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An investigation of structure in a turbulent boundary layer developing on a smooth wall MacAulay, Phillip N. 1990

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A N I N V E S T I G A T I O N O F S T R U C T U R E IN A T U R B U L E N T B O U N D A R Y L A Y E R D E V E L O P I N G O N A S M O O T H W A L L By Phillip N . MacAulay B. Sc. (Mathematics) Dalhousie University B. Sc. (Mechanical Engineering) Technical University of Nova Scotia A T H E S I S S U B M I T T E D I N P A R T I A L F U L F I L L M E N T O F T H E R E Q U I R E M E N T S F O R T H E D E G R E E O F M A S T E R O F A P P L I E D S C I E N C E in T H E F A C U L T Y O F G R A D U A T E S T U D I E S M E C H A N I C A L E N G I N E E R I N G We accept this thesis as conforming to the required standard T H E U N I V E R S I T Y O F B R I T I S H C O L U M B I A Nov. 1990 © Phillip N . MacAulay, 1990 In presenting this thesis in partial fulfilment of the requirements for an advanced degree at the University of British Columbia, I agree that the Library shall make it freely available for reference and study. I further agree that permission for extensive copying of this thesis for scholarly purposes may be granted by the head of my department or by his or her representatives. It is understood that copying or publication of this thesis for financial gain shall not be allowed without my written permission. Department The University of British Columbia Vancouver, Canada Date Qgc . /f, Vfib DE-6 (2/88) abstract The structure of a stable smooth wall zero pressure gradient turbulent boundary layer is investigated experimentally in order to determine the dominant outer region structure and to develop a hypothetical generalized boundary layer flow model. Three hot wire configurations, two vertically separated X-wires and a leading straight wire, a horizontal rake of 5 straight wires, and a vertical rake of 5 straight wires were used in the exper-iments, conducted at Reg = 8200. The basis for data reduction procedures came from crosscorrelations and the Variable Interval Time Average (VITA) technique. Three structure types are reported in the literature to be important: streaks and counter rotating streamwise vorticity, wall scaled hairpins or ring vortices, and large scale (0(6)) bulges. A simple pictorial model consisting of three Reg dependent interdeveloping stages, which integrate all three structure types, is presented and discussed in relation to the literature and experiments performed. The rake data indicate that the positive (du/dt) VITA detected velocity front has a scale much larger than that of the wall scaled eddies which typically have a scale of 100-300 y+, and that this velocity front exhibits characteristics that are consistent with the trailing velocity front described in the model. The general convection velocity from basic crosscorrelations and the convection velocity of the positive VITA detected velocity front both had values 90-100% of the local mean velocity over most of the boundary layer. Evidence of small scale structure concentration on the downstream edge of the trailing velocity front is presented. A new method used to determine the average structure inclination angle associated with the trailing velocity front is presented and demonstrates that the generalized structure inclination angle, calculated from basic crosscorrelations between vertically separated ii sensors, does not indicate structure shape, but is associated with the bulk flow associated with the structure. The new method appears to give results that are consistent with flow visualization and more accurately estimates the inclination angle associated with the most dominant feature of the outer flow, the positive VITA velocity front. Although the model presented is somewhat crude and further development and refinement are required, the model appears to agree with most data in the literature, as well as the present experimental results. iii Table of Contents abstract ii List of Tables vi List of Figures vii Acknowledgement xiii 0.1 Nomenclature . . . xiv 1 Introduction and Literature Review 1 1.1 Introduction 1 1.2 Boundary Layer Structure 4 1.2.1 Overview and Important Quantities 4 1.2.2 Inner Structure 7 1.2.3 The Outer Structure 11 1.2.4 Intermittent Region 24 1.2.5 Review of Important Structure Details 25 1.3 Reynolds Number Effects and Drag Reduction Methods 25 1.3.1 Reynolds Number Effects 25 1.3.2 Drag Reduction Methods 28 2 Experimental Apparatus and Procedure 30 2.1 Conditional Sampling ' . 33 2.1.1 uv Hole or Quadrant detection method 35 iv 2.1.2 Variable Interval Time Average (VITA) technique 36 3 Generalized Turbulent Boundary Layer Structural Model 52 3.0.3 Model Description 53 4 Experimental Results and Discussion 60 4.1 Correlations 60 4.2 Velocities Through V I T A Event Detections 67 4.3 Horizontal and Vertical Rake Data 79 5 Conclusions and Recommendations 120 5.1 Specific Conclusions 121 5.2 General Conclusions and Recommendations 122 Bibliography 124 Appendices 130 A Basic Boundary Layer Characteristics and Data Reduction Methods 130 B Potential Vortex Model Event Velocities 144 C Examples of Crosscorrelation Curves 147 v List of Tables Summary of Experimental Conditions vi List of Figures 1.1 Boundary Layer Regions 6 1.2 Sublayer Streak Structure: a)Cross Section View b)Side View 8 1.3 Pocket Vortex Structure (Ref.#17) 9 1.4 Typical Photographs of Streak Structure (Ref.#8) 10 1.5 Outer Structure at Low Ree (Ref.#4) 12 1.6 Stretch and Peel of Wall-Connected Hairpin 13 1.7 Falco's Typical Eddies and Bulges (Ref.#22) 15 1.8 Organized Hairpins (Ref.#4): a) Smoke Visualization b)Idealization 16 1.9 Structure Angle vs y/6: a)Subsonic b)Supersonic (Ref.#25) . . 17 1.10 Vorticity Surfaces Showing Cross-connection of Parallel Vortex Tubes (Ref.#34) 21 1.11 a)Formation of Ring Vortex from Necked Hairpin b)Hairpin-Ejection Structure 22 1.12 Spanwise Integral Length Scale at y+ = 15 (Ref.#23) 26 1.13 Inner and Outer Dimensions vs. Ree [Note: This figure was developed assuming a l/7th power law profile and a wall eddy scale of 100y+.] . . 27 2.14 Tunnel Sketch and Details 30 2.15 Traverse Mechanism 32 2.16 Wire Configurations: a)X-wires b)Horizontal Rake c)Vertical Rake 44 vii 2.17 Equipment and Data Pathway 45 2.18 Quadrant Detection Method 46 2.19 Example of VITA Event Detection (on u velocity) 46 2.20 Number of Events per unit time for each Quadrant as a Function of H (Ref#32) 47 2.21 Examples of ensemble-averages from: a)Quadrant#2 b)Quadrant#4 c)Positive VITA on u 48 2.22 a)Number of Events as a Function of (K) b)Number of Events as a Function of (T.) 49 2.23 Effect of K on VITA Ensemble-Averages: a)K=.5 b)K=.9 . . 50 2.24 Effect of T. on VITA ensemble-averages: a)T. = .24 b)T. = .12 . 51 3.25 Low Ree Outer Region Structure 53 3.26 Middle Reg Outer Region Structure 55 3.27 High Re6 Outer Region Structure 56 4.28 uv Probability Distribution at y/S = .07 61 4.29 Quantities used to Calculate the Generalized Structure Inclina-tion Angles 64 4.30 Generalized Structure Angles 66 4.31 Number of Events vs y/S 69 4.32 Examples of Possible Event Detection Locations 71 4.33 Ensemble-Averaged Positive Event Velocities: a)y/S = .024 b)y/£ = .07 73 4.34 Ensemble-Averaged Positive Event Velocities: a)y/5 = .185 b)y/6 = .412 74 viii 4.35 Ensemble-Averaged Positive Event Velocities: *)y/b" = -579 b)y/S = 1.03 75 4.36 Ensemble-Averaged Negative Event Velocities: ^)y/S = .024 b)y/6 = .07 76 4.37 Ensemble-Averaged Negative Event Velocities: a)y/£ = -185 b)y/S = .412 77 4.38 Ensemble-Averaged Negative Event Velocities: a)y/$ = 579 b)y/5=1.03 78 4.39 Horizontal Rake Ensemble-Averaged Positive Events, VITA wire#5: a)y/6 = .0477 b)y/6 = .093 81 4.40 Horizontal Rake Ensemble-Averaged Positive Events, VITA wire#5: &)y/6 = .165 b)y/6 = .277 82 4.41 Horizontal Rake Ensemble-Averaged Positive Events, VITA wire#5: &)y/6 = .488 b)y/S = .86 83 4.42 Horizontal Rake Ensemble-Averaged Negative Events, VITA wire#5: a.)y/S = .0477 b)y/S = .093 84 4.43 Horizontal Rake Ensemble-Averaged Negative Events, VITA wire#5: &)y/S = .165 b)y/S = .277 85 4.44 Horizontal Rake Ensemble-Averaged Negative Events, VITA wire#5: &)y/6 = .488 b)y/6 = .86 86 4.45 Vertical Rake Ensemble-Averaged Positive Events, VITA wire#l: B.)y/S = .109 b)y/S = .215 (note: y/S measured at wire#l) 88 4.46 Vertical Rake Ensemble-Averaged Positive Events, VITA wire#l: a)y/6~ = -443 b)y/6 = .654 (note: y/6 measured at wire#l) 89 ix 4.47 Vertical Rake Ensemble-Averaged Positive Events, V I T A wire#5: a)y/6 = .109 b)y/S = .215 90 4.48 Vertical Rake Ensemble-Averaged Positive Events, V I T A wire#5: a)y/8 = .443 b)y/6 = .654 91 4.49 Vertical Rake Ensemble-Averaged Negative Events, V I T A wire#l: a)y/5 = .109 b)y/S = .215 92 4.50 Vertical Rake Ensemble-Averaged Negative Events, V I T A wire#l: a)y/5 = .443 d)y/6 = .654 93 4.51 Vertical Rake Ensemble-Averaged Negative Events, V I T A wire#5: a)y/5 = .109 b)y/8 = .215 94 4.52 Vertical Rake Ensemble-Averaged Negative Events, V I T A wire#5: a.)y/6 = .443 b)y/S = .654 95 4.53 Effect of Spatial Averaging on Ensemble Event Traces 96 4.54 Horizontal Rake Subtracted Signals: a)y/6 = .277 b)y/6 = .715 . 103 4.55 Indication of Small Scale Structure Occurrence Relative to V I T A Events (Positive Events): a)y/S = .048 b)y/S = .093 104 4.56 Indication of Small Scale Structure Occurrence Relative to V I T A Events (Positive Events): a )y /£ = .165 b)y/6 = .277 105 4.57 Indication of Small Scale Structure Occurrence Relative to VITA Events (Positive Events): a)y/S = .488 b)y/6 - .86 106 4.58 Indication of Small Scale Structure Occurrence Relative to VITA Events (Negative Events): a.)y/S = .048 b ) y / £ = .093 107 4.59 Indication of Small Scale Structure Occurrence Relative to VITA Events (Negative Events): &)y/6 = .165 b)y/6 = .277 108 4.60 Indication of Small Scale Structure Occurrence Relative to VITA Events (Negative Events): a )y /£ = .488 b)y/S = .86 109 x 4.61 Horizontal Inclination Angle 110 4.62 Examples of Delay Time Distributions for Trailing Front Con-vection Velocity Determination: a)y/6 = .024 b)y/6 = .1 Ill 4.63 Examples of Delay Time Distributions for Trailing Front Con-vection Velocity Determination: &)y/S = .191 b)y/S = .418 . . . . 112 4.64 Examples of Delay Time Distributions for Trailing Front Con-vection Velocity Determination: a)y/5=.781 b)y/5=.933 . . . . 113 4.65 Average Trailing Front Convection Velocities 114 4.66 Example Distribution of Delay Times Between the Two X-wires for Calculation of Trailing Front Interface Angle 115 4.67 Front Inclination Angle 0 116 4.68 Ensemble-Averaged Correlations at Increasing Time Delays (r): a)Small r b)Large r 117 4.69 Effect of Increasing r on the Effective Lower Wire Position . . . 118 4.70 General Structure Inclination and Trailing Front Interface Angle 119 A.71 Mean Velocity Profile 131 A.72 Power Law Fit to Mean Velocity Data 132 A.73 Intensity Profiles 137 A.74 Length Scales: a)Integral b)Micro 138 A.75 Discrete Autocorrelation Parameters 139 A.76 Example Autocorrelation Curves 140 A.77 a)Calculation of Integral and Micro Time Scales b)Autocorrelation Vertex Parabolic Curve Fit 141 A.78 Crosscorrelations Between Horizontally Displaced Sensors . . . . 142 xi A. 79 Peak Delay Time Selection Method 143 B. 80 A vortex pair model for coherent large scale motions: a)Side View b)End View 145 B. 81 Distributions of velocity associated with the vortex pair model; a) Z=0 b)Z=2A (where the separation between the vortices =2A) 146 C. 82 Crosscorrelations on the u velocity between the leading straight wire and the lower X-wire 148 C.83 Crosscorrelations on the u velocity between; a)The two X-wires b) The leading straight wire and the upper X-wire 149 C.84 Crosscorrelations between the X-wires using the v velocity: a)Full data set b)Positive v data only c)Negative v data only . 150 C.85 Crosscorrelations between the X-wires using the uv velocity; a)Full data set b)Positive v data only c)Negative v data only . 151 C.86 Crosscorrelations between the X-wires using the u velocity; a)Positive u data only b)Negative u data only 152 C.87 Crosscorrelations of event detections between the leading straight wire and the lower X-wire 153 xii Acknowledgement I would like to acknowledge the help and support of my supervisor, Dr. LS . Gartshore, without who's patience I would not have been able to complete this work. I would also like to thank Dr. Salcudean who took the time to be interested in my progress and general well being. This work was funded in part by the Natural Sciences and Engineering Research Council of Canada. xiii 0.1 Nomencla ture x,y,z Coordinate directions t Time (x+,y+,z+) = xurjv,yuTIv,zuT11> Wall coordinates. c Hot Wire separation distance u,v,w Turbulent velocity components in x,y,z directions respectively p Turbulent pressure component U,P ... Mean quantities (long time averaged). p Density v Kinematic viscousity S — 899 Boundary Layer thickness Si Viscous sublayer thickness St Buffer region thickness K von Karman's constant uT = yTw/p Wall shear velocity. TW Wall shear stress Cf Wall skin friction coefficient r Measurement of time delay xiv Uoo Free stream velocity Ui Local mean velocity Ue Structure convection velocity Rex = xUoo/v Reynolds number based on distance from the originof the boundary layer. Reg — 6Uoo Iv Reynolds number based on the momentum thickness where: Res = SVoojv Reynolds number based on boundary layer thickness 8. Th Bursting period Tbg Bulge passing period 0(8) Order of delta H Level discriminator for the Quadrant technique Q Any turbulent quantity T* = Wool 8 = ST A Short time averaging time for the VITA technique 0 -Structure Angle te Integral time scale tm Micro time scale le Integral length scale xv lm Micro length scale Ruu u Velocity Isocorrelation contours Rvv v Velocity Isocorrelation contours xvi Chapter 1 Introduction and Literature Review 1.1 Introduction Solutions to turbulent flows have traditionally been sought by breaking the flow quantities into mean and fluctuating componants (U = U -fu ,P = P+p...) and then applying this parameterization to the generalized flow equations: the Navier-Stokes (N.S.) equations, continuity and an energy equation. Unfortunately this method gives rise to six new additional turbulent stresses in the N.S. equations. Further manipulation of the equations to solve for these six new second order stresses results in third order stresses and so on. This has been termed the closure problem and has prevented the formulation of exact solutions to turbulent flow problems. In order to deal with this, empirical relations for second, third or higher order quan-tities have been proposed. Unfortunately, these relations are to some extent flow specific and must therefore be checked experimentally for the flow in question. Traditionally, experimentalists have used mean flow profiles, space-time correlations and frequency spectra to investigate and determine these empirical relations. This has been useful, but it becomes very difficult to interpret these results without a clear idea of the particular physical structure of turbulence in the flow being investigated. The choice of which cor-relations to employ, and their directional orientations, is crucial for accurate prediction. Correlations are often used to determine characteristic length and time scales, however the final result is often very dependent on the directional orientation of the correlation 1 Chapter 1. Introduction and Literature Review 1 used and how the data are interpreted. For example, in a boundary layer, calculations using velocity correlations can result in quite different length scales, depending on the direction (x,y,z) and/or velocity component used. This indicates three dimensional struc-ture. Evidence from flow visualization and the orientational dependence of correlations has led to increasing interest in the determination of what have been termed turbulent or coherent structures. Coherent structures are vortical motions occurring in a quasi-periodic fashion, that develop in a deterministic manner and maintain spatial coherency over significant time and distance relative to their own length and time scales. Research in this area has led to the idea of further division of the time dependent quantities (u,v,p...) into relevent and irrelevent parts, where the relevent parts originate from the coherent structures and the irrelevent parts from the breakup and fossilization of earlier coherent structures and larger scale structures[l]. Understanding and quantifying these structures will enable the development of improved flow models and ultimately deterministic physical manipulation of the flow. Kline,Reynolds,Schraub and Runstadler [2] state: 'The structure of any turbulent flow reflects the local balance of turbulent production, transport, and dissipation of turbulent kinetic energy. It is im-portant that the mechanisms of these variables be understood.' Coherent structures have been identified and investigated in many flows through the use of : flow visualization (smoke, dye, hydrogen bubble, photosensitive additives), conditional sampling and correlations of hot wire and laser velocimeter data, and compu-tational methods such as large eddy simulations (LES) and direct numerical simulations (DNS). Chapter 1. Introduction and Literature Review 3 This work will concentrate on the identification and determination of coherent struc-ture in the outer region of a smooth wall, zero pressure gradient, turbulent boundary layer using constant temperature hot wire data. The motivation for this is: 1. To determine the dominant structure in the outer region of a boundary layer. 2. To develop a hypothetical generalized turbulent boundary layer flow model. Once a reasonable understanding of the structure and its development has been reached, existing passive and active methods of turbulence control can be improved and new ones developed. A discussion of drag reduction methods and their effect on the over-all boundary layer structure will be presented following a description of the generalized boundary layer structure. A difficulty with the subject of large turbulent structures, particularly those of the outer region, is the number of unconnected or loosely connected observations which have been reported from various experimental or numerical studies. The integration of these observations into a plausible model must be an important objective of every turbulence investigation, as it is of this thesis. The following sections of this thesis contain, in order: a review of boundary layer structure, a presentation of the experimental apparatus, a discussion of conditional sam-pling techniques, a general model structure which is suggested by most observations, a description of new experiments and their interpretation, and finally conclusions and recommendations. Chapter 1. Introduction and Literature Review 4 1.2 Boundary Layer Structure 1.2.1 Overview and Important Quantities The turbulent boundary layer may be divided into three general regions [3]: (Fig.1.1) 1. The Inner Region— Where useful descriptive quantities are: (x+,y+,z+) — xurjv,yurjv,zuTjv — Wall coordinates. uT — yr0/p — Wall shear velocity. r„ = —Wall shear stress. This region consists of: • Viscous sublayer— The inner region, extending from y+ = 0 —• 8, or y = 0 —• Si. This region has sometimes been called the laminar sublayer. Viscous forces dominate, but the flow here is not steady. • Buffer region— Viscous and inertia! forces in this region are of the same mag-nitude. This region extends from the upper viscous sublayer to the log region • Log region— The region of the boundary layer governed by the log law. (y+ ~ 25 —•> 200, depending on the Reynolds number of the flow). The inner region, at least for mean quantities, is considered to be independent of outer variables. There is some evidence to suggest that this is not completely valid as some effects appear to be outer variable dependent. This will be discussed later. 2. Outer or Wake region— Which uses the following quantities: Uoo — Free stream velocity. (y+ ~ 8 -> 25, 6, -> 6t). Chapter 1. Introduction and Literature Review 5 Sm = 6 —Boundary layer thickness, defined, somewhat arbitrarily, as the height at which the local mean velocity reaches 99% of the free stream velocity. Ret = xUgo/u — Reynolds number based on streamwise distance from the origin of the boundary layer. Reg = 9Uoolv — Reynolds number based on the momentum thickness where: U U JO t/oo L>oo Res = 8Uoo I v — Reynolds number based on boundary layer thickness 6. Inertial forces are dominant in this part of the flow which extends from the log region to the top of the boundary layer. 