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'1 IIHN'HHQ'WVM wk, .1?" 6'7 1*» r ‘WHEQC LIBRARY '- Michigan State = University ...-In w» - This is to certify that the dissertation entitled Transverse Vorticity Measurements In An Excited Two-Dimensiona1 Mixing Layer presented by Peter John Disimiie has been accepted towards fulfillment of the requirements for Ph. D. degree in Mechani ca] Engineering Qflfifégmc fl Major professor Date ggaa'z‘4sq / 98% MSU is an Affirmative Action/Equal Opportunity Institution 0-12771 IV4ESI_) RETURNING MATERIALS: ~ Piace in book drop to unnAmas remove this checkout from ...-uns-I-L. your record. FINES wii] be charged if book is returned after the date stamped below. RANSVRSE VORTICIT! NBASUREIENTS IN AN EXCITED NG-DIWSIONAL NIXING LAYER By Peter John Diainile A DISSERTATION Submitted to lichigan State University in partial fnlfillnent of the requirements for: the degree of DOCI‘OR OF PHILOSOPHY Depart-ent of lechanical Engineering 1984 3 I "7;.1 ‘/03 © Copyright by man man msxmn 1934 ABS'IIACI TRANSVHSE VORTICITY IEASUREIENTS IN AN EXCITED 'I‘O-DIIENSIONAL HIKING LAYER By Peter John Disinilc Transverse vorticity tine series have been obtained in a weakly excited. single-stream airing layer. Quasi-intantaneous vorticity tine series were obtained with a four-wire array and phase averaged transverse vorticity tine series were obtained with an X—array at each of the 414 points in the neasurenent grid. These data showed the regions of vortex fornation. amturation and decay. In addition to the detailed vorticity neasurenents in the raising layer. the upstrean tur- bulent boundary layer was also documented. The spatial locations of the distinctive vortex notions were found to be in good agree-ent with previous studies. Using the vorti- city field documentation. the spatial distribution and the temporal evolution of the prinary vortex notions in the airing layer were esan- ined. The spatial distribution revealed deep depressions 0‘ “1° Peter John Disimile vorticity contours en the high speed side of the mixing layer. The primary growth of the vertical structure was observed to be on the low speed side. In addition. it has been observed (over 19$ of the avail- able excitation cycle) that the core of the vertical structures appear to move at substantially different speeds. This detailed documentation of the vorticity field and the upstream turbulent boundary layer has also. i) produced information showing the tearing and fusing of vertical contours in the phase aver- aged plots and ii) shown the affects of excitation en the turbulent boundary layer . The quasi-instantaneous transverse vorticity measure-cuts indi- cate absolute values of peak vorticity which are an order of magnitude greater than those indicated by phase averaged transverse vorticity measurements. These large quasi-instantaneous transverse vorticity fluctuations indicate strong mixing throughout the core and periphery of the newly formed and saturated vertical structures. Althreugh the magnitude is approximately the same throughout these structures. the frequency of occurrence of these large fluctuations appears to be less on the low speed side of the newly formed vertex. I dedicate this Dissertation in nenery of my father. Peter Disimile ii AEINO'LEDGNENTS I would like to express ny appreciation to all the people that 1 have worked with during the past four years. Particularily. I would like to extend a warm thank you to the following people: 8. Kendall T. Skeltis l. lurawski J. Klewicki R. Iatsen J. Gafford S. Strachan R. Greene D. O'Reagan D. Iclenny S. Cary D. Smith P. Crowley R. Robb H. Pollack E. Gunckl e R. Aunan T. Gentner J. Peters 3. Fecia G. Statkievicx J. Daveust _ 1. Cole I. Brewer P. Hennessey B. Agar I. lose In addition. I would like to express my gratitude; 1b the men in the machine shop. especially D. Childs and S. Kurtx. Ib the people in DER. especially I. I. [roll and I. Perkins. Tb C. l" Klewicki fer the software development of PROCESS I and II. iii To S. Ali for acting as a vibration absorber. To 0. Ahned for an excellent drafting job. Tb C. B. Iark for the support. nourishment and encourage-cut she provided under very difficult conditions. 1b B. Curlett for the many long nights he spent cunehing data and helping me prepare this document. his hard work and dedication will never be forgotten. lb Dr. J. F. Fess for providing ne with the opportunity to design and construct a najer flow facility. To the NASA Ales Research Center. grant neniter: Dr. I. Inbesin. I would also like to express my appreciation to ny nether and brothers for a very special kind of encourage-cut they showed throughout my entire college career. To Rennie ny wife and friend. ny children. Ellie. Christopher and Michael it would not have been possible without your love. support and understanding. I thank you from the bottoa of ny heart and 1'. proud to be a part of you. iv TABLE OF CONTENTS LIST OF TABLES ................................................. viii LIST OF FIGURES .................................................. ix NOMENCLATURE ................................................... xiii CHAPTER PAGE 1 INTRODUCTION ...... l 1.1 Literature Review ..................................... 1 1.2 Present Experineut .................................... 4 1.3 Development of Facility ............................... 5 1.4 Objectives ............................................ 6 2 EXPERIIENTAL FACILITT'...................................... 7 2.1 Introduction .......................................... 7 2.2 Inlet Contraction highlights .......................... 7 2.3 The Boundary Layer Transition lodule .................. 8 2.4 The Entrainment ledule ............................... 10 2.5 Receiver/Fan Room .................................... 12 2.6 Computer Ioem/Labertory .............................. 12 3 Data Acquisition Facility ................................. 13 3.1 Introduction ......................................... 13 3.2 Pressure leasurement Facility ........................ 13 3.3 The Bet Iires ........................................ 14 3.4 Electronic Signal Conversion I Computer Facility 15 mBRIMTAL FACILITY MD Roma“ ......OOOOOOOOOOOOOOOOC 17 4.1 4.2 IntrOdnCtion 0.000.000.0000.........OOOOOOOOOOOCOOOOOO 17 heit‘tion loch‘ni” ......OOOOOOOOOOOO......OOOOOOOO. 17 4.3 not lire Alignment and Calibration ................... 19 4.4 4.3.1 LOU VQIOCIty Ctlibtdtion eeeeeeeaoeeeeeeeeeeeeea 19 4.3.2 Straight lire and Verticity PtOb. Ali‘n-ent eeeeeeeeeeeeeeeeeeeea........... 20 4.3.3 ant-'ir° c.11br‘tion eeeeeeeeeeeeoeeeeeeeeeeeeee 21 4.3.4 Hot-lire Positioning For Boundary Layer Surveys ......................... 22 Data Acquisition Strategy ............................ 23 ‘e‘el The Bound!!! L.y.r eeeeeeeeeeeeeeeeeeeeeeeeeeeee 23 4.4.2 n. Excitcd uix‘n‘ L.y°r ......OCCCOOOOOOOIOOOCO 24 UPSTRBAl BGINDARY LAYER RESULTS AND DISCUSION ............. 26 5.1 5.2 5.3 IntrOduct‘on 0.00.00.00.00......IIOOOCCOOCOO0.00.00... 2‘ Boundary Layer lean Velocity Profiles ................ 27 5.2.1 lid Plane lean Velocity Profiles ............... 27 5.2.2 Test of the Three-Dinmnsienality of the “O‘nv01001ty PtOfi-l.‘ ......OOIIOOOOOIOOOOOOOI. 29 5.2.3 The Influence of Excitation on the n..n v.10c1ty h0£il°3 ......OOIOCOOOOOOOOOOOO0. 30 5.2.4 The Influence of Phase Time on the “0“ v.1001t’ 0.00.00.00.00...OOOOOOCOO000...... 31 Streamvise Conponent of Turbulent Intensity .......... 32 5.3.1 lid Plane Turbulent Intensity Profiles ......... 32 5.3.2 The Three-Dinensienality of the Turbulent Int.n‘ity PtOfSIO' eeeeeeeeeeeeeeeeeeeeeeeeeeeee 32 5.3.3 Influence of the Phase Time on the Turbulent Int.n.tty PtOfil.‘ 00............OOOOOOOOOOOOOOO 33 vi RESULTS OF THE EXCITED lIXING LAYER INVESTIGATION ......... 34 6.1 6.2 6.3 6.4 6.5 6.6 Introanction 0.0.0.0.........OOOOOIOOOOOOOCCOO00...... 34 Spatial Distribution of the Phase Averaged Transverse Vorticity ................................. 35 Phase Averaged Streamwise v.1001ty PtOfil“ eeeoeeeeeeeeeeeeeeeeeoeeeeeeeeeeeaa. 4o Perturbed Phase Averaged Transverse vorticity contonr‘ ......OOOOCOOOOOO.........OOOOOOQQ. ‘0 Temporal Evolution of the Phase Averaged Transverse Vorticity ................................. 42 Quasi-Instantaneous Transverse Vorticity ............. 43 DISCUSSION OF VORTICITT IEASUEEIENTS IN AN “€11.”an mu 0.0.0..........COOOOOOOOOOOC.000...... 45 7.1 7.2 7.3 7.5 7.6 Intro‘uction 00.0.0000...0.0.0.000.........OOOOOOOOOOO 45 Phase Averaged Streamwise Velocity ................... 47 Evolution of the Phase Averaged Ttu'VOr‘. vorticity 0....0............OOOOOIOOOOOO... ‘8 7.3.1 Spatial Distribution of the Phase Averaged Transverse Vorticity ........................... 48 7.3.2 General Temporal Evolution of the Coherent vorticity conont‘ .........OOOOOOOOOOOOOOOOO.... 51 Global Evaluation of the Perturbed and I-wrtnrbod (.‘>1contonr‘ .0...OOOOOOOOOOOOOOOOIOO0.0 5‘ Phase Averaged Transverse Vorticity Time Series ...... 55 Quasi-Instantaneous Tiansverse Vorticity ............. 56 706.1 IntraduCtian eeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee 56 7.6.2 Quasi-Instantaneous Transverse vorticity Ti‘. soria. 0.0000000000000000...0.... 57 7.6.3 Quasi-Instantaneous Transverse vorti,°1ty sm‘ry 00...........OOOOOOOOOOOOO.... ‘0 vii 8 maUSIONS eeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee 62 WIXAMIC snmnmmNDITIONS eeeeeeeeeeeeeeeeeeeeeeeeeee 125 “Pmnlx B “mm DEVIATION 0? m3 I’M! vmmm eeeeeeeeeeee 135 APPENDIX C TEIPOEAL EVALUATION OF VOETTCITY CONTOUES ............. 144 was ...OCOOOOOOOOOOCOOOOOOOOO.......OOOOOOOOOOOO00.0.0.0... 153 viii LIST OF TABLES TABLE PAGE 6.1 Designation of the Phase Avgeraged Tine (i) for (uz)i contonr‘: '1 0.00.00.00.00........IOOOOOOOOOOOOOO0.... 39 6.2 Designation of the Phase Avgeraged Time (i) for i contonr‘: 'Pi ...0.0......OOOOOOOOOOOOOOOOOOO.....0... ‘2 6.3 Phase Averaged Transverse Vorticity Tine Series ............ 43 6.4 Quasi-Instantaneous Transverse Vericity .................... 44 A.1 Effect of Cubic Spline End Conditions on the Calculated Vorticity ............................... 127 3.1 st‘nd.rd ”0'1‘t10n‘ For x-.rr.y 0.0.0.0000.........IOOOOOOO 136 is LIST OF FIGURES Figure 1 Free Shear Flow Facility Floor Plan ......................... 2 Boundary Layer Transition lodule and Test Section ........... 3 Entrainment lodule .......................................... 4 Dual Cavity Throttling Chamber .............................. 5 lethod of Entrainment Velocity Determination ................ 6 Data Aquisition Facility .................................... 7a The Vorticity Probe ......................................... 7b A Typical Rot-lire Probe .................................... 8a Excitation lechanism (Isometric View) ....................... 8b Excitation lechanism (Side View) ............................ 8c Excitation lechanism (Support Fixture) ...................... 9a Schematic Representation of Excitation Intensity Determination ..................................... 9b Schematic Representation of Excitation Placement and levement ...................................... 10a Schematic Representation of Probe and Support Arm used for low speed calibration ................................... 10b Schematic Representation of the Probe Positioning Unit ...... 10c Schematic Representation of the Traverse lechanism .......... 11 A Visual Representation of the Ensemble Averaging Technique ......................................... l2 Schematic Representation of the leasurement Grid ............ 13a Clauser Plot of Data at X-4.5 cm. 2-0.0 cm ................. Page 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 13b 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 Law of the Vall Plot of Data at I-4.5 cm. 2-0.0 cm ......... Law of the Iall Plot of Data at I-25 cm. 2-0.0 cm .......... Law of the Iall Plot of Data at I-4.5 cm. 2-0.0. £30 on ..., Law of the Vall Plot for Data at I-4.5 cm. 2-0.0 cm. Bxcit.‘ .nd unoxcitGd ......OOIOOOOOO......OOOOOOOOCOOOOOOOO. Law of the Iall Plot for Data at I-4.5 cm. 2-0.0 cm; Ph.‘° Paint‘: 1' 1" 28 ‘nd 42 ......OIOOOO......COIOOOOOOOOO Streamwise Component of Turbulent Intensity for Data at I-4.5 cm. 2-0.0 cm. Excited and Unexcited .......... Streamwise Cempenent of Turbulent Intensity for Data at I-25 cm. 2-0.0 cm. Excited and Unexcited ........... Streamwise Component of Turbulent Intensity for D‘t. .t x=.405 c" z-o'o 6.. *20 CI eeeeeeeeeeeeeeeeeeeeeeeee Streamwise Component of Turbulent Intensity for Data at I-4.5 en. 2-0.0 on; Phase Points: 1. 7. 14. 28 and 42 ... Phase Averaged Transverse Vorticity (“2’13 kp.nd.d Initi‘l R.‘ion for '1 .........OOOOOOOOOOOOO00...... Phase Averaged Transverse Vorticity <‘x’i3 ."1.ndb)'63 ......0.0.......OIOOOOOOOOOOOOOO.......OOOOOOO Phase Averaged Transverse Vorticity (“s>i3 .)'63 .nd b)'125 ......OOOOOOOOOCOO0.0.000...0.00.00.00.00... Phase Averaged Transverse Vorticity (“2’13 .)'125 .nd b)'187 ....OOOOOOI0.0.00.0000...OOOOOOOOOOOOOOOOO. Phase Averaged Transverse Vorticity <01>13 ‘)'187 .nd b)'227 000............OOOOOOOOOOOOOOO0.0.00.0.0... Phase Averaged Transverse Vorticity (0‘)1; .)'227 ‘nd b)n89 ......OOOOOOOOIOOO0.0....00......I......... Phase Averaged Transverse Vorticity ('x)i3 .)'289 .nd b)"20 ......OOOOOO.........OOOOOOOOOOOOO0.0...... Phase Averaged Non-dimensional Velocity Profiles; For Phase Point. i-320 and at I-24.4. 39.6. 54.9. 70.1. 85e4g 100e6g 115e8g 131.1. 146e3 OI eeeeeeeeeeeeeeeeeee Phase Averaged Non-dimensional Velocity Profiles; 83 84 85 86 87 89 91 92 93 94 95 96 97 98 99 at 2-85.4 cm and i=1. 63. 125. 187. 227. 289 and 320 ........ 100 xi 31 32 33 34 35 36 37a 37b 38a 38b 39 40 41 42 43 44 45 Perturbed Phase Averaged Transverse Vorticity. i‘ .)m27 .“ b)msg 00......0.0.0.0.........OOIOIOOOCOCOOOOO. Perturbed Phase Averaged Transverse Vorticity. 