1、E FI LEcOPNATIONAL ADVISORY COMMITTEEFOR AERONAUTICSiITECHNICAL NOTE 3391FREE-FLIGHT MEASUREMENTS OF TURBULENT-BOUNDARY-LAYERSKIN FRICTION IN THE PRESENCE OF SEVERE AERODYNAMICHEATING AT MACH NUMBE_RS FROM 2.8 TO 7.0By Simon C. Sommer and Barbara J. ShortAmes Aeronautical LaboratoryMoffett Field, Ca
2、lif.#- -Washinc_onMarch 1955.r._21_JProvided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-NATIONAL ADVISORY COMMITTEE FOR AERONAUTICSTECHNICAL NOTE 3391FREE-F
3、LIGHT MEASIrREMENTS OF TURBULENT-BOUNDARY-LAYERSKIN FRICTION IN THE PRESENCE OF SEVERE AERODYNAMICHEATING AT MACH NUMBERS FROM 2.8 TO 7.0By Simon C. Sommer and Barbara J. ShortSUMMARYExperimental measurements of average skin friction of the turbulentboundary layer have been made on free-flying, holl
4、ow-cylinder models atMach numbers of 2.8, 3.8, 5.6, and 7.0, at conditions of high rates ofheat transfer. It has been found that for these high heat-transfer con-ditions, the ratio of skin friction to incompressible skin friction isapproximately 35 percent higher than zero-heat-transfer wind-tunnel
5、dataat Mach numbers of 2.8 and 3.8. Although no measurements of skin fric-tion have been made at zero-heat-transfer conditions at very high Machnumbers, the data of the present investigation indicate that this sametrend of increasing skin-friction ratio with increasing heat-transferrates will persis
6、t at Mach numbers as high as 7.The Rubesin and Johnson T method of calculating skin friction forlaminar boundary layers has been modified and compared to the data ofthis investigation and existing wind-tunnel data for conditions close tozero heat transfer. It has been found that values of skin-frict
7、ion ratiocomputed by this method agree well with the experimental values over awide range of Mach numbers and heat-transfer conditions.INTRODUCTIONThe present state of knowledge of the skin friction of turbulentboundary layers at supersonic speeds is primarily guided by the experi-mental data that e
8、xist. These data are fairly complete for conditionsclose to zero heat transfer at Mach numbers up to 4.5 (refs. i and 2).Unfortunately, there has been little experimental investigation of theeffects of heat transfer and further increases in Mach number on skinfriction. Theoretical estimates generall
9、y agree that skin frictionincreases with increasing heat transfer from the boundary layer to thewall, and decreases with increasing Mach number (e.g., refs. 3 through 7),but are not generally in agreement quantitatively. Since heat-transferrates will probably be large under conditions of free flight
10、 and sinceflight speeds of interest extend well beyond a Mach number of _.5, aProvided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-2 NACATN 3391program was initiated in the Amessupersonic free-flight wind tunnel tomeasure skin friction of the turbulent bo
11、undary layer under conditionsof large heat transfer and to extend the Machnumberrange for whichskin-friction data are available. The results of this investigation arereported herein. ISYMBOLSACDCDtCdtCFCF iCFLcmCpHhkmLMPratio of that part of the trip drag which results in removingCdtmomentum from th
12、e boundary layer to the total drag, - (seeCD Appendix B), dimensionlesstotal-drag coefficient, dimensionlesstrip-drag coefficient, dimensionlesscoefficient of that part of the trip drag which results in remov-ing momentum from the boundary layer (see Appendix B), dimension-lessaverage skin-friction
13、coefficient, turbulent flow, dimensionlessincompressible skin-friction coefficient, turbulent flow, dimen-sionlessaverage skin-friction coefficient, laminar flow, dimensionlessspecific heat of model materialj Btu/ib OFspecific heat of air at constant pressure, Btu/ib OFaverage heat-transfer coeffici
14、ent, Btu/sec sq ft OFwall thickness at base of model_ ftthermal conductivity of the_model material, Btu/sec sq ft F/ftlength of run of turbulent flow, ftlength of model, ftMach number_ dimensionlessstatic pressure, ib/sq ftiPreliminary results of the present investigation have been pre-sented in ref
15、erence 8.Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-NACATN 3391 3qRRb,RcRDrS$IStTTituXYYl_n5base pressure, ib/sq ftdynamic pressure, ib/sq ftReynolds number based on model length, dimensionlessReynolds numbers used in determining incompressible
16、skin-frictioncoefficient, dimensionlessReynolds number based on pipe diameter, subsonic pipe flow, dimen-sionlessradius of model from axis to wall center, ftsurface area, sq ftSutherland constant, ORStanton number, H . dimensionlessCPl01Ulabsolute temperature, ORinitial temperature of the model, ORt
17、ime, secvelocity in the x direction of air in the boundary layer, ft/secaxial distance, ftradial distance, fthalf-wall thickness, ftthermal diffusivity of the model material, km sq ft/secCm-_,YlHpositive roots of _ tan _ = - (values tabulated in Appendix IV,ref. 24), dimensionless kmboundary-layer t
