THE UN I V E RS I T Y O F M I C H I G AN COLLEGE OF ENGINEERING Department of Mechanical Engineering Heat Transfer Laboratory Technical Report No. 6 AN EXPERIMENTAL STUDY OF THE INFLUENCE OF LOCALIZED, NORMAL SURFACE OSCILLATIONS ON THE LAMINAR FLOW OVER A FLAT PLATE James M. Deimen John A. Cf-'rk ORA Project 05065 under contract witi'o AEROSPACE RESEARCH LABORATORIES, OAR AERONAUTICAL SYSTEMS DIVISION AIR FORCE SYSTEMS COMMAND WRIGHT-PATTERSON AIR FORCE' BASE, OHIO CONTRACT NO. AF 33(657)-8368 administered through: OFFICE OF RESEARCH ADMINISTRATION ANN ARBOR August 1965

irn y, This report was also a dissertation submitted by the first author in partial fulfillment of the requirements for the degree of Doctor of Philosophy in The University of Michigan, 1965.

ACKNOWLEDGEMENTS The authors are indebted to the many individuals who have contributed to this work. They would like to express their appreciation to Professors Vedat S. Arpaci, Wen Jei Yang, and Arnold M. Kuethe who served as members of the thesis committee. Special thanks are directed to Professor Kuethe for his encouragement, advice and his assistance in obtaining the use of the low turbulence wind tunnel of the Aerospace Engineering Department for an extended period. The research reported herein is part of the research program on "The Influence of Localized, Normal Surface Oscillations on the Steady Laminar Flow Over a Flat Plate# of the Aerospace Research Laboratories, Office of Aerospace Research, of the United States Air Force, whose support is acknowledged. The assistance of Dr. Max G, Scherberg of this laboratory is appreciated.

TABLE OF CONTENTS Page ACKN OWLBEGEMNTS ii LIST OF TABLES v LIST OF ILLUSTRATIONS vi NOMENCLATURE xii 'ABSTRACT xv CHAPTER I. Introduction and Literature Survey 1 II. Statement of the Problem 7 III. Experimental Equipment 12 3.1 Flat Plate Configuration 12 3.2 Oscillator 18 3,3 Membrane Dynamic Configuration 20 3,4 Hot Wire Anemometer 26 3e5 Wind Tunnel 27 IV, Measurement Procedure 30 V. Uncertainty Analysis 41 VI, Results of Measurements 46 6.1 Static Pressure on the Plate as a Function of x 0 46 6,2 Comparison of the Non.oscil1ating Laminar Flow Profiles with the Blasius solution 47 6.3 Tests for Locations of Interest in Oscillating Flcw 58 6,4 Comparison of Non-oscillating with Oscillating Profiles at the Same Velocities and Geometric Locat ions 61 6,5 Comparison of the Time Averaged Oscillating Profiles for Varios Values of x, 92 6,6 Comparison of the Time Averaged Oscillating Profiles for Various Values of Frequency, 112 iii

Page CHAPTER VII e Conclusions 123 APPENDIX 125 REFERENCES 128

LIST OF TABLES Table Page 3ol Natural frequency and first harmonic of membrane 25 4o.l Boundary layer thickness as a function of free stream velocity and distance from leading edge according: to Blasius 34 402 Frequency and probe location for mean velocity change at 241 40 5.1 Calibration velocity undertainty 45 5.2 Hot wire calibration uncertainty 45 5.3 Blasius "j uncertainty for > = 20 ft/sec and x = 8-inches 45 5o4 Dimensionless velocity uncertainty 45

LIST OF ILLUSTRATIONS Figure Page 2,1 Model of the flat plate 8 2,2 Analytical model of the disturbance 8 3,1 Flat Plate test apparatus mounted in tunnel test section 13 3,2 Electronic instruments 14 3.3 Micromanometer, oscillator and wind tunnel controls 14 3.4 Flat plate configuration 15 3,5 Detail of membrane configuration 17 306 Leading edge configuration 17 3,7 Mechanical oscillator drive 21 3.8 Motor control circuit for oscillator 22 3,9 Membrane configuration 22 3,10 Hot wire probe 25 3.11 Wind tunnel 28 4,1 Calibration curve of hot wire current Versus velocity 32 4,2 Plate for static pressure check 37 6,1 Percentage change in free stream velocity as a function of x, 48 6,2 Stead'y experimental profile compared to Blasius (x = 8t Uob 40) 49 6,3 Steady experimental profile compared to Blasius (x = 10, Uam 40) 50 6,4 Steady experimental profile compared to Blasius (x = 16, Lo= = 40) 51 6,5 Steady experimental profile compared to Blasius (x 23, (. w 40) 52 vi

Figure Page 6,6 Steady experimental profile compared to Blasius (x = 8, LLo —20) 53 6~7 Steady experimental profile compared to Blasius (x -,l10,L 20) 54 608 -Steady experimental profile compared to Blasius (x 169,Ul0L 20) 55 609 Steady experimental profile compared to Blasius (x = 239, a =20) 56 6o10 Composite of steady experimental profiles 57 6,11 Mean velocity change at = 2ol due to oscillation ( 4, 20) 59 6,12 Mean velocity change at = 24l due to oscillation ( Ucm = 40) 60 6l13 Comparison of velocity profiles with and without oscillation ( UeL = 40, x 8 f = 15) 64 6o14 Comparison of velocity profiles with and without oscillation ( LeC= 40, X 9o63, f =15) 6 5 6o15 Comparison of velocity profiles with and without oscillation ( L = 40 x -= 109 f 15) 66 6,16 Comparison of velocity profiles with and without oscillation (, = 40 x = 16, f = 15) 67 6.17 Cornparison of velocity profiles with and without oscillation ( L 40, x 23, f = 15) 68 6,18 Comparison of velocity profiles with and without oscillation ( tlA=b 40, x 8, f = 50) 69 6o19 Comparison of velocity profiles with and without oscillation ( U 409 x. 109 f= 50) 70 6~20 Comparison of velocity profiles with and without oscillation ( A.o = 409 x 169 f = 50) 71 vii

Figure Page 6.21 Comparison of velocity profiles with and without oscillation ( L0 = 40, x 23, f = 50) 72 6.22 Compariosn of velocity profiles with and without oscillation ( Uto = 40, x = 8, f = 75) 73 6,23 Comparison of velocity profiles with and without oscillation ( U4 = 40, x = 9.63, f = 75) 74 6.24 Comparison of velocity profiles with and without oscillation ( U = 40, x = 10, f = 75) 75 6.25 Comparison of velocity profiles with and without oscillation ( U = 409 x = 16, f = 75) 76 6.26 Comparison of velocity profiles with and without oscillation ( 0= 40, x = 23, f 75) 77 6.27 Comparison of velocity profiles with and without oscillation ( L = 40, x = 8, f 100) 78 6.28 Comparison of velocity profiles with and without oscillation ( Lao 40, x 10, f 100) 79 6.29 Comparison of velocity profiles with and without oscillation ( b = 40, x = 12, f = 100) 80 6,30 Comparison of velocity profiles with and without oscillation ( co 40, x = 16, f = 100) 81 6.31 Comparison of velocity profiles with and wit-hout oscillation ( LL 40 x = 23, f = 100) 82 6,32 Comparison of velocity profiles with and without oscillation ( LAco 20, x = 8, f = 15) 83 6,33 Comparison of velocity profiles with and without oscillation ( o=- 20, x = 9,63, f = 15) 84

Figure PLage 6034 Comparison of velocity profiles with and without oscillation ( do 20, x = 10, f = 15) 85 6,35 Comparison of velocity profiles with and without oscillation (,i= 20, x = 16, f = 15) 86 6,36 Comparison of velocity profiles with and without oscillation ( 1s 20, x 23, f = 15) 87 6~37 Comparison of velocity profiles with and without oscillation ( 't4 20, x 8, f = 50) 88 6.38 Comparison of velocity profiles with and without oscillation ( 4x 20, x = 10, f = 50) 89 6,39 Comparison of velocity profiles with and without oscillation ( = 20, x = 16, f = 50) 90 6,40 Comparison of velocity profiles with and without oscillation ( ~U 20, x = 23, f = 50) 91 6,41 Comparison of velocity profiles with and without oscillation ( iL = 20, x = 8, f = 75) 95 6.42 Comparison of velocity profiles with and without oscillation ( Lw 20, x = 9o63, f = 75) 96 6,43 Comparison of velocity profiles with and without oscillation ( iLZo 20, x =10 f =75) 97 6, 44 Comparison of velocity profiles with and without oscillation ( U = 20 x = 16, f =75) 98& 6.45 Comparison of velocity profiles with and without oscillation ( U0a= 20) x = 239 f = 75) 99 6,46 Comparison of velocity profiles with and without oscillation ( 4 = 20, x 8, f = 100)) l00 ix

Figure Page 6.47 Comparison of velocity profiles with and without oscillation ( eu 20, x = 10, f 1= 00) 101 6.48 Comparison of velocity profiles with and without oscillation W= 20, x = 16, f 100) 102 6049 Comparison of velocity profile with and without oscillation ( U, 20, x 23, f = 100) 103 6.50 Profiles as a function of x ( U.( 40, f = 15) 104 6,51 Profiles as a function of x 6( 4 -40, f = 50) 105 6,52 Profiles as a function of x ( UL = 40,, f = 75) 106 6.53 Profiles as a function of x ( U = 40, f = 100) 107 6.o54 Profiles as a function of x (,= 20, f= 15) 108 6055 Profiles as a function of x (: = 20, f = 50) 109 60.56 Profiles as a function of x ( U = 20, f = 75) 110 6.57 Profiles as a function of x ( Lc 20, f 1 L00) 111 6 58 Profiles as a function of frequency ( UtL= 40, x 8) 113 6.59 Profiles as a function of frequency 6( LL 40, x = 10) 114 6,60 Profiles as a function of frequency ( 4aOa = 40, x = 16) 115 6061 Profiles as a function of frequency (. 4 0, x 23) 116 6062 Profiles as a function of frequency (, = 20, x = 8) 117

Figure Page 6.63 Profiles as a function of frequency ( 4 20, x = 10) 118 6,64 Profiles as a function of frequency ( 4, = 20, x = 16) 119 6.65 Profiles as a function of frequency C( t = 20, x 23) 120 6.66 Oscillation Profile difference from Blasius profile ( W = 40, f 100) 122 A.1 Eccentric configuration 127 A.2 Counterweight configuration 127

NOMENCLATURE Small letters a thermal diffusivity b the uncertainty of a variable c conversion factorlb./ft2 to "Hg d the measured variable in uncertainty analysis e distance from membrane centerline f frequency go gravitational constant h center of gravity of a circular ring sector k diameter of inside crescent of eccentric 2c length of eccentric 9cw length of counterweight m! connecting rod crank end mass m2 connecting rod wrist pin end mass m shape factor of probability curve mt Vdimensionless shape factor of probability curve (mL2) r radius of counterweight ring s membrane tension t time u velocity component in x-direction v velocity component in y-direction w membrane deflection x distance along plate from leading edge y distance normal to plate z center of gravity of eccentric Xii

Capital letters B bore of eccentric D outside radius of eccentric F denotes function F3(X') geometric oscillation profile factor I outside radius of counterweight L distance of membrane centerline from leading edge P pressure R gas constant T temperature U' dimensionless velocity ( &/U,0, ) V velocity Xi dimensionless length (x/L) Re Reynolds Number with respect to distance from plate leading edge N hot wire resistance ratio Greek letters S laminar boundary layer thickness E amplitude of oscillating membrane!/ dimensionless membrane amplitude (E/L) Blasius variable p/IbD viscosity g/ kinematic viscosity amplitude frequency parameter Pohlhausen similarity parameter f -density X JI ea

AS/ steady disturbance function (exp L-m(/6- L)ZK ) WU circular frequency CO / dimensionless circular frequency (LoL/LC ) Subscripts co free stream Up- plate surface a air m membrane s static conditions o stagnation conditions B brass

Dissert at ion Abstract AN EXPERIMENTAL STUDY OF THE INFLUENCE OF LOCALIZED NORMAL, SURFACE OSCILLATIONS ON THE LAMINAR FLOW OVER A FLAT PLATE By James M, Deimen The purpose of this investigation is to study the effect of a finite localized surface oscillation on the mean value velocity profiles in the laminar boundary layer of a flat plate and compare the results with an analytic solution. The experimental program consisted of the design, construction and testing of a flat plate with a flexible membrane located in the surface and driven by an oscillating device. The flat plate was located in a low turbulence, low speed wind tunnel. The principal measuring instrument was a hot wire anemometer mounted on a bridge over the plate with its position normal to the plate controlled from outside the tunnel. Experimental data was taken at free stream velocities of 20 and 40 feet per second, The surface oscillation amplitude was 0.050 inches and the frequency range 15 to 100 cycles per second. The results of the investigation show that a definite change in the mean value velocity profile in laminar flow occurs and is a function of free stream velocity, frequency and location on the plate surface, In addition, early transition is promoted, The analytic solution is found to be qualitatively valid in the laminar flow region downstream of the membrane,