1 <>p d/dx alax 3(U)Idy angle in the XI-plane between velocity vector and axis of Irarray probe wavelength between newly formed and saturated vertex structure standard deviation quasi-instantaneous vorticity time step momentum thickness indicates a time averaged quantity quasi-instantaneous transverse vorticity phase averaged transverse vorticity phase or ensemble averaged quantity with respect to a specific phase: i this quantity has been perturbed summation derivitive with respect to I Spatial velocity gradient Spatial velocity gradient xvi CHAPTER 1 INTRODUCTION 1.1 Literature Review In a natural (unexcited) free shear layer. vorticity from the boundary layer is continuously shed from a backward facing step. This vertical fluid tends to roll-up (or fold) and to form discrete ver- tices. The roll-up of the vertical fluid is a result of the natural instability process. For the free shear layer this instability is of the Kelvin-Eelmhelts type. For convenience. these naturally oecuring discrete vorticies are termed ”unit vorticies" in the present discus- sien. Ihen periodic excitation is applied (at the separation lip) to a free shear layer. it causes a two-dimensional undulation of the separating boundary layer. This undulation is folloved by the agglom- eratien of the shed vorticity into a large. isolated. vertical structure downstream from the separation lip (Fiedler. Dsiomba. lens- ing and Resgen 1980 and Fiedler and Kerschelt 1979). An efficient agglomeration.may be accomplished by exciting the natural shear layer with a low frequency. long wavelength. periodic disturbance (lygnan- ski. Oster and Fiedler 1979. Re and Euerre 1984. Re and Ruang 1982). In addition to agglomeration and nonvlinear increases in width. excitation has been found to organise and generate larger vertical structures than would exist in a naturally oecuring shear layer. This organization is a result of the vertical structure being "locked” in space with respect to a particular phase (or time) of the excitation mechanism (Iygnanski.0ster and Fiedler 1979 and Fiedler. Korschelt and lensing 1978). Using temperature as a passive contaminant. Fiedler and Rorschelt (1979) measured the transverse space correlation of the temperature fluctuations in a two-dimensional jet. These results reveal a dramatic increase in the transverse spatial correlation and hence in the two-dimensionality of the excited case versus the natural shear layer. These large vertical motions (or structures) are often referred to as "coherent structures”. Russain (1983) defines a coherent struc- ture as "a connected. large-scale. turbulent fluid mass vith phase-correlated vorticity over its spatial extent. That is. underly- ing the three-dimensional random vorticity fluctuations characterising turbulence. there is an organized component of the vorticity which is phase correlated (i.e..ceherent) over the extent of the structure". The coherent structure properties can be educed by using phase averaging. Phase averaging is defined by the following operation: - “'m- 1m :1 12(x.x.z.-'r+t1). 'here ti is the time corresponding to a specific phase point (i) and T is the period (Russain 1970. Reynolds and Eussain 1970). In the foundation work of lensing (1981). the suppression of pairing of the large. isolated. vertical structures was obtained when the single stream shear layer was weakly excited. 'Specifically. the nixing layer is said to be weakly excited when a low frequency distur- bance is introduced into the flow with an excitation intensity of. I ?"]"‘/00 1 0.0078. Under these conditions lensing found that the subharmonic energy remained approximately one order of magnitude below the energy of the fundamental mode of the structure; this observation reveals that the pairing process. of the large scale motions. is suppressed for these conditions. In addition. lensing determined that for the case of a weakly excited flow. the vorticies would reach their maximum periodic energy level (become saturated) when the Streuhal number. St' based on X is approximately equal to 1. The downstream distance where this occurred is referred to as the saturation length (Feidler. Dxiomba. lensing and Resgen 1980. Feidler and lensing (1982). lensing 1981). 1.2 The Present Experiment In the present study the global vorticity distribution in an excited. plane. mixing layer was investigated. The simplest turbulent flow field in which this could be carried out was a non-reacting. sin- gle phase. isothermal. two-dimensional. inconpressible mixing layer. The single stream mixing layer. which has a greater spread rate and requires a shorter downstream distance to fully evolve (as compared to that of a two-stream mixing layer) was selected for the present work. There are many ways to introduce a periodic perturbation into the flow; among these are: the oscillating flap (Oster and 'ygnanski 1982). the vibrating ribbon (2aman.and Eussain 1981) and a loudspeaker (Feidler. Kerschelt and lensing 1978 and 2aman and Eussain 1981). In the present study a nev method. the reciprocating piston. was used to excite the mixing layer. This method assures a truly two-dimensional as well as a periodic perturbation (see section 4.2). In the present investigation. an excitation intensity of 0.00537 '35 4 Streuhal number. 3‘. (the expected location of the saturated structure) of 0.97 were selected based on lensing's finding. Setting th. excitation frequency, f.. equal to 15 Ex. the saturation length X. was determined to be 84 cm for a free stream velocity of 13 m/s. In addition. the approximate number of vorticies that would agglomerate vas calculated based on the frequency of the natural instabiliy. fu- Based on the existence of a turbulent boundary layer. the following mixing layer relationship is used to relate fn to the momentum thick- ness. 0; Ste . fn e 9/00, where Sta-0.024 (Drubka 1981 and Bussain and 2aman 1981) and U0 the free stream velocity. Once fn is obtained. the ratio fn/f° can be computed and is appreximatly equal to the number of unit vorticies expected to roll-up and form a large. vertical structure. In the present investigation approximately three unit vertices would agglom- crate. 1.3 Development Of The Facility In an effort to ensure high quality measurements in the present investigation. a flow facility was designed and constructed to provide the following conditions: a] the ability to control the flee rate and disturbance level of the entrainment flow. The objective was to ensure that the entrainment flow was essentially irretational. (This capability required the careful setting of the entrainment flow rate as described in chapter 2.) b] a universal turbulent boundary layer at the separation lip. 1.4 Objectives The primary goal of this study was to record and interpret the global distribution of phase averaged vorticity in the formation. saturation and decay regions in an excited. single-stream. free shear layer. In addition. both quasi-instantaneous and coherent transverse vorticity time series throughout the mixing layer were to be obtained and interpreted. A secondary objective of the study was to provide a test case for computer simulations of developing shear flows. The careful documentation of the turbulent boundary layer and the detailed vorticity measurements throughout the mixing layer will serve this objective. The detailed documentation of the flow field includes: 1) the determination of the relative magnitudes of the quasi-instantaneous transverse vorticity fluctuations in the non-linear. formation. saturation and decay regions of the weakly excited mixing layer. 2) the comparison of the quasi-instantaneous transverse vor- ticity to the transverse coherent vorticity in the non-linear. formation. saturation and decay regions of the excited mixing layer. 3) the affect of veak excitation on the upstream turbulent boundary layer. CHAPTER 2 EIPERIlENTAL FACILITY 2.1 Introduction A novel single stream. free shear layer flow facility was designed and constructed for the present study. From the floor plan. Figure 1. one can see a large suction tunnel which occupies the com- plete laboratory (6.81 m x 26.34 m). The volume between the fan outlet and the inlet of the zereth contraction serves as a high pres- sure (P - atmospheric pressure) settling chamber. The details of the flow facility are outlined below. 2.2 Inlet Contraction Highlights The overall contraction ratio (the inlet area of the aeroth con- traction divided by the entrance area of the test section) is 22.6:1. The fluid entering the xereth contraction is accelerated toward the test section through three. two-dimensional contractions. The first two. the xereth and the first contractions. are symmetric. They accelerate the fluid in the I! and XZ-planes. respectively. Upon exiting the first tvo stages of contraction and before proceeding through the final contraction. the fluid is passed through the primary turbulence manipulator section. The design of the primary and entrainment turbulence manipulators was based on the work of Leehrke and Nagib (1972 and 1976). In their work. the specific combination of an lid-8 honeycomb (d-3.175 mm) and multiple 30 mesh screens were found to considerably reduce the disturbance level of the exiting flow. Five screens. spaced at a distance of 12.7 mm. vere used to control the turbulence level upstream of the final contraction. The final asymmetric contraction. in the IY-plane and with an area ratio of 3.22:1. accelerates the fluid downstream. This contraction stage delivers the primary flow to the Boundary Layer Transition lodule (BLT). 2.3 The Boundary Layer Transition lodule The BLT is a constant area duct (50 cm x 80 cm). with one of its vertical side walls serving as the boundary layer conditioning sur- face. This surface manipulates the boundary layer before it separates from the backward facing step. The step (or separation lip) is the location where the mixing layer originates; this location also serves as the entrance to the test section. The conditioning of the boundary layer before it reaches the separation lip is a two-stage' process. First. to ensure that unwanted effects i.e.. Gortler and corner vor- tices. are prevented from reaching the test section. the boundary layer leaving the second contraction and approaching the BLT is removed. This is accomplished by using a separate fan. throttling valve and splitter plate. The splitter plate diverts the boundary layer fluid exiting from the second contraction and exhausts this unwanted fluid into the receiver. The plate has a parabolic leading edge (constructed from a redwood board) which has been fastened to the step side vertical wall. The leading edge and step side wall is dis- placed 2 cm inward (in the negative I direction) toeards the center of the primary flow. After the unwanted boundary layer is removed. the remaining flow continues over the leading edge and trip mechanism. A tripping mechanism is used to artificially thicken the boundary layer. In the present work. a number 16 open grit sandpaper was selected. Specifically. the sandpaper was located on the step side vertical wall immediately downstream of the leading edge and extended downstream for 60.5 cm (Figure 2). Choice and placement of the trip was based on the work of Ilebanoff and Diehl (1951) vho obtained a self-similar. mean velocity profile 170 cm downstream from the leading edge. The boun- dary layer continues to grow another 129 cm downstream before encountering the separation lip. The final 65.5 cm of the vertical wall upstream of the separation lip was constructed using Formica covered flakeboard. The motivation for this wall construction is as follows: a) The low thermal conductivity will minimise erroneous hot wire readings resulting from the additional heat loss to the wall. This extra heat loss can occur when the hot wire probe is brought into close proximity to the surface under investigation. For nenvconducting materials (materials with a lov thermal conductivity). such as Formica covered flake- board. the additional heat loss from the measurement probe to these surfaces is much smaller and can be considered 10 negligible for most practical boundary layer measurements (Bhatia. Durst and Jovanovic. 1982). b) The highly reflective Formica surface allows the use of an optical method in which the distance between the hot-wire and the wall can be accurately estimated (see section 4.3.4). 2.4 The Entrainment lodule The mixing layer. formed by a separating boundary layer. spreads laterally as it moves downstream in the test section. This lateral spread is associated with the entrainment of the surrounding fluid. In the present design. irretational fluid is continually drawn into the test section from the laboratory. That is. an irretational entrainment stream is introduced into the test section and a centrifu- gal fan (Chicago Blower. number 36.5 sea Airfoil Fan) returns the primary and entrainment flows to the laboratory from the receiver. This entrainment fluid must pass through the entrainment module and the entrainment turbulent manipulator section (Figure 3) before being engulfed and ingested into the mixing layer. This is in contrast with a conventional single stream free shear flow facility in which previ- ously sheared fluid is re-entrained in the test section without passing through the turbulence manipulators. In a conventional facil- ity. the level of residual vorticity in the entrainment stream increases to an equilibrium level for the laboratory. The disturbance level in a conventional tunnel cannot be controlled since the entrain- ment fluid is not passed through the turbulent manipulators. It is 11 this feature of the present facility that justified the time and expense for its development. The entrainment module was designed to provide a time indepen- dent. irrotational entrainment flow. with a constant velocity equal to that found in a natural mixing layer. This module consists of 155 flow conditioning units (each unit is a Dual Cavity Throttling Chamber: DCTC. Figure 4) followed by the entrainment plenum (a large settling chamber). The entrainment plenum is 2.44 m in height and 3.0 m in streamwise length. The DCTC is composed of two cavities which allow for the deceleration and the decay of the turbulent kinetic energy of the incoming flow. The flow rate is controlled by a slide mechanism on the front of the DCTC which adjusts the entrance cross sectional area: see Figure 4. Equalization of the flow non-uniformities can occur in the entrainment plenum before undergoing a 3.05:1 sudden contraction into the entrainment turbulent manipulator section. The entrainment flow rate was set such that the primary core flow passing through the test section experienced little or no streamwise acceleration (duoldx-O; see Figure 5 for measurement locations). Adjusting the slide mechanism on the DCTC's. the velocity difference [(Ug-U,)IU1] was minimized to less than 1 i at the measured points (U, is greater than U1 by approximately 1‘5). Placing a hot wire 112 cm downstream from the separation lip and approximately 2 cm away from the last entrainment screen. a dimensionless entrainment velocity. V./U° of 0.0395 vas measured (see section 4.3.1 for the calibration 12 technique). This is in good agreement vith the measured value of VglUo - 0.042. which was experimentally determined by Fiedler and Theis (1982) in a conventional flow facility. 2.5 Receiver/Fan Room The combined primary and entrainment flows exit the test section and enter the receiver. which serves as a low pressure plenum. This plenum allows for the isolation of the test section from pressure fluctuations originating at the fan; that is. the fluctuations that would be associated with the blade passing frequencies or rotor insta- bilities. The fan returns the primary plus the entrainment air to the laboratory as mentioned earlier. 2.6 Computer Room/Laboratory The laboratory also houses a computer room where a PDP 11/23 and various units of electronic instrumentation are located. This room is pressurized and air conditioned. The flow facility has been con- structed using vibration isolators. thereby minimizing the possibility of any disturbance being tranemitted to the test section while data taking is in progress. In addition. the computer room. viewing plat- form and the fan have been constructed and installed with vibration isolation in mind. Specifically. any disturbances originating at these locations must first be transmitted through plywood vibration absorbers and the concrete floor of the laboratory before being transmitted to the test section structure. CHAPTER 3 DATA ACQUISITION FACILITY 3.1 Introduction In the present study. direct velocity measurements were made with the use of hot-wire anemometry. A pitot-static pressure probe was used to monitor the tunnel speed and the hot wires were used to inves— tigate the velocity at specific locations in the boundary layer or the mixing layer. The data acquisition facility used for the mixing layer investigation is shown in Figure 6. 