18、hickness, ft boundary-layer momentlun thickness, Pl ul ulcoefficient of viscosity, ib sec/sq ft0 density of air, ib/cu ftProvided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-4 NACATN 3391_m density of the model material, ib/cu ftSubscriptsoiwExcept where
19、otherwise defined, the following subscripts apply:free-stream conditionsconditions at the outer edge of boundary layerconditions at wallSuperscriptconditions at which incompressible flow relations must be evalu-ated in order to represent compressible flowEQUIPMENT AND TEST CONDITIONSSkin friction wa
20、s obtained from measurements of the total drag ofspin-stabilized thin-walled tubes of the type shown in figure i. Testand tare models, identical except for length, were gun-launched underthe same conditions, and total-drag coefficients were computed fromdeceleration data. Deceleration of a model was
21、 computed from its time-distance history which was recorded by a chronograph and shadowgraphs(ref. 9). The difference between the total drag of a test model and thetotal drag of a tare model is, except for small corrections, a measureof the average skin-friction drag of the added length of the test
22、model.This tare-drag method of obtaining skin friction and this hollow-cylindermodel configuration were chosen because only small corrections -wererequired for the evaluation of skin friction. In addition, direct cor-relation could be made with flat-plate results inasmuch as the flowclosely resemble
23、d two-dimensional flow (boundary-layer thicknesses weresmall compared to the radius of the cylinder).Models and Model LaunchingThe models were made of 73 S-T aluminum, with 1.44 inches outerdiameter and 0.030-inch-thick walls. The outer and inner surfaces werepolished with successively finer polishi
24、ng papers, the last being 4/0polishing paper. The finish of some typical models observed with aninterferometer (ref. i0) showed the magnitude of the peak to valleyProvided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-NACATN 3391 5roughness to be approximat
25、ely 20 microinches; however, the root-mean-square height of the surface irregularities would be considerably smaller.Three nose contours, a double wedgewith a half-angle of i0 , a doublewedgewith a half-angle of _5, and a circular-arc profile with a tangenthalf-angle at the tip of 20 , each having a
26、 leading-edge thickness lessthan 0.001 inch were used. Boundary-layer trips (fig. 2), used through-out to promote turbulent flow over the surface of the models, will bediscussed later.The test models were 2.0 and 2.5 inches long. Tare models were 0.5inch long. Longer test models were desired to prod
27、uce a higher percentageof skin friction to total drag, but the model lengths were limited by twofactors. At the lower Machnumbers_the model length was limited to 2.0inches to prevent the shock wave from the leading edge from impinging onthe inside of the cylinder wall and causing interference with t
28、he boundary-layer flow. This limitation was of no consequenceat the higher Machnum-ber because of the smaller shock-wave inclination angle, but models over2.5 inches long failed structurally due to extremely high accelerationloads encountered in the gun.The models were launched from a standard 37-mm
29、rifled gun, the twistof the rifling being one turn in three feet corresponding to a helixangle of approximately 7.5 . The models, which were approximately 0.02inch smaller than the land diameter of the gun, were protected from therifling by plastic film wrappers which broke away from the models asth
30、ey emergedfrom the gun. A rifled aluminum disc, used to produce spin,was followed by a Neopreneseal which prevented powder gas leakage. Atest-model assembly is illustrated in figure 3- Muzzle velocities of3200 and 4400 feet per second were obtained by varying the powder chargesand resulted in peak a
31、ccelerations of 130,000 and 250,000 gs on themodels. The structural failure mentioned previously was observed onmodels 2.5 inches long at accelerations above 300,000 gs.Test ConditionsTests were conducted at nominal Machnumbersof 2.8 and 3.9 by fir-ing through still air at one atmosphere pressure wh
32、ere the free-streamstatic temperature was equal to ambient temperature. A nominal Machnum-ber of 7.2 was obtained by firing upstream through a Machnumber2 airstream where the free-stream 2 static temperature was about 56 percent ofthe ambient temperature. She free-stream Reynolds numberrange for the
33、tests was from 3xlOe to 9106 was usedin equation (2) to obtain results for comparison with the data.Colburn (ref. 19) and McAdams (ref. 20) have shown that if viscosityis evaluated at a film temperature (equivalent in purpose to the presentT), Tf = 1/2 Tw + 1/2 TI, the skin-friction equations for ze
