1、cc)to03 7 - 1,TECHNICAL NOTE 2974EXPERIMENTS ON MIXED-FREE- AND -FORCED-CONVECTIVEHEAT TRANSFER CONNECTED WITH TURBULENT FLOWTHROUGH A SHORT TUBEBy E. R. G. Eckert, Anthony J.Diaguila,andArthur N. CurrenLewis Flight Propulsion LaboratoryCleveland, OhioWashingtonJuly 1953. . . -Provided by IHSNot for
2、 ResaleNo reproduction or networking permitted without license from IHS-,-,-TECHLIBRARYKAFB,Nil!rjouIlllmlfllu!llllulllhu13DbbJC14NATIONAL ADVISORY COMMITTEEFOR AERONWTICSTECHNICAL lWD3 2974lZXl?ERIMENTSON MZXED-FREE- MU) -FORCED-CONVECTIVEHFAT TRWSFERCOIJNECTEDWITH TWBUWNT FLOW THROUGH A SHORT TUBE
3、By E. R. G. Eckert, Anthony J. Diaguila, and Arthur N. CurrenSUMMARYExperiments were conducted to obtain information on heat transferin turbulent, mixed-free- and -forced-convectionflow. This flow regimehas recently becom important in connectionwith certain engineeringapplications such as gas turbin
4、es and jet engines. The tivestigationwas made in a vertical ttie with a length-to-diameterratio equal to 5.The walJs of the tube were heated, and air was conductedthrough the _buoyanty forces connectedwith temperature - . . .-. _. Provided by IHSNot for ResaleNo reproduction or networking permitted
5、without license from IHS-,-,-2 NACA TN 2974differences in the fluid create the flow. Actually, such buoyanty forcesare always present in forced-flow heat transfer as well. Usually theyare of a smaller order of magnitude tham the external forces and may beneglected. In certain engineering application
6、s,however, this cannotbedone. It was, for titance, realized qtite early that the heat exchangein oil coolers is affected msrkedly by the free-convection currentssupqosed to the forced flow. This is caused by the low flow veloc-ities employed in such coolers. More recently, applications have becomehp
7、ortant in which very large free-convectionforces are present. Forcedflow through rotating components is always mibjected to centrifugalforces and Coriolis forces. In the presence of temperature differencesthese forces create strong free-convectionflows. Cooling of rotatingparts in gas turbties and j
8、et engines maybe considerably influencedbythese conditions. Emmples of such applications are cooling of rotatingturbine blades and of ram jets in helicopters.A limited number of experimental investigationshave been publishedand, from these, correlationsfor tied-free- and -forced-convectionheat trans
9、fer have been obtained. Experimental information on heat trans-fer in flow of o through tubes to obtain a relation for lmdnar heattransfer which included the free-convection effect is contained in ref-erence 1. In reference 2 is presented an analysis of laminar mixed-free-and -forced-convectionheat
10、transf in a vertical pipe, and in refer-ence 3 this analysis is comparedwith experimental information on oil andwater. Experhents on flow and heat trsnsfer of water through a cooledvertical pipe (L/d = 20) are described in reference 4. ( syabols aredefined in appendix A.) The results indicate that e
11、xpertients were con-ducted in the transition region between kminar and turbulent flow. Inreference 5 measurements on turbulent flow of water through a ttie withL/d = 52 show a considerable effect of free-convection currents. Cal-culations on lsminsr free and mixed flow for different configurationsan
12、d wall-temperature distributions are presented in references 6 and 7.However, the configurationswhich are important in engineering applica-tions are nmnerous. In addition to the geometry of the heat-transferringsurfaces,the tiection of the forced-flaw velocities relative to thefree-convectionforces
13、and the question of whetha the fluw is laminsr orturbulent are hportant. Kimwledge of even the most common configuration,namely, the flow through a circular tube, is very incomplete. Forhstance, no investigation is known in which the flow can with certaintybe eqected to be turbulent. In addition, it
14、 wiIl be shown in RESULTSAND DISCUSSION that, even in the flow regions which have been tivesti-gated, the recommended correlations are contradictory.The investigation described in this report was conducted at theNACA Lewis Mboratory to obtati information on heat transfer in themixed-free- and -force
15、d-comection regime for a configurationwhich pre-viously had not been investigated. The experimentwas conducted in acircular lmibewith forced flow through its interior,with free-convectionProvided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-NACA TN 2974 3h
16、)cooP.forces parallel or opposite to the forced-flow velocities, and with flowin the turbulent ramge. The apparatus used for this investigationwas sodesigned as to obtain local values of heat-transfer coefficient. Thelength-to-diameterratio of the te was 5. The te wall was heated bysteam to a unifor
