THE UNIVERSITY OF MICHIGAN INDUSTRY PROGRAM OF THE COLLEGE OF ENGINEERING EFFECTS OF COOLING ON TRANSITION IN THE BOUNDARY LAYER ON A HEMISPHERE. IN SIMULATED HYPERSONIC FLOW Roger DDunlap A dissertation submitted in partial ful:fillment of the requirements for the degree of Doctor o Philosophy in the University of Michigan 1961 Februlary 1961 IP - 499

Doctoral Committee o Professor Arnaold Mo Kuethe, Cochairmnan Associate Professor William Wo Willmarth, Co-chairman Associate Professor Thomas C. Adamsox, Jr o Mro James Lo Amick Professor Richard Bo:Morrison Professor Erich Ho Rothe

ACKNOWLEDGMENTS This investigation was partially supported by the United States Air Force under Contract Noos AF 49(638)-336 and AF 33(616)>6856, monitored by the Aeronautical Research Laboratories, Air Force Research Division, Air Research and Development Command. The author wishes to thank the doctoral committee for their efforts and especially Professors Arnold M. Kuethe and William W. Willmarth, co-chairman, who provided valuable guidance, advice, and encouragement throughout the course of the investigation. Helpful discussions with Mr. James Lo Amick are also deeply appreciated. Special appreciation is extended to Mr. A. M. Rickel of the Bendix Corporation Research Laboratories who took the photomicrographs and provided valuable information concerning the polishing of the model. The profilometer tracings were made through the courtesy of the Micrometrical Manufacturing Companyy, Ae,.. Arbor, Michigan. The assistance of Messrso Go E. Chmielewski, R.o Eo Deitrick, Ao JO Kuprenas, R. J. Brando, and F. L. Donovan in the construction and execution of the experiments is gratefully acknowledged. ii

TABLE -OF CONTENTS Page LIST OF FIGURES. o.. a. *.. e.. o *. e... e *...&.. 9 0. O e... iv CHAPTER I. INTRODUCTION....................................,.. 1 II. SOME EFFECTS OF COOLING, CURVATURE, AND ROUGHNESS ON BOUNDARY-LAYER TRANSITION...........................**** 7 III, FLOW SIMULATION AND SHROUD DESIGN,...,.,,,,.,,,, 17 Similarity Requirements for Boundary Layer FlowsSimplifications for Boundary Layer Transition Studies on Blunt Bodies in Hypersonic Flow........ 17 Shroud Design.,,,,,,,,,,,,,, 22 IV. EXPERIMENTAL APPARATUS AND METHODS.,......*,,,,,.,....... 29 General Wind:Tunnel Facility,,,,,,**.......**,,.. 29 Sphere and Associated Instrumentation. I,,,,....... 35 Preparation and Inspection of Model Surface....... 45 V. RESULTS AND DISCUSSION, * * * * Sees ** *... 51 Environmental Tests......................,*..... 52 Effects of Boundary Layer Cooling on Transition Caused by Roughness 59 Transition Experiments on a Highly Polished Model with Variable Boundary-Layer Cooling........ 70 VI. CONCLUDING REMARKS,,,,,,,,,,,,,,,,...... o f............ 88 APPENDICES..,...,.... * O.. *. *. 90 A, SIMILARITY PARAMETERS FOR BOUNDARY-LAYER FLOWS.. e..a * o.. a v... a..e.... a a 0.. a 0 - 91 B, CALCULATED PROPERTIES OF THE LAMINAR BOUNDARY LAYER ON A HEMISPHERE IN HYPERSONIC FLEOERENWES.......... oO........e4O............ 9 5o 10 111

LIST OF' FIGURES Figure Page 1 D.O-Distribution of Reynolds Number in the Boundary Layer Near the Nose of a Blunt BOdyO...Q.O.-*-..la..*O,.O. 10 2 Qualitative Variation of Critical Roughness Height with Boundary-Layer Coolingo 11 3.Effect of Cooling and'Roughness on Transition on a Sharp 100 Apex Angle Cone at Me 2 )70 (Data of van Driest and. BoisontlO ).....,o........ 13 4:Effect of Cooling on Transition on a Sharp 9.50 Apex Angle Cone at Mo o= 3,2 (Data of Jack et al( ) >*s64 14 5 Effects of Cooling on T- anition on Blun 13Qdies (Data of Diaconis et al 13)) and Stetson14)) 16 6 Range of Flow Simulation.... Q *,.............. 21 7 Coordinate System....00000000000*...... * *. *0 24 8 Aluminum Shroud Configuration with Sphere in Place (Dimensions in Inches).. @0 0000000 00000 28 9 Schematic Diagram of Air Supply System and Wind Tunnel Layout 30..... e 4 30 10 Photograph of Wind Tunnelo e o.......... o o o.o, 33 11 General Construction of Travelling:Periscope....... 34 12 Details of Sphere Instrumentation (All Dimensions in TInches.. 0... 00 0. 0 0 0.............000...Q 0..0 0 0 00. 37 13 Profilometer Tracing Across Thermocouple......0...O 38 14 Size and Construction of Pitot and Static Pressure Probes,.00 0.0 000 0. 0 00 0 00. 00.o 0 0 0o 00o0o o a.0 o e o a 42 15 Schematic Diagram of Cooling Procedure and Thermocouple Circulit, 000 0 0 0 0 0 0 0 os eo 44 16 Photomicrographs of Surface at a Magnification of 350 a) no relief, b) relief. 0 0 0... 0.,,,.,.O.. 48 iv

LIST OF FIGURES CONT'D Figure Page 17 Profilometer Tracings of Surface a) no relief, b) relief..,...,.,,........ 49 18 Measured Pressure Distribution on 9-Inch Diameter Sphere,,**,...*..*..D.,,V *0**.**'0#0 (... 53 19 Turbulence Level and Velocity Distribution in the Settling Chamber............................... 55 20 Typical Surface Temperature-Time Histories for Tests with Cooling...*...., ~...........****....*..* 58 21 Hot-Wire and Pitot Tube Measurements of Transition Caused by a.004" x.025" Diameter Disk..,..,....,,, 62 22 Hot Wire Fluctuation Distribution for TW/Ts = 1.0 and o0,8 (.004" x.025" Diameter Disk, 15~ Ahead of Wire ) ** 0 0 0 * * + 0* * 0* # 0* W* 65 23 Hot Wire Fluctuation Distributions for TW/Ts = 1.0 and 0.8, (two-dimensional ribbons 100 ahead of wire) a).004" x..030" ribbon and "smooth" surface....o..... 66 b ).006" x.030" ribbon......*,........,.....,,, 67 c).010" x.030" ribbon.,..,,,,,,,,,, 68 24 Calibration of Pitot Probe. *,.,,,.,,,,,,.,,,, 75 25 Records of Pp-P e Ps, and Tws During a Typical Transition Experiment...... *...4.,,,,,,.. 77 26 Correlation of Transition with CO2 Film....,......... 78 27 Local Transition Reynolds Numbers Based on Distance From the Stagnation Points, Rex, vs. TW/Ts..*...*.... 80 28 Local Transition Reynolds Numbers Based on BoundaryLayer Momentum Thickness, Reg, vs. Tw/Ts,,,,.. 4., 83 29 Local Transition Reynolds Number Based on BoundaryLayer Displacement Thickness, Reg*, vs. Tw/Ts. I..... 85 30 Variation of g with?? and Tw/Ts on a Hemisphere in Hypersonic Flow*,............................... 96 31 Variation of S' with 2' and Tw/Ts on a Hemisphere in Hypersonic Flow,..,,,,,.,,,.......,..... 97 v

LIST OF FIGURES CONJT ID Figure ePage 32. Variation of 9 with' and Tw/Ts on a Hemisphere 98 in Hypersonic Flow...........*..... 33. Variation of Cf~'~ae??j~w with ~ and. T/Ts on a Hemisphere in Hypersonic Flow.................... 99 34.Variation of qw with 7 and TW/Ts on a -emisphere in Hypersonic Flow...,.......... ~... *....... - 100 vi

NOMENCLATURE a speed of sound a2,a4 defined by Equation 11 b defined by Equation 8 -Cf local skin-friction coefficient, Cf = Cm mean specific heat of model material Cp pressure coefficient, Cp = a-_/ —:C specific heat at -constant pres.sure D diameter of body e' rms voltage- fluctuation h altitude in-the standard atmosphere k roughness height k. thermal. conductivity M Mach number Nu Nusselt number P pressure Pr Prandtl number q heat transfer rate, 8 -_ -_& r- radius in spherical coordiantesravg. mean radius-of a' hemispherical shell ar thickness of a hemispherical shell.R gas constant R radius:of mod-el.Re Reynolds number t time vii

NOMENCLATURE CONT tD T..; temperature u, v velocities in the ~ (or x) and r directions u' rms velocity fluctuation of u x distance along the surface of a body measured from the stagnation point y distance normal to a body surface ratio of specific heats boundary-layer thickness boundary-layer displacement thickness angle between the free stream direction and the normal to a body surface O boundary-layer momentum thickness /CC viscosity / -density density of model material shear stress, re = / stream function defined by Equation 6 Subscripts O initial value e local value just outside boundary layer k value at the top of a roughness element p value at point of measurement, pitot probe s stagnation value at the nose of a body w surface value aw adiabatic surface value viii

-I. INTRODUCTION -One of the most dif ficult problems' in the flow of a viscous fluid adjacent to a solid boundary is'that of predicting the transition from laminar to turbulent motion in the boundary layer, The transition process is governed by the non-linear terms in the Navier-Stokes equations and, according to experiment, may occur in one of two ways: 1) if the laminar boundary layer is- unstable to infinitesimal transient perturbations (termed linear instability), small disturbances, originatingat roughness- element$ or as turbulence in the outside strea, are amplified until the nonlinear terms in the governing equationS become large enough to determine the remainder of the flow process culminating in the turbulent layer, 2) if the disturbances in the laminar layer are initially so large that their subsequent behavior cannot be described by the theory for infinitesimal perturbations the non-linear terms in the equations describe the entire process. Therefore, the location of transition on a given body generally depends on the various disturbances present, such as. pressure waves, stream.turbulence, and surface rough= ness as well as-the flow-parameters govrerning the amplification of thbese disturbances., t is important for an understanding of the work to be described here to realize that if the disturbances are- large enough transition may occur in a linearly stable laminar layer. The stability of the laminar boundary layer to infinitesimal disturbances and the separate influences of Mach number, pressuxe gradient, heat transfer, and surface- crvature have been evaluated -theoretically by Tollmien, Schlichting, Goertler, Lees, Lin and others(l) -1

-2These stability theories, in addition to providing some understanding of the mechEanisms initiating the transition process for the important case when the disturbances are small, have served as valuable guides in designing, conducting, and interpreting experiments which verify and supplement our basic understanding of the transition phenomenon. Since the extension of the linear stability theories tocompressible boundary layers by Lees and Lin(23) in 1946, many experiments have been conducted to verify the theoretical predictions concerning the effects of thermal conditions at the surface on boundary layer stability. According to this theory, there is, in the absen'ce of surface curvature, a stabilizing effect of heat transfer from the boundary layer to the surface (boundary-layer- cooling) and therefore a corresponding delay in transition when it is, initiated by an instability to small disturbances. The experiments of many invest igators )n flat plates, cones and various bodies of revolution, over a wide range of Mach numbers, have indeed shown that cooling promotes higher transition Reynolds numbers while heating has the opposite effect, Recently, however, wind tunnel experiments by Jack, Diaconis, and Wisniewski(1 13) have shown a so-called "transition reversal", in which, when the degree of cooling exceeds a critical value, influenced by nose bluntness and surface roughness, transition Reynolds numbers were observed to decrease markedly. As the nose bluntness or roughness increased the critical degree of cooling decreased. Also, shock tube experiments by Stetson( ) have yielded low transition Reynolds numbers: for the highly cooled boundary layer on a hemisphere-cylinder configuration,

-5On the basis of observations such as these, s-ome controversy has arisen as to whether coolng may und.er some circumstances actually cause the boundary layer to become-linearly unstable.'The phenomenon is complicated by the fact that coolisng the boundary layer not only affects the stability to disturbances but, because of the relatively high density near the surface, the disturbance caused by a given roughness element will increase with cooling. This latter effect would, in itself, tend-to decrease the transition Reynolds numbers with increasing cooling. Further, if boundary-layer cooling occurs on a convex surface the resuting centrifiugal acceleration field tends to destabilize the flow. This tendency does not enter into the above mentioned stability theories. The relative importance of these various effects of cooling will be discussed qualitatively in the following section, and some typical experimental results will be presented. Although the effect of cooling in incre-asing the magnitude of disturbances from fixed roughness elements represents. a most plausible explanation for transition reversal, it has not yet been determined w1ether this is the proper explanation in all cases and there is a need for further experiments to answer specific quest ions. An important situation in which extreme boundary layer cooling occurs- s during the re-entry of a blunt body into the atmosphere at hypersornic speed. Under these circumstances unsteady boundary layer cooling exi5ts for a short perod of time while the heurface is cool and the stagnation temnperature high, Sincethe heat transfer rates associated with a turbulent boundary layer may be an order of magnitude higher thanL t ose in the laminar case, a knOwledge of the transition point

-4and its location as affected by the cooling iE of major'practical significance. Some attempts have been made to study transition under re-entry conditions by means of flight teStS (see, for example, References 15 and 16). Aside from the high cost and extreme instrumentation problems the interpretation of flight test data is hampered by the fact that marlny of the significant parameters vary simultaneously, so that finding the effect of any one presumes:a knowledge of the effects of the others. The purpose of the- work to be reported on here was to investigate- in the laboratory the effects of cooling on transition in the boundary layer on the nose of a blunt body under conditions similiar to those encountered during hypersonic re-entry, with. the aim of gaining some knowledge of the circumstances under which boundarylayer cooling may promote early transition. The first problem to be considered was that of producing a hypersonic environment which would facilitate the objectives of thegetransition studies. Important requirements were considered to be; 1) reaonable testing times and stagnation temperatures so that the details of the transition process may ultimately be studied, and 2) the ability to simulate low free stream turbulence and -small surface roughness so that the conditions of small d.isturbances may be realized, These requirements can be met by testing scale models in a wind tunnel, in which practical cooling rates can be achie-ed by ctooling the model and/or heating the stream. The maximum stagnation tempera;tures would perhaps be limited by the a-ailable instrentation.

