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An experimental investigation of the wall-pressure field during turbulent incompressible pipe flow Williams, Norman S.W. 1982

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AN E X P E R I M E N T A L I N V E S T I G A T I O N O F T H E W A L L - P R E S S U R E F I E L D D U R I N G T U R B U L E N T I N C O M P R E S S I B L E P I P E FLOW by NORMAN S.W. WILLIAMS B.A.Sc. , University of Waterloo, 1974 M . A . S c , University of Waterloo, 1976 A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY in THE FACULTY OF GRADUATE STUDIES (Department of Chemical Engineering) We accept this thesis as conforming to the required standard THE UNIVERSITY OF BRITISH COLUMBIA October 1982 ° Norman S.W. Williams, 1982 In presenting this thesis in part ial fulfilment of the requirements for an advanced degree at the University of Br i t ish Columbia, I agree that the Library shall make i t 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 f inancial gain shall not be allowed without my written permission. Norman S.W. Williams Department of Chemical Engineering The University of Br i t ish Columbia Vancouver, B .C . , Canada V6T 1W5 Date /4- ^ o ^ t * ^ * 2 19^5 Dedicated to my parents and to my nieces and neph ABSTRACT An optical technique was developed to make possible a study of the instantaneous structure of the turbulent wall-pressure f i e l d . The approach involved the use of real-time laser-holographic-moire interferometry. A moire fringe pattern generated by the holographic method was superimposed on the surface of a special ly-fabricated compliant pipe wal l . The compliant surface, in response to wall-pressure changes, introduces optical path length changes which are manifested by distort ions in the fringe f i e l d . The fringe distort ions, observed during flow, were recorded (framed area, 11 mm x 34 mm) by means of medium-speed motion photography. The amplitude of fringe distort ion provides a measure of the pressure magnitude at the wall. A 26.3 mm ID horizontal glass pipline (7.0 m long) supplied with d i s t i l l e d water from a constant head reservoir was used in the study. Photographs taken of the fringe patterns observed at a flow velocity (U) of 0.47 m/sec (Re^ = 12,300) were analysed. Results show that the wall-pressure f ie ld consists of a positive and negative pressure region. A s ta t i s t i ca l analysis reveals that the wall-pressure distr ibution is asymmetrical (Skewness = -0.29). - i i i -From an analysis of the pressure patterns, a relationship between the generation of wall-pressure fluctuations and known wall-layer flow characterist ics is inferred. A flow model is proposed to explain some aspects of the wall region dynamics and a mechanism for part icle detachment from a wall , during turbulent flow, is also presented. - iv -T A B L E O F C O N T E N T S Page A B S T R A C T i i T A B L E OF C O N T E N T S iv L I S T O F T A B L E S v i i i L I S T O F F I G U R E S x ACKNOWLEDGMENTS x i i i C H A P T E R 1 1 1. I N T R O D U C T I O N 1 1.1 Preamble 1 1.2 Classical background 3 1.3 Motivation for this study 5 C H A P T E R 2 8 2 . L I T E R A T U R E S U R V E Y 8 2.1 The Bursting Phenomenon 8 2.2 Wall-Pressure Fluctuations 12 2.3 Closing remarks 16 C H A P T E R 3 18 3. OB3ECTIVES O F T H E P R E S E N T STUDY 18 3.1 Statement of the Problem 18 3.2 Primary objectives 18 C H A P T E R I* 20 P R E L I M I N A R Y C O N S I D E R A T I O N S 20 i\A Feasibility Study 20 4.2 Making a Hologram 21 4.3 Suitability of the Compliant Material 21 - V -Page C H A P T E R 5 23 5. T H E V I S U A L I Z A T I O N T E C H N I Q U E : A H O L O G R A P H I C I N T E R F E R O M E T R I C A P P R O A C H 23 5.1 Visual izat ion Approach of this Study 24 5.2 The Ihterferometric Technique 24 5.3 Conventional Interferometers 25 5.4 Principles of Holography 25 5.5 Theoretical Foundations of Holographic Interf erometry 29 5.5.1 Mathematical Analysis of Holography 29 5.5.2 Holographic Interferometry 35 5.5.3 Application of the Moire Technique to Holography 36 C H A P T E R 6 45 6. E X P E R I M E N T A L A P P A R A T U S AND P R O C E D U R E 45 6.1 The Constant Head Flow System 45 6.2 Design Considerations for the Holographic Interferometer 47 6.2.1 Wavefront Division Holographic Interferometer (WDHI) 47 6.2.2 Amplitude Division Holographic Interferometer (ADHD 49 6.3 The Present Holographic Interferometer 51 6.3.1 Components of the Interferometer 51 (i) The Laser 52 ( i i ) Beamsplitter 53 ( i i i ) Mirrors 54 (iv) Lens-pinhole Spatial F i l te r 54 (v) Test Surface 56 (vi) Photoplate Holder 56 (vi i ) The Hologram 56 (v i i i ) Optical Bench 58 6.3.2 Design Parameters 59 (i) Design Angle 59 ( i i ) Coherence Length 60 ( i i i ) Beam Intensity Ratio 62 - v i -Page 6.4 Photoplate Processing Considerations 62 6.4.1 On-Site Processing i n a Liquid Gate 63 6.4.2 Hologram-Processing Supply Unit 64 6.5 The Photo-Optical Recording and Analysing Apparatus.. 64 6.6 Experimental Procedure 68 6.6.1 Gross Flow Experiments 68 6.6.2 Visualization Experiments 70 6.6.2.1 Laser Beam Alignment 70 6.6.2.2 Processing Solutions and Emulsion Pre-Treatment 70 C H A P T E R 7 73 7.1 Gross Flow Measurements 73 7.2 Wall-Pressure Fluctuations Measured with the Aid of the Holographic Interferometric Technique 74 7.2.1 Interferogram Interpretation 74 7.2.2 Data Reduction 75 C H A P T E R 8 77 8. E X P E R I M E N T A L R E S U L T S AND D I S C U S S I O N 7,7 8.1 Gross Flow Results 77 8.2 Hologram Experiments 77 8.3 Visu a l i z a t i o n Results 79 8.3.1 Observation of the Pressure Changes at the Pipe Wall 81 8.3.2 Measured Wall-Pressure Fluctuations 81 8.3.3 Temporal Variation of the Wall-Pressure 83 8.3.4 Instantaneous Wall-Pressure Fluctuations about the mean 89 8.4 Discussion of Results 89 8.4.1 Measurement Accuracy 98 8.4.2 A Few Words on the Present Technique 99 - v i i -Page C H A P T E R 9 9. S U G G E S T E D FLOW MODEL AND T H E P R A C T I C A L I M P L I C A T I O N S TOO 9.1 Proposed Flow Model 100 9.2 Pract ical Implications 103 C H A P T E R 1 0 106 1 0 . C O N C L U S I O N S AND R E C O M M E N D A T I O N S 106 10.1 Conclusions 106 10.2 Recommendations 107 1 1 . N O M E N C L A T U R E 108 1 2 . R E F E R E N C E S 113 1 3 . A P P E N D I C E S 121 A. The Compliant Pipe Wall 122 B. Calibration of the Dif ferent ia l Pressure Transducer.. 128 C. Error Analysis: Gross Flow Quantities 132 D. Interferometric Static Pressure Calibration of the Compliant Surface 134 E. Interferogram-Evaluation Technique 145 F. Estimation of the Effect of Wall Shear Stress on the Deformation of the Compliant Wall 147 G. Analysis of the Pressure Patterns of Wall-pressure fluctuations about the mean 151 H. Dynamic Calibration of the Compliant Wall 156 I. Treatment of Gross Flow Measurements 158 3. Movie Details 162 K. Treatment of Fringe Distortion Measurements 166 L. Development of the Interferometric Measuring Technique 187 - v i i i -LIST OF TABLES Page Tabl 2.1 Various Measurements of Turbulent Wall-Pressure Fluctuations on Smooth Flat Walls with Very Small Pressure Gradients 13 Table 6.1 Components of the Holographic Interferometer 52 Table 6.2 Manufacturer-Specified Characteristics of the Si lver Halide Emulsion 61 Table 6.3 Photo-Optical Recording and Analysing Apparatus 69 Table 6.4 Steps for Making a Hologram 72 Table 8.1 Flow Conditions for Visualization Runs 80 Table 8.2 Summary of the Analysis 97 Table A.1 Important Mechanical and Physical Properties of the Rubber Material 126 Table A.2 Load-Extension Data 127 Table B.1 Pressure Drop Data 131 Table C.1 Error Estimates of Gross Flow Quantities 133 Table D.1 Pump Characteristics 136 Table D.2 Summarized Static Pressure Calibration Data 142 Table D.3 Nozzle-Assembly Calibration Data 143 Table D.4 Static Pressure Regression Analysis 144 Table G.1 Frequency Table 153 Table G.2 Frequency Table 155 Table 1.1 Gross Flow Quantities 161 Table K.1 Instantaneous Fringe Distortions (downstream) 167 Table K.2 Instantaneous Fringe Distortions (upstream) 169 Table K.3 Instantaneous Fluctuations about the mean (downstream). 171 - ix -Page Table VIA Instantaneous Fluctuations about the mean (upstream)... 173 Table K.5 Instantaneous Wall-pressure Changes (positive pressure changes) 175 Table K.6 Instantaneous Wall-pressure Changes (negative pressure changes) 177 Table K.7 Instantaneous Wall-pressure Fluctuations about the mean (positive pressures) 179 Table K.8 Instantaneous Wall-pressure Fluctuations about the mean (negative pressures) 181 - X -LIST OF FIGURES Page Figure 5.1(a) The Off-Axis Hologram-Recording Arrangement.... 27 Figure 5.1(b) Image Reconstruction 28 Figure 5.2 Characteristic Curve of Amplitude Transmittance Versus Exposure 32 Figure 5.3 Schematic of the Test Section and Photo-Optical Set-Up 40 Figure 5.4 Side View of Specially-Constructed Pipe Section 41 Figure 5.5 P a r t i a l Pipe Section (Flat Piece Removed) 42 Figure 5.6 Test Section (in the Pipeline) Forming a Component of the Interferometer 44 Figure 6.1 Schematic of the Flow F a c i l i t y Integrated with the Holographic Set-Up 46 Figure 6.2 A Schematic Representation of a Wavefront Division Holographic Interferometer 48 Figure 6.3 A Schematic Representation of an Amplitude Division Holographic Interferometer 50 Figure 6.4 Spatial F i l t e r i n g of a "noisy" laser beam...... 55 Figure 6.5 Spectral S e n s i t i v i t y Curve for 10E56 ("Holotest") Emulsion 57 Figure 6.6 Liquid Gate-Plateholder and Precision-Mount Assembly 65 Figure 6.7 Flow F a c i l i t y and Adjacent Hologram-Processing Supply Unit 66 Figure 6.8 Hologram-Processing Supply Unit 67 Figure 7.2(a) Reference State Showing Base Fringe Pattern.... 76 Figure 7.2(b) Fringe Distortions During Flow 76 Figure 8.1 Fanning F r i c t i o n Factor - Reynolds Number Plot. 78 - xi -Page Figure 8.2(a) Interferogram Recorded at No Flow 82 Figure 8.2(b) Interferogram Extracted from Flow Sequence 82 Figure 8.3 Frequency Histogram of Wall-pressure Fluctuations 84 Figure 8.4 Spatio-Temporal Distribution of Positive Wall-Pressure Changes 85-86 Figure 8.5 Spatio-Temporal Distribution of Negative Wall-Pressure Changes 87-88 Figure 8.6 Instantaneous Wall-pressure Fluctuations about the Mean [Positive Pressure Changes] 90-91 Figure 8.7 Instantaneous Wall-Pressure Fluctuations about the Mean [Negative Pressure Changes] 92-93 Figure 9.1 Lift ing-Up Phase of Bursting 101 Figure 9.2 Photographs of L i f t ing Fluid Elements 102 Figure A.1 Flat-Piece of Test Section 123 Figure A.2 Arrangement for the Determination of the Young's Modulus of the Rubber Strip 124 Figure A.3 Load-Extension Plot 125 Figure B.1 Pressure Drop Measurement Set-up 129 Figure B.2 Di f ferent ia l Pressure Transducer Calibration Plot 130 Figure D.1 Schematic of the Conical Nozzle 135 Figure D.2 Nozzle-Assembly Calibration Plot 137 Figure D.3 Schematic of Nozzle-Surface Arrangement 138 Figure D.4 Relationship Between Fringe Distortion and Applied Pressure 141 Figure E .Ka ) Departures from Straight Lines (base fringes) Observed Upon Superimposition of an Interf erogram from the Flow Sequence 146 - x i i -Page Figure E.1(b) One Fringe Isolated to Show Upstream and Downstream Departures from the Straight Line of a Base Fringe 146 Figure F.1 Forces Acting on the Compliant (Wall) Surface.. 148 Figure G.1 Histogram of the Appearance of the Prominent Over-pressure Regions 152 Figure G.2 Histogram of the Appearance of the Prominent Under-pressure Regions 154 Figure H.1 Frequency-Response Plots from Impact Test 157 Figure K.1 Computer-generated Histogram of Wall-pressure Fluctuations 186 Figure L.1(a) Interferogram prior to 3et Application ( i n i t i a l state) 189 Figure L.1(b) Interferogram during 3et Application. 190 - x i i i -ACKNOWLEDGEMENTS The performance of any type of work often requires the help and/or co-operation of others. This project i s no exception and i t gives great pleasure to acknowledge those who contributed in different ways. F i r s t , the author wishes to express his profound gratitude to Dr. Donald W. Thompson for the constant encouragement and suggestions offered throughout the study. Secondly, my sincere thanks to Ms. Lystra M. Fletcher for her assistance with the tedious interferogram-reduction and photographic procedures. Acknowledgement i s due the people i n the E l e c t r i c a l and Mechanical Engineering departments who allowed me to use various pieces of their equipment. Also, to my former professor at the University of Waterloo, Dr. Dames D. Ford, for the confidence shown in me. Special thanks to the members of the department's work and electronics shops, the stores personnel and the secretaries for the i r invaluable help and co-operation. My brothers and s i s t e r s also deserve mention for their s p i r i t u a l input over the years. F i n a l l y , the f i n a n c i a l assistance provided by the National Research Council of Canada i s gratefully acknowledged. - viv -First turbulence random was made And spectra promptly measured And eddies lovably treasured All giving an impressive cascade Suddenly structure was paraded Spots, bursts and sweeps were sketched And after conditioning we anti-cascaded For older models could not be stretched Now we wonder if structure was originally made Or whether the turbulence did come first Could it be there's a scale of cascade And another for the nasty, tricky burst? Taken from a paper by V.W. Goldschmidt; Proc. of Symp. Structure and Mechanisms of Turbulence II, Berlin 1977 Notes in Physics. on Turbulence: #76, in Lecture CHAPTER 1 1. INTRODUCTION 1.1 Preamble In v i r t u a l l y every area of f l u i d mechanics complete understanding i s prevented by the onset or presence of turbulence. Most flows occurring in nature and in engineering applications are turbulent and thus the study of turbulence i s one of the most important branches of f l u i d mechanics. To date, however, i t i s not possible to solve turbulent flow problems — from f i r s t principles --with even the simplest of boundary conditions. A newcomer to the subject of turbulence quickly encounters the decomposition treatment of the unsteady flow, f i r s t proposed by Osborne Reynolds in 1895.^ The approach involves dividing the flow variables into a mean and a fluctuating part which, upon substitution into the Navier-Stokes equations, results in the so-called second-order (or Reynolds Stress) closure. Despite an enormous amount of research contributions which have led to various closure hypotheses,^"^ closing of the system of equations remains largely unrealized. To resolve the turbulence problem, some investigations followed a path aimed at understanding the physics of the turbulent motion. Notable in this regard i s a series of experiments conducted by the Stanford University research group (Kline and co-workers), in which flow - 2 -visual izat ion was used to study boundary layer flow. Their f i r s t paper, which appeared in 1967, gives results obtained from experiments which began in the late 1950's and is credited for in i t ia t ing a new direction to turbulence research. The most signif icant finding of Kline et al7 was the discovery of well-defined flow events inside the wall region. Since then, organized f lu id motions in the wall layer have been reported by other workers.8-10 Well-defined and persistent structures have also been observed in the outer flow region 1 1 > 1 ^ as well as in other shear f l o w s . 1 3 " 1 6 Evidence of the existence of organized structures suggests that their temporal behaviour may have a bearing on the development of the respective flow. As a result , a number of research groups are considering a deterministic approach to the study of turbulence. While information about coherent structures is sparse, at present, there is a growing optimism that continued effort to quantify their behaviour is the key to understanding the turbulence problem. Renewed emphasis is being placed on the use of flow v i s u a l i z a t i o n 1 7 ' 1 8 in this quest. The potential of this approach for identifying flow structure and reducing complex processes to simple pictures is well known. A brief account of the way in which the physical picture of turbulence has evolved, over the past several decades, is attempted in order to provide an appreciation for current research trends. - 3 -1.2 Classical background A cursory glance at the manner in which experimental techniques have influenced prevailing ideas on treating turbulent shear flows, over the past sixty years, reveals several d i s t i n c t periods of a c t i v i t y . In the twenties and t h i r t i e s turbulence research was aimed at r a t i o n a l i z i n g the idea of a turbulent viscosity c o e f f i c i e n t . This era was marked by the development of semi-empirical (phenomenological) theories, by L. Prandtl^ and G.I. Taylor,^ in which the Reynolds stresses were connected to the mean flow by an effective eddy v i s c o s i t y * or mixing length. Though the eddy concept played an important role in the construction of mathematical models, this abstract idea did not contribute to the understanding of the turbulent motion. By the f o r t i e s , hot-wire techniques became s u f f i c i e n t l y developed to enable measurement of velocity fluctuations and thus the various components of the Reynolds stress. The complexity of inhomogeneous turbulence, however, led Taylor^O and others to study the simpler, more academic homogenous isotropic f i e l d of turbulence. Interest in the s t a t i s t i c a l theory of turbulence, primarily attributed to Kolmogorov, 1 completely dominated the f i e l d in t h i s period. Further improvement in the hot-wire technique and associated electronic instrumentation led to concentrated studies, in the f i f t i e s , on the spectral d i s t r i b u t i o n of the turbulent ki n e t i c energy with *A concept introduced by Boussinesq 1^ in 1897. - 4 -emphasis on the fine structure of turbulence. However, the modes of inquiry failed to answer the basic question of how turbulence generates and maintains itself. A new outlook on turbulence followed the confirmation* of its intermittent nature by Corrsin and Kistler^ and Klebanoff25 i n the free-stream boundaries of turbulent flows and within a turbulent boundary layer, respectively. Townsend, in his book,^ 6 described turbulent flow as a system of large eddies, having dimensions comparable to the width of the flow, with smaller eddies containing most of the turbulent energy. He viewed the large structures and the small-scale turbulence as the main features of what he called the "double-structured" nature of turbulence. Townsend further drew attention to the important role of the large eddies in controlling transport and pointed out that these eddies should have a quasi-deterministic form. However, his study of the large eddy structure, using a time-averaged spatial correlation method, did not provide information to explain how the large eddies fit into the flow field. The last twenty years have seen a growing realization that the transport properties of turbulent shear flows are dominated by *Corrsin^ 2 w a s j- n e f i r s t to report that the outer edge of a jet is only intermittently turbulent and Townsend^ 3 later found this to be also true in the turbulent wake of a cylinder. - 5 -organized, non-random vortex motions. The form and scale of these coherent motions vary from flow to flow and different techniques7>8,12,13 n a v e D e e n used to identify and study them. In recent years our knowledge of the physics of the turbulent motion has increased tremendously and further improvements are expected when more measurements are made to f u l l y characterize flows. The new trend in experimental turbulence research i s to study the nature and dynamics of the ordered structures, or flow events, in an ef f o r t to determine what part they play in the development of the flow. E s s e n t i a l l y , t h i s approach requires the application of a r e l i a b l e technique that w i l l permit detection and measurement of those structures, or associated events, characteristic of the particular flow. 1.3 Motivation for this study I t i s remarkable that the f i r s t observations 7 -^ of organized motions were made in the wall region of turbulent boundary layer flows where the f l u i d motion i s most complex. The reason for t h i s may be attributed to the fact that t h i s region of flow has received the greatest attention over the years. It has been recognized, for some time, that the flow region in close proximity to a bounding surface plays an important role in the control of transport phenomena. The importance of t h i s region has motivated considerable research effort aimed at improving the understanding of the dynamics of the flow therein. - 6 -During the last several years a number of techniques have been employed to study the behaviour of the flow inside the wall region. These include photographing the movement of neutrally-buoyant solid particles 8> 1 1>27 and gas bubbles^,10,28 ± n the f l u i d , as well as making extensive anemometry measurements.29-34 Recently accumulated experimental results indicate that the f lu id motions in the v ic in i ty of a wall are part ia l ly of a deterministic nature. Researchers in this area are convinced that the observed coherent, repetitive events — called "bursting" — play an important part in turbulence generation and maintenance in wall-bounded shear flows. Bursting is composed of a sequence of ordered f lu id motions characterized in i ts latter stages by a violent and rapid eruption ("burst") of f lu id from the wall layer, followed by "inrushes" (or "sweeps") of high-speed f lu id from the outer region toward the wall . On the bases of observations 7 >8 >27 »28 a n cj measurements,29,34 ^ s n o v v f a i r l y well-established that the bursting process is cyc l ica l and is s t r i c t l y a sub-layer phenomenon that scales with wall variables; whereas the frequency of occurrence of bursts is believed to scale with outer flow parameters. Although a great deal of experimental evidence'-7>^8,35-37 confirming bursting has appeared over the last decade or so, no wholly satisfactory explanation of the phenomenon has yet emerged. The most cogent attempts, 1 1 ,28,38,39 t 0 ^ate, implicate pressure disturbances in the wall region as a probable cause of bursting. Experimental - 7 -findings imply that the flow events in the outer flow region are in some way responsible for the triggering of the wall-layer bursts. Also, i t i s well-known that the wall region i s affected by the outer flow through the agency of the pressure f i e l d . I t appears that before s i g n i f i c a n t progress in our understanding of wall turbulence can be expected, a clear understanding of the generation of wall-pressure fluctuations and i t s relationship to the flow in the wall region i s necessary. A survey of the l i t e r a t u r e reveals the need for more detailed information about the turbulent wall-pressure f i e l d . The present experimental programme was therefore devised to learn more about the structure and behaviour of turbulent wall-pressure fluctuations. - 8 -CHAPTER 2 2 . LITERATURE SURVEY The importance of f l u i d motions at a f l u i d - s o l i d boundary has been recognized since Prandtl^O proposed the boundary layer hypothesis i n 1904. Renewed interest in wall-bounded turbulent shear flows, in recent years, i s primarily due to the excellent v i s u a l i z a t i o n studies reported by Kline et a l , Corino and Brodkey 8 and Kim, Kline and Reynolds. 