3.2 Pressure leasurement Facility The pressure probe was mounted from the ceiling of the test sec- tion at I-15 cm and I--25 cm. A Validyne DP45-22 pressure transducer and CD12 transducer indicator were used to measure the difference between total and static pressure. 13 14 3.3 The Hot Iires All hot-wires were operated in the constant temperature mode. A straight wire was used for boundary layer surveys and a four-wire array (vorticity probe) was used in the mixing layer invesigation. The four-wire array is composed of: an I-array and a parallel array (Figure 7a). This probe. and its processing algorithms. are exten- sively described in Foss. Klewicki and Disimile (1984). The X-array is composed of two slant wires (in the II-plane). which are placed at 39'1341 438103 0‘ $45 degrees with respect to the probe axis and which are separated by approximately 1 mm. A. parallel' array is located below the Irarray by a distance of approximately 3.8 mm in the Z-direction and the two parallel wires are separated by a distance of 1.27 mm. The location of the Ivarray is such that the active portion is placed directly above the mid-point of the parallel array. The hot-wire probes were fabricated using 5 micron (diameter) tungsten wire. The ends of the tungsten wire were copper plated. The copper plating enables the wire to be soft-soldered to the tips of the jeweler's breaches (prongs. see Figure 7b) and it serves to isolate the active portion from the aerodynamic disturbance effects of the prongs. Although the wire was nominally 3 mm in length. the active portion was only 1 mm long. The hot-wires are connected to a bridge circuit incorporated in the DISA 55l01 anemometers and were set up vith a heating ratio of 1.7 . 15 3.4 Electronic Signal Conversion/Computer Facility The analog outputs of the four anemometers were input to a T81 1075!. 4 channel. simultaneous sample and held analog-to-digital (re- ferred to as AID) converter. This 12 bit AID converter has an input range of approximately 0 to +5 volts and a resolution of 1.2 milli- velts (that is. one least significant bit. LSB is equivalent to 1.2 millivolts). Connecting all four channels to a common signal. the AID we: found to have an accuracy of t2.4 millivolts (2 LI's). All four channels have matched 50 kHz low pass input filters. Also. this AID is equipped with a Direct lemory Access (DlA) interface. Iith a DEC DRVll-B interface module and DNA. the transfer of data directly between the AID and system memory can be accomplished. Once pro- grammed. this operation occurs without micropressor intervention. Once the AID is prepregrammed (i.e.. specification of starting channel. number of channels. number of samples and sampling rate) digitizing of the data can be initiated by either software control or external triggering. Ihen the external trigger mode is chosen. con- trol of the AID is transfered to an external device. This device can actuate the AID on the occurrence of a specific event. This feature of the facility was used in order to provide phase sampled measure- ments: the specific features of the phase sampling are described in section 4.4. The data acquisition system includes a computer/manual controlled traversing mechanism (Figure 10c). This system allows a probe to be 16 moved in the II-plane and to rotate about a 2-axis. Three stepper motors are used to drive the traverse. Communication between the motors and the computer takes place through the DEC DRVll interface module. The DEC DRVll and the DRVll-B interface modules are installed in a Charles River Data Systems PDP 11I23 microcomputer. All data are stored on a Digital RL02 10 megabyte hard disc. CHAPTER 4 EIPERIlENTAL FACILITY AND PROCEDURE 4.1 Introduction This chapter is divided into three sections: Excitation lechan- ism. Het lire Alignment/Calibration and Data Acquisition Strategy. 4.2 Excitation lechanism In the present investigation. periodic excitation of the separating. turbulent boundary layer was required. To accomplish this. an excitation mechanism was designed using a flat. rectangular piston moving in simple harmonic motion (see Figures 8a. 8b and So). This reciprocating motion was in the r Y—diroction (Figure 9a). The piston vas located immediately downstream of the separation lip (Fig- ure 9a and 9b). The excitation frequency. f., was set at approximately 15 B2. Fiedler and co-workers have shown that a precise frequency contel is not required since the shear layer response is the same over a wide range of frequencies. Hence. a hand adjusted. elec- tronic motor speed control was used to set the frequency to the nominal value of 15 Hz. 17 18 The simple harmonic motion. experienced by the piston. is a consequence of the approximately elliptical path travelled by the shoulder bolt (Figure 8a). The shoulder bolt fastens the connecting rod to the eccentric support fixture. which in turn is connected to the concentric support fixture. This fixture is able to communicate to the motor through the rotating shaft and the drive arrangement shown in Figure 8a. Selection of various eccentric support fixtures discretize the allovable excitation amplitude A! (the maximum dis- placement of the piston). In addition. a ”trip arm" is placed in betveen the eccentric and concentric support fixtures. The trip arm. in conjunction vith an infrared optical encoder. was used to actuate the AID converter. This is accomplished by allowing the trip arm to rotate and interrupt the infrared beam within the optical encoder. The arm is oriented such that the interruption of the infrared beam indicates the relative position of the excitation mechanism. Specifically. the interrupt signal corresponds to the first phase point (or sample). This is equivalent to an angular position of 90 degrees in the excitation piston cycle (Figure 9a). For the present work. the shoulder belt was located off-center at R-0.762 mm (the maximum.displacement of the piston). At a rotational speed of 15 Hz. this offset gives an excitation intensity of: P“ ‘ ‘l’ o 0039 v IUO] - . A second evaluation of the excitation intensity was provided by a hot-wire anemometer probe. The probe was positioned at I-1.5 cm. 19 2-0.0 cm and I-2.5 cm (i.e.. a displacement of approximately 13.3 mm into the excitation channel entrance Figure 9b). Setting the tunnel to the actual test conditions ("0'13 mls and 1.315 3;) the excitation intensity of: _ x/s [v"/U;] - 0.00537 was obtained Considering the difficulties in obtaining an accurate calibration of the hot-wire at very low velocities and the inherent problems of interpretting a hot-wire signal in an oscillatory flow. the agreement between these tvo values is acceptable. These results are interpret- ted to imply that the actual excitation intensity is nominally 0.0046. 4.3 Hot lire Alignment and Calibration 4.3.1 Low Velocity Calibration A low velocity calibration technique mas used to obtain calibration coefficients for use in the measurement of the entrainment velocity. The schematic showing the setup used in this technique is shown in Figure 10s: it makes use of the rotating probe support arm capability in order to obtain relative motion between the probe and the stationary air. In this technique. the hot wire was positioned on the probe support arm. normal to the direction of motion and diplaced a distance r away from the traverse pivot point (Figure 10a). Specifically. with the fan shut off (no primary or entrainment air flow) the probe support arm was rotated (through an angle of approxi- 20 mately 180 degrees) about the pivot point at a constant speed. Optical devices. placed at preselected angular positions (A7: go degrees). allowed the detection of the probe passage. The signals obtained from the optical devices were input to the computer together with the output voltage of the hot-wire. 'ith the use of software. the time interval (At) was computed. The velocity. experienced by the hot-vire probe. was determined from the relationship. U - r ’ A1 I At vhere r is the radial position of the hot-wire probe from the axis of rotation of the traverse device. Repeating this process several times at various speeds of rotation and fitting the data to the Collis and Iilliams (1959) equation. calibration coefficients were obtained for the low speed range: 0.32 mIs < U < 1.077 mIs. 4.3.2 Straight-lire And Vorticity Probe Alignment Alignment of the hot-wire probe for the boundary layer investiga- tions vas performed with the use of a surveyor's transit. In addition. the transit was used to align the four-wire array.' The par- allel array used in the vorticity probe was aligned to ensure a vertical orientation (vires in the IZ-plane). The vorticity probe. which contains both an I-array and a paral- lel array. was aligned such that the Irarray (horizontal and in IY-plane) was perpendicular to the parallel array (residing in the 21 IZ-plane). In addition. the active portion of the X-array is placed directly over the center of the parallel array. The parallel array was then positioned such that the distance between its two straight vires and the 2-axis extending up from the pivot point of the travers- ing mechanism were equal. when viewed through the transit. To ensure that the center of the vorticity probe is directly over the pivot point of the traverse mechanism. the probe support arm and probe assembly was rotated to +90 and -90 degrees (Figure 10b). At each angular position. the distance between the plane occupied by the par- allel array (only one wire visible when probe is positioned at tgo) and the Z-axis extending up from the pivot point are set to zero. This is accomplished by adjusting the support arm and the probe assem- bly (along the radii extending out from the pivot point axis). Once the hot-wires were aligned. the calibration procedure could begin. 4.3.3 Rot-lire Calibration An additional calibration of a straight wire and the vorticity probe were conducted in the test section. at I-l5 cm. I--25 on. 2-0 cm. At this location. the inviscid core flow occupies approximately the central 40 cm of the flow. The tunnel speed was monitored with a pitot static probe. For a single straight wire calibration. the hot wire voltage and tunnel speed were recorded for seven tunnel settings. The data were then made to fit the generalized Collis and Iilliams equation. 33-A+n-en 22 where O is the velocity: A. B and n are constants. Selection of n is based on the minimization of the standard deviation (of O) obtained using a least squares fit to the data. In a similar manner the four hot wire voltages of the vorticity probe vere recorded at a constant tunnel speed while the vorticity probe was rotated through 13 angles: 1 ' '42.'35.’30.-24.-18.-12.0.12.18.24.30.36.42. This procedure was repeated for seven fan settings. The calibration of the vorticity probe was obtained using the recently completed four-wire calibration procedure developed by C.L.Ilewicki (1983). 4.3.4 Hot-lire Positioning For Boundary Layer Surveys Once the single straight vire probe was aligned and calibrated and before the boundary layer surveys could be conducted. the determi- nation of the initial lateral position: To, of the probe near obtained. Using an optical technique. To could be accurately earl-at— ed. This was obtained by moving the probe close to the wall. determining the effective distance between the reflection of the hot-wire support prongs (as seen in the Formica) and the actual sup- port prongs. Ihen these prongs and their mirror image coincide. the prongs are touching the vall. Vith the knowledge that the hot wire is mounted at the center of the prong tip and the diameter of the prongs at the tip is 0.20 mm for the present probe. To was determined to be 0.10 mm. 23 4.4 Data Acquisition Strategy Data were recorded in the upstream boundary layer with a straight vire probe for both the excited and unexcited cases. In addition. the vorticity probe vas used to record data in the excited mixing layer. 4.4.1 The Boundary Layer In the boundary layer. hot-wire surveys (probe traversing later- ally in the I direction) were conducted at I-4.5 cm (upstream from the separation lip) at 2-0. $20 on and apatgaaa at I-25 cm and z-o on. All boundary layer investigations vere conducted with a free 'trOFI velocity “5 of nominally 13 nIs (as recorded by the pitot-static probe. section 3.2). Data was acquired using the computer controlled traversing mechanism (described in chapter 2) and appropriate software. The specific softvare used in the boundary layer investigations depended on whether the boundary layer was excited or natural. In either case the measurement locations were the same. The probe was indexed later- ‘117 (‘10- ‘0 and in the negative Y direction) through a total of 35 measurement locations to a final position of negative 7.86 cm (away from the step side wall). The measurement probe. initally located at Yo. was indexed as follows: the first 13 positions were incremented in intervals of 0.4 mm. the second 9 positions were incremented in intervals of 0.813 mm and the last 13 were incremented in intervals of 5.0 mm. 24 Ten thousand (10.000) samples were obtained at each of the 36 I locations in the unexcited case; these data were acquired over a time period of 10.24 seconds at a sampling rate of 977 Us. The resultant time series is then averaged over the 10.24 second time period; the mean voltage and its variance were obtained. In the excited case. the data acquisition was initiated upon interruption of the infrared beam of the optical encoder as described in section 4.2. Specifically. at any I-locatien an ensemble was created consisting of 1000 realizations (the begining of a realisation is marked by the rotation of the trip arm past the detection mechan- ism). Each realisation consisted of 56 samples (a time series 57.3 ms long) and were recorded at a sampling rate of 977 Rs. Once an ensem- ble was obtained. phase averaging (or an ensemble average taken with respect to a specific excitation phase angle) was performed. To obtain a phase average. the first sample (or phase point) of each time series would be added together and an average value determined for that phase point. Repeating this process for all remaining phase points. one obtains a phase averaged time series (Figure 11). 