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Effect of drag-reducing additives on pipe flow : Visualization with laser holographic interferometry Achia, B. Umesh 1971

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EFFECT OF DRAG-REDUCING ADDITIVES ON PIPE FLOW: VISUALIZATION WITH LASER HOLOGRAPHIC INTERFEROMETRY by B. UMESH ACHIA B. Tech., Indian I n s t i t u t e of Technology, 1968 A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF APPLIED SCIENCE i n the Department of" CHEMICAL ENGINEERING We accept t h i s t h e s i s as conforming to the r e q u i r e d standard THE UNIVERSITY OF BRITISH COLUMBIA December, 1971 In presenting t h i s thesis i n p a r t i a l f u l f i l m e n t of the requirements f o r an advanced degree at the University of B r i t i s h Columbia, I agree that the Library s h a l l make i t f r e e l y available for reference and study. I further agree that permission for extensive copying of t h i s thesis for scholarly purposes may be granted by the Head of my Department or by hi s representatives. It i s understood that copying or publication of t h i s thesis for f i n a n c i a l gain s h a l l not be allowed without my written permission. Department of CJ^-LnM*. The University of B r i t i s h Columbia Vancouver 8 , Canada Date £~£b-r'OtaA.Lj // > /'ffe  ABSTRACT The e f f e c t of turbulence damping polymer additive on the f l u i d flow structure near the wall region of a c i r -cular pipe was made v i s i b l e using real-time laser holographic interferometry. The interference fringes were recorded by high-speed motion photography. The gross flow behaviour of d i l u t e solutions of Polyox WSR 301 in d i s t i l l e d water was studied in a 2.63 cm pipe. It was observed that (i ) The onset of drag reduction occurred at a c r i t i c a l value of wall shear stress and Reynolds number. ( i i ) The f l u i d property parameter, 6, which governs the drag reduction capacity of the s o l u t i o n , had a power-law dependence on polymer concentration given by [23] 6 c Motion pictures of real-time holographic fringe displays for pure solvent and polymer solution were appraised i i q u a l i t a t i v e l y . Under sim i l a r flow conditions turbulent eddi in drag-reducing flow were observed ( i ) to show less small scale structure than thos in the pure solvent, and ( i i ) to burst from the wall region into the bulk flow with a lower frequency. i i i TABLE OF CONTENTS Page ABSTRACT. i i LIST OF TABLES v i i i LIST OF FIGURES ix ACKNOWLEDGEMENTS x i i PREFACE x i i i PART I DRAG REDUCTION Chapter 1 DRAG REDUCTION WITH POLYMERIC ADDITIVES. . . . 1 1.1 Introduction 1 1.2 Def i n i t i o n of Polymer Solution Drag Reduction 2 Chpater 2 REVIEW OF PREVIOUS WORK 6 2.1 Pipe Flow of Dilute Polymer Solutions. . . . 6 2.2 Measurement of Drag-Reducing Pipe Flow . . . 11 2.3 Nature of the Wall Region in Turbulent Flow 16 2.4 Theories of Drag Reduction 1° i v Page Chapter 3 EXPERIMENTAL APPARATUS AND PROCEDURE 23 3.1 Blowdown Flow Test Stand 23 3.2 Gross Flow Instrumentation 26 3.3 V i s u a l i z a t i o n Section 27 3.4 Experimental Procedure 28 3.5 Variables Studied 29 Chapter 4 RESULTS AND DISCUSSION 31 4.1 Gross Flow Data 31 4.2 V i s u a l i z a t i o n Studies 45 PART II HOLOGRAPHIC INTERFEROMETRY FLOW VISUALIZATION Chapter 1 HOLOGRAPHY AND FLOW VISUALIZATION 50 1.1 P r i n c i p l e of Holography. . 50 1.2 Holographic Interferometry 54 1.3 The Holographic Interferometer as a Flow V i s u a l i z a t i o n Tool . 55 1.4 Application of Moire" Techniques 56 Chapter 2 DESIGN CONSIDERATIONS FOR APPARATUS AND TECHNIQUES IN HOLOGRAPHY. . 59 2.1 The Laser. . 62 2.2 The Beam Expander and Spatial F i l t e r . . . . 63 2.3 The Optical Bench and Enclosure 64 v Page Chapter 2.4 The V i s u a l i z a t i o n Section 66 2.5 The Hologram 70 2.6 The Hologram Holder and On-site Processor. . 76 2.7 The Photo-Optical Recording System 79 Chapter 3 EXPERIMENTAL PROCEDURE 83 3.1 Laser Beam Alignment 83 3.2 Test Section Preparation 83 3.3 Recording the Hologram 84 3.4 Processing Sequence. 86 Chapter 4 RESULTS AND DISCUSSION . 88 4.1 Preliminary Studies 88 4.2 Exploratory Double-Exposure Studies 91 4.3 Refractive Index Enhancement 94 4.4 Observations with the Holographic Flow Vi s u a l i z a t i o n Interferometer. 96 4.5 The Photo-Optical Recording System 105 4.6 Improvements on the Present Arrangement. . . 107 CONCLUSIONS . . ' 108 RECOMMENDATIONS 110 GLOSSARY OF OPTICAL TERMS I l l NOMENCLATURE 112 REFERENCES 1 1 5 vi Page APPENDIX A Calibration of Flow Instruments A-l B Sample Calculation from Gross Flow Data. . . B-l C Motion Picture Data . C-l D Selected Data for Holography D-l E Scenario for Motion Picture E-l F Apparatus Drawings F-l v i i LIST OF TABLES Table , Page I Comparison of Polymer-Solvent Systems 40 II Hologram P r o c e s s i n g Sequence . .' 86 III S e l e c t i o n C r i t e r i a f o r a R e f r a c t i v e Index Enhancer 95 IV Motion Recording Instrumentation Data 106 A-I C a l i b r a t i o n Chart of the I n f u s i o n Pump . . . . . . . A-3 A-II I n t r i n s i c V i s c o s i t y Measurements A-7 B-I Gross Flow Data - D i s t i l l e d Water B-3 B-II to B-vi Gross Flow Data - Fresh Polyox S o l u t i o n , B-4 to 1 5 , 70 , 140 , 200 , 400 WPPM. . . . . . . . . . . . B-8 B-VH to B-IX Gross Flow Data - Degraded Polyox S o l u t i o n , B-9 to 1 40 , 200 , 400 WPPM B - l l B-X Slopes from the Prandtl-von Karman p l o t s B-12 C-I Motion Photography Data. C-2 v i i i LIST OF FIGURES Figure ~ Page 1 F r i c t i o n factors in smooth pipes 4 2 Line diagram of the blowdown pipe flow apparatus 24 3 Views of the apparatus 25 4 f vs Re plot showing flow regimes and con-centration effects of Polyox WSR-301 in d i s t i l l e d water (2.63 cm pipe) 33 5 Flow rate vs wall shear stress 34 6 a) Drag reduction on Prnadtl-von Karman co-ordinates (fresh s o l u t i o n s ; 0, 70 , 200 WPPM) 37 b) Drag reduction on Prandtl-von Karman co-ordinates (fresh s o l u t i o n s ; 15, 140 , 400 WPPM) 38 7 Effect of concentration on drag reduction. . . . 41 8 Drag reduction on Prandtl-von Karman co-ordinates (degraded s o l u t i o n s ; 140 , 200 , 400 WPPM) 43 9 Effect of age degradation on the polymeric parameter . 44 10 P i c t o r i a l representation of turbulent bursts from the pipe wall region 48 11 Generalized hologram recording 52 12 Holographic reconstruction 52 i x Figure Page 13 Holographic interferometer for pipe flow v i s u a l i z a t i o n (sectional elevation) 60 14 The holographic flow v i s u a l i z a t i o n apparatus . . 61 15 Beam expander-spatial f i l t e r assembly 63 16 Test section and infusion port . . . . . . . . . 67 17 Refraction at the pipe wall 68 18 On-site wet processing plateholder with a water immersed hologram 78 19 Cine recording in real-time holographic flow v i s u a l i z a t i o n 81 20 Schematic diagram of the hologram processing setup 85 21 Reconstructions from double-exposure holograms of a laboratory beaker with water. . 92 22 Double-exposure holographic interferometry setup 93 23 Holographic flow v i s u a l i z a t i o n interferometer showing co-ordinate axes and plane of f r i nge focus. . . 97 24 Examples of no-flow moire* fringe coding of the test section by hologram displacement 99 25 Fringe movements due to perturbations 101 26 Change in fringe aspect with viewing position 101 27 Flow c h a r a c t e r i s t i c s displayed by fringe d i s t o r t i o n s 102 28 Real-time flow i nterf erograms 104 x Figure Page A-l Pressure drop instrumentation A-2 A-2 Infusion pump c a l i b r a t i o n A-4 A-3 Preparation of Polyox solution . A-5 A-4 Determination of molecular weight of Polyox in solution A-8 D-l Characteristics of Kodak 649-F spectroscopic plate . . . . . D-l F-l Pipe i n l e t section F-2 F-2 On-site processing plateholder . . . . F-3 F-3 Plateholder frame F-4 F-4 Optical enclosure and stand F-5 F-5 Diffusing screen F-6 F-6 Test section d e t a i l s . . . . . . . F-7 xi i. ACKNOWLEDGEMENTS My sincere appreciation is due to Dr. Donald W. Thompson for his guidance and encouragement during the course of this work. I extend my gratitude - to my parents, whose philosophy, depicted by li n e s from Tagore's G i t a n j a l i Where tireless striving stretches its arms towards -perfection, Where the clear stream of reason has not tost its way into the dreary desert sand of dead habit.... . has provided a guideline for research. - to the s t a f f of the Chemical Engineering workshop for t h e i r unstinting co-operation that was v i t a l for this work, - and to many others who in smaller ways have stimu-lated thought but whom space l i m i t s mention. I am also indebted to the National Research Council of Canada for the f i n a n c i a l support of a Graduate Research Assistantship. xi i PREFACE Problem Outline - Scope The reduction of f r i c t i o n a l drag in turbulent flow due to the presence of certain additives in a l i q u i d has been very ac t i v e l y investigated in recent years. Polymer solution drag reduction is a phenomenon exhibited by very small quantities of certain long-chain polymers dissolved in a solvent and is widely known as the Toms phenomenon. The major problem in investigations has been the anomalous behaviour of conventional v e l o c i t y and turbulence measuring devices in drag-reducing systems. Hot-wire, hot-f i l m and Pitot probes have been found to give erroneous results (Part I, Chapter 2.2). Although a number of experi-mental studies have been done and some theories postulated, the mechanism of turbulence in drag-reducing flow s t i l l remains speculative. The wealth of gross flow data presently available in the l i t e r a t u r e i l l u s t r a t e s the wide range of parameters that govern drag reduction (Part I, Chapter 2.1). The various mechanisms postulated (Part I, Chapter 2.4) indicate one x i i i basic trend - that turbulence processes in the wall region are modified. The primary e f f e c t of long chain polymeric additives in turbulent boundary layer flow is believed to be a thicken-ing of the viscous sublayer adjacent to the w a l l , the s t r u c -ture of the remaining portion being l i t t l e changed. The polymer macromolecules seem to increase the hydrodynamic s t a b i l i t y of the viscous sublayer with reduced f r i c t i o n a l drag at the wal1. Flow v i s u a l i z a t i o n was proposed to obtain an i n -sight into the mechanism of eddy generation and d i s s i p a t i o n . The preferred method of investigating drag-reducing pipe flow would be one that interfered with the flow to the smallest degree. A sens i t i v e optical technique l i k e i n t e r -ferometry, which can display flow phenomena through r e f r a c t i v e index changes, offers an excellent approach for v i s u a l i z a t i o n . However, the use of conventional interferometry is severely r e s t r i c t e d by the physical configuration of such an experi-ment. The recent discovery of holography and the advent of holographic interferometry has added tremendous scope and f l e x i b i l i t y to interferometric measurements (Part I I , Chapter 1.2). Laser holographic interferometry, though s t i l l in a state of a r t , provides one with a powerful flow v i s u a l i z a t i o n x i v t o o l . The nature of the holographic recording process (Part I I , Chapter 1.1) allows the interferometric investigation of any test object ir r e s p e c t i v e of i t s optical q u a l i t y . A real-time interferometric fringe display of rapidly changing aperiodic phenomena l i k e f l u i d turbulence is impossible to follow with the naked eye. High-speed motion photography is essential to record the sequence of events for l a t e r study on an extended time base. Based on these precepts, an experimental holographic flow v i s u a l i z a t i o n f a c i l i t y was developed and used to study the nature of drag reduction. Plan of Work The purpose of this work was to: 1. Design and construct a single-pass, blowdown, flow test stand with instrumentation to handle d i l u t e polymer so l u t i o n s . A 2.63 cm i . d . glass pipeline with a constant head tank was to provide flow rates up to about Re = 25,000. 2. Design and set up a real-time laser holographic interferometer with provision for high-speed motion photo-graphy to v i s u a l i z e pipe flow turbulence near the w a l l . xv 3. Investigate the nature of drag reduction with * d i l u t e Polyox WSR-301 solutions in d i s t i l l e d water using gross flow data and motion pi c t u r e s . Presentati on The main body of this work is presented in two parts. In the f i r s t ( I ) , polymer solution drag reduction is discussed and results from gross flow data and v i s u a l i z a t i o n studies are presented. The second (II) contains d e t a i l s of the holographic flow v i s u a l i z a t i o n test stand with special procedures and apparatus required for this work. In addition to the t e x t , a s i l e n t 16 mm motion picture is a v a i l a b l e . It shows features of holographic flow v i s u a l i z a t i o n and i t s application to drag reduction studies. Pure solvent and polymer solution flows are q u a l i t a t i v e l y compared. Many features of the flow structure are aperiodic and can' be observed more f u l l y in motion picture sequences than in s t i l l photographs. * A high molecular weight, water soluble polyethylene oxide made by The Union Carbide Corp. xvi P A R T I DRAG REDUCTION 1 CHAPTER 1 DRAG REDUCTION WITH POLYMERIC ADDITIVES 1.1 Introduction While pumping gasoline-aluminum soap gels in 1945, Mysels [1] and co-workers observed an unexpected phenomenon. The highly viscous gel exhibited considerably less resistance to flow than untreated gasoline. Later in 1947-48, Toms [2] observed that very d i l u t e solutions (in order of parts per million) of polymethyl methacrylate in monochlorobenzene s i g n i f i c a n t l y reduced f r i c t i o n a l drag in turbulent pipe flow. This e f f e c t has since come to be widely known as the Toms phenomenon. The term 'drag reduction' was proposed by Savins [3]. He defined the drag r a t i o , DR, as the r a t i o of the pressure gradient for the solution in question to the pres-sure gradient for the solvent at the same flow rate in the same tube. 2 ( A P ) s o l u t i o n D R TAP7 (1) s o l v e n t Thus, a drag-reducing solution is characterized by a DR of less than unity. Drag reduction is known to occur in d i l u t e polymer s o l u t i o n s , soap solutions and s o l i d p a r t i c l e suspensions in pipe flow. Polymer solution drag reduction is a puzzling phenomenon, since the density and v i s c o s i t y of the s o l u t i o n , which are the relevant hydrodynamic properties, are l i t t l e d i f f e r e n t from that of the solvent. 1.2 Defin i t i o n of Polymer Solution Drag Reduction The general r e l a t i o n between shear s t r e s s , x, and shear r a t e , dU/dy, may be written as (2) n' = 1 n' < 1 n' > 1 Newtonian f l u i d Pseudoplasti c Di1atant 3 Dodge and Metzner [4] correlated the f r i c t i o n factors for turbulent flow through pipes by proposing a family of curves plotted against the generalized Reynolds number (Figure l a ) . They found that many non-Newtonian f l u i d s l i k e Carbopol 934, Attagel , clay suspension, ammonium alginate and polyvinyl alcohol f i t t e d this c o r r e l a t i o n which gave f r i c t i o n factors decreasing with decreasing n', the power-law index. However, carboxymethyl c e l l u l o s e (CMC) solution exhibited an anomalous behaviour of much greater drag reduction and f a i l e d to f i t the trend. This f a i l u r e was explained as being due to v i s c o e l a s t i c behaviour. Hershey and Zakin [5] replotted Toms' f r i c t i o n factor data against solvent Reynolds number (Figure l b ) . These plots immediately revealed the existence of drag reduc-tion in turbulent flow with f r i c t i o n factors below the curve of Nikuradse for Newtonian f l u i d s given by 1 f = 4.0 log(Re/f) - 0.40 (3) Therefore, i t can be said that the non-Newtonian f l u i d s of Dodge and Metzner [4] are not drag-reducing for while they delay laminar to turbulent t r a n s i t i o n , they do not cause the • 01 — • 001 ~~r RUN II - S D O P P . 1 P I S L-60 I N C Y C L O M C X H N C O - .009 I N C * T ' J S C o - . 0 3 3 I N : I l u a c •032 1NCM Tt;£ •OiS ISC1 TUSC • o s a I N C H ; U = E • 1 C 3 I N C * T U £ E • 5 0 3 I N C M IU5E • 3 S 9 I N C M T U S E 1 - 3 9 8 INC1 T U B E I GOO REYNOLOS NUMBER BflSEO ON SOLVENT VISCOSITY PLOT Of SOLVENT REYNOLOS NL'KSER VERSUS FANNING FRICTION FACTOR Figure l b . Drag-reducing l i q u i d s (Hershey and Zakin [5]) Figure 1. F r i c t i o n factors in smooth pipes. 5 skin f r i c t i o n to drop below the value for the solvent and exhibit higher drag after t r a n s i t i o n . In the l i g h t of these observations, polymer sol u -tion drag reduction may be defined as a reduction of skin f r i c t i o n , in turbulent flow, below that of the solvent alone and not simply lower than that of a Newtonian f l u i d with the same v i s c o s i t y as the polymer solution at a given wall shear s t r e s s . 