Direct Measurements of Skin Friction Citation Dhawan, Satish (1951) Direct Measurements of Skin Friction. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/1S03-8631. https://resolver.caltech.edu/CaltechETD:etd-09262002-155504 Abstract A device has been developed to measure local skin friction on a flat plate by measuring the force exerted upon a very small movable part of the surface of a flat plate. These forces, which range from about 1 milligram to about 100 milligrams, are measured by means of a reluctance measuring device. The apparatus was first applied to measurements in the low-speed range, both for laminar and turbulent boundary layers. The measured skin friction coefficients show excellent agreement with Blasius' and Karman's results respectively. The device was then applied to high-speed subsonic flow and the turbulent skin friction coefficients were determined up to a Mach number of about 0.8. A few measurements in supersonic floor were also made. The paper describes the design and construction of the device and the results of the measurements. Item Type: Thesis (Dissertation (Ph.D.)) Subject Keywords: (Aeronautics and Mathematics) Degree Grantor: California Institute of Technology Division: Engineering and Applied Science Major Option: Aeronautics Minor Option: Mathematics Awards: Caltech Distinguished Alumni Award, 1969 Thesis Availability: Public (worldwide access) Research Advisor(s): Liepmann, Hans Wolfgang Group: GALCIT, Caltech Distinguished Alumni Award Thesis Committee: Unknown, Unknown Defense Date: 1 January 1951 Record Number: CaltechETD:etd-09262002-155504 Persistent URL: https://resolver.caltech.edu/CaltechETD:etd-09262002-155504 DOI: 10.7907/1S03-8631 Default Usage Policy: No commercial reproduction, distribution, display or performance rights in this work are provided. ID Code: 3779 Collection: CaltechTHESIS Deposited By: Imported from ETD-db Deposited On: 27 Sep 2002 Last Modified: 22 Jul 2021 22:43 Thesis Files Preview PDF (Dhawan_s_1951.pdf) - Final Version See Usage Policy. 11MB Repository Staff Only: item control page

PIRLGT MEASUREMENTS OF SEIN FRICTION Thesis by Satish Dhawan In Partial Fulfillment of the Requiromonta For the Degree of Regtor of Philoscphy California Institute of Technology Pasadena, California 1951 ACKHOULEDGEIEUTS The author 4s deeply indebted to Dr. Hans Wolfgang Liepmenn who suggested and supervised this research. His guidance and intersst heve been throughout a constant source of inspiration. The author wishes to express his sincere appreciation to Dre G,. Be Milliian, Dre Be BE. Sechler ani Dr, P, 4. lLagerstram for their continued interest. Aclmowledgement is mide to the members of the Transonic Research Group at GALCIT for their cooperation and holp. In partiovlar dis-— cussions with Mr. Anatol Roshko and Dr. Julien Cole were very valuable. The entire credit of building the gicin friotion instrument is dus to manbors of the Aeronautics Machine Shop. In particular Mr. C. A. _ Bartsch was responsible for solving many of the difficult features on~ countered during the construction and design. It is a pleasure to acknowledge the contributions of Mrs. Dorothy Diamond and lirs. Beverley Cottingham in the preparation of the manu- seript umder rather trying olroumstances,. ABSTRACT A dovica has been develoved to measure local akin friction on a flat plate by measuring the forca azertad woon a vary mall moveable part of the surface of a flat plate. These foress, which ranze fron abouts 1 milligram te about 100 milligrams, are measured by means of a reluctance measuring device, The apparatus was Pirst applied to measurements im the low-speed range, both for laminar and turbulen’s boundary layers. Tha meaeured skin friction csefficients chow on eallent agreement with Blasiug’ and Karnan's results respectively. The devico wa then applied to high-speed subsonic flow and tho tur- bulent akin friction coefficients were determined up to a Maoh number of about 0.8. A few measurements in supersonic flow were also made. Tho paper desoribos the desien and conobtruction of tho dovise end the results of the measurements. 444 TABLS OF CONTSHTS Aalnowlodgoments Abstract fable of Gombenta Symbela I. Inbyrodustion Ii, Experimental Methods of Skin Friction Measurements le Be III. Development and Design of the Skin Friction Instrunont Ie Ze ' Bs &s Se Skin Prietion by the Velocity Profile Method Ae fhe Pitot (or Total Head) Tubs B.. The Stanton Tube G. The Hot-tire _Anenoneter D. The Interferoneter. | Yeasurement of Sidin Friction by Direct Methods A. Skin Friotion by a Heat transfer B. Direst Foros Measurement Effeot of Gaps — Measurement of Small Foross Bllect of Exbernel Vibrations and Temperature Changes | | Deseription Bleotronic Equipment and Ciroult Details I¥. Incompressible Plow Measurements le Ze Experimental Bquipment and getup Experimental Method 42 on on es! 12 16 16 18 20 20 26 at 29 80 30 32 Be iv A. Laminar Boundary Layer Be Turbulent Boundary lever Hesults and Disoussion A. landnar Boundary Layers Be furbulent Boumiary Layer Ve Compressible Flow Measurenents l. ‘Ranges of Wind Punnel 2, Experimental Procedure. Turbulent Boundary Se 4. c, Layer GH = 042 to M = O46) “As Pressure Gradients Be. Temperature BquiLtbetun + PY Gap Plows D. Errors Due to Defleations and Vibrations Re Ooourrense of Trangonic Regions and Shook Waves P. Alignment cf Foroe Blement Results of Measurements for Turbulent Boundary Layer at High Subsonic Speeds laniner Houmdary Layer Keasurenents Measurements in Supersonic Flow (MH = 1.24 to Ms 1.44) consluding Remarks References 55 My Sb og} 3b | ~y on STHBOLS hoeal skin friction coeificienty lesal skin frletlon coefficient in incompressible flow Blagius value for the local sicin friction coefficient = Ce- Cy, specific heat at constant prossure specific heat at constant volume enthalpy = 5/8 , ratio of displacement to momentum thiclness ratio of displacement to momentum thiekness in sompressible flow ratio of displacement tc momentum thickness in incompressible flow local Mach number free atroam Mach number local static pressure total head (impact pressure} local total head Prandtl munbes" Her = 4 e,, U? a aynomic pressure of frees stream heat Slow per unlit timo per unit area throuch the surface fas constant 2% Reynolds number static temporature of the fluid static temperature at outsides edge of boundary Layer stagnation tomperabure © RE wy p, Coe «f ie well tenperature velocity components in the boundary layer peraliel to tha surface affective velocity obtained from Stanton tubo reading volocity at oubside edes of boundary leyer valuo ab the wall omtput of transformer in volts coordinate along the surface in direetion of flow ccordinate normal to the surface o Coley , Tatio of specifics heats boundary layer thieiness displacement thielmess height above the wall y/ ve dimensionless coordinate norml to surface momentuna defect thickness mnonentum defect thiclmess in incompressible flow heat conductivity of the fluid coefficient of viscosity au/o = rinematic coefficient of viscosity coordinate along surface in vieinity of gap fluid density Pluid density at outside ede of boundary layer fluid density of the wmiform flow shearing stress at the surface (skin friction) I. INFRODUCTION An objact moving through a fluid experionces a drag foros which can bé decomposed into presstre drag and skin friction. This divi- sion is the samo whether the body moves with aupersonic or subsonic speeds. At present, wave drag and indused drag are by far better un~ dersteod both experimentally and theoretioally than skin frietion and boundary layer separation. This 1s partisularly true for supersonic velooitiea but it ia also ouriously enough true that experimental ine vestigations of akin friction in the subsonic range and in incompres- sible flew ere exqeedingly rere. —— Regent advances in the ‘design of high-speed afroraft and missiles ‘have shown that a more exact ImowLedge of skin friction (and heat transfer, which is related) 4s of great importence. Theory of the laminar boundary layer and of leninar akin friction beth sn low-speed and high-speed flow has been worked out toe considerable extent in the course of the last decade. In spite of the lack of detailed ex- “periments on laminar akin friction, it ig gonorally felt that the theoretioal results are adequate and ‘trustworthy up to Mach muber's of the order of four. Beyond this range, for hypersonio velocities, new effects such ag dissosiation, variable Prandtl number, ete. ap« pear and the prosent theory does not seem to be adequately explored, furbulent skin frietdon, on the other hand, presents a much more serious problem. Our understanding of turbulent shear flow, even in incompressible flow, is inadequate and it is ab present not possible to formilate 8 gompleta theory without regourse to empirical con- stants. Even if it 19 acaumcd that low-speed turbulent skin friction is Imown, say from Zarnan's logarithmic laws with empirically deter~ mined constants, the question of how to continue these laws to high valocities and to supersonic flow arises.. This. question was firat discussed by von Harmen in his Volta Gongress paper in 1955 (Rer. 1) and hag sinese then attracted a large nunber of investigations, for exemple, by Frankl and Voishel (Ref. 2}, Ferrari (Ref. 3), van Driest (Ref, 4), Li and Nagamatsu (Ref. 5), eto. The net result of all these investigations is & set ‘of akin friction versus Mach muber curves (at constant Reynolds number) which are bounded by vou" xermn's results for incompressible and ‘compresaible flows. That is, the gen- eral trend is a decrease of skin friction with Mach number as in laminar flow. However, this decrease may be larger or sualler de- pending upon the assumptions made ‘im the analysis. one of the as- sumptions made have a theoretically convincing reason, due to the present leok of kmowledge of turbulent flow. It turns out that von — orsan's original assumption, which is also the simplest, gives so fer the largest decrease in akin friotion with Mach numher; for ex- ample, the ratio of compressible to incompressible skin friction coefficient at a Mach number of two and a Reynolds number of ons million is approxiately 0.66 secording to von Karmin, - | Henes, 1t ia evident that the differences between various theo- ries are anything but minor, In fact, the differences at Mach number of the order of two are so large that performance computations based upon the one or the other of the theoretical skin friction ooerfi- elents result in very large, and sometimes decisive, differences. is ie clear, therefore, that besides the fundamental interest in tuvbulent boundary layers, the determination of high-speed skin frio- tion is of paremourt technical importance today. (Tho present investigation waa undertaken with the alm of devolop- ing an instrunent capable of measuring sicin friction in high-speed flow. The program consisted of four parte: {a) A eurvey of possible methods of determining askin friction with the aim of selecting the most promising one for further dovelopment . The result of this study suggested diract measurement of loaal skin friction. This is carried out by measuring the shear force ex- erted upon a onal movable part of a solid boundary by means of.a reluctance plokup. . {b) The danign and conatruction of tha deviea, inoluding de~ tailed studies of neoessary tolerances and sensitivities. (sc) The application of the device to skin friction measurements in ineompressible flow where the results can be compared both with measurements by other means and with theory. (a) Tha meagurament of sicin friction coefficients in high-speed and supersonic flow. The second part of (d) was, wmfortunately, not completely accom plished. Only a few measurements in supersonic flow with doubtful flew conditions were carried out. This is due te purely external reagona and viet dua too filure of the devices. Tha main aim of tha investigation was the development of the apparatus, a determination of its acouraoy and a denonatration of ite applicability. Further measurements using this type of apparatus are in progresa now, both eb GALOT? end