4.4.2 The Excited lixing Layer In the excited mixing layer. all the data were acquired using the vorticity probe. Although triggering of the AID vas accomplished by the identical method used in the excited boundary layer case. the sam- pling rate and the number of samples differed. A.measurement grid of 414 node points was established. The rectangular grid was defined by 25 9 lateral I 10°4t10333 ’7-3 S I i 17.1 cm and 46 I (or streamwise) locations: 12.25 S I 5 149.41 cm; see Figure 12. All mixing layer information was phase sampled with a sampling rate of 31.25 kHz. The data vere then stored in two fashions: l) a phase averaged time ser- ies (an ensemble average of 1000 events. see figure 11) and 2) 30 instantaneous time series. Each phase averaged time series is 320 samples (or 10.24 ms) long. All but tvo valanes of the instantaneous time series are 80 samples (or 2.56 ms) long. The I-42.73 cm and I-45.78 on mixing layer traverses are 320 samples (or 10.24 ms) long. The shortened instantaneous time series were a result of a typing error in the data acquisition software. CHAPTER 5 UPS'REAl BWNDARY LATER RESULTS AND DISCUSSION 5.1 Introduction Bot-wire traverses throughout the boundary layer were performed in order to determine the universality of the present turbulent boun- dary layer. The boundary layer data were processed and plotted in lav of the wall coordinates (U+,y+), 'hgrg at . file and 1* - rent/v ‘C vhere at is the friction velocity. Using a standard technique known as the Clauser plot (Clauser 1954). the data was plotted as U/Uo versus Y’UOIV and compared with the law of the vall. A value for the friction velocity U; can be determined by using. a]: up - uo[cf/2] . That is. the universal (law of the wall) curve can be replotted as a universal family of curves with the local skin friction coefficient. cf. as a parameter. The value of Cf is chosen by selecting the appropriate member from the family of curves which best fits the 26 27 acquired data near the wall. A typical Clauser plot is shown in Fig- ure 13a. In addition to the local mean velocity ‘U, an. atgaaaaiaa component of turbulent intensity was calculated and plotted against r/s. where 8 is the boundary layer thickness . The value of delta was approximated by 10 theta where the momentum thickness. O was obtained from o - I: omen—ulna) s! using Simspon's Rule for the numerical integration and the discrete U(I) values. The displacement thickness. 8. is determined using. 6‘ r J: (Hi/no) a! and Simspon's Rule of numerical integration. 5.2 Boundary Layer lean Velocity Profiles 5.2.1 lid Plane lean Velocity Profiles The friction velocity was determined for the first phase point of the excited boundary layer case. see Figure 13a. The insensitivity of the mean velocity profiles to the phase point is dicussed in section 5.2.4. The data were obtained at a location upstream from the separa- tion lip (X--4.5 cm) at 2-0.0 cm. The values of C: and U1 that were 28 determined for these conditions. are 0.0029 and 0.506 mIs. respective- ly. A comparison of the above Clauser plot to the one obtained for the unexcited case (not sheen) shoes negligible differences: namely. cf and U‘ were equal to 0.00285 and 0.501 mIs. respectively. ODGO Hg was determined. the boundary layer data were replotted in law of the wall coordinates (U+.Y+. Coles 1962.1968). as sheen in Fig- ure 13b for the excited case. These data show very good agreement with the law of the wall (Cole's line). 0* - 5.6 log1. 2* + 4.9 in the leg law region. The momentum thickness was determined to be 6.43 mm and the displacement thickness 8.83 mm for the excited case. This corresponds to a shape factor of approximately 1.37. In the unexcited case 9'5-53 II and 5.-8.99 mm corresponding to a shape fac- tor of 1.38. In addition. n'IUt is approximately equal to 2.57 for the unexcited case and 2.63 for the excited case. These results show that Tee additional characteristics of a fully-developed turbulent boundary layer have also been satisfied: a shape factor of 1.4 and n'Iut-2.5t0.25 (Bussain. 1983). The upstream boundary layer at I-25 on and 2-0 cm. Figure 14. has a shape factor. u'IUt and C: equal to 1.43. 2.68 and 0.0026 for the excited case. similarily 1.42. 2.80 and 0.0027 for the unexcited case. Comparing this upstream boundary layer to the boundary layer at the separation lip (I-4.5 cm) one can observe the following: the 29 upstream boundary layer exhibits an overshoot in the wake region and fair agreement in the log region. 5.2.2 Test Of The Three-Dimensionality Of The lean Velocity Profiles Additional boundary layer traverses eere obtained at the same upstream location (I=-4.5 em) but were displaced in the transverse direction along the surface of the step side plate. These traverses were used to examine the three-dimensionality of the boundary layer. . This information was processed in the same manner (Clauser plot to 40:01-139 Hg) and plotted in law of the wall coordinates. The addi- tional lateral traverses eere obtained at 2-r20 on (see Figure 15). The agreement between the three traverses and Cole's line in the lav of the wall region is good. Comparison of the momentum thickness. 0 shoes a maximum difference of 10 h between the three 2 traverses. It is inferred that the variation in theta is associated with the specific technique that was used to artifically thicken the boundary layer. Specifically. randomly distributed roughness elements (sandpa- per) were used to create the desired boundary layer thickness. This method of producing an artifically thickened turbulent boundary layer is knoen to generate greater three-dimensionality in the mean proper- ties than other tripping tripping mechanisms (Preston. 1958). It should be noted that the objectives of the present research required a relatively large value for the momentum thickness. This eould enable the excitation mechanism to produce the largest structure 30 possible at the selected value of f., The tcpogtgd three-dimensionalities are considered to be acceptable in the context of the objectives of the present investigation. 5.2.3 The Influence Of Excitation On The lean Velocity Profiles A comparison between the excited and unexcited turbulent boundary layer profiles obtained at (1.1.2) - (-4.5.I.0.0) cm are plotted in law of the eall coordinates (Figure 16). Again. good agreement is found in the log law region: hoeever. if attention is directed towards . the outer (or eake) region of the boundary layer. a difference between the two cases can be detected. That is. the mean velocity profile in the excited case undershoots the mean velocity profile in the unexcit- ed case in the outer region. This undershoot of the mean velocity profile indicates a reduction in O in the excited boundary layer case. This reduction is approximately 2$tbased on the calculated momentum thickness. A number of additional boundary layer traverses were recorded during the setting of the boundary layer bleed flee and all surveys consistently shoved a decrease in theta for the excited case from 1.5 to 8 percent. In the boundary layer traverse at X--25 cm. the velocity profile in the excited case is observed to undershoot that in the unexcited case in the wake region. A corresponding 3* drop in 0 has been found (Figure 14). Based on the observed effects of a low frequency. periodic exci- tation when applied to a free shear layer. a possible explanation for the decrease in theta in the turbulent boundary layer is presented. 31 A known feature of periodic excitation is its ability to organise and generate large vertical motions periodically spaced in time. That is. the naturally shed vertices from the separation lip are agglom- erated and regulated in space. It is hypothesized that the effect of this periodic flow interruption propagates upstream of the separation lip. tending to reduce the chaotic state of the flow by organizing and separating the large eddies present in a turbulent boundary layer. 5.2.4 The Influence Of Phase Time On The lean Velocity To examine the affect of the excitation phase angle on the mean velocity profiles. four phase points spanning the total excitation cycle were selected for comparison. These phase points are: 1.14.28 and 42; they are related to the position of the excitation mechanism throughout one complete cycle (Figure 9a). In Figure 17. the upstream traverse taken at 2-0 cm is sheen for six phase points. Although some scatter exists in the data no significant variations appear. This indicates that the effect of phase position of the excitation mechan- ism on the mean velocity profiles is negligible. 32 5.3 Streamwise Component of Turbulent Intensity 5.3.1 lid Plane Turbulent Intensity Profiles The streamwise component of turbulent intensity. .. .w [u' [no] in the boundary layer is plotted against TIb. where 6 (5'10 0) is the boundary layer thickness. In all plots of the excited turbulent intensity profiles the first phase point has been used. In Figure 18. both an excited and an unexcited boundary layer traverse. taken upstream of the separation lip (I-4.5 cm) at 2-0 cm. are shown. No major differences eere found between the two cases except at 115 greater than 1. In addition. the streamwise component of turbulent intensity for the last measurement point in the unexcited case is 0.5 5. The boundary layer traverses obtained at I-25 on for the excited and unexcited cases (Figures 19) shows slight data scatter for II6<0.7. 5.3.2 The Three-Dimensionality Of The Turbulent Intensity Profiles To indicate the degree of three-dimensionality in the turbulent intensity. the three traverses for the excited case are plotted in Figure 20. They eere taken at the same X-location. I-4.5 cm and at 2-0.+20 and ~20 cm. Again. the curves show good agreement except when I/e is greater than 1. This effect is apparently due to the variation in the free stream turbulent intensity. 33 5.3.3 Influence Of The Phase Time On The Turbulent Intensity Profiles To assess the affect of the phase time (point) of the excitation mechanism on the streamwise component of turbulent intensity. the pro- file obtained at I--4.5 cm and 2-0 cm eas replotted in Figure 21 with four additional phase points: 7.14.28 and 42. Considerable scatter is found among the various phase points when IIS exceeded 0.8. CHAPTER 6 RESULTS OF THE EXCITED lIXING LATER INVESTIGATION 6.1 Introduction This chapter presents the scheme used for processing the data and the results which have been obtained for the excited mixing layer: see chapter 7 for the discussion of the results. All results presented-in this chapter have been obtained by pro- cessing the data acquired using the four-eire array (i.e.. the vorticity probe shown in Figure 7a and described in section 4.3.2). These data were obtained over a rectangular measurement grid (des- cribed in section 4.4.2) with the probe positioned at the transverse position of 2-0 cm. The resulting data were stored as least signifi- cant bits (LSB's) and were used as input to a software package. PROCESS I. The algorithms. PROCESS I and PROCESS II. are discussed extensively in Foss. Kleeicki and Disimile. 1984. The outputs of PRO- CESS I are the following time series: the velocities. O, and Q‘ fro. the parallel array and the velocity Ox and the angle 1 from the X-array. 34 35 The following sections will present the phase averaged transverse vorticity. (0,). The spatial distribution and the temporal evolution of the phase averaged vorticity field will be evident in the contour plot representations of these phase averaged data. In addition.the quasi-instantaneous transverse vorticity. 03(r) will also be present- ed. 6.2 Spatial Distribution of the Phase Averaged Transverse Vorticity Figures 22 to 28 represent the phase averaged transverse vorticity, <0,>i. contours depicting the spatial distribution of the vertical motions in the mixing layer at a specific phase point (i). These spatial values of the phase averaged transverse vorticity. <0z>‘. eere obtained with the use of an algorithm called "VORTIS". The following items identify the signal processing steps used to obtain the (0‘). output: i) The digitized and phase averaged hot-wire voltages (81) and (E,) from the Iéarray eere used by Process I to calculate (Qx>i and (1).. ii) The values (°x>i and (1). were input to the processing routine "VORTIS" where (U). and (V). eere computed 36 (”)1 8 (QX>1 cog (1)1 (6.18) and (V>1 - <°x>i sin (1)1 (6.1b) for each phase point i at each of the (X.Y)-locations. iii) To determine the value of the phase averaged transverse vor- ticity. (“z>1- at a specific phase point and (X.I)-location. two spatial velocity gradients are required: a/ax]i and can/ark. These spatial velocity gradients were also calculated with the use of VORTIS. iv) Starting with the first phase point (i-l). all the (U). com- ponents of velocity for the first I-plane (all 9 I-measurement locations) were curve-fit eith the use of a cubic spline subroutine (included in VORTIS). The present cubic spline subroutine allows the user to select various end conditions. These end conditions are: a] The first derivative is equal to zero. b] The second derivative is equal to zero. c] The jump in the third derivative across the adjacent 37 interior point is forced to zero. The vorticity was calculated using all three end conditions and the respective values are compared in Appendix A. Except for the measurement points on the lateral boundaries. the vorticity values were found to be insensitive to the end conditions. The end condition corresponding to the second derivative equal to zero was selected for use in this study. The cubic spline subroutine curve-fits a cubic equation of the following general form between the data points: F1(r) - Ci(1.I)+Ci(2.I)‘B+C1(3.I)’B'I2+C1(4.I)‘B’l6 (6.2) where B - I—I(I). I - location where F1 is to be evaluated. Y(I) - actual I measurement location. i - phase point. The result of this curve-fitting operation is 8 sets of coeffi- cients (or 8 cubic equations) which are obtained for each of the I-planes. v) Taking the derivative of equation (6.2). eith respect to I. yields an equation for the determination of F'(I) at any Y-location: Fi'(!> - 01(2.I)+Ci(3.l)'E+C1(4.1)‘E’I2 38 The spatial velocity gradient alar]i can b. d.t.,.1n.d throughout the 46x9 measurement grid by repeating this calcula- tion for all 46 X-planes. vi) In a similar manner. all the phase averaged lateral velocity components. (V>i. for a specific I-plane were computed and stored in memory. Then. for a given I-plane a cubic spline was fit through each data pair at all 46 X-locations (the 46 locations correspond to the number of vaeasurement points in a single I-plane). The results are 45 sets of coefficients or 45 cubic equations. The general form is: 61(1) - Di(l.I)+Di(2.1)‘J+D1(3.I)‘J'I2+Di(4.l)‘J’I6 (6.3) where J - X-I(I). X - location where G1 is to be evaluated. 