6 CHAPTER 2 REVIEW OF PREVIOUS WORK 2.1 Pipe Flow of Dilute Polymer Solutions The factors affecting the level of drag reduction in pipe flow have been found to be: a) Polymeri c effects 1. Polymer concentration 2. Polymer type 3. Polymer-solvent combination 4. Degradation of polymer b) FIow parameters 5. Pipe diameter 6. Bulk mean velocity 7. Pipe wall roughness The abundance of information in the literature re-veals these parameters to be so closely interrelated that i t is d i f f i c u l t to predict the effect of each individually. 7 Polymer concentration. For a given polymer-solvent system and pipe, drag reduction has been observed to increase with increasing concentration [19,23,24,32,46] un t i l a maximum is reached [22,47]. After this point, the v i s c o s i t y of the solution becomes appreciably greater than the solvent and the f l u i d becomes non-Newtonian. Virk et al. [22] observed the l i m i t -ing drag reduction asymptote to be given by the equation f = 0.42 Re- 0'5 5 (4) The onset hypothesis of V i r k , based on a series of Polyox-water s o l u t i o n s , predicted ( x * )0 , 5 to be inde-w pendent of concentration and pipe diameter for a given macros molecule-solvent system. However, Whitsitt et al. [46] . found the c r i t i c a l shear stress at onset of drag reduction for Separan AP 30 solutions to be a strong function of con-centration, decreasing by a factor of 100 with concentra-tion increase from 10 to 250 WPPM. Effect of polymer type. The polymer type, characterized by i t s molecular weight and chain f l e x i b i l i t y , has been found to strongly 8 influence drag reduction. Virk et al. [22] suggested that the r a t i o of polymer molecular size and a c h a r a c t e r i s t i c length for turbulence at in c i p i e n t drag reduction is roughly constant. Liaw et al. [25] proposed a f l e x i b i l i t y and en-tanglement capacity c r i t e r i o n which allows the prediction of minimum useful molecular weights for drag reduction for any polymer species. In general, a polymer with higher molecular weight and greater f l e x i b i l i t y was found to be a more e f f e c t i v e drag reducer. Effect of solvent type. Good solvents were found to give greater drag r e -duction as compared with 'theta' or poor solvents due to the expanded nature of the molecules in the former. The more common systems that have been studied are polyethylene oxide (PEO) - water [22 ,26],polyacrylamide (PAA) - water [27], sodium carboxymethy1 c e l l u l o s e (CMC) - water [4,29,30], guar gum - water [31], polymethyl methacrylate (PMMA) -monochlorobenzene [ 2 ] , polyisobutylene (PIB) - cyclohexane and PIB - benzene [19], and polystyrene - toluene [19]. Polymer degradation The breaking up of long molecular chains reduces the molecular weight which in turn gives lowered drag reduction. 9 The most severe degradation is produced by mechanical shear but degradation can also be caused by thermal a c t i o n , u l t r a -sonic vibration and oxidation. Nearly a l l workers have considered this e f f e c t n e g l i g i b l e in the inter p r e t a t i o n of data. However, Paterson and Abernathy [32] have shown that during tests with high flow r a t e s , degradation can be severe for high molecular weight polymers. White [33] reported very rapid and high levels of degradation of PEO which he attributed to dir e c t oxidation i n i t i a t e d by high frequency turbulent eddies. The interaction of polymer with the solvent has been found by Patterson and Zakin [21] to strongly a f f e c t degradation rates of PIB in toluene and cyclohexane. The l a t t e r , a better solvent for PIB, showed a lower rate of degradation. Pipe diameter. A strong diameter e f f e c t was f i r s t reported by Savins [3] for the data of Toms [2], Drag reduction was observed to s t a r t at a lower Reynolds number in a smaller diameter pipe than in a larger one. At a given Reynolds number the f l u i d in the smaller pipe exhibited more drag reduction. However, the diameter e f f e c t was found to be 10 extremely weak when comparisons were made at constant bulk. v e l o c i t y . Rodriguez, Zakin and Patterson [43] presented a general correlation between f p / f v > equivalent to the drag 0 2 r a t i o and a Deborah number defined as llr/D * . The RZP correlation f i t t e d a large range of concentrations and pipe diameters. Velocity p r o f i l e . Elata et al. [31] modified the law of wall turbu-lent v e l o c i t y p r o f i l e by using an empirical Deborah number (U^ r i / v ) to obtain the equation u_ u. k *n V + 5.5 + a Jin v (5) Meyer [45] proposed a s i m i l a r equation in the form J _ / f 4 + — /2 /l Du log Re/f - 0.394 - — log *c r /2 v (6) w n which states that i f turbulent pipe flow data are plotted on Prandtl-von Karman coordinates, a straight l i n e should r e s u l t . The unique dependence of drag reduction on f r i c t i o n v e l o c i t y or wall shear stress at a given con-centration and independent of pipe diameter was shown by Whitsitt et al. [46] for Separan solutions in pipes 0.46 to 15.0 cm diameter. Pipe wall roughness. An increase in pipe wall roughness was found to reduce the effectiveness of a polymer as a drag reducer. Spangler [48] and Brandt et al. [49] found the f r i c t i o n in the f u l l y rough flow regime to be affected by wall conditions alone. 2.2 Measurement of Drag-Reducing Pipe Flow Anomalous behaviour of conventional probes. One of the primary obstacles in drag reduction investigations has been the d i f f i c u l t y in applying conven-tional measurement techniques to such systems [29,48,54,55, 56,57]. The use of impact and hot wire probes for turbulence 12 measurements in v i s c o e l a s t i c f l u i d s has been severely questioned. Pi tot tubes. The use of Pitot tubes together with Bernoulli's equation, which is used to determine the velo c i t y from mea-sured pressure difference in Newtonian f l u i d s , is question-able when applied to non-Newtonian f l u i d s because of possible effects due to normal stresses and shear dependent v i s c o s i t i e s . The theoretical analysis of As t a r i t a and Nicodemo [58] showed that a Pitot tube reading in a v i s c o e l a s t i c turbulent stream is made up of a f i r s t normal stress term, an integral normal stress term and a kin e t i c term, each of comparable order of magnitude. Experimental data shows that normal stress con-tributions are not neg l i g i b l e even in the central region of the pipe although turbulent flow conditions may e x i s t . Smith et al. [56] working with polyethylene oxide solution in a 3.21 cm i.d pipe observed that the discrepancy in Pitot tube readings increased with increasing absolute v e l o c i t y , polymer molecular weight, concentration of the polymer and decreasing Pitot tube diameter. The discrepancy was also found to be a function of the free stream s t r a i n rate. A s t a r i t a and Nicodemo [54] found Pitot tubes to give abnormally low readings, p a r t i c u l a r l y at small diameters. 13 Spangler [48] reported s i g n i f i c a n t errors in Pitot tube measurements with a 100 WPPM Polyhal1-water s o l u t i o n . When the measured p r o f i l e s were integrated and compared to the measured mass flow r a t e , an error of -14 per cent at high Reynolds numbers (1.5 x 10s) and -29 per cent at low Reynolds numbers (2.4 x 101*) were found which were believed attr i b u t a b l e to e l a s t i c e f f e c t s . Ernst [29] reported r e l a -t i v e l y small error of +7 per cent for 0.05 per cent CMC solution in pipe flow (0.65" and 1.427" i . d . ) . Spangler's 31 WPPM Polyhall solution showed an error of less than 5 per cent. Metzner and A s t a r i t a [60] indicated that the Deborah number, a dimensionless group representing a r a t i o of time scales of the f l u i d and flow processes, imposes r e s t r i c t i o n s on the macroscopic features of flows of v i s c o e l a s t i c f l u i d s around probes. One major e f f e c t is an appreciable thicken-ing of the boundary layer in the region of the leading edge or stagnation point of the object in the f l u i d . Depending on the object shape, this thickening may be present for appreciable distances into the veloc i t y f i e l d . Hot-wire and hot-film probes. A s t a r i t a and Nicodemo [54] observed hot-wire probes to be much less sensitive in drag-reducing l i q u i d s than in 14 Newtonian l i q u i d s . Hot-film measurements of Smith et al. [56] for cylinders in cross flow indicated poorer heat transfer in polymer solutions than in the solvent and ex-hibited abrupt tra n s i t i o n s over which the heat transfer c o e f f i c i e n t could vary t h r e e f o l d . The heat transfer was found to increase with increasing free stream s t r a i n rate and decreasing polymer molecular weight. Friehe and Schwarz [59] experimentally v e r i f i e d the operation of c y l i n d r i c a l and conical hot-film anemometers and Pitot tubes in d i l u t e polyacrylamide s o l u t i o n s . The c y l i n d r i c a l probe revealed reduced heat transfer and the Nusselt number independent of vel o c i t y in certain ranges. These anomalies of probes puts several drag-reduc-ing turbulent ve l o c i t y p r o f i l e data reported in l i t e r a t u r e [29,30,31,45] to severe question. Alternate methods. These l i m i t a t i o n s of conventional probes make the use of tracer p a r t i c l e techniques of rather d i r e c t i n t e r e s t . Metzner and A s t a r i t a [60] pointed out that i t seems probable that tracer p a r t i c l e s w i l l not follow v i s c o e l a s t i c flows unless the p a r t i c l e or bubble diameter is much smaller than the scale of flow being observed and the stretch rates of 15 the f l u i d do not change s i g n i f i c a n t l y over the p a r t i c l e diameter. These conditions impose r e s t r i c t i o n s on the use of suspended tracers to obtain instantaneous f l u i d v e l o c i t i e s in turbulent f i e l d s , whereas time average measurements may not be seriously a f f e c t e d . Seyer and Metzner [27] used bubble streak photo-graphy to measure axial and radial components of the instan-taneous v e l o c i t y vector in a polyacrylami de-water system. These measurements were used to calculate the time average axial v e l o c i t i e s as well as axial and radial turbulence i n t e n s i t i e s . The vel o c i t y p r o f i l e s checked with the measured bulk mean ve l o c i t y to within three per cent. The recently developed laser Dbppler velocimeter, which provides a more dir e c t means of ve l o c i t y measurement, without introducing any disturbance in the flow, is rapidly becoming popular in drag reduction measurements [62,63,64,65], The method is based on the observation of the Doppler s h i f t in frequency i n laser l i g h t scattered from sub-micron" size p a r t i c l e s suspended in the f l u i d . Goldstein et al. [62] measured the local v e l o c i t y of t r a n s i t i o n and turbulent pipe flow of 50 WPPM Polyox WSR-301 solution using 0.5 micron polystyrene spheres as s c a t t e r e r s . 16 Rudd [64,65] reported a more sensit i v e laser Db'ppl ermeter with a scattering volume of 10pm x 100pm x 1mm, the scattering being observed from the polymer molecules. The lOum resolution was in the d i r e c t i o n normal to the w a l l , thus enabling measurements closer to the wall than pre-viously obtained. A comparison of axial v e l o c i t y p r o f i l e s of solvent and polymer solution demonstrated a pronounced thickening of the viscous sublayer in the polymer s o l u t i o n . Fortuna and Hanratty [66] used an electrochemical technique which was a mass transfer analog of the hot-wire anemometer. . They reported that the presence of drag-reducing polymers reducesthe frequency and magnitude of fluctuations in the v e l o c i t y gradient at the w a l l . 2.3 Nature of the Wall Region in Turbulent Flow Newtonian f l u i d s . Experimental evidence in recent years overwhelmingly rejects the concept of the existence of a f u l l y developed laminar sublayer adjacent to the bounding surface of a turbu-lent shear flow f i e l d as postulated by Prandtl [6] and Taylor [7]. The time dependent viscous sublayer or p a r t i a l turbulence 17 concept is more widely accepted, although a s a t i s f a c t o r y theory completely defining turbulent shear flow is yet non-existent. Fage and Townend [ 8 ] , using an ultramicroscope to observe dust p a r t i c l e s adjacent to the w a l l , revealed that vel o c i t y fluctuations do not cease to exist even at the w a l l . Visual studies in the region of the viscous sublayer done by Kline and co-workers [9,10,11], Bakewell and Lumley [12] and Corino and Brodkey [13] serve in part to define the mechanics of Reynolds stresses. Q u a l i t a t i v e l y , in the region of the wall extending up to y+ = 30, the turbulent momentum transfer rates in a d i r e c t i o n perpendicular to the wall are seen to be governed primarily by large eddies that occur at random locations along the w a l l . The large eddies i n i t i a l l y appear as concentrations of low momentum f l u i d which subsequently eject a mass of f l u i d toward the main stream where the i d e n t i t y of the f l u i d is rapidly l o s t . Corino and Brodkey show that as much as 70% of the turbulent Reynolds stress can be accounted for by consideration of this flow. Kline and co-workers described the s o l i d boundary as being covered with islands of f l u i d hesitation with un-steady viscous flow. Turbulent fluctuations penetrate very 18 near to the surface at random i n t e r v a l s , the flow being dominated by viscous processes between penetrations. Bakewell's analysis showed that eddies occur as counter-rotating pairs with th e i r axes of rotation along the di r e c t i o n of mean flow. The ejection of low momentum f l u i d was i d e n t i f i e d with the r a d i a l l y directed flow between a pair of eddies. This eddy pair pattern which remains defined to the edge of the sublayer is associated with about half of. the total turbulent energy and is believed to control the radial momentum transport rates which exist in the wall regi on. Drag reducing f l u i d s . Wells and Spangler [14] experimentally demonstrated the importance of the wall region in drag reducing flow by inj e c t i n g polymeric additive at the tube wall and center-l i n e . Wall i n j e c t i o n was found to give almost instantaneous pressure drop while centerline i n j e c t i o n showed no observable drag reduction u n t i l the additive had time to diff u s e to the wa l l . Based on the visual observations in Newtonian f l u i d s , Seyer [15] deduced s i m i l a r i t y laws for boundary layer flow of drag-reducing polymer s o l u t i o n s . The analysis showed the 19 dependence of drag reduction on the e l a s t i c properties of the f l u i d and the importance of the f l u i d relaxation time in governing the turbulent processes in the wall region. It also indicated that the necessary concentration of polymer need only be maintained within the inner region of the boundary layer (y+ < 30) rather than throughout the entire boundary la y e r . 2.4 Theories of Drag Reduction Various mechanisms and hypothesis have been pre-sented to explain polymer solution drag reduction. i ) The e f f e c t i v e ' w a l l - s l i p ' theory of Oldroyd [34] was the e a r l i e s t attempt to explain the phenomenon and was put forward to explain the data of Toms [2 ] , It proposed the existence of an abnormally mobile laminar sublayer whose thickness was comparable to molecular dimensions and which caused apparent s l i p at the w a l l . Toms [35] l a t e r showed thi s model to fai1 . i i ) The effect of non-Newtonian v i s c o s i t y gradient was f i r s t discussed by Shaver and M e r r i l l [30] who conducted experiments on a series of free draining polymers of r e l a t i v e l y 20 high concentrations (0.1 to 1.5%). Since the shear rate is maximum at the tube v/all and zero at the tube center, a turbulent vortex must encouter an ever increasing v i s c o s i t y as i t moves toward the wall in a pseudoplastic l i q u i d . How-ever, this theory f a i l s to explain the presence of drag re-duction in very d i l u t e and apparently Newtonian polymer so l u t i o n s . i i i ) The effect of v i s c o e l a s t i c i t y of polymer solutions was postulated by Dodge and Metzner [4] to explain the anomalous results in turbulent f r i c t i o n measurements of t h e i r CMC-water so l u t i o n s . A s t a r i t a [36] suggested that turbulence in v i s c o e l a s t i c f l u i d s was less d i s s i p a t i v e and offered some order of magnitude calculations to support his proposal. Hershey and Zakin [5] proposed that turbulence suppression begins at a c r i t i c a l Reynolds number which is reached when a c h a r a c t e r i s t i c time of the flow is of the same order as the longest relaxation time of the polymer s o l u t i o n . Fabula [37] was able to relate drag reduction of a series of Polyox-water solutions to i n t r i n s i c v i s c o s i t y which is a function of molecular size in s o l u t i o n . However, the general a p p l i c a b i l i t y of such correlations to other systems has not been proved. Patterson and Zakin [21] presented a 21 predictive v i s c o e l a s t i c model for the reduction of turbulent energy di s s i p a t i o n which demonstrated that drag reduction may be predicted without the assumption of reduced turbulence i n t e n s i t y . A design chart was presented by Seyer and Metzner [27] for predicting drag reduction in PAA-water s o l u t i o n s . It covered a wide range of Reynolds numbers (0 to 60,000) and Deborah numbers (-2400) and a modest pipe diameter range (0.08 to 5.0 cm). The universal nature of this design method is yet to be tested. iv) Macromolecule-eddy i n t e r a c t i o n . Attempts have been made to characterize the interaction between poly-mer macromolecules and turbulent eddies by comparing t h e i r length or time s c a l e s . The length scale hypothesis of Virk et al. [22,24] characterized the macromolecule by the rms radius of gyration and turbulence by the wavenumber u*/v, while the time scale hypothesis [19,31,36] employed terminal relaxation time and wall shear rate as corresponding values. Calculations by Virk et al. have shown that the coiled polymer molecules are several orders of magnitude smaller than the turbulence microscale. To account for t h i s , shear-stretching and tangling of macromolecular c o i l s has been postulated. On the other hand the time s c a l e s , found to be of the same order, makes the time domain hypothesis more appealing. 