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Drag reduction of a rectangular prism through momentum injection Dobric, Andrew 1992

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DRAG REDUCTION OF A RECTANGULAR PRISM THROUGHMOMENTUM INJECTIONbyANDREW DOBRICB.A.Sc., University of British Columbia, 1990A THESIS SUBMITTED IN PARTIAL FULFILMENT OFTHE REQUIREMENTS FOR THE DEGREE OFMASTER OF APPLIED SCIENCEinTHE FACULTY OF GRADUATE STUDIESDepartment of Mechanical EngineeringWe accept this thesis as conformingto the required standardTHE UNIVERSITY OF BRITISH COLUMBIAAugust 1992© Andrew Dobric, 1992In presenting this thesis in partial fulfilment of the requirements for an advanceddegree at the University of British Columbia, I agree that the Library shall make itfreely available for reference and study. I further agree that permission for extensivecopying of this thesis for scholarly purposes may be granted by the head of mydepartment or by his or her representatives. It is understood that copying orpublication of this thesis for financial gain shall not be allowed without my writtenpermission.(Signature)Department of Mechanical EngineeringThe University of British ColumbiaVancouver, CanadaDate  September 2,  1992DE-6 (2/88)11ABSTRACTDrag of a two-dimensional rectangular prism in the presence of momentuminjection is studied experimentally. Moving Surface Boundary-Layer Control(MSBC), achieved here through a pair of rotating cylinders serving as momentuminjection elements, was investigated to assess the effect of:(i) tangential velocity (Uc ) of the cylinder surface with respect to thefree stream wind velocity (U);(ii) angle of attack (a) of the prism surface with respect to the freestream;(iii) roughness of the cylinder surface.As the wake-body interaction is an important aspect of the associatedaerodynamics, frequency of the shedding vortices, as reflected in the Strouhalnumber, was also monitored. Results suggest that, under optimum combinationsof the system parameters, a drag reduction of around 70% can be realized. Thestudy has considerable implication to the drag reduction of road vehicles,particularly the tractor-trailer truck configurations.111TABLE OF CONTENTSABSTRACT 	  iiTABLE OF CONTENTS 	  iiiLIST OF FIGURES 	 vLIST OF TABLES 	  ixNOMENCLATURE 	 xACKNOWLEDGEMENT 	  xii1 INTRODUCTION 	  11.1 Background 	  11.2 A Brief Review of the Relevant Literature 	  11.3 Scope of the Present Investigation 	  52 MODEL AND TEST PROCEDURES 	 82.1 Model and Support Arrangement 	  82.2 Wind Tunnel 	  102.3 Test-Model Configurations 	  102.4 Test Procedures 	  122.5 Flow Visualization 	  142.6 Data Analysis 	  16iv3 RESULTS AND DISCUSSION 	  173.1 Cylinders at Leading Edges	  173.1.1 Drag 	  183.1.2 Lift 	  353.1.3 Surface pressure and the Strouhal number 	  373.2 Cylinders at Top Edges 	  643.2.1 Drag 	  653.2.2 Lift 	  803.2.3 Surface pressure and the Strouhal number 	  813.3 Flow Visualization 	  1004 CONCLUDING REMARKS 	  1034.1 Summary of Results 	  1034.2 Recommendations for Future Work 	  104REFERENCES 	  106APPENDIX A: TYPICAL LIFT RESULTS 	  110APPENDIX B: ADDITIONAL PRESSURE DISTRIBUTION DATA . . 	  115VLIST OF FIGURESFigure 	 page1-1 Schematic diagrams explaining the pressure drag and vortexshedding frequency 	1-2 Configurations investigated in the wind tunnel test-program 	  72-1 A photograph showing the experimental set-up during the windtunnel tests 	  92-2 A schematic diagram showing the model dimensions (1, length; d,diameter; h, height) and distribution of the pressure taps 	  112-3 A schematic diagram of the closed circuit water channel facility usedin the flow visualization study. The dimensions are in mm 	  153-1 A schematic diagram showing rotating cylinders as momentuminjection units located at leading edges of the two-dimensional prism.Note the cylinders rotate in the opposite sense   183-2 Reference drag coefficient as affected by the angle of attack inabsence of the MSBC with smooth cylinders 	  193-3 Variation of the drag coefficient with the angle of attack as affectedby the momentum injection through the rotation of the smoothcylinders. Uc2 /U is changed systematically with Uel /U held fixedat:a) Uci /U 0; 	  21b) Uci /U = 1; 	  22c) UC1 /IJ = 1.5; 	  23d) Uci /U = 2 	  243-4 Plots summarizing the effect of momentum injection with smoothcylinders on the variation of CD with a 	  283-5 Reference drag coefficient as affected by the angle of attack inabsence of the MSBC with rough cylinders 	 30vi3-6 Variation of the drag coefficient with the angle of attack as affectedby the momentum injection through the rotation of the roughcylinders. Uc2 /U is changed systematically with Ucl /U held fixedat:Uci 	 = (); 	  31b) Uci /U 1; 	  32c) Ucl /U = 1.5; 	  33d) 	 /U = 2. 	  343-7 Plots summarizing the effect of momentum injection with roughcylinders on the variation of CD with a 	  363-8 Surface pressure distribution as affected by the momentum injectionUc2 /LT with Ucl /U held fixed at 0:a) a = 0'; 	  39b) a = 5'; 	  40c) a = 10'; 	  41d) a = 15'; 	  42e) a = 20'; 	  43f) a = 30'; 	  44g) a = 40'; 	  45h) a = 45° 	  463-9 Surface pressure distribution as affected by the momentum injectionUc2 /U with Uel /U held fixed at 2:a) cc = 0°, 	  49b) cc = 5'; 	  50c) a = 10'; 	  51d) a = 15'; 	  52e) a = 20'; 	  53f) a = 30°; 	  54g) oc = 40'; 	  55h) oc = 45° 	  563-10 Variation of the Strouhal Number with the angle of attack asaffected by the momentum injection:a) Uci /U = 0; 	  59b) Uci /LT = 1; 	  60c) UCi	 2. 	  613-11 Effect of momentum injection on the Strouhal number at a = 0 0 -45° 	  62vii3-12 A schematic diagram showing rotating cylinders as momentuminjection units located at the top edges of the two-dimensional prism.Note the cylinders rotate in the same sense   643-13 Reference drag coefficient as affected by the angle of attack inabsence of the MSBC with smooth cylinders 	  663-14 Variation of the drag coefficient with the angle of attack as affectedby the momentum injection through the rotation of the smoothcylinders. Uc2 /U is changed systematically with Uci /U held fixedat:a) Ucl /U = 0; 	  67b) Uci 	= 1; 	  68c) Ucl /U = 1.5; 	  69d) Uci /U = 2. 	  703-15 Plots summarizing the effect of momentum injection with smoothcylinders on the variation of CD with a 	  723-16 Reference drag coefficient as affected by the angle of attack inabsence of the MSBC with rough cylinders 	  733-17 Variation of the drag coefficient with the angle of attack as affectedby the momentum injection through the rotation of the roughcylinders. Uc2 /U is changed systematically with Ucl /U held fixedat:a) Ucl /I1 = 0; 	  74b) Uci /U = 1; 	  75c) Ucl /U = 1.5; 	  76d) Uci /U = 2. 	  773-18 Plots summarizing the effect of momentum injection with roughcylinders on the variation of CD with a 	  793-19 Surface pressure distribution as affected by the momentum injectionUc2 /IJ with Ucl /U held fixed at 0:a) cc = 60'; 	  82b) a = 75'; 	  83c) a = 90'; 	  84d) a = 105°; 	  85e) a = 120°. 	  86viii3-20 Surface pressure distribution as affected by the momentum injectionUc2 /U with Ucl /U held fixed at 2:a) a = 60'; 	  89b) a = 75'; 	  90c) = 90'; 	  91d) a = 105°; 	  92e) a = 120°. 	  933-21 Variation of the Strouhal Number with the angle of attack asaffected by the momentum injection:a) Uci /U = 0; 	  96b) Uci /U = 1; 	  97c ) UCi	 2- 	  983-22 Effect of momentum injection on the Strouhal number at a = 60° -120° 	  993-23 Typical flow visualization photographs for a rectangular prism, witha smooth surface cylinder for a = 30° 	  1013-24 Typical flow visualization photographs for a rectangular prism, witha smooth surface cylinder for a = 90° 	  102LIST OF TABLESTable page3-1 Reference drag coefficient corresponding to a = U c / U = 0 (smoothcylinders) 	 273-2 Drag coefficient as affected by the surface roughness (a = 0°) 	 373-3 Variation of the Strouhal number with the angle of attack andUc / U (0° < a < 45°) 	 633-4 Effect of the surface roughness on the drag coefficient (a = 90°) 	 803-5 Effect of the angle of attack and momentum injection on the Strouhalnumber (60° < a < 120°) 	 95ixNOMENCLATURECD	coefficient of drag; D / (1/2)pU2dhCL	coefficient of lift; L / ( 1/2)pU2dhCp	coefficient of pressure; (p - p.) / (p o - poo )Cpo	coefficient of pressure at tap n; (po - p> ) / (po - p.)D drag forceL lift forceU free stream velocityUc	surface velocity of the rotating cylinderUC1 , UC2 	 surface velocities of rotating cylinders 1 and 2, respectivelyRe 	 Reynolds number, Ud / vSt 	 Strouhal number, fdo / Uac 	 alternating currentd 	 width along cylinder surface edge, Figure 2-2do 	projected width normal to the flow, varies with a, Figure 1-2f 	 pressure fluctuation frequencyh 	 span of the model, Figure 2-21 	 length along the side surface, Figure 2-2n 	 pressure tap numberPb 	 base pressurefrontal pressurepressure at tap nstagnation pressurereference pressure far upstream of the modeldistance along circumference of the bodyangle of attackair viscosityair densityangular velocity of the rotating cylinderangular velocities of cylinders 1 and 2, respectivelyxixiiACKNOWLEDGEMENTSpecial thanks is extended to my supervisor, Dr. V.J. Modi, for his time andguidance throughout this project, whose insight has made this project athoroughly enjoyable experience.The assistance of Mr. Ed Abell, Senior Technician, Oliver B. Ying, andSimon St. Hill, with the installation of the instrumentation, is gratefullyappreciated.The investigation reported here was supported by the Science Council ofBritish Columbia, Grant No. 5-53762, and The Natural Sciences and EngineeringResearch Council of Canada, Grant No. A-2181.11 INTRODUCTION1.1 BackgroundEver since the OPEC crisis of the early 1970's, the world is beset by agrowing concern for energy conservation. The rapidly shrinking petroleumreserves