1(1) - actual X-measurement location. i - phase point (or time). vii) Taking the derivative of equation (6.3) with respect to X yields an equation for the determination of G'(X) at any I—locatien. Performing this set of operations for all I—planes (there are 9 I-planes). the spatial velocity gradient 0(V>IdX]i can be calculated throughout the 46x9 measurement grid. viii) Finally. the phase averaged transverse vorticity can be calculated at a specific phase point as: i - alar]i-a/ar]‘. (6.4) 39 These results were stored in a file containing the (1.1) coordinates and the magnitudes of (0‘). for the complete 414 point measurement grid. This file was then sent to the Cyber 750 mainframe computer where ('z>i contours were generated using the Surface II Graphics Sys- tem. A comparison of the contours obtained at the different phases (times) will give an indication of the temporal changes in the verti- city field. To allow for easy identification of the vorticity contour lines in the initial region of the excited mixing layer. an expanded view of this region is included in Figure 22. In Figures 22 to 28 the phase averaged transverse vorticity is plotted for a specific phase point of the excitation mechanism. These figures are labelled in such a fashion as to indicate the phase point which they represent. For example. Figure 23. containing the contours I1 and I63. represents the phase averaged transverse vorticity obtained at the 1st and 63rd phase point of the excitation mechanism. respectively. The following table presents a list of the figures and their respective phase points. Tible 6.1 Designation of the phase time (i) for (01>1 contours: Ii Figure 22: I1 (initial region) Figure 23: ‘I1 AND I63 Figure 24: I63 and I125 Figure 25: I125 and I187 Figure 26: I187 and 4'22? Figure 27: I227 and I289 Figure 28: I289 and I320 40 6.3 Phase Averaged Streamwise Velocity Profiles The phase averaged streamwise velocity component was calculated for each phase point. at all (IT) locations and fit eith a cubic spline using VORTIS. The resulting spline equations allow for the determination of the lateral distribution of non-dimensional velocity. This lateral distribution of the nondimensional streamwise component of velocity at the last phase point. (U(I)>,”/uo is plotted in Figure 29 for the following X-planes: X - 24.4. 39.7. 54.9. 70.2. 85.4. 100.6. 115.9. 131.1 and 146.4 cm. Also (U(I)>1IUo is plotted at I-85.4 cm (Figure 30) for the following phase points: i - 1. 63. 125. 187. 227. 289. and 320. 6.4 Perturbed Phase Averaged Transverse Vorticity Contours The contours of phase averaged vorticity exhibit many interesting f“titres. However. it eas recognized that some of the features may be “tifacts of the contouring routine or they may result from finite “lrle size affects. It was considered appropriate to test the sensi- ti'ity of the contours to perturbations of the measured voltages. The strategy used to investigate this sensitivity. was to select rando- you“. perturbationa to be added to the phase average voltages 41 random voltage perturbations to be added to the phase average voltages ((E1>,(E,>) at a given (I.I)-location. The technique used to generate the random perturbations is described below; it should be noted that the spatial locations. at which the perturbation was to be applied. was also randomly selected. This spatial randomness was to eliminate any bias in the spatial derivatives. The voltages at each of the 414 measurement locations were subjected to the folloeing perturbation process. T30 DOItBIBGd '01t4809 (BE) and (E?) eere obtained from the phase average 701t4208 (<31) and (E,>) and the average standard deviations (o, and c,) by the following operation: (E?) - (Ex) + K‘o1 (6.5a) (3P) . (3,) + [*o, (6.5b) where the values Of a: and o, are presented in Appendix B and I is the randomly selected multiplier with possible values of 0.t.0625. n.125. t.1875. $.25. The K multiplier eas selected by using the following procedure: i) a random number routine. with equal probability of selecting a value from a 0 to 1 line seament. was sampled. 11) if the sample vu vithin 0-5t0.2s. x was set to zero; if the sample was beyond the first range but within 0.5ro.41, I was set 42 t0 £0.0625. iii) a similar procedure was used for the other K values where the bounds are 0-5t0.47. 0.5to.49 and 0.5to.5. The routine. PERTAV. was used to create the perturbed data files that were subsequentlv input to PROCESS I and VORTIS. The output of VORTTS was then plotted as perturbed phase averaged transverse vorticity. (0%)1. contours usina Surface II graphics. The perturbed plots have also been labelled in a manner similar to the unperturbed contours. For example. in Figure 31 the contours IPl and IP63 represent the per- turbed phase averaged transverse vorticity acquired at the 1st and 63rd phase point of the excitation cycle. The following table presents a list of the figures and their respective phase points. Table 6.2 Designation of the phase time (i) for i contours: IPi Figure 31: 'P1 and IP63 Figure 32: IP63 and 'Pl25 Figure 33: 'Pl25 and IP187 Figure 34: IP187 and 'P227 Figure 35: 'P227 and IP289 Figure 36: IP289 and IP320 6.5 Tomporal Evolution of the Phase Averaged Transverse Vorticity Phase averaged transverse vorticity. (uz(x,y)) time series were obtained at all 414 (1.!) locations (see Figures 37 to 38). In order to obtain an accurate temporal historv at any given (X.I) location the 43 algorithm VORTTS was run for each discrete phase time: hence. 320 cal- culations were executed for the 10.24 ms sample time. (The discrete samples were separated by 0.032 ms.) In addition the output files from VORTIS had to be passed to the software package "VORTEl". This algor- ithm rearranges the phase averaged transverse vorticity files in such a manner II to prepare an (01(X.Y)) time series for each (X.I)-measuremcnt location. The temporal resolution of these time series is 0.032 ms. The following table presents a list of figures at the respective (3.!) locations. Tible 6.3 Phase Average Transverse Vorticity Time Series Figure 37a and b: X=48.8 cm and I-7.3 cm to 7.9 cm Figure 38a and b: I-84.4 cm and I--7.3 cm to 11.0 cm 6.6 Ouasi-Instantaneous Transverse Vorticity The quasi-instantanteous vorticity G‘(X,Y,t) is calculated using the instantaneous data obtained at each of the 414 (I.I.t) measurement locations and the algorithm PROCESS II (which is extensively discussed in Foss. 'lewecki and Disimile. 1984). To obtain an 0:(X,Y,t) time series it is essential that the four eire array (the vorticity probe) be used. Specifically. the stored instantaneous voltage time series is passed through PROCESS I whose output is read by PROCESS II. The output of PROCESS II is an irregular time series of o‘(x,!,r). Because of the size of the data set (there were 12.500 e'(r) plots available) only a few representative plots are being presented. They 44 are listed in table 6.4. Table 6.4 Quasi-Instantaneous Transverse Vorticity Figures 39 and 40: T-18.3 cm and I--4.3.-1.2 and 1.8 cm. Figures 41 and 42: X-34.6 cm and T--4.3 and -1.2 cm. Figures 43 and 44: T-42.7 cm and !--4.3 and -1.2 cm. Figure 45: Figure Figure Figure Figure Figure 46: 47: 48: 49: 50: I-45.8 cm and I-7.3. -4.3 and -1.2 cm. x-48.8 cm and Y--4.3. -1.2 and 1.8 cm. X-51.9 cm and I--4.3.-1.2 and I-1.8 om. I-58.0 cm and T--4.3.-1.2 and 1.8 cm. x-61.0 cm and T-—4.3.-1.2 and 1.8 cm. X-134.2 cm and I--4.3.-1.2 and 1.8 cm. CHAPTER 7 DISCUSSION OF VORTICITY lEASURElENTS IN AN EXCITED lIXING LATER 7.1 Introduction In the present section the detailed properties of the phase aver- aged vorticity field over 15% of the excitation cycle (and some aspects of the quasi-instantaneous vorticity time series from representive spatial locations) are examined. The phase averaged vor- ticity is created by the excitation of the separating boundary layer of a single stream mixing layer. Fieldler and coeorkers (1978. 1979. 1980. 1982) have extensively examined the general features of the excited mixing layer: the present results are in agreement with and extend their observations. A promi- nent feature of the phase averaged vorticity field is the existance of relatively large scale vertical motions at some distance downstream from the separation lip. It is important to emphasise that these ecll defined vertical structures would not be observed in the time (or ensemble) averaged data from an unexcited mixing layer. Such struc- tures. or coherent motions. are known to exist in an unexcited mixing layer. but spatial and temporal irregularity of their occurence would 45 46 not allow them to be discerned in a time (or ensemble) average representation of the flow field. Figure 51. shows a smoke photograph taken from the Dr.-Ing. Thesis of P. lensing (1981. photograph 3). The dimensionless phase averaged isotochs. UlU.-o.1 and 0.95, and the smoke photograph taken at the same phase time are superimposed showing that an instantaneous and the phase average representations of the flow are in good agreement. This is representative of the repeatabil- ity (in the flow behavior) that is created by the excitation process. From this figure (lensing's) the prominant features of the excited mixing layer can be identified: i) The mixing layer width. as defined by the 0.1 and 0.95 isotach contours. exhibits a sudden increase at a streamwise distance that is slightly upstream of the first identifiable vortex. ii) As the vertex moves dovnstream it grows in size and its per- iodic (or phase average) energy reaches a maximum at a location X' (St‘fil). At this location the vertical motion is said to be saturated. That is. the vortex has reached the end of the region of amplification and eill no longer be amplified. iii) Slightly upstream of the location of the saturated structure the mixing layer exhibits another rapid change in width. iv) A thin region of concentrated vorticity exists between the separation lip and the first formed vertical motion. In the present study this region is termed the "tongue". 47 Seven contour plots of phase averaged transverse vorticity. (0:)i have been selected for discussion. Each plot represents the phase averaged transverse vorticity field at a phase time i and the seven plots cover 15! of the excitation cycle. The evolution of the phase averaged transverse vorticity can be determined by a comparison of two or more contour plots. In addition. plots of the streameise component of velocity for several X-planes have been included for reference (see Figure 29). These considerations are dealt with in the folloeing sec- tion. 7.2 Phase Averaged Streamwise Velocity The non-dimensional phase averaged streameise velocity component. (U(I))1IUo is presented in Figure 29. An examination of these curves indicates the varying slope at the lateral end points of the measure- ment grid as the profile is plotted at subsequent downstream X-planes. The flattening or spreading out of the velocity profiles is apparent downstream of the separation lip. Figure 30 depicts the ("(I)>1IU° profiles obtained at an X-plane approximately aligned with the center of the saturated structure for successive phase times. This plot indicates that the streamwise nonrdimensional velocity profile at this specific X-plane is relatively independent of the phase time. 48 7.3 Evolution of the Phase Averaged Transverse Vorticity 7.3.1 Spatial Distribution of the Phase Averaged Transverse Vorticity The phase averaged transverse vorticity. (0‘). contours. are presented in Figures 22 to 28. These contours shoe the general features of an excited mixing layer. The insensitivity of some features of these <01)! contours to random perturbations in the flow is discussed in section 7.4. This insensitivity allows detailed exam- ination of these features eith the confidence that the perceived features are not an artifact of the contouring routine. A comparison of lensing's photograph 3 (Figure 51) to the phase averaged transverse vorticity: <7s>i' contours obtained in the present work indicate good agreement beteeen the general features of the two flow fields. A relatively thin region of vertical fluid. which extends from the separation lip downstream to the newly formed vertical structure. is also visible. This relatively thin. highly vertical. region is characterised by: i) the closed vertical contour lines (<'s)i‘14°'15° ...) and ii) a slight linear growth of the contour lines upstream of the closure region. As in section 7.1 item iv) above. this region is termed the tongue. There are two options for selecting a distance used in the nondi- mensional represention of the downstream distance (X): they are: i) use of the momentum thickness of the separation boundary layer. as has 49 been standard in the unexcited mixing layer. or ii) use of U/f° resulting in a Streuhal number based on X. The latter has been selected to slice direct quantitative comparison to the studies of Fiedler and coeorkers. In the present discussion Figure 28b will be used to compare the present work to that of Fiedler and coworkers. An examination of Fig- ure 28b (I320) indicates that the boundary layer "tongue" extends downstream to approximately X-42 cm or St,=o.4s. A rapid change in the width of the lower level vorticity lines on the low velocity side of the mixing layer is observed (see X-28 to 33 cm) in Figure 28b. After this rapid growth. the width of the mixing layer is approximate- ly constant. This region of approximately zero growth continues downstream to the nominal upstream boundary (X-43 cm. Stx-o.496) of the first fully formed vortex motion. The location of this first vor- tex is termed the region of "roll-up" by Fiedler and coworkers and it is preceded by another short segment of rapid growth in the width of the vorticity contours. The center of this first vertex is at Xzss cm or Stx=0.55. This value is in quite good agreement with the cor- responding location (Six-0.5) from the lensing study. A region of nominally zero growth exists downstream of the first newly formed vortex. This "constant" width region is terminated by another region of rapid growth just upstream of the saturated vertical structure. The position of this second vortex (X‘ugs cm) 1. in strik- ing agreement eith the equivalent vortex motion (the saturated vortex) 50 that was observed by Fiedler and coworkers [1980. 