A comparative study of the development of the turbulent near-wake behjnd a thick flat plate with both a circular and tapered trailing edge geometry.

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Lehigh University Lehigh Preserve Theses and Dissertations A comparative study of the development of the turbulent near-wake behjnd a thick flat plate with both a circular and tapered trailing
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Lehigh University Lehigh Preserve Theses and Dissertations A comparative study of the development of the turbulent near-wake behjnd a thick flat plate with both a circular and tapered trailing edge geometry. Ahmad Haji-Haidari Follow this and additional works at: Part of the Mechanical Engineering Commons Recommended Citation Haji-Haidari, Ahmad, A comparative study of the development of the turbulent near-wake behjnd a thick flat plate with both a circular and tapered trailing edge geometry. (1984). Theses and Dissertations. Paper This Thesis is brought to you for free and open access by Lehigh Preserve. It has been accepted for inclusion in Theses and Dissertations by an authorized administrator of Lehigh Preserve. For more information, please contact A COMPARATIVE STUDY OF THE DEVELOPMENT OF THE TURBULENT NEAR-WAKE BEHJND A THICK FLAT PLATE WITH BOTH A CIRCULAR AND TAPERED TRAILING EDGE GEOMETRY by Ahmad Haji-Haidari v A Thesis Presented to the Graduate Committee ' { of Lehigh University r r --K in Candidacy for the Degree of Master of Science in - * s~j v.. Mechanical Engineering Lehigh University 1984 ** 'S? ProQuest Number: EP76510 All rights reserved INFORMATION TO ALL USERS The quality of this reproduction is dependent upon the quality of the copy submitted. In the unlikely event that the author did not send a complete manuscript and there are missing pages, these will be noted. Also, if material had to be removed, a note will indicate the deletion. uest ProQuest EP76510 Published by ProQuest LLC (2015). Copyright of the Dissertation is held by the Author. All rights reserved. This work is protected against unauthorized copying under Title 17, United States Code Microform Edition ProQuest LLC. ProQuest LLC. 789 East Eisenhower Parkway P.O. Box 1346 Ann Arbor, Ml - v/ CERTIFICATE OF APPROVAL i This thesis is accepted and approved in partial fulfill «ment of the requirements for the degree of Master of Science in the Department of Mechanical Engineering and Mechanics. ay 9. iaf % date Professor in Charge Chairman of the Department -i.i / To My Family For the Years Apart -m - Acknowledgements The author wishes,to give warm sincere thanks to all those who in many Vays were involved in developing, organizing,.' '.: o ) conducting, and presenting this work,. In particular, the valuer ' able discussions with and helpful efforts, of Mr. E.A. Boguc/, and proof readings of Miss V.E. Dow are appreicated. The author also would like to thank Mrs. Donna Reiss for the prep-, aration of the typed manuscript. For their generosity in sharing their data, many thanks to Dr. R.W.. Patterson and his colleagues at United Technology Research Center. The continuous supervision, recommendations, encoura'ge-'^ ments, and unending patience of my thesis advisor, Professor C.R. Smith, are sincerely»appreciated. The continuing support of the National Science Foundation under the grant #MEA ,is gratefully acknowledged. iv~ J V TABLE OF CONTENTS TITLE CERTIFICATE OF APPROVAL DEDICATION. 21 i it i i i ACKNOWLEDGEMENTS TABLE OF CONTENTS LIST OF TABLES LIST OF FIGURES NOMENCLATURE ABSTRACT CHAPTER 1: INTRODUCTION 1.1 General 1.2 Laminar Flow 1.3 Turbulent Flow 1.4 Theoretical Investigations of a Turbulent Flat Plate Wake 1.5 Experimental Investigations of i Turbulent Flat Plate Wake 1.6 Overview 1.7 Present Study CHAPTER 2: EXPERIMENTAL ARRANGEMENT 2.1 Flow Facilities 2.2 Test Sections 2.3 Plate Support Arrangement 2.4 Visualization 2.5 Anemometry * v- (Table of Contents - cont.) ' -.-» Page CHAPTER 3: SHARP TRAILING EDGE * Introduction . 38 3i. 1 Hot Film Anemometry Measurement Visualization Studies 53 X3.2. 