-5However, in the-:tuaJl hypersonic -or supersonic wind tunnel s ll free stream disturbances and surface roughness become more diffiult to simulate~ At high speeds, pressure waves arising from the turbulent boundary layers on the tunel walls- are known to give rise to free stream disturbtances which may be- large enough to have an wbapreeiable effect on transition (7T9). he difficulties with respect to simulatin g small roughnriess stem from the fact that the boundary layers will be relatively thin because of the small scale of most wind tunnel models. These thin boundary layers, typically of the order of a few tenthousandths of an inch on a one inch diameter -spherical nose, impose severe limitations on the maximum roughness if transition due to roughness is to be avoided. The limitation becomes even more severe when one considers -the effect of cooling in increasing the effect of roughness. It was found for instance(15916) that transition Reynolds numbers, based on momentum thicknes9 on an 8-inch driameter hemisphere could be incrueased from values between 100 and 400 to between:900 and 12-00 by reducing the surface roughness from 25 rms microinches to less than 5 microinches. In the present investigation the problems of high free- stream turbulence and small mnodel size were overcome by simulation techniques. Specifiallly, t.he subsonic and low supersonic Mach number, pressureand velocity d.istributions which exist over most of the nose region of a blunt body in. hypersonic flow (on a sphere moving at Moc = -10 Me 1 at?7 = 440 and Me = 2 at 0 = 70.70) can be produced in a wind tunnel with

-6subsonic flow ahead of the body by a properly contoured shroud in the region of the nose. In such a "shrouded model" test the turbulence in the subsoni- "free-stream" can be kept at a low level, and size limitations on the model are reduced. Accordingly, the shroud technique was herein employed to Simulate the subsonic boundary layer Ion the nose of a 9-inch diameter hemisphere in hypersonic flow. The following chapters are devoted to a discussion of thehypersonic flow simulation, including a theoretical determination of the shroud contour, and a description of the experimental apparatus and techniques, followed by a presentatiqn and discussion of experimental results0 The experiments consisted of: 1) "environmental" tests which include the surface pressure distribution on the sphere resulting from the- shroud technique, turbulence levels in the wind tunnel and outside the boundary layer on the mo4el, correlation measurements between velocity fluctuations at the stagnation point, and temperaturetime histories of the model surface during tests with coolin g; 2) hotwire measurements of the transition caused by several roughness elements, showing qualitative effects of various combinations of cooling and roughness; and 3) effects of cooling on transition in the subic boundary layer when the surface is highly polished, determined by means of a small pitot probe at the surface. There are discussions of the roughness caused by dust in the airstream and by condensatio films (H20o, 2, and 02) at low model temperatures. * The idea of shrouding a model to simulate surface pressure and velocity distributions was first reported by Ferri(n 20

II. SOMB EFFECTS OF COOLING, CURVATURE AND ROUGHESS ON BODARY-AER TRANSITION -Experimental observations of the influence on transition of such factors as Mach number, pressure gradient, heat transfer, surface curvature fre-tretrem turbulence, and surface roughness have been reviewed and disuedsed in light of applicable stability theories by many authors(21-24). In this section attention will be devoted to a qualitative discussion of the effects of cooling in conjunction with convex surface curvature and. with surface roughness. A few of the experimental results pertaining to these effects will also be given. The effects of heat transfer on the stability of the laminar boundary layer to TollmiaenSchlichlting type disturbances was first evaluated theoretically be Lees and Lin in 1946(2P3). Their calculations showed that cooling stabilsized the boundary layer to disturbances of this type. On concave surfaces, transition may result from an entirely different instability mechanism. This so-called centrifugal instability results from the unstable distribution of the centrifugal acceleration field imn the boundary Zlyer on a surface with concave curvature, and was first recognized by Taylor(25) in connection with the flow between concentric rotating cylinders and later analyzed by Goertler(26) for boundary-layer flows. Experimental investigations by Liepmann (27) in subsonic flow, showed that increasing concave curvature does decrease the momentm thickness Reynolds number at transition in accordance with the predictions by Goertlero On the other hand, when the surface curvature was convex, Liepmann found that the Reynolds number of transi-7

-8tion, as well as the characteristics of Tollmien-Schlichting type disturbances, were little influenced by the stabilizing effect of the centrifugal acceleration field. As pointed out in a rough analysis by Lees(28), the density gradient and the resulting centrifugal acceleration field in a cooled boundary layer on a convex surface tends to decrease the stability of the flow but, even with infinite cooling, the criterion for dynamic stability remains satisfied. Whether the transition point in the compressible boundary layer on a convex surface is appreciably influenced by the decreased stability.caused by cooling (in contrast to the results:of Liepmann for an incompressible flow without heat transfer) has not been determined. Turning now to the influence of cooling on the m.gnitude of disturbannces, it will be shown that the transition reversal phenomenon can be caused by the effect of cooling in causing an increase in the magnitude of d.isturbances from fixed roughness elements. The effects of roughness on transition have been explored by many investigators (a comprehensive discussion of past methods- of correlating the data, as well as a successful new method, has recently been given by Potter and Whitfield(29)). Various parameters, such as k/Es, Rek = and Rek f(Mk) (where k = roughness height,,,4,/,f&and.Mk are the density, veelocity, viscosity, and Mach number, respectively, at the top of the roughness, and f(Mk) is a monotonic increasing function of Mk) have been found. to correlate the data well. For purposes of the qualitative discussion here, the roughness Reynolds numbers Rek, will be-used. It has been Observed by many investigators that as

-9Rek is increased above a certain critical value (magnitude of disturbance from the roughness element exceeds a threshold value) the transition. point begins to move upstream until, for large enough Salues of Rek. it occurs immediately behind the roughness element. Boundary layer cooling may be iden:tifLed. wiLth an increase in Re because of t:he resulti-ng increase in the density and velocity ase ell as a decrease in the viscosity at the peak of a given element. Thus early transition or transition reversal may be caused by the cooling. An illustration of -the effect that cooling may have on Rek is given in Figure 1 which shows the distribution of Re*/Reg through the boundary layer near the nose of a blunt body. For small roughness elements (small'/g ) it is seen that Rek may be increased by an order of magnitude as a result of cooling. In accordance with the above discussion, three ranges of roughness heights, dependent on the cooling rate, would be expected. This is illustrated qualitatively in Figure 2 which shows the effect of'increasing cooling.n decreasing. the threshold roughness heghtt necessary'to cause transition.i In general a curve such as that shown would 8also depend on the type of roughness element and its location on This deduction assumes that Rek increases faster tIan than e critical marlue of ReC, Although little data is available, the observabtions of Braslow, anox, and Horton30O) on cones and flat plates indicate that the critical value of Rek is essentially independent of heat transfer, They also report transition reversals caused by -the effect of cooling in. increasing Rek to s-upereritical values, Thee distributions were computed from the boundary-layer solutions of Cohen and Reshotko(3l) for the case of stagnation poinrt flow on a body of revolut;ion..

-.0' I, 0.10 Tw 0.2,4.6.8 1.0 Figure 1. Distribution of Reynolds Number in the Boundary Layer Near the Nose of a Blunt Body.

Res CONSTANT LLJ~~~~~~~~I H~~~~~~~~~~~~~~~~~~r * THRESHOLD ROUGHNESS HEIGHT Li FOR TRANSITION z crr TURBULENTI LAMNI NAR ZERO' INFINT INCREASING BOUNDARY LAYER COOLING -— C COOLI COOLING Figure 2. Qualitative Variation of Critical Roughness Height with BoundaryLayer Cooling.

-12the body as well as Reynolds number, However, for illustrative purposes we may ident'ify -the thhree ranges of roughness height as those corresponding to regions I9 II., and III in -the figure. For region I'the roughness is large enrouh so that transition always occurs at t he roughness independ.ent of the cooling. In region 1I transition may or may not occure, depending on'the cooling rate, while in region III the rougl-mess is small enough so that the value of Rek remains subcritical up to the maximum cooling rate, One phase of the experimental re saults to follow will demonstrate these roughness regimes, Before proceeding to the present work a few of the transition results, of other investigators will be gitveno The purpose here is to illustrate some examples of th? opposing trends of the influence of cooling which have been reported. Data of van Driest and Boison( on a sh.rarp 10~ apex angle cone at Me- 2.70 is shown in Figure 3, In this and the following figures the local Reynold.s numbers at transition, based on conditions at the ed.ge of the boundary layer and. distance from the stagnation. point, is given as a unction of the ratio of wall temperat'ue to adiabatic wall temperature. With a smooth surface (rs roughnress approx;ately 10 microinc.ches) and. the.0005 inch trip the transition Reynolds number in.creased. with cool-ing land approached the line i.ndicating complete stability to two-dimensional disturbarinces, TrazMsition reversasl esulting with the o0019.002, a:nd.004 inch trips is also apparent, Observations due to Jack et al (12) on a sharp 950 apex:anrgle cone at Mw= 3012 is given in Figure 4, They obtain data similiar to that of van Driest, tending asymptotically to complete stablizatt on at a slightly lower temperature ratio, However they also

1.0 TEMPERATURE RATIO FOR COMPLETE STA0.4 so...'- X 0.0005"'0.002", 0.8 _' 0.004" |_ | —- I TRIP LtlON | 0.4 I I I... I I 11 0 2 4 6 8 10 12.106 ~ReX~' x eX00005 AUeX Figure 3. Effect of Cooling and Roughness on Transition on a Sharp 100 Apex Angle cone at Me = 2.70 (Data of van Driest and Boison(lO)).

I.0 0 0.8...L I.. 0 * TRANSITION ON CYLINDER 0 TRANSITION ON CONE 0.6 0.4. 0.2 I I I, 0 2 4 6 8 10 12'106 4UeX Rex= Figure 4. Effect of Cooling on Transition on a Sharp 9.50 Apex Angle Cone at M = 3.12 (Data of Jack et al(12))

-15find a reversal at lower temperature ratios without placing a trip on the surface (rms surface roughness was 12 microinches). At these temperatures both CO2 and H20 films, of undetermined thickness were on the surface. The authors concluded. however, that transition reversal could not be attributed. primarily to surface roughness. An examiple- of the effects of cooling on blunt nosed models (convex surface curvature ) is presented in Figure 5. Wind tunnel data of Diaconis et al(l3) for a hemisphere-cone-cylinder at Mo = 3.12 is shown together ith the shoc:k: tube results of Stetson(4) (M C = 1,5- 2.49) for a hemisphere cylindere On the blunted conecylinder transition reversal ocaurred at higher temperature ratios than for the sharp cone tests of the same author's (Figure 4). The surface roughness was < 16 microinches. At these temperatures, a frost film, of undetermined thickness- was on the surface. The shock tube data of Stetson also'show low transition Reynolds numbers at the lower temperature ratios. The rms surface rqughness of the':0.25-inch-radius hemisphere-cylinder was less than 1 microinch, but the heat-transfer gages used to detect transitioon protru.ded 12 mi-croinches above the surface. Observations of early transition promoted by boundary layer cooling,- uch as those presented' above, stimulated the investigation to be presented in the foliowingi pages.

