1、j.I.1NATIONALADVISORYCOMMITTEEFOR AERONAUTICSTECHNICAL NOTE 3287HEAT TRANSFER FROM A HEMISPHERE-CYIXNDEREQUIPPED WITH FLOW-SEPARATION SPIKESBy Jackson R. Staider and Helmer V. NielsenAmes Aeronautical LaboratoryMoffett Field, Calif.WashingtonSeptember 1954.: :):,-L“.) .,!.1IttProvided by IHSNot for
2、ResaleNo reproduction or networking permitted without license from IHS-,-,-IEurllJJUItA-u,NM.JNAI101WLADVISORY COMMITTEE FOR AERONAUTI( IllnmllllllmmulOOhL23bTEC91?ICALNOTE3287HEAT TRANSFER FROM A HEMISPHERE-CYIJI!DEREQUIPPED WITH FLOW-SEPARATIONSPIKESBy Jackson R. Staider and Helmer V. NielsenTests
3、 were conducted to determine the effects on average heattransfer, average recovery temperature, and pressure distribution causedby attaching spikes to the front of a hemispherical-nosedbody of revolu-tion. The investigationwas concernedprimarily with a series of conical,-nosed spikes of semiapex ang
4、le 10 and length to body-diameter ratio 0.5to 2.0. In addition, the effect on heat transfer of capping the spikeswith flat disks and blunt cones of semiapex angle kOO was also investiga-ted at a Mach number of 2.67 and a Reynolds number of 2.85fio5.The range of investigationwas from Reynolds number
5、1.55 to 9.85x05(based on body diameter) and from Mach number 0.12 to 5.04.Although the tests confirmedprevious results which showed a reduc-tion of drag on attaching spikes to a hemispherical nose at supersonicspeeds, it was found that the rate of heat transfer is approtelydoubled regardless of spik
6、e length or configuration. It was also foundthat this increase in heat transfer is confined almost entirely to theforward half-area of the hemisphere. Average temperature-recoveryfac-tors are lowered slightly on the addition of spikes, decreasingwithincreasing spike length. At a Mach number of 1.75
7、the 2-inch spikereduced the recovery factor by 3 to 5 percent, depending on the Reynoldsnumber; at a Mach number of 2.67 the reduction was from 5 to 10 percent.For the hemisphere without spikes it was found that the Nusseltnunibersmeasured at subsonic and supersonic airspeeds could be correlatedas a
8、 function of Reynolds nuniberalone, provided the air properties wereevaluatedbehind the normal shock waves. Thus, it is possible to predictsupersonicheat transfer from a hemisphere by using subsonic data. . . . . . -. ._ _ . .Provided by IHSNot for ResaleNo reproduction or networking permitted witho
9、ut license from IHS-,-,-2INTRODUCTIONrNACA TN 3287nInterest has been expressed in the use of spikes protruding infront of blunt bodies as a means of reducing their drag. Mair (ref. 1)and Moeckel (ref. 2) examined, in some detail, the mechanism of flowseparation ahead of two-dimensionaland axially sy
10、mmetricbodiesequiFpedwith various length skes and found appreciable drag reduc-tions at supersonic speeds. ,In view of the drag reductions resulting from the use of spikes,it was apparent that informationwas needed concerning the effect ofspikes on heat transfer to blunt-nosed bodies. Consequently,t
11、heFresent investigationwas undertaken to measure the heat-transfer andrecovery-temperaturecharacteristicsof a hemispherical-nosedcylinderwith and without drag-reduction spikes over a range of Mach nunibersandReynolds numbers.NOTATIONA%Ddhk1MNuPQResurface area of hemispherical nose, sq ftpressure dra
12、g coefficient,dimensionlesspressure coefficient,drag, lbdiameter, ftaverage heat-transferthermal conductivity,spike length, fttiensionlesscoefficient,BTU/see, sq f%, %?BTU/see, sq ft, Ol?/ftMach number, dimensionlessNusselt number, , dimensionlesspressure, lb/sq ftheat rate, BTU/seevpdReynolds numbe
13、r, , dimensionless Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-NACA TNrTvQ7PPnorDm3287Tr - Tmtemperature-recoveryfactor, , dimensionlesso wtemperature, %? absvelocity, ft/secangle with the longitudinal axis of theratio of specific heats (1. for a
14、ir),viscosity, lb-sec/sq ft”mass density, slugs/cu ftSubscriptsconditions at the nose of the modelstagnation conditionsrecovery conditionsreferred to a characteristicdiameterfree-stream conditionsmodel, radiansdimensionlessDESCRIXTIONOF EQUWind Tunnelsused in the presentThree wind tunnels werefirst
15、was the Ames 6-inch heat transfer tunnel, a return-type, continuousinvestigation. Theoperation tunnel. It is described in detail in reference 3. The secondwas the Ames 10- by l the other was machined to form a cone of 10 semiapex angle.In order to avoid conduction of heat along the spikes, they were
16、 madeof Micarta which has a loy value of thermal conductivity. When thespikeswere not used, a small headless screw was used to plug theorifice in the model.Power to the heat-transfer model was suppliedby a 20-wattelectric heater made by winding Advance wire about a small threadedTransite cylinderwhi