34、ro heat trans-fer in smooth pipes could be applied to flow with heat transfer. TheDrew, Koo, and McAdams equation (ref. 19),CF : 0.0014 + 0.125 RD -s2 and the Karman-Nlkuradse equation (ref. 21),!= 2 logio(RD 4_-4_F)-0.8Jf cFProvided by IHSNot for ResaleNo reproduction or networking permitted withou
35、t license from IHS-,-,-NACA TN 3391 19were both evaluated at the film temperature, as defined above. The Drew,Koo, and McAdams equation, and the K_rm_n-Nikuradse equation gave resultsat RD = 105 that differed very slightly from the results of equation (2).Skin-friction ratio, as determined from equa
36、tion (2) agreed well with theexperimental skin-friction results of reference 21 and was slightly higherover the entire range of wall-temperature ratios when compared to theheat-transfer results of references 21 and 22. It appears probable thatequation (2) can be used to predict skin-friction ratio a
37、t subsonic Machnumbers.Comparison of the T method with experimental results of refer-ence 23.- For Mach numbers above 4.5 there is very little experimentaldata available against which to check the T method other than the dataalready presented in the preceding sections of this paper. In fact, theonly
38、 additional data in this Mach number range known to the authors arethe data of reference 23. Unfortunately, these data are not for flat-plate conditions, being a set of measurements of the turbulent boundarylayer on a nozzle wall at Mach numbers of 5.0, 6.8, and 7.7. The valuesof local skin-friction
39、 coefficients and the corresponding values of localincompressible skin-friction coefficients were based_ in reference 23,on the same R e (Reynolds number based on momentum thickness). It wastherefore necessary for comparison with the present results to re-evaluatethe local incompressible skin-fricti
40、on coefficients so that the values oflocal skin-friction coefficients and the corresponding values of localincompressible skin-friction coefficients, cfi, were based on the sameR z (Reynolds number based on length of run of turbulent flow on a flatplate). The resulting expression for local incompres
41、sible skin-frictioncoefficient based on RI and derived from the K_rm_n-Schoenherr equa-tion iscfi =0.0293 0lg 1( cf/cfi )Ro cf/cfi )ROwhere Re and (cf/cfi)R e are the values given in reference 23.The experimental results in the ratio of skin friction to incompres-sible skin friction, cf/cfi , are sh
42、own in figure 13 and are comparedwith skin-friction ratio as determined by use of equation (2) for thetemperature conditions of the experiment. It can be seen that althoughthe data show no definite trends of the effect of heat transfer on skin-friction ratio, the level of the data is in fair agreeme
43、nt with theresults from the T method. The T method predicts a large changein skin-friction ratio between zero-heat-transfer conditions and condi-tions where the wall-temperature ratio is unity; however, for the heat-transfer conditions of the experiment, the T method predicts a rela-tively small cha
44、nge in skin-friction ratio. The measured changes inskin-friction ratio are, in general, of the same order of magnitude toProvided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-20 NACA TN 3391be expected from the T method; however, in some cases, the changes
45、are of opposite sign.Predicted effect of Reynods number on skin-friction ratio.- Thepredicted effect of Reynolds number on skin-friction ratio was investi-gated by evaluating equation (2) at standard isothermal altitude condi-tions, and using the procedure described previously. The effect ofReynolds
46、 number on skin-friction ratio at Mach numbers of 2 and _, atTw = TI and Tw = Tr_ is shown in figure lb. It can be seen that at aMach number of 2, over the wide Reynolds number range from 106 to lOS_that the predicted Reynolds number effect on skin-friction ratio issmall. In fact_ the magnitude of t
47、his predicted effect over the Reynoldsnumber range from 3106 to 30i06 is so small, less than 2 percent, thatit would be difficult to confirm experimentally. This prediction isconsistent with the results of Chapman and Kester (ref. i) where noReynolds number effect on skin-friction ratio was detected
48、 at Hach num-bers up to 3.6. At a Mach number of 8, however_ the predicted effectof Reynolds number on skin-friction ratio over the Reynolds numberrange from 3i0 e to 30xlO 6 is the order of 5 to i0 percent. Over theReynolds number range from 106 to i0s, the predicted effect is the orderof i0 to 25
49、percent. This analysis was made to caution the reader aboutthe validity of the assumption that skin-friction ratio is invariant withReynolds number. Since the Reynolds numbers encountered in high-speed,high-altitude fliht can be expected to be in the order of several hun-dred millions, the application of equation (2) with the ass