'Plan View Studies 55 ^2^2 Side-view Horizontal Bubble-wire a Mixing in the Region 0 X + b Mixing in the Region X+ Summary of the Visualization Studies CHAPTER 4: t ROUND TRAILING EDGE WAKE. 88 * 4.1 Hot-film Measurements ' Visualization Studies Side-vieift Hydrogen Bubble-wire Visualization a Visualization Studies for 0 X a-l Upstream Penetration of. the Back-flow la-2 Recirculating Flow Penetration Across the Wake a-3 Structures Within the Separated Shear Layer b Visualization Results for 3.0 X Plan-view, Hydrogen Bubble-wire^ Visualization a Plan-view Visualization Near the Trailing Edge b Plan-view Visualization for X 3.0, 0.0 Y Summary of the Visualization Studies 137 CHAPTER 5: DISCUSSION 141 5*1 General Sharp Trailing Edge 142 5,2.1 Immediate Effect of Wall Disappearance, X + &* -VI (Table of Contents - cont.) Page Centerline vs. Turbulent Boundary ' Layer Profile a Transformation of Y + to X b Similarity in the Flow Developmen tv Wake Profiles: Sharp vs. Round Trailing Edge Results \ Comparison Between WRC Measurements and Present Studies Velocity Profiles. * Heat Transfer Measurements Flow Induced Oscillation Future Considerations, 176 CHAPTER 6: CONCLUSlpNS 178,REFERENCES ** 182 APPENDIX A -Visualization Results for the Initial Test Plate 190 APPENDIX B - Anemometer Calibration and Drift Compensation. 195 APPENDIX C - Visualization of Secondary Vortices in the Separated Boundary Layer at' Re L =1.6xl APPENDIX D - Fluid Dynamic Attenuation of Source*of Oscillation. ' 201 APPENDIX E - Selected Experimental Data 206 VITA 2*14 -vn- i LIST OF TABLES Table Page I Physical characteristics of the plates. 28 E,l Experimental data, boundary l^er profiles 207 of mean velocity prior to separation at X=-2.0 of the sharp trailing edge..' -^.2 Experimental data, mean velocity profile 208 in the' wake of the sharp trailing edge. E.3 Experimental data, turbulence intensity 210 profiles in the wake of the sharp trailing edge. E.4 Experimental data, the sharp trailing edge 212 centerline mean velocity profile. '^ E.5 Experimental data, boundary layer profiles 212 of mean velocity prior to separation at X=-3. ) of the round trailing edge; E.6 Experimental data, mean velocity profile 213 in the wake of the round trailing edge. E.7 Experimental data,- turbulence intensity 213 profiles in the wake of the round trailing edge. vnr l; ST OF FIGURES Page Figure 2.1 Side-view schematic of water channel 21, flow facility. '.'- Figure 2.2 Schematic representation of the test 24 plate with the round trailing edge in place. Figure 2.3 Schematic diagram of the two trailing,, 25 edge geometries, a) circular (D=10 cm), b) taper (total included angle 9 ). Figure 2.4 Schematic Of the plate mount. 29. Figure 2.s5 Photograph of? the water channel (look- 31 VJ ing upstream)', traverse platform, video system, two TV cameras-, and the test ^ section in the plate. Figure 2.6 Schematic of the hydrogen bubble-wire 33 probe supports, a) horizontal,^ t b) vertical. * * Figure 2.7 Schematic of the anemometry system. 36 Figure '3.0a Side-view schematic showing the refer- 39 ence coordinates used for both trailing edges. Figure 3,0b Schematic showing the hydrogen bubble- 39 wire orientation for the round trailing edge (identical orientation employed for sharp trailing edge). Figure 3.1 Boundary layer profiles of mean velocity 41 prior to separation.at X=-2.0 of sharp trailing edge. Re[_=8.27xl0 5, Re e = 2\5xl0 3. J ) Figure 3.2 Mean velocity profiles in the wake of 43 x= sharp trailing edge. X=0.0, O 'I 1.0, A X=2.0, X=4.0, V X=8.0, ix--i?.o. ix- (List of Figures - cont.) ; - -Pise Figure 3.3 Wake mean velocity profiles plotted 44 in wall parameters behing the sharp trailing edge. X=0.0, O X=1.0, A X=2.0, O X=4.0, V X=8.0, B0 X=12.0. Figure 3.4 Center!ine velocity;o Andreopoulos 46 & Bradshaw. Re 9 =13.6xl0 3,. * J Ramaprian et al. Re Q =2.4xl0 3,, A Chevray & Kovasznay Ren-1.58xl0 3, and D present Re e =2.5xl0 3. Figure 3.5 Key integral parameters for the sharp 49 - trailing edge wake. H; A Anderopoulos & Bradshaw, O Chevray & Kovasznay,. D