1、, - %NATIONALADVISORYCOMMITTEEFOR AERONAUTICSTECHNICAL NOTE 4018k2AE! CC3PI: %?m 1AFWL “”ETHNICAL LW3WWWWLAFJWWB t N 9 M+INFLUENCE OF TURBULENCE ON TRANSFEROF HEAT FROM CYLINDERSBy J.Kesth and P. F. MaederBrown UniversityWashingtonOctober 1957.8“ltY,Provided by IHSNot for ResaleNo reproduction or ne
2、tworking permitted without license from IHS-,-,-.,TECH LIBRARY KAFB, NMlH NATIONALADVISORYcolmITTEE FOR AERONAU2 IllllllllllllllilllllllllllulitlJb7iOg“ TECHNICAL NOTE 4018 .-INFLUENCE OF TWWULENCE ON TRANSFEROF HEAT FROM CYLINDERSBy J. Kestin and P.This report deals with the problemturbulence on th
3、e transfer of heat fromF. Maederof the influence of free-streama cylinder in forced convectionat very low Mach numbers but at large Reynolds nunibers. In particular,an attempt is made to determine whether the sole influence of tuxhlenceis to s”ft the point of lsminar separation in mibcritical flow,
4、or thepoint of transition in supercritical flow, and thus effect a change inthe rate of heat transfer. It is shown that this is not the case andthat varying the free-stream turbulence affects local rates of heattransfer.The results are presented in the form of curves of R against Xand against (where
5、 is Nusselt number, = is Reynoldsnumber, and is Stanton number, all basedon mean properties); eachcurve has been plotted for a constant value of turbulence intensity, thetemperature effects having been elhinatedby the use of integral meanvalues of the thermodynamic properties of the fluid over the b
6、oundarylayer. The eerimental results unmistakably demonstrate that in thesubcritical range the Nusselt nuniberis not independent of the intensityof turbulence.An attempt to correlate the variation of the Nusselt nuniberat con-stant Reynolds and Prandtl nuniberswith the Taylor parameter A doesnot lea
7、d to a useful result. Thus, the intensity of turbulence seemsto be the prhsry parameter, at least in the small range of scale valuesL= 0.162 to 0.574 centimeter covered.This paper presents a survey of related analytical and experimentalwork and shows that the present tentative conclusions find ample
8、 supportin previous investigations. It is also pointed out that an oscilhtionin the free stream has a different effect on the velocity profile andon the temperature profile in the boundary -yer which may cause depar-tures from Reynolds analogy, inasmuch as the latter is proved for steadyflow only. H
9、ence, it is thought that the Reynolds analogy is a limitinglaw for zero turbulence intensity.Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-2 -. NACA TN 4018. .-4. INTRODUCTION -”It has been known for some time that eerimental results on thetransfer
10、 of heat reported by different observers show divergenceswhichexceed the respective experimentalerrors. Tt is clear that a system-atic influence is at work, and the present report shows that in therange of turbulent flow the structure of the turbulent stream exertsa profound influence on the rate of
11、 heat transfer in otherwise similarflows. A dimensional argument of the shnplest kind can be used to showthat this may be so.It will be recalled that in the elementary derivation of the lawsof similarity which apply in forced convection (refs. 1 to 4) the exter-nal flow is always described by specif
12、ying only one velocity Um, thefree-stream velocity. This constitutesan adequate description incases when the external flow is laminar or, in other words, when itsturbulence intensity e = O. However, when the external flow is tur-bulent, the laws of similarity implyl in addition, a similarity in ther
13、andom fluctuations in the streams. Present-day experimental evidenceseems to show that an adequate degree of similarity is achieved whenthe intensity of turbulenceand the scale of turbulenceJwL= G(y) dJ- (2)0are fixed in value. rHere (u )2 denotes the root mean square of thelongitudinalvelocity fluc
14、tuation, G(y) is theG= 1%gcorrelationfactor(3)for fluctuations U1 and U2 occurring at a distance y apart. Theintensity of turbulence is a measure of the amplitude of the random fluc-tuations in the stream, and the scale of turbulence serves as a roughmeasure of the size of eddies present in the stre
15、am.-.Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-lUlC14TN 4018 30The preceding description of the turbulent free stream disregardsthe frequency of the rsadom fluctuations, it being implied, as is wellknown from the TolJmien-Schlichtingtheory of t
16、he origin of turbulence(ref. ), that the random fluctuations cover a wide range of frequenciesof which a given band is amplified at a given Reynolds nuniber(4)The remaining frequencies are dsmped out and need not be considered.A clear understanding of the influence of turbulence on the rateof heat t