9 These studies revealed that the f l u i d motions within such flows exhibit a d e f i n i t e sequence of ordered events. A number of investigators have since confirmed the existence of coherent wall region motions and have also made measurements to characterize them. This survey aims to cover only those contributions which pertain most to the present study and i s not intended to be a complete review. Excellent comprehensive reviews may be found in References 41-44. 2.1 The bursting phenomenon Using the hydrogen-bubble technique in a turbulent (water) boundary layer, photographs taken by Kline and his co-workers showed that near the wall alternating regions of high and low velocity developed which were elongated in their streamwise extent, thus - 9 -appearing "streaky" in structure. The low-speed "streaks" were seen to (i) slowly l i f t away from the wall, ( i i ) often to begin a growing osc i l l a t ion , and ( i i i ) to f ina l ly break up into more chaotic motion. This whole sequence of events was termed "bursting" by Kim et al who estimated that practical ly a l l the turbulence production, given by -puv 8U/3y, occurred during that phase. Kline and his colleagues also inferred, from their experiments, that the turbulent momentum transport and production take place intermittently in time and space through small-scale bursting motions. Quantities such as the l i fe-t ime of streaks, the average distance between streaks and the burst rate were measured by Kline et al to characterize the wall region flow. A similar ordered sequence of events was observed by Corino and Brodkey. They used a high-speed movie camera, that could be moved with the flow, to photograph a region of a particle-marked pipe (water) flow. The events observed by them began with a gradual deceleration of the f lu id nearest to the wall. The flow within this decelerated region was seen to exhibit a very small velocity gradient so that there were regions of high shear at i ts edges. A large scale high-velocity f lu id mass, from further upstream, then appeared to accelerate the decelerated f l u i d . This phase was immediately followed by ejection of f lu id from the decelerated region outwards from the wall . The sequence of motions ended with the high-speed f lu id mass, moving with a velocity greater than the mean, "sweeping" the f ie ld of retarded f l u i d . Corino and - 10 -Brodkey also estimated that the largest part of the Reynolds stress was produced during the short ejection periods. Several l a t e r investigations,^»31>45A6 u s i n g hot-film or hot-wire anemometry techniques, have given quantitative support to the estimate made by Corino and Brodkey with regards to the large contribution to the Reynolds stress during the ejection (burst) periods. The recognizable flow patterns, described in the foregoing paragraphs, were seen to repeat themselves in time intervals randomly spread around an average time. Using different burst-detection schemes Laufer and Badri Narayanan-^ and Rao et al^9 agree that the mean frequency of bursts scales with 6 and U,,,, suggesting an association between the wall and outer region of a turbulent boundary layer with regards to bursting. Their scaling, however, i s contrary to Meek's,^ and also that implied by Kline et al and Achia,-^ which suggest scaling with wall variables. Nychas, Hershey and Brodkey^* and Of fen and Kline, 27** i n t h e i r visual studies, observed d i s t i n c t and i d e n t i f i a b l e events in the wall and outer region as part of a deterministic sequence which occurred randomly in time and space. The presence of transverse vortices was *A technique similar to that used by Corino & Brodkey but in a turbulent boundary layer (water) over a f l a t plate. •They used the combined dye-streak-hydrogen bubble technique in a f l a t plate turbulent (water) boundary layer set-up. - 11 -considered by Nychas et al to be the most signif icant feature of the outer flow region. They observed that, in most cases, the appearance of these outer region vortices preceded the ejection of small-scale f lu id elements from the wall. The Offen and Kline technique enabled the observation of the beginning and growth of a disturbance (originating in the outer region) upstream of, and prior to, the l i f t -up of low-speed f lu id from the wall . They and Nychas et al believe that a "cause-and-effect" relationship exists between the events of the outer region and the wall-layer bursts. Furthermore, the apparent repetitive nature of the flow pattern and the results of earl ier findings prompted Offen and Kline to conclude that the bursting process is c y c l i c a l . In a later paper, Offen and K l i n e 3 8 presented a model to explain the bursting phenomenon. Their model views the low-speed wall streak as a sub-boundary layer within the conventionally-defined turbulent boundary layer and the l i f t -up stage of bursting as the separation of this inner boundary layer due to a temporary local adverse pressure gradient. The low-speed streak, according to Offen and Kline, is believed to be subjected to a pressure osci l la t ion — probably imposed by wallward moving f lu id ("inrushes") on the sublayer. From their observations, Nychas et al believe that the ejection event is closely associated with the transverse vortex motions of the outer flow region. They feel that these (convected) vortices induce conditions in the wall region that cause f lu id eruptions to occur. - 12 -Prat u r i and Brodkey,^7 i n a more recent paper, reported on t h e i r use of a stereoscopic technique which permitted viewing of the three-dimensional aspects of the flow. These authors are convinced that the outer region events i n i t i a t e the wall region turbulent a c t i v i t y , in agreement with the postulates of Nychas et a l , Offen and Kline, and others. However, they, too, were unable to account for the mechanism responsible for triggering the wall-layer bursts. To understand t h i s phenomenon, i t seems natural to consider the momentum equation. As the wall i s approached, the i n e r t i a l forces i n the f l u i d become vanishingly small so that the pressure and stress contributions would be the only s i g n i f i c a n t terms i n the equation. In view of the ideas of Nychas et a l , Offen and Kline, Praturi and Brodkey, and others, i t i s conceivable that the eddies in the outer flow region create pressure-field effects on the sub-layer f l u i d causing eruptions of f l u i d elements therefrom. 2 .2 Wall-pressure fluctuations Research on pressure fluctuations in turbulence has been pursued both t h e o r e t i c a l l y ^ 8 - ^ and experimentally^2-61 since the late f i f t i e s . The majority of measurements of pressure fluctuations were made beneath a turbulent boundary layer with a i r as the working f l u i d (see Table 2.1). These early studies were primarily directed towards an understanding of structural vibrations that are believed to result in - free J • tream i — — Investlfttor Flow medium U » |m/»«c) 1 C D l ' / o | d |mm) t* | m m | d 3* U r u C D m / « « c | » r V n ' e H ! 1 Hirriion (1958) A i r 90 ) . 1 1 . ( 1 .1 0. 04 1. 2 348 3. I- 10 1 9. 5- I C ' 3 1 3.0 | WlllmarUi (1959] A i r 1.1 1. 035 13 • 103 5 .5 . - . 0 - 3 1. 32 Skucriyk and Had*!* (I960) Water ( 11. 5 3.1 3. 1 0. 034 0. 22 2750 17 • 10 3 1. 8- 1 0 ' 3 0.77 j ' B'lll and Wiltia(19C1) Wi ler 6.7 S. • 4. 1 1. 1 0. 95 1. 0 4. 3 0. 035 0. 037 0. 23 0. 22 0C5 924 II • 10 J 4. 3- I0 5 5. 6 • I0" 3 s - . o - J 2.4 j 1.8 W!\!marlh and WooIdridfe (1961) A i r 82. 1 0. 01 4. 1 1 1 . 9 0. 33 0. 0326 2. 03 562 38 • I0 5 5. 6- 10"' 2. 64 8 0. 3 0. 03 6. 0 546 60 . I0 3 3. 9 Scn l ln i C.9S3] Air 100 1 1. 8 3. 1 0. 5 0. 035 7. 0 741) 32 . | 0 5 7- 10 3 :. 9 WllUnarlh and Rooi (1963) A i r • 1 . J 0. 01 1. > 1 5. J 11. 1 0. 132 0. 441 0. 032 6 2. 03 196 711 36 • I0 3 5. 4- 1 0 ' ' 4. 7- 10* 3 1. 54 3. 20 :« 1. 55 0. 0394 0. 95 101 4.3- 10 3 Scl-.loemer (19(1) A i r 0.1 1. < 3. 84 0. 41 0. 0317 1. 24 131 5.6- 10 3 4. G • 10 1. 46 3. t 0. 19 0. 1)327 3. 27 ' 1S9 :? • I0 3 s . i o - 3 2. 45 Dull (1S67) A i r 100 0.75 0. 74 1 . 1 0. 36 0. 035 3. 52 1 112 10 • 103 4. 6- 10" J I. 2 i i 7. 85 0. 101 0. 0363 0. IS 45 t.2- 10 1 10. 6- 1 0 " 3. 6 BlJlte f.970) Air so 0. 15 0. 79 7. 1 0. 113 0. 033 1. 65 61 17 • 10 3 7. t- 1 0 ' ' 3. 6 Wl lU (19701 Ai r 38 3. 3 0.1 0. 17 18 2 • 10S 10. 9- 10"' 3. 1 E.-r.mt'rUn| (197!) 1 Air 1. 5 < 1 I; 1' 9. 1 Ve 0. 46 1. 93 0. 04 0. 34 4 7 202 9. 3- 10", 5. 3- 10 3. 9 1. 66 Table 2 .1 : Various measurements of turbulent wal l -pressure f luc tua t ions on smooth f l a t walls with very small pressure q r a d l e n t s . * •Taken from Reference 64. - 14 -the genera t i on or t r ansmi t t ance of a i r c r a f t cab in n o i s e , or even to cause s t r u c t u r a l f a t i g u e . A l l measurements of p ressure f l u c t u a t i o n s p r i o r to 1970 were made by means of e l e c t r o - m e c h a n i c a l t ransducers f lush-mounted w i th the bounding s u r f a c e . The a t t enua t i on of the pressure s i g n a l , apparent ly due to the c a n c e l l a t i o n of p ressure changes over the face of the t r a n s d u c e r , i s we l l - documen ted . 6 ^ B l a k e 6 3 and Emmerling e t a l ^ repor ted two independent se t s o f r e s u l t s obta ined by us ing p inhole-microphone dev ices to measure pressure f l u c t u a t i o n s at the w a l l of a wind t u n n e l . The two d i f f e r e n t s e t s of measurements show a cons ide rab le i nc rease i n the i n t e n s i t y of the w a l l - p r e s s u r e f l u c t u a t i o n s , compared to r e s u l t s p r e v i o u s l y o b t a i n e d . Th is f i n d i n g l ed Emmerling et al to conclude t h a t , compared t o a f l u s h t r ansduce r , a p inhole-microphone system enables cons ide rab le improvement i n pressure r e s o l u t i o n . Emmerling et a l , however, d id not mention the p o s s i b l e e f f e c t of i n t e r a c t i o n of the f low i n the p inho le w i th the boundary- layer f low or wi th the f low s t r u c t u r e s that produce the p r e s s u r e . B u l l and Thomas 6^ have s i nce performed exper iments i n which they used p i e z o e l e c t r i c and p inho le t ransduce rs of the same diameter i n the same f l o w . The i r r e s u l t s show tha t the i nc rease i n p ressure i n t e n s i t y , when t ransduce rs of smal l d iameters are used, i s not near l y as dramat ic as repor ted by Emmerling e t a l . On the b a s i s of t h e i r f i n d i n g , B u l l and Thomas conclude t h a t : - 15 -.... the flow disturbances created by a pinhole are localized so that the incorrect spectra obtained from pinhole measurements and genuine boundary layer spectra both scale with wall variables .... This conclusion offers a plausible explanation for the very strong dependence of the root-mean-square (r.m.s) pressure on transducer s i z e , shown by Emmerling et a l , when transducer diameter i s scaled with wall variables. Clearly, more information about the wall-pressure f i e l d i s required for adequate characterization and an improvement in our understanding of the wall region dynamics. For example, knowledge of the temporal behaviour of wall-pressure fluctuations would be helpful. Emmerling 6 6 designed an optical device to study the structure of wall-pressure fluctuations under a turbulent boundary layer in a wind tunnel. His apparatus consisted, b a s i c a l l y , of a f l e x i b l e l i g h t - r e f l e c t i n g transducer plate, flush-mounted to form part of the wind tunnel wall and which also served as a component in a Michelson interferometer. This apparatus enabled Emmerling to study what he interprets to be pressure-causing flow structures. He estimated the convection velocity (u"c) of some structures, r e l a t i v e to the flow v e l o c i t y (U^), to be as low as U„/Um = 0.40*. *A value of Uc/U00 = 0.20 i s reported in a lat e r paper 6 7 resulting from Emmerling's study. - 16 -A convection velocity of 0.40 U implies that these structures travel close to the wall. Emmerling's results seem to suggest a connection between these flow structures and the generation of wall turbulence. However, he was unable to establish any kind of relationship between the convection velocity of these structures and the observed wall-pressure patterns. The available information on the turbulent wall-pressure f ie ld is clearly quite l imited. This is not caused by a dearth of experimental investigations, but rather by the extreme d i f f i c u l t i e s that beset the experimenter in this f i e l d . Wall-pressure fluctuations are of small magnitude and i t is extremely d i f f i c u l t to separate them, when conventional transducers are used, from other spurious signals present in the system. These d i f f i cu l t i es are further compounded by the fact that pressure f luctuations, in turbulence, are of sizes ranging from a few times the boundary layer thickness down to scales of the order of v / U * . 6 2 2.3 Closing remarks Workers in this area are trying to develop a physical model to explain the nature of bounded turbulent shear flows. Only when an adequate mechanistic picture is obtained wi l l i t be possible to mathematically model these flows for applications of technical - 17 -i n t e r e s t . Unfortunately, t h i s picture i s far from being completely clear. An understanding of the physical processes actually occurring in such flows i s indispensable for progress toward an an a l y t i c a l description of them. Even short of that, knowledge of these processes would be helpful for understanding and coping with p r a c t i c a l problems i n which turbulent flow i s prominent. - 18 -CHAPTER 3 3. OBJECTIVES OF THE PRESENT STUDY 3.1 Statement of the problem The present study was speci f ica l ly undertaken to gain insight into the mechanisms of the generation of boundary layer wall-pressure fluctuations in order to elucidate some aspects of the flow in the wall region. 3.2 Primary objectives From the statement of the problem, i t is clear that i t is necessary to obtain information about the structure of the wall-pressure and i ts variation with time. Measurements made at a single point and conventional time-averaged analyses are, therefore, not of great u t i l i t y since they cannot provide data about the repetitive events that are now known to be important. For the present study, an optical approach with the feature of enabling the extraction of quantitative information from visual records is considered. Both the need for such methods and their usefulness are amply demonstrated in the research papers 6 8 from a recent f lu id dynamics symposium. - 19 -The primary objectives of the present study were: 1. to develop a technique which would permit visual izat ion and measurement of the fluctuating pres-sure at a pipe wall during turbulent flow of water, and 2. to determine the relationship between the pressure fluctuations and the flow in the wall region. - 20 -C H A P T E R 4 4 . P R E L I M I N A R Y C O N S I D E R A T I O N S A f a i r amount of i n i t i a l experimentation was necessary before the actual pipe flow study was even attempted. This chapter outlines only those experiments and considerations that are important to the main experimental programme. 4 . 1 Feasibility study F e a s i b i l i t y experiments were performed to ascertain the s u i t a b i l i t y of a laser-holographic interferometric approach for the present study. F i r s t , a simple hologram-interferometer was designed for use in making practice holograms. The next step was the implementation of interferometry. It was necessary to apply the technique to detect small timewise changes on the surface of an object. A thin (2mm-thick) layer of a transparent polymeric (rubber) material*, formed on a Plexiglas plate, was used as the object in the interferometer. It was established that deformation of the coating, resulting from the impingement of a submerged laminar water j e t , could be detected and was measurable. *This material was formulated as a part of t h i s work. - 21 -4.2 Making a Hologram The principle of holography is presented in Chapter 5 and is therefore not given in this section. Severe building vibration proved to be a nuisance in the early attempts to make a hologram in this laboratory. This hazard was circumvented by using a very fast exposure time (fraction of a second) with high laser (output) power. Holograms were made of various pieces of laboratory glassware. Considerable effort was made to obtain a holographic image of optimum f ide l i t y for interferometry (see Appendix L) . 