1、NffCt050TiLIBP RY No. 1050R. HEAT TRANSFER OVER TEE CIRCUMI_F_RENOE OF A HEATEDCYL!ND_ iN _NSVERSE FLOi_By Ernst Schm_t and Karl WennerForschung auf dem Geblete des IngenieurwesensVol. 12, No. 2, _iarch-April 1941 / _ Z l:!wa shing ton_m_Ir_i_ I943Provided by IHSNot for ResaleNo reproduction or netw
2、orking permitted without license from IHS-,-,-ii-ZIProvided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-NATIONAL ADVISORY COMMITTEE FOR AERONAUTICSTECHNICAL MEIORANDUM NO. 1050HEAT TRANSFER OVER TEE CIRCUMFERENCE OF A HEATEDiCYLINDER IN TRANSVERSE FLOWBy
3、Ernst Schmidt and Karl WennerSUMMARYA method for recording the local heat-transfer coeffi-cients on bodies in flow was developed, The cylinder sur-face was kept at constant temperature by the comden_tion ofvapor except for a narrow strip which is heated separatelyto the same temperature by electrici
4、ty. The heat-transfercoefficient at each point was determined from the electric-heat output and the temperature increase. The distributionof the heat transfer along the circumference of cylinderswas recorded over a range of Reynolds numbers of from 5000to 426,000. The pressure distribution was measu
5、red at thesame time. At Reynolds numbers up t_ around lO0,00 highmaximums of the heat transfer occurred in the forward stag-nation point at 0 and on the rear side at 180 , while ataround 80 o the heat-transfer coefficient on both sides ofthe cylinder behind the forward stagnation point manifesteddis
6、tinct minimums. Two other maximums occurred at aroundll5 behind the forward stagnation point between 170,000and 423,000. At 428,000 the heat transfer at the locationof these maximums was almost twice as great as in the for-ward stagnation point, and the rear half of the cylinderdiffused about 60 per
7、cent of the entire heat. The testsare compared with the results of other experimental andtheoretical investigations.INTRODUCTIONWhile the following measurements on the distributionof the heat transfer along the circumference of cylindershad been made by the machine laboratory of the Danzig*“W_rmeahg
8、ab_ (bet den Umfang tines angeblasenen geheiztenZylinders.“ Forschung auf dem Gebiete des Ingenieurwesens,vol. 12, no. 2, R_arch-April 1941, pp. 65.73.Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-2 _NACA 2echnical _emorandum No. 1050Technical Inst
9、itute in 1935-33, their publication hadbeen held in abeyance p_nling their extension to stillhigher Reynolds nullbets, iieanWhile Krujilin (reference I)in 1938 published siuilar me_sure_Gents at about the sameReynolds numbers the results of w._ich are qualitativelyin agreement with our own experimen
10、ts. Hc too observedat high Reynolds nunlbers the markedly defined maximum ofthe heat transfer at ii0 to 120 behind the forward st_-nation point. But quantitatively there are considerablediscrepancies. At Re = 39,500 his reported heat transferin the forward stagnation point is 30 percent greaterthan
11、in our te_ts and at Re = 425,000 it is 35 percent.His valucs are too high by about the sane amounts comparedto the measurements of all the other observers whoseaverages are in good agreement with ours. The calculationof the heat transfer in the forward stagnation point ofcylinders by Squire (unpubli
12、shed b_t mentioned in “l_iodernDcve!opmcnts in Fluid Dynar.ics _t vol. 2, Oxford, 1938,p. 631) is also in agreement with our experiments.TEST iETHOD AND EXPERII,iENT- a is the heating ele_zent in form of a hollow,rectangular copper bar, housing the heating coil b.The thermocouplem c soldered to the
13、heating elementpass through pipe d to the outside, The hea_ing elementis so supported in box e by means of the pertinax strapsf as to leave between beth an isolating air space boundedby polished metal surfaces. The surfac9 temperature ofthe vapor-heated cylinder part is measured at four pointsg in t
14、ubing h along the circhmfcre_ce, soldered fromthe inside to the cylinder wall. The tubing h Passes _through the vapor chamber to a hole in the cylinder bymeans of which the prossuro distribution along the cir_cumference can be d_terminedo The vapor for heating thecylinder is fed tilrough tu_e i in s
15、uch aiounts thatalways an excess flows off thrQugh pipe k into a con_densator to prevent air from entering the vapor chamber.The electric heating of the copper bar is so ad-justed that it assumes the same temperature as the vapor-heated cylinder portion. The temperatures were recordedwith soft-solde
16、red manganin-constantan thermocouples of0.3 millimeter in diameter by means of a Wolff compensatoraccording to Diesselhorst. Four to six thermocouplesProvided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-4 NACA Technical Memorandum No. 1050each were employ