at the Jet Propuleion Laboratory. fhe research was sponsored by the National Advisory Comittee for Aeronautied and. conducted at GALCIT as part of a long range in- vestigation of boundary layer phenomena at high speeds. II, EXPERIMEN2AL METHODS OF SKIN FRICTION MSASUREMENT Under the asawaption of continum flow and nowslip at the solid eur foe the intensity of alein friction 7 at amy poimt on a golid surfaco ins flowing gas is given by aa ae pw gosffielent of viscosity whore us Velooity component in the boundary layor parallel to the surface -y # goormdinate norma) to the surface ‘Por the flow of (gases at temperatures and pressures at which the mean - . free paths of the gas molecules are sual compared to the physical d~ mensions of the eysten,. the slip at the eolia boundary is negligible. The following discussions will apply to eases where these conditions are realized. ; | | fhe above expreasion for skin friction is valid for laminar and, because of the existence of the sublayer, also for turbulent boundary layers. In goneral, experimental attempts at measurement of the skin friction may be elassified into taro main types: . (2) Those which endeavor to determine the components of the . right hand side of the above equation. (b) Those which rely on & bul néagurement of the skin friction iteekt, oF soma other piystoat quantity related to. Ate i. Skin Friction by the 1 Velocity Profile Method In the first type of measurement the physical quantities to he meagured aye tho viscosity 4 and the velocity in the boundery layor, ‘u« Kinetie theory and experiment indicate the viscosity coefficient te be a function of the absolute temperatura alone. Thus a lecal measurement of the wall temperature (with, say, a sensitive thormo- couple) is sufficient to define / H)yso* The measurement of the ve-~ locity ag a fimotion of the normal coordinate y is, however, a more complicated procedure, Measurement of tho looal velocity in moving fluide ia extremely difficult and up to the present time no really satisfactory direct methods exiat for application to the observation of high-speed flows. The only Imown published mesuranents of local velocity of interest to fluid mechanics are those of Fage end Townend (Ref. 6) who used an ultramicroscope with a rotating objectiva ta ob- eerve boundary layer flow in a water channel. For most aerodynamic ‘investigations the local veloolty is not found directly but related quantities like dynamic pressure, meses flow, density, eto. are meas- ured. To obtain velocity fron such neagurenents one requires addi- tional informetion about the flow, For exemple, consider the three most extensively used instru- monte, the pitot tube, the hotewire anemometar and the interferometer. In order to obtain volocity from the reading of s pitot tube ons must lmow the local static pressure and density, For the hot-wire ane- mometer the local denaity is required, ‘while information about the local temperature is necessary for the “interferometers In the case of the boundary layer, theoretical considerations borne out by experi- nents, show that the variation of pressure normal to the aurface is negligiblee On this assumption the experimental determination of stetic pressure in tha boundary layer ie aimplified to a Iconk meag- urement on the surface. {Since the pressure is measured et the will and tts variation is small the essumption of constant through tho bomdary layer introduces only second order errors in a skin fPrietion mensurenont.) However, for the inatriments mentioned above, for each “determination of velocity one would still have to make at least one additional measurement apart from the reading of the instrunent ‘itself. In determining ekin friction from the glope at the wall of a measured velocity prefila, errors in measurenent af the profile di- reotly affect 7, « A method which is not so sensitive to the portion of the velocity profile in the immediate noighborhood of the wall is provided in principle by Zarman's momentum integral. The basic con- sideration underlying thie 4e the fact that the Prietional forse on the gurface must appear as a momentum defect in the rest of the bound- ary layer. For the case of steady two-dimensional flow past a flat surface one obtaing e,u* dx @ U dx , dx where ¢ , U are the density and velocity just outside the boundary layor and 9 and & are defined bys 6 2 momentum defect thiclmesa = ou /- a) dy a © u § = displacement thiclmess & \ ( /- <) roy end x is the coordinate in the direction of the flow. Several pro~ Pilas in the region of determination of 7, would now have to bs measured go that the derivative of @ with respect to x oan be found. This methed, while not sonsitive to errors in 4 close to the well, involves ‘she added complication of lmowing U , ep, and 9 as functions of x. Its application is more practical in the case of uniform flow past a Flat plate when the presaure gradient in the x-direction is also garo and the above exprassior redusad to % _ de p.U% dx Tho use of this method dees not, however, eliminate the difficulties in the determination of velocity from a pressure or momentum meaagure- Notes on Instruments used in the Measurement of Velooity Profiles A. The Pitet (or Total Head) Tube The specialized form usually used for bowmdary layer measurensnts consists of a small bore tube (of the order of 0.05 inch diameter ) with its mouth flattened owt to form a narrow rectangular opening. | The impact prasasure at tha mowth As proportional to pur and is usu- ally measured on a mercury or alcohol manometer. As mentioned before, in order to obtain velocity from the reading ef such an instrument one needs a lmowledse of either ep or 7. Por non-dissipative flows with specds below the speed of sound, the assumption of isentrapic deceler- ation at the tube mouth ia closely ful filled end the velooity u is related to the impact pressure p by | z= u=~|2Cp % {r (=) s - here i, = stagnation temporature Pp = local statis pressure xs 2 s Cp and Cy being the specific heats at con- stant pressure and constant volume respectively The stagnation temperature 7, may bo measured at some conveni- ent reference point in the flew, for example, in the case of a wind ‘tunnel, in the reservoir or settling chamber. At supersonic speeds a shook wave appears in front of the tube mouth and the entropy loss. through this must be taken inte account. By assuming tho ahapo of the shock wave to be straight and normal to the flow direction the ve- locity can still be caleulated by use of the woll-lnown Rayleigh pitot tube formula +i +/ ! 2x - ¥-/ ( m2 yot) #1 Pp Py ; _s (Cpa) | where M is the local Mach munber just ahead of the tube (in front of the shoak wave) p the impaot pressure reading of the tube (behind tha ‘normal shook wave). The two pitot tube formulas become identical atMel, | For a akin friction determination with a pitot tube one would then have to imow the followings | (a) The impact pressure indicated by the tube aa a function of y within the boundary layer. (b) The static pressure at the point of measurement. (co) The temperature distribution in the bomdary layer. 10 By asguming the total temperature to be constant through the boundary layer tho temperature meaguroment is very much gimplified, but such en assumption causos some error in the value of the shearing stress. This assumption amounts to taking the value of the Prandtl] number Ps Ae Since for eotual cases A. </ ( Por air 0.724) the error is not larze at lew spesds but inereasss rapidly with in- creasing Hach number, an approximte estimate of the error in 7, caused by such an assumption may be readily obtained. For points in the boundary layer very dose to the wall the flow may be considered incompressible eo that. the pitot tube reads A= 0+ put. The pres sura p is measured on the surface and is approximately constant through the boundary layer. From this RT dn, f(42-yn2 For y—~ 0, (2-9 —~ 0 and the second tern on the right hend side ig nogligible as compared to the first. Therefore, for small values of y- | te. 7 Also the viscosity coefficient is approximately pole so that the shear stress at the wall =/, 24) «7 Bow y? Tw G7 FOR) “2op 11 "8 sor turbulent where /(F,) is nearly 4 Ye for laminer and 6F. boundary layers. Henes, by using ‘y= 4% the shearing stress would be direetly in error, For the typical case of an insulated flat plate at M 41.5 this error would amount te approximately Bi. AS ’ Righer Mach numbers tha arrors would ba even greater. it is interesting to note the improvement in adcuracy if an ace. tual measured value of the wall temperature 7y is used for the de« termination of % . Tho orrors in H| due to temporature are Yiw practically eliminated. The main limitetion now is in the determina} tion of a . Due to the finite size of the pitet tube, 4 cannot dy |w be mensured right up to the wall. Another error introduced by the finite siza of the pitet tube in boundary layer moasuremonts is due to the transversal total pressure gradient in the boundary layer. The | average indicated by the tube does not correspond to the velocity at the conter of the tube but to that at sone point which is shifted. from the center towards the ragion of higher voloaity. In a measure- ment of the volocity profile in a given boundary layor, this error is emphasised for pointe close to the wall, For a tube with a reotangu~ lar opening of 0.005" this shift is of the order of 0.001" in a ve~ Lovity gradiunt om #109 ¢t./seo. per foot (representative of a typical laminar boundary layer at Mach number 41,4 and Reynolds nun- ber based on a 10 om. length = 108), In actual use the shif can bs approximately ascounted for (see Ref. 7 for details). : Be Tho Stanton Tube The Stanton tubo is a modification of the pitot tube which gives en indication of the shearing stress on a surface. It consists of a 12 small tube with a hole in its side (see sketch). Tho tube projects & gmAL1 distance (of the order of 0.605") from tho surface on which the friction is to be measured and the opening in the sida of U a the tuba facas the direstion of = ~ = $$ $ret flow. The end of the tube is eed ae = sround flat to form a razor meee PEPE EF TEFL ELE EERATEE FECES PEEL EG sharp lip with the opening. For a distanee € very close to the anrface (this would have to be within the laminar sublayer in flows with turbulent boundary layers) we have approximately . Ug ; . 7) 8 pw —e * (Ow He) (Zac) whers - Ue is the effective velocity corrasponding to the tube prassura reading and the subssript w denotes conditions at the walle The sur~ faca tube may thus be usefully employed for indications of changes in % (see Ref. 8 for example of use). However, because of tho unpre- aise definition of the quantity . Ue as measured by the tube and the oxtrene sonsitivity to Cy, tho hoight of the tube above the surface, this method is not recommended for absolute measurement of 7, « G.. The Hot-Nire Anenonater _ The hot-wire anemometer depends for its measurement of velocity on the hest loss from a very ‘gnall dianeter (of the order of 0.0005") wire which is heated electrically. For a given temperature differ. ences between the heated wire and the surrounding air the amount of heat transferred is proportional to the squares root of the mss flow e4 + In order to fini the velocity u from the mass flew one wust kniow the density P+» For the neasurenment of mean velocity in bound~ ary layors at low spesds, where the effects of compressibility can be neplected, the hot-wire anemomster is used as a calibrated instrument. fhe calibration is performed under controlled conditions, for oxample, in © wind tunnel with a low turbulence Isvol. In this range the sen- sitivity and accuracy cf this instrument are well established. At high apeeds the lew of heat transfer deviates considerably from the ono at low speeds. In particular, the effects of temperaturs end don- sity gradients on the reading of the instrument under these conditions aro not yet established (see Ref. 9 for some recent work on this sub- ject). Since a hobewire has to be calibrated wider conditions which eannot be exactly reprodused during boundary layer measurements sud effects may cause large changes in the calibration constants, Until the behavior of hotewires in high-speed, particularly supersonia, flow is woll established it io felt that this instrument is unsuitable for procise measurements of boundary layer Clow at high speeds... 