T.7..WIND TUNNEL _ _ _ _ _ _ _ (REF. 13) 0.6 * TRANSITION ON CYLINDER 0 TRANSITION ON CONE 0.4 l 0.2 SHOCK TUBE (REF. 14) 0 1 2: 3 4'106 PeU X Rex e Figure 5. Effects of Cooling on Transitign 9n Blunt Bodies Data of Diaconis et al 13) and

!II. FLOW SIMULATION AID SHROUD DESIGN S.mila.arity Reqmirements for Boundary Layer F'Lows - Simplifications for Bcnun3d yada'ayer Transit:ion Studies on. Blunt Bodies in Hypersonic Flow The Cri~danental] guides fo:r the design of any wind tunnel facility are the non-dimensional similarity parameters, derived from the governing physic:a. e'q(uations., -blch w miust have the same values for two sets of testing conditi!.ons if the detailed flow fields are to be non-dimensionally identical. In the present investigation, it was desired to study the bourdary laye:r flow wi h occurs over the- nose region of blunSt bodies at lyperso-ic speeds. Aco rdingly, the important similarity parameters for this -study are those associated with the boundary-layer equations. It %Wll be sho<wn below that within certain limitations, when conditions at the stagnation point are used for forming the similarity parameters (as opposed to the usual "free-stream"' conditions) the "'free-stream" Mach number drops out of' the problem. This result is a consequence of the- Mach number independ.ence principle (50) The choice of reference conditions at -the stagnation point and the relative u;rimportance of Mach number as a Thich -"ree-stream"' conditions no longer have significance. A straig':t~forward dime:nsional analysimS:o the boundary layer equations, given in Appendix A, shows that when the following conditions are realized:n two fow fields.: 1, TI e bodies are geometrically similar. 2. The fluid.s'act as non-reacting gases. 3 v -Oer'the range of temperatures encountered, the dependence on temperature of the viscosity, thermal conductivity, and -17

specific heats can be represented with sufficient accuracy by power laws. 4. The Prandtl number and ratio of specific heats, based on stagnation conditions, are constant. 5. The flow along the edge of the boundary layer can be considered isentropic, then the important similarity parameters for comparison of the boundary layer flows are 1. The Mach number distribution, IVe(S), along the edge of the boundary layer; 2. Either the Nusselt number distribution, N[o(D), along the wall or the wall temperature ratio, rw (); 3. The stagnation Reynolds number, Aed - s where x is measured from the stagnation point along the body in a meridian plane and D is the body diameter. Thus, with the above __T T restrictions, the local boundary layer profiles and will have the same functional dependence on the non-dimensional co-ordinates in any two flows in which these similarity parameters are the same. Although, in general, the Mach number distribution along the edge of the boundary layer of a given body implies a unique freestream Mach number, an exception occurs for the case of blunt bodies in hypersonic flow, In this case, the Mach number and pressure distributions at the edge of the boundary layer are those associated with Newtonian flow and become independent of free stream Mach number over most of the nose region. Actually, the modified Newtonian theory shows that the ratio of surface pressure coefficient to its value at the

-19stagnation point is independent of free- -stream Mach number thr-gh therelation --- - = = 5 a? (1) However, in the hypersonic flow regime is negligible c0ompared to unity and can also be nle cted. compared to e/PS:ver a -considerable portion of the- nose region of a blunt body., Thus, the pressure and Mach number distributions are given quite accurately by the equations = - C? (2) an-d Ml-= YTt csI-) (3) in the'vicinity of the nose- -of a blunt body in hypersonic flow. Experiments on hemispheres (References 33-38, for example) show that the pressurssure distribution given by Equation - i ve'.-ty accurate over most of the nose region. For example, the data of Reference 34 shows less than 15% deviation from Equation 2 up to; = 45 when Moo - 2.0, and nearly perfect agreement up to? = 650 for Ma:= 4.15. Thus, for the purpose -of studying the-boundary layer over the nose of a blunt body in hypersonic (and moderate supersonic) 1flow when real gas effects and free-stream entlroVpy gradients are of minor importance, the important similarity paraetePrs, based on stagnation

-20point conditions, are Reynolds number, <, and either the wall temperature ratios, (, or the Nusselt number, Nuw( ).Thecharacteristic veloc'ity.in the problem is the speed of sound, and free stream conditions have little significance. Real gas effects., such as dissociation and ionization and the attendant heat and mass transfers in a multicomponent reacting gas will undoubtedly have some effect on the laminar boundary-layer stability. However, the purpose here was to study the circumstances under which cooling may actually promote a decrease in transition Reynolds number, a phenomenon which has been observed in wind tunnels(11-13) under ambient stagnation conditions, as well as in the shock tube(14) where the temperatures ranged as high as 10,000 R, Therefore, failure to simulate the real gas effects associated with high temperature levels was considered to be of only minor consequence, at least for a first approximation to the effects of cooling and roughness on transition. The effect of not simulating thp local "free-stream" vorticity and entropy gradient associated with the bow wave could not be assessed apriori. On the basis of the arguments presented above, a wind tunnel facility for boundary layer transition studies on a hemisphere in simulated hypersonic flow was designed by shrouding the model so that the Mach number distribution given by Equation 3 could be realized. The analysis used in designing the shroud is presented in the next section. Since in the -use of the tunnel the supply air was unheated, boundary layer cooling was effected by filling the model with various coolants such as liquid nitrogen, In Figure 6 the range of simulation

24 h= I10,000 FT. 90,000 70,000 50,000 30,000 10,000 "21 - _ _ 0._ I _ E II I I I.... I r I I I l l8 -0.2 1 1 l5.-153 w LIQUID NITROGEN LIMIT7 0.25- z F 9 l _ / I I2'/,2,////////// x ////////////s////:/// 7 X,9 //,R %/2'/,' i -'Id' { ~'51 1 iZ 6 |0.73 6 WgO 3 Icn Tw'300dqz I oL 1 I 0 I 1X i II 1 105 2 3 5 7 o106 2 3 5 7 107 2 3 5 7 o108 STAGNATION REYNOLDS NUMBER PER UNIT LENGTH, Res /DFT. Figure 6. Range of Flow Simulation

-22provided by the facility is given in terms of the stagnation Reynolds numbers and wall temperature ratios for a re-entry body (Tw = 3000~R) at various altitudes and Mach numbers. Shroud Design The following analysis predicts the contour of an axisymmetric shroud enclosing a hemisphere on which, for choking flow, the pressure and Mach number distributions are those for hypersonic flow (Equations 2 and 3). A hemisphere was chosen partially because the spherical coordinate system facilitates the analysis. The design of the shroud contour was carried out in two steps. First, an approximate solution for the incompressible, irrotational flow field was found in the region 0 ~ -' 45~, and, second, the resulting contour-was corrected for compressibility near the sonic region (Me = 1 at ~ - 440) assuming one-dimensional flowe Experimentally the spherical surface is convenient because by rotating a sphere a single probe serves for determining a distribution over a meridian plane. The contour downstream of the sonic point could also be designed by the method of characteristics. However, this refinement was considered unnecessary because boundary-layer transition was expected to occur in the subsonic region with the testing conditions available. Further, the free stream turbulence generated by the turbulent boundary layer on the shroud would probably seriously affect the transition on the model.

-23Proceeding to the incompressible problem, the irrotationality condition and conservation of mass, expressed in spherical coordinates, (see Figure 7) are, respectively, and In view of Equation 5 a stream function, 31r( A), can be defined by rJ2 _ (6) The irrotationality condition, Equation (4), expressed in terms of 3 leads to the following linear equation h) rb - The boundary conditions to be supplied with Equation 7 are thaty is zero on the stagnation streamline and the surface of the body, and, in addition, that the velocity distribution derived from Equation 3 exists along the body surface. Mathematically, the irrotational flow of an incompressible fluid in a "simply connected" region is uniquely determined when either the stream function or the normal component of velocity is known at every point of the boundary(39). In the present application on the other

-4.4= CONSTANT SHROUD ~f~r'~=0 "' = Fgre 7- Coordinate System. Figure 7. Coordinate System.

-25hand the problem is to determine the shape of the shroud streamline (Figure 7) such that the hypersonic:velocity distribution (Equation 3) will exist over the spherical surface in the range 0A --- 44~. LWhile we cannot show that the shroud shape so determined represents a unique solution, the agreement with experiment is excellent (see Section V). The velocity distribution corresponding to Equation 3 is approximated by the first term of its series expansion. Then the boundary conditions on the zero streamline, for 0' ~ L- on a sphere of radius R, become a(ro) -O (r (8) Although no straightforward analytical methods appeared to exist for solving Equation 7 with conditions 8, an approximate closedform solution was obtained by making a few minor simplifications. Since in the range O- 2 ~-~ both sinr and cot$' are given to within 1% by the first two terms in their series expansions, Equation 7 becomes, to a high degree of approximationr Varicda' - (9) with the boundary conditions (to9) 1- O ( r_> R) (10)

-26In attempting a power series solution of the form to the above problem, it is found from Equations 10 that the first and third. boundary conditions are satisfied if CL,(r) =o ( ( 3) (12) so that the stream function can be written in the relatively simple form 3It?) c (, ) -7~ L2 (t y (v) t 1 (13) By substituting Equation 13 into Equation 9 and applying the boundary conditions, Equation' 10, the following two simultaneous differential systems result for determining a2(r) and a4(r) r2 z ~ LC, = - g Gly 3, (R) =- _- (i4) az (R) = o and - o 3 l (R) _ RS (15) QW'(R) = O

-27After solving these equations (Cauchy type) the stream fIction given by Equation 13 is determined. The final result may be aitten _~ A 4(16) Thus, the (incompressible) shroud contour for any given volume flow is given implicitly by setting ~ = constant in this equation. The shroud contour - - (r) is then found by specifying 3 and r and solving the quadratic in x for values of. In Figure 8 a scale drawing of the shroud based on the above analysis is shown, Corrections for the effects of compressibility, as mentioned above, have been incorporated. The figure shows that the effect of compressibility is appreciable only in the immediate vicinity and downstream of the sonic point 2 = 44o0 For ] > 45~0, the gap between the shroud. and the sphere surface is slightly greater thar. hat specified by theory. This increase in gap was provided so that boundary layer growth would not influence the position of the sonsic point,

NOTE: DOTTED LINE INDICATES SHROUD CONFIGURATION BASED ON INCOMPRESSIBLE FLOW. 18 1 /-SUPPORT STR~ r 24 Figure 8. Aluminum ShrouJ Configuration with Sphere in Place (Dimensions in Inches)

iV. EXPERIM/ENTAL APPARATUS AID METHODS General- Wind Tunnel Facility A schematic diagram showing the general layout and construction of the wind tunnel facility is given in Figure 9. This facility was erected at the Aeronautical Engineering Laboratories of the Department of Aeronautical and Astronautical Engineering, University of Michigan. AS- indicated in the figure, two air supplies and efxhaust systems have been employed. Stagnation pressures of one atmosphere an.d less canal be -obtainaed by usiang air from a 15,000 cubic- foot dry air storage and exhausting into vacuum tanks having a total volume of 13,000 cubic feet, Pressures up to 8.5 atmospheres (structural limit of the tunnel) can be obtained by regulating from a 375 cubic foot 2500 psi. high pressure system and exhausting into either the vacuum tanks or the atmosphere. Both air supplies are unheated. Air dryer's in both systems use activated alumina as the desiccant. The lowest dewpoints obtainable with the atmospheric supply, as well as the length of time they can be maintained, are quite dependent on the atmospheric humidity. Practical dewpoint temperatures range from -400F in the summer to -60OF in the winter with this system. In eontratt, the high pressure dryer', the installation of which was brought asbout during the present investigation, is independent of atmospbaric conditions and is capable of lower dewpoints. Dewpoin ts in the range -700F to -10CiF (measured at one atmosphere pressure), corresponding to specific humidities of 1.8 x 10(5 to 8.9 x 10-7 pounds of water vapor per

PRESSURE REGULATOR 500 PSI SAFETY DIAPHRAM TO 2500 PSI AIR _ MECHANICAL SEPARATOR I0 x 6 EXPANSION 16 x 10 EXPANSION 28 MESH SCREENS TO DRY AIR STORAGE II: (PRESSURE= AMBIENT; DEW POINT =-600F MINJ - THROTTLING VALVE I LIGHT SOURCE 18 AND COOLING FAN " 0 PERISCOPE 150 PSI SAFETY DIAPHRAM 10:1 HONEYCOMB7 I/ I: I H ON EVCOM B7 16 x 12 REDUCER 28 MESH SPHERE SUPPORT BRACKET SAND TRAVERSE MECHANISM *ii-116.~, TO ATMOSPHERE OR VACUUM TANKS 2-1/2 L12 1e 2 I12. 17-1/2 pL \12 x 8 REDUCER ~/ 1 ~- 60 — 18 - 24 - 14 FILTER PAPER Figure 9. Schematic Diagram of Air Supply System and Wind Tunnel Layout.

-31pound of air, were usually obtained. No provisions are incorporated for removing carbon dioxide from the air. The supply air is throttled. Figure 9, to produce- stagnation pressures between 0.1 and 8.5 atmospheres. Steady flow conditions -could be established in minimum times of about one second with the atmospheric supply and two to three seconds with the high pressure system. When the high pressure supply is used the air passes through a mechanical separator which traps large scale rust and dirt (95% of all particles larger than 10 microns in size, accordilng to the manufacturer) which may have accumulated in the storage tanks and. lines prior to the dryer installat ion. After pressure regulation, the air enters a 16-inch diameter 5-foot long settling chamber through the diffusers shown. Screens are provided at the junction of the two diffusers to prevent flow separation. The settling chamber contains a 10:1 (length to widthratio of the cells) honeycomb, 2~ inches thick four 28-mesh screens of.0065f' wire Air samples taken from the high pressure supply showed a condensation temperature for dry ice of approximately -2300F which corresponds closely to that pred.icted on the basis of the carbon dioxide content in the standard atmosphere (.03% by volume). However, several analyses of the compressed air showed. that the CO2 content varied up to as much as 30 times that in the atmosphere The corresponding "1specific humidity" for CO2 ranged from 4.5 x 10-4 to.5 x 102 pounds of CO2 vapor per pound of air, so that for the limiting temperatures in these tests (condensation of liquid oxygen around -300~PF depending on the pressure) the problem of frost build-up on the model surface was of minor importance compared to the condensation of C02 in affecting boundary-layer transition. A discussion of the effects of frost and CO2 on transition is given in the Results and Discussion, Section Vo

-32diameter, and a paper dust-filter* at the entrance. After passing through the 2-foot long test section the air is exhausted to either the atmosphere or vacuum tanks, depending on the pressure level. A scale drawing of the test section interior showing the shroud contour and sphere is given in Figure 8. Figure 10 is a photograph of the wind tunnel. The reducer downstream of the test section can be unbolted and lifted out of position, as shown, providing access to the model and its instrumentation. The photograph also shows a travelling periscope mounted on the downstream end of the settling chamber. The general construction and operation of this device is sketched in Figure 11. The main purpose Of the periscope, whose field of view covers a region up to 200 from the stagnation point, is to provide a means of checking for ice and carbon dioxide formation on the sphere. It is also a convenient device for determining accurately when an instrument on the surface is at the stagnation point. When flow measurements are being made the periscope is retracted so that the bottom is flush with the wall of the settling chamber. The tunnel weight flow (in pounds per second), based on measured -velocities in the settling chamber, is approximately.17 times the stagnation pressure (in pounds per square inch absolute) for the The purpose of the filter is to remove fine scale rust and dirt not trapped by the mechanical separator. The paper, called 5 ply Airmat, is manufactured by the American Air Filter Co., Louisville 8, Kentucky. The dynamic pressure at the filter was 10,000 to 50,000 times that for which it is normally used so that it had to be backed by screens to provide physical strength. It was found necessary to remove the oil normally in the filter since the particles which did get through would stick to the model quite readily, A surprising amount of rust was stopped by the filter under these circumnstances.