and fast disappearing rain forests make the efficient utilization of energyone of the most pressing issues of our time. Over the years, there has been agrowing interest in increasing the lift and decreasing the drag through the controlof the boundary-layer associated with the streamline as well as bluff bodies. This,in turn, has reflected on the vortex shedding and wake characteristics of the body.Introduction of the Moving Surface Boundary-layer Control (MSBC) representsone approach to minimize drag thus contributing to the efficient use of the naturalresources.1.2 A Brief Review of the Relevant LiteratureEver since Prandtl's introduction of the boundary-layer concept, there hasbeen concerted effort aimed at reducing its adverse effects. Methods includingsuction, blowing, vortex generators, etc. have been researched at length andapplied in practice with some degree of success. Much of the literature on these2topics has been reviewed by Goldstein 1 , Lachmann 2, Rosenhead 3 ,Schlichting 4, Chang 5 , and others. However, the use of Moving SurfaceBoundary-layer Control (MSBC) has received less attention, relatively speaking.The main goal is to delay, or even prevent, separation of the boundary-layerfrom the body. A moving surface accomplishes this by:- retarding the growth of the boundary-layer through reduction ofrelative motion between the surface and the free stream;- injecting momentum into the boundary-layer.A practical application of the boundary-layer control has been demonstratedby Alvarez-Calderon and Arnold 6, who carried out tests on a rotating cylinderflap to develop a high-lift airfoil for STOL-type aircraft. The system wassuccessfully tested in flight on a high-wing research aircraft. Also, NorthAmerican Rockwell designed the OV-10A aircraft which was flight tested atNASA's Ames Research Center 7 ' 8 ' 9. Cylinders, located at the leading edgesof the flaps, were rotated at high speed with the flaps in the lowered position, tostudy the landing characteristics.For understanding of the parameters affecting the boundary-layer controlprocess, Tennant et al. 10, 11 conducted tests with a wedge-shape flap havinga rotating cylinder at the leading edge. Flap deflection was limited to 15°, andeffect of the gap-size between the cylinder and the flap surface investigated.However, the ratio of the cylinder's surface velocity with respect to the free streamvelocity was limited to 1.2.3Through a comprehensive wind tunnel test-program involving a variety ofairfoils with one or more cylinders forming the moving surfaces, along with thesurface singularity numerical approach and flow visualization studies, Modi et12, 13, 14, 15al. 	 and Mokhtarian 16 have shown the concept to beremarkably effective. Results indicated an increase in the maximum liftcoefficient by at least 200% and a delayed stall angle to 48°.The basic concepts involved in the pressure drag reduction are indicated inFigure 1-1. Shown is a bluff body, a two dimensional prism, located in a freestream at zero angle of attack. Here, p f and Pb are the pressures on the front andrear surfaces, respectively. By increasing the base pressure, p h , or decreasing thefrontal pressure, pf , one can reduce the pressure drag of the body. Reduction ofthe bluff body drag has been investigated by Modi et al. 17, 18, 19, 20 andYing 21 using the momentum injection through MSBC. Ying has also reviewedthe associated literature at considerable length.Another relevant aspect of the bluff body aerodynamics and associateddynamics is its potential for vibration when exposed to a fluid stream. A commonexample is that of transmission lines humming in a breeze. Vortex resonance,galloping, flutter and buffeting are some examples of such fluid-structureinteraction instabilities. A vast body of literature exists in the area including thecontributions by Blevins 22, Den Hartog 23, Vickery and Watkins 24, andmany others. Cermak 25 and Welt 26 have provided excellent overviews ofcontributions in this area. Of course, the end objective would be to suppress, or , 1.........1110. 	1 ■110-..■100.  Bluff Body  .........1110.-	.......DragFigure 1-1 	 Schematic diagrams explaining the pressure drag and vortex shedding frequency.145at least minimize, the resulting oscillations. Zdravkovich 27, 28 , Wongong 29 ,Kubo et al. 30 , and others have reviewed this literature quite effectively.A circular cylinder best demonstrates the phenomenon of shedding vortices,and the associated Strouhal number, observed with bluff bodies. The Strouhalnumber (St) is the ratio of the vortex shedding frequency (f) and the exposeddiameter of the body (do ) to the free stream velocity of the fluid (U). A classicalpaper of particular interest is that by Fage and Johansen 31 where the flowbehind an inclined flat plate is investigated, including the aerodynamics andfrequency of shed vortices. The suppression of these shedding vortices with theuse of moving surface boundary-layer control has been investigated by Kubo etal. 32, 33.1.3 Scope of the Present InvestigationThe present study builds on this background and investigates applicationof the Moving Surface Boundary-layer Control (MSBC) to a two-dimensionalrectangular prism. An organized wind tunnel test-program explores the effect ofMSBC on:(i) the lift and drag forces;(ii) the surface pressures; and(iii) the vortex shedding frequency;associated with the prism. A diagram of the different configurations investigated6is presented in Figure 1-2. The important parameters used during the MSBCstudy are the angle of attack (a) of the model with respect to the free stream winddirection; the cylinder surface roughness; and the ratio of the cylinder's surfacevelocity (Uc ) to the free stream wind velocity (U). This ratio (U c /U) and theangle of attack were systematically varied during the experiments for two cylindersurface roughness conditions. A flow visualization study compliments the windtunnel test-data.60 °< u< 120 °-45 0< ot< 45 °Figure 1-2 	 Configurations investigated in the wind tunnel test-program.82 MODEL AND TEST PROCEDURES2.1 Model and Support ArrangementThe model used in the present test-program is a modified version of thatemployed in the previous work 21 investigating the flow around bluff bodies.Figure 2-1 shows the model, supported by the strain-gauge balance, during atypical wind tunnel test. The rotating cylinders were integrated into arectangular Plexiglas prism with, approximately, a 2 mm gap between the cylinderand the body. The surface of the cylinders was flush mounted with the bodysurface to prevent abrupt pressure gradients. End-plates were provided at the topand bottom of the prism model to minimize edge effects, thus promoting the two-dimensional flow condition.The 25 4 mm diameter rotating drill-rod cylinders were connected by sewingmachine belt drives to high speed variac controlled 1/8 hp ac motors. The angularvelocity (w) of the cylinders was measured with a hand-held tachometer (Shimpo),thus providing the surface velocity Uc .The rectangular prism, with the attached cylinders and motors, wassuspended via two perpendicular flexible steel plates and a nylon bushing froman aluminum frame The whole system can be rotated on the bushing in thehorizontal plane to alter the angle of attack of the model. Strain gauges wereFigure 2-1 	 A photograph showing the experimental set-up during thewind tunnel tests.10attached to each flexible steel plate to measure the deflection of the prism in twonormal directions.2.2 Wind TunnelThe wind tunnel used in the experiments was a suction-type with amaximum speed of 50 m/s. The tunnel speed can be adjusted by a Variactransformer and was measured using a pitot static tube, placed at the contractionsection of the tunnel and connected to an inclined alcohol manometer. The motorand fan are positioned downstream of the test-section. Upstream of the test-section is a contraction-section with a ratio of 10:1. The entrance to the windtunnel is provided with a series of honeycomb and wire screen panels to promoteuniformity of the velocity profile and reduce turbulence. The peak turbulenceintensity in the test-section was around 0.5%. The square test-section, 45 x 45cm, has Plexiglas window inserts for easy viewing of the model.2.3 Test-Model ConfigurationsVariations in the experimental set-up ranged from the two rotatingcylinders at the leading edges of the rectangular cross-section prism, with thecylinders rotating in opposite directions, to the cylinders at the upper edges of thebody, with the cylinders rotating in the same direction (Figure 2-2). TheyI = 100 mm•+STap #1 	 -0.0332 	 -.0163 	 0.0004 	 0.0165 	 0.0336 	 0.1997 	 0.2248 	 0.2479 	 0.27410 	 0.30011 	 0.32412 	 0.35013	 0.45014 	 -F. 0.50015 	 -0.45016 	 -0.35017 	 -0.32418 	 -0.30019 	 -0.27420 	 -0.24721 	 -0.22422 	 -0.19954321ClC222 21 20 19 18 17 167 8 9 10 11 121314'15d =89.5 mmh = 420 mmFigure 2-2 	 A schematic diagram showing model dimensions (1, length; d, diameter; h, height) and distribution ofthe pressure taps.12provided the basis for studying the effects of momentum injection under differentorientations of the model. The angle of attack (a), with respect to the free streamwind velocity, was changed in 5-degree increments from 0° to 25°, followed bytests at 30°,40°, and 45° for the leading edge cylinder configuration. For the topedge cylinder arrangement, the angle of attack was varied from 75° to 105° in thesame 5° increments as before, and in 15° increments in the 60° — 120° range.In each case, the speed of the cylinders was independently varied to studyits influence on the drag, lift, pressure distribution, and Strouhal number. Ingeneral, it was anticipated that higher cylinder rotation speeds would lead tolower drag values up to a limit. There may also be some optimal