17、m temp=ature. The Reynolds nuniberbased on the averageforced velocity and the ttie diameter could be veried between 36)CL03and377X103. The Grashof nmdoer based on the tube length and the temperaturedifferencebetween the tube wall and the ah in the tube varied between109 ad 30In addition, a survey is
18、 presented of the results of previous invest-igations and the information obtained from it is combinedwith theresults of the present experhents so as to obtain consistent correlationsin a large range of the mixed-flow regime.APPARATUSBasic ConsiderationsThe large free-convectionforces present in the
19、 applicationswhichwere mentioned in the introduction cause the Grashof nunibers,whichchsxacterizethe free-convectionflow, to become very large (of theorder of magnitude of 1012). The influence of free convection on heattransfer is expected to be especially lsrge when the free-convectionforces are pa
20、rallel or opposite to the forced-flow Mlrection. The cool-ants most widely used are ah and water with a Prandtl nmiber between 1and.10. Although the influence of the Prandtl number is comparativelysmall, experiments, in order to be useful for these applications, shouldbe conductedwith a fluid having
21、 a Prandtl number near this range, withvery lsrge Grashof nuubers, and with the described direction of the bodyforces. The large Grashof nmibers in the applications sre causedbylsrge body forces (centrifugalforces and Coriolis forces). Such aforce field is complicated by the fact that the accelerati
22、on causing thebody forces varies locally in direction and magnitude. In experimentsdesignedto obtain basic information, it is desirable to have a shpleforce field with loctiy constant acceleration as represented by thegravitationalfield. In addition, many experimental dMficulties areavoided when sta
23、tionary eqtipment is used h which the free-convectioncurrents are generatedby the gravitationalfield of the earth. Thebuoyant forces connectedwith the gravitationalfield, however, wemuch smaller and special attention has to be dtiected to meanE by whichlarge Grashof numbers can be obtained. The Gras
24、hof nmiber can beincreasedby increasingthe CUmensions of the experimental apparatus,byincreasingthe temperature Mfferences which are imposed on the fluid,or by choosing the proper test fluid. A survey revealed that with afixed temperature difference approximatelythe same Mmensions of the. - - . Prov
25、ided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-4 NACA l?N29,74test setup are necessary for water and for compressed air tith a pres-sure near 100 pounds per square igch as a test fluid. For most othereasily available fluids, an apparatuswith lsrger dime
26、nsionsmust be usedto produce the same Grashof nunikrs. Only the use of liquids near theircritical state and of liquid metals would produce the same Grashof ntiersin sma13er equipmqt. This possibility, however, was discarded becausethe Prandtl nuniberof liquid metals and of liquids near their critica
27、lstate is too far from 1. In addition, such liqyids would introduce seri-ous clifficulties into the experimentalion. It was therefore decided touse compressed air as the test fluid.The test apparatus then had to consist essentially of a verticaltibe of large -nsion through which ah was conducted in
28、an upward ordowuward direction. The walls of the ttie were heated. Steam was usedfor this purpose in order to obtati a uniform temperatureon the largetnibesurface.Me ArrangementThe apparatus (fig. l(a) which was used for the tests to bedescribedwas aheady available in its essentialparts from previou
29、sinvestigationson free-convectionheat transfer. Various componentP-Sare designatedby letters on this figure to simplifyreferences in thetext. The appsratus consists essentially of a vertical tube and two1A. The over-aJJ-dimensions of the tube are: height, l+ feet;coversoutside diemeter, 24 inches; a
30、nd wall thickness 3/8 tich. The tube wasfabricated from mild steel and coated with zinc on the inside and out-side surfacesto prevent corrosion. The inside surfacewas ground smoothafter the coating i?asapplied. The height of the remaining roughnessalong the axial length adjacent to the steam chanibe
31、rswas measured andfound not to exceed N. 007 inch. This dimensionwas assumed to be suffi-ciently small to consider the surface as hydraulically smooth (ref. 8).W at approximately 80 F and with pressures from atmospheric to125 pounds per sqysre inch absolute could be introduced either throughthe inle
32、t line into the bottom cover or through the inlet line into the top cover. It could also be removed through the exhaust lines, Ct, or D. proper adjustment of the valves in the air lines,dHf erent flow conditions could be produced. Upwsrd flow of the ahthrough the tube was obtainedby admitting the ai
33、r through into thebottom cover. It then had to pass through a dense screen E before Itentered the tube proper. It left the tube through another screen Etito the top cover and was discharged through the exhaust line Ct. Toobtain duwnward fluw in the tube, afi was admitted through the line into the to
