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Aerodynamics of several slender and bluff bodies in presence of momentum injection Deshpande, Vijay S. 2000

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A E R O D Y N A M I C S O F S E V E R A L S L E N D E R A N D B L U F F B O D I E S I N P R E S E N C E O F M O M E N T U M I N J E C T I O N V U A Y S. DESHPANDE B.E., University of Mysore, India, 1986 A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF APPLIED SCIENCE / in The Faculty of Graduate Studies Department of Mechanical Engineering We accept this thesis as conforming to the required, standard THE UNIVERSITY OF BRITISH COLUMBIA January 2000 © Vijay S. Deshpande, 2000 In presenting this thesis in partial fulfillment of the requirements for an advanced degree at the University of British Columbia, I agree that the Library shall make it freely available for reference and study. I further agree that the 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. Date: l&.ihJ.OTUMTto. JlO OO The University of British Columbia Department of Mechanical Engineering 2324 Main Mall Vancouver, B.C., Canada V6T 1Z4 A B S T R A C T The concept of Moving Surface Boundary-layer Control ( M S B C ) , as applied to a two-dimensional Joukowski airfoil as wel l as three-dimensional cube, water-tank and building models, is investigated through a planned wind tunnel test-program at a subcritical Reynolds number of 2.5 x 10 5. High speed rotating cylinders served as momentum injection elements and controlled the key parameter U c / U , where U c is the cylinder surface velocity and U represents the free-stream velocity. In case o f the two-dimensional airfoil, a single rotating cylinder replaced the nose of the airfoil. Results suggest that the concept is quite promising leading to an increase in lift by around 100 % and the delay in stall from 10° to 35°. It led to the rise of lift to drag ratio by 167 %. The momentum injection also resulted in an increase in the Strouhal number, at all angles o f attack (a), thus rendering the airfoil to behave as an effectively more slender body, even at a high a . In general, effect of the cylinder surface roughness was to further increase the Strouhal number by a small amount. The three-dimensional cube model, with an edge length o f W , carried two momentum-injecting elements at the vertical edges o f the front face. The study with basic cube in presence o f the M S B C provided, for the first time, the fundamental information concerning pressure distribution and forces which should serve as a reference in future. A t a = 0 and U c / U = 4, a reduction in drag by around 67% is indeed impressive. The Den Hartog criterion for galloping showed an improvement in stability with an increase in the momentum injection. The cube model when supported by a pillar served as a water-tank to assess the effect o f height (H). Two heights were considered: H = 2 W and H = 3W. A t the lower height, the i i effect of Uc/U was to reduce the drag at virtually all angles of attack, however, the decrease was substantially less compared to that observed for the basic cube. This is primarily due to the lateral flow created on the side faces of the tank because of the gap formed by the proximity of the ground. This adversely affects reattachment and separation of the boundary-layer. However, at the higher height (H = 3W), the trend reverses as expected. Now the reduction in drag is significantly higher even compared to that for the basic cube case. Both the tank models were found to be susceptible to galloping instability for 75° < a < 90°, even in presence of the momentum injection. Tests with the building models assesses the effect of aspect ratios (A.R. = 2, 3) on the pressure distribution and forces, using the basic cube as the top element. In general, irrespective of the A.R., the influence of momentum injection is to reduce the drag, almost at all a. However, the decrease in C D is less at a higher aspect ratio. Perhaps the most important effect of the higher A.R. is the building's susceptibility to galloping. This can be eliviated by injecting momentum over greater height of the building compared to 33% in the present case (H = 3W). The fundamental information of long range importance presented in the thesis should serve as a reference and prove useful to industrial aerodynamicists as well as practicing engineers. iii T A B L E O F C O N T E N T S A B S T R A C T n T A B L E O F C O N T E N T S iv LIST O F S Y M B O L S vii LIST O F FIGURES ix LIST O F T A B L E S xiv A C K N O W L E D G E M E N T xv 1 INTRODUCTION 1 1.1 Preliminary Remarks 1 1.2 A Brief Review of the Relevant Literature 2 1.3 Scope of the Investigation 14 2 M O D E L S AND T E S T P R O C E D U R E S 18 2.1 Two-Dimensional Airfoil Model 18 2.2 Three-Dimensional Cube Model 22 2.3 Tank Models 28 2.4 Three-Dimensional Building Models 28 2.5 Test Procedures 32 2.6 Presentation of Results 39 3 T W O - D I M E N S I O N A L AIRFOIL 41 3.1 Pressure Distribution (Smooth Cylinder) 41 3.2 Force Components 55 3.3 Effect of the Cylinder Surface Roughness 64 3.4 Strouhal Number 68 iv 4. BASIC CUBE MODEL I 75 4.1 Pressure Distribution: Plane-1 I 77 i 4.2 Pressure Distribution: Plane-2 83 4.3 Pressure Distribution: Plane-3 90 4.4 Drag and Side Forces 94 4.5 Galloping Instability 99 5 WATER-TANK MODELS : EFFECT OF HEIGHT 101 5.1 Pressure Plots 101 5.2 Drag and Side Forces 103 6 BUILDING MODELS: ASPECT RATIO EFFECTS 123 6.1 Pressure Distribution 125 6.2 Drag and Side Force Coefficients 145 6.3 Galloping Instability 153 7 CLOSING COMMENTS 158 7.1 Contributions 158 7.2 Major Conclusions 159 7.3 Recommendations for Future Studies 161 LIST OF REFERENCES 164 APPENDIX I INSTRUMENTATION USED IN THE STUDY 174 APPENDIX II PRESSURE PLOTS FOR THE BASIC CUBE MODEL 176 APPENDIX III PRESSURE DISTRIBUTION PLOTS FOR THE 189 WATER-TANK MODELS WITH H = 2W AND v H = 3W APPENDIX IV PRESSURE PLOTS FOR BUILDING MODELS 232 WITH H = 2W AND H = 3W vi LIST OF SYMBOLS A reference area; C x span in case of 2-dimensional airfoil model, W x H for 3-dimensional models AR aspect ratio of three-dimensional bluff body, H/W C airfoil chord Cc axial force coefficient, Fc/(l/2) p U 2 A C D drag coefficient, D/(l/2) p U 2 A C L lift coefficient, L/(l/2) p U 2 A C N normal force coefficient, FN/(1/2) p U 2 A Cp mean pressure coefficient, (P-Poo)/(l/2) p U 2 Cs side force coefficient, S/(l/2) p U 2 A d diameter of rotating cylinder D drag force Fc force parallel to the chord F N force normal to the chord fv frequency of vortex shedding H height of building or water tank model L lift force P static pressure at the surface of a model Pa, free-stream pressure P„ static pressure at the pressure tap location n vii Re,Rn Reynolds number, pUC/u or pUW/p. S side force on a three-dimensional model St Strouhal number, f vC/U t time U free-stream air velocity Uc surface velocity of rotating cylinder Uc/U momentum injection parameter W side of the square cross-section of three-dimensional models X distance along chord of airfoil X/C nondimensional length along the chord of airfoil a angle of attack p air density u dynamic viscosity of air viii LIST OF FIGURES 1-1 Flettner applied the Magnus Effect to ship propulsion in 1924 when he fitted two large vertical rotating cylinders on the deck of the "Buchau" [25]. 5 1-2 The practical application of moving wall for boundary-layer control was demonstrated by Favre in 1938 [26]. Using an airfoil with the upper surface formed by a belt moving over two rollers, he was able to delay separation until the angle of attack reached 55°, where the maximum lift coefficient of 3.5 was realized. 6 1-3 The North American Rockwell's OV-10A aircraft in flight demonstrating a successful application of the rotating cylinder as a high-lift device. 8 1-4 Various rotating-cylinder configurations studied with the two-dimensional Joukowski airfoil model by Modi et al. [43]. 10 1-5 Application of the moving surface boundary layer control (MSBC) procedure to Bluff bodies such as a flat plate at a large angles of attack, rectangular prisms, and tractor-trailer truck configurations [44,45]. 11 1-6 Representative flow visualization pictures taken by Modi et al. [44] showing, rather dramatically, successful control of the boundary-layer separation through momentum injection. 12 1-7 Models used in the wind tunnel test-program: (a) two-dimensional airfoil; (b) cube; (c) water-tank; (d) building. 15 1- 8 A schematic diagram showing the scope of the investigation. 17 2- 1 A schematic diagram showing the two-dimensional Joukowski model during the test-program. 19 2-2 Photographs showing details of the pressure taps and pressure conducting tubings. 20 2-3 Detailed schematic of the rotating cylinder and the drive mechanism. 21 2-4 Schematic diagram showing details of the pressure taps near the rotating element. 23 ix 2-5 Rotating cylinders with three different types of surfaces used in the test-program. 24 2-6 Photograph of the two-dimensional Joukowski airfoil model assembly showing pressure conveying tubes, momentum injecting circular cylinder and a drive motor. 25 2-7 (a) Schematic diagram of the basic cube model showing distribution of taps; (b) A photograph of the basic cube model with pressure conveying tubings and two momentum injecting circular cylinders. 26 2-8 Two tank models studied in the test-program to evaluate the influence of height. 29 2-9 Photograph of a tank model, with H = 3W, showing the two rotating elements for momentum injection, support column and pressure conveying polyethylene tubes. 30 2-10 A set of three prism models with the aspect ratio of 1, 2 and 3. 31 2-11 Photograph of the building model with a height reaching three times the side of the square cross-section. Note, the basic cube with rotating cylinders forms the top section of the model. 33 2-12 A schematic diagram of the low speed, low turbulence, closed circuit wind tunnel used in the test-program. 34 2-13 The water-tank model with H = 3W undergoing wind tunnel tests. 35 2-14 A schematic diagram showing the instrumentation set-up during pressure measurements. 37 2- 15 Instrumentation layout for the measurement of vortex shedding frequency. 38 3.1 Typical pressure distribution plots for a conventional Joukowski airfoil as obtained by Modi et al. [43]. These results serve as reference to assess the effect of airfoil modifications and cylinder rotation. 42 3- 2 The effect of airfoil modification in absence of momentum injection. The change in pressure distribution resulted in a slightly lower value of the Climax as shown in Figure 3-6(a). 44 3-3 Pressure plots showing the delay in stall brought about by the cylinder rotation. 45 x 3-4 Pressure distribution on the Joukowski airfoil as affected by the momentum injection and angle of attack: (a) a = 0; (b) a = 30°; (c) a = 50°; (d) a = 90°. 46 3-5 Effect of angle of attack and momentum injection on: (a) peak suction pressure and average wake pressure; (b) location of the peak suction and boundary-layer separation. 53 3-6 Variations of force coefficient with angle of attack and momentum injection: (a) lift coefficient (CL); (b) drag coefficient (CD); (C) enlarged view of the region near origin; (d) (CL/CD); (e) normal force coefficient (CN); (f) chordwise force coefficient (Cc). 56 3-7 Geometry of various force coefficients. 63 3-8 Variation of lift and drag coefficient with angle of attack for Uc/U = 3: (a )CL ; (b )C D ; ( c )CL/C D . 65 3-9 Effect of momentum injection on the strength and frequency of pressure signals in the wake: (a) time-histories of pressure signals for Uc/U = 0 and 3; (b) frequency spectra as obtained using the FFT. 69 3-10 Variation of the Strouhal number as affected by the momentum injection using: (a) smooth cylinder; (b) cylinder, with splines; (c) deep-spline cylinder. 70 3- 11 Summary of the influence of surface roughness and momentum injection on the Strouhal number variation with a. 73 4- 1 The cube model, with momentum injecting rotating elements and 76 pressure taps, located in the test-section during wind-tunnel experiments. 76 4-2 A schematic diagram showing, quite approximately, some features of the complex flow associated with a sharp-edged cube. 78 4-3 Pressure distribution on plane-1 as affected by the momentum injection and angle of attack: (a) a = 0; (bi) a = 45°; (02) a = 45° (reversed rotation); (c) a = 90°. 79 4-4 Pressure distribution for plane-2 showing the effect of a and Uc/U: (a) a = 0; (bi) a = 30°; (t>2) Schematic diagram showing the Vortex V at the edge P2 and a pair of conical vortices formed at the corner CR.; (c) a = 60°; (d) a = 90°. 8 4 xi 4-5 Pressure distribution for plane-3 as affected by Uc/U and a: (a) a = 0; (b) a = 45°; (c) a = 90°. 91 4-6 Force coefficients as affected by the angle of attack and Uc/U: (a) C D ; (b )C S . 95 4- 7 Flow past a two-dimensional square-section cylinder at a = 15° in absence of momentum injection: (a) sketch of separating streamlines; (b) flow visualization by Yokomizo and Modi [61 ]. 98 5- 1 Water tank-models during wind tunnel tests: (a) H = 2W; (b) H = 3W. 102 5-2 Pressure distribution in plane-1 as affected by the momentum injection at a = 0: (a) basic cube (H = W); (b) water tank (H = 2W); (c) water tank (H = 3W). 104 5-3 Pressure plots for plane-2 as affected by the momentum injection at a = 0: (a) basic cube (H = W); (b) water tank (H = 2W); (c) water tank (H = 3W). 107 5-4 Effect of momentum injection at a = 0 on pressure distribution in plane-3: (a) basic cube (H = W); (b) water tank (H = 2W); (c) water tank(H = 3W). 110 5-5 Effect of the water-tank height on the pressure distribution at a = 0: (a) Uc/U = 0; (b) Uc/U = 4. 113 5-6 Forces on the water-tank model with a height of H = 2W: (a) C D ; (b) C S . 116 5- 7 Variation of forces on the tank model at H = 3 W: (a) C D ; (b) C S . 120 6- 1 A family .of three building models, with an aspect ratio equal to one, two and three, used in the wind tunnel test-program to assess the effect of momentum injection. 124 6-2 Pressure plots in plane-1 at a = 0 as affected by the momentum injection: (a) aspect ratio = 1; (b) aspect ratio = 2; (c) aspect ratio = 3. 126 6-3 Pressure plots for plane-1 at a = 60° as affected by the momentum injection: (a) aspect ratio = 1; (b) aspect ratio = 2; (c) aspect ratio = 3. 129 6-4 Pressure plots for plane-1 at a = 90° as affected by the momentum injection: (a) aspect ratio = 1; (b) aspect ratio = 2; (c) aspect ratio = 3. 