MSU LIBRARIES Q—v RETURNING MATERIALS: PIace in book drop to remove this checkout from your record. FINES wiII be charged if book is returned after the date stamped beIow. .9— ”iii I [55‘ apt-23 1 I.“ 31"" 3&1}! iv L . W3» 31".}..23 " & In ..'L a " «J. '.>. .'.-wk ' . » ' -.,. .‘. ‘ , ~ g- “:3 f 3*." EW- -. . . - I «I: - .- ’ ' :-: .’. .'. P "~ "m ufb‘lln — b .18 A STUDY OF INTERMEDIATE SCALE MOTIONS IN THE OUTER REGION OF TURBULENT’BOUNDARY LAYERS By David Bruce Signor A THESIS Submitted to Michigan State University in partial fulfillment of the requirements for the degree of MASTER OF SCIENCE Department of Mechanical Engineering 1982 A: contri' trnnsf bonnda condit visual coherc long 1 typic, IWand. Vorte “lube numbe ABSTRACT A STUDY OF INTERMEDIATE SCALE OOHERENT MOTIONS IN THE OUTER REGION OF TURBULENT BOUNDARY LAYERS By David Bruce Signor An experimental investigation was performed to determine the contribution of intermediate scale coherent motions to the momentum transfer in the outer region of zero pressure gradient turbulent boundary layers. Simultaneous hot-wire anemometry and visual data was conditionally sampled with selection based primarily on the visualization. Nommalized Reynolds stress peaks contained within the coherent motions, termed "typical eddies". were found to be twice the long time normalized mean value. The momentum transfer produced by the typical eddies is directly related to the growth of the turbulent boundary layer. The data strongly suggests that the typical eddies are vortex rings. The normalized typical eddy length scales are Reynolds number dependent, while the normalized velocity scales are Reynolds number independent, for the Reynolds number range of 700 < Re ( 4000. Sub a—-I>'WI__ A STUDY OF INTERMEDIATE SCALE OOHERENT MOTIONS IN THE OUTER REGION OF TURBULENT BOUNDARY LAYERS Submitted by: David B. Signor T M.S. Candidate Approved by:. 486$.“— R. E. Falco Associate Professor Thesis Advisor IO M» ca; C. R. St. Clair. Jr. Acting Chairperson Department of Mechanical Engineering 8-1/‘8’2 Date Lfi—H 3'2. Date 9434-). Date ACKNOWLEDGEMENTS I would like express my appreciation to my parents for their continual support and encouragement throughtout my college career. I would like to recognize the support of the Air Force Office of Scientific Research under Contract F49620-82-K-0003. monitored by Captain Michael Francis, and the Office of Naval Reaseach under Contract N0001477C0348. monitored initially by Ralph C00per and subsequently by Robert Whitehead. I would like to express my gratitude to my thesis advisor, Dr. Robert E. Falco for his guidance throughout my graduate studies, and to my thesis committee~ for their helpful suggestions. Also, I would like to express my sincere appreciation to the following people whose contributions to this work are too numerous to list: Brian Leary. Nelson Maldonado, Brian Agar, Jeff Lovett. Doug Little, Jan Martin and. last but not least, Brenda Betts. iii TABLE OF CONTENTS Page LIST OF FIGURES ................................................ vi LIST op TABLES .... ..... ........................................ xii LIST OF SYMBOLS ................................................ iii CHAPTER 1 INTRODUCTION ............................................ 1 2 DESQIPTION 0F EXPERIMENTS .............................. 5 2.1 Experimental Apparatus ............................. 5 2.2 Data Acquisition ................................... 7 2.2.1 Acquisition of Visual Data ..--.~.--.----..~- 7 2.2.2 Acquisition of Mean Velocity Profile Data-------------------~-----------o- 7 2.2.3 Simultaneous Acquisition of Vorticity Probe 'ndVisul D‘ta eeeeoeeeeeeeeeeoeeeeeeo 10 Dat 2.3. 2.3. 2 3 2.3 a Reduction and Analysis Techniques ............. 14 Mean Velocity Profile Data .................. 14 vorticity Probe Dgtg ........................ 17 Conditional Sampling of the Visual Data °---- 21 2.3.3.1 Length Scale Data Sampling---------- 21 2.3.3.2 Vbrticity Probe Data Samplingo-o-ooo 22 “NH 3 mull“ .’....0.00.00.00.00.000000IOOOOOOOOOOOOOOOO.'.... 24 3.1 M°.n veloc1ty PrOfile D‘ta eeeeeeeeeeeeeeeeeeeeeeeee 24 3.2 Overall Impressions of the Visual vortiCity PrObe Dat‘ 0.0.0....OOOOOOOOOOOOOOOOOOOOO. 27 3.3 Length Scale D‘t‘ 0.000.000.0000...OOOOOOOI....00... 29 3.4 Typical Eddy Velocity Scale Data ................... 31 3.4.1 velocity Scale Statistics ................... 32 3.4.2 Individual Reynolds Number Velocity Scale Data ......................... 33 3.4.3 Data Averaged Over the Reynolds Number Range ................................ 39 3.4.4 Grand Ensemble Averaged iV 5 C0! APPENT APPEN APPEN APPEN APPE} velocity scale Data00000000000000000000000000 3.5 Accuracy . ......... ...... .......... ... ...... ........ 4 DISCUSSION ............... ....... ...... ...... 4.1 Discussion of Results .............................. 4.2 5 CONCLUSIONS APPENDIX A APPENDIX B APPENDIX C APPENDIX D APPENDIX E REFERENCES Comparison of Data with other Researcher's Work ................... 00.000.00.0000.000000000000000000.000000000000000 Description of Computer Pragrams . .......... ........ Sample Hot-Wire Calibration ......... Example of Collis and Williams coeffiCients A, B, ‘ndN 0.000.000.00000000000000000 \ Data Points Sampled Within the Typical Eddy......... Parameters used in the Nommalization of the Vorticity Probe Data ............ 41 44‘ 47 47 51 53 167 180 181 182 185 186 Figure 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.9 2.10 2.11 3.1 3.2 3.3 3.4 3.5 3.6 3.7 LIST OF FIGURES Page Turbulence Structure Laboratory Wind Tunnel ... ------ .. 54 Laser optics of fall 1980 turbulent boundary layer Vi‘uliZ‘tion 0 00000000 00000000000000.0000 0000000 55 Velocity profile data acquisition, reduction \ and analysis program sequence ............... ...... .... 55 Schematic of vorticity probe (four views) ...... ....... 57 Vorticity probe data acquisition. reduction and .MIY‘is prosrm sequence 0.000000000000000000.00000000 58 Laser optics of fall 1981 and winter 1982 turbulent boundary layer visualization ........ ........ 59 Typical eddy distances used in reducing the vorticity prObe dat‘ 0000000.0000000000000000000 0000000 60 The eight defined zones of the typical eddy ........... 51 Examples of distorted typical eddies ............. ..... 52 Typical eddy length scales ................ ............ 53 Acceptable orientations for conditionally sampling zones 7 and 8 ................................ 54 y vs U. unshifted y values. fall 1979 data ............ 55 y vs U. unshifted y values, fall 1981 data ............ 66 y vs U. shifted y values, fall 1979 data . ........... .. 57 y vs U. shifted y values. fall 1981 data ..... ......... 68 we vs filo... fall 1979 an. ...... . ....... 69 y/G vs U/UD. fall 1981 data ............ .......... ..... 70 Clauser plot, fall 1979 data ..... . .................... 71 vi 3.8 3.9 3.10 3.11 3.12 3.13 3.14 3.15 3.16 3.17 3.18 3.19 3.20 3.21 3.22 3.23 3.24 Clauser plot. fall 1981 data .......................... + u vs y+. using u fall 1979 data .............. ..... ‘CO’ u+vsy+.n81ngu f‘ll 1981 d‘t' oeeeeeeeeeeeeeeeeee tcf + + n V' y . “Sins urn, f.11 1979 d't' 0.0000000000000000. u+ vs y+' using“ fa111981 data 00000000000000.0000 tn' _ s (U'un-UHuto vs (yutc)/(6 0;). fall 1979 data ........... _ a (Un-UHutc vs (yutc)/(8 ug). fall 1981 data ........... (U,—'fi)/n,c vs (yrum)/(s‘u.,), fin 1979 data . ..... (Ug-UUutn vs (yutn)/(5.Ug). fall 1981 data .. ...... ... Cxt and Cyt Normalized with O ......................... cxt and cyt Normalized with 599 ....................... (Cxtutp/p) vs R9 ...................................... (Cytutp/u) vs R9 ...................................... Ensemble averaged data of u'IU; conditionally sampled to the typical eddies, for four Reynolds numbers. The vertical axes correspond to the normalized eddy smoke boundaries. One vertical division is 0.015. Zones 1-4 are sho'n. 000000.00...0.000000000000000...000000.00...0.00 Ensemble averaged data of u'lug conditionally sampled to the typical eddies, for four Reynolds numbers. The vertical axes correspond to the normalized eddy smoke boundaries. One vertical division is 0.015. Zones 5-8 are ‘hO'ne 000000000.00000000000000000000.0000000000.0.0.00 Ensemble averaged data of v'IU; conditionally sampled to the typical eddies, for four Reynolds numbers. The vertical axes correspond to the normalized eddy smoke boundaries. One vertical division is 0.012. Zones 1-4 are .ho'n. 0.000.000.0000.000000000000000...0000000000 ..... Ensemble averaged data of v'lUg conditionally sampled to the typical eddies, for four Reynolds numbers. The vertical axes correspond to the nommalized eddy smoke boundaries. One vertical division is 0.012. Zones 5-8 are ‘ho'n' eeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeea vii 72 73 74 75 76 77 78 79 80 81 82 84 85 86 87 88 3.2! 3.2 3.25 3.26 3.27 3.28 3.29 3.30 3.31 3.32 Ensemble averaged data of u'v'/(Uwz) conditionally sampled to the typical eddies, for four Reynolds numbers. The vertical axes correspond to the normalized eddy smoke boundaries. One vertical division is 0.0006. Zones 1-4 are shown. .................................. 89 Ensemble Averaged Data of u'v'/(U;2) conditionally sampled to the typical eddies. for four Reynolds numbers. The vertical axes correspond to the normalized eddy smoke boundaries. One vertical division is 0.0006. Zones 5-8 are shown. .................................. 90 Ensemble averaged data of (dv'ldx)-(O/Ug) conditionally sampled to the typical eddies. for four Reynolds numbers. The vertical axes correspond to the normalized eddy smoke boundaries. One vertical division is 0.03. Zones 1-4 are shown. .................................. 91 Ensemble averaged data of (dv'ldx)o(O/U;) conditionally sampled to the typical eddies. for four Reynolds numbers. The vertical axes correspond to the normalized eddy smoke boundaries. One vertical division is 0.03. Zones 5-8 are shown. .................................. 92 Ensemble averaged data of (du'ldy).(O/U§) conditionally sampled to the typical eddies. for four Reynolds numbers. The vertical axes correspond to the normalized eddy smoke boundaries. One vertical division is 0.03. Zones 1-4 are shown. ........................... ....... 93 Ensemble averaged data of (du'ldy)-(O/Ug) conditionally sampled to the typical eddies. for four Reynolds numbers. The vertical axes correspond to the normalized eddy smoke boundaries. One vertical division is 0.03. Zones 5-8 are shown. .................................. 94 Ensemble averaged data of (wz')-(O/Ug) conditionally sampled to the typical eddies. for four Reynolds numbers. The vertical axes correspond to the normalized eddy smoke boundaries. One vertical division is 0.04. Zones 1-4 are shown. .................................. 95 Ensemble averaged data of (wz')o(O/Ug) conditionally sampled to the typical eddies, for four Reynolds numbers. The vertical axes correspond to the normalized eddy smoke boundaries. One vertical division is 0.04. viii 3.33 3.34 3.35 3.36 3.37 3.38 3.39 3.40 3.41 3.42 3.43 Zones 5-8 are shown. .................................. 96 Ensemble averaged data of (s ')-(e/Ug) conditionally sampled to the typical eddies, for four Reynolds numbers. The vertical axes correspond to the normalized eddy smoke boundaries. One vertical division is 0.03. Zone; 1-4 are shown. .................................. 97 Ensemble averaged data of (s ')-(6/U;) conditionally sampled to the typical eddies, for four Reynolds numbers. The vertical axes correspond to the normalized eddy smoke boundaries. One vertical division is 0.03. Zones 5-8 are shown. .................................. 98 The ensemble averaged u'IUo data shown in Figures 3.21 and 3.22 averaged over the four Reynolds numbers. Zones 1-8 are shown. One vertical division is 0.008. ..................... ...... 99 The ensemble averaged v'lUg data shown in Figures 3.23 and 3.24 averaged over the four Reynolds numbers. Zones 1-8 are shown. One vertical division is 0.008. ........................... 100 The ensemble averaged u'v'/(U;2) data shown in figures 3.25 and 3.26 averaged over the four Reynolds numbers. Zones 1-8 are shown. One vertical division is 0.0004. .................... ..... . 101 The ensemble averaged (dv'dx)-(O/Ug) data shown in Figures 3.27 and 3.28 averaged over the four Reynolds numbers. Zones 1-8 are shown. One vertical division is 0.01. ............................ 102 The ensemble averaged (du'ldy)-(O/U;) data shown in Figures 3.29 and 3.30 averaged over the four Reynolds numbers. Zones 1-8 are shown. One vertical division is 0.014. ......... ..... . 103 The ensemble averaged w '/(OIU;) Data shown in Figures 3.31 and 3.32 averaged over the four Reynolds numbers. Zones 1-8 are shown. One vertical division is 0.03. ............................ 104 The ensemble averaged s '/(O/Ug) Data shown in Figures 3.33 and 3.34yaveraged over the four Reynolds numbers. Zones 1-8 are shown. One vertical diVi‘ion i‘ 00012. 00000000000000.0000...0.000 105 Mean flow field of an ideal typical eddy -- ----------- . 106 Grand ensemble average over zones 1-6. zones ix 3.44 3.48 3.50 3.51 3.52 4.1 4.2 1-8. and zones 7.8 of u'IUo. One vertical diV1820ni80.006. 0000.00000000000’00000000000000000000 107 Grand ensemble average over zones 1-6, zones 1-8. and zones 7.8 of v'IUO. One vertical dIVi‘ion 1‘ 00008. 00000000000000.00000000000000 000000 108 Grand ensemble average over zones 1-6, zones 1-8. and zones 7,8 of u'v'/(U;2). One vertical diVi‘ion 1‘000004. 00000 00000 00000000000000.000000000 109 Grand ensemble average over zones 1-6, zones 1-8. and zones 7.8 of (dx'ldx)-(6/Ug). One vortic‘l diVi'ion 1‘ 0.01. 00000000..0000.00.00.000000 110 Grand ensemble average over zones 1-6, zones 1-8. and zones 7.8 of (du'/dy)-(O/Ug). One vertic‘l diVi‘ion is 0.012. 000000000000000000000 000000 111 Grand ensemble average over zones 1-6, zones 1-8, and zones 7.8 of wz'O/Ug). One Vertical DiViSion180.02. 0.000000000000000000.000.000.00....00 112 Grand ensemble average over zones 1-6, zones 1-8, and zones 7.8 of sxy'(O/U;). One vertical diVi‘ion 180.01. 0..000.00.000.0000000000.00.0.0000...113 Grand ensemble averages over zones 1-6 of: u’lU;, v'IUg, '(OIUon ). (du' Idygs o(O/U¢ ). (dv'ldx)-(O/Ug). s:¥(O/U: ). u' v '/(U, The vertical lines represent the normalized eddy boundaries. ..................................... ...... 114 Grand ensemble averages over zones 1-8 of: u'lflg, v'lUg, '(O/Uo ). (du' Idyg) -(O/Uo ). (dv'ldx).(e/ug). ::¥(e/u: ), u v [(0 The vertical lines represent the normalized eddy boundaries. ........................................... 115 Grand ensemble averages over zones 7, 8 of: u'IUg. v'IUg. '(O/UO ). (du' ldyg; W(O/ (dv'ldx).(e/ug). H:¥(e/u ).’ u v [(0 The vertical lines represent the normalized eddy boundaries. ........................................... 116 Example of a typical eddy in a turbulent boundary layer. 0; = 3.27 ft/s. The probe is 3 inches from the wall. ......................... ...... 117 Example of a typical eddy in a turbulent boundary layer. 0; = 3.27 ft/s. The probe is 3 inches from the Wall. and is intersecting the eddy in zone 2. ................................ ....... 118 4.3 4.4 4.5 4.6 4.7 4.8 Ezmmple of a boundary layer. typical eddy in a turbulent U” = 3.27 ft/s. The probe is 3 inches from the wall. and is intersecting the eddy in zone 4. Example of. a boundary layer. typical eddy in a turbulent U; = 3.27 ft/s. The probe is 3 inches from the wall. and is intersecting the eddy in zone 4. Example of a boundary layer. typical eddy in a turbulent U; = 3.27 ft/s. The probe is 3 inches from the wall. and is intersecting the eddy in zone 6. ....00.000.000.000.........OOOOOOOOOOOO Falco's definition of typical eddy zones nom‘lizedbythe Cyt length ......OOOOOOOOOOOOOOOOOOO. Falco's normalized ensemble averaged Reynolds stress u'v'/(Ug2) for his five zones of the typical eddy. One vertical division is 0.0004. %=1232 ......OOOOOOO0O.............OOOOOOOOOOOOOO0.0 Falco's normalized grand ensemble a eraged distribution of u'IUQ, v'lUw. u'v'/(U; ) R0 = 1232. I0.00.........OOOOOOOOOOOOOCOOOO...... xi 119 120 121 122 123 124 LIST OF TABLES Table 2.1 Collis and Williams Coefficients -- -------- . ooooooooo .. ..... 125 2.2 y-Positions of the Vorticity Probe . ------- ----. .......... .. 123 2.3 Fall 1979 Mean Velocity Profile Parameters, output from LINVP8 eooeeeeaeaeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee 129 2.4 Fall 1981 Mean Velocity Profile Parameters, output from LINVP8 eeeooeeeeeaeeeeeoooeeeeoeeeeeeeeaeeeeeeee 133 2.5 Fall 1979 Mean Velocity Profile Parameters, output from VELPR1 oeoeeeeeesoaooeooooeeeeeeeeeeaeeeeeeoeoee 137 2.6 Fall 1981 Mean Velocity Profile Parameters, Output fro“ VELPRI eseeaeaeeeaeeeeeeeeeaeeeeoeooo........... 141 2.7 Correction Coefficients CP and CN '°°°'---------------o-o-o- 145 3.1 Summary of Fall 1979 Mean Velocity Profile Parameters °°---- 146 3.2 Summary of Fall 1981 Mean Velocity Profile Parameters ------ 147 3,3 1yp1¢.1 Eddy Length scgle Data ................... ......... . 148 3.4 ”can Values from the Long Time Records °-°-------------.