2D, ‘Interferometer | | This instrument measures directly the change in density with ref- erence to somo kmown value (see Ref, 10 for an account of the theory of operation of this instrument). Since the interrerometor leaves the flow undisturbed, it seems, at first sight, to be the ideal instrument — for twoedimensional boundary layer measurements, There are, however, sorious Limitations ta its uso for such work. These are due to: (a) Brrors arising from the refraction of the Light travorsing 14 the boundary layaz. . (bo) Presence of side wall boundary layers in wind tumels. {o) Transverse contamination of laminar boundary layers. The errors due to refraction are quite complex. Ag a ray of Light traverses the boundary layor it traces a aurved path instead of a straight one due to the existence of density gradients in the bowd~- ary layer. Thus two types of errors are introduced aa a result of re- “fraction. The first 4s in the optical peth length of the ray.and tho “gonond in the position to whioh the indicated density corresponds. Further ersors result from the fact that due, to. refraction a pay of | Light which enters the ‘tunnel at right-ongles to the side wall leaves the test section at “an ‘angle to the exit window or well. fThie causes ‘refraction through ‘the windort, so that the . Location of the apparent _ onigin of the ray is further in ereor. A more couplets discussion of these errors may be found in Refs. 1 and 12. It is sufficient to note here that investigations of the magnitudes of the refraction or- ror show that the inateated donaity profiles in boundary layer meas- . urements with an interferometer may be in error to the extent of - epproxinately 108. The second Limitation, that of the presence of tunnel wall -bound- ary layer, affects the moasured density aince the interferometer beam “traverses both the wall density Field aa woul ag the one being gtudied. One method of minimising this error is to pass the reference beam of the interferomter algo through the test section and thus cancel the effect of the wall boundary Leyers (Ret. 13). Tho third limitation is of primary consequence in leninar boundary 16 layor measurements. It 1s woll kmown (Ref. 14) that external distur- beness can cause transition of laminar flow to tho turbulent tyne. Observations of laminar boundary layere on flat plates show that dus to transverse contamination of the sides there are always régions of turbulent flow. Again the interferometer beam integrates the density in these regions as part of the laminar boundary layer and hence gives erroneous indications. | | The above discussion shows that accurate measurement of density in a boundary layer with an intorferometor is far from simple. Ap- proximate mothods of correction have been devised by various workers | (Refs. 11, 12 and 15). It is felt that the techniques so far developed ‘are inadequate, partioularly for taking the rather serious refraction error into account. in addition to these difficulties in the measure- ment of density one still has tho basic problem, mentioned before, ef obtaining velocity froa the reading of the instrument. Knowing 0» one still neods the distribution of the static temperature through the voundary layor for a galoulation of uw. “One may prooged to use theo- retically caloulated temperature distributions in the boundary layer (for example, in Ref. 16) or alternatively use a pitot tube to aupple- ment the interferometer. In this conneation the use of a total head tube is considered to be an improvenent over the first method of as~ auning theoretical Alstribublons of temperature in the boundary layer, and using tho interferonoter ag a primary measuring instrument. The yveading cf a pitot tube (apart from errors due to Pinite size) ie pre- portional to eu? and, for all practical purposes, is independent of theoretical assumptions. Hence this, with an acqurate independent moasurement of Ce» should give a fairly relieble dsteraination of the voloolty. 25 Measurement of Skin Friction by DirocsS Mothcads Tha above discussions show that experimental determination cf sin friction by the Indirect method of velocity distribution moas- moment in thin boundary layers io subjeet to many orrorg, The shear ing otress 7, has to bo dotermined by differentiation, either of measured velooity profiles or of slowly varying parameters (the loss of momentum in the boundary layer). Bvon when the quantities to be differentiated are thonselves measured couparatively accurately the reoults of differentiation van bo quite inaccurate. The second type of akin friction measurement, relying on a di- reot of bulk measurement, may be performed in principle in two ways: (a) By a heat transfer measurement. . -' {b) By a direct force determination. A, Siin Friction by a Heat Tranefer Measuranent Tha first method depends on Reynolds’ analogy between the trans- port of momentum and the transfer of heat. If 9g, is the heat flow por unit time from a unit area of the surface, and & is the host conductivity of the fluid, then ; aT xk (—— Go (ar a0 where 7 is the local temperature. The analogy with the expression for tha intenaity of skin friction is at onee apparent. “For the case Cp i k of two-dimensional flow with the Prandtl] nurber =/ the 1? temperature 7 is a paraholie function of the veloalty u alene, In such a case the heat flow g end tho wall shearing stress 7, may be explicitly related by an expression (Ref. 17) of the form: p | & - Ww t “fare 7, = temperature of frce strean, 7 = wall temperature ‘U m velocity of free stream mM, * Mach numbor of frea stream In the above relation assumptions cf laminar flow and equal ore dore of magnitude for the viesoug ond thermal boundary layers are in- herent. It is easily sean that estimates of skin frictlon can be ob- tained by imegurenent of g, and the othar quantities involved. For eases when the Prandtl number differs from unity but is constant and the flow is turbulent, similar relations between the heat trensfer and the akin frietion may be derived (Ref, 18). These relations, how- aver, are not exact and although they do indicate the existence of « rolationship between 9, and Z% , they are by themselves not reliable enough to form the basis of measurements for @, . In such cases oeli- bration procedures have to be relied upon. H. Ludwieg (Ref. 19) has euccacs fully used this principle for the measurement of wall shearing gtresses in turbulent flows at low speeds. His instrument consists of a gmall electrically heated element flush with the gurface on which tho measurement is te be made and thormally ingulated from it. 4, is measured by the amount of eleobrical energy supplied to the element. The temporabures of the clement and the free stream arc meagured by 18 thermocouples. It must be pointed out that in this case the general rolation betwoon g, and 7, must be modified to account for the fact that the thersal layer end the friction leyer do not originate at tho sens point. Ludwheg calibrated hie instrument by measurements of g, with known values of the friction foros, so that his measurements are not affeated by theoretical assumptions on the relation betwoon 7, and g . The use of this type of instrument for high-speed flow in- vestigations has, however, one sarious drawback. It ia extremaly dif} ficult to provide known shearing streases for calibration purposes. For instance, it is no longer possible to use the mown relation at low speeds between pressure drop in a two-dimensional charmel and the shearing stress on the walls. Furthermore, it is open to question whother a heat tronsfer inetrment calibrated in flows with fully de- veloped turbulent boundary layers can be used for the measurament of skin friotion in laminar flows, and vice versa. On account of these difficulties it was felt that a method noasuring the shear foree di- reatly would be superior to the heat trensfer method. | B, Direct Porce Moacuremant In principle this method is very simple. The orietional force 4s allowed to move e smill element of the surface in the direction of the flow, and against some restcring force. This movement is cali- brated to indicate the magnitude of the force. This method was used vy early investigators like Froudo and Kempf in determining the fluid resistance of bodies in water. A more recent application is that of Schul tz<Grunow (Ref. 20), who used it for measurements of Z% ina low-speed wind tunnel. Since thie method does not roly on any 1s physical assumptions regarding the neture of the boundary leyer flow it is inherently very suitable for surface friction MGASUTEMnonts ¢ There are, however, several difficulties and possible sources of er- ror in the actual usa of this principal, especially for applications to supersonic flow. The moving element has to be separated from the rest of the eurface by small gapse These may cause changes in the ve- locity and pressure distribution in their immediate vicinity and ‘se distort the measurements, Again, for local measurements the forae element has to be very emall compared to tho dimensions of the body on which the friction neasurenente are to be mde. This is of spoc- ial importance in cases where there are large pressure predients in the direction of flow. The magnitude of the friction forces on a anall element are bound to be small so that the force measuring mech- anism has to be extremely sensitive. Investigations of these diffi- culties showed that nevertheless the direct foree measuroment method was quite feasible and practical, 20 II. DEVELOPMENT AND DESIGN OF THE SKIN FRICTION LNSTRUMENT Although the principle underlying the direst measurenent of skin prietion (es outlined in tho lact seotion) is quite etraightformard ite actual applisation to flow measurementa is far from simpie. This is especially true for measurements at high speeds. An instrument based on this principle cen be used with confidence only after rather extensive investigations and considerations of the features likely to introduce errors in the measurement. This section will be coucerned with the investigations ungertaken to evaluate the applicability of the direct skin friotion measurement method and the design of an in- strument based on the results of these investigations. The main features to be investigated in determining the ectuel feasibility of the method my be briefly summed up as follows: {a) Effect of the zaps in the surface on the skin friction meas- urement. | | (bo) The practicability of accurately measuring small forces with apperatus having extremely small physical dimensions. (ce) The effect of external vibrations and temperature changes on the instrument during measurement. 