22 The s t r a i n energy hypothesis of Walsh [38] postu-lated that drag reduction occurs when s t r a i n energy convec-tion from the highly strained wall region becomes comparable to the kinetic energy d i f f u s i o n . v) The additive adsorption theory was f i r s t pro-posed by El'perin et al. [39,40] to explain the Toms e f f e c t . Based on t h i s , a model proposed by Bryson et al. [41] postu-lates modification of the flow layers immediately adjacent to the wall by an increase in the sublayer thickness due to adsorbed polymer aggregates. Adsorption measurements of Arunachalam and Fulford [41] indicated increased additive concentration at the pipe wall than at the center. Axial dispersion studies of Kenny and Thwaites [51] on Separan AP-30 in water revealed the constant velocity gradient region near the wall to be doubled by the presence of polymer molecules. Although the adsorption of polymers on surfaces has been well established [52,53] the inter a c t i o n of a so thickened sublayer and a turbulently flowing f l u i d stream is not c l e a r l y understood. 23 CHAPTER 3 EXPERIMENTAL APPARATUS AND PROCEDURE 3 .1 Blowdown Flow Test Stand A blowdown pipe flow apparatus with a single pass method of testing was designed and constructed to obtain gross flow data and to conduct v i s u a l i z a t i o n studies on the drag-reducing polymer s o l u t i o n . A diagram and views of the apparatus are shown in Figures 2 and 3. The 160 l i t r e reservoir tank T was connected to a regulated compressed a i r supply to provide constant head blowdown during flow t e s t s . The flow section F consisted of commercial QVF pyrex glass pipe 2.63 cm i.d and 7m long made up of two 3m and one Im sections bolted together with flanges. The i n l e t to the pipe from the tank had a conical converging section B which was connected to the bottom of the tank. , The gaskets and pipe j o i n t s were c a r e f u l l y aligned to reduce t h e i r possible action as disturbance generators. The test section for v i s u a l i z a t i o n studies was located over Legend T B F: H C Reservoi r tank Pipe i n l e t section Glass pipeline Holography setup Collecting tank P l , p 2 p w v 0 A D s o l e n o i d v a l v e p r e s s u r e t a p s s o l u t i o n i n l e t w a t e r i n l e t v e n t o v e r f l o w r e g u l a t e d a i r i n l e t d r a i n i n g o u t l e t H •305 CM F o o Figure 2. Line diagram of the blowdown pipe-flow apparatus 26 200 pipe diameters downstream of B so that motions observed were not influenced by entrance e f f e c t s . The entry length f o r f u l l y developed turbulent flow may be predicted by the equation [16] ^ - = 0.693(Re)0 , 2 5 (7) Hinze [17] points out that this r e l a t i o n gives values less than that experimentally observed. Nikuradse observed that 25 to 40 pipe diameters were s u f f i c i e n t for disturbed e n t r i e s . In this setup, the f i r s t s t a t i c tap was located over 40 d i -ameters downstream of entry, which would s a t i s f y the most extreme requirement for measurement and v i s u a l i z a t i o n . The l i q u i d discharged into a c o l l e c t i n g tank C which was open to the atmosphere. The end of the pipe was turned up s l i g h t l y with a 30° connector so that the entire pipeline remained f i l l e d with l i q u i d at no-flow (see also Part I I , Chapters 1.2, 2.4, 3.2). 3 . 2 Gross Flow Instrumentation Pressure drop measurement. A Statham PM280 b i - d i r e c t i o n a l pressure transducer was connected across the central 3m pipe s e c t i o n . Wall taps 27 (3mm dia.) were c a r e f u l l y d r i l l e d into Plexiglas rings aligned and fixed at the flange l o c a t i o n s . The pressure drop was recorded continuously during a flow test on a Sargent-Welch model SRG s t r i p chart recorder. Before each set of flow t e s t s , the transducer and recorder were calibrated as out-lined i n Appendi x A . Flow rate measurement. Flow rate was measured by timing a known volume of e f f l u e n t . 3 .3 V i s u a l i z a t i o n Section Figure 16 shows d e t a i l s of the flow v i s u a l i z a t i o n section. Part II presents in detail the holographic tech-nique and instrumentation developed for this study. Some dye tracer studies were done with the same setup. A 0.4mm wall s l o t located about 8cm upstream of the v i s u a l i z a t i o n section served as an in j e c t i o n port both for the dye and r e f r a c t i v e index enhancer for holographic studies. The s l o t was inc l i n e d at 85° to the upstream side of the flow axis and made in a teflon sleeve S machined and aligned with the glass pipe F. 28 A plenum chamber P which enclosed the s l o t was e f f e c t i v e in damping out i n e r t i a l effects of the i n j e c t a n t . A metered quantity of the injectant was introduced by means of an infusion pump (Sage model 355, Appendix A.2). Various methods were explored (Part I I , Chapter 4.3) for enhancing the r e f r a c t i v e index of the f l u i d near to the wall so that the interference fringes could be modulated. Infusion of a small flow of f l u i d with a d i f f e r e n t r e f r a c t i v e index through a wall s l o t was preferred to generating a tem-perature gradient or allowing material to dissolve from a soluble w a l l . The l a t t e r methods pose p r a c t i c a l d i f f i c u l t i e s / while the former has the advantage of di r e c t comparison with the dye marker technique. 3.4 Experimental Procedure The tests were conducted at room temperature (22°C) with pure d i s t i l l e d water and with polymer solutions prepared as described in Appendix A.3. The flow rate was measured by timing the c o l l e c t i o n of 4 l i t r e s using a stopwatch read-able to 0.2 sec. The flow r a t e s , presented as corrected to the nearest ml/sec, are estimated to be within ± 1.5 per cent. The pressure drop across the 305 cm length of pipe was 29 continuously recorded. The value of the pressure drop could be read to 0.5 mm of water on the recorder chart. The test l i q u i d . D i s t i l l e d water solutions of the polymer were the obvious choice for these single pass tests to minimize cost and to eliminate handling and disposal problems. The use of an organic solvent would require a closed test loop with a pump. This is especially undesirable due to the rapid degradation of polymer solutions in a high shear environment l i k e that in a pump. Tests were made using drag-reducing Polyox WSR-301 solutions having a concentration range of 0-400 WPPM. Solu-tion preparation and handling were standardized for a l l batches since these operations are known to affect the drag-reducing properties. The method adopted for this work is outlined in Appendix A.3. The polymer was characterized by i t s molecular weight determined from i n t r i n s i c v i s c o s i t y measurements (Appendix A.4). 3 . 5 Variables Studied  Gross flow A series of Polyox concentration 15, 70, 140, 200 and 400 WPPM were tested to observe the eff e c t of concentration 30 on the extent of drag reduction. One batch could provide at least 8 good data points v/hen run twice through the system. Test runs were also made after aging the solutions for two weeks to observe the ef f e c t of degradation. The solutions were stored in the c o l l e c t i n g tank C during the aging period. V i s u a l i z a t i o n studies were done with both the non-drag-reducing pure solvent and drag-reducing solution using holographic interferometry. 31 CHAPTER 4 RESULTS AND DISCUSSION Gross flow tests were f i r s t conducted to observe the nature of drag reduction in this flow system. V i s u a l i -zation studies were done after the flow regimes were defined by these t e s t s . 4.1 Gross Flow Data A sample ca l c u l a t i o n is shown in Appendix B with tables l i s t i n g calculated values f o r each concentration. Calibration of the apparatus with d i s t i l l e d water gave points lying close to the l i n e defined by the equation [16] f = 0.046 ( R e ) "0 , 2 (8) in the turbulent regime (Figure 4; Table B-I). The data was in good agreement with published f r i c t i o n factors for com-mercially smooth pipes. 32 Calculation of Reynolds number. Al l f r i c t i o n factor data are plotted against s o l -vent (pure d i s t i l l e d water) Reynolds number. Due to the s l i g h t non-Newtonian nature of s o l u t i o n , the question of which is the proper Reynolds number to use becomes apparent. Ernst [29] and Meyer [45] proposed s l i g h t variations in de-fi n i n g v i s c o s i t y to account for the importance of the wall region. Ernst assumed a power-law ve l o c i t y p r o f i l e to be va l i d at the wall and calculated the local v i s c o s i t y from wall shear stress using measured viscometric data. The problem in dealing with the v i s c o s i t y in turbulent flow, which is e s s e n t i a l l y very small as long as the solution is d i l u t e , the additional e f f e c t of v i s c o e l a s t i c i t y and choice of a suitable shear rate for comparison j u s t i f y the use of a solvent v i s c o s i t y based Reynolds number. This value is pre-c i s e l y defined, ea s i l y computed and allows di r e c t comparison with Newtonian data. The data obtained from the gross-flow studies are shown in Figure 4 in the form of a conventional Fanning f r i c t i o n factor-Reynolds number plot and in Figure 5 as a flow rate vs. wall shear stress p l o t . Figure 4 shows the regimes in drag — reducing flow. .015 T -LAMINAR—H—TRANS IT ION-O .010 .009 .008 .007 I 1 1 •TURBULENT WITH NO DRAG REDUCTION * Re ~ .006 »—< cc u_ CD .005 .004 .003 f = T_6A Re cr- A- _ Turbulent smooth f = 0 . 0 4 6 ( R e ) -°-2 TURBULENT WITH DRAG REDUCTION \ \ \ \ Legend • WATER O 70 WPPM • 200 WPPM A 400 WPPM \ \ \ \ \ \ \ Drag Reduction ^/Asymptote (Virk et a l . ) = 0 . 4 2 ( r \ e ) -° -5 5 10 15 20 REYNOLDS NUMBER (xl 0 J) Figure 4. f vs Re plot showing flow regimes and concentration effects of Polyox WSR-301 in d i s t i l l e d water (2.63 cm pipe) 25 co CO FLOW RATE Q ml/sec 35 1. laminar Re < 2200 2. t r a n s i t i o n 2200 < Re < 4000 3. t u r b u l e n t Newtonian 4000 < Re < 9000 4. t u r b u l e n t drag-reducing Re > 9000 The 'onset' of drag reduction is c l e a r l y revealed in both the p l o t s , indicating the presence of a c r i t i c a l value of Reynolds number, Re, and wall shear s t r e s s , x , below which the d i l u t e solutions follow the Newtonian curves, independent of polymer concentration. Although no data was found in the l i t e r a t u r e for direct comparison with this p a r t i c u l a r system, the trends of the flow regimes were observed to be s i m i l a r . The onset Reynolds number appears to decrease s l i g h t l y (Re = 11,000 to 8000) with increasing polymer concentration. Virk et al. [22] observed a c r i t i c a l concentration (of 500 WPPM in a 3.21 cm pipe with Polyox W301-water) above which the solution did not exhibit a Newtonian turbulent flow regime. Instead the results followed an asymptote (shown in Figure 4) i n d i -cating that the c r i t i c a l wall shear stress was reached in the t r a n s i t i o n flow region. The c r i t i c a l value of Re and x may be considered e s s e n t i a l l y constant over the range of concentrations studied. 36 The extent of drag reduction after onset was found to be a function of Reynolds number, giving a higher per-centage reduction in f r i c t i o n with increasing Re. The maxi-mum Re in this study was limited to 25,000 by virtue of apparatus design. The effect of polymer concentration. The data for fresh solutions at the f i v e concentra-tions studied are presented on the Prandtl-von Karman plots in Figures 6a and 6b. This representation shows three im-portant features of polymer solution drag reduction: 1. the onset of drag reduction, 2. the semi-logarithmic l i n e a r i t y after onset and 3. the dependence of the slope [ d ( l / / f ) / d log(Re/f)] on polymer concentration after onset. Figures 6a and 6b indicate the onset of drag reduc-tion to occur at a rather well defined value of Re/F, which is weakly dependent on polymer concentration, being about 800 ± 100 for Polyox WSR-301 in this system. T T T T r T r Fresh solutions of Polyox WSR-301 in d i s t i l l e d water. Legend O 200 WPPM Polyox • 70 WPPM A 0 WPPM Newtonian turbulent flow — = 4.0log, Re/f~0.40 /f _ 0 -Or JZL J L J I I I , I 6 7 8 Re/f (x 10"2) 9 10 15 Figure 6a. Drag reduction on Prandtl-von Karman co-ordinates Re/f (x lO"2) Figure 6b. Drag reduction on Prandtl-von Karman co-ordinates. 39 The semi-1ogarithmic l i n e a r i t y of polymer solution data, f i r s t pointed out by Elata and Tirosh [44] and Meyer [45], is apparantly a rather general feature of drag reduc-t i o n . Virk and Baher [23] associated a unique' slope, Sp, v/ith each polymer concentration, which was observed to increase with increasing concentration. The data exhibits some scatter which causes minor ambiguity with respect to onset, since the inters e c t i o n of the best straight l i n e representing the polymer solution with the solvent l i n e generally d i f f e r s from the point at which the polymer solution data departs from the solvent l i n e . However, the difference in onset due to this is small. The difference in slope between the polymer solution and pure solvent l i n e s , denoted as 6 = s p _ s s [23], may be considered equivalent to the f l u i d property parameter, of Elata et al. [31] and Meyer [45]. Figure 7 shows a log-log plot of 6 vs. polymer concentration obtained from this work (s o l i d points) and compared with a wide range of data of other workers (Table I ) . Data obtained in this work is seen to follow the power-law relati o n s h i p (eqn. 9) 6 cc c0'5 (9) The polymer-solvent systems over a concentration range of one to three decades c l e a r l y reveals a slope of 0.5 in every case. Table I Comparison of Polymer-Solvent Systems Entry Polymer-Solvent System Mol. wt. (x 10- 6) Pipe id cm Source 1 Polyethyleneoxide - water (WSR-301) 2.5+ 2.63 this work 2 (W205) 1.3 0.953 Virk and Baher [23] 3 (N750) 0.63 0.292 Virk [22] 4 Polyacry1 amide El98 - water 4.7 0.953 Virk and Baher [23] 5 Polymethy1 methacry1 ate - monochlorobenzene 2.3 0.404 Toms [2] 6 Polyisobutylene - cyclohexane 0.93 1 .30 Rodriguez [43] 7 Polydimethylsiloxane - toluene 11.0 0.272 Liaw [25] [determined experimentally from i n t r i n s i c viscosity measurements - Appendix A] 42 The data of this work represents an upper extreme pipe diameter value and a mid-range molecular weight (Table I ) . The proportionality law is believed to have a constant which is c h a r a c t e r i s t i c of the polymer, solvent and possibly pipe [23]. Based on the argument that drag reduction is a wall e f f e c t , Elata [31] and Meyer [45] point out, by analogy to turbulent Newtonian flow, that the wall region is governed by f r i c t i o n scales independent of pipe diameter. The data as shown in Figure 7 appears to indicate t h i s , since no diameter e f f e c t is readily noticeable. The trend with polymer molecular weight seems more evident, with the nature of the solvent also being an impor-tant parameter. Considering only the data from entries 1 to 3 in Table I, which compares PEO of d i f f e r e n t molecular weights in water, the data of this work ( l i n e 1) would be expected to f a l l above l i n e 2 in Figure 7, assuming total independence of pipe diameter. Since i t f a l l s between li n e s 2 and 3 the present data may suggest the interaction of some other polymeric parameter. The s c a r c i t y of data for pipes of over 2.0 cm diameter and differences in the methods of solution preparation, handling and testing make any d i r e c t comparison of data d i f f i c u l t . The e f f e c t of degradation by aging of the solutions is shown in Figure 8. When compared with fresh solution data 20 T 18 J _ / f 14 T i 1 1 r Degraded s o l u t i o n s of Polyox WSR-301 in d i s t i l l e d water. Legend A 400 WPPM Polyox O 200 WPPM O 140 WPPM Newtonian t u r b u l e n t flow 1 Re/I (x l O " 2 ) CO Figure 8. Drag r e d u c t i o n on Prandtl-von Karman c o - o r d i n a t e s . Figure 9. Effect of age degradation on the polymeric parameter. 