CHAPTER I Introduction and Literature Survey Although a large number of boundary layer studies both theoretical and experimental have been conducted and reported, only a relatively small number have been concerned with the effects of an artificial time varying disturbance located in the boundary layer region. This is a report of an experimental.study of one such type of disturbance, namely the effect of an oscillatory disturbance in the boundary layer induced by the oscillatory movement of a small region normal to the surface of a flat plate. The flat plate is located in a steady parallel flow field with no pressure gradient. This experimental study is based upon a theoretical study conducted by Na (56) in which the disturbance is an oscillating bulge in the flat plate transverse to the mean velocity of the flow and sinusoidally varying in amplitude with respect to time. The literature survey was conducted with two primary objectives. First, to review previous theoretical and experimental research concerning disturbed boundary layer flows along a flat plate. Primary interest was centered upon the laminar profile and transition regions. Second, to study and analyze the techniques utilized by previous investigators, in their studies of turbulent flow and boundary layer flow. Emphasis was placed on hot wire anemometry technique since this method of measurement is

used for this investigation. The following paragraphs contain brief resumes of the more important references. Liepmann and Dhawan (43,16) studied the skin friction due to the laminar boundary layer. They utilized a flat plate with a small moveable section in its surface. Movement of this section gave a direct indication of skin friction. The flat plate was mounted in a wind tunnel of low turbulence level (0~03%). 'With a hot wire anemometer they studied the effect of small gaps in the plate surface and the Tollmien-Schlichting waves, They also studied the pressure gradient due to the leading edge of the flat plate. Schubauer and Skramstad (67) conducted an experiment in which they found the Tollmien=Schlichting waves as predicted by the Tollmien-Schlichting stability theory. In order to obtain the low turbulence levels necessary, extensive experimental work was performed to find the best combination of screens and cloth for the tunnel settling chamber and to isolate the test section from the rest of the tunnel, The results of their turbulence measurements and the effect of fan noise on turbulence are given in the report, They developed the method of producing oscillations in the boundary layer by electrodynamically vibrating a thin metallic ribbon in the boundary layer. Dryden, Schubauer, Mock and Skramstad (17) experimentally determined tables of turbulence level versus mesh length for various screens and developed corrections for

wire length when the wire length and the scale of turbulence are of the same order. Schubauer and Klebanoff (65) conducted a detailed investigation of the transition region with naturally and artificially induced turbulence spots, They used the vibrating ribbon flat plate and wind tunnel of reference (67) and devel oped a method of dual mounting for two hot wires so that a turbulent spot could be observed with respect to time and distance simultaneously. They compared their experimental results in regard to turbulent spot movement and calming effect with Emmons (20), Emmons (20) developed a probability transition theory from observations of turbulent spots on a tilting water table. He then applied this theory to transition on a flat plate with fair results. Charters (5) conducted experiments to investigate the effect of transverse contamination of laminar boundary layer flow by turbulence. He studied the edge effect of the wind tunnel walls with the flat plate fastened to the walls and also the turbulent wake of a rod or airfoil set perpendicular to the plate in the boundary layer. He found that the transverse effect spread linearly with distance downstream. Liepmann and Pila (44) conducted studies on the effect of roughness elements and heating on the boundary layer of a flat plate mounted vertically in the flowo Their method of reducing wind tunnel turbulence level is given in

the report including the components and measurement so Blasius profile measurements were taken with both hot wire and total head tube, In additionr temperatures were taken with the hot wire. Dryden (18) gives a very detailed account of problems met in hot wire boundary layer measurements and includes leading edge effects and heat loss due to the proximity of the hot wire to the wall. He includes a detailed study of the effect of a pressure gradient along the surface of the plate and a thorough investigation of the laminar,.transition and turbulent flow regions. MlcPhail (46) conducted measurements to determine the effect of the wind tunnel contraction section on the turbulence components and turbulence level. In addition9 he studied the effect of fan noise on the turbulence level~ Klebanoff and Tidstrom (39) utilizing the vibrating ribbon technique to induce vibrations in the boundary layers made measurements of fluctua iLon in the laminar boundary layer just upstream of transition. They used two hot wires mounted in two positions with simultaneous observation on an Qscilloscope to observe the movements of turbulent spots. Hill and Stenning (34) measured boundary layer profiles on a flat plate in a mainstream flow possessing pressure oscillations which were varied over a wide frequency range. They compared the profiles with oscillations to those without and found no change in the mean values from the theoretical or experimental Blasiub profiles0

Moore and Ostrach -(54) developed a theoretical analysis of the-boundary layer.,,profiles due to the oscillation of a plate about its steady mean velocity. They found a second order quasisteady effect on the mean boundary layer velocity profiles in compressible flow, Kestin, Maeder and Wang (37) developed a theoretical analysis of the boundary layer equations including first and second order effectso Their solutions are in the form of infinite series of trigonometric functionso Computer calculations indicate that oscillations due to a free stream turbulence level of 5% would produce a second order effect of only 0025% on the mean velocity profile. Klebanoff, Tidstrom and Sargent (38) present detailed measurements of boundary layer instabilities including secondary vortex streaming both for naturally and artificially induced oscillations in the boundary layer. A vibrating ribbon was used to induce oscillations and two hot wires were used to simultaneously pick up two components of the velocity for display on an oscilloscope. Criminale and Kovasznay (12) developed a theoretical analysis of the growth of a three dimensional wave packet begun by an impulsive instability and located in a Blasius boundary layer flow, Greenspan and Benney (23) have recently developed a theoretical analysis which indicates a sudden growth of secondary oscillations in flat plate boundary layer flow0 Their linearized analysis possesses good agreement with

the experimental observations of sudden violent velocity changes in the transition region as indicated by Klebanoff, Tidstrom and Sargent (38).

CHAPTER I I Statement of the Problem The problem is purely experimental in nature, conducted primarily to ascertain the validity of a mathematical model by Na(56), A physical system was designed and constructed to approximate the mathematical model o The mathematical model including the basic assumptions and results of the perturbation analysis developed by Na are as follows. Let a semi-infinite 'flatt plate be placed in a flow of constant velocity such that the mean pressure gradient on the surface of the plate is zero (Figure 2ol)o The following assumptions are made. a) Let L, the distance of the localized disturbance from the leading edge, be signiftcantly greater than the boundary layer thickness b, ioeo, e L >, ~, such that leading edge effects can be neglected. b) Let the fluid be incompressible so t.hat the induced pressure waves travel with infinite velocity~ c) Let the surface of the plate be given by the probability curve.for the two dimensional space-wise coordinates (Figure 202) and the time-wise periodic disturbance by complex notation for a steady periodic disturbance. Therefore, the surface may be given by the following expression: y = exp- g =m (x - L)2 + i;tw (2ol)

8 y / 0 Figure 2.1 Model of the flat Plate Figure 2.2 Analytical model of the disturbance

d) The effect of localized oscillations on the potential flow is neglected. The potential.flow is assumed to be a flow of constant velocity e) The velocity component of the plate in the x direction is zero. The continuity, momentum and energy equations for Cartesian coordinates can be thus expressed, Continuity, b~a._~ ~(2,2) Momentum, (2o3) Energy, 'T' rLe a.T + ~a3 ' (2.4) The boundary conditions are, AO_. /ft- (s-LY L) tfJ LL:e o aT=,T~v3., ~pIC-;~~

10 The final result obtained by Na expressing the equation for the velocity profile in the boundary layer under perturbed conditions is, ~/ - E6 / -= - 2M U! 1, c (2,6) where, and F3(Z) = zx (: 1)X-0.2sg z.50 - ( XK)'(XX'-~) 2G ' (X 1Z);- o, 25] + 2 rm> X'(2X -A )1(2.7) The primes denote non-dimensional quantities and - is the Blasius non-dimensional variable, defined as ~i3 The first three terms on the right s ide are an approximate representation of the boundary layer laminar profile over a flat plate with no oscillation, i e,, the zeroeth order solution (36,59). This non-oscillatory case may also be represented by the Blasius profile (2). The purpose of this investigation is the effect of the last term. Scrutiny of this term reveals that it may be divided into E,,/ /Re multiplied by a geometric quantity. Therefore, the effect of this term can be investigated by the alteration of the amplitude and frequency

11 of the bulge in the plate. Since the frequency enters to the fourth power, the effect of frequency alteration will be sudden and rapid. The experimental program is concerned with two comparisons. a) A comparison of the mean velocity profile with oscillation with the mean measured velocity profile without oscillationo b) A comparison of the mean velocity profile with oscillation with the prediction of the perturbation theory. Since the small perturbation solution is very restrictive in regard to the size of ' W /Re the theoretical solution is not expected to hold when the last term reaches a few percent of the sum of the first three terms. The experimental investigation utilizes relatively large values of amplitude and moderate values of frequency, i.e,, on the order of the boundary layer thickness at the bulge and frequencies up to 100 cpso In effect, a finite disturbance is introduced into the boundary layer. Therefore, the theoretical solution is only a qualitative indication of the physical problem when applied to finite disturbances.

CHAPTER III Experimental Equipment The experimental program is conducted in a low speed, low turbulence wind tunnel of the Aerospace Engineering Department. Inside the tunnel test section is a flat plate assembly with a flexible membrane located in the surface~ The principal measuring instrument is a boundary layer hot-wire probe located on a bridge over the plate (Figure 3o,),; The flat plate and supporting assembly is mounted vertically with the flexible membrane drive mechanism mounted on one side of the tunnel test section wall and the hot-wire position control passing through the opposite wall. The roof of the test section is removable glass panes to allow adjustment and visual inspection. Views of the electronic instruments and controls are shown in Figures 3.2 and 3.3, 3.1 Flat Plate Configuration The plate is 13 inches by 31 inches, 6061-ST6 aluminum plate *- inches thick (Figure 304), The plate is split at the membrane location 9 inches from the leading edge with the downstream section fastened to the T-section rails and the leading edge section moveable to facilitate adjustment of the membrane tension. The membrane is glued to the clamping bars on the underside of the plate (Figure 3.5). The dimensions of the downstream section are based upon the length of the membrane across the plate. Charters (5) 12

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~'~4.~ ~ 31-IN. 9.0-IN. -1 3/8-IN. - - 9l — I ~ FLOW 10 IN. A -_ -- -13 IN. __ /- | ~~~/ __ FLOW OSCILLATING MEMBRANE LEADING EDGE A A' T RAIL Figure 3.4 Flat plate configuration

16 found that an edge effect would expand over the surface of a plate with a constant angle of less than 100 in the downstream directiono Therefore, for a 100-angle and 8-inches membrane length the edge effects would meet at a downstream distance of approximately 22 inches. The membrane is 10-inches long to insure two dimensional flow over the full central 8-inches. The supporting structure allows the plate to be adjusted for angle of attack and pivots approximately at the membrane location. The structure holds the plate rigidly 12-inches from the wall approximately in the center of the tunnel test section. The leading edge is symmetric and razor sharp, with each surface approximately parabolic (Figure 306). The plate surface was hand sanded with #250 wet sandpaper to obtain a satin finish before the plate was split at the membrane locationo The T-rails insure that there is no change of elevation on the plate at the membrane, The membrane clamping bars are shimmed to adjust the membrane level with the plate, The gap in the surface between the membrane and the plate is less than 1/16-inches which is less than the 1/8-inches tested by Liepmann and Dhawan (16.43). The membrane material is a thin very elastic rubber cnommonly known as rubber dam. The surface roughness is comparable t o the 'surface roughness of the plateo The width under tension is 1 3/8-in. Glued to the centerline of the membrane is the aluminum driven link of the oscillating linkage.