1. Effect of Gaps That the gaps between the surface of ths flat plete and the force element may have some effect on the force measured is quite clear fron the fact thet in the gaps the condition of no-slip et the surfece is no longer satisfied. The break in the continuity of the boundary my 21 de regarded as a sudden disturbance in the slope of the velocity pro~ file et the wall (thet is, tho shearing stress 7). The magnitude of thie disturbance ovidently depends on the dimonsiong of the slot ag woll as the characteristics of the flow in its vicinity. The fact that for small surface gaps the disturbance in pressure is negligible forms the basis of the well-known method smployed in the measurement of static pressures in moving fluids. Since pressure and velocity disturbances are related, it is reasonable to expect that for small gaps the associated velocity disturbance would also be small. In or- der to substantiate this heuristic reasoning and to arrive et a some- whet more precise idea of the "smallness" of the gaps which would not disturb the. velocity profile, tests were mde on flat plates with ‘slote in the surface. A slot width of 0.01" was used for the study in supersonic flow. This slot dimension was chosen as being © practi- cal one for actual use in tho instrument to be developed. Ths flow over the plate surface was observed by means of Schlieren photographs. Figs. 1 and 2 are typical Schlieren photographs of the flow past the slots with leminar and turbulent boundary layer respectively. It was found that the plate surfece and the element had te be in the same plane to almost an optical degree of flatness before the shook waves dispappoared on the Sohlieren. The laminar boundary layer photograph (Pig. 1). indicates no detectable disturbances due to the presence of the slots. In the turbulent case (Fis. 8) (thero being a steepor ve- losity gradient at the plete surface) very faint waves can be seen originating at the gap locations. In order to estimate tho strength of these waves, an attempt was mado to measura the pressurs rise a2 through them by means of a 0.04" diameter static pressure prebs and an alcohol manometer. No indication of pressure variation could be obtained, Since experience with eimilar probes has shown the instru- ment to be an extrencly sensitive one, it was concluded that the ef- fect of the slots was negligible, This conclusion was further oon firmed by a detailed exploration of velocity profiles in the vicinity cf & satple slot. The profiles on a flet plate with a relatively large slot of about 0.2 em. were measured with a 0.0005" diameter platinum hotewlre. Since the boundary layers at high speeds are too ‘thin to ellow accurats profile determination, these measurements were carried out in a low-speed wind tunnel, The boundary layers were relatively thick (ebout 1 om.) and the hot-wire measurements quite ecourate, In onder to retain some measure of dynamical pini larity with the slot in the high speed tunnel, the Reynolds number based on the gap width and free stream velooity, denaity, and viscosity wae kept approximately the seme in the two cases. The results of these. moasturements are shown in Fig. 8. The slope and shape of the velecity profiles in the vicinity of the slot, end henee the shearing stress, is seen to be essentially unaltered by the presence of the slot. it je interesting to mote the profile measured in the pap itself. A . emall finite velocity is indicated at the wall level but the slope of he rest of the profile is not sensibly affected. The profile immedi- ately behind the slot does not indicate any trace of the disturbance. The velogity profiles shown in Pig. 5 are for a turbvlent boundary leyor on the flet plate. The effoct of the gap on a surface with leminsr boundary layer would be even less. 2. Measvuremens of Small Forces Almost all the usual motheds employed in the measurement of small forces have oue comwsaon feature In that they ell ubllize «a small linoar or angular movement preduced by the force being measured c- mainst some mechanical reatcring force. The principal methods avail- eble are: (a) Mechanical devices ugiligzing the torsion of a thin wire. (b) Optical mothods. (a) Resistance wire gaged. (da) Reactance gages. The mochanical torsion wire is essentially very simple and is utilized extensively in laboratory measurements of small forces (for example, surface tension of Liquids). Considerable effort was ex- pented in an attempt to employ this method for the measuremet of _ kin friction forces, 4 tost sotug, however, showed that it could not be used to advantage with complicated levor systems which would éestroy the simplicity and accuracy of the method. "Among the optical methods, the use of interferometry for the eee curete meusuresent of small displacements is well known. The oxtranc sensitivity of this method, however, requires alnost perfect vibra- tion isclation of the optical elements and thus makes a practical ap- plication in a case like the present extrenely difficult. Fwo other optical methods were investigated. The first of these employed opti- cal levers to magnify small anguler changes, while the second used the fact that the width of the diffraction pattern from a narrow rectanguler slit is proportional to the width of the slit. While ex- tremoly simple in their epplication, these mothods were found to be not accurate enough. | The resistance strain gece, extensively used in experimental struehoral analysis and recently also in wind turnel balance systems, works on the principle that a change in strain in a thin conducting wires is accompanied by @ chance in electrical resistance of the wire. Since the percentage change in resistence is of the same order of magnitude as the percentage strain and the wire material cannot be stregeed beyond ites elastia limit, rather elaborate aleotrisal eauipe ment is necessary for precision measurements with this type of cage. Its use is further complicated by the necessity for temperature com- . pensation, for changes in temperature would directly affect the rosis- tance of the strain gage wire. A test apparatus employing the wire strain gage showed that this method did not heve the accuracy or sta~ bility required for the measurement of small forces of the order of 100 milligrans,. | | ‘The reactance type gage is similar to the resistance gage inae- much as it also employs a mechanical movement to produce a corres- ponding change in an electrical quantity. Im this case, however, it is possible for the percentage shange in reactance to be several or» ders of magnitude larger than the percent mechanical change. The change in reactance can thus be easily and accurately measured. The particular form of reagtance gage or pick-up chosen for the present application is a small 5/16" diameter, 7/16" long variable differun- tial transformer monufactured commercially (Schaevitz Engineering 25 Company, Camlen, New Jersey). It consists (see Fig. 4) ossentially of three coaxial coils, one primary and two seconderios., A emalt iron ore forma the controlling element of the transformer, The primary ooil is energized with high frequency (20 HO) AsG. so that the sole- noidal fores on the core is effectively eliminated. The output of the secondary coils cotmected in opposition is a function of the oore posi- ‘tion (Fig. 5). The sensitivity of the transformer is of the order of 0.03 volte por 0,001" eore dieplaconent at & volte input to the pri- mery. This corresponds to a full-scale deflection on a Hewlett-Packard - Vaouua Tube Volimeter. The output change is large enough for measure- nent of core movenents less then 1/10,000 of ai inch to approximately 1% accuracy. 3. Bfifeot of External Vibrations end Temperature Changes Since the skin friction instrument was intended for use in wind | tumels which are always subject to vibrations, actual measurements of the frequencies and amplitude of the tunnel vibrationa were made with a standard vibration analyser. These measurements showed that the predominant external frequencies wore at approximately 200 cyclos/sec. and 20 cyelos/sec, The maximm omplitude of vibretion wae about 0.001" et the lower frequency. In view of this the core suspension systen of the instrument was designed with a natural frequency much lower (about 5 cycles/sec. ) than the external vibrations. Since the external vibrations ectually have a continuous frequency spectrum rather than just discrete frequencies, it ia impossible to entirely eliminate the effect of these vibrations. Asa result the transformer 26 core may oscillate to a smll extent about some mean position or my be effectively displaced from te rest position, It ia therefore im portant to operate on a part of the output curve (Fig. §) such that the onciilations do not mike the gore cross the minimum or "sero" point of the curve. The effect of the external vibrations was further minimized by viscous damping and distribution of the miss of the ose gillating system eo that ite center of gravity and center of percus- sion were approximately coincident. . The transformer pickup was tested for temperature effects and it was found thet temperature changes of + 20% have no effect on the out- | ; put. In the actuel design one further precaution would be required, . ‘The Link system carrying the core must be av designed that therm ‘ ghanges leave the oore position unaffected. | “Mo ewmuarise the above investigations the following design re- quirements were set up for the shearing instrument. | (a) The instrument 4g to be used primarily for two<d mensional neasurements. in the GALT 4" x 10" Trangonic Wind Tunnel (see Ref. 21 for description). The mall size of the test section demands that _ the instrument be of extremely small dimensions. | (b) The moving clement and the flat plate must et all tines be et the same level. Even amll inelinetions {of the order of 1/50th ofa degree) of the element would introduce large errors in tne measured forces. ‘the gaps between the ‘force element and the plate surface must be ag small as possible. (a) The foree measuring system must be sensitive enough to mens- ure akin friction forces in both laminar and turbulent boundary layers 27 in the aveilable range of iach number ané Reynolds number (M & 0 to 1.5 and Reynolds number « 104 to 10°), ‘This corresponds ¢o shearing stresses ranging from approximately 1 milliprem/eq. om. to about 1 gran/sq. or. | {a} The instrument readings must be immune to vibrations from the tunnel and to temperature changes. 4. Desoription The instriment developed da showm schematically in Fig. 7. The flat plate used for the measurements 1s supported from the esiling of the tunnel. ‘The small 0.2 om. x 2.0 cu. moving element is supported by a spocially designed four-bar linkege which allows it to translate in the plene of the plate without rotation. The rectangular slot in the plate thru which the foree element is exposed to the flow has ac- oureately lepped sides. fhe gaps at the leading and trailing edge of the element are approximately 0.004" and 0.008" respectively. The . alenent is lepped flush with the surface of the plate after assembly. The degrees of flatness is checked by means of interference fringes. The flexure links in the suspension system can be replaced by Links of various thickness (0.005", 0.01", 0.025") thus providing a large ranze of variation of the restoring foree. Movement of the force sle- mont is conveyed to the core of the transformer by a non-conducting rod and matal yols arrangenent. The transformer is held in position Oy & brass cago which oan be adjusted for position by moans of set ecrews. The linkage assembly seats in recesses in the flat plate sun- port which also gerves as a stream-lined windshield. The damping of 28 the force clement is obtained by two dampers which are carried by the yoke of the flexure link assembly and ere immersed in Dow Corning Silicone Fluid ef 500 centistokes viscosity. The area of the surface ef the dampers was adjusted to provide slightly less than critical — damping to the pact lieting system. The masa of the domping syehem is also utilized to obtain coincidense of the center of percussion and center of gravity of the Linknge. - fhe effectiveness of damping and vibration isolation can be seen from the sample calibration curve in Fig. 8. Calibration of the instrument is obtained by moans of & pule ley arrangemont with jewel bearings. The pulley wos conetrueted from magnesium (for lightness) and balanced in rotation so that it intro- duced no errors in calibration. The frictional torque of the jewel bearings is of the order of 10°6 igi@e-om. and henes is negligible. A eingle fibre nylon thread provided the means of attaching small frac- tional woights to tho linlmge’ during ealibration. Sample calibretions indicating the rapestibility end linearity of the force measuring system may be seen in Pigs. 9 and 10. The entire force linmge and coil systen is enclosed in the windshield which hss a frontel area of 1/4" x 2 1/2". When in use, the inside of the windshield is sealed off from the flow, exoepting for the gaps around the force clement 4tseif. These gaps serve as vente for equalization of presswre be- twoon the inside and outside of the foree element, The solectrical leads are likewise senled. During cperdtion, the pressure across the gaps could be observed on an alochol manometer. One lead of the manometer was