---- 151 3.5 RMS Values from the Long Time Records ...-.................. 156 3.6 Grand Ensemble Averaged Data from Zones 1-6 ................ 150 3.7 Grand Ensemble Averaged Data from Zones 1-8 ................ 151 3.8 Grand Ensemble Ayeraged Data from Zones 7 and 8 -- ------- ... 152 4.1 Normalized Mean and Peak Values within the Typical Eddies. Compared to the Long Time Mean Values .............................. ...... ....... 163 4.2 Peak Values Within the Typical Eddy. it R9 = 729.9 164 4.3 Peak Values within the Eddy, Compared to the Long Time nus VRIUOS eeoeeesoeoeeeeeeeeeeeeeoeaeaeaeeaeeeeeeeeeeO 166 xii LIST OF SYMBOLS Collis and Williams parameter Collis and Williams parameter Local skin friction coefficient Correction coefficient Correction coefficient Typical eddy length scale Typical eddy length scale Streamwise velocity gradient at the wall Anemometer output voltage Clauser's pressure gradient parameter Shape factor Flow rate Correlation coefficient Reynolds number based on distance from the wall Reynolds number based on momentum thickness Fluctuating spanwise strain rate Total streamwise velocity Average streamwise velocity Free stream velocity Friction velocity based on the wall shear stress Friction velocity based on the skin friction coefficient Fluctuating velocity component in the x direction xiii Nondimensional velocity (U/ut) Fluctuating Reynolds stress Fluctuating velocity component in the y direction Streamwise velocity at 99% at the edge of the boundary layer Fluctuating 2 component of vorticity Nondimensional distance from the wall (yutp/n) Typical eddy length scale Boundary layer thickness Density Momentum th ickne s s Viscosity ivx INTRODUCTION CHAPTER 1 Experimental investigations of turbulent boundary layers have been _ extensive throughout the last half of this century. Initial studies involved interpretation of measurements of spatial and power spectra of turbulent velocities. Papers dealing with this topic include: Townsend (1951). Klebanoff (1954). Grant (1958). and Trintton (1967). Willmarth and Wooldridge (1962. 1963) and Willmarth and Tu (1967) obtained space-time correlations between turbulent velocity components and fluctuating wall pressure. Structural models were proposed based on these methods of analysis. These models are useful. but the determination. of unique flow structures from the space-time correlations obtained from long time averages is difficult. Coherent motions in the turbulent boundary layer have also been investigated using flow visualization. These coherent motions are of two general types: (1) bursting processes originating from the wall. and (2) bulges at the turbulent/nonturbulent interface. Hams (1963) used dye and hydrogen bubbles in water. Other investigators who used this technique were: Schraub et a1. (1964. 1965). Kline et a1. (1967). Kim et a1. (1968. 1971). and Grass (1971). Fiedler and Head (1966) and Falco (1974. 1977) also used visual techniques to examine coherent turbulent structures. Corino and Drodkey (1969) used a high speed movie camera to track the motion of individual particles in the flow. This technique allowed them to observe the sweep phenomenon. Kim et al. (1968. 1971) estimated that all the Reynolds stress occurred during bursting periods in the region 0 ( y* < 90. Corino and , 2 Brodkey (1969) estimated that 70% of the Reynolds stress was produced in this same region. While flow visualization studies reveal the flow structure to the human eye or movie cameras. obtaining quantitative measurements of the Reynolds stress is difficult. Bot-wire measurements supplement visual results by providing quantitative data. Investigators who have used this technique include: Rao. Narasimha. and Badri Narayanan (1971). Laufer and Badri Narayanan (1971). and Willmarth and Lu (1971). Kovasznay. Kibens. and Blackwelder (1970) pioneered the technique of conditionally sampling velocity measurements. This technique has been subsequently used by : Wallace. Eckelmann. and Brodkey (1972). Willmarth and Lu (1972. 1973). and Wallace and Eckelmann (1974). A more recent investigation was that of Purtell (1978). who investigated u-component fluctuations and spectra. The general purpose of this investigation was to examine the typical eddy. which is a coherent motion observed by Falco (1974) as bulges protruding into the non-turbulent region. in the outer region of tubulent boundary layers. Kovasznay et a1. (1970) investigated three dimensional bulges along the turbulent/nonrturbulent interface. They observed large fluctuations in the normal (v') velocity component within these events. These three dimensional bulges are assumed to be the typical eddies of this investigation. because they exist in the same location (outer region of the boundary layer). and exhibit the same behavior (large v' fluctuations). Specifically the objectives of this investigation were: (1) to examine the contribution to momentum transfer made by the typical eddy in the outer region of turbulent boundary layers. (2) to add evidence 3 to the idea that the events observed by Falco (1974). which were termed "typical eddies". are vortex rings. and not hair pin vortices as proposed by Head and Bandyopadhyay (1981). and (3) to document the mean flow field of the typical eddies over the range of Reynolds numbers of this investigation. Increased knowledge about items (1). (2). and (3) will result in a better understanding of turbulent boundary layers. This understanding is essential to successful modification of boundary layers for numerous technical applications. Hot-wire data was collected in the outer region of turbulent boundary layers at momentum thickness Reynolds numbers (R9) of 729.9. 1397. 2376. and 3116. A stream-wise cross section of the turbulent boundary layer was illuminated using a vertical plane of laser light and vaporized mineral oil ("smoke”) introduced upstream of the data collection point as a flow marker. Length scales of the typical eddy were determined from high speed movie film data records. The eddies observed in the films appeared as cross sections of vortex rings. The most frequently observed orientation of the eddies was that of a vortex ring convecting itself in the upstream direction and away from the wall. The typical eddies are very dynamic. They appear to be continually changing shape and orientation. as they are formed. evolve. collide into one another. and decay. They tend to roll over on themselves. similar to rigid body dynamics. caused by the velocity gradient in the boundary layer. The determination of mean velocity scales from the hot-wire signals involved conditionally sampling the typical eddies. based primarily on the visual data. The conditionally sampled portion of the typical eddy furthest from the wall (top lobe. defined in section 4 2.3.3.1) was based entirely on the visualization. The portion of the eddy closest to the wall (bottom lobe) was often partially obscured by the smoke filled boundary layer. When the bottom lobe was visible. but partially masked by surrounding smoke. the hot-wire signals were used to confirm its existence. The turbulent boundary layer parameters obtained from mean velocity profiles were used to normalize the length and velocity scale data. CHAPTER 2 DESCRIPTION OF EXPERIMENTS Three types of experiments were performed during this investigation. The first type of experiment involved flow visualization only (fall 1980). The second type was the collection of mean velocity profile data. which involved calibration and use of a single hot-wire probe. The third type was the collection of simultaneous hot-wire and visual data. preceded by calibration of a 4-wire probe (hereafter called the vorticity probe) capable of measuring spanwise vorticity. This chapter contains a discussion of the experimental apparatus used in the three types of experiments. the data acquisition techniques. and the data reduction and analysis techniques. 2.1 Experimental Apparatus All three experiments of this investigation were conducted in the Turbulence Structure Laboratory (TSL) low speed wind tunnel. shown in Figure 2.1. As far as possible. the same measurement equipment was used in all of the experiments. The pertinent equipment utilized in each experiment will be mentioned in the description of each experiment. The primary apparatus used in the first type of experiment (fall 1980. visualization only) were: a Redlake Locam model 50-002 16mm pin registered high speed movie camera with a Schneider-Kreuznach Zenon 1:0.95/25 lens and Kodak High Speed 7250 Tungsten color film. a Coherent (1-8 Supergraphite argon ion laser. a C.F. Taylor model 3020 smoke generator. and a Melles Groit cylindrical lens with enhanced aluminum coating and front silvered cylindrical mirrors. The second type of experiment was the mean velocity profiles of which there were two sets. The fall 1979 mean velocity profile and hot-wire calibration data was collected using a TSI digital voltmeter. a single hot-wire probe and a Disa 55M10 constant temperature standard bridge anemometer. and two micromanometers. The mean velocity profile and calibration data. which were collected during the fall of 1981. required the use of a simultaneous sample and hold. 50kHz analog to digital converter (hereafter referred to as 'the A/D'). a\P1essey LSI-11/23 computer (hereafter referred to as 'the computer'). a MKS Baratron model 146E—0.1 pressure transducer. and a Keithly voltmeter. in addition to the voltmeter. and anemometry utilized in the fall 1979 mean velocity profile data collection. The third type of experiment (simultaneous hot-wire and visual data collection) was the most involved of the three types and incorporated the use of the following equipment: a vorticity probe (designed by Dr. J.F. Foss and fabricated by B.E. Agar). the A/D. the computer. the Coherent argon ion laser. the same Melles Groit cylindrical lenses and mirrors used in the fall 1980 visualization. four Disa 55M10 anemometers. the MKS Baratron pressure transducer. the T81 voltmeter. a Keithly voltmeter. a Validyne pressure transducer. the smoke generator and the Redlake Locam high speed movie camera with the same lens and film as used in the fall 1980 visualization experiments. 2.2 2.2. not SUI depe Bar: eacl sec1 The inj: the tr a: In the bot: qu wit 2.2 197 dlt 2.2 Data Acquisition 2.2.1 Acquisition of Visual Data The first experiment was the collection of visual data. which did not involve hot-wire anemometry. Visual data was recorded at free stream velocities of 3.24. 5.93. 10.2. and 19.2 ft/sec. for the purpose of determining the typical eddy length scales and their Reynolds number dependence. The flow speed in the wind tunnel was monitored with the Baratron pressure transducer and T81 voltmeter. The boundary layer of each flow speed was tripped at the entrance of the first working section of the wind tunnel with a 1/2 inch outer diameter circular rod. The turbulent boundary layer was marked with vaporized mineral oil injected at the entrance of the first working section. just upstream of the trip. The laser beam was directed into the wind tunnel and transformed into a vertical laser sheet by a series of mirrors and lenses. shown in Figure 2.2. This vertical laser sheet was aligned in the x-y plane. and allowed a cross-sectional side view of the turbulent boundary layer to be photographed with the high speed camera. The data acquisition position was at the downstream end of the second working section (refer to Figure 2.1). The camera was mounted horizontally. with the lens three feet from the vertical plane of laser light. 2.2.2 Acquisition of Mean Velocity Profile Data Two "sets" of mean velocity profile data were collected. The data for the first set of four profiles was collected during the fall of 1979 and will be referred to as "the fall 1979 mean velocity profile data". The data for the second set of four profiles was collected during the fall of 1981 and will be referred to as ”the fall 1981 mean velocity profile data". The mean velocity profile and hot-wire calibration data of fall 1979 was collected using the Disa anemometry and the T81 voltmeter mentioned in section 2.1. The hot-wire calibration consisted of collecting simultaneous average voltages from the hot-wire. and pressure readings from the micromanometers. The averaging capability of the T81 voltmeter was used with a 100 second time constant. The TSI voltmeter then required 400 seconds of averaging time for each data point. The pressure readings were converted to velocities via the Bernoulli Equation. The hot-wire voltages were then plotted against the micromanometer velocities to form the calibration curve. The hot-wire calibrations of fall 1979 were conducted in a calibration tunnel separate from the main Turbulence Structure Laboratory wind tunnel. The acquisition of the fall 1979 mean velocity profile data was similar to the acquisition of calibration data. The differences were. the main wind tunnel was utilized and pressure data was not recorded for each data point. Four sets of mean velocity profile data were collected at free stream velocities of 3.24. 5.93. 10.2. and 19.2 ft/sec. A 1/2 inch outer diameter circular rod was positioned at the upstream end of the first working section to trip the flow. Prior to the collection of data the y position of the probe was measured as carefully as possible using a telescope and graduated rule arrangement. Refer to Figure 2.2 for the orientation of coordinate axes. The pressure measurements made during the experiment were used only as a check on the free stream velocity in the wind tunnel. The TSI 9 voltmeter was used to collect hot-wire voltages. again using 400 seconds of averaging time per data point. The mean velocity profile and hot-wire calibration data of fall 1981 was collected using the A/D and computer mentioned in section 2.1. The program sequence used in the hot-wire calibration and data collection process discussed below is shown in Figure 2.3. Descriptions of the programs used throughout this investigation are located in Appendix A. The hot-wire calibration involved the following steps. The AID was calibrated by adjusting the ranges. offsets. and gains of the channels to be used to settings apprOpriate for the range of velocities to be measured. Then the Turbulence Structure Laboratory (TSL) program ADCAL was run which: (1) communicates to the A/D the channel numbers and delays to be used. (2) communicates to the direct memory access board (DMA) the number of words to transfer and where to store them. and (3) synchronizes the A/D output with the input voltages. The hot-wires used in the collection of the mean velocity profiles of fall 1981 were calibrated in the TSL main wind tunnel. Prior to the hot-wire calibration the turbulence trip was removed and the hot-wire was positioned in the center of the wind tunnel (y-z plane) at the same x location as the mean velocity profile data acquisition. The hot-wire calibration data was collected using the TSL program RUNlSK. Program CALFIT was then used which determined the coefficients (A. B. n) of the Collis and Williams relation: (E2 = A + no“) based on a least squares curve fit through the calibration data. The calibration curves were visually inspected via program CALDRW. which plots the calibration data and the least squares curve fit. Normally the hot-wire calibration 10 data was collected the day before the mean velocity profile data was collected. This allowed the calibration data to be examined in sufficient detail to insure that good calibration data had been obtained. Calibration data from the highest speed. which is typical of the calibrations at all four speeds. is shown in Appendix B. Four sets of mean velocity profile data were collected at free stream velocities of 3.27. 6.10. 