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500 WATT LAMP FORCED-AIR COOLED) CONDENSING LENSES 3 x 1/2 PLASTIC WINDOW (EYEPIECE OF SIMILAR CONSTRUCTION) EYEPIECE TO VIEWER PLANE MIRROR 9ICLOWER PERISE 1.5 x 2.12 ELLIPTICAL FIRSTSURFACE PLANE MIRROR Figure 11. General Construction of Traveling Periscope.

-35conditions of the experiments. At the maximum. allowable tunnel pressure of 125 psi, the high pressure storage sysztem, containing approximately 4700 pounds of air at 2500 psi and 700F, would be emptied in 3.3 minutes. This represents the minimum length of run for the facility. When running from the atmospheric supply the vacuum tanks limit the length of run with chocked flow to about 9 minrutes, nearly independelnt of stagnation pressture. A Bourdon-type gage, a 60.inch mercury manometer, and straingage-type transducers were used -separately an.d n iconjunction, where applicable or necessary, to measure and reord. tunnel stagnation pres sures. A thermocouple upstream of the settling chamber was used to measure stagnation t;emperatures. The sphere and its associated instrumenation. are discussed below. Sphere and. Associated Instrumentation The 9-inch diameter sphere was machined in two hemispheres from solid 60/40 brass forgings. The purpose of this method, as opposed to casting the hemispheres, was to avoid, as much as possible, gas holes in the final machined. surface. The wall thickness is 1/4 inch except in the region of the support stru6ts where it gradually increases to a maximum thickness of 3/4 inch.. The installation of the sphere in the shroud permits fore and aft movement of +1/4 inch. By means of this adjustment the pressure distribution onr the hemisphere ca. be varied somewhat from the Newtonian case. This was not done, however, in the present study. Six 3opper-constantan thermoc-ouples are installed within 0.020 inches of the outside surface at lP in:tervals, as shown in

-36Figure 12. Also shown in this figure is the location and construction of two hot-wire probes and a pressure tap. The purpose of using two hotwires was to measure correlations of the fluctuations at the stagnation point outside the boundary layer. When boundary-layer disturbances were being studied the wire nearest the thermocouples was removed and a plug inserted in its place. The second wire was then turned 1800 so that any roughness caused by the plug or thermocouples would be downstream and therefore would not influence the measurements. Originally it was planned to use both the thermocouples and the hot-wire to detect boundary-layer transition. The thermocouples were installed before the final.010 inch was machined from the surface so that a smooth finish would result after final machining. However, this.did. not happen. Several gas pockets formed at the constantan connection, appearing as deep pits after machining. Also, the action of the lathe cutting tool was such that a slight depression existed in the softer soldered region. This is illustrated in Figure 13 which shows a profilometer tracing across one of the thermocouple junctions. Subsequent methods of filling the depressions, such as by soldering or copper plating and then polishing, were not considered satisfactory in view of the importance of roughness in these experiments. Thus, the thermocouples were used mainly as a means for measuring the surface temperature as a function of time during the cooling and heating All profilometer measurements reported in this paper were made courtesy of the Micrometrical.Manufacturing Company, Ann Arbor, Michigan.

6 THERMOCOUPLES FROM 100 TO 600 A 4.5 THERMOCOUPLES B ~B 0~~~~~~~~~~~~0 ~5 L_ C~ _ _ SUPPORT STRUT 22 PRESSURE TAP HOT WIRE PROBES FRONT VIEW SECTION A-A (HORIZONTAL PLANE OF SPHERE).020!'0 - 0 -SOFT SOLDER REMOVABLE PLUG.00 1.3 ~~~~/ --—,o SOFT SOLDER.040 CERAMIC 40 TUBE ~ ~ ~ 1/8 COPPER TUBE TUBE.010 WIRE INSULATION 40002 PLATINUM OR TUNGSTEN COPPER WIRE.010 CONSTANTAN WIRE WIRE SECTION C-C S E CT I0N B-B ~S ~E ~C ~T IO ~N B-B ~PRESSURE TAP DETAILS (X2) THERMOCOUPLE DETAILS (X4) HOT WIRE PROBE DETAILS (X2) Figure 12. Details of Sphere Instrumentation. All Dimensions in inches.

PROFICORDER _.00250",i.40" IS1~~~~~ — B-1 —..I,_ l?_ 1 P CHART No. 9_.87 Figure 13. Profilometer Tracing Across Thermocouple.

periods of a test. When transition experiments were conducted, these surfa;3e therm.ocouples were alwys downstream of the measuring station, Use of the hot-wire anemometer to obtain quantitative inform:ation concerning boundarylayer flu-ctuations presented an extremely dii'ffticult eeerimental problem in tLhe present case~ Immersed in the cooled bond.ary layer between the Estagnation point and the sonic'position ( - 440), the hot-wire ean experienrce a ide range of "local freest:ream" c.nd.tions upon which its response will depend; viz. Nusselt nurber., Reyriolds number, Mach umber, and, stagnation temperature. In general, a hotswire in compressible flow is sensitive to fluctuations in vpLocity, temperature, and. density, and its mean square output'is depend.ent, in additionr, on cross correlations between thes:e variables. When viewed in terms.of vorticity, entropy, and sound., the numnber of wuknowrn quantities making up a single measurement can usually be redu.ced froam six to three or four by neglecting correlations between sound and e:ntropy or vorticity and in the proper circumstances by neglecting soand altogether. To extract a sn.gle fluctuation, then, eq4ires at least three o:r four measurem.ents for.i -ch the sensitivi.ties to the varsious lucetuatitons are vaTried between measurementls by varying'the wire heating. For a given wiLre, these sensitivities generally depend on the localQ Nubsselt number MEach number,, Reynold. numbler9 recovery factor', (nonl.inear ) ariation of wire resistance with temwperature, temnperature loading, and. various derivatives between these vairia'bles. Because the dependence on the above-variables can vary RefeceUn@ gives an excell.ent discussion of the hot-wire in compre~il fL:z< *nO

-40greatly among individual wires (end loss effect and method of construction) a given wire must first be subjected to a series of calibration tests~ Thus, preparing a wire to make measurements and extracting information in a compressible flow is not an easy task - especially in view of the breakage which is often encountered, In the present application the real difficulty comes in knowing what the conditions are at the wire. Assuming (machine) calculations have been made so that the boundary-layer variables are known as a function of space and time while the model heats up, it is then necessary to know exactly where the wire is in the boundary layer and to be able to place it back in the same position if it should break. The difficulty here is due to the thinness of the boundary layer which varied from about.002 to.008 inches in the range of conditions tested. In view of the expected difficulties in seeking quantitative information of fluctuations in the boundary layer, the hot wire was used in these initial investigations as a tool for viewing the overall type of fluctuations (regular or random) present and their relative amplitudes at various angular stations and under different conditions of boundary-layer cooling. It also served to measure "free-stream"' turbulence distributions and for measurements of the "free-stream" velocity correlations at the stagnation point. A Shapiro-Edwards hot-wire set was used in conjunction with an oscilloscope and tape recorder for viewing and recording the signals. Even as a qualitative instrument the high mortality of the hot-wires at relatively low dynamic pressures made it desirable

to seek a more rugged instrument. Since the thermocouple method had been abandoned and no windows existed in the tunnel, a surface pitot-tube appeared to be the next possibility as a transition probe. Such an instrument was developed to detect the inreasee in total pressure near -the surface when transition occurred. This instrument is called a — Stanton-tube when the ratio of tube height to boundary-layer thickne ss is small, and c be used to measure skin friction at the surfaAe. The small thickness of the boundary layer under consideration made it impractical to satisfy this requirement so that the tube served only as a transition indicator Evren to serve this function it was necessary to make the height of the probe as small as ppssible, constistent with a reasonable response time, if it was to be fairly senitive to transition. The lower limit on size was determined mainly by physical limitations in construct ion. Figure 14 shows the size and construction of the pitot-tube, a static tube- beside it, and the pressure leads. The tube was made by copper plating a horseshoe shape sh aoundpe ar static prese tap, insertin a 001l-inch brass shim painted with silver conducting paint, and then plating a thin cover. After removing the spacer the paint was dissolved by sucking a thinner through the.openingo The l/2-nch copper tubing was placed around the 1/8-inch presure leads to insulate them frm. the liquid nitrogen which filled the inside of the sphere, Before this was done, liquid oxygen would form inside the pressure leads and cause See Reference 41 for example.

-428 COPPER LEADS 2 COPPER TUBE PITOT TUBE CONFIGURATION NOT DRAWN TO SCALE. SCALE -t- I STATIC ORIFICE.032 DIA. A A- -\ S L, 5 -ad.002 PITOT TUBE PITOT TUBE TOP VIEW SHOWS ENTIRE PITOT TUBE SCALE, 5J 1 CONFIGURATION. Figure 14. Size and Construction of Pitot and Static Pressure Probes.

-43erratic readings. The static and pitot pressures were measured differentially by a strain-gage-type pressure transducer whose output was measured. continuously on Sanborn pen recorders. A -schematic diagram showing the method used to cool the sphere,, together with a typical thermocouple circuit, is given in Figure 15. Two coolantss dry ice mixed with acetone and liquid nitrogen, were used-. The corresponding minimum wall temperatures attainable were 110 F with dry icea etone and 320 F with liquid nitrogen. The dry ice-acetone mixture was emptied into the sphere by hand and removed with a avacuum pump. Liquid nitrogen was pumped into the mod.el from a self pressurizting (22 psi) 110 liter container and left to evaporate at the end of a run, The cooling procedure consisted of filling the sphere until the d.esired. nitial temperature was reached and. then starting the tunnel. While pre cooling to the lowest temperatures, the model would be exposed to the essentially- stagnant d.ry air in the tunnel for a few mrlnutes during which the surface temperature was below the dewpoint temperature of the air. For a dewpoint of -75~F the total amount of water in the air contained by the tunnel is about 10Q5 pounds. Even assuming all of this water could d.eposit on the surface only! 6 results in a uniform layer about 10 inches thick. Therefore9 water cordensation prior to a run was n.ot considered. to be of importance in influencing the data taken. Examination of the stagnation point Of more importance is the condensation of CO2 that may take place while ste ady flow conditions are being established during start up. ThMis is d.iseused in -Se t0ion V.

-44 - I DRY ICE -ACETONE I MIXTURE SPHERE FILLED WITH LN2 I —-\ EXHAUST TO THERMOCOUPLE ATMOSPHERE MEASURING JUNCTION COPPER LEADS SELECTOR SWITCH CONSTANTAN'- LEAD 1 LN2RECORDING iREFERENCE POTENTIOMETER JUNCTION 110 LITER PRESSUH20 AND ICE RIZED CONTAINER Figure 15. Schematic Diagram of Cooling Procedure and Thermocouple Circuit.

J45region of the surface through the periseope never showed any visible evidence of frost just prior to starting the tunnel. Actually, when the air de, wpoint was about -70F or! ess, a minute or so of run time was:required before the frost was visibleo However, if a relatively short run was made the sphere would. e allowed to warm to a temperature above the air dewpoint before making a second run. T.he internal cooling of the modlel was not forced but depended on the natural -heat tran.sfer from the coolant reservoir inside0 Althouegh this reservoir could be maintained during a run, the heat transtfer from t;he air was usually much greater th th than that to either the dry ice-acetone or liquid nitrogen so that the surface temperature would. increase as the run progressed. For the coldest tests the temperature rise was of the order of 5 to 100F/sec at the stagnation point for the first 10 to 15 secon-d. P.eparat i-on an.d.Drtspection of Modei Surface In many exerimental boundary-layer studies the combination of Reynolds number, Mach number and body lengths are such that the boundary-layer thickness isL large enoaug so' that the avoidsace of rough ness effec-ts on transitlon does not require a highly polished surface. High Reynolds nubers per unit Length, whiclh tend to reduce this thickne~s, are usua.lly associated -with h'gh MaCh lnumber's, which. have the opposite e2ffect. One important exception is-'the case at hand, that is, boundary layer studies on blaunt bodies in hypersonic flow. Here the unit Reynolds numbers mbers are relatively high because of the high."freestlreamn Mayc;h number wrile the Mach nmbers at the edge os tclhe boundary layer are.!o near the nose. Thus, typas tboundary layer thicknesses

-46on the 9-inch hemispherical nose were only a few thousands of an inch. Since the effect of boundary-layer cooling is to cause a given roughness height to be even more effective in promoting transition it becomes a necessity to pay close attention to the surface finish. Mechanical hand polishing was the method used for preparing the surface after final machining. The entire hemisphere was sanded and rough polished until no deep scratches could be seen. The final polish was concentrated only in a region bisected by the meridian on which the measurements were made. This region was considerably larger than the "transverse contamination zonet, in which transition caused by roughness at the edge of the zone would spread to the measurement meridian within the latitude range of the tests. A conservative estimate for this half angle of spread of transition was taken to be 100. Chromic oxide and aluminum oxide, having particle sizes ranging from 15 microns initially down to 0.1 microns for the last polish, were used in the final polishing stages. It was found that special care had to be taken in applying the final polish to the brass surface in order to avoid so-called relief polishing, wherein the grain structure of the hard and soft phases polish at different rates and give an etching effect, which can result in significant surface roughness. The relief polishing was kept at a minimum by using a cloth without nap, such as silk, for most of the polishing operations, and polishing only a short time with the softest cloths to take out scratches made with the silk. There is, then, a limit other than time to which an alloy such as brass can be polished. If one continues to polish

-47with the finest powders. and softest cloths available, relief polishing will begin to appear before "all" scratches from the harder cloths containing no nap have been obliterated. Figures 16 and 17 show.photomicrographs and profilometer tracings, respectively, which illustrate the type of surface obtained where relief polishing resulted compared to that final.ly obtained using the polishing procedure outlined above. BOth. s~ua es had been polished to the point where no scratches were visible to. the n aked eye. Figure 16a was made.with the microscope and lighting directed normal to the surface, while the lighting in Figure 16b was directed at a slight angle to the surface normal so as to accentuate the ruggedness of the relief polish. The grain structure is still visible in Figure 16a but shows up mainly due to the differential staining of the phases. rather than differential height and shape. The black spots are app!rently blow holes in the surface. These photographs and profile tracings show a considerable difference in surface roughness between'the two polishing techniques. Both microscopic examinations and profilometer tracings were used to inspect the surface finish. The stylus used with the profilometer was.0007 inches in diameter and had 1 gram of applied pressure..The traces were, of course, carried out in a region where the groves due to the stylus could not influence transition at the position of measureAll photomicrographs were made through the courtesy of Mr. A. M. Rickel of the Bendix Corporporation Research Laboratories,'Detroit, Michigan'.