17、ch was then fitted inside the hemisphere. Tem-peratures were measured by four iron-constantanthermocouples insertedin the nose within 1/16 inch of the surface at 90 intervals on acircle of 11/16-inch diameter concentricwith the axis. A fifththermocouplewas placed within 1/8 inch of the stagnationpoi
18、nt - asclose as was possible without breaking through to the central orifice.The hemispherical nose was attached-to the cylindrical afterbodyby means of a 2-1/k-inch-long,hollow, internal support shaft of stain-less steel, 3/8 inch in CLkmeter,which was passed through a l/2-inch-long, 7/8-inch-disme
19、terMicarta bushing threaded directly in the after-body. In order to determine the axial heat conduction, three thermo-couples were provided at equally spaced intervals along the axis of thesupport shaft. At the outer rhn of the hemisphere, heat conduction tothe stainless-steelafterbody was minimized
20、 by reducing the area ofcontactbetween these parts to less than 0.009 square inch. This wasaccomplishedby chamfering the internal edge of the afterbody to athickness less than 0.003 inch.For a second series of tests the hemisphere consisted of two sectorswhich divided the surface area into halves. T
21、he copper frontal sectorwas heated as befoye while the stainless-steelrear senentwas unheated.Heat flow to the latter segment was minimized by reducing the area ofcontactbetween the two sectors to less than 0.223 squ thesame tests for the frontal hal.f-sreaof the hemisphere; and pressure-distributio
22、n tests.Average heat-transfer rate and recovery temperature for the entirehemisphere were obtained by measuring the voltage and current to theheater, the body temperatures, and the stagnation temperature of thewind tunnel. All temperatureswere obtained with iron-constantanthermo-couples using the te
23、mperature of melting ice as a reference. They wereread on an indicatingpotentiometer. Measurement of support-shafttemperatures enabled the determination of the amount of heat leakagealong that meniber. During the initial tests, an air space of approxi-mately 0.002 inch was maintained between the nos
24、e and the cylindricalafterbodypreventing heat leakage h that direction. Later tests withthe nose firmly in contactwith the cylinaerqs chamfered edge revealedan increase in total heat leakage of less than 1 percent. All subsequentinvestigationwas therefore conducted with the nose and afterbody in fir
25、mcontact.For each physical configuration (differentlength of spike) thepower input to the heater was varied in six approximately equal stepsfrom O to a maximum of almost 20 watts. A typical correspondingrangeof nose temperatures (dependingon the Reynolds number) would be from50F to 160F.The phase of
26、 the investigation concernedwith obtaining average heattransfer and recovery temperature over the frontal half-area of the hemi-sphere was conducted in the same manner as the first phase. Because theheat path for conductionbetween the hemisphere sectors was very smallcompared to the heat path for fo
27、rced convection to the air stream, heatleakage between these sectors was neglected. . - . . _ -.Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-. . . .6 NACATN 3287Pressure distributionswere measured only at Mach numbers of 1.75and 2.67. When no spik
28、e was attached, the pressure at the stagnationpoint (q= O) couldbe measured tith the orifice then available at thatpoint. However, when spikes were in place, the first station availablefor measurement was at q = fi/12radians (15).The stisonic tests were conducted in the 2- by 5-foot duct, thesuperso
29、nictests at Mach nuuibersof 1.75 and 2.67 in the Ames 6-inchheat-transfer tunnel, and those at a Mach number of 5.04 in the Ames 10-by 14-inch supersonictunnel.Average heat-transferDATA REDUCTIONcoefficientsand average recovery tempera-tures were found from the equationQ = hA(Trby the method of leas
30、t squares using- Tn) (1)the six different sets of measuredvalues of Q and Tn found for the six values of power input. Anequivalent graphicalmethod is to plot Q/A as a function of Tn; theheat-transfer coefficient then will be given by the slope and therecovery temperaturewill be found at the intercep
31、twhere Q/A = O.Over the range of temperatures used in this investigation (” F to190 F), it was found that the heat-transfer coefficient,h, was inde-pendent of the nose temperature. Therefore, in the above-mentionedgraphicalmethod, the data points formed a straight line.In obtaining the heat transfer
32、 over the front half-area of thehemisphere, the same equations and the same procedure were used as forthe entire hemisphere. Both of these sets of results were then employedto calculate the heat transfer for the rear half of the hemispherebyuse of the equationNU2 = 2N - Nu= (2)The subscripts 1, 2, d
33、 t refer to the front sector, rear sector, andtotal hemisphere, respectively. This equationwas obtained from a simple “heat balance assuming that both seents have the same average recoverytemperature. The average recovery temperature can be defined as thetemperature assumed by the nose when the net