combinations ofthe cylinder speeds which may minimize the drag.To begin with, the lift and drag measurements were carried out withcylinders having a smooth surface. This was followed by tests with rough surfacecylinders. The surface roughness was characterized by eight, 2 mm deep, equallyspaced, triangular grooves in the direction parallel to the axis of the cylinders.The vortex shedding frequency study also used the smooth and rough cylinderconfigurations, however, the latter resulted in the higher Strouhal Number values.2.4 Test ProceduresThe test procedures involved are rather conventional and straightforward.For the drag and lift measurements, bridge amplifier meters and digital13voltmeters were utilised, while for the pressure data, a Scanivalve and a personalcomputer were the main data acquisition and processing tools.At the beginning of the drag/lift experiments, the bridge amplifiers neededwarm-up before use. Under the no-load condition of the model, when the straingauges are not influenced by any bending forces, the bridge amplifiers wereadjusted so as to provide zero readings on the voltmeters to serve as a reference.A simple loading device was then attached to the sides of the wind tunnel inpreparation for the strain gauge transducer calibration. This involved the use ofa light-weight string, connected to the midsection of the model, which was placedover a sheave bearing on the calibration apparatus. Weights were attached to thestring providing a known force in one direction and the corresponding voltagerecorded. The procedure was repeated for the other strain gauge transducer uponrotation of the model by 90°, thus providing calibration for the forces measuredin two orthogonal directions.Now, the wind tunnel was turned on and the power adjusted to a desiredspeed for the tests. The cylinder angular velocity was set using the tachometer.The tunnel's free stream velocity was adjusted to remain constant, thusmaintaining a desired Reynolds number (Re) irrespective of a and U c / U. Theoutput voltages of the two transducers were read, followed by an analysis of thedata to give drag and lift coefficients.For the pressure measurements, the taps, located at the mid span of themodel, were connected to a Scanivalve pressure transducer (pressure transducer14#PDCR23D-lpsid and signal conditioner #SCSG2±5V/VG), which provided ananalog signal proportional to the measured pressure. It may be emphasized thatchanges in cylinder speed and angle of attack influence the free stream velocitydue to blockage effects. In the present study, the wind speed was held constantirrespective of the model condition to facilitate comparison at a fixed free streamReynolds number.2.5 Flow VisualizationThe wind tunnel test results were complemented by an extensive flowvisualization study carried out in the laboratory of Professor T. Yokomizo at theKanto Gakuin University, Yokohama, Japan. The design of the models wassupplied to Professor Yokomizo and the models were constructed in his machineshop. The tests were carried out by Dr. Yokomizo, Dr. Modi and twoundergraduate research assistants.The flow visualization study was carried out using a closed-circuit waterchannel facility. The models were constructed from Plexiglas and fitted with twin,hollow, smooth surface cylinders driven by compressed-air motors. A suspensionof fine polyvinyl chloride powder was used as a tracer in conjunction with slitlighting to visualize streak lines. Both the angle of attack and the cylinder speedwere systematically changed, and still photographs as well as videos were taken.Figure 2-3 shows a schematic diagram of the test arrangement.SHEET LIGHTMODELHONEYCOMBCDLt)zMIRROR	 SOURCE OF LIGHT SLIT  	 \500 130 	 2630Figure 2-3 	 A schematic diagram of the closed circuit water channel facility used in the flow visualization study.The dimensions are in mm.IPCDC\JCr)PI162.6 Data AnalysisSignals from the two force transducers were sent to a pair of bridgeamplifiers and displayed on two voltmeters. The voltage measured was directlyproportional to the model deflection. The relationship between the voltage and theforce was found to be linear.With the addition of a personal computer, frequency analysis was possiblethrough monitoring of the pressure fluctuations at the surface of the model. Thepressure taps, distributed around the mid-section of the body, along with areference static pressure tap, were connected to a Scanivalve. The pressure signal(voltage) was read into the computer through the use of an analog-to-digital cardand was stored for further analysis. Each sample consisted of five seconds of 100Hz information, read by the computer using a data acquisition program developedby Seto 34. Preliminary calculations suggested the sample frequency of 100 Hzto be adequate for the intended information.With reference to the stored information, a program was written todetermine the mean value of the pressure measured at each tap. The coefficientof pressure at tap n (Cpn , n = 1 to 22) is based on the pressure at tap n (pa)compared to the ambient pressure (R.) and the dynamic pressure ( 1/2pU2 ),P„ Pm P„ PmC -  Pn1 	 /I —PI—p U22173 RESULTS AND DISCUSSIONDuring the entire experimental program, the wind speed was maintainedat approximately 5 m/s (corresponding to Re -., 40,000). The wind tunnel's Variaccontrolled motor was adjusted to maintain a constant free stream dynamicpressure as pointed out before, while the cylinder's rotational speed held fixed, tooffset any blockage and drag reduction effects on the upstream flow.3.1 Cylinders at Leading EdgesThe experimental set-up where the rotating cylinders are placed on theprism face exposed to the free stream is shown in Figure 3-1. It indicatespositions of the two cylinders and their respective rotation directions, as well asreference for the pressure tap position, s, along the perimeter. Here the angle ofattack ranges from -25° to 25° for the force measurements and from 0° to 45° inthe frequency study.Figure 3-1 A schematic diagram showing rotating cylinders as momentuminjection units located at leading edges of the two-dimensionalprism. Note the cylinders rotate in the opposite sense.3.1.1 DragSmooth CylindersTo begin with, the drag results were obtained with the cylinders heldstationary providing the case which serves as reference to assess the effect ofmomentum injection and surface roughness (Figure 3-2).With the model at a = 0° and the cylinders rotating at the same speed (butin opposite directions) the flow field should be symmetrical. The results confirmedthis observation for both the smooth and the rough cylinders at four different180 	 5 	 10 	 15 	 20 	 252.45	 2.38	 2.13	 2.35 	 2.64	 2.914CD3--\-15 	 -10 	 -5 	 0 	 5 	 10 	 15 	 20 	 25210-25	 -205Figure 3-2cy 0Reference drag coefficient as affected by the angle of attack in absence of the MSBC with smoothcylinders20speed ratios. Only when the surface velocities (U ci , Uc2 ) of the two cylindersdiffered did the drag results deviate from the symmetric case.Another case of symmetry in the CD variation, as against the flowsymmetry, occurs when the pair of angular velocities are interchanged at a = 0°.This is apparent in the results presented in Figure 3-3. Note the interchange ofUcl and Uc2 ( i.e. Uci / U = 0 and Uc2 / U = 1 changed to Uci / U = 1 andUC2 0).A remark concerning the blockage effect would be appropriate here. Severalclassical procedures for blockage correction of streamlined bodies are available,and have been used in practice with some success depending on the situation.However, their application to bluff geometries has proved to be of questionablevalue. The problem is further complicated for the case of unsteady flows withseparation, reattachment and reseparation. In absence of any reliable procedurefor the blockage correction, the results are purposely presented here in theuncorrected form. This is not a primary concern in the present study as theobjective is to assess the influence of the MSBC at the same blockage, i.e. relativevalue of the drag without and with the cylinder rotation.With the cylinders stationary at a = 0°, the drag coefficient (C D ) of therectangular prism was 2.45 (Figure 3-3(a)), which is higher than the classicalvalue of 2.1 for a sharp edged square prism due to the wall confinement effects.For small angles of attack (a up to around 10°), the drag coefficient diminishes asthe flow on the top face reattached and that on the bottom face remains attached51CD0-25 	 -20 	 -15 	 -10 	 -5 	 0 	 5 	 10 	 15 	 20 	 25Variation of the drag coefficient with the angle of attack as affected by the momentum injectionthrough the rotation of the smooth cylinders. Uc2 /tJ is changed systematically with U ci /U held fixedat: a) Uel iU = 0.Figure 3-3X UC2/t-i= 0	 Uc2/U=1	 Uc2/U= 1.5XX UC2 = 24 -It /U = 13 -11 -25	 -20	 -15	 -10	 -5 	 0 	 5 	 10 	 15 	 20 	 25cv 0Figure 3-3	 Variation of the drag coefficient with the angle of attack as affected by the momentum injectionthrough the rotation of the smooth cylinders. U c2 /U is changed systematically with U ci /U held fixedat: b) 11c1 /1.1' = 1.C D01-25	 -20	 -15	-10	 -5 	 0 	 5 	 10 	 15 	 20 	 25az °Figure 3-3 Variation of the drag coefficient with the angle of attack as affected by the momentum injectionthrough the rotation of the smooth cylinders. U c2 /U is changed systematically with Uel /U held fixedat: c) Ue l /U = 1.5.5CD1 	 1 	 1 	 i 	 1 	 I	 I	 1 -25	 -20 	 -15	 -10	 -5 	 0 	 5 	 10 	 15 	 20 	 25ceFigure 3-3 Variation of the drag coefficient with the angle of attack as affected by the momentum injectionthrough the rotation of the smooth cylinders. Uc2 /U is changed systematically with 11 c1 /tT held fixedat: d) Uci /U = 2.025due to a favourable pressure gradient. This leads to a reduced wake width whichis apparent from the