3. Intermittent region— In this region the flow is alternately turbulent rotational and irrotational due to the irregular shape of the interface between the turbulent bound-ary layer flow and the irrotational free stream. The intermittent region is usually included with the outer region as it includes the somewhat artificial boundary £ 9 9 . Various relations have been developed from theory and experimental results to predict the mean velocity profile. The two important basic relations are: 1. The linear viscous sublayer relation, U uTy — = — = y+ which applies to the very near wall region, y+ < 5. 2. The log law, U 1 urv — = - In + C UT K V where K is von Karman's constant. Thi6 relation applies to the log region. Chapter 1. Introduction and Literature Review 6 u Note: The extent of the various regions depends on the Reynolds number of the flow Figure 1.1: Boundary Layer Regions Other more complicated functions have been employed to model both of these regions and the buffer region. Most use some type of weighting function, forcing the relation to converge to the sublayer relation close to the wall and to the log law farther from the wall. A l l of these functions use adjustable constants that fit the particular flow conditions being modeled. Basic scales of the flow are considered, but the actual flow structure is not. The mean profile suggests that there are at least three separate mechanisms to be considered. The near wall structure, the outer structure and the intermittent region structure. It should be noted that what is being termed the outer structure is important for the outer and the upper inner regions, and that all of the structure is probably interrelated. The overall boundary layer structure has been found to be Reynolds number dependent, especially for Reg < 3000. This point will be discussed later. The generalized Chapter 1. Introduction and Literature Review 7 structure description given here is for Reg > 5000. 1.2.2 Inner Structure A large body of research has been done on turbulent boundary layer and channel and pipe flows in the last 15 to 20 years. Much of this work has concentrated on the inner or near wall region. Structure in the near wall region appears to be similar for all wall bounded shear flows. Differences are present, but appear to be related to the outer regions. The inner structure appears to consist of sublayer streaks associated with counter-rotating streamwise vorticity. These give rise to an instantaneous inflexional velocity profile which becomes unstable, resulting in ejections/bursting. A sublayer streak is an elongated region, up to 1000x+ in length, 20 to 40 z+ across, of locally accelerated or retarded fluid, aligned with the mean flow (Fig.1.2). This structure has been observed and studied in boundary layer, channel, and pipe flows. Streaks have been visualized using smoke injected at the wall [4], suspended sand particles in the near wall region [5], hydrogen bubble visualization in pipe flow [6] and in channel flow [2], suspended particulates in pipe flow [7], and dye injection in channel flow [8]. Streaks have also been identified using hot wire rakes [9], from numerical Large Eddy Simulations (LES) [10], velocity correlations [11], and numerical calculations using generalized lagrangian mean equations [12]. Most researches indicate that the streaks are caused by, or occur in conjunction with, elongated regions of streamwise vorticity. These have been identified using flow visualization [4, 6], from correlation measurements using hot wires [13, 14], vorticity probe data [15], LES data [10, 16], and calculations using the lagrangian mean equations [12]. Average dimensions and orientations of these structures are reported as shown in Fig.1.2. A slightly different wall structure has also been proposed [17]. It also includes regions of decelerated fluid and counter-rotating vorticity, but in a more specific pattern termed Chapter 1. Introduction and Literature Review 8 Counter rotating vorticity Low speed streak - ~ 100 z+ Low speed streak U Low speed streak Counter rotating streamwise vorticity Figure 1.2: Sublayer Streak Structure: a)Cross Section View b)Side View Chapter 1. Introduction and Literature Review 9 a pocket. This pocket supposedly forms from the interaction of the wall layer with a sweep, where a sweep is denned as a local downrush of higher velocity fluid from above. This interaction results in the formation of leading and trailing horseshoe or hairpin vorticies, resulting in streaks and smaller vortex structures (Fig.1.3). The basis of this Primary hairpin vortex Figure 1.3: Pocket Vortex Structure (Ref.#17) structure came from flow visualization, hot wire measurements, vorticity measurements and correlations. Oldaker and Tiederman, [8] while investigating streak formation using dye injection, describe a similar sequence in the development of streaks. They observed that the initial disturbance to the near wall region appeared as a depression or valley in the dye layer, and that the streaks developed as extensions or combinations of these initial depressions. The depressions were thought to have been caused by small scale sweeps near the wall. The authors presented flow visualizations of sublayer streaks which clearly show streamwise elongated structure (Fig.1.4). Once the counter-rotating/streak structure has formed, it initially slowly grows in strength and begins to lift away from the wall. This has been observed in flow visualiza-tions [7, 6] and numerical simulations [16, 12]. A point is reached where the local mean velocity profile becomes unstable, probably inflexional and therefore inviscidly unstable. Chapter 1. Introduction and Literature Review 10 Figure 1.4: T y p i c a l Photographs of Streak Structure (Ref.#8) The strength of the structure then grows exponentially, fluctuates and bursts. A burst is an area of violent upthrust of near wall fluid into the outer layer. Another term used to describe this phenomenon is an ejection, which refers to a single coherent upthrust of fluid. A burst usually consists of one or more ejections described as originating from the same streak structure. Inflexional velocity profiles have been associated with streak liftup and bursting by several authors [7, 6, 11, 18]. Bursting results in narrow spanwise, 30 to 50 z+, regions of retarded fluid possessing positive vertical velocity. Sweeps, which can be described as regions of positive u and negative v, follow and interact with the bursts, resulting in thin regions of very high shear, with magnitudes that have been estimated to be several orders of magnitude larger than at the wall [19]. These regions, and the whole of the inner structure have been shown to be responsible for a large percentage of turbulence production and dissipation (dissipationoc p(dui/dxj)2). Bursting appears to originate in the upper viscous sublayer and buffer region. The peak intensities of u 2 , v 2 , and w2 all occur in the region where bursting appears to be the predominant structure. Corino and Brodkey [7] indicate that although bursting occurs only~ 18% of the time, it was responsible for most of Chapter 1. Introduction and Literature Review 11 the turbulence production. Up to 77% of the total uv stress has been associated with quadrant II or ejection events, and 55% with the trailing sweeps, quadrant IV events. The remainder (—32%) is associated with the other two quadrants [20]. Quadrant division of the uv stress refers to division of the uv velocities by the sign of the u and v velocities. Therefore, quadrant II events have -u and +v velocities and quadrant IV events have -|-u and -v velocities. Many researchers have attempted to quantify an average frequency of occurrence or period for bursting and to determine the appropriate non-dimensional scaling. Visual, conditional sampling, tracer contamination and autocorrelation methods have all been used and compared attempting to resolve this. A reliable and accurate method of mea-surement of the bursting frequency could be used to determine the effect of anti-drag de-vices and controls, as lower bursting frequencies indicate reduced turbulence production and skin friction. Scaling for the bursting frequency on outer variables TBUOO/8 ~ 2 —» 7 has been reported [6, 21, 20, 22], but inner variable scaling has also been presented [18]. Significant problems occur in determining the bursting frequency, related principally to the detection method, thresholds and criteria, and the fact that most measurements have been done at low Reg. A strong Reg dependence in the inner region has been noted [23]. 1.2.3 The Outer Structure The outer structure has been examined by a number of researchers, both to describe the structure and to determine its relation to the inner structure. It has become apparent that the flow is quite Reg dependent. This has caused a certain amount of confusion because most flow visualization experiments have been most successful at low Reg, and a significant proportion of other experiments have therefore been performed at low Reg, to allow for comparison with the flow visualizations. Experiments performed at higher Reg do not compare very well with the low Reg results on several points, most probably Chapter 1. Introduction and Literature Review 12 Figure 1.5: Outer Structure at Low Reg (Ref.#4) due to differences in structure. Head and Bandyopadhyay [4] performed flow visualization experiments at a number of Reg (600 —• 9600), using smoke injected near the wall as a contaminant. They deter-mined, quite conclusively, using illumination planes at 45" and 135° to the wall, that at least at low Reg the outer structure consists of hairpin type vortex structures inclined downstream at an average angle of ~ 45°(Fig . l .5) . At higher Reg, these structures appear to conglomerate into larger bulge structures, consisting of many vortex hairpins, and at much higher Reg it appears that only the tips of these hairpins survive as discrete entities within the larger bulge structure (which shall be discussed later). Head and Bandyopadhyay conjecture that these hairpins are related to the wall structure (streaks, etc.) as continuations of the streamwise counter rotating vorticity, which stretches or peels away from the wall (Fig.1.6). The dimensions of the hairpin structures were found to be Ree dependent and it was estimated that the spanwise dimension scaled at ~ 100z+, [4] which agrees roughly with the spanwise spacing of the streaks and counter-rotating vorticity in the wall region. An Chapter 1. Introduction and Literature Review Figure 1.6: Stretch and Peel of Wall-Connected Hairpin argument in support of the importance of the 45° inclination angle was presented. 'In a shear flow parallel to the wall, the downstream angle o /45° represents the direction of the principal axis along which the strain is one of pure extension and the rate of stetching is a maximum, and it must surely be significant that the characteristic angle of the hairpins is so close to this value. The direct effect of the shear flow will be to rotate the hairpin back towards the wall, and this effect can only be resisted by the induced velociy that each limb of the hairpin induces on the other. The angle at which the hairpin sets itself will thus be a result of these two conflicting effects. Initially the angle may be greater than 45°, but at some stage dissipation will reduce the induced velocities and the hairpin will rotate back towards the 45° angle. At the same Chapter 1. Introduction and Literature Review 14 time the rate of stretching will increase, and so tend to increase the induced velocity; thus, so long as the angle that the hairpin makes with the surface is greater than 45", the situation remains stable. Once the hairpin has been rotated to an angle less than 45°, however, the rate of stretching will decrease and there will be nothing to prevent the angle reducing further, with ever-increasing rapidity as dissipation proceeds. \4] Various ages of these structures would be present at any one time, the older structures having progressed as high as the top of the boundary layer and eventually dissipating, while newer more vigorous structures rise from the lower levels. For all Reg, but especially at high Reg, the tips of these structures appeared to be the most obvious features. It was difficult to relate the tips in a physically connected fashion to the near wall region at high Reg, although they still maintained characteristics very similar to the low Reg structures. Falco [22] also performed flow visualization experiments with smoke, and took simul-taneous hot wire measurements. He commented that the bursting and outer bulge passing period were of the same order of magnitude, but different in value by ~ | (bulge passing TbgUeo/S ~ 2.5, bursting TbUoo/S ~ 5), and if the two are related this difference needs explaining. His description of the outer structure consisted of bulges of two different kinds, dependent on their inner velocity patterns, and typical eddies which he described as ring vortex structures which typically occurred, or were observed, at the trailing edges of the bulges (Fig.1.7). These typical eddies were strong producers of uv stress and con-vected along the bulge interface with time. The typical eddies reportedly scaled on wall variables (100 to 200y+), over the various Reg experiments that he performed. Although he divided the bulges into two catagories, both exhibited sweep type velocities at their trailing edges. Chapter 1. Introduction and Literature Review 15 u Figure 1.7: Falco's Typical Eddies and Bulges (Ref.#22) Falco also occasionally observed what he termed a superburst, which was a rapidly growing disturbance originating in the lower boundary layer regions, and he conjectured that perhaps this was the start of a new bulge structure. The superburst structure appears quite similar to the organized hairpin motions observed by Head and Bandy-opadhyay [4],(Fig.1.8). Falco's experiments spanned Reg =(1000 to 5000), but most of his observations seemed to be derived from the lower Reg experiments. A number of researchers have tried to show quantitatively that the outer structure of the boundary layer consists of hairpins or similar structures, and to determine the average inclination angle of these structures. Alving and Smits [24], using hot wires with vertical separation, calculated crosscorrelations between the two wires at Reg > 5000, and using an estimated structure convection velocity ~ .8(7/, where Ui is the local mean velocity, Chapter 1. Introduction and Literature Review 16 a) Figure 1.8: Organized Hairpins (Ref.#4): a) Smoke Visualization b)Idealization determined average structure inclination angles at various values of y/6 (Fig.1.9a). The convection velocity is a measure of the propagation velocity of the coherent structures, which can be quite different from the local mean velocity. Alving and Smits also deter-mined that the measured structure angle was sensitive to wire separation, for separation values of < .18. They believe that at smaller wire separations, small scale structure influences the correlations and therefore the angle. The interpretation of what this angle represents is slightly unclear in view of the multiplicity of structure scales in the outer layer. The authors speculate that the angle approaches 90° at y/6 = 1 due to the tendency of the hairpins to bend upstream at their tips, as seen in Head and Bandyopadhyay's flow visualizations. Experiments done in supersonic boundary layers [26] using shadowgraphs and crosscorrelations (Fig.1.9b), Chapter 1. Introduction and Literature Review 17 •A 10 08 0.6 04 4 0.21 a • .023 a) « « . 0 4 4 • « . 0 4 9 • B.OSS « » . 0 7 8 . s.io 0 • • « . l l It • • . 1 6 o " • . 2 1 • • • = i 8 • • « • «= .28 • x • o o M e • e • # • * e H x • O K * • a > I t M y% M • «. |/<J = 0.08 m • • • 0.0ft • A . g/<J - 0.21 • • b) * • A _ • e • m- • A • • •• • • • L r u, u B 0 10 20 30 40 50 60 70 • (degrees) Figure 1.9: Structure Angle vs y/6: a)Subsonic b)Supersonic (Ref#25) Chapter 1. Introduction and Literature Review 18 show well ordered structure inclination angle ~ 45° to the wall. It would seem that the structure is of similar form, but somewhat more ordered in supersonic flows. Tritton [27] did a fairly extensive study of correlations of the u, v and w velocities throughout a boundary layer at Reg ~ 2600, using two hot wires with various separa-tions and directions of separation. Most of the correlations indicate a general structure having a scale of ~ 100 —• 200y+, and an average structure angle of ~ 39° between y/S = .106 —• .187. One interesting result was that although the crosscorrelations on u indicate a downstream inclination to the structure, this was not at all apparent from the crosscorrelations on the v velocity, which indicated vertical orientation. The crosscorre-lations on v also indicated a much narrower overall structure. Moin and Kim [10], from a Large Eddy Simulation (LES) of channel flow, showed that for the main body of the flow, the vorticity was concentrated in the xy plane at ~ 40° —• 60° to the horizontal, which indicates that the strongest vorticity was associated with angles around 45°. They indicated that vortex stretching due to mean strain was a maximum at 45° and was a dominant flow mechanism. In the yz plane, vorticity was aligned with the y axis, but with significant vorticity still apparent in the z direction over most of the boundary layer. The vorticity in the z direction might have been due to the heads of hairpin vortex structures. Two-point correlations indicated preferred structure angle of ~ 45° and also indicated that the structure was of a counter-rotating nature. The authors presented instantaneous vorticity plots and vortex filament traces showing hairpin-like structure in support of their counter-rotating hairpin conjecture. Antonia, Browne and Bisset [28] did a study of the effect of Reg on the isocorrelation contours of u (Ruu) and v (Rvv), determined with an eight X-wire array in the xy plane. The Ruu contours indicated considerable streamwise structure extent, with a downstream preferred inclination. The Rvv contours indicated much smaller streamwise extent and little to no structure inclination. The authors comment that this indicates the presence Chapter 1. Introduction and Literature Review 19 of at least two or more scales of coherent motion in the flow, where the largest structure dominates the Ruu contours and the smaller the Rvv. The Ruu isocorrelations were found to be more strongly influenced by Reg than the Rvv isocorrelations, especially for Reg < 5000. Sabot, Saleh and Compte-Belot [35] studied pipe flow. They suggested that coherence in the horizontal direction is due to the passage of large structures, and that vertical coherence is due to the smaller structures. Lu and Willmarth [20] estimated, from shear stress probability plots, that the average structure angle should be ~ 20°, and that the stress was concentrated in the II and IV quadrant throughout most of the boundary layer. Chen and Blackwelder [29] used temperature contamination, and simultaneous hot wire and cold wire rake measurements to examine a stably- stratified, wall heated, bound-ary layer. Using a conditional sampling technique, The Variable Interval Time Average (VITA) technique, to be described in more detail later, they were able to define coherent fronts in the flow, where the fronts represent rapid changes in temperature. They detected four times as many hot-to-cold fronts as cold-to-hot fronts, and observed that the former were much more abrupt, spanned a large portion of the boundary layer, and were skewed downstream. The cold-to-hot fronts were explained as background "noise", and deter-mined not to be as important as the hot-to-cold fronts. These fronts did not allways strike all the wires and the authors conjectured that this was due to limited spanwise extent of the structure. Examination of their results indicates that the structure angle across the boundary layer was ~ 48°, with low local angles near the wall and higher angles in the mid and upper regions. A front passing frequency was calculated and nondimensionalized with outer variables to be Fb6/Uoo = .38 which gives a nondimensional period of ~ 2.6. This value was found to be reasonably constant across the boundary layer. Comparing simultaneous X-wire data with the cold rake data indicated that the temperature fronts Chapter 1. Introduction and Literature Review 20 coincided in a general way with a velocity front observable in both the u and v ensemble averaged velocity signals. This was also shown by Subramanian, Rajagopalan, Anto-nia and Chambers who performed a similar experiment with temperature contamination [ 4 1 ] . The front coincidence was not exact, and the temperature fronts lagged behind the velocity fronts, especially near the wall. The hot-to-cold temperature fronts consisted of a slow increase in temperature fol-lowed by a rapid decrease, and the corresponding velocity fronts consisted of a slow decrease in u, (increase in v), followed by a rapid increase in u (decrease in v). This indicates that the fronts consisted of a slow upwelling of fluid followed by a more rapid downrush, or 6weep motion. The average streamwise spacing of these fronts was ~ 38, and the experiments were performed at Reg ~ 2600. Jovic and Browne [30] performed VITA conditional sampling experiments using a yz rake spanning ~ 8 in both directions. They determined that a significant number of the V I T A detected structures spanned 8 in both the y and z directions. Alfredson and Johansson [31, 32] used the V I T A technique to detect structures in channel flow. They showed that fronts occurred at all levels from y + = 2.8 upwards, and from ensemble averages of the u velocity, they showed that the fronts were similar in form at all y/6 locations, with the fronts detected at lower levels being more strongly sweep dominated. Melander and Hussain [34] have done a numerical simulation of the joining of two counter-rotating vortex tubes, similar to the counter- rotating vorticity found in the wall region. Their study showed that if the vortex tubes are subject to a disturbance that causes them to come in contact with each other, they may then cross-connect forming horseshoe type vortex structures (Fig.1.10). In the wall region, the upstream side of cross-connected streamwise vorticies would be just the type of structure needed to develop into a horseshoe vortex. Another result of this kind of effect could be the formation of ring vortex structures through necking of an already existing disturbed hairpin vortex Chapter 1. Introduction and Literature Review 21 (F ig . l . l l a ) . Hama [33] showed that a parabolic vortex tube (which is very similar in form to cross-connected wall vorticity, or the leading hairpin of Falco's pocket structure) aligned with the horizontal, will lift up due to its own induction and form something which looks very similar to the hairpin structures of Head and Bandyopadhyay (Fig.1.6). Figure 1.10: Vorticity Surfaces Showing CroBS-connection of Parallel Vortex Tubes (Ref.