17 MEMBRANE PLATE SURFACE KNIFE 4 CONNECTING ROD CLAMPING BAR Figure 3.5 Detail of membrane configuration Figure 3.6 Leading edge configuration Figure 3.6 Leading edge configuration

18 3.2 Oscillator The device to oscillate the membrane in the plate surface required the most effort in the development of the test apparatus. The initial goals of the investigation were set high and required an oscillating device with a frequency range of 10-1000cps and with an amplitude greater than 0o010 inches. In addition the driving device would have to be located within an area less than one inch below the plate or outside the tunnel test section. The frequency requirement indicated that an electromagnetic device would be most promising. The first test device utilized a 0.001 inches aluminum foil membrane above a specially constructed D.C. electromagnet. The membrane lay parallel to the magnetic field lines. An electric AoC. current oscillating at the desired frequency was passed through the membrane in a direction perpendicular to the magnetic field lines. Thus, an electromotive body force was developed in the membrane with its direction perpendicular to the plane of the membrane. The intensity of the oscillating disturbance generated was so small that a stethoscope had to be utilized to hear the sound. Therefore, a second electromagnetic oscillator of similar design was constructed but with an iron foil membrane of 0.003 inches thickness. The effectiveness of the superior magnetic permeability is partially nullified by the increase in stiffness and inertia in comparison with the aluminum foil, The electromagnet was operated to produce a magnetic flux ten times that necessary to produce magnetic

saturation in the foil. The signal was audible but of such low intensity that the oscillation amplitude was insufficient for the purpose of this investigation. Since the iron foil was magnetically saturated and thickening of the foil would increase the stiffness and inertia, the only alternative would be to increase the A.C. current level. Sufficient current for an appreciable oscillating amplitude would cause severe heating of the membrane. Heating of the membrane could not be permitted since heating a section of the plate would induce a change in the air flow over the plate that could not be tolerated. Therefore, the electromagnetic oscillator was abandoned. Brief consideration was given to various forms of fluid powered oscillators but the best approach seemed to center on a mechanical oscillator with a frequency range of 10-200 cps. Therefore, a mechanical oscillator was constructed as follows, The membrane is driven from outside the tunnel by a connecting rod of aluminum tubing 14-inches long, At the crank end the rod length is adjustable. The crank is an eccentric with a 9/16-inches connecting rod needle bearing. Eccentrics with 0,050 inches and 0,010 inches were constructed but only the 0,050 inches was used in this investigation. The connecting rod is connected to the driven link under the membrane with a small journal bearing. Dual counterweights on either side of the needle bearing complete the reciprocating mechanism.

20 The total reciprocating unbalance is less than 1/20 poundmass and the rotating unbalance is less than 1/20 pound mass. The counterweights approximately eliminate the rotating unbalance and shift the angular position of the maximum reciprocating unbalance. See Appendix for the design of theeccentric and counterweightso The eccentric is driven through a gearbox (Figure 3~7) The gearbox has interchangeable spur gears with possible ratios of 10 to 1, 4 to 1 and 2 to 1. The gearbox is driven by a shunt wound, 24 volt D.C, 10,000 RPM, Robbins and Myers, Hp. aircraft motor. The motor is capable of sustained operation over a range of 5000 to 12000 RPMo With the gearbox the useful frequency range is 10 to 100 cps. In addition, the eccentric can be mounted directly on the motor shaft for frequencies from 100 to 200 cps. A thin iron disk with six teeth is mounted on the motor shaft~ Continuous monitoring of the motor speed is obtained with an Electro Model 3010-A magnetic pickup and a Hewlett-tiackard Model 522-B electronic counter. Two 12-volt storage batteries are connected in series through a rheostat to control the motor speed by control of the motor voltageo Figure 308 shows the control circuitry. 3,3 Membrane dynamic configuration The instantaneous shape of the membrane at either maximum or minimum position is assumed to be triangular (Figure 3.9). Also shown is the analytical curve used by Na(56) to describe the surface,

21 Figure 3.7 Mechanical oscillator drive

22 RHEOSTAT 12 V KNIF:E | a 12 V SW ITCH Figure 3.8 Motor control circuit for oscillator.0500 IDEALIZED FORM ANALYTICAL OF ACTUAL MEM- SHAPE (56) IN. 02 50.012.5.7.6.5.4.3.2.1 0.1.2.3 4.5.6.7 - eIN. + e IN. Figure 3.9 Membrane configuration

23 y= Eexp -m(x - L)22 (3.1) In Figure 3.9 the analytical curve is made to equal the idealized triangular shape at 0.3 inches from the centerline of the membrane. The corresponding value of m' is 535 and the resulting analytical shape closely approximates the actual shape. In fact any value of m' from 400 to 1000 will cause the analytical shape to closely approximate the actual triangular shape. The possibility of harmonics in the shape of the membrane was checked analytically and experimentally. The experimental check consisted of observing the membrane in operation over the frequency range with a Strobotac stroboscopic light. No harmonics appeared in the membrane. In addition the membrane was simultaneously checked for rocking about the wrist pin and no rocking was observed. The analytical check utilized the following membrane equation, a 1 a2w (33) Wb(L~~ - at"~~ ~(3,2) which, for this case, reduces to a.___ -- - a_... — (3.3) where, z. =S (3,4)

24 The center of the membrane is displaced as ( sin sj t. The following steady state solution is applicable, ALV~= F(X:+~)p~v I~ ~(3~5) The steady equation then takes the form, F'~~)4- r'eat = Ma( 4 )We) (3e3.6) The boundary conditions are as follows Uc --!..A -' =O (3.7) The solution for: is, = e..~ (codas,,o Q; LO) 3.. tH5(3.8) and, w,{(,,_ -..,., L ( 3. 9) The membrane density = 0o0359 Lbm/in3. Table 3.1 indicates the elongation from a one inch relaxation length, the corresponding tension, the fundamental natural frequency and the first harmonic, Operation of the oscillating membrane was limited to elongations between * and 3/8 inches with frequencies below 200 cpso

25 FUNDAMENTAL FIRST ELONGATION TENSION NATURAL — HARMONIC FREQUENCY FREQUENCY Ibf.250 INCHES 27.5 /IN2 217 cps 434 cps lb1.375 INCHES 42.5 /INZ 246 cps 492 cps Table 3.1 Natural frequency and first harmonic of membrane Figure 3.10 Hot wire probe

26 3,4 Hot-wire anemometer The hot-wire probe is mounted on an aluminum bridge spanning the plate and clamped to the rails underneath the plate (Figures 3.1 and 3.4). The bridge may be clamped at any location along the plate, Mounted on the bridge is an assembly that may be clamped at any spanwise position on the bridge. This assembly contains a Starr-ett micrometer head for positioning the probe at any location normal to the plate. The micrometer head can be turned from outside the tunnel with a shaft passing through the tunnel test section wall. Various probes may be accommodated by the micrometer assembly. The hot wire probe utilized for this investigation is shown in Figure 3o10, Two curved stainless steel surgeons needles are mounted in a streamlined plastic block which in turn is mounted on the end of a i-inch aluminum rod which fits into the micrometer assembly. Soft soldered across the tips of the stainless steel needles is the hotwire itself. The hot-wire is a 0o0002 inches diameter tungsten wire 0.050 inches long. Since the length to diameter ratio of the hot wire is 200 to 1 the thermal end effects of the wire when heated may be ignored. The electrical leads are soldered into the eyes of the needles. The hot-wire instrumentation consists of a Flow Corporation Model HWB3 constant current anemometer which includes the wire current circuit, galvanometer circuit, bridge circuit and voltage amplifier. This control unit utilizes a four-wire circuit where two leads to the hot-wire

27 carry the current for the hot-wire and the other two leads are for measurement of the hot-wire voltage with the galvanometer. The output voltage of the hot wire can be fed into the amplifier which includes a compensating circuit for the thermal lag in the hot-wire. The output of the amplifier is fed through a 7 kc low pass filter to a Dumont Model 322 oscilloscope. The oscilloscope continuously monitors the instantaneous voltage drop across the hot wire as compensated and amplified. In this investigation the purpose of the oscilloscope is to enable a qualitative instantaneous understanding of the flow characteristics at each data point of each velocity profile. Measurements of RMS voltage and current are made with the galvanometer of the control unit. The temperature of the air in the wind tunnel is measured simply by means of a thermometer inserted through the roof of the tunnel test section. 305 Wind Tunnel All preliminary developmental testing was performed in a wind tunnel with a test section of 2 feet by 2 feet cross section and 4 feet in length. Unfortunately this tunnel does not possess a calming section ahead of the convergent section. Gross instabilities are present in the air flow thus preventing its use for quantitative measurement in this investigation. The wind tunnel used to obtain the results of this investigation is shown in Figure 30110 The calming section

9' 6 12' -12 10' 2.5- 3' 2 FT I0 FT 2 ____.__ __ _ _ _ _ _ __ --- —— ____ ___ _ lo10~~~~~~~~~~~~~~~~~~~~~~O CONVER UPSTREAM DOWNSTREAM DIVERGENT CALMING GENT FAN FA N CHAMBER SECTION TEST SECTION TEST SECTION SECTION SECTION Figure 3.11 Wind tunnel

29 of the tunnel contains three turbulence screens followed by a 25 to 1 convergent section. Two test sections in series are located downstream of the convergent section. The test section cross section area is 2-feet by 2-feet and 12-feet in length, The downstream test section is utilized for this investigation. Downstream of the test section is the divergent section leading to the axial flow fan, The fan is driven by a field controlled series wound DoC, motor. The tunnel is capable of producing velocities ranging from 10 to 50 feet per second through fully open test sectionso The velocity of the free stream in the tunnel test section can be kept within 0,001 inches of water in terms of the dynamic head, The free stream turbulence level of the tunnel is approximately 0,05% at 20 feet per second and 0,1% at 40 feet per s econdo For continuous monitoring of the test section free stream velocity and the calibration of the hot wire probe an F.Wo Dwyer pitot static tube is utilizedo The pitot static tube is connected to a Merriam micromanometer Model 34FB2 TM, A three way valve in the tubing leading from the stagnation point tube is included with one branch open to the ambient barometric pressure, Thus, either the dynamic head inside the tunnel test section or the difference between the tunnel test section static pressure and the ambient barometric pressure can be measured,

Measurement Procedure The operation of the hot-wire and associated equipment for the purpose of quantitative velocity measurements requires painstakingly careful measurement technique. The following procedure was developed specifically for the experimental program of this investigation but contains methods common to most hot-wire procedureso The measurement procedure may be divided into three major categories,: a) hot-wire calibration procedure, b) profile measurement procedure, c) determination of the locations of interest in the boundary layer of the flat plate. The hot-wire is calibrated with a pitot static tube and micromanometer. The hot-wire probe is mounted in a fixture fastened to the pitot tube with the hot-wire in a plane normal to the end of the tube and about 4-inches from the tube. The pitot tube is mounted about 7-inches from the tunnel test section wall where the tunnel free stream air flow is uniform. The following expression derived from Bernoulli s equation and the perfect gas laW is used to determine the tunnel air speed. o -P ) 2goRTs PsV2 (4 1) (Po -Ps) is the dynamic head and is measured by the micromanometer in inches of watero The gas constant R is 53035 pounds force feet per pound mass degree Rankin 30

31 and go is 32.174 pounds force per pound mass. Ts is the static temperature of the air in the tunnel test section as indicated by an ice bath calibrated mercury thermometer. Since the tunnel wind speed is always below a Mach number of 0.05 the static temperature and stagnation temperature are essentially alike. The static pressure inside the wind tunnel is measured with the micromanometer by comparing the static pressure of the pitot tube with the ambient outside the wind tunnel and subtracting from the corrected barometric pressure as measured by a mercury barometer. The hot-wire is operated at a resistance ratio of 1,6. The cold resistance is set with the galvanometer and bridge circuit, Then the hot wire heating current is switched on and balanced with the bridge circuit. Finally the wire current is measured with the galvanometer. A typical calibration curve of current versus velocity is shown in Figure 4.1, Hot-wire calibration is affected by aging of the hot-wire and by dirt depositing on the wire, thus causing a change in the convection heat transfer. Large changes in wind tunnel operating termperature will also cause changes in calibration. Therefore the calibration of the hot-wire is checked before and after each series of tests on each testing dayo The flat plate is mounted vertically in the tunnel test section with a minus -X degree angle of attack with respect to the geometric center plane of the tunnel, The measurement of profiles with the plate at angles of attack from 00 torso indicate that profiles most

32 70 60 N= 1.6 MA 50 40 I 0 10 20 30 40 50 V FT/sEc Figure 4.1 Calibration curve of hot wire current versus velocity

33 closely approximating the theroetical Blasius profile at all plate locations occur with the -~o angle of attack. The reason for the small angle of attack may be the slight asymmetry in the flow due to the necessary supporting structure of the plate. The measurement of profiles is as follows. The probe bridge is clamped to the plate with the hot-wire located at the desired distance downstream of the leading edge. The probe is adjusted toward the plate until the tip of the probe and its reflection in the plate just meet. Then the probe is adjusted outward to the first data point location. The wind tunnel air velocity is adjusted to the appropriate velocity as monitored by the pitot tube and micromanometero The tunnel velocity is checked and corrected for each data point. Por non-oscillatory profiles the membrane is kept level with the plate surface. The locations for the data points of each profile are determined in the following way. Table 441 gives the theoretical laminar boundary layer thickness ( i ) as defined by 99/ of the free stream velocity, The boundary layer thickness for the appropriate plate location and free stream velocity is divided by ten and the first data point location is taken at approximately 10% of the boundary layer thickness~ In addition two or three points are taken at the same interval beyond the boundary layer to insure that the free stream has been reachedo A final point is taken at least 3/4-inches from the plate to insure that the other free stream measurements are

