l a n d r , , r . A l s o 2  r, = { tx - (xy+A)] + [y 2  ;  r  (y- - A ) ] }* 2  r  y  = {fr/ - (xy- A ) ] + [y,-- (yy+A)] }* 2  2  2  The x and y velocity c o m p o n e n t s can then b e calculated by  V  vx  =  v  t  c o s  0  +  v  n  s i n  w h e r e )3 is t h e a n g l e b e t w e e n t h e p a n e l a n d t h e x - a x i s .  0  APPENDIX 4  REGRESSION METHOD USED FOR  COMPARING  TWO PRESSURE COEFFICIENT DATA SETS  T h i s r e g r e s s i o n m e t h o d w a s u s e d b y Flay, E l f s t r o m a n d C l a r k [14] f o r c o m p a r i n g c a r pressure distributions  m e a s u r e d in d i f f e r e n t w i n d  tunnel  configurations  to  an  equivalent  reference pressure distribution. A  linear r e g r e s s i o n analysis, u s i n g a l e a s t - s q u a r e s t e c h n i q u e ,  is p e r f o r m e d  on  a  r e f e r e n c e - t e s t a n d a c t u a l d a t a s e t , o n a v e l o c i t y basis, t o o b t a i n t w o c o e f f i c i e n t s : a b l o c k a g e c o r r e c t i o n factor, C F , a n d an associated standard deviation, S D . T h e b l o c k a g e correction factor is t h e v a l u e b y w h i c h t h e s l o t t e d - w a l l f r e e s t r e a m s p e e d m u s t b e d i v i d e d t o g i v e t h e  best  agreement with the equivalent reference-test pressure distribution. The standard deviation can b e r e g a r d e d as t h e r e s i d u a l e r r o 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 r e s s u r e d i s t r i b u t i o n . For pressure-tap n u m b e r  / , t h e n o r m a l i z e d v e l o c i t y is c a l c u l a t e d u s i n g  (I"  (A4.1)  Cp;)*  f o r b o t h p r e s s u r e d a t a s e t s . T h e c o e f f i c i e n t s C F a n d S D o f t h e l i n e a r r e g r e s s i o n are o b t a i n e d t h r o u g h a l e a s t - s q u a r e s fit. Let V r , / = ;  1,...,N  b e the set of n o r m a l i z e d reference velocities a n d V t h e actual ;  v e l o c i t y s e t . T h e c o r r e c t e d v a l u e s , V c - , are o b t a i n e d t h r o u g h t h e l i n e a r r e g r e s s i o n  V  for w h i c h the coefficients A ,  and A  2  C /  = A, + A  V. ;  are c a l c u l a t e d t o m i n i m i z e t h e s u m o f t h e  b e t w e e n V c - a n d t h e r e f e r e n c e v a l u e s Vr -. f  2  7  69  (A4.2)  differences  70  T h a t is  N Z /si  (vr - (A, + A ;  V-))  2  is m i n i m i z e d .  2  (A4.3)  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 h e s t a g n a t i o n p o i n t t h e v e l o c i t y is n e c e s s a r i l y z e r o in b o t h the reference a n d slotted-wall data sets. Therefore  d dA  A  2  2  N I P i  (Vr - (A ;  Vj))  = 0  2  2  (A4.4)  is n o w c a l l e d C F ( b l o c k a g e - c o r r e c t i o n f a c t o r ) a n d is u s e d t o o b t a i n e d t h e c o r r e c t e d p r e s s u r e  c o e f f i c i e n t s C p - as f o l l o w s c ;  (1 -  Cp ) = cj  CF  2  (1 -  C  P /  )  (A4.5)  T h e q u a l i t y o f t h e o v e r a l l fit o f t h e s l o t t e d - w a l l d a t a t o t h e r e f e r e n c e - t e s t d a t a is j u d g e d o n the value of the standard deviation :  1 S D = [ N  To summarize, the  N Z  /i  (C  P f /  - Cp  c /  )  2  P  (A4.6)  i  blockage correction factor  C F is a m e a s u r e o f  b e t w e e n a slotted-wall and a reference-test data set; A value of C F =  the  correlation  1 r e s u l t s in n o b l o c k a g e  correction. C o n s e q u e n t l y , the ideal configuration of the Tolerant w i n d tunnel s h o u l d p r o d u c e C F ' s c l o s e t o unity. A n d , the standard deviation S D indicates the error b e t w e e n the c o r r e c t e d and reference pressure distribution; 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 of slotted-wall data.  APPENDIX 5  GRADED OPEN AREA RATIO  This a p p e n d i x derives t h e e x p r e s s i o n s u s e d t o o b t a i n varying o p e n areas a l o n g t h e w i n d axis. A c o m p l e t e l y d e f i n e d slotted-wall c o n f i g u r a t i o n requires, in a d d i t i o n t o wall l e n g t h a n d slat s i z e , t h r e e p a r a m e t e r s : t h e O A R w h i c h f i x e s t h e n u m b e r o f g i v e n - s i z e slats t o b e u s e d , t h e o p e n - a r e a d i s t r i b u t i o n a n d finally a n initial c o n d i t i o n w h i c h c a n , f o r e x a m p l e , b e t h e s i z e o f t h e first s l o t . Let a  0  ,a ,...,a 1  n  b e the size of t h e slots w h e r e the subscripts indicate t h e slot n u m b e r  i n c r e a s i n g i n t h e d o w n s t r e a m d i r e c t i o n . F o r a s l o t t e d - w a l l c o n t a i n i n g n slats, t h e r e w i l l b e ( n + 1) s l o t s . A l s o , l e t L b e t h e l e n g t h o f t h e w a l l a n d c t h e c h o r d o f t h e a i r f o i l - s h a p e d slats. T h e o p e n a r e a r a t i o is t h e n d e f i n e d as  1 OAR = - { L  n Z /=o  a } = 1;  n»c — L  (A5.1)  F o r a d i s t r i b u t i o n o f o p e n areas v a r y i n g l i n e a r l y w i t h t h e s l o t n u m b e r , w e h a v e  a,- = a  0  i = 1,2,...,n  + b«i  (A5.2)  w h e r e b is t h e s l o p e o f t h e l i n e a r v a r i a t i o n . T h e o p e n - a r e a r a t i o c a n n o w b e w r i t t e n as  1 OAR = - { L  n Z /'=o  or 71  ( a  0  + b « i ) }  (A5.3)  72  1 O A R = — { ( n + 1) a L  0  n 2 /=o  + b  i}  (A5.4)  And since  n Z  i = i n (n + 1)  /:0  (A5.5)  the expression for O A R b e c o m e s  1 OAR = - { ( n + 1)[a  + inb]}  0  (A5.6)  a n d t h e s l o p e b c a n 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 r e q u i r e t h e o p e n areas t o i n c r e a s e 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 t h e r e f o r e h a v e  b  £  0  or  O A R * L - (n+1) a  0  £  0  (A5.8)  Thus w e have  OAR* L 0  <  a  0  *  (A5.9) n+ 1  or, using e q u a t i o n (A5.1)  73  L 0  £  a  0  n«c (A5.10)  * n + 1  w h e r e t h e 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 b u t i o n . O n e c a n n o w d e f i n e a p a r a m e t e r , AORT, w h i c h r e l a t e s t h e s i z e o f t h e 0  tn  slot ( a ) to the 0  e v e n l y - s p a c e d slot size, s u c h that  L -  n«c  AORT =  (A5.11) n+ 1  T h e v a l u e o f A O R T is t h e r e f o r e a l w a y s g r e a t e r 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 (linear) v a r i a t i o n o f o p e n areas o n l y o n e p a r a m e t e r n e e d t o b e g i v e n : AORT. T h e n , f o r a g i v e n A O R T , t h e s l o t s i z e a  0  a n d t h e s l o p e b o f t h e l i n e a r d i s t r i b u t i o n is  c a l c u l a t e d . F o r t h e s p e c i a l c a s e w h e r e A O R T = 1 w e h a v e b = 0 w h i c h is t h e 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 . m e a s u r e d f r o m t h e n o z z l e exit t o t h e l e a d i n g e d g e o f t h e slat S/  n u m b e r i , c a n t h e n b e c a l c u l a t e d as f o l l o w s  (A5.12)  i-i x . = a s  0  +  2  (a.