4.3 Suitability of the compliant material In addition to satisfying the general requirements of Section 4.1, more specif ic considerations were necessary. It was very important, for example, to determine i f the coating developed would be suitable for the pipe flow study. The coating is a si l icone rubber compound which possesses appreciable wear and water resistance. Because of i ts transparent nature i t was conducive to direct transmission holography6^ a n ( j ? therefore, did not require the application of any special l ight -ref lecting layer that would be susceptible to degradation with use. Since this compliant material is to be used to form the pipe (wall) surface, i ts influence on the adjacent pipe flow was also of - 22 -great concern. It is well-known that a hydro-elastic instabi l i ty in the form of a wave structure [e.g. the Rayleigh wave 7 0] may develop at a compliant surface-l iquid interface. However, Hansen and Hunston 7 1 show that such waves occur only when the quotient, U > 1.41 [4.1] where: bulk flow velocity, m/sec shear modulus, N/m density of the flowing f l u i d , kg/m3 The calculated value of this non-dimensional parameter varied from 0.02 to 0.04 over the flow range of this study. Another important requirement is for the excitation pressure forces and the response of the compliant surface to be in phase. This condition is met i f the fundamental frequency of the compliant wall is higher than the frequency range of the turbulent wall-pressure fluctuations to be studied. As outlined in Appendix H, the compliant surface developed for this study sat is f ies this speci f icat ion. U G - 23 -C H A P T E R 5 5 . T H E V I S U A L I Z A T I O N T E C H N I Q U E : A H O L O G R A P H I C I N T E R F E R O M E T R I C A P P R O A C H V i s u a l i z a t i o n approaches d i f f e r from other experimental methods mainly because they render certain properties of a flow f i e l d d i r e c t l y accessible to visual perception. As a result, insight into a physical process may be improved considerably i f a pattern produced by, or related to, the process can be observed. When compared to a measuring probe, a v i s u a l i z a t i o n technique offers many advantages. For example, the l a t t e r has the a b i l i t y to enable study of a flow variable without physically interfering with the flow. In contrast, a measuring probe w i l l disturb the flow to some degree. Also, whereas a probe provides data for only one point, a v i s u a l i z a t i o n device gives details of an area of the flow system under investigation. The value of a v i s u a l i z a t i o n approach i s greatly enhanced i f quantitative data can be derived from the associated pattern observed. This added capability i s a d e f i n i t e asset to current trends in experimental turbulence research where questions have been raised concerning the adequacy of measurements which u t i l i z e instrumenta-tion's ,72 a n c j analyses 73-76 n o t suited to the coherent and intermit-tent nature of turbulent flows. - 2 4 -5.1 Visualization approach of this study It is clear that a detailed study of the wall-pressure f ie ld can be best made by recording i ts instantaneous development over an area of the bounding surface. To this end, a visual izat ion technique combined with cine-photographic recording seems appropriate. This study was therefore aimed at obtaining pictures to show the pattern of the fluctuating pressure on the wall of the pipe bounding the flow. It was the hope that quantitative data, from the visual records, would provide insight into the mechanisms of the generation of wall-pressure fluctuations. 5.2 The interferometric technique Interferometry is a non-perturbing measuring procedure which is of special value in obtaining information about a system, without the necessity of making physical contact. In general, a l l interferometric techniques are sensitive — even to sl ight changes that may occur in the surroundings. It is required, therefore, to construct an interferometer that is sensitive to the quantity to be measured but relat ively insensitive to the disturbing effects of the environment. - 25 -5.3 Conventional interferometers A number of a u t h o r s 7 7 - ^ have presented excellent treatises on the use of conventional interferometers (eg. Michelson's, Mach-Zehnder's) as optical measuring devices in many applications. Conventional interferometry, however, i s unsuitable for use i n the present study because the technique i s limited to test sections with o p t i c a l l y f l a t and p a r a l l e l windows and requires precise o p t i c a l components. The discovery of holography has made possible an interferometer which i s not dependent upon the use of precision optics. The holographic technique i s therefore quite useful in studies u t i l i z i n g complicated geometries. 5.4- Principles of Holography Dennis Gabor's principle of wavefront reconstruction i s now universally know as holography. The essential elements of the theory of holography were worked out by Gabor in 1948.^1 The essence of Gabor's work involved the recording of the wavefront emanating from an object. At any point on a wavefront there exists a certain amplitude and phase r e l a t i v e to other points. By recording both the amplitude and phase a l l pertinent o p t i c a l information about the object i s captured. - 26 -Recording of phase as well as amplitude is achieved by making the object wavefront interfere with another wavefront, which can be either f la t or spherical , called the reference wave or reference beam. The interference fringes so produced are recorded on a (conventional) photographic medium which is then called a 'hologram' -- a derivation from the Greek word 'holos' meaning 'the whole' i . e . the whole information. A fundamental requirement for the holographic process is the condition that the light source used be temporally and spatially coherent. It was, therefore, not unt i l the advent of the laser — a light source which sat isf ies the coherence requirement — and the efforts of Leith and Upatnieks 8 2 > 8 3 that the practial u t i l i t y of Gabor's invention was real ised. Holography is a two-step method of optical imagery. Complete wavefront recording is accomplished so that a l l optical information about an object is retained for subsequent re t r ieva l . In the f i r s t step, a microscopic fringe pattern, resulting from the interference between the mutually coherent object wave, (5, and the reference wave, ft, i s photographically recorded [see Figure 5.1 (a)]. The next step — the reconstruction stage — involves the illumination of the recorded interference pattern, (called the hologram), by the reconstruction beam, ->-' . R, in order to reconstruct the original object wave [See Figure 5.1 (b)]. An observation of this reconstructed wavefront yields a view of - 27 -R: Reference wave O: Object wave Figure 5.1(a): The off-axis hologram-recording arrangement. - 28 -R': R e c o n s t r u c t i o n wave Figure 5.1(b): Image reconstruction. - 29 -the ob jec t that i s p r a c t i c a l l y i n d i s c e r n i b l e from the o r i g i n a l . When used in combinat ion wi th i n t e r f e r o m e t r y , the ho log raph ic techn ique makes a v a i l a b l e a method fo r o p t i c a l , i n t e r f e r o m e t r i c measurements, on su r faces of n o n - o p t i c a l q u a l i t y , s e n s i t i v e to o p t i c a l pa th leng th changes down to one- tenth of a wavelength of l i g h t . Ho lograph ic i n te r fe romet ry t he re fo re o f f e r s great p o t e n t i a l f o r use i n the v i s u a l i z a t i o n and measurement of sma l l su r face changes. 5 .5 Theoretical foundations of holographic interferometry A mathemat ical account of ho lograph ic image format ion and i t s a p p l i c a t i o n to i n t e r f e r o m e t r y , i n t h i s s tudy , i s presented in t h i s s e c t i o n . 5.5.1 Mathemat ical a n a l y s i s o f holography The process of holography has a l ready been desc r ibed as the s u p e r p o s i t i o n of two mutual ly coherent wavefronts i n c i den t on the same photographic medium. The ampl i tude of the re fe rence and ob jec t wavefronts may be desc r i bed by the complex f unc t i ons - 30 -i * R (x,y) a R (x,y) = Ap (x,y) e [5.1(a)] and i^O (x,y) a0 ( x ' y ) = A0 ( x ' y ) e [5.1(b)] where: a amplitude d i s t r i b u t i o n A amplitude modulus <)> phase of wavefront x,y co-ordinate axes in hologram plane R reference (beam) wavefront 0 object (beam) wavefront Since the reference and object waves are mutually coherent, the intensity in the hologram plane, I (x,y), i s obtained by adding the amplitudes, given by equation [5.1], and multiplying by the complex conjuguate, I(x,y) = ( a R + a Q) ( a R + a Q ) * [5.2] which, upon expansion, yields *This superscript asterisk i s used to denote the complex conjuguate. - 31 -2 2 1 •(*>y) = A R + A Q + A Q A R e + e [5.3] For optimal f i d e l i t y of the reconstructed image holograms are made within the exposure range, indicated in Figure 5.2, described by the equation A t = b - 3E [5.4] where b i s the intercept of the straight l i n e on the ordinate and 3 (the slope) i s the emulsion constant. The amplitude transmittance of a l i n e a r l y recorded hologram i s related to the intensity d i s t r i b u t i o n at the hologram plane by, A t (x,y) = b - 3 T £ I(x,y) [5.5] since E = T I [5.6] (Tg. i s the exposure time). By substituting the expression given by Equation [5.3] into [5.5] the f i n a l amplitude transmittance becomes, Figure 5.2: Characteristic curve of amplitude transmittance (A.) versus exposure (E). - 33 -A t ( x , y ) = b - 3T £ ( a Q + a^) ( a Q + a R ) * b - 3T r ~2 2 i ( W " ^ V ^ A R + A 0 + A 0 A R 6 + A 0 A R e [5 .7 ] Upon r e - i l l u m i n a t i n g the hologram wi th the o r i g i n a l re fe rence beam a lone , the t ransmi t t ed wave at the hologram i s g iven by *(x,y) = a R ( x , y ) . A t ( x ,y ) bA R e e r E A R e i^p f~2 2  J LAR + A0 + A0 A R i<VV a 4 -u*0-*Rn + A Q A R e [5 .8 ] By expanding and r e - a r r a n g i n g Equat ion [5 .8] the f o l l o w i n g equat ion r e s u l t s , iKx.y) = jb-(AJJ + A Q J P T ^ A ^ 1 ^ A 2 R 3T E A o e 0 A 2 R T A i ( 2 W R E o e [ 5 .9 (a ) ] - 34 -Since in practice the reference beam is made suff ic ient ly uniform, A R may be considered essentially constant across the hologram. 2 By setting the factor of the second and third terms in Equation [ 5 .9 (a)] equal to k, the equation may be re-written as i<t> i<j) i(2<|> -<|> ) * (x,y) = [b - (A| + A ) gT F] A_e R - kA e 0 - kA e R 0 [5.9(b)] I I l ° I i _ ! I (i) ( i i ) ( i i i ) Term (i) in the above equation is the attenuated reconstructing wave. The terms ( i i ) and ( i i i ) represent the f ine- l ine structure of the hologram that causes i t to act l ike a di f f ract ion grating. The second term represents a wave identical to the original object wave, except for the constant factor, and is thus responsible for the primary, virtual image of the object. Except for i ts intensity, this reconstruction is theoretical ly identical to the object. An observer looking through the processed plate would therefore seem to see the object located in i ts or iginal posit ion. Term ( i i i ) represents a second reconstruction on the opposite side of the photoplate. This conjugate reconstruction is always present but is not in focus when the primary reconstruction is in focus. The presence of the conjugate image can degrade the primary image and is a major obstacle in Gabor-type holograms. However, this problem - 35 -i s solved by using the now well-known " o f f - a x i s " ^ 1 approach for making holograms. This geometrical arrangement results in s p a t i a l l y separated primary and conjugate reconstructions, as shown in Figure 5.1 (b), which do not interfere with each other. 5.5.2 Holographic interferometery Holographic interferometry involves the formation and subsequent interpretation of the macroscopic fringe pattern which appears when a wave, stored in a hologram at some e a r l i e r time, i s later reconstructed and caused to interfere with a comparison wave. Single- and double-exposure holographic interferometry are descriptive labels attached to variants of the interferometric method which can make possible the study of surface change. With the double-exposure method, two exposures are sequentially recorded on the same hologram. Any change in the surface between exposures w i l l result in a "frozen" fringe pattern over the surface of the object. The single-exposure method enables what i s called a " l i v e " fringe or real-time study. This method requires only one exposure to be made to obtain the v i r t u a l image of the object. In t his interferometer, the v i r t u a l image obtained during the f i r s t exposure represents a reference state to which the object, as i t undergoes changes with time, i s compared. The v i r t u a l image, therefore, performs a function similar to the reference arm in a conventional interferometer. - 36 -Interference between the wavefront from the hologram and the actual object wavefront produces a " l i v e " fringe pattern. This l i v e fringe f i e l d provides the real-time capability of the technique for studying instantaneous changes. The storage or time-delay aspect, described above, gives the holographic method a unique advantage over conventional interferometry. This aspect relieves the stringent requirements for perfect o p t i c a l elements, required in conventional interferometry, since phase d i s t r i b u t i o n due to o p t i c a l imperfections in the test section and other components are also holographically recorded. 5.5.3 Application of the moire technique to holography There exists considerable confusion in the f i e l d of holographic interferometry with regards to the quantitative interpretation of observed fringe patterns.^5>86 Most authors tend to derive the i r own methods of interpretation which are usually limited to their particular application. The relationship between the observed fringe pattern and the quantity studied i s often complicated by the complex nature of the fringe structure. In general, fringe interpretation i s a very d i f f i c u l t , tedious and time-consuming exercise. The moire concept introduced by Pastor^ 7>88 and used by Achia i s adopted for use i n t h i s study. This approach provides a tractable geometric method for real-time holographic interferometric fringe pattern interpretation. - 37 -Moire patterns commonly refer to the patterns seen when two similar screens or high frequency gratings are nearly superposed. Since a hologram may be considered to be a complicated high frequency d i f f r a c t i o n grating, the application of the moire technique to holography suggest i t s e l f Chau and Mulianey^O used double-exposure holographic interferometry, with moire fringes, to examine flow phenomena. Their approach, however, does not have the real-time feature and i s therefore unsuitable for application in the present study, where interest l i e s in studying instantaneous changes. In real-time holographic interferometry, the interference of the wavefront of the v i r t u a l image (comparable to the "stored" grating), recorded at an i n i t i a l time, t ^ , with the actual object wavefront (analogous to a " l i v e " grating) w i l l produce v i s i b l e interferometric fringes. The fringe f i e l d represents the projection, in the direction of the object wavefront, of the moire pattern generated at the hologram plane. Small r e l a t i v e changes in optical path lengths between the test surface and i t s v i r t u a l image, due to changes at the surface, w i l l appear as distortions of the fringes seen through the hologram superimposed upon the surface. The observed fringe pattern i s due to a variation in phase difference in the reconstructed wavefront, coming from the hologram, and - 38 -the actual object wavefront. The phase difference engendered i s related to the opt i c a l path difference (OPD) between the two waves according to, OPD = — (<|>0 - <j>R) [5.10] 2TT Interference maxima occur when, OPD = mX [5.11] By equating Equations [5.10] and [5.11], * 0 - <t>R = 2mir [5.12(a)] or, <t>0 - 4»R = nir [5.12(b)] I f the object suffers a change at a later instant of time, in real-time modality [with the same reference wave but with a perturbed object wave incident on the hologram], the new hologram i s " l i v e " — i.e . i t i s not recorded — and may be defined as, <t>0 - <t>R = n'TT [5.13] - 39 -the moire structure produced in the holographic plate gives, (4>0 - 4>R) - Up - <t>R) = (n-n')TT [5.14(a)] By l e t t i n g (n-n') = N , the above equation becomes, <l>0 - 4>0 = NTT [5.14(b)] representing the phase difference in the wavefront emanating from the object at different times. 5.6 The object in the present study The object (or test surface) in the interferometer used in t h i s study i s an area of a specially-fabricated compliant pipe wall. Figure 5.3 i s a schematic diagram of the Plexiglas pipe section and the photo-optical set-up. The pipe section, about 1.3 m in length, was constructed of the same inside diameter as the upstream and downstream glass pipeline, except for the f l a t wall (exaggerated in the fig u r e ) . A side view of a 0.33 m length of the pipe section i s presented i n Figure 5.4. This section consists of a removable f l a t piece (see Figure 5.5) in which a cavity i s machined. The s i l i c o n e rubber compound, formulated in this study (see Appendix A), f i l l s the cavity flush with i t s edges to form a smooth, uniform compliant pipe (wall) surface. cross-section Figure 5.3: Schematic of the test section and photo-optical set-up Figure 5.4: Side view of specially-constructed pipe section. Figure 5.5: P a r t i a l pipe section ( f l a t piece removed). - 43 -The s l i g h t deviation from roundness of the pipe i s gradual to prevent the development of secondary flows. The test section was ca r e f u l l y aligned and inserted into the pipeline (see Figure 5.6) to form a part of the interferometer. The bordered area (11mm x 34mm) seen on the exterior pipe wall i s the actual v i s u a l i z a t i o n location in t h i s study. The border aided in focussing for photographing the fringe pattern and i t also served as a spatial scale. Figure 5.6: Test section (in the pipeline) forming a component of the interferometer. - 45 -CHAPTER 6 6. EXPERIMENTAL APPARATUS AND PROCEDURE The apparatus consists, b a s i c a l l y , of a constant head flow system integrated with a holographic interferometer. Achia 9^ gives a complete description of the flow f a c i l i t y and therefore only the salient features, changes and/or si g n i f i c a n t modifications are presented in t h i s section. 6.1 The constant head flow system The flow f a c i l i t y i s shown schematically in Figure 6.1. A unidirectional d i f f e r e n t i a l pressure transducer, model PL-280TC-2.5, manufactured by Gould Inc., Oxnard, C a l i f o r n i a , replaces the transducer used by Achia. A 160-litre reservoir, pressurized with compressed a i r , provided a constant head to supply the pipeline with water via a globe valve, a remote control solenoid valve and a conical-shaped flow straightener. The horizontal glass pipeline (26.3 mm ID), 7.0 m long, included a section 3.05 m, i n length, for pressure drop measurements. The f i r s t s t a t i c pressure tap was i n s t a l l e d at a distance of more than 40 pipe diameters downstream of the pipe i n l e t . The water, from t h i s single-pass system, was directed to an open c o l l e c t i n g tank after i t s passage through a 30° connector. This Legend f.s -flow straightener p.t : pressure transducer s : solenoid valve Holography set-up HS*--cr—a collecting tank water inlet overflow. power source — «•—(J laser head vent a i r reservoir PX -p-ON Figure 6 . 1 : Schematic of the flow fac i l i t y integrated with the holographic set-up. - 47 -connector was f i t t e d to the discharge end to ensure that the pipeline i s kept f i l l e d with water. The test section was inserted into the pipeline at over 200 pipe diameters downstream of the flow straightener. Hinze 4 1 recommends an entry length of 40 pipe diameters (Nikuradse's value) as a minimum for ensuring fully-developed turbulent flow. 6 . 2 Design considerations for the holographic interferometer Two fundamentally different designs were considered for the present interferometer, namely — the wavefront division and the amplitude division variants. 6.2.1 Wavefront d i v i s i o n holographic interferometer (WDHI) A wavefront division holographic interferometer was considered for use in th i s study. (A schematic representation of a WDHI i s given in Figure 6.2). The upper portion of the expanded beam goes d i r e c t l y to the photoplate while the rest of the beam passes through the diffusing screen, DS, to diffusely illuminate the test surface. The portion of the beam which cleared the pipe served as the reference beam R, and the lower portion formed the object beam, 0. 48 -Legend D-S : diffusing screen L-G : liquid gate M : mirror O '• object beam R : reference beam SF-BE : spatial filter-beam expander Figure 6.2: A schematic representation of a wavefront d i v i s i o n holographic interferometer. - 49 -Alignment of t h i s interferometer, which uses a single beam, i s re l a t i v e l y simple. However, a major drawback of the WDHI i s the i n a b i l i t y to vary the reference - object beam intensity r a t i o (R/0), especially during reconstruction, to attain a 1 : 1 balance in brightness between the test section and i t s v i r t u a l image in order to optimize fringe v i s i b i l i t y (contrast). Optimization of fringe contrast, with the WDHI, can only be obtained by the precise development of the photoplate to a spe c i f i c photographic density. 