#34) An important feature of the hairpin structure originating at the wall as cross-connected vorticity, or as the leading edge of a pocket formation, is that lift up of this type of struc-ture would produce most of the features of an ejection or burst. The reverse flow through Chapter 1. Introduction and Literature Review 22 Figure 1.11: a)Formation of Ring Vortex from Necked Hairpin b)Hairpin-Ejection Structure the centre of the lifting hairpin/horseshoe would produce a region of retarded fluid of narrow spanwise extent, moving away from the wall, and the interaction of this fluid with the surrounding fluid would produce a large amount of uv stress. These were the predominant features of a burst (Fig.1.11b). Furthermore, both the cross-connected or pocket structures could form due to the interaction of a near wall sweep impinging on the counter-rotating vorticity in the wall region, thus accounting for the presence of the near wall sweeps as an important feature of the structure as described by a number of researchers. Moin and Kim [10] go so far as to say: Chapter 1. Introduction and Literature Review 23 'Using conditional sampling criteria, we show that the bursting process is indeed associated with hairpin vortices surrounding the region where low speed fluid ts ejected from the wall region.' A number of researchers have conjectured that there must be some communication between the inner and outer structure. Some have suggested that the wall layer bursts grow into outer layer bulges; others that the passage of the outer layer bulges result in sublayer bursts. In addition there is the hypothesis that both are the result of an overall flow instability. Blackwelder and Kaplan [11], from an experiment conducted in a boundary layer using hot wires, commented that bursting phenomenon appear to be linked to outer bulges, but scale on inner variables. Antonia and Rajagopalan [36] used a wall shear stress probe and hot wires to investi-gate structure in duct flow. They used electronic filtering to separate the small and large scales, and determined that the correlations used to determine convection velocity were insensitive to filtering, and thus that the small and large scale structure must have had similar convection speeds. Willmarth [37], experimentally determined the wall pressure pattern associated with bursting. His results indicate that before bursting occurred, when the wall layer had a strong streaky nature, that it was subjected to a local adverse pressure gradient. Due to the large scale of this pressure pattern, he concluded that this was due to the passage of large structures and hence that bursting could be linked to the outer large structure. He also found that the wall pressure patterns were divided into two groups, those with convection velocities typical of the outer structure, and those with speeds typical of the wall region. Chapter 1. Introduction and Literature Review 24 Thomas and Bul l [38] also conducted a study of the wall pressure patterns, in con-junction with wall shear stress pattern and hot wire measurements. Their measurements were filtered into high and low frequency components. They compared and correlated the results from all three sensor types in a boundary layer for which Reg ~ 10200. They found that the high frequency shear and pressure patterns correlated with each other, and must therefore occur in a connected fashion. Comparison of low frequency pressure and velocity patterns demonstrated that they were linked. The high frequency shear, pressure and velocities all correlated with both the low frequency velocity and pressure patterns, indicating that the high frequency (small scale) activity was concentrated and associated with the large scale structure. A n idealized version of this interrelation was given. The authors note that the frequency of occurrence of the pressure patterns was very similar to the bursting frequency. One objective of Thomas and Bull's study was to determine if bursting could be caused by the large scale streamwise pressure pattern. The authors concluded, based on dimensional arguments, that the adverse pressure gra-dient imposed by the large scale streamwise pressure fluctuation was not great enough to be primarily responsible for bursting. They did not investigate the y or z pressure gradients however and concluded that these could conceivably be much greater than the streamwise gradients and could therefore have a strong effect on bursting. Finally, they observed that there exists a strong link between the low and high frequency patterns, and thus a link between the outer and inner structure. 1.2.4 Intermittent Region The wavy interface structure of the intermittent region 16 most likely related to the bulge structures, as the intermittence frequency [39] is of the same magnitude as the bulge passing frequency. This is perhaps not surprising, but it is further evidence of the interrelation of the overall boundary layer structure. Chapter 1. Introduction and Literature Review 25 1.2.5 Review of Important Structure Details In summary, the structure of tubulent boundary layer flows, and to a certain extent pipe and channel flows, appears to consist of a number of different structures and different scales of structures: 1. In the near wall region there exists evidence for streaks and counter-rotating vor-ticity. 2. In the log and outer regions, wall-scaled hairpins or ring vortex structures, which, according to most of the available evidence, originate in or just above the near wall region and are tied to sublayer streaks and bursting in some fashion. 3. Large scale, 0(6), structure spanning most of the boundary layer, which has as its most distinguishing feature an abrupt trailing u velocity front. How the wall-scaled eddies form from the structure in the wall region, and their re-lation to the large scale outer structure, is still uncertain. A tentative mechanism has been presented that accounts for both hairpins and ring vortices by cross-connecting vor-ticity. Visual evidence in support of hairpin and ring vorticies has been presented. This does not exclude the possibility of other structure or different production mechanisms, but hairpin and ring structure does explain much of the available data and observations. The structures appear to be linked in some way to each other, and all appear to exhibit some Reg dependence. The greatest dependence seems to be for low Reg < 3000 —> 5000. 1.3 Reynolds Number Effects and Drag Reduction Methods 1.3.1 Reynolds Number Effects McLean [23] has shown that the spanwise integral scale is not constant at a set y + = 15, and that there exists a strong Reg dependence of the spanwise integral scale for Reg < Chapter 1. Introduction and Literature Review 26 3000 (See Fig.1.12). This observation violates the idea of viscous scaling in the wall region, an integral feature of the law of the wall. e IX) ae ae 0.4 02 0.0. 7*« 15 o « • RFB B JHH e prtttnt * Robinson • Ulemi t l el. O present £ present e*0 o» 0 e*0 o « 0 o«-O.I5 o«-0.26 0 2 0 0 0 4 0 0 0 _ 6 0 C O 6 0 0 0 lOOOO Figure 1.12: Spanwise Integral Length Scale at j / + = 15 (Ref.#23) Reynolds number dependence has also been observed in the velocity isocorrelations Ruu, Rvv, as previously mentioned, and has been observed in flow visualizations in the form of structure differences between low and higher Reg. The fact that a number of quantities, including 6 o m e inner region characteristics, appear to scale on outer param-eters argues for Reg dependence. This is on the surface surprising, but if one examines the relative scale of some of the structures, as a function of Reg, a tentative explaination may be offered as follows. The inner streak/burst,hairpin structure appears to scale, at least dimensionally, on inner variables at ~ 100 —* 200y +. For low Reg values these wall scaled structures Chapter 1. Introduction and Literature Review 27 are similar in scale to the boundary layer thickness, and could therefore be responsible for most of the turbulent momentum exchange in/through the boundary layer. As the boundary layer thickens, Reg increases, the scale of the wall structure becomes orders of magnitude smaller than the boundary layer thickness. Hence one would intuitively believe that for large Ree, the wall structure can no longer be responsible for all of the outer boundary layer dynamics and momentum exchange (Fig.1.13). There must there-fore develop additional larger scale structures to control the outer layer dynamics. The development of the bulges as important structures could account for much of the appar-ent Ree dependence and the dependence of some of the inner structure characteristics on Ree. 0.5 0.4 . 0.3 . Meters 0.2 . 0.1 . 0 .. 0 1 2 3 4 5 6 7 8 9 10 Re9 THOUSANDS Figure 1.13: Inner and Outer Dimensions vs. Ree [Note: This figure was developed assuming a l /7th power law profile and a wall eddy scale of lOOy+.J Chapter 1. Introduction and Literature Review 28 1.3.2 Drag Reduction Methods Reduction of the drag resulting from turbulent boundary layer flow has become an exer-cise in control of the turbulent structure. The three important passive methods are: 1. Riblets and Grooves 2. Large Eddy Break-up Devices (LEBUs) 3. Polymer Addition Riblets consist of small grooves of specific cross-section, usually ~ 15y+ in width and height, oriented in the direction of the flow. These devices have been reported to have achieved up to 8% drag reduction. One theory on why they are effective, even though they can double the surface area, is that they displace the streamwise vortex and streaky structure higher into the flow. The explanation offered for this effect is that the riblets have a damping effect on the streamwise vorticity. Increased streak spacing has also been suggested. L E B U s consist of thin ribbons or airfoils, at a set distance above the wall, which span the flow. These devices appear to decrease the skin friction and entrainment downstream of their locations, but at the same time they do add device drag. Net drag reductions of 5 —• 10% have been reported. It has been suggested that LEBUs disrupt the large scale outer structure. Polymer additives are long-chain polymers added to the flow in dilute quantities, 50-200 ppm. The presence of these additives has been shown to increase the length scales in the wall region and reductions in drag of up to 50% have been reported in some cases. An effect of the presence of the polymer is to increase the streak spacing and also the lifetime and length of the streaks. Up to double the normal streak spacing has been reported. The bursting frequency from each streak structure appears to remain the same, however Chapter 1. Introduction and Literature Review 29 fewer streaks leads to fewer bursts. The increase in streak spacing is explained as being due to the increased resistance of the dilute polymer solutions to vortex stretching, thus inhibiting streak formation. In the polymer solutions it has been suggested that the weaker streak forming disturbances are damped out and only the stronger disturbances persist [8]. Interactive methods of drag reduction aimed at controlling the wall eddy structure have been attempted by Roon and Blackwelder [40]. They suggested the use of riblets with suction to try to inhibit low speed streak lift-up. This method has led to a reduction in the number of detected lifting/bursting streaks, decreasing detections with increasing suction. Decreased detections indicate lower bursting rates and thus lower skin-friction. Other interactive methods being investigated include selective wall heating and structure control by interaction with added eddy structure. In order to obtain as clear a picture as possible for the overall structure of the bound-ary layer, it was necessary to examine many pieces of evidence and then try to develop a model that does not exclude or violate any of the existing data. It was difficult to try to interrelate the available data, but this integration is necessary for the development of a model or framework from which further studies can be planned. The lack of a coherent framework in the literature was preceived as a serious deficiency, especially for people new to the field. The previous discussion has covered most of the important features and ideas, but it is not to be thought in any way all inclusive. Chapter 2 Experimental Apparatus and Procedure The experiments were performed in an open circuit, smooth wall, boundary layer wind tunnel at the Mechanical Engineering Dept. of the University of British Columbia (Fig.2.14). Important details of the tunnel were as shown. Key 1. --Screens 2. -Honeycomb Flow Stralghteners 3. -Boundary Layer Trip (2cm X 15cm) 4. -Traverse Mechanism 5. -Wall Static Pressure Taps 6. -Adjustable Roof 7. -Hot Wires (3 Configurations) 8. ~Neutral Zero Pressure Gradient Boundary Layer 9. --Pitot Tube Figure 2.14: Tunnel Sketch and Details 30 Chapter 2. Experimental Apparatus and Procedure 31 (Too ~ 4 m/s 699 ~ .33 m. /Zefl ~ 8390 fle6 ~ 82500 Cf ~ .0035 (From Clauser Plot) uT - y/T^p ~ 0.334 m/s 100y+ ~ 0.0048 meters = 0.0145(y/g)  Table 2.1: Summary of Experimental Conditions The test section of the tunnel was ~ 30 meters long, ~ 2+ meters in height and ~ 2.4 meters across. The boundary layer was tripped at the beginning of the test section using a 2 cm high wedge, 15 cm long, spanning the width of the tunnel. The distance from the last screen to the trip was > 2 meters, indicating the boundary layer developing along the floor would already have become turbulent, having a Rex > 5x10 s even before the trip was reached. The trip was used to artificially thicken the boundary layer and ensure a fixed origin, reducing any upstream transition fluctuation dependence. The boundary layer was allowed to develop over 24 meters after the trip. By this distance any structure produced by the trip will have decayed to insignificance as the measurement station was > 1000 trip heights downstream. The height of the roof of the test section was adjusted to maintain zero pressure gradient conditions in the test section, < .06 Pa/m locally and < .15 Pa over the length of the tunnel. This was done by measuring the test section pressure using wall pressure taps distributed at 2.4 meter intervals along its length, and adjusting the roof until the pressure difference between all taps was less than ~ .15 Pa, as measured with an inclined alcohol manometer. The free stream velocity was measured using a pitot tube. A l l hot wire configurations were calibrated relative to the pitot tube using the relation: U = AVnjrBt where n = .45, and A and B were determined using a least-squares fit to the hot wire calibration data. In all cases a least-squares fit producing a calibration coefficent of .998+ was required, or the calibration was repeated until this was attained. Wire configurations were traversed Chapter 2. Experimental Apparatus and Procedure through the boudary layer using a simple manual traverse mechanism (Fig.2.15). 32 •90 cm 5 cm Figure 2.15: Traverse Mechan i sm The larger supporting members were at least 90 cm, > 18 support diameters' down-stream of the hot wires, and produced less that 1% blockage by area. Three Bets of wire configurations were used to take the data: 1. Two vertically displaced X-wires and a leading straight wire (See Fig.2.16a). 2. A horizontal rake of five straight wires (Fig.2.16b). 3. A vertical rake of five straight wires (Fig.2.16c). In all cases standard D A N T E C hot wires were used having active sensor lengths ~ 1 —• 1.5 mm, operating at 80% overheat. Accuracy in vertical positioning using Chapter 2. Experimental Apparatus and Procedure 33 the traverse was ~ ± .5 mm. Hot wire data was taken using five D A N T E C 56C17 hot wire bridges and 56N20 signal conditioners. Low pass filtering was at 3000 Hz. Data digitization was at 1000 Hz, 40000 point continuous records, on all channels. This was done using a Data Translation (DT2801A) 12 bit analogue to digital board installed in an I B M X T computer. The data files were then stored on magnetic tape on a V A X 750 computer, which was also used for program development and data manipulation (Fig.2.17). A l l results and figures were produced using the above data sets. The wall skin friction coefficient C / , and the shear velocity uT were determined using universal curves for inner turbulent boundary layers on a smooth wall (Clauser 1954). 2.1 Conditional Sampling Conditional sampling identifies repeated features termed events in the time dependent signals of turbulent flow. This can be done using the same time history or other time histories as the detector signal. A particular signal characteristic is identified as the event detector and a detector function is developed to identify it. Whenever this signal criteria is identified by the detector function, the desired time histories around the detection are saved, centered on the event detection. This procedure is implemented for the whole data record length, and the events are summed and averaged to produce ensemble-averaged event signals. The ensemble-averaged signals may then be used to determine typical characteristics or trends for the events. This has been done by other researchers using velocity, pressure, temperature, and shear stress signals. A number of detector functions have been developed for this purpose and deciding which, if any, is superior depends on the nature of the structure being sought, and Chapter 2. Experimental Apparatus and Procedure 34 has been a topic of considerable discussion. A detector function should possess several characteristics: • A high probability of detecting the desired structures present in the flow. • A low probability of detecting false strutures; producing a detection from a signal which is not related to the desired structure. • The detector function must provide for time centering of the structures to enable the calculation of a useful ensemble-average. • The calculated ensemble-averaged signals should not be a function of the detector function, only of the structure present in the flow. All of the detector functions developed use one or more level or duration discrim-inators. The fact that all the methods use a discriminator of some type immediately introduces a certain bias to the results, and raises the question, 'What is the best dis-criminator value?'