10.7. and 17.5 ft/sec. The 1/2 inch outer diameter cylindrical rod was used to trip the boundary layer for the three lowest speeds. A 1/16 inch rod was used to trip the boundary layer at the highest speed. The reason for the different trip size at the highest speed was that the flow was observed to be naturally turbulent. The 1/16 inch diameter trip was used to insure fully developed turbulent flow and to fix the point of transition. The position of the trip was 18 inches from the upstream and of the first working section and 14 feet upstream from the point of data collection. Prior to collection of mean velocity data. the y position of the single hot-wire was measured with a magnifying lens and ruler with 1/100 inch graduations. The AID would then be recalibrated and program ADCAL rerun on the day of mean velocity profile data acquisition. The mean velocity profile data was collected with the TSL program RDN18K. 2.2.3 Simultaneous Acquisition of Vorticity Probe and Visual Data Simultaneous vorticity probe and visual data was obtained during the fall of 1981 and winter of 1982. at the same four free stream velocities as the mean velocity profiles of fall 1981 mentioned in section 2.2.2. of and sch is cal vel red to cal ori loo pro' tha cal the wt. °bt. dir. the (n) den 11 The vorticity probe consisted of four individual hot-wires. Two of the hot-wires were parallel to one another (the "parallel wires”) and the other two hot-wires formed an "X" when viewed from the side. A schematic of the vorticity probe. along with the critical dimensions. is shown in Figure 2.4. The calibration of the vorticity probe was similar to the calibration of the single hot-wire calibrations of the fall 1981 mean velocity profiles. The sequence of vorticity probe data acquisition. reduction. and analysis programs is shown in Figure 2.5. Again. refer to Appendix A for a description of these programs. Prior to calibration. the vorticity probe was rotated 90 degrees. from its orientation during the experiment. about the x-axis (clockwise when looking downstream). and placed in a special fixture which allowed the probe to be rotated about the line passing through the crossing of the "x-wires”. and orthogonal to the plane of the "x-wires". The four hot-wires were calibrated over the range of velocities that they would encounter during the experiment. The vorticity probe calibration involved collecting data over the range of velocities while the probe axis was parallel to the x-axis (refer to Figure 2.2). and at a velocity in the center of the range of velocities while the probe was rotated 5 and 10 degrees about the crossing of the x-wires. The data obtained when the probe axis was parallel to the x-axis (aligned directly into the flow) was input to program CALFTT which determined the coefficients in the Collis and Williams relation. The exponents (n) of the four hot-wires (which comprise the vorticity probe) as determined by CALFIT. were generally different than the 0.45 value predicted by Collis and Williams. All combinations of A and B for 12 values of the exponent (n) from 0.3 to 0.99. at intervals of 0.01 were inspected for each hot-wire. An example of the range of coefficients and standard deviations for 0.3 < n < 0.99 is located in Appendix C. The standard deviation of the curve fit using n = 0.45 was found to be insignificant. Thus. an exponent of 0.45 was used for each hot-wire of the vorticity probe at the four flow speeds. The coefficients (A and B) chosen by CALFTT and the actual values used in the data reduction are shown in Table 2.1. The calibration data obtained when the vorticity probe was rotated to 5 and 10 degrees about the crossing of the x-wires was input to Program CPCN. which determined the coefficients CP and CN. These coefficients are used later in the experimental data reduction process to correct for small deviations from the ideal 45 degree angle shown in Figure 2.4. Further information about the calibration of this type of vorticity probe is available in the M.S. thesis by J.A. Lovett (Michigan State University. 1982). During the collection simultaneous vorticity probe and visual data. the turbulence trip sizes. location. and position of data collection were all the same as in the mean velocity profile experiments of fall 1981. The same Redlake Locam movie camera was used as in the fall 1980 visualization experiments. Also the same camera settings (f-stop. shutter angle. and framing rate) were used with minor corrections intended to improve the readability of the films. The vorticity probe was positioned in the outer region of the boundary layer for the four flow speeds. The exact locations are included in Table 2.2. The camera was mounted horizontally. with the tip of the vorticity probe in the downstream third in the field of view. The lens 13 was approximately 3 feet from the laser sheet. The laser beam was directed into the wind tunnel. using a series of mirrors and lenses. and transformed into a vertical sheet of light aligned parallel with the streamwise direction of the flow (in the x-y _ plane). This arrangement is shown in Figure 2.6. The "smoke" which was introduced into the flow through 1/4 inch diameter holes located at the upstream end of the first working section. became entrained in the turbulent boundary layer and served to mark the flow. The vertical sheet of laser light cut through the boundary layer between the ”x-wires". and "parallel-wires”. This allowed the cross-sectional side view recorded on the high speed film to be as highly correlated as possible with the spatial derivatives obtained from the vorticity probe signals. The visual data was matched to the vorticity probe data by means of a computer controlled digital counter. (hereafter refered to as the "clock"). which counted the number of data points being collected. The clock was positioned such that it appeared in the films. Several data "takes" were recorded at each flow speed. A take consisted of the acquisition of 18000 data points. The sampling rates of the A/D at the four flow speeds were 1000. 2500. 5000. and 16000 Hz. Forty five hundred data points per channel per take were recorded at each flow speed. Each take is considered to be a "long time" data record. based on the number of boundary layer thicknesses which passed the probe during each take. 14 2.3 Data Reduction and Analysis Techniques The methods of reducing and analyzing the mean velocity data and the simultaneous vorticity probe and visual data are discussed in this section. The method of reducing and analyzing the visual data (without the vorticity probe) is not discussed. since the same method was used to reduce the visual data of the simultaneous experiment. 2.3.1 Mean Velocity Profile Data The mean velocity profile data of fall 1979 was reduced by hand from voltages to velocities. The mean velocity profile data of fall 1981 was reduced from voltages to velocities on the computer with the TSL program CONVOL. The fall 1979 and fall 1981 mean velocity profile data was analyzed in the same manner. The boundary layer parameters determined from the fall 1979 mean velocity profiles were used to normalize the length scale data. The boundary layer parameters determined from the fall 1981 mean velocity profiles were used to normalize the velocity scale data. Refer to the program sequence shown in Figure 2.3. Each profile was plotted in y vs C coordinates using program LINVP8. This program calculated du'ldy at the wall by means of a linear curve fit through the data. The slope at the wall was then used to calculate the friction velocity. The values of the friction velocity obtained by this procedure will hereafter be referred to .as “rn' Several runs of LINVP8 were conducted. with different combinations of points in the linear curve fit. The output of LINVP8 for the fall 1979 and fall 1981 mean velocity profile data is shown in Thble 2.3 and Thble 2.4. respectively. The output files and 15 corresponding plots were then inspected. and values of u...n for each velocity profile were chosen based on the following critera: (1) the first data point in the linear curve fit must be far enough away from the wall so that the conductive heat transfer effect due to the close _ proximity of the probe to the floor of the wind tunnel is negligible. (2) the y+ value for the last point in the linear curve fit should be as low as possible. (note: a value of y.‘. = 7 is typically considered to be near the edge of the linear region. but if the data remained linear beyond this value then the curve fit was extended). (3) the standard deviation of the linear curve fit should be relatively low. (4) the y-intercept should be within the expected error in the positioning of the hot-wire. which is approximately 0.005 inches. (5) there should be as many points in the linear curve fit as possible. and (6) the value of ut should experience small changes as the number of n points in the linear curve fit is changed. After this analysis. the y intercept obtained was considered to be the position y = 0. and the y values in the data files were shifted to reflect this. This was done to correct for errors in positioning the hot-wire probe during data acquisition. and all subsequent calculations and plots were made using the y-shifted data. The values of utn did not change as a result of shifting the y values. but there was a favorable effect on the Clauser and u+ vs. y* plots discussed in section 3.1. Program VELPRl was then used to determine other necessary parameters. such as 699. the displacement thickness( 5. ). momentum thickness( 0 ). Reynolds number( R9 ). and the shape factors R and G. Again several iterations were necessary. The number of input points was changed for each run of VELPRl. The number of input points in 16 these iterations bracketed the data point with the largest velocity. which occured at approximately the location of delta free stream. The output parameters of VELPRl are shown in Table 2.5 and Table 2.6 for the fall 1979 and fall 1981 mean velocity profile data. respectively. Program LINVP7. which generated plots of Y/O vs 6/05 was then run on both the fall 1979 and fall 1981 mean velocity profile data. The four sets of mean velocity profile data collected during fall 1979 were plotted on the same plot. as were the profiles of fall 1981. This was done to check for internal consistency of the two sets of mean velocity profile data. A Clauser plot (1)/lla vs Rey) was created for both sets of profile data with program LGAXS4. The skin friction coefficient(cf) of each profile was read directly from these plots. and each profile was checked for a well developed log region. The next step in the analysis of the mean velocity profile data was the creation of the u+ vs y+ plots. with the program UYPLS3. Both sets of profiles were ploted using utn (from LINVP8) and “to (using cf from the Clauser plot). These plots allowed the data near the wall to be examined for errors in the estimates of ut There was an apparent n' error in the u, estimates before the y values of each profile were shifted to cause the y-intercept of the linear curve fit to be zero. The data in the outer region was examined for collapse on the Coles line when utc was used. The last program to be run in the analysis of the mean velocity profile data was VELP51. This program plotted (IL-TIMEno vs (yut)/(6.U°). which allowed the data in the outer region to be examined for internal consistency. The fall 1979 and fall 1981 data was plotted 17 on separate plots using both “I and “r n c' 2.3.2 Vorticity Probe Data All of the vorticity probe data obtained from the simultaneous vorticity probe and visual data acquisition experiments discussed in section 2.2.3 was reduced (by necessity) on the computer. Refer to the program sequence shown in Figure 2.5. The vorticity probe data was reduced from the "raw" form (bits per millivolt) to velocities with the TSL program CDNVOL. The velocity outputs from CONVOL. for the ”parallel wires" were related to the wire voltages by means of the Collis and Williams relation (E2 = A + as“). The velocity outputs from CDNVOL for the "x-wires" needed to be corrected using the coefficients CP and CN mentioned in section 2.2.3. The correction of the ”x-wire" velocities was done in program VELRED. The majority of the data reduction was also performed with program VELRED. The inputs to program VELRED were: the sampling rate of the A/D. the critical wire distances. and the CP and CN coefficients. The values of the coefficients CP and CN which were used for the vorticity probe are included in Thble 2.7. The output of VELRED was 14 quantities all of which were calculated from the four basic hot-wire signals. These quantities were the fluctuating component of velocities. and velocity derivatives (ie. fluctuation - total - mean). The fluctuating quantities which were examined in detail were; u'. v'. u'v'. du'ldy. dv'ldx. wz'. and sxy'. A subroutine which "smoothed" the data and also removed "bad" data points was contained in program VELRED. The smoothing technique was a five point moving average. The 18 technique of removing "bad" data points was to compare the distance between each data point and its neighbors with the standard deviation of the long time record. If a data point was greater than one standard deviation from its neighbors. then it was replaced with the average of its two neighbors. There were never more than twenty bad data points per 4500 point record. This subroutine operated only on the velocity components themselves (ie. u'. v'. and the fluctuating u components of velocity from the two parallel wires). The derivatives were not directly smoothed. but since they were calculated from "smoothed" signals. they were much easier to correlate with the visual data than they would have been if the velocity components had not been smoothed. The data smoothing was necessary because the sampling rate was slow enough to allow 'noise' to contaminate the derivatives. The 'bad data points' in the long time records are believed to be the result of oil droplets leaving the hot-wires. The long time record of these quantities for each "take" and each Reynolds number was plotted using the TSL program PLOTTR. The next step in the data reduction process was the "reading" of the movies. This critical step in the data reduction process involved conditionally sampling the visual portion of the data. from which the velocity scales were determined. The conditional sampling of visual data is explained separately in section 2.3.3. The process of reading the films was as follows. The clock numbers appearing in the films as the downstream and upstream boundaries of the eddies contacted the vorticity probe were recorded. These two clock numbers corresponded to the "front" and ”back" of the eddies. respectively. The distances shown in Figure 2.7 were measured *I 19 on the film for each eddy that was sampled. The average length scale cxt was used to calculate the average number of data points recorded during the passage of a typical eddy past the vorticity probe. Sample calculations. the number of data points sampled within cxt' and the number of boundary layer thicknesses which passed the probe. during a data record. for the four flow speeds. are located in Appendix D The distances Cyt. cyb' Cpt' and Cpb were used as inputs to programs PFILM and PBFILM which separated the data obtained from reading the films into eight defined zones of the typical eddy. shown in Figure 2.8. A clear understanding of the definitions of the typical eddy will be essential to understand the plots discussed in section 3.3. These eight zones refer to the y position of the eddy through which the vorticity probe passed. during the simultaneous vorticity probe and visual data acquisition. Zone 1 was defined to be the region immediately above the eddy. beginning at a vertical line tangent to the front of the tap tobe. and ending at the vertical line tangent to the back of the eddy. Zones 2 through 5 are of equal thickness in the y direction. They begin at the front of the eddy and end at the back. The lower boundary of zone 5 corresponds to the observed bottom of the top lobe. Zone 6 is the region between the two lobes. beginning at the vertical line tangent to the front of the top lobe of the eddy and ending at the back of the eddy. Zones 7 and 8 are of equal thickness in the y direction. The top of zone 7 corresponds to the tap of the bottom lobe. The bottom of zone 8 corresponds to the bottom of the bottom lobe. The TSL program ENSMB4 was used to ensemble average the portions of the vorticity probe data records which corresponded to the passage 20 of typical eddies (as observed in the movies). Ensemble averages of the vorticity wire data for each zone of the typical eddy were obtained. The ensemble averaged signals were then normalized using both u.m and the free stream velocity (0;) at each Reynolds number. The parameters used to normalize the seven fluctuating quantities are shown in Appendix E. These normalized data records were plotted using program EDYPLT. The differences between normalization using u.m and the free stream velocity were negligible. The normalization using 0, was used in the final plots (discussed in section 3.1) since the free stream velocity is a more readily obtainable flow parameter lhan the friction velocity “rn‘ The normalized data from each of the seven quantities of interest was then averaged over the four Reynolds numbers using program ENSENS. These normalized data records were plotted using program EDTPLT. The data in the plots produced with EDYPLT (discussed in sections 3.4.1 and 3.4.3) has been scaled by ENSMB4 such that the points where the vorticity probe contacted the downstream and upstream boundaries of the eddies are indicated by vertical lines with tick marks on them. The tick marks on the vertical axes denote increments in the magnitude of the signals. The direction of time is from left to right. thus the flow is from right to left. in these plots. Each division of the horizontal axis represents 20 data points. of which every fifth was plotted. There are twice as many data points shown before and after the eddy. as there are inside the smoke boundaries. The final step in the reduction of the vorticity probe data was the calculation of a ”grand ensemble average" of the sampled typical eddies. This consisted of averaging the data from zones 1 through 6 21 together. averaging