-48_ a. no relief b. relief Figure 16. Photomicrographs of Surface at a Magnification of 350

/ I-' t- a) NO RELIEF.oooo000025 I.010" I /~ ~~~ Ii,~~~. NO.... b) RELIEF Figure 17. Profilometer Tracings of Surface.

-50ment. One or two traces were assumed to be typical of the entire polished surface prior to placing the model in the wind tunnel. The best surface obtained had an rms roughness less than one microinch according to profilometer measurements, Figure 17a. Although this is undoubtedly on the low side due to deficiencies of (42) this type of instrument on very smooth surfaces, it is indicative of a high quality finish, In this report) rms roughness reported in connection with the present study were those obtained with a profilometer. It should be pointed out that an rms roughness measurement on a "smooth" surface, regardless of how accurate the method used in obtaining it, is very often only indicitive of the care used in pblishing rather than an important aerodynamic parameter characterizing the roughness. That is, the relatively few scratches, pits, and protrusions often present during and after, if not before, a wind tunnel test may be of much more significance in effecting boundary-layer transition than the many smaller irregularities which usually make up the sample rms measurement. During tests with the smoothest surface some microscopic inspections were made of small dust particles deposited near the stagnation point. These are discussed with the experimental results which follow.

V. RESULTS AND DISCUSSION The experimental results to be described, below are presen.ted in three parts. First are the -tests which check and describe the "environmental" conditions u;d.er which the boundarylayer transition studhies were conducted.. They include the surface pressure d~istrfbution on the sphere resulting from the shroud tec'hique, turbulence leveLs in. the wind tunnel and outside the boundary layer on the mod.el, correlation measurements between velocity fluctuations at the stagnation point, and temperature-time histories of the model surface during tests with boundary-layer cooling. The second. and third parts are -concerned with the investigations: of transition in moderately cooled. boundary layers. Wben these studies were first begun the pressure range was limited to a maximumn of one atmosphere while the high pressure d.riers and dirt sepa.rators were being'installed. Accord.Jingly, a series of preliminary experiments were run at a constant stagnation Reynolds number, Re --- of approximatei.y 4 3 x 106 Dry ice and, acetone was used as the coolant so that the m.inimum ratio of wall temperature to stagnation temperature was about 0.72. The hoto-wire an.emometer served. to determine the character of fluact'uat ions in the bournd.ary layer. Although "-naturali" transition was not observed in the subsonic bounddary layer under these cond.itionas, some experimen rts' were made to ascertain the effects of'boundary-layer cooling n: the d.isturban es caused by various two-and three-dimensional single roughness elements glued. to the surface.

t~~~~~~~~ PS r o Re 2.92 10 (Ps O Re:180 X106 (P5:47.3psia) C.5T.1.2-80 -70 -60 -50 -40 -30 -20 -10 0 10 20 30 40 50 60 70 80 rq- DEGREES Figure i8, Measured Pressure Distribution Dn 9-inch Diameter Sphere.

occur a few degrees ahead of the theoretical position ( =43.80). This error is probably a result of the simple one-dimensional correction used in the neighborhood of the sonic point. That is, the deviation from one-dimensional flow, due to the curving boundaries of the shroud and sphere, causes the sonic line near the sphere to move upstream of the minimum area. While pressure distribution measurements were being made, a one percent low frequency oscillation in stagnation chamber pressure was observed. This was traced to intermittent separation in a curved inlet pipe which in turn was coupled with an unsteadiness in an upstream valve. After eliminating this fluctuation the turbulence level distribution at the shroud inlet was that shown in Figure 1-9. Measurements of the velocity profile are also shown. The rms mainstream velocity fluctuations in the axial direction are about 0.3% of the centerline velocity. A turbulent boundary layer extending about 2 1/2 inches from the wall is also apparent. The turbulence level is reduced considerably as the flow passes over the nose of the sphere. Measurement in the "free-streamn outside the boundary layer, at a height of.071 inches from the surface, showed the rms streamwise velocity fluctuations to be less than 0.1% of the local velocity in the range 7~y ~' 460. Although the gap between the shroud and sphere reaches a minimum of 3/8 of an inch in the sonic region, the shroud boundary layer, 2 1/2 inch thick in the settling chamber, does not appear to introduce unreasonable values of'"free-stream" turbulence in the range of the investigation. The relatively low "f'ree-stream"' turbulence level is important particularly

-55 -' U' 100 U - TURBULENCE LEVEL, 100 u lO VELOCITY PROFILE,' 2.8- FT. 49 SEC. 2.40 2.0 1.6 0 1-X —-— * —--.1.2- - 1.0.8.4 -6 -4 -2 0 2 4 6 HORIZONTAL DISTANCE FROM CENTERLINE - INCHES Figure 19. Turbulence Level and Velocity Distribution in the Settling Chamber.

-56because no quantitative information of the effect of "free-stream" turbulence on transition, pertaining to the present study, is available at present. Recent measurements by Kuethe, Willmarth, and Crocker of the correlation between velocity fluctuations on opposite sides of the nose of hemispheres have shown the occurence of a random, low frequency, stagnation point motion. In subsonic flow, they found high negative correlations to exist at ~70 from the stagnation point when the hot-wire frequency band was 0.1 to 20,000 cps. At M- =2.44 nearly zero correlation was reported for the frequency range 10 to 20,000 cps, although significant negative correlation did exist when the frequency band was restricted to the range 0.1 to 50 cps. Of basic interest in itself, the stagnation point motion is also significant since it represents a source of disturbance to the boundary layer flow which could be of importance in the transition process. In the present shrouded sphere tests the correlation was 0 measured at the same angular position, ~7, with the hot wires.05 inches from the surface. Measurements were made with the wire compensated to respond in the frequency range 0.1 to 20,000 cps and without compensation which limited the high frequency response to about 300 cps. In these frequency bands, no appreciable motion of the stagnation point was found. Further measurements still need to be made to determine whether a motion, whose amplitude is small compared to the overall rms fluctuation level, exists at low frequencies, as in the supersonic case above, or whether the stagnation

-57point remains fixed due, perhaps, to the "confining" effects of the shroud-. on the main stream flow0 Finally, the model wall temperature-time histories will be considered. Results for typical testing conditions are presented in Figure 20 whAich shows the time variation of the difference between in;tantaneous and. initial wall temperature at the stagnation point, divided by the difference between the air stagnation temperature and initial wall temperature. Data are shown for both liquid nitrogen and d.ry ice-acetone coolants. The effectiveness of the coolants is shown by comparison with the corresponding theoretical time variation of the temperature ratio neglecting the heat transferred by lateral conduction, and assuming that the inside wall is insulated. The opposite extreme of infinite cooling is, of course, represented by the abcissa, Tw - Tw The results show that the heat transferred to the coolant from -the model was generally small in comparisonr with that transferred to the model from the air. Nearly equilibrium conditions were established. only at the lower heating rates with the dry ice-acetone coolant, It is seen that the experimental points for the liquid nitrogen data have a nearly exponential variation with time, if the net heat transferred to the wall per second is modified to be a constant fraction of thiiat transferred from the air, i.e., qws is replaced by.qws w'here o< is less than one, then the modified theoretical curve he exponential solution is based, on a constant mean specific heat for the metal and results from the fact that qws/Ts-Tw is very nearly indepenxdent of Tw. The theoretical heat transfer at the stagnation point, q.w w'as computed from t:he solution of:References 31 and 32.

THEORETICAL VARIATION WHEN HEAT TRANSFER 0 DUE TO LATERAL CONDUCTION AND COOLANT ___ CORRESPONDS TO EXPERIMEN IS NEGLIGIBLE COMPARED TO THAT OF AIR TAL CONDITIONS IN Ts 5000F 0 P5:52.7 psi* TT:o307'F.8 0 P5528.7 psia ST~ W T,, = 3LIQ. N2 COOLANT.8 Ps,=28.7 psia,Ts-T T 25aOF K Ps: 12.6 psic sTs-,Two'I470F -DRY ICE-,ACETONE COOL'T K[estj'9-~~~e.6 0~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~0 9ws r I`'400 K low Tw -T 0 TS 10 r15 20 25 30 3 40 T s - T.4...............TI E.SC N 0 5 10 15 ~ 2~~~~~~~~~~~~~~~~~~-0 NOW0354 Figure 20. Typical Surface Temperature -Time Hist~ories for Tests with Cooling.

-59can be made to fall on the data. This results in a "figure of merit" for the cooling effectiveness. For example, the solid curve will fall on the corresponding data if qwS is replaced by 0.65 qws, that is, about 35% of the heat transferred from the air was absorbed by the coolant. With the experimental techniques used for cooling and for detecting transition (Section IV), the minimum wall temperatures for which transition data could be obtained were limited by the temperature rise during the establishment of steady flow conditions and the instrument response. The time required for the pitot tube to reach equilibrium was about 3 seconds. If the model was cooled to liquid nitrogen temperature (140~R) initially the stagnation point temperature would rise to about 155 R in three seconds. For an air stagnation temperature of 500 R, the corresponding minimum value of Tw/Ts was O.31. Actually, the minimum wall temperatures for which reliable data could be obtained will be seen to be nearer 2500R because of the condensation of carbon dioxide on the model surface at lower temperatures. Effects of Boundary-Layer Cooling onTransition. Caused by iRoughness A series of transition experiments, carried out at a constant stagnation Reynolds number of approximately 4.3 x 106, were made to verify the qualitative effects of cooling on boundary-layer transition caused by various roughness elements. As pointed out in Section II, three ranges of roughness height, dependent on the stagnation Reynolds number, angular position from the stagnation. point, and amount of boundary layer cooling, are expected. The three ranges arg (see Figure 2)

-60o1) the roughness may be small enough so that transition does not occur either with or without a given amount of cooling, or 2) the roughness may be of such a height that transition occurs only when the boundary layer is cooled, or 3) the roughness is large enough so that transition always occurs, independent of the amount of cooling. The data to be presented, illustrating the above ranges of roughness, were obtained with the same hot wire heated to nearly the same temperature. Since the angular position of the wire from the stagnation point was varied by rotating the sphere, the wire height from the surface was exactly the same in all of the tests. This ** distance was between.002 and.003 inches. The boundary layer thickness varied from.0057 inches at? = 0~to.0078 inches ati? = 450, nearly independent of the small amount of cooling. The wall temperature was nominally 0.8 of the stagnation temperature for the tests with cooling. The hot wire data is given in terms of the rms wire voltage fluctuations as a function of wire position from the stagnation point. Although no attempt was made to calibrate the hot wire and decompose the voltage signal into the various flow fluctuations (Section IV), it should be Other data with different hot-wires showed the same general effects of cooling. However, the fluctuation levels were not sufficiently repeatable due to the difficulties experienced in locating the wire at the same height in the relatively thin boundary layer. The boundary layer thickness, displacement thickness, momentum thickness, heat transfer, and skin friction for the laminar boundary layer were computed using the techniques and solutions of References 31 and 32. Their variation with?? and Tw/Ts is shown in Appendix B.