1982]; see item ii of Section 7.1. For a weakly excited flee. they found that the nondi- mensional downstream distance where the saturated structure is located 18 3°14t°d ‘0 StI. Interpolating Stx from lensing's work (1981) for a similar excitation intensity the following was obtained: St: - f. 9 X‘ I Uo 8 0.97 (where St‘-O.97 is based on an approximate excitation intensity of 0.0052 as compared to 0.00537 in the present investigation). For the present investigation a 3t. a 0.98 was determined. Farther downstream the periodic energy of the saturated structure starts to decay. with little or no increase in the width of the shear layer. The distance beginning at the location of the saturated structure and extending downstream to a location ehere the Stx 51.5 is termed the decay region (Chapter 1) by Fiedler. et.al. For the present work. the decay starts at approximately X-85 cm and extends downstream to X-140 cm (to the center of the decayed structure). This is equivalent to Stx u1.6, which differs by 6.6 I»from the value found by Fiedler and coworkers [1980.1981.1982]. At this position. X-140 cm (the end of the decay region). another rapid change in the shear layer width is observed; beyond this position. it is inferred (from the observations by Fiedler. et.al.) that the shear layer will slowly assume the character of a natural shear layer. Bence. any noticable effect of excitation is found to persist only up to a streameise position of approximately 140 cm. 51 7.3.2 General Tbmporal Evolution of the Coherent Vorticity Contours The temporal evolution of the coherent vorticity. (oz)1 can be qualititively obtained by a comparison of Figure 22 and 28 (each con- tour plot represents a specific phase time. i). The detailed observations obtained from such comparisons are listed in Appendix C. The following observations are based upon a net evaluation of these separate observations. From the phase averaged transverse vorticity contours it has been observed that the lower level vorticity contour lines. from the high speed side. make deeper depressions into the mixing layer (at X-42 and 73.2 on) than their counterparts on the low speed side. Accompanying this depression of the vorticity lines is an increase in the phase averaged lateral velocity (V) on the upstream side of the depression by approximately 25 I (of. the (V) value of the fluid in the region 'hOtO 93° (0,) contours are "parallel" to the X axis). In a compli- mentary way the growth and shrinkage of the concentrated vortidal structure (vorticity values from 80 to 160) appear to be more dominant on the low speed side. The average structure velocity (U. was obtained for the newly formed vortex. the saturated vortex and the decayed vortex using the ratio ALIAt. The displacement: AL is the doenstream distance a spec- ific vertical structure moved in the sample time interval: At. The average structure velocities were determined to be: 52 U, - 0.70 mIs for the newly formed structure 'U‘ - 5.51 mIs for the saturated structure U‘ - 1.76 IIs for the decaying structure As suggested by the velocity values. the translation of the three structures are quite different over the observation time of 15 percent of the complete cycle. The newly formed vertex moved 0.72 cm. the saturated vortex.moved 5.64 cm and the decayed structure moved 1.7cm. If the 320th phase point is used to establish a characteristic "wavelength". it is noted for reference that the distance between the newly formed and the saturated vertex is 36.5 cm. The velocity of the saturated structure. quoted above. is an average value: a more detailed examination of the time dependent posi- tion of the structures center is presented in Figure 52. The slope of this curve indicates the core velocity of the saturated structure. These velocities vary an order of magnitude and appear to indicate that the core has undergone periods of large acceleration and decel- eration. The positions obtained by this method are estimates. in as much as they depend upon the somewhat arbitrary selection of "the ver- tex center”. The dashed curve in Figure 52 is based upon the center of the saturated structure using the perturbed contours. This curve shows greater scatter but the trend is similar to that for the meas- ured data. The perturbed results suggest that the non-uniform 53 translation of the vertex core may be an strongly influenced by the data processing procedures. In a similar manner. it can be determined that the front and the back of the large. saturated. vertical struc- ture move at different speeds. Specifically. the front velocity. Uf ‘5-43 '1' and th' back.velecity. 0; -3.86 mIs. Evidence of this is also found in a flow visualisation study preformed in an axisymmetric mixing layer by Hussain and Clark (1981). The lateral location of the boundary layer tongue and of the centers of concentrated vertical fluid appear to be distributed sym- metrically around the IZ-measurement plane where I--1.2 cm. If a measurement plane were aligned eith the separation lip (at I-O) it is possible that symmetry eould exist around that plane. This is a result of the large spatial velocity gradient. [ aUIdI ivy-0 , that exists at the separation lip and its influence on all points doenstream. There are two dominant vortex interactions ehich have been observed in the present experiment. They are the "tearing and fusing” of vertical fluid masses. The tearing process appears to be related to the deep incursions of the lover level vertical fluid from the high speed side of the mixing layer. The extent to which the vorticity contour lines are torn and the size of vertical fluid mass which is 54 separated is related to the distance doenstream from the separation lip. That is. the farther downstream the structure is located when this tearing process takes place. the greater is the number of vorti- city contour lines that are torn and the larger is this separate fluid mass. The fusion process is one in which two or more vertical fluid masses are brought close to each other. fuse and become one vertical mass. 7.4 Global Evaluation of the Perturbed and Unperturbed <"s’i Contours The purpose of this section is to summarise the inferences that are based on the data perturbations. Recall from section 6.4 that the perturbed phase averaged transverse vorticity. (elz’)1 contours were derived in the same manner as (at)! with the exception of the random addition or subtraction of a random voltage perturbation to the data before the processing stage. This random constant (‘3. took on the discrete values from 0 to t .25; in increments of 0.06253. where 3' is the time averaged standard deviation (discussed in section 6.4) of the unprocesed data. The spread of the mixing layer in both the perturbed and unperturbed cases are approximately the same. In addition. the locations of the concentrated vertical structures are also similar and the vortex interactions observed in the unperturbed case can still be observed in the perturbed contours. In general the only differences in the two cases are the magnitudes of vorticity; that is the level of vorticity in structures in the perturbed case appear to be greater than the unperturbed case by approximately 10 I. The deep depression 55 of loeer level vorticity lines in the region between the tongue and the newly formed vertex is also present. Therefore. it is concluded that in general. the major features. observed in the unperturbed case. are “robust" results and are not altered by perturbations to the ori- ginal data. It should be noted that. in general. larger perturbation levels led to more "closures" of the vorticity contours. See the large X values of Figures 28 and 36 as examples of the "closure" effect. 7.5 Phase Averaged Transverse Vorticity Time Series An investigation into the phase averaged transverse vorticity. (0,). time series in Figures 39a and 39b to 40s and 40b. provides quantitative information in support of the events observed in the (0,)! contours. Note that these time series extend over 15.4 percent of the full cycle. An examination of Figures 39a and 39b (Xn48.8 cm and Ib-7.3. -4.3. -1.2. 1.8. 4.9. 7.9 and 11.0 on) shows the level of phase aver- aged transverse vorticity variation to be of the same order at the center of the newly formed vortex (Y-1.2 cm) and on the vortex peri- phery located at I-1.8 on; the variation is considerably reduced at I--4.3 cm. A similar comparison has been made for the saturated structure (Figures 40a and 40b). The center of this structure is located at 1285.4 cm (and ire-1.3. -4.3. -1.2. 1.8. 4.9. 7.9 and 11.0 cm). The results indicate approximately the same magnitude of phase 56 averaged transverse vorticity variation at the structure center (T--l.2 cm) and its peripheries located at I--4.3 and 1.8 cm. Therefore it can be concluded from the phase averaged transverse vor- ticity time series that the center of the saturated structure is relatively calm on the average and that the (“2) variations in the concentrated vertical core is of similar magnitude as the (“2) varia- tions on the vortex peripheries. 7.6 Quasi-Instantaneous Transverse Vorticity 7.6.1 Introduction Thirty sets of high-rate (32 us) data samples were collected at each point in the measurement grid. The majority of these sets are 2.5 ms in duration: two X-planes. as noted below provide 10 ms dura- tion records. The transverse vorticity is computed for small (1 1 mm x 1 mm) micro-circulation domains from these data. The resulting out- put is an irregular function of time as a result of the convected displacement which defines the length of the domain. Therefore. the output is termed a quasi-instantaneous time series of the transverse vorticity. Prior investigations of excited shear layers have not employed direct measurement of vorticity: hence. the results of this section are unique observations. The plots of quasi-instantaneous transverse vorticity ('z) shown are representative of the thirty sets of time series at any given (X.I)-measurement location. unless othereise specified. Specifically. 57 the representative plots were derived using the folloeing procedure: i)the mean and standard deviations were evaluated for each of the thirty time series. ii)a single time series. which had a standard deviation and a mean value that were similar to the average of the group of thirty. was selected as the representative case. It is recognised that this process provides only a qualitative basis for the comparisons of the phase averaged and the instantaneous vorticity values. Boeever. these comparisons are quite instructive and they are included herein for this purpose. 7.6.2 Quasi-Instantaneous Transverse Vorticity Time Series Figure 39 is a representative plot of 01(1) for three lateral locations in the tongue region at x-18.4 on. Their respective phase averaged values for the first phase point are included on the figure for reference. Large excursions of the vorticity at the center of the tongue are evident in this figure. The representative excursions near the high speed edge of the tongue. Y--4.3 cm are relatively small (2100 s") ehereas the low speed edge of the tongue exhibits inter- mediate level excursions. The limited data for the low speed side is indicative of the number of time steps which are required to form a complete circulation micro-domain. Figure 40 shoes tee additional time series at X-18.4 on: these where selected to represent the extreme cases for minimum excursions 58 at the centerline and relatively large excursions at the high speed edge. It is interesting to note that the excursion levels. for the two I locations. are approximately the same. Figures 41 and 42 are for X-33.6 cm. The former presents the representative conditions at X-33.6 cm and the latter Figure 42 shoes two traces for which the excursion levels. at the high speed edge of the tongue and near the tongue centerline. are quite similar. The excursions are. again. seen to be quite large with respect to the phase averaged values. In the region between the tongue's end and the neely formed vor- tex (X-39.7 to 45.8 cm) the net convective transport of loeer level vertical fluid from the high speed side can be observed in the phase averaged transverse vorticity contours. An examination of the a: ti-g series (Figures 43 and 44) which where obtained at 1-42.7 on. show high levels of vorticity fluctuations at the lateral locations: the high speed edge of the tongue (I--4.3 cm) and in the central region of the strongly vertical region (-1.2 cm). Unlike the tongue region. in which the excursions at the edge regions were small eith respect to those near the centerline. the intermediate valanes exhibit excur- sions which are large at both centerline and at lateral I-locations:-4.3 cm. It is considered to be significant that the quasi-instantaneous vorticity values show a distinctively different behavior in a region of the flow field where the phase averaged cone tours contours also exhibit a distinctive change. 59 Relatively large vorticity fluctuations can be observed in the neely formed vortex (at X-48.8 cm. !-4.3 on. see Figure 45). In addition. ‘50 0; fluctuation activity in the center of this new vortex (at I--1.2 cm) is approximately the same order of magnitude as the adjacent lateral positions on the periphery of the vertical structure. At the next downstream measurement plane (X-51.9 on. Figure 46) the peak level of the a z excursions. at Y--1.2 and 1.8 cm. are also of the same order of magnitude. An examination of the complete set of the instantaneous records reveals that the frequency of the at fluctua- tions at I-1.8 cm is systematically less than that at the central core and the high speed edge of the active region. Figures 47 to 49 present a series of representative “z(‘) distri- butions at the streameise locations: 58.0. 61.0.79.3 and 134.1 cm respectively. Althreugh detailed differences exist. each of these stations can be characterised by similar magnitudes of peak excursions at the three lateral locations and by the relatively lower frequency of fluctuations at the I--1.8 on locations. The at excursions in Fig- ure 45 through 48 are quite large eith respect to their respective phase averaged values. In general the average level of the transverse vorticity fluctua- tions in the decaying region (X-134.1 cm. Figure 50) are smaller than at the upstream locations. Occasional oz spikes of approximately 40 times the phase average transverse vorticity have been found in a number of the time series at this Xrlocation. 60 7.6.3 Quasi-Instantaneous Transverse Vorticity Summary The peak quasi-instantaneous transverse vorticity fluctuations in the tongue region reach a maximum in the core. These values of quasi-instantaneous transverse vorticity. at are approxiaately 20 times larger than the phase averaged transverse vorticity. <“s’i . This confirms the concern regarding the possibility of ensemble aver- aging smearing out the peak values of vorticity (Dimotakis. Debussy and Ioochesfahani.1981). In addition there were realizations in which 0, in the core region were of the same order of magnitude as a values s at the laterally adjacent measurement points outside the concentrated tongue. The quasi-instantaneous vorticity time series. although limited in scope. can be used to infer some basic features of the vertical regions. It is considered to be instructive that the fluctuation lev- els.across the newly formed and the saturated vortex motions are relatively large. This indicates that the entire vertex is a region of strong "activity". In contrast. Iygnanski. Oster and Fiedler (1979). have shown that the thermal field. in the core region of a large forced vortex motion. is relatively "inactive" whereas the boun- daries of the vortex exhibit large temperature gradients and temperature fluctuations. The difference beteeen these two measures of the excited mixing layer can be attributed to the different response in the vertical and in the thermal properties of a flow eith intense. small scale. vortex motions. Specifically. it is inferred 61 from the vorticity measurements that the relatively high frequency and strongly fluctuating vorticity values are representative of such a flee. For a given amount of thermal energy (supplied in the upstream boundary layer) a flow field with energetic small scale motions would lead to enhanced heat transfer between adjacent fluid elements; hence. the imbedded temperature variations would be smoothed out by the enhanced diffusive effects. In addition it has been found that the frequency of occurrence of these vorticity fluctuations varies throughout the newly forming structure. That is. the vorticity fluctuations on the low speed side (I-1.8 cm) of the mixing layer are characterized by smaller frequency fluctuations in comparison with the fluctuation frequencies of the I--1.2 and -4.3 on locations. Conversely the frequency of occurrence (Of these 0, fluctuations) appear approximately the same throughout the saturated structure. In general. lower levels of ”z are found in the decay region. Iith the exception of an ocassional e spike. this decaying process appears to be quite violent at times generating fluctuations of at approximately 40 times the phase averaged transverse vorticity. CHAPTER 8 CONCLUSIONS From the examination.of the eeakly excited and unexcited turbu- lent boundary layers. the following has been determined. The mean velocity profiles obtained from the turbulent boundary layer surveys show good agreement with Coles law in the logorithmic region. This agreement in the mean velocity profiles will enable computational fluid dynamists to apply modeling techniques to the excited mixing layer using Coles lae as a valid initial approximation to the velocity profile in the turbulent boundary layer. In addition. a slight reduc- tion in the momentum thickness was obtained in the present work when the boundary layer eas excited. The prominent features of the phase averaged field: the tongue. the newly formed vortex. the saturated vortex and the decaying vertex. that were observed by Fiedler and coworkers are also observed in the present study. Using the 320th phase point as a representative condi- tion. these last three structures appear at the nominal Streuhal number locations of: St,-f,'1/Uo - 0.55. 