132 xii 6-5 Variation of pressure plots in plane-1 as affected by the aspect ratio and momentum injection: (a) a = 0; (b) a = 60°; (c) a = 90°. 136 6-6 Variation of pressure plots in plane-2 as affected by the aspect ratio and momentum injection: (a) a = 0; (b) a = 60°; (c) a = 90°. 139 6-7 Variation of pressure plots in plane-3 as affected by the aspect ratio and momentum injection: (a) a = 0; (b) a = 60°; (c) a = 90°. 142 6-8 Variation of force coefficients with a in presence of momentum injection for a building with an aspect ratio of 2: (a) CD; (b) Cs. 147 6-9 Pressure plots in plane-1, for H = 2W, as affected by the momentum injection: (a) a = 75°; (b) a = 90°. 149 6-10 Variation of force coefficients with the angle of attack for a building of H = 3W: (a) C D ; (b) C s • 154 II-l Pressure distribution plots for the basic cube in: (a) plane-1, a = 15°, 30°, 60°, 75°. 177 II- 2 Pressure distribution plots for the basic cube in: (b) plane-2, a = 15°, 45°, 75°. 181 U-3 Pressure distribution plots for the basic cube in: (c) plane-3, a = 15°, 30°, 45°, 60°, 75°. . 184 III- l Pressure plots for the tank model with H =2W: (a) plane-1, a = 15°, 30°, 45°,45°R, 60°, 75°, 90°; (b) plane-2, a = 15°, 30°, 45°,45°R, 60°, 75°, 90°; (c) plane-3, a = 15°, 30°, 45°,45°R, 60°, 75°, 90°. I 9 0 III- 2 Pressure plots for the tank model with H =3W: (a) plane-1, a = 15°, 30°, 45°,45°R, 60°, 75°, 90°; (b) plane-2, a = 15°, 30°, 45°,45°R, 60°, 75°, 90°; (c) plane-3, a = 15°, 30°, 45°,45°R, 60°, 75°, 90°. 211 IV- 1 Pressure plots for the building model with H =2W: (a) plane-1, a = 15°, 30°, 45°,45°R, 60°, 75°, 90°; (b) plane-2, a = 15°, 30°, 45°,45°R, 60°, 75°, 90°; (c) plane-3, a = 15°, 30°, 45°,45°R, 60°, 75°, 90°. 233 IV-2 Pressure plots for the building model with H =3W: (a) plane-1, a = 15°, 30°, 45°,45°R, 60°, 75°, 90°; (b) plane-2, a = 15°, 30°, 45°,45°R, 60°, 75°, 90°; (c) plane-3, a = 15°, 30°, 45°,45°R, 60°, 75°, 90°. 253 xiii LIST OF TABLES Table 3-1 Effect of angle of attack on the front stagnation point location. 51 Table 3-2 Variation of peak suction pressure, separation location and average wake pressure as affected by the angle of attack and momentum injection. 52 Table 4-1 Effect of momentum injection on galloping stability. 100 Table 5-1 Stability prediction for the water-tank model at H =2W. 118 Table 5-2 Prediction of stability, based on the Den Hartog criterion, for the water-tank model at H = 3W. 122 Table 6-1 Comparison of drag reduction for the cube, water-tank and building models at Uc/U = 4. 152 Table 6-2 Comparative stability results for three buildings as affected by the aspect ratio, angle of attack, and momentum injection. 156 xiv ACKNOWLEDGEMENT I would like to express my sincere thanks to my supervisor, Dr. V.J. Modi, for his support and guidance throughout my stay at the University of British Columbia. The models were fabricated in the Mechanical Engineering workshop. Assistance of Mr. Tony Basic, Mr. Doug Yuen, Mr. Dave Camp and Mr. John Richards, in the design and construction of the models is gratefully acknowledged. Many thanks are due to my friends in the Vibration and Controls Laboratory, especially, Vince den Hartog and Dr. Prasad Patnaik, for their constructive comments and help. xv 1. INTRODUCTION 1.1 Preliminary Remarks A wide variety of engineering structures are susceptible to flow induced vibrations. From large aspect ratio lighthouses, industrial chimneys, cooling towers, raised water tanks and antenna masts to bluff bodies like buildings, bridges and iced transmission lines as well as aerodynamically shaped aircraft wings and control surfaces, are known to oscillate under the action of wind. Offshore structures, such as oil-drilling platforms, have also exhibited undesirable oscillations under the combined effects of wind and waves. These oscillations are of engineering concern because of their potentially destructive effects. Industrial chimneys have shown visible cracks due to excessive wind loading, lighthouse and building windows have experienced damage, and iced transmission lines are known to have severed from their towers. The most dramatic example is the collapse of the original Tacoma Narrows Bridge, in Washington State, U.S.A. The bridge was destroyed in 1940, after only a month of operation, through a torsional instability induced by a 67.2 km/hr (42 mph) wind blowing for an hour. A combination of critical wind velocity and low structural damping produced catastrophically large oscillations. At times, human comfort, rather than structural integrity, determines the limits on the allowable amplitudes and oscillation frequencies. Tall buildings, like the World Trade Center in New York, can sway up to 30 cm in high winds at the top. These vibrations are usually at frequencies of less than 1 Hz and often not severe enough to compromise the structural integrity of the building. However, the occupants have experienced symptoms akin to sea-sickness, vertigo and disorientation. These problems have also been reported by occupants of air traffic control towers [1]. Vibrational accelerations must be less than 0.15g for human 1 comfort. In the past, when safety margins were not clear, engineers overcompensated their calculations by factors of two, five or an order of magnitude to err on the side of safety. Advances in metallurgical sciences and computer-aided designs have tended to reduce the safety margin and permitted construction of structures with lower stiffness. This often makes them susceptible to wind, earthquake, as well as ocean waves and current excited oscillations. In addition, the tendency today is to build higher and longer structures. The heights of the tallest buildings and the spans of the longest bridges in the world change routinely. The vibrational energies of such structures are difficult to dissipate due to the inherently lower damping. Lower safety margins, lighter materials, with the tendency toward taller buildings and longer bridges all conspire to create structures, which are quite prone to vibrations. The twenty-first century would witness super-tall buildings (> 1,000 m) and extra long span bridges (> 2,000 m), as pointed out by Kubo et al. [2,3]. For a long time, the adverse influence of wind induced vibrations was not appreciated or considered minor. Several major failures and the current building trends have raised sufficient concern and focussed attention on the engineering relevance of flow induced instabilities. Even today, building codes in most countries are still at the evolutionary stage so far as the wind effects are concerned. A vast body of literature accumulated over years has been reviewed by several authors including Wille [4], Marris [5], Morkovin [6], Parkinson [7], Cermak [8], Welt [9,10], Modi et al. [11], Seto [12] and Munshi [13]. 1.2 A Brief Review of the Relevant Literature Obviously, the forces and moments responsible for vibration of structures are governed by pressure distributions on their surfaces which, in turn, depend on the character 2 of the boundary-layers and their separation. Hence, ever since the introduction of the boundary-layer concept by Prandtl, there has been a constant challenge faced by scientists and engineers to minimize its adverse effects and control it to advantage. Methods such as suction, blowing, vortex generators, turbulence promoters, etc. have been investigated at length and employed in practice with a varying degree of success. A vast body of literature accumulated over years has been reviewed rather effectively by several authors including Goldstein [14], Lachmann [15], Rosenhead [16], Schlichting [17], Chang [18], and others. However, the use of moving wall for boundary-layer control has received relatively little attention. This is indeed surprising as the Associate Committee on Aerodynamics, appointed by the National Research Council, specifically recommended more attention in this area, almost three decades ago [19]. Irrespective of the method used, the main objective of a control procedure is to prevent, or at least delay, the separation of the boundary-layer from the wall. A moving surface attempts to accomplish this in two ways: it prevents the initial growth of boundary-layer by minimizing relative motion between the surface and the free stream; and it injects momentum into the existing boundary layer. The injection of momentum helps in keeping the flow attached to the surface in the region of adverse pressure gradient thus delaying its separation. Newton was probably the first one to observe the effect of moving wall boundary-layer control on the trajectory of a spinning ball [20], although the basis of the effect was not fully recognized. Almost 200 years later, Magnus [21] studied lift generated by circulation and utilized the effect to construct a ship with a vertical rotating cylinder replacing the sail. Swanson [22] and Iverson [23] have presented excellent reviews of literature on the Magnus 3 effect. As early as in 1910, Prandtl himself demonstrated his "ship of zero resistance" through flow around two counter-rotating cylinders [24], while Flettner [25] applied the principle to ship propulsion in 1924 when he fitted large vertical rotating cylinders on the deck of the 'Buchau' (Figure 1-1). A little later, in 1934, Goldstein [14] illustrated the principle of boundary-layer control using a rotating cylinder at the leading edge of a flat plate. However, the most practical application of moving wall for boundary-layer control was demonstrated by Favre[26]. Using an airfoil with upper surface formed by a belt moving over two rollers (Figure 1-2), he was able to delay separation until the angle of attack reached 55° where the maximum lift coefficient of 3.5 was realized. After a lull of more than twenty years (1938-1960), during which the tempo of research activity as indicated by important contribution in the field remained dormant, there appears to be some signs of renewed interest in this form of boundary-layer control. Alvarez-Calderon and Arnold [27] carried out tests on a rotating cylinder flap to evolve a high lift airfoil for STOL-type aircraft. The system was flight tested on a single engine high-wing research aircraft designed by Aeronautical Division of the Universidad Nacional de Ingenieria in Lima, Peru [28]. Around the same time Brooks [29] presented his preliminary results of tests on a hydrofoil with a rotating cylinder at the leading or trailing edge. For the leading edge configuration only a small increase in lift was observed, however, for the latter case a substantial gain in lift resulted. Motivation for the test-programme was to assess improvement in the fin performance for torpedo control. Along the same line, Steele and Harding [30] studied the application of rotating cylinders to improve ship maneuverability. Extensive force measurements and flow visualization experiments were conducted using a water tunnel and a large circulating water 4 5 Sir* £ o E •8 B'g 5 g S ° O bO e .s « > •o o a s > a o -° 8 -° ^ s .s £ I 8 P3 00 CD w o in m "O U l --4—» C*H o o JB C =3 C * 8 H U N CA I-i &! o u o u o i E channel. Three different configurations of rudder were used. The rotating Cylinder: (i) in isolation; (ii) at the leading edge of a rudder; (iii) combined with a flap-rudder, the cylinder being at the leading edge of the flap. From the overall consideration of hydrodynamic performance, mechanical complexity and power consumption, the configuration in (ii) was preferred. An application to 250,000 ton tanker showed the power requirement for 1 m diameter cylinder rotating at 350 rpm to be around 400 kW. Of some interest is the North American Rockwell's OV-10A (Figure 1-3) which was flight-tested by NASA's Ames Research Center [31-33]. Cylinders, located at the leading edge of the flaps, are made to rotate at high speed with the flaps in lowered position. The main objective of the test-programme was to assess handling qualities of the propeller-powered STOL-type aircraft at higher lift coefficients. The.aircraft was flown at speeds of 29-31 m/s, along approaches up to -8°, which corresponded to the lift coefficient of about 4.3. In the pilot's opinion, any further reductions in the approach speed were limited by the lateral-directional stability and control characteristics. Excellent photographs of the airplane on ground, showing the cylinders in position, and in flight have been published in the Aviation Week and Space Technology [34,35]. Around the same time Tennant presented an interesting analysis for the two dimensional moving wall diffuser with a step change in area [36,37]. The diffuser incorporated rotating cylinders to form a part of its wall at the station of the area change. Preliminary experiments were conducted for the area ratio up to 1:2.5, which showed no 7 8 separation for appropriate moving surface to diffuser inlet velocity ratio. Tennant et al. [38] have also conducted tests with wedge shaped flap having a rotating cylinder as the leading edge. Flap deflection was limited to 15° and the critical cylinder velocity necessary to suppress separation was determined. Effects of increase in gap-size (between the cylinder and the flap surface) were also assessed. No effort was made to observe the influence of increase in cylinder surface velocity beyond Uc/U = 1.2. Subsequently, Tennant et al. [39] have reported circulation control for a symmetrical airfoil with a rotating cylinder forming its trailing edge. For zero angle of attack, the lift coefficient (CL) of 1.2 was attained with Uc/U = 3. Also of interest is their study concerning boundary-layer growth on moving surfaces accounting for gap effects [40,41]. It is important to point out that virtually all the studies used two-dimensional models in the investigations. Even the design of OV-10A was based on two-dimensional data ! This was the state of development with respect to the moving surface boundary-layer control when Modi et al. entered the field in 1979 [42]. The subsequent contributions to the literature are essentially from his group which undertook a planned, comprehensive investigations with two-dimensional airfoils (Figure 1-4) as well as two- and three-dimensional bluff bodies (Figure 1-5) involving a flat plate (two-dimensional), rectangular prism (two-dimensional), and tractor trailer truck configurations (three-dimensional). The extensive wind tunnel test-programme, complemented by numerical simulations and flow visualization (Figure 1 -6) showed : (i) significant increase in the lift of an airfoil by as much as 195%, with the stall delayed to 48° [43]; (ii) reduction in the pressure drag of the flat plate by 75% [44]; 9 Leading-Edge Cylinder The Basic Configuration 0.05 C Trailing-Edge })iu>67C Cylinder Rear Upper-Surface Cylinder Upper (. o.38 c Leading-Edge^ Cylinder/^f^ Forward Upper-Surface Cylinder 0.05 C Figure 1-4 Various rotating-cyUnder configurations studied with the two-dimensional Joukowski airfoil model by Modi et al. [43]. 