6.2.2 Amplitude d i v i s i o n holographic interferometer (ADHI) An amplitude division holographic interferometer requires more op t i c a l components and also presents one with a more d i f f i c u l t alignment procedure, compared to i t s wavefront division counterpart. Amplitude d i v i s i o n i s brought about by the introduction of a beamsplitter into the path of the incoming laser beam. With t h i s arrangement, i t was necessary to steer the reference beam over the pipe, with the aid of a couple of mirrors, along i t s path to the photoplate (see Figure 6.3). The variable beamsplitter f a c i l i t a t e d adjustment of the intensity during both the recording and subsequent reconstruction stages of the holographic process. This feature of the ADHI s i g n i f i c a n t l y reduces the problem faced with the WDHI in obtaining suitable fringe contrast, necessary for interferometry, and far outweighs i t s alignment d i f f i c u l t i e s . Figure 6 . 3 : A schematic representation of an amplitude d i v i s i o n holographic interferometer. - 51 -In consideration of its capability, an ADHI was selected for use in this study. The essential features of this interferometer are: 1. a beam dividing device, 2. a means of directing the divided beams along different paths, and 3. a beam recombining system The components which perform the above-listed functions are described in the next section. 6 . 3 The present holographic interferometer 6.3.1 Components of the interferometer A schematic arrangement of the optics is given in Figure 6.3 and the various components are listed in Table 6.1. (i) The Laser For holography only lasers which operate in the single TEM mode^ ^ a r e useful. The highest degree of coherence — both spatial and temporal — is obtained with operation in the mode. - 52 -Table 6.1: Components of the Holographic Interferometer Component Specifications Laser Beamsplitter Mirrors Lens-pinhole sp a t i a l f i l t e r Photoplate holder Diffusing screen Test surface Optical bench A Spectra-Physics (water-cooled) argon-ion, model 164 with model 265 power source ( e x c i t e r ) ; Spectra-Physics model 89 etalon inserted i n o p t i c a l cavity. 3odon model VBA-200, continuously variable density. Front-silvered variety supplied by Edmund S c i e n t i f i c Co. Spectra-Physics model 332 with 4 mm focal length lens and 6.8 y pinhole aperature. Constructed from Plexiglas; see Figure 6.6. Made from finely-ground commercial glass. Details in Section 5.6 and Appendix A. Gaertener S c i e n t i f i c Corp. Model 210. - 53 -A 2-W argon-ion laser provided the coherent l i g h t for t h i s interferometer. To ensure an adequate coherence length, for holographic interferometry, a stable uniphase, single frequency output was achieved by i n s t a l l i n g an etalon inside the laser cavity. These improvements, however, are obtained at the expense of output power. With the laser operating at a wavelength of 488 nm (blue l i g h t ) , the maximum obtainable power output was about 800 mW. ( i l ) Beamsplitter In an ADHI of n o p t i c a l paths n - 1 beamsplitters are required. Therefore, a standard two-beam ADHI such as that designed for t h i s study, requires only one beamsplitter. A beamsplitter divides an input (incident) l i g h t beam into two components emerging in different directions — usually at right angles to each other. The r e l a t i v e i n t e n s i t i e s of the two emergent l i g h t beams are fixed by the characteristics of the beam s p l i t t e r — i . e . a beam s p l i t t e r i s capable of r e f l e c t i n g and transmitting an incident beam in a certain c h a r a c t e r i s t i c r a t i o . The reflection/transmission r a t i o (R/T) i s usually expressed as a percentage. A variable-ratio beamsplitter, essen t i a l l y a p a r t i a l l y silvered mirror whose r e f l e c t i v i t y i s made variable by means of a simple rotation to change the point of incidence of the incoming beam, was the type used in the present unit. I t s v a r i a b l e - r e f l e c t i v i t y capability was extremely - 54 -useful in balancing the beam-intensity r a t i o between the object and reference beams at the hologram-recording plane and also to maximize fringe v i s i b i l i t y for interferometry. ( i i i ) Mirrors Mirrors of the front-silvered variety were used. In th i s interferometer, the mirrors pick up the beams leaving the beamsplitter and direct them along the desired paths to the photoplate. (iv) Lens-pinhole spatial f i l t e r I t i s important, for holographic interferometry, to have an op t i c a l l y clean laser beam for the recording of the fine d e t a i l s of interference and the subsequent observation of d i f f r a c t i o n patterns. A lens-pinhole spatial f i l t e r transforms a collimated, "noisy" laser beam into an expanded beam with a smoothly-filtered wavefront having a Gaussian intensity d i s t r i b u t i o n . The instrument consists of a pinhole movable along the x- and y-axes and a short focal length expanding lens, movable along the z-axis, as shown schematically in Figure 6.4. The power of the lens controls the divergence of the beam while the diameter of the pinhole aperature determines the degree of f i l t e r i n g . The lens focuses the input laser beam into the pinhole which passes only the central portion of the beam, thus behaving l i k e a low-pass f i l t e r . ^ 3 Figure 6.k: Spatial filtering of a "noisy" laser beam. - 56 -(v) Test surface As described in Section 5.6, the test surface i s a specially-constructed compliant pipe (wall) surface. Details of the compliant surface are given in Appendix A. (vi) Photoplate holder Exact re-alignment of the processed plate i s a c r i t i c a l step for the successful implementation of real-time holographic interferometry. The problem i s all e v i a t e d , in th i s study, by using a device which holds the plate in place by means of stainless steel-leaf c l i p s . This plate holder device i s designed to sli d e into a cavity which forms the l i q u i d gate used. With the plate held in place photographic processing i s performed i n si t u . ( v i i ) The hologram In any holographic interferometer the hologram-recording plate performs the beam recombining function. The main difference between holographic emulsions and that used i n conventional photography i s the grain s i z e . The former i s extremely fine-grained and hence i t s resolution i s considerably better than that of photographic emulsions. High resolution orthochromatic plates with maximum spectral s e n s i t i v i t y in the blue-green region (see Figure 6.5) were used in t h i s - 57 -10 E M M O t O O wavelength (nm) Figure 6.5: Spectral s e n s i t i v i t y curve* for 10E56 ("Holotest") emulsion. *From: Technical B u l l e t i n -- Agfa-Gevaert.^^ - 58 -work. The plates are manufactured by Agfa-Gevaert Scientia under the trade name "Holotest". ( v i i i ) Optical bench Since making a hologram involves the recording of a complex stationary microscopic interference pattern, a vibration-free work surface i s desirable. As a rule of thumb a movement of about A/4 of a component, during exposure, w i l l o b l i t e r a t e the hologram (X i s the wavelength of the l i g h t used). A l l components comprising the interferometer, except the laser, were mounted securely to a special o p t i c a l bench. This bench, equipped with steel r a i l s , enabled the use of magnetic bases to provide anchorage for the components they supported. The bench was supported, in turn, by a heavy steel table. Between the table and the bench was sandwiched a s t r i p (« 3 mm-thick) of neoprene rubber to suppress the transmission of vibration from the floor to the work bench. To reduce the effects of a i r currents in the laboratory on the op t i c a l apparatus, the components susceptible to such effects were housed in an enclosure (1.5 x 0.75 x 1.0m) made from Celotex. With the room l i g h t s turned o f f , t h i s enclosure also served as a darkroom for handling and onsite processing of the photographic plates. - 59 -Owing to i t s weight and the lack of bench space, the laser was placed on a separate mechanically stable bench. It was necessary to cover the laser head with a sheet of p l a s t i c to prevent dust or other foreign particles from getting to i t s internal optics. 6.3.2 Design parameters (i) Design angle A char a c t e r i s t i c parameter for any holographic system i s i t s design angle, i . e . the average angle at which the reference beam crosses the object beam at the photoplate. Once the design angle i s chosen so have the resolving power of the photographic emulsion and i t s effective speed. Modulation Transfer (MF) i s the term used to define resolving power in terms of spatial frequency.* The information that an emulsion must record i s very fine. This d e t a i l (microscopic interference fringes) i s a function of the design angle. To estimate the resolution requirements of the emulsion, the fringe frequency to be photographically recorded may be calculated from the equation •Modulation transfer describes the a b i l i t y of an emulsion to record the s p a t i a l frequency of a test subject and consequently defines the resolving power (or resolution capability) of that emulsion. - 6 0 -f = I sin (6/2) [6.1] where 6 i s the angle between the reference and object illumination beams and X i s the wavelength of the l i g h t . The calculated frequency must be reasonably lower than the manufacturer-specified resolution capacity of the emulsion (see Table 6.2). For the maximum design angle of the present interferometer, the calculated s p a t i a l frequency of 1900 lines/mm i s reasonably lower than the rated value (2800 lines/mm) of the "Holotest" 10E56 emulsion used. This emulsion consists of fine grains (0.08 - 0.03 ym) of s i l v e r halide compounds dispersed in gelatin.^5 ( i i ) Coherence length Although a laser i s usually thought of as a coherent source, only a laser which o s c i l l a t e s in a single a x i a l and transverse mode emits l i g h t that i s highly coherent-- in both space and time. In general, coherence length i s determined by multiplying the coherence period by the velocity of l i g h t . The etalon f i t t e d inside the laser (head) ensures an adequate coherence length of the argon-ion laser used in the present study. The path traversed by the object beam and that of the reference beam, measured from the beamsplitter to the centre of the photographic plate, Table 6 . 2 : Manu fac tu re r -Spec i f i ed C h a r a c t e r i s t i c s of the S i l v e r Ha l i de Emuls ion Emulsion Thickness (Mm) Subst ra te Record ing Wavelength Range Speed ° (uO/m 2) L i m i t i n g R e s o l u t i o n ( l ines/mm) 10E56 ("Hole-test") 6 g l a s s (NAH) 3 or thochromat ic ' 3 0.05 2800 NAH means n o n - a n t i h a l a t i o n backed See range i n F igure 6.5 a l s o c a l l e d " reco rd ing s e n s i t i v i t y " - 62 -was made as closely equal* as possible (within 10 cm) in order that the maximum coherence length of the laser might be u t i l i z e d . ( i i i ) Beam intensity ratio In order to optimize fringe contrast, the reference-object beam intensity should be in balance during readout (reconstruction). A ft/ft r a t i o of about 5:1 i s considered suitable by a number of workers-^>69,97-99 ^ n holography. 6.4- Photoplate processing considerations I t i s recommended that holograms be developed immediately after exposure, since the extremely fine grains of the emulsion may be subject to latent image fading.95 The preservation of hologram quality affects the f i d e l i t y of the image and i s dependent on the emulsion treatment steps. Quite complicated procedures have been published many of which include involved preconditioning^^ and emulsion-hardening^ steps, prior to exposure,and often incorporate an elaborate bleach process''^,103 a f t e r development. Bleaching practices are known to ->• •* *The use of equal 0 and R paths enhances the resolving power of the photographic emulsion.96 - 63 -cause the formation of a low frequency phase pattern which d i f f r a c t s unwanted l i g h t into and around the holographic image. This "noise" l i g h t usually takes the form of a v e i l i n g glare that reduces the contrast of the image. A f a i r l y rapid and uncomplicated procedure which does not require many processing steps was used herein. The emulsion i s subjected to the bare minimum number of processing solutions, so that phase changes from surface r e l i e f and gelatin thickness variations of the glass-backed emulsion are eliminated. 6.4.1 On-site processing inside a l i q u i d gate The l i q u i d gate i s the same as that used and described by Achia. The photoplate holder f i t s exactly into the l i q u i d gate and serves to maintain the photoplate in the same position during hologram-recording, processing and reconstruction. For emulsion exposure and during the subsequent read-out stage, the plate was kept immersed in fresh d i s t i l l e d water inside the gate. Many holographers recommend the use of a l i q u i d gate^-+-107 for signal-noise (S/N) improvement in the holographic image. I t i s believed that immersion of the plate in d i s t i l l e d water, prior to exposure, serves to relieve anisotropic stresses in the emulsion introduced during i t s manufacture. There i s also reasonable evidence i n t h i s work which suggests that the pre-soaking of the emulsion enhances i t s s e n s i t i v i t y . - 64 -Figure 6.6 shows the l i q u i d gate. Processing solutions, from an adjacent set-up [Figure 6.7], were sequentially introduced to and withdrawn from the bottom of the gate by means of a compressed nitrogen-(vacuum) suction system. The photographic plate was placed inside the gate with the emulsion side facing the object to be recorded. The l i q u i d gate was mounted on a unit designed to provide micrometer controlled translation and rotational displacements. This whole assembly was affixed to the optical bench by means of a magnetic base as shown in Figure 6.6. 6.4.2 Hologram-processing supply unit This unit i s a modification of the one used by Achia and described in his thesis. In the present unit [see Figure 6.8] glass bottles were used to store the photographic solutions just prior to use. Also, the valves through which the solutions pass were changed to standard (glass) stop cocks. These changes prevented the need for frequent maintenance of the unit and are very important since hologram processing i s c r i t i c a l and cannot tolerate interruption for making repairs or other adjustments. 6.5 The photo-optical recording and analysing apparatus A v i s u a l i z a t i o n approach requires some means of recording the observed events to obtain a permanent record for later study. Details Figure 6.6: Liquid gate-plate holder and precision-mount assembly. Figure 6 . 7 : Flow f a c i l i t y and adjacent hologram-processing supply unit. Legend o: overflow S: fresh sol'n S': used sol'n ®: glass stopcock A A A distilled water Figure 6 . 8 : Hologram-processing supply unit. to vacuum - 68 -of the cine-photographic equipment, accessories and the motion picture analyser used are given in Table 6.3. The photographing was done by means of a stationary camera mounted on a heavy-duty tripod, independent of the optical bench. 6.6 Experimental procedure The main experiments performed in the study were the gross flow and the visualization runs. The l a t t e r includes the hologram-making procedure which i s presented in a concise point form, herein, since i t is an important part of the central study. 6.6.1 Gross flow experiments The d i f f e r e n t i a l pressure transducer was calibrated as outlined in Appendix B. I t s ca l i b r a t i o n was checked prior to each run. D i s t i l l e d water from the reservoir in Figure 6.1 was used in a l l runs. Following visual routine checks on the system, flow in the pipe was i n i t i a t e d and allowed to attain a constant pressure drop (AP signal was continuously recorded). At that point, the flow rate was measured by timing the c o l l e c t i o n of about 10 l i t r e s of water, using an L.C.D. stopwatch. Flow rate measurements are estimated to be within ±1.5 percent. - 69 -Table 6.3: Photo-Optical Recording and Analysing Apparatus Camera: 1 . Bolex H-16 medium-speed, variable shutter supplied with extension tubes. Remote control operation. 2. Red Lake Labs Hycam K2054AE, high-speed (1/2.5 shutter) with: - glass r e t i c l e (with cross-hairs) - 30x c r i t i c a l focussing eyepiece Lens: 75 mm, f/1.9 cosmicar. Tripod: Hercules, model 5302 heavy duty. Motion picture analyser: LW International, model 224A photo-optical analyser projector with calibrated viewing screen. - 70 -6.6.2 Visualization experiments The v i s u a l i z a t i o n runs could only be performed when building vibration was reduced. This reduction was achieved after workshop hours and when other pieces of heavy equipment in the building were not operating. Certain preparations for the performance of the v i s u a l i z a t i o n experiments were necessary. 6.6.2.1 Laser beam alignment The laser was turned on and allowed to warm up at least 12 hours before a run. Beam alignment was performed with the laser operating 1 0 8 below 100 mW, recommended for safe operation with respect to skin exposure (Note: Special safety goggles were worn!). For making holograms, i t was determined by t r i a l that the laser should be turned up to at least 200 mW (on blue l i n e ) . Preliminary study indicated that uncontrollable building vibration necessitated the use of high output power which enabled the use of an attendant fast exposure time. 6.4.2.2 Processing Solutions and emulsion pre-treatment The photographic processing solutions were carefully prepared (instructions given in Reference 109) and placed in th e i r respective holding bottles, at room temperature. - 71 -To promote hypersensitivity and also to relieve emulsion stress, the photoplate was immersed in d i s t i l l e d water inside the l i q u i d gate prior the the start of the experiment. This pre-soaking duration (» 1 hour) i s believed to be adequate in ensuring that the emulsion equilibrated with the system before a hologram was made. The procedure described in sub-Section 6.6.1 for the gross flow runs i s essentially the same as that used for the v i s u a l i z a t i o n runs. Precautions exercised in both cases are outlined in the section. The system was allowed to equilibrate for at least 12 hours. The pipeline was checked to ensure that there were no trapped a i r bubbles inside and a hologram of the test surface was made, following the steps l i s t e d in Table 6 A. A moire fringe grid of desired frequency and orientation was generated by means of a controlled micrometer translation of the hologram. The fringe grid which covered the test surface was recorded on 16 mm movie fil m before the flow was started and the instantaneous fringe pattern, observed during flow, was s i m i l a r l y recorded. For observation and analysis of the recorded fringe display, the motion-picture analysis projector (details of the instrument given i n Table 6.3) was used. - 72 -Table 6 A Steps For Making a Hologram Step No. Process So lu t ion Remarks 1 Emulsion Pre-soak D i s t i l l e d Water Agfa-Gevaert (102 mm x 127 mm) g l a s s -backed 10E56-NAH plates suppl ied by New-port Research Corp. Pre-soaked for W -60 minutes. 2 Exposure D i s t i l l e d Water Laser operated on b l u e l i n e ; 1/120 s e c a exposure at 200 mW s e t t i n g . 3 Development Kodak D-19 2-3 min. durat ion (optimum obtained by t r i a l ) ; plate density observable with the aid of a s a f e l i g h t . * Stop Kodak SB-5 15-30 sec . dura t ion . 5 F i x C Kodak rapid f i x e r with hardener 2-3 min. dura t ion . 6 Rinse D i s t i l l e d water 1-2 washes, 5 min. dura t ions . 