- + c)  i = 2,3,...,n  (A5.13)  i = 1,2,...,n  (A5.14)  After simplification, w e get  x  = i . a  0  +(i-1)c +  *i(i-1)b  APPENDIX 6  INSTRUMENTATION  Pressure Transducer Barocel 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 i g n a 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 1 0 1 5 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  Scanivalve 48-ports ( S C A N I V A L V E C o r p . ) M o d e l 48J9-2273  Pressure Lines Polyethylene tubing (INTRAMETRIC) Inside 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 S c a n i v a l v e ="1 m ( 3 ft.) S c a n i v a l v e t o p r e s s u r e t r a n s d u c e r » 2 m (6.5 ft.) Manometer Betz Water M i c r o m a n o m e t e r (Max-PLANCK-INSTITUT f u r Stromungsforschung Cottingen) S m a l l e s t d i v i s i o n : 0.1 m m H  a  O  Averaging Voltmeter Time D o m a i n Analyser (Solatron, S C H L U M B E R C E R ) Smallest division : 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 S m a l l e s t D i v i s i o n : 0.2 % o f r a n g e ( 2 0 , 1 0 0 , 2 0 0 , 5 0 0  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 . Ltd., England)  Hz)  APPENDIX 7  ERROR ANALYSIS  T h i s s e c t i o n d e s c r i b e s in d e t a i l t h e e v a l u a t i o n o f e x p e r i m e n t a l e r r o r s o n r e d u c e d d a t a s u c h as d y n a m i c p r e s s u r e , v e l o c i t y , R e y n o l d s n u m b e r , p r e s s u r e c o e f f i c i e n t a n d S t r o u h a l n u m b e r . T h e m e t h o d u s e d h e r e is t e r m e d u n c e r t a i n t y analysis a n d p r o v i d e s relative 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 variable, Y, related t o s o m e i n d e p e n d e n t variables, x , , x , . . . , x 2  n  , by  t h e f u n c t i o n Y = f ( x , , x , . . . , x ) , t h e u n c e r t a i n t y o f t h e r e s u l t s is 2  n  9f  3f  eY = [ ( —  ex,)  9x,  where e x , , e x , . . . , e x 2  n  2  , ex )  +...•+(—  3x  n  2  ]*  (A7.1)  n  are t h e u n c e r t a i n t i e s o r p r o b a b l e e r r o r s o f t h e v a r i a b l e s x , , x , . . . , x 2  n  ,  respectively. T o u s e u n c e r t a i n t y a n a l y s i s it is n e c e s s a r y t o o b t a i n t h e e r r o r a s s o c i a t e d w i t h e a c h i n d e p e n d e n t v a r i a b l e . S u c h u n c e r t a i n t i e s are d e t e r m i n e d s o m e t i m e s f r o m t h e p r e c i s i o n o f a n instrument, o r f r o m the e x p e r i e n c e of the experimenter. T h e f o l l o w i n g t a b l e s u m m a r i z e s t h e u n c e r t a i n t i e s in t h e b a s i c v a r i a b l e s , a n d f o r m s t h e basis f o r t h e s u b s e q u e n t c a l c u l a t i o n s .  eK,  ± 1 %  eK  ±  2  1 %  ± 0.002 volts ± 0.003 volts eH„  ± 0.003 volts  Table A7.1 : Uncertainties in basic values.  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 t h e e x p r e s s i o n u s e d t o calculate t h e pressure coefficients,  P i " C p . = i + J. K  H  n "  (A7.2)  »q„  t h e u n c e r t a i n t y i n Cpy b e c o m e s  -  1  eC  P /  = [( — K  P; n  1  2%  _ H  e H „ > » + (- -^— eK )*  + (- ^-feo, )  n  P /  K  P; n  _H  e >» + ( —  2  K l q  2%  K  n  T h i s r e l a t i o n s h o w s that m a x i m u m e r r o r w i l l o c c u r w h e n q  F  2  n  n  (A7.3)  2  is t h e l o w e s t , w h e n t e s t i n g t h e  l a r g e s t m o d e l ( 1 2 i n c h e s i n d i a m e t e r ) a n d w h e n (py - H ) is largest, g e n e r a l l y c o r r e s p o n d i n g t o n  t h e b a s e p r e s s u r e . T h e u n c e r t a i n t y at t h e s t a g n a t i o n p o i n t ( C p = 1), w h e n (py - H ) = 0 a n d f o r n  K  2  = 0.985 and q  n  = 0.179 volts c o r r e s p o n d i n g t o a typical test f o r a 1 2 - i n c h d i a m e t e r cylinder,  l e a d s t o e C p = ± 0 . 0 2 o r a b o u t ± 2 % . T h e s a m e c a l c u l a t i o n b u t i n c l u d i n g a b a s e p r e s s u r e py = -  0.377 volt and a total head H  n  = 0.308 volt c o r r e s p o n d i n g t o a testing o f the s a m e 12-inch  c y l i n d e r b e t w e e n s o l i d w a l l s g i v e s e C p = ± 0 . 0 8 . F o r t h e s e c o n d i t i o n s t h e b a s e p r e s s u r e is C p  D  = - 3.0 w h i c h t r a n s l a t e s t o p e r c e n t a g e e r r o r o f a b o u t 3 % .  Uncertainty in Dynamic Pressure, q  The relation b e t w e e n q  n  , t h e d y n a m i c pressure o b t a i n e d in t h e n o z z l e a n d e x p r e s s e d in  v o l t s , a n d q , t h e t r u e d y n a m i c p r e s s u r e o f t h e t e s t s e c t i o n i n p s i u n i t s , is g i v e n b y  q (psi) = K , ( m m H  2  0 / volt) q  n  ( v o l t s ) C (psi / m m H  2  0 )  (A7.4)  w h e r e K , is a c a l i b r a t i o n v a l u e a n d C is u s e d t o c o n v e r t t h e u n i t s . A g a i n u s i n g e q u a t i o n ( A 7 . 1 ) t o  78  obtain a measure of the uncertainty, w e get  eq = [ ( q C e K , ) n  2  + (K  1  C eq  n  )  2  ] ^  (A7.5)  or in terms of percentage  -  =  q  [(  ) +(—) F 2  K,  2  •  (A7.6)  q„  w h i c h gives f o r the lowest w i n d s p e e d an error of a b o u t ± 2 %.  Uncertainty in Reynolds Number, Re  T h e g e n e r a l e x p r e s s i o n f o r R e is  Uh Re  (A7.7)  V  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 t h e d y n a m i c p r e s s u r e  U = V -  (A7.8)  thus,  h / q Re =  (A7.9)  In c a l c u l a t i n g t h e e r r o r in R e w e n e g l e c t t h e u n c e r t a i n t y i n t h e m o d e l s i z e h b u t i n c l u d e a n e r r o r in t h e k i n e m a t i c v i s c o s i t y v a n d d e n s i t y p d u e t o t e m p e r a t u r e v a r i a t i o n s . A p p l y i n g ( A 7 . 