pressure measurements and flow visualization study resultspresented later. Beyond this critical angle, the separation point on the top facemoved upstream towards the leading edge of the prism with a correspondingincrease in CD. The plot has mirror symmetry about the a = 0° line as expected.With the top leading edge cylinder stationary (U ci = 0) and the bottomcylinder set into motion (Uc2 > 0), there was clear reduction in the drag for allnegative values of a. The momentum injection promoted the boundary layer toremain attached further along the surface towards the trailing edge. The lowestCD value of 1.58 corresponding to a = —5° represents a drag reduction of 34%.Even at a = —25° and Uc2 /U = 2, the change in CD from 2.91 to 1.99 amounts toa reduction of 31.6%. The corresponding reduction at a = 0° is 17.6%.On the other hand, for a > 0° the drag coefficient increases significantly.The pressure drag represents a cumulative effect of complex interactions betweenthe separation and reattachment conditions, pressure distribution and projecteddimension normal to the flow. Now the injected momentum carries theaccelerated boundary layer on the bottom face further along the direction normalto the flow resulting in a wider wake. The largest C D was 4.52 (a 55.3% increasefrom the base value) measured at a = 25°. Thus with the single cylinder rotation,injection of momentum on the leeward face results in reduction of the drag whilethat on the upstream face leads to an increase in the drag coefficient.Figure 3-3(b) shows the effect of additional momentum injection on the26upper face of the prism through rotation of the upper leading edge cylinder(Uci X = 1). With Ucl /UT T= - C2 /U 1 the CD plot is symmetrical about a = 0°as expected. The reduction in drag for this case is 14.3% at a = 0° and anincrease in drag of 55% at a = 25°. Validity of the earlier observation concerninginjection of the momentum on the upstream or leeward face and its effect on dragis strikingly apparent here. Note a significant increase in the drag at a negativea, particularly at higher values, due to injection of the momentum on theupstream face. However, at a positive angle of attack, the upper cylinder rotationhas a beneficial effect in reducing the drag. Of course, as expected, the effectbecomes progressively small at higher a. Note, at Ucl /LT = 1 and Uc2 /U = 2, thereduction in drag with respect to the reference case (Uci = UC2 = 0) is 24.9% ata = 0° , 28.9% at a = -25°, and an increase in drag of 1.7% at a = 25°. The lowestCD occurred at a = -5° as in the previous case (Figure 3-3(a)). The lowest dragcoefficient of 1.45 at Um /U = 1, Uc2 /U = 2 represents a drag reduction of 39.1%from the corresponding no rotation case (also at a = -5°).With a further increase in Um , similar trends persisted with minorvariations due to a number of complex interactions between a variety of factorsgoverning the flow as pointed out before. The results for U cl /U = 1.5 and 2 arepresented in Figures 3-3(c) and 3-3(d), respectively. With both the cylindersrotating at a relative speed of 1.5, the lowest CD = 1.65 at a = ±5° represents adrag reduction of 30.7% with respect to the no rotation case. The correspondingreduction at a = 0° is 31.2%. Similar results with U cl /U = 2 in Figure 3-3(d) are27apparent, however, with minor discrepancy in absolute values due to vibrationproblems. A viscous damper was introduced, however, it did not completelyeliminate the problem.To summarize, with smooth cylinders, the best condition corresponded toUC2 1 and Uc2 /U = 2 at a = 5°. The drag reduction was 40.8% with respectto the Zero Angle and Velocity (ZAV) condition. The corresponding reduction withrespect to the Stationary Cylinder Same Angle (SCSA) case amounts to 39.1%.On the other hand, the maximum reduction in CD at a = 0° is 24.9% at1-1C1/U = 1 and Uc2 /U = 2. A comparison of cylinder rotation velocities with theresulting drag reductions with reference to the ZAV condition are presented inFigure 3-4 as well as Table 3-1.Table 3-1 Reference drag coefficient corresponding to a = U c / U = 0(smooth cylinders)Um/U= Uc 2 / U CD (a = 0°) change from ZAV0 2.45 —1 2.10 —14.3%1.5 1.93 —21.2%2 2.19 —10.6%:4, -----------2X ti c iti=01 	 -1-- 	Uc /U=1	  Uc /U=1.5	--- H 		 Lic /U=20-25; 	 1 	 t 	 1 	 I 	 I	 1 -20	-15	 -10 	 -5 	 0 	 5 	 10 	 15 	 20 	 25CDc oFigure 3-4 	 Plot summarizing the effect of momentum injection with smooth cylinders on variation of CD with a.29Rough CylindersAs in the smooth cylinder case, the rough cylinders exhibited symmetryabout a = 0° for identical cylinder speeds (but opposite in sense). Figure 3-5displays the reference drag coefficient data with no rotation of the rough cylinders.In Figure 3-6(a), with Ucl / U = 0, similarities are evident with reference to thesmooth cylinder case in Figure 3-3(a). For a > 0°, there is a decrease in the dragfor all Uc2 / U > 0 as compared to a drag increase for Uc2 / U = 0. The lowestdrag occurred at a = —5° with Uc2 / U = 2. Note with roughness the minimum CDis 1.01 compared to 1.58 for the smooth cylinder case, a reduction of 36%.It may be pointed out that, for stationary cylinders, the presence of splinesto provide roughness results in a larger separation angle leading to a wider wakeand higher drag compared to the case of smooth cylinders.Figures 3-6(b) through 3-6(d) display the results when both the cylinders,with surface roughness, are operating. In all the cases, there are substantial dragreductions, particularly at low angles of attack. With U cl / U = 1.5 andUC2 / U = 2 at a = 10° the lowest drag recorded was CD = 0.60. As can beexpected, the same value was also obtained in the symmetric configuration ofUci / U = 2, Uc2 / U = 1.5 at a = —10°.With both the cylinders rotating at the same angular rate, the drag valuesfor the rough cylinders showed a higher percentage reduction than the0 	 5 	 10 	 15 	 20 	 252.28 	 2.49	 2.79 	 3.19 	 3.78 	 4.37-20 -15 -10 -5 04CD3215 	 10 	 15 	 20 	 250-25Figure 3-5cv 0Reference drag coefficient as affected by the angle of attack in absence of the MSBC with roughcylinders.0 	 I 	 1 	 I 	 I 	 I 	 I 	 I 	 I 	 I -25	 -20	 -15 	 -10 	 -5 	 0 	 5 	 10 	 15 	 20 	 25Figure 3-6ley 0Variation of the drag coefficient with the angle of attack as affected by the momentum injectionthrough the rotation of the rough cylinders. Ue2 X is changed systematically with Uci /U held fixedat: a) Ucl /U = 0.NUC1 /U= 1>< 	 uc2/1-J=0uc2/ u= i5NN 	 \ U c2 / U = 1.5N	 zN 	 ---a- uc2/u=zN 	 zN 	 zN 	 v2 -10-25 	 -20 	 -15	 -10 	 -5 	 0 	 5 	 10	 15 	 20 	 25a°CDFigure 3-6	 Variation of the drag coefficient with the angle of attack as affected by the momentum injectionthrough the rotation of the rough cylinders. Uc2 /U is changed systematically with Uci /U held fixedat: b) Uci /U 1. 	 cA:ND4UC2/U=0Uc2/U=1Uc2/U=1.5 //Uc2/U=2/><I N N\NNUC1 /U = 1.50-25	 -20 	 -15	 -10 	 -5 0 	 5 	 10 	 15 	 20 	 255vu °Figure 3-6	 Variation of the drag coefficient with the angle of attack as affected by the momentum injectionthrough the rotation of the rough cylinders. Ue2 fU is changed systematically with Uci /U held fixedat: c) Ucl X = 1.5.XUC1 /U = 2UC2/U= 0Uc2/U=1UC2/L1= 1.5 X5 	 10 	 15 	 20 	 25-25 	 -20 	 -15 	 -10 	 -5 	 05NNN4 -N,NNC DFigure 3-6ceVariation of the drag coefficient with the angle of attack as affected by the momentum injectionthrough the rotation of the rough cylinders. Uc2 /U is changed systematically with Uci AI held fixedat: d) Uci /U = 2.35corresponding smooth cylinders case. These results are displayed in Figure 3-7,and summarized in Table 3-2 for a = 0. It is apparent that the highest dragreduction of around 70% can be achieved for U c TU = 1.5. There is a possibilityof further improvement in the performance by optimizing the surface roughnesscondition of the momentum injecting elements. The pressure distribution resultsprovide further appreciation of the flow field, particularly with respect toseparation and reattachment.Figure 3-7 summarizes more useful information, from practical applicationconsiderations, for several identical values of the speed ratios. In general (exceptfor —12° < a < 12° and Uc /U = 2), the momentum injection leads to a significantreduction in drag as shown for a = 0 in Table 3-2. Even for a = ±25°, thereduction in drag at Uc /U = 2 is around 35%.3.1.2 LiftDuring the wind tunnel tests, through measurements of two orthogonalforces it was possible to determine the lift acting on the model. Although not theobjective of the present study, which focuses on the effect of momentum injectionon the drag, the lift results were also obtained (Appendix A). As the momentuminjection attempts to delay the boundary-layer separation, the effect, in general,is to increase lift at a given a.0 	 1 	 i 	 1 	 i 	 I 	 1 	 I	 1 	 I -25	-20	 -15	 -10	 -5 	 0 	 5 	 10 	 15 	 20 	 25ceFigure 3-7	 Plot summarizing the effect of momentum injection with rough cylinders on variation of C D with a.Table 3-2 Drag coefficient as affected by the surface roughness (a = 0°)UC1 / U = UC2 / U Cylinder Type CD % reductiondue toroughness% reductionwrt ZAV(smooth*)0 smooth 2.45*rough 2.28 6.9 6.91 smooth 2.10rough 1.21 42.4 50.61.5 smooth 1.93rough 0.73 62.2 70.22 smooth 2.19rough 0.95 56.6 61.23.1.3 Surface pressure and the Strouhal numberThrough a systematic variation of the angle of attack (a) and themomentum injection parameters Ucl /U , Uc2 TIJ, a considerable amount ofinformation was obtained pertaining to the surface pressure distribution. Forconciseness, only some typical results useful in establishing trends are presented3738here with further details recorded in Appendix B. It must be pointed out that,due to the obvious practical difficulty, the pressure information at the location ofthe rotating elements are missing. However, this does