7 Viewing D i s t i l l e d water Fresh d i s t i l l e d water added fo l lowing r i n s e . Note: A gentle passage of nitrogen was used for ag i ta t ion in steps 3-6, i n c l u s i v e . a L a s e r output-end f i t t e d with a var iab le exposure time m e t a l - l e a f s h u t t e r . b A 7-1/2 W red s a f e l i g h t suppl ied by Sy lvan ia . Af ter 1 min. in the f i x i n g bath, the hologram may be i l luminated to observe the image. - 7 3 -C H A P T E R 7 7 . M E A S U R E D Q U A N T I T I E S AND DATA R E D U C T I O N In this chapter the equations for the gross flow parameters, used to define the flows, are given and an outline of the fringe interpreta-tion and data reduction procedure i s also presented. 7 . 1 Gross flow measurements The volumetric flow rate (Q) and the corresponding pressure drop (AP) over a length (L) of the pipe were measured d i r e c t l y , as described in sub-Section 6 . 6 . 1 . From these two quantities, the following parameters were calculated: ( i ) the Reynolds number based on pipe diameter (Re.), [ 7 . 1 ] ( i i ) the Fanning f r i c t o n factor ( f ) , f = 2 T / P U 2 [ 7 . 2 ] o - 74 ( i i i ) the mean wall shear stress ( T 0)> T Q = 1/4 d [7.3] and, (iv) the f r i c t i o n (shear) velocity (U„), = /T7p [7.4] * o (Error estimates for gross flow quantities are presented in Appendix C). 7.2 Wall-pressure fluctuations measured with the aid of the  holographic interferometric technique I t was necessary to relate the observed fringe distortions to the pressure magnitude which causes the d i s t o r t i o n s . Such a relationship i s shown in Figure D.4 obtained from an interferometric s t a t i c pressure c a l i b r a t i o n of the compliant wall, as described in Appendix D. 7.2.1 Interferogram interpretation The interferogram may be interpreted as a d i s t r i b u t i o n of phase differences which appears as a grid of macroscopic interferometric - 75 -fringes. These fringes, generated prior to flow, are superimposed upon the compliant surface thereby providing a reference (datum) for measuring wall-pressure changes in terms of fringe d i s t o r t i o n s . Figure 7.1 (a) i s a sketch of the reference state ( i . e . prior to flow). The deviations from straight lines (observed during flow), sketched in Figure 7.1 (b), provide a measure of the pressure associated with the change at the surface and also give an indication of the direction of change. 7.2.2 Data reduction The amplitude of fringe distortions was measured and used in conjunction with the amplitude of fringe d i s t o r t i o n versus pressure plot. Measurements were made from consecutive interferograms (movie frames) projected on a screen frame-by-frame (see Appendix E). Knowledge of the photographic framing rate and the s p a t i a l scale, of the framed area, enabled further determination of spatial and temporal characteristics of the wall-pressure fluctuations. - 76 -5 4 3 2 1 f : fringe spacing F i g u r e 7 . 2 ( a ) : Reference s t a t e showing base f r i n g e p a t t e r n . F igu re 7 . 2 ( b ) : F r inge d i s t o r t i o n s dur ing f l o w . Flow direction - 77 -CHAPTER 8 8. EXPERIMENTAL RESULTS AND DISCUSSION The r e s u l t s of the main v i s u a l i z a t i o n study and a u x i l i a r y exper iments are presented and d i scussed h e r e i n . 8.1 Gross flow results Gross f low runs were performed to check the f low system. The c a l c u l a t e d parameters — f r i c t i o n f a c t o r ( f ) and Reynolds number ( R e ^ ) , from the present s tudy , are p l o t t e d along wi th those of Ach ia i n F i gu re 8 . 1 . The graph shows reasonable agreement between the two se t s of data which f o l l o w the Newtonian tu rbu len t f low smooth-tube l i n e desc r i bed by the equat ion [see e . g . Knudsen and K a t z 1 1 0 or K a y s 1 1 1 ] , f = 0.046 Re ~ 0 , 2 [8 .1 ] d 8.2 Hologram experiments The main f a c t o r s of concern i n making holograms were: ( i ) the exposure t ime, and ( i i ) the emulsion development t ime . (x1(T 3) 1 T" 10 9 8 7 6 f Re. O • 4 — Q 6 f =0.046 R e d - 0 - 2 O Achia's A The present study 2 "3 4 t 6 7 3 3 10 15 R e d ( x l 0 - 3 ) Figure 8.1: Fanning f r i c t i o n factor - Reynolds number plot 20 - 79 -These two factors control the (optical) density d i s t r i b u t i o n of the photoplate and thus the fringe contrast. A trial-and-error approach was used to determine the emulsion exposure and subsequent development duration which enabled the use of a f a i r l y wide range of reference-object beam ratio for making suitable holograms. A R/0 r a t i o of about 5:1 up to 10:1 was found to be satisfactory in t h i s work. 8.3 Visualization results The flow conditions for the v i s u a l i z a t i o n runs are l i s t e d in Table 8.1. These runs were i n i t i a l l y planned to cover the range of Achia's study to enable some comparison with his results. Only the movie for the run at Re^ = 12,300 was f u l l y analysed and the results are presented in th i s chapter. At 7,500 _< Re^ < 12,300 fringe distortions were not pronounced. It i s believed that the associated pressure changes in this flow range did not induce adequate response of the compliant material. [The use of two other compliant surfaces of the same material, but of thicknesses k mm and 6 mm, did not show any noticeable change in the degree of fringe d i s t o r t i o n s ] . In the case of flows at Re^ > 12,500, flow induced vibrations resulted in considerable fringe movement. The fringes were also observed, on occasion, to lose v i s i b i l i t y . There i s a strong suspicion that the severe reduction i n v i s i b i l i t y may be due to wall-pressure changes beyond the tolerance of the present interferometer. Table 8.1: Flow Conditions for Visualization Runs Fluid Reynolds Number (Red) Friction Factor (f) Flow Rate (Q x 106) Bulk Velocity (U) Friction Velocity (U») Pressure Drop (AP) (AP/L)x103 Distilled water (at 20° C, v*1.0x10-V) sec 7,500 0.0079 (m3/sec) (m/sec) (m/sec) (mm H20/3.05m of pipe) (K Pascal/m) 155.0* 0.29 0.018 15.65 50.33 12,300 0.0072 254.27 0.47 0.028 37.88 121.82 15,000 0.0068 310.08 0.57 0.033 52.61 169.19 a> o - 81 -8.3.1 Observation of the pressure changes at the pipe wall An actual interferogram of the test surface i s shown in Figure 8.2 (a). With flow in the pipe, the base fringes were f i r s t seen to move about their i n i t i a l position in a "rocking" mode showing only s l i g h t distortions in the upstream di r e c t i o n . More pronounced and larger d i s t o r t i o n s then appeared along with the small d i s t o r t i o n s . The presence of small scale distortions of varying sizes, appearing as " j i t t e r s " (or serrations), i s cha r a c t e r i s t i c of the instantaneous wall-pressure changes observed. A value as low as 0.40 mm in the transverse (Z) direction was obtained for the smallest size j i t t e r s observed. This value provides a measure of the minimum resolution of the compliant wall. Large fringe distortions (in the upstream direction) of varying amplitude appeared near the bottom of the frames (interferograms) [see Figure 8.2 (b)]. In the same frames, prominent medium-size fringe distortions (in the downstream d i r e c t i o n ) , whose amplitude also changed with time appeared near the top. The timewise changes in the amplitude of the fringe distortions recorded were converted to instantaneous pressure changes and are presented in the next section. 8.3.2 Measured wall-pressure fluctuations Details of the interferogram-evaluation procedure are given in Appendix E. The approach used i s somewhat similar to that of - 82 -F igu re 8 . 2 ( a ) : In ter ferogram recorded at no f low ( i . e . i n i t i a l s t a t e ) . z o y Flow direction F i g u r e 8 . 2 ( b ) : In ter ferogram ex t rac ted from a f low sequence ( R e d * 12 ,300) . - 83 -Glassman.0-5 The reference (base) fringes were a r b i t r a r i l y numbered from right to l e f t (the flow d i r e c t i o n ) . The results presented are of measurements made from consecutive interferograms selected from a sequence. A frequency histogram of the wall-pressure changes i s presented in Figure 8.3. The pressure d i s t r i b u t i o n i s skewed to the l e f t (skewness = -0.29) indicating that more events occur with high amplitude and negative sign than with high amplitude and positive sign. 8.3.3 Temporal variation of the wall-pressure The instantaneous pressure changes at the pipe wall are presented in Figures 8.4 and 8.5 as spatio-temporal plots. These plots are constructed from measurements made at the fringe locations indicated thereon. [Fringe spacing - 5 mm in the x- d i r e c t i o n ] . A study of the pressure patterns of the positive pressures [Figure 8.4] reveals d i s t i n c t phases which bear higher pressure values, on an average, than in other frames. A similar random appearance of higher magnitude pressure phases i s also evident in the patterns of the negative wall-pressure changes [Figure 8.5]. Although in some instances (frames 7, 9, 13, 16, 23) higher positive pressures are seen to occur at the same time with higher magnitude negative pressures, t h i s coincidence was not always true (see e.g. frames 10, 26, 47). Skewness : -0-29 Kurtosis : -1-12 120 + 100 tv JO E 80+ 60+ 40 20 -16 -14 -12 -10 -8 -6 Pressure (ubar) Figure 8.3: Frequency histogram of wall-pressure fluctuations. F i g u r e 8 . 4 : S p a t i o - t e m p o r a l d i s t r i b u t i o n o f p o s i t i v e w a l l - p r e s s u r e c h a n g e s (U = 0 . 4 7 m / s e c : t ime between f rames = 0 . 0 1 6 s e c ) . - 88 -- 89 -8.3.4 Instantaneous wall-pressure fluctuations about the mean Measurements of the amplitude of fringe distortions at each fringe location were standardized (see Appendix K). The time average fringe d i s t o r t i o n at each location was determined. In each case, the respective mean value was subtracted from the instantaneous and the result converted to the corresponding pressure. These values, plotted in Figures 8.6 and 8.7, are actually wall-pressure fluctuations about the mean. Figure 8.6 shows quite cl e a r l y under-pressure (see frames 1-3) and over-pressure (e.g. frames 8, 10), as well as under- and over-pressure (e.g. frames 11, 12) phases. In Figure 8.7, over-pressure (e.g. frames 9, 10), under- and over-pressure (e.g. frames 16, 17) and under-pressure (e.g. frames 49, 50) phases are also evident. A s t a t i s t i c a l evaluation (see Appendix G) of over 60 consecutive frames reveals a mean time interva l of 0.16 sec. between the appearance of prominent over-pressure regions of the positive wall-pressure changes. For the negative wall-pressure changes, the mean time interva l between prominent under-pressure regions i s 0.21 sec. 8.4- Discussion of results The vast majority of publications on wall-pressure measurements that have appeared are of mean values. As a resu l t , only a limited comparison can be made between the present results and those of other investigators. - 90 -Flow direction '1 m m P 1 1 1 H 4 3 2 1 Fringe number 10 bar] 5 Q) - 0 sur -5 w o --lo- CL - 91 @ " 7 ^ X X I @ " ^ 60) •^7 V" - X — . Ficn.re 8 6- Instantaneous wall-pressure fluctuations F lgu.e 8.6. 1 ^ ^ ^ [ p o s U l v c p r e s s u r e changes] - 92 -- 9k -The negative skewness of the wall-pressure d i s t r i b u t i o n [Figure 8.3] i s consistent with the trend depicted by the data reported by Din k e l a c k e r . 1 1 2 I t i s shown that the t h i r d moment (skewness) of wall-pressure fluctuations, measured by means of electro-mechanical pressure transducers, becomes negative as transducer diameter decreases. This finding i s evidence that the present device provides adequate sp a t i a l resolution. It may be of interest to note that the pressure patterns of the present study bear some resemblance to the wall-pressure f i e l d associated with a turbulent spot, obtained in a recent study by Mautner and Van A t t a . 1 1 ^ These authors state that the wall-pressure signature of a turbulent spot consists of positive-pressure regions and a central negative-pressure region. In his model of boundary layer turbulence, B l a c k 1 ^ asserted that the wall-pressure f i e l d comprises a positive pressure region and a negative pressure region. The present results offer support to the ideas of Black, but i s inconsistent with the results reported by Emmerling. The l a t t e r observed the occurrrence of both positive and negative pressure fluctuations in the same region. The photographs obtained in the present study show quite c l e a r l y a region of positive pressures and a region of negative pressures. The longer time interva l (0.21 sec) between the appearance of under-pressure regions (characteristic of the negative wall-pressure changes) compared to that (0.16 sec) of the over-pressure regions of the positive - 95 -pressures suggests that the former effects may be due to events occurring at some distance from the wall. This belief i s in accord with the findings of others (e.g. B u l l 6 ^ and Dinkelacker et a l . 6 7 ) . Achia estimated that the time interva l between wall-layer bursts in water (Re^ - 11,000) was 0.14 sec. This value shows a remarkable agreement with the time interva l between what appears to be prominent random over-pressure regions of the positive wall-pressure changes in this study. Such an agreement implies some connection between the two events. This idea i s not new. Einstein and L i ^ , based on their theory, pointed out that the periodicity of the flow structure in the wall layer should be reflected in the wall-pressure. In order to explore the believed relationship, the following analysis was made. According to Rao et al the mean burst period scales with outer flow parameters (U m and 6) as By replacing U by pipe bulk velocity (U) and 6 by pipe radius (r ) and oo o substituting the values from the present study, Equation [8.1 (a)] gives * 5 [8.1 (a)] -^=5.7 r o [8.1 (b)] using Achia's values, TU/r = 4.5 i s obtained. - 96 -The above results seem to suggest that the time interval between wall layer bursts (from Achia) and the prominent over-pressure regions of the positive wall-pressure changes both scale with outer parameters. This result would lend credence to the prevailing idea of an interaction between the wall layer and the outer flow (core region) with regards to bursting. In fact , Emmerling came to this conclusion. However, B l a c k 1 a l s o showed that based on wall parameters (U* and v) the following relationship holds, = 116 [8.2] Using Achia's data, Equation [8.2] gives a value of 87.5 compared to 125.4 obtained for the present data. (It is of interest to note that upon substitution of Emmerling's data into Equation [8.2], TU*/v = 112 resul ts ) . The result of the foregoing analysis (see Table 8.2) does not seem to favour one set of scaling parameters over the other. Consequently, the actual scaling is an open question. Nevertheless, i t appears as i f the bursting occurrences, observed by Achia, are related to the generation of the wall-pressure changes of this study. The actual connection, however, remains to be determined. There is therefore a definite need for more work in this area. In order to ascertain the believed association between the generation of wall-pressure fluctuations and. bursting, a visual izat ion Table 8.2: Summary of the Analysis Investigation Experimental Details T + _ TU*2 V Reference 35 Distilled water, 0.026 m ID pipe (Red * 11,000) U = 0.42 m/sec [wall-layer bursts] C f - TR Uco 6 - 5 (Rao et al ) = 116 (Black) 4.5 87.5 The present study Distilled water, 0.026 m ID pipe, (Red * 12,300) U = 0.47 m/sec [pressure fluctu-ations] 5.7 125.4 - 98 -approach which w i l l permit simultaneous observation of the development of wall-pressure fluctuations and wall layer bursting should be considered. The results from such a study might also reveal the physical process(es) responsible for the negative and positive wall-pressure changes observed in this study. Such an investigation has the potential of providing much needed information to improve the present understanding of wall turbulence. 8 . 4 . 1 Measurement accuracy Considerations of the measurement accuracy include: ( i ) the effect of wall shear stress ( i i ) movement of the fringes, resulting from vibration and a i r currents in the room, and ( i i i ) error in measuring fringe distortions Point ( i ) ; An estimate of the effect of the wall shear stress (see Appendix F) indicates that the displacement caused by wall shear i s negligible. Point ( i i ) : Vibration and a i r current effects cause some fringe movement but do not cause fringe d i s t o r t i o n . Fringe movement at the flow analysed was i n s i g n i f i c a n t compared to the degree of fringe d i s t o r t i o n observed. - 99 -Point ( i i i ) ; The amplitude of fringe distortions was measured with an accuracy of ± 0.5 mm. 8.4.2 A few words on the present technique Although quantitative data were not obtained over a range of Reynolds number, the technique served its intended purpose. Despite the present laborious data-reduction procedure, this device provides a useful basis for qualitative and quantitative study of the structure and behaviour of the turbulent wall-pressure field. - 100 -CHAPTER 9 9. SUGGESTED FLOW MODEL AND THE PRACTICAL IMPLICATIONS The present model i s based on the pressure patterns observed in th i s study, the contributions of other workers in the area and current knowledge of bounded-flow dynamics. 9.1 Proposed flow model I t i s well-established that turbulence generation and maintenance take place in the wall region v i a the bursting process. The present model aims to provide a physical picture to explain certain aspects of bursting. The negative wall-pressure fluctuations are believed to be due to suction created by vortices in the outer flow region, consistent with the postulate of Nychas et a l . I t i s suspected that vortex suction induces lifting-up of low-speed f l u i d elements from the wall [see Figure 9.1, taken from the bursting sequence sketched by Corino and Brodkey, and Figure 9.2 from Achia and Thompson^ 6]. When a l i f t e d f l u i d tongue [a term used by L e v i ^ 7 ] reaches some c r i t i c a l distance from the wall, eddies are believed to form downstream in i t s wake — probably in accordance with the ideas of Levi. Oldaker and Tiederman^7 reported that essentially no streamwise v o r t i c i t y was observed, in their study, u n t i l a streak l i f t e d from the - 101 -Figure 9.1: Lift ing-up phase of bursting [Taken from Corino and Brodkey8] - 102 -Figure 9.2: Photographs of l i f t i n g f l u i d elements [From Achia and Thompson^^] - 103 -wal l . I t i s the motion of these eddies that presumably cause the o s c i l l a t o r y motion of the low-speed streaks observed by Kline and his co-workers, and others. The violent break-up stage of bursting i s possibly due to the destruction of the eddies formed by the low-speed "tongues" and the faster flow in the outer region. Fl u i d i s returned to the wall via the "sweep" event, described by Corino and Brodkey, as a consequence of continuity. 9.2 Practical implications There i s widespread interest i n predicting and con t r o l l i n g the rate at which p a r t i c l e s , suspended in a flowing l i q u i d , deposit on conduit walls. Such knowledge i s of great importance in understanding fouling in heat exchangers and reverse osmosis membranes, contamination of nuclear power f a c i l i t i e s and thrombus formation in vascular prostheses or other a r t i f i c i a l organs. Cleaver and Y a t e s ^ ^ developed a model for deposition of p a r t i c l e s , from a turbulent flow, based on the idea that p a r t i c l e s are convected to the wall by the "downsweep" phases of the bursting process. Their model removes several objections of previous theories,119-121 which were based on the concept of " f r e e - f l i g h t " of p a r t i c l e s across the viscous sublayer, and allows a satisfactory prediction of deposition rate. - 104 -The problem of p a r t i c l e removal has received less attention. Cleaver and Y a t e s ^ 2 2 ' 1 2 3 a ^ s o linked p a r t i c l e removal with the bursting occurrence. Their theory adequately describes certain aspects of removal but the detachment mechanism remains unclear. In addition to postulating a detachment mechanism, these authors considered the effect of re-entrainment^ 2 3 on p a r t i c l e deposition. They argued that the l i f t force generated by f l u i d shear i s incapable of dislodging p a r t i c l e s from a f l a t surface. Consequently, they feel that re-entrainment occurs as a result of wall-layer bursts. The finding of 1 ?u Bowen "-^  that no re-entrainment occurs under laminar flow conditions offers some support to the Cleaver and Yates hypothesis. A similar reasoning has been used by CJacksonl 2^ t o explain the entrainment of large sedimentary particles in deep a l l u v i a l flows, by Sumer and Oguz^ 2 6 for p a r t i c l e suspension close to a wall and also by E p s t e i n ^ 2 7 in the case of deposit removal in heat exchanger fouling. To understand the effect of re-entrainment on p a r t i c l e deposition rate, Cleaver and Yates further proposed that a minimum shear velocity (U*) must be attained before any re-entrainment w i l l occur. A model^ 2, resulting from Emmerling's work, has been recently proposed. This model i s based on the generation of "tornado-like" vortices which are somewhat similar to Theodorsen's "horse-shoe" v o r t i c e s ^ 2 8 . I t i s suggested that i f the limbs of a distorted vortex contact the surface they w i l l act l i k e miniature tornadoes to suck up any matter present thereon. - 105 -The pressure pa t te rns observed i n the present study suggest a d i f f e r e n t mechanism fo r p a r t i c l e removal from a w a l l . The negat ive w a l l - p r e s s u r e f l u c t u a t i o n s , p o s s i b l y due to vor tex s u c t i o n , cou ld conce i vab l y induce an updra f t which e f f e c t s l oosen ing of p a r t i c l e s . These p a r t i c l e s may then be e x p e l l e d from the w a l l r e g i o n , i n sympathy wi th a b u r s t , when the c r i t i c a l shear v e l o c i t y of a g iven p a r t i c l e - f l u i d system i s exceeded. - 106 -CHAPTER 1 0 1 0 . CONCLUSIONS AND RECOMMENDATIONS 1 0 . 