1 ) o n (A7.9) w e g e t  79  eRe — = [(i Re  eq - ) q  -ev  ep 2  p  )  2  +(  ,  — )  2  v  F  (A7.10)  a n d t h e e r r o r i n v a n d p is e s t i m a t e d f o r a v a r i a t i o n o f 1 0 ° F a b o u t t h e s t a n d a r d 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  lb/ft  3  v = 1.64 ± 0 . 0 6 x 1 0 " * f t / s e c 2  w e obtain an error 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 t h e S t r o u h a l n u m b e r is g i v e n b y  f h St = — U  (A7.11)  w h e r e f is 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 . 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 ( A 7 . 8 ) . H e n c e ,  f h / i p St =  (A7.12)  a n d t h e e r r o r i n St b e c o m e s  eSt ef — = [( - ) St f  2  +  eq - ) q  2  +  ep — ) p  2  . P  (A7.13)  F o r a n e r r o r i n f r e q u e n c y e s t i m a t e d t o b e n o m o r e t h a n ± 2 % , t h e r e s u l t i n g e r r o r o n t h e St is ± 2 . 5 %.  80  Uncertainty in Drag Coefficients,  Because t h e drag coefficients are o b t a i n e d f r o m integration of t h e surface pressure d i s t r i b u t i o n a n d t h e r e f o r e d e p e n d o n t h e i n t e r p o l a t i o n m e t h o d u s e d , it is d i f f i c u l t t o c a l c u l a t e its e r r o r . H o w e v e r , it is e s t i m a t e d , b a s e d m a i n l y o n t h e e r r o r i n 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):  Physical a n d basic transform planes f o r a circular cylinder 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.  0.0  30.0  60.0  X/h Figure  4.1 :  P r e s s u r e d i s t r i b u t i o n o v e r a n o r m a l flat p l a t e in unconfined flow comparison of n u m e r i c a l c a l c u l a t i o n in t r a n s f o r m p l a n e w i t h analytical solution. G i v e n C b = - 1.38, N = 7 0 p  4.2 :  90.0 BETA  120.0  150.0  Pressure distribution o v e r a circular cylinder in unconfined flow : comparison of numerical calculation in transform plane with analytical s o l u t i o n . Given C  p  o  = - 0.96, 0  S  = 80° , N =  70  180  Figure  4.3  :  V a r i a t i o n o f s o u r c e s t r e n g t h w i t h n u m b e r o f p a n e l s in transform  p l a n e , f o r flat p l a t e a n d c i r c u l a r c y l i n d e r  unconfined flow.  in  O  a  ii  Frtw Air (AiNtrttoal) Numerical Calculation  Tr— Air (Analytical) Numerical Cofculotlsn  8  -0.5  -0.3  —I  -o.i  r—  o.i  —1— 0.3  0.5  X/h a normal flat plate Figure 4.4 : Pressure distribution over in unconfined flow : comparison of numerical calculation in physical plane with analytical solution. Given C = - 1.38, N = 60 po  0.0  Figure 4.5  —I 60.0  -1— 30.0  —I 90.0 BETA  -1  120.0  150.0  Pressure distribution over a circular cylinder in unconfined flow comparison of numerical calculation in physical plane with analytical solution. Given C = - 0.96, p* = 80° , N = 60 p D  s  180.0  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 | gQ.5  Q, CIRCULAR CYLINDER  Cpb, FLAT PLATE  era c 3  13 3 .. sr  c  £§.< 2.5" ^ = = § 9,  n  S{ 2.CT  2 "° Q.T3 2 ^ •< to 3 = C 2 3 2 ~ n Q T3 O  If * fO  (B  Cpb, CIRCULAR CYLINDER  Given  C p  CF =  0.6749  D  =  ?-  -0.3  —I— -0.3  -I  1  0.1  -0.1  -  -I— 0.3  0.S  X/h Figure  4.7 :  P r e s s u r e d i s t r i b u t i o n o v e r a n o r m a l flat p l a t e i n s o l i d - w a 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 n u m e r i c a l c a l c u l a t i o n in p h y s i c a l p l a n e w i t h analytical s o l u t i o n .  Figure  4.8  :  Corrected pressure distribution over a n o r m a l flat p l a t e in s o l i d - w a l l c o n f i n e d f l o w : comparison of corrected numerical c a l c u l a t i o n in p h y s i c a l p l a n e w i t h free-air analytical s o l u t i o n .  co co  -3.65  -3.575  -3.60 -3.570-  -3.55-3.565-3.50  XI D_  -3.560-  a  -3.45  -3.555 -3.40  -3.550  -3.35  -3.545  10  i  20  30  -3.30 40  50  Wall Length  N Figure  4.9 :  Variation of base pressure coefficient w i t h n u m b e r of panels o n solid walls, for a normal flat plate m o d e l i n c o n f i n e d f l o w . Given C = - 1.0 , h / H = 1/3 , W a l l L e n g t h = 12 p  o  Figure  4.10 :  10  15  Variation of base pressure coefficient with w a l l l e n g t h , f o r a n o r m a l flat plate in c o n f i n e d flow. Given  C  pD  -  -  1.0  N ( m o d e l ) = 8 0 , N(wall) =  ,  h/H 20  =  1/3  ,  co U3  OT C  Correction Factor O  p In  b  z o§ o <  f £  2 oo  •hP © Is II  I  • o o O 7T -1  Qi  o  3/  n 3 on O  3 o Q.  _ o ^ ST  CD O o Q  CD  p  o A.  00 O  3  06  3"  p In'  p  p  p  Given C ~ - 0.96 , 0 C F = 0.7827 pb  7-j  1 30.0  0.0  1 80.0  1 90.0  1 120.0  1  1 150.0  160.0  BETA Figure  4.13:  Pressure distribution over a circular cylinder in solid-wall c o n f i n e d flow : c o m p a r i s o n  of  numerical calculation in physical plane w i t h f r e e - a i r analytical s o l u t i o n .  i  i  0.0  30.0  1 60.0  S  1 90.0  = 8 0 ° , h / H = 1/3 ,  1 120.0  1 150.0  1 160  BETA ure  4.14  :  Corrected  pressure  distribution  over  a  c i r c u l a r c y l i n d e r in s o l i d - w a l l c o n f i n e d f l o w : comparison calculation  of in  corrected  physical  analytical s o l u t i o n .  plane  numerical with  free-air  -2.51  -2.50-  -2.49  -2.48-  X)  o_  a  -2.47  -2.46-  -2.45  - 2 . 4 4 -r 0  T" 10  I  20  30  40  50  Wall Length  N Figure  4.15 :  Variation of base pressure coefficient with  Figure  4.16 :  Variation of base pressure coefficient with  n u m b e r of panels o n s o l i d walls, for a circular  w a l l l e n g t h , f o r a c i r c u l a r c y l i n d e r in c o n f i n e d  c y l i n d e r m o d e l in c o n f i n e d f l o w .  flow.  Given C  Given C  p  o  = - 1.0 , 0  W a l l Length = 12  = 8 0 ° , h / H = 1/3 ,  p  o  = - 0.96 , 0  $  = 8 0 " , h / H = 1/3 ,  N ( m o d e l ) = 80 , N(wall) = 20  era c  Base Pressure, Cpb  —T  z a2 3 f ™ 3=• 0  Q.  3  llOao  °  II  1' o  Z O *T 3.  w  w  2 era a; d (t Q | '  3 o Per"  cu  _^ i/i  O » - "O  cu n  in  "OS  _ <n 0. C —*  O CD 03 O  i-o  -S 9- 23 3"  Correction Factor o  o  o  cn  •vi  £6  o  00  o  o  09  in  o  (O  o  o  (O  in  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  4.19  :  T h e o r e t i c a l v a r i a t i o n o f b a s e p r e s s u r e 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 4  s i z e s o f flat p l a t e 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 t e s t s e c t i o n .  