not affect the drag (andlift) data as they are measured directly through strain gauge force transducers.More importantly, the results provided better appreciation as to the physicalcharacter of the flow particularly with reference to the boundary-layer separation,reattachment, and base and frontal pressures. The fluctuating character of thepressure due to the shedding Karman vortices also helped in arriving at thecorresponding Strouhal number.For the analysis of pressure distribution around the rectangular prism, onemust try to interpret the pressure coefficients (Cp ) at each pressure tap.Although the pressure information is incomplete, it may help explain drag and liftvariations observed through the force measurements. Major changes in CD andCL can be correlated with pressure variations in certain regions over the bluffbody.The first set of pressure values studied were for the case, as before, whereUc /1-J. = 0 while the second cylinder is progressively rotated at higher speeds.The results are presented in Figure 3-8. The objective is to assess the effect ofmomentum injection on the pressure distribution at a given angle of attack. Asin the case when both the cylinders are stationary and a = 0°, there should not beany lift since the flow field is symmetric. This is apparent in Figure 3-8(a). Withthe momentum injection into the boundary-layer (U c2 / U > 0), there is a drop inX u c2/ u =0	  U c2 / U = 1q U c2 / U = 20Op- 1q q/-\'' X-2W Ixxxxxxx-3-0.5	 -0.4 	 -0.3	 -0.2 	 -0.1	 0 	 0.1	 0.2	 0.3	 0.4	 0.5SFigure 3-8	 Surface pressure distribution as affected by the momentum injection Uc2 /U with Uci /U held fixedat 0: a) a = 0°.X XSFigure 3-8	 Surface pressure distribution as affected by the momentum injection Ue2 /U with Ucl /U held fixedat 0: b) a = 5°.X Uc2/U=0	  u c2 iu= 1q Uc2/U=20- 11- 1/N.-2 - XXvXxxC p-3	1 -0.5 	 -0.4 	 -0.3 	 -0.2 	 -0.1 	 0 	 0.1 	 0.2 	 0.3 	 0.4 	 0.5SFigure 3 -8 	 Surface pressure distribution as affected by the momentum injection U c2 X with Ucl /U held fixedat 0: c) a = 10°.-0.4 	 -0.3 	 -0.2 	 -0.1 	 0 	 0.1 	 0.2	 0.3 	 0.4	 0.5SFigure 3-8	 Surface pressure distribution as affected by the momentum injection U c2 /U with Uci 1U held fixedat 0: d) a = 15°.-3-0.5 	 -0.4 	 -0.3 	 -0.2 	 -0.1 	 0 	 0.1	 0.2 	 0.3 	 0.4	 0.5SFigure 3-8	 Surface pressure distribution as affected by the momentum injection U 2 /U with Uel /U held fixedat 0: e) a = 20°.10Cp- 1-2-3-0.5 	 -0.4 	 -0.3	 -0.2 	 -0.1	 0 	 0.1 	 0.2 	 0.3	0.4 	 0.5SFigure 3-8	 Surface pressure distribution as affected by the momentum injection Uc2 /U with Uci /U held fixedat 0: f) a= 30°. X U c2 /U=0U c2 / U=1q Uc2/U=2**ic p-1-2-3-0.5 	 -0.4 	 -0.3 	 -0.2 	 -0.1 	 0 	 0.1 	 0.2	 0.3	0.4	 0.5SFigure 3-8	 Surface pressure distribution as affected by the momentum injection Uc2 with Uci /U held fixedat 0: g) a -= 40°.-0.4	 -0.3 	 -0.2 	 -0.1 	 0 	 0.1 	 0.2 	 0.3	 0.4 	 0.5SFigure 3-8	 Surface pressure distribution as affected by the momentum injection Uc2 /LT with Uci /LT held fixedat 0: h) a = 45°.47pressure immediately behind the rotating cylinder (s < — 0.20) due to an increasein the local air speed. Further along the surface, the energy from the momentuminjection is dissipated into the boundary layer to create a higher pressure, witha resulting increase in Cp in the wake and on the sides of the body. This wasreflected in the drag coefficient decreasing from 2.28 to 1.20 (U c2 iU = 0 and 2,respectively). Also, the variation in Cp when 1.1c2 /U is increased from 0 to 1 isgreater than that for the Uc2 /U changing from 1 to 2. The drag results alsoshowed the similar trend.With an increase in the angle of attack, the pressure distribution changesmarkedly (Figure 3-8(b)). The top face of the body (0.20 < s < 0.37) seems to bein a constant pressure zone, most likely a separation region produced by the flowdetaching from the top cylinder, which is not rotating. The bottom face shows alow pressure region just behind the cylinder in the case where there is no rotationof the second cylinder. This is due to the accelerated flow. As the second cylinderstarts rotating, the pressure increases due to the momentum injection as describedbefore, the effect becoming quite apparent in the wake on the top face atUC2 /Ur = 2. As for the a = 0° case, the drag of the body decreased with theintroduction of the momentum injection.The same trend persists for a = 10°. At a = 15° (Figure 3-8(d)), thepressure distribution in the region —0.37 < s < —0.20 is essentially uniform. Thereis only a small area of low pressure just behind the lower stationary cylinder.With the rotation of the lower cylinder, the flow on the bottom face remains48essentially attached. The added energy does become apparent through anincrease in the pressure in the wake region.At higher angles of attack the pressure distributions exhibit similarcharacter. Of particular note is the Cp distribution when a = 45°. Here thepressure on the top and the rear faces (0.20 < s < 0.55) is essentially constant.This indicates that the entire region is in the wake. The energy from themomentum injection results in higher pressures as Uc2 iL1 increases.With an additional momentum injection through the rotation of the topcylinder (Uc1 /I5 = 2), the pressure plots are further affected (Figure 3-9) in theexpected fashion. The observations here are very similar to those discussedearlier,however, a few explanatory comments would be appropriate.For a = 0°, as expected, there is a low pressure region in the vicinity of thecylinders, due to local acceleration of the flow. Further along the top and bottomfaces, the decrease in the fluid speed due to convection of the momentum andenergy dissipation, the pressure shows a slight increase. On the bottom face, withthe second cylinder not rotating, the pressure is essentially constant correspondingto only minor changes in velocity in the separated region. With the momentuminjection on the top face, the similar behaviour was observed. The sameobservations can be made as given for the case of Um / U = 0 for Ucl / U = 2.The effect of raising the momentum injection level to Um. /U = 2 has astriking effect on the pressure plots. As can be expected, for a = 0° and1-/C2 /1-J 0, results are similar to those for the case where U cl /15 = 0 andX u c2 iu=o	  u c2 /u=iUc2iu= 2±±LJXxx     XXfXEl II II XXX X,4}xXX Cp-3-0.5 	 -0.4 	 -0.3 	 -0.2 	 -0.1 	 0 	 0.1	 0.2	 0.3	0.4	 0.5SFigure 3-9	 Surface pressure distribution as affected by the momentum injection Uc2 /U with Ucl /U held fixedat 2: a) a = 0°.X Uc2/u=0uc2/U=1q Uc2/U=2Xzfl-3-241--0.5 	 -0.4 	 -0.3 	 -0.2 	 -0.1 	 0 	 0.1 	 0.2 	 0.3 	 0.4 	 0.5SFigure 3-9	 Surface pressure distribution as affected by the momentum injection U e2 /U with Uci /U held fixedat 2: b) = 5°.opX-2-3X X1X uc2/u=0	  u c2 iu=iUc2/U=20Cp4]-0.5 	 -0.4 	 -0.3 	 -0.2 	 -0.1 	 0 	 0.1 	 0.2 	 0.3 	 0.4	 0.5SFigure 3-9 	 Surface pressure distribution as affected by the momentum injection Ue2 /IJ with Ucl /U held fixedat 2: c) a = 10°.-3-2X0CpX uc2/U=0 	 ti c2 iu=iEl Uc2iu=2zX Xdu XXX XXX XECJOELIll q-0.5 	 -0.4 	 -0.3 	 -0.2 	 -0.1 	 0 	 0.1	 0.2	 0.3 	 0.4 	 0.5SFigure 3-9 	 Surface pressure distribution as affected by the momentum injection Ue2 /U with Uci /U held fixedat 2: d) a = 15°.xXIL-1>< X 	 qX Xx X XX xII 	1X U c2 / U = 0U c2 / U = 1[1] U c2 / U = 20CpL11 F-1-2-3-0.5 	 -0.4 	 -0.3 	 -0.2 	 -0.1 	 0 	 0.1 	 0.2 	 0.3	 0.4 	 0.5SFigure 3-9 Surface pressure distribution as affected by the momentum injection Uc2 /U with Uci /U held fixedat 2: e) a = 20°.X uc2/u =0uc2/u=iuc2iu=2XxX x Xgr.±±63:1[4:th-3 	 I 	 I -0.5 	 -0.4 	 -0.3 	 -0.2 	 -0.1 	 0 	 0.1 	 0.2 	 0.3	0.4	 0.5SFigure 3-9	 Surface pressure distribution as affected by the momentum injection U 2 /LT with Uci /LT held fixedat 2: f) a = 30°.Cp-0.5	-0.4	-0.3	-0.2	-0.1	 0	 0.1	 0.2	 0.3	 0.4	 0.5SFigure 3-9	 Surface pressure distribution as affected by the momentum injection 13-c2 X with Uci /U held fixedat 2: g) a = 40°.X uc2/u=0	  u c2/u=iq Uc2 /U=2- 1X X 	 XXXXXXX Xth-2-3-0.5 	 -0.4 	 -0.3 	 -0.2 	 -0.1 	 0 	 0.1 	 0.2	 0.3 	 0.4 	 0.5SFigure 3-9	 Surface pressure distribution as affected by the momentum injection Uc2 AI with Ucl /C1 held fixedat 2: h) a = 45°.0Op57UC2/U = 2, presented earlier. Note, on the lower face, the pressure is uniform asthe second cylinder is not rotating. However, on the top face, due to themomentum injection, there is a remarkable recovery of pressure. As Uc2 / U isincreased, the pressure on the lower face also shows a significant increase inpressure.With the angle of attack set at 5° (Figure 3-9(b)) and Uc2 /U = 0, thepressure on both the top and the bottom face increases significantly, and so doesthe base pressure. This reflected in a large reduction in drag as seen before. Thefluid is now directed towards the upper cylinder, where the momentum injectionis being applied. This causes a reduction in the flow around the bottom side of thebody resulting in the higher pressures.With the introduction of momentum injection through the lower cylinder,the local fluid speed around the body increases and the pressure drops. The fluidflux is now divided and, for a given U ci /LT, the relative increase in momentum islarger at the top face, and hence the pressure drop. This character is alsoapparent in the Cp distributions at higher angles of attack.As apparent from the pressure plots, the base pressure for an increase ina tends to drop with the inclusion of the second cylinder's rotation. This isevident at both Uc2 /U = 1 as well as 2. However, complex interactions in the flowfield reflect in the associated drag differently. For the lower level of momentuminjection corresponding to Uc2 X = 1, seen in the drag, the drag increases,however, at a higher energy level (Uc2 /U = 2), CD diminishes.58With respect to the