1 Conclusions The present technique permits v i s u a l i z a t i o n and measurement of turbulent wall-pressure fluctuations. Using t h i s device a study of the structure and behaviour of the pressure f i e l d at the pipe wall i s made possible. Analysis of the pressure patterns provides insight into the causation of some features known to be characteristic of wall-bounded flows. Based on the results of thi s study, the following main conclusions are drawn: 1. The wall-pressure f i e l d i s characterized by a region of positive pressures and a region of negative pressures. 2. The wall-pressure d i s t r i b u t i o n shows an asymmetry (negative skewness). 3. A relationship exists between the generation of the positive wall-pressure fluctuations and known wall-layer c h a r a c t e r i s t i c s . - 107 -10.2 Recommendations The following recommendations are suggested for future study: 1. An effort should be made to improve the present manual interferogram-evaluation technique. The p o s s i b i l i t y of incorporating a semi-automatic data-reduction technique, such as the one described in Reference 129, might be explored. 2. The design of an experimental arrangement which would allow observation of bursting at the wall and, at the same time, the instantaneous wall-pressure development should be considered. - 108 -11. NOMENCLATURE amplitude d i s t r i b u t i o n A cross-sectional area (m ) V A R amplitude modulus A t amplitude transmittance AN area of nozzle (m ) b intercept on ordinate in Figure 5.2 d pipe diameter (m) dN diameter of nozzle (m) E Exposure (u3/m ) E modulus of e l a s t i c i t y [Young's modulus] (N/m2) f s p a t i a l frequency in Equation [6.1] (lines/mm) f frequency in Figure H.1 (HZ) f frequency of events in table G.1 f Fanning f r i c t i o n factor F y force acting in y- direction (N) F s shearing force (N) G shear modulus [modulus of r i g i d i t y ] (N/m2) h nozzle-to-surface distance (mm) i , k integers (or constants) - 109 -K reciprocal of s e n s i t i v i t y in Equation A.1 (Kg/mm) k constant K Bulk modulus [reciprocal of compressibility] (N/m2) ^x^y'^z dimensions in the x-, y- and z directions (mm) L length of pipe (m) rrn c e l l mid-points in Equation [G.1] m,n, n, N constants 0 object (beam) wavefront p,po pressure (ybar) /~^2 root-mean-square pressure (N/m2) P w perimeter of wall (m) AP pressure drop (mm of water) AP/L pressure drop per unit length of pipe (K Pascal/m) q O T dynamic pressure of flow (N/m ) flow rate of nozzle assembly (m /sec) Q pipe flow rate (m /sec) r^ nozzle radius (m) r pipe radius (m) o R reference beam R1 reconstruction beam - 110 -Re^ Reynolds number based on pipe diameter 5 area of compliant wall exposed to the flow (m ) t time (sec) t . i n i t i a l time (sec) 1 T tension in Equation (F.1] (N/m) T mean time interva l in Equation [8.1 (b)] (sec) Tg mean time between bursts (sec) exposure time (sec) + T dimensionless time U M boundary layer freestream velocity (m/sec) U bulk pipe velocity (m/sec) ,U f r i c t i o n (shear) velocity (m/sec) U c convection velocity (m/sec) v nozzle velocity (m/sec) q V volume of l i q u i d (m ) Greek Letters a angle of i n c l i n a t i o n (in Appendix F) (degrees) 3 slope of A vs E plot (m2/y0) 6 boundary layer thickness (mm) A error (or change) in a quantity 6 twice angle between R & 0 beam (degrees) K slope of load vs extension plot (Kg/mm) - 111 -A wavelength (nm) u micro- (= 10"6) v v i s c o s i t y (kg/m-sec) T 180° P > P [ _ » P M density (kg/m ) a standard deviation o variance £ sum of T Q mean wall shear stress (N/m ) <j> phase of wavefront i> transmitted wave phase angle Superscripts/Subscripts + made non-dimensional A assembly c convection d based on diameter D deformation i i n i t i a l I l i q u i d M material N nozzle 0 object - 112 -R reference s s t a t i c , shearing t transmittance w wall x,y,z co-ordinate directions T shear ( f r i c t i o n ) - 113 -12. 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S t e i d e l , R.F., Introduction to Mechanical Vibrations, 2nd ed., Wiley (1979). 144. Halliday, D., and Resnick, R., Physics, parts I & I I , Wiley (1960). 145. C o l l i e r , R.O., Burckhardt, C.B., and L i n , L.H., Optical  Holography, Academic Press (1971). - 121 -13. APPENDICES - 122 -APPENDIX A A.1 The compliant pipe (wall) surface A.1.1 Formation of the compliant surface 0.02 kg. of the Dow Corning 721-silicone rubber compound was k 3 completely dissolved in 10" m of the solvent Varsol. The resulting clear mixture was poured into a cavity that was machined in the f l a t piece wall of the Plexiglas pipe section (see Figure A.1). The mixture was allowed to set at room temperature and formed a smooth uniform transparent layer (2.0 mm x 12.7 mm x 263.5 mm) bonded to the r i g i d substrate. A mix of the same consistency was poured into a specially made Teflon mould to produce a s t r i p of the same dimensions as the wall layer. This s t r i p was used to determine the mechanical and physical properties of the material. A.2 Determination of the moduli of Elasticity  and Rigidity of the material The rubber s t r i p was fixed at one end (see Figure A.2) and known weights were attached, in turn, to i t s lower free end. The extension of the material was measured by means of a telescope cathetometer and the results plotted in Figure A.3. 2 6 9 mm-F igure A .1: F l a t - p i e c e of t e s t s e c t i o n . - 1 2 4 -t t t t.t t.t A t ' ' ' ' ' L it w Figure A.2: Arrangement for the determination of the Young's modulus of the rubber s t r ip . Extension, &2 (mm) F igure A.3: Load vs ex tens ion p l o t . - 126 -From the slope (K) of the load-extension graph, the modulus of e l a s t i c i t y (E) of the rubber was obtained as E a [A.1] where: &x = length of rubber s t r i p in streamwise direction (m) A = cross-sectional area of the rubber s t r i p (m ). For an isotropic e l a s t i c material the Young's (E), shear* (G) and bulk (K) moduli are related by the equation130 G ~ [1 + G/3K] [A.2] For a soft s o l i d G«K, so that the term G/3K-H) and Equation [A.2] reduces to, G = 1/3 E [A.3] Table A.1 Important Mechnical and Physical Properties of the Rubber Material E (N/m2) G (N/m2) K[= s e n s i t i v i t y " 1 ] (kg/mm) PM (kg/m3) 6.13 x 105 2.04 x 10 5 6.02 x 10" 3 920 *Also called modulus of r i g i d i t y . - 127 -Table A . 2 : Load-ex tens ion Data X Y X 2 XY 0 .3 2.0 0.09 0.6 0.6 4 .0 0.36 2.4 1.0 6.0 1.0 6.0 1.3 8.0 1.69 10.4 1.7 10.0 2.89 17.0 2 .0 12.0 4 .0 24.0 E 10.03 60.4 Y = 6.02 X (Regress ion through the o r i g i n ) - 128 -APPENDIX B Calibration of the differential pressure transducer A schematic of the flow pressure drop (AP) measuring system i s given in Figure B.1. The system was checked against the s t a t i c c a l i b r a t i o n plot (Figure B.2), prior to each run, by the following procedure: 1. Close valves 1 and 2 which connect the system to the pipeline. Open valves 3 and k to connect water manometer across the pressure transducer. Ensure balance in water columns. 2. Switch on power source* for the pressure transducer and set at 5-V. 3. Switch on recorder, turn to STANDBY mode and select desired span and chart speed. k. Turn recorder control to PEN, short recorder terminals and use ZERO control knob for mechanical zeroing. 5. Remove short and connect transducer leads. 6. Use resistance bridge control for fine zero adjustment, i f necessary. 7. Adjust manometer to create a known AP (mm of water) across the transducer and note the corresponding recorder respone. 8. Repeat step 7 for 3 or 4 different AP values and compare with o r i g i n a l c a l i b r a t i o n plot, obtained by a similar procedure. *Anatek model 50-1S, manufactured by Anatek Electronics Ltd. - 129 -water » manometer p r e s s u r e t r a n s d u c e r b r i d g e r e s i s t o r r e c o r d e r F igu re B.1: P ressu re drop measurement set Pressure drop (mm of water) Figure B.2: Static pressure drop c a l i b r a t i o n plot. - 131 - • Table B . 1 : P ressu re Drop Data X Y XY X 2 5.0 0.05 0.25 25 10.0 0.112 1.12 100 15.0 0.190 2.85 225 22.0 0.275 5.05 484 27.0 0.330 8.91 729 32.0 0.390 12.48 1024 36.0 0.444 15.984 1296 40 .0 0.500 20.0 1600 46.0 0.570 22.22 2116 53.0 0.670 35.51 2809 59.0 0.740 43.66 3481 66.0 0.824 54.384 4356 Z 411.0 5.095 227.418 18245 N = 12; X = 34 .25 ; Y = 0.42 Y = 0.013 X - 0.015 - 132 -APPENDIX C Error Analysis; Gross-flow Quantities Flow rate (Q) Error calculations are based on a flow Re. = 10,000. d About 10 l i t r e s of water were collected during a run. The volume of water was measured (accuracy ± 5 ml) by means of a graduated cylinder of rated capacity 1000 ml. The accuracy of timing the c o l l e c t i o n of water, based on the operator's response to start and stop the clock, i s estimated to be about ±0.4 sec. At Re d « 10,000 (Q « 225 x 10" 6 m 3/sec), the error in Q (= V/t) i s calculated according to A Q = A V + V ( A t ) [ c > 1 ] where the positive sign i s used in order to obtain the maximum error.* Hence AQ = 3.15 x 10 nrr/sec which i s equivalent to an error in Q of 1.40%. A similar approach was used to estimate the error in the other quantities. [The physical properties (p,v) of the water were assumed constant — negligible temperature change during a run]. Error estimates are l i s t e d in Table C.1. *See References 131, 132. - 133 -Table C.1: Error Estimates of Gross Flow Quantities Quantity Symbol Percent Error Flow rate Q ± 1.4 Pressure drop AP ± 2.0 Bulk velocity U ± 2.0 Reynolds number Re . d ±3.0 F r i c t i o n factor f ±5.0 Mean wall shear stress T 0 ± 3.5 F r i c t i o n (shear) velocity u * ± 1.8 - 134 -APPENDIX D Interferometric static pressure calibration  of the compliant surface One end of a 0.12 m long glass tubing (3-mm bore) was car e f u l l y drawn out to form a conical nozzle, 1 mm ID (see Figure D.1). A variable speed syringe pump (details of operation in Table D.1), connected to the other end of the glass tubing, was used to calibrate the nozzle assembly. The system flow rate (Q.) was determined by timing the c o l l e c t i o n A of a known quantity of water. Three such measurements were made at each pump setting and a mean value calculated. (Figure D.2 i s a plot of flow rate versus pump setting). As shown in Figure D.3, the nozzle was f i t t e d inside the Plexiglas test section so that i t s t i p was positioned normal to the compliant wall at a h = 2r^. A nozzle-to-surface distance which gives h/r^ >_ 1.0 i s recommended by Scholtz and T r a s s ^ ^ for no induced external flow and negligible jet spreading. I t has been shown^^ that with such an arrangement, the t o t a l a x i a l jet pressure i s constant and i s equal to the stagnation pressure. - 135 -Figure D.1: Schematic of the conical nozzle. -, 136 -Table D.1 Pump Characteristics Type Operation Details Sage model 355 Flow rate fixed by syringe syringe pump with size and combined settings 50 ml B-D p l a s t i c of flow rate d i a l and range syringe. switch located on face of pump. A range setting of x 1/10 was used i n t h i s study. O 20 40 60 80 Pump Setting (% ) F igure D.2: Nozzle-assembly c a l i b r a t i o n p l o t . - 138 -test section Figure D.3: Schematic of nozzle-surface arrangement. - 139 -D.1 Pressure calibration D.1.1 Experimental procedure The pipe section and the nozzle assembly were f i l l e d with d i s t i l l e d water and the set-up allowed to equilibrate. After about eight hours, a hologram of the surface was made and a base fringe pattern of the same orientation and spacing, as before, was generated and photographed. Upon operation of the submerged j e t , a fringe d i s t o r t i o n was observed at the point of application. The fringe pattern was again photographed. The procedure was repeated at pre-determined pump settings and the corresponding flow rates were noted. D.2 Relationship between amplitude of fringe  distortion and applied pressure From the flow rate of the nozzle assembly (Q.), the nozzle A v e l o c i t y was calculated v N = QA/AN [D.1] By applying a mechanical energy balance (Bernoulli's equation) between the t i p of the nozzle and the surface (where the velocity at - .140 -impingement = 0 (stagnation poi n t ) ] , the stagnation pressure i s obtained by P s = 1/2 Pv^ [D.2] For each pump setting (or Q^), and, thus p g, was calculated. The amplitude of fringe d i s t o r t i o n , due to jet impingement, was obtained by the procedure outlined in Appendix E. A graph of amplitude of fringe d i s t o r t i o n versus applied pressure (Figure D.4) was constructed. (Pressure s e n s i t i v i t y of the technique i s 3.3 ybar/mm). F i g u r e 0.4: R e l a t i o n s h i p between f r i n g e d i s t o r t i o n and a p p l i e d p r e s s u r e . Applied Pressure (ybar) - 142 -Table D.2: Summarized Static Pressure Calibration Data Q A[x 10 6] (m3/sec) P s (ybar) Amplitude of Fringe Distortion (mm) 0.013 1.45 0.50 0.022 3.92 1.25 0.028 6.48 2.00 0.033 8.82 2.75 0.038 11.72 3.50 0.044 15.68 4.70 - 143 -Table D.3: Nozzle-Assembly Calibration Data X Y XY X 2 10 0.013 0.13 100 20 0.028 0.56 400 40 0.055 2.2 1600 60 0.080 4.8 3600 80 0.11 8.8 6400 E 210 0.286 16.49 12100 N = 5 ; X = 4 2 ; Y = 0.057 Y = 0.0014 X - 0.0018 - 144 -Table D.4: S t a t i c P ressure Regress ion A n a l y s i s X Y X 2 XY 1.45 0.50 2.10 0.73 3.92 1.25 15.37 4.90 6.48 2.00 41.99 12.96 8.82 2.75 77.79 24.26 11 .72 3.50 137.36 41.02 15.68 4.70 245.86 73.70 Z 520.47 157.57 Y = 0.30 X (Regress ion through the o r i g i n ) - 145 -APPENDIX E Interferogram-evaulation technique An interferogram of the i n i t i a l state ( i . e . before pipe flow or j e t impingement of the surface) was projected* for viewing. The straight l i n e (base) fringes were traced onto a graduated screen. Each interferogram recorded during flow [or from the jet impingement (calibration) experiments] was projected on the same screen. From the superimposition of an interferogram recorded of the surface change upon the trace of the base (reference) fringes, the dis t o r t i o n s were observed as departures from the straight lines of reference (see Figure E . 1 ) . The projector was operated in the single frame mode to enable measurements of the fringe distortions on each frame. Fringe d i s t o r t i o n s were measured as fractions of the fringe spacing. *See Table 6.3 for d e t a i l s of the analysing projector. - 146 -5 4 3 2 1 — borders of base fringes 1,2,5 shown as broken lines ( ) Figure E-1(a): Departures from straight lines (base fringes) observed upon superimposition of an interferogram from the flow sequence. y——amplitude of downstream distortion X amplitude of upstream distortion Figure E .1(b): One fringe isolated to show upstream and downstream departures from the straight l i n e of a base fringe. - 147 -APPENDIX F Estimation of the effect of wall shear on the  deformation of the compliant surface The deformation ( y n ) , of the compliant wall due to the pressure exerted by the turbulent flow, may be described by ( P s H x y D = ~ p - f — [ F . D where: .2' p = pressure (N/m ) S = exposed area of compliant wall (m ) &x = length of compliant wall in streamwise direction (m) P^ = perimeter of compliant wall (m) T = force per unit length of compliant wall (N/m) By making a s t a t i c force balance normal to the compliant wall, the angle of i n c l i n a t i o n (a) between the compliant wall and the r i g i d Plexiglas substrate (see Figure F.1) i s obtained: - 148 -FLOW DIRECTION < Figure F.1: Forces acting on the compliant wall surface. - H 9 -EF y = 0: T(sin a) P w = PS [F.2] or, sin a = J2| [F.3(a)] W Combining Equations [F.1] and [F.3 ( a ) ] , sin a = y D/£ x [F.3(b)] Therefore, for a maximum deformation Equation [F.3 (b)] yields a = 0.4° -- the maximum i n c l i n a t i o n angle. By replacing p in Equation [F.3 (a)] by the r.m.s pressure, ( D 2 ) ' S sin ex = ( p > [F.3(c)] W According to the l i t e r a t u r e (see e.g. Table 2.1), ( P 2 ) 1 7 2 - 3T Q [FA] - 150 -Equations [F.3 (c)] and [F.4] may be combined to give, 3T S sin a = — ° - [F.3(d)] The shear stress at the wall exerts a shearing force (F g) upon the compliant wall. F g causes an increase in the tension of the material where i t i s bonded to the Plexiglas substrate upstream and a corresponding decrease where i t i s bonded downstream. In the worst case, the increase in tension i s F T (SL St, ) I % ° z x x A change in tension changes the deformation by, A yD = ± yD [F.5(a)] Equations [F.3 (d)], [F.4] and [F.5(a)] give . 2 Ay D = ( £ x + £ z ) v D sin a = 9 ym. I 3& X and thus can be considered negligible. - 151 -APPENDIX G Analysis of the patterns of wall-pressure fluctuations about the mean From the observed events a histogram was constructed in each case. [Data l i s t e d i n Tables G.1 and G.2]. The mean time interval between the appearance of the prominent over- or under-pressure regions was calculated as follows, and thus the standard deviation (a) was also calculated. It would seem reasonable to expect a relationship between streak l i f e - t i m e (Achia's study) and the persistence of the pressure patterns of this study. However, Achia's estimate of streak l i f e - t i m e (=0.1 sec) i s an order of magnitude lower than the time of persistence (=1 sec) of the pressure patterns observed in the present study (at about the same Reynolds number). Achia's analysis, however, i s based on an auto correlation at a single point whereas the present treatment involves observations at several points. Further work to ascertain the connection between the two events i s suggested. k [G.1] The variance, approximated by, - 152 -(A C > H - 2 o JQ E 3 0-1 0-2 0-3 Interval between events (s) 0-4 Figure G.1: Histogram of the appearance of the prominent over-pressure regions (Positive wall-pressure changes). , - 153 -The 95% confidence l i m i t s are: T ± 1.96 o//N Table G.1: Frequency Table C e l l Mid-Points (m.) C e l l Events (f.) f .m. l l f .m. l l 0.05 4 0.20 0.0099 0.15 3 0.45 0.068 0.25 1 0.25 0.063 0.35 2 0.70 0.25 Total 10 1.60 0.39 a = 0.12 T = 0.16 ± 0.03 sec - 154, -to *•> c 0) > «•- o I O 4) .O E 3 z 0-1 0-2 0-3 Interval between events (s) 0-4 Figure G.2: Histogram of the appearance of the prominent under-pressure regions (Negative wall-pressure changes). - 155 -Table G.2: Frequency Table A l l Mid-points On.) 1 C e l l Events < v f .m. l I f .m.2 l l 0.05 2 0.10 0.005 0.15 2 0.30 0.045 0.25 3 0.75 0.19 0.35 2 0.70 0.25 Total: 9 1.85 0.49 The 95% confidence l i m i t s are: T = 0.21 ± 0.03 sec. - 156 -APPENDIX H Dynamic Calibration of the compliant wall Dynamic c a l i b r a t i o n serves to determine the frequency - response of the compliant wall. Calibration was acheived by using an impulse testing device. The apparatus consists of a Bruel & Kjaer accelerometer - impulse hammer set, type 4332/35, coupled to the Nicolet 660 A frequency analyser and the Tektronik 4662 interactive p l o t t e r . A thin layer of s i l i c o n grease, recommended in the Instruction Manual,135 w a s u s e d for mounting the accelerometer to the compliant (wall) surface. The special hammer was used to s t r i k e the compliant surface as close as possible to the accelerometer. [The accelerometer was placed at three different locations and the surface struck a t o t a l of ten times in each case]. After each impact a frequency range was scanned. A t y p i c a l frequency-response plot i s shown in Figure H.1. The f i r s t resonant peak i s at 23.0 Hz. With the r e l a t i v e l y low flow velocity of the present study, the cha r a c t e r i s t i c frequency range of wall-pressure fluctuations calculated according to Black f = 0.0089 U2/v [H.1] i s 2 - 10 Hz. - 157 -F R E Q U E N C Y ( H Z ) coherence = 0-987 F igu re H .1 : Frequency-response p l o t s from impact t e s t . - 158 -A P P E N D I X I Treatment of gross flow measurements Pipe diameter (d) = 26.29 mm Pipe Bulk velocity, U(m/sec) = 4Q/Trd = 1.84 x 103Q Reynolds number, Re d = = 4.84 x 107Q Mean Wall shear stress (T ) , o x _ d ( A P ) = 2.16 x 10"3 AP r . . , x p . „ x g/g„ o 4L Lmm of water] water 3 3 c or, x (N/m2) = 0.0211 AP r _ . , o [mm of waterj i - • I - - 4 - - e 0 / , -> -> - i n - 5 — [ m m °* water J Fanning Fr ict ion factor, f = =- = 4.22 x 10 ~ PU U -'159 -Shear v e l o c i t y , U*(m/sec) = [ T 0 / P ( w a t e r ) ] . 