commected to a static pressure orlifics on the plete just ahend of the element and the other indieated the pressure inside the 29 windshield 5. Blectronio Equipment and Ciroult Details 4 bloak diagram of the manner of use of the skin friction instru- ment is shown in Fig. 6. A precision Hewlett-Packard low frequency . oscillator ected as the power supply for the differential transformer. The output from the aseondarias commected in opposition was read on a Howlott~Packard Vacuun Tube Voltmeter to on accuracy of $1. Since the output is directly proportional to the input, the letter wag al- ways kept at the sane fixed Value before taking a skin friction read- ing. In order to avoid errors introdused by switching, a second vaouun tube voltmeter was used to read the input to the primary coil of the transformer. the variable resistence of 20,0000 (show in “Pig. 6) across the secondary colle of the transformer mit wes found ugeful in reducing the magnitude of the output at the "balance point” (symmetrical core position) to approximtely 0.001 volts. This ef-— | ‘fectively increased the range of readings on the voltmeter soale. N18) IV. ZINCOMPRESSIBIE FLOT LEASURELIENTS At low speeds the assumption of insompreasibility of the alr is a close approximation end leads to considereble simplification in theoretical treatment of the boundary leyer equations. This bs espec~ -4elly important for the case of leminar flow past a flat plate at gero incidence, for in this case an exact solution of the Prandtl equetions is possible. This is the well«lnown Blasius solution. For the muigh more conpliceted oase of turbulent flow, theoretical solutions of the equations are not possible. However, as shown by Prandtl, von Karman and others, even for turbulent flow important theoretical deductions regarding the skin friction and nature of the boundery leyer flow can be made. | The logarithmic lew for skin friction at high Reynolds num~ pers ip a well-inown exemple, | In order to establish the general validity of the present method of measurement, the skin friction instrument was adapted for measure- ments in lowespeed flow. Twa typas of flow wore investigated, the so- called Blasiugs flow and fully developed turbulent flow past a flat plete. It is believed that the reyults of this investigution, upurt fron confirming the eoouracy of the method of measurement, have some interest and valuo of their own. 1. Experimental Equipment and Setup The general experimental arrangement for the low-speed measure- monts 1g shown in Fig. 11. The GALCIT “Correlation” tunel was used for this investigation. This is a speaislly designed wind tunnel for _ turbulence meesurements, with & very low free etrosm turbulenoe level (u’ f¥ of tho order of 0.03%). Sinee the mognitude of the shoering stress 7, at the low speeds. and Reynolds numbers (U & 400 cm,/sea. to 1600 om./sec. and Reynolds numbers about 6 x 10% to 6 x 10°) is extramaly amall, being of the order of 1 milligram/sq. ems, the small (0.2 x 2-0 om.) element of the instrument was replaced by a larger one measuring 1.15 om. x 6.5 om. Phosphor Bronze 0.005" thick by 1/4" wide flexure links were used instead of the regular 0.01" thick links. This increased the sensitivity of the fores measuring system by a feetor of epproximtoly 4, The instrument ws attached to the flat plate by means of e metal yoke, as showm in Fig. 11. The surfece used for the low-speed bound~ ary layer measurements was a sharp nosed 12" x 86" flat plate made cut of B/l6" thick plastic material. The surface of this plate had a highly poliched Minish. Thare was, however, come irregularity present in the form of waviness in the surface. Mo attempt wis made te remedy this because the amplitude of the surface waves wes too small (of the order of 0.005" in a length of 2") to be of any significance. The shearing stress instrument could be Leoated in two elternetive posi- tions on tho plato. The ohange in position allowed an additional veriation in the Reynolds number (that ie, in eddition to the change rade possible by free stream velocity changes). The measuring ele- ment consisted of a small piece of the plastic (identical with the plete mterial) rectangular in shape and attached to the force link ege co that the lower surface of this clement was flush with the sur~ rounding plate surface. The element was separated from the rest of 52 the surface (on all four sides) by a 1/62" wide gap. That the elemont was really Plush with the plate surfsoe could be checked accurately by means of an optical arrangement consisting of a reflecting surface and 8 magnifying lens. ‘The force linlmgs systen was shielded and serled off from the flow by a streamlined brass ehield. Total head profiies could be measured at either looation of the choar stress measurenent by means of a total head tube and a portable micrometer head with a least count of 0.01 ema, The total head tube dimensions are shown in Pigs 12. A precision alechol manometer of the Zahn type was used for the mene urenent of pressures. Total head or statia presaure traversas could be made in the direction of flow by means of & motorized tra- VOTE. “2. Dperimentel Method A. Yeminar Boundary Layer | In order to establish the type of boundary layer flow, velooity profiles were measured on the surface of the plate for a range of ve- locities covering the Reynolds number range over which the shearing ~ fores was to be measured. These profiles (Fig. 12) showed good agres- menb with the theoretical Blacius profile. That the flow was indood laminar was further cubstantiated by observing lewinar boundary layer oscillations (Pollmion-Sehlichting waves) by means of a 0.0005" dia- moter platinum hct-wlre placed near the surface of the plete (approxi- mately at a distance of 0.1 om.). The regular isminar oseilletions could be changed to randem turbulent Pluobuations by introducing dis- turbances in the boundery layer ahead of the point of measurement. In 58 acciticn to substantisting the pressure profile measurements, this | preoaution served another significant purpose: it removed any suspi- Gion that the foroe of friction measured by the shearing stress in- atrument was due to anything other than pure laminar Plow. It is Imown thet laminar flow does not break down at a definite (timeeinde- pendent) distance from the leading edge. Transition to turbulent flow is evidenced by the appearance of "bursts" of turbulent fluctuations (see Ref. 22) superposed on the laminar oscillations, In case such "yursta" were present, the fores neaeurenents would not correspond to purely leminer friction. The actual shearing force measurement consisted of taking the difference of voltmeter readings with end without flow for each point measured. This process eliminated any poseible errors due to sere shift in the measuring system, In the earlier steges ef the expori- mente , the instrument was calibrated before and after each sot of _ shearing force measurements. Since the calibration (Fig. 9) did not perceptibly changes, this process was later réplaced by one of making periodic cheeks. The calibration remained constant during the entire duration of the measurenents to better than 1%. it was not possible to fulfll] exactly the comiition of zero prece sure gradiont required by Blesius flow. However, the devistion from ap ax ments reported, and it was possible to adjust the plete in pitch to = O wee small (> lass then 1%) in the range of the measure- give apprexiiaately a constant fevorable pressure gradient. This ws actually measured and the force measurements sorrested accordingly when making tho comparison with theory (see page 36). ' 84 Since the forces measuring system of the skin friction instrument is essentially a suspension it is affected by tilt of the instrument. In srder to determine and account for the error introduced by changes in the attitude of the inetrument due to deflection of the flat plate, the following procedure was adopted, The element was covered with a streamlined shield which left 46 free to move but shielded it com- pletely fron the flowe The difference between tho "no flow and "with flow” readings then gave the effect of the plate tilt. This error was determined for the entire range of velocities since the plate deflesc~ tion is dependent on the air loads of the system. Fig. 13. shows the effect of plate tilt on the instrument. The mean curve of Fig. 13 was then used to sorrect the instrument readings. The oaximum correction was less than 10%, The scatter in Fig. 15, at about 1300 om./sec. free strean velovity, is due to excessive vibrations indused by reso- nanse with e natural mode of oseilletion of the tunel. ‘The above procedure of correction was necessary enly for the measurements made at the forward location (x = 28.6 oms.) of the instrument. For the rear Location (x = 58.0 cms.) the plate support was modified to in- crease its rigidity. This effectively eliminated any plate tilt. As will be noticed from Pig. 14, the scatter of the experimental points is considerably less at the rear lecation than in front. Dur- ing all tho measurements preaautions were taken to ensure that there was no flew thru the gaps between the force element and the plete. This waa done by sealing the windshield onto the plete and checking © the pressure differanea between its inside and the plata surface an an aloohol U-tuba. 35 B. Turbulent Boundary Layer Tae experinental procedure for the skin friction measurements on the flat plate with turbulent boundary layer was essentially similer to that adopted for the laminar case, The boundary layer was tripped, that is, made turbulent, by a roushness slement at the leading edge. The type of flow was identified by the shape of the velocity profile (seo Fig. 12) as well as by the random fluctuations shown by a hot- wire placed close to the flat plate surface, That the particular manner in which the boundary layer was tripped was of no essential importance to the skin friction measurements was ascertained by eaus- ins the transition in different ways ( for example, raising the free stream turbulence level with the help of wire soreens in the tumel; or alternatively by adjusting the plate orientation so that the stag- nation point on the leading odge was located on the side opposite to _the surface of moasurement). In all the measurements reported here the boundary layer was tripped by a single roughness element, a wire, at the leading edge of the flat plete. ‘This method wes adopted in praferanca to the others beeauses it gave a eonvenient method of fis- ing the point of transition almost at the leading odge of the flat plete. Thus, we climinate any arbitrariness about the length enter- ing into the calculation of the Reynolds mmber of the turbulent boundary layer flow. That the boundary layer was really turbulent clicse to the lending edge was confirmed by a total hend tube survey in the direction of flow with the tube touching the plate. The change from laminar to turbulent flow ia then indicated as a sharp rise in total head loss by the totel head tube, 36 8. Results and Disoussion A. Laminar Boundary Layer The direct’ skin friction measurements are shown in Fig. 14. They cover a range of Reynolds numbers from abowt 6 x 10* to 6x 105. In comparing the experimental values with theory, the values of the | shearing stress, as indicated by the instrument, were sorrested for experimental error due to plmte deflection and the effect of pressure gradient, The method of correction for plate deflection has been dis- cussed before. It applied only to the measurements at the forward lo- cation (x = 286), sinoe at the rear location there was no deflection of the plate and supports. The effect of pressure gradient was taken into account by use of Karman's integral relation for the boundary layer. Since oe was not exactly sero its magnitude was ascertained by actual measurement. Fig. 15 shows. these pressure gradient moasure- ments. It will be noticed from Fig, 15 that at any given value of free stream velocity at the point of measuremant a , has vary nearly a constant value over the entire length of the flat plete. Using this fast, the momontum integral