Table 4.1 Boundary Layer Thickness As A Function of Free-Stream Velocity and Distance From Leading Edge According to Blasius (2) x In. 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 U0c! 20 8.070.099.121.140.157.171.185.198.210.222.232.243.253.262.271 in. ft. 30.057.081.099.114.128.140.151.162.172.181.190.198.206.214.222 sec. 40.050.071.086.099.111.121.131.140.149.157.164.172.179.185.192

35 correct. Some profiles measured are in the transition zone and therefore require more data points than the thirteen or fourteen above. The procedure is similar in that equidistant points are taken receding from the plate until the free stream velocity is reached and checked as above. At each data point the following procedure is carried outa) the probe is adjusted to the appropriate distance normal to the plate, b) the air stream temperature is checked and recorded, c) if the air stream temperature has deviated more than 0,50 Fahrenheit from the value at the previous data point then the hot-wire cold resistance is rechecked, d) the hot-wire is balanced with a resistance ratio of 1.6, e) the hot-wire current is read and recorded with the galvanometer, f) if the oscillator is operating then the motor speed is read and recorded from the electronic counter, g) the hot-wire current is recheckedo The oscillating profile is always measured immediately after the non-oscillating profile measurement thus insuring the most accurate possible comparison, Quantitative measurement with the hot-wire anemometer is an art that requires much experience before the best results can be consistently obtained~ The raw data are in terms of wire current in milliamperes, From the hot-wire calibration curve the velocities

36 may be read. The,velocity and the geometric position of the hot-wire are reduced to non-dimensional form as, L~,>z, = t W )(402) where 7 is the Blasius similarity parameter and a. equals 0416373 x 10-3 feet per second squared, the kinematic viscosity of air. The values of e1"/tc4 are plotted versus ~?* The static pressure gradient along the surface of the plate is checked with an aluminum flat plate of similar configuration to the test plate (Figure 402)0 The plate for the pressure check contains static pressure taps two inches apart along the length of the plate~ With the tunnel in operation and the plate at a minus ~O-angle of attack, the static pressure at each tap is compared with the ambient barometric pressure utilizing the micromanometer. The changes in the pressure difference read on the micromanometer are introduced into the following expression which is derived from Bernoulli's equation along a streamline~ dV 0- (4 3) f~V where o 075 Lbf/ft3 V is in feet per second PI is in inches of mercury C is the conversion factor 700727 lbf/ft2/"Hgo The static pressure at the plate surface must be assumed equal to the static pressure in the streamlines just beyond the

37 i1 -. i 4. i Figure 4.2 Plate for static pressure check

39 The fourth term may be differentiated with respect to and set equal to zero to obtain, -_ (53.799) F3(Z') (1-9 9 +8g )=0 or (S_22r8<2 _3 (4.4) The root of interest in this equation is = 0,422 which is the location of the maximum or minimum effect as determined by the sign -of F3(X'), Thus, the largest absolute effect may be expected at about 42% of the boundary layer thickness or * = 2.1. On the basis of this analysis the following procedure is followed. The probe is located at a given value of x and y corresponding to T = 2,1, The wind tunnel is operated at the appropriate velocity and the hotwire current balanced with the oscillating membrane turned off. The hot-wire current is measured. Immediately thereafter the oscillating membrane is turned on and the wire current rebalanced and remeasured, This procedure is repeated for various frequencies, velocities and locations on the plate starting with x = 4-inches downstream to x = 22-inches (Table 4.2)

40 Table 4.2 Frequency and Probe Location for Mean Velocity Change at = 21ol x inches 4 6 8 10 11 12 14 16 18 19.5 40 40 40 40 40 40 40 40 40 40 40 Freq. 50 50 50 50 50 0 50 50 50 50 ft c p.o s. 56 56 56 56 56 56 56 56 56 56 sec 108 108 108 108 108 108 108 108 40 40 40 40 40 40 40 40 40 40 Loyd Freq. 50 50 50 50 50 50 50 50 50 50 20 c.p.So 56 56 56 56 56 56 56 56 56 56 ft. 108 108 108 108 108 108 108 108 108 108 sec.

CHAPTER V Uncert ainty Analysis This chapter concerns both the inaccuracies associated with the actual construction of the test apparatus and the uncertainties involved in the measurement procedure for the profile data points, A single sample analysis (14) for uncertainties will be applied to the procedure for the reduction of data. The micromanometer reading accuracy for the dynamic head is estimated at + 0.001 inches of water. The micromanometer accuracy for static pressure measurement is also + 0,001 inches of water, The result of the mercury thermometer calibration in an ice bath was 32.7 ~F0 The 0.70F is assumed to hold over the entire range of the thermometer and is taken into account in obtaining the raw data for the calibration curves. The reading accuracy of the thermometer is + 0,1~Fo The uncertainty of the calibration points may be ascertained with a single sample uncertainty analysis. The uncertainty interval for each result may be computed with the following expression, bph= ( ad the functo ) u o ( dt ha rf (5m1) where F is the function used to compute the result from the raw data, di is a measured variable and bi is the uncertainty of the ith variable. Equation 4,1 rearranged 41

42 into the following form is used to compute the velocity, Nam (P -Ps T -Ad P 2erO s Ts/? (5o2) Equation 5,2 is substituted,into equation 5,1 and the resulting expression divided through by equation 5,2 to give the following expression, V PO2 P -MS X i W (F b)s(S Table 5,1 indicates the uncertainty interval for various velocities, The geometric position of the hot wire is accurate to + 0,050 inches in x and +0,005 inches normal to the plate, The hot-wire current is measured to an accuracy of ~-milliampere by balancing the galvanometer, Table 5,2 indicates the percentage inaccuracy as a function of velocity as read from the calibration curve for a hot-wire resistance ratio of 1,6, The raw cali= bration data of the hot-wire is applied directly to the calibration curve, Since the oscillating drive is a moving mechanical device, play was present when the linkage was first assembled due to inaccuracies in the manufacture of the parts, After completion of all the tests for this investigationn wear of the moving parts had increased the playo A fair estimate of the inaccuracy in the oscillating

43 amplitude is + 0.005 inches which is 10% of the 0.050 inches amplitude of oscillation used in this investigation. Angular play of the eccentric gear in the gear box never exceeded 5~ with respect to the motor pinion when the gear box was used for the lower frequencies. The oscillating frequency always remained within + 3% of the desired frequency. Extraneous vibrations are produced in the whole test plate from the tunnel test section wall to which the test plate is attached. Tunnel wall vibration originates from two sourceso A slight rotating unbalance in the wind tunnel fan produces vibrations along the entire wind tunnel. This effect is minimized by conducting all experimental tests at wind tunnel velocities which minimize the effect. When the oscillating drive mechanism is operating the reaction force of the reciprocating masses is transmitted to the tunnel test section wall and thence to the plate. The amplitude of the vibrations produced in the whole plate by the above effects always remained less than 5% of the amplitude of the oscillating membrane. The uncertainty of the profile curve results may be ascertained with a single sample uncertainty analysis. The position of the probe is calculated in terms of the Blasius(2) non-dimensional similarity parameter, (5o4)

44 The expression for ' may be substituted into equation 5.1 and the resulting expression divided by ~ to obtain bt - be ~ $+ A ~ % X + 1(5.5) Table 5,3 indicates the uncertainty interval for a typical,T at a velocity of 20 feet per second and x = 8 inches. The uncertainty interval in the non-dimensional velocity Z/ 4 /a- may be determined, also by substituting into equation 5.1 and dividing through by LL/ to obtain LII Za + Q(5.6) Table 5.4 indicates the uncertainty for typical dimensionless velocities.

45 Table 5.1 Calibration Velocity Uncertainty V 10 ft/sec 20 ft/sec 30 ft/sec 40 ft/sec bv + ~283 +.o148 +o.102 +o.078 Table 5 2 Hot Wire Calibration Uncertainty V 10 ft/sec 20 ft/sec 30 ft/sec [40 f:t/sec AV +2.5 +2 5 +1 65 +1.25 Table 5.3 Uncertainty for uo= 20 ft/sec and #A = 8 inches t 1 1.0371 2.075 3. 111 4.150 5.187 by +o178 +,192 + 213 +__.240 +.270 Table 5.4 Dimensionless Velocity Uncertainty,1.00 |075.50 525

CHAPTER VI Results of Measurements The results of this investigation may be divided into six categories. Ao Static pressure on the plate as a function of x, Bo Comparison of the non-oscillating laminar flow profiles with the Blasius (2) solution. C. Tests for locations of interest in oscillating flow, Do Comparison of non-oscillating and oscillating profiles at the same velocities and geometric, locations. Eo Comparison of oscillating profiles as a function of x at constant frequency and flow velocity. F. Comparison of oscillating profiles as a function of frequency with x and flow velocity constant, The first and second categories concern the fidelity with which the physical system approximates the theoretical model, The final four categories concern the effect produced by the oscillating disturbance. All results found in this study are for free stream velocities of 20 or 40 feet per second0 6ol Static pressure on the plate as a function of xo The static pressure data from the static taps of the flat plate constructed for the pressure gradient check are reduced with equation 4o3,, divided by the free stream velocity. 46

47 The percentage change is plotted as a function of distance along the plate surface from the leading edge. The resulting velocity gradient is assumed to occur midway between the pressure taps. Figure 6.1 is the plot for tunnel velocities of 20 feet per second and 40 feet per second, It may be noted that the maximum velocity gradient is slightly larger than 1% at 40 feet per second and always less than 1% at 20 feet per second, Thus, the assumption of a zero free stream velocity gradient is valid. 6.2 Comparison of the non-oscillating laminar flow profiles with the Blasius(2) solution,, A better check of the actual laminar flow velocity profiles along the plate as compared with the theory by Blasius(2) is afforded in Figures 6.2 through 6o10, The solid curve is the Blasius solution. The figures indicate that the measured profiles at the values of x as shown closely approximate the theory for both the 20 and 40 feet per second free stream velocities, Therefore, the physical system constructed quite closely approximates the theory for laminar boundary layer flow with no artificially induced disturbances in the boundary layer and for zero pressure gradient, Of course, random instantaneous disturbances are always present in the free stream and boundary layer as observed on the oscilloscope,

0 +1 0 o 8 o 0 0 0 INCo -I 0 40 /SEC t O 20 IF/SEC 3 5 7 9 11 13 15 17 19 21 23 25 -, INCHES Figure 6.1 Percentage change in free stream velocity as a function of x.

1.0 0.8 FT U00 = 40 YSEC 0.6 K- = 8.0 IN. BLASIUS UoO 10 EXPERIMENTAL DATA 0.4 0. 2 0 I 2 3 4 5 6 7 8 9 10 '7) = y~~ Figure 6.2 Steady experimental profile compared to Blasius (x = 8, u00 = 40)

0.8 uo - 4o F/SEC 0.6- x = 10.00 IN. u - BLASIUS uCO 1 0 (E EXPERIMENTAL DATA 0. 4 0.2 v t i I I I I I I I I I 0 1 2 3 4 5 6 7 8 9 10 "1 Y Figure 6.3 Steady experimental profile compared to Blasius (x = 10,uco = 40)

1.0 0.8 - u0= 40 FT/SEC 0.6 - x =16 IN.. BLASIUS U_ ueo Q 0 EXPERIMENTAL DATA 0.4 0.2 0 I 2 3 4 5 6 7 8 9 10 igure 6.4 Steady experimental profile compared to Figure 6.4 Steady experimental profile compared to Blasius (x = 16, uoO = 40)

1.0 0.8 0.6.~~~~~~~~~~~~0 40 FT, UQ) 40 'SEC 0. 6 x =23 IN. u - BLASIUS U00 0 EXPERIMENTAL DATA 0.4 0.2 0 I 2 3 4 5 6 7 8 9 IC vX Figure 6.5 Steady experimental profile compared to Blasius (x = 23,uCO = 40)

1.0 0.8 u0 = 20 /SEC x =8 IN. 0.6 fBLASIUS U 0 EXPERIMENTAL DATA U00 0.4 0.2 0/ 0 1 2 3 4 5 6 7 8 9 10 = y Figure 6.6 Steady experimental profile compared to Blasius (x = 8,uoo =20)

1.0 0.8 -u o = 20 FT/SEC x =IOIN. 0.6 BLASIUS Us / O EXPERIMENTAL DATA UoO 0.4 Q 0.2 0 I 2 3 4 5 6 7 8 9 10 =: Y uo VX Figure 6.7 Steady experimental profile compared to Blasius (x = 10, U o0 =20)