45 in Figures 6a and 6b, the magnitude of the slope is seen to be markedly decreased showing a lesser drag-reducing e f f e c t of the degraded s o l u t i o n s . The semi-logarithmic l i n e a r i t y of slope on the Prandtl-von Karman plot is s t i l l observable. Figure 9 shows the effect of degradation on the 6 vs. C r e l a t i o n s h i p . The same power-law relati o n s h i p holds reasonably well for the degraded s o l u t i o n s . The onset of drag reduction appeared to be unaffected by degradation, the onset value of Re/f remaining about 800 ± 100 as in the case of the fresh s o l u t i o n s . The flow regimes observed with both fresh and degraded solutions were i d e n t i c a l , with the l a t t e r having a lower drag reducing e f f i c i e n c y . 4.2 V i s u a l i z a t i o n Studies On establishing the flow regimes from gross-flow data, v i s u a l i z a t i o n of the physical nature of drag reduction was done with the holographic technique. A q u a l i t a t i v e description is presented, quantitative measurements being beyond the scope of this t h e s i s . The description is based on visual observations and analysis of motion picture records of real-time holographic fringe displays of the flow. This was done in the d i f f e r e n t regimes with both Newtonian ( d i s t i l l e d 46 v/ater) and drag-reducing s o l u t i o n . This study was confined to Re < 10,000 due to low laser l i g h t i n t e n s i t y which limited the motion picture frame rate. Although the framing rate was not as high as desired for optimum conditions (100 pps as compared with 400 pps - Appendix C), s a t i s f a c t o r y records were made displaying some physical aspects of drag-reducing flow. These features are shown in the companion motion p i c -ture (Scenario - Appendix E). In laminar flow (Re < 2000), the enhancer was ob-served to stay close to the wall and was not detectable in the bulk of the flow. Disturbance of the flow caused small ripples within this l a y e r , which smoothed out r a p i d l y . Both Newtonian and drag-reducing flow revealed this trend. During t r a n s i t i o n (2000 < Re < 4000) intermittent turbulent bursts were separated by laminar regimes. Blobs of f l u i d were seen to erupt from the wall layer into the bulk. These bursts were conservative in nature. As the flow was increased to Reynolds numbers above 4000, the f l u i d elements ejected from the wall layer became more frequent and broke up more e n e r g e t i c a l l y . The turbulence was characterized by the abrupt movement of ejected elements into the bulk of the flow, the process being local in nature' and random in space and time. The motion of the vortices from the wall towards the centerline was along a s l i g h t l y curved center!ine a) Newtonian flow ( d i s t i l l e d water) pipe wall ' ' ' ' ' ' ' ' ' ' ' ' s cen ter1i ne < ^ 1 flow d i r e c t i o n b) drag-reducing flow (Polyox solution) Figure 10. P i c t o r i a l representation of turbulent bursts from the pipe wall region under s i m i l a r flow conditions. 48 path directed downstream (Figure 10). This mixing of f l u i d from the wall region with the core created a great deal of turbulent motion within the bursts, which destroyed the iden t i t y of individual f l u i d elements. This general descrip-tion was followed by both Newtonian and drag-reducing flow as turbulent flow conditions set i n . However, as the Reynolds number was increased, the turbulence phenomena in the Polyox solution gradually departed from that of water. This departure may be described as a more 'conserva-t i v e ' nature of the v o r t i c e s , shown p i c t o r i a l l y in Figure 10. The fi l a m e n t - l i k e smaller bursts accompanying the larger structure were markedly absent, in d i c a t i n g t h e i r suppression. The rate of ejections was also observed to be s l i g h t l y less than during Newtonian flow. This departure in flow behaviour was observed s l i g h t l y before (Re - 6000) the 'onset' of drag reduction, as defined by the gross-flow s t u d i e s , when f r i c t i o n factors begin to f a l l below the Newtonian f r i c t i o n factor l i n e . It became more evident with increasing Re to the 'onset' range (9500 ± 1500). Supporting evidence. ' In contrast to gross-flow s t u d i e s , very few v i s u a l i -zation studies have been done on drag-reducing systems. The 49 observations of this work may be p a r t i a l l y substantiated by some investigations made under widely d i f f e r e n t conditions. Gadd [26] conducted a simple experiment by i n j e c t i n g coloured jets of water and 30 WPPM Polyox solution into stag-nant pools of l i q u i d s . The Polyox j e t showed much less d i f -fusion than the water j e t , in d i c a t i n g a suppression of small scale eddies in the polymer s o l u t i o n . Giles and P e t t i t [61] observed flow i n s t a b i l i t i e s in Polyox solutions using dye streams in c a p i l l a r y tubes 1.5mm d i a . The s t a b i l i t y of the flow, indicated by dye filament breakup, increased monoton-i c a l l y with polymer concentrations. Shaver and M e r r i l l [30] studied highly pseudoplastic (n'= 0.61) CMC solutions by dye i n j e c t i o n at the pipe wall and c e n t e r l i n e . Wall i n j e c t i o n showed that horseshoe v o r t i c e s , which formed at or near the wall and t r a v e l l e d r a d i a l l y into the core, were r e l a t i v e l y fewer and less well developed than in the Newtonian solvent. With centerline i n j e c t i o n the dye stream remained intact at a distance far downstream in pseudoplastic flow, while rapid dispersion was present in the Newtonian case. Seyer [15] reported Tanner's visual observations of the growth of turbulent spots in drag-reducing flows over f l a t plates at high Reynolds number (~ 105). At a given Reynolds number, the growth angle of a turbulent spot was markedly reduced from that of the Newtonian case. P A R T II HOLOGRAPHIC INTERFEROMETRY FLOW VISUALIZATION 50 CHAPTER 1 HOLOGRAPHY AND FLOW VISUALIZATION 1.1 Pri n c i p l e of Holography Holography or wavefront reconstruction was f i r s t reported by Gabor [57] in 1948. However, optical holo-graphy was beyond pr a c t i c a l application for the lack of a coherent l i g h t source u n t i l the advent of the laser in 1958. Leith and Upatnieks [68,69,70] l a t e r demonstrated various aspects of holography. Due to the spec i a l i z e d nature of holography a b r i e f outline of i t s mechanism and features would be in order. Holography is a two-step imaging process. The f i r s t step consists of photographically recording the i n t e r -ference pattern between an object wavefield and a reference wavefield. In the second step, this recorded pattern is used to reconstruct the o r i g i n a l object wavefield. Figures 11 and 12 show generalized holographic recording and recon-struction geometries. The amplitude of a l i g h t wave at a plane may be defined by a complex function as 51 u, x = A , . e (x,y) (x,y) (x,y) (10) where A: Amplitude modulus cj>: phase. A photographic plate in the hologram recording optics is exposed to a l i g h t amplitude d i s t r i b u t i o n A R e + AQ e , the l i g h t i n t e n s i t y being I = 1C|,R it}>0 AR e + AQ e (11) Assuming that the this intensity d i s t r i b u t i o n plitude transmittance afte r photographic emulsion recording has a l i n e a r response, the am-development is given by (12) T = Tn - kl when illuminated by the reference wave. Figure 11. Generalized Hologram Recording. (The object may be r e f l e c t i n g or transmitting) Figure 12. Holographic Reconstruction. The reconstruction beam is ide n t i c a l to the reference beam. Either a real image or a v i r t u a l image is seen at position shown. 53 Upon expanding T = T R - k 1<|>0 An e R + A„ e ( 1 3 ) = T R - kAR - kAQ2 + 2k AR AQ cos (<(>0-<pR) (14) unmodulated object and reference i n -tens i t i es The fine l i n e structure of the hologram that causes i t to act l i k e a d i f f r a c t i o n grating is represented by the term i U 0 - 4 > R ) 2k AR AQ cosU0-<J>R) = k A R AQ e (D + k A R A Q e 0 R ( 1 5 ) ( i i ) Term (i) represents the reference int e n s i t y modu-lated by the object amplitude and is the v i r t u a l image of the object. 54 Term ( i i ) is the real or conjugate image coming into focus in front of the hologram. The presence of both a real and vi r t u a l image is c h a r a c t e r i s t i c of a l l holo-graphic processes. The v i r t u a l image formed by a hologram is a r e p l i c a of the o r i g i n a l object, exhibiting three-dimension and par-allax e f f e c t s . It appears at that location in space where the object existed during the recording process. 1.2 Holographic Interferometry This a b i l i t y of a hologram to record an object and accurately reconstruct i t at a l a t e r instant provides a powerful means of performing interferometry [72,73,74]. Real time holographic interferometry (also known as 'stored beam' or ' l i v e fringe') is done by superimposing the reconstructed v i r t u a l image on the o r i g i n a l object. This is achieved by accurate repositioning of the processed hologram in the recording setup. The v i r t u a l image of the i n i t i a l condition serves in the same way as the reference arm of a conventional interferometer while the object is under t e s t . This aspect relieves the stringent requirement for perfect optical com-ponents and matching of the optical paths. Perturbations in the test section such as mechanical displacement or r e f r a c t i v e index change due to either 55 concentration or temperature or density gradients, appear as an interferometric fringe pattern. These fringes may be observed and recorded in real time by viewing through the hologram. 1.3 The Holographic Interferometer as a Flow  V i s u a l i z a t i o n Tool The holographic interferometer may be considered as a common path interferometer except that the test and comparison beams are separated in time [75]. Its unique feature is wave storage; the comparison wave, containing information of the i n i t i a l conditon, being stored in a holo-gram [73]. Flow v i s u a l i z a t i o n is possible with double-exposure and real-time methods, the drawback of the former being i t s i n f l e x i b i l i t y . In this method,two holograms are sequentially recorded on the same photoplate and any d i f -ference in the two situations appears as a frozen-fringe pattern. In the real-time method only one exposure is necessary. A flow disturbance inside a transparent pipe can produce variations provided that r e f r a c t i v e index gradients are present in the flowing l i q u i d . This disturbance can be made v i s i b l e by generating related amplitude effects as in an interference fringe pattern. 56 A hologram made at the no-flow condition includes the unwanted phase disturbances caused by imperfections in the optical components and the test section envelope. The reconstruction cancels these disturbances and fringe move-ments represent only those due to perturbations in the flow. Secondary effects due to mechanical movement, acoustic vibrations and thermal gradients are also present i f not properly i s o l a t e d . 1.4 Application of Moire Techniques Moire patterns commonly refer to those patterns observed when two s i m i l a r screens, sets of rulings or high frequency gratings are superposed. Since a hologram can be considered as a complex d i f f r a c t i o n g rating, the a p p l i -cation of moire techniques to holography suggests i t s e l f [76]. Small r e l a t i v e displacements of the rulings appear as large movements of the moire f r i n g e s , making the tech-nique useful to measure extremely small movements. Real-time hologram-moire interferometry [77] is analogous to superposing a recorded grating on a ' l i v e ' grating. In the reconstruction, fringes are observed in the extended volume behind the hologram in the d i r e c t i o n of the object wavefront. These fringes are the projection 57 of moire fringes generated and observed on the hologram plane [78]. The hologram at time t 0 is produced by the inter-ference of object and reference wavefronts which can be defined considering only the phase terms in the equation of two i n t e r f e r i n g wavefronts as <P0 - <PR = rn-ir (16) At a l a t e r instant of time t', the perturbed object wave and the same reference wave is given by YQ - <j)R = rn'ir (17) The moire of the fringes observed or located at the hologram is V*R 4 - 4 = NTT or (18) 58 which represents the phase difference in the object beam at d i f f e r e n t times. Exact realignment of the hologram in the record-ing optics gives a condition where <{> = <p'Q. Then, N = 0, which represents null f r i n g e s . A system of moire* fringes of desired orientation and frequency can be generated by controlled movement of the hologram. The unperturbed flow test section can be coded with i n i t i a l moire" f r i n g e s . Phase va r i a t i o n in the flowing stream is vi s u a l i z e d as real-time d i s t o r t i o n s of this fringe system which retains high v i s i b i l i t y over large optical path length d i f f e r e n c e s . 59 CHAPTER 2 DESIGN CONSIDERATIONS FOR APPARATUS AND  TECHNIQUES IN HOLOGRAPHY The essential features of the interferometer are: 1. A beam d i v i d i n g system, 2. means of taking the divided beams along d i f f e r e n t paths to form test and r e f e r -ence beams, and 3. a beam recombining system. In a holographic interferometer, the recording plate performs the th i r d function. Figure 13 shows the sectional elevation of the flow v i s u a l i z a t i o n holographic interferometer used in this study. An off-axis Fresnel holography setup with wavefront d i v i s i o n was used to conserve the available laser l i g h t for high-speed motion photography. Figure 14 shows a view of the apparatus. The apparatus consisted of the following major components : SF/BE 50 • -fj-SF: BE: D E P H A: W: B C s p a t i a l f i l t e r b eam e x p a n d e r d i f f u s e r i n d e x m a t c h i n g e n c l o s u r e p i p e w i t h f l o w m e d i u m h o l o g r a m h o l o g r a m h o l d e r w a t e r g a t e P l e x i g l a s w i n d o w s f i l m p l a n e o f H y c a m V7T7 a p p r o x i m a t e d i s t a n c e s i n cm S c a l e 1:2 Figure 13. Holographic interferometer for pipe flow vi s u a l i z a t i o n (sectional elevation). Figure 14. The holographic flow visualization apparatus. B: optical bench H: hologram C: Hycam camera P: pipe I: enhancer infusion line L: laser 62 1. The laser (L) 2. Beam expander and spatial f i l t e r (SF/BE) 3. Optical bench and enclosure 4. The v i s u a l i z a t i o n section (P, D, E) 5. The hologram (H) 6. Hologram holder and on-site processor 7. The Hycam camera (C) 2 .1 The Laser The nature of the hologram recording process demands a highly coherent l i g h t source. A high degree of temporal coherence is required to produce a stationary primary fringe pattern (see glossary) at the recording plane. A l s o , the coherence length of the laser must be greater than the d i f -ference in optical path length between the reference beam (R) and object beam (0). A continuous wave helium-neon gas l a s e r , the Spectra Physics 124A (15mW) with a model 255 exciter was the l i g h t source. It emits a 1 mm diameter collimated o monochromatic beam at a wavelength of 6328 A (cherry-red). The laser was tuned to an output of 22mW as measured with a Spectra Physics 401-C power meter. A Prontor-press leaf shutter was screwed onto the laser head to control exposure 63 times while recording holograms. A pneumatic shutter r e -lease was used for remote operation. 2.2 The Beam Expander and Spatial F i l t e r Spatial f i l t e r i n g of the beam is done to remove d i f f r a c t i o n patterns caused by dust p a r t i c l e s on the optical components in the beam path. It is accomplished by focusing the beam through an aperture which is close to the d i f f r a c -t i o n - l i m i t e d spot size of the focusing lens. col 1i mated laser beam cone-shaped expanded beam lens pinhole Figure. 