0.98 and 1.6 respectively. These values are in good agreement with the corresponding values reported by Fiedler and coworkers. The phase averaged vorticity contours indicate the deep depres- 62 63 sion of vorticity lines on the high speed side of the mixing layer. In addition. the dominant growth and shrinkage of the vertical fluid masses seem to be more predominant on the low speed side of the mixing layer. It has also been observed (over the available 155 of the exci- tation cycle) that the cores of the vertical structures move at different speeds. Specifically. the saturated structure appears to move with a much larger average velocity. including periods of rela- tively large acceleration and deceleration. The existance of vortex interactions. such as tearing and fusing of vertical contours has also been observed. The measurement of quasi-instantaneous transverse vorticity in the tongue and farther downstream in the vertical structures. have shown peak values of transverse vorticity excursions which are an order of magnitude larger than those of the phase averaged transverse vorticity. This sheds considerable light on the vertical activity within the concentrated vortex. In addition. these large instantane- ous transverse vorticity fluctuations appear to have the same order of magnitude both in the concentrated region and the periphery of the vertical structures. Although the peak values of the quasi-instantaneous transverse vorticity. throughout the vertical structure. are of the same order of magnitude. their frequency of occurrence is not. Specifically. the occurrence of these large excur- sions is less frequent on the low velocity side of the mixing layer in the newly formed vortex. FIGURES 64 an: ocean 5:33“ to; unemm noun a one»: x\\\\\\ \.\\ \ R in“ .31 n 35.2 2;: 1.3.72.5 >>Iv .1. >.._1 mOZm hzwihmaao< udhhost. \‘ hop-25 nauauuoufl. 5150 H2:— v onus:— _..Il|.' . .( 8 8 Q. 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I I I? ON p v w . O. O. o. In “a 99 Y POSITION (m) -0.05 0 0.05 0.10 0.15 I I I l I II II d O X: 146.3011 X= I3” cm ‘\\ x=nsacm \ X =I00.6¢m X=05.4 cm l ./ Ill Iol LJHIOI I II «Fl 0 T— X=70.I cm a L - I x-sepcm %— X=39.6¢m — A L X=24.4 cm -Z.@73 -0.@13 0.048 0.108 0.189 Y PoslIlon ' (m3 Figure 29 Phase Averaged Non-dimensional Velocity Profiles; For Phase Point. i-320 and at 1-24.4. 39.6. 54.9. 70.1. 85.4. 100.6, 115.8, 131.1. 146.3 on 100 v POSITION (m) - 0.05 0 0.05 010 l1 II I II I I 0.15 o -o -- JILIIII III—I «4.6 O cDI I l—Iol l l-Iol l l-IOI II IIIIITIIII I'I‘ i=320 I: 289 I: 227 I: I87 I=I25 i=1 1 -0.073 -0.@.1.3 0.048 0.108 @189 Figure Y PoslIlon (m) 30 Phase Averaged Non-dinensional Velocity Profiles; at l-85.4 on and i=1, 63, 125. 187. 227. 289 and 320 . 101 nemkan an. 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J...” 127 Thble A.1 Effect of Cubic Spline End Condition on the Cslculstcd Vor- ticity 1(cl) Y(°-) <~.>(s") <0,>/<.,> s <..>/<..> s 12.3 —7.3 19.33 100.00 -235.50 12.3 -4.3 42.73 —12.31 27.76 12.3 -1.2 237.63 0.57 -1.53 12.3 1.3 162.13 0.16 0.76 12.3 4.9 -32.44 -4.01 -1.11 12.3 7.9 6.99 -24.46 5.44 12.3 11.0 -4.21 -33.49 9.74 12.3 14.0 -0.73 -227.40 41.10 12.3 17.1 -0.61 -100.00 290.16 15.3 -7.3 17.35 104.33 -207.33 F? 15.3 -4.3 47.15 -10.24 20.66 1, 15.3 —1.2 236.15 0.55 -1.04 J 15.3 1.3 160.94 -0.32 0.37 g 15.3 4.9 -29.10 1.62 —0.43 15.3 7.9 6.40 6.56 -1.25 w -... 15.3 11.0 -3.03 12.66 0.97 15.3 14.0 -0.07 623.57 -942.36 15.3 17.1 -0.35 21.13 193.32 13.3 -7.3 11.79 104.66 -57.76 13.3 -4.3 59.36 -5.53 3.01 13.3 -1.2 224.91 0.40 -0.23 13.3 1.3 146.47 -0.14 0.10 13.3 4.9 -13.04 -0.22 —o.22 13.3 7.9 5.03 -2.56 0.20 13.3 11.0 -1.32 -9.09 3.33 13.3 14.0 0.27 -11.11 -114.31 13.3 17.1 -0.50 -76.00 266.00 21.4 -7.3 7.22 101.30 259.97 21.4 -4.3 70.53 -2.79 -7.11 21.4 -1.2 213.01 0.25 0.64 21.4 1.3 137.43 —0.12 -0.27 21.4 4.9 -4.35 1.33 2.30 21.4 7.9 2.90 0.34 -1.72 21.4 11.0 0.05 30.00 100.00 21.4 14.0 0.75 -4.00 -29.33 21.4 17.1 0.32 63.75 234.37 24.4 -7.3 9.31 93.56 307.20 24.4 -4.3 77.39 -3.01 -9.90 24.4 -1.2 199.40 0.32 1.03 24.4 1.3 136.13 -0.12 —o.40 24.4 4.9 7.61 0.53 1.34 24.4 7.9 1.97 -1.02 -1.52 24.4 11.0 1.35 0.74 0.74 24.4 14.0 0.31 —9.33 1.23 24.4 17.1 0.67 33.31 -4.43 27.5 -7.3 3.16 66.91 466.54 27.5 -4.3 33.91 -1.74 -12.16 27.5 27.5 27.5 27.5 27.5 27.5 27.5 30.5 30.5 30.5 30.5 30.5 30.5 30.5 30.5 30.5 33.6 33.6 33.6 33.6 33.6 33.6 33.6 33.6 33.6 36.6 36.6 36.6 36.6 36.6 36.6 36.6 36.6 36.6 39.7 39.7 39.7 39.7 39.7 39.7 39.7 39.7 39.7 42.7 42.7 42.7 42.7 42.7 42.7 42.7 42.7 42.7 45.8 I “Q.HQ‘HH O 0.. h4h4h4 O O .1- I .s-q-a-qu-a.snn1a 0 O O O hihibi O O h4h4h4 I O O O O O O O #43494 I O O O O O C O I Jb~l~labh|~lOshiFla-I~IJ4FI~IO4FIhi O Iaid13¢:‘O‘OGIt9iniutd¢3¢:\olotnlozniuid<3¢3\olochIOiuand1313‘O‘DGDIotniutdGaibloiotll0¢ntnldl3h4h4 O p 131 2.84 16.77 72.64 126.13 118.25 86.34 51.93 27.64 9.35 4.06 16.32 61.39 109.75 103.93 76.06 46.77 24.86 8.04 3.82 4.43 44.83 92.04 86.90 70.68 47.63 27.25 10.30 4.53 5.17 43.26 89.17 81.46 64.99 55.09 27.30 10.56 6.27 -0.74 30.77 69.39 64.90 59.01 53.13 27.91 10.00 5.96 7.47 27.79 61.69 57.13 53.01 48.55 30.98 120.77 103.94 -6.43 1.00 -0.29 0.13 -0.17 0.98 -10.80 92.86 80.27 -5.72 0.87 -0.25 0.12 -0.24 1.37 -15.30 119.37 287.81 -7.63 1.00 -0.29 0.13 -0.25 1.28 -12.72 107.95 248.94 -7.98 1.04 -0.31 0.15 -0.27 1.87 -17.90 112.12 2167.57 -13.94 1.66 -0.49 0.20 -0.30 1.86 -19.50 122.15 300.54 -21.66 2.61 -0.77 0.30 -0.37 1.81 -49.30 203.34 -12.58 1.94 -0.56 0.21 -0.10 0.14 -1.39 11.33 192.71 -13.73 2.06 -0.58 0.20 -0.02 -0.48 5.97 -47.91 672.69 -17.80 2.33 -0.66 0.21 -0.08 0.00 0.39 '3.53 473.89 -15.16 1.97 -0.58 0.18 0.00 -0.40 4.26 -26.95 2951.35 ~19.01 2.26 -0.65 0.19 -0.04 -0.18 2.00 -12.25 220.75 -15.90 1.91 -0.56 0.17 -0.12 0.42 97.6 97.6 100.6 100.6 100.6 100.6 100.6 100.6 100.6 100.6 100.6 103.7 103.7 103.7 103.7 103.7 103.7 103.7 103.7 103.7 106.7 106.7 106.7 106.7 106.7 106.7 106.7 106.7 106.7 109.8 109.8 109.8 109.8 109.8 109.8 109.8 109.8 109.8 112.8 112.8 112.8 112.8 112.8 112.8 112.8 112.8 112.8 115.9 115.9 115.9 115.9 115.9 115.9 I I L ~l 0 . ”DONNNHOOUQONuwHOOUUQNWuI-iOODUQRUWHOOUUONWN #43444 . 0 0 . . 0 IIIHHH I I «bIdId-b-d-dubIfl-d-bIHIfl-b'd-4.bId-Q-LIHIH 0.00.0.0... 0 Fihihi -4-e«bId-q 0 Al hlhihi 0 «q-e.buu~q-bnu . .3- “‘3'.“ o 132 13.55 6.40 19.31 45.96 66.32 56.56 57.74 50.57 30.20 16.14 9.65 35.33 42.57 62.21 67.65 57.90 50.80 35.35 17.60 10.70 37.18 51.22 63.51 62.19 60.60 51.40 33.25 21.12 10.78 43.00 53.66 66.18 67.25 62.06 44.76 37.97 22.00 9.81 50.11 59.69 66.69 60.60 61.07 50.53 38.11 24.69 15.81 55.97 61.18 76.49 74.75 66.24 52.36 -15.42 121.56 144.17 -16.23 3.02 -0.95 0.35 -0.44 2.32 -15.86 98.86 114.21 -25.39 4.66 -1.17 0.45 -0.49 2.15 ~15.74 96.26 110.81 -21.55 4.66 -1.30 0.45 -0.53 2.44 -13.97 102.13 99.74 -21.41 4.65 -1.25 0.42 -0.54 1.82 -11.45 95.41 97.63 -21.96 5.28 -1.60 0.54 -0.67 2.78 -15.80 92.03 85.03 -20.84 4.47 -1.24 0.48 -0.67 -3.62 28.44 114.03 -12.84 2.38 -0.74 0.23 ~0.16 0.66 -4.58 28.19 7.33 -1.62 0.29 -0.09 0.03 -0.04 0.20 -1.48 8.79 22.73 -4.41 0.96 -0.27 0.12 -0.23 1.17 -6.91 50.46 25.35 -5.44 1.19 -0.33 0.15 -0.34 1.32 -8.32 69.52 18.50 -4.17 1.00 -0.31 0.11 -0.20 0.94 -5.43 31.56 1.57 -0.38 0.08 -0.03 0.05 -0.19 115.9 115.9 115.9 118.9 118.9 118.9 118.9 118.9 118.9 118.9 118.9 118.9 122.0 122.0 122.0 122.0 122.0 122.0 122.0 122.0 122.0 125.0 125.0 125.0 125.0 125.0 125.0 125.0 125.0 125.0 128.1 128.1 128.1 128.1 128.1 128.1 128.1 128.1 128.1 131.1 131 .1 131.1 131.1 131.1 131.1 131.1 131.1 131.1 134.2 134.2 134.2 134.2 134.2 343434 ~a~3a-34 0 .* 343434 0 . 0 . 0 0 . 343434 0 0 IHHH -d-4-hId-d-5Ifllflub-d-dubIfl-d-bldId-b-d-d.bIfl-dubldld 0... . .4» 343434 I I I 343434 ~l~aas34~aJ~3434au~1~2au34~3a-3434 0 . . 0 0 0 . 0 0 . 0 0 . . 0 A . UQNQDWHOOUDGNQ’WHQOUWUNO’WH000%“NuwHOOUDNNwUI-‘OOOUQNQDWHOO I .34444 . 133 34.76 23.99 16.25 58.87 63.55 72.99 69.95 53.33 49.38 35.11 20.60 20.08 42.35 49.52 58.56 65.52 58.40 47.56 40.79 28.81 17.29 41.25 56.72 68.14 71.91 65.74 50.12 42.04 31.56 25.40 43.80 59.52 73.55 69.24 66.69 51.83 40.49 31.42 21.70 32.64 48.56 72.01 65.27 61.34 52.35 39.90 31.78 26.98 40.17 59.39 78.19 73.92 63.26 3.05 -16.22 89.29 86.22 -21.40 5.01 -1.44 0.69 -0.95 4.22 -26.50 101.44 101.02 -23.14 5.26 -1.30 0.53 -0.86 3.19 -16.73 103.93 79.42 -15.48 3.46 -0.93 0.46 -1.06 4.26 -21.07 97.64 76.94 -15.17 3.29 -0.98 0.42 -0.87 3.83 -18.30 98.85 87.65 -15.77 2.87 -0.89 0.47 -1.03 4.69 -21.81 95.92 75.85 -13.82 2.78 -0.87 0.44 1.04 -5.54 30.40 7.90 -1.97 0.47 -0.13 0.00 0.14 -0.83 5.34 -20.42 -4.58 1.05 -0.22 0.03 0.05 -0.38 1.62 -8.61 53.50 35.22 -6.86 1.53 -0.40 0.12 -0.08 0.14 -0.70 3.11 26.14 -5.14 1.13 -0.33 0.15 -0.29 1.28 -6.05 32.76 26.23 -4.76 0.83 -0.28 0.08 -0.13 0.50 -2.30 10.16 33.78 -6.01 1.32 -0.31 0.19 134.2 134.2 134.2 134.2 137.2 137.2 137.2 137.2 137.2 137.2 137.2 137.2 137.2 140.3 140.3 140.3 140.3 140.3 140.3 140.3 140.3 140.3 143.3 143.3 143.3 143.3 143.3 143.3 143.3 143.3 143.3 146 .4 146.4 146.4 146 .4 146.4 146.4 146.4 146.4 146.4 149.4 149.4 149.4 149.4 149.4 149.4 149.4 149.4 149.4 7.9 11.0 14.0 I 34 ~l~l 0 0 «434 . HOODUQNWIHHOOWDONUWHOO‘OUONumHOOUWONWuflOO‘DOBNm I343434 ~3~Ia-34~Ia.3434a. 0 0 . 0 I . 0 343434 Iu-b-q-a-sIa-a-quoa . PHI-l .Qd‘I-‘QJH . I «a-4.uIa-a.LIaIu . . . 0 HHH .0 Q‘HQ..‘H§ o HHH 134 48.71 40.05 36.32 28.29 41.40 57.67 77.99 85.94 61.86 44.27 46.65 36.38 26.00 38.98 52.01 79.97 83.83 61.38 44.24 45.01 38.51 25.85 7.75 23.77 51.40 55.32 52.91 47.64 35.78 33.60 27.92 13.91 28.24 43.90 52.70 41.17 40.90 40.79 28.08 30.96 40.28 65.11 80.20 71.38 65.71 50.15 43.38 36.47 25.79 “1.17 4.97 “20.37 97.56 77.63 “14.70 3.08 “0.69 0.57 “1.15 3.88 “18.31 95.58 76.86 “16.42 2.30 “1.04 0.13 “1.31 4.11 “18.15 100.43 289.81 “17.25 5.49 0.85 2.00 “0.97 6.15 “23.21 105.59 182.53 “49.36 “5.92 “7.72 “6.46 “2.81 4.88 “31.13 100.61 100.00 24.30 24.25 17.37 17.27 2.71 6.50 “15.00 100.00 “0.18 0.82 “3.30 15.87 12.51 “2.90 0.22 “0.30 “0.08 “0.54 1.31 “6.46 33.54 2.46 1.50 1.04 0.61 0.85 0.02 1.84 “7.24 41.20 88.52 “23.94 “4.55 “3.90 “3.14 “1.91 0.17 “4.23 15.83 150.32 31.13 27.54 13.57 15.72 7.68 1.25 9.44 “21.25 “55.04 “73.38 “51.22 “38.86 “36.48 “22.89 “7.15 29.39 APPENDIX B STANDARD DEVIATION 0F TEE.X“AIRAI VOLTIGES An evslution of the sensitivity of the vorticity contours to per- turbations in the nessured voltsges required the develop-eat of perturhstion vslues for vires one snd two of the X-srrsy. The instsn- tsneous tine series volts;es vere used to oreste estimates of the stsndsrd deviution. I?) vslues ss shown in the following relation- ihip3- th. thlt (0)1 is the stsndsrd devistion based upon the phsse sversged voltsge (8)1 end the instsntsneous voltsge. Bi for the i th phsse point. as 1/2 («pi-[1130 2n“ Inn, 4391’] 2/2 <¢3>i.[1’30 2:: [‘83 ’(Bg>la] The stsndsrd devistions st ouch phsse_point were then sversged over 311 phsse points resulting in 01 und 0,. see Tshle 8.1. 135 I on 12.3 12.3 12.3 12.3 12.3 12.3 12.3 12.3 12.3 15.3 15.3 15.3 15.3 15.3 15.3 15.3 15.3 15.3 18.3 18.3 18.3 18.3 18.3 18.3 18.3 18.3 18.3 21.4 21.4 21.4 21.4 21.4 21.4 21.4 21.4 21.4 24.4 24.4 24.4 24.4 24.4 24.4 24.4 24.4 24.4 27.5 27.5 27.5 27.5 I on I NI e 0 QNflwHOOWDONWWHOOUUQNWNHOODUQNNWHOOVDGNQNHOOUWQNUW 343434 3.3434a-I~aa.34~Ias3434¢. . 343434 I 0 0 0 . 0 0 0 . I I «bId-d-bIdIH-b-d-dcblfl-d 0 0 . 0 343434 0 . I HH-de-bHd-LHchdd‘HQ-LHHQQQ 0 343434 I 0 . 0 0 0 0 0 0 343434 I 0 0 0 . . 0 0 0 136 Ihble 8.1 Stsndsrd Devistion for errrsy Voltsges 31(IV) ;3(") 5.99 51.48 100.85 193.03 87.78 109.83 113.52 102.32 120.81 6.09 40.13 169.56 174.94 54.53 33.21 35.10 30.04 34.10 10.15 42.32 143.41 236.84 52.14 40.64 29.78 28.39 31.34 6.02 53.67 207.68 209.53 68.13 30.61 20.80 21.56 31.05 9.92 47.21 138.13 250.32 64.88 36.26 23.63 26.44 15.07 13.81 49.91 187.14 206.01 6.66 30.91 78.16 146.61 117.98 95.70 101.29 116.19 130.81 5.77 31.12 118.67 137.18 75.00 36.43 50.91 48.85 57.09 6.42 34.64 79.82 170.64 98.69 59.67 42.05 36.09 47.02 7.87 40.43 105.04 186.78 90.86 51.39 53.65 29.17 39.11 9.67 33.92 110.28 191.77 117.37 63.07 44.29 33.07 21.06 12.14 38.34 116.33 158.00 27.5 27.5 27.5 27.5 27.5 30.5 30.5 30.5 30.5 30.5 30.5 30.5 30.5 30.5 33.6 33.6 33.6 33.6 33.6 33.6 33.6 33.6 33.6 36.6 36.6 36.6 36.6 36.6 36.6 36.6 36.6 36.6 39.7 39.7 39.7 39.7 39.7 39.7 39.7 39.7 39.7 42.7 42.7 42.7 42.7 42.7 42.7 42.7 42.7 42.7 45.8 45.8 45.8 343434 -a-d.bIn-a.h 0 J- 343434 . 0 0 . 0 0 0 343434 I 0 0 0 . . 0 0 . I Nd‘fld‘HI-‘dfislddbth‘HI-i 0 .i I 343434 I 343434 34an~a~aas34~1as3434 0 0 . 0 . . 0 0 343434 I I ~l~l04h|~204h|h|04~l~llbhi~304hl 0 0 . 0 0 0 . 0 0 waHOODUONuUI-iOOUUQNUWHOOUWGNNUHOOWUflNUWHOOOQQNODUHOOIDO I 3.4 0 137 105.75 44.05 27.47 14.14 8.49 10.77 45.74 181.38 206.88 120.79 57.71 36.11 27.67 14.11 11.02 48.80 186.48 259.00 159.51 78.00 45.37 28.73 18.66 11.48 69.10 169.96 292.91 128.13 96.68 66.98 33.21 22.43 11.28 9.77 33.50 52.42 172.78 127.81 236.79 263.01 196.42 8.54 12.43 50.43 46.56 1“ .42 110.15 238.48 154.10 308.35 10.82 8.26 33.10 102.87 67.88 46.59 31.10 18.51 11.45 33.49 113.79 184.12 111.26 59.45 55.75 31.83 21.69 13.27 43.77 121.06 194.91 156.41 83.73 43.39 31.59 24.73 11.01 45.69 91.52 206.74 140.66 62.75 50.84 43.84 21.79 14.13 1‘02, 36.10 28.09 67.96 88.26 118.75 181.56 201.20 16.78 16.51 30.66 34.68 104.68 82.54 167.40 155.70 258.29 16.77 13.87 35.21 27.5 27.5 27.5 27.5 27.5 30.5 30.5 30.5 30.5 30.5 30.5 30.5 30.5 30.5 33.6 33.6 33.6 33.6 33.6 33.6 33.6 33.6 33.6 36.6 36.6 36.6 36.6 36.6 36.6 36.6 36.6 36.6 39.7 39.7 39.7 39.7 39.7 39.7 39.7 39.7 39.7 42.7 42.7 42.7 42.7 42.7 42.7 42.7 42.7 42.7 45.8 45.8 45.8 343434 . . 0 0 0 343434 I . . 0 0 . . 0 0 I -q-q-3Ia-4.uuuIn.u-4-4.344-4.3 :1 I ub-d-d-bId-d-filflId 0 0 0 I I343434 . 0 NOWHOOVUNNUDNHOO‘ODONWUHOOUVGNQUHOOWUQNQWHOOUDQNODWHOOIDD 343434 0 . 0 . . I Q~I¥HQ§HH§QQLHQO4HH O I I343434 0 0 0 0 0 0 0 “4.3-9‘34‘3‘3". 0 343434 0 . 0 I I4.3 . 