17、ed on both the copper bar and the cylinder.Originally all temperatures were measured against one coldjunction, but later on only the difference between theCylinder and :the copper bar was determined for simplicity,Where, n view of the small difference in this range thecalibration curve of the thermo
18、couples could be regarded “_s_ straight line with a slope 0.02126 C at O.001 -millivolt.2_eair-temperature was measured by a heat-resistant ther-mometer inserted laterally in the jet; it ranged between20 and 26 C in the different te_ts and _n one test wascons ta_t to 0.I .The hcating element can be
19、turned as indicated infigure 1 through any desired angle _p in respect to theflow direction by turning the whole tubeabout its axisand a graduated disk. By turnln- the tube the pressuretest station of tubin_ h is _oved with it and suppliesthe pressure distribution p over the circumference,The “outPu
20、t of the heatir_,z clement ascertained with pre-cision am_etcr and voltmeter gives the heat transfer ofthe part of the cylinder surface occupied by it. Halfthe area of the small gap filled with bakelite bet_eenheating clement awl cylinder is counted as heating _urfacc.The cylinder with the heating c
21、lement was mountedupright in the air stream of a rectangular nozzle of500 millimeters in width _,nd 250 millimeters in h_:i_.ht,an_ht. A. Betz ventilator with diffuser in a secondopening of the same wall pushed the air from the largerinto the smaller room from which it was returned throught_ic nozzl
22、e into the first. Stilling surfaces assureddisturbance-free air flow into the nozzle. In an earlierstudy with tl_e same nozzle arrangement Hilpert (reference2) proved that the employed nozzle gives _n air stream of.very uniform vclocity distribution. The flow velocity“ co_._.!d be varied between 2 _
23、nd 33 motors per second bymoans of the ventilator. To assure a fairly constant airstream with respect to time, the ventilator ._as.driven from two separate storage batteries_ one feeding the field,the other the armature, x_Cr addin_ an aopropriate number ofcells to the armature battery the rotationa
24、l speed in the_ri_ature circuit cO_Id be varied within wide limits with-o:,t variable rheostat _nd kept very constant.The airspeed was determined from the pressure dif-ference of the t_o rooms before and behind the nozzle andal_o _ith a Prandtl pitot tube.Provided by IHSNot for ResaleNo reproduction
25、 or networking permitted without license from IHS-,-,-NACA Technical Memorandum.No. 1050 5The pressure dfstribution on the cylinder circum-ference was determined by the cited orifice of 1 milli-meter, the static pressure Po in undisturbed flow andthe equivalent pressure of the test chamber, respecti
26、vely,into which the jet entered, serving as reference pressure.The pressures were recorded with a micromanometer filledwith xylol, calibrated by means of a Levy-type pressurebalance (reference 3), and supplemented at high pressuresby an Askania _Tater-column minimeter.EXPERIMENTAL CYLINDERSIThe cyli
27、nders were 50, 1O0, and 250 millimetersin diameter. The dimensions of the heating elements areappended in table I. The 50-millimeter cylinder wasfitted in the nozzle with its axis parallel to the 600-millimeter long nozzle edge; but in one test with Re =8290 it stood upright, that is, parallel to th
28、e shortedge of the nozzle.End disks of 250-millimeter diameter insertedperpendicular to the axis on the cylinder removed thedisturbing effect of the cylinder ends on the flow.The 100- and the 250-millimeter cylinder were mountedwith their axis at right angles to the longitudinaledges of the nozzle.
29、The 800-millimeter long exitedges of the nozzle were lengthened by flat plates ofcardboard through which the ends extended into the testcylinder The distance from cylinder axis to nozzle-exit opening amounted to 165 millimeters on the 50-millimeter cylinder and to 360 millimeters on the twoothers. F
30、igure 3 is a photograph of the setup showingthe nozzle a and the 100-millimeter cylinder b.Directly belo_ the electrically heated boiler for pro-ducing the vapor is indicated as thick cylinder cwrapped in aluminum foil, An estimate of the effect of the end disks per- _pendicular to the axis of the t
31、ube on the basis of theBlasius equation for laminar-boundary-layer thicknesson a flat plate gave at the lowest airspeed a thicknessof 0.75 centimeter. Since the ends of the heating ele-ments were always about 50 millimeters from the end disks,its effect does not extend as far as the heating element.