-61pointed out that, with the conditions outlined above, the wire sensitivities had nearly the same variation with position from the stagnation point in all of the tests. The voltage fluctuations are therefore comparable. Measurements were made with two types of disturbances glued to the surface. They were, 1) a.004" x.025" dia. disk placed 15 ahead of the wire, and 2) three ribbons,.004",.006"' and.010" high,.030" wide, and approximately 1 1/2" long, placed 100 ahead of the wire. In addition, data was taken with no disturbance added to the surface. In this case the rms surface roughness was 10 to 15 microinches, with pits ranging up to 100 microinches in depth. Typical fluctuation levels at transition are shown in Figure 21. The difference between total and static pressure in the boundary layer is, also given. Distributions are shown for the case of no disturbance placed on the surface, and for the case when the.004 inch disk was placed 15 ahead of the sensing probes. It should be emphasized that in this figure and the ones to follow the angular position of the probe was varied by rotating the sphere. Consequently the roughness elements rotate at the Same time. It can be seen that with the disk forward of 15 to 200 (probe angle 30 to 35 degrees) the disturbances caused by the disk are damped before they reach the hot wire. In this region, the rapid rise in fluctuations is interpreted as indicating the occurence of transition. This interpretation is The total head tube opening spanned the boundary layer between.0015 and.0045 inches from the surface, This tube was not mentioned in the description of the experimental apparatus (Section IV) since it was only used for a few measurements.

X JOO4",025" DIA. DISK, 150 V [AHEAD' OF PROBE 6 6 gSMOOTH" SURFACE Tw 5 Ts >cr~~~~~~~~~~~~~~. U PITOT- STATIC TUBES - AP U3 0) ~ _ cn0 8 t3 "_-~~~~~~~~~~~~~~~~~~~~~~~-2 (I) V 0 W >I w Ig! z I 0 n: i t o I % CL a. 1 2 _ _ _ _ _ I d 2 4 Ut ~~~~~~~~~~~~~~~~2 - 1 w I t 0 ~~~~~~~~~~-J 01~ ~ 0 0 0 10 20 30 40 50'p-ANGULAR POSITION OF PROBE, DEGREES Figure 21. Hot-wire and Pitot Tube Measurements of Transition Caused by a.004' x.025" Diameter Disk.

-63verified by the pitot pressure measurements which indicate much higher velocities (skin friction) in the lower portions of the boundary layer. Subsequent increases in the angle show a decreasing fluctuation level at the wire and an increasing deviation from the laminar pitot pressure distribution. For these angles the pitot pressure results are consistent with the development of a fully turbulent boundary layer at the probes as the transition point moves closer to the disturbance. The fluctuation distributions in the transitional and turbulent regions depend, among other things, on the Mach number(29'45) pressure gradient(43) and, as will be seen, the type of trip Of course, they also depend on the relative position of measurement which, in this instance, changes considerably in the thicker transitional and turbulent boundary layer. However, the rather large decrease in indicated fluctuations is probably caused by the fact that the high frequency response of the hot-wire amplifier was cut off at 10,000 cps to keep the noise low, An estimate of the turbulent frequencies to be expected in this case shows, however, that much of the energy is contained. above the frequency range used. For example, on the basis of (46) measured energy spectrums in the turbulent boundary layer at low speed on a flat plate, it is estimated that for the measurements shown, near 90% of the turbulent energy is contained in fluctuations above 107 000 cps. The rising voltage fluctuations at the largest angles for the smooth surface is caused in part by the increasing wire sensitivity to percentage reloity fluctuations at the higher speeds. Also, the sound level may be increasing near the sonic region. The

pitot pressure distribution indicates, however, that transition does not occur up to 42 = 45~ for the smooth surface condition. Cooling of the boundary layer causes the position of transition due to the disturbance in Figure 21 to move forward, as illustrated in Figure 22. Hot wire fluctuation levels are given for Tw/Ts = 1.0 and 0.8. Transition with boundary layer cooling occurs about 50 ahead of the position without cooling, in accordance with the roughness regime II of Figure 2, Section II. Oscillograms of the fluctuations are also shown in Figure 22. In the transition region, frequencies ranging up to about 2500 cps can be seen. These frequencies are considerably lower than those corresponding to disturbances of the order of the boundary layer or disk size, being transmitted at the free stream speed ( 10sec., t~e, 5 x 105 sec.-). Presumably, they are associated with DDsl< turbulent bursts in the initial stages of transition. The effect of small boundary layer cooling rates on transition caused by the three two-dimensional ribbons is given in Figures 23a-23c. Figure 23a also shows results for the smooth surface. These results illustrate the three ranges of roughness discussed previously in Figure 2. Thus, transition did not occur on the smooth surface, with or without cooling. The roughness of the smooth surface therefore falls in regime III. When the.004 and.006 inch disturbances were introduced transition occurred and the effect of cooling was to move it further forward, Figures 23a and 23b. These roughness elements therefore fall in regime IIo For example, with the.004 inch ribbon transition did not occur at 2 = 35~ until the boundary layer was cooled.

-6520 350 ( I I ~ 8oXn Tw w.8 -J TS Ts _ —J |AMPLIFICATION I __E__ — 1.O IN ALL 6 * TRACES. o7 I - 1Tw 4- TT S LL T o Ts 0 10 20 30 40 50 ANGULAR POSITION OF HOT -WIRE, DEGREES WIRE Figure 22. Hot Wire Fluctuation Distributions for Tw/T= 1.0 and 0.8, (.004" x.025" Diameter Disk, 150 Ahead of Wire)

7 TS }.004" x.030" RIBBON 10~ T AHEAD OF WIRE d W TW 0 5 I.8 >__ Ts, T o 0 I 9 4 Ts "SMOOTH" 49 r( SURFACE Tw 10 20 30 = 5I ro wire) 4(a).004" x 030" ribbon, and "smooth" surface. IjI 1.0 and 0.8, (two-dimensional ribbons 100 ahead of wire) (a).o04-" x.030"l ribbon, and 9"smooth" surface.

-677 11.3 WIRE REL. TW POSITION AMPL' F'TION TS 6 150 1.0.8 50 5 27~.5 I0 _-j:z 3l.006"x.030" RIBBON 10~.0 AHEAD OF WIRE H 2 ~- 0 TS TW TS 0 10 20 30 40 50 I -ANGULAR POSITION OF HOT -WIRE, DEGREES WIRE Figure 23. (continued) (b).00oo6" x -.030" ribbon

.010" x.030" RIBBON 100 AHEAD OF WIRE 0 Tw Tw Z T' o 4 Ts UL 3 WIRE Figure 23. (continued) 0 0 10 20 30 40 50'7- ANGULAR POSITION OF HOT- WIRE, DEGREES WIRE Figure 23. (continued) (c).010" x.030" ribbon

-69Finally, in Figure 23c the transition point moved furthest forward with the.010 inch -disturbance and there was no appreciable effect of cooling. This roughness element therefore falls in regime I. In addition to the effects of cooling it may be noted that the initial stages of transition are quite similar for both the twoand three-dimensional disturbances as evidenced by the oscillograms in Figures 22 and 23b. Also, with the relatively large.010 inch ribbon disturbance height (disturbance height = 1.7), the fluctuation amplitudes at boundary layer thickness transition (below 10,:000 cps) were considerably less when compared to those resulting with the smaller disturbance. In all of the measurements with applied roughness the exact position of transition was found to vary somewhat between experiments where the only change was to replace the disturbance with a (supposedly) identical one. This indicates that the manner in which the elements were glued to the surface was highly critical, Also the increased surface pitting with time may have introduced some scatter into the experiments. However, in the data given in Figures 21-23 the disturbance element was not changed between the tests with and without cooling. Two extraneous effects were encountered in the earlier tests. During these tests regular voltage fluctuations appeared which were traceable to vibration of the hot wire supports. Since the fluctuation thus generated f was considerable compared to the overall signal, it was necessary to support the hot-wire terminals near the tips to eliminate this spurious signal. Also, when the air dewpoint was unusually high, boundary-layer transition would. occur due to the roughness caused by frost forming on the surface, The hot wire records were quite striking in this instance. At the beginning of the tests,

-70the boundary layer was turbulent as far forward as 12.5 from the stagnation point, Then as the surface temperature slowly rose the boundary layer passed rather suddenly through the transitional to the laminar state. At the end of the test the flow was laminar at least to the largest angles investigated (? = 45~)* This type of result could not be reproduced when the air dewpoint was. close to or below the initial wall temperature (- -60~F). In conclusion, the data presented has qualitatively demonstrated the combined effects of cooling and roughness on boundary layer transition. The stagnation Reynolds number was held constant and-one (relatively small) boundary layer cooling rate was used. The results indicate that a given amount of surface cooling does not affect transition if the roughness is small, or large, but that there iS an intermediate range of roughness for which cooling hastens transition. The width of this range and its position in the roughness scale is probably a function of Reynolds number and distance from the stagnation point. In the following section, experiments are described in which the Reynolds number and surface cooling were varied and the surface roughness was kept as small as possible. Transition Experiments on a Highly Polished Model with Variable Boundary-Layer Cooling. — "_ _,.' -.,, -'.'.. X.... i,,.:~.,...- " The purpose of the experimemts to be discussed here was to gain further knowledge of the circumstances under which cooling of the boundary layer may promote early transition on a blunt body, One effect of cooling is to increase the Reynolds number at the peak of a

-71given roughness element. Therefore, a decrease in transition Reynolds number will occur with boundary-layer cooling if, as a consequence of the cooling, a particular roughness Reynolds number exceeds a critical value. On the other hand, according to our present notions, there appears to be no reason to expect a large reduction in transition Reynolds number due to the effects of cooling on boundary-layer stability. As pointed out in Section II, existing small disturbance theory predicts increasing stability to Tollmien-Schlichting disturbances with increasing cooling, for surfaces without curvature. There is a destabilizing effect of the density gradient in the cooled boundary layer on a convex surface, but rough analysis indicates that the flow in the centrifugal acceleration field remains dynamically stable even if the surface temperature is decreased to O0R. In an effort to determine the effects of cooling on boun-: dary layer stability, experiments were conducted in which the roughness of the model surface was made as small as possible. The results show that, for small roughness, there is little change in transition Reynolds number with cooling for the range of parameters investigated. The surface roughness was minimized by giving the model an extremely smooth polish (approaching 1-microinch rms, Section III) and placing paper dust filters in the airstream. In addition, the model was continually monitored throughout the test program so that the effects of any change in surface roughness, caused by pitting, deposition of small dust particles, and formation of frost or carbon dioxide

-72could be detected. Estimates* of the order of magnitude of frost film thickness to be expected when the surface was cooled below the air dewpoint ( - -75 F) gave a uniform layer thickness of about 1 microinch per second of fun time at the highest mass flow rates. The roughness caused by the frost would, of course, depend on the crystalline pattern and the way in which it was distributed over the surface. However, the rough estimates indicated that for a short run the build up would be of the order of the surface roughness itself, and the frost was expected to have negligible influence. Observations of the surface by means of the periscope showed no visible signs of the frost during a short run. AS far as the transition observations were concerned, no noticeable change in the trend of the data was found when the surface was cooled below the deFpbiht as long as the low dewpoint was maintained. An analysis of several air samples showed the percentage of carbon dioxide to vary up to as much as 30 times that for the standard atmosphere. These unusually high amounts of CO2 were probably caused by contaminated intake air at the compressors and/or partial oxidation of the oil during compression. At the tunnel pressures, and these percentages of C02, dry ice would condense on the model surface for temperatures in the range 230~R to 250 R. The estimates assumed that all of the water vapor in the velocity boundary layer up to a given-angle from the stagnation point deposited uniformily over the included surface area. The results were found to be nearly independent of the angular location chosen. These estimates are conservative as to the total amount of water that could reach the surface when the Lewis number and Prandtl number are equal to one, i.e., when the diffusion boundary-layer thickness is equal to the velocity boundary-SAyer thickness.

Estimates similar to those for frost, gave uniform layer thickness of from 25 to 1000 microinches per second of run time. For the lowest model temperatures, in contrast to the case with the frost layer, the CO2 became clearly visible as the tunnel established steady conditions. As will be pointed out, the records of transition from turbulent to laminar flow were often visually correlated with the disappearance of the condensation film as the model warmed. The maximum cooling range for which reliable data was obtained was thus limited to the range in which C02 was observed to condense. Low transition Reynolds numbers (as much as 50% below the highest values observed) were also found to occur as a result of the roughness caused by minute dust particles sticking to the model within about 100 of the stagnation point. Microscopic examinations of six of the larger particles showed their heights to vary from.00075 inches to.0020 inches. The non-repeatibility of the data when the particles were removed suggested that the low transition Reynolds numbers were caused by these roughness elements. This conjecture was also supported by a calculation of the- critical roughness height for a particle at 10~o For example, using a critical roughness Reynolds number of 700 and a tunnel pressure of 40 psia, the critical roughness height for a particle at 10~ is.0023 inches when TW/Ts = 1.0 and.0013 inches when Tw/Ts= 0.5. In the present investigation, supercritical roughness Reynolds numbers of 640 and 1015 were measured for two-dimensional ribbons at 10~ and 12~, and a value of 465 was found for a three-dimensional disk at 120. Reference 47 gives values between 625 and 770 for spherical roughness elements at 10~ on a 10 foot diamneter hemisphere in subsonic flow.