10 Two dimensional flat plate a L u U C Two dimensional rectangular prisms H L/H = 0 . 3 , 1 , 2 , 4 U Tractor-trailer truck configuration <b 0Uc ;//>>y//////y/y//////////////////// Figure 1-5 Application of the moving surface boundary layer control (MSBC) procedure to bluff bodies such as a flat plate at a large angles of attack, rectangular prisms, and tractor-trailer truck configurations [44,45]. 11 12 (iii) reduction in the pressure drag of rectangular prisms by around 55% [44]; (iv) reduction in the pressure drag of highway truck models by 24% [45]. Modi has presented a detailed review of this class of problem [46]. Based on the literature review, following general observations can be made: (i) Although there is a modest body of literature aimed at aerodynamics of slender and bluff bodies in presence of the MSBC, most of it is confined to two-dimensional models. (ii) Circular cylinders, serving as momentum injecting elements, are considered to have smooth surface. Effect of surface roughness on the efficiency of the momentum injection process has received virtually no attention. Even for two-dimensional airfoil, reliable information on this aspect is not available. (iii) One of the effects of momentum injection is to delay separation and interfere with the formation of the organized Karman vortex street. However, there are hardly any studies aimed at influence of the MSBC on the Strouhal number. It is indeed surprising that even for a two-dimensional airfoil, this important information of far-reaching consequence is not available. (iv) Effect of the MSBC on the aerodynamics of three-dimensional prisms has received little attention. Most of the results have been obtained through tests with models of tractor-trailer truck configurations. Obviously, for real-life applications to buildings and other civil engineering structures, fundamental aerodynamic information is of central importance for this class of geometries. 13 1.3 Scope of the Investigation With this as background, the thesis investigates, through wind tunnel tests, aerodynamics of slender as well as bluff bodies in presence of the MSBC at a subcritical Reynolds number of 2.5 x 105. It attempts to address comments concerning lack of information made earlier (page 13). Thus the focus is on obtaining new information of fundamental importance concerning the surface loading which would be responsible for vortex induced and galloping type of instabilities. Both the two-dimensional (airfoil) as well as three-dimensional (square cross-section prisms) models are used (Figure 1-7) in the carefully planned test-program. The plan of study has four related aspects or phases. The first phase focuses on the two-dimensional study using an airfoil model. The second phase deals with a three-dimensional study of a cube, resting on the ground, which gives reference information for the studies in phases three and four. Phase three emphasizes, through the model of a cubic tank, effect of height while, in phase four, the focus is on the aspect ratio of a building with square cross-section. To begin with, in Chapter 2, design and construction of models for the wind tunnel experiments as well as the test-methodology are described. It is followed by the test-results and their discussion for a two-dimensional model of a symmetrical Joukowski airfoil (chapter 3). This provides vital missing information as pointed out in (ii) and (iii) on page 13. Chapters 4 to 6 attempt to address some of the issues raised in observation (i) and (iv). Chapter 4 studies, for the first time, aerodynamics of a cube in presence of the MSBC. The information serves as reference for investigations in Chapters 5 and 6. The focus in 14 15 Chapter 5 is on the effect of height on the pressure distribution, drag and side force on a cubic tank-like structure. The influence of the aspect ratio of a building, with square cross-section, on its aerodynamics is the subject of Chapter 6. The thesis ends with a brief review of important conclusions, significant original contributions and suggestions for future study. Figure 1-8 schematically shows the plan of study. 16 S3 H Z H o o w u z w Cfl g Cfl Q O ca fa fa P z o H u fa 1-5 z fa c z fa »-Cfl fa > fa 1/3 fa o Cfl u i u o ffe cfl *•£ o u CA u a u by c o | o o u cfi oo c o 0 3 & o e CO 00 17 2. MODELS AND TEST PROCEDURES As pointed out before, the wind tunnel test-program has four distinct phases involving streamlined as well as bluff bodies (Figure 1-7): (i) two-dimensional Joukowski airfoil; (ii) cube; (iii) water-tank; and (iv) building. The cube model also forms the basic element in the water-tank as well as the building aerodynamic studies. It serves as a water-tank, located at two different heights, for the study in (iii), and as the top section of the building, with two different aspect ratios, for the investigation in (iv). This chapter describes the models as well as test-procedures. 2.1 Two-Dimensional Airfoil Model Figure 2-1 shows schematically a symmetric, two-dimensional Joukowski airfoil during wind tunnel tests. It is 16 % thick with a chord length of 370 mm. The rotating cylinder diameter is 10 % of the chord length and is located at the leading edge of the airfoil. A 1/4 h.p, variable speed, AC motor drives the cylinder. 43 pressure taps, 0.5 mm in diameter, are located at the upper and lower surfaces of the airfoil (Figure 2-2). The gap between the rotating cylinder and the body of the airfoil is typically 1.0-1.5 mm. The bluffhess of the airfoil is a function of the angle of attack (a). At zero angle of attack the airfoil behaves as a streamlined body. As the angle of attack is increased the bluffhess also becomes larger. Thus at a large angle of attack, typically near and beyond the stall, the airfoil behaves as a bluff body. Variation of the lift, drag, lift to drag ratio and Strouhal number with the angle of attack in presence of the MSBC are of primary interest in this study. The details of the model and a motor coupling to the rotating element are shown in Figure 2-3. The measurement of pressures at the surface of the cylinder, rotating typically at 6,000 - 12,000 18 Figure 2-1 A schematic diagram showing the two-dimensional Joukowski model during the test-program. 19 Figure 2-2 Photographs showing details of the pressure taps and pressure conducting tubings. 20 1/4 H.P., 3.8 AMP (Variac Control) No Load RPM:22,000 High Speed Bearing Rotating Leading Edge Cylinder 3.8 cm diam. Fenner Coupling Pressure Taps 38 cm C h o r d , Max. Thickness 6.4 cm ot 1/4 Chord Position High Speed Bearing Lower Support Bracket Figure 2-3 Detailed schematic of the rotating cylinder and the drive mechanism. 21 rpm, presents a challenge. The problem was resolved by keeping the pressure conveying tubes, located in narrow grooves, stationary while the cylinder rotated (Figure 2-4). Thus the pressure was measured not at the surface of the cylinder but in a close proximity of it. As the pressure taps remained immersed in the boundary-layer, they provided good estimate of the static pressure. As can be expected, the surface character of the rotating cylinder would affect effectiveness of the momentum injection process. To assess the influence of the surface roughness, three different cylinders were used as shown in Figure 2-5: (i) smooth surface; (ii) 10 equally spaced, axially parallel splines with a depth equal to 5% of the cylinder diameter (D, 37 mm in all the cases); (iii) cylinder with four deep splines each having a depth of 0.27D. A photograph of the entire airfoil model with a drive-motor is presented in Figure 2-6. 2.2 Three-Dimensional Cube Model A schematic diagram of the basic cube model is shown in Figure 2-7(a). It is a 203 x 203 x 203 mm (8 in) hollow wooden box with aluminum rotating cylinders, 50.8 mm (2 in) in diameter, at two adjacent vertical edges. The rotating cylinders are hollow and have smooth surface. For this and other three-dimensional models, only smooth surface cylinders were used as the results with the airfoil provided some appreciation concerning the influence of the surface roughness. The model was provided with 76 pressure taps, distributed over five faces covering three orthogonal planes, as shown in Figure 2-7(a). Horizontal Plane-1, parallel to the flow, has 33 pressure taps. For a two-dimensional model, i.e. if the model is extended vertically to the tunnel walls as a square prism, this will be the pressure information normally obtained. 20 pressure taps in Plane-2, normal to the flow direction at a = 0, provide information at a section downstream of the front face. Vertical Plane-3, aligned with the flow 22 MODEL STATIONARY PRESSURE RINGS LEADING-EDGE PRESSURE LINES ROTATING LEADING-EDGE CYLINDER Figure 2-4 Schematic diagram showing details of the pressure taps near the rotating element. 23 Outs ide D i a m e t e r (D) = 3 7 m m Groove Wid th Groove D e p t h Spline 4.5 m m 2 m m Wid th = 10 m m D e p t h = 10 m m Deep —spline Smooth Figure 2-5 Rotating cylinders with three different types of surfaces used in the test-program. 24 Figure 2-6 Photograph of the two-dimensional Joukowski airfoil model assembly showing pressure conveying tubes, momentum injecting circular cylinder and a drive motor. 25 26 27 at a = 0, carries 22 pressure taps. Like Plane-1, it monitors pressure variations in the downstream direction, but in a vertical plane. The bottom face of the cube model rest on a surface and hence carries no pressure taps. The cylinders are belt driven by two independent 1/4 h.p. DC motors (maximum current = 50A) mounted inside the cube. The desired power is provided by a DC supply with a variac. An opening in the bottom face of the model serves as an exit for the pressure tubing and electrical cables connecting to the externally located instrumentation. For the cube as well as other three-dimensional models (water-tank, building), the pressure data were complemented with drag and force measurements using a six component strain-gage balance. A photograph of the basic cube model is presented in Figure 2-7(b). 2.3 Tank Models The basic cube model was mounted on a hollow, circular cross-section, aluminum column to form a tank model as shown in Figure 2-8. The column also served as a conduit for pressure tubings and electrical wires. The tank was so located as to reach two different heights of 2W and 3W, where W is the length of one of the edges of the cube. Thus with the cube model resting on the ground and at two different heights, results can be obtained for H/W = 1, 2, 3. Figure 2-9 shows a photograph of the tank model with H = 3W. 2.4 Three-Dimensional Building Models The basic cube model described earlier was also used to form a part of the set of three prisms with square cross-section as shown in Figure 2-10. Motivation here was, as mentioned before, to study system aerodynamics as affected by the aspect ratio. The set of prism may represent, in an idealized fashion, buildings of varying heights. Note, the basic cube with 28 2 9 30 31 rotating cylinder forms the top section of the building. As W = 203 mm, the tallest prism has a height of 609mm. Figure 2-11 shows photograph of the prism with H = 3W. 2.5 Test Procedures Wind Tunnel The wind tunnel used in the test-program is shown in Figure 2-12. It is a closed circuit tunnel with a test-section of 0.91 x 0.68 x 2.60 m. The test-section is provided with 45° corner fillets varying from 0.152 m x 0.152 m to 0.121 m x 0.121 m to partly compensate for the boundary-layer growth. The tunnel contraction ratio is 7:1. The wind speed can be varied from 1-45 m/s. A wire screen at the inlet to the test-section ensures uniform velocity with a spatial variation of less than 0.25%. The intensity of turbulence in the test-section is less than 0.1%. The wind speed can be determined using a Betz manometer having an accuracy of 0.1 mm of water. A 230 V, 57.2 A, 15 h.p., DC motor driving a commercial axial-flow fan powers the wind tunnel. A Ward-Leonard system is used for the speed control of the electric motor. A six-component pyramidal force balance placed below the test-section supports the model under test. The output of the force balance load cells are six electrical signals (one each for the lift, drag, and side force; and the pitch, yaw and roll moments) which are transmitted to the computer based data acquisition system. Details of the instrumentation used during the experiments are given in Appendix I. Figure 2-13 shows a typical water-tank model during wind tunnel tests. Measurement of Pressure Distribution The mean pressure distribution around the body was measured using pressure taps provided on the circumference of the model. The pressure taps were connected to a scanivalve pressure transducer system. The scanivalve has 48 pressure ports and is driven by 32 Figure 2-11 Photograph of the building model with a height reaching three times the side of the square cross-section. Note, the basic cube with rotating cylinders forms the top section of the model. 33 34 Figure 2-13 The water-tank model with H = 3W undergoing wind tunnel tests. 