15. Beam expander-spatial f i l t e r assembly A Spectra Physics model 332 spatial f i l t e r with a 4 mm focal length lens and 6.8 micron pinhole was used. It expanded the collimated laser beam to a s p a t i a l l y f i l t e r e d cone-shaped output beam having a Gaussian i n t e n s i t y d i s t r i b u t i o n . 64 2.3 The Optical Bench and Enclosure Since a hologram is a recording of a system of stationary primary interference f r i n g e s , a movement of one-half fringe width during recording can cause the fringes to be blurred out. This results in a distorted recon-structed image or no image at a l l . Hence there is the need for extreme s t a b i l i t y of the optics with, no r e l a t i v e movement between the components. The common sources of disturbances in the labora-tory may be a) f l o o r v i b r a t i o n s t r a n s f e r r e d to the work s u r f a c e , b) inadequate r i g i d i t y of the o p t i c a l mounts, c) a i r movements due to v e n t i l a t i o n , d) temperature changes, e) a c o u s t i c a l disturbances A heavily constructed stand and enclosure for the optics were necessary since the laboratory, situated on the second f l o o r of the b u i l d i n g , was not designed for optical work. The table frame (Figure F-4) was of welded tubular steel with l e v e l l i n g bolts at each l e g . A 1.2 cm thick 150 kg steel plate (1.5 x 0.75 m) rested on the frame. 65 Between the plate and frame was sandwiched a 3mm thick s t r i p of hard neoprene rubber to suppress transmission of high frequency vibrations from the f l o o r . A Gaertner S c i e n t i f i c Corp. model 210 op t i c a l bench rested on the table. The optical bench is made up of nine p a r a l l e l steel r a i l s mounted on a 5 cm thick steel table. A pneumatic suspension system, housed in a r i g i d metal frame, supports the ta b l e . In this study, the bench was bolted to the metal frame as done during i t s transpor-tation instead of being allowed to f l o a t on the suspension. The f l o a t i n g of the bench was undesirable since any d i s -turbance would cause too much r e l a t i v e motion of the optics with the p i p e l i n e . Also, i f the pipe were clamped to the f l o a t i n g bench i t s movement would cause bending and s t r e s s -ing of the glass. The complete holography system was enclosed in a box (1.5 x 0.75 x 1.0 m) made of black hardboard mounted on a metal frame. The base of the frame rested on a hard rubber s t r i p along the edges of the t a b l e . The enclosure served as a miniature darkroom inside which the hologram could be exposed and processed without removal from i t s holder. It minimized dust s e t t l i n g on the optical components and isolated a i r movements in the laboratory. It protected 66 both the unwary observer from looking d i r e c t l y into the laser beam and the optics from accidental mishandling. 2.4 The V i s u a l i z a t i o n Section A section of the glass pipeline which traversed the optical bench was used for flow v i s u a l i z a t i o n . Figure 16 shows the detail s of the test section and the i n j e c t i o n port for the r e f r a c t i v e index enhancer. Refractive effects of the glass w a l l . Due to i t s c i r c u l a r cross-section and r e l a t i v e l y thick wall (3mm), the glass pipe acts as an imperfect c y l i n d r i c a l lens. When f u l l of water, the inner wall sur-face of the pipe is not v i s i b l e . The lens e f f e c t due to the glass wall was overcome by enclosing the test section in a rectangular glass housing f i l l e d with glycerine (n = 1.474) which nearly matched the r e f r a c t i v e index of the pyrex glass pipe (n ~ 1.475). Figure 17 shows the e f f e c t of r e f r a c t i o n at the w a l l . Since this study involved the use of water as the flow medium the r e f r a c t i v e effects due to i t could not be avoided. An ideal setup would be one simi l a r to Corino's Figure 16. Test section and infusion port x = 0.712 mm (b) gly c e r i ne (n = 1.474) pyrex glass x < .003 mm (c) tr i c h i o r e t h y l e n e t r i chioroethylene (n = 1.475) pyrex glass n : i n d e x of r e f r a c t i o n r e l a t i v e to a i r . x : d i s t a n c e from the w a l l f o r t o t a l i n t e r n a l r e f l e c t i o n P i p e i . d . = 2.63 cm , o.d 3.31 cm (not to s c a l e ) Figure 17. Refraction at the pipe w a l l . a) u n e n c l o s e d p i p e b) w i t h r e f r a c t i v e i n d e x m athcing e n c l o s u r e c) i n d e x matched e n c l o s u r e and flo w medium. 69 [13] studies where trich1oroethy1ene (n = 1.475) was used -^as both the flow medium and envelope f l u i d for wall turbu-lence studies in a c i r c u l a r glass pipe. Use of diffused i l l u m i n a t i o n . Leith and Upatnieks [71] have shown that the reconstruction of deep, three-dimensional objects can be greatly improved by illuminating the object with diffused l i g h t while the reference wave remains plane or s p h e r i c a l . A d i f f u s e r , when introduced between the l i g h t source and the object, oblit e r a t e s many defects of direct coherent beam i l l u m i n a t i o n . An image formed by a coherent wave is contaminated with d i f f r a c t i o n patterns of each scattering structure in the beam path; such as dust p a r t i c l e s on sur-faces, bubbles and s t r i a t i o n s in the glass and a i r - g l a s s interface r e f l e c t i o n s . The d i f f u s e r introduces redundancy by spreading the collimated beam in a l l d i r e c t i o n s , r e s u l t i n g in the information from each object point reaching a l l points on the hologram. It ensures that the complete v i r t u a l image is v i s i b l e from a l l parts of the hologram, which allows the observer to view a 3-D object or phenomenon from d i f -ferent perspectives. The hologram can be scratched or 70 spotted with d i r t without serious loss of information. A l s o , the photoplate is more uniformly illuminated so that i t s dynamic exposure range is not exceeded at any point. The choice of a proper d i f f u s e r is e s p e c i a l l y important during visual or photographic imaging since speckle, a spotty pattern due to s e l f interference of l i g h t from many scattering elements in the d i f f u s e r , can be very ob-jectionable i f present above a certain l i m i t . A special two-layer d i f f u s e r was constructed (Figure F-5) from 3mm thick glass plates ground f i n e l y on one s i d e . 2.5 The Hologram The hologram is the most important component of this interferometer. Its quality and the f i d e l i t y of the reconstructed image are maximized by careful processing steps that maintain the dimensional s t a b i l i t y of the photo-graphic emulsion. Choice of the recording medium. The hologram recording medium used throughout this study was the Kodak 649-F Spectroscopic p l a t e . It is an 71 extremely fine grained and very high resolution (>2000 l i n e s / mm) panchromatic emulsion with good red s e n s i t i v i t y [83]. Its 15 micron thick emulsion is coated on a 1 mm thick x 102 x 127 mm glass plate for r i g i d support. The inherent slowness of this emulsion (ASA index of 0.003; [79]) was advantageous in this study since the laboratory was not t o t a l l y dark. The emulsion tolerates considerable stray l i g h t . Since exposure times for this study were \ to \ second, there was no need to resort to a faster emulsion (eg. Agfa-Gevaert 10E70, 8E70). Plate exposure f a c t o r s . Exposure time. The ideal exposure time for a hologram is that r e -quired to produce a pattern with transmitted i n t e n s i t y vary-ing uniformly about the midpoint of the straight l i n e portion of the T/E curve (Appendix D). The swings in exposure must stay within the l i n e a r region in order that the recorded primary fringes reconstruct an image of maximum brightness and minimum d i s t o r t i o n . Exposure in the nonlinear region results in deteriorated image quality termed intermodulation noise [80]. 72 The recommended exposure for the Kodak 649-F emulsion is about 1100 ergs/cm2 [81]. An exposure time range of \ to \ second and development in Kodak D-19 for Z\ to 5 minutes were found to su i t this study. Processing effects are discussed in Chapter 4 of Part I I . Beam balance r a t i o . The ideal reference beam to object beam r a t i o is that which produces the highest v i r t u a l image to object i n t e n s i t y . Carrol [82] determined an optimum beam power ratio of 4:1 using Kodak 649-F p l a t e , for maximum fringe v i s i b i l i t y in a holographic interferometer where the beam power ratios during recording and readout were kept the same. The present study had this feature since the need to use a l l the available l i g h t prohibited the use of beam attenuators. A r a t i o in the range of 4:1 to 10:1 has been found to be s a t i s f a c t o r y . Angle between beams. The spatial frequency of a primary fringe pattern is given by f = | Sinf- (19) 73 where 8 is the angle between the object and reference beams. The emulsion f a i l s i f this frequency exceeds i t s r e s o l u t i o n . The highest spatial frequency possible with this experimen-tal configuration was found to be well within the resolution l i m i t of > 2000 lines/mm for Kodak 649-F plates [83]. Processing considerations. The basic processing sequence for the exposed photoplate follows that for normal photography, employing a developer, stop bath and f i x e r . In a d d i t i o n , special steps are used to meet certain hologram requirements. The sequence is outlined in Chapter 3.4 of Part I I . Emulsion shrinkage. Development and f i x i n g of the emulsion results in some of the s i l v e r bromide being converted to metallic s i l v e r while the rest is washed away. The emulsion volume is thus reduced and being bound to a r i g i d glass backing i t causes changes in the emulsion thickness [84], The t h i c k -ness is t y p i c a l l y reduced by 15%-20% for Kodak 649F plates [85]. Emulsion shrinkage results in a distorted recon-structed image (surface r e l i e f noise) and colour s h i f t towards shorter wavelengths. 74 Yu and Gara [87] have shown that emulsion thickness variations do not a f f e c t the recording stage but seriously degrade the reconstructed image. They suggested that immer-sion of the hologram in a l i q u i d gate during recording and readout would improve the f i d e l i t y of the reconstructed image. The need for plate drying after processing is avoided and this eliminates emulsion cracking. A l s o , stresses induced in the emulsion during factory drying procedures are relieved by immersion. When plates without antihalation backings are used, undesired internal r e f l e c t i o n s from the rear glass surface give spurious fringe patterns. The use of a l i q u i d gate with an index of r e f r a c t i o n close to that of glass (1.475) greatly reduces these r e f l e c t i o n s . Dreskin and Langone [86] used a mixture of toluene and inhib i t e d methyl chloroform (2.25 : 1.0) as a suitable index-matching l i q u i d to back the photoplate. . In this work, d i s t i l l e d water was used as the l i q u i d gate since the emulsion side of the photoplate was also immersed. Although the r e f r a c t i v e index (1.333) was d i f f e r e n t from that of the glass backing (1.47) or Plexiglas (-1.48) windows of the plateholder, secondary r e f l e c t i o n s were found to be less than that for plates exposed in a i r . 75 Bleaching of holograms. Holograms recorded as s i l v e r images with normal fi l m development techniques have a usual d i f f r a c t i o n e f f i c -iency of about 4%. By reducing the s i l v e r concentration i t is found to give e f f i c i e n c i e s of up to 30%. Bleaching pro-duces a pure r e l i e f pattern consisting only of varying gelatin thickness with no l i g h t absorbing material present, resul t i n g in a brighter reconstructed image [88]. Most of the common bleaches involve the oxidation of s i l v e r , con-verting i t to an ion (Ag - e -»- Ag+) which readily reacts with a suitable negative ion in the bleach solution to pro-duce an insoluble s i l v e r s a l t . Chromic, c u p r i c , f e r r i c and mercuric s a l t s , in which the metal ion can reduce i t s valency and act as the oxidizing agent, are generally used. Various bleaches have been t r i e d and th e i r mechanisms and results discussed in detail [89,90,91,92]. Bleaches used in this study are l i s t e d in Appendix D. Bleached holograms have a tendency to darken with time when exposed to ambient l i g h t because of the formation of printout s i l v e r . McMahon and Maloney [91] have shown that the s t a b i l i t y against printout darkening is e s s e n t i a l l y determined by the s i l v e r halide of which the recording is formed; AgCl being the poorest in this respect while AgBr is 76 considerably better and Agl exhibits a very high degree of resistance. Printout darkening could, however.be used to some advantage in obtaining good fringe contrast as d i s -cussed in Chapter 4.1 of Part I I . Hardening of the emulsion prior to or afte r de-velopment has been found to e f f e c t i v e l y decrease the l i g h t s e n s i t i v i t y of reaction products of bleaching by producing a r i g i d matrix. Laming et a l . [93] reported the use of a chemical hardening solution followed by oven baking of the hologram at 180-250°C for 30-45 minutes. In this work, a formaldehyde solution was used for prehardening [92] since the plate was always immersed in a water gate. 2.6 The Hologram Holder and On-site Processor A problem in this real-time holographic i n t e r -ferometry study was the accurate relocation of the processed hologram in the recording o p t i c s . Since the interferometer was very sensitive to extremely small displacements, a null fringe condition was possible only by the exact realignment of the hologram after photographic processing. The simplest solution to this problem was to process the hologram at i t s recording l o c a t i o n , or on s i t e . 77 A holder was designed and b u i l t to meet the f o l -lowing needs; ( i ) an on-site wet processing tank for holo-grams, ( i i ) an immersion tank for the photoplate in a water gate, and ( i i i ) a precision relocating holder for holograms processed outside the recording o p t i c s . Descri pti on The assembled plateholder, shown in Figure 18 con-sisted of three u n i t s ; the tank (A), the photoplate frame (B) and the precision carriage mounts with a magnetic base (C) . The tank body was made of a 24 mm thick U-shaped Plexiglas slab with 3 mm sheets forming i t s transparent windows. An angular groove milled along the sides and bottom of the tank body mated with corresponding angular edges of the photoplate frame. The tank volume was such that a minimum quantity (325 ml) of solution was required for each processing step. The tank had one tube connection (D) serv-ing both as the i n l e t for fresh solution and a i r for a g i t a -t i o n ; and as an outlet for the used s o l u t i o n s . The channel from this tube connection runs along the bottom of the tank, to which i t was connected by a series of 14 d i s t r i b u t o r holes for uniform a i r burst a g i t a t i o n . An overflow pipe and a Figure 18. On s i t e wet processing plateholder with a water immersed hologram. 79 drip tray protected the optical bench from accidental so l u -tion s p i l l a g e . The frame was designed to hold the standard 102 mm x 127 mm x 1 mm Kodak 649-F Spectroscopic p l a t e . The plate was loaded by s l i d i n g i t down the,two guide r a i l s , which provided just enough clearance for i t s thickness, and then gently forced into s t a i n l e s s steel leaf springs along the bottom edge. This retaining mechanism held the plate without stressing i t . For plate removal after an experiment, the guide r a i l s were unscrewed and l i f t e d out because the emul-sion on the edges of the processed plate tended to bind with the Plexiglas r a i l s and the plate could not be ea s i l y s l i d out. The frame was lowered and raised in the tank with the help of two screw-on rods at the top. The plateholder assembly was mounted on three pre-c i s i o n micrometer stages, two tr a n s l a t i o n a l and one r o t a t i o n a l . The whole unit was secured to the optical bench with a mag-netic base. Tygon bottles and tubing with brass valves were used to handle the photographic s o l u t i o n s . (The detailed drawings appear in Appendix F.) 2.7 The Photo-Optical Recording System This served as a means for recording the chaotic rapid motions of turbulent flow which were displayed as 80 real-time pertrubations of the moire* f r i n g e s . The rapid motions were studied on an extended time base by the use of high-speed motion photography. Camera. A Red Lake Labs, model K20S4AE 16 mm Hycam was used to record the real-time fringe d i s p l a y . It was mounted independent of the optical bench on a Hercules model 5302 heavy duty t r i p o d . A 30x magnifying viewfinder and a ground glass focusing gate were essential for sharp imaging of the f r i n g e s . Lighting and optical arrangement. Figure 19 shows the layout of optical elements with the optical power in milliwatts indicated in the beam path. The optics were arranged to reduce l i g h t losses so that the highest possible framing rate could be used. Power meter measurements on the unexpanded beam indicated that 20-25% of the incident beam power was l o s t on r e f l e c t i o n . Hence, wavefront d i v i s i o n holography was preferred to amplitude d i v i s i o n . Although the l a t t e r pro-vides the f l e x i b i l i t y of monitoring recording and readout beam power ratios by the use of a variable density beam 81 / M Legend L: l a s e r S: s h u t t e r M: m i r r o r SF: s p a t i a l f i l t e r BE: beam expander D: d i f u s e r P : pipe E: e n c l o s u r e H: hologram C: Hycam camera (numerals i n the beam path i n d i c a t e o p t i c a l power i n m i l l i w a t t s ) Figure 19. Cine recording in real-time holographic f1ow vi suali zati on . 