0.032 T 1 / 2 o For Re d < 2000: f ( t h e o r e t l c a l ) = ^ d For Re d > 2000: f ( t h e o r e t i c a l ) = 0.046 Re"' [See Table 1.1] The measured quantities (Q and AP) were used to calculate the pertinent gross flow parameters, as indicated above. The computer program used for these calculations i s presented on the next page. MICHIGAN TERMINAL SYSTEM FORTRAN G ( 2 1 . 8 ) MAIN 0 9 - 1 9 - 8 2 16:40:47 PAGE P 0 0 1 0001 0002 0003 . 20 0004 2 0005 0006 0007 0008 0009 0010 001 1 0012 31 0013 0014 0015 0016 0017 30 0018 0019 32 0020 16 0021 0022 3 0023 0024 7 0025 0026 0027 0028 0029 0030 0031 0032 •OPTIONS IN •OPTIONS IN • S T A T I S T I C S * I O ( 1 0 ) , D P ( 1 0 ) . I R ( 1 0 ) . V ( 1 0 ) . T ( 1 0 ) , V I ( 1 0 ) . F T ( 1 0 ) . F E ( 1 0 ) DIMENSION 1,DPK(10) 1 = 1 READ(5 ,2 ) 1 0 ( 1 ) ,DP( I ) F 0 R M A T ( I 6 , 1 X . F 6 . 2 ) D P ( I ) = D P ( I ) * 1 0 IR( I )=48.374*10(1) V ( I ) = 1 . 8 4 * I O ( I ) / ( 1 0 * * 3 ) T ( I ) = . 0 2 1 1 * D P ( I ) V I ( I ) = S O R T ( T ( I ) / 1 0 0 0 ) I F ( I R ( I ) . L T . 2 0 0 0 ) G 0 TO 30 F T ( I ) = 0 . 0 4 6 / ( I R ( I ) * * 0 . 2 ) F E ( I ) = 4 . 2 2 * D P ( I ) / ( ( V ( I ) * * 2 ) * ( 1 0 * * 5 ) ) DPK( I )=DP( ' l ) *3 .216 1 = 1 + 1 I F ( I . G T . 1 0 ) G 0 TO 32 GO TO 20 F T ( I ) = 1 6 . 0 / I R ( I ) GO TO 31 WRITE(6, 16) F O R M A T ( ' I ' ) WRITE(6 ,3 ) F0RMAT(56X, 1 . ' 6 ' ) WRITE(6 ,7 ) F0RMAT(24X, 1 , ' U * ' , 7 X , ' F 2 2 X , ' ( K P A S C / M ' , 4 X 3 . 4 X . ' E X P T L ' / 3 8 X , 'GROSS FLOW Q U A N T I T I E S ' / ' + ' . 5 5 X . 2 K ' _ ' ) / 2 3 X , 8 5 ( ' _ ' ) / 2 9 X 0 ( * 1 0 ) ' , 8 X . ' D E L T A P , 8 X , ' F ' / 2 5 X , ' 3 ' , 5 4 X ' ( M / S E C ) ' , 9 X , ' 2 ' , 4 X , ' * 1 0 ) , 7 X , ' R E ' , 4 X , ' TAU Z E R O ' , 7 X (M / S E C ) ' , 2 X , ' ( M M H 0 ) ' . (NEWTON/M ) ' , 3 X . ' ( M / S E C ) ' . 2 X , ' T H E O ' / ' + ' , 2 3 X . 8 5 ( ' _ ' ) ) , 1 2 X , ' U ' 2 ' / 2 3 X , ' D P K ( K ) . V ( K ) . I R ( K ) , T ( K ) . V I ( K ) , F T ( K ) , F E ( K ) 5 X . F 6 . 2 , 6 X . F 6 . 3 , 3 X . I 5 . 4 X . F 7 . 3 . 5 X . F 6 . 3 , 1X, DO 11 K=1,10 W R I T E ( S , 5 ) I 0 ( K ) , 0 P ( K ) 5 F 0 R M A T ( 2 5 X , I 3 , 7 X , F 4 . 1 1.5) 11 CONTINUE WRITE(6 ,33) 33 F O R M A T ( ' I ' ) RETURN •• END E F F E C T * ID ,EBCDIC,SOURCE.NOLI ST,NODECK.LOAD,NOMAP E F F E C T * NAME = MAIN . LINECNT = 60 SOURCE STATEMENTS = 32.PROGRAM SIZE = 2F8 1734 • S T A T I S T I C S * No e r r o r s 1n MAIN NO DIAGNOSTICS GENERATED .000 .000 .500 .000 .000 . 200 6 .000 7 .000 8 .000 9 . 0 0 0 9 . 2 0 0 10.000 11.000 12.000 12.050 12.100 12.200 13.000 13.200 14 .000 15.000 16.000 17.000 17.200 19.000 2 0 . 0 0 0 20 .200 2 0 . 4 0 0 2 0 . 6 0 0 2 4 . 0 0 0 25 .000 26 .000 27 .000 28 .000 3 1 . 0 0 0 32 .000 33 .000 34 .000 0\ o': T a b l e 1.1 GROSS FLOW QUANTIT IES Q ( * 1 0 ° ) ( M 3 / S E C ) DELTA P (MM H 2 0 ) (KPASC/M 1 Q 3 ) U ( M / S E C ) RE TAU ZERO (NEWTON/M ) U* ( M / S E C ) 39 1 . 1 3. 54 0 . 072 1886 48 1 . ,8 5 . 79 0 . 088 2321 60 2 , .8 9 . .00 0 . , 1 10 2902 73 3 , .8 12 , .22 0 . . 134 3531 87 5, .5 17 . 69 0 . . 160 4 208 136 1 1 .2 36. .02 0. .250 6578 155 15 .0 48 .24 0. .285 7497 226 28 .6 91 .98 0 .416 10932 258 37 . 5 120 . 60 0 .475 12480 346 63 .5 204 . 22 0 .637 16737 0 . 0 2 3 0 . 0 3 8 0 . 0 5 9 0 . 0 8 0 0 . 1 1 6 0 . 2 3 6 0 . 3 1 6 0 . 6 0 3 0 .791 1 . 340 0 . 0 0 5 0 . 0 0 6 0 . 0 0 8 0 . 0 0 9 0 .01 1 0 . 0 1 5 0 . 0 1 8 0 . 0 2 5 0 . 0 2 8 0 . 0 3 7 THEO EXPTL 0 . 0 0 8 4 8 0 . 0 0 9 7 6 0 . 0 0 9 3 4 0 . 0 0 8 9 8 0 .OO867 0 . 0 0 7 9 3 0 . 0 0 7 7 2 0 . 0 0 7 16 0 . 0 0 6 9 7 0 . 0 0 6 5 8 0 .00901 0 . 0 0 9 7 4 0 . 0 0 9 6 9 0 . 0 0 8 8 9 0 . 0 0 9 0 6 0 . 0 O 7 5 5 0 . 0 0 7 7 8 0 . 0 0 6 9 8 0 . 0 0 7 0 2 0 .00661 - 162 -APPENDIX 3 Movie details Kodak 4x R 449 reversal 16 mm B/W movie f i l m was used. This emulsion type (ASA 400) was found to provide the best resolution of the fringe pattern with the present laser l i g h t i n g condition. The (s i l e n t ) movie uses descriptive t i t l e s to give an outline of holography and the implementation of the real-time interferometric approach used in the study. The integrated flow & holographic appartus and the specially-fabricated test section are shown. Schematic drawings of the test section and the photo-optical set-up are included to show how the technique works. This section i s followed by an actual flow sequence which shows the instantaneous fringe distortions due to pressure changes at the surface. - 163 -Section 1 : FLOW VISUALIZATION with laser holographic interferometry to supplement Ph.D. thesis e n t i t l e d : v An Experimental Investigation of the  Wall-Pressure f i e l d During  Turbulent Incompressible Pipe Flow by Norman S.W. Williams Supervisor: Prof. Donald W. Thompson Chemical Engineering Department University of B r i t i s h Columbia Vancouver, CANADA V6T 1W5 Financial support provided by the National Research Council of Canada under grant A 4936. - 164 -Section 2 Holography a two-step method of optical imagery image formed by the super position of two mutually coherent wavefronts Step 1 RECORDING [ o f f - a x i s recording geometry shown] Step 2 RECONSTRUCTION [shown diagramatically] Section 3 : Holographic Interferometry - generation and interpretation of an interferometric fringe field Real-time ('live' fringe) approach 'live' fringes serve to code object surface (initial state) timewise change at surface visualized as distortion of fringe field, necessary to relate fringe distortion to the surface change cine-photographic recording of fringe pattern The technique permits visualization and measurement of the fluctuating pressure exerted at the pipe wall during flow. - 165 -Section 4-: [A schematic of the integrated flow f a c i l i t y & holographic apparatus i s shown followed by views of the actual set-up. A specially-constructed compliant pipe (wall) surface was used i n the study. Views of the Plexiglas test section are shown]. Section 5; [Schematic representation for the implementation of the technique i s shown followed by an actual flow case for Re d = 12,300 (U = 0.47 m/sec) at 60 fps] THE END - 166 -Appendix K Treatment of Fringe Distortion Measurements K.1 Instantaneous fringe distortions Measured values of fringe distortions are tabulated - see Tables K.1 (downstream distortions) and K.2 (upstream d i s t o r t i o n s ) . The time average value of the fringe d i s t o r t i o n (f^) at each location, over the flow sequence, was determined by, ?d=VT £ f d ( V C K - 1 ] where f , (t.) i s the instantaneous fringe d i s t o r t i o n , [ f , (t.) - f.] d 1 d i d values were also calculated and are presented in Tables K.3 and K.4. Using Figure D.4, the fringe distortions (Tables K.1 and K.2) were converted to instantaneous wall-pressure changes at the different fringe locations (see Tables K.5 and K.6). S i m i l a r l y , values of the instantaneous wall-pressure fluctuations about the mean were calculated and are l i s t e d in Tables K.7 and K.8. (The computer programs used for these calculations are also included). - 167 -Table K.1 INSTANTANEOUS FRINGE DISTORTIONS f doWTIS tream 1 FRINGE NUMBER 3 2_ 1 3. 79 0, 79 3. 57 0.77 1 . 26 1 . 99 2 .05 1.73 1 . 26 1 .26 0.77 0. 57 1 .67 1 .95 1 . 64 1 . 26 0.69 0.57 1 . 26 1 . 99 0.47 0.47 0 . 79 0.57 0.79 0 . 57 O. 57 . 0 . 69 0 .63 26 26 57 0' 47 69 26 79 57 6 1 O O 47 69 79 26 26 1 1 O . ' 1 . O. O. O. O . 0. O. O. O. 1 . 1 . 0.79 . 26 .73 .73 . 26 0.46 0.47 O. 77 1 . 58 1 . 26 1.73 1 .64 1.73 1 .99 1 . 58 1 .26 0.79 1 . 99 1 . 64 1 . 26 1 . 58 . 0.63 1 . 26 O . 79 O . 47 0 . 79 O. 4 7 1 . 67 6.79 0 . 57 0.79 26 26 79 3.79 1 . 26 3 . 63 0 . 79 1 . 26 1 . 26 1 . 26 1 . 58 1 . 1 . 0 . 26 6 1 0 47 47 77 73 57 O .0 0.57 0.69 O 1 .64 O. 79 1 . 26 1 .67 0. 79 1 . 73 0. 79 0 .47 0 .79 1 . 58 1-64 26 73 99 99 1 .73 0.47 O. 79 ' 1 . 99 1 .64 1 . 58 26 1 . 67 . 0.47 1.99 1 .95 1 .58 1 . 26 1 .99 1 .26 • •1 . 23 0.79 0.57 0.63 0. 79 O . 79 0 . 69 O.O 1 . 26 0 . 79 O . 47 0 . 57 0.63 0 . 79 0.77 0.46 O . 63 0.47 0 .47 67 1 . 26 0.63 0.57 0.63 0.47 0. 79 0 . 79 1 .26 0.60 1 O. 0 47 47 3.63 3.57 3. 57 0. 57 0.77 0.57 0. 79 1 .26 1 .67 1 . 99 1 . 95 1 . 26 0.63 0.47 0.79 0 .47 0.0 .0. 79 0.47 1 . 26 0.57 0.69 O. 47 0 . 69 0.63 0.0 0.0 0.0 O .47 O . 47 O. 79 0.47 0.0 O .47 0.57 0.0 0.63 O . 47 O .47 O.O 0.47 0.63 0.47 0.0 0.0 0. 47 0.79 0.79 0.57 0.57 - 168 -Table K 54 0.79 55 0.47 56 1 . 99 57 0 . 63 58 0. 79 59 0.0 60 1 . 99 6 1 1 . 26 62 0. 79 63 0.79 64 1 . 26 65 1 .73 66 0.47 67 0.57 68 0. 47 69 0. 57 70 1 . 67 7 1 1 . 26 72 . 1 .67 73 ' 0.47 74 - 0.69 75 . 0.79 76 1 . 26 77 1 . 26 78 O . 79 79 1.73 80 1 .99 8 1 1.73 82 0 . 79 83 1 . 26 84 1 . 26 85 .1 . 99 86 1 . 73 87 1 . 58 88 1 . 26 89 1 . 26 .1 (con t ' d ) 0. 63 0.63 0.0 1 . 73 0.47 0.0 o. 79 0.0 0.69 0. 57 1 . 26 0.0 1. 58 0.63 1 .26 0. 79 1.26 1 . 26 0. 47 1 .99 0.0 1. 26 0.57 1 . 58 1 . 89 0 . 79 O. 47 V. 26 0.60 0.79 1 26 0.0 2 .05 0 47 1 .99 0.47 0 79 0.69 1 . 26 1 26 0 . 79 0 .47 1 67 0.57 0. 79 1 26 0.79 0 . 79 0 47 1.26 0.57 0 79 • 1 . 64 0. 79 o 79 1 . 26 0.0 1 26 0 . 47 0. 63 1 67 0.79 1 . 26 1 67 1 . 26 0.63 1 26 O . 79 O . 47 1 99 0.47 0.0 0 . 79 1 . 67 0.0 0 . 57 1 . 58 0. 47 0 .0 0.69 0 . 47 0 .0 1 . 26 0 . 47 0 . 57 1 .67 0. 47 0 . 57 . 0.60 0 . 79 0 . 79 1 . 26 0.63 1 . 26 0 . 79 0.0 1 . 26 0. 79 0.0 0 . 79 1 . 64 0.63 1 . 26 0.0 0 . 57 0 . 79 0 .47 0.47 - 169 -Table K.2 INSTANTANEOUS FRINGE DISTORTIONS [ u pStream] FRAME NUMBER 5 4 FRINGE NUMBER 3 2 1 1 -2 .05 0 . 0 - 1 . 26 -2 . 7 1 0 . 0 2 -2 .05 - 1 . 26 - 1 . 26 - 0 . 63 - 1 . 36 3 -2 .05 - 1 . 58 -2 . 7 1 -2 . 7 1 - 0 . 47 . 4 - 1 . 26 - 1 . 26 -2 . 59 -2 . 68 - 0 . 6 3 5 - 1 . 26 - 1 . 26 -2 . 05 -2 . 68 - 0 . 63 6 . - 1 . 26 - 0 . 79 -2 . 68 -2 . 68 - 0 . 6 3 7 -2 .05 - 1 . 26 -2 . 68 - 4 . 73 - 0 . 6 3 8 - 2 . 0 5 - 0 . 79 -2 . 7 1 -2 . 2 1 - 1 . 26 9 0 . 0 0 . 0 - 1 . 32 -4,. 10 - 2 . 1 4 10 0 . 0 0 0 0 0 - 0 . 88 0 . 0 11 - 1 . 7 3 0 0 -2 05 - 0 . 50 - 0 . 50 12 - 1 . 26 - 0 95 - 0 57 -4 10 -2 . 77 1 3 0 . 0 0 0 - 3 31 -3 69 O . O 14 - 1 .26 . -1 26 ' -2 1 1 -4 10 - 3 .09 15 0 . 0 0 0 -2 05 -3 34 0 . 0 16 - 1 . 2 6 -1 26 -2 7 1 -4 26 -2 . 74 17 - 1 . 29 -1 29 -2 7 1 -4 10 - 2 . 7 1 18 - 0 . 8 8 0 0 - 1 7 7 -3 63 • - 1 .32 19 - 1 . 29 0 0 - 1 26 -2 05 -2 .05 . 20 -2 .08 -2 ' 08 -2 08 -3 34 - 1 . 26 2 1 - 1 . 26 -1 26 -2 74 . -3 34 -2 ..08 22 -2 .11 -2 1 1 -2 7 1 -4 10 - 0 . 63 23 -2 .68 - 1 26 -2 68 -4 10 - 1 . 7 3 24 - 1 . 26 - 1 26 -2 74 -3 72 - 1 . 2 6 25 -3 .31 -2 7 1 - 1 26 -3 7 2 - 1 . 32 26 - 1 . 32 -4 10 . -2 68 - 0 79 -2 .05 27 - 1 . 26 - 0 88 -2 74 -4 16 -2 . 74 28 - 0 . 4 7 -2 68 -2 68 -4 10 - 1 . 26 29 -2 .05 -3 63 -2 84 -0 79 - 1 . 29 30 -3 . 66 -2 08 -2 74 - 1 80 - 0 . 8 2 31 -2 .68 -0 60 -2 08 -4 04 - 2 . 1 1 32 - 2 . 1 0 - 1 73 - 1 39 - 1 25 -2 . 79 33 - 1 . 26' -2 70 - 1 77 - 1 26 -2 .05 34 -2 .05 - 1 84 -2 7 1 -3 63 - 2 . 1 1 35 - 1 . 80 - 1 26 -2 7 1 -3 28 - 1 . 3 1 36 - 1 . 7 3 - 1 73 -4 16 -2 02 -2 .02 37 -2 . 10 - 1 73 -2 7 4 . -2 74 - 1 . 77 38 -1 .81 - 1 . 26 -2 .05 -4 19 -2 . 77 39 . - 2 . 0 5 - 1 .86 -2 .68 -3 34 - 2 . 1 8 40 : -2 .11 - 1 . 83 -2 . 74 -3 . 4 1 -2 . 68 4 1 - 2 . 7 7 - 1 . 77 -2 . 76 -3 66 - 1 . 29 42 -2 .68 -2 . 68 -2 . 1 1 -2 .65 - 1 . 80 43 -2 . 62 -3 . 34 -2 . 77 -3 . 63 0 . 0 44 -2 .71 -2 . 1 1 -2 .7 1 -4 . 23 - 1 . 77 45 -2 .71 - 1 . 29 -2 . 77 -4 .98 0 . 0 46 -2 .11 - 1 .61 -2 .62 -2 . 62 0 . 0 47 - 1 . 7 7 - 1 . 29 -4 . 26 -4 .92 0 . 0 48 -2 . 74 - 1 . 92 -2 . 8 1 -3 . 63 - 1 . 77 49 - 2 . 6 8 -2 68 -2 . 68 -4 . 23 - 0 . 8 2 50 - 2 . 6 8 -2 .05 -2 .81 -2 .81 - 0 . 5 7 51 -1 .86 - 0 . 85 -2 .08 -1 . 26 0 . 0 52 -2 .52 -2 . 18 -2 . 7 1 -3 .63 0 . 0 53 -2 . 74 -2 .05 - 1 .26 -2 .65 - 0 . 8 2 - 170 -Table K.2 ( con t ' d ) 5 4 . - 1 2 6 5 5 -o 8 5 5 6 -2 8 4 5 7 -2 8 1 5 8 -2 18 5 9 -2 1 1 6 0 -2 18 6 1 -2 7 1 6 2 - 3 3 1 6 3 - 3 3 4 6 4 -2 0 8 6 5 -2 0 5 6 6 -2 7 7 6 7 -2 6 8 6 8 -3 4 7 6 9 -2 7 1 7 0 -2 4 9 7 1 - 1 8 9 7 2 -2 6 8 7 3 - 3 7 2 7 4 -3 7 2 7 5 -4 3 5 7 6 -4 1 0 7 7 - 3 6 6 7 8 -2 8 4 7 9 -2 6 2 8 0 - 1 2 6 8 1 - 1 7 3 8 2 - 1 7 0 8 3 -2 7 7 8 4 - 3 .6 3 8 5 -3 7 2 8 6 -4 1 0 8 7 -4 10 8 8 - 3 7 2 8 9 -3 6 3 - 0 5 7 - 0 8 8 - 0 8 5 - 1 2 6 -2 1 1 -2 1 1 -2 0 8 -2 0 8 - 1 2 9 -2 8 1 - 1 2 6 -2 5 9 - 1 8 9 -2 1 4 -2 0 8 -2 0 8 - 1 2 6 -2 6 5 - 1 8 9 - 3 2 8 - 1 2 6 - 3 3 4 -2 0 5 -2 0 5 - 1 9 2 -2 7 1 -2 6 8 -2 6 8 -2 0 8 - 3 3 1 -2 0 8 - 3 7 5 -2 0 5 -4 13 - 0 8 2 -2 7 4 - 1 8 0 -2 7 1 -2 6 8 - 3 7 2 - 1 9 9 -4 10 -2 0 5 - 3 2 5 - 1 7 3 -2 7 7 -2 8 4 -2 8 4 -2 18 -2 7 7 -2 6 2 - 3 6 3 -. 1 7 3 -2 6 8 - 1 2 6 ^2 6 8 - 1 7 0 -2 7 7 - ,1 8 6 -2 5 9 -2 1 1 -2 5 9 -2 . 18 -2 6 8 - 1 . 2 6 - 1 7 3 - 1 . 2 6 - 1 . 7 3 - 1. . 2 9 -2 . 5 9 - 1 . 2 6 -2 . 6 8 0 0- 0 0 0 0 0 0 - 1 2 6 - 0 5 7 -2 7 7 0 0' -2 8 1 0 0 -3 37. - 0 6 3 - 3 3 1 0 0 - 3 18 - 0 6 3 -2 6 5 - 0 7 9 - 3 2 8 - 0 7 9 -2 1 1 - 0 5 7 -2 6 8 0 0 -4 2 9 - 0 7 9 - 3 3 1 - 0 5 0 -2 8 1 - 0 5 0 - 3 3 1 - 0 8 2 -2 0 5 0 0 - 3 3 7 0 0 -4 13 - 1 2 6 - 1 9 9 - 1 2 6 -2 5 8 - 0 6 0 -2 8 4 0 0 -2 7 7 0 0 -2 8 4 0 0 - 1 6 1 -o 5 7 -2 0 5 - 0 5 7 -2 1 1 - 0 8 2 - 3 3 4 -o 7 9 -2 14 - 0 5 7 -2 0 5 - 0 5 0 - 3 . 3 4 0 0 -4 . 1 0 0 0 -2 . 0 5 0 0 -2 . 6 8 - 0 7 9 - 1 . 2 9 0 0 - 1 . 6 1 0 .O - 171 -Table K.3 l N _ S i m m o ^ ^ [downstream] FRAME NUMBER 1 2 3 4 5 6 7 8 9 10 .1 1 12 13 14 15 16 17 18 19 20 2 1 22 23 " 24 25 26 27 28 29 30 3 1 32 33 34 35 36 37 38 39 40 4 1 42 43 44 45 4 6 47 48 49 50 51 52 53 - O . 25 - O . 25 - 0 . 4 7 - O . 27 0 . 2 2 0 . 9 5 1.01 0 . 6 9 O 0 - 0 - 0 O 0 O. 0 . - O . - 0 . O. 0. - 0 - 0 - 0 - O -0 - 0 - 0 22 22 27 47 63 9 1 60 . 22' . 35 . 47 .22 . 95 . 57 57 25 47 25 47 . 47 -0 . 35 - 0 . 4 1 0 .22 22 . 47 .04 . 57 . 35 0 . 22 - 0 . 25 - O . 47 -O . 43 - 1 . 04 - 1 .04 -O . 57 - 0 . 35 - 0 . 25 22 . 22 -0 . 25 O . 22 0 . 6 9 0 . 6 9 0 . 2 2 0 . 6 0 •0 . 25 FRINGE NUMBER 3 2 -- 0 . 5 6 - 0 5 5 - 0 . 2 5 O. 55 O. 24 O. 0 . 0 . O. 7 1 62 7 1 96 0 . 55 0 . 24 •0 .23 O. 96 0 . 6 2 O . 24 O . 55 - 0 . 39 0 . 24 - 0 . 23 55 0 . 23 0 . 5 5 0 . 65 0 . 2 3 45 •0 .23 0 . 24 0 . 24 -O . 23 - 0 . 2 3 - O - O - O - O 24 39 23 ). 24 D.24 D . 24 D.55 0 . 24 0 .41 1 .02 55 55 O. 25 0 .71 •0 .45 • 1 .02 02 45 0 . 33 0 . 2 4 0 . 6 5 0 . 2 3 0 .71 - O - 0 - 1 - 0 - 0 . 2 1 -0 . 52 2 1 58 64 . 26 .74 .99 .99 0 .74 - 0 . 52 - 0 . 2 1 0 . 9 9 64 58 26 67 52 0 . 9 9 0 . 9 6 0 . 5 8 O. 26 0 . 9 9 0 . 26 O . 23 - 0 . 2 1 - 0 . 4 3 - 0 . 37 - O - 0 - O - 0 2 1 2 1 30 00 26 2 1 .52 . 43 . 37 . 2 1 .22 . 54 . 37 52 52 67 26 .37 0 . 4 3 37 52 2 1 21 0 . 26 0 . 4 0 - 0 - O - O 1 - 0 . 5 9 - 0 . 1 1 - 0 . 1 1 0 .04 - 0 . 0 2 - 0 . 0 2 - 0 . 0 2 0 . 1 9 - 0 0 . 1 - 0 - 0 02 20 67 08 40 37 67 .04 . 1 1 . 20 . 1 1 D.59 3. 20 0.11 0 .67 . 0 .02 0 .11 0.11 0.11 0 .04 0 . 5 9 0 . 5 9 •0. 59 1 1 - 0 - 0 . - 0 - 0 11 20 1 1 59 1 1 02 . 59 .04 . 1 1 . 1 1 . 59 0 .11 0 .04 1 1 0 . 5 9 0 . 5 9 1 1 O. 20 0 . 2 0 0 . 0 2 •0 .02 - 0 . - O i i III t i i i II i t i II o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o — ooooo 10 M cn <n to to K> M cn \t> 01 ro to ro w C J ai cn w cn. cn tn a i u ro J O M to O M *>. 10 cn ro i i i i i i i i i III II II II i 0 0 0 0 0 0 0 0 - - 0 o o o o o o o o o o o o o o o o o o o o o o o o o U4Ut»l>UUlUlN)UOlIJ01«'UIUItUUUlI>CllIiUUIliIi-Jt.UlUUlOllO-.(D u O ^ •* "* . i i i o o i o - o o . o i o i o o i o o o a> o o - 173 -Table K . 4 INSTANTANEOUS FLUCTUATIONS ABOUT THE MEAN [upstream] FRAME FRINGE NUMBER UMBER 5 4 . 3 2 1 1 0.18 1.61 .1.24 0.16 0. 95 2 0. 18 0. 35 1 . 24 2 . 24 -0.41 3 0. 18 .0.03 -0.2 1 0. 16 0. 48 4 0. 97 0. 35 ' -0.09 0. 20 0. 32 5 0.97 0. 35 0.45 0. 20 0.32 6 0.97 0.82 -0. 18 . 0. 20 0. 32 . 7_ 0. 18 0.35 -0.18 - 1 . 85 0. 32 8 0.18 0.82 -0.21 0.67 -0.3 1 9 2 . 23 .' 1.6 1 1.17 -1.22 -1.19 10 2 .23 1.61 2 . 50 1 . 99 0. 95 11 0.50 1.61 0.45 2 . 37 0 .44 12 0. 97 0. 67 1 . 93 -1.22 -1.83 13 2 .23 1.61 -0.81 -0.81 0.95 14 . 0.97 0. 35 0. 38 . -1.22 -2.14 15 2.23 1.61 0.45 -0.47 0.95 16 0. 97 0. 35 -0.2 1 - 1 .38 - 1 .79 17 0.94 0. 32 -0.2 1 -1.22 - 1 . 76 18 1 . 35 1.61 O. 73 -0.75 -0. 38 19 0.94 1.61 1 . 24 6.83 -1.10 20 0.15 " -0^47 0.42 -0.4 7 -0.3 1 2 1 0.97 0.35 -0. 25 -0.47 -1.13 22. 0.12 -0. 50 -0.21 -1.22. . 0.32 23 -0.4 5 0. 35 -0. 18 -1.22 ' -0.79 24 0.97 0.35 -0.25 -0.8 5 -0.31 25 - 1 .08 -1.10 1 . 24 -0.85 . -0. 38 26 0.91 -2 . 49 -0.18 2.09 -1 . 10 27 0.97 0.73 -0.25 - 1 . 29 - 1 . 79 28 1 . 76 - 1 .07 . -0.18 -1.22 -0.3 1 29 0. 18 -2.01 -0 . 34 2 . 09 -0 . 34 30 -1.43 -0.47 . -0.25 1 .08 0. 13 31 -0.4 5 1.01 0.42 -1.16 -1.16 32 0. 14 -0.12 1.11 1 . 63 -1.84 33 0.97 - 1 . 08 0.73 1.61 -1.10 34 0.18 -0.23 -0.21 -0.75 -1.16 35 0.44 0. 35 -0.2 1 -0.40 -0.36 36 0. 50 -0.12 - 1 . 66 0. 86 - 1 .07 37 0. 13 -0. 12 -0. 25 0. 13 -0.82 38 0.42 0. 35 0.45 - 1 . 32 -1.83 39 O. 18 -0 . 25 -O. 18 -O. 47 - 1. 23 40 0. 12 -0.22 -0 . 25 -O. 53 -1.73 4 1 -0.54 -0. 15 -0. 26 -0. 78 -0. 34 42 -0.45 - 1 .07 0. 38 0.23 -0.85 43 -0. 38 -1.73 -0.28 -0. 75 0. 95 44 -0.48 -O. 50 -0.2 1 - 1 . 35 -0 .82 45 -0.48 0. 32 -0. 28 -2.11 0.95 46 0. 12 0.00 -0. 12 0. 26 0. 95 47 0.47 0. 32 - 1 . 76 -2.04 0.95 48 -0.5 1 -0.31 -0.3 1 -0.75 -0.82 49 -0.45 . -1.07 -0. 18 - 1 . 35 0.13 50 -0.45 -0.44 -0.3 1 0.07 0. 38 51 0. 37 0. 76 0.42 1.61 0.95 52 -0. 29 -0. 56 -0.2 1 -0.75 0.95 53 -0.51 -0.44 1 . 24 0. 23 O. 13 174 -Table KA (cont'd) 54 0 97 1 04 1 6 1 2 88 0 95 55 1 38 0 76 1 24 2 88 0 95 56 - 0 6 1 -o 50 0 38 1 61 0 38 57 -0 57 - 0 47 0 42 0 10 0 95 58 0 06 0 32 - 0 31 0 07 0 95 59 0 12 0 35 - 0 09 - 0 50 0 32 60 0 06 - 0 28 0 35 - 0 44 0 95 61 - 0 48 - 0 47 0 42 - 0 31 0 32 62 -1 08 0 35 - 0 15 0 23 0 16 63 -1 1 1 - 0 28 - 0 78 - 0 •40 0 16 64 0 15 0 35 - 0 85- 0 76 0 38 65 0 18 - 0 44 0 45 0 20 0 95 66 - o 54 - o 31 - 0 21 - 1 4 1 0 16 67 - 0 45 -1 07 - 0 18 - 0 44 0 44 68 -1 24 - o 47 - 0 81 0 07 0 44 69 - 0 48 - 0 47 -1 25 - 0 44 0 13 70 - 0 26 - 0 44 -1 63 0 83 0 95 7 1 0 34 0 79 - 0 25 - 0 50 0 95 72 - 0 45 - 0 19 - 0 2 1 - 1 25 - 0 3 1 73 -1 49 -1 07 -1 22 0 89 - 0 31 74 -1 49 - 0 38 -1 60 0 20 0 35 75 -2 12 - 0 44 - 0 75 0 04 0 95 76 -1 87 - 0 12 - 0 28 0 10 0 95 77 -1 43 -1 23 - 0 34 0 04 0 95 78 - - 0 6 1 . - 0 56 - o 28 1 27 0 38 79 - 0 38 -'1 01 -1 13 0 83 0 38 80 0 97 - 0 12 - 0 18 0 76 0 13 8 1 0 50 0 35 - 0 18 - 0 47 0 16 82 0 53 - 0 09 - 0 28 0 73 0 38 83 - 0 54 - 0 25 - 0 09 0 83 0 44 84 -1 39 - 0 50 - 0 09 - 0 47 0 95 85 -1 49 - 0 56 - 0 18 -1 22 0 95 86 -1 87 0 35 0 76 0 83 0 95 87 -1 87 0 35 0 76 0 20 0 16 88 -1 49 0 32 - 0 09 1 58 0 95 89 -1 39 0 35 - 0 18 1' 27 0 95 - 175 -Table K.5 [positive pressure changes] INSTANTANEOUS WALL PRESSURE CHANGES FRAME NUMBER 1 2 3 4 5 6 7 8 9 10 1 1 12 13 14 15 16 1 7 18 19 20 2 1. 22 23 24 25 26 27 28 29 30 3 1 32 33 34 35 36 37 38 39 40 4 1 42 43 44 45 46 47 48 49 50 51 52 53 FRINGE NUMBER 3 ?_ 1 50 50 80 45 00 30 50 50 00 00 45 1 . 80 5 . 30 20 20 00 20 . 80 .00 . 30 .50 •1 . 50 2 . 50 80 50 80 80 20 00 00 00 1 . 80 0 . 0 1 . 50 2 . 20 4 .00 2 . 50 1 . 80 1 . 95 0 . 0 0 . 0 50 20 50 00 00 50 00 .50 .50 .00 . 20 1.45 1 . 50 2 .45 5 . 00 4 .00 5 . 5 . 5 . 6 . 5 . 4 . 2 . 6 . 5 . 4 . 5 . 2 . 4 . 2 . 1 . 2 . 1 . 5 2 1 2 4 4 2 2 4 2 2 4 4 4 5 4 50 20 50 30 00 00 50 30 -20 00 00 00 00 50 50 . 50 . 50 . 30 . 50 . 80 . 50 .00 .00 . 50 . 50 .00 .00 . 50 .OO .00 .00 .00 .OO 1 . 95 0 . 0 2 . 5 0 1 . 50 1 . 50 2 .45 5 . 50 1 . 80 0 . 0 0 . 0 1 . 80 2 . 2 0 4 . 00 5 . 3 0 2 . 50 5 . 50 2 .50 1 .50 2 .50 5 .00 5 . 2 0 4 .00 5 . 50 30 . 30 .50 1 . 50 2 . 50 30 20 OO .00 . 30 1 . 50 6 . 30 20 00 00 30 00-90 50 80 00 .50 . 50 . 20 .0 .00 . 50 1 . 50 80 00 . 50 . 45 1 . 45 2 .00 1 . 50 1 . 50 5 . 30 4 .00 2 .00 1 . 80 2 .00 1 .50 2 .50 2 . 