1.04  0.020  1.020.015-  f  1.00  0.98  f  0.010-  0.960.005  Blockage Ratios 0.94  o  83%  (Sin.)  19.4 X Cftn.) + X  23.0 X OK) 33.3 X Win.)  c  0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9  0  1  l  0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8  Theoretical variation of b l o c k a g e c o r r e c t i o n f a c t o r as a f u n c t i o n o f O A R f o r 4 Sizes o f flat p l a t e 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 .  0.9  Open Area Ratio  Open Area Ratio 4.20 :  C  0.000  0.92  Figure  cccdc  Figure  4.21 :  Theoretical variation of standard  deviation  as a f u n c t i o n o f O A R f o r 4 s i z e s o f flat p l a t e 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 section.  test  0.30  -0.95  rfiHc  7  0.28-  o °  -1.00-  :.++++ . : X  /  0.26-  c *o Q) O  0.24  O  -1.10  CD  V. V)  0.22  V) <D \CL  Blockage Ratios:  (i  O A + X  0.20-  -1.15-  6.3 % In.) 13.8 X O K )  O A  -1.20  4.22 :  0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9  0  0.1 0.2 0.3  function of  OAR  for  4  sizes  o f c i r c u l a r c y l i n d e r 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 of t h e test s e c t i o n . Given C  po  = - 0.96, 0  S  I I I I 0.4 0.5 0.6 0.7 0.8  Figure  4.23  Theoretical variation of pressure coefficient at (3 =  6 0 ° as a f u n c t i o n o f OAR  80°  for 4 sizes  o f c i r c u l a r c y l i n d e r 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 .  =  I 0.9  Open Area Ratio  Theoretical variation of pressure coefficient  at0=3O°asa  (3 In.) (3 In.) 23.0 X (9 In.) 33.3 X (12 In.)  X  Open Area Ratio Figure  8.3 X 13.8 X  -f  25.0 X (9 K) 33J X (ttln.)  0.18 0  Blockage Ratios  Given C  p  o  = - 0 . 9 6 , p* = s  80°  Pressure Coefficient at 70 era c  3  CM  cn  o  O  i  2. 2J-  n 3  ro  -ca 3  cr j II « ~" <= o £ < i 5= 3 W  o S Q. W 3.  "* S 5'3 | §  •ca cn  3  II  o  a  p  § p.  1  2.  CL o>  I  O «  co  <D Q  •a o 8.02 - j ~ jo > a ro O o 3 ro2 o  oo  o  1  25T " 3. 3  c  IS)  cn i  I  =: 52. ° N  3"  cn u M u U w b M  o  a  M CO a 3" p p  O ba o  X-  a M  *  o  ^  o o  w Q O  (0  o—=— Base Pressure Coefficient ao c  I  3 UI  cr a. pj-  cn  o cn i  o  o o I  O  %:1 n ro  ro2 3 ro  o i  O  ho  9"8 2  M  o  O  O  a ii a 2 •O Si- TJ 5- _ ll < o « 2. a» 09 S 5 o 0 cu3.  P j  CM  1  o C.  oo 3* -  1  o-  ~ i Q.  as  n  3 ro 2,3  1/1  2 5 "  in fO ~"  3  g.  ro?o ro  Z6  cn  Q  o  5-2 p p  13.8  tu O  (D  2S.0  ii  3  x + t>o 00 33.3  81  3  p  M  *  X  M a p 3 3  a  o o X*  Id M * JO o? a  rX^>+^....>,CL. x  -xN,^  p  cn  1.02  0.06  0.05-  0.04-  0.03-  £  0.02-  0.01-  c  o»96 f 0 Figure  j j j j i i i i i • | 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1  4.26 :  0.00  l  p  o  S  N  c  c I  r  c  c I  ^  ^  t  \  0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9  Open Area Ratio  Theoretical variation of b l o c k a g e c o r r e c t i o n f a c t o r as a f u n c t i o n of O A R f o r 4 s i z e s o f c i r c u l a r c y l i n d e r 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 . Given C = - 0.96 , 0 = 8 0 °  c  Open A r e a Ratio Figure  4.27 :  Theoretical variation of standard  deviation  as a f u n c t i o n o f O A R f o r 4 s i z e s o f c i r c u l a r c y l i n d e r 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 t h e test s e c t i o n . Given C  pD  = - 0.96 , B  g  =  80°  of  Figure  5.1  :  The closed-circuit " G r e e n " w i n d tunnel.  -I  —• 6M. |<—  §  i  i  i  i  i  1 1-  rn  77777?  '/777777777777777777777777777777777777777f/'  Figure  5.2 :  Pressure tap positions o n the floor a n d in the p l e n u m .  TOO  *>•  -ft*!a I'll  PI'l  7  Pressure tops  20'  13  ,  1  I  12"  •  1' 4 2-  •H —I—14—-U - L i { - — L - H - L i i 12  dia.=  Figure  5.3  3,5,9,12  IN.  Pressure tap positions o n m o d e l s .  101  r r r r r/.  V V  +  ^ ^ ^ ^ ^ ^-  -t- +  j,—y •» +. - H — K 4 •> 4 4 t - »  •++•-)• 4T/  i- + + * + +4- + -»-4.t-»--*-t-+-»- + +-»- + + -f + + -t--t--t 4- + + + + + + + + + + 4 + + + 4 + +.-t-4- + 4 + + + + - f 4 + - f + ++ + +  07777777777777777777777777777777777777777^  • •+--f + +- + +• + + + + ++ + + + -»• + 4 +  + +++ + +  Figure  5.4  :  Tuft positions 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 tunnel for s m o k e f l o w visualization.  4  b f •rinnntol R M U V S  / A  e  1 4  A  4 —  •  4 A \  wkKkagt m•ckaoa  M b t S.S t M b 1 10.4 I ickapi Mh> t SS.S I Ok Ana V « e 4 0 * -to  4 \ •  >J|IWtb i * 1 LIMITS' 1 W • b . mlBob Opan i• T M M b 10.000 Mob 1W b i 1 O.t  o  e  0 e  A  A  Egparlmonlal RnuHs O A 4  \  Obckag* Ikh i l l 1 Sbckog* Ik 10.4 f Sbckogt tkfie 1 SS.S »  A  «o 1  \  *b> - t o •nmiMi lb, H.OOiB* l b . •< SW* 1 18 0*wn A r w M b I0.S44 Ptab faalbfi t 0.0  \  \  • I.OSiD* lob. ojf Stata 1 10 Opm Area Rail1 10.417 1 0.0  e  5; A  A  *  A  A  A  *  S  A  A  A  A  O  A  A  A  O A  O A  A  O A  O A  A  A  •  A  4  •  •  • •  •  4 • 4  • +  +  +  A  A  4 4 • •  e A  • •  e A  A  A  • 4 4  +  4  n  (b) -«.S  A  O  •  (a) -«.9  A  O  R.I  I.I x/h  Figure  o.s  o.s  -4.3  6.1 (a) t o ( m ) : Re = I O 5  -1 -O.S  .1  x/h  I 0.1  —r— o.s  (c) 1.9  -O.S  -O.S  0.1  O.S  O.S  x/h  P r e s s u r e d i s t r i b u t i o n o v e r 3 d i f f e r e n t s i z e s o f flat p l a t e m o d e l . —  o ro  1 *•  Expertmenol Rtiudt O HeehOM • ft Do t B.S 1 A •teckooa Ratio l 18.4 1 iH» I 93.9 1 — AnayHc* Cpt» -ia RtynoWi rfe* > l.00«»» Iti. of SWl < M Optn A rvo Ha>l) 10.480 i 0.0  feynoMi i*. tl.M>»> Mb. o» SWt i 13 Opwi V M Mto I0.4S3 I 0.0  \ A  \ \ I KqmeMi f*. il.00«»» Mb, ef SWi i 19 OpwiAraaMlo lO.SM • 0.0  1*  id •  * + + +°  Id  +  •A * A A A A A * A+ A  (e)  o.s  Figure  -0.9  *  .0+ A  +  + t»  A  ft -O + + +<S. * * A * +  A  (f)  -0.9  -0.1  x/ri  0.1  0.9  0.9  -0.9  -fl.3  T  -0.1  x/h  r—  0.1  —r—  0.9  0.9  6.1 (a) t o ( m ) : P r e s s u r e d i s t r i b u t i o n s o v e r 3 d i f f e r e n t s i z e s o f flat p l a t e m o d e l . Re = 1 0 s  o co  O A 4 — Mb. of Vjti t » Open A T M Ml* 10.563 M i PMUhn i 0.0  Mb. of Stall  1  i  RvynoMj nb.  II  Mb. ef Stall  Opon Arw Mto i0.9 - • - • i o.O  ?  Experimental Resutrt Ibckosi Ratio i 6.9 I Btodcoa* Ro)k> i 10.4 t Modeopt 1Mb i 93.9 I Anahffkol Cpb- -IO • 1.00 if)*  i 10  Open Arie RaHo iO.B99 i 0.0  3  3 =J - * — .  A  »  °  A  +  A  •  •—>  -0.9  •  .Uf.  (g)  -0.8  *  -0.1  »  A A  — — I «/h 0.1  Figure  °  A  — I —  0.9  J  + • + + 4 4 4 ++ t •  . — * -  »  ta I o i  A A  -0.9  -0.9  -I  -0.1  x/h  • 4 + + • (&  (h) 0.8  3  9  —1— 0.9  -i 0.9  A  A #  4 4+4+ + B  D -0.9  -0.9  *3  —r— o.i  -0.1 x/h  A  —i—  0.9  0.9  6.1 (a) t o ( m ) : P r e s s u r e d i s t r i b u t i o n s o v e r 3 d i f f e r e n t s i z e s o f flat p l a t e m o d e l . 5 Re = 10  o  p  in o'  Expcclrmrrld Rttulti  o o"  tfactlOBJ* Ro•No  A \  \  "™~ AnoiyiloQlf ( Ipba - t O Rvynolds nb* Mb. of State  1 1  \  1.80 »»» 9  Op*Mi Arvo RoH ) 10.872  ?-  T"  \  I 8.9 I A Btockoou Rinto I 18.4 I *4* Btodtofljt RiMo t 33.9 «  O  PW*) PotiftOfl  +  • • + • • A  a  *  * c?  1  I LOOKS' Mb. al StaN I0 Open Ano Mh> 10.708 I 8.8  ?H  0.0  + • • + + +  3d  +  • + • +  6  +  i nb. rl.00i«>» Nb. ef SW* I 7 Open Ana Rotto t0.74S • 0.8  + + + + +  •A—A  -A  8  + ++  +  -0.9  T -8.1  +  * + ++  +  +  T" o 7-  ie (j) 7-O.S  (K) -0.9  -0.1  x/h  o.i  Figure  0.3  0.5  -8.9  -0.1 x/h  8.1  —1— 8.9  (1) 8.9  D.9  —r— e.i x/h  -1—  e.s  8.9  6.1 (a) t o ( m ) : P r e s s u r e d i s t r i b u t i o n s o v e r 3 d i f f e r e n t s i z e s o f flat p l a t e m o d e l . Re = 1 0 s  o  Figure  6.1 (a) t o ( m ) : Re =  10  P r e s s u r e d i s t r i b u t i o n s o v e r 3 d i f f e r e n t s i z e s o f flat p l a t e m o d e l . s  i  o CTl  -|  O Btockogo Katie i 8.3 I A Blockage Ratio t 18.4 I + Blockage Ratio t 33.3 I  *•>. of Stato t 89 Opm Area Ratio 10.000 Petition t 0.0  St*-*. O O O O O g A A  Q  ° °o  O O O OO  I J$ *  * * * * * * A  . ++  A  A  +  O  o  O  (a)  -s.o  Mb. of State t 18 Open Area Rotto 10.344 Plato Position i 0.0  O Btoekag* Ratio i 8.3 I A Btockoge Ratio t 19.4 I + Blockage Ratio i 33.3 I  -3.0  p.  O.  N.  A +  (b)  T  -1.0  1-  1.0  3.0  S.O  -3.0  y (feet)  Figure  6.2 (a) t o ( d )  -3.0  T  -1.0  y (feet)  :  i— 1.0  F l o o r s t a t i c p r e s s u r e d i s t r i b u t i o n s f o r 3 d i f f e r e n t s i z e s o f flat p l a t e  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 l o t ) .  -1— 3.0  S.O  O Btoekoy* Ratio s 8.3 A Btockag* Ratio : 18.4 + Btockag* Ratio I 33.3  I I I  Nb. of Stahj i 13 Opm Area Raho :0.526 < 0.0  O Btocfcago Ratio i 8.3 A Btockag* Ratio « 19.4 4 Bbckog* Ratio I 33.3  Nb. of Stall i 8 Opm Ar*a Ratio 10.708 Pkit* Position i 0.0  I I 1  t * o-  m O O 0 0  o  * *J  ° o o  i  I O U  2  3  is*  _6o o o  o  o  I  a.  H  <=!  +  +  X  k.  + +  0L  N .  7-  (c) -3.0  -3.0  Figure  -1.0  T— 1.0  y (feet)  6.2 (a) t o ( d ) :  I— 3.0  5.0  -5.0  -3.0  I 1.0  1—  1.0  y (feet)  — l — 3.0  5.0  F l o o r s t a t i c p r e s s u r e d i s t r i b u t i o n s f o r 3 d i f f e r e n t s i z e s o f flat p l a t e 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 l o t ) .  —• CO  e m*  Nb. of Stall i 99 Opm Area Ratio 10.000  O Blockage Rone t 8.3 A Btockog* Ratio I 19.4 + Btockog* Ratio s 33.3  s  O Blockage Ratio i 0.3 A Blockage Ratio i 19.4 + Blockage Ratio t 33.3  0.0  + A.  + A  KA.  4.  o o o o o o o  °  O O O  A O A  8.  7  u  Nb. of S M * t IB Opm Aroa Ratio : 0.344 Plate Position i n.O  I I I  4  +  8. u  A3 O  a. e o -  a  +  7  +  e  u ti.  + A A  4  e  T-  Ti  (a)  -20.0  -12.0  Figure  .0  Vh  4.0  ~T 12.0  b) 20.0  •20.0  -12.0  T— 4.0  y/h  6.3 (a) to (d) : Floor static pressure distributions for 3 different sizes of flat plate model positioned at center (non-dimensionalized plot).  I 12.0  20.0  -. o VD  O Blockage RaHo t 8.3 A Blockage Ratio i 19.4 + Btockog* Rone t 33.3  Nb. of Stat. i 13 Open Area Ratio :0.326 Plato Peottton t 0.0  I I I  O Blockage Ratio i 8.3 f A Blockage Ratio I 19.4 I + Blockage Ratio i 33.3 I  Nb. of Stato t 8 Open Area Ratio 10.708 P*** PooRlon i 0.0  *  Is^ A f f l  ^"AB o o o 6  O © O <D © O  ix  Ii o  a o  11 '  ++  •H-  e  S o  U  B  a  A  O  r  A  p re.  Ti  (c) -20.0  (d) -12.0  -4.0  Figure  y/h  4.0  12.0  20.0  -20.0  I  -12.0  ~1 -4.0  4.0  y/h  6.3 (a) to (d): Floor static pressure distributions for 3 different sizes of flat plate model positioned at center (non-dimensionalized plot).  12.0  20.0  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  V a r i a t i o n o f b a s e p r e s s u r e 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 z e s o f flat p l a t e m o d e l p o s i t i o n e d at c e n t e r .  0.85  5.0  0  0.4  0.1 0.2 0.3  0  0.5 0.6 0.7 0.8 0.9  0.1 0.2 0.3  Open Area Ratio Figure  6.5  :  Variation function  of  of  front  O A R for  drag  m o d e l p o s i t i o n e d at c e n t e r .  1  Open Area Ratio  coefficient  3 sizes of  0.4 0.5 0.6 0.7 0.8 0.9  flat  as  a  plate  Figure  6.6 :  V a r i a t i o n o f d r a g 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 z e s o f flat p l a t e m o d e l p o s i t i o n e d at c e n t e r .  _,  ro  113  0.28  o.io  4 0  Figure  6.7  :  i  i  0.1  0.2  i  i  i  i  i  0.3 0.4 0.5 0.6 0.7 Open A r e a Ratio  i  i  0.8  0.9  I  1  V a r i a t i o n 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 z e s o f flat p l a t e m o d e l p o s i t i o n e d at c e n t e r .  0.10  1.10  0.09-  0.08-  C  0.07  o o  0.06  *>  <D Q  "2  Blockage Ratios : O A -f  8.3 X  (3  In.)  19.4 »  (7  In.)  33.3 %  (12  In.)  0.05  O  TJ C CJ  to  0.04^  0.03-  +  I  ...Y. .+../.\i../..V.  0.02  A  0.01  0.00  0  0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9  1  -a  +  o0  0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9  Open A r e a Ratio  Open Area Ratio Figure  6.8  :  V a r i a t i o n o f b l o c k a g e - c o r r e c t i o n f a c t o r as a f u n c t i o n o f O A R f o r 3 s i z e s o f flat p l a t e m o d e l p o s i t i o n e d at c e n t e r .  Figure  6.9  :  V a r i a t i o n o f s t a n d a r d d e v i a t i o n as a f u n c t i o n of  OAR  for  3  sizes  p o s i t i o n e d at c e n t e r .  of  flat  plate  model  1  Ratio i 8.3 * Ratio t 19.4 I Pockogo Ratio t 33.3 I  »*• °< Slot* t 99 Opon Aroo RaMo :0.000 Position t 22.0  Nb. of SWo > 18 Opon Aroa Ratio 10.344 i 22.0  O Blockage Ratio ! 8.3 I A Btockog* Ratio t 19.4 I 4 Block age Ratio : 33.3 I  4  4  A  A  •  4  A  O A +  Q Q O O O O Q Q A J A  A A A A  AA  a  "E o l o  O  1 .  o  A  o  0  0  A* .  4  0  o o o o  A A A +  +  +  o  0  **A A +  4  3  k.  + +  a.  ++  +  i  T-  (a) -3.0  -3.0  y (*•«*)  —f— +  3.0  (b) 5.0  -s.o  i—  -3.0  y* (••*)  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).  