the data from zones 7 and 8 together. and averaging the data from zones 1 through 8 together. These three averages were over the range of Reynolds numbers of this investigation. ‘ 2.3.3 Conditional Sampling of the Visual Data 2.3.3.1 Length Scale Data Sampling The length scale data was obtained entirely by flow visualization. Refer to Figures 2.2 and 2.6 for the shape and orientation of an ideal typical eddy. Since the population of these "ideal" eddies is small compared to the population of all eddies in the boundary layer. a method of conditionally sampling was necessary. The conditional sampling of typical eddies was based on: (1) shape. (2) orientation. (3) observed internal fluid motion and. (4) y/B greater than 0.5. All four conditions were met (for each segment of data sampled. The shape and orientation of the eddy needed to be "close" to that of ideal. Granted. this method of sampling is subjective. but the sample size of 200 eddies per Reynolds number was sufficient to remove this inherent subjectivity. This conclusion is based on the observation that the differences in length scales from a sample size of 100 eddies per Reynolds number to a sample size of 200 eddies per Reynolds number was less than 10 percent. Examples of eddies that would have been considered too distorted or of improper configuration to include in the length sample are shown in Figure 2.9. The length scales; Cx. Cy, and Ye are defined graphically in Figure 2.10. Cxt was defined to be the horizontal distance from a vertical tangential line drawn at the downstream edge of the top lobe 22 of the eddy to the point where this horizontal line intersected the upstream edge of the top lobe. Cyt was defined to be the vertical distance from a horizontal tangential line drawn at the upper edge of the top lobe to a horizontal tangential line drawn at the bottom of the top lobe. Yc was simply defined as the distance from the floor of the wind tunnel to the horizontal line defining cxt' 2.3.3.2 vorticity Probe Data Sampling The quanitative signals obtained from the vorticity probe were selectively sampled based primarily on the visualization. and then these samples for each Reynolds number were ensemble averaged as discussed in section 2.3.2. The data at the two lowest Reynolds numbers were conditionally sampled based entirely on the visualization. The data at the highest two Reynolds numbers. however. was sampled with reference to both the visual data and the long time records discussed in section 2.2.3. The long time records of the fluctuating signals were a helpful aid in the sampling of data at the two highest Reynolds numbers due to the difficulty in reading the respective films. The data for zones 1 through 6 was sampled using the same criteria as in the sampling of the 1980 visual data. discussed in section 2.3.3.1. The ensemble averages of the signals in these zones closely represent what physically occurs as the average "typical eddy" passes the vorticity probe. The data for zones 7 and 8 do not represent this average picture as well. This is due to the differences in the sampling techinque for zones 7 and 8 as compared to zones 1 through 6. One of the objectives of this investigation was to determine whether typical eddies are vortex rings or hair pin vortices. The data 23 for zones 7 and 8 was sampled then. with the intent of choosing "good" examples of typical eddies (based on the visualization). This procedure. while providing substantial evidence that the typical eddies of this investigation are vortex rings. does not rule out the possibility that an occasional vortex hair pin may exist in turbulent boundary layers. The criteria for sampling eddies which struck the vorticity probe in zone 7 or 8 were: (1) visual indication of a bottom lobe. supported by (2) signals from the long time record. The orientation criterion was relaxed to the point where eddies orientated as shown in Figure 2.11 would be acceptable. but the distorted eddies shown in Figure 2.9 would still not be sampled. The eddy shown in part a of Figure 2.11 is thought to be responsible for some of the anomalous signals discussed in section 3.4. The eddy shown in Figure 2.11b has rotated through the orientations shown in Figure 2.11c. and 2.11a. sequentially. CHAPTER 3 RESULTS 3.1 Mean Velocity Profile Data The results of the mean velocity profile data analysis (as described in section 2.3.1) presented in this section are intended to indicate the internal consistency of the data. The pertinent velocity profile parameters for the fall 1979 and fall 1981 data are summarized in Tables 3.1 and 3.2. respectively. The values of R9. up. 699. 6.. 0. H. and G were calculated with program VELPRl. The shape factors H and G were used as a diagnostic check on the mean velocity profile data. The fall 1979 and fall 1981 data plotted as y vs U) are shown in Figures 3.1 and 3.2. respectively. The y values of the data in these two plots have not been shifted as discussed in section 2.3.1 (to have zero y-intercept). The lines drawn through the data in Figures 3.1 and 3.2 are the best curve fits as determined by the procedure outlined in section 2.3.1. The values of the shear stress at the wall (du/dy-w). “tn' and y+ for the last point in the curve fits (unshifted y values) are included in Tables 3.1 and 3.2 for the fall 1979 and fall 1981 data. respectively. Notice that y.'. 8 10.7 and 12.6 for the last point in the curve fits through the fall 1981 data at U; of 6.1 and 10.7. respectively. Also notice that the data for these profiles appears quite linear out to the noted y+ values. which may be considered outside the wall region. (refer to Figure 3.2 and Table 3.2). The fall 1979 and fall 1981 data was again plotted as y vs E. but with shifted y values are shown in Figures 3.3 and 3.4. respectively. The y values of the data at U; = 19.2 ft/s of fall 1979 were shifted by 24 25 +0.05 inches based on a curve fit through three data points. This data was not considered close enough to the wall to yield an accurate value of u . Thus. u tn tn for the fall 1979 data at U; = 19.2 ft/s was determined by correlation with the other mean velocity profiles of this investigation. The y values of the fall 1981 data were all shifted less than 0.01 inches. which brought the y intercept of the curve fits to zero. (urn/0;) and (utc/U;) for each profile were calculated. The values are included in Tables 3.1 and 3.2. (11,:c /U;) decreased by 16% over the range of flow speeds for both the fall 1979 and fall 1981 data. (utn/U;) decreased by 46% and 22% over the range of flow speeds for the fall 1979 and fall 1981 data. respectively. urn at U; = 19.2 ft/sec appears to be too small. since (1) it is less than “t of the /0;) fall 1981 profile at U;=l7.5 ft/sec. and (2) the decrease in (“tn as noted above. for the fall 1981 data. is approximately twice that of the fall 1979 profiles. The fall 1979 and fall 1981 mean velocity profile data was plotted as 170 vs U7U;. these plots are shown in Figure 3.5 and Figure 3.6. respectively. The fall 1979 data for the three lowest Reynolds numbers collapse very well. while the data at the highest Reynolds number lies near the other three. but crosses over at approximately Y/G = 5.0. There was no data collected above Y/O = 10.0 for the three lowest Reynolds numbers of the fall 1979 data. The fall 1981 mean velocity profile data collapses quite well when plotted as Y/G vs UYU;. There is more scatter than in the fall 1979 plot which is caused by the shorter time record used in the fall 1981 mean velocity profiles. Approximately 30 seconds of averaging time was used for the fall 1981 26 data compared to approximately 7 minutes for the fall 1979 data. Thirty seconds of data contains several boundary layer thicknesses for any of the profiles. but fluctuations in the free stream velocity due to fluctuations in the fan speed did not average out over this short period of time. The skin friction coefficients for both the fall 1979 and fall 1981 mean velocity profiles were determined by plotting U/U; vs Rey (Clauser plot). and are included in Tables 3.1 and 3.2. respectively (following Clauser 1954). The fall 1979 velocity profile data is shown in Figure 3.7. All four profiles have a well developed log \region. The data for the 10 ft/s and 19 ft/s should not lie so close together. The 10 ft/s data would be expected to be slightly higher and the 19 ft/s data slightly lower. but the resulting error in “1c is not noticeable when the data is plotted as uI vs y+. or in the second type of Clauser plot I (U;-'I—J)/u.r vs (Tut)/(6.U;) ]. The fall 1981 velocity profile data plotted on the Clauser plot is shown in Figure 3.8. These four profiles appear as would be expected. with well developed log regions. The log region of the 17.5 ft/s profile is not as well deve10ped as the three lower speed profiles. but as with the fall 1979 data. any resulting error in “to is not noticeable when the data is normalized and plotted as uf vs y+. or as (0.16) ln.‘ y. (Tut) / M‘s.) . The u+ vs y+ plots for the fall 1979 velocity profile and fall 1981 velocity profile data using “to are shown in Figures 3.9 and 3.10. respectively. Both sets of mean velocity profiles collapse very well and lie slightly above the Coles line. Note also that. with the exception of the lowest speed fall 1979 profile. the data near the wall 27 is to the right of the u+ = y+ curve. The n? vs y+ plots for the normalized fall 1979 and fall 1981 velocity profile data using u are shown in Figures 3.11 and 3.12. tn respectively. Now both sets of mean velocity profile data collapse on the u? - y+ curve. but lie above the Coles line. with the exception of the lowest speed fall 1979 velocity profile. There is no immediately apparent collapse of the data above y.'. = 30. Both sets of mean velocity profiles were plotted as (U;4U)/ut vs (Yut)/(6.U;). using both “rc and “tn' shown in Figures 3.13 through 3.16. The plots with “r for both sets show the data collapsing c slightly better than with urn' Neither the use of “re or utn places the data outside the acceptable range for this type of plot. 3.2 Overall Impressions of the Visual Vorticity Probe Data The visual data that was recorded simultaneously with the vorticity probe data was generally of good quality. As the free stream velocity increased. however. the details on the film became more difficult to resolve. This is due to the limitations of light for illumination which required the exposure time of the camera to be slower than desirable. The eddies in the boundary layer with U; = 3.2 ft/s were clear and distinguishable. Many of the eddies that were sampled were at the outer edge of the boundary layer. and thus had the further advantage of being silhouetted against smoke free fluid. The sampled eddies contained entirely within large scale motions were generally harder to distinguish. 28 The visual data taken at U; 8 3.2 ft/s revealed that the boundary layer is composed of approximately 80 percent eddies. or vortices. These eddies are continually evolving. and colliding into one another. They also are constantly being created and destroyed. They occur in all possible orientations and distortions of the basic ring shapes. The orientation described in section 2.3.3.1 is the most frequently encountered. The orientation of second highest frequency is when the eddy has rotated 45 degrees clockwise from the orientation of highest frequency so that the eddy is now convecting itself directly away from the wall (as shown in part A of Figure 2.12). The visual data at a free stream velocity of 6.1 ft/s was nearly as clear as that at 3.2 ft/s. The visual data at the two highest speeds (free 'stream velocities of 10.2 and 17.5 ft/s) contained considerably less detail than at the lower speeds. The eddies at the three highest flow speeds behaved similar to those at the lowest flow speed. That is. the eddies continued to populate approximately 80 percent of the boundary layer. They were constantly being created and destroyed. and they were continually evolving. The eddies at a free stream of 17.5 ft/s were sampled with the vorticity probe data used as a reference. This was necessary since only the outline of the eddies could be distinguished. and the rounded shape of a smoke filled protrusion into the smoke free fluid may not. in fact. be an eddy. Thus the signals were used to confirm that what visually appeared as an eddy also had fluctuating u and v components of velocity which corresponded to those of a vortex. Another method of confirming that the events being sampled were eddies which met the criteria discussed in section 2.3.3.1 was to rapid 29 advance the projector forward and reverse at the area of interest. This allowed the actual fluid motions to be seen. whereas looking at any given frame of film revealed. at best. the instantaneous picture. This technique was most necessary at the two highest speeds. where the internal details of the flow were less clear. The typical eddies of this investigation appear as vortex rings in the visual data over the range of Reynolds numbers investigated. Hair pin vortices were not observed in any of the films. 3.3 Length Scale Data The typical eddy length scales of this investigation were found to be on the order of the Thylor microscales. These length scales are considerably smaller than those of the large scale motions. which are on the order of 1.6 699. The physical length scales cxt' Cyt' and Yc (refer to section 2.3.3.1 for definitions) were measured with sample sizes of 100 and 200 eddies. The magnitudes of the average length physical scales for both sample sizes. and the percent change in Cx' and Cy are included in Table 3.3. Also included in Table 3.3 are the fall 1979 boundary layer parameters used in normalizing the length scales (for reference). and the normalized length scales. The statistics of the length scales for the sample with 200 eddies is also included in Table 3.3. for reference. The changes in the physical length scales from a sample size .of 100 to 200 are sufficiently small that significant changes for larger sample sizes is not expected. The best estimates of CI and Cy will be taken from the sample of 200 eddies. The error bars on the data in the figures discussed below. reflect the percent change in length scales. 30 and not the error in the estimates of the normalizing parameters. The length scales Cxt and Cyt normalized with momentum thickness (0). and plotted against Reynolds number (R9). shown in Figure 3.17. reveal the Reynolds number dependence of the length scales. Note that the length scales normalized with 0 (outer layer parameter). decrease by approximately 32 percent over the range of Reynolds numbers of this investigation. The equations for the linear regression curve fits through the data are included in Figure 3.17. Both curve fits had a correlation coefficient of R = -0.98. The length scales normalized with 599 (outer layer parameter). shown in Figure 3.18. decreased by approximately 44 percent over the range of Reynolds numbers. The typical eddy length scales do not scale on outer region parameters. as concluded by inspection of Figures 3.17 and 3.18. If they did. there would be no trend with Reynolds number. The length scales Cxt' and Cyt were then normalized with utn (inner layer parameter). and the kinematic viscosity(u/p). Cxt normalized with u; and ut is shown in Figure 3.19. The curve fits of n 0 the data normalized with “re used all four data points. while the curve fit through cxt normalized with utn utilized only the three lowest Reynolds number data points. The highest Reynolds number point was omitted because it was not colinear with the other three data points. Recall that urn at this Reynolds number was obtained from a data correlation. and not from direct measurement. The curve fit was used to predict a value of (Cxtutnp/u) at R9=3827. u was then calculated tn to be 0.584 ft/s. and du/dy-w = 2056. These values are more consistent with the fall 1981 velocity profile at R0 = 3116. for which du/dy-w = 1700 (refer to Table 3.2). Whereas using “tn = 0.516 at R9 = 3827. 31 from the data correlation. the corresponding value of du/dy-w is 1600. Thus the estimate of utn from the data correlation was low by approximately 12%. The length scale Cy normalized with utn and are 3.20. Again. the data normalized with u.m is linear over the entire is shown on Figure range. but Cy normalized with “r at R9=3827 is low. u was predicted n tn to be .517 from the curve fit through the three lowest Reynolds number data points. The data shown in Figures 3.19 and 3.20 indicates that the length scales do not scale with the inner layer parameter u‘. 