relation may be written for a given point ass aCr H+2 dp Che G dz where aCe = Cy - & ig the differenes of the local sicin friction acefficient from the Dlesius value Cy, H wvatio of displacement to momentum thislmess / q =>, U*= dynamic pressure of free strean dp 3, # constant pressure gradient over the flat plate Thus for a fixed valve of *% and g, imowing the pressure gradient end using the Blasius value of 4 = 2.605, the effect of pressure gradient san be estimmted. That the use of the Blasius value for 4 is justified for the purpose of such calculations may be seen from ‘the profiles of Fig. 12, which show that for the small values of <. the departure from the Blasius profile is alight. Al the measured valuos of C; shown in. Pig. 14 heve been corrected for the effect of. pressure gradient in the marmer outlined above. The menitute of the maximum correction was of the order of 8% in c . The agreement with the theoretical straight lines of Blasius is scen to be excellent. Tho exporimontal points show in Pigs 14 aro the results of several observations taken at differont times and to some axtent indicate the repeatability of tho measurements. Also shown on the same figure are values of CG obtained from the rome of Fig. 12 by nee suring the slope at the wall and correcting for & effect. From the discussion it is evident why the few scattered experi«- ments on flat plate skin friction often give too large values of Cy The reason for this is the extreme sensitivity of the laminar leyer to pressure predients. If the pressure gradient is slightly norative the layer is stable and laminar, but the skin friction toa high. If the pressure gradient is slightly positive, turbulent "bursts" ere likely to appear and Cc, is moasured too large again. B. Turbulont Boundary Layer The measurements of local skin friction with turbulent bowidary layer on the plate were also corrected for pressure gradient effect | in a mauer similar to the one adopted for the laminar case, For the purposes of this correction, values of 4 and 6 were obtained by assuming a power law velocity profile in the boundary layer with a power index of 1/7, The magnitude of tha corrections in this cease was of the order of 2% in G. Fig. 14 shows the excellent egreanent between the experimental values and the theoretical curve given by Karman for tho skin friction on a flat plate with turbulent boundary leyer. This agreement is believed to be fortuitous to some extent, for the constants in Karmin's logarithmic relation FE = A+B 406, afece are not predioted by theory but have to be determined from experiment. The value of A and &, ag found from the present experiments, Wee -Oe91 and 45,05 respectively as compared te 1.7 and 4415 in Karmn's forma. This difference in the constants is perhaps to bo attributed to the fact that 4 and 3 ero not absolute constants but depend some- what on the conditions of experiment, for example, on Reynolds number, ete. One can only conclude that the logaritlulc forsmle of Karman is | a fair approximation for incompressible flow. Due to the Limited renge of the tunnel turbulent boundary leyer flow at Reynolds numbers higher than 6 x 10° could not be studied. ‘V. GOMPRESSIBLE FLO MEASUREMENTS It was originally intended to investigate two simple reprosenta- ‘tive types of viscous compressible flow, namely the steady laminar and turbulent flows on an insulated flet plate with zero pressure gradient. It has already been pointed out that even in the incompressible flow moasuremonts gonsidorable diffioulties were ensounterod in obtaining experimental conditions which closely epproximted the conditions form- ing the bagis of theoretical analyses. In the case of the compressible _ flew meacurenents, the additional Limitations imposed by small size of the wind tumiel and by the effects agoompanying compressibility were sonstimes so severe that they resulted in either changing some of the original aims or even abandoning them. For instance, it wes highly desirable to obtain skin friction measurements for the case of a lemi- nar boundary layer, for vhioh rather extensive theoretical information “4s available. Experimentally, however, it was found impossible to maintain leninar ‘flor without rather strong favorable pressure gradi- ents (see pags 47). Hence, the noasurenente in the laminar case had to ve restricted to a single set of measurements of skin friction with known pressure eradiente. If the following pages indicate a lack of completeness and continuity it is lergely a result of features in- herent in the phenemenon being investigeted. 1. Range of Wind Tunnel fhe investigations were carried out in the 4" x 10° GALCIT Trun- sonic Wind Turmel. This is ea continuously operating close return type ‘uunnel equipped with air filter, silien gel dehumidifMer, and a flexi- ble nozzle (Ref. 21). The Mach number range of this wind tumel exe tends from about M= 0.25 to KX = 1.5. Since ell the skin friction moasuronents wero carried out at a fixed looation of the force meag- uring element, the possible moans of Reynolds munber control wore limited to: oe a | (a) Voloeity changes (b) Stagnation temperature changes (6) Stagnation pressure changes | | Of these, the last two leave the Mach number waffected and hence ars very suiteble for isolating Reynolds nuaber effects from Mach number | effects, Unfortimately, the rango of. Roynolde mumber variations pos- sible by these means wes extremely limited in the prosent caso, and for all. practical purposes changes in Reynolds number were possible only through Mach number changes. The available renge of Reynolds numbers was thus confined to approximately Re Sx 105 to 1.2 x 10°. Gince oxpeorimontal limitetions severely Linited the investigation on laminar boundary layers, the main part of the compressible Slow meas- urements were confined to turbulent boundary layer flow. 2, Bxperimental Procedure. Turbulent Boundary Layer (If = 0.2 to Me 0.8) | fhe size of the flat plate and the general arrengemont is shows in Pig. 7. It will be noticed that the flat plete has a sharp lead- ine edge, one side of the plate (the measuring surface) being parallel to the flow. For the oase of the hich subsonic flow mossuromenta, 41 this configuration served to produce turbulent boundary layers start~ ing at the leading edge of the plate, the stagnation point in this range being on the surface opposite to the measuring surface. How- ever, in order to remove army doubt regarding the nature of boundary | . layar flow for mast of the turbulent boundary lnyer mensuremants, a 0-005" dianster steel wire oanented about 0.2 om. from the leading edge of the plate was used as @ trip. Figs 16 shows that the experi~ mentel points with and without the wire trip agree very woll. Ag shown in the sketoh (Figs 7), the flat plate does not quite span the width of the wind tunnel. Previous experience in investigating high epeed flow phenomenon hed indleated that the side wall boundary layer effects were minimized by shortening the span of two-dimensional models an enount equal to the displacement thicimess of the. boundary layers In the present case this anounted to approximately 1/4" on either side of the flat plate. Detachable side piscos cauld be in-- stalled on the flat plate so that it effectively spanned the entire spar of tha tunnel. As a matter of precaution, skin friction measure- monte were made both with and without these side pieces. Fig. 16 shows the agreement between these measurements. Fig. 17 shows repre- sontativo velocity profiles meagured with a tetal head tube end com- puted on the bagis of constant energy per uit mase through the bound- ary layer, The turbulent boundary layor akin friction moasuremants shown in Fig. 16 are the resulte of some eight separate sets of obser- vations. During these moasurements every effort wae mde to eliminate or account Por errors which might affeot the reliability of the re- sults. The following points were especially important. a2 A. Pressure Gradients Fig. 18 shows representative pressure distributions measured with a statie pressure probe and an aleshel micromanometer. Since the | probe travel was limited, it was not possible to ebtain the pressure distributions over the ertire length of the plate. However, it is known from previous calibration shecks of the flow in the tunnel that the flow 1s quite smooth, so that the pressure distributions shown in Fig. 18 extend continuously in either direction, As sean in Fig. 18 the pressure gradients are quite small but not sero. To estimate the _ effect of these small pressure gradients on the measured skin friction, use wes again made of the Farman momentum integral. It was assumed for these computations thet the turbulent boundary layer profiles oould be represented by s power lew, Justification for this is apper- ent from Fig. 17. The momentum integral reletion for compressible flow may be written es. de 6. 4 she dp 7% 5 @-a) * ra z] where. the symbols have their usual meanings. Tt is well imown thet es a first approximation O, the momentum thiclmess, may be said ta be unaffected by compressibility effects (equivalent to an assumption of pus constant). Using this and neglecting the effect of pressure gradients on @ and “ ome may write | A. = Hi; {v- aa (+ )| * where H, = 0 compressible ig the shape parameter for compressible flow end 4, the sane for incompressible flow. Assuming a 1/7th power " yelooity profile we can use the incompressible flow values of & and 4; given by Us a; 0.036 (4) 45 a H; 4286 The effect of pressure gradiont then may be approximetely determined by writing the integral relation as 8; dp =- -me at AC, = {(z M )+He} a ox where do acy = {¢ -2 xy and using the approximate values for AH, and @ from above, and ‘ dp T ux from Pig. 18. These calculations show that the maximum error in tho local skin friction cooffieient is lesa than 1%. | B. ferperature Equilibriun in order to realize the condition of zero heat transfer on the flat plate it is extremely important that thormal conditions be stable _during operation of the wind tunnel. The method of supporting the flat plete along its centerline by a thin strut minimized any losses duo to conduction. In addition, the measurements were carried ont with the stagnation temperature of the air in the neighborhood of the room temperature. The stagnation temperature could be maintained con- stant to epproxinately 21°C. The usual time taken by the skin fric- tion instrument rendinzs to steady down was of the order of two min- utes or ao efter tha tunnel Plow and the stagnation temperature head stabilized. That conditions on the flat plate had really reached the state of sero heat transfer was confirmed by a calibrated thermocouple probe touching the surface of the plate. The thermocouple cutput wes read by a precision Leeds and Borthrup petembioneter on which temper- etare chanzes of abouts 0.01°C could be easily detected. It was Pound that if anjr changes in stagnation temperature were mede, thermal equil- librium on the plate was attained after two or three minutes of stab- dlisation. During the period of stabilizstion the effect on the skin friction was observed to be strikingly lerge. It is for this reason that these preceutiona are strongly stressed here. As a poimt of ine terest, the temperature recovery on the plate, as indented ‘by the thermocouple probe, is shown in Pig. 19. Also show for somperison is the usual empirical relation for temperature recovery oma flat plete with a turbulent boundary layer. The results in Fig. 19 are to | be regarded only as of a qualitative nature, since ne ace ont is taken of the effect of the probe itself on the temperature recevery. The main reason for theso measurements was to confirm thet thermal equi- libriwn had been reached on the plate. On the basis of these experi- ments, the usual procedure followod was to let conditions stabilize for over ten minutes or so before recording the skin friction read- ingse Gc. Gap Plows During ell the moasurenents reported here there was no flow $hrough the gaps separating the forco eloment from the plate. This wes ascertained by moans of an alcohol U-tubs which, for all the re- ported measurements, indicated less than 0.5 om. of alcohol differsnece in pressure across the geps between the inside of the shield and the outside flow. In order to determine the degres to which the skin friction readings were affected when there wma flow through the gaps, m or a test sotup was arranged. Any desired pressiwa difference could be maintained across the gaps by means of s suotion pump arrangenent con~ nected to the inside of the sealed windshield of the skin friction in- strument. It was found that with no flow in the tunnel, pressure dif- feronoos of about 6 ons of eleche! saused an. error of about 8% in the reading of the instrument. This waa true regardless of the diroction of the pressure difference. Of course these values would be somewhat different under actual flow conditions. But they certainly would not change by an order of magnitude and since during the measurements the pressure difference was alweys less shan iff om. of aloohol, only negligible errors could have been ‘caused. | D. ferore Due to Deflections and Vibrations _ These effecta were checked for in a minnor similar to ono adopted -during the incompressible flow neasurenonts. The force clement was covered ‘up with a streamlined shield protecting it from the flow but leaving it completely free to move. If any deflection of the etruo- . sure supporting the instrunent ocourred it would show up as o reading. A similar effect would be producod in the case’ of imperfect vibration igolation. 