3.0  3.0  Nb. of Start i 13 Open Ar*o RoHo t0.526 PW* PoslHon i 22.0  O Btocfcog* Roflo i 8.9 I A Btockog* Ratio l 19.4 I + Wochop*> rtoHo t 33.3 t  + A  O Btockaoa Ratio t 8.3 A Btoekog* Ratio i 19.4 4 Btockag* Ratio I 33.3  Nb. of Stat* it Opon Aroo Ratio :0.708 i 22.0  I I I  i  +  +  O A +  "E  o o  oO  M M  O O O A  •St  a  o  ° A A + +  O  A  S o  O +  3  +  +  +  + +  %  a.  T-  0  +  A  « o.  A  ° o  O  A  3  O  D.  * *  n  A  §  -. i  A  A+  O  N .  T-  (c) -S.O  (d) -3.0  Figure  .0  . I.O x  6 . 1 0 (a) t o (d) :  i 3.0  S.O  -S.O  -3.0  -1.0  ~i—  y (feet)'  3.0  5.0  F l o o r static p r e s s u r e d i s t r i b u t i o n s f o r 3 d i f f e r e n t s i z e s o f flat p l a t e  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 h e c e n t e r ( d i m e n s i o n a l i z e d p l o t ) . CTi  I*, of State i 99 Open Area Ratio 10.000 l 22.0  Ratio i 8.3 t Hotle i 19.4 I Ratio i 33.3 f  Nb. of Stall i 18 Open Area Ratio :0.344 Plate Position t 22.0  O Blockage Ratio i 8.3 J A Blockage Ratio I 19.4 I + Blockage Ratio I 33.3 I  + A  + A +  •f'B  b o  O  ° ooooo o &  A S A A  AA  8. a  A  e  9  o ~  V  (b)  (a) -30.0  -22.0  Figure  -14.0  -6.0  o o o o o oo  2.0  10.0  -30.0  I  -22.0  I -14.0  1 , -6.0 L  6.11 (a) t o ( d ) : F l o o r static p r e s s u r e d i s t r i b u t i o n s f o r 3 d i f f e r e n t s i z e s o f flat p l a t e m o d e l p o s i t i o n e d at 2 2 i n c h e s u p s t r e a m o f t h e c e n t e r ( n o n - d i m e n s i o n a l i z e d plot).  i—  2.0  10.0  O Btockog* Ratio i 6.3 A Btockog* Ratio I 19.4 4 Btockog* Ratio i 33.3  J I I  Nb. of Stall I 13 Opon Aroa Ratio 10.326 Plato PMStton : 22.0  Nb. of Stall j 8 Optn Aroa Ratio 10.708 Plat* Pocltton t 22.0  O Btockog* Ratio t 8.3 % A Btockog* Ratio t 19.4 I 4 Btockog* Ratio i 33.3 I  4  A  4  4  0»  Of O  O O  o o o oo  o  o o o o o o o oo 4  s.  4  u  4IA O A  4  a °.  T-  T-  (c) -30.0  -22.0  Figure  -14.0  y/h  -6.0  —\— 2.0  (d) 10.0  -30.0  -22.0  -14.0  /.  yA  -6.0  2.0  10.0  6.11 (a) t o (d) : F l o o r static p r e s s u r e d i s t r i b u t i o n s f o r 3 d i f f e r e n t s i z e s o f flat p l a t e m o d e l p o s i t i o n e d at 2 2 i n c h e s u p s t r e a m o f t h e c e n t e r ( n o n - d i m e n s i o n a l i z e d plot). CO  119  -1.0-  -1.5-  c O  0>  o  o  © »_ 3 f/>  CO  d>  o  CO  00  0.3 0.4 0.5 0.6 0.7 Open A r e a Ratio  Figure  6.12  :  V a r i a t i o n o f b a s e p r e s s u r e 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 z e s o f flat  p l a t e m o d e l p o s i t i o n e d at 2 2 i n c h e s u p s t r e a m o f t h e c e n t e r .  0.85  0.45  I 0  j  i  |  j  j  j  j  j  j  0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9  I  i 0  1  Open Area Ratio  Open Area Ratio Figure  6.13  :  Variation of  function  of  front  O A R for  drag  coefficient  3 sizes of  flat  as a plate  m o d e l p o s i t i o n e d at 2 2 i n c h e s u p s t r e a m o f the center.  1 1 1 1 1 i 1 i i 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9  Figure  6.14 :  V a r i a t i o n o f d r a g 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 z e s o f flat p l a t e m o d e l p o s i t i o n e d at 2 2 i n c h e s u p s t r e a m o f t h e c e n t e r .  r 1  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  : V a r i a t i o n 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 z e s o f flat p l a t e m o d e l p o s i t i o n e d at 2 2 i n c h e s u p s t r e a m o f t h e c e n t e r .  0.10  C  .o ~o  *>  Q) Q  "S O  TJ C D  in  v.uv n 0  1  1  1  1  1  1  1  1  1  0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9  r  0  1  i  i  6.16 :  V a r i a t i o n o f b l o c k a g e - c o r r e c t i o n f a c t o r as a function  of  O A R for  3 sizes of  flat  plate  i  i  i  i  i  Open Area Ratio  Open Area Ratio Figure  i  i  0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9  Figure  6.17:  V a r i a t i o n o f s t a n d a r d d e v i a t i o n as a f u n c t i o n of  OAR  for  m o d e l p o s i t i o n e d at 2 2 i n c h e s u p s t r e a m o f  positioned  the center.  center.  at  3  sizes  22  of  inches  flat  plate  upstream  model of  the  1  Experimental O A + X —  Results  Blockage Ratio : Blockogt Ratio : Blockog* Ratio : Btockaga Ratio : Roshko, Raf. 20  Reynolds nb« Nb. of Skill Opon Arta Ratio  A  A  A  A  A  A + X —  1.00 xK>» 99 0.000  O O O © o A  Experimental  8.3 X 13.8 % 25.0 * 33.3 X  Btockaga Ratio : 13.8 I Blockage Ratio : 25.0 I Blockog*) Ratio : 33.3 I Roshko, Rof. 20  Reynolds nb* Nb. of Slati t Opon Aria Ratio  O O  A  A  A  + + +  X  60.0  X  90.0  120.0  150.0  180.0  Beta  Figure  6 . 1 8 (a) t o ( m ) Re = 1 0  : 5  Results  Pressure distributions o v e r different sizes o f circular c y l i n d e r m o d e l .  1.00 x t t ' 18 0.344  Experimental  Results  Experimental  A Btockog* Ratio : 13.8 X + Btockog* Ratio : 25.0 X X Btockog* Ratio : 33.3 X — Roshko, R*f. 20 Reynolds nb. Nb. of Slats Open Aroa Ratio  90.0  A Blockage Ratio : 13.8 X + Btockog* Ratio : 25.0 X X Btockog* Ratio : 33.3 X — Roshko, Rof. 20 Reynolds nb. Nb. of Stats : Opart Aroa Ratio  1.00 x » » 16 0.417  120.0  150.0  160.0  Bota  Figure  6 . 1 8 (a) t o ( m ) : Re = 1 0  Pressure distributions o v e r 4 sizes o f circular c y l i n d e r m o d e l . 5  Results  1.00 x » »  IS  0.453  Experimental A + X —  Results  Btockog* Ratio : Btockog* Ratio : Btockog* Ratio : Roshko, R*f. 20  Reynolds nb. Nb. of Slats Open Area Ratio :  90.0  Beta  Figure  -i— 120.0  Experimental  13.8 X 2S.0 X 33.3 X  A + X —  1.00 xlO* 14 0.490  150.0  6 . 1 8 (a) t o ( m ) : Re = 1 0  Btockog* Ratio : 13.8 X Btockog* Ratio : 2S.0 X Btockog* Ratio : 33.3 X Roshko, Ret. 20  Reynolds nb. Nb. of Slats Open Area Ratio  180.0  0.0  90  Pressure distributions o v e r 4 sizes o f circular c y l i n d e r m o d e l . s  Results  1.00 xlO* 13 0.526  180.0  Figure  6 . 1 8 (a) t o ( m ) : Re =  10  Pressure distributions o v e r 4 sizes of circular cylinder m o d e l . 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  120.0  150.0  Beta  Figure  160.0  Beta  6 . 1 8 (a) t o ( m ) : Re = 1 0 *  Pressure d i s t r i b u t i o n s o v e r 4 sizes o f circular c y l i n d e r m o d e l .  180.0  Figure  6 . 1 8 (a) t o ( m ) : Re = 1 0 *  Pressure distributions o v e r 4 sizes of circular cylinder m o d e l . £ 00  120.0  Figure  6 . 1 8 (a) t o ( m ) : Re = 1 0 *  150.0  180.0  Pressure distributions o v e r 4 sizes of circular cylinder m o d e l .  