. All of the schemes exhibit detection frequency dependence on the discriminator value, and therefore determination of typical event occurrence frequencies or periods can not be done with certainty using these methods. Typically the discrim-inators are adjusted until the frequencies match those of visual studies, but even this is a dubious practice. It would seem that conditional sampling of this type has limited usefulness. However, it can be used to identify typical event structure with a certain amount of confidence, as long as the detector fuction meets the previously mentioned criteria. It should be mentioned that the ensemble-averaged signals can be thought to only be reliable for times close to the event detection centering time. Far from the event center, age and orientation of the structure relative to the detection sensor, and the three dimensional nature of the structure, are important and therefore the ensembled values can be taken only as typical trends in the signals [41]. Chapter 2. Experimental Apparatus and Procedure 35 The two most generally used and accepted single point detection methods (single point meaning that the detector signal comes from a single point in the flow) are the Variable Interval Time Average (VITA) method and the uv Hole or Quadrant method. These will be discussed and compared to indicate the reasoning behind the choice of method used for this study. Other single point methods do not appear to offer significant advantages over the VITA or Hole methods and are not as well used or documented. Multiple point detection schemes have been developed using rakes of sensors (Chen and Blackwelder [10] and Jovic [30]). These methods have not been used in this study. It has been noted that VITA detections correspond to rake detections much better than do uv Hole detections. 2.1.1 uv Hole or Quadrant detection method The uv Hole method has been used by Lu and Willmarth [20] and assumes that the events, bursts/ejections and sweeps, are important uv stress producers, and that most of the uv stress produced will lie in the second and fourth quadrants, ie (+u,-v) sweeps and (-u,+v) bursts. This effect can be seen in a uv quadrant plot. The uv stress is skewed, resulting in the larger portion being found in the second and fourth quadrants. This has been observed to be the case throughout the boundary layer, although it is most noticable near the wall. The uv Hole method makes use of this by determining that an event has occured when: I «v ( t ) |> Hurm.vrm. and is centered at the point where | uv(t) | is maximum for the detected excursion. The uv Hole method selects events from the areas shown in Figure 2.18, centered on the maximum value of the uv stress during the time that it exceeds the stated criteria. The value of (H) used determines how much of the data will be Chapter 2. Experimental Apparatus and Procedure 36 excluded, or the size of the hole region. Lu and Willmarth determined the best value for the constant (H) by examining the % contribution to the total uv stress from each of the four quadrants, that exceeded the detection level. They found that for their experi-ments, a value of (H ~ 4 —• 5) effectively eliminated any contributions from the first and third quadrants, while still maintaining a significant contribution from the second and fourth. This was determined to be an effective value for (H). Further decomposition of the conditional data into second and fourth quadrant ensemble-averages, giving typical second and fourth event characteristics, was also done. 2.1.2 Variable Interval Time Average (VITA) technique Blackwelder and Kaplan have used this method of event detection to examine wall struc-ture in a turbulent boundary layer. The basic VITA method compares the long time average (rms) value of a turbulent quantity with a short-time-averaged variance of the same quantity. When the short-time-averaged variance exceeds (K) times the long time (rms) value, where (K) is the detection level constant, an event is said to have occurred. The variance is defined as: va-r(xut,T,) = Q 2 ^ , t, T,) - [Q(xitt,T.)]2 Where the (xi) denotes position of the sensor, (t) the time at the end of the short time averaging window, and (T, = *£/«,/£) the short time averaging time, or window width. The (~) symbol denotes a short-time-average quantity where the short-time-average is defined as: Q{xi,t,T.) = i - f Q(xiyt)dt 1. Jt-T. and an event is detected when, ™r > K(Qrm.)2 Chapter 2. Experimental Apparatus and Procedure 37 The V I T A technique searches for rapid sustained excursions in a turbulent quantity. These changes may be further subdivided into positive and negative slope events, deter-mined by the sign of dQ/dt for the event. The detected events are ensemble-averaged to produce typical event signals, where the ensemble-average is defined as: The events are centered about the (Us), where the (Us) refer to the event detection times, and (N) is the number of event detections used to calculate the average. The (r) refers to ensemble time (time removed from the event center). Ensemble averages may be performed on the quantity used for the detection scheme or on any simultaneously measured quantity once the event times (Us) have been determined for the data record. Determining the best values of (K) and (T„) to use in the V I T A detection scheme is a tricky problem and will be discussed later. Subramanian and Rajagopalan [41] compared the VITA, Hole, Rake, and other meth-ods of event detection with simultaneous flow visualization. They determined that while the V I T A method did not detect all visual events, it had a low probability of produc-ing false detections. They also found that the Hole method produced ensemble event histories that were quite different from those of the VITA, Rake, or any other of the tested methods. They recommend the VITA technique as one of the better single point detection schemes. Bogard and Tiederman [21] also compared single point detection methods. They recommended the Hole method as a burst detection method for use in determining the bursting frequency. They also indicate that the V I T A technique has a low probability of producing false detections, but that the number of events detected was very sensitive to the value of the threshold (K) and was therefore perhaps not a good method of 1 N Chapter 2. Experimental Apparatus and Procedure 38 determining the bursting frequency. Blackwelder and Kaplan [11] performed the V I T A technique on a pseudo turbulent signal to try to show that the ensemble-averages produced using V I T A were not a function of the V I T A detection scheme, and only of the flow structure. Their results indicated that V I T A produced ensemble averaged signals that most likely were not a function of the VITA scheme. They also indicated that the resultant ensemble-averages were only weakly dependent on (T») with a bias towards stronger shorter duration events with decreasing (T*). The value of (K) appeared only to affect the amplitude of the ensemble-averaged signals, not their shape, and the results collapsed when scaled with (Kv?)*. Figure 2.19 is an example of event detections using V I T A on the u velocity. Two detected events from the data shown are identified, and the regions used for calculation of ensemble averages, centered on V I T A event detections, are outlined. A l l three velocity signatures can and will be used to produce ensemble averages from the events derived from the u velocity. This figure is fairly representative of typical velocity signals, although the events did not usually occur this close to each other. Several points may be demonstrated from this figure: 1. VITA detected large, rapid, fairly sustained (~ 0.025 s. which translates to ~ 1/36 in the streamwise direction) rises in the u velocity. 2. Most detected events were positive, du/dt > 0, and were preceded by a period of sustained retarded u velocity. 3. Activity can be observed in the v and uv velocity signals prior to and during the u velocity events. 4. As observed by Alfredsson and Johansson [32], large uv peaks not occurring near u velocity V I T A events are accompanied by peaks in the v velocity signal and could Chapter 2. Experimental Apparatus and Procedure 39 therefore be detected using VITA on the v signal (See far right of figure). A n observation that can be made from this figure, and others like it, is that the v velocity contains higher average frequency content than the u velocity. This has been noted by a number of authors. It appears that the u velocity signal acts as a filter for the uv velocity. Peaks in uv most often occur during the low frequency excursions in the u velocity. This is perhaps not on the surface surprising, but if one assumes that the u signal is indicative of large scale structure, it seems clear that while the uv signal could be used to detect the same events, the uv signal would not properly provide for large scale event centering. The uv peaks appear to be located in the region preceding the V I T A u velocity detections, but at different times relative to the u signal event from event to event. This has also been observed by Alfredsson and Johansson [32]. Their results, taken in a water channel having a Reynolds number based on channel width ~ 7500 (Reg < 2000), show that the ensemble-average of all u velocity V I T A events was very similar to the ensemble-average of only the positive events. They also found that there were fewer negative events than positive, and the negative event ensemble-averages indicated event structure of shorter duration. The authors also performed the V I T A technique on the v velocity. They determined that the v events were of shorter duration than the u events, and, using the same discriminator value K , that v events were three times as frequent as u events. The short-time-averaging time, (T„), which gave a maximum number of v events was significantly shorter than that for the u events, further indication that the v events were of shorter duration. We postulate that the v VITA and uv Hole detections are most likely due to the hairpin/ring vortex structures which would be of shorter duration than the bulge structure. Gartshore [42], based on a potential flow model of a hairpin vortex (see Appendix#B), indicated that the positive v, negative u velocity peaks (quadrant II Chapter 2. Experimental Apparatus and Procedure 40 events ) associatated with the model vortex, would be fewer in number, due to structure area considerations than the quadrant IV events, but would on average be much stronger. They would therefore be more likely to be detected using higher Hole discriminator (H) levels. Therefore, at lower (H) values, there should exist a greater number of quadrant IV detections than quadrant II detections, but at high (H) values this should be reversed. A trend of this nature is quite clear in the data of Alfredson and Johansson [32] (Fig.2.20), in a plot of the number of detected events per quadrant at y+ = 50, for different values of (H). Another point of importance is that, as Bogard and Tiederman [21] have shown, multiple events of short duration can occur associated with the breakup of a single streak structure. These events (ejections, hairpins?) may be grouped as one burst by setting a minimum event detection time separation. This could be related to the observation that there are a larger number of v velocity detections and that they are of shorter duration, the v velocity detections being dominated by the smaller multiple structures, and the u velocity detections by the overall larger bulge structure. Alfredsson and Johansson [32] made some interesting observations on the two detec-tion schemes: • The quadrant methods ensemble-averages indicated structure of shorter duration than that of the V I T A method, indicating a bias towards smaller scale structure. • Only 50% of V I T A events using K = 1.0 corresponded to quadrant events using H = 4.0, but more than 90% had a quadrant detection associated with them using H = 2.0 and the two methods of detection did not coincide, but were related. In general, for u accelerations (positive V I T A u velocity events), which were by far the most common, the quadrant detections occurred prior to the V I T A detections Chapter 2. Experimental Apparatus and Procedure 41 with an average lead time'of ~ 10 viscous time scales (i//u*). This put the quad-rant detections well downstream of the V I T A accelerations, in the area of retarded flow found before the VITA events. The authors concluded that the VITA tech-nique gave better representations of the actual event realizations. Figure 2.21a,b,c demonstrates the differences in the ensemble-averages between the two sampling methods. The V I T A technique was chosen as the conditional sampling method for this study for the following reasons: 1. V I T A ensemble-averages do not appear to be a function of the sampling technique. 2. V I T A gives ensemble representations which are closer to those of the typical events. 3. The VITA technique searches for two criteria, rapid and sustained changes in the selection quantity, while the uv Hole method is in reality only a level conditioner and therefore does not provide for event centering as well as the VITA method and is not as selective about what it accepts as an event. 4. The V I T A method can be applied to one quantity at a time, while the uv Hole method requires both the u and v velocities, which means that all detection sensors must give both velocities. This increases the complexity of the apparatus and the cost. For this study V I T A was applied to the u velocity signals. The values of (K) and (T.) to use depends on the size and strength of the structure being sought. (T») should be of the same order as the typical event characteristic time scale, in this case a large sustained velocity change, and (K) should be chosen large enough to minimize invalid event detections, (assuming that valid events give, on average, stronger VITA signals) and small enough that a reasonable number of events are detected. Chapter 2. Experimental Apparatus and Procedure 42 As previously indicated, the choice of appropriate values of (T„) and (K) has been considered by several investigators. Some study of this issue was done to observe the effects of the variations of these parameters on the number of events detected, and the appearence of the resultant ensemble-averages as a function of the parameters. The following was noted: 1. As K increases, the number of both positive and negative V I T A events decreases (Fig.2.22a). 2. The effect of increasing (K) on the ensemble-averages indicates that larger (K) values tend to select events with faster, larger deviations (stronger events). This effect may be observed in Figure 2.23a,b for both positive and negative events. 3. The effect of (T«) on the number of events detected was quite weak for the range of (T.) examined, but peaked around T» = 0.2 (Fig.2.22b). The ensemble-averages reflect the tendency of larger values of (T*) to bias towards events of longer dura-tion (Fig.2.24a,b). The choice of T. = UooT/S = 0.2 requires the detected velocity change to have streamwise dimensions of 0.28 or less. Slower changes will be longer than the short-time-average window and would be unlikely to produce events. Ob-servation from the present results indicate that on average, the actual dimensions of the detected accelerations are shorter than the window length used to detect them. The values of (K) and (T„) chosen for the experiments to follow were K=0.6 to 0.8 and T. = 0.2. Values in this range appeared to satisfy the stated criteria. Bogard [43] has modified the V I T A technique to incorporate a level criteria to attempt to determine each event duration. Different events have at least slightly different shapes and durations due to age and orientation of the structure as it passes the detection Chapter 2. Experimental Apparatus and Procedure 43 sensor. The modified technique detects in the same way, but then uses a level criteria to determine the end of the event. In this way each event may be scaled in order to produce a more representative ensemble average. This method was not attempted, but is mentioned here as a possible further extension on the conditional sampling technique. An important point to note about the selection of (K) and (T») is that the values chosen do not affect the overall shape of the resultant ensemble-averages, and therefore unless quantitative results are required, the precise values used, as long as they are within a reasonable range, should not seriously effect trends in the data. The majority of this work only attempts to give trends and it was therefore considered that the values of (K) and (T«) as described should be effective. Chapter 2. Experimental Apparatus and Procedure 44 TWO X-WIRES + UPSTREAM NORMAL WIRE T IX-wireC3,4) 3. 5mm-I 33mm I jX-yireCI.2) Normal u i r a C S ) T Y A —• X HORIZONTAL RAKE OF FIVE NORMAL WIRES b) VERTICAL RAKE OF FIVE NORMAL WIRES I  T~, W I R E J T ~ T * f ^ X ^ WIRE»2~ f ^ C U WIRE»3 17. I n n , '  WIRE#4 — — — — — v * 31 .3 Figure 2.16: Wire Configurations: a)X-wires b)Horizontal Rake c)Vertical Rake Chapter 2. Experimental Apparatus and Procedure 45 Hot wires 5 channels 5 Dantec 56c17 CTA hot wire bridges and 56n20 signal conditioner units 12 bit analogue to digital conversion @1000 Hz. per channel. (Data Translation DT2801A) Figure 2.17: Equipment and Data Pathway Chapter 2. Experimental Apparatus and Procedure 46 V uv Probabi l i ty C o n t o u r s Figure 2.18: Quadrant Detection Method 1 1.1 1.2 1.3 1.4 1.5 TIME (S) Figure 2.19: Example of VITA Event Detection (on u velocity) Chapter 2. Experimental Apparatus and Procedure 47 Figure 2.20: Number of Events per unit time for each Quadrant as a Function of H (Ref#32) Chapter 2. Experimental Apparatus and Procedure 48 Figure 2.21: Examples of ensemble-averages from: a)Quadrant#2 b)Quadrant#4 c)Positive V I T A on u Chapter 2. Experimental Apparatus and Procedure 49 Figure 2.22: a)Number of Events as a Function of (K) b)Number of Events as a Function of (T„) Chapter 2. Experimental Apparatus and Procedure 50 1.5 U Urms 0.5 v "rrrw - 0 . 5 . *rms -1 .5 . T, = .2,K = .5 v/6 = .185 ENSEMBLE u VITA ENSEMBLE v ENSEMBLE uv .08 - . 0 6 - .04 1 1 1 . 02 0 .02 TIME ( S ) .04 .06 .08 1.5 U urms 0.5 v "rma 0 . ut/ Tp.— urms -0.5 -1.5 T. = .2,K = .9 ENSEMBLE u VITA ENSEMBLE V ENSEMBLE uv - . 0 8 - . 06 - . 04 - .02 H 0 TIME ( S ) 1— .02 .04 .06 .08 Figure 2.23: Effect of K on V I T A Ensemble-Averges: a)K=.5 b )K=.9 Chapter 2. Experimental Apparatus and Procedure 51 Figure 2.24: Effect of T; on V I T A Ensemble-Averages: a)T* = .24 b)T. = .12 Chapter 3 Generalized Turbulent Boundary Layer Structural Model This chapter develops a generalized, simplified, pictorial, descriptive model of the outer structure of a smooth wall turbulent boundary layer. It is rather remarkable that the author knows of no equivalent model described in the literature. The author believes this to be a serious deficiency in the literature. The model developed here is very useful as a framework into which further development and refinement may be placed, in addition to enhancing our understanding of the existing results. Discussion and observations to improve on the model are obviously an ongoing necessity. It is somewhat unusual to present the results before the experiments, but in this case it is necessary because understanding the experiments and their interpretations would be difficult at times without a framework into which to place the ideas. At the time that the experiments were performed, the overall model did not exist, which proved to be a major obstacle. We hope that presenting it in this manner will make understanding and interpreting the material much easier. Following discussion of the model, the experimen-tal results will be presented, and we will indicate why we feel that the model agrees with the results and the literature. The model has been developed to describe the effects and structure in the outer region of the turbulent boundary layer and incorporates a duality of scales coupled with Reynolds number dependence. 52 Chapter 3. Generalized Turbulent Boundary Layer Structural Model 53 3.0.3 Model Description The full model consists of three interrelated structure organizations which develop one into another as Reg increases. 1. Initially at low Reg < 1000, the outer structure appears to consist of hairpin type vortices. At these Reg values, the hairpins, which have lateral dimensions of in-fluence of the order of 100 —* 200y +, and which, according to most evidence, are related to the sublayer streaks and bursting, are of similar scale to the overall boundary layer thickness (see Fig.3.25). This size should enable these structures to be the dominant transporters of momentum in the outer layer, and would closely link the outer and inner regions. Vortex Structure Figure 3.25: Low Reg Outer Region Structure Chapter 3. Generalized Turbulent Boundary Layer Structural Model 54 2. As the Ree rises (roughly, 1000 < Ree < 3000), the wall region and therefore the scale of the hairpin structures (100 —• 200y+), independent of Reg, becomes smaller relative to the boundary layer thickness (8) than for the low Reg case. This is due to the fact that the thickness grows more rapidly than the wall layer (Bee Fig.1.13). As this occurs, and the hairpins become small compared to 8, they would become inefficient as the dominant structure. Large amounts of stretching or peeling of the vorticies would be necessary for the hairpins, as distinct entities, to span the boundary layer. In order to maintain the momentum exchange, another organization or structure would be necessary. The suggested form of this is that the hairpins organize or are organized into groups, maintaining their coherency at a scale similar to 8, even though singly they are an order or more of magnitude smaller (see Fig.3.26). This kind of organization has been occasionally observed (see Fig.1.8). 