35 a solenoid controller. As there were 43 pressure taps in case of the Joukowski airfoil model, only one scanivalve was used. On the other hand, for the pressure measurements of three-dimensional models, two scanivalve units were required as the total number of pressure ports were 76. In the steady state, the pressure conveying tubes had little effect on attenuation and phase response of the signal [47, 48]. The output signal from the scanivalve transducer is directed to the signal conditioner, amplifier and finally to a computer through analog to digital (A/D) interface card. A schematic diagram of the experimental set-up is shown in Figure 2-14. The pressure signals were sampled at a frequency of 25 Hz. Each set of sampled data is then averaged to obtain the mean pressure and the corresponding pressure coefficient ( C P ) . Force Measurement For the two-dimensional airfoil model, the mean pressure field around the surface of the body was integrated to obtain the aerodynamic lift and drag force coefficients (CL, CD). However, for the three-dimensional models direct force measurements were made using the platform type load-cell balance. The sensitivity of the platform balance was in the range of 0.135 mV/kgf to 0.315 mVTkgf depending on the direction of the force. The readings obtained from the load cell, sensing side and drag forces, were reduced to their dimensionless form (C s, CD). Measurement of Strouhal Number As the flow separates from the body, a vortex is formed and is subsequently shed in the wake. Figure 2-15 shows the schematic of the test set-up for the measurement of frequency of shed vortices. A disc probe [49] is inserted in the wake at approximately 1.5 times the chord of the airfoil from the leading edge, to obtain the pressure signal. The signal 36 u Presure Tubes Signal Conditioner & Amplifier Model / / / ^ Model Support Port Display Unit o o Scanivalve Scanivalve Controller A / D Interface Card Data Figure 2-14 A schematic diagram showing the instrumentation set-up during pressure measurements. 37 Damping Bottle i Disk Probe Polythylene Tube, Length=l .5m Barocel Pressure Transducer Signal Conditioner Fil ter Data Acquisition System Figure 2-15 Instrumentation layout for the measurement of vortex shedding frequency. 38 is fed to a large empty bottle and to one end of the barocel pressure transducer. The bottle acts as a damping device for the fluctuating pressure signal. The dampened pressure signal is conveyed to a differential pressure transducer (Barocel). The pressure transducer thus responds only to the fluctuating portion of the pressure signal. Output of the pressure transducer is collected in a PC based data acquisition system after signal conditioning and amplification. The data is sampled at the rate of 60 hertz. By performing the Fast Fourier Transformation (FFT) analysis on the pressure signal, a spectrum of frequencies is obtained, with the dominant peak representing the frequency of shed vortices. It is converted into the dimensionless form to obtain the Strouhal number. Measurements such as pressure, force and Strouhal number were conducted in the angle of attack range of 0 to 90° for the two-dimensional airfoil. The effect of surface roughness of the momentum injecting element was also assessed for the airfoil. However, for the three-dimensional models, the focus was on the rotating cylinders with smooth surface. Important changes occur in the flow character as the angle of attack is increased from zero. In the case of three-dimensional models, the stagnation point shifts from the front face to the adjacent face at a critical angle of attack. In the cube-based models studied here, this occurred at a « 45° when reversal in the direction of the momentum injection would become necessary. The momentum injection parameter Uc/U was varied from 0 to 3 in steps of one unit during tests on the two-dimensional airfoil model, and from 0 to 4 in case of three-dimensional bluff bodies. Presentation of Results The relatively large angles of attacks used in the experimental result in a considerable blockage of the wind-tunnel test-section. For the airfoil model a = 90°, it was the highest 39 encountered in the present test-program reaching a value of 40.6 %. The peak blockage values for the basic cube, tank and building models were 9.3 %, 12.6 % and 27.9 %, respectively. The wall confinement leads to an increase in local wind speed at the location of the model, thus resulting in an increase in aerodynamic forces. Several approximate correction procedures have been reported in literature to account for this effect. However, these approaches are mostly meant for streamlined bodies with attached flow. A satisfactory procedure applicable to a bluff body offering a large blockage with separating shear layers is still not available. With rotation of the cylinder(s), the problem is further complicated. As shown by the pressure data and confirmed by the flow visualization [44], the unsteady flow can be separating and reattaching over a large portion of the top surface. In absence of any reliable procedure to account for wall confinement effects in the present situation, the results are purposely presented in the uncorrected form. The main objective of the study is to assess the effect of momentum injection, which has been observed to be essentially independent of the Reynolds number in the subcritical range [44]. Thus mechanism of delay in separation due to the MSBC is virtually unaffected by the blockage, which would raise the local Reynolds number. Furthermore, the major interest is in assessing relative influence of the momentum injection at a given blockage. 40 3. TWO-DIMENSIONAL AIRFOIL This chapter presents test-results for a symmetrical Joukowski airfoil, of 16 % thickness, in presence of the Moving Surface Boundary-layer Control (MSBC). To begin with, pressure and force data, as affected by the angle of attack and momentum injection parameter Uc/U, are presented and discussed. Here, the surface of the rotating cylinder is smooth. Next, the effect of the surface roughness on the airfoil loading is assessed using smooth, splined and deep-splined cylinders as momentum injecting elements. Finally, the attention is directed to the Strouhal number and its variation with the MSBC and the surface roughness. Al l the tests were carried out at a Reynolds number of 2.5 x 105. As can be expected, through a systematic variation of the angle of attack (a = 0 - 40° at an increment of 5°, 50°, 70°, 90°; occasionally intermediate values as deemed necessary), Uc/U (0, 1, 2, 3), and three surface characteristics for the rotating cylinder, the amount of information obtained is literally extensive. Only some typical results are presented here to retain clarity and help establish trends. 3.1 Pressure Distribution (Smooth Cylinder) Figure 3-1, which serves as a reference, shows pressure distribution on the surface of a conventional Joukowski airfoil, i.e. without rotating cylinder replacing its nose, as obtained by Modi et al. [43]. Due to practical difficulty in locating pressure taps in the cusp region there is an apparent discontinuity in the pressure plots near the trailing edge. However, the region has little importance in the present discussion. Pressure loading on both top and bottom surfaces of the airfoil are presented (clear symbols for bottom surface). It is apparent that the airfoil, in absence of any modification to its nose geometry, stalls at an angle of 41 -2.5 -2 -1.5 H -1 'P -0.5 0 f 0.5 0 0.2 0.4 ^ 0.6 0.8 1 Figure 3-1 Typical pressure distribution plots for a conventional Joukowski airfoil as obtained by Modi et al. [43]. These results serve as reference to assess the effect of airfoil modifications and cylinder rotation. 42 attack of 12°. The modified airfoil has its nose replaced by a circular cylinder approximately matching the local curvature. Its diameter extends to 10 % of the chord as mentioned earlier. Furthermore, it introduces a gap, between the cylinder and the rest of the airfoil, thus permitting communication between the bottom and top surfaces. As can be expected, presence of the cylinder with Uc/U = 0 would affect the pressure distribution adversely (Figure 3-2) and resulted in a slightly lower peak lift as discussed later. However, with an injection of momentum, the situation changes dramatically as shown in Figure 3-3. The delay in stall brought about by the cylinder rotation is apparent. For a = 15° and with Uc/U = 0, the airfoil would stall based on the results in Figure 3-2. However, with Uc/U = 2, the flow reattaches thus delaying the stall and the associated pressure collapse. Figure 3-4 shows a sample of representative results for the effect of momentum injection at several angles of attack: a =0, 30°, 50° and 90°. Only the two extreme values of Uc/U = 0 and 3 are used in the plots for clarity. The results bring to light several interesting points of information: (i) In general, momentum injection affects the pressure distribution on both upper as well as lower surfaces of the airfoil. The most noticeable effect is on the suction pressure peak at the cylinder location. (ii) An increase in the momentum injection tends to increase the negative pressure peak and delays the boundary-layer separation. (iii) As expected, the front stagnation point moves downstream with an increase in the angle of attack, however, its location is virtually unaffected by the momentum injection. This is in sharp contrast to an isolated rotating cylinder, 43 -2.5 0 0.2 0.4 0.6 0.8 1 X/C Figure 3-2 The effect of airfoil modification in absence of momentum injection. The change in pressure distribution resulted in a slightly lower value of the C^max as shown in Figure 3-6(a). 44 0 0.2 0.4 0.6 0.8 1 X/C Figure 3-3 Pressure plots showing the delay in stall brought about by the cylinder rotation. 45 46 47 48 -2.5 Uc/U X/C Figure 3-4 Pressure distribution on the Joukowski airfoil as affected by the momentum injection and angle of attack: (d) a = 90°. 49 immersed in a free stream with its axis normal to the flow. Table 3-1 summarizes the stagnation point location as affected by the angle of attack. Information concerning approximate location of the separation point as suggested by the near constant pressure in the wake, the average wake pressure, as well as the peak suction pressure are listed in Table 3-2. The results in Table 3-2 are also plotted in Figure 3-5 to have better appreciation of trends. In general, without momentum injection, the peak suction pressure gradually diminishes with an increase in the angle of attack (Figure 3-5a). The effect of momentum injection is to increase the suction pressure (i.e., to make it more negative), at all angles of attack, by a significant amount. For example, at a = 50°, the Cp = -3.95 represents an increase in the negative pressure (i.e. suction) by approximately 220 % due to a momentum injection corresponding to Uc/U = 3. Note, the minimum Cp is reached at a = 50° beyond which the pressure tends to increase (i.e. the suction decreases). The effect of an angle of attack on the average wake pressure is relatively small. The momentum injection was found to reduce the average wake pressure by a small amount at all angles of attack. So far as the location of the peak suction pressure is concerned, it showed clear forward movement with an increase in the angle of attack (Figure 3-5b). However, it is virtually unaffected by the momentum injection. Of course, the main effect of the momentum injection is to move the boundary-layer separation point, on the top surface, downstream as seen in the range a = 15° - 90°. For example, with Uc/U = 0, the boundary-layer separates at « 7.8 % of the chord for the airfoil at a = 30°. However, with Uc/U = 3, the separation moves to 52 % of the chord length. For the airfoil at a large angle of attack (a > 70°), the effect of Uc/U on the separation location becomes relatively small. 50 Table 3-1 Effect of angle of attack on the front stagnation point location. a Front Stagnation Point Location, % of chord length 0 0 30° 7 50° 20 70° 36 90° 47 51 Table 3-2 Variation of peak suction pressure, separation location and average wake pressure as affected by the angle of attack and momentum injection. a Uc/U Peak Suction Separation Location, % chord Average Base c P Location, % chord c P 10° 0 7.9 -2.12 Near Trailing edge -0.05 3 7.9 -2.33 Near Trailing edge -0.08 30° 0 1.4 -1.72 7.9 -0.80 3 1.4 -2.80 52.0 -0.76 40° 0 1.4 -1.85 7.9 -0.93 3 1.4 -3.50 42.0 -0.74 50° 0 1.4 -1.58 7.9 - 0.90 3 0 -3.95 24.0 -0.72 70° 0 0 -1.23 6 -0.81 3 0 -3.50 15 -0.63 90° 0 0 -0.73 0 -0.52 3 0 -1.86 11 -0.58 52 53 12 10 o SZ O c o *-t—' G3 O O _J c o o CO CD <u CL 8 0 Peak Suction Location Uc/U \ \ ^ ^ \ Separation A 0 \ \ / Location x 3 * \ \ -\ \ Uc/U = 3 -Uc/U = 0 \ \ ---i & — — i — — ^ 0 20 40 60 80 a 100 90 80 70 60 50 " D i_ O JO O c o *-t—' CD O O _ J c o CD 40 CD a. o C/) 30 20 10 0 Figure 3-5 Effect of angle of attack and momentum injection on: (b) location of the peak suction and boundary-layer separation. 54 3.2 Force Components Pressure plots were integrated to obtain the lift and drag information as affected by the momentum injection parameter, Uc/U, and angle of attack (Figures 3-6 a, b, c). The basic (i.e., unmodified) Joukowski airfoil has a maximum lift coefficient of around 0.88 (Figure 3-6a). However, with modification, bluffness of the cylinder and the associated gap cause the C L , max to diminish. Note, the slope of the lift curve remains virtually unaffected. In absence of the cylinder rotation the modified airfoil stalls at around 12° giving uniform pressure distribution on the top surface as seen before (Figure 3-1). The stall sets in rather abruptly as shown by a sudden drop in lift. However, with the cylinder rotation, a large well-developed suction peak at the leading edge of the airfoil suggests a delay in the stall. In fact the results show the stall to occur around 35° (Uc/U =3) with an increase in the lift coefficient by about 103 %. An increase in speed beyond Uc/U = 3 improved the situation only marginally suggesting the existence of a critical speed ratio beyond which momentum injection through a moving surface appears to have little effect. Note also that the effect of rotation is to extend the lift curve without affecting its slope, and flatten the stall peak. Figures 3-6(b) and 3-6(c) present information about the drag variation with angle of attack in presence of the M S B C . Three distinct ranges of the angle of attack can be identified: (i) for 0 < a < 8°, the effect of momentum injection is favorable and seems to reduce C D ; (ii) for the angle of attack in the range of 20°- 45°, the effect of cylinder rotation is not well defined; 55 56 1.6 Figure 3-6 Variations of force coefficient with angle of attack and momentum injection: (b) drag coefficient (CD). 