5 0 4 .00 1 .90 0 . 0 1 . 50 1 . 50 2 .00 1 . 80 1 . 80 80 45 1 . 80 2 . 5 0 4 .00 5 . 30 6 . 30 6 . 20 4.. OO 2 .00 1 . 50 2 . 50 1 . 50 0 . 0 2 . 50 . 1 . 50 4 .00 1 . 80 2 .20 1 . 50 2 . 20 00 0 .0 .0 1 . 50 1 . 50 2 . 50 1 . 50 0 . 0 1 . 50 1 . 80 O . O 00 50 .50 .0 1 .50 00 50 0 0 1 .50 2 .50 2 . 50 1 .80 1 .80 O O O co o o u i u i c j c n o i O O c M cn C J o C J co cn co cn cn O cn ui o C J o cn o C J m cn O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O I—' CD c n o c n o O c n c n m o O o o c n c j O c j u O c n c n c n O C J O c n c n O O O O i ^ c n o c D c n c n O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O o o a. 0\ u i O w u n J O i o u O i o O u u n i i O u n i i o u O u i o u u u O i o c n c i i u O O O O U O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O o o o o ^ - u O O " « - * J - ' - ' 0 0 ' W ' ' W O " - u U i * ' ' - ' i l i k > J i i | O i > < ' O w O O L n c D O O O O < ^ c n c ^ c n c n O O c n o O O O c n c D c n c n c n o u i c n c n c n O O O O O i o O O O O O O O O O O O O O O O o o o o o o o o o o o oo o - 177 -Table K.6 [Negative pressure changes] INSTANTANEOUS WALL PRESSURE CHANGES FRAME NUMBER 1 2 3 4 5 6 7 8 9 10 1 1 12 13 14 15 16 17 18 19 . 20 2 1 22 23 24 25 26 2.7 28 29 30 3 1 32 33 34 35 36 37 38 39 40 4 1 42 43 44 45 46 4 7 48 49 50 5 1 52 53 FRINGE NUMBER 3 1 -6 . 50 0 . 0 -4 .00 -6 . 50 -4 .00 -4 .OO -6 . 50 - 5 . 0 0 . -8 . 60 - 4 .00 -4 .00 - 8 . 2 0 -4 .00 -4 .00 -6 . 50 -4 .00 - 2 . 5 0 -8 . 50 -6 . 50 -4 .00 -8 . 50 -6 . 50 -2 . 50 -8 . 60 O . O 0 . 0 -4 . 20 0 . 0 0 . 0 0 . 0 -5 . 50 0 . 0 -6 . 50 -4 .00 -3 .00 - 1 . 8 0 0 . 0 0 . 0 - 10 .50 -4 . 00 -4 .00 -6 . 70 0 . 0 0 . 0 -6 . 50 -4 .00 - 4 . 00 -8 . 60 - 4 . 1 0 - 4 . 1 0 - 8 . 6 0 -2 . 80 0 . 0 -5 . 60 - 4 . 1 0 0 . 0 -4 .00 -6 . 60 - 6 . 6 0 - 6 . 6 0 - 4 . 0 0 ' -4 . 00 .-8 . 70 -6 . 70 -6 . 70 - - 8 . 6 0 -8 . 50 -4 .00 -8 . 50 -4 .00 -4 .00 -8 . 70 - 10 .50 -8 . 60 -4 .OO -4 . 20 - 13 .00 -8 . 50 - 4 . 00 -2 .80 -8 . 70 - 1 . 50 -8 . 50 -8 . 50 -6 . 50 - 1 1 .50 -9 . 00 - 1 1 .60 -6 . 60 -8 . 70 -8 . 50 - 1 . 90 -6 . 60 - 6 . 6 5 - 5 . 50 - 4 . 4 0 - 4 . 0 0 " -8 . 55 - 5 . 60 -6 . 50 -5 . 70 -5 . 50 - 6 . 6 7 75 50 70 -8 . 80 -8 . 50 -8 . 30 -8 . 60 -8 . 60 -6 . 70 -5 . 60 -8 . 70 -8 . 50 -8 . 50 -5 . 90 -8 .00 -8 . 70 85 .00 . 50 . 50 .00 . 90 -5 . 80 - 5 . 60 -8 . 50 - 1 0 . 6 0 -6 . 70 -4 - 5 -4 -6 10 10 10 10 -8 . 50 - 6 . 5 0 -2 . 70 - 6 . 9 0 - 6 . 50 -8 . 60 -8 . 60 - 1 3 . 2 0 -8 . 70 -6 . 50 -8 . 50 -8 . 70 - 8 . 7 5 -6 . 70 - 8 . 8 0 -8 . 60 -8 . 80 -8 . 30 - 13 . 50 -8 .90 -8 . 50 -8 . 90 -6 . 60 - 8 . 60 -4 .OO -8 . 60 -2 .00 -8 .60 -8 . 50 -8 . 50 -8 . 50 - 1 5 . 00 -7 . 00 - 1 3 . 00 -2 . 80 - 1 . 60 - 13 .00 - 1 1 . 70 - 1 3 . 0 0 - 1 0 . 6 0 - 1 3 . 5 0 - 13 .00 - 1 1 .50 -6 . 50 - 1 0 . 6 0 - 1 0 . 6 0 - 1 3 . 0 0 - 13 .00 - 1 1 .80 - 1 1 . 80 -2 . 50 - 13 . 20 - 1 3 . 00 -2 . 50 - 5 . 70 - 12 . 80 -3 . 95 -4 .00 - 1 1 . 50 - 1 0 . 4 0 -6 . 40 -8 . 70 - 13 .30 - 10 .60 - 10 .80 - 1 1 . 60 -8 . 40 - 1 1 . 50 - 13 .40 - 15 .80 -8 . 30 - 1 5 . 6 0 - 1 1 .50 - 1 3 . 4 0 -8 .90 -4 . 00 - 1 1 . 50 -8 . 40 0 30 50 00 00 00 .00 .00 . 80 .0 . 60 -8 . 80 0 . 0 9 . 80 0 . 0 8 . 70 8 .60 -4 -6 -4 -6 -2 20 .50 .00 .60 .00 -5 . 50 - 4 . 00 -4 . 20 -6 . 50 -8 . 70 -4 -4 -2 .00 . 10 . 60 -6 . 70 -8 . 85 -6 . 50 -6 . 70 - 4 . 1 5 -6 . 40 -5 . 60 -8 . 80 -6 . 90 -8 . 50 -4 . 10 - 5 . 70 0 . 0 60 O O O 60 -2 .60 - 1 .80 0 . 0 0 . 0 -2 .60 - 1 7 8 -Table K.6 (cont'd) 54 -4 00 - 1 . 80 55 -2 70 -2 . 70 56 -9 00 -6 . 70 57 -8 90 -6 60 58 -6 90 -4 10 59 -6 70 -4 00 60 -6 90 -6 00 61 -8 60 -6 60 62 - 1 0 50 -4 00 63 - 10 60 -6 00 64 -6 60 -4 00 65 -6 50 -6 50 66 -8 80 -6 10 67 -8 50 -8 50 68 - 1 1 00 -6 60 69 -8 60 -6 60 70 -7 90 -6 50 7 1 -6 00 -2 60 72 -8 50 -5 70 73 - 1 1 80 -8 50 74 - 1 1 80 -6 30 75 ' - 13 80 -6 50 76 - 13 00 - 5 50 77 - 11 60 -9 00 78 -9 00 -6 90 79 -8 30 -8 30 80 -4 .00 - 5 50 8 1 - 5 . 50 -4 .00 82 -5 .40 - 5 .40 83 -8 .80 - 5 .90 84 - 1 1 . 50 -6 . 70 85 - 1 1 .80 - 6 . 90 86 - 13 .00 -4 .00 87 - 13 .00 -4 .00 88 - 1 1 .80 -4 . 10 89 - 1 1 . 50 -4 .00 -2 . 80 0 . 0 0 . 0 -4 . 00 0 . 0 0. O -6 . 70 -4 . 00 - 1 . 80 -6 . 60 -8 . 80 0 . 0 -8 . 90 -8 . 90 0 . 0 -8 20 - 10. 70 -2 00 -6 80 - 10 50 0 0 - 6 60 - 10 10 -2 00 -8 40 -8 40 -2 50 - 10 40 - 10 40 -2 50 - 10 60 -6 70 - 1 80 -6 50 -8 50 0 0 -8 60 - 13 60 -2 50 -8 50 - 10 50 - 1 60 - 1 0 50 -8 90 - 1 60 - 1 1 90 - 10 50' -2 60 -13 10 -6 50 0 0 -8 70 - 10 70 0 0 -8 60 - 13 10 -4 00 - 1 1 80 -6 30 -4 00 -13 00 -8 50 - 1 90 - 1 0 30 -9 00 0 0 -8 80 -8 80 0 0 -9 00 -9 00 0 0 -8 80 -5 10 - 1 80 - 1 1 50 -6 50 - 1 80 -8 50 -6 70 -2 60 -8 50 - 10 .60 -2 . 50 -8 .80 -6 .80 - 1 .80 -8 . 20 -6 . 50 - 1 .60 -8 . 20 - 10 .60 0 .0 -8 . 50 - 13 .00 0 .0 - 5 . 50 -6 .50 0 .0 -5 . 50 -8 . 50 -2 . 50 : 8 . 20 -4 . 10 0 .0 -8 . 50 -5 . 10 0 .0 -179 -T a b l e K.7 [ P o s i t i v e p r e s s u r e s ] INSTANTANEOUS WALL PRESSURE FLUCTUATIONS ABOUT THE MEAN FRAME NUMBER 1 2 3 4 5 6 7 8 9 10 1 1 12 13 14 15 1G 1 7 18 19 20 2 1 22 23 24 25 • 2G 27 28 29 30 3 1 32 33 34 35 36 37 38 39 40 4 1 42 43 44 45 46 47 48 49 50 5 1 52 53 FRINGE NUMBER 4 3 2 1 - 0 . 80 -1 .79 - 0 . 66 I - 1 .86 - 0 . 8 0 - 1 .74 - 1 .66 - 0 . 36 - 1 . 50 - 0 . 7 9 - 0 . 66 - 0 . 36 - 0 . 8 5 1 .76 1 . 84 0 .14 0 . 70 0 .76 2 .04 - 0 . 0 6 3 .OO 2 .26 0 .84 - 0 . 0 6 3 . 20 1 .96 2 . 34 - 0 . 0 6 2 . 20 2 .26 3 .14 0 . 59 0 . 7 0 3 .06 3 .14 - 0 . 0 6 0 . 70 1 .76 2 . 34 0 . 64 - 0 . 8 5 0 .76 - 1 . 66 2 .14 -1 .50 - 0 . 7 4 - 0 . 66 3 .44 2 .00 3 .06 3 .14 4 .44 2 .90 1 .96 2 .04 4 . 34 1 . 90 0 . 7 6 1 . 84 2 .14 0 . 7 0 1 . 76 0 .84 0 . 1 4 - 1 , 1 0 - 1 ,24 2 .14 - 0 . 36 - 1 . 50 0 . 7 6 - 1 . 66 0 . 6 4 0 . 70 - 0 . 7 4 3 .14 - 0 . 36 3 .OO - 1 . 7 4 3 .04 - 1 . 86 - 1 . 80 - 0 . 7 4 1 . 84 0 . 6 4 - 1 .80 - 1 .74. 0 .84 - 0 : 3 6 - 0 . 80 2 .06 3 .14 2 .14 - 1 . 50 - 0 . 7 4 0 .84 - 0 . 0 6 - 0 . 8 0 - 1 . 4 4 0 .74 0 . 34 - 1 . 50 - 0 . 7 4 - 0 . 6 6 - 0 . 36 - 1 . 50 0 . 7 6 - 1 . 36 0 . 34 - 1 . 1 0 0 . 7 6 - 1.. 16 0 . 1 4 - 1 . 30 - 0 . 7 4 - 0 . 6 6 - 1 .86 0 . 70 - 0 . 7 4 - 0 . 66 - 1 . 86 0 . 70 0 . 76 - 0 . 9 6 - 1 . 86 - 1 . 50 - 1 . 2 4 - 3 . 1 6 - O . 36 -3 . 30 - 0 . 7 4 0 .84 - 0 . 36 - 1 . 80 0 .76 - 0 . 66 0 .64 - 1 . 1 0 0 .76 - 1 .66 - 0 . 36 0 . 70 0 . 7 6 - 1 . 36 - 1 . 8 6 - O . 80 1 .76 - 1 . 1 6 - 0 . 36 - 1 . 50 0 .76 - 0 . 6 6 - 0 . 0 6 - 1 . 35 - 1 . 29 - 0 . 7 1 - 1 . 86 -3 . 30 -3 . 24 - 1 . 7 1 0 . 1 4 -3 . 30 - 1 . 7 4 - 1 . 1 6 - O . 36 - 1 . 8 0 . - 1 .74 - 1 . 66 - 0 . 36 - 1 . 1 0 - 0 . 7 9 - 1 . 66 - 1 , 86 - 0 . 8 0 2 .26 2 .14 - 0 . 36 0 . 7 0 - 1 .44 0 . 8 4 0 . 1 4 0 . 70 - 3 . 2 4 - 1 . 1 6 - 0 . 36 - 0 . 8 0 - 3 . 2 4 - 1 . 36 - 1 . 86 0 . 7 0 - 1 . 4 4 - 1 . 1 6 - 1 . 8 6 2 . 2 0 - 1 .04 -1 .66 - 0 . 36 2 . 20 0 .76 - 0 . 6 6 0 . 6 4 0 . 7 0 2 .06 - 0 . 6 6 0 . 6 4 1 . 90 - 0 . 7 4 0 . 84 - 0 . 0 6 - 0 . 8 0 2 .26 - 1 . 26 - 0 . 0 6 - 180 -Table K.7 (cont'd) 54 - 0 . 80 - 1 . 24 - 1 . 16 - 1 . 86 55 - 1 . 80 2 . 26 - 1 . 66 - 1 . 86 5G 3 .00 - 0 . 74 -3 . 16 • 0 . 34 57 - 1 . 3 0 - 1 . 4 4 0 . 84 - i .86 58 - 0 . 8 0 1 . 76 - 1 . 16 2 . 14 59 -3 . 30 - 0 . 74 0 . 84 2 . 14 60 3 .00 - 1 . 7 4 3 . 14 - 1 . 86 6 1 . 0 . 70 0 . 76 - 1 . 36 3 . 14 62 - 0 . 80 2 . 76 - 0 . 66 - 0 . 36 63 - 0 . 80 0 . 76 - 1 . 26 0 . 64 64 0 . 70 0 . 76 -3 . 16 4 . 64 65 2 . 20 - 1 . 74 3 14 -o . 36 66 - 1 . 80 - 0 . 7 4 -o 96 2 14 67 - 1 . 50 0 . 76 - 0 66 - 0 36 68 - 1 . 80 2 .06 - 1 36 0 64 69 - 1 . 50 0 . 76 - 0 66 0 64 70 2 .00 - 1 .74 0 84 - 0 06 7 1 0. 70 - 0 . 74 2 04 0 64 72 2 .00 - 0 . 7 4 0 84 - 1 86 73 - 1. 80 0 . 76 - 1 66 0 14 74 . - 1 . 10 2 .06 - 0 66 2 14 75 . - 0 . 8 0 2 .06 0 84 0 14 76 0 . 7 0 0 . 7 6 - 0 66 - 0 36 77 0 . 70 3 .06 -1 66 - 1 86 78 - 0 . 80 - 0 . 74 2 14 - "1 86 79 2 . 20 - 1 . 4 4 1 84 - 0 36 80 3 .00 -3 . 24 - 0 96 - 0 36 8 1 2 .20 - 3 . 2 4 d . 84 - 0 36 82 - 0 . 80 - 1 . 4 4 2 . 14 - 0 . 36 83 0 .70 - 1 . 4 4 - 1 . 26 0 . 64 84 0 . 7 0 - 0 . 74 0 . 84 0 . 14 85 3 .00 0. 76 ' - 0 . 66 - 1 . 86 86 2 . 20 0 . 76 - 0 . 66 -1 . 86 87 1 . 70 - 0 . 74 2 . 04 0 . 14 88 0 . 70 0 . 76 -3 . 16 - 0 . 06 89 0 . 70 - 0 . 7 4 - 1 . 66 - 0 . 36 - 181 -Table K.8 [Negative pressures] INSTANTANEOUS WALL PRESSURE FLUCTUATIONS ABOUT THE MEAN FRAME FRINGE NUMBER NUMBER 5 4 3 2 1 0 58 5.11 3 92 0 52 3 01 2 0 58 1.11 3 92 7 12 - 1 29 3 0 58 0 .11 - 0 68 0 52 1 5 1 4 3 08 1.11 - 0 28 0 62. 1 01 5 3 08 1.11 1 .4 2 0 62 1 01 6 3 08 2 .61 - 0 58 0 62 1 01 7 0 58 1.11 - 0 58 - 5 88 1 01 8 0 58 2 .61 - 0 68 2 12 -o 99 9 7 08 5 .11 3 72 -3 88 -3 79 10 7 08 5 .11 7 92 6 32 3 01 1 t 1 58 5 .11 1 42 7 52 1 4 1 12 3 08 2 .11 6 12 - 3 88 - 5 79 13 7 08 5 . 11 -2 58 -2 58 3 01 14 3 08 1.11 1 22 -3 88 -6 79 15 7 08 5.11 1 42 - 1 48 3 01 16 3 08 1.11 - 0 68 -4 38 -5 69 17 2 98 • 1.01 - 0 68 -3 88 - 5 59 1 8 4 28 5.11 2 32 -2 38 - 1 19 19 2- 913 5 .11 3 92 2 62 -3 49 20 0 48 - 1 . 4 9 1 32 -•1 48 - 0 99 2 1 3 08 1.11 - O 78 - 1 48 -3 59 22 0 38 - 1 . 5 9 - 0 68 -3 88 1 01 23 - 1 42 1.11 - 0 58 -3 88 -2 49 24 3 08 1.11 - 0 78 -2 68 - 0 99 25 - 3 42 - 3 . 4 9 3 92 -2 68 - 1 19 26 2 88 -7 . 89 - 0 58 6 62 -3 49 27 3 08 2 .31 -o 78 -4. 08 -5 69 28 5 58 - 3 . 39 - 0 58 -3 88 - 0 99 29 0 58 - 6 . 3 9 - 1 08 6 62 - 1 09 30 -4 52. - 1 . 4 9 - 0 78 3 42 0 4 1 3 1 - 1 42 3.21 1 32 -3 68 -3 69 32 0 43 - 0 . 39 3 52 5 17 -5 84 33 3 08 - 3 . 4 4 2 32 5 12 -3 49 34 0 58 . - 0 . 7 4 - 0 68 -2 38 -3 69 35 1 38 1.11 - 0 68 - 1 28 - 1 1 4 36 1 58 - 0 . 39 -5 28 2 72 -3 39 37 0 4 1 - 0 . 3 9 - 0 78 0 42 -2 59 38 1 33 1.11 1 42 -4 18 -5 79 39 0 58 - 0 . 79 - 0 58 - 1 48 -3 89 • 40 0 38 - 0 . 69 - 0 78 - 1 68 -5 49 4 1 - 1 72 - 0 . 4 9 - 0 83 -2 48 - 1 09 42 -1 42 -3 . 39 1 22 0 72 -2 69 43 -1 22 - 5 . 4 9 - 0 88 -2 38 3 01 44 - 1 52 - 1 . 5 9 - 0 68 -4 28 -2 59 4 5 - 1 52 1.01 - O 88 -6 68 3 01 46 0 38 0 .01 - 0 38 0 82 3 01 47 1 48 1.01 - 5 58 -6 48 3 01 48 -1 62 - 0 . 99 - 0 98 -2 38 -2 59 49 - 1 42 -3 . 39 - 0 58 -4 28 . 0 4 1 50 - 1 42 - 1 . 39 - 0 98 0 22 1 2 1 5 1 1 18 2 .41 1 32 5 12 3 01 52 - 0 92 - 1 . 7 9 - 0 68 -2 38 3 01 53 -1 62 - 1 . 39 3 92 0 72 0 4 1 - 182 -Table K.8 (cont'd) 54 3 .08 3 .31 55 4 . 38 2 . 4 1 5G - 1 . 92 - 1 . 59 57 - 1 .82 - 1 .49 58 0 .18 1 .01 59 0 . 38 1 . 1 1 60 0 . 18 - 0 . 89 6 1 - 1 . 52 - 1 . 49 62 -3 .42 1 . 1 1 63 - 3 .52 - 0 89 64 0 .48 1 1 1 65 0 58 - 1 39 66 - 1 72 - 0 99 67 - 1 42 -3 39 68 -3 92 - 1 49 69 - 1 52 - 1 49 70 - 0 82 - 1 39 7 1 1 08 2 5 1 72 - 1 42 - o 59 73 -4 72 - 3 39 74 -4 72 - 1 19 75 -6 72 - 1 39 76 -5 92 - 0 39 77 -4 52 -3 89 78 - 1 92 - 1 79 79 - 1 22 - 3 . 19 80 3 08 - 0 . 39 8 1 1 58 1 . 1 1 8 2 1 . 68 - o . 29 83 - 1 . 7 2 - 0 . 79 84 -4 . 42 -1 . 59 85 -4 . 72 -1 . 79 86 -5 . 92 1. 1 1 87 -5 . 92 1 . 1 1 88 -4 . 72 1 . 01 89 -4 . 42 1 . 1 1 5 . 12 9 . 12 3 .01 3 . 92 9 . 12 3 .01 1 .22 5 . 12 1 . 2 1 1 . 32 0 . 32 3 .01 - 0 . 98 0 . 22 3 .01 - 0 . 28 - 1 .58. 1 .01 1 . 12 - 1 . 38 3 .01 1 . 32 -o . 98 1 .01 - 0 48 0 .72 0 . 5 1 -2 48 -1 . 28 0 .51 -2 68 2 .42 1 . 2 1 1' 42 0 62 3 01 -o 68 -4 48 O 51 -o 58 - 1 38 1 4 1 -2 58 0 22 1 4 1 -3 98 - 1 38 0 4 1 - 5 18 2 62 3 01 - 0 78 - 1 58 3 01 - 0 68 -3 98 - 0 99 -3 88 2 82 -o 99 -5 08 0 62 1 1 1 -2 38 0 12 3 01 - 0 88 0 32 3 01 - 1 08 0 12 3 01 - 0 88 4 02 1 2 1 -3 58 2 62 1 2 1 - 0 58 • 2 42 0 4 1 - 0 . 58 - 1 48 0 5 1 -o. 88 2 32 1 . 2 1 - 0 . 28 2 . 62 1 . 4 1 - 0 . 28 - 1 . 48 3 . 01 - 0 . 58 -3 . 88 3 . 01 2 . 42 2 . 62 3 . 01 2 . 42 0 . 62 0 . 5 1 - 0 . 28 5 . 02 3 . 01 - 0 . 58 4 . 02 3 . 01 - 183 -DIMENSION X ( 5 ) . G T ( 5 ) . N ( 5 ) , W ( 5 ) , A V G ( 5 ) INTEGER J DO 11 1=1,5 X ( I ) = 0 GT( I ) =0 N( I )=0 1 1 CONTINUE W R I T E ( 6 . 6 ) 6 F O R M A T ( ' 1 ' ) WRITE(6 , 16 ) • 16 FORMAT(50X , ' INSTANTANEOUS FRINGE D I S T O R T I O N S ' / ' * ' , 5 0 X , 3 2 ( ' _ ' ) / ' 0 ' , 1 3 6 X . 6 0 ( ' _ ' ) / 3 6 X , ' | ' , 2 X , ' F R A M E ' , 3 X . ' | ' , 1 8 X , ' F R I N G E NUMBER' , 19X, ' 2 | ' / 3 G X , ' | ' , 2 X . ' N U M B E R ' , 2X , ' I ' , 5 X , ' 5 ' , 9 X . ' 4 ' , 9 X , '3 ' , 9 X . ' 2 ' ,9X , ' 1 ' , 4 3X. ' | ' / ' + ' . 3 6 X . 6 0 ( ' _ ' ) / 3 6 X , ' I ' , 10X, ' | ' . 5 0 X . ' j ' ) 21 R E A D ( 5 , 1 )J ,W 1 F 0 R M A T ( I 4 , 2 X , 5 F 6 . 2 ) I F ( W ( 1 ) . E O . 1 O 0 ) G 0 TO 44 DO 22 1=1,5 X ( I ) = W ( I ) * 0 . 3 1 5 3 G T ( I ) = G T ( I ) + X ( I ) N ( I )=N( I )+1 22 CONTINUE W R I T E ( 6 , 3 7 ) J , X 37 F O R M A T ( 3 6 X , ' | ' . 4 X , I 2 . 4 X . ' | ' , 5 ( 2 X , F 6 . 2 , 2 X ) , ' | ' ) GO TO 21 44 DO 69 I = 1 , 5 A V G ( I ) = G T ( I ) / N ( I ) W R I T E ( 6 , 4 7 ) I , G T ( I ) ,AVG( I ) 47 F O R M A T ( 1 4 . 2 F 1 0 . 2 ) 69 CONTINUE. END END DIMENSION W(4) , Z ( 4 ) . X B A R ( 4 ) , Y ( 4 ) X = 0 ' XBAR( i ) = 3 . 3 0 XBAR(2) = 3 .24 , . XBAR(3 ) = 3. 16 XBAR(4 )=1 .86 W R I T E ( 6 , 6 ) 6 F O R M A T ( ' 1 ' ) W R I T E ( 6 . 1 6 ) 16 F0RMAT(45X , ' INSTANTANEOUS FLUCTUATIONS ABOUT THE MEAN' 1 / ' + ' . 4 5 X , 4 1 ( ' _ ' ) / ' 0 ' . 4 1 X . 5 0 ( ' _ ' ) / 4 1 X . ' | ' . 2 X , ' F R A M E ' . 3 X . ' | ' , 1 3 X . ' 2FRINGE N U M B E R ' . 1 4 X . ' | ' / 4 1 X , ' | ' , 2 X , ' N U M B E R ' . 2 X . ' | ' , 5 X . ' 4 ' . 9 X 3 . ' 3 ' , 9 X . ' 2 ' . 9 X , ' 1 ' . 4 X , ' j ' / ' + ' , 4 1 X , 5 0 ( ' _ ' ) /4 1 X . ' | ' , 1 0 X . ' | ' 4 , 4 0 X . ' | ' ) , 1 1 R E A D ( 5 . 1 )J ,W 1 FORMAT( I 4 , 2X . 4 F 6 . 2 ) IF(W( 1 ) . E O . 100JGO TO 33 DO 22 1=1.4 Z ( I ) = ( W ( I ) - X B A R ( I ) ) * 0 . 3 1 5 3 Y( I ) = Z( I )* * 2 X = X + Y( I ) 22 CONTINUE W R I T E ( 6 . 2 ) U . Z 2 F O R M A T ( 4 1 X . ' | ' . 4 X . I 2 . 4 X , ' | ' . 4 ( 2 X , F 6 . 2 . 2 X ) , ' | ' ) X = 0 GO TO 1 1 33 STOP END END - 184 -C I M E N ' S I O N X (4 ) , GT( 4 ) . N(4 ) , W( 4 ) , AVG(4 ) INTEGER J DO 11 1=1.4 X ( I )=0 G T ( I ) = 0 N( I ) =0 11 CONTINUE W R I T E ( 6 , 6 ) 6 F O R M A T ( ' 1 ' ) W R I T E ( 6 , 1 6 ) 16 FORMATf49X . ' INSTANTANEOUS WALL PRESSURE C H A N G E S ' / ' + ' . 4 9 X , 3 4 ( ' _ ' ) / ' 10 ' . 4 1 X , 5 0 ( ' _ ' ) /4 1X, ' | ' . 2 X , ' F R A M E ' , 3 X , ' | ' . 1 3 X , 'FRINGE NUMBER' , 14X, ' 2 | ' / 4 1 X , ' | ' . 2 X , ' N U M B E R ' . 2 X . ' | ' , 5 X , ' 4 ' , 9 X , ' 3 ' . 9 X , ' 2 ' , 9 X . ' 1' ,4 3X, ' | ' / ' + ' ,4 1X.50( ' _ ' ) /4 1X. ' | ' . 10X, ' | ' , 4 0 X . ' | ' ) 21 READ(5 , 1 )U,W 1 F 0 R M A T ( I 4 , 2 X , 4 F 6 . 2 ) I F ( W ( 1 ) . E O . 1 0 0 ) G O TO 44 DO 22 1=1,4 X ( I )=W( I ) GT( I )=GT( I )+X( I ) N ( I )=N( I )+1 22 CONTINUE W R I T E ( 6 , 3 7 ) u , X 37 F0RMAT(4 1 X . ' | ' . 4 X . I 2 , 4 X , ' | ' , 4 ( 2 X . F 6 . 2 , 2 X ) , ' | ' ) GO TO 2 1 44 DO 69 I=1.4 AVG(I )=GT(I ) / N ( I ) W R I T E ( 6 , 4 7 ) I . G T ( I ) , A V G ( I ) 47 F O R M A T ( 1 4 , 2 F 1 0 . 2 ) 69 CONTINUE END END DIMENSION W ( 5 ) , Z ( 5 ) , X B A R ( 5 ) . Y ( 5) x=o XBAR ( 1) = - 7 . 0 8 XBAR(2 ) = - 5 . 1 1 X B A R ( 3 ) = - 7 . 9 2 XBAR(4 ) = - 9 . 12 X B A R ( 5 ) = - 3 . 0 1 W R I T E ( 6 . 6 ) 6 F 0 R M A T ( ' 1 ' ) W R I T E ( 6 . 1 6 ) 16 FORMAT(38X. ' INSTANTANEOUS WALL PRESSURE FLUCTUATIONS ABOUT THE MFA 1N' / ' + •' . 38X , 5 5 ( ' _ ' ) / ' 0 ' . 36X .60( ' _ ' ) / 36X . ' | ' . 2X , ' FRAME ' , 3X . ' | ' . 18X , ' 2FRINGE N U M B E R ' . 1 9 X . ' | ' / 3 6 X , ' | ' , 2 X . ' N U M B E R ' . 2 X , ' | ' , 5 X . ' 5 ' . 9 X . ' 4 ' . 9 X 3 . ' 3 ' . 9X , ' 2 ' , 9X , ' 1 ' ,.4X , ' | ' / ' + ' , 36X .60( ' _ ' ) /36X . ' | ' . 10X . ' | ' 4 , 5 0 X . ' | ' ) 1 1 RE A D ( 5 , 1 )U,W 1 FORMAT( I 4 , 2 X ,5F6 . 2 ) I F ( W ( 1 ) . E O . 1 0 0 ) G 0 TO 33 DO 2 2 1=1.5 Z( I )=W( I ) -XBAR( I ) Y ( I ) = 2 ( I ) * • 2 X = X +Y ( I ). • 22 CONTINUE V = X / 5 V I=SORT(V) W R I T E ( 6 , 2 ) J . Z 2 F0RMAT(36X, ' | ' . 4 X . 1 2 . 4 X , ' | ' , 5 ( 2 X , F 6 . 2 . 2 X ) . ' | ' ) X=0 GO TO 11 33 STOP END END - 185 -K.2 Wall-pressure d i s t r i b u t i o n The values of the instantaneous wall-pressure fluctuations (changes) over the flow sequence were used in the construction of a frequency histogram. A b u i l t - i n computer command was invoked. This command generates a plot (see Figure K.1) and analyses the data to determine the skewness and kurtosis. <HISTOGRAM HISTOGRAM MIDPOINT - 1 6 . O O O - 1 5 . 000 - 1 4 . 000 - 1 3 . 000 - 1 2 . 000 - 1 1 . 000 - 10 .000 - 9 . 0 0 0 0 - 8 . 0 0 0 0 OOOO - 6 . 0 0 0 0 - 5 . 0 0 0 0 -4 .0000 - 3 .0000 -2 .0000 - 1 . OOOO O. 1 . OOOO 2 . OOOO 3 . OOOO 4 . OOOO 5 . OOOO 6 . OOOO 7 . OOOO u -Q 3. * -7 m to 1) u C L VAR=1 INTERVAL=24: ( -16 ,7 )> COUNT FOR 1. TOTAL (EACH X= 2) 1/1 m £ Z m cn co c ;o H O C I cn 2 +X 1 +X . • 2 +X 23 +XXXXXXXXXXXX 12 +XXXXXX 22 +XXXXXXXXXXX 13 +XXXXXXX 60 +XXXXXXXXXXXXXXXXXXXXXXXXXXXXXX 47 + XXXXXXXXX.XXXXXXXXXXXXXXX 4 1 +XXXXXXXXXXXXXXXXXXXXX 53 *XXXXXXXXXXXXXXXXXXXXXXXXXXX 17 +XXXXXXXXX 63 +XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX 14 +XXXXXXX 32 +XXXXXXXXXXXXXXXX 2 +X 73 +XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX 2 +X 127 +XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX 6 1 +XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX 65 +XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX 32 +XXXXXXXXXXXXXXXX 35 +XXXXXXXXXXXXXXXXXX 2 +X 00 ( INTERVAL WIDTH= 1.0000) Figure K . 1 : Computer-generated histogram of w a l l - p r e s s u r e f l u c t u a t i o n s . - 187 -Appendix L Development of the Interferometric Measuring Technique In large part, this work involved a stepwise approach in the development of the present technique. An outline of the different aspects involved, which were essentially of an exploratory nature, i s presented herein. Hologram Making Various bleach processes^,98,100-104 w e r e t r i e d , in the early attempts, in order to enhance the d i f f r a c t i o n efficiency and thus the image quality of the holograms. In the present work, bleached holograms were observed to become tanned upon exposure to ambient l i g h t . This finding, along with those described in Section 6.4 led, to the development and use of the present procedure (see Table 6.4) for making amplitude holograms. I n i t i a l jet impingement - surface deformation experiments To test the a p p l i c a b i l i t y of the technique, a clear j e l l o solution was prepared and poured into a rectangular cavity (10mm deep) where i t was allowed to set. The impingement of a jet of a i r onto the material, covered with moire fringes, showed di s t o r t i o n of a fringe at the point of impingement. This d i s t o r t i o n was s t i l l seen when the jet - 188 -was turned off since the material suffered a permanent deformation. A thin piece of transparent membrane skin stretched over a similar cavity was also used. With this arrangement, surface deformation was also permanent. The results of these experiments indicated that a perfectly e l a s t i c (Hookean) material was necessary for use. In addition, the material was required to be transparent and s t r u c t u r a l l y soft but r i g i d from the standpoint of the turbulent pressure forces in the pipe flow study. The compliant material In terms of a v a i l a b i l i t y and cost, a s i l i c o n e rubber compound, manufactured by Dow Corning, seemed appropriate for the present work. A number of organic solvents (e.g. carbon tetrachloride, chloroform) were t r i e d in early attempts to dissolve the material. The solvent varsol was found to effect complete dissolution to produce a homogenous, clear solution. The next step involved trying different procedures for coating the surface of a Plexiglas plate to obtain a uniform layer. A coated surface was used in subsequent jet-impingement studies in a i r and i n water. Figure L.1 i s an example of the test r e s u l t s . Figure (a) shows the reference fringes superimposed upon the surface and in Figure (b) the d i s t o r t i o n i n the fringe f i e l d , due to impingement of the j e t , i s seen in the region to the l e f t . ure L.1(a): Inteferogram p r i o r to j e t a p p l i c a t i o n ( i n i t i a l s ta te ) - 190 -- 191 -Vibrational s t a b i l i t y for interferometry In addition to the reasons outlined in Section 6.2, an amplitude d i v i s i o n holographic interferometer was chosen since t h i s arrangement was found to provide improved s t a b i l i t y to vibrations. This finding may be rationalized in the following manner. With the present design, the two beams from the beam s p l i t t e r to the photoplate are important. Since the components through which these two beams pass are fixed to the same bench s i g n i f i c a n t r e l a t i v e motion i s suppressed. In the case of the wavefront d i v i s i o n counterpart, however, the beam from the point of the laser (head) i s also important in t h i s regard. Therefore, motion of the laser r e l a t i v e to any of the other components causes fringe movements. 

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