present, e; Andreopoulos & BradshawA, Chevray & Kovasznay 4 present. Figure 3.6 Turbulence intensity profiles. in the 51 wake of sharp trailing edge. D X= 0.0, O X=1.0, A X=2.0, O X*4.0, V X=8.0, ffl X= Figure 3.7 Streamwise location of hydrogen-bubble 54 probes.. Figure 3.8 Plan^view showing low-speed streaks 57 , over the flat plate. X w -j re =-1.25, ; ^ Y wire =10, FHB-120 HZ, ^ f Figure 3.9 PIan^view visualization of low-speed 60 streaks accompanied with a streak spacing histogram, a) Flow over the plate Vyire = ~ 600 Y wire =10» and b) Picture obtained in the wake at X^-jre^30 ' Y^i re =10. Same magnification as 3.9a. Fi.gure 3.'10 Variation of mean spanwise streak spacing 61 with X both on the wall and in the wake. O Y + 5; yvlo -x- \ (List^j0f Ngures -; cont.) Page igure 3.11 Variation of scale and disturbance from the trailing edge in the neighborhood of centerline behind sharp trailing edge. 63 FigDfe 3.12 Similarity in scales of turbulence structures in the logarithmic region of the boundary layer upstream and down- -stream of the trailing edge. wi re = 130, xj 1r^-600; b) Y:- Yj ire =270, -* - Xwire (same magnification). 66 Figure 3.13 Side-view photographs showing boundary layers merging, wake interaction, and mixed ajid unmixed regions: 69 a Figure 3.14 Side-view illustration of mixing process in the vicinity of the trailing edge, Xji re =0,0, FUB=120 Hz. aj Shear layers merge in a thin wake, b) intense interaction of boundary layers involving outer wake fluid; c) schematic representation of more common mixing process. 72 Figure 3.15 Side-view photographic sequence with schematics showing flow developments with distance, from the trailing edge at.same y location. 79 Figure 3.16 Characterization of the most detectable behavior at the instantaneous interface.at the mixed and unmixed region. Three sttiematic representations of the behavior showing: a) an amplifying, sinuous * interface, b) a rapid breakdown of the wake interface, and c) a thru, smooth, nonoscillating interface. 83 Figure 3.17 Breakdown at the wake increases. X + 200. interface as X 85 XV (List of figures - cont.) Figure 3.18 Flow structure In the vicinity at the 87 trailing edge. Figure 4.1a Boundary layer profiles of mean velo- 90 city at X=-3.0, Re L =7-6xl0 5, Re 0 =* 1.62xl0 3. Figure 4.1b Turbulence intensity profile at X=-3, 91 Page a v* -* Figure 4.2 Development of mean velocity profiles 93 in the wake of round trailing edge t compared with upstream boundary layer profiles. X=4.0, O X=8.0, A X= 12.0, X=-3.0. Figure 4.3 Short segments of the anemometry signal 95 at selected downstream locations illustrating the effect of vortex shedding on_ the velocity, behavior. Figure 4.4\ Turbulence intensity profiles in the wake.97 of round trailing edge. X= 4.0, O X= 8.0, A X=12.0, Re L =7.6xl0 5, Re Q =1.62xl0 3. Figure 4.5 Turbulence intensity profiles in the wake 99 of round trailing edge with low cut-off frequency'at 1 Hz. X=4.0, O X=8.0, A X=12.0, Re L =7.6xl0 5, Re e =l.62x10. Figure 4.6 Turbulence intensity profiles due to 101 shedding in wake of round trailing edge, O X=4.0,O X=8.0, A X=12.0, Re e = I,62xl0 3, Re^.SxlO 1 *---experimental ' data, Bloor & Gerrard (1966); X=12.0 in the wake of a circular cylinder Re d =1.6xl0\ Figure 4.7 Side-view schematic of wake development 104 for circular trailing edge. -xn- (List of figures - cont.j Figure 4.8 Flow behavipr'in the vicinity of the * 106 trailing edge. Figure 4.9 Schematic of separation bubble for 108 circular trailing edge. Page Figure 4.10 a) Side-view visualization of vortex 112 shedding in the wake of the circular trailing edge, b) Schematic of effects of vortex.shedding on the wake immediately behind the trailing edge. Figure 4.11 Side-view visualization of small scale ^ 114 structures Viding in perimeter of Strouhal c vorte*. ' Xj ire =170, HBF=60 HZ, Strouhal period=l.62 (Note t*=t/t Strouhal). Figure 4.12 Side-view illustration of small-scale 119 disturbance detected between 3 X 12 ^wire^*' v wire = 2«a) Schematic representation of these^disturbances in relation to a