57 58 59 60 61 (iii) for a > 45°, the M S B C clearly reduces the drag. The flow visualization study referred to earlier [44] clearly showed reduction in the wake width with an increase in Uc/U suggesting decrease in the pressure drag. Equally important parameter, from performance consideration, is the ratio C L / C D presented in Figure 3-6(d). The improvement in the C i / C D was observed with the M S B C over the entire range of the angle of attack used in the test-program. However, its dramatic rise in the range 0 < a < 10° is rather impressive. Note, the peak value of 16.22 at Uc/U = 3 (a = 5°) represents an increase of 167 % compared to the no rotation case. As the present study involves an airfoil at high angles of attack and the momentum injection is approximately along the chordwise direction, normal (CN) and chordwise (Cc, sometimes referred to as axial) force components can also help in understanding variations of C L and CD- Note, the lift and drag components can be expressed quite readily in terms of C N and Cc as (Figure 3-7): C L = C N COS a - Cc sin a ; (3.1) C D = C N sin a + Cc cos a. As expected, the C N plots in Figure 3-6 (e) display some similarity with the trends observed for the lift variation (Figure 3-6a). However, the chordwise component of the force (Cc, Figure 3-6f ) bears no resemblance to the variation of drag coefficient indicated in Figure 3-6(c). At very high angles of attack beyond stall (a > 40°), the lift decreases with an increase in the angle of attack, however, in the same range, the drag continues to increase. This may be attributed to a larger contribution to C D from C N (Eq. 3.1). Furthermore, for a > 40°, C D decreases with an increase in the momentum injection, as there is a drop in C N at a higher Uc/U. 62 = Resultant Force Coefficient Figure 3-7 Geometry of various force coefficients. 63 3.3 Effect of the Cylinder Surface Roughness One would expect the cylinder roughness to have some effect on the momentum injection process and hence on the aerodynamics of the airfoil. To assess this influence, extensive test-program using three distinct surface conditions (smooth, spline, deep-spline), described in Chapter 2 was undertaken. Detailed pressure plots and force information was obtained as affected by the angle of attack and momentum injection. For conciseness, only the lift and drag information is presented here for Uc/U = 3, the highest value used in tests with the airfoil (Figure 3-8). At the outset, it is apparent that the effect of surface roughness on CL before stall (i.e. a < 35°) is within the experimental error (approximately + 3 %) and hence negligible (Figure 3-8a). However, for a > 35°, there is a well-defined trend: increase in the surface roughness seems to affect lift generation process adversely. So far as the drag coefficient is concerned, for a < 35°, it is slightly reduced by presence of the surface roughness (Figure 3-8b). The spline-geometry appears to perform better in terms of drag reduction. However, for a > 35°, the trend is not well-defined. Perhaps the CL/CD plot in Figure 3-8(c) is more informative. It clearly points out the undesirable effect of the surface roughness, i.e. higher CL/CD is attained with the smooth surface cylinder rotating element. Note, with the spline and deep-spline configurations, the peak value of CL/CD (a « 6°) diminished from 16.2 (smooth) to 12.3 (spline) and 8.4 (deep-spline) representing a drop of 24 % and 48 %, respectively. Thus, at least for the aircraft application, the use of smooth surface cylinder is preferred. In the case of the prototype study with the OV-10A mentioned in Chapter 1 (page 7), the momentum injecting circular cylinders had smooth surfaces. 64 1.6 h 1.2 h 0.8 0.4 0 0 20 40 60 a0 80 Figure 3-8 Variation of force coefficients with angle of attack for Uc/U = 3: (a) CL-65 Figure 3-8 Variation of force coefficients with angle of attack for Uc/U = 3: (b) CD-66 3.4 Strouhal Number As mentioned in Section 2.5, the vortex shedding frequency was obtained by performing the Fast Fourier Transform (FFT) analysis of time-dependent pressure signals. The trailing vortices cause pressure fluctuations as they are convected downstream in the wake. A disc probe, described at length by Modi and Dikshit [49] was used to obtain the fluctuating pressure in the wake of the airfoil model. The probe was placed at a distance of around 0.5C from the airfoil's trailing edge. Figure 3-9(a) compares the typical pressure signals as affected by the momentum injection of Uc/U = 0 and 3. It is apparent that momentum injection weakens the pressure signal suggesting reduced strength of shedding vortices. Figure 3-9(b) shows the frequency spectrum as obtained by the FFT. For Uc/U = 0, the characteristic vortex shedding frequency is about 4.8 Hz whereas at Uc/U = 3 it increases to around 5.9 Hz. Thus with the momentum injection, the effective bluffhess of the airfoil, at a given angle of attack, seems to reduce resulting in a higher Strouhal number. The tests were conducted over a range of the angle of attack and in presence of three cylinder roughness conditions as before. The Strouhal number data as affected by the angle of attack, momentum injection and surface roughness are presented in Figures 3-10 and 3-11. Several general trends can be discerned as follows: (i) In general, in absence of momentum injection, the Strouhal number is expected to decrease with an increase in the angle of attack due to an increase in bluffhess. The presence of humps in the region of 15° < a < 50° for the rough cylinders, particularly for the case of Uc/U = 3, may be attributed to a tendency of the separated shear-layer to reattach. This also reflects as a reduction in effective bluffhess. 68 3 Frequency, Hz Figure 3-9 Effect of momentum injection on the strength and frequency of pressure signals in the wake: (a) time-histories of pressure signals for Uc/U = 0 and 3; (b) frequency spectra as obtained using the FFT. 69 0.7 0.6 h 0.5 0.4 St. 0.3 0.2 0.1 0 0 Streamlined Object Approaching an Airfoil [50] j Flat Plate with Rounded Edges [50] J I L J L L Uc/U —B— 0 1 —A— 2 - e - 3 20 40 60 a _ L I L 80 Figure 3-10 Variation of the Strouhal number as affected by the momentum injection using: (a) smooth cylinder. 70 71 72 0.7 0.6 h 0.5 T 0.4 St. 0.3 0.2 h 0.1 0 0 20 40 60 80 a Figure 3-11 Summary of the influence of surface roughness and momentum injection on the Strouhal number variation with a. 73 Irrespective of the roughness condition, effect of the momentum injection, at a given a, is to increase the Strouhal number. Thus, as pointed out before, the airfoil behaves as a relatively more slender body. For a given Uc/U, the increase in the Strouhal number tends to be slightly higher for the rough cylinders compared to the smooth surface case. This is particularly noticeable for the deep-spline cylinder (Figure 3-11). For the airfoil at a = 0 and Uc/U = 3, increase in the Strouhal number for the smooth surface case was around 24 %, and 36 % for the deep-spline cylinder. For a = 90°, the airfoil should approach a flat plate. In the present study (smooth surface cylinder, Figure 3-10a), for Uc/U = 0, the Strouhal number is 0.15 while for a flat plate with sharp edges it would be 0.18 [51]. On the other hand, for Uc/U = 3, the present airfoil has St = 0.41. For a flat plate with rotating cylinder at each edge and Uc/U = 3, the corresponding Strouhal number would be 0.6 [46]. Note, at a = 90°, the rise in the St from 0.15 at Uc/U = 0 to 0.43 at Uc/U = 3, for the deep-spline cylinder, represents an increase of 185 % ! Spectacular reduction in the wake width as observed through flow visualization by Modi et al. [52], increase in the C L / C D ratio obtained in the present study (Figure 3-8 c ), and rise in the Strouhal number observed here tend to substantiate beneficial effects of the momentum injection. 74 4. BASIC CUBE MODEL Interest in flow past cylinders with rectangular cross-sections has been primarily because the information has application to the design of a class of buildings [53-57]. Furthermore, wind profiles around buildings may significantly change the local micro-climate affecting pedestrian comfort and pollutants' dispersion. A cubic structure is a particular case of such rectangular prisms. It has also received some attention because of its simple, symmetric geometry and similarity with low-rise buildings and cab of a tractor-trailer truck. However, both rectangular prisms with large aspect ratios and cubic structures, when resting on ground and exposed to wind, create rather complex flow patterns revealing several nodes and saddle points. In the present study, as pointed out earlier, a cubic model serves as a basic element to assess the influence of the MSBC on the aerodynamics of water-tank and building models. As such investigation of a cube with momentum injection has not been reported in the industrial aerodynamics literature, a comparative assessment of the data is not possible. Results for sharp-edge cube (in absence of the MSBC) when available are presented to help appreciate the effect of rounded corners (due to presence of cylinders) and momentum injection. Figure 4-1 shows the cube model, of 20.3 cm (8in) side, during wind-tunnel tests. One of the major challenges faced is the concise presentation of the large amount of information obtained during the test-program. The cube was provided with 76 pressure taps distributed over three mutually orthogonal planes 1, 2 and 3 as pointed out earlier (Figure 2-7a). Pressure measurements were carried out at a = 0 - 90° in a step-size of 15° and for five different values of Uc/U (0,1,2, 3,4). Thus pressure information at 380 points on the surface 75 The cube model, with momentum injecting rotating elements and 76 pressure taps, located in the test-section during wind-tunnel experiments. 76 of the cube is measured. This is repeated at seven different angles of attack! Thus the information available is literally overwhelming. As the objective is to establish trends, results helpful in achieving that goal are appropriately selected and presented in the main body of the thesis. Remaining data are given in Appendix II. A legend drawing is included with each pressure plot to assist in locating positions of pressure taps on the surface. Before presenting the pressure data, it would be useful to give a rather approximate description of this extremely complex flow. Consider a sharp edge cube, in absence of the MSBC and at a = 0, as shown in Figure 4-2. The approaching flow rolls up near the front face of the cube to form a horseshoe vortex along two sides (top and bottom faces in the plan view). The flow separates at edges of the windward face, and reattaches some distance downstream on the top and side faces. The flow then recirculates behind the cube. These are merely the gross features. The detailed character of the flow is a subject of controversy. 4.1 Pressure Distribution: Plane-1 Figure 4-3 shows distribution of pressure at ports (taps) in the central horizontal plane parallel to the flow, as affected by the angle of attack as well as momentum injection. Figure 2-7(a) in Chapter 2, which identifies the three orthogonal planes selected for distribution of pressure ports, five faces of the cube of interest, and pressure tap numbering system, is essential to decipher trends. As expected, for a = 0, the plots are symmetrical about the stagnation point at tap 17 with large suction peak at the rotating cylinders. The stagnation region is rather wide, almost extending between taps 15-19. Increase in the negative peak pressure at the rotating cylinder with an increase in Uc/U is also as anticipated. In general, the effect of momentum injection is to increase the pressure on the sidewalls (faces B and C) as well as on the leeward face (face D), i.e. in the near wake. This 77 Plan View Side View S Separation Point S T J , S D Upstream and Downstream Stagnation Points R s Reattachment Point Figure 4-2 A schematic diagram showing, quite approximately, some features of the complex flow associated with a sharp-edged cube. 78 79 80 81 82 would suggest reduction in the drag with momentum injection. Drag results presented later (Figure 4-6a) substantiate this observation. Figure 4-3(bi) shows pressure plots for a = 45°. Note, the stagnation point has moved significantly to the right (viewing from the front in the direction of the flow) and is now located on the surface of the right cylinder. Otherwise the trends are similar to those observed before and the base pressure continues to rise with an increase in Uc/U. As the stagnation point is located on the cylinder, its rotation would oppose the flow in some region. To alleviate this situation, the direction of rotation of the right cylinder (normally counter clockwise) was reversed for a > 45°. The results with reversed (i.e. clockwise) rotation for the right cylinder are presented in Figure 4-3(b2). Although the general trends remain essentially the same, local variations are present, particularly in the wake. Figure 4-3 (c) presents pressure plots for a = 90°. Note, now the windward face is B and the stagnation point is at tap 27 on face B. Again the suction pressure peaks are present over both the rotating cylinders as the stagnation point has moved away from the right cylinder. 4.2 Pressure Distribution: Plane-2 For a = 0, plane-2 is orthogonal to the flow direction, removed a distance W/2 (10.15 cm) downstream from the face A. The pressure ports involved are from 33 to 54. Figure 4-4 (a) shows the pressure data as affected by the momentum injection at a = 0. The main feature of interest is the tendency of the flow to reattach in presence of increasing momentum injection resulting in the progressive rise in pressure at taps 33-39 on the face B and taps 48-54 on the face C. 83 84 85 u Figure 4-4 Pressure plots for plane-2 showing the effect of a and Uc/U: fa) Schematic diagram showing the vortex V at the edge P2 and a pair of conical vortices formed at the corner CR. 86 o 87 The flow on the face E is rather interesting. For Uc/U = 0, fluid slowly accelerates, from stagnation, vertically on the face A and separates at the top sharp edge (Pi) creating the negative pressure. With rotation of the cylinders, suction created on the windward face A causes the incoming flow to accelerate. Now the flow at a higher velocity separates at the top edge as before creating pressure that is lower than that for the Uc/U = 0 case. For a = 30° (Figure 4-4bi), the character of the flow has two major features: (i) for Uc/U = 0, the separation angle for the shear layer at the left cylinder is higher than that at the right cylinder. This is schematically shown in Figure 4-4(b2). This results in a relatively higher pressure on the face B (taps 33-39) compared to that at the face C (taps 48-54). The momentum injection has only marginal effect in these regions. It tends to increase the pressure slightly on the face B suggesting possible reattachment. On the other hand, the injection of momentum merely increases the velocity causing the pressure to diminish at the face C. (ii) The presence of a peak in the region corresponding to taps 39-41 is an outcome of two effects: • The lateral vertical flow on the face B separates at the sharp top edge P2, creating a vortex (V) and a corresponding low pressure region. • Also at the rounded top corner (CR) two conical vortices (CV) are formed as indicated in Figure 4-4(b2). The one on the right would interact with vortex V (both of the same direction) giving rise to a suction peak as observed. 