1.0 0.8 U9co 20 ~EC x 16 IN. 0. 6 -BLASIUS u 0 EXPERIMENTAL DATA U00 0.4 (.1w 0.2 0 0 1 2 3 4 5 6 7 8 9 10 7) = yu Figure 6.8 Steady experimental profile compared to Blasius (x = 16, uc =20)

1.0 0.8 F TjE uq00 20 'E x 23 IN. 0.6 - BLASIUS u 0 EXPERIMENTAL DATA U00 0.44 o. 2 0~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~0 0 I 2 3 4 5 6 7 8 9 IC 71 =Y uo Figure 6.9 Steady experimental profile compared to Blasius (x = 23, u c 20)

1.0.8 - BLASIUS EXPERIMENTAL.~6 L J ~~~o u =40 F1SEC X 8 INCHES 0 uo 40 FSEC= 10 INCHES 40 /SEC X= 10 INCHES U FT 1 U = 40 /SEC,= 16 INCHES 4 0 UnO= SEC,X=3 INCHES FTSE o.2 u 20 FTSEC, 8 INCHES FT.2C d < u oo'= 20 SEC,x I0 INCHES ' V uao =20 FT/SEC, 16 INCHES > )uoo = 20 FT/sEC,X=23 INCHES O IC I 1 I I J 0 2 3 4 5 6 7 8 9 10 UOD 77 =Y U/' Figure 6.10 Composite of steady experimental profiles

58 603 Tests for locations of interest in oscillating flowo All oscillating data was obtained with a membrane amplitude of + 00050 incnes. The membrane centerline is 9-inches from the leading edgeo For a free stream velocity of 20 feet per second the theoretical laminar boundary layer thickness is 0o149 inches. Therefore, the oscillating amplitude is 33% of the boundary layer thickness. For a free stream velocity of 40 feet per second the boundary layer thickness is O105 inches and therefore the oscillating amplitude is 48% Hernce, the disturbance is a finite disturbance in amplitudeo Figures 6o11 and 6,12 indicate the results of the measurements made to determine the locations of interest on the plateo The measurements were made at 2-inch intervals of x except immediately downstream of the oscillating membrane where the measurements were made one inch apart. The last position was at 19.5 i nches because of mechanical dif f iculties underneath the plate. The location of the probe from the surface of the plate always corresponded to a value of ~ of 2.1, The data are plotted as the change in mean velocity due to the oscillating disturbance as a percentage of the free stream velocity versus plate location x. The positive percentages indicate an increase in velocity. The lines at + 2.5% indicate the accuracy band of the hot wire anemometero The- centerline of the oscillating membrane is the location 9=inches from the leading edge, as shown,

%O/ou00 20 FTs +20 +10 AU LAuE a X1100 ___ ___ _0_ _ [ 50 CPS q 56 CPS -20 -20 108 CPS, OF MEMBRANE l I I I I I I I 4 6 8 10 12 14 16 18 20 X, INCHES Figure 6.11 Mean velocity change at 7 = 2.1 due to oscillation (uoo = 20)

% ~~FT uOa = 40 FSEC + 20 +10 A Au A UCO 0 _I 0 0 O -IO 0 40 CPS 0 50 CPS o -20 <: 56 CPS A 108 CPS L OOF MEMBRANE 4 6 8 10 12 14 16 18 20 X, INCHES Figure 6.12 Mean velocity change at 17 = 2.1 due to oscillation ( uoo = 40)

61 Figure 6.11 for 20 feet per second indicates that there is no significant effect upstream of the membrane for any of the frequencies checked, Immediately downstream for frequencies of 50 cps and above a definite decrease in the velocity is to be notedo At 14=inches and beyond there is a definite increase in the velocityo The instantaneous hot-wire signal on the oscilloscope indicated turbulence spots at locations 16-inches and downstream~ Figure 6.12 for 40 feet per second also indicates no significant effect upstream of the membrane except for one point at 108 cps and 8-inches, Downstream of the membrane the effect at the lower frequencies is less disc ernable, At 108 cps, however, a definite decrease occurs immediately downstream with an increase at 12=inches and thereafter~ Turbulent spots were noted on the oscilloscope from locations 14-inches downstream at a frequency of 108 cps, In reference to the Tollmien-Schlichting stability theory (64) the disturbances of this investigation lie entirely within the damping region to the left and below the neutral curve, The neutral curve applies to disturbances of vanishingly small amplitude whereas this investigation concerns large amplitude disturbances, 6,4 Comparison of non-oscillating with oscillating profiles at the same velocities and geometric locations, Figures 6,13 through 6,49 compare the mean value profile for oscillating flow with the profile for nonoscillating flowo Figures 6,13 through 6,o17 are for a

62 free stream velocity of 40 feet per second and an oscillating frequency of 15 cps. There is nosignificant difference in the profiles except those at x = 9~63 and x = 10-inches which exhibit a consistent decrease in -velocity. Figures 6.18 through 6.21 are at 40 feet per second and 50 cps. There is no significant change at x 8-incheso However, at x = 10-inches there is a consistent decrease in velocity. At x - 16-inches there is an increase in velocity near the wall and a decrease in velocity near the edge of the boundary layer. This oscillating profile exhibits an increase in the boundary layer thickness. However, no turbulent spots were noted on the oscilloscopeso The profile at x 23-inches is a definite transition profile with turbulent spots observed on the oscilloscopeo Figures 6~22 through 6026 are at 40 feet per second and 75 cps. Again no significant change is noted at x = 8 inches, However, at x = 9063-inches a consistent decrease in velocity is noted and at x = 10-inches a large decrease in velocity is apparent in combination with a thickening of the boundary layer. No turbulent spots were noted on the oscilloscope at this location. However, at x = 16-inch es the flow has gone into transition with attendent turbulent spotso The flow is further into transition at x 23-inches.

Figures 6,27 through 6.31 are at 40 feet per second and 100 cps, No significant change is noted at x = 8-inches. At x 100-inches a consistent decrease in velocity can be noted and at x 12-inches, the velocity increases near the wall and then decreases as the edge of the boundary layer is approached. No turbulent spots were observed on the oscilloscope at this location, Howevert at x = 16-inches the velocity increases over a larger portion of the boundary layer and the boundary layer. 'is thicker, A few beginning turbulent spots were noted xon the o,scilloscopeo At x 23-inches tran'sition flow has again occurred. No boundary layer separation was noted at either x = 9,63-inches or x = 0-inches, x = 9,63-inches is the downstream edge of the oscillating membraneo Figures 6,32 through 6,36 are for a velocity of 20 feet' per second and a frequency of 15 cps. There is no significant change in the profiles except at x ' 23-inches where the oscillating profile is consistently decreased. Figures 6,37 through 6,40 are for 20 feet per second and 50 cps, There is no significant change in the profiles at x = 8 or x 10inches, At x 16=inches the velocity increases near the wall and near the edge of the boundary layer but does not increase in the central portion of the boundary layer, Apparently this profile occurs just upstream of the location where the velocity profile is fully increased, No turbulent spots were preesent on the oscilloscope, At x 23=inches a transition profile occurs with turbulent spots appearing on the oscillscope,

1.0 0.8 U co= 40 FTSE 0.6x8 IN. 0.6 - 0 NO OSCILLATION U V f=15 C.P.S.,=.050 IN. BLASIUS 0.4 0.2- 0 0 0 1 2 3 4 5 6 7 8 9 10 Figure 6.13 Comparison of velocity profiles witb and without oscillation (u00 =40, x=8, f=15)

1.0 0.8 |]< Uoo:40 F/EC O0~~~~. 6 40F 0.61 -/ x 9.63 IN. u 0 7 O NO OSCILLATION UoO 04V7 f= 15 C.P.S., E=.050 IN. 0. 4 - BLASIUS 0.2 0 1 2 3 4 5 6 7 8 9 10 7)= y v X Figure 6.14 Comparison of velocity profiles with and without oscillation (uoo =40, x=9.63,f=15)

1.0 0.8 U co=40 FSEC x 10 IN. 0.6 X 0 NO OSC ILLATION U UoO 0 f= 15 C.P.S.,E=.050 IN. 0.4 BLASIUS 0, 4~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~0 0.2 0 2 3 4 5 6 7 8 9 10 71 = Yu~ Figure 6.15 comparison of velocity profiles with and without oscillation (u0040, x10, f15)

1.0 0.8 / ='40 F/EC x =16 IN. 0.6 - 0 NO OSCILLATION u | V f=15 C.P.S.,=.050 IN. UO | BLASIUS 0. 4 0.2 0 1 2 3 4 5 6 7 8 9 10 =Y y Figure 6.16 Comparison of velocity profiles with and without oscillation (UoO =40,x=16, f=15)

1.0 0.8 U = 40 FT/E co 7SEC x =23 IN. 0.6 0 NO OSCILLATION u V f=15 C.P.S.,E=.050 IN. UOO BLASIUS 0.4 0.2 0 0 I 2 3 4 5 6 7 8 9 10 Figure 6.17 Comparison of velocity profiles with and without oscillation (uco =40, x=23, f=15)

1.0 0.8 uo = 40 FT/SEC x =8 IN. 0.6 0 O NO OSCILLATION u V f=50 C.PRS.,=.050 IN. Uoo I BLASIUS 0.4 0. 2 0 L... I I I I I! I I I I 0 I 2 3 4 5 6 7 8 9 10 D =Y > Vx Figure 6.18 Comparison of velocity profiles with and without oscillation (uco =40, x=8, f=50)

1.0 0.8 -I 40F SEC 0.6 - x =10 IN. u 0 NO OSCILLATION oU 0 V f=50 C.P.S.,E=.050 IN. 0.4 BLASIUS 0.2 0 I 2 3 4 5 6 7 8 9 10 v Y Figure 6.19 Comparison of velocity profiles with and without oscillation (uO =40, x=10, f=50)

1.0 0.8 0Uco 40 /SEC x. = 16 IN. 0.6 NO OSCILLATION |7V f=50 C.P.S.,E=.050 IN. UV u I /- BLASIUS 0.4 7/. 0.2 I I I, I I I. I I Iit 0 I 2 3 4 5 6 7 8 9 10 X) =>Y Figure 6.20 Comparison of velocity profiles with and without oscillation (u00 =40, x=16, f=50)

1.0 0.8 U co = 4057SE 0.6 x = 23 IN. u I U~ O NO OSCILLATION U00 V f=50 C.P.S.,e=.050 IN. 0.4 BLASIUS 0.22 0 1 2 3 4 5 6 7 8 9 10 7) = > n Y~v Figure 6.21 Comparison of velocity profiles with and without oscillation (uco =40, x=23, f=50)

1.0 0.8 u c = 40 '/SEC 0.6 v x =8 IN. 0 NO OSCILLATION UC0o | A V f=75 C.P.S., =.050 IN. O0.41 - ~ -.. --- — BLASIUS 0.2 o0 2 3 4 5 6 7 8 9 I = 6y onovo Figure 6.22 Comparison of velocity profiles with and without oscillation (Uo =40, x=8, f=75)

1.0. 0.8 u 40 F1T 0.6 x =9.63 IN 0 NO OSCILLATIO N U uao I V f=75 C.P.S.,e=.050 IN. -. 4 BLASIUS 0. 4 0. 2 0 2 3 4 5 6 7 8 9 10 = y Figure 6.23 Comparison of velocity profiles with and without oscillation (uWo 40, x=9.63, f=75)

1.0 0.8 - u oO = 40 F/SEC 0.6 - x =10 IN. ~7u | / Q)0 NO OSCILLATION UaO Av f=75 C.P.S.,E=.050 IN. 0. 4 / ---- BLASIUS 0.2 0 I 2 3 4 5 6 7 8 9 10 = YX Figure 6.24 Comparison of velocity profiles with and without oscillation (u c =40, x=10, f=75)

1.0 V V V V~7 vv ~7FT I~7 u v o/Y ~ UCO =40 FSEC 0.6 - x =16 IN. 0 NO OSCILLATION _ V Uoo 0v f-75 C.P.S.,E=.050 IN. 0.4 BLASIUS 0.2 0 2 3 4 5 6 7 8 9 10 =y UoY Figure 6.25 Comparison of velocity profiles with and without oscillation (uco =40, x=16, f=75.)