The influence of dust particles on the transition data was reduced by removing the oil from the paper filter so that the particles had little tendency to stick to the model. In addition, the surface was cleaned when any specks of dust could be seen. When real gas effects are of only minor importance, the laminar boundary layer on geometrically similar blunt bodies in hypersonic flow is characterized by a Reynolds number behind the bow shock wave and the ratio of wall to stagnation temperatures. Therefore, if the roughness (and all other disturbances) are also scaled, we would expect, in general, the nondimenlsional location of transition to be a function of Reynolds number and temperature ratio. Stated in another way, the locaal transition Reynolds number should generally depend on the non-dimensional location of transition as well as ion the temperature ratio. In the experiments reported here the observations were made at a fixed angular position, and the transition Reynolds number determined as a function of temperature ratio. Transition was detected with the pitot pressure probe described in Section III. Typical calibration data showing the difference in pitot minus static pressures between the laminar and'turbulent boundary layer is shown in Figure 24. The turbulent boundary layers were obtained by- using a.0025 inch ribbon trip placed 50~ 15~, and 25~ ahead of the probe. It can be seen that the turbulent pitot pressure was fairly insensitive to the trip location, which reflects the slow rate of growth of the turbulent boundary layer in the subsonic region. When the measured pressure difference is divided by the stagnation pressure, the resultant drmensionless parameter o~has littlte dependence on

tRIP POSITION DEGREES AHEAD OF PROBE PS " 30 pSa P 50 tsid 5 ~0 15 C ] 25 V v NO TRIP 0.20 1 Tw - I TRIP HEIGHT =.0025" Ts.16..12 (i, ae'].12 0 TURBULENTT.08 BUL..T{.04 LAMINAR 0 30 35 40 45 50 A- NGULAR POSITION OF PROBE) DEGREES Figure 24. Calibration of Pitot Probe.

-76the stagnation pressure level, The increase in measured pitot pressure when the boundary layer changes from laminar to turbulent is seen to be more than 100% for the 35, 40, and 45 degree angular locations. Typical data obtained during a given run are reproduced in Figure 25. In this run the flow began laminar at the lowe-st temperatures, changed to turbulent when the stagnation pressure was increased, and then, at constant stagnation pressure, returned to the laminar state as the surface temperature increased. The values of Lp/ps for both laminar and turbulent flows correspond closely to the values found when the probe was calibrated at Tw/T:s 1, The record does in fact indicate that the change in boundary layer temperature close to the surface has negligible effect on the average pitot pressure over the subtended portion of the layer, In contrast to the data of Figure 25, when the initial wall temperature was decreased slightly to the range in which C02 condensed on the model surface, the flow started out turbulent even with a 25% reduction in stagnation pressure (Reynolds number), as is shown in Figure 26. In this run the model was observed through the periscope and. the time at which the C02 did not extend beyond 2Z = 200 (limit of field of view) was noted. This observation correlates with the change The first peak in the pressure difference, P -P, is caused by the slower response time of the pitot probe compared with that of the static tube, during start-up. Thus, for the first few seconds the pitot probe remains at nearly atmospheric pressure while the static tube follows the rapid negative to positive variation of static gage pressure.

-77300 _ 200 — a100.. I _ _... __.l 2 20 0 10 20 30 40 TIME SECONDS Figure 25. Records of P-P Ps, and Tw Durirng a Typical Transition Experiment

-78300. 0 0.. I 100 40 0Q -7 TIME AT WHICH GCODID NOT EXTEND BEYOND r 200 illl'20 30 40 TIME, SECONDS Figure 26. Correlation of Transition with C02 Film.

-79from turbulent to laminar flow indicated by the pressure records. That is, the roughness caused by the CCO film promoted turbulent flow at a lower Reynolds number unt il the film did not extend beyond some angle between 200 and 45~. The fact that the CO2 film disappeared last at the stagnation point as the body warmed is of course caused by the higher heat transfer rates (greater evaporation rates) in the turbulent boundary layer. Most of the transition data was taken at the 45O anglar position, with a few measurements at 4 and a single measurement at 30~. The data is presented in Figure 27 in terms of the lodal transition Reyrnolds: number based o distance from the stagnation -point, Rex, as a function of Tw/Ts. Results are also given of some other investigations with hemispheres in supersonic flow for which transition was observed ahead of the 900 point. In the range 1' Tw/Ts 0.05 the present data show little effect of cooling on the local transition Reynolds number at 40~ and 45~0 For Tw/Ts <.5 the scatter, as well as a reduction in Rex, is caused largely by the presence of varying amounts of CO2 on the surface. Although data in which dust particles were definitelyy nown to be influencing transition are not shown, there is still some scatter in the present data outside the range in which CO2 condenses on the surface. These lower values of Rex did not correlate with the increasing surface abrasi:on at the Stagnation point i.e., with increasing testing time with the- same surface. The scatter may therefore -reflect the influence of minute dust particles. In fact, it is possible that the small

-80CO2 SOLIDIFIES (THIS INVESTIGATION) 7I 2 —- -,300{ 1~06 * PRESENT DATA D: =9" = 45" is " " " - 30~ REF. 15 (FREE FLIGHT), D 8",' = 608 75~ 5.I v0,o 48 (WIND TUNNEL), =19", 500 75o O *. 49 a -:2", 30~ a 40 V V.' 14 (SHOCK TUBE), 2-, 45 3*I05 I I I 1I 0.2.4.6.8 1.0 Tw Ts Fi:tIgure?7. Local Trans:ition Reynolds Numbers Based on Distance Fromn the S-tagnaatlon Point, exs vs.'.w/Ts.

decrease in Rex wit]h cooling may be caus-ed. by the increasing importance of any dust particles present as the surface is cooled. All the data from other sources shown in Figure 27 are for rms surface roughness reported -to- be less than 5 microinche,, except that of Reference 48 which reported a value of 10-15 microinches. The level of Rex at TW/T5 1 for the prese:ct investigation is seen to be somewhat higher than that of Reference 48. This result may accordingly be attributed to the differences in surface roughness. Agreement between the present data and the flight teSt re-sults of Reference 15, for which transition occurred at the 60 and 75 degree location, is alsao apparent for TW/Ts near. 0.5. The recent wind tunnel data of Reference 49 which extends to- a lower temperature ratio than that reached here also indicate an independence of Re-:with cooling. There is, however, a factor of about 2 3/2 in the levels of Rex between their data and the present data. This- disagreement may be due to differences in abs-olute surface roughness and/or free stream turbulence levels. With an unheated. airstream it was not possible to check the range of'temperature ratios correspon4ing t-o the shock tube data of Stetson( ). These data show considerab.ly lower values of Rex at the low temperature ratios. Although the rms surface roughness was less than 1 microinch, the heat transfer gages used to detect transition were approximately 12 microinches in height. A typical value of Rek at the top of the gage located at 30~ was estimated. to be about 130. While The stagnation point boun:dary-layer disStributions,- Figure 1, were used in this calculation.

-82no information is available on the critical value of Rek under these circumstances, this value does lie in the range of critical values found in the experiments of Reference 48 on a 19-inch diameter hemisphere without cooling As was pointed out previously, any local transition Reynolds number such as Rex, Re Rep- Re, or Rey, would be expected to depend on the angular location and temperature ratio. This dependence was given in terms of Rex in Figure 27, where the disagreement between data taken under dynamically similar conditions (present data and that of Reference 49) must reflect a difference in the simulation of boundary layer disturbances, viz0 free stream turbulence and sound, and surface roughness. It is.of interest to view the transition data in terms of Reg and.Re5s which are based on characteristic lengths which depend on the cooling and are generally more characteristic of a boundary layer than is the distance x. The variation with Tw/Ts of Re9 at transition is given in Figure 28. All the data of Figure 27 is shsown except for the present investigation for which only the highest values are given, A small increase in Reg with cooling is indicated by the present data for transition at 450 in the range e5 ~ Tw/Ts l 1. Comparison with Figure 27 shows that Reg is less dependent than Rex on angular position at the lower angles but more dependent at'the higher angles, corresponding to the manner in which 9 varies with? as opposed to the linear variation of x (see Appendix B) As pointed out in Section II, Reference 30 found little effect of cooling on the critical value of Rek for transition on cones and flat plates in supersonic flowo

1400 * PRESENT DATA,, ~ 45, i!,,, 40,,.~ 30' 1200 a - REF. 15, 60~175 0 A" 48, 58~-75~ 1 0 " 49, = 30~&40, V " 14, 45~ 1000 800, v0 000 400 V V V~0 200 0.2.4.6.8 1.0 TW Figure 28. Local Transition Reynolds numbers Based on Boundary-Layer Momentum Thickness, Reg, Vs. Tw/T8

The data of Figure 28 is given in Figure 29 in terms of the variation of Rear at transition. All of the data indicates a rapid decrease in RegS with decreasing Tw/Ts. This behavior reflects the rapid decrease in Y~with cooling, the effect of which also tends to center the data about a nearly straight line decrease in Re pg-. The flight data (Reference 15), for which transition occurred at 60 and 75 degrees on an 8-inch diameter hemisphere with rms surface roughness between 0 and 5 microinches, shows considerably higher values of Reg5 as well as Re9. This result may reflect either a smaller absolute roughness and free:stream turbulenc-e compared with the roughness and stream turbulence in the wind tunnel tests, or a difference in the stability characteristics and transition process at the higher angles. It is not possible, on the basis of the- few unaclasiEfied results shown, to determine whether a particular Reynolds number is most significant for describing transition on "smooth" hemispherical bodies in hypersonic flow. However, concerning the correlation in terms of Re o, one notes that ~ is practically constant on a hemisphere when Tw/Ts is very small (see Appendix B), In view of this and the fact that changes little after the first 20 to 30 degrees, a correlation in terms of Repg-: becomes of little use as far as predicting the location of transition is concerned. A knowledge of the location of transition, especially when Tw/Ts is small (high heat transfer), is important from the standpoint of those aspects of a design dictated by the heat transfer rates~ The results of the present experiments are summarized as follows:

-852400 20 PRESENT DATA,' = 45 U400 —-4., 30 2000 Xa REF. 15,N: 60 a 750 -... 0 (" 48, = 58~ —75 o 11 49, 30a40 V " 14, =45~ 1600 0. 200 ___ ~ 60~0 0 _ 0.2.4.6.8 1.0 Tw Ts Figure'-!9. Local Transition Reynolds Number FPsed( on Boundary-Layer Displacement Thicklness, Reg., rs. Tw/Ts

-861, In the- cooling range investigated, when the roughness wag small, little effect of cooling was found. on trans-Ltion when it occurred at 40 and 45 degrees from the stagnation point. Thuas, the stbFility of the subsonic boundary layer is not appreciably decreased. by the cooling. 2. The. values'of Rex and Reg were 5 x 106 to 6.3 x 106 and. 600 to 7Q00, respectively, for transition at, 45 in the range -0.5. Tw/Ts ~ 1.0o While there was no'"transition reversal"' in the subsonic boundary layer, neither was there a siganificant increase in Rex xor Ree which would have been predicted on the basis of the stabilizing effect of cooling on Tollmien-Schlichting type disturbances on a flat plate. The failure- to: find an increase in Rex or Reo with cooling could have possibly been caused by the increased magnitude of the disturbances from rouIghness elements still present, which then cause transition in the coaoler more stable boundary layer as soon as smaller disturbances from the same roughness elements in the warmer less stable layer. Theeffect of cooling in destabilizing thq. flow in the centrifugal acceleration fie-ld may also have b:een of importance under these -circum stances (Section II). There i. clearly a need for more experimentation to investigate these effects in detail. Since the hypersonic pressure distribution was not simulated for angles greater than 45, no. data was taken at the higher angles. To Actually, the pressure gradient begins to deviate from that for hypersonic'flow around 400 (Figure 18)o That this did:not have any appreciable eff-ect on the transition Reyn olds numbers 0is indicated by comparison with the data at 40O. Therefore, we conclude that the results at 45~ are applicable to a hemisphere in 4hypersonic flow,

-87deternine whether the turbulent obseryations at 450 may have resulted from a rapid. shift of transition to a position near the nose, the pitot probe was placed at 300 and the tunnel pressure increased until 0 transition occurred. To obtain transition at the 30 position it was necessary to increase the pressure 10 to 15 percent above the values necessary to obtain transition at 40 and 45 degrees. Therefore, when the boundary layer first became turbulent at 45 ~ it was indeed laminar over most of the upstream portions of the hemisphere. That is, transition did not suddenly move close to the nose at might happen if, says e cetrifgal instability were to deelop at the nose where the density gradients are large, or if a roughmess element near the nose became sapercritical.

VI. CONCLUDING REMARKS The main results of this investigation are summarized as follows: io Simulation of the stubsonic boundary layer'on a hemisphere in hypersonic flow for the purpose of studyi.ng boundary layer transil tion has been acecmplished using the shroud technique. A mathematical analysis was developed for predicting the shroud. contour which would cause the hypersonic pressure distribution -to prevail up to the sonic point (2 = 44 ). The measured pressure d.istribu'tion on the shroud.ed hemisphere was in excellent agreement with the Newtonian d.istribution specified in the analysis. 20 Experiments with small cooling rates', in which roughness elements were pla-ed on the model, have qualitatirvely demonstrated the combined effects of cooling and. roughness on boundary layer transition. The results indicate that a given amount of cooling does not affect transition if the roughness is small: or large, but that there is an intermed.iate range of roughness where caoling hastens transition. 3. An essential feature of transition studies with boundary layer cooling is the close control of surface roughness. In the present exper ments this in-wolved, in addition to having a highly polished surface,. the necessity for lovR water vapor dew:pQint., the avoidance of carbon d.ioxide condensation f ilms, and special filtering of the airstream to remove most of the d.ust particles. 4. When the roughness was smll, little effect of cooling was found. on transition occurring 40 and 45 degrees fromr the stagnation

-89point. The values of Rex and Re- were 5 x 106 to 6.3 x 106 and 600 to 700, respectively, for transition at 450 in the range 0.5 - TW/Ts - 100 It is concluded that the stability of the subsonic boundary layer is not appreciably decreased in this cooling range.