89 At a = 60°, a positive pressure close to Cp ~ 0.75 suggest proximity to the stagnation condition as discussed earlier, while the rest of the region is essentially in the wake created by the flow separating at the edge P 2 (Figure 4-4c). At a = 90°, plane-2 becomes aligned with the flow. As expected, pressure taps 33-39 suggest proximity to the stagnation region, while the rest of the taps are essentially in the wake caused by the flow separating at the edge P2 (Figure 4-4d). 4.3 Pressure Distribution: Plane-3 For a = 0, vertical plane 3 is aligned with the flow direction (Figure 4-5a). To begin with, let us consider the reference case with no momentum injection. As can be anticipated, the windward face A has high positive pressure, close to the stagnation condition. The stagnation point is located at tap 59. The flow separates at the top sharp edge Pi with reattachment downstream on the face E in the vicinity of port 66. It separates again at the edge P4 with the face D in the wake. The effect of momentum injection is to promote suction leading to acceleration of the flow approaching the edge Pi. This higher energy is reflected in the higher pressure, with an increase in Uc/U, on the top surface E as well as in the wake. At a = 45° the effect of momentum injection becomes more apparent. As the stagnation region moves towards the right cylinder, the positive pressure is significantly lower. Rotation of cylinders creates suction region on the face E which also tends to reduce the pressure at ports 55 to 63. A large value of Uc/U leads to higher suction, i.e. a lower pressure. This is quite evident on the front face A. A significant increase in pressure on the top face E and essentially the same wake pressure are also apparent. Note, because of the angle (a = 45°), the velocity component normal to the edge Pi is relatively small. Hence the pressure on the 90 91 92 top face E (at ports 64 to 68) is higher compared to that for a = 0. However, as the flows from the sides and the top face reunite in the wake, the pressure there is essentially the same as before. At a = 90°, plane-3 is normal to the incoming flow and located at a distance W/2 downstream from the windward face. The effect of momentum injection on the face A is quite evident. It shows a small rise in Cp with an increase in Uc/U. However, taps 69-76 on the face D are devoid of the direct momentum injection. In fact, they are in the separated flow from the sharp edge P5. Rotation of the upstream cylinder tends to cause suction on the face B, which would accelerate the flow leading to slightly higher velocity and the associated lower pressure as obtained here (taps 69-76). Perhaps the feature of some interest is the pressure peak in the region covered by taps 63-66 (face E). It appears to be the combined effect of reattachment of the flow separated at the edge P2 and the asymmetry caused by the momentum injecting cylinder. Note, the peak is not at the center but has shifted slightly in the direction of the face A. 4-4 Drag and Side Forces Detailed pressure measurements provided useful information concerning several parameters including the stagnation region, separation of boundary-layer and reattachment, suction peak pressures as affected by a and Uc/U, as well as the near wake pressure. However the flow, even for a relatively simple geometry represented by cube, is indeed complex. The pressure data were complemented by force measurements. Figure 4-6 shows variations of drag and side force coefficients (CD and Cs, respectively) as affected by the angle of attack and momentum injection. 94 95 96 To begin with, for reference, consider the variation of drag in absence of momentum injection. At a = 0, the drag of the model is slightly lower (CD = 1-08) than that for a sharp edged cube (CD = 1.18) as obtained by Bearman [59] and quoted by Blevins [60]. A slightly lower value of C D for the present case is due to two rounded edges, formed by the momentum injecting cylinders, on the windward force. A small reduction of drag in the range 0 < a < 15° may be attributed to the reattachment of the flow on the face B as indicated in Figure 4-7. At a = 60°, C D reaches the maximum value of 1.54 and subsequently it decreases reaching a value of 1.0 at a = 90°. Note, the geometry of the windward face normal to the flow at a = 90° is slightly different from that at a = 0. This may be responsible for a slight difference in the C D values at a = 0 and 90°. With the injection of momentum there is dramatic decrease in C D at all angles of attack. In the pressure plots, this was reflected in the appearance of large suction peaks at cylinder locations and increases in the wake pressure. At a = 0 and Uc/U = 4, the change in C D from 1.08 to 0.36 represents a decrease by 67 %. Similarly, for a = 60° and 90° the reduction in drag coefficient was found to be 56 % and 45 %, respectively. * At Uc/U = 0, the side force varies in a fashion that is similar to that observed for the drag: Cs increases with a, reaches a peak value of around 0.27 at a = 45°, and then diminishes. Again the difference in the side force value at a = 0 and a = 90° is attributed to the asymmetry caused by the presence of a cylinder. With momentum injection, the Cs value increases at all a. For a = 45° and Uc/U = 4, the rise in Cs is round 159 %. At a = 90°, the increase is even higher (~ 900 %). However, in general, the side force values are significantly lower, by around 50 %, compared to the C D data for the same a and Uc/U. 97 Flow past a two-dimensional square-section cylinder at a = 15° in absence of momentum injection: (a) sketch of separating streamlines; (b) flow visualization by Yokomizo and Modi [61]. 98 4-5 Galloping Instability Bluff bodies are susceptible to vortex resonance and galloping types of instabilities. Vortex resonance refers to the forced vibration condition where the vortex shedding frequency coincides with the system's natural frequency. On the other hand, galloping is the self-excited phenomenon where the force depends on the motion itself and acts in the direction of the motion. The amplitude of oscillations grows until the rate at which the energy is extracted from the fluid-stream balances the rate of dissipation of energy. Den Hartog [62] has presented an approximate criterion for the galloping instability as (dC s/da)+C D<0. Two-dimensional prisms are known to gallop at small angles of attack [13, 63]. With the measured drag and side force information in hand, one can assess the galloping stability of the cube resting on ground. Table 4-1 presents the necessary information. Note that even in absence of momentum injection, the cube is stable. In general, the effect of Uc/U is to increase stability for a < 15°. However, for a > 15°, momentum injection tends to reduce the stability. This aspect would be of considerable interest during the study of water-tank and building models. A word of caution is appropriate. The approximate criterion of Den Hartog was derived for two-dimensional bluff bodies. Here it is applied to a three-dimensional object. Although for large aspect ratio structures it has worked quite well, it has never been applied to such small aspect ratio body. On the other hand, one would expect the stubby object like cube to be stable and Den Hartog's criterion predicts it to be so. 99 Table 4-1 Effect of momentum injection on galloping stability. a 0 Uc/U C D dCs/da C D + dC s/da 0 1.07 0.178 1.248 0 2 0.52 1.833 2.353 4 0.36 2.455 2.815 0 1.02 0.437 1.457 15 2 0.73 0.858 1.588 4 0.51 1.222 1.732 0 1.26 0.418 1.678 30 2 0.95 0.172 1.222 4 0.61 0.181 0.791 0 1.53 -0.176 1.354 60 2 1.11 0.201 1.311 4 0.67 0.038 0.708 0 1.45 -0.318 1.134 75 2 1.24 0.185 1.244 4 0.66 0.102 0.764 0 1.02 -0.43 0.59 90 2 0.82 -0.28 0.54 4 0.55 -0.067 0.483 100 5. WATER-TANK MODELS : EFFECT OF HEIGHT The study with the cube model in Chapter 4 provided fundamental information, which can serve as reference in a variety of situations. A cubic water-tank is now considered. It is supported by a circular cylindrical pillar (5.08 cm diameter) at two different heights: H = 2W and H = 3W, where W represents the length of the cube-edge. An airfoil shaped shroud surrounded the support during experiments to minimize interference caused by the presence of the support. The objective is to assess the effect of the height of the tank above the ground on the mean surface pressure distribution and forces (drag, side force) as affected by the angle of attack and momentum injection. Figure 5-1 shows the tank at two different heights during wind tunnel tests. The tests were conducted at a subcritical Reynolds number of 6.7 x 104. As mentioned earlier in Chapter 2, the free-stream turbulence intensity in the test-section is less than 0.1 % and the boundary-layer thickness is less than 8 mm. In the discussion of results, the cube faces (Figure 4-4b2) are often referred to as follows: face A upstream or windward face ; face B or C side faces ; face D downstream face ; face E top face. 5.1 Pressure Plots In general, the pressure distribution in the three orthogonal planes I, II and III remained quite similar to those observed for the basic-cube case in Chapter 4. Variations in local values were noticeable, particularly at the suction peaks associated with the cylinder rotation, as well as on the sidewalls and in the wake pressure; however character of the plots 101 Figure 5-1 Water tank-models during wind tunnel tests (a) H = 2W; (b) H = 3W. 102 remained essentially the same. Figures 5-2 through 5-4 help illustrate this point. They show pressure distributions on planes 1, 2 and 3, respectively, as affected by the tank height, for the case of a = 0. Results for the basic cube model resting on ground (i.e. H = W) from Chapter 4 are also included to help comparison. It is apparent that the variation in the tank height has virtually insignificant effect on the trends followed by the pressure plots. However, there are variations in the numerical values in certain regions as mentioned earlier which would affect the drag and side force. This point can be better appreciated from Figure 5-5 where the height variation is emphasized for two values of momentum injection parameter, Uc/U = 0 and 4 at a = 0. One can arrive at similar conclusion from pressure plots at other angles of attack. The pressure plots were obtained in the angle of attack range of a = 0-90° with a increasing in a step of 15°. In light of the above observation, these results are purposely not included here. However, they are presented in Appendix III to permit access to details if and when needed. It is indeed surprising that such basic information for cubic tank, even in absence of momentum injection, does not seem to be reported in open literature. 5.2 Drag and Side Forces To recapitulate, for the basic cube resting on ground, i.e. H = W, the effect of momentum injection was to reduce the drag coefficient at all angles of attack. On the other hand, the side force increased with Uc/U at a given a. Application of the Den Hartog criterion showed the cube to be statically stable at essentially all angles of attack except for 75° < 90°. In general, the level of stability reduced with an increase in the angle of attack and momentum injection. With this as background, the attention was focussed on evaluating the 103 104 105 106 CL I I I o 107 108 109 110 I l l 112 113 114 effect of height on forces experienced by the water tank and the resulting character of stability. Water-Tank at a Height H = 2W Figure 5-6 presents results for the drag and side force coefficients for the tank at H = 2W. In absence of momentum injection, the variation of Co with a is similar to that observed for the cube (H = W) except for the peak value attained, which is slightly lower (Co.max = 1.4 as against 1.54 for H = W). Also the drop in C D in the range 0 < a < 15° is no longer present. This suggests that the absence of ground leads to lateral flow on the side faces preventing reattachment observed earlier (Figure 4-7). As before, in general, the effect of momentum injection is to reduce the drag at virtually all a, however, the reduction is significantly less compared to the basic cube case (Figure 5-6a). The reduction in drag at a = 0 and Uc/U = 4 is now 34 % as against 67 % observed for the cube. The corresponding reductions at a = 60° and 90° are 27 % and 10 % (compared to 56 % and 45 %, respectively for the cube), respectively. Thus efficiency of the momentum injection in promoting reattachment and delay of separation seems to reduce due to proximity of the ground. Absence of the ground seems to induce wider wake. The side force results are shown in Figure 5-6(b). The increase in side force, at a given a, with momentum injection is similar in character to that observed for the cube case, however, now the increase is significantly higher, particularly at Uc/U = 4. The presence of negative slopes for 45° < a < 60° (Uc/U = 0) and a > 75° (Uc/U = 2, 4) suggest reduced stability or even possible instability. Table 5-1, which presents prediction of instability based on Den Hartog's criterion, substantiates this observation. 115 Figure 5-6 Forces on the water-tank model with a height of H = 2W: (a) Cp • 116 Table 5-1 Stability prediction for the water-tank model at H = 2W. ct° Uc/U C D dC s/da C D + dCs/da 0 0.96 0.26 1.22 0 2 0.65 1.417 2.067 4 0.63 2.128 2.758 0 1.09 0.50 1.59 . 