1.0 0.8 - V =40FlS -/ U = 00 FSEC 0.6 - x =23 IN. u |Q O NO OSCILLATION UOO 1 Jv f=75 C.P.S., =.050 IN 0. 4 BLASIUS 0.2 0 I I I I I I I I 0 1 2 3 4 5 6 7 8 9 10 D =y J/iri v7X Figure 6.26 Comparison of velocity profiles.. with, and without oscillation (u c0 =40, x=23, f=75)

i.0 0.8 FT U (X)40 U00 SEC 0.6 - x:8 IN. 0 NO OSCILLATION UCO V f= 100 C.P.S.,E=.050 IN. 0.4 - BLASIUS o. 2~ eL~siu0.2 0 0 1 2 3 4 5 6 7 8 9 10 Figure 6.27 Comparison of velocity profiles with and without oscillation (u00 =40, x=8, f=100)

0.8 /V0~~~~U = u 40 T/SEC x = 10 IN. O NO OSCILLATION U uC) O g V 7v f 100 C.P.S.,E =.050 IN. 0.o ~~~~~~~~~~~~4 4BLASIUS 0.2 X0 I2 3 4 5 6 7 8 9 10 Figure 6.28 Comparison of velocity profiles with and without oscillation (Uoo =40, x=10, f=100)

1.0 0.8 -I c = 40 F'sEc 0.6 ) 7/ x =12 IN. __0.6 V 0 NO OSCILLATION uoo | />) V f=100 C.P.S.,E=.050 IN. U00 BLASIUS 0.4F 17 0.2 0 1 2 3 4 5 6 7 8 9 10 7 =Yuo Figure 6.29 Comparison of velocity profiles with and without oscillation (uo0 =40, x=12, f=100)

1.O 0.8 - Uoo 4oFTSEC x =16 IN. 0.6 0 O NO OSCILLATION u v' f = 100 C.P.S., -=.050 IN. BLASIUS 0.4 oo 0.2 0 1E 1, I I I I i i I I i I 0 1 2 3 4 5 6 7 8 9 10 Figure 6.30 Comparison of velocity profiles with and without oscillation (u co =40, x=16, f=100)

1.0 0.8 v v Uo = 40 FT x = 23 IN. O. 6 7 Q0 NO OSCILLATION u | V f = 100 C.P.S.,E =.050 IN. U%0 _.i. _ BLASIUS 0. 4 0.2 0 0 I 2 3 4 5 6 7 8 9 10 v X Figure 6.31 Comparison of velocity profiles with and without oscillation (uo0=40, x=23\, f=100)

1.0 0.8 FT 0a=0 SEC 0.6 - x 8 IN. 0 NO OSCILLATION U00 v f= 15 C.P.S.,=.050 IN. 0.4 - BLASIUS 0.2 0 1 2 3 4 5 6 7 8 9 10 7) = y o 17 Y~1/ Figure 6.32 Comparison of velocity profiles with and without oscillation (u c 20, x=8, f=15)

1.0 0.8 -20= Fl Uco 2 F/SEC 0.6 / x =9.63 IN. u 0 O NO OSCILLATION U0 Xv f = 15 C.P.S., =.050 IN. 0.4 - BLASIUS 0.2 o 1 2 3 4 5 6 7 8 9 10 Figure 6.33 Comparison of velocity profiles with and without oscillation (Uco=20, x=9.63, f=15)

1.0 0.8 FT co '20 /SEC x =10 IN. 0.6 0 NO OSCILLATION U f f=15 C.P.S.,e=.050 IN. UOO U00I~ BLASIUS 0. 4 0.2 0 I 2 3 4 5 6 7 8 9 10 17Y Figure 6.34 Comparison of velocity profiles with and without oscillation (uo=20, xl10, f=15)

1.0 0.8 -CUoo-20 FI/SEC x =16 IN. 0.6t 0 NO OSCILLATION u V f=15 C.P.S.,E=.050 IN. Uoo BLASIUS 0.4 0o 0.2 0f lI, I I I I, l I i 0 2 3 4 5 6 7 8 9 10 Figure 6.35 Comparison of velocity profiles with and without oscillation ( uo =20, x=16, f=15)

1.0 0.8 0a.0 SEC 0.6 - x =23 IN. 0 NO OSCILLATION U UoO /V 7 f=50 C.P.S.,E=.050O IN 0.4 - BLASIUS 0.24 0. 0 0 I 2 3 4 5 6 7 8 9 10 = y Y/I Figure 6.36 Comparison of velocity profiles with and without oscillation (u 00 =20, x=23, f=15)

1.0 0.8 FlIs U 20E FT/SEC 0.6 F 2 x =8 IN. 0 NO OSCILLATION uao | vO f=50 C.P.S.,E=.050 IN. /o- 4BLASIUS 0.4 0.2 0 I 2 3 4 5 6 7 8 9 10 7)'=yq y vX Figure 6.37 Comparison of velocity profiles with and without oscillation (u a =20, x=8, f=50)

1.0 0.8 =20 FT/ co U 2 SEC 0.6 /7 x =10 IN. 0.6 - O NO OSCILLATION UaO V,v f=50 C.P.S.,E=.050 IN. BLASIUS 0. 4 0.2 0 1 2 3 4 5 6 7 8 9 10 D y Figure 6.38 Comparison of;.velocity profiles with and without oscillation (u o0=20, x=10, f=50)

1.0 -0.8 IO 20FTSEC 0x =16 IN. O NO OSCILLATION U Uoo v f=50 C.P.S.,E =.050 IN. o 0.4i - BLASIUS 0.2 -0.2 0 2 3 4 5 6 7 8 9 10 7=Y - yi Figure 6.39 Comparison of velocity profiles with and without oscillation (u co 20, x=16, f=50)

1.0 0.8 u o O20 FEC x =23 IN. 0.6 0 NO OSCILLATION u v f=50 C.P.S.,E=.050 IN. UOO BLASIUS 0.4 0.2 0 0 I I, I I I I I I 0 1 2 3 4 5 6 7 8 9 10 VX Figure 6.40 Comparison of velocity profiles with and without oscillation (uOo =20, x=23, f=50)

92 Figures 6.41 through 6.45 pertain to 20 feet per second and 75 cps, At x = 8 and x = 9.63-inches there is no significant change in velocity. At x = 10-inches the velocity consistently decreaseso At x = 16-inches the velocity is consistently increased throughout the boundary layer. No turbulent spots are present on the oscilloscope. A transition profile occurs at x = 23 -inches. Figures 6,46 through 6,49 are for 20 feet per second and 100 cpso There is no significant change in the profile at x = 8-inches. At x 10-inches the velocity is consistently lower. At x = 16-inches the profile increases in velocity near the wall and decreases near the boundary layer edge. A transition profile occurs at x = 23-inches. 6.5 Comparison of the time-averaged oscillating profiles for various values of x, Figures 6.50 through 6.57 are a comparison of the oscillating profiles as a function of x with frequency and velocity held constant, All profiles of this comparison are at x values of 8, 10, 16 and 23-inches, Figures 6.50 through 6.53 are at a free stream velocity of 40 feet per second, Figure 6050 indicates that at a frequency of 15 cps all four profiles follow the theoretical Blasius (2) solution closely, At 50 cps in Figure 6,51 the profiles at x = 8 and 10-inches follow the Blasius profile closely but at x = 16-inches an increase in velocity near the wall and a decrease in velocity near the edge of the boundary

layer are apparent. The boundary layer also thickens in this profileo At' x: 2'3 inches'the transition profile occurs. Figure 652' at 75 cps more clearly indicates the progress of the phenomenono At x = 8=inches the profile closely approximates the Blasius (2) profile whereas at x l i0=inches the velocity is seen to decrease and the boundary layer thickeno The profiles at x 16 and 23 -inches are both transition profileso Figure 6~53 at 100 cps clearly illustrates the phenomenon. The profile at x 8-inches is close to the Blasius profile. At x ~ 10-inches the decrease in velocity is apparento At x 16-inches the increase in velocity near the wall and the thickening of the boundary layer is apparent, At x 23 -inches transition has already occurredo The thickening of the boundary layer while the flow is still laminar may be explained as a similar effect to that which occurs with a stationary bulge in the plate surface, A stationary bulge will cause an acceleration and subsequent deceleration in a laminar boundary layer. Figures 6~54 through 6o57 are at a free stream velocity of 20 feet per second,, Figure 6054 shows that at 15 cps all the profiles except x = 23=inches follow the Blasius profile closely. The profile at x = 23-inches tends to decrease in velocity. Figure 6~55 at 50 cps indicates that the profiles at x 8 and 10Binches follow the Blasius profile but at x 16~inches the profile begins its increase in velocity leading to the transition velocity of x 23 Zinches0

Figure 6.56 at 75 cps presents the clearest picture of the phenomenon. Again the~profile at x = 8-inches follows the Blasius profile. At x = 10-inches the velocity decrease is clearly showno At x = 16-inches the velocity increase over the entire profile in the laminar boundary layer is apparent. Finally at x = 23-inches the transition range has been entered, Figure 6-57 at 100 cps again indicates the phenomenon. The profile at x = 8-inches follows Blasius, The profile at x = 10-inches shows the decrease in velocity. The profile at x - 16-inches indicates the increase in velocity near the wall and the decrease in velocity near the boundary layer edge. This profile apparently occurs after the fully increased velocity profile and just before the transition zone at x = 23-inches, The experimental results just presented indicate that the analytic solution of Na (56) is qualitatively valid downstream of the membrane. The solution by Na indicates a decrease in the velocity profile and then a subsequent increase in the profile, The analytic solution cannot give any indication of the onset of transition but the experimental evidence shows transition occurs just downstream of the profile where all velocities exceed the Blasius profile, The assumption in the analytic solution (56) that no separation exists downstream from the membrane is shown to be valid by the experimental laminar flow profiles at x = 9.63 and l0linches,

1.0 0.8 UGO=20 FT/$ cO ZOF~SEC x =8 IN. 0.60 0 NO OSCILLATiON Uco | X v f=75 C.P.S., =.050 IN. Uoo BLASIUS 0. 4 0.2 0 I 2 3 4 5 6 7 8 9 10 =y Uo Figure 6.41 Comparison of velocity profiles with and without oscillation (uco=20, x=8, f=75)

I.0 0.8 Uo = 20 F/SEC 0.6 - x = 9.63 IN. 0 NO OSCILLATION Uoo v f =75 C.P.S.,E =.050 IN. 0. 4 - BLASIUS 0.2 0 I 2 3 4 5 6 7 8 9 10,n Y X Figure 6.42 Comparison of velocity profiles with and without oscillation (u 0o =20, x=9.63, f=75)

1.0 - =02 FT/ 0.6 x =10 IN. ___u~~ 0| / ~~O0 NO OSCILLATION U ~~~~UOO~ ]: I~ /B~ v f= 75 C.P.S.,E =.050 IN. 0.4 - BLASIUS 0.2 without oscillation (u =20, x 10, f=75)

1.O0 0.8 -V CO SEC Uo =0 FT/SEC x = 16 IN. 0.6 0 O NO OSCILLATION U V V f 75 C.P.S., =.050 IN. UOO 0.4 - BLASIUS 00. 4 0.2 0 I 2 3 4 5 6 7 8 9 10 /= y Figure 6.44 Comparison of velocity profiles with and without oscillation (uo =20, x=16, f=75)

1.0 0.8 o. BLASIU u aO 20 F~SEc 0.2 0 1 2 3 4 5 6 7 8 9 10 "?~ = Y /iN.i Figure 6.45 Comparison of - velocity profiles with and without oscillation (u00=20, x=23, f=75)

0.8 ua0=20 co 7SEC 0.6 - x =8IN. 0 NO OSCILLATION UoOU 7 f= 100 C.P.S., E=.050 IN. 04 - BLASIUS 0~~~~~~~~~~~~~~~~~~~ 0. 2 0 I 2, 3 4 5 6 7 8 9 10 1~~~ 1/ Figure 6.46 Comparison of velocity profiles with and without oscillation ( ucC=20, x=8, f=100)

1.0 0.8 co =20 /SEC 0.6 x = 10 IN. 0 NO OSCILLATION Uoo | X v f= 100 C.P.S.,E=.050 IN. 0.4 i BLASIUS 0. 2 0 I 2 3 4 5 6 7 8 9 10 ny Figure 6.47 Comparison of velocity profiles with and without oscillation (u c =20, x=10, f=100)

I.O 0.8 -0.6 v U0 20 FTSEc x 16 IN. u 0 NO OSCILLATION U7 f = 100 C.P.S., E =.050 IN. 0.4r t BLASIUS 0.2 -7 0 2 3 4 5 6 7 8 9 10 lvX Figure 6.48 Comparison of velocity profiles with and without oscillation (u c0=20, x=16, f=100)

0.8 | v ff Uco = 20 F/SEC 0.6 - x =23 IN. u 0 NO OSCILLATION u% 1 V7 V f = 100 C.P.S., E =.050 IN. 0.4 - BLASIUS 0.2 0 1 2 3 4 5 6 7 8 9 10 7= y 1/X Figure 6.49 Comparison of velocity profiles with and without oscillation (uoO =20, x=23, f=100)