3.4 Typical Eddy Velocity Scale Data The velocity scale data obtained from the simultaneous vorticity probe and visualization experiment was analyzed with three techniques. The first was to plot each normalized fluctuating quantity. derived from the conditionally sampled vorticity probe data. The data at the four Reynolds numbers. for a given quantity and zone. were each plotted on a single plot. using program EDYPLT. This technique allowed the data to be inspected for trends with Reynolds number. and the relative position of the peaks in the fluctuating signals to be correlated with the smoke boundaries of the typical eddies. The results of this technique are discussed in section 3.4.2. The second technique. which is discussed in section 3.4.3. was to average the data for a given quantity and zone for the four Reynolds numbers together. The data for each zone and a given quantity was then plotted on a single page. with a separate time axis for each zone. This technique allows the mean flow field picture of the typical eddy (over the Reynolds number range of this investigation) to be seen more 32 clearly than with the first technique. This technique also allows the relative magnitudes of the fluctuating quantities to be compared over the eight zones. The third technique is the grand ensemble averages of the vorticity probe data over both Reynolds number and zone. The data from zones 1 through 6. 1 through 8. and zones 7 and 8. was averaged and plotted in two ways. The first method of plotting the grand ensemble averaged data was on the same graph as was used in the first technique. Again. this type of plot is useful in examining the relative magnitudes of the grand ensemble averaged data. The second method of plotting was to plot all seven quantities for a group (1-9- zones 1-6) of grand ensemble averaged data on the same page. using program PLOTTR. The relative phasing of the quantities can be seen using this method of plotting. This method. however. does not show the relative magnitudes well. The grand ensemble averaged data is discussed in section 3.4.4. 3.4.1 Velocity Scale Statistics The mean values of the seven quantities of interest were composed for each long-time record at each flow speed. The dimensional mean values were then averaged over all the takes for a given flow speed. The dimensional long-time mean values of u'. v'. s '. du'ldy. dv'ldx. xy wz'. and u'v' are shown in Table 3.4. The dimensional long-time RMS values of the seven quantities at R9 = 729.9 are shown in Table 3.5. The long time mean and RMS values will be referenced later with respect to the peak values measured within the eddies. 33 3.4.2 Individual Reynolds Number Velocity Scale Data This section is a review and discussion of the hot-wire data which was recorded for the eight zones of the typical eddy discussed in section 2.3.2. Fourteen fluctuating quantities were produced from the four hot-wire raw voltage signals. seven of these quantities were examined in detail. Since there are seven quantities and eight zones. there are fifty-six combinations to be examined. The plots of this data are shown in Figure 3.21 through Figure 3.34. Each plot contains the normalized data for the four Reynolds numbers (R9 = 729.9. 1397. 2376. and 3116). which are also indicated in the figures. Refer to Appendix E for the parameters used in the normalization. The values of the normalization parameters were obtained from the fall 1981 mean velocity profiles. The figures will not be referenced directly in this section. but to gain a full appreciation of the data the reader should follow the figures referenced by zone and quantity in the text. Also there are three important ideas to keep in mind while reading this section: (1) the data indicates no trend with Reynolds number. over the range of Reynolds numbers investigated. (2) the maximum values of the fluctuating signals of the typical eddy lie within the vertical lines in the figures. which correspond to the smoke boundaries of the eddy. (refer to section 2.4.2) and (3) the data indicates that the typical eddies of this investigation are vortex rings. with their characteristic flow field. The u' and v' signals for the eight zones indicate the basic flow field within and nearby the eddy. thus they will be discussed in combination. As an eddy passes just below the probe (zone 1). the v’ signals are generally negative with relatively small magnitude. whereas 34 the u' signals are positive above the eddy with slightly larger magnitude. The v' signals are negative since the flow around the eddy is moving toward the wall. The fluctuating u' signals are positive since the flow above the eddy is moving past the eddy in the +x direction and since the negative vorticity of the top lobe is inducing positive u fluctuations. As an eddy strikes the probe just inside the top lobe and above the center of negative vorticity (zone 2). the v' signals begin to collapse and show the characteristic downward. then upward. motion of the fluid. Note that the negative and positive peaks of the v' signal lie within the smoke marked boundaries of the eddy. The u' signals for zone 2 are slightly positive which indicates the probe is above the center of negative vorticity. The v' signals for zones 3 and 4 appear quite similar. as they should. since these two zones bracket the center of negative vorticity. Note that the v' signals collapse very well. indicating no Reynolds number dependence over the range of Reynolds numbers investigated. within the accuracy of these measurements. The u' signals for zone 3 reveal that the positive fluctuations induced by the nearby center of negative vorticity are canceled by negative fluctuations due to the relative bulk motion of the eddy in the negative x direction. The u' signals in zone 4 are beginning to show a small. negative trend within the eddy. This adds evidence to the idea that the center of negative vorticity lies between zones 3 and 4. since in zone 4 the negative bulk motion of the eddy and the u' fluctuations induced by the negative vorticity now add in the negative direction. instead of cancelling as they did in zone 3. This is assuming that the negative bulk motion of the eddy is the same for zones 3 and 4. which is reasonable. The v' signals in zone 5 become 35 more scattered and show less of a negative fluctuation as the the eddy first strikes the probe. The u' signals in zone 5 have a distinct negative trend within the eddy. The v' and u' signals for zone 6 remain quite similar to the signals in zone 5. As the eddy strikes the probe in zone 7 suddenly the v' signals take on a very different shape than in zones 2 through 5. The v' signals in zone 7 and 8 show a distinct positive peak just as the eddy strikes the probe followed immediately by a negative peak before the eddy has completely passed the probe. This is the first indication of a very important idea. that the typical eddies of this investigation are vortex rings. When viewed in the cross-sectional side view of the visualization. these vortex rings appear as a vortex pair. Refer to Figure 2.9. which shows the top and bottom lobes of an ideal typical eddy. The bottom lobe of the eddy. which contains the center of positive vorticity is not always visible next to the top lobe. This is for two reasons: (1) the visualization is not perfect which tends to mask the bottom lobes which also tend to be buried in surrounding smoke. and (2) the mean vorticity of the boundary layer is negative which tends to shorten the life of the bottom lobe and decrease its magnitude. A possible explanation for the inconsistencies of the v' signals in zone 8. for the two highest Reynolds numbers. is that the eddies tend to group together so that just after the passage of an eddy another immediately follows. The u' signals for zone 7 are negative. but have lost the distinct negative fluctuation of zones 4. 5. and 6. The u' signals for zone 8 are slightly negative. but do not show any variations as the eddy passes the probe. This indicates that in zone 8 the u' signal due to the internal fluctuations of the eddy are approximately equal to the 36 negative of the relative eddy velocity. The u'v' signals (Reynolds stress) for zones 1 through 4 appear as small fluctuations about the long time mean value of -0.000634 (normalized average over all four speeds and all takes that were read). This indicates that although the u' and v' signals are highly correlated near the center of vorticity. there is on average no difference in magnitude between the momentum transfer within the eddy (for zones 2 through 4) and the momentum transfer in the boundary layer at the y position of the probe. The u'v' signals for zones 5 and 6 indicate that there is approximately three times as much Reynolds stress in these zones as in the boundary layer. The u'v' signal in zone 7 has a negative peak of the same magnitude as in zones 5 and 6. but the peak is shifted toward the downstream portion of the eddy. This indicates that the momentum transfer caused by the typical eddy is concentrated in zones 5. 6 and 7. which is consistent with the flow field of the eddy. The u'v' signals in zone 8 indicate (similar to the signals in zones 1 through 4) there is no marked difference between the momentum transfer in zone 8 as compared with the boundary layer at the y position of the probe. The increase in scatter in the highest Reynolds number data is due to the small sample size. Note that the u'v' signals for all eight zones have no apparent trend with Reynolds number. The dv'ldx signals in zone 1 indicate no strong fluctuations. -as expected. since the v' signals of zone 1 are generally constant. The dv'ldx signals of zones 2 through 6. however. show a distinct negative peak at the center of vorticity. Recall that the v' signals for these zones show a negative fluctuation followed by a positive fluctuation. 37 Thus. dv'ldt would have a positive peak at the center of vorticity. and dv'ldx correspondingly shows a negative peak. The dv'ldx signals in zone 3 and 4 also show slight positive fluctuations at the front and back of the eddy. which corresponds to the v' signal fluctuations at the front and back of the eddy. The dv'ldx signals in zone 6 begin to show an increasingly positive peak at the upstream edge of the eddy. This positive peak is increased even further in zone 7. and the negative peak has essentially disappeared. The dv'ldx signals in zone 8 appear very similar to the v' signals in zone 7. with slightly more scatter. Again as with zones 1 through 5 the dv'ldx signals in zones 7 and 8 are consistent with the fluctuating v' signals. Note that the dv'ldx signal shows no trend with Reynolds number in any zone. The du'ldy signals for zone 1 are generally zero. since the probe is in the outer region of the boundary layer (y/899 is approximately 0.8. refer to Table 2.2) and there is essentially no vorticity above the eddy. There is no distinct fluctuations in the du'ldy signals in zone 2. except the peak in the highest Reynolds number data. which may be explained by the decreased size of the eddies and the difficulties in determining exactly where the eddie strikes the probe due to the relatively poor visualization at this speed. The du'ldy signals have a distinct positive peak in zones 3 and 4. which is consistent with the idea that these two zones bracket the center of negative vorticity. The du'ldy signals decay in zone 5 and in zone 6 have become esentially zero. The du'ldy signal is not expected to have any distinct peaks in zone 6. since in this region the fluid is generally moving in bulk motion. The du'ldy signals in zones 7 and 8 generally appear as the negative of the signals in zones 3 and 4. with the exception of the 38 large positive peaks in the two higher Reynolds numbers in zone 7 which may be explained by the sampling methods discussed in section 2.3.3. Again there appears to be no Reynolds number trend in the du'ldy signals through the eddy. Also note that the magnitudes of the du'ldy and dv'ldx signals are approximately equal. The vorticity signals show no distinct peaks in zone 1. as expected. The vorticity in zone 2 begins to show the negative peak associated with the center of negative vorticity located between zones 3 and 4. The very large negative peak in vorticity. at the highest Reynolds number. is a result of the inconsistently large positive peak in du'ldy at this Reynolds number and zone. As mentioned earlier. this is not believed to indicate a Reynolds number dependence. but rather the difficulties in sampling at this Reynolds number. The large negative peaks in vorticity in zones 3 and 4. clearly indicate that the center of negative vorticity lies. on average. between these two zones. The decrease in the negative vorticity peak in zone 5 from that in zone 4. further indicates that the center of vorticity lies above zone 5. The vorticity in zone 6 has a small negative peak indicating either that this region is dominated by the negative vorticity of the top lobe. or sampling errors in distinguishing the bottom edge of the top lobe. Note that the peaks in the fluctuating vorticity for zones 1 through 6 lie within the boundaries of the eddies marked by smoke. This indicates that the eddies are well defined by the smoke marker. The vorticity in zones 7 and 8 has distinct positive peaks near the center to the upstream portion of the eddy. This indicates quite clearly that the typical eddies of this investigation are vortex rings and not vortex hair pins extending to the floor as suggested by other 39 researchers (Willmarth and Tu 1967). The negative peaks in vorticity in the two highest Reynolds numbers in zone 7 also add evidence to the vortex ring idea. These negative peaks are due to the sampling methods discussed in section 2.3.3.2. Note. as is the case with the previously discussed quantities. that there is no trend with Reynolds number in the fluctuating vorticity signals in any of the eight zones. The strain rate signals in zone 1 are generally scattered with a slight hint of a positive peak at the upstream edge of the eddy. The strain rate signals in zone 2 do not contain any distinct fluctuations except for the two highest Reynolds numbers. which is probably due to the difficulties in data sampling. The strain rate fluctuations in zones 3 and 4 have a clear positive peak at the upstream edge of the eddy. This positive peak persists in zones 5 and 6. but there is more scatter in the data. The positive peak in strain rate in zones 3 through 6 corresponds to compression of the fluid.thus suggesting that on average there is a stagnation point located on the upstream edge of the eddy which varies from zone 3 to 6 for the eddies that were sampled. The strain rate signals in zones 7 and 8 have too much scatter to indicate the existence of other stagnation points. Indeed. a second stagnation point is not expected. Again note. as with the other quantities. that there is no apparent trend with Reynolds number in the fluctuating strain rate over the range of Reynolds numbers investigated. 