laminar cell , b) spanwise * oriented structures downstream of a laminar cell , and c) streamwise oriented structures upstream of a' laminar cell . Figure 4.13 Top and oblique views illustrating the 122 * ' streamwise vortex stretching caused by *^ like rotation Strouhal vortices. ' Figure 4.14 The vertical bubble-probe locations where^ 125 visualization studies were done. Figure 4.15 Top-view bubble-wire visualization of 129 the decelerating-accelefating flow in the inevprent boundary layer separation region wire just off the wall and 9 downstream of tangency between flat plate and circular trailing edge Strouhal ' - period x=l,62 sec. -xiii- J (List-of figures - cont.) Figfire 4.16 Far field-view photographs showing 131 a) stagnant pockets in incipient boundary layer separation, wire location same as figure 4.15, b) low-speed streaks just above the surface and upstream of separation point X=-4, F HB =120 Hz. Figure 4.17 Effect of pressure gradient on velocity 132 field, particularly qn low-speed streaks. Figure 4.18 Plan-view photograph along with a 136 schematic illustrating axial vortex pairs downstream of the circular trailing edge, Xw ire =4, Y wire =l, FHB=120 HZ. Figure 4.19 Detected flow characteristics in the 138 vicinity of the circular trailing edge. Figure 5.1 Sharp trailing edge centerline velocity 148 profile vs. a turbulent boundary layer profile obtained over a fl$t plate. S Johansen & Smith (1983) Re e =1350, present fte e =2500. Figure 5.2 Comparison of centerline velocity relax- 152 at ion vs. X. present, U*=0.032i'. fj present U , O Andropoulos and Bradshaw [5] U*=*Q.035 (equation 5#!). Figure 5.3 Sharp trailing edge; linear growth of 155 centerline velocity for X + 100, present U*=0.032, present U*=0.037 Q H Johansen & Smith (1983). Figure 5.4 Centerline velocity in the wake a the 158 sharp trailing edge; comparison with the law-gf-the-wall and a turbulent boundary layer profile. Figure 5.5 Ratio of mixing scales in the wake to -163 thru of boundary layer, as a function of nondimensional distance. Page -xi v- ' (List of figures - cont.) T Page Figure 5.6 The wake mean velocity profiles behind 167 both sharp and circular trailing edge. A sharp trailing edge, O circular* trailing edge. UTRC [57]round T.E. - H UTRC X=9.0, and X=13.0. Figure 5.7a Heat transfer characteristics (Stanton 172 number) measured along the arc bf cir-' Ocular trailing edge for conditions dynamically similar to those.of prelent study.. Figure. 5.7b Model of separated flow behavior near 172 the circular cylinder trailing edge'' illustrating the appearance of a'small - stagnant bubble on the surface; ' ( Figure A-l Plan-view sequence showing the generation, growth, coalescence, and formation of ( small scale spanwise structures developing in the wake of a 1.25cm thick flat plate with a circular trailing edge. F HB =120 Hz, We 34 ' Y wire= u St ^ Figure A-2 Far-field (side-view visualization of 193 trailing edge behavior for identical visualization-conditions; a) initial laminar boundary layer 5=0.83, b) initial turbu- \ lent boundary layer 6=2.5cm, X w -j re =0.2. ' Figure B-2 Typical linearization curve used for 197 anemometer measurements. The top curve shows the voltage output at the start of each run; the bottom curve/ Q shows the effects of djift at the end of the run.. v^- -XV- NOMENCLATURE ' '. U 2. CF Skin friction coefficient = rrr-z f. Strouhal frequency FMD Hydrogen bubble-time line frequency h Thickness at the tip of the tapered geometry +. hv. H Nondimensional thickness E V,L Test section (plate or chord) length L Nondimensional length scale M Mach number. H Total number of data samples Re., Re Re Reynolds number based on the plate or chord u o L length =- - Reynolds number based on momentum thickness /' Re g Re. Reynolds number based on boundary layer thick- ness V Reynolds number based on the plate thickness t ^ V Plate initial thickness T Strouhal shedding period u Time-averaged, local streamwise velocity UQ, Time-averaged, local wake centerline velocity & d&. -XVI' (Nomenclature - cont.) U Free stream