3. Finally as the Reg becomes large (> 5000), the wall scaled eddies, hairpins or necked hairpins (ring vortices, see Chapter 1), become very small compared to 8 and can not maintain the outer layer dynamics on their own. Therefore the secondary larger structure becomes dominant. These have been sometimes termed bulges. The bulges scale on the outer variables and so they grow at the same rate as 8 and therefore maintain their coherent nature and importance indefinitely, independent of further increases in Reg. Figure 3.27 is a schematic of this structure. A bulge consists of an upwelling of BIOW moving fluid and wall scaled eddies which circulate up the trailing edge. This circulation could be driven at least in part by the wall scaled eddies themselves, as the counter-rotating vortex structures would propagate backwards relative to the mean flow due to their own self induction. The areas where VITA events occur, and the sign of the events, are indicated on Chapter 3. Generalized Turbulent Boundary Layer Structural Model 55 U Middle Reynolds number, inner structures becoming small compared to outer structure Re =3000 6 Figure 3.26: Middle Reg Outer Region Structure the diagram at the edges of the bulge. Leading and trailing the bulge are sweep motions. Motions of this type would be required by continuity, but their positions as shown would explain much of the observed characteristics of the structure. The leading sweep could also act as the trailing sweep for the next downstream bulge, and vice-versa, assuming that the bulges occur close enough together. The top bulge interface should coincide with the intermittent interface, or would be closely related to it. Therefore, the intermittent interface should have a scale similar as the bulge structure, and also the bulge passing and intermittent interface transition occurrence frequencies should be related. Chapter 3. Generalized Turbulent Boundary Layer Structural Model 56 Wall eddy structure U small compared to outer 'Bulge' structure Figure 3.27: High Reg Outer Region Structure The wall eddies would congregate at the trailing bulge interface or front due to the following considerations: • The bulge is internally a region of retarded fluid rising from below. • The trailing sweep is an accelerated region of fluid sweeping down from above. • The area where the two interact results in a large velocity gradient. As the wall eddies approach this gradient, propagating backwards in the retarded fluid, they would penetrate it until their self-induced negative velocity is balanced by the higher local velocity due to the sweep. At this point they would stop relative to the gradient interface and assuming that they possess the correct orientation, as indicated on the figure, propagate upwards due to the bulge Chapter 3. Generalized Turbulent Boundary Layer Structural Model 57 circulation and their own self-induction. The shape of the bulge interface itself should help to align the eddies in the required direction, and the eddies indicated origin as necked hairpins would also give the required orientation. The stronger structures would penetrate more deeply than the weaker ones, resulting in a zone of intense small scale activity. As these structures convect upwards, dissipating as they rise, they would be replaced by new ones from below. The indicated form of the wall-scaled eddies is a ring vortex, possibly formed from a cross-connected hairpin (see Chapter 1). Other vortex structures, such as full hairpins, would be possible, but due to their elongated nature they would be very susceptible to distortion resulting in the loss of well defined vertical extensions, or legs, causing them to closely resemble ring type structures. Flow visualization shows that at high Reg, the only well denned small scale vortex structures are what appear to be the tips of hairpins, which can for all practical purposes be described as rings. The integration of the sweep fluid with the bulge would cause local acceleration of the retarded bulge fluid and local retardation of sweep fluid. This high-low speed fluid mix must be displaced in the vertical and/or spanwise direction by fluid from below, otherwise the structure could no longer evolve and grow. Displacement in the vertical direction would place the mixture in a higher velocity region due to the mean gradient, and this fluid could therefore undergo further acceleration by additional sweep fluid. The effect of this would be that the bulge would grow vertically and horizontally and would require continuous replenishment of retarded fluid from below, giving the whole bulge an overturning circulation and causing continual momentum exchange. Chapter. 3. Generalized Turbulent Boundary Layer Structural Model 58 The passage of some part of the bulge structure must cause conditions in the wall region facilitating the formation of new wall structures, maintaining the supply of wall-scaled eddies and retarded fluid. The bulgeB would of course be three-dimensional and could occur in an interrelated way, such that the trailing and leading sweep motions might be related to the leading or trailing sweep motions of other structures. A two-dimensional array in the xz plane of interrelated structures is also a possibility, but it seems clear that individual bulges should have a spanwise scale of similar order as their streamwise scale, which is of the order of 8. The bulges should have a life cycle, new ones continually forming to replace the older weaker structures, weakened by age or interaction with each other and the sweeps. The (—u —• -fu) events should be much stronger and more coherent due to the nature of the trailing interface as compared with the leading interface (+u —* —u) events. The high velocity sweep overtaking the retarded bulge would result in a larger more clearly defined interface than at the leading edge of the bulge, except near the top of the bulge, where the preceding sweep would correspond with the intermittent interface, resulting in a well defined (-fu —> —u) event. Therefore, using the same detection criteria (K , T*), for most of the outer region one should detect a greater number of positive, (—u —> -fu) V I T A events, than negative (-fu —• —u). This assumes that V I T A detections are principally due to bulge interface interactions. Further discussion and interpretation of V I T A events may be found in section 4.2. In the intermittent region, the number of positive and negative events should be almost equal in contrast to the above comment. It has not been our intention to clearly delineate three Reg regions. Rather, the three proposed strutures must blend together over large Reg ranges, with the middle Reg structure simply being the transition from the low to high Reg structure. The Chapter 3. Generalized Turbulent Boundary Layer Structural Model 59 model described takes into account the observed Reg dependence of the flow structure, an important and heretofore confusing factor, and it agrees with most of the present observations and those in the literature. Chapter 4 Experimental Results and Discussion The mean velocities and intensities for the boundary layer, at the measurement location, were plotted and compared to published values. These basic boundary layer character-istics, and a discussion of the basic data reduction methods, can be seen in Appendix A. This chapter will present and discuss the results of conditional sampling and data manipulation from the three wire configurations, and relate these to the model presented in Chapter 3. The fluctuating velocities in the uv plane are skewed. Figure 4.28 is an example of a probability distribution of the u and v velocities, where umam is the maximum deviation of the u velocity from the local mean. It shows that the uv stress is concentrated in the Becond and fourth quadrants. This is fairly typical over most of the boundary layer. This figure indicates that the fluctuating u and v velocities are in some fashion linked to each other and therefore do not strictly exhibit random behavior. The presence of some type of structure in the flow could account for this, and much of the techniques to follow are an attempt to define the nature of this structure. 4.1 Correlations Basic crosscorrelations can be used to give an indication of the general structure of the v flow. The croBscorrelation function can be thought of as an indication of similarity in the velocities between the sensor locations, as a function of delay time (r), where (r) is the difference in time, or the offset, between the data sets being correlated (See Appendix A). 60 Chapter 4. Experimental Results and Discussion 61 1 v "max 0 - 1 0 u i Umax Figure 4.28: uv Probability Distribution at y/6 — .07 The delay time at which the crosscorrelation is a maximum indicates the average time delay between the data sets for which the velocities, at the two measurement locations, were most similar. This information can be used to determine characteristics of the flow structure. Interpretation of this data can be difficult, and conclusions somewhat risky unless one already has a good idea what the structure should be. Once this has been determined, the correlation data can be used to support the structure assumptions. For example, Tritton's [27] study of the correlations in a boundary layer at low Reg ~ 2600, if examined in terms of hairpin type vortex structure, quite strongly supports scaling in the order of 100 —• 200y+. If one did not already have a model in mind, the data would have been difficult to interpret. - % = .07 y+ = 513 Quad.II -u,+v Quad.I : +Uy+v ; . Quad.Ill - u , - v ' Quad.iv ; +u y-v [ — i — : — i — i — i _i_ i i i i i i i i Chapter 4. Experimental Results and Discussion 62 Basic crosscorrelations on the u velocity for all y/8 locations were performed between: 1. The leading straight wire and the lower X-wire. 2. The two X-wires. 3. The leading straight wire and the upper X-wire. Crosscorrelations were also performed using the v and uy velocities acquired with the two X-wires. Crosscorrelations from the leading straight wire and the lower X-wire were used to get a measure of the average convection velocities. It should be noted that these can be quite different than the local mean velocities. This was done using a peak selection method (see Appendix A) . The peak delay times, evaluated using this method, should give an indication of the time taken for the significant structures in the flow to travel from wire-to-wire. The calculated convection velocities were quite similar to the local mean velocities (£/j), in this case (95-100% of U{). Examples of all crosscorrelation results can be found in Appendix C. Crosscorrelations between the upper X-wire and the leading straight wire, and between the two X-wires were used to determine what shall be termed a "generalized structure inclination angle". Alving and Smits [24] made this determination in a Ree ~ 6000 boundary layer flow, and found the angle was dependent on wire separation, for separations less than ~ .IS. The X-wires in this study were set at AS to avoid this problem. The explanation forwarded for this effect [24] was that the smaller scale structures begin to influence the correlations for small separation distances, which biases the results towards larger angles. From the description of the small scale structure in the literature, having scales of influence of 100 —• 300y +, the separation distance would be important at low Reg, but should become less so at higher Ree, since the thickness growth rate is considerably larger than the wall scale growth rate. The generalized structure inclination angle was determined making use of the same peak selection method mentioned previously. A peak delay time for each crosscorrelation Chapter 4. Experimental Results and Discussion 63 curve was determined, and the inclination angle was calculated using the relations: 9 = arctan^OZZ/nU^) for crosscorrelations between the two X-wires, and 9 = orctan(.033/(.0533 - T3Uei)) for crosscorrelations between the leading straight wire and the upper X-wire. Figure 4.29 is a diagram of the relevent quantities, where Uc stands for the convection velocities. Uc was taken to be equal to the local mean velocities, due to the close similarity between the two, and due to scatter in the calculated convection velocities, which would have produced additional scatter in the inclination angle results. Figure 4.30 shows the generalized structure inclination angle as a function of y/S. This figure indicates that the bulk velocities of the structure are most similar for small angles near the floor, and are almost vertically correlated in the intermittent region. These angles do not determine the 6hape of the overall structure, they only indicate the orientation in which the velocities are the most similar. This should be related to the shape of the dominant structure in the flow, but it does not determine it. Crosscorrelations of the v velocity between the X-wires indicates that the preferred direction of similarity is approximately normal to the wall for all tested y/S locations, for the wire separation used. This effect has been noted by other authors. Examination of the curves also indicates that the crosscorrelation peaks are not as strong and of reduced duration for the v velocities compared to the u velocities. It has been generally noted that the v velocity has a higher frequency content than the u velocity, and must therefore be associated with smaller scale activity. For this reason, or if the v velocity correlations are associated with a smaller part of the overall structure than the u velocity, one would expect the correlation peaks to be narrower and of lower magnitude. Exactly why the Chapter 4. Experimental Results and Discussion 64 Upper X-wire Figure 4.29: Quantities used to Calculate the Generalized Structure Inclination Angles v velocity correlations exhibit only vertical angular dependence is difficult to explain. The above does not really account for it. The size of the small wall eddy structures depicted in the model for the experimental conditions used should be ~ .005 —> .015m. In comparison, the vertical wire separation distance was .03m. Thus the effects of the small structures are most likely not the only cause for the observed characteristics in the v velocity crosscorrelations, as the small scale structure should not generally span both of the wires. The only other explanation that might account for this effect is that the v velocities must not be strongly linked to the shape of the large scale structure, or that any (+) angular orientation, from one part of the structure, is balanced by an equal (-) contribution from anouther. This area needs further consideration. Crosscorrelations on Chapter 4. Experimental Results and Discussion 65 the uv velocities from, the two X-wires, exhibited characteristics similar to those of the v velocities. The time records of the instantaneous u crosscorrelations, at set time delays, were examined and it appears that areas of high correlation are associated with VITA detec-tions, but that the two did not generally coincide. The high correlation regions indicated strong correlation over long time scales, indicating structure of the order of S or more. Several further subdivision of the velocities were attempted, to determine if they would effect the crosscorrelations. The u and v velocities were subdivided into positive and negative contributions. This should determine whether the sign of the velocities had an effect on the correlation characteristics, which could indicate association with different parts of the overall structure. Crosscorrelations on the v velocities were mostly uneffected by this division. A slight biasing of the correlations towards positive angles was associated with the positive v velocities, and the positive v velocity's correlation peaks were wider than the negative v velocity's peaks, a weak indication of association of the positive v velocities with larger structure. Similar effects were noted in the uv velocity crosscorrelations, based on selection on the sign of the v velocity. Division of the u velocities also did not significantly effect their crosscorrelations. It did indicate that negative u velocity may be associated with larger structure, and with slightly lower inclination angles, but these trends were weak. Generalized structure angles were computed to compare results from correlations calculated using only the pos-itive u velocity data, and only the negative u velocity data (see Fig.4.30). The positive u velocity data resulted in slightly higher angles, but the differences were small. The V I T A technique was also used to attempt to determine more from the correlations. In general this was not very successful either, except that it was determined that the peaks in the crosscorrelations, and therefore bulk inclination in the flow, were not principally Chapter 4. Experimental Results and Discussion 66 0 . 8 0 . 6 _ y/s 0 . 4 . 0 . 2 . a a A L L ° D P O S I T I V E DATA ONLY ° ° N E G A T I V E DATA ONLY o A o A • O A D O A D D O A OA • A O O A a O A • D o A • AO A O A • C A • a o • O 0 1 0 2 0 3 0 4 0 5 0 6 0 7 0 8 0 9 0 0' Figure 4.30: Generalized Structure Angles associated with the gradient regions of the structure, which result in VITA events. Win-dows of data, up to 2T. in length were selected, centered on VITA detections, and were crosscorrelated using data from the the two X-wires. The results indicated little or no angular dependence. This was confusing, as the original hypothesis suggested that the angle associated with the peak of the crosscorrelation curves would be a direct result of the bulge interfacial regions. A slightly different method using crosscorrelations at set time delays was developed that we feel does give a good indication of the inclination of the interfacial gradient fronts, and will be discussed later. Crosscorrelations of the times of the actual VITA detections between the X-wires, Chapter 4. Experimental Results and Discussion 67 also failed to indicate a preferred delay time, although it should be noted that for the correlation experiments discussed up to this point, no distinction between positive and negative VITA detections had been made. Although this may have introduced uncer-tainty to the results, it could not have been wholly responsible for the almost total lack of preferred delay time found in these crosscorrelations. Crosscorrelations of VITA events between the leading straight wire and the lower X-wire, using the same method, were quite successful, and again indicated that the convection velocities of the VITA fronts were quite close to the mean velocities. The basic crosscorrelation experiments indicated: 1. The average convection velocities were 95 — 100% of the local mean velocities. 2. There is an angular dependence to the flow structure associated with the u veloci-ties, but not with the v or uv velocities, over the distance correlated. 3. The crosscorrelation peaks indicating angular dependence, were not directly asso-ciated with VITA detected events. 