1.0 0.8 0. 8: < o~~~~~~u o= 40 FT/SEC uEl4O F/SEC f = 15 C.P.S. 06 =.050" 12]c e~ [~f~ ~x = 8.0" 0 U 10.0"A 16.0" V 0.44 23.0" E BLASIUS ~ 0.2 0 I I! I I I I I l I 0 1 2 3 4 5 6 7 8 9 10 ii - y vx Figure 6.50 Profiles as a function of x (uoO =40, f = 15)

1.0 -c 'E 0.8 [ E] Z u(! =40 F SEC f =50 C.P.S. 0.6 - 0 E =.050" u0 x =8.0" O UO 10.0" A 16.0 V 23.0" 0 o BLASIUS 0 0.2 0 1 2 3 4 5 6 7 8 9 10 = y Figure 6.51 Profiles as a function of x (u x: = 40, f = 50)

1.0 0.8 3 El[Elv uI=4O FT, Ed v p/ f31~~ Uo40 4FT/sEC f =75 C.P.S. 0.6 E =.050" u 7 x 8.0" 0 U- 10.0" A 16. V 0.4- El 23.0" E3 BLASIUS - 0.2 0 1 2 3 4 5 6 7 8 9 10 v x Figure 6.52 Profiles as a function of x (uo = 40, f = 75)

0.8- v 0 pa U =o040 FTSEC f = 100 C.P.S. 0.6 3, E =.050" U ' x8.0" O Uo 10.0" O I~~~~~~3~~~~~ Em 16.0" v 0.4 - 23.0" 0 BLASIUS - 0.2 0 I I I I I I I I 0 1 2 3 4 5 6 7 8 9 10 = yU Figure 6.53 Profiles as a function of x (uoo = 40, f = 100)

1.0 - 0.8 eUoO-20FT/E f = 15 C.P.S. 0.6 E =.050," x = 8.0" U 10.0" 16.0" V 0.4 23.0" 0 BLASIUS U 0 0 1 2 3 4 5 6 7 8 9 10 1= U Figure 6.54 Profiles as a function of x (u o = 20, f = 15)

1.0 - Ox= 0 0. 6 - h Uo 020 FTEC U E7 ci r f -50 C.P.S. uO r e =.050" x =8.0" O 0.4 -16.0" o Eo f23.0" Q1 0. 2 0.2 BLASIUS 0 _ I ] I i I I I I I 0 2 3 4 5 6 7 8 9 10 Figure 6.55 Profiles as a function of x (u O = 20, f = 50)

I.0 0.8 V 0.6 U =20 FT U ~~~~~~~~~~~~~~~~~~~c S EC __ f =75 C.P.S. E.050" 0.4 ~ x =8.0" 0 10.0" A 16.0" V 23.0" ol 0.22 BLASIUS 0 1 2 3 4 5 6 7 8 9 10 = Y Figure 6.56 Profiles as a function of x ( u00 = 20, f = 75)

1.0 0. 81= 20 ~Z U 20 FT/SEC 0.6 7 /f = 100 C.P.S. 0.6 -V X o: e.050 C.P.S. Uu0| a 7 / x = 8.0" O 10.0" 0.4 - 16.0" V7 23.0" 0 ] BLASIUS 0.2 7 0 1 2 3 4 5 6 7 8 9 10 VX Figure 6.57 Profiles as a function of x (ucO= 20, f = 100)

112 6,6 Comparison of the time averaged oscillating profiles for various values of frequency. Figures 6.58 through 6065 are a comparison of the oscillating profiles as a function of frequency with x and velocity held constant. Figures 058 through 6e,61 are at a free stream velocity of 40 feet per second. Figure 6,58 indicates that at x = 8-inches the profiles all closely approximate the Blasius profile. At x 10inches in Figure 6.59 the profile for 75 cps decreases most markedly from the Blasius profile. At x = 16-inches in Figure 6060 the profile for 15 cps closely approximates the Blasius profile. The profiles for 50 and 100 cps show the increase near the wall and the thickening of the boundary layer. The profile for 75 cps is a transition profile and shows the most deviation. The profiles at x = 23-inches in Figure 6.61 6are transition profiles except for 15 cps which is a laminar profile closely approximating the Blasius profile. It is apparent that the maximum effect of the oscillation occurs at a frequency of 75 cps with a free stream velocity of 40 feet per second. Figures 6062 through 6~65 pertain to a free stream velocity of 20 feet per second. In Figure 6o62 the profiles at x = 8-inches again indicate a clouse approximation to the Blasius (2) profile. At x 10=inches in Figure 6o63 the profiles progressively decrease from the Blasius profile as the frequency increases from 15 to 100 cps, At 75 cps a slight thickening of the boundary layer may be noted. Figure 6064 at x 16 inches indicates a progressive

1.0 - 0.8 - U0 =40 FT/SEC O. 6L - x =8.00" e =.050" U UOUa~~~~~~~~~O ~f = 100 C.P.S. 0 75 C.P.S. A 0.4- 50 C.P.S. V l Q(E) 15 C.P.S. 0 l BLASIUS 0.2 0 I 2 3 4 5 6 7 8 9 10 Figure 6.58 Profiles as a function of frequency Figure 6.58 Profiles as a function of frequency (u x = 40, x = 8)

1.0 0.8 u (! 40 FT/S a! m a va~U0400 F SEC 0.6 x = 1000" E =.050" U Uoo f 100 C.P.S. 0 75 C.P.S. A 0.4- do 50 C.P.S. V 15 C.P.S. E BLASIUS 0.2 0 I 2 3 4 5 6 7 8 9 10 = YX Figure 6.59 Profiles as a function of frequency ( uO = 40, x = 10)

1.0 0.8 U = 40 - 'SEC x = 16.00" 0.6 E =.050".U Lp ~Jf =100 C.P.S. O UCO 1 75 C.P.S. A 50 C.P.S. V 0.4 - i 5 C.P.S. EJ BLASIUS 0. 2 - 0 0 I 2 3 4 5 6 7 8 9 10 =~ > Figure 6.60 Profiles as a function of frequency (u =0 40, x = 16)

1.0 0.8- E o ] ^~V (i' 7 / UaO _40 FTSEC x =23.00" 0.6'-, E] E.050" u -f =100 C.P.S. 0 UoO O 75 C.P.S. A 0.4 50 C.P.S. V 15 C.P.S. El BLASIUS 0.2 0 I 2 3 4 5 6 7 8 9 10 71 x Figur.e 6.61 Profiles as a function of frequency (u o = 40, x = 23)

0.8 -00 SEC x =8.00" E =.050" _u__ ] in f = 100 C.P.S. O lU0 75 C.P.S. A 0. 4 50 C.P.S. V / 15 C.P.S. 0E i-s BLASI US 0.2 0 1 2 3 4 5 6 7 8 9 I1 n=Y vX Figure 6.62 Profiles as a function of frequency ( u c = 20, x = 8)

1.0 - 0.8 - uo = 20 FTsEC x = 10.00'' 0.6.~ ~ E =.050" u__ f = 100 C.P.S. O 75 C.P.S.A 0.4 50 C.P.S. V 15 C.P.S. 0 ] BLASIUS 0.2 0 1 2 3 4 5 6 7 8 9 10 Figure 6.63 Profiles as a function of frequency ( uc = 20, x = 10)

I.0 A~ 0.8 0 A ~~~~~~~~u00 20 FSE 0.6 x 16.00" UOO ~~~~~~~~~~~~f 100 C.P.S. 0 75 C.P.S.A 50CPS15 C.P.S.0 -0. 2 -,40' ~~~~~~~~~BLASIUS 0. 0 I 2 3 4 5 6 7 8 9 1 n o~~~ vx Figure 6.64 Profiles as a function of frequency ( u = 20, x = 16)

1.0 A A 0.4 Oe V0 C.v uCo = 20 F7SEC 7x = 23.00 0.6 ):5Q 0( E =.050" U f 1 00 C.P.S. ) 75 C.P.S. A ~~~~~~~~~~~~0.4 ~~50 C.P.S. V 15 C.P.S. 0 BLASIUS 0.2 0 I 2 3 4 5 6 7 8 9 I0 = y Figure 6.65 Profiles as a function of frequency ( u c=o 20, x = 23)

121 increase in the velocity profile from 15 to 75 cps, At 100 cps the profile has begun the decrease in velocity near the edge of the boundary layer o In Figure 6065 for x 23=inches the profiles are transi'tion profiles except for the profile at 15 cps which is laminar but decreased from the Blasius profile. There appears to be no frequency within the range of frequencies studied that produces a maximum effect for a free stream velocity of 20 feet per secondo Figure 6066 is the difference between the Blasius theoretical solution (2) and the experimental velocities for the typical case of LAm = 40 feet per second and i~ = 100 cycles per secondo The plot is velocity difference divided by the free stream velocity versus the Blasius t. Only the profile at x = 10hinches appears to have a minimum near ~ = 21l as predicted by the analytical solution of Na (56). The transition profile at x = 23=inches has a maximum at t4l 1 and a minimum at about t = 4o5o The profiles at x = 12 and 16 have maxima at about - = 1.5 and minima at about = 3o,50 The profile at x = 8-inches also exhibits a small maximum and minimum but this may be open to question because of the accuracy of the measuring equipment.

uo=40FT/SEC X =8.00 INCHES 0 o 0 10.00 INCHES A 02f = 100 C.P.S. 12.00 INCHES 0.2 Vov V 16.00 INCHES V OV 0O 0: 23.00 INCHES 03 O V Au 0 O O AA O<>.00000 00 0-.2 0 -.4 0 I 2 3 4 5 6 7 8 9 10 77 =Yu Figure 6.66 Oscillation Profile difference from Blasius profile (u 00 = 40, f = 100)

CHAPTER VII Conclus ions Several definite conclusions may be made from the results of this investigation. 1. The analysis by Na(56) indicates that the maximum change in the mean value velocity profile for this type of oscillating flow occurs at?2 A 2.1. Fig. 6.66 shows that the maximum change in the experimental mean value velocity profiles occur at differing values of Nevertheless the experimental investigation shows that measurements made at various x and. = 2.1 will indicate the location of profiles in the oscillating flow that deviate from the Blasius (2) flow. 2, Separation will not occur behind a finite oscillating surface disturbance as large as 48% of the boundary layer thickness for velocities in the range tested, i.e., 20 to 40 ft/sec. This conclusion implies that the geometric shape of the disturbance is similar to the probability curve. 3. A definite change in the mean value velocity profile occurs for an oscillating disturbance of finite amplitude and is a function of free stream velocity, frequency, and position downstream from the disturbance, Immediately downstream of the disturbance the mean velocities at various " decrease. Subsequently, further downstream the mean velocities increase with respect to the mean 123

124 profile velocities without the disturbance. The analysis by Na(56) for very small disturbances also indicates the downstream decrease in mean velocities and the subsequent increase. Unfortunately, quantitative values obtained from the theory do not adequately predict the geometric location on the plate for the decrease or increase. Therefore, the analysis by Na can only be considered qualitatively valid for disturbances of finite magnitude in the region downstream from the membrane. 4. The data for 40 ft/sec indicate a maximum change in the mean value velocity profiles at 75 cps. The entire range from 50 to 100 cps lies below the neutral, stability curve in the damping region. Thus, the maximum in the experimental data is not explained by the stability theory. 5. Thickening of the laminar boundary layer occurs for an oscillating surface disturbance in a similar manner to the thickening for a stationary bulgeo The present investigation indicates a thickness of up to 45% in excess of the boundary layer without the disturbance. The boundary layer edge is defined as 99% of the free stream mean velocityo 60. Early transition from laminar to turbulent flow is definitely promoted in the frequency range of 50 cps to 100 cpso

APPENDIX Eccentric and connecting rod design and balance. The eccentric configuration is shown in Figure A-1 and the counterweight configuration in Figure A-2. Center of gravity for eccentric. (A-1) 2. Eccentric unbalance DF/4SB ( D sons t7S where YB = 0.3048 Lbm/in3 The connecting rod rotating unbalance is mt E where mn is the connecting rod crank end mass (0.050 Lbm). The connecting rod reciprocating unbalance is 2m2 E where m2 is the connecting rod wrist pin end mass (0,050 ibm). The total eccentric and connecting rod unbalance is, (A-4) 125

126 The counterweight ring unbalance is, The total unbalance is, 4 PQocD f LL,, t2 ins ( + g7r W ) The unbalance of the counterweight is, 0 (o.oo0 73f s r(h5)L -"w (A=7) The total unbalance is set equal to the unbalance of the counterweight and the resulting expression solved for outside radius I with 6 a specified parameter. Therefore, for each eccentric a set of counterweights must be constructed. The resulting expression is a cubic equation in I with the parameter, as follows, gj-7Z8sf 6-L f5i354E~ d — ~~ (A-8) For an eccentric with a stroke of = 0050 inches the outside radius I is 0O803. inches.