34、p cover, entered the te through the screen on top of theProvided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-NACA lN 2974tube, left it through the lower screen, and wasthe bottom cover through the exhaust line .convectionheat transfer, air was admitted in
35、to5finally discharged fromFor a study of free-the top cover through and removed from the upper portion of the the through D. In thisway cool air was continuously supplied to the upper portion of the ttie.Free-convection currents transported the cool air into *he heated por-tions of the te amd replac
36、ed the warm-air layer which flowed upwardalong the heated wall.The amount of air conducted through the tube was measured by anorifice in the air-supply line. In order to assure that the air enteredthe tube proper with a constantvelocity, the screens E were made verydense. They consisted of a l/8-tic
37、h-thickFiberglas mat between twol/4-inch-mesh, 23-gagewire galvanized screens. The screens produced apressure drop of 5 pounds per sqgare tich at the lowest air flow investi-gated. Measurements of temperature and velocity profiles in the lnibeindicated that the screens fulfilled their purpose.The su
38、rface of the ttie was heated with low-pressure steam super-heated by throttling to 2 or 3 F above the saturationtemperature; thepressure ranged from 1 to 3 inches of mercury above atmospheric pressure.Four openhgs F along the length of the insulated stesm jacket Gsurroundingthe the were used to dist
39、ribute the steam uniformly through-out the jacket. A steam trap on the main condensate line and a throttlevalve on the steam supply line were used to obtain the desired steampressure.Sixteen condensate c-ers H, 7+ inches wide, were arranged alongthe length of the heated section of the lxibe;therefor
40、e, only part of thecircumferenceof the ttie was covered by them. The chaaibersvaried inlength from 6 inches at the top of the tfie to inches at the bottomand trapped only the condensatewhich developed on the section of thethe wti enclosed by these chanibers.Erom each cwer, l/2-inch-dismeter lines, s
41、hown in figure l(b), cszriedthe condensate through thesteam jacket to the condensatemeasurtig apparatus. The exposed portionof these lines (J in fig. l(a) was heavily insulated to reduce heatlosses.Condensate Measuring ApparatusThe condensate from the condensate chambers was measured on aburette boa
42、rd (K in fig. l(a). Each chaniber H was connected to aQburette L graduated in tenths of a milliliter. A spherical condensateTcollector M, l; inches in diameter, and a petcock arrangement N at the. . - - _ . .Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IH
43、S-,-,-6 NACA TN 2974top of the burette were necessary because direct connectionsbetween theburettes and the lines from the condensate chaubws H would permitsteam to fill the portion of the burettes not used up by condensate andthus provide an exposed area for steem condensationwhich would varywith t
44、he amount of condensate in the burettes. The burettes were insu-lated by two layers of air between two Plexiglas tidaws at the frontand an insulatingboard at the rear. Nevertheless, the condensationcaused by the heat losses from the burettes proved inconvenient in theftist runs made with direct conn
45、ectionsbetween burettes and condensatelines. The spherical container M, which was installed after thisexperience, was emptied into the burette as soon as the condensate levelhad risen to out 1/4 inch above the level inticated in figure l(a);this provided a rel it indicated a temperature difference o
46、f approximately1 F. This temperature clifference was disregarded. The accuracy of thepotentiometer, the calibration accuracy, and the reading accuracy togetheradded up to an error in the wall-temperature measurement of +2.0 F. Thedifferencebetween the temperatures tidicatedby the thermoco.es in thes
47、team jacket and in the wall was between 0.5 and 1 F. Steam tempera-tures were estimated to be accurate within . 5 F. Readings of the tem-perature of the heated atr at a specified location, however, repeatedonly within the radiative heat loss may be different.However, it will be shown later in this s
48、ection that this loss is verysmall. By neglecting the difference in the radiative heat flow occurringduring the heat-transferruns and the heat-loss runs, equations (2)to(4) can be ccmibined=wh-wh+ (5)In this equation w is the amount of condensate collected during a heat-tiansfer run, w is the smount
49、 collected during a heat-loss run, and is the convectiveheat transfer in a heat-loss run. value of is small comparedwith the other terms in equation (5) tider the test,.conditions set up in the heat-loss runs and can be determinedby the fol-lowing approximate calculation. Since no informationon the specificconfigurationus
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