Strouhal number analysis, the measured frequencies forthe various combinations followed the expected trend as suggested by the dragresults: an increase in the Strouhal number with a decrease in the effectivebluffness. The frequency data (Figures 3-10, 3-11 and Table 3-3), show theStrouhal number (St) variation as affected by the angle of attack and cylinderrotation speed. With the injection of momentum the Strouhal number shows adistinct increase in the range a 5 10° as the wake is narrowed and the bodybecomes effectively more streamlined. However, at higher angles of attack(a 15°), the cylinder rotation has virtually no effect on the vortex sheddingfrequency. This can be expected because of the larger separating angles of theshear layers requiring a vertical component of the momentum to reduce the wake-size as against the tangential component provided by the present arrangement.0	5 	 1 0 	 15 	 20	25 	 30	35	40	45Figure 3-10 Variation of the Strouhal Number with the angle of attack as affected by the momentum injection:a) Uci /U = 0.0.50.450.4St 0 .350.3 -X	 f)XX Lic2 / U = 0	  UC2 / U = 1q 	 C2 U = 200 	 5 	 10 	 15 	 20 	 25 	 30 	 35 	 40 	 45Figure 3-10 Variation of the Strouhal Number with the angle of attack as affected by the momentum injection:b) Uel /U = 1.0.250.20.150.10.05XSt0.25 -0.40.35D0.2 -0.15 -0.1 -0.05 -0X Lic2 / U = 0	  UC2 / U = 1q UC2 U = 20 	 5 	 10 	 15 	 20 	 25 	 30 	 35 	 40 	 45Figure 3-10 Variation of the Strouhal Number with the angle of attack as affected by the momentum injection:c) Ucl /U = 2.0.15 -0XX U cU c /U=1q U c /U= 25 	 10 	 15 	 20 	 25 	 30 	 35 	 40	 450.4 	0.350.3 -St0.25 -0.2 -0.1 -0.05-0Figure 3-11 Effect of momentum injection on the Strouhal number at a = 0° - 45°.Table 3-3 Variation of the Strouhal number with the angle ofattack and Uc / U (0° < a < 45°)Angle(a°)Uci / U .Uc2 /U. 0Uci/U.Uc2 /U.1Uci /U.Uc2 /U.20 0.184 0.328 0.3505 0.202 0.362 0.38610 0.273 0.327 0.32015 0.281 0.287 0.30520 0.284 0.286 0.29630 0.291 0.283 0.29240 0.295 0.290 0.28745 0.291 0.291 0.29563U643.2 Cylinders at Top EdgesThe experimental arrangement for rotating cylinders at the top edges isillustrated in Figure 3-12. It shows position of the two cylinders and theirrespective direction of rotation, which is the same (clockwise) as against theprevious case. Reference for the circumferential position (s) is the same as before.Here the angle of attack (a) ranges from 75° to 105° for the force measurementsand from 60° to 120° for the frequency measurements.Figure 3-12 A schematic diagram showing rotating cylinders asmomentum injection units located at the top edges of thetwo-dimensional prism. Note the cylinders rotate in thesame sense.653.2.1 DragSmooth CylindersTo simulate the effects of rotating cylinders along the top surface of a two-dimensional rectangular prism in a fluid stream, the configuration with75° 105° was used. A reference drag coefficient plot without any momentuminjection is shown in Figure 3-13. Note, the smallest drag is not at a = 90° as onewould intuitively expect but occurs at around 95° because of the reattachment ofthe separating shear-layer at the bottom face. It should be emphasized that thesituation is not the same at a = 85°.It should be recognized that now the momentum injection is at the two topedges. The flow field is rather complex as the fluid flux is divided unevenlybetween the top and bottom sides depending upon the level of the momentuminjection. Contribution to the separation region, and hence the wake, is alsodifferent. The complex character of the flow is further accentuated at the top facedue to the momentum injection leading to a delay in separation, perhapsreattachment of the separated shear-layer and even reseparation. Add to this theeffect of the angle of attack and one has a rather challenging flow field foranalysis. Fortunately, the general trends are rather well established.In general, the highest drag coefficient is associated with a = 75°(Figure 3-14). This is due to separation at the lower edges where there is nocy 0Figure 3-13 Reference drag coefficient as affected by the angle of attack in absence of the MSBC with smoothcylinders.CUC 1 /U = 0Uc2 U = 0Uc2 / U = 1	  Uc2 / U = 1 .5Uc2 / U = 20 	75 	 80 	 85 	 90 	 95 	 100 	 105ce °Figure 3-14 Variation of the drag coefficient with the angle of attack as affected by the momentum injectionthrough the rotation of the smooth cylinders. Uc2 /U is changed systematically with Uel TU held fixedat: a) Uci /U = O.5C2UC2 / U = 01 - 	 1 	 UC2 / U = 1UC2 / U = 1.5El- Uc2 U = 20 	75 	 80 	 85 	 90 	 95 	 100 	 105cv oFigure 3-14 Variation of the drag coefficient with the angle of attack as affected by the momentum injectionthrough the rotation of the smooth cylinders. Uc2 X is changed systematically with Ucl /IJ held fixedat: b) Uci /U = 1.5	  Uc2 / U = 01 - 	 UC2 / U = 1	  UC2 / U = 1.5f=3. Uc2 / U = 220 	75 	 80 	 85 	 90 	 95 100 	 105cv oFigure 3-14 Variation of the drag coefficient with the angle of attack as affected by the momentum injectionthrough the rotation of the smooth cylinders. Ue2 /U is changed systematically with tic]. /U held fixedat: c) Uc 1 /U = 1.5. cs)C D3UC1 /U = 1.5UC1 /U = 2\100	105C	 UC2 / U = 0- UC2 / U = 1X 	  UC2 / U = 1.5-R 	 . Uc2 / U = 20 	 1 	 1 	 1 75 	 80 	 85 	 90 	 95u oFigure 3-14 Variation of the drag coefficient with the angle of attack as affected by the momentum injectionthrough the rotation of the smooth cylinders. Uc2 TU is changed systematically with Uci /LT held fixedat: d) Uci (U = 2. -.4071momentum injection. As can be expected, now the lower face contributesrelatively higher to the drag than the upper face. Even at higher angles of attack(a up to 100°), the upstream cylinder is successful in delaying separation,resulting in a narrower wake and a reduction in the pressure drag. The optimumconfiguration leading to the maximum drag reduction (from the reference valueat Ucl /UaUC2	=corresponds= 90°) co 	 to Uci. /U -C2 	1.5 at a = 90°.Here, a change in CD from 3.07 to 2.06 amounts to a decrease of around 33%.Figure 3-15 summarizes performance of the momentum injection at the top edges.Rough CylindersIn general, with the rough cylinders at the top edges of the prism andUc /U = 0, the drag was observed to be higher than that in the correspondingsmooth cylinder cases (Figures 3-16, 3-13). This may be attributed to the splinesurface geometry of the cylinders (particularly the leading edge cylinder) leadingto a turbulent separation at a higher angle. With the momentum injection, thereis an overall decrease in drag compared to the corresponding smooth cylinder case(Figure 3-17, 3-14). It is of interest to note that, with Uc2 /U = 0, injection ofmomentum through rotation of the trailing edge cylinder (Uci /U > 0) hasvirtually no effect on the drag. This is understandable, as now the rear cylinderis submerged in the wake of the leading edge cylinder rendering it essentiallyineffective.C D—X Lic /U=0  tic /U=1X Lic /U=1.5Lic /U=20 	75 	 80 	 85 	 90 	 95 	 100 	 105Figure 3-15 Plot summarizing the effect of momentum injection with smooth cylinders on variation of C D with a.cv 0Figure 3-16 Reference drag coefficient as affected by the angle of attack in absence of the MSBC with roughcylinders.75 80 85 90 95 100 105116L0*0U c2UC 1 /U = 0Uc2 / U = 0UC2 / U = 1	  UC2 / U = 1.5- 	 Uc2 / U = 20 	C Dcv oFigure 3-17 Variation of the drag coefficient with the angle of attack as affected by the momentum injectionthrough the rotation of the rough cylinders. Uc2 /13 is changed systematically with U el /U held fixedat: a) Uc i. /LT = 0.CD	  UC2 / U = 0	  UC2 / U = 1	  UC2 / U = 1.5-E3 Uc2 / U = 2075 	 80 	 85 	 90 	 95 	 100 	 105cy 0Figure 3-17 Variation of the drag coefficient with the angle of attack as affected by the momentum injectionthrough the rotation of the rough cylinders. Uc2 /U is changed systematically with U el /U held fixedat: b) Uel /U = 1.CDUC2 / U = 0UC2 / U = 1	  UC2 / U = 1.5UC2 / U = 20 	75 	 80 	 85 	 90 	 95 	 100 	 105cv oFigure 3-17 Variation of the drag coefficient with the angle of attack as affected by the momentum injectionthrough the rotation of the rough cylinders. U c2 /LT is changed systematically with Uci /U held fixedat: c) Ucl /U = 1.5.5	 UC2 / U = 01	UC2 / U = 1	  UC2 / U = 1.5UC2 / U = 20 	75 	 80 	 85 	 90 	 95 	 100 	 105Figure 3-17 Variation of the drag coefficient with the angle of attack as affected by the momentum injectionthrough the rotation of the rough cylinders. Uc2 /U is changed systematically with Ucl /U held fixedat: d) Ucl /U = 2.78The optimum configuration resulting in the maximum drag reduction wasUCi /U = 1 . 