82 s p l i t t e r and additional mirrors, much of the useful l i g h t i s 1 o s t . Lens,. The minimum distance between the object and camera was limited by the location of the hologram. A 75 mm Cosmicar lens with a 10-15 mm extension provided a f i e l d of view of about 25 mm x 35 mm. The lens-extension tube system also f a c i l i t a t e d location of the plane of focus of the interference f r i n g e s . A l l motion pictures were taken with this lens. In addi t i o n , a 150 mm Takumar lens was employed for magnifica-tion and focusing during visual observation. Fi Im. The low inte n s i t y of the expanded laser l i g h t placed severe requirements on the type of f i l m used. To follow the sequence of motions, a higher speed f i l m was desired so that an increased framing rate could be used. However, a compro-mise between speed and resolution had to be made. Table C-I shows the d i f f e r e n t films used and the results obtained. The effect of d i f f e r e n t factors is discussed in.Chapter 4.5 of Part I I . 83 CHAPTER 3 EXPERIMENTAL PROCEDURE 3 .1 Laser Beam Alignment The laser was allowed to warm up for at least one hour before an experiment. Figures 13 and 19 show the arrange-ment of the beams. The collimated beam was ref l e c t e d from mirror M and aligned to pass just over the top of the test s e c t i o n , so that on expansion, a portion of the beam went d i r e c t l y to the photoplate H while the rest of the beam passed through the d i f f u s e r D. The lower half d i f f u s e l y illuminated the pipe P to form the object beam 0 while the upper served as the reference beam R. The beam expander and pinhole were then c a r e f u l l y aligned with a power meter. The shutter S was closed and the exposure timer ring set to the desired p o s i t i o n . 3. 2 Test Section Preparation The i n i t i a l condition to be hoiographically recorded was with the entire pipeline f i l l e d with d i s t i l l e d water at 84 laboratory conditions. The index matching enclosure surface was c a r e f u l l y cleaned with solvent to remove dust and grease. The pipe surface was s i m i l a r l y treated before f i l l i n g the enclosure with glycerine. The d i f f u s e r was adjusted so that i t backlighted the test section as viewed through a l l points at the photoplate l o c a t i o n . 3.3 Recording the Hologram The photoplate was fixed in i t s frame and immersed in the tank with the emulsion side facing the l i g h t source. The tank cover was secured. The plate was usually allowed to normalize in d i s t i l l e d water for about 30 minutes and then exposed while s t i l l immersed. To process the p l a t e , measured volumes of solutions were sequentially introduced from pressurized bottles and withdrawn under suction. Figure 20 shows the schematic processing setup. Three sol u -tion bottles were used for the processing sequence requ i r -ing a developer, stop bath and f i x e r in quick succession followed by washing. The other steps are shown in Table I I . air vacuum Legend P : photographic plate E ! darkened enclosure w : distilled water s •  fresh solution s' : used solution ® : valve Figure 20. Schematic diagram of the hologram processing setup. 86 3.4 Processing Sequence The processing sequence with the solutions and processing times is outlined for Kodak 649-F p l a t e s , the solutions being at room temperature ( 2 2° C ) . Table II Hologram Processing Sequence STEP SOLUTION TIME 1 . Normali ze d i s t i l l e d water 1/2 hour 2. Expose d i s t i l l e d water v a r i a b l e , depending on l i g h t i n t e n s i t y 3. Preharden Kodak SH-5 10 min. 4. Wash d i s t i l l e d water 5 min. 5. Develop Kodak D-l9 or HRP 4 to 5 min. 6. Stop Kodak SB-5 1/2 - 1 min. 7. Fix Kodak rapid f i x e r 2 min. 8. Wash two water washes 5 min. each 9. Bleach (for Kodak EB-2 or t i l l pattern dense patterns) Kodak R-l0 cleared 10. Clearing wash Kodak S-13; s o l n . B 2 min. 11 . Final wash two water washes 5 min. 87 From step 4 on, gentle a i r burst agitation was used. The formulae for the special treatment solutions are given in Appendix D. After a l l the processing steps, the tank was re-f i l l e d with d i s t i l l e d water and the hologram was ready for viewing as a part of the interferometer. 88 CHAPTER 4 RESULTS AND DISCUSSION 4 .1 Preliminary Studies To develop a holographic system for flow v i s u a l i z a -tion a number of preliminary f e a s i b i l i t y studies were done, the major aims being, ( i ) to obtain a d i s t o r t i o n free v i r t u a l image of the transparent pyrex glass pipe test section and ( i i ) to optimize the use of available laser l i g h t to enable the highest possible framing rate for motion photography. Holograms of various r e f l e c t i n g and transparent objects were made to test the f i d e l i t y and r e p r o d u c i b i l i t y of reconstructed v i r t u a l images. Observations from these studies are summed up in the following generalized statements. The reference beam to test beam in t e n s i t y r a t i o and the angle between the beams could be varied with great l a t i t u d e , the c r i t i c a l factor being the exposure time. The optimum time was ea s i l y determined by a step wedge exposure method. Both over- and under-exposed plates were found 89 undesirable. The former however could be bleached to give phase holograms. Of the bleaches used (Appendix D) , the chromic R-10 bleach was found to be the fastest (2 to 4 minutes) even with very dense patterns. Thus bl eached, hoi ograms be-came tanned in the course of time due to printout darkening. The cupric bleach (EB-2) gave a blue t i n t to the hologram and was found to be very much slower than the chromic bleach, requiring up to 45 minutes in some t e s t s . The e f f e c t of dust and s t r i a t i o n s in the labora-tory glass were t o t a l l y eliminated by using diffused back-l i g h t i n g . The choice of the d i f f u s e r was governed by the tolerable speckle, which becomes more severe as the grain size of the d i f f u s e r increases. The special d i f f u s e r (Figure F-5) gave a better compromise between low speckle and l i g h t loss than coarse ground g l a s s , dense white polyethylene sheet or l e n t i c u l a r screen. During interferometry i t was observed that i r r e -spective of speckle s i z e , the dark fringes appeared as con-tinuous dark lines and the speckles appeared only within the bright f r i n g e s . Unlike the observation of p a r a l l e l f r i n g e s , convoluted fringes become d i f f i c u l t to distinguish from the speckle i f the speckle size is not considerably 90 less than the fringe spacing. In such cases, the use of high contrast processing does l i t t l e to improve fringe c l a r i t y [97]. During on-site bleaching in the interferometer, the fringes were observed to gradually lose contrast and sometimes even disappear. However, when printout darkening took place, the fringes would reappear. For optimum fringe contrast, the hologram pattern must have a certain density i f other means of monitoring beam ratios are unavailable. This density (not measured qua n t i t a t i v e l y ) could be obtained by two means in the flow v i s u a l i z a t i o n interferometer: ( i ) Exposure for \ sec. and development for 3% min. in D-19 or ( i i ) Exposure for \ s e c , development for 5 min. in D-19, bleaching to clear in R-10 and then allowed to printout darken. Holograms normalized and exposed in a water gate were observed to give brighter reconstructed images than those exposed in a i r and dried after processing. About \ hour of immersion prior to exposure was found to be adequate. Processed holograms kept immersed in the water gate for periods of 4 to 6 weeks showed no sign of image quality de-t e r i o r a t i o n or loss of fringe contrast. 91 4.2 Exploratory Double-Exposure Studies Holograms of laboratory glassware were made and methods of r e f r a c t i v e index enhancement were explored. The objects were backlighted through a ground glass d i f f u s e r . Double-exposure holographic interferograms of perturbations in f l u i d s enclosed within poor quality glass envelopes showed the p o s s i b i l i t y for s i m i l a r real-time interferometry. Figures 21a and 21b are photographs of reconstruc-tions from the double-exposure holograms showing the eff e c t of heat and concentration gradients in water. The holograms were exposed for a total time of 2 sec.; 1 sec. to record the i n i t i a l c ondition, a 5 sec. interval when the perturbation was introduced ( i . e . current passed through filament or a drop of acetone put in the water), followed by another 1 sec. exposure to record the perturbed s t a t e . The r e s u l t i n g re-fr a c t i v e index changes showed up as interference bands. Figure 22 shows de t a i l s of the recording, reconstruction and photographic geometry typical for such st u d i e s . The optical path lengths shown in the recording geometry reveal a path difference of about 20 cm, demonstrat-ing the long coherence length of the l a s e r . The photographs were taken with a 200 mm lens and extention tubes on 35 mm, 400 ASA fi l m at f4.0 with 20 sec. exposure time. Figure 21. Reconstructions from double-exposure holograms of a laboratory beaker with water. a) Temperature gradients from a heated filament b) Concentration gradients of dissolving acetone Figure 22. Double-exposure holographic interferometry setup. 94 4.3 Refractive Index Enhancement These experiments demonstrated the use of either heat or concentration to enhance r e f r a c t i v e index and hence produce related interference e f f e c t s . In actual flow v i s -u a l i z a t i o n , the choice of a suitable enhancer was governed by the following requirements. a) When introduced i n t o the flov/ing stream i t would not a f f e c t the p h y s i c a l flow p r o p e r t i e s (p or u) of d i s t i l l e d water or d i l u t e Polyox s o l u t i o n s ; or re a c t chemically w i t h them. b) The r e f r a c t i v e index enhancement would be such that a l a r g e An was p o s s i b l e v/ith a very s m a l l amount of the enhancer. A number of organic l i q u i d s and solutions were tested for this purpose. Solutions of propylene glycol (CH2OHCHOHCH3) in water were found to s a t i s f y the require-ments best. Table III l i s t s some of i t s solution properties along with that of warm water, an otherwise most l i k e l y choice. A d i l u t e propylene glycol solution is seen to be better than the l a t t e r by virtue of a higher An for a given Ap. The infusion of the enhancer during flow tests was done by means of a calibrated infusion pump. 95 Table III Selection C r i t e r i a for a Refractive Index Enhancer a) Propylene glycol Wei ght % 2 0 n An x 10" 0.0 1.5 6.5 1.0000 1 .0012 1.0050 1.3330 1.3346 1.3398 0 16 68 b) Warm water Temp. °C P t n An x 10* 20 30 40 50 0.9982 0.9956 0.9922 0.9880 1.3330 1.3319 1.3305 1.3289 0 11 25 41 (data taken from the CRC Handbook of Chemistry and Physics^ 50th ed.) 96 The rate of infusion of the enhancer into the flow was governed by the flow v e l o c i t y of the stream. Visual tests were conducted with the 6.5% propylene glycol solution by varying the flow rate and enhancer infusion rate of the enhancer. At a Reynolds number of about 10 ,000 (Q^225 ml/sec) the infusion rate was about 0.03 ml/sec for v i s u a l l y observed fringe modulation. This corresponds to a bulk d i l u t i o n of the flow by 1 in 7000. Moreover, this value represents an upper l i m i t , since direct visual observation of flow patterns at higher flow rates are d i f f i c u l t . A high-speed photo-graphic recording of the modulated fringes 'sees' the en-hancer induced flow patterns more readily than the eye. Typical d i l u t i o n s of the order of 1/10,000 were used. At lower flow rates, proportionally less enhancer infusion was required, which was adjusted by d i a l l i n g the infusion pump. 4.4 Observations With the Holographic Flow V i s u a l i z a t i o n  Interferometer Moire* fringe coding. the Figure 23 shows the schematic v i s u a l i z a t i o n and recording setup. perspective view of By on-site processing Figure 23. Holographic flow v i s u a l i z a t i o n interferometer showing co-ordinate axes and the plane of fringe focus. 98 or accurate relocation of the hologram, a superposition of the v i r t u a l image on the object was possible so that no i n i t i a l moire" fringes were present (N = 0). This condition was very sens i t i v e to the s l i g h t e s t disturbance (pipe v i b r a -tions during flow, building v i b r a t i o n s , small temperature fluctuations) and was found d i f f i c u l t to maintain. However, the formation of an i n i t i a l moire* fringe pattern by controlled displacement of the hologram provided a method of 'coding' the test s e c t i o n . This imaged coding does not physically disturb the flow being v i s u a l i z e d . Nature and location of f r i n g e s . The spatial frequency, orientation and s e n s i t i v i t y of the coded pattern could be adjusted by displacing the plateholder on i t s micrometer controlled t r a n s l a t i o n stages. Figure 24 (a to d) shows some examples of possible moire" fringe patterns which could be altered to any desired p o s i -t i o n . The s e n s i t i v i t y of the interferometer to pertur-bations decreased as the hologram displacement was made larg e r . Hologram movement of up to 2 mm in the ± x-direction could be tolerated before the fringes became i n v i s i b l e . This happened when the fringe frequency became so high that i t merged with the speckle of the backlighting d i f f u s e r . 99 Figure 24. Examples of no-flow moire* fringe coding of the test section by hologram displacement. a) in the -x direction from null position b) near nul l - f r i n g e condition c,d) in the +x direction 100 The s t a t i c fringes came into focus very near the v e r t i c a l axial plane (y-axis) of the pipe. This feature f a c i l i t a t e d focussed viewing of both the fringes and the wall region of the pipe where v i s u a l i z a t i o n was of i n t e r e s t . Interpretation of f r i n g e s . Fringes in hologram interferometry can be i n t e r -preted in the same manner as in c l a s s i c a l interferometry. However, the complexity in object shape, which made the object wavefront undefinable, did not permit a geometrical solution for the moire* fringe d i s t o r t i o n . Hence, the need for a q u a l i t a t i v e approach to interpret fringes became necessary. The fringes were found to d i s t o r t due to two major reasons, ( i ) r e f r a c t i v e index enhanced flow and ( i i ) vibration of the pipe due to the flowing l i q u i d . Observations showed that the nature of fringe motions due to ( i ) and ( i i ) were d i s t i n c t l y d i f f e r e n t . The enhancer in the flowing l i q u i d caused the fringes to ' s w i r l ' and 'wave,' the kind of motion one would observe in a tracer marked f l u i d stream. Mechanical movement caused the fringes to be shif t e d bodily to d i f f e r e n t o r i e n t a t i o n s . These descriptions are i l l u s t r a t e d in sketches and photographs in Figure 25 and 27. The motions are more readily appreciated when observed as real-time motion p i c t u r e s . 101 Figure 25. Fringe movements due to p e r t u r b a t i o n s . t e s t s e c t i o n l e f t of normal normal view r i g h t of normal Figure 26. Change in f r i n g e aspect with viewing p o s i t i o n . 