1% was found that the installation of the instrument in ' %he wind turmel was porfeatly rigid and that the vibration isclation ani damping quite adequate, so that no errors were introduced on those BOCOUNTE s E. Qsourrence of Transenic Regions and Shook Veves Tho upper limit (approximately M = 0.8) of Mach mmber for the hich aubsonio flow measurements reported here was set by the appear- ance of shook waves near the leading ede of the flat plate. It was found that with the appearence of a transonic shock et the leading eigo of the plate no sudden chances sould be observed in the skin ariotion at the point of moagurszent. Nevertheless, in order to re- tein clean experimental condition’ it was desided to restrict the meagurenente to flow without shook waves. FP. Alignment of Foros Blenent During the courge of the experinents reported here the alignment ef the foroa elemant with the rast of tha plete surfees was pericdi- cally cheoked optically by moans of interference fringes, During the entire period of measurencnt the alignment remained the same to within +11 x 10%inches (corresponding to a fringe movement of one fringe width of Caiimiua light), | ae Se Results of Measurements for Turbulent Boundary leyer at High Subsonia Speeds Tne experimental values of local skin ?riotion coefficient Gg measured by the skin friction instrument are shown in Fig. 16. in computing the skin friction cvefficiont and the Reynolds mimber, free stroan Valuos of density and viscosity have been used. As seen the experimental points lie quite olose to (but definitely below) the curve for incompressible flow, showing thet the ‘effect ef compressi-~ bility in the range of Mach numbers up to BH = 0.8 is quite amall but in the expected direction. The experimental seatter is of the order of © 5% abowt the moan. Ag briefly mentioned before, the effect of heat transfer on the skin friction was found to be quite importent. Guantitativa 47 measurements of this effect were not possible with the present equip- mont, bub in general the following was observed: If after equilibriun conditions had been attained in the Wind tumel the stagnation tem- perature in the settling chember wes lowered, the skin friction read- | ing showed & warked increases. The magnitude of this increeasa seened to depend on the rate of heat trenefor for it eould be controlled te — some extent by controlling tho rate of cooling of the air in the settling ehember of the tunnel. Roughly speaking (for no precise measurements could be obtained), during the period of heat transfer ' the skin friction changed by about 50% of the steady state (zero heat transfer) value. Raising the stagnation temperature resulted in lower skin friction readings. On roattainaont of steady conditions, the skin friction alwnys regained its zero heat transfer value. As indi- gated by these observations, tho resultant effect of heat transfer from or to the flat plato is the opposite of what one sxpects fron theoretical considerations. Ho explanation has been found for this enomalous behavior. 4 Laminar Boundary Layer Measurements | a hae beon mentioned before that due to experimental diffioul- ties it was not possible to obtain laminar boundary layers of suffi- ecient extent without favorable pressure gradients, There are several reasons for thie. “Laminer bounde ry layers are notoriscusly soneitive to loading edge conditions. For supersonic flow measurements it is necessary te usc the type of “half-wedge” leading edge employed in the present experiments (soe Ref. 23). This type of leading edge is not vary suitable for subsonic work, for it requires the stagnation point to be on the side of the eur face of measurement, In the present setup this would require the flat plate to be ot a relatively large pesitive angle of attack. This wee not feasible. Por the case of supersonic flow with an attached bow wave this difficulty would ba obviated (actually, in the supersonic flow measurements other effoots prevented any reliable measurements of akin friction with laminar boundary Layora : seo Peg 59). 4&5 an alternative for obtaining Lemi- nar boundary Layers on the flat plate, a special attachment wee sade for modifying the nose shape. 4s seen in the eocompanying skoteh, this served the earlier mentioned purpose of fixing che stagnation . | Circular Aros Nose Attachnent [ | \ a - \ aneurin Surface Stagnation Point of Flat Plate point where desired. With this attachment laminar boundary leyers could be obtained on the fiat plate at low subsonic Hach numbers {about Ho = 0.3). At higher subsonic Mach numbers, however, the dis- turbance caused by the joint between the nose attachment and the loading sdge of the flat plate wag suffioient to cause transiticn ahead of the point of measurement. In spite of all efforts to min the joint smooth, laminar boundary layers sould not be maintained past the force element. The only way laminar boundary layers sovld be ob- tained with this oonfiguration was with the help of stabilising pros- - gure gradients in the direction of flew. The favorable pressure a sama” ao gradient was produced by altering the shape of the wind tumnel well opposite the flat plate with the help of e tapered hardwood blook. The scheme is shown in the aceompanying sketch. The pressure grad~ ients prevailing over the flat plate were then meesured for each Mach } Tunnel Ceiling Skin Priction $ al tastremont —~- Flow — Rardwood Bleek Tunnel —\ Floor ~~f rmumber at which the skin friction was measured. Representative pres= sure distributions om the flat plate are shown in Pig. 20. The slcin friobion poasurexonts are presented in Fig. 16, As a point of inter- est, the skin friction coefficients aro also shown after ‘epproximtely allowing for the measured pressure gradient; these points are seen to | be approximately 15% above the Blasivus curve for M= 06. Ths = affagt cnaleviation was carried out in a manner similar to thet for the turbulent case. Although these messurenents cannot be used for comparison with the cases computed by theory they are believed to be ef soma value. It will be noticed that in spite of the lars devia- tion from the condition of sero pressure gradient and the orudo method for allowing for preasure gradient effeet, the experimental values follow the general trond indicated by laminar boundary layer theory ronsonably closely. 5. Transition Measuremnts During the attempts te preduce laminar boundary layers a few measurements of skin friction were mde with transition to turbulent flow ocsurring on the flat plate. {> the author's Inowladge direct measurements of local eidn friction in the region of transition have . never been reported. The measurements presented here are guite quali~ tative and do not conclusively demonstrate any results. These meas< urements were made under conditions of negligible pressure sradiants with the flat plate leading edge adapted for laminar flaw (see page 48). Schlderen observation of the boundary layer showed that at low Hach numbers (about 0,25) the boundary leyer was leminar from the leading edge up to approximtely a distance of one contineter past the force element. The corresponding skin friction was quite close to the Blasius ourve for ineompressible Flow. Increasing Mach nunber (end hones the Reynolds mumber) had the effect of rapidly increasing . . the skin friction wrtil et about M = 0,6 the measurexents approached the turbulent values. At the sams time the appearance of the bound- ary layer in tha neighborhood of tha point of measurement could be seen to change gradually from the typical thin, sharply defined lani- nar boundary layer to ea thicker end less sharply defined turbulent one. Thess moasurements are showm in Pig. él. A little reflection will show that the prise in local skin friction as measured by the instriment and indicated by Fig. 21 cannot be explained even quali- tatively by the concept of steady transition at a critical Reynolds number, even if one considers transition to cocur over a rerion and F) 6 Sl and not at a point » One reasommble explanation may be edvanoed if - the transition phenomenon is regarded ag the result of a statistical | apposrance of turbulent spots. This point of view, that is, thet there, ig no "transition boundary layor™ but that the observed transi- tion region consists of internittently occurring laminar and turbulent flow, was first mentioned by Dryden (Ref. 2¢) and further substan- ‘tated by Liepmann - (Ref. 25). The occurrence of transition from this ‘viewpoint has recently been discussed by Professor E. W. Emnona of ‘Harvard University, whe related the interaittent transition phenomencn to Charters* contamination and developed from there a phenomonological theory of the transition sone. Turbulent spots occurring in a random fashion my be regarded to ba always present in any type of flow, In fully developed turbulent flow the probability approaches unity, With this picture of transition the following explanation of tho present measurements seems to ba plausible. When the fores clement ia in leminar flow there are hardly any turbulent "bursts" in the flow and “4f there aré, the chanoes of one trevelling across the element is exe ocedingly omall. Ag ‘the Reynolds nunber increases the rate of anpeoar- ance of the turbulent spots ahead of the slement increases rapidly and with it the number passing over the force éslement, Due to the considerably higher shearing forces associeted with turbulent motion, the instrument indicates grenter skin friction. It my be nontioned thet during the transition measurements reported here the readings of tho instrument were quite steady and repeatable. This is to be ox~ pected since duo to the inertia of the force olemont and linkage, tho instrument rendings would not follow rapid fluctuations but indicats an average. 