ro  130  0.3  0.4  0.5  0.6  0.7  Open Area Ratio  Figure  6.19  : V a r i a t i o n o f p r e s s u r e c o e f f i c i e n t at ft = 5 0 ° a s a f u n c t i o n o f O A R f o r 4 s i z e s o f c i r c u l a r c y l i n d e r 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 .  Pressure Coefficient at 100  Pressure Coefficient at 180  ecra  o o ro  —  US 5 ST  CD  tt»  t 3' ?  ST Q  S  3  8  3 ro o  3-. 2 o <= §1:  O  TJ > O T:  5"  ro n  2 ro  o Q.  S - a ro .U  Q. »  N  fa  Le L  s. "  II  x + >o CD cn O Q  ? > Qb o  O  u  CO  o  ?  f  2o "  u o <o M - " M * a) X  V  O  o  M  m  s  10 3  3  ? ??  ..4-+$'  ;  .^AKAAQASAQA c .92 a> o  -0.1-  O  CD o o c  O A  .2  Blockage Ratios  +  X  u.e  «  (s '"•)  K  (S  23.0* 33.3 X  In.)  (tin.) (12  In.)  -0.4  -0.5 0.1 0.2  0.3  OA  0.5  0.6  0.7  0  0.8 ti!9  Open Area Ratio Figure  6.22  : V a r i a t i o n o f f r o n t d r a g 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 4 s i z e s o f c i r c u l a r c y l i n d e r 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 the test s e c t i o n .  0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9  Open A r e a Ratio Figure  6.23  : V a r i a t i o n o f rear d r a g 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 for 4 sizes of circular c y l i n d e r 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 .  1  2.4  0.24  0.23-  0.180.170.160.15-  Blockage Ratios : O A  8-5 *  (3  '"•)  13.8 X  (5  In.)  +  25.0 %  (9  In.)  X  33.3 X  (12  In.)  0.14-  0  i i i i r i i i r 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9  0.13  1  I  0  6.24 :  V a r i a t i o n o f d r a g 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 for 4 sizes of circular cylinder  I  I  I  i  i  Open A r e a Ratio  Open Area Ratio Figure  I  0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9  model  p o s i t i o n e d at t h e c e n t e r of t h e test s e c t i o n .  Figure  6.25 :  V a r i a t i o n 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 of O A R for 4 sizes of circular cylinder 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 .  I 1  1.10  0.04 O  Blockage Ratios : 0.02-  0.75-1-—I 0  I  I  I  i  I  I  I  I  6.26 :  0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9  of  OAR  for  4  sizes  (3  In.)  (3  In.)  +  23.0*  (9  In.)  X  33.3 X  (12  In.)  1  0  0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9  Open Area Ratio  V a r i a t i o n o f b l o c k a g e - c o r r e c t i o n f a c t o r as a function  8.3 X 13.8 X  0.00  Open Area Ratio Figure  O A  of  circular  c y l i n d e r 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  of  Figure  6.27 :  V a r i a t i o n o f s t a n d a r d d e v i a t i o n as a f u n c t i o n of O A R for 4 sizes of circular cylinder 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 .  t h e test s e c t i o n .  co  Experimental © A + X —  Results  Blockoge Folio : Blockoo* Ratio : Blockage Ratio : Blockage Ratio : Roshko, Ref. 20  8.3 13.8 25.0 33.3  Reynolds nb. Nb. of Slots : Open Area Ratio :  O  °  Q  A  A  S I  X  %  1.00 xlO' 99 0.000  O  O  O  O  O  O  A  A  A  A  A  A  O  O  A  A  I  I  A  A  + * + + + + + + + +  x M  x  90.0  x X X x x X X  120.0  150.0  180.0  I80.0  Beta  Figure  6.30  (a)  to  (rh)  :  Pressure  distributions  circular-cylirider-splitter-plate m o d e l . Re = 1 0  5  over  different  sizes  of ^  Pnaxurm Coefficient -2.3  -2.0  -1.5  1.3 -4,  -1.0  8-  cm  c  u> o  3  S--  x+ 3 0 OD OD OD OD  Ss--  8 ?cT?? 3  S  I  o — 0  S-  am a a ai a  A  n a  o  ro  (a 3 ^  S3  apis?  II  o 3  I ft) to  tllO  8'  ui (/> t/i C -i ro  a.  S'  3 .  O" C  o 3  VI  rVessurev Coefficient  O <  n  -2.3  N  -2.0  1.5  -1.5  -4,  . a.  O  c 3  a. ro i  in  •a ro  X + 0> G  3D OD C P OD OD  o ;  (* "8  iiii!  *»  ?  ^ aaaa  30X3)3)  o  5" 5" 5" 5"  p  K>  Jo  Mill  w ro  8"  • ui • ut a «• x  3  ai tn ui CU O CO M  >* M * •  00  Experimental O A + X  \  —  Btockog* Blockog* Btockog* Btockog*  Ratio Ratio Ratio Ratio  : : : :  O A + X  8.3 X 13.8 X 25.0 X 33.3 X  —  Roshko, R*f. 20  Reynolds nb. Nb. of Slats : Open Ar*a Ratio :  'A  Experimental  Results  »  *  *  *  x  x  x  Ratio Ratio Ratio Ratio  : : : :  8.3 X 13.8 X 25.0 X 33.3 X  Roshko, Ref. 20  Reynolds nb. Nb. of Slats : Open Area Ratio :  i .00 xtO* 14 0.490  *  Blockage Blockoge Btockog* Blockage  Results  1.00 « » ' 13 0.S26  1 !  )  X x  '(e) '  0.0  '(f)  r-— '  90.0  h—  1  60.0  1  90.0  '  1  120.0  '  1  150.0  180.0  0.0  30.0  60.0  90.0  120.0  150.0  180.0  Beta  Beta  Figure  <-  6 . 3 0 (a) t o ( m ) :  Pressure distributions o v e r 4 sizes o f circular-cylinder-splitter-plate  m o d e l . Re = 1 0  5  Lo CO  1.3  Results  Experimental  0  Experimental  —1  O A + X  e>"  o  Ratio Ratio Ratio Ratio  : : : :  8.3 I 13.8 I 25.0 * 33.3 %  Roshko, Ref. 20  Reynolds nb. : 1.00 xtO Nb. of Slats : 11 Open Area Ratio : 0.599  ^  -0.5  o~  —  Btockaga Btockoge Btockogt Btockaga  Results  \  8  — i 8 8 i 8—1—I—8—8—<  e  — • i-  J  H  0-0  (g) '  I——' 30.0  1  1  60.0  Figure  1 '  90.0  Ma  1  1  120.0  1 • 150.0  wt ' ( h ) 160.0  1 I  1 I— — I — I —I< 0-0 30.0  ' 1  60.0  1  1 H i1 1 1 —  90.0  1  120.0  1  1 ' 1 1  150.0  1  180.0  Beta  6.30 (a) t o ( m ) : Pressure distributions o v e r 4 sizes o f circular-cylinder-splitter-plate m o d e l . Re = 1 0 s  co  Experimental O A + X  Blockage Blockoge Blockoga Btockaga  Rollo Ratio Ratio Ratio  Results 6.3 13.8 2S.0 33.3  X X X X  —• Roshko, Raf. Ray no kit nb. Nb. of Skits t Opan Area Ratio  1.00 K10* 9 0.672  I44I4XL  1BO.0  Figure  6 . 3 0 (a) t o ( m ) :  Pressure distributions o v e r 4 sizes o f circular-cylinder-splitter-plate  m o d e l . Re = 1 0  5  Experimental Btockog* Btockog* Btockog* Btockog*  Results  Ratio Ratio Ratio Ratio  : : : :  8.3 X 13.8 X 25.0 X 33.3 X  Roshko, R*f. 20 Reynolds nb. Nb. of Slats Op*n Area Ratio  1.00 x « » 8 0.708  IXLOJJLl B  I  H  B  C  I  B  B  G  S  -  B*fa  Figure  6 . 3 0 (a) t o ( m ) :  Pressure distributions o v e r 4 sizes o f circular-cylinder-splitter-plate  m o d e l . R e = 10  s  m  150.0  Figure  6 . 