102 Figure 27. Flow c h a r a c t e r i s t i c s d i s p l a y e d by f r i n g e di s t o r t i ons . a) wavy motion in laminar flow b) breakup in t r a n s i t i o n c,d) spots and e j e c t i o n s i n turbulence 103 A further complication to fringe analysis arises from the three-dimensionality of the hologram interferometer due to the use of a diffuse object. When viewed from d i f -ferent angles, the parallax between the object and i t s re-construction changed causing the aspect of the fringes in the i nterf erogram to change (Figure 26).' Fringe movement was related not only to the perturbation but also the view-ing angle. A l l observations in this study were made by view-ing in a plane perpendicular to the z-axis through the holo-gram. Observations of flow v i s u a l i z a t i o n of drag-reducing flow are discussed in Chapter 4.2 of Part I. F l e x i b i l i t y in v i s u a l i z a t i o n studies. The imaged moire* fringe pattern which could be adjusted by controlled hologram displacement gave a b u i l t - i n f l e x i b i l i t y to any v i s u a l i z a t i o n study. By changing the grid orientation and frequency, d i f f e r e n t aspects of the f 1 ow were observed. An i n i t i a l no-flow grid with a low fringe frequency was very sensitive to perturbations. Figure 28a shows an i n i t i a l pattern with fringes nearly p a r a l l e l to the flow. In Figure 28b, the r e f r a c t i v e index enhanced flow shows a 104 Figure 28. Real-time flow interferograms showing a) i n i t i a l no-flow moire* fringes b) a turbulent burst seen during flow c) altered high frequency moire* fringe grid at no-flow viewed closer to the pipe wall d) the fringe distortion indicates flow velocity profile. 105 turbulent spot bursting away from the pipe w a l l , i t s boundary and structure v i s i b l e in good d e t a i l . Further displacement of the hologram changed the grid to a d i f f e r e n t orientation and higher frequency (Figure 28c). This revealed the ve l o c i t y p r o f i l e of the index en-hanced portion of the flow as in Figure 28d. A turbulent eddy now appeared as a blob moving across the g r i d . 4.5 The Photo-Optical Recording System The data of this system is summarized in Tables IV and C-I. The l i m i t i n g factor on the frame rate for high-speed recording of real-time fringes was the low laser l i g h t i n t e n s i t y . This was further limited by the f-number used for framing since a low number did not accommodate the l a t e r a l movement (along z-axis) of the fringe plane, due to a limited depth of f i e l d . The disadvantage of using a high aperture was that the speckle of the d i f f u s e r came into focus on the f i l m giving a very grainy appearance to the f r i n g e s . When coupled with very high speed f i l m ( i . e . Kodak 2485 processed in MX 542-1 to give 8000 ASA) the inherent f i l m grain further deteriorated the image. From a series of tests the best combination of adequate depth of f i e l d with low f i l m grain 106 Table IV Motion Recording Instrumentation Data Camera: 16mm Hycam; 1/2.5 shutter. Lens: 75mm, f 1.9 Cosmicar with 15mm extension tube. Pipe axis to f i l m plane distance: 48 cm. Field of view: 32mm x 24mm Estimated l i g h t i n t e n s i t y = 10 meter candles at f i l m plane. Lens opening: f 4.0 / Film (Kodak 2485): at 1000 ASA. Framing speed: 100 frames/sec. Exposure time/frame: 1/250 sec. Acces sori es a) Timing l i g h t generator with 10,100 and 1000 pips/sec. b) Ground glass focusing gate. c) 30x c r i t i c a l focusing eyepiece. d) Glass Reticle with cross h a i r s . 107 and speckle noise was found to be 100 frames/sec at f 4.0 with f i l m processed at 1000 ASA. These values are strongly dependent on the hologram density, which was controlled by the processing techniques (described in Chapters 3.4 and 4.1 of Part II) to obtain optimum fringe contrast. The l i g h t incident on the f i l m was estimated at about 10 meter candles. This represents only a f r a c t i o n of the total laser l i g h t since a large portion is l o s t in the undiffracted part of the reference beam. 4.6 Improvements on the Present Arrangement. 1. Increased laser output power could provide a much higher framing rate which is essential for studies at higher flow v e l o c i t i e s . 2. A method of having the hologram integral with the test section is d e s i r a b l e . This would eliminate or greatly reduce the fringe movements due to small r e l a t i v e movements between the pipe and the hologram. 3. A refinement to the existing setup with provision for stereoscopic viewing of the flow phenomena could give three-dimensional information. This may be done by using two holograms at d i f f e r e n t angular locations to observe a single point in the region of i n t e r e s t . 108 CONCLUSIONS Drag reduction studies with d i l u t e solutions of Polyox WSR-301 in d i s t i l l e d water revealed: 1. The existence of d i s t i n c t flow regimes. 2. The onset of drag reduction was weakly depen-dent on polymer concentration and degradation. It occured over a narrow range of Reynolds number (9500 ± 1500) and wall shear stress (4.0 ± 1.0 dynes/cm2). 3. The extent of drag reduction after onset, governed by the polymer property parameter 6, was observed to follow the power-law relationship with concentration given by 6 cc c 0- 5 A new application of holography to real-time l i q u i d flow v i s u a l i z a t i o n was demonstrated. V i s u a l i z a t i o n of drag-reducing flow with the holographic interferometer revealed: 109 1. Apparently less d i s s i p a t i v e eddies during turbulent flow of polymer solution as compared to water. 2. The eddies'to be ejected from the wall region into the bulk flow with a r e l a t i v e l y lower frequency. n o RECOMMENDATIONS A continued visual investigation of the wall region using holographic techniques should be conducted: (i) to obtain quantitative information of the frequency, scale and structure of turbulence in d i l u t e polymer solutions and ( i i ) to obtain information which might reveal the cause of turbulence suppression in such systems, which may correlate the local ejection sequences with polymeric and flow parameters. Simultaneous laser Doppler anemometry and laser holographic v i s u a l i z a t i o n , combined with high-speed o s c i l l o -graphy, would be valuable in formulating a detailed quanti-tative physical picture of turbulence in the wall region during drag reduction. I l l GLOSSARY OF OPTICAL TERMS Fringe pattern: alternate dark and bright bands of l i g h t . Primary Interference fringes: a microscopic fringe pattern recorded on the hologram as a r e s u l t of interference between object and reference beams. Secondary Interference fringes or moire* fr i n g e s : those fringes r e s u l t i n g from a difference between two conditions in the reconstrcuted imagespace. Fringe width: distance between the centres of two consecutive bright or dark bands. One fringe width represents an optical path length difference of one wavelength. Sta t i c f r i n g e s : A moire* fringe pattern with no flow inside the pipe. Dynamic fringes : Movement of the s t a t i c fringes due to r e -f r a c t i v e index enhanced flow or v i b r a t i o n . 112 N O M E N C L A T U R E Symbol Uni ts A cross section area cm2 A R , A Q amplitude modulus of l i g h t beams C , c polymer concentration in weight parts WPDM per m i l l i o n D pipe diameter cm DR drag r a t i o , per cent drag reduction f Fanning f r i c t i o n factor I i n t e n s i t y k constant of proportionality M polymer molecular weight m,m',N integers n' flow behaviour power-law index n r e f r a c t i v e index An r e f r a c t i v e index difference AP pressure drop cm of water Q bulk flow rate cm3/sec Re Reynolds number r relaxation time sec S slope o f l i n e 1 1 3 Symbol Uni ts T transmittance U bulk mean ve l o c i t y cm/sec u local v e l o c i t y cm/sec du/dy shear rate s e c- 1 x,y,z co-ordinate directions °=,<5 polymeric property parameter B cone angle of the beam degrees 6 angle between beams degrees p density gm/cm3 Ap density difference gm/cm3 n absolute v i s c o s i t y gm/cm sec [n.] i n t r i n s i c v i s c o s i t y dl/gm v kinematic v i s c o s i t y cm2/sec x shear stress dynes/cm2 Subscri pts w: wall s: solvent cr: c r i t i c a l p: polymer r e l : r e l a t i v e R: reference beam sp: s p e c i f i c 0 : object beam v: viscous *: onset 114 Legend to symbols used in figures BE beam expander BS beam s p l i t t e r C camera D d i f f u s i n g screen E r e f r a c t i v e index matching enclosure F d i r e c t i o n of flow H hologram I infusion point for r e f r a c t i v e index enhancer L expanding lens M mirror 0 object beam R reference beam P pipe SF spatial f i l t e r 115 REFERENCES Part I 1. 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Opt. Soc. Amer. 59, 1530 (1969). 88. Altman, J.H., Appl. Opt., 5, 1689 (1966). 89. Russo, V. and S o t t i n i , S., Appl. Opt., 7, 202 (1968). 90. L a t t a , J.N., Appl. Opt., 7, 2409 (1968). 91. McMahon, D.H. and Maloney, W.T., Appl. Opt., 9, 1363 (1970). 92. Pennington, K.S. and Harper, J.S., Appl. Opt., 9, 1643 (1970) . 93. Laming, F.P. et al., Appl. Opt., 10, 1181 (1971). 94. Lamberts, R.L. and Kurtz, C.N., Appl. Opt., 10, 1342 (1971) . 95. Hariharan, P. and Ramanathan, C.S., Appl. Opt., 10, 2197 (1971). 96. Waddell, J.H., Proc. SMPTE Symp. High-Speed Photog., Hollywood, C a l i f . , Oct. 1951. 97. Tanner, L.H., J . Phys. E: S c i . Instrum. , 2 , 51 7 (1968). A-1 APPENDIX A CALIBRATION OF FLOW INSTRUMENTS A.1 D i f f e r e n t i a l Pressure Transducer A schematic diagram of the AP measurement trans-ducer (Statham PM 280) is shown in Figure A l . A s t a t i c c a l i b r a t i o n of the transducer was done before each set of flow test runs with the aid of a water manometer. Procedure: 1. The input pressure lines were closed (valves 1 , 2) and the transducer connected across the manometer. 2. The transducer bridge resistance was adjusted to bring the recorder pen on the s c a l e . 3. Gain on the recorder was adjusted by t r i a l for best pen response with minimum noise. 4. The water columns in the manometer were balanced and then the recorder pen zeroed to a convenient p o s i t i o n . 5. The water manometer was then adjusted to a known AP cm water (say 5 cm). 6. With the mV span set at ImV, the recorder variable span was adjusted for a pen movement of 5 scale divisions (recorder span = 10 divs = 240 mm). The manometer AP was changed to d i f f e r e n t values to establish l i n e a r i t y of the calibrated s c a l e . The valves 1 and 2 were opened after c a l i b r a t i o n . The recorder pen movement was checked for r e p r o d u c i b i l i t y by switching. A constant maximum error of less than 0.5 mm of water was observed. 3 ® low pressure side •cal i brati ng-water manometer Statham PM280-TC transducer ® 4 •0" 2 High pressure side bridge r e s i s t o r Sargent Welch Recorder Fi gure A l . Pressure drop measurement setup. A-3 A.2 Calibration of the Infusion Pump (Sage model 355) Syringe: 50 ml B/D p l a s t i c syringe Liquid : d i s t i l l e d water Each flow rate was an average of three readings obtained with a graduated cylinder and stopwatch. The c a l i b r a -tion chart and curves are shown in Table A-I and Figure A2. Table A-I Calibration Chart of the Infusion Pump Number Dial Setting % Flow rate ml/sec. x 1 x 1/10 1 100 1 .345 0.140 2 80 1 .100 0.109 3 60 - 0.0801 4 50 0.665 -5 40 0.545 0.053 6 20 0.275 0.027 7 4 - 0.0045 Dial Setting % Figure A2. Infusion pump calibration chart. A-5 A. 3 Preparation of Polyox Solutions Solutions of Polyox WSR-301 in d i s t i l l e d water were prepared by d i l u t i n g master batches made as follows. 1. Dry Polyox powder was weighed accurately to 0.0001 gm on a Mettler balance. 2. A glass beaker containing about 200 ml of dis^ t i l l e d water was s t i r r e d by a magnetic s t i r r e r at about 500 rpm. Small amounts of the powder were dusted into swirling l i q u i d to disperse the pa r t i c l e s (Figure A3). This wetting action greatly reduced th e i r tendency to coagulate. Polyox WSR-301 powder —1000 ml beaker i s t i l l e d water magnetic s t i r r e r Figure A3. Method of Polyox dispersion. 3. These dispersed solutions containing about 1 gm of Polyox per batch were transferred into a 2.5 I master batch solution b o t t l e . 4. The dispersion was gently s t i r r e d (about 60 rpm) u n t i l complete di s s o l u t i o n in 2.5 I of d i s t i l l e d water. Master batches thus prepared were diluted to the test run batch quantity (153 £ / r u n ) . The solution was allowed to mix thoroughly for about 12 hours with a i r agitation, in the reservoir tank. Error in designating concentration values to test batch solutions is estimated at less than ± 2 WPPM. It may arise from small differences in the total volume of water in the batch. A.4 Characterization of Polyox WSR-301 Solutions The Polyox used in these studies was characterized by i t s molecular weight determined from i n t r i n s i c v i s c o s i t y measurements. r i _ lim nsp  [ n ] " C-0 C A-7 The molecular weight was determined from the expression [50] [n] = 1.25 x lO"1* M 0- 7 8 Table A-II I n t r i n s i c Viscosity Measurements (on freshly prepared Polyox WSR-301 - d i s t i l l e d water solutions in a 50-series Cannon-Fenske Viscosimeter at 25°C) Concn. C WPPM Draining time t sec Relati ve Vi scos i ty n _ t \ ~ *<> Reduced Vi scos i ty 0 t = 265.0 0 1 .000 -145 317.0 1 .1962 13.53 290 386.0 1 .4566 15.74 465 490.0 1.8490 18.25 580 540.0 2.0434 19.27 -1 1 ' 1 1 1 ' 1 — r - 1 ' — — — o — I n t r i n s i c viscosity [nl = 1 2 - 2 ^ • gm * Molecular weight of Polyox in fresh solution M = 2.5 x 106 1 1 1 I . I . I i 1 0 200 400 600 Polyox Concentration C WPPM Figure A4. Determination of molecular weight of Polyox in s o l u t i o n . B-1 APPENDIX B SAMPLE CALCULATION FROM GROSS FLOW DATA A l l calculations are based on the solvent Reynolds number. Pipe diameter D = 2.629 cm c/s Area of flow A = 5.429 cm2 Bulk mean velocity U = §• = 0.184 Q (B.l) M S € C where Q is the volumetric flow r a t e . Solvent Reynolds No. Re = p jj D (B.2) where p and y are the density and v i s c o s i t y of water. D o 1.0 x 2.629 x 0.184 Q  K e 0.01 = 48.426 Q (B.3) Wall shear stress D AP  Tw 4L B-2 where AP = c m' o f W a t e r 305 cm. of pipe T = 2.11 AP • . (B.4) W cm. water T Fanning F r i c t i o n factor f = P U2/2gc 1 cm water = 980.64 dynes/cm2 AP f = 4.188 w a t e r (B.5) U The theoretical solvent f r i c t i o n f a c t o r , f s , is given by the equation f = 0.046(Re)" 0' 2 (B.6) ( v e r i f i e d by apparatus c a l i b r a t i o n with d i s t i l l e d water.) Percentage Drag Reduction = 100 (B.7) DRAG REDUCTION STUDIES - EFFECr OF POLY HER CONCENTRATION SYSTEM : POLYOX WSR 301 IH DISTILLED HATER (FRESH) PIPE DIAMETER : 2. 63 CMS PRESSURE DROP ACROSS 3 05 CM LEN3TH POLYMER CONCENTRATION 0. WEIGHT PARTS PER MILLION 0 ML/SEC DP CH H A T E R U : H / S E C RB SOLUTION HE ROOT F 1/ROOT f TH FO DYNES/CM 2 SOLVEIIT 9 10 37.00 SO.00 70.00 100.00 115.00 1211.00 177.00 209.00 295.00 3'40.00 0. 10 0.20 0.35 0.70 0.90 1.00 1.95 2.75 1.85 S. 15 6. 82 9.21 12. fl9 . 18.12 21.18 22. 8U 32. 61 38.50 51.31 62. 63 1792. 2121. 3 389. 1812. 5568. 6001. 8 570. 10120. 11281. 16163. 0.009016 0.0098 75 0.008817 0.338610 0.038100 0.008028 0.007683 0.037771 0.036879 0.006567 170. 11 210.58 318.26 150.08 510. 31 537.95 751.21 892.09 1181.71 1331.07 10.53 10.06 10.65 10.76 10.91 11. 16 11.11 11.31 12.06 12.31 0. 21 0.12 0.009682 0.71 0.009052 1.18 0.038129 1.90 0.008196 2. 11 0.008071 1. 1 1 0.007519 5.80 0.007273 10.23 0.006789 12.98 0.006599 Table B-I. Gross flow data - d i s t i l l e d water. co i CO DS A G R E D U C T I O N S T U D I E S - E F F E C I OF POLK HER C O N C E N T R A T I O N S Y S T E M : P O L Y O X WSH 301 I N D I S T I L L E D WATER ( F R E S H ) P I P E DI AM ET ER : 2 . 6 3 C H S ' P R E S S U R E DROP A C R O S S 3 OS CM L E N G T H POLYMER C O N C E N T R A T I O N : 1 5 . H E I G H T P A R T S PER M I L L I O N Q M L / S E C 6 1 . 0 0 121 . 0 0 1 1 0 . 0 0 1 6 7 . 0 0 2 1 0 . 0 0 2 0 2 . 0 0 3 0 8 . 0 0 •4 0 0 . 0 0 DP CM WATER 0 . 5 0 0 . 9 5 1 . 2 5 1 . 7 0 2 . 5 5 3 . 9 0 4 . 7 0 6 . 6 0 U : M / S E C 14. 92 22.2<) 2 5 . 79 3 0 . 7 6 3 8 . 6 8 5 1 . 95 5 6 . 7 U 7 3 . 6 8 HE 3 9 2 2 . 58 5 9 . 6 7 7 9 . 8 0 8 6 . 1 0 1 6 8 . 1 3 6 5 4 . 1 4 9 1 3 . 1 9 3 6 8 . S O L U T I O N 0 . D 0 9 K 0 7 0 . 0 0 8 0 0 9 0 . 0 0 7 8 7 2 0 . 0 0 7 5 2 4 0 . 0 3 7 1 3 7 0 . 0 0 5 8 9 8 0 . 0 0 6 1 1 5 0 . 0 0 5 0 9 2 BB ROOT F I / R O O T F TW FO DR D Y N E S / C H 2 S O L V E N T P E R C E N T 3 8 D . 3 9 5 2 4 . 3 3 6 0 1 . 1 5 7 0 1 . 4 0 8 5 9 . 0 4 1 0 4 3 . 6 6 1 1 6 6 . 2 5 1 3 8 2 . 0 2 1 0 . 3 1 11. 17 1 1 . 2 7 1 1 . 5 3 1 1 . 8 4 1 3 . 0 2 1 2 . 7 9 1 4 . 0 1 1. 05 0 . 0 0 8 7 9 1 2 . 0 0 0 . 0 0 8 1 1 3 2 . 6 4 0 . 0 0 7 8 8 0 3 . 5 9 0 . 0 0 7 6 0 7 5 . 3 8 0 . 0 0 7 2 6 6 8 . 0 2 0 . 0 0 6 6 5 0 9 . 9 2 0 . 0 0 6 7 3 0 1 3 . 9 3 0 . 0 0 6 3 6 8 - 7 . 0 1 .3 0 . 1 1. 1 1 . 8 1 3 . 9 9 . 1 2 0 . 3 Table B-II. Gross flow data - 15 WPPM fresh Polyox solution. CD I DRAG REDUCTION STUDIES - EFFECT OF POLYMER CONCENTRATION SYSTEM : POLYOX HSR 301 IN DISTILLED HATER (FRESH) PIPE DIAMETER : 2.63 CMS PRESSURE DROP ACROSS 305 CH LENGTH POLYMER CONCENTRATION : 70. HEIGHT PARTS PER MILLION a ML/SEC UP u CH HATER CM/SEC HE SOLUTION RE ROOT F 1/ROOT F TH FO DR DYNES/CH2 SOLVENT PERCENT 75.00 1IV.00 DO.00 267.00 323.00 3 6 1.00 111.00 170.00 0.15 0.85 2.05 3.70 * .85 5.85 7. 30 8.10 13. 82 21.00 35.00 19. 18 59. 50 67.05 81.79 86.58 3631. 5520. 9200. 12928. 15610. 17625. 21198. 227 57. 0.009875 0.338073 0.037009 0.006106 0.005738 0.035150 0.031571 0.001691 360.87 195.97 770.23 1031.77 1181.71 1301. 