5, UC2 /15 = 2 with a = 95°. Here there was a drag reduction of around49%, with the CD decreasing from 3.16 to 1.60. For the a = 90° case, the largestdecrease was realised for Ucl AT = 1.5 and Uc2 it.T = 2, leading to a CD value of1.60, a 45.8% reduction.With the rectangular prism set at a = 90°, the average drag for fourdifferent values of Uc2/U (averaged over the values of U ci ) were obtained andpercentage reductions compared with the corresponding smooth cases. Theseresults are presented in Table 3-4. It is evident that, in general, for the casesconsidered, an increase in the leading edge cylinder speed appears to effect thedrag reduction favourably. Figure 3-18 summarizes the drag reductioninformation for the rough cylinder cases at four different values of U c /U. Note,for Uc /U = 2 and a = 90°, the drag reduction of around 37% is indeed impressive.CDu 0Figure 3-18 Plot summarizing the effect of momentum injection with rough cylinders on variation of C D with a.80Table 3-4 Effect of surface roughness on the drag coefficient (a = 90°)UC2 / U Cylinder Type CD % reduction*0  smooth 3.21*rough 2.85 11.41 smooth 2.60rough 1.95 39.31.5 smooth 2.29rough 1.83 43.02 smooth 2.46rough 1.80 43.93.2.2 LiftDuring the wind tunnel tests, through measurements of two orthogonalforces, it was possible to determine the lift acting on the model. Although not theobjective of the present study, the lift results were also obtained (Appendix A).As the momentum injection attempts to delay the boundary-layer separation, theeffect is to increase lift at a given a.813.2.3 Surface pressure and the Strouhal numberWith the rotating cylinders at the top edges of the rectangular prism, bothrotating in the same direction, the flow field lacks symmetry as against theprevious case with cylinders at the leading edges and rotating in the oppositesense. Also, the two bottom edges are sharp, providing a distinct separation pointnear s = —0.38 for a 90°.To begin with, the case with the trailing edge cylinder held stationary wasconsidered with the leading edge cylinder velocity varied systematically. Thepressure data results, presented in Figure 3-19, clearly show an increase in thebase pressure with an injection of momentum suggesting a corresponding decreasein the drag coefficient as shown earlier by the force measurements.With both the cylinders stationary and a = 60° (Figure 3-19(a)), there seemsto be a separation region just downstream of the leading edge cylinder(-0.05 < s < 0.00) caused by the flow detaching from the surface of the cylinder.There is reattachment due to the positive pressure gradient promoting the flowto move along the surface before detaching again at the location of the trailingcylinder. With the introduction of momentum injection, the first separation regionis eliminated due to the increased energy in the flow near the body. Thisincreased energy is also reflected in the overall increase in the pressure coefficientaround the whole body.As the angle of attack is increased to a = 75° (Figure 3-19(b)) and with the0o p- 1X Uc2/U=0Uc2/U=1q Uc2/U =2-2Xq DOX XDI] qX X-3-0.5 	 -0.4 	 -0.3 	 -0.2 	 -0.1 	 0 	 0.1 	 0.2 	 0.3	0.4	 0.5SFigure 3-19 Surface pressure distribution as affected by the momentum injection Uc2 /U with Ucl /U held fixedat 0: a) a --= 60°.XXX u c2 / u = 0c2 / U = 1U c2 / U = 2qElE1 ['Et1I	X XX XX X X /-\-3-0.5 	 -0.4 	 -0.3 	 -0.2 	 -0.1 	 0 	 0.1 	 0.2 	 0.3 	 0.4 	 0.5SFigure 3-19 Surface pressure distribution as affected by the momentum injection U c2 /U with Uci. /U held fixedat 0: b) a = 75°.10-20CPqED Ei ED Ej  	 +	 [\•/ X 	44. XX-2-0.4 	 -0.3 	 -0.2 	 -0.1 	 0 	 0.1 	 0.2 	 0.3 	 0.4 	 0.5SFigure 3-19 Surface pressure distribution as affected by the momentum injection U c2 /U with Um /U held fixedat 0: c) a = 90°.	 oo-1 - qF1     -3-0.5XXX X XI1LP X u c2/ti =U c2/ U = 1q U c2/ U = 2  [i]al LX XXXXXXXXXxxX uc2/u	  U c2 / U = 1U c2 / U = 210C P-2 /  X-3-0.5 	 -0.4 	 -0.3 	 -0.2 	 -0.1 	 0 	 0.1	 0.2 	 0.3	0.4	 0.5SFigure 3-19 Surface pressure distribution as affected by the momentum injection U 2 /U with Ucl /U held fixedat 0: d) a = 105°.C p1X u c2 u o	  U c2/ U = 1q U c 2 / U = 2    Ei   OM ELME] 	 ■ 	XXX X xX X Rim R. - 1-2-3-0.5 	 -0.4	 -0.3 	 -0.2 	 -0.1 	 0 	 0.1	 0.2	 0.3 	 0.4 	 0.5SFigure 3-19 Surface pressure distribution as affected by the momentum injection U c2 /U with Ucl (U held fixedat 0: e) a = 120°.87two cylinders stationary, there appears a large separation bubble. Reattachmentoccurs near the trailing edge and the Cp tends to the wake pressure as sapproaches +0.05. With the introduction of the momentum injection, theseparated region is eliminated and the overall pressure distribution about therectangular prism increases as before.At a = 90°, the pressure plots show interesting features, hence furtherinterpretation of the Cp data (Figure 3-19(c)) is in order. Along the surface of thebody, near s = 0, the pressure is nearly uniform and very close to that recordedin the wake region behind the body (0.20 < s < 0.35), indicating the absence ofreattachment upstream of the trailing edge cylinder, hence, this area is a part ofthe wake. With the momentum injection, the flow is accelerated and remainsattached, with a significant level of pressure recovery and a higher value of thebase pressure.For a =105°, there is a distinct separation from the leading edge cylinder,as shown in Figure 3-19(d). The separation region is quite apparent from thenearly uniform and identical pressure coefficients in the range —0.05 < s < 0.05and 0.20 < s < 0.35, for the three cases of Uc2 iU studied. Even with theseparation, the momentum injection continues to increase the pressures aroundthe body, except at the surface directly exposed to the free stream. The bottomface (0.38 < s < 0.62) is partially exposed to the free stream and experiences thedecrease in pressure corresponding to an increase in the surface velocity. Theremay be a separated region at the corner (s = 0.38), but this could not be detected88due to the lack of pressure data in that area.Figure 3-19(e) shows the surface variation of C p at an angle of attack of120°. The trends are similar to those as in the case of a = 105°. Once again,there is a positive pressure gradient along the bottom face (surface opposite tothat of the two cylinders), and the wake region extends from the upstreamcylinder (s = —0.12) to s = 0.38, with an increase in the wake pressure due to themomentum injection.With the addition of momentum injection due to rotation of the downstreamcylinder, located at s = 0.12, the pressures increase dramatically at all angles ofattack as indicated by the data in Figure 3-20. For the case of a = 60°(Figure 3-20(a)), there is a small separation region just behind the upstreamcylinder (up to s = 0), followed by the reattachment. In this region between thetwo cylinders, the flow is accelerated as apparent from the positive pressuregradient. Beyond the trailing edge cylinder, the wake is formed, suggestive thatthe flow is no longer attached even with the cylinder rotating at U cl / U = 2.There is relatively little difference in the pressure data between UC 2 / U = 0 andUC2 / U = 1, but the effect of momentum injection becomes more apparent atUC2 / U = 2. A possible explanation for this situation may be associated with thecomplex character of the local flow in the vicinity of the upstream cylinder. Note,the power input is proportional to the cube of the velocity. When UC2 / U = 1,there is little difference in the local speeds along the surface, but when this ratiois increased beyond unity, a greater amount of energy is being supplied to the10C P- 1-2-3-0.5 	 -0.4 	 -0.3 	 -0.2 	 -0.1 	 0 	 0.1	0.2	 0.3 	 0.4 	 0.5SFigure 3-20 Surface pressure distribution as affected by the momentum injection Uc2 /U with Ucl /U held fixedat 2: a) a = 60°.10C P- 1-2-3-0.5 	 -0.4 	 -0.3 	 -0.2 	 -0.1 	 0 	 0.1 	 0.2	 0.3	0.4	 0.5SFigure 3-20 Surface pressure distribution as affected by the momentum injection U e2 with Uel /1..T held fixedat 2: b) a 75°.1X uc2/U= 0uc2/U=1q uc2/U=2q qXC D1 	 F,ii 	 L-1\-/ X.--,-1 -qqqqqIII 	 III XXX X XX X-2  -3-0.5 	 -0.4 	 -0.3 	 -0.2 	 -0.1 	 0 	 0.1 	 0.2 	 0.3 	 0.4 	 0.5SFigure 3-20 Surface pressure distribution as affected by the momentum injection Uc2 /I.J with Lie' /U held fixedat 2: c) a = 90°.I 	 I 	 t 	 t 	 1 	 t 	 t 	 t 	 1 01X uc2/u=0± u c2 iu=iq uc2iu=2X —C D q [ME qDOMMXXXXXXX      -2 -     -3-0.5 	 -0.4 	 -0.3	 -0.2 	 -0.1 	 0 	 0.1 	 0.2 	 0.3 	 0.4 	 0.5SFigure 3-20 Surface pressure distribution as affected by the momentum injection Uc2 X with Ucl /U held fixedat 2: d) a = 105°.1L0p- 1-2X Uc2/U=0	  UO2/U=1Uc2/U=2LEJEJDELIEJX 	 I F>i<>< XXXXT 1-3-0.5	 -0.4	 -0.3	 -0.2	 -0.1	 0	 0.1	 0.2	 0.3	0.4	 0.5SFigure 3-20 Surface pressure distribution as affected by the momentum injection Ue2 /U with Ucl /U held fixedat 2: e) a = 120°.94flow.A large separation region is apparent along the surface containing the twocylinders when a = 75° and the leading edge cylinder is stationary, indicating anadverse pressure gradient near the upstream edge (Figure 3-20(b)). The flow mayattempt to reattach further along the surface, but this cannot be certain withoutdirect measurements in this region. When Uc2 / U is increased, the Cp values inthis region are fairly constant indicating a near balance of the positive pressuregradient with the dispersion of the concentrated energy from the downstreamcylinder.At a = 90° and Uc2 /U = 0, separation occurs on the surface between thetwo cylinders (Figure 3-20(c)). With the momentum injection, the wake pressureis slightly higher than the pressure along the surface near s = 0. Here, unlike thecase where a = 60°, the difference in the change in pressures for the upstreamcylinder's surface velocity ratio between 0 and 1 is greater than that between 1and 2. This may be due to the flow remaining attached to the surface of the twocylinders (rather than injecting momentum into the fluid stream) with therotation of the second cylinder.In Figures 3-20(d) and 3-20(e) there is a marked wake region beyond theupstream cylinder as the top face moves from the free stream (a > 90°). Themomentum injection does tend to increase the average pressure around the body,as expected, but no other effects can be distinguished from the data available.With respect to the Strouhal number analysis, the frequencies measured for95the various combinations resembled what was expected. The frequency data(Table 3-5, Figures 3-21 and 3-22) show the Strouhal number (St) as a functionof the angle of attack and cylinder rotation speed. With the injection ofmomentum into the flow, in most cases the St was found to increase as the wakeis narrowed and the body becomes effectively more streamlined. As in the caseof —45° a 5_ 45°, the effectiveness of the momentum injection is limited to acertain range of angles of attack. The most significant change in St occurred ata= 90° (an increase of 29.5%), while at other angles of attack it was