3 0 (a) t o ( m ) :  180.0  Pressure distributions over 4 sizes of circular-cylinder-splitter-plate  m o d e l . Re = 1 0  s  ro  143  0.0  X  1.6  1 0  i  0.1  i  i  i  i  0.2  0.3  0.4  0.5  i  0.6  i  0.7  i  0.8  |  0.9  1  Open Area Ratio Figure  6.31  : V a r i a t i o n o f p r e s s u r e c o e f f i c i e n t at B = 5 0 ° as a f u n c t i o n o f O A R f o r 4 s i z e s o f c i r c u l a r - c y l i n d e r - w i t h - s p l i t t e r - p l a t e 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 t e s t section.  -2.0-1—1  0  1  1  I  I  1  l  l  o«  l  0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9  1  -2.0  Open Area Ratio Figure  6.32 :  V a r i a t i o n o f p r e s s u r e c o e f f i c i e n t at B = 1 0 0 ° as a f u n c t i o n of O A R for 4 sizes of circular-cylinder-with-splitter-plate model 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 t e s t s e c t i o n .  A  :  :  i  i  I  0  :  I  •  : .  :  1  1—r——i  :  :  :  :  1  r—  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 :  V a r i a t i o n o f p r e s s u r e c o e f f i c i e n 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 z e s o f circular-cylinder-with-splitter-plate model 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 t e s t s e c t i o n .  —• -P»  2.0  - 0 . 4 — t — i — i — i  0  i  i — r — i — I  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.  X  i  0  1  1  1  1  1  i  i  i  i  r  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  : V a r i a t i o n o f d r a g 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 4 s i z e s o f c i r c u l a r - c y l i n d e r - w i t h - s p l i t t e r - p l a t e 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 t e s t section.  0.10  -I—I  1  I  I  ~i  0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9  6.37 :  of  OAR  for  4  circular-cylinder-with-splitter-plate  I  I  I  I  I  Open Area Ratio  V a r i a t i o n o f b l o c k a g e - c o r r e c t i o n f a c t o r as a function  1  0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9  Open Area Ratio Figure  1  sizes  of  model  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  6.38 :  V a r i a t i o n o f s t a n d a r d d e v i a t i o n as a f u n c t i o n of  OAR  for  4  sizes  circular-cylinder-with-splitter-plate  of model  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  6.39  :  G e n e r a l f l o w p a t t e r n in t h e p l e n u m s f o r n o r m a l o p e r a t i o n .  -Pa CD  Pressure Co«yfflclWit -0.4  -0.8  -0.2  x+  0.0  -4—  —I  X+  an  X 4X  3! c  X  uoo>  3  X  09 DO  o  4-  X  ifi <"> n n «a  2 " —»  + •  X  en  s*  •  at  w  I  §W  Prtmufti Coofflcktnt  5'  CL _ ro ~  -0.8  -0.4  0.0  -0.2  -4—  -I—  0.4  0.2  -4—  -4—  0.8  .X + B-3  i . .  Bock Block Block Block  3"  IA  3 ro  5" S 9 3  TJ.  OJ _ j-» T J rB  +  SB  5* 5*6" 5*  era  -g_  O.S  -4—  »o  fill  ? S.  0.4  0.2  -I—  3 ro  1  s  3  g,  •s-s-s-s  ° 1 _  •?  X-0B X4-09  ,ff 6-5* 6"  X+  • apito ' uibia 0  1  z-  X X X X  +  DO  f5  0>O  +  D> Q  +•  P> 8  +  ><3  ft I" 5*  . CT  2- ft S* 3  2  c  ro o. 5a. 3"  •0.8  _  * rT  o •> ro  ro »  1  1  0.0  —— I  m  x* 00  ,6-5-6-6-  I  X X  tm_  o  0.4  0.2  »  an 'tm 8.3 13.8 25.0 33.3  ro _ ui o  -0.2 -I  III!  3  ro * 5- ro  -0.4  -I  X  x 4-  t»a  4-  e>8  +  ra  +  ra  o*  O.S  Nb. of Soli Opon Aroo Ratio  I  14 0.490  Nb. of Skjti : Opon Ar*o Ratio :  O Btockog* A Btockog* 4 Btockog* X Btockog* i—' -3.0  Ratio t Ratio : Ratio : Ratio : r  6.3 I3.B 25.0 33.3  •  +  *  *  X  X  f I I I  4 X  s.o  1  Figure  fi  (d)  -'y CM) °  6.40  13 0.526  Nb. of Slat* : 12 Open Ar*a Ratio : 0.563.  4  * 8 2 2 2 8 X  -s.o  : :  s.o  (a)  to  9.0  (I)  O Btockog* Ratio : A Btockog* Ratio t 4 Btockog* Ratio : X Btockog* Ratio : -1 ' r  +  4  X  X  X  8.3 I 13.8 I 25.0 I 33.3 f  -s.o  :  Plenum  ?-  (e)  s.o  pressure  circular-cylinder-with-splitter-plate section.  8 s 8 4  model  4  A O  s.o  distributions  -S.O  for  p o s i t i o n e d at t h e  6  O Btockog* Ratio : A Btockog* Ratio : 4 Btockog* Ratio : X Btockog* Ratio : -I ' r  -s.o  4  sizes  center of  the  of test  a  gfifi  *  4  4  4  *  X  X  8.3 I 13.B J 25.0 < 33.3 I  (f)  s.o  s.o  Nb. of SMI Open A S M Ratio  : t  11 0.599  Nb. of Stall Op*n Ar*o Ratio  X A  O  -5.0  A  O  s  O Btockog* Ratio : A Blockag* Ratio : 4 Btockago Ratio s x Btockog* Ratio : -t-t-9.0 - r 0  10 0.635  Nb. of Stat* i Open Aroa Ratio i  9 0.672  + A  a  a  a  a  • x  + x  • *  8.9 I 13.8 1 25.0 I 33.31  -1-  (W°  Figure  O  O Btockog* Ratio t A Btockog* Ratio : + Btockog* Ratio : X Blockag* Ratio : -r•+9.0 -9.0  (g) 9.0  6.40  5.0  (a)  A  e  to  (I)  :  Plenum  A  if 4  + x  •  + x  -I-  pressure model  A  e  a  e  e 4  + x  8.3 J 13.8 I 25.0 I 33.3 I  circular-cylinder-with-splitter-plate section.  a  a  4  x  X  O A 4 X  (h) 9.0  a  s.o  distributions  Blockag* Blockag* Btockog* Blockag*  -s.o  for  p o s i t i o n e d at t h e  -s.o  4  Ratio : Ratio : Ratio : Ratio I -+-  sizes  center of  the  8.3 13.8 25.0 33.3  of test  I I I 1 -t-  4  a 4  x  (D 9.0  9.0  Nb. of Stall : 8 Opto Ar*a Ratio i 0.708  4 X A  Nb. of Stall : 7 Op*n Ar*a Ratio i 0.745  X  Nb. of Stats : 0 Opsn Aroa Ratio : 1.000  X  4  4  A  o  A A  O  X  O  6  4 X  e  e  4 X  4 *  6  A  O  A O  X  i  A  4 X  9  et-  ?-  Bloekago Btockog* Blockag* Blockag* -5.0  -1-  Ratio : Ratio : Ratio Ratio :  8.3 I 13.81 25.0 J 33.3 I  7  O A 4 X  (j) 5.0  S.O  9.0  Blockag* Btockog* Btockog* Blockag*  Ratio Ratio Ratio Ratio  8.3 13.8 25.0 33.3  j I I I  -r-  (k) 9.0  -3.0  a A 4 X S.O  Btockog* Btockog* Btockog* Btockog* -t-9.0  9.0  Ratio t Ratio : Ratio : Ratio : -r-  8.3 f 13.8 I 25.0 X 33.3 I •+-io 1.0  r ('••»)  -s.o  Figure  6.40  (a)  to  (I)  Plenum  pressure  drcular-cylinder-with-splitter-plate section.  I «I  model  distributions  for  p o s i t i o n e d at t h e  4  sizes  center of  the  of test  (1) 9.0  5.0  Figure  6.41  :  General flow pattern in the p l e n u m s for e x t r e m e c o n d i t i o n s .  154  CD  O  Nb. of Slots : Open Area Ratio : Plate Position :  12 0.563 22.0  c  75 9  +  O  u  O  o  O +  O  ©  ©  O  to  3  CM  a.  o _  O A +  -5.0  Blockage Ratio : Blockage Ratio : Blockage Ratio : —I— -3.0  -1.0  8.3 J 19.4 X 33.3 Z  (feet)  y Figure 6 . 4 2  T— 1.0  I— 3.0  S.O  P l e n u m p r e s s u r e d i s t r i b u t i o n s c o r r e s p o n d i n g t o t e s t i n g o f n o r m a l flat p l a t e s at 22 i n c h e s u p s t r e a m o f t h e t e s t s e c t i o n c e n t e r . O A R = 0 . 5 6 3  

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