13 1153.16 1559.13 10.06 11.13 11.91 12.19 13.20 13.55 11.79 11.60 0.95 0.308928 1.79 0.00821 1 1.33 0.007113 7.81 0.006925 10.23 0.006667 12.31 0.006509 15.10 0.006256 17.72 0.006185 •10.6 1.7 5.1 7.5 13.9 16. 3 26.9 21.1 C O I cn Table B-111. Gross flow data - 70 WPPM fresh Polyox solution DRAG REDUCTION STUDIES - EFFECT OF POLK KER CONCENTRATION SYSTEM : POLYOX HSR 301 IN DISTILLED HATER (FRESH) PIPE DIAMETER : 2.63 CMS PRESSURE DROP A:ROSS 305 CM LEN3TH POLYMER CONCENTRATION :' 140. HEIGHT PARTS PER MILLION Q DP U RB ML/SEC CM WATER CM/SEC SOLUTION RE ROOT F 1/ROOT F TH FO DYNES/CS 2 SOLVENT DR PERCENT 101).00 150.00 213.00 263.00 321).00 370.00 444 .00 454.00 o.ao 1.45 2.40 3. 15 4. 15 4.90 i.S5 6.00 19.H9 27. 63 39.24 48.45 60.42 68. 16 81. 79 83.63 5229. 7263. 10 313. 12 7.34. 15882. 179 15. 2149 8. 21983. 0.008466 0.007955 0.006530 0.005621 0.034761 0.00441.8 0.003538 0.033593 481. 16 647.78 833.39 954.77 1095.89 1190.80 1278.69 1317.70 10.87 11.21 12.38 13.34 14.49 15.04 16.81 16.68 1.69 0.008300 3. 06 0.007772 5.06 0.007246 6.65 0.006946 8.76 0.006646 10.34 0.006488 11.92 0.006256 12.66 0.006228 -2.0 -2.3 9.9 19. 1 28.4 31.9 43.4 42. 3 Table B-IV. Gross flow data - 140 WPPM fresh Polyox solution. CO I DRAG REDUCTION STUDIES - F.FPECT OF POLYMER CONCENTRATION SYSTEM : POLYOX WSR 30 1 IN DISTILLED WATER (FRESH) PIPE DIAMETER : 2.63 CNS PRESSURE DROP ACROSS 305 CH LENGTH POLYMER CONCENTS ATI ON : 200. WEIGHT PARTS PER MILLION 3 UP U RE ML/SEC CM WATER CM/SEC SOLUTION RE ROOT F 1/ROOT F TW FO DR DYNES/CM 2 SOLVENT PERCENT 78.00 155.00 190.00 226.00 313.00 357.00 396.00 506.00 0.'4j 1.50 2.00 2.55 3.85 1.55 5. 10 7.00 11. 37 28.55 35.00 141. 63 57.66 65.76 72.95 33.21 3777. 7505. 9200. 10913. 15155. 17286. 19171. 21501. 0.009130 0.007707 0.036838 0.006101 0.001851 0.031107 0.031011 0.003375 360.87 658.85 760.78 875.72 1055.53 1117.19 1211.86 1123.28 10.17 11.39 12.09 12.50 11.36 15.06 15.78 17.21 0.95 0.008858 3. 15 0.007721 1.22 0.007113 5.59 0.007160 8. 12 0.006709 9.60 0.006535 10.76 0.006100 11.77 0.006091 -3. 1 0.2 7.8 10.6 27.7 32. 6 37.3 11.6 Table B-V. Gross flow data - 200 WPPM fresh Polyox solution. C O ^4 OR AG REDUCTION STUDIES - EFFECT OF POLYMER CONCENTRATION SYSTEA : POLYOX WSR 301 IN DISTILLED HATER (FRESH) PIPE DIAMETER : 2.63 CMS PRESSURE DROP ACROSS 30S CM LENGTH POLYMER CONCENTRATION : 400. HEIGHT PARTS PER MILLION 0 DP U RE ML/SEC CM HATER CM/SEC SOLUTION RE ROOT F 1/ROOT P TH FO DR DYNES/CM 2 SOLVENT PERCENT H6.00 134.00 181.00 201).00 270.00 396.00 444 .00 500.00 0. 55 1. 15 2.00 2.05 2.90 4.25 5.25 5.85 15. 84 24.68 33. 34 38. 32 49. 74 72.95 81. 79 92. 10 41 64. 64U8. 8764. 10071. 13073. 19 174. 21498. 24210. 0.039179 0.007905 0.007535 0.335849 0.0349 10 0.003345 0.003287 0.032888 398.95 576.89 760.78 770.23 916. 10 1109.01 1232.60 1301.13 10.44 11.25 11.52 13.08 14.27 17.29 17.44 18.61 1. 16 0.008687 2.43 0.007949 4.22 0.007485 4.33 D.0072BO 6. 12 0.006910 8.97 0.006400 11.08 0.006256 12.34 0.006109 -5.7 0.6 -0.7 19.7 28.9 47.7 47. S 52.7 Table B-VI. Gross flow data - 400 WPPM fresh Polyox sol u t i o n . co i CO DRAG REDUCTION STUCIES - ElfECT OF POLYMER CONCENTRATION SYSTEM : POLYOX HSR 301 IN DISTILLED HATER (DEGRD) PIPE DIAMETER : 2.63 CMS PRESSURE DROP ACROSS 305 CM LENGTH POLYMER CONCENTRATION : 100. HEIGHT PARTS PER MILLION Q DP U RE ML/SEC CM HATER CM/SEC SOLUTION RE ROOT F 1/ROOT P TM FO DYNES/CH2 SOLVENT DR PERCENT 10 11 73.00 0.00 13.15 3535. 0.009265 310.23 10.39 0.81 0.008976 -3.2 128.00 1. 10 23. 58 6198. 0.008287 561.21 10.98 2.32 0.008023 -3.3 172.00 1. 80 31. 68 8328. 0.007510 721.71 11.51 3. 80 0.007562 0.7 190.00 2.05 35.00 9200. 0.007009 770.23 11.91 1.33 0.007113 5.1 200.00 2.30 36.81 9681. 0.007097 815.81 11.87 1. 85 0.007337 3.3 212.00 3. 25 11. 58 11718. 0.006850 969.80 12.08 6. 86 0.007063 3.0 266.00 3.50 19.00 12880. 0.006106 1006.11 12.80 7. 38 0.006931 11.9 32 1.00 1. 70 59. 13 15513.- 0.005630 1 166.25 13. 33 9. 92 0.006675 15.7 310.00 5.20 62.63 16163. 0.005552 1226.71 13.12 10.97 0.006599 15.9 388.00 6.00 71.17 18787. 0.001920 1317.70 11.26 12.66 0.006127 23.5 122.00 7. 10 77.71 20133. 0.001921 ' 1133.11 11.25 11. 98 0.006320 22.1 CO I Table B-VII. Gross flow data - 140 WPPM degraded Polyox soluti on DRAG RELUCT ION STUCIES - EFFECT OF POLYMER CONCENTRATION SYSTEM : POLYOX USR 301 IN DISTILLED HATER (DEGRD) PIPE DIAMETER : 2.63 CHS PRESSURE DROP ACROSS 305 CM LENGTH POLYMER CONCENTRATION : 200. HEIGHT PARTS PER MILLION Q HL/SEC DP U RE CM HATER CH/SEC SOLUTION BE ROOT F 1/ROOT F TH FO DR DYNES/CH2 SOLVENT PESCENT 200.00 250.00 202.00 115.00 370.00 445.00 500.00 2.35 3. 15 3.d5 4.70 5.55 6.40 7.85 36.84 46.05 51.95 63.55 68. 16 81.97 92. 10 9684. 12105. 13654. 16705. 17915. 21547. 24210. 0.007252 0.006221 0.005976 0.004874 0.005004 0.003989 0.003876 824.66 954.77 1055.53 1166.25 1267.33 1360.92 1507.22 11.74 12.68 12.94 14.32 14. 14 15.83 16.06 4.96 0.007337 6.65 0.007017 8. 12 0.006850 9. 92 0.006579 11.71 0.006488 13.50 0.006253 16.56 0.006109 1.2 11.3 12.8 25.9 22.9 36.2 36.6 Table B-111. Gross flow data - 200 WPPM degraded Polyox solution. co i o DRAG REDUCTION STUDIES - EFFECT OF FOLK HER CONCENTRATION SYSTEM : POLYOX HSR 301 IN DISTILLED HATER (DEGRD) PIPE DIAMETER : 2.63 CHS PRESSURE DROP ACROSS 305 CH LENGTH POLYHEB CONCENTRATION : 400. HEIGHT PARTS PER MILLION 0 DP U RE F RE ROOT F 1/ROOT F TH FO DR ML/SEC CM HATER CM/SEC SOLUTION DYNES/CR2 SOLVENT PERCEI 1 312.00 3. 75 57.17 15107. 0.001755 1011.74 11.50 7.91 0.006713 29.2 2 1 12.00 5.15 75.89 19919. 0.003963 1255.86 15.88 11.50 0.006350 37.6 3 170.00 6. 75 86.58 22757. 0.003772 1397.61 16.28 11.21 0.006185 39.0 Table B-IX. Gross flow data - 400 WPPM degraded Polyox solution. DO I B-12 Table B-X Slopes from the Prandtl-von Karman Plots ( F i g s . 6a, 6b, 8) Polyox concentration WPPM 6 fresh solutions 6 . degraded solutions 15 4.3 -70 8.5 -140 15.1 17.8 200 18.9 11.7 400 24.3 9.1 CT * 1 • c d ( l / / f ) Slop of a l i n e ; S = —- -— d(log Re/f) Slope of the Newtonian l i n e ; Sg = 4.0 -5 = Sn - Sc P s C-1 APPENDIX C MOTION PICTURE DATA Motion picture data of experimental runs is sum-marized in Table C-I. Certain sections are presented in the companion motion picture (scenario - Appendix E). Desirable framing rate in 16 mm motion recording for sharp reproduction [96] * « , m o r / . ^ - 40 x speed of subject (cm/sec) frames/sec width of f i e l d (cm) ~ Considering a flow Reynolds number of about 10,000 (at the onset of drag reduction in this sytem) , bulk v e l o c i t y U * 40 cm/sec f p s = H ^ i O - 500 The l i m i t a t i o n s of f i l m grain ( f i l m speed = 1000 ASA) object resolution (f number = 4.0) and available laser l i g h t i n t e n s i t y (= 10 meter candles) in turn limited the framing speed to 100 f p s . TABLE C-I. SUMMARY OF MOTION PICTURE DATA r l l m typo Hologram c o n d i t i o n s Lena F i l m i n g c o n d i t i o n s Othor data P.crarks •..•,-o/r.orr..a :,roc-jr.sod ASA & attachments •it l i g h t f p o * exp* f .no. ::•>•< 73 Kodak 24-35 b/w .v.-.-;,t!v M.-.h-nr.ec'l .'.CA v.-.riaUi In 1X642-1 dev. / . n i n at 22'C. f o r 1000 ASA Developed on s i t e . Exposure i DOC. Developed i n D-19 f o r 5 min a t 22°C. 75 mm Cosmicar on Hycam K20S4AE. O b j e c t - f i l m plant d i s t . of 1,5 ra 8.0 25 t o 400 1/62 t o L/1000 1.9 The t e s t s e c t i o n wan not in d e x matched. Tho t o t a l frame a r r a was not u t i l i z e d . I'pto 50 fps s u c c e s s f u l l y framed. A mirror removed t o improve l i g h t i n g c o n d i t i o n s . / 11 II Hologram o f (1) bloachod on s i t e i n R-10 t o c l e a r . it 10.0 II II . 1.9 Acetone used f o r flow i n d e x enhancer i n wator. Improved hologram d i f f r a c t -ion e f f i c i e n c y enabled a 100 f p s rato.Acetone l a y e r s s t r a t i f i e d . .-•A 71 n II Sot o f hologram oxpo:inre3; t , f : p l , l i »"C mado.bost f r i n g e c o n t r a s t w i t h ooc exp. bleached t o c l e a r . 150 mm Takumar T 29 mm oxtn. a t 2.5 m from object - 32 to 75 l/BO to L/180 Warm wator at 50* C f o r index enhuncor. S t r a t i f i c a t i o n o f warm l a y n Good f r i n g e readout and focus piano at pipe c e n t e r . K.r 71 " it Hologram processed on s i t e nn i n ( 1 ) . 75 mm Cosnicar i -10 mm extn. tube 8.0 50 L/125 1.9 t o 5.6 I n f u s i o n of lCSS p o l y -g l y c o l - w a t o r s o l u t i o n Good f r i n g e rod-.ilr.tion. Best r e s o l u t i o n a t f 4 . 0 . f A-.r 71 n II Hologram o f (4) bleached. it LO.O 50 nnd 100 1/125 and 1/250 4.0 ic 1.9 I n f u s i o n o f 6.555 poly g l y c o l a t 0.014 ml/s a t f l o w Re o f 3300, 5100 and 6300. Good r e a l - t i m e d i s p l a y of flow. Scenes i n c l u d e d i n companion motion p i c t u r e (scene 1 to 5i sc e n a r i o i n appendix E ) , t. J'in 71 H 0 Hologram.of (5) kept immer-sed i n tho tank f o r 0 wooks. F r i n g e v i n l b i l i t y and con-t r a s t r e t a i n e d . n 100 1/250 1.9 I n f u s i o n of 1.5% poly g l y c o l s o l u t i o n . f i l m s l i g h t l y overdcvelope.l i n d i c a t i n g higher framing c o n d i t i o n s . 7 Aug 71 it it Hologram processed o u t s i d e the r e c o r d i n g o p t i c a . II - tt ti It Tost s o c t i o n enclosed i n an indcx-matching_ g l y c o r i n o bath. Wall r e g i o n made v i s i b l e with t r a v e r s i n g f r i n g e s o f high v i s i b i l i t y . ? l i p 71 It In HX6/.2-1 dov, 4 rein at 32 C for 8000 ASA Hologram as i n (7) and bleached In R-10. n 12.0 50 lA2!> 1.9 t o 22.0 I n f u s i o n of 1.531 po l y d l y c o l . W a l l r e g i o n viewed. Cood f r i n r . e readout o f turbulence s t r u c t u r e s . Largo i n c r e a s e i n framing speo.l but u n d e s i r a b l e g r a i n incas of f i l m . 9 S'/p 71 Kodak T r i - X rev-e r s a l f i l m 160 ASA I I 75 mm Cosmicar + 15 mm extn. tube - 16 1/40 . 1.9 F r i n g e modulation i n wator and Polyox s o l -u t i o n s recorded. Sharp r e c o r d i n g o f s t a t i c f r i n g e s . Flow f r i n g e s l a c k d e t a i l duo to low f p s . !7 71 H'j'J.-ik 7W.» Eictachrome h*. ph-spoed c o l o r r e v . 125 A2A 500 ASA II II 12.0 50 1/125 2.8 1.5* p o l y g l y c o l s o l n . i n f u s i o n i n d i s t i l l e d wator and 400 WPPM Polyox s o l u t i o n . Comparison of Newtonian and drag-reducing polymer s o l u t i o n flow was p o s s i b l e . Scenes i n c l u d e d i n sec, 6 of s c e n a r i o i n appendix E. ll Cct 71 Yi<Ar:< 7277 4-X rev.b/w /.OO ASA 1000 ASA n II 100 and 150 1/25C 1/375 4.0 it n Flow d e t a i l s not s a t i s f a c t -ory duo t o i n s u f f i c i e n t l i g h t . • Kia-Mng a t tho Hycam f i l m piano on a Honoywoll Pentax 3/21 l i g h t m e t e r * frar.en por second as d i a l l e d on tho Hycara 0 expoouro por frame i n seconds (1/2.5 s h u t t e r on Hycan) D-1 APPENDIX D SELECTED DATA FOR HOLOGRAPHY a) Density vs. log E curve b) T/E curve Fi gure Dl. Characteristics of Kodak 649F plates developed for 12 min in D-19 [90] D-2 Formulae for Special Treatment Solutions Hologram prehardener, Kodak SH-5 [92] Sodium s u l f a t e , anhydrous 50 g/1 Sodium carbonate, monohydrate 12 g/1 0.5% antifogging agent (optional) 40 ml/1 Formaldehyde (added just before 5 ml/1 use) Hologram bleaching solution - chromic bleaches Kodak R-9 [94] Potassium Dichromate 9.5 g/1 S u l f u r i c a c i d , cone. 12.0 ml/1 Kodak R-l0 [88] Soln. A: Ammonium Dichromate 20 g/1 S u l f u r i c A c i d , cone. 14 ml/1 * Soln. B: Sodium Chloride 45 g/1 or Potassium Bromide 92 g/1 or Potassium Iodide 128 g / l+ 1 part A + 1 part B + 10 parts of d i s t i l l e d v/ater before use. * Russo and S o t t i n i [89] suggest 1/10 part for better r e s o l u t i o n . ^Hariharan and Ramanathan [95] suggest 2 g/1 for lesser s t a i n i n g . D-3 Hologram bleaching solution - cupric bleach. Kodak EB-2 [92] A: Copper s u l f a t e , crystals 120 g/1 C i t r i c A c i d , monohydrate 150 g/1 Potassium Bromide 7.5 g/1 B: 3% Hydrogen Peroxide s o l n . 1 part A + 1 part B mixed just before use. Hologram wash s o l u t i o n s , Kodak S-13 [94] A. Stain remover. D i s t i l l e d water 750 ml Potassium Permanganate 2.5 g S u l f u r i c A c i d , cone. 8.0 ml water to make 1 1 B. Clearing s o l u t i o n . Sodium b i s u l f i t e 10 g/1 E-1 APPENDIX E SCENARIO FOR MOTION PICTURE Film T i t l e Made by HOLOGRAPHIC INTERFEROMETRY FLOW VISUALIZATION B. U. ACHIA to supplement the thesis submitted in pa r t i a l f u l f i l m e n t of the Master of Applied Science degree in Chemical Engineering. University of B r i t i s h Columbia, Vancouver, Canada. Thesis Advisor Or. D. W. Thompson Research support: National Research Council of Canada Grant, Type of f i l m 16 mm, s i l e n t , The motion p i c t u r e , part black/white and part colour, shows some aspects of real-time holographic interferometry flow v i s u a l i z a t i o n of l i q u i d in a c i r c u l a r cross-section pipe. The flow of drag-reducing d i l u t e Polyox solution is E-2 compared with that of d i s t i l l e d water. Normal projection (16 frames/sec) shows a l l the events (taken at 50 or 100 frames/sec) in slow motion. Introduction a) The experimental method and setup, the region of interest and the framed area are shown 40 mm flow 52 mm-pipe o.d 35 mm (Kodak 2485 high-speed recording, b/w negative fi l m processed at 1000 ASA) Scene Description 1 Moire* fringe grid - s t a t i c pattern - no flow. A moire" fringe g r i d i s superimposed to traverse the test section. The pipe does not have a r e f r a c t i v e index-matching enclosure. The fringe movement i s due to bu i l d i n g v i b r a -t i o n (50 frames/sec, f 4.0). E-3 Scene Description 2 Moire fringe grid - dynamic pattern - no flow. The s t a t i c pattern of Scene 1 i s shovm to d i s t o r t due to finger pressure on the pipe (100 frames/sec, f 1.9). 3 Flow with r e f r a c t i v e index gradients. The i n i t i a l pattern of Scene 1 i s modulated by the infusion of 6.5% polyglycol s o l u t i o n § 0.014 ml/sec (100 frames/sec, f 1.9). Two flow conditions are shown. a) at Re = 3300 b) at Re = 6300 The flow patterns are r e a d i l y v i s i b l e as r e a l -time fringe d i s t o r t i o n s . 4 Reoriented i n i t i a l moire* fringes - no flow. The hologram i s displaced s l i g h t l y so that the fringes reorient p a r a l l e l to the pipe a x i s . This new pattern has a lower frequency and higher s e n s i t i v i t y than that shown i n Scene 1. 5 Flow with induced gradients. The fringe d i s t o r t i o n c l e a r l y reveals the bursts of turbulently flowing l i q u i d . Re = 3500 (100 frames/sec, f 1.9). E-4 Scene Descri ption Color: V i s u a l i z a t i o n of drag-reducing flow of d i l u t e Polyox s o l u t i o n . mm flow 3 2 mm —r pipe w a l l c r o s s w i r e s The frame measures 24 mm x 32 mm. The pipe wall i s made v i s i b l e by the index matching en-closure. (Kodak 7242 high-speed Ektachrome pro-cessed at 500 ASA. 75 mm Cosmicar lens with 15 mm extension.) Laminar, t r a n s i t i o n and turbulent flow of d i s t i l l e d water and drag-reducing 400 WPPM d i l u t e ' Polyox solu t i o n are compared. In turbulent flow, the bursts from the wall region into the bulk are observed to be d i f f e r e n t i n Newtonian and drag-reducing flow. Taken at 50 frames/sec, f 2.8 with wall i n f u s i o n of 1.5$ pol y g l y c o l s o l u t i o n at 0.02 ml/sec. The ' j i t t e r ' of the fringes i s due to very small amplitude v i b r a t i o n of the pipe due to flowing l i q u i d , giving r e l a t i v e movement between the pipe and the hologram. Turbulent bursts i n drag reduction are seen to be characterized by less v i o l e n t mixing action and r e l a t i v e l y lower frequency than i n Newtonian flow of the pure solvent. APPENDIX F APPARATUS DRAWINGS Pipe i n l e t section On s i t e processing plateholder Plateholder frame Optical enclosure and stand Diffusing screen Test section d e t a i l s Dimensions in mm Seale 1:3 SECTION X-X ELEVATION I n l e t f i t t i n g S: Brass s h e l l 2mm t h i c k D r a i n f i t t i n g F: Flange f o r 1 i n . QVF pipe Test s e c t i o n connection X: Thermowell Figure F l . Pipe i n l e t section. Detail - A major dimensions in MM Scale 1 :2 Legend A : Retai ni ng spri ng B: Guide r a i l material - Plexiglas Photoplate Frame Figure F-3. Photoplate frame. •150-O o o E: Enclosure for the optics 0: Gaertner 210 optical bench T: Iron slab for table top F: Tubular table frame in in CM L P S Levelling bolts Pipe axis Remote release for shutter Dimensions in cm Scale 1:50 cn Figure F4. Optical enclosure and stand. dimensions in mm Scale 1:1 Figure F5. Diffusing screen for object illumination. h — y 20 70 2 8 0 s e c t i o n z-z F : QVF g l a s s pipe a : end p l a t e s ( t e f l o n ) E : E n c l o s i n g box b : backing p l a t e s (aluminum) I • I n f u s i o n l i n e c: t e n s i o n rods P Plenum chamber ( P l e x i g l a s ) d: i n s e r t S Sleeve ( t e f l o n ) r : o - r i n g s e a l s W 0.4 mm w a l l s l o t g : g l y c e r i n Dimensions i n mm ~p Figure F 6 . Test section d e t a i l s . 

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