velocity outside boundary layer or wake * u ^,u' Root mean square of the streamwise velocity flucrms -. v tuations \ ,v' root mean square of the *normal velocity fluctu- ations u 1 v' Reynolds -stress ' U-, U Friction or shear velocity 7 TO. J * IL U Nondimensional friction velocity = rp U., Nondimensional boundary layer streamwise velocity v = u + T Uf, Nondimensional wake center!ine streamwise velocity \. ~ o~. x ' Streamwise coordinate X Nondimensional streamwise coordinate + * X Nondimensional nensional streamwise, coordinate xu T Jjt v.. ' ' y Normal coordinate Y Nondimensional normal coordinate a ^ -it + - ' r: yu Y Nondimensional normal coordinate i : » \- z Spanwise coordinate -XV11- ^ i o (Nomenclature - cont.) Z Nondimensional spanwise coordinate = n*r + zu Z Nondimensional spanwise coordinate s - T Greek 5 Boundary layer thickness 6 Displacement thickness 6- Inner wake thickness, ref. [5] e Momentum thickness on the plate 9 Momentum thickness at the trailing edge e. Momentum thickness jax far wake used in ref. [63] X Spanwise spacing between low-speed streaks X Mean value of X - + *u X Nondimensional mean streak spacing =. - v Kinematic viscosity Y Temperature intermittency r Euller constant Strouhal shedding period tf -xvm- ABSTRACT The effects of botfv a circular and tapered trailing*edge geometries on the velocity field and turbulence structure in the near-wake of a simulated gas turbine type blade geometry are examined using both hydrogen bubble flow visualization and hot-wiijp anemometry j easure- ments. With a circular trailing edge and Re[_=7.6xl0 5, the flow de- taches in an. incipient separation zone at 93.6 e 99,' generating a separation bubble which extends to 1.5 X 3 downstream. From detailed studies of the flow b&havjor in the near-wake separation bubble-re- gion,.a model for flow behavior within the separation bubble is devel- oped; the ramifications of the model on surface heat transfer are V demonstrated by. comparisxm with an independent study conducted at UTRC,, The'wake flow behavior behind the circular trailing edge is very p Sfstrongly dominated by Strouhal vortex sheading with St=0.21. ualization results indicate that, the turbulent structures entering The vis-, the wake from the separating turbulent boundary layers are strongly affected by vortex stretching effects generated by like-rotation Strouhal vortices. This results,an the development of an intense mix- ing process within a short distance fr.om the trailing edge and, is sug- gested as providing a substantial contribution to the high turbulence intensity levels encountered in the turbulent wake of this and similar bluff bodfes. This rapid slretching-mixing interaction is also sug- gested as the stimulus for an observed rapid lateral spreading of.the wake.- This elevated mixing process causes the wake defect velo- city to recover very quickly, such that the wake centerline velocity v ^reaches over 80% of the freestream^velocity approximately ten boundary - ' V ^ ',., layer thicknesses downstream of the trailing edge P A second study was done wi.th a tapered trailing edge geometry which yields a nonoscillating smooth merging of the two shear layers. Tests were conducted for 1^=8.2xl0 5 which is slightly higher than for the circular trailing edge case. The outward spreading of the wake is observed to occur quite slowly, with the mixing process essen- tially limited to interactions at the interface between the two separ- ated shear layers. A significant finding of this study is that the mixing process and the relaxation of the centerline velocity profile ;.' demonstrate behavior very similar to thdse of a turbulent boundary layer. Both hot film anemometry measurements and flow visualization results indicate that froth velocity behavior and turbulence structure vary with X in a ma atmer strikingly similar to the way the corre- sponding flow characteristics change with Y within a turbulent b dary layer. From the hot-film measurements, two separate regions'^an be distinguished alo
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