127 D =0.5625 IN. - B =0.283 IN. ~!< ~ D \k =D-2E k 'c =0.9375 IN. z Figure A.1 Eccentric configuration 15'1 D = 0.5625 IN. \r = 0.3438 IN. < r < \ ~cw =0.500 IN. z Figure A.2 Counterweight configuration

REF.ERENCES 1. Benney, D.Jo, "A Non-Linear Theory for Oscillations in a Parallel Flow"L J. Fluid Mech. 10, 2 Mar0 1961, 209-236. 2. Blasius, Ho, "Grenzschichten in Flussigkeiten mit kleiner Reibung" Zeit Mathe? Physo 56, 1908, p.1, Also NACA, TM # 1256. 3, Bolt Beranek and Newman, Inc. "Effect of Localized Acousstic Excitation on the Stability of a Laminar Boundary Layer."D Cambridge, Massachusetts, January 15, 1962. 4. Chang, PoK, "Drag Reduction of an Airfoil by Injection of.Sound Energy pt J, Aerospace Sci. 28, 9, Sept, 1961, 742-743. 5. Charters, o,C,, "Transition Between Laminar and Turbulent Flow by Transverse Contaminationi", NACA TN #891, March 1943, 6. Cheng, S o,, "Some Aspects of Laminar Boundary Layer Flows", Quarto Appl. Math. 14, 4, Jan, 1957, p. 337-352. 7. Cooper, Ralph Do and Tulin, Marshall Po "Turbulence Measurements with the Hot Wire Anemometer",. AGARD # 12 August 1955, North Atlantic Treaty Organization. 8, Corcoran, WmHo,, Opfell, J.oB and Sage, BH,, Moment um Transfer in Fluids, Academic Press Inc,, 1956. 9, Corsin, S. and Uberoi, M.S, O"Spectra and Diffusion in a Round Turbulent Jet," NACA Rept, 1040, 1951. 10. Corsin, S. "Extended Applications of the Hot Wire Anemometer". NACA TN 1864, 1949, 11o Corsin, So "Investigation of Flow in an Axially Symmetrical Heated Jet of Air", NACA Wartime Rept,. 94, 1946 12, Criminale, W,O,, Jr. and Kovasznay, LoSoG., SThe Growth of Localized Disturbances in a Laminar.Boundary Layer"_J. Fluid Mech, vol. 14, pt. 1 Sept, 1962, p. 59-80 13. Davies, EoBo and Young, AoDo "Streamwise Edge Effects in the Turbulelnt Boundary Layer on a Flat Plate Finite Aspect Ratio", AoRoC, R&M #3367 128

129 14. Dean, Robert C. Jr., et al. "Aerodynamic Measurements" Massachusetts Institute of Technology, Summer Session 1952. 15. Dhawan, S. and Narasimha, R. "Some Properties of Boundary Layer Flow during the Transition from Laminar to Turbulent Motion" J. Fluid Mech,, 3,4, Jan. 1958, 418-436. 16, Dhawan, S. "Direct Measurements of Skin Friction". NACA Rept. 1121, 1953. 17. Dryden, HL., Schubauer, GB,, Moc, WoCo and Skramstad, HoK, "Measurements of Intensity and Scale of Wind Tunnel Turbulence and Their Relation to the Critical Reynolds Number of Spheres"o NACA Rept. 581, 1953. 18, Dryden, Ho.L, "Air Flow in the Boundary Layer near a Plate", NACA Rept. 562, 1936. 19, Dryden, HoLo,, and Kuethe, AM., 'The Measurement of the Fluctuations of Air Speed by.the Hot Wire Anemometer", NACA Rept. 320, 1929, 200, Emmons, HoW., "The Laminar Turbulent Transition in a Boundary Layer, Part I#. Jour, Aero. Sc, Vol. 18, 7, July 1951 p o 990-998, 21. Ferri, Ao., Kuchemann, D. and Sterne, L.oHG, Progress in Aeronautical Sciences Volume II, Boundary Layer Problems New York, Pergamon Press, Inc. 1962, 22. Gault, Donald E,, "An Investigation at Low Speed of the Flow over a Simulated Flat Plate at Small Angles of Attack Using Pitot Static and Hot Wire Probes," _NA TN 3876, March 1957, 23. Greenspan, H.Po and Benney, Do,J,, "On Shear Layer Instability, Breakdown and Transition". Fluid Mech volo 15, pt, 1, 133-153, 240 Grohne, D. "On the Spectrum of Natural Oscillations of Two Dimensional Laminar Flows," NACA /TM 14170 25. Hall, A.A., "Measurements of the Intensity and Scale of Turbulence"t ARC R&M 1842, 1938, 26. Hall, A.A. and Hislop, G.S., "Experiments on the Transition of the Laminar Boundary Layer on a Flat Plate"~ ARC R&M 1843, 1938,0 270 Hansen, Mo "Velocity Distribution in the Boundary Layer of a Submerged Plate" NACA TM #585,

130 28. Hassan H.A,, "On Unsteady Laminar Boundary Layers". J, Fluid Mech. vol. 9, pt 2, October 1960, po 300-3040 29, Hassan, H.A. "On a Solution to the Unsteady Laminar Boundary Layer" o/Space ci, 27, 6, pp 474=476 (Readers Forum) June 1960o. 30o Hayasi, N,, '"On the Approximate Solution of the Unsteady Quasi-two-dimensional Incompressible Laminar Boundary Layer Equations". Physics Socie.ty of apan, J, Vol,, 17, Jan. 1962, po 203-212. 31, Hayasi, No, "On Semi-similar solutions of the Unsteady Quasi two-dimensional Incompressible Laminar Boundary Layer Equat ions"o Phics. Society of J J o VOl o 17, Jan, 1962 po 194=203 32. Hayasi, N., "On Similar solutions of the Unsteady Quasi= two-dimensional Incompressible Laminar Boundary Layer Equations',,o khysics Society of Japan, J. volo 16, Nov, 1961.p 2316-2329.13 33. Hildebrand FoBo,, Advanced Calculus for Engineers, P"rent.iss-Hall, Inc..1949, 7T-". 34, Hill, P,Gand Stenning, A,H,, "Laminar Boundary Layer in Oscillatory Flown ASMB Trans. 82B (Jo Basic Engn.) 3, Sept, 1960, p. 593=608, 35, Hinze, J.0.o, Turbulence An Introduction to its Mechanism and Theor..McGraw.. Hi1 1959, 360 Holstein, H, and Bohlen, To OEin.-Einfaches Verfahren zur Berechnung Laminarer Reibungschlichten die dem Nahungsansatz von K, Pohlhausen genugen," Lilienthal=Bericht S 10, 1940, P, 5 — 37. Kestin, J o, Maeder, P F, and Wang, HE,, "On Boundary Layers Associated with Oscillating Streams", A Res Secto A. volo 109 no. 1, 19619 po 122, 38, Klebanoff, PSo,, Tidstrom9 K oDo and Sargent, LoMo "The Three Dimensional Nature of Boundary Layer Instability"o. FluidM vol. 12, pt, 1, Jan. 1962 p. 1:'34, 39, Klebanoff, P.S, and Tidstrom, K,D., "Evolution of Amplified Waves Leading to Transition in a Boundary Layer with Zero Pressure Griiea nt," NASA TN D:195 Sept, 19590 400 Knudsen, James G, and Katz, Donald L,, Fluid namics and Heat Transfer, McGraw:Hill, 1958

131 41, Kovasznay,,. L O"Calibration and Measurement in Turbulence Research by the Hot Wire Method," NACA TM 1180, 1947. 42, Laufer,.J, "The Structure of Turbu lence in Fully Developed: Pipe Flow." NACA Rept, 1174, 1954, 43, Liepmann, HoW. and Dhawan, So "Direct Measurement of Local Skin Friction in Low Speed and High Speed Flow." Procedure of the First U, S, Nat. Cong r of Appl, hMechanics, 1 51, p o 869,o 44. Liepmann, HWo and Fila, GH,, "Investigation of Effects of Surface Temperature and Single Roughness Elements on Boundary Layer TransitiCan" NACA Rept. 890, 1947. 45, Lighthill, M,J,, 9"The Response of Laminar Skin Friction and Heat Transfer to Fluctuations in the Stream.Velocity" Proc. Roy S$OC, A-224, 1954 po 1o 46, MacPhail, DoC, "Turbulence Changes in Contracting and Distorted Passages", ARC R&M 2437, 1951, 47. Mark, Richard M, "0On Shear Flow Past Plates",, Fluid Mech, vol. 14, Ppt. 3, Nov. 1962, p. 452-462, 48, Martin, EDo "Note on the Three Point Boundary Value Problem for the Blasius Equation," Jo Aero/Space Sci, vol. 29, no 9, Sept 1962, p. 1133-1134 49. Martinelli, RC, anq Randall, R,D,, "The Behavior of a Hot Wire Anemometer Subjected toa Petiodic Velocity" ASME Tm ns, Jan, 1946, 50,0 -McClure, JoDo, "On Perturbed Boundary Layer Flows" Appendix A "Stability of a Flexible Surface Exposed to Potential and Laminar ViscousaFlows" MIT Fluid Dynamics Research Lab, Rept, 62-2 (AFOSR 62- 18) June 1962, 51o Mechel, F, Mertens, Po and Sehilz, F, "Research on Sound Propagation in Sound Absorbent Ducts with Super Imposed Air Stream" Physihalisches Institut der Universitat Gottingen, Technical Report No, 2, Contract No, AF-61(052)-112 Wright Air Development Center 52, Mitchner, Morton "Propagation of Turbulence, from an Instantaneous Point Disturbane. " J, Aero Sci, volo 21 no, 5, May 1954 (Reader s Forum) po 350-351, 53, Moore, P oKo and Ostrach, S. "Displacement Thickness of the Unsteady Boundary Layer" J, o Aeroo Scio vol.o 24 no, 1, Jan 1957 (Reader's F orum) p o 77~78,

132 54. Moore, FoK and Ostrach, S. "Average Properties of Compressible Laminar Boundary Layer on Flat Plate with Unsteady Flight Velocity." NACA TN 3336 Dec. 1956. 55. Moore, F.K, "Unsteady Laminar Boundary Large Flow"t NACA TN 2471, 1951. 56. Na, Tsung Yen "The Influence of Localized Normal Surface Oscillations on the Steady, Laminar Flow over a Flat Plate" PhoD Thesis, University of Michigan. 57. Ostrach, Simon "Compressible Laminar Boundary Layer and Heat Transfer for Unsteady Motions of a Flat Plate" NACA TN 3569, 1955o 58. Pai, Shih-I Viscous Flow Theory, I - Laminar Flow, D, Van-Nostrand Co0, Inc. 1956 59, Pohlhansen, Ko "Zur Haberumgsweisen Integration der Differentialgleichung der Laminaren Reibungsschzicht" ZAMM 1, 1921, p 252. 60. Richardson, E/G,, "The Correction of Hot Wire Readings in a Boundary Layer for Proximity t the Solid Boundary" J. Aero Sci. vol., 23, no. 10, Oct. 1956 (Reader's Forum) p.0 9.0-971 61. Sandborn, V.Ao, #An Equation for the Mean Velocity Distribution of Boundary Layers" NASA Memorandum 2-5-59EB. 62. Sandborn, V.A., #Application of the.Hot Wire Resistance Temperature Transducer to the Measurement of Transient FlowQuant ities" ASME Symposium on Measurementss in Unsteady Flow, May 1962, 63, Sato, H, and Kuriki, K. "The Mechanism of Transition in the Wake of a Thin Flat Plate Placed Parallel to a Uniform Flow." J. Fluid Mech, II, 3, Nov. 1961, p. 321-352. 64, Schlichting, H. Boundary Layer Theory, 4th edo McGrawHill, 1960, 65, Schubauer, GB and Klebanoff, P.S., "Contributions on the Mechanics of Boundary Layer Transition", NACA TN 3489, 1955, 66,0 Schubauer, GB, and Kelbanoff, PoS. "Investigation of Separation of the Turbulent Boundary Layer"~ NACA Rept. 1030, 1951 (Formerly NACA TN 2133)o

133 67. Schubauer, G.Bo and Skramstad, H oK, "Laminar Boundary Layer Oscillations and Stability of Laminar Flow o" NBS Research Paper #1772 or, J0 Aero Scio 14, 69, 1-47 or, NA'CA Rept. 909, 68. Schubauer, G.B. and. Klebanoff,?,S. "Theory and Application of Hot Wire Instruments in the Investigation of Turbulent Boundary Layers". NACA ACR 5K27, W786, 1946. 69.:Squire, HB,o "Heat Transfer Calculation for Aerofoils" ARC R&M, 1942, po 19860 70,o Vrebalovich, Thomas "1Application of Hot Wire Techniques In Unsteady Compressible cFlows" ASMIE Symposium on Measurement in Unsteady Flow May 1962.

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