32、Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-NACA Technical _emorandum No. 1050TESTING PROCEDUREAND EVALUATIONAfter an initial run of the motor and after the airstream had become constant with respect to time, the heatoutput of the copper bar was
33、regulated so that its tem-perature in the steady state was the same as that of thevapor-heated portion of the cylinder surface. To savetime, small but constant temperature variations up to-_0.4 were at times tolerated during the adjustment,The small:_thermal Interchar. ge Q_ involved betweenheating
34、barand vapor-heated surface was obtained by:special calib-ration tests and applied as correction.The amount of heat diffused by radiationQs = Os?(Tw!lO0)“ - (TLflO0)must be deducted from the electrically measured heatoutput Qg.F radiating surface, tho.t is, the heat-diffusingsurface of the copper ba
35、r inclusive of half thebakelite-coated clearance space in square metersCs :-4.96 kilocalories per soua_e meter per hour (deg K)_,the radiation factor of the absolutely black bodyemission ratio of the polished copper surface, which.with consideration of tie more radiriting half ofthe clearance space
36、was appraised at O.10Tw = 273 + i00 temperature at the surfaceTL := 273 + 24 surrounding temoeratureTable II contains the effective quantities of theradiating surfaces of t.he heating bars and the valuesof the radiation-diffused heat quantities Qs for thedifferent tubes.Allowance for the corrections
37、 Q% and Qs theabsolute values of which range at small Re between0 an! 4 percent, at large Re between 0 and 3 percentof the he_,ting performance, affords the heat transfer= Qg-Q_-Qs of the heating element and thus theheat-transfer coefficient according to equation (1).Provided by IHSNot for ResaleNo
38、reproduction or networking permitted without license from IHS-,-,-NACA Technical Memorandum _o. 1050 7The airspeed follows from _ : _-2g AP/7. whereAP (kg/m a) is the pressure difference between pressureand suction space before and behind the nozzle, g =9.SI meters per second per second, the gravita
39、tionalacceleration, and 7 (kg/m 3) the specific gravity of air.In table III the individual values of the readings andthe results computed therefrom are given for a test onthe 10C-mi!limeter cylinder at Re = 39,800. (P-Po isdifference of pressure p at location _ of the tubecircumference and of the st
40、atic pressure Po in undis-turbed air stream,)Tile principal data of the tests are collected intable IV. The calculation of Nu and Re was basedon the planimeteredlaverage values of k = 0.0241kilocalories per meter per hour per degree Centigradeand D : 19.4 X 10 -6 square meters per second between2_ 0
41、 an_ i000 C. _RESULTS OF TESTSIn figures 4 to 6 the dimensionless Nu obtainedfrom the experiments arc shown plotted against the angle%o for different Re. Starting from the stagnation pointthe heat-transfer coefficient _ drops to a distinct minimumclose before q_ = 90 o and then rises again, which is
42、 soto much higher values as Re is greater.It is to be noted that the test points give the localaverage value of _ over the width of the heating bar.Hence at places whorc the heat-transfer coefficients plot-ted against qo have a minimum, th.e _urve of the localheat-transfer coefficient must extend be
43、low the meast_rodvalues and vice versa.The peculiar distribution is even plainer in thepolar diagrams of figure 7. At around _ = 115 dis-tinct maximums of the heat transfer occur for Reynoldsnumbers above 200,000, and which at Rc = 426,000 arealmost twice as high as in the stagnation point. Onthe re
44、ar of the cylinder at _ = 180 the heat-transfercoefficients for Reynolds numbers of from 25,000 to426,000 arc greater than in the forward stagnation_Oint.Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-8 NACA Rechnic_l i_emorandum No. 1050These pheno
45、mena._rc _ot known at the time of ourexperiments, since measurements of this nature at suchlare Reynolds numbers Vere up to then unavailable, al-though Krujilin had published simils, r results in 1938(reference i).In general, the measurements were limited to halftile cylinder circumference; but as a
46、 c:heck on the sym-metry several check masurements of the heat transferand the pressure distribution were carried out_over theentire circumference without, however, manifesting anysubstantial differences between both halves.The pressure distribution at dlferent Re meas,ured on the heated tube is giv
47、en in figure 8. TI_ominimum of the pressure distribution lies before the minimum of the heat-transfer coefficient indicated withAt Re between 180,00 and 400,000, that is, in_min“the so-called critical-resistance region in which themarked drop of the resistance coefficient occurs, theknown strong pre
48、ssure minimum is seen at _ closelybelow 90. The very small low pressure at the back isprobably attributable to the insufficient width of thejot compared to tube diameter. The jet is to some ex-tent split by the cylinder.Interesting para_llels arc obtained when the distri-bution of the heat-transfer
49、coofficibnt is compared wishrmcasurcmcnts of the shear-stress distribution on the-_allof a circular cylinder as made by Fage and Falkncr (refer-once 4) with a Stanton-t_pe_ _ exploring tube. Besides theheat-transfer-d_stribution together with the correspondingpressure distribution by our measurement