APPENDICES -90

APPENDIX A SIMILARITY PARAMETERS FOR BOUNDARY-LAYER FLOWS Consider the steady boundary-layer flow of a non-reacting perfect gas about a body of revolution. The boundary-layer equations which govern the motion can be written for the coordinate system shown as: 2< ( ) +-s, (g-r ) O (A-l) axus U_- e t g (A-2) 2x-r = s (k) - U a Pe tyla\d (A-3) p U/t?7T- (A-4) * Assume the surface nearly isothermal so that ck a(, y -91

-92These equations are non-dimnensionalized in terms of the boundary-layer profiles as follows: Define the 4on-dimensionxal quantities, shown by superscript * to be X + x V D D X= -5 -S ). _e (A-5) Then the governing equations can be written - ~~~~~~~~~ ~~~~~ (A~y me el;B" iP (pt u"i t lef r@)' +P Ctr Ta,/ jt Cie el- (A-6) 2% ie -t-Re -' t/o5 C 51U@ dLC) (A-7)

(+ =I~rv4 (L'zI U(*+ &XL ~e /e (A-8) and (=1 (A-9) w~here Rer= xel Equations (A_6) to (A-9) are four simultaneous equations for determining the four unknowns u*, v, T*, 7* All other parameters appearing are either giyen constants or known functions. Applicable boundary conditions supplied with these equations are W%'40) = 2/(X,) O Xc) TU(X) I+ /z ) T+ L - / (A-l ) and ) 9 (XJ- (A-9) Tz

-94Assuming that k, /4, and Cp vary as powers of the temperature over the range of temperatures for two flow fields, k*,/ Y*, and Cp* are unique functions of T*. Further, if any gradients in entropy along the edge of the boundary layer are neglected then all the terms in square brackets become functions of Me(x*) only. Thus, for two flows in which Prs and ~Ys are the same, the non-dimensional velocity, temperature, and density distributions in the boundary layer on geometrically similar bodies will be identical functions of the nondimensional coordinates provided the similarity parameters Me(X*), Tw/Ts (x*) or Nuw(x*), and Res are the same.

APPPENDIX B CALCULATED PROPERTIES OF TIE LAMINAR BOUDUNRY LAYER ON A HEMISPEIERE IN HYPERSONIC FLOW The following figures show the variation of i,, -, Cf and qw with 72 and Tw/Ts for a hemisphere in hypersonic flow. The parameters were computed using the methods and solutions due to Cohen and Reshotko(31',32). w is a constant of proportionality between viscosity and temperature given by the- relation -,-95

-962.8 2.4 2.0 1.6J. 1.2,.. 0.8 0 10 20 30 40 50 60 - - DEGREES Figure 30. Variation of 6 with I and Tw/Ts on a Hemisphere in Hypersonic Flow.

-97Tw.0.6 — 1.0 0.4 0.__ t_..... 0 10 20 30 40 50 60 - DEGREES Figure 31. Variation of b* with r and TW/Ts on a Hemisphere in Hypersonic Flow.

-980.36 0.32 TW'- 0 TS~.2 0.28 0.24 0.20 0.16 0.12 0 10 20 30 40 50 60,- DEGREES Figure 32. Variation of @ with r and Tw/Ts on a Hemisphere in Hypersonic Flow.

-993.0 2.5 32.0 1.5 - 1.0 0 10 20 30 40 50 60.- DEGREES Figure 33. Variation of Cf pUwUe TR with r and Tw/TS on a Hemisphere in Hypersonic-Flow.

-1000.8. TW 0 0.6. /.. 0.4 1.0...,T$ 0.2 0 10 20 30 40 50 60, - DEGREES Figure 34. Variation of qw with, and Tw/Ts on a Hemisphere in Hypersonic Flow.

REFERENCES 1. See for instance: Lin, C. C. The Theory of Hydrodynamic Stability. Cambridge University Presis, (1955). 2. Lees, L., and Lin, C. C. "Investigation of the Stability of the Laminar Boundary Layer in a Compressible Fluid." NACA TN 1115, 1946. 3. Lees, L. "The Stability of the Laminar Boundary Layer in a Compressible Fluid." NACA Report No. 876, 1947. 4. Eber, G. R. "Recent Investigations of Temperature Recovery and Heat Transmission on Cones and- ylinders in Axial Flow in the N. 0. L. Aeroballistics Wind Tunnel." J. Aero. Sci., 19, (1952), 1-6* 5. Higgins, W., and Pappas, C. C. "An Experimental Investigation of the Effect of Surface Heating on Boundary-Layer Transition on a Flat Plate in Supersonic Flow." NACA TN 2351, 1951. 6. Liepmann, H. W., and Fila, G. H. "Investigations of Effects of Surface Temperature and Single Roughness Elements on Boundary Layer Transition." NACA TN 1196, 1947. 7. Scherrer, R. "Boundary Layer Transition on a Cooled 200 Cone at Mach Numbers of 1.5 and 2.0." NACA TN 2131, 1950. 8. Czarnecki, K. R., and Sinclair, A. R. "Preliminary Investigation of the Effects of Heat Transfer on Boundary Layer Transition on a Parabolic- Body of Revolution (NACA RM-10) at a Mach Number of 1.61." NACA TN 3165, 1954. See also NACA TN 3166 by same authors. 9. Jack. J. R. and Diaconis, N. S. "Variation of Boundary Layer Transition on Two Bodies of Revolution at a Mach Number of 3.12." NACA TN 3562. 10. van Driest, E. R., and Boison, J. C. "Experiments on Boundary Layer Transition at Supersonic Speeds." J. Aero. Sci., 24, (1957),885-889. 11. Diaconis, N. S., Jack, J. R., and Wisniewski, R. J. "BoundaryLayer Transition at Mach 3.12 as Affected by Cooling and Nose Blunting." NACA TN 3928, 1957. 12. Jack, J. R., Wisniewski, R. J., and Diaconis, N. S. "Effects of Extreme Surface Cooling on Boundary Layer Transition." NACA TN 4094, October, 1957. -101

-10213. Diaconis, N. S., Wisniewski, R., J,} and Jack. J. R. "Heat Transfer and Boundary Layer Transition on Two Blunt Bodies at Mach Number 3.12." NACA TN 4099, October, 1957. 14. Stetson, K. F. "Boundary-Layer Transition on Blunt Bodies with Highly Cooled Boundary Layers." J. Aero. Sci., 27, (1960), 81-9o. 15. Hall, J. R., Speegle, K. C., and Piland, R. 0. "Preliminary Results from a Free-Flight Investigation of Boundary-Layer Transition and Heat Transfer on a Highly Polished 8-InchDiameter Hemisphere-Cylinder at Mach Numbers up to 3 and Reynolds Numbers Based on a Length of 1 Foot Up to 17.7 x 106." NACA RM L57D18c, May, 1957. 16. Garland, B. J., and Chauvin, L. T. "Measurements on Heat Transfer and Boundary-Layer Transition on an 8-Inch-Diameter HemisphereCylinder in Free Flight for a Mach Number Range of 2.00 to 3.88." NACA RM L57504a, April, 1957. 17. Morkovin, M. V.'"On Transition Experiments at Moderate Supersonic Speeds." J. Aero. Sci., 24, (1957). 18. Laufer, J. "Aerodynamic Noise in Supersonic Wind Tunnels." JPL Progress Report 20-378, February 27, 1959. 19. Amick, J. L. "Supersonic Tunnel Design for Transition Studies." Paper presented at 14th STA Meeting, October 17-19, 1960. 20. Ferri, A., and Libby, P. A. "A New Technique for Investigating Heat Transfer and Surface Phenomena Under Hypersonic Flow Conditions." J. Aero. Sci., 24, (1957), 464-465. 21. Kuethe, A. M., and -Schetzer, Jo D. Foundations of Aerodynamics. New York: John Wiley and Sons, Second Edition, (1959), Chapter 15. 22. Dryden, H. L.'Some Aspects of Transition from Laminar to Turbulent Flow."' Lecture Series No. 34, The Institute for Fluid Dynamics and Applied Mechanics, University of Maryland, November, 1955. 23. Gazely, C. "Boundary-Layer Stability and Transition in Subsonic and Supersonic Flow." J. Aero. Sci., 20, (1953), 19-28. 24. Czarnecki. K. R., and Sinclair, A. R. "Factors Affecting Transition at Supersonic Speeds." NACA RML53I18a, November, 1953. 25. Taylor, G. I. "Stability of a Viscous Liquid Contained Between Two Rotating Cylinders." Phil. Trans. Roy. Sco. London: A223, (1923), 289-343.

-10326. Goertler, H. "Ueber eine dreidimensionale Instabililaet laminarer Grenyschichten an knokaven Waenden." Ges. d. Wiss., Goettingen., Nachr. a. d. Math,, Bd. 2, Nr, 1, 1940, (Translated in NACA TM 1375, June, 195). 27. Liepmann, H. W. "Investigations of Boundary-Layer Transition on Concave Walls." NACA ACR 4J28, 1945. 28. Lees, L. "Note on the Stabilizing Effect of Centrifugal Forces on the Laminar Boundary Layer Over Convex Surfaces," J. Aero. Sci., 25, (1958)0 29, Potter, J. L., and Whitfield., J.. D "Effects of Unit Reynolds Number Nose Bluntness, and Roughness on Boundary Layer Transition." AEDC-TR-60-5, March, 1960. 30. Braslow, A. L., Knox, E. C., and Horton, E A, "Effect of Distributed Three-Dimensional Roughness and Surface Cooling on Boundary-Layer Transition and Lateral Spread of Turbulence at Supersonic Speeds," NASA TN D-53, October, 1959. 31. Cohen, C. B.13,, and Reshotko, E, "Similar Solutions for the Compressible Laminar Boundary Layer with Heat Transfer and Pressure Gradient." NACA Report 1203, 1956. 32. Cohen, C. B,, and Reshotko, E. "The Compressible Laminar Boundary Layer with Heat Transfer and Arbitrary Pressure Gradient." NACA Report 1294, 1956 33. Oliver, R. E. "An Experimental Investigation of Flow Over Simple Blunt Bodies at a Nominal Mach Number of 5.8." J. Aero. Sci., 23, (1956). 34. Beckwith, I. E., and Gallagher, J. J. "Heat Transfer and Recovery Temperatures on a Sphere with Laminar, Transitional, and Turbulent Boundary Layers at Mach Numbers of 2.00 and 4.15." NACA TN 4135, December, 1957. 35. Cooper, M., and Mayo, E. E. "Measurements of Local Heat Transfer and Pressure on Six 2-Inch-Diameter Blunt Bodies 6at a Mach Number of 4.95 and at Reynolds:Numbers Per Foot to 81 x 106." NASA Memo 1-3-59L, March, 1959. 36. Kemp, N. H., Rose, P. H., and. Detra, Ro W. "Laminar Heat Transfer Around Blunt Bodies in Dissociated Air," AVCO Research Report 15, May, 1958. 37. Boison, J..C. "Experimental Investigation of the HemisphereCylinder at Hypervelocities in Air." AEDC-TR-58-20 (ASTIA Document: AD-204392), November, 1958,

-lo438, Kendall, Jr.,, J. M. "Experiments on Supersonic Blunt-Body Flows." CIT, Progress Report No. 20-372, February, 1959. 39. Lamb, H. Hydrodynamics. New York: Dover Publications, (1945), 42, 40. Morkovin, M. V. "Fluctuations and Hot-Wire Anememetry in Compressible Flows." AGARDograph 24, NATO, November, 1956. 41. Trilling, L.., and Hakkinen, R. J. "The Calibration of the Stanton Tube as a Skin-Friction Meter." 50 Jahre Grenzschichtforschung. Edited by H. Goertler an4 W. Tollmien, Braunschweig: Friedr, Vieweg und Sohn, (1955). 42. Wilkins, M. R., and Darsaw, J. F. "Finishing and Inspection of Model Surfaces for Boundary-Layer-Transition Tests." NASA Memo 1-19'59A, February, 1959. 43. Kuethe, A. M., Willmarth, W. W., and -Crocker, G. H. "Stagnation Point Fluctuations and Boundary Layer Stability on Bodies of Revolution with Hemispherical Noses." Presented at AGARD Boundary Layer Symposium, London, England, April 25-29, 1960. 44. Kuethe, A. M., Willmarth, W. W., and Crocker, G. A. "Stagnation Point Fluctuations Near the Nose of Bodies of Revolution." Physics of Fluids, 2, (1959). 45. Potter, J. L., Whitfield, J. D.o and Strike, W. T. "Transition Measurements and the Correlation of Transition Sensitive Data."f AEDC-TR-59-4, February, 1959. 46. Favre, A. J., Gaviglio, J. J., and Dumas, R. "Space-Time Double Correlations and Spectra in a Turbulent Boundary Layer, Journal of Fluid Mechanics, 2, (1957). 47. Peterson, J. B., and Horton, E. A. "An Investigation of the Effect of a Highly Favorable Pressure Gradient on Boundary-Layer Transition as Caused by Various Types of Roughnesses on a 10-Foot Diameter Hemisphere at Subsonic Speeds." NASA Memo 2-8-59L, April, 1959. 48. Bandetlini, A. and Isler, W. E. "Boundary-Layer-Transition Measurements on Hemispheres of Various Surface Roughnesses in a Wind Tunnel at Mach Numbers from 2.48 to 3.55." NASA Memo 12-25-58A, March, 1959. 49. Cooper, M., Mayo, E. E., and Julius, J. D. "The Influence of Low Wall Temperature on Boundary-Layer Transition and Local Heat Transfer on 2-Inch-Diameter Hemispheres at g Mach Number of 4.95 and a Reynolds Number Per Foot of 73.2 x 10." NASA TN D-391, July, 1960. 50. Hayes, W. D., and Probstein, Ro F. Hypersonic Flow Theory. New York: Academic Press Inc,, (1959).

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