3.4.3 Data Averaged Over the Reynolds Number Range The results of the previous section indicated there was no trend with Reynolds number for any of the seven quantities examined. The 40 data discussed in this section has been averaged over the Reynolds number range of this investigation. The magnitudes of the signals were weighted by the number of eddies in a given zone. The fluctuating u component of velocity is positive in zones 1 and 2. and becomes increasingly negative through zone 6. as shown in Figure 3.35. The u' signal is tending to become less negative in zones 7 and 8. The u' signal. then indicates the flow is passing over the top of the eddy. and the eddy is convecting itself upstream. relative to the mean flow. The v' signals shown in Figure 3.36 clearly indicate the downward. upward motion of the fluid in the top lobe. and the upward. downward motion in the bottom lobe. This alone (i.e. wiflhout any information about the vorticity) suggests that the typical eddies of this investigation contain regions of positive vorticity. The u'v' signals shown in Figure 3.37 indicate that the momentum transfer caused by the typical eddy is concentrated in zones 5 through 7. This is consistent with the idea that typical eddies are vortex rings. The dv'ldx signals shown in Figure 3.38 indicate that v' is changing most rapidly in zones 3 and 7. dv'ldx in the top lobe (zone 3) is negative. which is consistent with the downward. upward motion indicated in Figure 3.36. dv'ldt in zone 3 would have a strong positive peak corresponding to the negative peak in dv'ldx. The strong positive peak in dv'ldx for zone 7 agrees with the upward. downward motion of the bottom lobe. The du'ldy signals shown in Figure 3.39 reveal a strong positive gradient in the top lobe. and a strong negative gradient in the bottom 41 lobe. This is very indicative of a vortex pair. The vorticity signals shown in Figure 3.40 give a very strong indication that the typical eddy is a vortex ring. There is a clear region of negative vorticity centered in the top lobe and a clear region of positive vorticity in the bottom lobe. It is difficult to determine whether the magnitude of the vorticity in the bottom lobe is due to the sampling technique discussed in section 2.3.3.2. or whether this is a true indication of the average strength of vorticity in the bottom lobe. Small regions of very strong positive vorticity in the bottom lobe would indicate that the vortex ring is becoming stretched towards the top lobe. rather than the idea that the bottom lobe is simply defusing. as might be expected. The strain rate signals shown in Figure 3.41. strongly suggest a stagnation point along the upstream side of the top lobe. Again. this is consistent with the vortex ring idea. The ideas discussed in this section are summarized in Figure 3.42. which shows the mean flow field around and within an ideal typical eddy. 3.4.4 Grand Ensemble Averaged Velocity Scale Data The data discussed in this section has been normalized and averaged over the Reynolds number range and over three groupings of the zones of the typical eddy. The intent of this procedure is to allow the typical eddy to be examined as a coherent entity. and to compare the magnitudes of the averaged quantities within the eddy to the magnitudes of the long time averaged quantities. A long time data record implies many boundary layer thicknesses past the vorticity probe 42 during the data acquisition period. The exact amount of time in each long time record was discussed in section 2.3.2. The normalized grand ensemble averaged u' and v' signals are shown in Figures 3.43 and 3.44. respectively. These two figures indicate that the eddy is convecting itself upstream (in the relative sense). and away from the wall (in the absolute sense). The strength of the normalized u' and v' signals are comparable over the entire eddy (zones 1 through 8). The u' and v' signals in zones 7 and 8 appear to be significant. but this information is clouded by: (l) the sampling technique discussed in section 2.3. and (2) the number of eddies in zones 7 and 8 combined is approximately one fifth the number of eddies in zones 1 through 6 combined. The normalized grand ensemble averaged u'v' signal is shown in Figure 3.45. u'v' averaged over the top lobe (zones 1 through 6) and the entire eddy (zones 1 through 8) shows fluctuations about the long-time mean value of -0.000634 and a minimum value of -0.00114 in the center of the eddy. Similar to the u' and v' signals. the u'v' signal in zones 7 and 8 appears significant. This significance may be reduced. however. for the reasons mentioned above. The dv'ldx signal shown in Figure 3.46 clearly indicates the changes in v' with respect to x. dv'ldt is also readily inferred. Note that the positive maximum for zones 1-6 and 1—8 is at the right vertical axis (which corresponds to the upstream edge of the eddy). dv'ldx in zones 7 and 8 appears similar to the negative of dv'/dx in zones 1-6. The du'ldy signal shown in Figure 3.47 indicates a positive gradient centered in the top lobe. There is a significant negative 43 gradient in the bottom lobe. but again the absolute magnitude of this peak may be misleading. The normalized grand ensemble average of wz' shown in Figure 3.48 reflects a central idea of this investigation. The typical eddy contains regions of positive and negative vorticity. This would not be expected to be observed in hair pin vortices. The strain rate signal shown in Figure 3.49 strongly suggests a stagnation point located on the upstream edge of the typical eddy. There also is a slight positive peak at the downstream edge of the eddy. but this is probably not a true stagnation point. The relative phasing of the three groups of normalized grand ensembled data is shown in Figures 3.50. 3.51. and 3.52. Each signal is bracketed by two solid lines. which are the maximum and minimum of the signal for the segment of data plotted. Each signal has a third solid line associated with it. This line has tick marks on it. and is the line indicating zero magnitude of the signal. There are two rows of closely spaced dots. (which may appear as solid lines) for each signal. The locations of these dotted lines represent plus and minus one RMS from the mean line. The RMS lines can be distinguished from the maximum and minimum lines because the data crosses the RMS lines. but not the the maximum or minimum lines. The sixth line of interest for each plot is dashed. which represents the mean of the signal over the segment of data plotted. Each figure also has two vertical lines which cross all of the signals. These correspond to the smoke boundaries of the eddies. The maximum. minimum. mean and RMS values for the signals shown in Figures 3.50. 3.51. and 3.52 are included in Tables 3.6. 3.7. and 3.8. respectively. The time and flow directions 44 are indicated in the figures. The items to be noted from Figures 3.50 and 3.51 are: (1) the u'v'. wi'. dv'ldx. du'ldy. and u' signals have peaks centered between the smoke boundaries. (2) the strain rate signal has its peak at the upstream smoke boundary. and (3) the v' signal has both negative and positive peaks within the smoke boundaries. The items to be noted in Figure 3.52 are: (1) the positive vorticity peak is located within the smoke boundaries. (2) the v' signal is approximately the negative of the v' signal in zones 1-6. and (3) the u'v' peak is shifted from the center of the eddy to the upstream smoke boundary. which is consistent with the mean flow field shown in Figure 3.42. Item (1) is significant because it indicates that the smoke boundaries of the eddies correspond to the outer edge of the vortex. Item (2) indicates that the v fluctuations are similar in the tOp and bottom lobes. 3 .5 Accuracy This section contains a brief discussion of the maximum errors resulting from the instrumentation and calculations. Errors resulting from the conditional sampling technique have not been calculated. The errors due to sampling. however. are assumed to be small. This assumption is based on the data shown in Figures 3.21 through 3.34. The data in these figures indicates no trend with Reynolds number. even though the samples for the four Reynolds numbers each contain. a different number of eddies. Larger sample sizes are desirable. but they are not expected to significantly change the results. The A/D was tested with a 3.75 volt input. The output was 3.75 i .003 volts. or x .085 in the converted anemometer voltages. This 45 translates into 1.25% and 0.76% error in the streamwise and normal velocity components. The pressure transducer contributed a maximum of 1.3% error to the free stream velocity. The error of the A/D due to sampling rate is about 0.0rs and will be neglected. The largest standard deviation in the calibration curves was .0313 (volts)2 which was at the lowest flow speed. This standard deviation translates into a .06% error in the velocity using the Collis and Williams parameters. at this flow speed. The errors due to the calibration curve at successively higher flow speeds were .01%. .002%. and .0005%. The sum of the above errors is at most 2.69% and 2.1% for the streamwise and normal velocity components. respectively. This will be approximated by 2% for both components. The error in u'v' was less than 4% based on 2% error in u' and v'. The error in the spatial derivatives (du'ldy and dv'ldx). wz'. and sxy'. due to errors in the measured distances of the vorticity probe are as follows. The distance between the parallel wires was .044" t .0025". which resulted in at most 6.49 error in du'ldy for all four flow speeds. The instantaneous total U-component of velocity from the x-wire was used as the convection velocity in the calculation of dv'ldx. Thus the error in dv'ldx resulted from the error in v' and U. and was less than 4%. The error in '2' and ‘xy' was calculated to be less the 8%. The error in the normalization parameter U; was approximately 2% from above. The error in the normalization parameter was calculated to be $.05 inch or 11%. The normalization parameter was calculated to be which was greatest at the slowest flow speed. This was based on the 46 standard deviation of the estimates of 0 shown in Table 2.6. Thus the error in the du'ldy. dv'ldx. wz'. and ‘xy' data shown in Figures 3.21 through 3.52 is 20% at most. The error in u'. v'. and u'v' signals shown in these same figures is estimated to be less than 5%. The estimated error in utn shown in Tables 3.1 and 3.2 was calculated from the standard deviation in the linear curve fits through the data near the wall. The estimated error in “en shown in Tables 3.1 and 3.2 was calculated using an estimated error in cf of t.00005. \ CHAPTER 4 DISCUSSION 4.1 Discussion of Results One of the major ideas of this investigation is that typical eddies are coherent features. existing in the outer region of turbulent boundary layers. which cause the significant fluctuations in the velocity components. The typical eddies of this investigation were also observed to cause the significant peaks in Reynolds stress and vorticity. The coherence of the typical eddies is verified in the visual data records. Clearly visible typical eddies in a turbulent boundary layer with a free stream velocity of 3.27 ft/s are shown in Figures 4.1 through 4.5. Part (a) of each of these figures is a print from the high speed films. Part (b) is a schematic which shows the outline of the area of interest in the print. The red clock numbers in the prints are backwards. because the prints have been reversed. so that the time (left to right) and flow (right to left) directions in these prints will be consistent with the plotted data (in Figures 3.21 through 3.52). The vorticity probe can be seen in the prints. Note that the) bottom lobe of the typical eddies is visible in each figure. Note also that the eddies in Figure 4.1 through 4.4 are very close to the ideal shape and orientation described in section 2.3.3. The eddy outlined in the upper portion of Figure 4.1b is not striking the probe. but it is a good example of an eddy with both top and bottom lobes. The eddy shown in Figure 4.2 is striking the probe in zone 2. The eddies shown in Figures 4.3 and 4.4 are striking the probe in zones 4 or 5. The typical eddy shown in Figure 4.5 which is closest to the 47 48 vorticity probe is an example of an eddy striking the probe in zone 6. The importance of the typical eddy is seen by comparing the magnitude of the fluctuations inside the eddy to the long-time mean and RMS values. The normalized mean and peak values of u'v' and wz' within the eddies in zones 1-6. 1-8. and 7-8 are compared to the long-time mean values (shown in Table 3.4) in Thble 4.1. The mean and peak values of u'v' compared to the long-time normalized mean value of -0.000634 are seen to be approximately 1.5 and 2.0. respectively. Thus the typical eddies of this investigation make a significant contribution to the momentum transfer in the outer region of turbulent boundary layers. Two items must be kept in mind when considering that the sampled typical eddies. on average. contain Reynolds stress peaks which are twice the long time mean. First. the sampling critera was based primarily on the visualization. The eddies which were clear and distinct enough to be sampled. however. often had small peaks in u'v'. so that the factor of two difference between the Reynolds stress within the eddies compared to the long-time mean represents the average contribution made by the eddies. not the maximum contribution. Second. the large scale motions were observed to be comprised almost totally (80%) by typical eddies in some state of evolution. or decay. The eddies which were too distorted to sample. frequently contained u'v' peaks on the order of 20 times the long time mean. This suggests a picture of the physical boundary layer where the typical eddy is responsible for essentially all of the momentum transfer in the outer region. (for 700 < R9 ( 4000). Thus the rate of boundary layer growth is determined by the number and strength of the typical eddies in the outer region. The origin of the typical eddies is speculated to be 49 connected to bursts moving outward from the wall. These bursts. then entrain fluid and produce vortex rings (much like smoke rings blown from a persons mouth). The typical eddies are stable. coherent events. which propel themselves away from the wall. and persist until they either reach the non-vortical fluid in the free stream and decay. or are destroyed by colliding with other typical eddies. The vorticity contained within the the typical eddy is on the order of 103 times the mean vorticity in the outer region. While this number is quite large. it is not surprising. since du/dy at nine tenths of 699 is essentially zero. It is important to note that dv'ldx contributes significantly to the vorticity. A comparision of the mean and peak values within the typical eddy was made with the long-time mean values for the seven quantities of interest. This proved to be non-meaningful as the long time mean values for most of these quantities is essentially zero. A more meaningful comparision was made between the peak values within the eddies in each zone. and the long time RMS values. at R9 = 729.9 (refer to Table 3.5). The normalized and dimensional peak values within the typical eddy are shown in Table 4.2. Since the typical eddy velocity scales were concluded to be R9 independent (refer to section 3.4.2 and Figures 3.21 through 3.34). the comparision of peak values within the eddy to the long-time RMS values. shown in Table 4.3. were made at only one Reynolds number (R9 - 729.9). The ratios shown in Table 4.3 are generally of the order of 1.0 in zones 4. 5. 6. 7. and 8. being slightly lower in zones 1; 2. and 3. Again two items (mentioned above) should be kept in mind when considering these ratios: (1) the 50 magnitudes of the fluctuations in the sampled eddies represent an average over their lifetimes. not an estimate of the maximum they contain. and (2) the outer region is comprised of approximately 80% typical eddies. Thus. all of the significant velocity fluctuations in the outer region are correlated with the passage of the typical eddies. The mean length scales Cxt and cyt shown normalized with inner and outer region parameters in Figures 3.17 through 3.20. exhibit a distinct Reynolds number dependence. If a coherent feature (typical eddy) decreases in scale with increasing Reynolds. then due to its smaller physical size. it might be expected to contribute less \to the momentum transfer at these higher Reynolds numbers. The contribution to the normalized momentum transfer. as shown in Figures 3.25 and 3.26. of the typical eddy. however. is not seen to decrease over the momentum thickness Reynolds number range of this investigation. Furthermore. none of the normalized fluctuating quantities investigated appear to have any trend with Reynolds number. as shown in Figures 3.21 through 3.34. The mean flow field of the typical eddy shown in Figure 3.42 is deduced from the data shown in Figures 3.35 through 3.41. The mean flow field is seen to be that of a vortex ring. The event referred to as a typical eddy may be postulated to be flow structures other than a vortex ring. with similar behavior. Indeed. the data of this investigation is limited by Reynolds number range and sample size. thus it cannot conclusively rule out the existence of other structures with similar behavior. Data taken from an array of four vorticity probes placed a mean length scale (Cyt) apart. in conjunction with both vertical and horizontal planes of illumination would be very useful in 51 determining if other structures existed. The data of this investigation does suggest -very strongly. however. that the typical eddy is a vortex ring. Once this conclusion is made. a model of the origin (mentioned above). growth. and decay of vortex rings in the outer region could be developed. This model would be very useful as a starting point in understanding the outer region dynamics of more complex flows (i.e. non-zero pressure gradient and higher Reynolds number). Additional information about the relative phasing of the normalized grand ensamble averaged signals is obtained by plotting the data as in Figures 3.50. 