4.2 Velocities Through VITA Event Detections Our interpretation of the signifigance of the VITA detected events is that the positive slope u velocity events coincide with the trailing gradient interface seen in the model, and the negative slope events most probably with the leading interface. This is obviously an idealization, and some of the detected events would be the result of random patterns or what will be considered noise. Structure-to-structure variations caused by orientation and age differences are to be expected, and for this reason, the ensemble-averaged velocities can only be thought to represent the trends in the velocity signals, especially at times far removed from the event centers. The important point to note is that there will be Chapter 4. Experimental Results and Discussion 68 a large degree of variability from event-to-event, but that the ensemble-averaged event velocities should still indicate general characteristics of the structure. The number of positive VITA detections was greater than the number of negative detections at all wires for the majority of the boundary layer, except in the intermittent region where they became almost equal (see Fig.4.31). The interpretation of the events gives an explanation for this. The trailing interface is characterized by high speed fluid interacting with lower speed fluid rising from below. The area of interaction should result in mixing and acceleration of the low speed fluid by the higher speed fluid, and displacement of the mixed fluid vertically by the circulation from below. The mixed fluid is displaced to a region of higher average velocity, due to the mean gradient, and therefore undergoes further acceleration. This front must be three dimensional and the slower moving fluid, or bulge, may be surrounded by faster moving sweep fluid. This kind of interaction would result in a much more abrupt and intense gradient than interactions of the opposite nature, high speed sweep fluid leading low speed bulge fluid, which occurs at the leading interface of the bulge. Use of the same detection parameters for both positive and negative detections should result in a greater number of positive detections. It is believed that the trailing interface interaction is one of the most coherent and easily detected characteristic of the bulge structure, and the feature that the VITA technique detects. In the intermittent region the situation should be slightly different. We assume that the intermittent interface coincides in a general way with the bulge top interface. This has not been proven, but the data strongly suggest it as the bulge-passage and intermittent-transition frequencies are of similar magnitude, and examination of time records of veloc-ity in the intermittent region, indicates that the VITA events are related to the intermit-tent transitions. Bearing this in mind, the positive and negative events should coincide with the transitions from rotational to irrotational fluid. These interfacial regions should Chapter 4. Experimental Results and Discussion 69 1.2 y 6 i . 0.8 . 0.6 . 0.4 0.2 *-.-j3*i:-j POS. SLOPE XWIRE 1,2 Q--- Q NEG. SLOPE XWIRE 1,2 o-'-opOS. SLOPE LEADING WIRE *--*NEG. SLOPE LEADING WIRE °--°POS. SLOPE XWIRE 3,4 * - " v NEG. SLOPE XWIRE 3,4 20 1^ 40 60 80 100 120 140 # OF EVENTS Figure 4.31: Number of Events V B y/S be quite distinct, regardless of the sign of the transition, and therefore there should be an approximately equal number of positive and negative events in the intermittent region, which is reflected in the data. Typical velocities from events detected with the X-wire wire set have been produced for all y/S locations. Figures 4.33, 4.34, and 4.35 are examples of ensemble-averaged positive event velocities at several y/S locations, and figures 4.36, 4.37, and 4.38 give ensemble averaged negative event velocities at the same locations. Several trends have been observed: Chapter 4. Experimental Results and Discussion 70 1. For most of the boundary layer, especially for the lower regions, the ensemble-averaged positive events are stronger and of greater duration than the negative events, indicating that the positive events are associated with, or are derived from, structure of greater coherency. Because the positive ensemble-average event veloc-ities exhibit greater spatial coherency, they should aho be more similar to each other at greater times removed from the event detections. The positive events can be seen to be associated with a strong trailing acceleration, or sweep, which is most apparent for low y/S values. The negative events are also to a certain extent associated with a sweep motion which precedes the events, but this association is not as strong as with the positive events. 2. The general form of the positive events appears to be similar across the whole of the boundary layer: a region of retarded fluid up to ~ S in length, followed by a region of accelerated fluid of slightly reduced extent. The retarded fluid is associated with positive v velocity, especially near the event detections, indicating that an upwelling of fluid exists in this region. The sweep fluid is associated generally with slight negative velocities. 3. The negative events appear almost as a mirror image of the positive events about the event detection time, except that the the duration of the coherent nature of the ensemble-averages is reduced. These events have been interpreted as coinciding with the leading interface, but the events exhibit significant positive v velocities, which is somewhat at odds with this interpretation. The bulge structure has been described as growing away from the wall, and if the wires passed through the leading interface of the top of a newly growing bulge, a strong negative event, which would also be associated with large positive v velocity, could result, as the top portion of a newly growing bulge should exhibit significant vertical velocity. Further down Chapter 4. Experimental Results and Discussion 71 the front of the bulge, the negative events should be weaker and not necessarily associated with strong v velocity, as this part of the bulge interface need not be growing vertically and is most likely not very coherent (see Fig.4.32). This is Figure 4.32: Examples of Possible Event Detection Locations naturally only speculative, but it does account for the features of both event types, and the fact that the positive events are stronger, and detected more frequently. 4. In the intermittent region, the positive and negative events become approximately equal in number, strength, and duration. These events would be associated with the tips of the bulges and as mentioned, should also be associated with the intermittent transitions. In this region, the sweep motions do not appear to be as important, and the transitions from or to the sweeps simply cause the velocities to return to approximately mean values. The negative regions of the ensemble-averages, Chapter 4. Experimental Results and Discussion 72 associated with the internal section of the bulge structure, are quite pronounced, especially in the upper intermittent levels. The mean gradient is very low here, and therefore large positive fluctuation velocities, caused by fluid descending from above would be unlikely, while large negative velocities would be quite possible as a result of rising fluid from below. This effect is reflected by the gradual loss of importance of the sweep motions in the ensemble-averages as a function of distance from the wall. The opposite is somewhat true of the negative velocity regions associated with the bulge. We believe that the event velocities and trends correspond with those that would exist for the model presented. Caution must still be exercised in interpreting these types of results. Spatial averaging effects due to structure orientation as it passes the detection wires, and the inclusion of detections that do not correspond to true structure, but are the result of random interactions, will tend to diminish the definitiveness of the ensemble-averages, especially at times far removed from the event detections. Figure 4.33: Ensemble-Averaged Positive Event Velocities: a)y/8 b)y/S = .07 Figure 4.34: Ensemble-Averaged Positive Event Velocities: a b)y/S = .412 Chapter 4. Experimental Results and Discussion 2 1.5 J 1 J U vrms 0.5 t*rnw uv -°-5 *rms -1 .5 a) y/S = .579 ENSEMBLE u V I T A ENSEMBLE v ENSEMBLE uv „ , - v - v / " "'\ A. tA^'> A' / \\' 'V i i 1 — i - . 0 8 - . 0 6 - . 0 4 .02 0 .02 TIME (S) .04 . 06 T .08 Figure 4.35: Ensemble-Averaged Positive Event Velocities: a)y/5 b)y/S = 1.03 Chapter 4. Experimental Results and Discussion 76 1 . 5 J u urms 0 . 5 v urms o 4 ~ - 0 . 5 UV urms - 1 . 5 J - 2 y/6 = .024 ENSEMBLE uVITA ENSEMBLE v • • - ENSEMBLE uv \_- " v ' '- / -%/' V y i i i i i r — . 0 8 - . 0 6 - . 0 4 - . 0 2 0 . 0 2 . 0 4 I . 0 6 . 0 8 TIME ( S ) 1 . 5 U v-rms 0 . 5 V Urms o J uv "°-5 *rms - l • 1 . 5 b) y/6 = .070 ENSEMBLE u VITA ENSEMBLE v ENSEMBLE uv I I - . 0 8 - . 0 6 1 I . 0 4 - . 0 2 . 0 2 . 0 4 . 0 6 . 0 8 TIME ( S ) Figure 4.36: Ensemble-Averaged Negative Event Velocities: a)y/8 = 024 b)y/6 = .07 Chapter 4. Experimental Results and Discussion 2 1 .5 1 y/6 = .185 ENSEMBLE u V I T A ENSEMBLE v ENSEMBLE uv U v-rms °-5 - !'•;"' '-• ~v 0 urms uv "°-5  urms - l \ ;' V\ ,\ - 1 . 5 -V A ' »> - 2 i i i i - . 0 8 - . 0 6 - . 0 4 - . 0 2 1 1 1 1 1 0 .02 .04 .06 .08 TIME (S ) 2 TIME (S) Figure 4.37: Ensemble-Averaged Negative Event Velocities: a b)y/t? = .412 Chapter 4. Experimental Results and Discussion 2 1.5 u urms 0.5 Urms urms o J -0.5 a) -1.5 -2 y/6 = .579 ENSEMBLE u V I T A ENSEMBLE V ENSEMBLE uv 1 , \ AT' II ' • Jiv : / \ f! . 'r<F/ \r 1 1 1 1 T— r— r - . 02 0 .02 TIME (S) .04 T .06 T .08 Figure 4.38: Ensemble-Averaged Negative Event Velocities: a b)y/6 = 1.03 Chapter 4. Experimental Results and Discussion 79 4.3 Horizontal and Vertical Rake Data The horizontal and vertical rake data were analysed to determine some of the spatial characteristics of the V I T A detected velocity fronts at a number of positions in the boundary layer. The initial objective was to determine if the VITA detections were associated with small scale intense activity, or were a result of large scale structure interaction. The wire separations were chosen in order to make this determination. The important small scale activity, according to the literature, should have spanwise dimensions ~ 4 —»• 10mm, (100 —» 200y+) for the experimental conditions used. The instantaneous streamwise velocities would exhibit large local gradients over the spanwise scale of the structures, for the small scale structure, as the proposed form of the structure is of a counter-rotating nature. This characteristic will be used to link the small and large scale structure. Wire#5 of the horizontal rake was used to detect V I T A u velocity events. The signals from all five wires were ensemble-averaged using the detections from wire#5. Figures 4.39, 4.40, and 4.41 give results for positive events, and Figures 4.42, 4.43, and 4.44 for negative events. The curves indicate that the event trends in the u velocity seen at wire#5 are very similar to those for the other wires, for the majority of the boundary layer. Very near the wall, the similarity is not as strong. Near the wall, the ensemble averages would include a larger number of new structures. These would be of smaller scale than fully developed bulges, and could account for the decreased similarity between the wires. It appears that the detected structure has a lateral scale of at least twice the rake span, or > 15mm, and that it is quite likely much greater. Similarity in structure spanning 8 in the spanwise direction has been detected by Jovic and Brown [30], using the V I T A technique with a horizontal rake of hot wires. This is of a scale much greater than the small scale structure and therfore indicates that the V I T A detected fronts have Chapter 4. Experimental Results and Discussion 80 large lateral scales and must therefore be associated with large structure. The results do not preclude the possibility that the small scale structure is in some way responsible for V I T A detections by intensifing the gradients locally, but it does demonstrate that the most noticeable feature is of large scale. Therefore, if the V I T A detections are caused in some way by the small 6cale structure, it must also in general be associated with the large scale fronts as is indicated in the model. The negative ensemble events, from the horizontal rake, do not appear to be quite as similar as the positive ensemble events over the span of the wires. This would result if the negative events contain a greater percentage of random interactions, compared to valid event detections. The nature of the negative events as hypothesized, might result in this situation if one assumes that random interactions would result in the same number of false positive and negative events. There were fewer total events in the negative ensemble-averages and therefore these would contain a greater percentage of false detections, which would result in degradation of the ensemble plots. Results from the vertical rake indicate several trends (see Figs 4.45 to 4.52): 1. Detections at the lowest wire (wire#5) do not correspond as well to large scale coherent structure above, as detections at the upper wire correspond to structure below. This can be observed in both the positive and negative slope ensemble-averaged detections, and would be expected from structure which grows away from the wall, especially if the strongest detections occurred near the tops of the large scale structure, as has been hypothesised. 2. Coherency over the span of the wires is indicated, although degradation of the slope of the gradient interface as a function of distance from the detector wire occurs. This effect does not necessarily indicate a weakening in the front as a function of distance from the detection wire. Another cause of the reduction in slope of the Chapter 4. Experimental Results and Discussion 81 T I M E ( S ) 1 J 0 . 5 U Urms - 0 . 5 • 1 - 5 J b) - 2 y/S = .093 W I R E 1 W I R E 2 [\ W I R E 3 jA W I R E 4 .••'Vv — W I R E 5 VITA Vr^ 1 ^ Jll V T . 0 8 - . 0 6 - . 0 4 - . 0 2 0 . 0 2 . 0 4 . 0 6 . 0 8 T I M E ( 5 ) Figure 4.39: Horizontal Rake Ensemble-Averaged Positive Events, VITA wire#5: a)y/£ = .0477 b)y/S = .093 b) - . 0 8 - . 0 6 - . 0 4 - . 0 2 0 .02 TIME (S) .04 ~1 .06 .08 Figure 4.40: Horizontal Rake Ensemble-Averaged Positive Events wire#5: a)y/S = .165 b)y/S = .277 , VITA Chapter 4. Experimental Results and Discussion 83 0 . 5 U - 0 . 5 - 1 - 1 . 5 a) 2 J U urms o - l b) y/6 = .86 WIRE 1 WIRE 2 WIRE 3 WIRE 4 WIRE 5 V I T A H i /J T - . 0 8 - . 0 6 - . 0 4 - . 0 2 0 T I M E ( S ) i i i r . 02 . 0 4 . 0 6 . 0 8 Figure 4.41: Horizontal Rake Ensemble-Averaged Positive Events, V I T A wire#5: a)y/8 = .488 b)y/8 = .86 Chapter 4. Experimental Results and Discussion 84 y/6 = .0477 WIRE 1 WIRE 2 - . 0 8 - . 0 6 - . 0 4 - . 0 2 0 .02 .04 .06 .08 TIME (S) y/6 = .093 WIRE 1 WIRE 2 - . 0 8 - . 0 6 - . 0 4 - . 0 2 0 .02 .04 .06 .08 TIME (S) Figure 4.42: Horizontal Rake Ensemble-Averaged Negative Events, VITA wire#5: &)y/8 = .0477 b)y/6 = .093 Chapter 4. Experimental Results and Discussion 85 y/6 = .165 WIRE 1 - . 0 8 - . 0 6 - . 0 4 - . 0 2 0 .02 .04 .06 .08 TIME (S) y/6 = .277 WIRE 1 WIRE 2 A - . 0 8 - . 0 6 - . 0 4 - . 0 2 0 .02 .04 .06 .08 TIME (S) Figure 4.43: Horizontal Rake Ensemble-Averaged Negative Events, V I T A wire#5: a )y /£ = .165 b)y/6 = .277 Chapter 4. Experimental Results and Discussion 86 it Urms o b) -2 y/6 = .86 WIRE 1 WIRE 2 WIRE 3 WIRE 4 WIRE 5 V I T A .08 -.06 -.04 I I r~ .02 0 .02 TIME (S) .04 .06 .08 Figure 4.44: Horizontal Rake Ensemble-Averaged Negative Events, V I T A wire#5: a)y/6 = .488 b)y/8 = .86 Chapter 4. Experimental Results and Discussion 87 ensemble curves will arise from spatial averaging due to front-to-front variation in the vertical angular orientation. An example of this is demonstrated in Figure 4.53. A saw tooth front shape is assumed as the original profile, as indicated, and ensemble-averages of uniform distributions, spanning .05 and .1 seconds, containing 50 and 100 of these original profiles, have been calculated. This was done to model a distribution of angles, or 'jitter' from front to front, which would result in the front reaching the wires at varying delay times relative to the time it reaches the detection wire. These ensemble-averages exhibit similar degradation to that seen in the vertical rake ensemble-averages. In order to observe the relationship between the small and large scale structure, the horizontal rake data was analysed in the following manner. The fluctuating signal from wire#5 was subtracted from the simultaneous fluctuating signals of all five wires. Fig-ure#4.54a,b i6 an example of the resultant subtracted signals. These signals were then used as an indication of small scale activity, as they are a measure of the gradients in the velocities between wire#5 and the other wires. The wire separation distances were smaller than the expected size of the important small scale structure, but the rake span was of similar scale. Therefore the subtracted signals should be related to structure having a scale somewhere in the range of scales produced by the important small scale activity. Smaller scale structure will not greatly effect the subtracted signals, and larger structure will result in low gradients across the rake span, and should not have a large impact. This is by no means intended as a quantitative measure, however it should give an indication of where in time the small scale structure is concentrated. The subtracted signals were squared and normalized by their respective long time squared averages. These signals were then ensemble- averaged using the event detections from wire#5 as the event centers. The resultant ensemble-averaged signals were quite noisy and were Chapter 4. Experimental Results and Discussion 88 Figure 4.45: Vertical Rake Ensemble-Averaged Positive Events, VITA wire#l: a)y/5 — .109 b)y/8 = .215 (note: y/S measured at wire#l) Chapter 4. Experimental Results and Discussion 89 Figure 4.46: Vertical Rake Ensemble-Averaged Positive Events, VITA wire#l: *)y/6 = .443 b)y/S = .654 (note: y/S measured at wire#l) Chapter 4. Experimental Results and Discussion Figure 4.47: Vertical Rake Ensemble-Averaged Positive Events, V I T A wire a)y/5=.109 b ) j / / £= .215 Chapter 4, Experimental Results and Discussion TIME (S) TIME (S) Figure 4.48: Vertical Rake Ensemble-Averaged Positive Events, VITA wire &)y/6 = .443 b)y/S = .654 Chapter 4. Experimental Results and Discussion 92 V I T A — W I R E 1 y/6 — .109 W I R E 2 - . 0 8 - . 0 6 - . 0 4 - . 0 2 0 . 0 2 . 0 4 . 0 6 TIME ( S ) TIME ( S ) Figure 4.49: Vertical Rake Ensemble-Averaged Negative Events, VTTA wire#l: a ) y / £ = . 1 0 9 b ) y / £ = . 2 1 5 Chapter 4. Experimental Results and Discussion - . 0 8 - . 0 6 - . 0 4 - . 0 2 0 . 0 2 . 0 4 . 0 6 . 0 8 TIME (S) - . 0 8 - . 0 6 - . 0 4 - . 0 2 0 . 0 2 . 0 4 . 0 6 . 0 8 TIME (S) Figure 4.50: Vertical Rake Ensemble-Averaged Negative Events, V I T A wire# l a)j//5 = .443 d)y/6 = .654 Chapter 4. Experimental Results and Discussion 94 l -I 0 . 5 U Urms - 0 . 5 - 1 - 1 . 5 a) W I R E 1 W I R E 2 W I R E 3 W I R E 4 VITA j ^ I R E 5 ^ O v - - / y/6 = .109 A / \ / \ . 0 8 - . 0 6 - . 0 4 - . 0 2 0 . 0 2 T I M E ( S ) . 0 4 . 0 6 . 0 8 1 J W I R E i y/6 = .215 W I R E 2 W I R E 3 T r T ™ . W I R E ^ V I T A — W I R E 5 - 1 . 5 b) - 2 i i i 1 r - . 0 8 - . 0 6 - . 0 4 - . 0 2 0 n r 1 r— • 0 2 . 0 4 . 0 6 . 0 8 T I M E ( S ) Figure 4.51: Vertical Rake Ensemble-Averaged Negative Events, V I T A wire#5: a)y/6 = .109 b)y/6 = .215 Chapter 4. Experimental Results and Discussion T I M E ( S ) 0 . 5 - 1 . 5 b) - 2 W I R E l y/S = .654 W I R E 2 W I R E 3 A , R T M L W I R E 4 / \ VITA W I R E 5 / \ / ' ' \l I I I I 1 I 1 1 T" - . 0 8 - . 0 6 - . 0 4 - . 0 2 0 . 0 2 . 0 4 . 0 6 . 