around 10%.Table 3-5 Effect of the angle of attack and momentum injection onthe Strouhal number (60° < a < 120°)Angle(a° )Um / U =Uc2 / U = 0Um / U =Uc2 / U = 1UCi / U =Uc2 / U = 260 0.274 0.257 0.27775 0.258 0.274 0.28390 0.190 0.233 0.246105 0.281 0.298 0.294120 0.272 0.295 0.3030.4XXX Uc2 / U = 0	  UC2 / U = 1UC2 U = 20.350.3St0.25 -0.20.15 -0.10.05Ci0 	60 	 75 	 90 	 105 	 120Figure 3-21 Variation of the Strouhal Number with the angle of attack as affected by the momentum injection:a) Ucl /U = 0.0.40.35 -0.3St0.25a0.2 --0.15 -0.1 -0.05 --X Lic2 / U = 0	  UC2 / U = 1q UC2 = 2WW060 75	 90	 105	 120ce ,Figure 3-21 Variation of the Strouhal Number with the angle of attack as affected by the momentum injection:b) Uci /U = 1.XX Uc2 / U = 0UC2 / U = 1UC2 U = 20.40.3575 	 90 	 105 	 120ce °Figure 3-21 Variation of the Strouhal Number with the angle of attack as affected by the momentum injection:c) Uel /LT = 2.0.3St 	 '-0.250.20.150.10.050600.40.350.3St0.250.2Li}XXX ti c /U= 0—I -	(Jc /U-= 1U c /U= 20.150.10.050 	 1 	 I 60 	 75 	 90 	 105 	 120a°Figure 3-22 Effect of momentum injection on the Strouhal number at a = 60° - 120°.1003.3 Flow VisualizationIn conjunction with the research completed here, flow visualization studieswere performed. A water tunnel model with scaled dimensions to that used in thewind tunnel tests was utilized. Figures 3-23 and 3-24 show dramatic effects ofmomentum injection as applied to a rectangular prism. The drag reduction andpressure distributions from the wind tunnel experiments seem to be validated bythe flow visualization study shown.102Uc / U 0Uc / U -- 2Uc / U -- 4_ 	--.-- 	 `7--------..._ 	 '---'''7...-=-, -••••,, --- --,„..,.._	 _ 	 -... -..--,-7-__. 	 ___- --- ------- --- 	 **---- -:-+--- ': -------- •.-- -4:--Z,41.444,--` ‘t":---NNI, ,,.,,y----.404.____.;.. ,,,.-' - ,,_--x,,,,.  `- ,...*:-........■1-..: '-- - -.4,.. otti-.....Figure 3-24 Typical flow visualization photographs for a rectangular prism,with a smooth surface cylinder for a = 90°.1034 CONCLUDING REMARKS4.1 Summary of ResultsThe study, aimed at assessing the effect of momentum injection on the fluiddynamics of a two-dimensional rectangular prism, has provided information offundamental value and far-reaching consequence never reported before. Detailedmeasurements of the pressure distribution, force and Strouhal number clearlysuggest that the MSBC can significantly reduce the drag of the prism. Effectively,it affects the bluffness of the body, thus changing its Strouhal number, which canbe used to advantage in controlling the fluid-structure interaction instabilitiessuch as the vortex resonance and galloping.With the momentum injection through smooth cylinders at the leadingedges, a drag reduction of around 39% was realized at a = —5° with U cl / U = 1and Uc2 / U = 2. Further reduction can be achieved through the use of cylinderswith surface roughness. With the spline geometry used in the present study, adrag reduction of 75% was achieved with Um / U = 1.5, Uc2 / U = 2 and a = 10°.With the momentum injection at the top face, the leading edge cylinderplayed the dominant role in governing the boundary-layer separation. The MSBCwith the smooth cylinders reduced the drag coefficient with respect to the basevalues by up to 36% (Uci / U = 0, Uc2 / U = 2, a = 105°). Introduction of the104surface roughness further improved the performance by around 39% (U ci /U = 1.5,Uc2 /II = 2, a = 90°).The pressure data helped explain the trends predicted by the forcemeasurements. Their time dependent variations formed bases for calculation ofthe vortex shedding frequency and the associated Strouhal numbers. Both thepressure and Strouhal data, in general, substantiated the trends predicted by theforce data, and provided better appreciation of the flow field. An increase in theStrouhal number with the momentum injection suggests effective reduction inbluffness of the body, leading to a narrower wake and corresponding reduction inthe drag.4.2 Recommendations for Future WorkThe investigation reported here represents only a small step in explorationof the new field with exciting possibilities. As can be expected with any emergingarea of research, there are numerous avenues one can pursue to have a betterunderstanding of the governing process at the fundamental level. A few issuesdemanding immediate attention, which are likely to be of practical value, areindicated below:(i) Uc /LT range should be extended further, to the level of at least 4, to arriveat a limiting value beyond which the momentum injection has little effect.(ii) Effect of surface roughness in improving efficiency of the MSBC needs more105attention.(iii) Cross-section (1/d) of the rectangular cylinder should be changedsystematically to cover a wide range of rectangular prisms. For a small 1/d(- 0.1), this will yield a widely investigated plate type geometry, while l/d4 - 6 will tend toward trailer-type configurations presently underinvestigation 35 .(iv) The present model should be modified in several ways to:(a) include more pressure taps in the vicinity of the rotating elementsto better predict the pressure distribution in that critical region;(b) provide arrangement for constructing rectangular prisms withdifferent 1/d in a modular fashion;(c) 	 incorporate rotating elements at other locations.(v) For assessment of the overall efficiency, it would be useful to monitor thepower input precisely. For better appreciation, it would be useful topresent information also in terms of saving in power for probableapplication to truck configurations.(vi) Several alternate approaches to boundary-layer control should also beexplored for relative assessment of effectiveness. Of particular interest arethe application of fences on the front face; oscillating flap at the leadingedges; communication of the front stagnation pressure to the rear face, etc.These concepts are only in the preliminary stage of development in Dr.Modi's laboratory, and show considerable promise.106REFERENCES[1] Goldstein, S., Modern Developments in Fluid Mechanics, Vols. I and II,Oxford University Press, 1938.[2] Lachmann, G.V., Boundary Layer and Flow Control, Vols. I and II,Pergamon Press, 1961.[3] Rosenhead, L., Laminar Boundary Layers, Oxford University Press, 1966.[4] Schlichting, H., 1968, Boundary Layer Theory, McGraw-Hill Book Company.[5] Chang, P.K., Separation of Flow, Pergamon Press, 1970.[6] Alvarez-Calderon, A., and Arnold, F. R.,"A Study of the AerodynamicCharacteristics of a High Lift Device Based on Rotating Cylinder Flap",Stanford University Technical Report RCF-1, 1961.[7] Cichy, D.R., Harris, J. W., and MacKay, J. 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Davenport,in press; also Journal of Wind Engineering and Industrial Aerodynamics,in press.109[33] Kubo, Y., and Yasuda, H., "Surface Pressure Characteristics of a SquarePrism Under Aerodynamic Response Control by Boundary LayerAcceleration", Proceedings of the Conference on Flow-Induced Vibrations,Brighton, U.K., May 1991, Paper No. C416/101, The Institution ofMechanical Engineers, pp. 411-416.[34] Seto,M.,"Flow Interference Effects Between Two Circular Cylinders ofDifferent Diameters", M.Sc. Thesis, The University of British Columbia,1990.[35] St. Hill, S.,"Effect of Boundary-Layer Control on the Drag of a Cube-TypeTruck Configuration: Wind Tunnel and Prototype Tests", M.A.Sc. Thesis,The University of British Columbia, November 1992.APPENDIX A: TYPICAL LIFT RESULTSItoC L-3-25	 -20	 -15 	 -10 	 -5 	 0 	 5 	 10 	 15 	 20 	 25ce °Plot summarizing the effect of momentum injection with smooth cylinders on variation of C L with a.>< Uc iti=oU c / U = 1U c / U = 1.5U c / U = 22C L1-3 	-25	-20	 -15	-10	 -5	 0	 5	 10	 15	 20	 25cv 0Plot summarizing the effect of momentum injection with rough cylinders on variation of C L with a.X- 1U c /U= 0U /U= 1U C /U=1.5U c /U= 2-2 --33075 	 80 	 85 	 90 	 95	100 	 105ce °Plot summarizing the effect of momentum injection with smooth cylinders on variation of C L with a.2 -CL0-1X— u c iu=o	  uciu=i-2 -U c / U = 1.5 	 =4>XX u c iu=2-375 	 80 	 85 	 90 	 95X100 	 105u °Plot summarizing the effect of momentum injection with rough cylinders on variation of C L with a.APPENDIX B: ADDITIONAL PRESSURE DISTRIBUTION DATAI ISX Uc2/U=0	  tic2 iu=iq Uc2/U=2XXq I XX 	• L ElXXXXX0Op-2-3-0.5	 -0.4 	 -0.3 	 -0.2 	 -0.1 	 0 	 0.1	 0.2 	 0.3 	 0.4 	 0.5SSurface pressure distribution as affected by the momentum injection Uc2 iU with Um /U held fixed at 1: a) a =ElX u c2 / u = o	  U c2/ U = 1U c2 / U = 2c p           0q*          -3-0.5 	 -0.4 	 -0.3 	 -0.2 	 -0.1 	 0 	 0.1	 0.2	 0.3	 0.4 	 0.5SSurface pressure distribution as affected by the momentum injection Uc2 /13 with Uci /U held fixed at 1: b) a = 5°.-3-0.5	 -0.4	 -0.3	 -0.2	 -0.1 0	 0.1	 0.2	 0.3	 0.4	 0.5SSurface pressure distribution as affected by the momentum injection U c2 /U with Uci /U held fixed at 1: c) a = 10°,S-3-0.5 	 -0.4	 -0.3	 -0.2 	 -0.1 0 	 0.1 	 0.2 0.3	 0.4 	 0.5Surface pressure distribution as affected by the momentum injection U c2 /U with Uci /U held fixed at 1: d) a = 15°.10Cp-1-2-3-0.5	 -0.4	 -0.3	 -0.2	 -0.1	 0	 0.1	 0.2	 0.3	 0.4	 0.5SSurface pressure distribution as affected by the momentum injection Uc2 /U with Uci /U held fixed at 1: e) a = 20°.10C p- 1-2-3-0.5	 -0.4	 -0.3	 -0.2	 -0.1	 0	 0.1	 0.2	 0.3	 0.4	 0.5SSurface pressure distribution as affected by the momentum injection U c2 /U with Uci /U held fixed at 1: 0 a = 30°.10Cp-1-2-3-05	 -0.4 	 -0.3 	 -0.2 	 -0.1 	 0 	 0.1 	 0.2	 0.3 	 0.4 	 0.5SSurface pressure distribution as affected by the momentum injection Uc2 /U with Ucl /U held fixed at 1: g) a = 40°.SSurface pressure distribution as affected by the momentum injection Uc2 AI with Ucl X held fixed at 1: h) a = 45°.

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