3.51. and 3.52. These plots show peaks in wz'. u'v'. dv'ldx. du'ldy. and u' centered between the smoke boundaries for zones 1-6 and 1-8. whereas the positive peak in strain rate. indicating a local stagnation point is located on the upstream boundary of the eddy (zones 1-6). The v' signal shows that the fluid in the downstream half of the top lobe (zones 1-6) is moving down and the fluid in the upstream half of the top lobe is moving up. This downward and upward pattern is reversed in the bottom lobe. 4.2 Comparison with Other Researcher's Work The data of this investigation was. on a limited scale. compared with the data obtained by Falco (1974). Falco's definitions of the typical eddy zones were slightly different than the definitions put forth in section 2.3.2 of this investigation. His zones are shown in Figure 4.6. He was unable to resolve the bottom lobe in the visualization and thus did not obtain data corresponding to zones 7 and 8 of this investigation. Falco’s ensemble averaged u'v'/U;2 at R9 = 52 1232 for the five zones defined in Figure 4.6. is shown in Figure 4.7. He measured u'v' peaks of 0.0016 and 0.0014 in zones 4 and 5. respectively. which correspond to the peaks of .0016 in zones 5 and 6 shown in Figure 3.37. Falco's long-time mean value of u'v' was zero. since his x-wire was approximately one boundary layer thickness from the wall. Falco's normalized grand ensemble averaged data over the top lobe of the typical eddy is shown in Figure 4.8. His peak values and signal shapes for u' and v' are very similar to the normalized grand ensemble averaged data of zones 1-8 of this investigation shown in Figures 3.43 and 3.44. The relative magnitudes of the u'v' peak of Falco's data and that of this investigation. shown in Figures 4.8 and 3.45. respectively. are both approximately -0.0006. The data of this investigation has a larger negative mean value for the reason mentioned above. The close agreement between the two sets of data. lends support to the accuracy of both. CHAPTER 5 CONCLUSIONS The typical eddy length scales Cxt and Cyt do not scale on inner or outer layer parameters. and exhibit a distinct decreasing trend with . increasing Reynolds number for 700 < R9 < 4000 (refer to Figures 3.17 through 3.20). The normalized. fluctuating velocities and velocity derivatives of the typical eddy. however. have no apparent trend with Reynolds number. (refer to Figures 3.21 through 3.34). Thus. although the typical eddies of this investigation are of physically smaller size at the upper end of the Reynolds number range. their normalized effect on the outer region of the boundary layer is constant over the Reynolds number range. The typical eddy has been shown to be a coherent structure existing in the outer region of turbulent boundary layers. (refer to Figures 4.1 through 4.5). The typical eddy contains peaks in normalized Reynolds stress. which is a measure of momentum transfer. on the order of two times the normalized long-time mean value. This is an average result over the eddies lifetime. not an estimate of the peak magnitudes within the eddy. Typical eddies which contained 20 times the long-time mean u'v' have been observed. The momentum transfer produced by the typical eddy determines the rate of boundary growth. The typical eddy is the cause of the significant velocity fluctuations in the outer region of turbulent boundary layers. The typical eddies of this investigation are concluded to be vortex rings. based both .on the visualization. (see Figures 4.1 through 4.5). and the fact that they contain regions of positive and negative vorticity. (see Figure 3.40). The mean flow field of the typical eddy is shown in Figure 3.42. 53 FIGURES 54 3mH> mafia 3w; nah Hearse ucflfi >u0umuonmq musuosuum mucmaspnse H.N wnswfim .J. > ez_on .o.: zo_._._m_:ou< Skull)“ k mzou >mzo: mzmmxum 3.11::i [I L 2e_kurdazou rm. .O.m||||.|' . leall .o.=~ 1 .m.:~||||iu j...ulll.....m.MWHBII....|!.... :oflummwamsww> umzma zpmvcsoa unwasnusu owaa Hana mo mowumo ummmq N.N madman mommzz 855$ mzmn x523 20$ 20 09 ~29“: _ mmmfi WT Illll (NI. _ ¢ .lml. — u mood nmzz a F . . .. A S\\\\\\\\\\\N\\\\\\\N\\\\\\\\\\\\\\\\\\\\\\\\\\\_\\\\\\\K_.._ Sam 4405C _ .em _ i no .9) 1E. . _ fl _ zodlllv CLO / /1J/H_ G _ Illaem.mW/;H”WV_ Ill/I _ Lhr” _ x _ mzmn_ m > \_ :om5¢n \ gong: 2030236 56 CALIBRATION PROGRAMS Data Acquisition ADCAL computer and AID synchronization RUN18K collects urwire calibration data Data Reduction OONVOL converts bits/millivolt to voltages Data Analysis CALFIT determines Collis and Williams parameters CALDRW visual check of calibration data MEAN VELOCITY PROFILE PROGRAMS Data Acquisition ADCAL computer and AID synchronization RUN18K collects mean velocity profile data Data Reduction CONVOL converts bits/millivolt to velocities Data Analysis LINVP8 plots y vs U. for four profiles simultaneously VELPRl determines various mean velocity profile parameters LINVP7 plots y/O vs U/U; LGAXS4 plots U/U; vs Rey + UYPLS3 plots uf vs y VELP51 plots (U;-?U)Iut vs (y-ut)I(6.-U;) Figure 2.3 velocity profile data acquisition. reduction. and analysis program sequence. 57 )r ' \ L/‘N L h \ A .Am3mw> unemV |i / J! mm<0 mm-<——- (AL/Bo. I... 2.0m .v m... X< . wmomn. enema muwuauno> mo uwumEmrum ¢.N muswwm FL: ..eeodfiq m_x<.mmomn 39%?de _ a? m _ mi x . 58 CALIBRATION PROGRAMS Data Acquisition ADCAL computer and AID synchronization RUN18K collects vorticity probe calibration data Data Reduction CONVOL convert to voltages Data Analysis CALFIT determines the Collis and Williams coefficients CALDRW visual check of calibration data VORTICITY PROBE PROGRAMS Data Acquisition ADCAL computer and AID synchronization RUN18K collects vorticity probe data Data Reduction CONVOL convert to velocities CPCN calculates the CP and CN parameters for the x-wires VELRED calculates the long time record of fluctuating quantities PFILM.PBFILM separates the information recorded from the films into eight groups corresponding to the eight zones of the typical eddy ENSMB4 selects. scales. and averages the segments of the data records produced by VELRED which correspond to typical eddies striking the vorticity probe NORMAL normalizes the ensembled vorticity probe data ENSENS averages the vorticity probe data over the range of Reynolds numbers Data Analysis PLOTTR plots the long time records. and the ensembled data ‘ MAXMIN determines the maximums. minimums. means. and RMS values of the ensembled and normalized data EDYPLT plots the ensembled and normalized data Figure 2.5 Vorticity probe data acquisition, reduction. and analysis program sequence. 59 :ofiummfiamsmfi> uozma xumvcson ucofisnuuu Nmma poucfiB use Hmma Hfimm mo mofiuao momma o.~ mpswfim acméz A] .. 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I 3 3 DI ...... .... I 4h“: ea: I: he: ovzv g ,=u=u I! 99 3O Eddies Zone 1 87 Eddies Zone 2 l A 111 Eddies W " Zone 3 " " 140 Eddies § § 1 . . = A4— Zone 4 ‘F 90 Eddies ' - - :44 Zone 5 A 107 Eddies +H—H—H—H—‘ v Zone 6 p 4F 60 Eddies Zone 7 ‘ L T I U 55 Eddies ‘44 Zone 8 #— ‘ d d d Ju- db .‘L 1!- 1. db co- 4. u“- +- J 1 r 4 f Figure 3.35 The ensemble averaged U'/Um data shown in Figures 3.21 and 3.22 averaged over the four Reynolds numbers. Zones 1—8 are shown. One vertical division is 0.008. 3O Eddies Zone 1 87 Eddies Zone 2 111 Eddies Zone 3 140 Eddies Zone 4 90 Eddies Zone 5 107 Eddies Zone 6 60 Eddies Zone 7 55 Eddies one 8 Figure 3.36 The ensemble averaged V'/Uw data shown in Figures 3.23 and 3.24 averaged over the four Reynolds numbers. Zones 1-8 are shown. One vertical division is 0.008. 101 30 Eddies Zone 1 87 Eddies : ; . ; . . : ... 4+ : ._4 111.1 : : . ..+ :e— Zone 2 0 ‘xv L—p — —— — —+ —— — — ‘ . " ' lll Eddies A A 1 A L 1 1 l A 1 l A j l A L 1 1 Li I 1 zone 3 1 1 u I I I r 1 1 fi“ fj ' ' ' ‘ ' '—' ' I 1L J» _ — —— A L — — — _— — Zone 4 W b . l 90 Eddies 1 _A A 4 A A J l 1 1 l l J J J_._ zone 5 V 1 V T 1 1 j at 1 fl j I j 1 I —' j—vfi ‘ *7 db 1b 4‘ . 107 Eddies —~+ % 41; § ; : : 4 . *~+—‘ %*%7: ; : % 4 £_:;— Zone 6 1 V fir — _ — — ‘ — — —P — _ _ — — L f 0 60 Eddies Zone 7 db G. qb 55 Eddies Zone 8 Figure 3.37 The ensemble averaged u'v'/(Umz) data shown in Figures 3.25 and 3.26 averaged over the four Reynolds numbers. are shown. One vertical division is 0.0004. dicate the longtime mean value of 0.000634. Zones 1-8 The dashed lines in— 102 I 9 3 > E L T m NAM 1“}. :k. “AL 30 Eddies Zone 1 87 Eddies Zone 2 111 Eddies Zone 3 140 Eddies Zone 4 90 Eddies Zone 5 107 Eddies Zone 6 60 Eddies Zone 7 55 Eddies Zone 8 Figure 3.38 The ensemble averaged (dv'dx)*(6/Um) data shown in Figures 3.27 and 3.28 averaged over the four Reynolds numbers. Zones 1—8 are shown. One vertical division is 0.01. 30 Eddies Zone 1 87 Eddies Zone 2 111 Eddies Zone 3 140 Eddies Zone 4 90 Eddies Zone 5 107 Eddies Zone 6 60 Eddies Zone 7 55 Eddies Zone 8 Figure 3.39 The ensemble averaged (du'/dy)*(6/Um) data shown in Figures 3.29 and 3.30 averaged over the four Reynolds numbers. Zones 1-8 are shown. One vertical division is 0.014. 104 L A A J J. L au- 4%. d d A U 1 fi A J 1' . A n1};::$:::::::i 1' v 1 V / fl 1 V U ////.\\13\\ T W 1 j I T V J L 30 Eddies Zone 1 87 Eddies Zone 2 111 Eddies Zone 3 140 Eddies Zone 4 9O Eddies Zone 5 107 Eddies Zone 6 60 Eddies Zone 7 55 Eddies Zone 8 Figure 3.40 The ensemble averaged Wz'/(6/Um) data shown in Figures 3.31 and 3.32 averaged over the four Reynolds numbers. One vertical division is 0.03. are shown. Zones 1-8 105 30 Eddies Zone 1 87 Eddies Zone 2 111 Eddies Zone 3 \ 140 Eddies Zone 4 90 Eddies Zone 5 107 Eddies Zone 6 60 Eddies Zone 7 55 Eddies Figure 3.41 The ensemble averaged Sxy'/(0/Uw) data shown in Figures 3.33 and 3.34 averaged over the four Reynolds numbers. Zones 1—8 are shown. One vertical division is 0.012. 106 SMOKE ’ . BOUNDARY Flow Direction Figure 3.42 Mean flow field of an ideal typical eddy 107 Zones 1-6 tycoons»! ounns IN! V . m 7 0 . 4T ‘ o 1 o . 0 . u w Zones 1-8 lounns fl 0 ¢ ‘VfiV—vfi *‘v '_T 'V V —1 «Dunn: um .. ‘ Flow Figure 3.43 Grand ensemble average over zones 1-6, zones 1-8, and zones 7,8 of U'/Um. One vertical division is 0.006. 108 v w Zones 1-6 maxi... SW. 4 Time 5 1 E 3 . Flow atoms “5 ' Figure 3.44 Grand ensemble average over zones 1-6, zones 1-8, and zones 7,8 of v'lUm. One vertical division is 0.008. Time WM 109 Zones 1-6 fifij j fi v w 14' V V V ' a W j_' v v j ‘v’fifi‘v *v V v owns 815 Flow «— Figure 3.45 Grand ensemble average over zones 1-6, zones 1-8, and zones 7,8 of u'v'/(Um**2). One vertical division is 0.0004. WI. 110 Zones 1-6 54m») WI. v Zones 7 and 8 DLM .119 14 0% “ U 0 . I ‘2 .- H'w‘fi j ' ' ' .‘j 7 . w 0' “9% an; '5' Flow 4— Figure 3.46 Grand ensemble average over zones 1-6, zones 1-8, and zones 7,8 of (dv'/dx)*(6/Um). One vertical division is 0.01. Time ——> 111 Zones 1-6 om: A 1 Flow Figure 3.47 Grand ensemble average over zones 1-6, zones 1-8, and zones 7,8 of (du'/dy)*(6/Um). One vertical division is 0.012. Time ——> 112 Zones 1-6 ' m Zones7and8 ‘V 115 Flow «— 7".\x.!‘\~e . 4<~ f 4\ C: E :: u'v' W"\ 1 U002 \ I I 0' s. p tg"".“'=ar - a ------ A -‘,-..b--------;'--- “w. ----- «'43-- Wz'(e/u..) ' W 1 v o a: f \‘ .‘ ‘1 ' \ .' ‘. :5. A L._ ‘ ' 23.111 .AL .' Ella/U) M’WY‘LEQK-XV‘ " i----.:_- _-_-_ ‘3' ---- dx m ‘5 ' x. n/ ‘?Hu; ’ \ I Q I" if I t ‘ d ML L LWL“ - *7 L * A - fiw/u-) :Qu--.‘.¢.“.$ ....... p ooooooooo b.... 03‘..----.'«---. ,1 °. .-°’ ‘. g \ fifr r f w :W"\ 4” .-f. f . j Sxy'(6/Um) "- "'3 W“: 71"“ '''' ' ‘ 72° """ ‘ ‘ ' ' V‘ wauzfiéz‘i' fi Figure 3.51 Grand ensemble averages over zones 1-8 of: Sxy'*(6/Um), (du'/dy)*(6/Um), (dv'/dx)*(6/Um), Wz'*(6/Um), u'v'/ The vertical lines represent the normalized eddy boundaries. U'/Uw, V'/Um, 116 Time Flow .____.. .'.... \7 7 03 / 11....— , ‘ Wz' (e/um) "WK """" f " " """"" ”$1.. ......... -1 .- ...‘ . ...-oncoooooo .-- --.--.oo y'afLfir"), "7 41:; ”all"; ?;¢r[~.irc. Ha Sxy' (e/Um) “I ‘. 3o, -’h I. ”r 7"»7 (x: if..- 01* -i/ L\-.--;;_' ::::;;;;J7‘<:°"°"'"""7')""':;}’-‘===*"“‘:L m mv—vvv-vv-vvvv" vvwvvv ' vvvvvvvvvvvvwv' } (j \- . l A L _._u.' \ AJ/ 11.. _ \47 Figure 3.52 Grand ensemble averages over zones 7,8 of: U'/Uw, V'/Um, SXY'*(6/Uoo). (dU'/dy)*(6/Um). (dv'ldx)*(e/U..), Wz'*(e/U..), U'V'/ (Um**2). The vertical lines represent the normalized eddy boundaries. 117 «U00 (b) chm rr'rilrvc'rrryrlr vrr'vr'vrrr’,, '7rr—r Figure 4.1 Example of a typical eddy in a turbulent boundary layer. Uan = 3.27 ft/s. The probe is 3 inches from the wall. 118 (a) (b) 'I’II'V'I'V"(IVI’I’Ir'rr'I’VI'I’7' rfi—r— Figure 4.2 Example of a typical eddy in a turbulent boundary layer. Um = 3.27 ft/s. The probe is 3 inches from the wall, and in inter— secting the eddy in Zone 4. 119 (b) I’,””",””I””’I'I'IIIVVIVIVIV'I' Figure 4.3 Example of a typical eddy in a turbulent boundary layer. Um = 3.27 ft/s. The probe is 3 inches from the wall, and is inter- secting the eddy in Zone 4. 120 @Am ... “A 'l’lrlr r r " ”"rrzr,r,,,,,”' rrr: Figure 4.4 Example of a typical eddy in a turbulent boundary layer. Um = 3.27 ft/s. The probe is 3 inches from the wall, and is inter- secting the eddy in Zone 4. 121 (a) (b) r’r77rrrrrrrrrrrr’rrrr’lrr,r’rrfi—f-V Figure 4.5 Example of a typical eddy in a turbulent boundary layer. Um = 3.27 ft/s. The probe is 3 inches from the wall, and is inter- secting the eddy in Zone 6. 122 cuwcmauko mcu >2 vmuwflmfiuo: mmcou xwvm Hmowa%u mo cofiufiawwmv m.oonm o.q muswfim m3w>mm ,/// . r. . e . \Iy \ \ ~3u>u3 \\\\\. a till. I . do. no 390.. . \ J\ IIH. h 03m>mu J/////// .////// unuq o; /, nulw- ... 1:. fl Au. l\ . no. m / 123 .NmNH .qooo.o ma coflmfl>au HmUfiuum> MEo .sccw amongsu ecu we meON m>ww mm: new ED\.>.= mmmpum meoczwm vowmpw>m anEmmco wwNHHmEpc: m.ouamm ~.q opswwm N _1 \ mm” I‘lllll Auu1xauunw. A:|u:::|)(\\\\\uniu __uVJ\0 . xxx». 0 . . . 0 0 .|+1|:‘. .ronnrrb . s|||mw maaIIl\Ia\aIIIIII\lllllnuuu||||||||\||111Ir N n_ V1 ullll _ meEwmzm l 4m>mg z_¢mm§DZ 124 .NMNH n om .m8:\.>.: .8=\.> .8:\.5 mo coausnauuwfiv wowmum>m mHaEmmcm vcmuw wwNfiHmEuoc m.ooamm w.q muswwm «30:; cocooi.. N8: .>.= 38:; ulunlnnl. UI. |.:1IIILIIIIIIII|I! .Iu, HwuIlIhurmulllllIIIllnlummmmmumlmmumurllll No.0 . . . 1....l.luu.l..l...u.llfllllllllll 1 d d d \I No; 1 mm. > 300+ l . 59:4 «0.: 4 filmy! l nNHnmuIm HA I .l .l nl |||||| l ....h.\1 I g 3: .nn ... cacao-cu 3 pong: TABLES 125 Table 2.1 Collis and Williams Coefficients This table contains the values of the Collis and Williams coefficients calculated with program CALFIT. and the values used in the data reduction. for the four flow speeds of this investigation. The standard deviations of the curve fits calculated by CALFIT are also included. The Collis and Williams relation is: E2 = A + B-Qn. where E is the hot-wire output voltage. 0 is the flow velocity, A. B. and n are the Collis and Williams coefficients. The hot-wire associated with a set of parameters is denoted by; TOPBPAR. BOTrPRR. BACK-X. or. FORrX. These represent the tap parallel wire, the bottom parallel wire, the x-wire which is slanted downstream, and the x-wire which is slanted upstream, while the probe is in the experiment orientation shown in Figure 2.4. U; = 3.27 ft/s Values determined with CALFIT: A B STD n WIRE: 9.967 2.146 0.018108 0.53 TOP-PAR 9.914 2.168 0.016648 0.52 BOT-2K8 10.34 1.854 0.015845 0.52 BACK-X 10.34 2.248 0.019801 0.49 FORPX Table 2.1 (continued) 0; = 3.27 ft/s Manually chosen values: A 9.373 9.393 9.896 10.04 B 2.718 2.669 2.283 2.538 U; = 6.10 ft/s Values determined with CALFIT: A B 12.02 0.7543 11.90 0.7487 10.10 1.9840 12.24 0.7526 U, = 6.10 ft/s 126 STD 0.031344 0.027307 0.024931 0.023292 STD 0.01936 0.01958 0.008750 0.01213 Manually chosen values: A 9.243 9.143 9.604 9.796 B 2.817 2.796 2.391 2.583 05 = 10.7 ft/s Vhlues determined with CALFIT: A 6.212 6.330 7.335 6.883 B 5.240 5.172 4.388 4.935 U; - 10.7 ft/s Manually chosen values: A 9.628 9.695 10.18 10.11 B 2.497 2.467 2.098 2.347 STD 0.030122 0.030002 0.009133 0.023073 STD 0.013208 0.012938 0.011119 0.014503 STD 0.013056 0.012942 0.011418 0.014216 WIRE: TOP-PAR BOTLPAR BACK-X FORrX WIRE: TOP-PAR BOT-BAR BACK-X FORrX WIRE: TOP-PAR BOT-PAR BACK-X FOR?! WIRE: TOPbPAR BOT-PAR BACKFX FORrX WIRE: TOP-PAR BOTLPAR BACK-X FORrX Table 2.1 (continued) 0; = 17.5 ft/s Values determined with CALFIT: A 11.82 11.72 13.19 11.89 B 1.418 1.447 0.640 1.511 U; = 17.5 ft/s Manually chosen values: A 9.872 9.947 10.332 10.459 B 2.538 2.473 2.137 2.351 127 STD 0.004546 0.004326 0.004492 0.003893 STD 0.005116 0.004867 0.006326 0.004207 WIRE: TOP-PAR BOGLPAR BACK-X FORrX WIRE: TOP-PAR BOT‘PAR BACK-X FORrX 128 mm.N Na.u malz on» «o .uoaea.om Ioououououl .oo.\au. a: ...aoaas as» A..a.aac cannon opens cocoonueo can: u a N." oaaah 129 wwwnc.o hunc.c mchvoc.o vcmcc.c an».w¢~ unwmn.c ov.a cu w chnc.o ommc.o aaaece.c Hanoo.c anv.mvu mmwnn.o um.a a v owvuo.o aww¢.c chemoc.c omwco.° cmv.vvn muchH.° va.w w v wae~c.o «Hao.c Heoeoe.c “ano¢.o cae.e¢H “can“.o as.» a m meaao.o ausc.o eunaoo.c nnmce.o mac.um~ caan~.o «a.p a m «aafio.o «eso.° «soooc.c «Hoco.c oev.sm~ oe~e~.c an.“ s m 23 Cid: 3: 27...: Aux: Gamma: amazuuu .. macaw amazunnunam mmoqm.anm . ae\ue .. a . amzHa loam unnunO .auouefluunm ouuuoum ham00nu> use: aha" mush m.N nunsa 130 mauflc.ou nuvo.c saveoc.c wamco.c men.uau «anfiu.o H».« e a mpaoo.cu nano.o unavoo.c muncc.o muv.mcn npmuu.c "a.s m N ununc.on mue°.c aesvco.c «uncc.c nas.mau ccefiu.o 4m.m e a pcoac.ou oo¢¢.c mfipmoo.c Hauco.c «aa.mau avuuu.c ea.” n a sumac.on mano.o nsnuec.c neucc.° vuc.«am Hucmu.c as.“ e H mucfic.cu ~cv°.c “cemoo.c Havoc.c can.mau nfiuuu.o sm.m m a .aa. A«\..nac Anna Au\..aav A.\HV Aoomwuuc «BEA .. 23m Euném Bedlam . ~88 .. a . 23+.» .25 emu: neuoce.o u .a\=v oo.\uc as.“ u 4: Aeonaasaao. m.“ cap.a 131 ehwcc.cl abdo.c kuvoo.c shaco.c www.mhw nvmmm.° «v.w n N Hhmoo.cl NOH¢.o movuoo.o Nunac.o Nwm.fith cwmvm.o 50.5 v N schoo.eu ew~c.c semeoc.° «aficc.c cup.~ne afiaum.o ca.a e a canoo.cn nsfio.o caaacc.c Hmfloc.c oea.vae ~e~mn.¢ an.» n a Hmmoo.ou us~o.° manhoo.c upcco.o mvn.anp unavn.o so.“ 4 fl socco.°n aefio.o thHeo.c uwcco.o ceu.cas mmuvm.o ma.“ m a Aaav Au\u.e«v Anus Au\u.a«v Auxnv Accumuuv «ES.» . . 23m ELI—am Bedlam . he}... . . a . 53+» .83 Se: “cacao.o u .a\=a umm\am «.93 u a: Aeouuauaooc m.u sagas 132 m¢»mc.cu HVHo.o eamamo.c pHeoc.c Hma.H»~ scepn.o mm.HH » H »¢nso.°: HuHo.c H»eemo.c HHwoo.o was.Ham memo¢.o «H.cH w H eevnc.ou aaoo.c Hunene.o »»ncc.c H».~H~H eeuvv.c Hc.a n H nocmo.c- mecc.o ccoocc.c cacao.o c~.H»»H euuen.c »H.~ u H An: Ania: 2.3 A335. 3:. Aoommflv «BE-» .. 23m «BEAAS $8.515 . 3:3. .. a . 