0 8 T I M E ( S ) Figure 4.52: Vertical Rake Ensemble-Averaged Negative Events, VITA wire a)y/S = .443 h)y/S = .654 Chapter 4. Experimental Results and Discussion 96 Figure 4.53: Effect of Spatial Averaging on Ensemble Event Traces Chapter 4. Experimental Results and Discussion 97 smoothed using an averaging window equal to T». The actual value used should not be very important in this situation. The above was done for positive and negative events. The results (Figs. 4.55 to 4.60) indicate that the small scale structure is concentrated, to a certain extent, about the VITA events. The positive events exhibit small scale concentration before the event center time, associated with the downstream side of the trailing front of the bulge. The negative events appear to be associated with structure centered about the event detections. A certain portion of these peaks, very close to the event centers, will be due to variation in the large scale front geometry. From observations of the ensemble-averaged horizontal rake velocities (see Figs. 4.39-4.44), the front appears to be quite coherent across the horizontal rake and does not appear to exhibit much three-dimensionality in terms of horizontal inclintation (see Fig.4.61). If the fronts did possess large and varying horizontal inclination then the ensemble-averages at wires#l—4 (see Figs. 4.39-4.44) would exhibit significant signal degradation due to spatial averaging. Since it appears that only small inclinations are involved, which would result in small time scale signals, centered on the event center time, the peaks observed in the subtracted, squared, normalized, ensemble-averaged traces could not be caused solely by horizontal inclination. Examination of the subtracted signals themselves (see Fig.4.54a,b) demonstrates that the events are generally associated with a number of peaks in the subtracted signals, suggesting that the activity is due to a number of small structures, and not as a result of one large one. When comparing the positive and negative event results, it is important to keep in mind the hypothesized origin of each type of event, as has been discussed. In this context, the results of the small scale structure experiments generally support the model structure presented in Chapter 3, indicating that small scale activity is concentrated near the positive event interface. Other evidence of this link between the different scales of structure exists in the literature, Falco [22] and Thomas+Bull [38]. Chapter 4. Experimental Results and Discussion 98 The presence of the strong peak associated with the negative events indicates that small scale structure should be present near the top of the bulge, on the leading front, but this is quite speculative, as the nature of the negative events is somewhat unclear. One final note on these results is that the small scale activity associated with the positive events, was distributed over larger time scales than the negative event data, and if com-pared to the ensemble-averaged velocity traces, it appears that the small scale activity occurs in a region preceding the trailing front. This agrees with the hypothesis that the small wall eddy or ring vortex structures propagate backwards in the flow, and are then concentrated by the trailing front, as described in Chapter 3. The positive trailing front events are the most easily detectable part of the overall structure. Estimates of the convection velocities of these fronts were made in order to determine if they differed from the overall convection velocities determined from the direct crosscorrelations. Data from the leading straight wire, and the lower X- wire, were analysed as follows: • Positive VITA events were detected at the leading straight wire, and the times corresponding to the maximum in the VITA variance for each event was determined. • The maximum in the variance at the lower X-wire, following a detection at the leading straight wire, over a time record twice that expected from the local mean velocity, was determined. The delay time (r) between the maximum variance at the leading straight wire and the lower X-wire then determined the convection velocity for the front, Uc = .0533/r. • Distributions of delay times at each y/S location were determined, and the most probable delay time from each distribution was used to calculate an average con-vection velocity for the positive VITA events, or trailing front interface. Chapter 4. Experimental Results and Discussion 99 Examples of the distributions of delay times can be seen in Figures 4.62 to 4.64. Figure 4.65 is a plot of the front convection velocities at different levels in the boundary layer, calculated in the described manner. The calculated velocities were ~ 95 —• 100% of the local mean velocities, as were the original overall convection velocities. In retrospect, from observation of the ensemble-averaged velocities through the positive events, this is not surprising, as the ensemble averaged velocities pass through the local mean value as they cross the event fronts. Further investigation of the fronts vertical inclination angle was attempted using the same method used to determine the front convection velocity, except that it used detections at the upper X-wire and attempted to determined the delay time between maximums in the variances at the two X-wires. This method resulted in very flat dis-tributions, (see Fig.4.66), from which a most probable delay time would not have been meaningful. The reason for the failure of the method is unknown. The large scale motion is clearly coherent over the span of wires, as seen in the results from the vertical rake data. Angular variation from front to front, and small scale structure, which would to a certain extent affect when the maximums in the variances occurred, should have an effect and would result in some flattening of the distribution, but may not fully explain this. The average structure inclination angles, determined from crosscorrelations, indicate al-most vertical orientation of the structure in the upper regions of the boundary layer. The fronts themselves, from flow visualizations, must eventually lean back downstream to correspond to the tops of the bulges (see Fig.4.67), assuming that the bulge trailing interfaces, from visualization, and velocity front interfaces are a result of the same struc-ture. Thus the peak in the correlation curves between the two X-wires must be dominated by other aspects of the structure than the front interface itself, especially near the top of the boundary layer. To investigate this, ensemble-averages of crosscorrelations at var-ious time delays (r), where in this case r refers to the crosscorrelation delay time, were Chapter 4. Experimental Results and Discussion 100 calculated, centered on positive events detected at the upper X-wire. Figure 4.68a,b is an example of these ensemble-averaged crosscorrelations. The correlations are quite poor very close to the event fronts, and the majority of the peak in the basic crosscorrelation must therefore come from regions removed from the front itself. From the figures, it appears that the areas of largest correlation are associated with the regions before the event, or inside the bulge, with some contribution from the trailing sweep. Based on this we believe that the peaks in the basic crosscorrelation curves indicate similarity of the bulk velocities associated with the structure, and that structure angles determined from these curves do not necessarily give a good indication of the shape or outline of the structure. Examination of the ensemble-averaged u velocity crosscorrelations at different time delays, did suggest a method which could be used to get an idea of the basic shape of the trailing edge of the bulge, or the shape of the front associated with the positive VITA detections (see Fig.4.68a,b). As the two X-wires approach the trailing front of the bulge, the correlation increases, reflecting greater similarity in velocity between the two wires. When the top wire (X-wire(3,4)) crosses the front, an event is detected and the correlation abruptly falls (see centers of Fig.4.68a,b). When the lower X-wire penetrates the front, the correlation rises again due to the coherent nature of the trailing sweep. As the correlation time delay (r) is increased, velocities at the upper wire are compared to velocities from the lower wire location, at later and later times relative to the upper wire velocities. This is similar to displacing the lower wire farther and farther upstream of the upper wire (see Fig.4.69). Increasing r has only a limited affect on the ensemble-averaged correlations, except near the event center time. At the event, the extent and magnitude of the negative peak in the ensemble-averaged crosscorrelations changes. For r = 0, the negative peak is large because it takes significant time for the lower wire to pass through the front after the upper wire (see Fig.4.69, State 1). As r increases, Chapter 4. Experimental Results and Discussion 101 the time delay between the time when upper and lower wires pass through the front decreases, and therefore the magnitude and extent of the negative peak decreases (see Fig.4.69, State 2). Finally when r becomes large enough that the lower wire on average passes through the front before the upper wire, the negative slope region of the ensemble averaged crosscorrelation begins to march backwards in time at a rate similar to the change in r , as it i6 no longer associated with the positive V I T A detections occuring at the upper wire, which determines the event centering time, but is now initiated by an event, or crossing of the front, at the lower X-wire. The time delay r , just before this occurs, was taken as the value used to calculate the front inclination angle, in the same way as was done using the peak time from the basic crosscorrelation curves. 0 = arctan(.033/(TUc)) Again, the local mean velocities were used instead of the calculated front convection velocities, as the two were quite similar. The determination of the value of r to use was somewhat subjective, as it was done visually by comparing the ensemble-averaged correlation curves (see Fig.4.68a,b). This determination was somewhat difficult in the region y/S ~ .6 —* .8. In all cases a conservative value was chosen which may have biased the results towards higher angles, especially in the region mentioned. Figure#4.70 shows both the general structure, or bulk motion inclination angle, and the front inclination angle. The front inclination angle is quite different, especially in the upper regions of the boundary layer, and indicates structure boundary shape similar to the model, and to that seen in flow visualizations. It should be mentioned that these angles represent only an average of the detected fronts occurring at the upper wire location. The values given would be affected by the age and orientation of the detected fronts, and therefore also of the V I T A parameters used. These effects should be greatest in the middle of the boundary layer. The upper Chapter 4. Experimental Results and Discussion 102 and lower regions should be dominated by old and new structures respectively, while the middle regions would contain a greater mixture. This may account for the observation that the determination of the value of r was more difficult in the middle regions, but was quite clear in the upper and lower regions. The results presented in this chapter do not prove the existance of any of the structure discussed, and are not intended in that light. The results do appear to be consistent with the model described in Chapter 3, and therefore can be said to be supportive of it. Ensemble-averaged velocities have indicated that the typical velocities through the positive and negative VITA events, are consistent with the trailing and leading bulge interfaces in the model. Crosscorrelations have indicated that the velocities are most similar at an angle inclined downstream for the u velocity, but not for the v or uv velocities, which is somewhat surprising. A new method of utilizing the crosscorrelations, indicated that angular dependence, which is consistent with flow visualization of the bulges, exists and also indicates that the angles associated with the basic crosscorrelations are not primarily due to the event fronts. Data from the horizontal and vertical rake indicate that the VITA detected events are due primarily to large scale structure. Small scale structure concentration, has been shown to be associated with the VITA fronts, and is consistent with the model. Chapter 4. Experimental Results and Discussion 103 Wire#l - Wire#5 y/6 = .715 rfrt\r*4\/\r*t/^^^ — > - ^ ^ r } i \ \ r j J ' ^ ^ Wire#2 - Wire#5 Wire#3-Wire#5 Wire#4-Wire#5 Wire#5 - Wire#5 b) Wire#5 VITA Event Detections i i i i i r~ 6 6.1 6.2 6.3 6.4 6.5 6.6 6.7 6.8 6.9 7 TIME (S) Figure 4.54: Horizontal Rake Subtracted Signals: a)y/5 = .277 b)y/6 = .715 Chapter 4. Experimental Results and Discussion 104 - . 0 8 - . 0 6 - . 0 4 - . 0 2 0 .02 .04 .06 .08 TIME (S) (0-EVENT DETECTION) 1.4 J i 1 I I 1 i 1 r-- . 0 8 - . 0 6 - . 0 4 - . 0 2 0 .02 .04 .06 TIME (S) (0-EVENT DETECTION) Figure 4.55. Indication of Small Scale Structure Occurrence Relative to VITA Events (Positive Events): a)y/6 = .048 b)y/6 = .093 Chapter 4. Experimental Results and Discussion 105 a) 1 > I I I 1 I 1 1 - . 0 8 - . 0 6 - . 0 4 - . 0 2 0 . 0 2 . 0 4 . 0 6 . 0 8 T I M E (S ) ( 0 - E V E N T D E T E C T I O N ) 1.5 . Figure 4.56: Indication of Small Scale Structure Occurrence Relative to VITA Events (Positive Events): a)y/8 = .165 b)y/8 = .277 Chapter 4. Experimental Results and Discussion 106 TIME (S) (O-EVENT DETECTION) Figure 4.57: Indication of Small Scale Structure Occurrence Relative to VITA Events (Positive Events): &)y/6 = .488 b)y/8 = .86 Chapter 4. Experimental Results and Discussion 107 TIME (S) (O-EVENT DETECTION) 1.5 . TIME (S) (O-EVENT DETECTION) Figure 4.58: Indication of Small Scale Structure Occurrence Relative to VITA Events (Negative Events): &)y/6 = .048 b)y/6 = .093 Chapter 4. Experimental Results and Discussion 108 TIME (S) (O-EVENT DETECTION) - . 0 8 - . 0 6 - . 0 4 - . 0 2 0 . 02 .04 . 0 6 .08 TIME (S) (O-EVENT DETECTION) Figure 4.59: Indication of Small Scale Structure Occurrence Relative to V I T A Events (Negative Events): a.)y/S = .165 b)y/S = .277 Chapter 4. Experimental Results and Discussion 109 Figure 4.60: Indication of Small Scale Structure Occurrence Relative to VITA Events (Negative Events): a)y/6 = .488 b)y/S = .86 Chapter 4. Experimental Results and Discussion 110 VITA Front Horizontal Rake -Wlre#1 -#2 -#3 -#4 -#5 Detection Wire a—Horizontal Inclination Figure 4.61: Horizontal Inclination Angle Chapter 4. Experimental Results and Discussion 111 Figure 4.62: Examples of Delay Time Distributions for Trailing Front Convec-tion Velocity Determination: a)y/S — .024 b)y/S = .1 Chapter 4. Experimental Results and Discussion 112 Figure 4.63: Examples of Delay Time Distributions for Trailing Front Convec-tion Velocity Determination: a)y/6 = .191 b)y/6 = .418 Figure 4.64: Examples of Delay Time Distributions for Trailing Front Convec-tion Velocity Determination: &)y/6 = .781 b)y/6 = .933 Chapter 4. Experimental Results and Discussion 114 1.2 1-(Ui-Ue)/Ul Figure 4.65: Average Trailing Front Convection Velocities Chapter 4. Experimental Results and Discussion 115 0 . 5 . — y/6 = .070 0 . 4 . 0 . 3 . P(r) 0 . 2 . 0 . 1 _. 0 0 . 0 0 5 . 0 1 . 0 1 5 . 0 2 . 0 2 5 . 0 3 . 0 3 5 . 0 4 T (S) Figure 4.66: Example Distribution of Delay Times Between the Two X-wires for Calculation of Trailing Front Interface Angle Chapter 4. Experimental Results and Discussion 116 Figure 4.67: Front Inclination Angle 0 Chapter 4. Experimental Results and Discussion 117 1.5 C(r) 0.5 0 . - 0 . 5 . 0.15 1.5 C ( r ) l . 0.5 . -0.5 -1 _L b) CORR. (T- .024) CORR. (T- .026) CORR. (T- .028) CORR. (T- .030) CORR. (T- .032) CORR. (T - .034) -0.1 ^ 5 •j-r r j - . 0 5 1 0 TIME (S) .05 0.1 0.15 Figure 4.68: Ensemble-Averaged Correlations at Increasing Time Delays (r): a) Small r b)Large r Chapter 4. Experimental Results and Discussion 118 Figure 4.69: Effect of Increasing r on the Effective Lower Wire Position Chapter 4. Experimental Results and Discussion 119 Figure 4.70: General Structure Inclination and Trailing Front Interface Angle Chapter 5 Conclusions and Recommendations The object of this thesis was to determine the dominant structure in the outer region of a stable, smooth wall, turbulent boundary layer, and to develop a simplified pictorial turbulent boundary layer flow model. The literature indicated that the structure of the boundary layer is Reg dependent, especially for Reg < 3000—5000, and that there are at least two important scales of motion: wall-scaled, and outer-variable-scaled structure. It was also indicated that the two important motions are in some manner interrelated. A certain lack of cohesiveness in the literature was noted, and an attempt was made to link the numerous observations. The model that was developed came about as a result of evidence from the literature, and, to a certain extent, from the experiments performed and observations made from a number of tests. The experimental results of this work are intended only as indicators of trends and characteristics of the flow structure. Errors in the results are very difficult to assess, as the use of the conditional sampling technique, VITA, and the other selective methods employed, introduces uncertainty at a level much higher than others present, and which is impossible to evaluate. As an indication of the uncertainty present in the results, the convection velocity and structure angle data appear to exhibit fluctuations, or scatter, of the order of 5-10%, and one must therefore assume that the uncertainty is of at least this level. It is also likely that the results are to a certain extent dependent on the VITA paremeters (K, 71*) used, but this dependence should not greatly affect the basic trends, only the magnitudes. 120 Chapter 5. Conclusions and Recommendations 121 The conclusions of this work can be broken down into two groups: specific and general. The specific conclusions apply to high Reg flows and come directly from the experiments, while the general conclusions are derived from both the literature and the results of the experiments performed. 5.1 Specific Conclusions 1. Results from the rake experiments indicate that the large scale velocity front is coherent on a scale greater than the expected size of the important small scale structure, and it has been indicated in the literature that it has a scale similar to the boundary layer thickness in the vertical and spanwise directions. 2. Both the convection velocity of the large scale velocity front, and the general convec-tion velocity derived from the basic crosscorrelations, are both typically 95 —* 100% of the local mean velocity. 3. Results from the subtracted horizontal rake data indicate small scale structure concentration is present at the inside edge of the large scale trailing velocity front. 4. The ensemble-averaged, event centered, crosscorrelations at set time delays indicate that the peaks in the basic crosscorrelation curves are not directly related to the delineating velocity fronts of the large scale bulge structure, but to the regions preceding and following the interface events. Therefore, the structure inclination angles calculated from the basic crosscorrelations must indicate similarity in bulk velocities as opposed to angular inclination of a specific feature of the structure. 5. One can obtain the local average inclination angle of the trailing velocity fronts us-ing VITA through the ensemble-averaged crosscorrelations as described in Chapter Chapter 5. Conclusions and Recommendations 122 4, and the relation attained agrees with the basic structure observed in flow visual-izations in the literature. This relation was quite different from that obtained from the basic crossocrrelations, especially in the intermittent region. 5.2 General Conclusions and Recommendations An important focus of this work was the development of the overall structure model presented in Chapter 3. The model incorporated Reg dependence and the dual scale nature of the structure observed in the literature. Arguments were presented to account for features observed in the experiments and literature, and to attempt to properly fit them into the model. The model as described should be useful as a tentative description of the outer region structure, and in some respects interrelates of the whole of the boundary layer structure. At present the model is somewhat crude and is lacking in several areas. In order to improve upon this, several areas of investigation could prove useful. 1. The model presented is essentually two dimensional. Further investigation into the spanwise structure would be useful in determining the average shape of the structure. 2. A larger number of wires in the form of a vertical rake might be used to distin-guish between old and new structures, by determining the vertical extent of each individual structure. This assumes that the structures originate at the wall. 3. Flow visualization of the intermittent interface, compared to simultaneous velocity measurements, could be used to determine the relation between the bulge structure and the intermittent interface. This relation may seem obvious, but has not been proven. Chapter 5. Conclusions and Recommendations 123 4. Closer examination of the region close to the large scale velocity fronts could lead to confirmation of the structure of the small scale activity concentrated in this area. The importance of work of this nature is not derived from specific results and con-clusions, but from the improved understanding of the nature of the flow that is being examined. It is important in that it provides a basis from which can be developed intere-lations between the specific flow in question and other turbulent flows, and can be used to suggest areas of investigation for turbulence control experimentation. For example, determining the mechanism linking the formation of the large and small scale structure would be of great value. Disruption of this mechanism could easily be used to reduce the wall shear stress and therefore the drag. Bibliography [1] J.O.Hinze, 2nd. Edition, pg.614-707, McGraw-Hill Inc. [2] Kline S.J., Reynolds W.C. , Schraub F .A . , Runstadler P.W., The Structure of Tur-bulent Boundary Layers, J. Fluid Mech., Vol. 30,pp.741-773, (1967) [3] H . Schlichting, 6th. Edition, pg.523-606, McGraw-Hill Inc. [4] Head M.R. , Bandyopadhyay P., New Aspects of Turbulent Boundary Layer Struc-ture, / . Fluid Mech., Vol. 107, pp.297-338, (1981) [5] Grass A . J . , Structural Features of Turbulent Flow over Smooth and Rough Bound-aries, J. Fluid Mech., Vol 50,pp.233-255, (1971) [6] K i m H.T. , Kline S.J., Reynolds W.C. , The Production of Turbulence in a Turbulent Boundary Layer, J. 