6. Measurements in. Supersonic Flow (H = 1.24 to B= 1.44): Due to experimental difficulties it was possible to mke measure~ | ments of skin friction in supersonic flow only for the case of cur- - bulent leyers. Since lesiiner boundary layers could not be consia- | tently nainteined over the measuring element, no measurements of laminar skin friction at supersonic speeds are reported here. The ._ inability to maintain leninor boundary layers over the flat plate way due principally to the > et ‘Size of the wind tumel and does not re- ‘flest in any manner on the skin friction instrument. | ‘Byen in the cage of the turbulent: boundary layer measurements. the range of supersonic Hach number's with attached nose shock wave on the plate wos Limited to M& 1.87 to HE LAs. Below about M = 1.38 a detached bow wave formed ahead of the leading edge, The flow eon figuration in the neighborhood of the nose with a detached ahook WEVS was such that an expensian occurred sxound the leading edge followed | by a compression shook. Fig. 22 ie a spark Schlieren of this config- uration. The second compression shook wave near the leading edge of the plate is due to the 0.005" diameter wire used as a trip for the — “boundary layer, That there were no sudden changes caused in skin frlotion due to the bow wave dotachnent may be seen from Fig. 28 where the skin friction measurements are shown in the form of ratio & Cy ‘ Cf, the incompressible value for the same Reynolds mumber. Some of where C,; ig the local measured skin friction coefficient and the subsonic measurements ure aleo show on the same figure. During comes the measurements in supersonic flow shown in Fig. 23 it was not possi- ble to obtain conditions of zero pressure gradients in the direction of flow. The Mach number distribution over the plate departed from the required uniforn one to such an extent as to render. the results quite umreliable for comparison with theory. Harman's surve for ture bulent skin friction in compressible boundary layer over a Flat plate ‘ig included in Fig. 23 only for the sake of interest. Although the experimental points lie quite close to this curve, Lt cannot be gon- eluded that compressibility lowere the local skin friction coefficiont by an amount given by Kermen'e empiricel ourve. ‘The siin friction measurements presented do, however, represent the actual surface shearing forces present under the conditions of measurement. CONCLUDING REMARIS _ It has been shown thet an instrument for the direct measurement of local skin friction can be successfully developad if sufficient eare is taken. | Measurements of laminar and turbulent siin friction on a flat plate at zero angle of attack and low-speed flow gave excellent agreement with Blasius' and von Farman's skin friction laws respec- tively. . Moaouromonte of turbulent skin friction on a flat plate in hich- speed flow showed that for subsonic flow the skin friction did not depend much on Hach number though a slight, expected, decrense af Cy is noticoable. | | | The fow meaauroments so far mede in gupersonic flow (H ~ 1.4) ware taken in the prosence of a pressure pradient and honeo aro net “ag eagily and reliably compared with theory as are the other measure- ments reported here. The very notiesable decrease in skin friction is believed to be real. ‘The determination of exact quantitative velues, however, requires a thorough check under both conditions. i. 2. $. ae Be Ve. Oe 20. li. 12. 65 “ee von Karman, Th.: The Problem ef Resistance in Compressible: Fluids. Proce Volta Songress, 1086. Frank and Yoishel: ‘turbulent Friction in the Boundary Layer of a Flat Plate in a get neta Tr Compressible Plow at t Eigh Ferrari, Ces study of the Boundary Layer at Supersonic sposde in Turbulent Flowi Case of Flow ee a Flat Plate. Quarterly _ of Applied Yethomatias, Vol. 8, Ho. 1, 1950. You Driost, EB. Ret Turbulent ‘Boundary Layor an dempronetbie ‘Lh, Te Ye and Kigonateu, H. Tet Effects of Density Fluctuations on the Turbulent Skin Friction of an Insulated. Flat Plate at. _ High Supersonic Speeds... To appear shortly in Jour. 4ero. Sod. 8 Fage, Ae and ‘Townend, H. G. Bet Examination or Turbulent Flow ; with an a Uliramicroscope. _ Prove: Boys Boas London, Kerten A, Vols Young, A, Dy and ens, J. Hei The Behavior of a Pitot tube in & Transverse Total Pressure. Gradient. ARC Technical Report, R. end Me 2770, 1957. - Page, A. and Sargent, Re Pat - ace awe ‘ant Boundary Layer Phe- nomenon Hear a Flat Parteoes . Frogs: Roy. Boos ‘Tandon, Series A, Rovagensy, Le §. Ou The Robes J Anemometer in buperecnie Flow. Jou, Acro. Sol., Septenber 1060, 00 Gooderum, P. Be, Wood, @ P. and Brevoort, Me ‘Sst “Investigation ; with an Interferomter of tho Turbulent Hiscing of e Froe Super~ sonic Jet. NACA T.M. 1857, 4pril 1968. Ladenburg, R, and Wachtel, Ge Des Further Interferometric Studies of Bouxlary Layer, Along Flat Plates, Palmer Physical laboratory, Princeton University Report, Contract Ho. R7 our 599, Ded. 1949. ~ Blue, Re Fes Interferoncter Corrections and Measuremonte of . laninsr Boundary Layers in Supersonic Streams. RACA T.H. 2110. . ‘Aghkenas, H. I, and Bryson, A. Ee: Design end Performance of a Simple Interferomoter for Wind Tunnel Measurements. dour. Acide. Sei,, Yol. 18, Ho, 2, Feb. 1081. : a, 18. is. 17. i8. 19. 20, | ‘Ble 22. 24. Charters, A. C.t Transition Between Laminar and Turbulent Flow by fransverse Contamination. ACA T.H, 891, Merch 1045. Bershader, Dy: An Interferometric Study of Supersonio Channel Flow, Review of Solentific Instruments, Vol. 20, Ho. 4, 1949. Ladenburg, Re end Bershader, D.: Interferometric Studiss on laminar end Turbulent Boundary Layers Along a Plane Surface in) Swoersonic Velooities. U.S. Neval Ordnance Laboratory Report Ho. 1138 (Symposiun on Exporimental Compressible Flow) May 1060. von Karman, Th. and Teien, H. 8: Boundary layer in Compresai- ble Fluids, dour, Aero, Sole, April 1958. von Farman, The: Amplogy Between Fluid Frietion and Heat Trans~ Per. Prone. ASME, 1059, Ludwieg, H.: Ein Gerat sur Mesesung der Vendschul spannung que polenter Reibmgsschichten. Inge-Arch. Aveileble as NAGA T if. * ‘ Schulte-Grunow, Fes’ Roues Reibungswideratandegesets fur Glatte Platten. Larerahrforschung, Voi» 27, No. 8, 1960. Avelable es NACA &.M. 986. Dhawan, 5. and Roshke, Avs A: Flexible Hogzle for a Small Super- gonio Wind Tunnel» Jour. Aords + Scie, Vol. 18, ppe 2536258, April A961. , Emons, He Wo: The Leminar « furbulent Transition in a , Boundary Layer (Part I), sours Aero. Sol. 1961, ° Bumons, H. W, and Bryson, A. E.: The Leminar - Turbulent Transi~ tion in a Boundary Layer (Part II), First U.S. Netional Congress of Applied Mechanies, Chisago, T1l., 1951. Ldepmann, He We, Roshlo, A. and Dhawen, S.: On Reflection of Shock Weve from Boundary Layers, HAGA T.N. 2334, April 1951. Dryden, Hes Air Flow in the Boundary Layer Near a Plate. HAGA FoR. B62. ; Liepmann, H. W.: Investigations on Leminar Boundary Layer Sta- ‘bility and Transition on Curved Boundaries. NACA Wartime Report Wal07 (declassified). Laminer Boundary layer , M # 1.4 Pigs 2 : Flow from Left to Right furbulent Boundery Layer MS 1.4 Pig. 2 Effect of Slots in Plate (Arrows Indicate the Position of Slots) 58 VELOCITY PROFILES ON FLAT PLATE WITH TURBULENT BOUNDARY LAYER AND SLOT Ry= 410% R, = 1000 ee ae 0 4a Pe te B=- 1.05 cm. | -0.55 cm. ~0.20 cm. cje (6) CM. +0.25 cm. +0.75 cw. eo o e oo — | b-_— X =10. . | X= 10.3 cm =i $=0.25 cm. = Luo FiG. 3 Ow Oteg' 38 O05 8 ——_ 0 7 59 7" pe—— _L. —___») 16 PRIMARY wa Z, RS | MAGNETIC ———ae a NON ~MACNETIC SPINDLE b--—4 LEADS ouTPUT SECONDARIES DIFFERENTIAL TRANSFORMER FIG. 4 OUTPUT VOLTS | | | | MINIMUM | | PORTION OF CURVE USED POINT — \ | ] | i -007" ie) .007" CORE DISPLACEMENT SKETCH OF OUTPUT CHARACTERISTICS OF DIFFERENTIAL TRANSFORMER FIG. 5 vV.T. VOLTMETER ™ OSCILL a, 20,000N a [~~ / > ene 7 | [ input \ 3 : OUTPUT \ CONSTANT VOLTAGE > 4 \ ~~ TRANSFORMER plex up V.T. VOLTMETER CIRCUIT USED FOR SKIN FRICTION INSTRUMENT FIG. 6 60 NO\LOIGI NIMS JO “WIS Z£ °9O!4 LINSNSYXNSV3AW LOSYIO YO LNSWAYLSNI JO HOL3YS LHOISM NOILLVYgIV> > M014 LN3N313 3904 _\ r~“—— wa 2'O ae a ae Kc, a hac gurthnne lh io AaMIN 4 NONLVYaINVO SZ SYNIT. 3YNX3I4 N\ ‘ 7S om WN Zaye 1v714 a O13)HS a GNIM LLL ZONITI32 T3BNNNL [ SM3YDS ONILSNOy “— 3g09 YSWYXOASNVYHL JTIBVIYVA 61 EFFECT OF VIBRATIONS ON CALIBRATION OF SKIN FRICTION INSTRUMENT 700 600 ©- 500 a) = & 400 ~ ° 0 — = = § o to 300 a— Q wa 4 200 —o- © STATIC CALIBRATION @ DYNAMIC CALIBRATION VIBRATION FRENQUENCY + 25 Y/s 100 o T | | ! om: 0 0.02 0.04 0.06 0.08 0.10 AV - VOLTS FIG. 8 62 CALIBRATION OF SKIN FRICTION INSTRUMENT 25 FORCE — MILLIGRAMS 20 0.0005 x INPUT — 5 VOLTS AT 20KC T, = 39.25 x AV DYNES /SQ. CM. + LINKS A © FORCE. INCREASING e FORCE DECREASING g 0 OO! 002 003 004 005 AV « VOLTS FIG. 9 006 63 CALIBRATION CURVE OF SKIN FRICTION INSTRUMENT 0.0!" x -_" STECL LINKS 16 To= 38.3 x10°x AV DYNES /SQ.CM. 1000 900 J 800 L WORKING RANGE MILLIGRAMS y 700 & fe) | nn © oO - 300 ya ® REPEATS 200 100 Ol 02 03 .04 05 Av ~ VOLTS FIG. 10 06 07 64 1) ‘Old TANNAL NOLLWTAHNOD (2x $2) LIOWS NI NOLLYTIWLSNI 3LWId Lv JO HO13vS ,LLLLLALLAALLALAALLAALAAAAAAAALL LAL LLLLLALLAL LLL ALLA LALA LO yools sownna_! MOTs Z2°ON 1°ON NOlLLYO07 NOILVDO7 ONIENS WAN ONIUNSW3N 3d0ud (WD 9S) ,22 SYNSS3IYd WILL WWD 9°82) Ea { a \ L AN3W3T3 39x04 av3H UA z,| | oe ul YSISWOYNDIN ul l | Lo —__ re eee sdou L_ n¥ _. QUSIHSONIM ONILYOddNs SLLLLL 2 La LLLLLLLLLL NLLLLLLLL x J a i TF: SENL-N TWOHOOTIW OL ANO SOWA WOYLD3ST3 ONINSD VWNNAL tI 65 ZI Old XAl pad ia) 8 d 9 G v c 2 fe) 0 3 NOISN3WIG I Zen. OW3H IWLOL »L100°0 I. ————— ° "0 alZoo'o fo nea 4 | © Li2¢ | ed o 7; - fete | i a | qe 41170 3903 ONIGVST Iv gg & ! te } sa O3ddidL YAW AYVONNOg gO 612 =" --e- sLNFTINGYNL ; ° / snisv7a — ° i sw6G=« = OLX Z'9. e % n fexa <OlXZO'E © YWNIAY7 “O79 | : fo) fa} SWo Ged = * {fovxeie ° ° / zal ,OIX L762 0 Tg 3S £0 “ 7 e LS fe gO [| _4 _ Wa Ol NO14 FIGISSAYDNOONI dive IWl4a NO S314d0ud HSAVT AYVONNOG 66 0002 008! 009] OO el Old ‘Oas/Wo = 9 vl 002 | OOO! 008 O09 Cov an A a am FIWd iv14d JO NOLLDST450 YO4s NOILLOSYYOD 2000 vOOO" 9000" 8000" 100° SINOA — AV 67 LOCAL SKIN FRICTION IN INCOMPRESSIBLE FLOW (M = Q) Ol | 8 6 BLASIUS _| i a 4 al ie Coe : Po Pw 7 v7 a KARMAN fe) ; ogo we ans) fo} @ aah 00l Sy ct) 8 re _ 6 4 «FROM PROFILE MEASUREMENTS o DIRECT SKIN FRICTION MEASUREMENTS © X = 28.6cM. a DIRECT SKIN FRICTION 3 MEASUREMENTS _X = 56 en. Rererel| 104 2 4 6 8 102 2 4 6 8 68 OL Og OS Ov OE O02 Ol 95 c9S=N | —la—# oo far OO aft fOY Cc IcB=N : TR oe coc Ses a —~ {Ol (e} Sool=n lo lo _+o-_— —_ oe tO or | oO een=n b> gee to OO J or 6b | “Vv fe) eo0el=n a ee . — O1 ; 10] Besi=N ot . 2s a re Ol Q ‘236/SM26 1791 = L ' ro or | | MO 1s 3 1gISSSYdAWODNI Sividd Iv14d V NO SNOLLOGIMLSIG SYNSS Sud x QIXQE OIXO7z Baixo QO!1000' Or looy tov OY OslO00’ L \ jOZzZOO)” ‘ YaAV7 AYVONNOG YVNINYT OveZ000 IN3ICVeD SenSSsed YC4 NOLLDSYYOD 69 Ot O14 XY Legis 6 + z Qleereas » € z rae] (INSIQVYS BYNSS3ud YO4 G3LIIVYOD) YaAV ANVONNOG YYNINWT = ® CLN3IOVYSD 3YNSS3Yd 3AILWO3N) YIAVT AHWONNCA YWNINVT oO (LNZIGvV¥o 3yuNSS3¥d ON3Z) Y3AV7 AMWONNOG LNIINBYNL ° a snisw1a e (O=W) YVNINVT le P 4h pS dial Sui” AilM 0 dI¥L 3YIM LNOHLIM @ NYU S350 30S HAM © 7 ERR 0 221% |, (O=W) LNA TINGYNL i rs p= | (g'0 OL ZO=W JONVY YSGWAN HOVW) MOTs OINOSENS N Sivd Iv14s V NO NOILLOldd NS TWW207 Oennreo 70 TURBULENT BOUNDARY LAYER VELOCITY PROFILES ON FLAT PLATE cle 0} @, oe ra “s) e Y o ° oO @ (e) ° ®2 M=0.4I, R=69xI0° ® M= 0.635, R=94xI0° ° M= 0.795, R= 1.08xI0° I/7 -cl(X% —pyrc (S) 2 4. 6 8 To) 12 14 r=) 71 REPRESENTATIVE PRESSURE DISTRIBUTIONS ON FLAT PLATE WITH TURBULENT BOUNDARY LAYER SUPERSONIC FLOW — FLOW | 0.1 oa] = q 0 ae oe -0.! 3 2 O l 2 3 | xX ems. FROM ELEMENT on , q M=0.52 -Oll 3 2 l 6) l 2 3 | X ews. FROM ELEMENT | Ol ——o__] TO ee ee Oe nena M=0.34 -0.1 3 2 0 | 2 3 Xemus. FROM ELEMENT FIG. 18 72 TEMPERATURE RECOVERY ON FLAT PLATE WITH TURBULENT BOUNDARY LAYER ZERO HEAT TRANSFER im 1.0p- SS ee ep eee eee co) re) ° O° Tw To 0.9 °o EXPERIMENTAL V3 o-l yao Tw, t+ Pa) “ESM To 1+ iy M2 | 0.8 07 : — (0) O.l 0.2 0.3 0.4 0.5 0.6 0.7 0.8 MACH NUMBER FIG. 19 73 REPRESENTATIVE PRESSURE DISTRIBUTIONS ON FLAT PLATE WITH LAMINAR BOUNDARY LAYER SUBSONIC. Fl OW ~ FLOW a oh Me= . be +. 0.68 , i ee -O <) 3 2 | ‘@) | 2 3 X ows. FROM ELEMENT M=.375 [-O—-—5___] = 0 CO a -o1 + 2 | omn | 2 3 X cms. FROM ELEMENT 0.1 Ap 0 eee eee M= 0.48 -O. | ‘3 2 |. 8) | 2 3 X cms. FROM ELEMENT FIG. 20 74 TRANSITION ON A FLAT PLATE M+0.24 TO M+0.6 0.005 -— We {oma te 0.004 == TURBULENT Pape 0.003 zo ° 0.002 5 . [) 0.001 J bp LAMINAR | o PAY (M=0) PA ‘_ TN 0.0005 ms 3 4 5 6 7 89g L§ 2 2.5 2xio§ 10° R ate 6 oe de , Vik Fla a uv low Pas & f G4 eren Photograph of a 3 che Sehi3 76 EFFECT OF COMPRESSIBILTY ON LOCAL SKIN FRICTION ON A FLAT PLATE TURBULENT BOUNDARY LAYER REYNOLDS NUMBER # 106 L2 I (oe) le] Ong oo Q wel Xx ° -——— —~I9 ° oP ° lo ° ° so. _| , \ , a KARMAN | M=0 Wi . NOSE SHOCK Co _| Ge KARMAN DETACHED 8 | —-——~__] COMPRE Ce ssiple NOSF SHOCK y ATTACHED 06 0.4 0.2 °5 0.2 0.4 0.6 0.8 1.0 l.2 1.4 16 18 20 FIG. 23