17、ransfer is very importsnt in my engineering applications.It may lead to methods of controlling the rates of heat transfer fromsolid bodies to fluid streams, whether in the direction of increasingthem, for example in boilers or heat exchangers, and thus improvingtheir efficiency or in the direction o
18、f reducing them in order to pro-tect the metal walls from deteriorating and burning out at high tem-peratures. The problem is also important in the calibration of high-temperature probes, inasmuch as the correction factors to be appliedto them depend to a great extent on the rate of heat transfer fr
19、om thestream to the probe.Probably the greatest experimental effort has been spent in meas-uring mesm coefficients of heat transfer from cylinders in crossflow.This case is, perhaps, not of the greatest importance so far as applica-tions in aerosmics are concerned, but it constitutesthe simplestexpe
20、rimental arrangement. Since, in addition, the experimental materialavailable for comparison is abundant, it seems reasonable to begin theinvestigationwith this case.-This investigation has been conducted under the sponsorship adwith the financial assistance of the National Advisory Committee forAero
21、nautics. The authors are indebted to Professor L. S. G. Kov PV2dynamic headresistanceReolds mmiberReynolds numbergas constant1=based on mean propertiesstandard resistancefrontal areaStanton ntierStanton numberwall thiclmessbased on mea propertiestotal temperatureatmospheric temperaturetemperature me
22、asured in settling chambersurface temperaturetemperature of body,of cylinderfree-stream temperaturetime.potential velocityProvided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-6 NMX l?N4018Um tree-stream velocityuouvVmvVowwWow=X,yaEeAAvvPvUlongitudinalvelo
23、city componentlongitudinalvelocity component in steady-state solutionfluctuating longitudinalvelocity componentvoltagemeasured voltagetransverse velocity componenttransverse velocity Component h steady-state solutionvelocitymeasured velocityvelocity along center linefree-stream velocitycoordinates o
24、f cylindricalbodymean coefficient,ofheat transferintensity of turbulencetemperature ratioTaylor parsmeter (eq. (6)wavelength of sound wavedynamic viscositykinematic viscositydensity of fluidangle at which transition occurs on “cylinderfrequency of oscillationa71a15a71a15.Provided by IHSNot for Resal
25、eNo reproduction or networking permitted without license from IHS-,-,-NACA TN 40187MCKGROUND OF PROBLEM.A short discussion is now presented of the relationships whichmust be eected to exist, with the usual assumption that the structureof the turbulence in the external stream may be overlooked, excep
26、t inthe consideration of the position of the point of lamim separationor of the point of transition.The first question which poses itself is an inquiry into the rela-tion between the purely aerodxc parameters and the thermodynamicparameters in the flow. It is well known (refs. 5 to 7) thatin therang
27、e of incompressibleflow the temperature field in the stream abouta solid body, and hence the mean coefficient of heat transfer, is deter-mined solely by the velocity field when the Prandtl nmnber is constant.On the other hand, the velocity field is independent of the temperaturefield. Consequently,
28、the Nusselt nunber Nu = $ must be expected todepend on the same parameters as the drag coefficient CD because theNusselt number represents an integrated effect of the temperature fieldand the drag coefficient represents an integrated effect of the velocityfield.It willbe recalled that the drag coeff
29、icient is a function.-of one variable, the free-stream Reynolds number Rem, in the subcriti-cal and supercritical ranges of Reynolds numbers, whereas h the witi-.f cal range it also depends on the turbulence of the stream. This maybe taken as evidence that the field of flow remains sensibly unaffect
30、edby turbulence, except in the critical range, and, by the preceng argu-ment, the same might be expected to be true of the Nusselt number.As far as can be ascertained, no exact numerical data concerningthe overall effect of turbulence on the flow past a cylinder in therange of criticalReynolds nuibe
31、rs are available. However, the problemhas been studied with great thoroughness in relationto spheres,notablyby Dryden and Kuethe (ref. 8), Dryden (refs. 9 and 10), Dryden, Schubauer,Mock, and Skrsmstad (ref. n), and Platt (ref. I-2). It was studied withspheres because,.beforethe advent of sensitive
32、and reliable hot-wireanemometers, the turbulence in a tunnel was usually specified by indi-cating that Reynolds number for which the drag coefficient of a sphereattained the conventional value CD = 0.3. (The lowest value for asphere is about =0.1, insteadof = 0.36 for the cylinder.)In the absence of
33、 direct measurements on cylinders it is permissible tosuppose that the type of relationship to be expected is identical withthat for a sphere,the only difference being in the nunerical VSheS.involved.Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-8T