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B . , Bisset D .K. , Effect of Reynolds Number on the Organised Motion in a Turbulent Boundary Layer, Private Communication [29] Chen Chyan-Hai P., Blackwelder R.F. , Large-Scale Motion in a Turbulent Boundary Layer: A Study Using Temperature Contamination, J. Fluid Mech., Vol. 89,pp.l-31, (1978) Bibliography 127 [30] Jovic, Browne, Coherent Structures in a Boundary Layer and Shear Layer of a Backward-Facing Step, Seventh Symposium on Turbulent Shear Flows, (August 1989) [31] Johansson A . V . , Alfredsson P.H. , On the Structure of Turbulent Channel Flow, J. Fluid Mech., Vol. 122,pp.295-314, (1982) [32] Alfredsson P.H. , Johansson A . V . , On the Detection of Turbulence-Generating Events, / . Fluid Mech., Vol. 139,pp.325-345, (1984) [33] Hama F.R. , Progressive Deformation of a Curved Vortex Filament by its Own In-duction, Physics of Fluids, Vol 5,pp.ll56-1162, (1962) [34] Melander, Hussain, Cut and Connect of Two Antiparallel Vortex Tubes: A New Cascade Mechanism, Seventh Symposium of Turbulent Shear Flows, (August 1989) [35] Sabot J . , Saleh I., Compte-Bellot, Effects of Roughness on the Intermittent Mainte-nance of Reynolds Shear Stress in Pipe Flow, Physics of Fluids, Vol. 20,pp.150-155, (1977) [36] Rajagopalan S., Antonia R .A. , Some Properties of the Large Structure in a Fully Developed Turbulent Duct Flow, Physics of Fluids, Vol. 22,pp.614-622, (1979) [37] Willmarth W.W. , Adv. Applied Mech., Vol. 15, pp.159, (1975) [38] Thomas A.S.W. , Bull M . K . , On the Role of Wall-Pressure Fluctuations in Determin-istic Motions in the Turbulent Boundary Layer, J. Fluid Mech., Vol. 128,pp.283-322, (1983) [39] Kovasznay L.S.G. , Kibens V . , Blackwelder R. F. , Large-Scale motion in the Inter-mittent region of a turbulent boundary layer, J. Fluid Mech., Vol.41,pp.283-325, Bibliography 128 (1970) [40] Roon J .B. , Blackwelder R.F. , The Effect of Longitudinal Roughness Elements and Local Suction upon the Turbulent Boundary Layer, Private Communication [41] Subramanian C.S., Rajagopalan S., Antonia R .A . , Chambers A . J . , Comparison of Conditional Sampling Techniques in a Turbulent Boundary Layer, J. Fluid Mech., Vol.123, pp.335-362, (1982) [42] Gartshore I.S., Models for the Large Coherent Structures in Turbulent Boundary Layers, I.M.S.T. Internal Note, December (1987) [43] Morrison J.F. , Tsai H . M . , Bradshaw P., Conditional-SampHng Schemes for Turbu-lent Flow, based on the Variable-Interval Time Average (VITA) Algorithm, Experi-ments in Fluids, Vol. 7,pp.173-189, (1989) [44] Smits A . J . , Watmuff J .H. , Large Scale Motions in Supersonic Turbulent Boundary Layers, A Survey of Measurements and Measurement Techniques in Rapidly Dis-torted Compressible Turbulent Boundary Layers, Ch. 3, (1988) [45] Smits A . J . , Spina E.F. , Alving A . E . , Smith R.W., Fernando E . M . , Donovan J.F., A Comparison of the Turbulence Structure of Subsonic and Supersonic Boundary Layers Physics of Fluids A, Vol. 1, pp.1865-1875, (1989) [46] Kreplin H.P., Eckelmann H . , Behavior of the Three Fluctuating Velocity Compo-nants in the Wall Region of a Turbulent Channel Flow, Physics of Fluids, Vol. 22,pp.l233-1238 (1979) [47] Narahari K . , Narasimha R., Narayanan M . A . B . , The "Bursting" Phenomenon in a Turbulent Boundary Layer, / . Fluid Mech., Vol. 48,pp.339-352, (1971) Bibliography 129 [48] Bose T.E., Wheaton K.R., Vortex Models of a Psuedo-Turbulent Shear Flow, Sev-enth Symposium on Turbulent Shear Flows, (August 1989) [49] Coustols E., Cousteix J., Experimental Manipulation of Turbulent Boundary Lay-ers through External and Internal Devices, Seventh Symposium on Turbulent Shear Flows, (August 1989) [50] Riedeger S., Influence of Drag Reducing Additives on Turbulent Shear Flows, Sevent Symposium on Turbulent Shear Flows, (August 1989) Appendix A Basic Boundary Layer Characteristics and Data Reduction Methods The data for this experiment were taken with a number of different hot wires and con-figurations (see Chapter 2). Before these more complex experiments were performed, the basic mean characteristics of the boundary layer, at the measurement station, were determined to ensure that the boundary layer was well behaved. The nature of the ex-periments did not require extremely preciese measurements, due to the qualitative nature of the investigation, but they were performed as carefully as possible. Experiments were performed at night to minimize any effects of changes in the build-ing characteristics which might affect the open circuit design tunnel. Any small holes or irregularities in the development length of the tunnel were covered. It should be noted that there were occasional irregularities, which could not be totally removed, which lo-cally would be inconsistent with the smooth wall assumption. How much of an affect these had is unknown. Although the irregularities would have disturbed the sublayer somewhat, because this work is concerned with the upper layer, these occasional irregu-larities should not have been significant. The wall for a distance of at least 1.2 meters upstream of the measurement position can be considered to be smooth. When wire sets were moved to a new vertical location, any vibrations in the apparatus were allowed to decay for at least 1 to 2 minutes. Figure A.71 shows the mean velocities derived from two vertically displaced straight hot wires, traversed through the boundary layer. There appears to be a slight difference in the curves from each of the two wires. This could be due to the calibrations or drift in 130 Appendix A. Basic Boundary Layer Characteristics and Data Reduction Methods 131 1.2 1.2 1.4 Figure A.71: Mean Velocity Profile the sensors, which were quite new. All wires were operated for a number of hours before tests were run, which should have limited drift, but drift is a possibility as the difference seems to be greater at lower y/6, and the data was taken from the top of the layer down. All numerical experiments were performed using the fluctuating components only and the resultant error, in magnitude only, of these values would only be ~ 2%, which should not seriously affect the results in any way. The mean velocities were fit to a power law: i r = c 1 ( v )» The exponent determined from the power law fit was found to be ~ 1/6.5 which is in good agreement with the expected value of 1/7 for a smooth wall (see Fig. A.72). The intensities (Vu*) were determined, plotted, and compared to tabulated values Appendix A. Basic Boundary Layer Characteristics and Data Reduction Methods 132 -1.8 -1.6 -1 .4 -1.2 -1 -0.8 -0.6 -0.4 Log10(y) ' Figure A.72: Power Law Fit to Mean Velocity Data from Hinze [1]. Good agreement can be seen over much of the boundary layer, although there does exist some discrepancy for the upper 1/3, where the tabulated values are lower than the experimental data. This could be due to higher free stream intensity and to some extent error in the determination of (8), which i6 somewhat arbitrary (see Fig. A.73). One set of points, indicated on the Figure, appears to have been in error. Exactly what the difficulty was here is not known. This point is therefore somewhat suspect. The wall shear velocity was determined from Universal curves for inner turbulent boundary layers on a smooth wall [Clauser 1954]. Preston tube determination of the shear velocity was attempted, but the velocities were so low that accurate pressure mea-surements were difficult with the equipment available, and this was abandoned. De-termination of the exact value of the wall shear was not of major importance to the Appendix A. Basic Boundary Layer Characteristics and Data Reduction Methods 133 performance of further experiments so, this should not affect the results. The integral (te) and micro (tm) timescales were calculated and the related length scales (le = teUi/6) and (7m = tmUi/S), where Ui is the local mean velocity, were plotted (see Fig. A.74a,b). The mean velocities were fit to a power law: Uoo _r(Uy i The exponent. This was done using autocorrelation curves calculated from the u velocity data sets. Autocorrelations give an estimate of the selfsimilarity of a flow parameter, at a point, as a function of the time delay between data points. The autocorrelation (A(r)), where (r) is the time delay, is defined as: 1 rT A ( X » T ) = ^ r T ^ = / * + T)]rf< lU[Xi)2 Jo or in discrete form, as the data was discrete, assuming a straight line fit between data points: A ( x . T ) 1 A +l)u( 8 < >/ + m + l) U(XJ, I + 1)U(XJ, I + m) U(XJ, I)U(XJ,I + m + 1) U(XJ, I)U(XJ, I -f m) 6 + 6 + • 3 J where: N = the number of data points m = r/At (r must be an integer number of At) At =data step size = 1/frequency n = N — m — 1 (see Fig.A.75) Figure A. 76 is an example of several autocorrelation curves at different y/S, calculated as described. These curves were also determined for longer time delays, attempting to Appendix A. Basic Boundary Layer Characteristics and Data Reduction Methods 134 discern a large scale structure passing period from the location of the second peak in the curve. This proved to be impossible to do with any amount of confidence because the position of this peak varied widely even for adjacent y/S sensor locations. The integral time scale was calculated in the normal fashion, by integration of the autocorrelation curve up to the first zero crossing (see Fig.A.77a). The micro time scale was also determined in the standard way by fitting a parabola to the vertex of the autocorrelation curve and extrapolating the fitted curve to its t intercept (see Fig.A.77a). The curve was fit using a weighting function on the first four calculated autocorrelation points. The weighting function values were: 1, 2/3, 1/3, 0.000001 for points one to four and 0.000001 for the next 6 points. Figure A.74b shows an example of a curve fit using this procedure. The micro length scale behaves as one might expect, with the smallest scales found near the wall, increasing in size with increasing distance from the wall, and finally falling off towards free stream values in the intermittent region (see Fig.A.74b). The inte-gral length scale data exhibited much more scatter, perhaps due to inaccuracies in the technique, and was strongly affected by the onset of intermittency for y/S > .6 (see Fig.A.74a). This can be explained by the presence of a transition between rotational fluid convecting from below, and irrotational fluid being entrained from above. These demarkations produce strongly defined regions, and would therefore bias the calculated scales towards this large scale structure. For the main body of the flow, the integral length scale was found to be ~ 1/26, and the micro length scale varied from ~ .03 —» .115. The significance of these scales is somewhat unclear. The integral scale is generally thought to indicate the average large scale, and the micro scale a measure of the average small scale. It appears that while the integral, or large scale, does not change much across the boundary layer, the micro scale undergoes a significant trend. The simplest expanation of this is that the small scale structure predominantly originates near the Appendix A. Basic Boundary Layer Characteristics and Data Reduction Methods 135 wall and is convected upwards, dissipating as it rises, causing the shift towards larger scale. The integral scale remains constant, BO the large scale must be similar across most of the boundary layer. Alternatively, the measurements of scale were only done in the middle and outer layers. In the inner region, the integral scale may decrease significantly, reflecting an increase in importance of the smaller scales. Crosscorrelations and variations of the crosscorrelation method were used to deter-mine convection velocities and structure angles. The basic crosscorrelation method, which is similar to the autocorrelation method, will be presented, and a method for determining the center of a peak in the crosscorrelation curve, or any other curve. The crosscorrelation gives an estimate of the similarity of a flow parameter between two points in the flow, as a function of correlation delay time (r). For these experiments, the u, v, or uv velocities at different points in space (simultaneous data records) were used. The crosscorrelation is defined as: 1 rT C(xiy zit T) = • /=EEE / t)u{Xj, t + r Ts/ul^^vJx~yJo )}dt or in discrete form, using the same symbols and method as the autocorrelation calcula-tion: C ( M i , r ) = 1 ^ . J + l H ^ J + m + l) U(XJ, I -f 1)U(XJ, I + m) u(xj,I)u(xi, I + m + 1) U(XJ, I)U(XJ, I + m) £ C O Figure# A.78 is an example of the crosscorelations between two horizontally separated sensors, which should give an indication of the convection velocity between the two sensors, which can be quite different from the mean velocity. The delay time (r) of the peaks in the curves represents the average time for the structures to pass from sensor to Appendix A. Basic Boundary Layer Characteristics and Data Reduction Methods 136 sensor. A reliable repeatable method of estimating the delay time, or the peak position, was necessary, and was developed. The method operates with discrete data, but to simplify the discussion this point will be ignored, the difference between the disscussion and the reality being a number of interpolations between adjacent data points. The peak delay times were selected as follows (see Fig.A.79): 1. The maximum point of the curve was determined (Pi). 2. The points on either side of the maximum point at 90% of the maximun peak value were determined (Sj, S>). 3. The area bounded by the two points and the correlation curve was calculated (A). 4. The point on the curve at which 1/2 of the calculated area (A) was reached was found and designated as the peak of the curve (Pj)-5. The delay time (r x) corresponding to (P 2) was used as the peak delay time. This method was used whenever a peak delay time waB calculated from time dependent data. In this section we have presented the basic data and experimental methods. This is not a complete discussion of methods, but is the basis upon which others were developed. Appendix A. Basic Boundary Layer Characteristics and Data Reduction Methods Figure A.73: Intensity Profiles Appendix A. Basic Boundary Layer Characteristics and Data Reduction Methods 1.6 A A A 1.4 A A A A 1.2 A 4 1 A A y/s A A 0.8 A A A A 0.6 A A A A 0.4 A A AA 0.2 -A A A 0 & a) ( 1 1 1 1 1 J 0.1 0.2 0.3 0.4 0.5 1 0.6 1 1 1 0.7 0.8 0.9 1 TeUc/6 1.6 • a • 1.4 • • • • 1.2 - • • a o y/6 a n • • 0.8 -0.6 - • a a Q 0.4 - • • 0.2 - S n 0 ° 0 • a 0 i i i .02 .04 .06 1 08 i 1 0.1 0.12 0.] TmUc/6 Figure A.74: Length Scales; a)Integral b)Micro Appendix A. Basic Boundary Layer Characteristics and Data Reduction Methods Straight line fit between data points u(1) u(N-2) u(3) u(I+m+1) \ u(I+m)/ u(I+1) ^ 1=1 i=2 =3 i _ U(N-1) U(N) 1=1 I=J+1 l=I+m lefcm+1 | = N - 2 l=N-1 l=N Figure A.75: Discrete Autocorrelation Parameters Appendix A. Basic Boundary Layer Characteristics and Data Reduction Methods l \~"~~ i i i r 0 .02 .04 .06 .08 0.1 0.12 0.14 0.16 0.18 T IN SECONDS Figure A.76: Example Autocorrelation Curves Appendix A. Basic Boundary Layer Characteristics and Data Reduction Methods 141 0.5 0.4 J 0.3 0.2 0.1 -0.1 a a EXPERIMENTAL DATA LEAST SQUARES FIT y=y/Ar V ' b) l 0.5E-3 T .001 .0015 .002 TIME IN SECONDS I .0025 .003 Figure A. 77: a) Calculation of Integral and Micro Time Scales ^Autocorrelation Vertex Parabolic Curve Fit Appendix A. Basic Boundary Layer Characteristics and Data Reduction Methods 0.8 0.7 C(r) 0.6 0.4 : :— yi6--— Y /<£-. : — y/S-. — y/S--— y/Sm• - . ^ ~ ' 022 036 049 063 077 090 y y ... ^ ^ / * ^ ' , - ' / . / y / ' / y y' y y'y" ' y y / y . . V v N V 0 .005 .01 .015 .02 .025 .03 T ( S ) Figure A.78: Crosscorrelations Between Horizontally Displaced Sensors Appendix A. Basic Boundary Layer Characteristics and Data Reduction Methods 143 Figure A.79: Peak Delay T ime Selection Method Appendix B Potential Vortex Model Event Velocities Appendix B contains several figures from a paper by Gartshore, Models for Large Co-herent Structures in Turbulent Boundary Layers (Ref#42). These figures indicate how the fluctuating velocities would be affected by the passage of a potential hairpin vortex structure (see Fig.B.80a,b). The velocities indicated in Figure B.81a,b are very similar to those obtained when using the Hole or Quadrant detection technique (see Chapter 2). This is by no means conclusive evidence, but it is consistent with the idea that the Quadrant detections could be the result of small scale vortex structures, and not directly due to the large 6cale velocity front proposed to be the cause of the VITA and Rake detections. 144 Appendix B. Potential Vortex Model Event Velocities 145 a) A vortex model for coherent large scale motions in a turbulent boundary layer. s h e e r s I b) Flow pattern in the x-z, on cross-flow plane, following the vortex pair. Figure B.80: A vortex pair model for coherent large scale motions; a)Side View b)End View Appendix B. Potential Vortex Model Event Velocities 146 Figure B.81: Distributions of velocity associated with the vortex pair model; a)Z=0 b ) Z = 2 A (where the separation between the vorticies =2A) Appendix C Examples of Crosscorrelation Curves Contained in this appendix are examples of the correlations used to determine convection velocity, bulk structure inclination, and angular orientation of the velocity components. These were discussed in Chapter 4. The data for these correlations was taken with the two X-wires and the leading straight wire wire set. Figure C.82 is an example of the crosscorrelations between the leading straight wire and the lower X-wire, and wa6 used to calculate the average convection velocity. Figure C.83a is an example of the crosscorrelations between the two X-wires, which wa6 used to calculate average structure inclination. Figure C.83b is an example of the crosscorrelations between the leading straight wire and the upper X-wire, which was also used to calculate average structure inclination. Figure C.84a-c demonstrates that the v velocity crosscorrelations do not exhibit any preferred inclination, as the peaks in the crosscorrelation curves between the X-wires are centered on zero time delay. This is true for the full data sets, and for correlations calculated on the positive and negative v velocity data only. Figure C.85a-c shows that the same is true for correlations calculated using the uv velocity, and for correlations calculated using uv data separated into positive and negative sets by the sign of the v velocity. Figure C.86a,b demonstrates that the sign of the u velocity does not have a great effect on the crosscorrelations between the two X-wires and therefore does not have a strong influence on the average structure inclination. Finally, figure C.87 is an example of crosscorrelations of event detections between 147 Appendix C. Examples of Crosscorrelation Curves 148 the leading straight wire and the lower X-wire. This was then further broken down, as described in Chapter 4, to produce event convection velocity distributions which showed that the average event velocities were very similar to the average convection velocities calculated from the basic crosscorrelations between the leading straight wire and the lower X-wire. 0 . 9 0 . 8 C (T ) 0 . 6 YlS--YlS--Y/<J-. Y/S--104 117 131 172 199 . 240 //•'/ • ,/yf ' s /" V N ; \ ^ \ ^ \ >^ 0 . 005 .01 . 0 1 5 .02 . 025 .03 T IN SECONDS Figure C.82: Crosscorrelations on the u velocity between the leading straight wire and the lower X-wire Appendix C. Examples of Crosscorrelation Curves 149 0 . 4 5 . a) .01 0 .01 T IN SECONDS .02 .03 0 . 8 b) y/6-y/S-y/S-y/6-y/S-. 104 .117 .131 . 172 . 199 .240 .03 . 02 - . 0 1 0 T IN SECONDS .01 .02 .03 Figure C.83: Crosscorrelations on the u velocity between; a)The two X-wires b)The leading straight wire and the upper X-wire Appendix C. Examples of Crosscorrelation Curves 150 0 . 5 0.65 0.65 Figure C.84: Crosscorrelations between the X-wires using the v velocity: a)Full data set b)Positive v data only c)Negative v data only Appendix C. Examples of Crosscorrelation Curves 151 0.43 -0 .1 - . 075 - . 0 5 Figure C.85: CroBscorrelations between the X-wires using the uv velocity; a)Full data set b)Positive v data only c)Negative v data only Appendix C. Examples of Crosscorrelation Curves 152 0.7 C ( T ) 0.5 in - - - lit -"- Y/< Y/< - -— Y/( »-.104 y=.ii7 j=.131 5-.172 S=.199 $-.240 s s ^ *" ' " ' X-> a) -0.1 -.075 -.05 -.025 0 .025 .05 .075 0.1 T IN SECONDS 0.9 0.8 0.7 Y/tf-.104 Y/«5-.U7 Y/t5=.131 Y/tf-.172 Y//5=199 YM-.240 b) -0.1 -.075 -.05 .025 0 .025 T IN SECONDS .05 .075 0.1 Figure C.86: Crosscorrelations between the X-wires using the u velocity; a)Positive u data only b)Negative u data only Appendix C. Examples of Crosscorrelation Curves 153 o.i - . 0 2 - 0 . 1 - . 0 7 5 - . 0 5 - . 0 2 5 0 . 025 .05 . 075 0 . 1 T IN SECONDS Figure C.87: Crosscorrelations of event detections between the leading straight wire and the lower X-wire 

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