15 2 0.98 1.60 2.58 4 0.84 1.904 2.744 0 1.29 0.596 1.886 30 2 1.09 0.958 2.048 4 0.92 0.917 1.837 0 1.36 -0.401 0.959 60 2 1.35 -0.208 1.142 4 1.01 0.051 1.061 0 1.18 -0.019 1.161 75 2 1.14 -0.840 10.3 4 0.91 -0.720 0.19 0 0.93 -0.413 0.517 90 2 0.96 -1.788 -0.828 4 0.83 -1.192 -0.362 118 Water-Tank at a Height H = 3W Force results for the cube supported by the cylindrical column of length H = 3W are presented in Figure 5-7. In absence of momentum injection, the results are quite close to those for the case of H = 2W except for small local differences. However, with an injection of momentum there is a dramatic decrease in drag at all angles of attack. This in sharp contrast to the small reduction in CD observed at H = 2W compared to that for the basic cube. Now, for a = 0 and Uc/U = 4, the reduction in CD is 67 %, the same as that for the ground-based cube. The corresponding reductions in C D at a = 45° and 90° are 65 % and 69 %, respectively, which are even higher than those observed for the basic cube case (57 % and 45 %, respectively) This suggests improvement in the momentum injection efficiency as the tank moves away from the ground beyond a critical distance with the boundary-layer separation from the side walls delayed resulting in the observed reduction in CD-So far as the side force variation is concerned (Figure 5-7b) the behavior, in absence of momentum injection, is similar to that observed for the H = 2W case (Figure 5-6b). However, a rise in Cs with Uc/U for a given angle of attack is somewhat lower, although the trends are quite comparable. Furthermore, with an increase in Uc/U, the critical a for the onset of a negative slope is slightly delayed (from a = 45° for Uc/U = 0 to a = 60° for Uc/U = 4) suggesting stability over a wider range of the angles of attack. Of course, at a higher a (a > 60°), the system becomes unstable, i.e. prone to the galloping type of self-excited oscillations even at Uc/U = 4 (Table 5-2). 119 120 121 Table 5-2 Prediction of stability, based on the Den Hartog criterion, for water-tank model at H = 3W. a 0 Uc/U C D dCs/da C D + dC s/da 0 0 0.94 0.713 1.653 2 0.62 1.375 1.995 4 0.31 2.116 2.426 15 0 1.17 0.417 1.587 2 0.8 1.430 2.230 4 0.44 1.490 1.930 30 0 1.30 0.306 1.606 2 0.98 0.896 1.876 4 0.43 0.688 1.118 60 0 1.39 -0.363 1.027 2 1.25 -0.458 0.792 4 0.69 -0.344 0.346 75 0 1.27 -0.183 1.087 2 1.08 -0.987 0.093 4 0.49 -0.917 -0.427 90 0 1.07 -0.745 0.325 2 0.89 -1.490 -0.60 4 0.34 -1.277 -0.937 122 6. BUILDING M O D E L S : A S P E C T R A T I O E F F E C T S Flow past buildings has been a subject of considerable study for quite sometime. Leonardo de Vinci (1452-1519) is said to have sketched flow pattern behind a rectangular bluff object showing surprisingly accurate vortex pattern. Nowadays design of tall buildings routinely involves model tests to predict forces and dynamic response characteristics [8, 64-68]. Structures with rectangular cross-sections, treated as two-dimensional as well as three-dimensional bodies, have also received attention [69-76], however, in majority of cases, the focus has been on specific geometries, turbulence character of the incoming flow and time dependant loading. Surprisingly as it may seem, even in absence of momentum injection, a systematic study of a square prism in laminar flow, with emphasis on the aspect ratio effect on the mean loading, remains virtually unexplored. This information, of course, is of fundamental importance, as it would serve as reference to assess the effect of geometric modifications, free-stream turbulence, etc. The objective here is to study, through a planned program, detailed mean pressure distribution and forces on a family of three square cross-section prisms (cylinders), with aspect ratios of 1, 2 and 3 (Figure 2-9), in presence of the MSBC. The basic cube model studied in Chapter 4 serves as the key element. Note, besides changing the aspect ratio, the models also vary the length of the rotating element with respect to the height of the model, from 100 % for cube to 33 % for the building with an aspect ratio of 3. The momentum injecting cylinders had smooth surfaces. Figure 6-1 shows photographs of the three building models tested. A set of buildings with three aspect ratios, the angle of attack ranging from 0-90°, and variation of momentum injecting parameter (Uc/U) affecting 76 pressure taps, distributed 123 over three orthogonal planes at the cube, naturally lead to a vast amount of information. As mentioned earlier, concise yet informative way of presenting the results posed a challenge. Only some selected data helpful in appreciating features of the complex flow are reported here with the rest included in Appendix IV. 6.1 Pressure Distribution Figure 6-2 shows pressure plots for a = 0, in plane-1, as affected by the momentum injection and aspect ratio (A.R.). As expected, the pressure distribution is symmetrical about the stagnation point at tap 17 for all Uc/U values. The suction peaks at cylinder locations clearly show the effect of momentum injection: with an increase in Uc/U the suction peak pressure becomes progressively more negative at three aspect ratios used in the test-program. On the other hand, pressures on the sidewalls and in the wake show small increase at a higher Uc/U, again at all aspect ratios. Thus trends in the pressure plots remain essentially the same, irrespective of the aspect ratio, except for small variations in local numerical values. The main discemable effects of the A.R. are: (i) increase in the negative (suction) peak pressure with an increase in the aspect ratio; (ii) lower pressure on the side faces as the aspect ratio increases; (iii) reduction in the wake pressure at higher A.R. Obviously, these pressure variations will affect the force coefficients CD and Cs associated with the buildings of three different heights. Figures 6-3 and 6-4 present similar information in plane-1 for a = 60° and 90°, respectively. Results in Figure 6-3 substantiate the above comment concerning the trends remaining virtually unaffected by the aspect ratio. Note, the stagnation point moves to the 125 126 127 128 129 130 131 132 133 134 upstream cylinder (tap 23). Remarks in (i) and (ii) are still valid, however, the wake pressure is clearly higher for the tallest building at Uc/U = 4. Figure 6-4, for a = 90°, considers the case when the momentum is injected only on the side face A. The stagnation point has moved to tap 27 for the three aspect ratio values. The main effect of the aspect ratio is in the wake pressure, which shows a significant increase at Uc/U = 4 for A.R. = 3. This would suggest a reduction in the drag at a = 90° with momentum injection. Perhaps it would be more informative to present aspect ratio effects in the same figure to assess their relative importance somewhat directly. This is shown in Figures 6-5 to 6-7. Figure 6-5 presents aspect ratio effects, without (Uc/U =0) with momentum injection (Uc/U = 4) for three angles of attack (a = 0, 60°, 90°) in plane-1. Figures 6-6 and 6-7 provides similar information for plane-2 and plane-3, respectively. To begin with, consider the A.R. effect in absence of momentum injection (i.e. Uc/U = 0) and at a = 0 as shown in Figure 6-5(a). Several points of interest are apparent: (i) Magnitude of the positive pressure as well as the extent of the positive pressure region on the windward face diminishes with an increase in the aspect ratio. (ii) The suction peak at the cylinder location increases; i.e. the pressure becomes more negative with an increase in the A.R. The results in (i) and (ii) would suggest a higher aspect ratio to reduce the drag at a = Uc/U=0. (iii) The base pressure shows a significant decrease at a higher A.R. This, in turn, would reflect on an increase in the pressure drag. 135 . 5 I ; —; : : : : ; 1 1 5 9 13 17 21 25 29 1 Port Number Figure 6-5 Variation of pressure plots in plane-1 as affected by the aspect ratio and momentum injection: (a) a = 0. 136 25 29 1 Figure 6-5 5 9 13 17 21 Port Number Variation of pressure plots in plane-1 as affected by the aspect ratio and momentum injection: (b) a = 60°. 137 Plane-1 a = 90° Uc/U = 0 1 25 29 1 5 9 13 17 21 Port Number Figure 6-5 Variation of pressure plots in plane-1 as affected by the aspect ratio and momentum injection: (c) a = 90°. 138 0 CP -1 - Plane-2 ct = 0 Uc/U = 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 A.R. = 1 - B H B B— B &—B B -¥ — A A &—-a £_ -2 ^ x ^ - x — x — x - ~X^-"X -A & &- -A A A A A & " . . . . . . - N ^ . . . . - x ^ x - x— x-^ 2 1 H 1 1 1 1 1 \ Plane-2 a = 0 c Uc/U = 4 I I I I 33 Figure 6-6 37 49 53 41 45 Port Number Variation of pressure plots in plane-2 as affected by the aspect ratio and momentum injection: (a) a = 0 . 139 33 37 41 45 49 53 Port Number Figure 6-6 Variation of pressure plots in plane-2 as affected by the aspect ratio and momentum injection: (b) a = 60°. 140 0 -3 1 k 0 cP -1 -2 -3 33 Figure 6-6 37 H—I—I—h—I—HVW Plane-2 a = 90° Uc/U = 0 H h 1 1 1 1 1 1 h A.R. = 1 : — B B B — ? B -•A A *"A X_^x : y x — x— x—x— x— * Plane-2 a = 90° Uc/U = 4 49 53 41 45 Port Number Variation of pressure plots in plane-2 as affected by the aspect ratio and momentum injection: (c) a = 90°. 141 Plane-3 a = 0 Uc/U = 0 1 k g s - K - H Plane-3 cc = 0 Uc/U = 4 0 C P -1 -2 -3 -4 55 Figure 6-7 59 71 75 63 67 Port Number Variation of pressure plots in plane-3 as affected by the aspect ratio and momentum injection: (a) a = 0. 142 1 h Plane-3 a = 60° Uc/U = 0 0 13 9 ? 9 T 9 =^=° 1 2 -3 2 1 r-0 Plane-3 a = 60° Uc/U = 4 1 h x x—-x—x—x^ i . _Sv - - . _ ^ x-^-x^-^x^-x^-x—»-x^-x 3 1 1 1 1 55 >ure 6-7 59 71 75 63 67 Port Number Variation of pressure plots in plane-3 as affected by the aspect ratio and momentum injection: (b) a = 60°. 143 55 Figure 6-7 59 63 67 Port Number 71 75 Variation of pressure plots in plane-3 as affected by the aspect ratio and momentum injection: (c) a = 90°. 144 Thus effects in (i) and (ii) are entirely opposite to that suggested in (iii). The same trend continues with the momentum injection of Uc/U = 4. Hence the effect of A.R. at a = 0 is likely to be insignificant. This is substantiated by force results presented later in Figure 6-8(a) and 6-10(a). For a = 60° (Figure 6-5b), the effect of momentum injection is rather dramatic. Suction peaks at the downstream cylinder are larger, with distinctly lower pressures in the wake, without and with momentum injection, for higher aspect ratio building. This would indicate an increase C D with A.R. at a = 60°. Similar conclusion can be drawn from plots in Figure 6-5(c) for a = 90°. Figure 6-6 for pressure distribution in plane-2 clearly shows that with an increase in the aspect ratio, effectiveness of the momentum injection in promoting reattachment diminishes. This, of course, is expected, as now the sharp edge portion of the building is greater, while the region covered by the MSBC remains fixed. Resulting lateral flow in the vertical direction tends to delay attachment. Plane-3 is not directly affected by the momentum injection, and essentially the stagnation condition prevails over the front face (Figure 6-7a) at a = 0. The flow separates at the top horizontal edge Pi and the base pressure is distinctly lower for the larger aspect ratio building. This would tend to increase the drag, particularly at a = 90° where the effect is quite distinct. The drag results in Figures 6-8(a) and 6-10(a) substantiate this observation. 6.2 Drag and Side Force Coefficients Figure 6-8 presents variation of C D and Cs with the angle of attack and momentum injection for the building with an aspect ratio of 2. Corresponding results for the basic cube (A.R. = 1) and the water-tank model (H = 2W) were presented earlier in Figures 4-6 and 5-6, 145 respectively. They will be helpful in understanding the present set of data. To begin with, consider the case of Uc/U = 0. It is apparent that the C D data are significantly higher at all values of the angle of attack compared to those for the basic cube. The same is true with respect to the water-tank model (Figure 5-6). This can be expected because of the sharp edges of the square cross-section prism extending over a longer distance in the present case. Of interest is the drop in C D with a in the range 0 < a < 15°. Similar drop was observed for the basic cube (Figure 4-6) but not in the case of water-tank (Figure 5-6). As explained before (p.97), this is attributed to the reattachment of the separated boundary-layer on the face B (Figure 4-7). Presence of ground in the case of the basic cube and bottom section of the building in the present case promotes reattachment. However, the tank being supported by a pillar does not provide such base. The flow below the tank induces lateral flow on the face B which prevents the reattachment, thus leading to a higher drag, in this range of a, for the tank. The rise in drag in the range 75° < a < 90° represents a different trend from that observed for the basic cube or the tank. This can be explained quite readily by comparing the pressure plots for a = 75° and 90° in plane-1 as given in Figure 6-9. Note, the base pressure (taps 5-10) for a = 75° is distinctly higher than that at a = 90°. Furthermore, average pressure on the windward face (taps 24-29) is slightly lower for the a = 75° compared to that at a = 90°. These differences would lead to an increase in the drag at a = 90°. The reduction in drag with momentum injection at all angles of attack follows the expected trend. However, the drop is relatively smaller for the present case as summarized in 146 147 148 149 150 Table 6-1 for a - 0 , 45° and 90°. This may be attributed to: (a) inherently higher drag due to sharp edges extending over a longer distance; (b) relatively smaller length, in relation to height, of the momentum injecting elements. Variation of the side force coefficient with a in Figure 6-8(b) has several features of interest. (a) There is a change in the direction of the force (Cs < 0) showing a dip in the range of 0 < a < 28°. This was not present in the basic cube or the water-tank study. Note, the Cs becomes progressively more negative with an increase in Uc/U, in this range of a. In his study with a two-dimensional square prism with rotating cylinders extending over the entire length, Munshi [13] observed a similar dip in the lateral force coefficient in the angle of attack range of 0 < a < 15°. It appears to be associated with sharp edges of the building extending over a longer length compared to the basic cube and tank-models. Similar plots for a higher building of H = 3W presented in Figure 6-10 substantiate this observation. Note, the peak pressure now is even more negative. Obviously, presence of steep negative slopes in the Cs plot suggests possible galloping instability of the building in the range of 0 < a < 15° and 75° < a < 90°. Square prisms are known to be unstable in certain ranges of a [63, 77]. (b) In general, the effect of momentum injection shows relatively small increase in Cs, when an increase is present (40° < a < 80°). (c) There is a steep decline in the side force with an increase in Uc/U for 75° < a <90°. • 151 Table 6-1 Comparison of drag reduction for the cube, water-tank and building models at Uc/U = 4 Model Reduction in C D , % a = 0 a = 45° a = 90° Basic Cube 66.4 56.5 46.1 Tank, H = 2W 34.4 25.2 10.2 Building, H = 2W 30.1 26.5 31.2 152 Force data for the building with Ft = 3W are presented in Figure 6-10. The variation of C D follows trends that have some similarity with those for the H = W and H = 2W cases (Figure 6-10a). However, the trends are somewhat distorted because a larger portion of the total drag is now contributed by the sharp edged section of the building (66 % of the total height). The rotating cylinders extend only to H/3 and hence have relatively less influence in governing the overall aerodynamics of the structure. Note, a reduction in drag coefficient for 0 < a < 15° is now possible only with the momentum injection (Uc/U = 2, 4). The peak drag continues to occur in the vicinity of a = 45° as for the H = 2W case. The effect of momentum injection on drag reduction at a = 45°, where the wake is likely to be the widest, seems to be relatively negligible. The side force data (Figure 6-1 Ob) show trends which are essentially similar to those observed for the H = 2W case. The effect of momentum injection is to reduce the side force coefficient in the range 0 < a < 55°. Similar variation was observed in the H = 2W case for 0 < a < 30°. It is of interest to recognize that the effect of momentum injection is clearly stabilizing for 60° < a < 90°. 