137 105.75 44.05 27.47 14.14 8.49 10.77 45.74 181.38 206.88 120.79 57.71 36.11 27.67 14.11 11.02 48.80 ' 136.43 259.00 159.51 78.00 45.37 28.73 18.66 11.48 69.10 169.96 292.91 128.13 96.68 66.98 33.21 22.43 11.28 9.77 33.50 52.42 172.78 127.81 236.79 263.01 196.42 8.54 12.43 50.43 46.56 144.42 110.15 238.48 154.10 308.35 10.82 8.26 33.10 102.87 67.88 46.59 31.10 18.51 11.45 33.49 113.79 184.12 111.26 59.45 55.75 31.83 21.69 13.27 43.77 121.06 194.91 156.41 83.73 43.39 31.59 24.73 11.01 45.69 91.52 206.74 140.66 62.75 50.84 43.84 21.79 14.13 14.29 36.10 28.09 67.96 88.26 118.75 181.56 201.20 16.78 16.51 30.66 34.68 104.68 82.54 167.40 155.70 258.29 16.77 13.87 35.21 45.8 45.8 45.8 45.8 45.8 45.8 48.8 48.8 48.8 48.8 48.8 48.8 48.8 48.8 48.8 51.9 51.9 51.9 51.9 51.9 51.9 51.9 51.9 51.9 54.9 54.9 54.9 54.9 54.9 54.9 54.9 54.9 54.9 58.0 58.0 58.0 58.0 58.0 58.0 58.0 58.0 58.0 61.0 61.0 61.0 61.0 61.0 61.0 61.0 61.0 61.0 64.1 64.1 138 I3444I4 ~I-sau34~aas34 0 0 . .1 II43434 ubIflIH-L-d-d-FIH-Q-LIHId 0 0 0 0 0 0 0 O I343434 I ##4##.“ 000...... 343434 0 0 Qd-hI-IQI‘H 0 I 1 .- . . umuoouooouuuncouwoonuuucouwooumuuocoooonuuwoooouwuuuoouflow 343434 I .LIa-q-LI444 0 O . 0 0 0 0 I I h|04~l~l I343434 «b-d-d-bld~dcbld .000... 51.93 172.71 129.66 235.84 263.23 196.71 17.86 59.90 140.31 267.31 278.81 97.68 49.23 29.87 24.04 23.71 92.99 190.99 269.88 212.24 153.74 59.53 33.17 21.64 24.13 103.19 215.56 268.28 180.59 140.68 68.70 37.25 31.18 18.44 92.81 187.03 237.15 285.61 101.35 50.04 33.61 25.68 21.04 116.20 192.34 227.86 204.89 113.73 45.35 40.01 25.38 57.05 118.25 28.74 67.96 89.22 119.81 181.59 201.02 22.04 31.56 106.02 210.44 220.65 86.11 93.74 73.05 53.05 22.87 57.53 138.68 194.04 182.24 122.05 99.68 78.20 59.59 17.83 51.75 148.01 136.32 173.33 139.70 120.79 77.37 66.39 19.78 55.19 118.50 164.80 148.43 149.78 98.59 81.07 42.58 26.57 64.85 120.25 125.17 151.06 136.03 115.15 81.20 52.63 31.06 62.28 64.1 64.1 64.1 64.1 64.1 64.1 64.1 67.1 67.1 67.1 67.1 67.1 67.1 67.1 67.1 67.1 70.2 70.2 70.2 70.2 70.2 70.2 70.2 70.2 70.2 73.2 73.2 73.2 73.2 73.2 73.2 73.2 73.2 73.2 76.3 76.3 76.3 76.3 76.3 76.3 76.3 76.3 76.3 79.3 79.3 79.3 79.3 79.3 79.3 79.3 79.3 79.3 82.4 I dd‘HQ-fiHH 0 I343434 3* upcouoeouqu-ocbeeouuuucoooeoubuuocoueouuuuooweoouuuuoouweon 343434 0 0 0 ~a~2au34~aa-3434 . I I 343.. . . . . 343434 . 0 QQ-bI-‘dubI-I 0 I “Q‘HQ‘HH e o e e “0"“ 0e I “Q‘HQ‘HH‘ e IIIHHH so so 343434 0 I . ~4-d-hId-4-LIflId-b . 139 179.95 272.80 223.87 156.02 87.38 32.84 36.64 76.97 133.40 186.87 242.79 253.32 180.79 134.79 47.91 44.61 41.92 140.13 215.16 206.09 204.68 165.68 132.11 69.87 55.08 59.23 132.35 202.13 249.30 251.86 231.32 133.35 113.99 64.76 31.95 111.48 185.99 253.97 249.57 201.90 130.55 102.31 80.54 73.87 117.65 179.95 237.23 250.64 268.51 209.91 124.84 76.99 26.94 98.17 158.78 179.51 151.50 111.71 64.32 44.68 38.93 69.43 92.66 140.76 178.79 128.27 134.54 74.80 51.67 28.69 76.47 115.92 138.13 200.53 177.20 118.92 107.52 70.84 25.86 83.60 133.27 145.58 143.79 200.63 144.96 86.73 84.23 32.56 72.46 106.00 184.83 201.84 206.88 105.88 114.19 94.67 38.79 69.74 119.46 155.33 231.14 197.20 183.44 103.31 86.57 33.21 82.4 82.4 82.4 82.4 82.4 82.4 82.4 82.4 85.4 85.4 85.4 85.4 85.4 85.4 85.4 85.4 85.4 88.4 88.4 88.4 88.4 88.4 88.4 88.4 88.4 88.4 91.5 91.5 91.5 91.5 91.5 91.5 91.5 91.5 91.5 94.5 94.5 94.5 94.5 94.5 94.5 94.5 94.5 94.5 97.6 97.6 97.6 97.6 97.6 97.6 97.6 97.6 97.6 140 IHHH I; I‘Qd‘HQ.HH e e e e e o e e I ..4 . . . 0 0 HOODOGNWO’HOOQDONwWHOOOUQNqu-‘OGIOIONNUWHOODUQNGDWHOCUUQNm 343434 0 0 0 0 I ~844§H~I¥HH§-I~I§H~I§H . 343434 I 0 . 0 . 0 0 0 . 51' 343434 0 0 ~a~aau34~aa.34 0 I 34.3 ee 343434 0 . 0 0 . 0 343434 II -4-hId-4-LIHIfl-b-d-d-bIH-QILIH ......0 100.64 194.65 250.18 274.86 200.12 168.91 132.26 75.10 29.23 41.56 178.10 236.00 269.14 289.96 215.78 135.61 73.00 37.52 83.42 221.65 212.28 315.33 243.60 184.56 146.28 69.28 38.35 75.27 130.92 218.81 213.86 181.66 210.81 165.06 76.34 62.42 58.35 184.65 215.69 279.20 278.02 237.93 117.06 95.32 61.08 115.31 149.82 222.56 290.78 260.72 215.74 98.42 160.56 68.43 152.94 172.52 214.38 189.49 155.90 117.13 100.72 37.39 54.02 94.94 161.75 174.11 222.81 192.86 123.89 86.37 28.02 62.40 96.40 138.30 195.33 186.90 157.61 113.26 89.99 22.86 43.32 91.42 141.53 206.52 186.31 180.19 162.94 105.08 31.93 44.89 101.33 124.15 176.70 176.02 159.97 129.18 103.55 38.30 53.57 113.48 138.18 145.07 216.67 151.14 143.14 122.54 1‘ I. I' I \ 100.6 100.6 100.6 100.6 100.6 100.6 100.6 100.6 100.6 103.7 103.7 103.7 103.7 103.7 103.7 103.7 103.7 103.7 106.7 106.7 106.7 106.7 106.7 106.7 106.7 106.7 106.7 109.8 109.8 109.8 109.8 109.8 109.8 109.8 109.8 109.8 112.8 112.8 112.8 112.8 112.8 112.8 112.8 112.8 112.8 115.9 115.9 115.9 115.9 115.9 115.9 115.9 115.9 141 QQLHd0HHO~I 0 I34343- .... .1- 00000034mun-40°90ueonuuuoceoeouuuuoowoeouuuuoooueou4.5003460000034040» 343434 0 . . . . . 343434 I 0 0 . 0 0 0 0 . I QQ-bHflthchQd-SHQ‘HH . II .1. use. HHH .0 -a-a.3I-4-LI4 . I 343434 I 343. 0 . 0 0 . 0 0 0 II fiHd‘HH‘QQ‘HQ‘I-I‘ ....... 3434 52.62 179.52 213.89 244.21 259.78 236.62 233.81 129.39 85.70 65.49 190.63 239.14 286.22 267.17 264.22 248.58 161.54 110.41 81.57 155.38 239.60 260.49 283.23 226.21 228.74 161.47 136.70 140.92 176.52 178.98 216.33 261.32 212.03 236.09 198.13 159.16 110.07 177.42 170.49 223.36 230.46 232.35 195.81 178.63 123.60 141.10 175.62 194.75 214.67 279.29 224.67 225.37 188.48 45.36 110.56 114.96 142.34 163.12 155.46 181.93 152.66 126.79 45.38 80.66 94.31 120.96 162.52 162.13 195.81 156.53 147.45 41008 78.28 90.71 136.90 149.72 159.10 192.97 181.54 179.86 56.01 90.04 115.59 121.45 142.42 163.99 158.75 159.49 159.05 40.74 73.15 102.06' 113.99 151.78 199.91 174.29 200.08 179.13 66.83 91.74 91.60 132.23 185.22 173.66 203.87 224.33 115.9 118.9 118.9 118.9 118.9 118.9 118.9 118.9 118.9 118.9 122.0 122.0 122.0 122.0 122.0 122.0 122.0 122.0 122.0 125.0 125.0 125.0 125.0 125.0 125.0 125.0 125.0 125.0 128.1 128.1 128.1 128.1 128.1 128.1 128.1 128.1 128.1 131.1 131.1 131.1 131.1 131.1 131.1 131.1 131.1 131.1 134.2 134.2 134.2 134.2 134.2 134.2 134.2 142 H ~3~l . 0 3 343434 0 0 0 . 0 0 I QQQHQ-‘HH-‘Q‘I‘H4‘HH 0 343434 0 0 O . 0 . 0 OUOGNU‘DHOOUUQNGWHOOUBNNNU’HBOQUNN‘DNHOOUUQNUWHOOQUQNNWH 343434 I 3.1 0 0 . . . 0 -4-4.3Ia-4-5Ia 0 .Ll HHH eeeeee I QQ-FHQ%HH&~I~I4LH~204H 0 343434 I 000.... . I § 0 I 34~Ias3434 . . 34 179.06 170.59 205.91 242.33 257.11 245.54 272.79 236.31 265.71 186.71 117.86 167.72 193.50 246.25 213.43 295.09 236.78 233.13 183.23 145.05 157.93 184.89 241.08 287.88 223.91 307.54 195.56 185.82 94.82 133.70 153.03 237.90 177.05 256.77 257.41 283.41 173.52 104.54 119.34 196.96 203.08 264.09 274.74 278.80 235.26 198.15 139.34 180.76 184.09 234.13 299.85 189.79 257.81 168.92 78.46 122.04 125.87 145.25 147.68 195.34 217.26 245.21 210.27 61.20 70.43 113.10 115.62 128.72 205.55 206.35 187.95 133.34 62.34 77.59 106.65 153.68 187.77 205.73 240.21 182.47 193.79 76.51 74.07 106.87 123.42 199.23 211.86 246.53 226.72 166.87 82.29 85.79 130.39 141.61 160.35 233.29 187.33 236.63 167.00 71.80 109.34 111.92 146.68 177.01 202.97 215.62 134.2 134.2 137.2 137.2 137.2 137.2 137.2 137.2 137.2 137.2 137.2 140.3 140.3 140.3 140.3 140.3 140.3 140.3 140.3 140.3 143.3 143.3 143.3 143.3 143.3 143.3 143.3 143.3 143.3 146.4 146.4 146.4 146.4 146.4 146.4 146.4 146.4 146.4 149.4 149.4 149.4 149.4 149.4 149.4 149.4 149.4 149.4 143 3434 4d-d-h 0 0 II-II-IH Ii fiI-‘chQQ-FHd‘I-‘H 0 00.00.... HOOUQQNWWHOOQQONWNHOOQBQNWU’HOODWONQWHOOQUflNqu-lO 343434 ~I~Iau34~a 0 343434 I I .3 0 0 0 0 0 0 0 0 343434 I 0 0 0 0 0 0 0 . I ~4-4.3Iu-a.bIaI-.s-q-4-hIn-a-sIaIn . I “0““.3‘3“ . .0 343434 245.46 186.02 66.69 118.50 187.87 243.38 243.34 253.67 293.85 248.60 241.04 92.39 109.16 198.92 219.13 212.21 233.46 281.93 291.09 256.15 65.23 124.01 139.08 168.29 255.79 217.44 247.23 295.49 192.44 64.58 104.19 147.65 237.59 255.21 279.55 260.50 288.94 274.92 64.51 104.11 147.83 237.44 255.97 280.04 261.03 288.89 274.62 235.45 180.48 73.03 101.53 102.69 148.67 221.89 142.48 238.52 171.36 165.36 62.64 76.13 106.81 140.84 191.21 174.92 203.29 198.46 194.66 56.78 85.14 89.30 125.46 158.47 205.47 169.81 206.39 182.54 53.57 68.02 120.75 140.30 158.41 175.86 235.50 204.06 246.19 53.56 67.79 120.91 140.63 158.80 175.38 235.48 204.31 246.09 1311 APPENDIX C TEMPORAL EVALUATION OF VORTICITY CONTOURS A conpsrison of the nsjor festures of the vorticity contours hss been nude in order to ohtsin s quslitstive evslustion of the tenporsl evolution on s glohsl scsle. The contour plot of (az>1+1 is referred to the sinilur contour plot st phsse tine i. Figure (23) (I63 vith respect to '1) AIIn the tongue region note: l)the shrinksge of the <0z>-200 contour line st 1-24 on. 2)the lovenent dovnstresn of thc (uz)-180 contour line st IP37 on. end B)In the intcrfsce hetveen tongue end the nevly for-ed vorticsl 8821102“. 11080: 1)the sepsrsting of the (u:)-130 contour line st 1-42 cm. snd 2)th0 thIIGOIOnt 0f the <0,>-120 contour line on the high speed side st X!42 on. 144 145 C)In the newly formed vortical structure notc: 1)th° 01°38‘t103 0‘ th' <0,>-140 contour line at IP51 on. and 2)the tanslation of the ('r>'15° contour line at 1950 on. D)2egion between the ncwly formed and isolated vortical structure is noted: 1)the equidistant separation of the <0z>8100 contour line of two vortical notions; the snallcr vortical fluid mass is centered at 1-70 on and the larger at X-79.5 on. a)the structure at 1’70 on experiences a slight redistribution. b)the structure at 1-79.5 on translates downstream. 2)the inward movement of the 90 line at 1'74 c- on the high speed side. E)1n the large isolated structure note: 1>srovth of the -120 and 130 contour line at 1439 cu 2)growth of the <0'>-90 contour line at 1991.5 on F)In the region between 1-98 and 1-150 on note that: 1I-60 contour line at 19106 c- is being pinched and 2)the tearing of <0:>-70 contour line at 1'132 cn. 146 Figure (24) (I125 with respect to I63) A)In the tongue region note: l)the tearing and isolation of <0z>n190 11a. gt 1334 on. 2>¢oppr444£on of the <4,>-130 line at 1430 cu. B)In the interface region between the tongue and the newly formed vortical structure note: 1)reuniting of the (“2"130 contour line at X!42 cn. 2)receding of the (uz)-120 contour line at XF42 cm on the high speed side. C)In the newly formed vortical structure note: 1)growth of the (”z>'14° contour line at IF48 on on the low speed side. and 2)th0 birth 0f th. <0,>-160 contour line at XF48 on. D)In the region between the newly formed and isolated structure note: 1)shrinkage of the snall vortical parcel (at X370 on) on the front. back and top. 2)tearing 0f th‘ (0,)390 contour line at 1‘73 on. 3)incursion of <0,)-80 contour line at 1:73 on on the high speed side. 147 E)In the large isolated structure note: 1’3118ht increase in (0,):130 contour line at 1:82 cn, and 2)the slight increase in the 100 line at 1:88 cn. F)In the region between 1:98 and 1:150 on: 1)Tearing of the 60 line st 1:122 c- fron high and low speed side. Figure (25) (I187 with respect to 1125) A)In the tongue region note: 1)shrinkaae 0f thO (flz)-230 contour line at 1:15.5 cn 2)pinching down of (01>:180 contour line at 1-32 cm fro- low and high speed sides. 3>srovth of <4,>-130. 170, 160. and 150 contour lines at 1:33 to 1:41 cl B)In the interface region between the tongue and the newly forned vortical notion note: l)outward novenent of 130 line at 1:42 cn to high speed side. C)In the newly forned vortical structure note: 1’810'th Of (0,)-150 and 160 contour lines at 1:48.5 cn 2)shrinkage of the (01>:140 cotour line at 1:48.5 on. 148 D)1n the region between newly formed and isolated structure note: 1)Fusiug of the 100 line upstream to the newly formed vortical structures. 2)further inward movement of <0,>:80 contour line at 1:73 cm from high speed side. E)1n the large isolated structure note: l)slight shrinkege of (“2"130 contour line st 1:80 on. F)In the region between 1:98 cm and 1:150 cm note: 1)pinching off of (uz)-60 contour line at 1:122 cn from the low and high speed side. Figure (26) (I227 with respect to I187) A)In the tongue region note: 1)pinching down of the (at):180 contour line at 1:34 on. B)In the interface region between the tongue end the newly formed vortical motion note: l)slight outward movement of the (n‘>:120 contour line toward the high speed side (1:42 cm) 2)slight outward movement of the (“2"130 contour line toward the high speed side (1:42 cm). ‘- - -. . 149 . C)In the newly formed vortical structure note: 1>continnod srovth of the <-,>-150 and 160 lines at 1349 cm. towards the low speed side. D)In the region between the newly formed and isolated structure note: l)oontinued shrinking of vortex at 1:70 on 2)inward movement of (Uz)-80 contour line at 1874 cm from high speed side. E)In the large isoleted structure note: l)shrinkege of the (uz>-l20 contour line at 1:80 cm. 2)shrinkage and translation of (uz)-130 contour line at 1-80 cm. F)In the region between 1:98 cm and 1:122 cm note: 1)comp1ete tearing of (uz>-60 contour line at 1:120 cm. Figure (27) (I289 with respect to I227) A)In the tongue region note: l)shrinkage of the (“2"180 contour line at 1:38 cm and 2)decay of the (e:>-190 bubble at 1:36 cm. 150 B)In the interface region between the tongue and the newly formed vortical motion note: 1)receding of the (mz>:120 and 130 contour lines at 1:43 cm. toward the high speed side. C)In the newly formed vortical structure note: 1)growth of the <0z>:150 and 160 contour lines at 1:48 em. 2)elongation of the (mz>-100. 110. 120 and 130 contour lines in the range of 56 to 64 cm and 3)birth of a (m:>-170 contour line. D)1n the region between the newly formed and isolsted structure: l)tusing of the isolated (uz)-100 contour line at 1:70 cm to the upstream (uz>:100 contour line of the formed vortex st 1-65 cm 2)inward movement of <0,>-80 contour line on high speed side at 1-73 cm E)In the large isolated structure note: “detonation of the <44,>-120 contour line et 1-30 cm 2)shrinkage of the (uz)-130 contour line at 1:85 on F)In the region between 1:98 cm and 1:150 cm: l)shrinkage 0‘ (0,):80 contour line at 1:140 cm 151 Figure (28) (I320 with respect to I289) A)In the tongue region note: l)shrinhage of the (mz>:220 contour line at 1:18 cm, 2)the growth of (mz>:190 contour line at 1:27.5 cm, 3)shrinkage of (oz):180 contour line at 1830.5 cm and B)In the interface between tongue and the newly formed vortical motion note: 1)receding of (uz):130 contour line to high speed side at 1:42.5 om C)In the newly formed vortical structure note: 1’810'th 0‘ (01>:150. 160 and 170 contour lines at 1:48 cm. D)In the region between the newly formed and isolated structure note: 1>couplote testing of the <4,>- 30 contour line at 1-73 cm 2)inward movement from high speed side of the (“2)‘70 contour line at 1:73 cm. B)In the large isolated structure note: l)tnbttlntill reduction of the (0‘)-120 canton: ling gt X‘86 c. 2)s1ight increase in (oz):130 contour line at 1:86 on 152 F)In the region betveen 1:98 and 1:150 cm: 1)pinch1na down on (Oz):50 contour line from high and low speed at 1:110 om 2)the fusing of the (0‘)-60 contour line at 1:122 cm. IEFMCES REFERENCES Bhatia. J.C..Durst. F. and Jovanovic. J. (1982) Corrections of hot-wire anemometer measurements near walls. I. Fluid lechanics 122. 411-431. Brown. 6 and Reshko. A. (1974) On density effects and large structures in turbulent mixing layers. J.Fluid Iechanics 64. 775-816. Clauser. 0.E. (1954) Turbulent boundary layers in adverse pressure gradients. J. Aeronautical Sci. 21. 91.108. Coles. D. 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