34、rate of heat flow to or fromthe nose is zero.The pressure drag of the unspiked hemisphere was calculatedly inte-grating the pressure distribution about the nose using the expression“Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-NACA TN 3287 7m/2D.d
35、2fP sin Q cos Tdq20The drag coefficientwas based on the projected frontal area of themodel and thus was calculated from3-(/24Cn= r P sin Q cos 9 dq(3)(4)2 doYpmMcuWhen spikes were attached to the nose of the model,integrationwas changed to exclude the frontal areatheoretical.pressure drag on a 10 co
36、ne as obtainedthe lower limit ofof the spike. Thefrom reference 5 wasadded to obin the totai pressure drag of the hemisphere-spike combina-tion. In all cases the skin friction along the spike was neglected.DISCUSSION OF RESULTS.According to Fage (ref. 6), the point of transition from laminarto turbu
37、lent flow in the boundary layer of a sphere always occurs on therear hemisphere at Reynolds numbers from 1.57x105 to 4.24x105. Sincethe Reynolds numbers of Fagels experiments correspond closely to thoseof the present tests (based on conditionsbehind the normal bow shockwave), the boundary layer on t
38、he unspiked hemisphere can be assumedlaminar.The experimentallydeterminedvalues of average heat transfer forthe unspiked hemisphere are shown in figure 2. It is to be noted thatwhen the air-stresmproperties are evaluatedbehind the normal shockwave, there is excellent correlationbetween the supersoni
39、c and subsonicresults of this expertient. Thus it is possible to predict supersonicheat transfer for this configurationfrom the subsonic dataJ-.Since the average heat transfer from a hemisphere cannot be corre-lated directly with that from a sphere (due to the phenomenon of separa-tion), only a limi
40、ted amount of data is available for comparisonwiththe present results in figure 2. There were three subsonic tests whichinvolved an identical experimental technique; namely, passing steamthrough a hollow sphere,balancing the temperature of a small indepen-dently heated plug to that of the remainder
41、of the sphere, and measuringthe power input to the plug, thus determining the local heat transfer tothe air stresm. The values thus found may then be integrated over thesurface of the front half of the sphere to obtain average heat-transfercoefficients.- - . .- -. .- . Provided by IHSNot for ResaleN
42、o reproduction or networking permitted without license from IHS-,-,-8(ref.%NACA TN 3287first of these tests was conductedby Lautman and Droegewho, in 1950, obtained Nusselt nunibersfor the front half of asphere which are approximately 50 percent above those obtained in thepresent experiment. Their w
43、ork, however, was supersededby that ofXenakis, Amermm, andhlichelson (ref. 8) who tested the same model(alongwith two other spheres of different dimensions)but improved theinstrumentation. The latter used values of the thermal conductivity ofair based on an average of the wall and air temperatures.
44、Therefore,it was necessary to adjust their Nusselt ners to free-stream valuesin order to enable comparisonwith the present work. Unfo thesecond was the use of guy wires which were attached to the supports justbelow the models. The effects of these methods of support on the airflow about a sphere are
45、 not negligible (ref. 9) and may easily contributeto an increase in heat transfer from the sphere.The third test was conductedby Cary (ref. 10) Who obtained localvalues about a sphere which, when integrated over the front half weapproximately percent below those obtained in this investition.The reas
46、ons for the great discrepancybetween Carys results and thoseof references 7 and 8 are not known and cannotbe determined from theinformation in reference 10. It is noteworthy, however, that a thin- shelled iron sphere was used instead of a copper one as in the othertests. The presence of a condensati
47、onfilm tithin this sphere wouldquite likely produce nonuniform surface temperatureswhich would greatlyaffect the heat-transfer data. ,.,Korobkin (ref. 11) presents experimentalresults obtained for ahemisphere-cylinderin a supersonicblow-down wind tunnel which arebelow those of this experiment. Howev
48、er, his data are admittedly inerror due to axial conduction of heat in the model. When his experi-mental data me corrected as described in reference 11, they are inessential agreementwith the preseht data. Korobkin also used unpublishedresults of Sibulkin to obtain e theoretical solution for local h
49、eattransfer about a hemisphere. When this is adjusted to the exact solutionat the stagnationpoint (ref. 12), it results in a curve of Nu#-li2about a hemisphere whi, when integrated, correspondsvery closely withthe present results.The reasons for the discrepancybetween the results of previous einvestitions is tifficult to establishbeca
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