53+» .33 $3» eeHcco.o u Aa\=c omm\»m a.»H u 1: AeouuHunoo. m.u oHpaa 133 moamc.c :nmnc.¢ mnaoc.o naono.c wamoo.o auacc.c Nnuoc.c hnnoo.c hNooo.c nauoc.o npnoo.o onvcc.o ohnoc.° Andy mNHzHIH wm>zHA Iouu unnuuc namo.° NHOH.¢ acafi.e naoH.o anH.c mann.o #:Nn.c mnaa.¢ nwnn.c HHNH.° N»HH.° tha.o oenn.c AM\u.umv Hmtanc.o echono.° wanenc.c wwhunc.c auwcnc.o vaomcc.o cowhc°.o huphoc.o Nonaoc.o anamoo.o nuanoc.c hmmhco.c aunaoo.c Addy Hwonc.c anhuc.° hcafi°.o annao.o enmuc.c. ccHH¢.c occnc.c oeoac.c o~c~c.o ncwco.c Nnmoc.c hHHHc.o navnc.c Auxu.u«v mmoqm NNHZHIHInHm mmOAmlnHm nnwouooc.c .4 emc.mmu awn.wHH nou.acu mae.m°u onn.ceu nem.eon new.aa www.mOH cah.voH mno.am non.ncn chn.NoH cah.won ..\Hv »e\ae u Aa\av Hwavn.c VNHVH.° catnu.c aammn.c nuanu.o acvmn.c wcaun.c «cumu.o «humu.c cHaNn.° «bomu.c unumn.c maunn.c Aomwnuc. mw.a ac.m aw.n Vb.” Nb.h «0.x ch.h au.h an.” pw.h «a.» av.w ma.n am «as: HaaH HH.» v.~ .Haus 134 seucc.o «anc.c »~o»oo.o oHeoo.c we».MHm s»aun.e en.~H «H 4 seeec.c conc.c neHooc.c »nmoo.c van.»~m n»mmu.c »e.HH NH 4 cHocc.e nnmc.o soonc¢.c anmcc.c nes.»nm omamu.o ae.cH HH 4 a»occ.o »emo.c opveo°.c Hneco.c «44.n4m pucea.c am.a oH v »ueoo.o unnc.c nnHaco.o unecc.e asc.va mpan~.c an.» a e spHco.on pnec.c eHwaco.e Hvsoo.o »HH.H»« aseHu.o ov.» a v pnuoc.cu ome°.o nHmuuo.c apuuc.c Hmo.n»a ameHH.o Hm.e e e sneoo.ou anvo.c Hepsce.o 4H»co.o ma».eeu «HHHN.o an.» a m »»nco.on nevo.o aauHHo.c OMHHo.c omc.am~ oe»cu.o «H.» » m ca»oo.c- n»vo.c Haaseo.c »nseo.o a°¢.anu amncu.c 4H.» m N nN=H°.ou ncno.o evmoHc.o »»eHo.c H4».»n~ mn»»H.e p».v » a oecHo.cu sumo.o «shuHo.o chHc.o a»¢.nH~ s»»nH.c eu.v e H ¢~»°c.en ae¢°.o mnnHHc.c oech.¢ u»a.nv~ c»noa.o co.¢ » a 25v :\u.u.: 25V AuxaLHuv :\Hv Aeeaxuuv zquHu» macaw uuezHu»uaam maohmnnam »e\ae up: am aouu unnuuc ha.m hn.m mo.m at.” “a.“ :5 as Hu.m un.m no.m wa.u cm.u Anxuv magm> thhnn eeHcoo.c u Aa\=. av he nv mv Hv .mhm mc .92 (SHE nl 88.: a :35 u 3: .uuouoa-uam ouauoum humoo~o> use! mama much n.N onfiuh 138 as.» ev.H «H.nenH cemv.o mane.o »F.m ha.» an «a.» ne.H n».¢e~H ae~¢.o »»He.o um.m Ha.» pm »».» we.H aa.HecH nmem.¢ nomn.o “a.” as.“ mm mm.» »V.H on.»me ~»mu.c vaun.o nH.~ »~.n mm He.p mm.H ue.HHv maeH.o hmeu.o m¢.H »a.c Hm Auwv Aumv Aufiv Au\uv u a an e .a «as »»3m> .m»» mo .cz HEB ($22» In meHoco.c u Aa\=v aco.c « cmu.¢ u up: AuoaumunOev m.u euneh 139 we.» nu.» ma.» mm.h me.“ at." av.“ vv.H u».acp~ ma.thu ww.Nmuu hh.mmmn ex an.¢ cm.m wc.m mm.« «H ...w hc.on om.a «v.o mm.» Aa\mv «QAN> . pmmn.° sanp.c :36 2.3.: pHam.c cec».c anau.c »HH¢.° Andy .qu c .a Banana neHcco.c u .a\=. mm mm an av mam no .92 .nlapmzHunu ac°.c « aem.c a a»: Avonumuuoov m.N empeh 140 ah.m an.» an.» an.» cm.a on.“ an.“ nm.a ch.ouwm om.mvwm on.manu hw.Van on “ham. Hewm. hum". noun. Aumv @ o HE... S... 8.2 o cv»e.c an." oa.aH e 23... Ha." «HdH c ee»u.o no." an.»H Aumv Adm. Aaxmv .a saw ashfi» season eeHcoc.c u .a\=v Avonauuuoov an an an nu m.N swash 141 ea.» ma.” ha.» on.a we.» an." on.n at.“ we.“ a¢.n Nv.avn mm.emn ta.muh wh.evh hu.vmn ea chem.c acen.c av.m eH.m VHmm.c sacn.o »V.n »H.n «Hmv.c heme.o as.” nu.m manv.c e»»e.c ep.m ¢~.n as»m.¢ «amn.o Hm.n «H.m AuH. .uH. .aH. A.\u. e .o «as aahm> Humane nuueHoco.o u Aa\=. av av mv mv A? man :6 .oz .njupmzHuuu noo.o « «NH.o u up: Hmm3m> scum «agape ..uono-su.m .HHuoum »uaooHo> a..: H~»H HH.» e.~ .Haaa 142 an.» «a.» aa.h na.h ha.h ha.h wa.b an.” 9%.” nv.H nv.u at." wv.H wv.~ mm.aw¢u hw.N¢mn hw.hnmn mn.hamu nw.mmmn Hh.muau an.hhun cu eamm.o n»vn.c mm.m ca.m «mvv.c neve.c es.n Ho.» asve.o aHme.o a».m uo.e n»n¢.° ceee.o «a.m we.» Hs¢¢.e acne.o e».n Ha.» emmv.c mane.° ee.m aa.n »»~e.c HHue.c Hn.m as.“ AeHv AaH. .aH. Aa\u. c .o as» ash~> Humane «HpeHooo.c u .a\=v ~°.c fl av 5% mt av at an an .m»» me .oz nuuapmzHuuu vu.c u up: Avonumuaocv w.n cuppa 143 mm.» an.m «n.n mm.» mw.m mm.w av.H OV.H c¢.H av.H NV.“ NV.” aa.omau cm.whmu cw.mvnu an.chHN «v.55aa mh.nwhn on :36 can... 36 2.3 nevc.o vune.o sH.v He.°H Ham¢.c enHe.c ao.v an.cH soH¢.o a»»m.¢ e».n av.cH 82.5 2%... He...” 35H necm.o «mav.c »o.m Hu.oH .aHe AaHV .aHv ..\u. o .o as» a»4m> . »baa=o «HueHooo.c u .a\av Hm av av mv me He mam no .cz nsJapmszun eoe.o « oem.o u up: Avouaauaeev w.N eunah 144 om.HH n».H mm.»cmu Hc»~.o nan.o e4.“ «a.eH a. eu.cH H».H Hn.nnmu u»m~.o oe¢¢.o on." Ha.»H »e ev.¢H a¢.H ma.»Hau enum.o sHac.c c».~ 4H.»H n4 an.cH »v.H ea.omau eamm.o ¢aa¢.c as." Hu.pH mv »~.cH e¢.H H».amom anvm.c »acu.c on." ea.»H H4 «u.oH e¢.H nm.eHHn eenm.c naH».° as.“ Hm.»H an mu.OH e¢.H 4a.a»on oHnm.° aHH».e we." ea.»H hm «o.OH »¢.H n».ncna p»»~.c cpnc.o em.H as.eH mm ands Ian .aHV A.\cv e m ea c .o as» aa3m> .maa mo .oz Banana unlapmzHun- »eeHoco.o u .a\av ec.o « 4n.o u up: Amonuuuuoov w.N o—aafi 145 Thble 2.7 Correction Coefficients CP and CN The following correction coefficients. CP and CN. were input to program VELRED, to correct for the slight misalignment of the "x-wires". Ideally the x-wires are perpendicular to each other. and inclined at 45 A degree angles with respect to the mean flow. The values of CP and CN for the ideal case are +1 and -1. respectively. Re C? CN 729.9 0.849 -0.762 1397. 0.953 -0.815 2376. 1.003 -0.997 3116. 1.016 -1.097 Thble 3.1 R9 1],,‘, (ft/s) 899 (inches) 6. (inches) 0 (inches) H G du/dy at the wall y* at the last point of the du/dy calculation (prior to y shift) (u/pg (ft /sec) utn (ft/sec) “to (ft/sec) cf t 0.00005 u l0; tn u In, 1c Summary of Fall 736.9 3.24 3.97 0.673 0.453 1.49 6.57 157.4 £0.25 7.30 1.66E-4 0.1617 t0.0001 0.155 $0.001 0.0046 0.0499 0.0478 146 1365. 5.93 3.77 0.658 0.456 1.44 7.92 320. £3. 5.82 1.65E-4 0.230 10.008 0.258 10.002 0.0038 0.0388 0.0435 2742. 10.2 4.38 0.759 0.534 1.42 8.63 740. $34. 7.06 1.65E-4 0.349 $0.008 0.407 10.005 0.0032 0.0342 0.0399 1979 Mean Velocity Profile Parameters 3827. 0.515 0.397 1.30 8.79 0.768 10.007 0.0032 0.0269 0.040 Thble 3.2 U; (ft/s) (inches) 5 (inches) 0 (inches) G du/dy at the wall y+ at the last point of the du/dy calculation (prior to y shift) (u/p; (ft Isec) urn (ft/sec) “1c (ft/sec) °£ : 0.00005 urn/U; utc/Ug Summary of Fall 729.9 3.27 3.72 0.667 0.451 1.48 8.17 99. $7. 7.67 16.8E-4 0.129 $0.005 0.162 $0.001 0.0049 0.0394 0.0495 147 1397. 6.10 3.92 0.666 0.459 1.45 7.95 340. $38. 10.7 16.7Er4 0.238 $0.013 0.266 $0.002 0.0038 0.0390 0.0436 2376. 10.7 4.17 0.616 0.444 1.40 8.51 776. $26. 12.57 16.7EF4 0.360 $0.006 0.448 $0.003 0.0035 0.0336 0.0419 1981 Mean Velocity Profile Parameters 3116. 17.5 2.93 0.519 0.357 1.46 10.2 1700. $400. 13.4 16.7E-4 0.536 $0.06 0.643 $0.006 0.0027 0.0306 0.0367 148 Thble 3.3 Typical Eddy Length Scale Data Reference. Fall 1979 Mean Velocity Profile Parameters: R9 736.9 1365. 2742. 3827. U; (ft/s) 3.24 5.93 10.2 19.2 (m/s) 0.987 1.81 3.11 5.85 699 3.97 3.77 4.38 4.20 (inches) (meters) 0.101 0.0957 0.111 0.107 0 (mm) 11.5 11.6 13.6 10.1 (feet) 0.0377 0.0380 0.0445 0.0331 uto 0.0472 0.0786 0.124 0.234 (m/s) utn 0.0494 0.0701 0.106 0.157 (m/s) (p/g) 1.54E95 1.53Er5 1.53Er5 1.54Er5 (m /sec) Percent change in Cxt and Cyt from sample size of 100 to 200 Cxt -6 -7 +3 +9 cyt '3 '6 +5 +6 Length scale data. sample size = 100 eddies ext (mm) 27.6 26.0 21.4 14.1 cyt (mm) 17.5 16.5 13.7 9.6 '3 (mm) 94.0 103. 103. 103. c 149 Table 3.3 (continued) Length scale data. sample size = 200 eddies (physical/scale) cIt (mm) 25.93 24.20 22.07 15.46 6,, (mm) 17.03 15.55 14.39 10.22 '7; (mm) 90.66 100.4 102.3 101.1 (in) 3.57 3.95 4.03 3.93 Ext/0 2.26 2.09 1.62 1.53 Eytle 1.43 1.34 1.05 1.01 ic/e 7.33 3.66 7.52 10.0 Ext/699 0.257 0.252 0.199 0.144 Egt/sgg 0.163 0.162 0.130 0.0955 70/69, 0.397 1.049 0.922 0.945 (Ext-uTc-p)/u 79.6 124. 179. 235. ('§t-utc.p)/p 52.2 79.9 117. 155. 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Nam.ma coHumuanmo mufizuuom mHaEmm 9 xfivcmam< 2181 Appendix C Example of Collis and Williams Coefficients A, B, and N. 2 N E = A+B~Q E: voltage Q: flowrate (FT/S) 2 STD: standard deviation in (volts) 0100 01 17000 1 0: 3.239 0- 3.003 070-0.007032 0-0.30 0100 01 17000 2 0- 3.000 0- 3.313 070-0.000001 0-0.31 0100 01 17000 3 0- 0.107 0- 3.190 070-0.000730 0-0.32 0100 01 17000 4 0- 0.303 0- 4.009 070-0.000303 0-0.33 0100 01 17000 3 0- 0.074 0- 4.011 070-0 000439 0u0.34 0100 01 17000 0 0- 7.224 0- 4.332 070-0.000299 0-0.33 0100 01 17000 7 0- 7.330 0- 4.111 070-0.000100 0-0.30 0100 01 17000 0 0- 7.007 0- 3.007 070-0.000027 0-0.37 0100 01 17000 9 0- 0.103 0- 3.077 070-0.003097 0-0.30 0100 01 1700010 0- 0.444 0- 3.401 070-0.003771 0-0.39 0100 01 1700011 0- 0.717 0- 3.290 070-0.003030 0-0.40 0100 01 1700012 0- 0.900 0- 3.120 070-o.003331 0-0.41 0100 01 1700013 0- 9.210 0- 2.903 070-0.003419 0-0.42 0100 01 1700014 0- 9.440 0- 2.014 070-0.003312 0-0.43 0100 01 1700013 0- 9.002 0- 2.071 070-0.003211 0-0.44 0100 01 1700010 0- 9.073 0- 2.330 070-0.003110 0—0.43 0100 01 1700017 0-10.073 0- 2.412 070-0.003027 0-0.40 0100 01 1700010 0-10.200 0- 2.294 070-0.004944 0-0.47 0100 01 1700019 0-10.432 0- 2.102 070-0.004009 0-0.40 0100 01 1700020 0-10.029 0- 2.077 070-0.004000 0-0.49 0100 01 1700021 0-10 799 0- 1.970 070-0.004740 0-0.30 0100 01 1700022 0-10.903 0- 1.004 070-0.004000 0-0.31 0100 01 1700023 0-11.121 0- 1.793 070-0.004042 0-0.32 0100 01 1700024 0-11.272 0- 1.711 070-0.004000 0—0.33 0100 01 1700023 0-11.410 0- 1.032 070-0.004370 0-0.34 0100 01 1700020 0-11.330 0- 1.337 070—0.004330 0-0.33 0100 01 1700027 0-11.094 0- 1.403 070-o.004340 0-0.30 0100 01 1700020 0-11.023 0- 1.410 070—0.004340 0-0.37 0100 01 1700029 0-11.930 0- 1.334 070-0.004334 0-0.30 0100 01 1700030 0-12.072 0- 1.293 070-0.004370 0-0.39 0100 01 1700031 0-12.190 0- 1.233 070-0.004393 0-0.00 0100 01 1700032 0-12.304 0- 1.101 070-0.004020 0-0.01 0100 01 1700033 0-12.413 0- 1.129 070-0.004070 0-0.02 0100 01 1700034 0-12.320 0- 1.079 070-o.004721 0-0.03 0100 01 1700033 0-12.024 0- 1.032 07D-0.004770 0-0.04 0100 01 1700030 0-12.724 0- 0.907 070-0.004044 0-0.03 0100 01 1700037 0-12.023 0- 0.943 070-0.004910 0-0.00 0100 01 1700030 0-12.910 0- 0.904 070—0.004997 000.07 0100 01 1700039 0-13.000 0- 0.000 070-0.003004 0-0.00 0100 01 1700040 0-13.097 0- 0.029 070-0.003177 0-0.09 0100 01 1700041 '0-13.103 0- 0.794 070-0.003277 0-0.70 0100 01 1700042 0-13.200 0- 0.700 070-0.003301 0-0.71 0100 01 1700043 0-13.349 0- 0.729 070-0.003491 0-0.72 0100 01 1700044 0-13.429 0- 0.090 070-0.003007 0-0.73 0100 01 1700043 0-13.303 0- 0.009 070-0.003727 0-0.74 0100 01 1700040 0-13.300 0- 0.041 070-0.003031 0-0.73 0100 01 1700047 0-13.034 0- 0.013 070-0.003979 0-0.70 0100 01 1700040 0-13.720 0- 0.390 070-0.000111 0-0.77 0100 01 1700049 0-13.793 0- 0.300 070-o.000247 0-0.70 0100 01 1700030 0-13.002 0- 0.343 070.0.000307 0-0.79 0100 01 1700031 0-13.929 0- 0.320 070-0.000329 0-0.00 0100 01 1700032 0-13.993 0- 0.499 070—0.000073 0-0.01 0100 01 1700033 0.14.030 0- 0.479 070-0.000023 0-0.02 0100 01 1700034 0-14.117 0- 0.400 070-0.000974 0-0.03 0100 01 1700033 0-14.177 0- 0.442 070-o.007127 0-0.04 0100 01 1700030 0014.230 0- 0.424 070-0.007203 0-0.03 0100 01 1700037 0-14.293 0- 0.407 070-0.007440 0-0.00 0100 01 1700030 0-14.340 0- 0.391 070-0.007000 0-0.07 0100 01 1700039 0-14.403 0- 0.370 070-0.007702 0-0.00 0100 01 1700000 0-14.430 0- 0.301 070-0.007923 0-0.09 0100 01 1700001 0-14.300 0- 0.347 070-0.000091 0-0.90 0100 01 1700002 0-14.339 0- 0.333 070-0.000237 0-0.91 0100 01 1700003 0-14.009 0- 0.320 070-0.000423 0-0.92 0100 01 1700004 0-14.030 0- 0.300 070-0.000394 0-0.93 0100 01 1700003 0-14.700 0- 0.290 ITO-0.000703 0-0.94 0100 01 1700000 0-14.733 0- 0.204 070-0.000937 0—0.93 0100 01 1700007 0-14.790 0- 0.273 070-0.009110 0-0.90 0100 01 1700000 0-14.043 0- 0.203 070-0.009203 0-0.97 0100 01 1700009 0-14.007 0- 0.233 070-0.009439 0-0.90 0100 01 1700070 0-14.930 0- 0.243 070-0.009033 0-0 99 182 APPENDIX D Data Points Sampled Within the Typical Eddy The typical eddy length scale Cxt was measured during the reading of the films taken simultaneously with vorticity probe data. as mentioned in section 2.3.2. The mean value of Cxt was used' to calculate the number of points sampled with a typical eddy at each flow speed. The purpose of this was to verify that there were enough points sampled with the typical eddy to allow accurate derivatives to be calculated. A sample of the calculations made is shown below for U; = 3.27(ft/s). The results of these calculations, for the other flow speeds, will be stated. Reference information 00 : 3.27 ft/s Cxt : 30.9 mm 0.1014 ft 599 3 3.72 in 0.31 ft Total Data Points: 18000 Sampling Rate : 1000 Hz Points/Channel : 4500 Time for passage of an average size eddy: (0.01014 ft) ‘ ( s/3.27 ft) Data points/average size eddy: (0.0310 s) ‘ ( 1000 points/s) = 31.0 Time for passage of one boundary layer thickness: (0.0310 s 9 3.72 in)/(O.1014 ft ‘12) Data points/899: (0.0948 s) ‘ ( 1000 points/s) = 94.8 0.0310 s 0.0948 s 183 Number of boundary layer thicknesses which pass the probe in the long time record: 4500 points/ (94.8 points/delta) Duration of the long time record: (4500 points)/(1000 points/s) Reference information Time Data Time Data U0 C xt 599 3 Total Data Points: Sampling Rate Points/Channel 6.10 ft/s 25.36 mm 0.0832 ft 3.92 in 0.327 ft 18000 2500 Hz 4500 for passage of an average size eddy points/average size eddy for passage of one boundary layer thickness points/599 Number of boundary layer thicknesses which pass the probe in the long time record Duration of the long time record 47.5 899/record 4.5 s 0.0136 s 34.0 0.0534 s 133.5 33.7 1.8 184 Reference information: U. : 10.7 ft/s Cxt : 25.34 mm 0.0831 ft 699 : 4.17 in 0.347 ft Total Data Points: 18000 Sampling Rate : 5000 Hz Points/Channel : 4500 Time for passage of an average size eddy : 0.00777 s Data points/average size eddy : 38.83 Time for passage of one boundary layer thickness : 0.0325 s DItC points/599 3 162.5 Number of boundary layer thicknesses which pass the probe in the long time record : 27.7 Duration of the long time record : 0.9 s Reference information: U; : 17.5 ft/s cxt : 18.82 mm 0.0617 ft 599 ' 2.93 in 0.244 ft Total Data Points: 18000 Sampling Rate : 16000 Hz Points/Channel : 4500 Time for passage of an average size eddy : 0.00352 s Data points/average size eddy : 56.4 Time for passage of one boundary layer thickness : 0.0139 s Data points/599 : 222.9 Number of boundary layer thicknesses which pass the probe in the long time record : 20.2 Duration of the long time record : 0.28 s 185 APPENDIX E PARAMETERS USED IN THE NORMALIZATION OF THE VORTICITY PROBE DATA fluctuating dimensional normalizing quantity units factors v' ft/s 1/Ua 1/utn u' ft/s 1/U, 1/“tn u'v' (ft/s)2 (1mg)2 (l/utn)2 dv'ldx 1/s GIU, 0/1;tn du'ldy 1/8 O/Uo O/utn 'z' 1/s OIU. O/utn sxy' 1/s OIU, O/u.cu Note: the values of the normalization parameters were otained from the fall 1981 mean velocity profiles, and are included in table 3.2 REFERENCES 10. 11. 12. REFERENCES Brodkey, R.S., Wallace. J.M. and Eckelmann, H. 1974. J. Fluid Mech.. 63. 209. Corino, E.R. and Brodkey. R.S. 1969. A visual investigation of the wall region in turbulent flow. I. Fluid Mech.. 37. 1. Falco, R.E. 1974. Some comments on turbulent boundary layer structure inferred from the move- ments of a passive contaminant. AIAA Paper 74-99. Falco. R.E. 1977. A structural model of the turbulent boundary layer, in "Proceedings of the 14th Annual Meeting of SES." Nev. 14-16. Lehigh University. Fiedler, H.. and Head, M.R. 1966. "Intermittency Measure- ments in the Turbulent Boundary Layer," J. Fluid Mech. 50, 719-735. Grant, H.L. 1958. J. Fluid Mech.. 4. 149. Grass. A.J. 1971. Structural features of turbulent flow over smooth and rough boundaries. J. Fluid Mech.. 50. 233. Hams, F.B. and Nutant. 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Kibbens, V. and Blackwelder. R.F. 1970. Large scale motion in the intermittent region of a turbulent boundary layer. J. Fluid Mech.. 41. 284. Laufer. J. and Narayanan, M.A.B. 1971. Mean period of the turbulent production mechanism in a boundary layer. The Physics of Fluids. 14.1. 182. Lovett. J.A. 1982. M.S. thesis. Michigan State University. Lu, 8.8. and Willmarth. W.W. 1973. Measurements of the structure of the Reynolds stress in a turbulent boundary layer. J. Fluid Mech.. 60. 481. Purtell, L.P. 1978 The turbulent boundary layer at low Reynolds number. Ph.D. thesis, University of Maryland; University Microfilms cat.no. 79-06663. ' Rao, K.N.. Narasimha. R.. and Badri Narayanan. M.A. 1971. J. Fluid Mech.. 48. 339. ‘ Schraub. F.A.. et a1. 1964. "Use of Hydrogen Bubbles for Quantitative Determination of Time Dependent Velocity Fields in Low Speed Water Flows." Report MD-10. Thermosciences Div.. Mech. Engrg. Dept.. Stanford University. Schraub. F.A. and Kline. 8.1. 1965. ”A Study of the Structure of the Turbulent Boundary with and without Longitudinal Pressure Gradients." Stanford University. Mech. Engng. Dept. Rep. MD-12. ' Townsend. A.A. 1951. Proc. Camb. Phil. Soc.. 47. 375. Tritton. D.J. 1967. J. Fluid Mech.. 28. 439. Wallace. J.M.. Eckelmann, H.. and Brodkey, R.S. 1972. J. Fluid Mech.. 54. 39. ‘ ‘ Willmarth. W.'. and Lu. 8.8. 1972. Structure of the Reynolds stress near the wall. I. Fluid Mech.. 55. 65. Willmarth. '.W. and Tu. 8.1. 1967. Phys. Fluids. 10. 8134.- Willmarth. '.W. and Wooldridge. C.E. 1962. J. Fluid Mech.. 14. 187. ‘ ' Willmarth. W.W. and Wooldridge. C.E. 1966. AGARD- NATO Rep. no. 456.