34、heReyaoldsstale ofNACATN 4018preceding investigationsshowed that the value of the criticalnumber depends to a marked degree on the intensity and on thethe turbulence in the free stream. However, as shown by Taylor .R(ref. 13) and Wieghardt (ref. 14) the criticalReynolds nuniberdependson the single p
35、arameter(5:which will be called the Taylor parameter. In order to prove this propo-sition, Taylor used an arguhent based on the statistical theory ofturbulence, and Wieghardt used a simplified estimate of orders of mag-nitude. In both arguments, the essential assuion consists in recog-nizing that th
36、e position of the point of transition is determinedbythe turbulent fluctuations in the pressure gradient. The correctnessof this assumption was confirmed experimentally in reference 11 byshowing that the criticalReynolds nunikr is a unique function of theTaylor parameter A from equat$on (5). The cor
37、relation has been madefor spheres of different dismeters, all points tracing a single curvewithin the experimentalerror.There are no reliable data about the angle Q at which transitionoccurs on a cylinder at differentvalues of the Taylor parameter A,but it may be noted that trsmsition shifts downstr
38、eam as A is increased.The criticalReynolds number has a lower value for higher values of A, ?and, in the case of a cylinder, it ranges from approximately Rem = 3X105.at high values of A to approximately Rem = 5 x 10 at lower values a71of A.In an endeavor to determine the independentvariables of the
39、prob-lem, the following view may be taken: The Nusselt number (or the Stantonnuniber)varies locally around the circumference of the cylinder, itsvalue at any point being determinedby the temperature gradient at thewall at the point under consideration. In turn, this temperature gra-dient is determin
40、edby the velocity profile, and the velocity gradi-ent at the wall determines the local coefficient of skin friction. Con-sequently, the mean Nusselt number could be evaluated if it were pos-sible to determine the position of the point of separation, laminar orturbulent, and of the point of transitio
41、n, if it exists, and if it werepossible to evaluate the local Nusselt numbers from the velocity field.In addition, it would be necessary to evaluate the variation of thelocal Nusselt nunber in the wake.From what has been said before it is known that, in the rapge ofReynolds nunbers where the boundar
42、y layer is laminar, the position of thepoint of separation is insensitiveto the value of the Taylor parsm =hence, the mean Nusselt number should depend on the Reynolds number alone,unless the turbulence parameter A affects the local temperature gradi-ent without affecting the velocity profile, or un
43、less it affects the rate ,-Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-NACATN 4018 9of heat transfer to the wake. Similarly, in the rsmge of Reynolds num-bers when the boundary layer is composed of a lsminar and a turbulentportion, the mean Nusse
44、lt number must be expected to depend on bothvariables Rem and A; for very high Reynolds numbers, when the posi-tion of the point of transition and that of turbulent separation ceaseto be influencedby A, the mean Nusselt number must be expected todepend on the Reynolds nuuiberalone, unless the struct
45、ure of the tur-bulent stresm affects the local temperature gradient or the rate ofheat transfer in the weke or both.The present investigationwas undertaken with the explicit objectof obtaining experimental data against which such conclusions can betested. In particular, the aim of this investigation
46、 is to verifywhether the only effect of a variation in the intensity and scale ofturbulence is to change the positions of the points of separation and/orthe point of laminar-turbulenttransition in the flow or whether thechange penetrates deeper into the boundary layer thus effectihg localvalues or,
47、in other words, whether it affects the temperature yield orthe velocity field or both.Since the aerommic aspects of the problem have, so far, beendiscussed on the basis of experiments with unheated streams it is per-tinent to remark here that, strictly speaking, it is necessary to con-sider an addit
48、ional similarity psrsmeter, namelyTo - Te =Tm(6)where To denotes the surface temperature of thecylinder and T.denotes the free-stream temperature. In postulating “incompressible”flow it is implied that the limiting case when the te erature ratio(3+0 is being considered. In actual fact, when e 70, th
49、e fluidbecomes heated or cooled along its path of flow in the boundary layer,and compressibility effects wi manifest themselves even at relativelylow speeds.When presenting experimental data on the transfer of heat betweenwalls and stresms it is customsry to correct for the influence of thistemperature parameter by employing m