6.3 Galloping Instability As before, one may now proceed to assess the building stability, based on Den Hartog's criterion, as affected by the aspect ratio, angle of attack and momentum injection parameter Uc/U. This information is presented in Table 6-2. Meteorological data about the wind direction and velocity being normally available, building designer can use the information on instability to advantage to assure safety. Based on the results following general remarks can be made: 153 0.5 0 Uc/U 0 2 4 0 15 —1 r— 30 45 a 0 60 75 90 Figure 6-10 Variation of force coefficients with the angle of attack for a building of H 3W: (a) C D . 154 155 Table 6-2 Comparative stability results for three buildings as affected by the aspect ratio, angle of attack, and momentum injection. Building <x° Uc/U C D dCs/da C D + dCs/da Basic Cube, H = W, A.R. = 1 0 0 1.07 0.178 1.248 4 0.36 2.455 2.815 45 0 1.38 0.141 1.521 4 0.60 -0.001 0.599 90 0 1.02 -0.430 ' 0.590 4 0.55 -0.067 0.483 Building,, H = 2W, A.R. = 2 0 0 1.63 -0.720 0.910 4 1.14 -1.528 -0.388 45 0 2.00 0.162 2.162 4 1.47 0.649 2.119 90 0 1.73 -1.776 -0.046 4 1.19 -3.210 -2.02 Building,, H = 3W, A.R. = 3 0 0 1.60 -4.584 -2.984 4 1.23 -16.27 -15.04 45 0 2.07 0.286 2.356 4 2.05 0.573 2.623 90 0 1.85 -0.477 1.373 4 1.48 -0.859 0.621 156 (a) Although the basic cube of A.R. = 1 is stable at a = 0, 45° and 90°, without as well as with momentum injection, the situation changes at the higher A.R. (b) In general, the effect of an increase in the A.R. is to make the building progressively less stable or even unstable. This suggests a need for momentum injection over greater height of the building as the A.R. increases. Note, in the present case, rotating cylinders extend only up to 50 % of the height for the building with an A.R. = 2. It covers only 33 % of the building height when the aspect ratio is 3. (c) Momentum injection generally reduces stability of the buildings with A.R. = 2 and 3. Of course, as mentioned before, the basic cube is always stable. (d) Tall buildings with square cross-section are susceptible to galloping type of instability at a = 0. These conclusions are based on Den Hartog's approximate criterion. It does not account for building's inherent structural damping which would tend to improve the stability. 157 7. CLOSING COMMENTS Contributions The main contributions of the thesis may be summarized as follows: (i) The focus of the thesis has been on determining fundamental information of lasting value, with reference to the Moving Surface Boundary-layer Control (MSBC). Results obtained promise to serve as reference and form a basis for further developments in the field for a long time. (ii) The two-dimensional study with a Joukowski airfoil provides detailed information concerning the pressure distribution, forces and Strouhal number as affected by the angle of attack, momentum injection parameter Uc/U and surface roughness of the rotating elements. Such a comprehensive study, using the same model and wind tunnel test-facility, leading to consistent set of unique data represents an important contribution. Of particular significance are the results for the surface roughness and Strouhal number. (iii) The investigation of the basic cube model in presence of the MSBC, which has never been reported before, is of far-reaching significance. The results obtained lay a sound foundation for further study and should serve as a fundamental reference. They should prove useful to the community of industrial aerodynamicists and practicing engineers. (iv) The fluid dynamics of a water-tank in presence of the MSBC, as affected by the height, provides valuable new information of practical importance. 158 (v) For tall structures, and supertall buildings planned in the early next century, investigation of the aspect ratio effects in presence of the MSBC represents an important development. 7-2 Major Conclusions The thesis presents results of a rather fundamental study aimed at the MSBC as applied to a two-dimensional airfoil, a basic cube, two configurations of a water-tank and buildings with two different aspect ratios. More important conclusions based on the test-program may be summarized as follows: Two-Dimensional Airfoil (ai) The momentum injection has significant effects on the pressure distribution. It creates a large suction peak at the cylinder location, as well as affects the position of the boundary-layer separation. In general, the wake pressure increases with an increase in Uc/U suggesting a reduction in the pressure drag. (a2) Force results suggest a large increase in the maximum lift coefficient and delay in stall with the momentum injection. For Uc/U = 3, the stall was delayed from a = 10° to a = 35° with the peak lift coefficient showing an increase of nearly 100 %. The corresponding rise in C L / C D was by 167 % ! (a3) Irrespective of the angle of attack, the effect of momentum injection is to increase the Strouhal number. Thus the airfoil behaves as an effectively more slender body, even at a high angle of attack. This would reflect in a smaller wake width and hence a reduction in the drag. In general, an increase in the Strouhal number for given a and Uc/U was slightly higher with the surface roughness. 159 Basic Cube (bi) With an increase in the angle of attack, the front stagnation point moves downstream. This requires reversal in the direction of rotation of one of the cylinders to promote reattachment and delay of separation for a > 45°. In general, with an increase in Uc/U, the suction peak pressure as well as the wake pressure increase suggesting a reduction in drag. (b2) Independently measured (as against pressure integrated) force results, in presence of the M S B C , showed considerable reduction in drag at all angles of attack. At a = 0 and Uc/U = 4, the reduction in CD was around 67 %. The corresponding values for a = 60° and 90° were 56 % and 45 %, respectively. (b3) Den Hartog's approximate criterion shows the cube to be stable in galloping, even in absence of momentum injection, at all angles of attack. In general, the stability margin improves with an injection of momentum. Water-Tank (ci) For the tank at a height of H = 2W, the effect of momentum injection is to reduce drag at virtually all angles of attack, however, the decrease is significantly less compared to that observed in the basic cube case. Thus, at a small height, a gap created by the proximity of the ground results in lateral flow on the side walls of the tank. This, in turn, appears to reduce efficiency of the momentum injection in promoting reattachment and delay of the boundary-layer separation. However, for H = 3W, the trend reverses. Now the cube is sufficiently far away from the ground and the flow on the top and the bottom faces are essentially similar (except for presence of the supporting 160 pillar at the bottom face). This reflects favorably on the drag reduction, which is significantly higher, even compared to that for the basic cube case. (C2) The water-tank models are prone to galloping instability at high angles of attack (a > 75°) at both the heights tested, even with momentum injection. Note, the Den Hartog criterion does not account for the structural damping. Furthermore, sloshing motion of water in the tank can help dissipate energy and restore stability [11]. Building Models ( d i ) Pressure distributions and hence the force coefficients (CD, CS) are significantly affected by the aspect ratio (A.R.) of the building. An increase in the A.R. is generally accompanied with a small decrease in the wake pressure, thus suggesting a slight increase in drag. However, as with the basic cube and water-tank, the C D decreases with the momentum injection at all angles of attack, although the reduction is relatively smaller in the present case. (d2) As can be expected, a higher aspect ratio makes the building susceptible to the galloping instability. This suggests a need for momentum injection of over greater height of the building as against the 33 % (H = 3W) and 50 % (H = 2W) in the present study. 7-3 Recommendations for Future Studies The thesis represents a small step in understanding challenging fluid dynamics of a group of bluff bodies. Even here, the aspects covered are rather limited. Several avenues for further investigations with the MSBC, which are likely to be enlightening as well as satisfying, are indicated below: 161 (i) The present set of results have focussed on laminar flow. In practice, building will be partly or even completely submerged in the ground boundary-layer. There is a scope for extending the present study to account for the boundary-layer profile as well as scale and intensity of turbulence. (ii) For better appreciation of the complex character of the flow, inherent to this class of problems, extensive flow visualization study should complement the wind tunnel test results. (iii) Effect of the cylinder length as a fraction of the building height should be explored systematically to arrive at the minimum value needed for the MSBC to be effective in achieving the desirable effect. (iv) The study aimed at the influence of surface roughness should be pursued further with a larger variety of surface conditions. The momentum injection range should be extended to Uc/U < 1. (v) Application of the MSBC tends to suppress vortex shedding and modifies variation of the resultant force with the angle of attack. These suggest a possibility of suppressing both vortex resonance and galloping type of instabilities with an application of the MSBC. A few preliminary studies in the area have been reported, however, considerable scope exists for systematic investigation of the problem, with both two - as well as three - dimensional structures. (vi) Significant improvement in the C L / C D for an airfoil with the MSBC suggests possible application of the concept to control surfaces (hydroplanes) of submersibles or Automated Underwater Vehicles (AUVs). This represents a 162 new area of application. International Submarine Engineering Research Ltd., Port Coquitlam, B.C. has shown interest in application of the MSBC to maneuvering control of the AUVs. Such application to a prototype may be a desirable step in assessing practical applicability of the MSBC concept. (vii) Application of the MSBC to a rotating helicopter blade should be explored to prevent its stall. If successful, it could open a new area of application with far-reaching effects. (viii) Mathematical approaches should be developed to predict dynamical response of structures, during vortex resonance and galloping, in presence of the MSBC and accounting for damping. 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Thesis, University of British Columbia, Vancouver, B.C., Canada, 1966. 173 APPENDIX I : SPECIFICATIONS FOR INSTRUMENTATION USED IN THE STUDY (i) High Speed A.C. Motors (Dumore Corporation, U.S.A.) - Catalogue No. 6-021, Model 8551, Superflex-623G; - Specifications: 115 Volts, 3.8A, 0-60Hz, 1/4 h.p., 22000 rpm (no load) (ii) High Speed DC Motor (Astro Flight Inc., U.S.A.) -Power 1000 Watts; - Max. Current 35A; - Speed 17,000 rpm. (iii) Digital Tachometer (Shimpo, Japan) - Model DT-205B; - Range = 6 - 30,000 rpm; - Accuracy = 2 rpm. (iv) D.C. Power supply (Epsco Inc., U.S.A.) -Input: 115 Volts, 50-60Hz; - Output: 0 - 16 Volts, 8 A maximum . (v) Variable Transformer (Ohmite Manufacturing Company, U.S.A.) - catalogue No. VT8 - F; - Input: 120 Volts, 50 - 60 Hz; - Output: 0 -140 Volts, 7.5 A, D.C. 174 (vi) Pressure Measurement System (Scanivalve Corporation, U.S.A.) - Model J (500 psi) scanivalve transducer; - CTLR2/s2-s6, solenoid controller; - SCSG2, signal conditioner; - Accuracy, 2.5381 x 10 ~3 mV/N/m2. (vii) Barocel Pressure Sensor (Datamatics Inc., U.S.A.) -Type 550 ; -Range 10psi (690N/m2); - Resolution , 10"6 PSI (6.9 x 10 "5 N/m2). (viii) Platform Balance (Aerolab Inc. U.S.A.) -Lift: 0.135 mV/kgf; - Drag: 0.233 mV/kgf; - Side Force: 0.315 mV/kgf. (ix) A/D Input-Output System (Data Translation Inc., U.S.A.) - DT 2801 Series ; - Number of Channels = 8 or 16 ; - A/D Resolution = 12 bits ; - Maximum Gain = 8 ; - A/D input = 13.7 kHz. (x) IBM PC/486 compatible computer for data acquisition and reduction. 175 APPENDIX II: PRESSURE PLOTS F O R T H E BASIC C U B E M O D E L 176 177 178 179 181 182 185 186 187 APPENDIX III: PRESSURE DISTRIBUTION PLOTS F O R T H E W A T E R - T A N K M O D E L S W I T H H = 2W AND H = 3 W 189 190 191 192 193 194 195 196 198 199 2 0 0 2 0 1 202 203 204 205 208 209 210 211 212 213 214 216 217 218 219 220 221 CL 1 » I o 222 223 224 226 227 229 CN T - O T - CN CO o. i i i O 230 231 A P P E N D I X I V : P R E S S U R E P L O T S F O R T H E B U I L D I N G M O D E L S W I T H H = 2 W A N D H = 3 W 232 233 234 235 .236 237 238 239 240 241 243 CN T - O 1 - CN CO Q. 1 1 1 o 244 245 246 2 4 8 249 250 o 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 o 274 

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