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National Advisory Committee for Aeronautics • 1 NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS REPORT 1040 SPECTRA AND DIFFUSION IN A ROUND TURBULENT JET By STANLEY CORRSIN and MAHINDER S. UB EROI 1951 RfPRODUCED BY NATIONAL TECHNICAL INFORMATION SERVICE US DEPARTMEN T OF COMMERCE .. SP RINGF iElD. VA. 22 161 r------ -------. REPORT 1040 SPECTRA AND DIFFUSION IN A ROUND TURBULENT JET By STANLEY CORR IN and MAHINDER S. UBEROI The Johns Hopkin: niversity I I I \ \ REPRODUC EO BY NATIONAL TECHN ICAL INFORMATION SERVICE u.s. DEPART MENT Of COMMERCE r SPRI NGfiElD . VA . 22161 I L ational dvisory Conlmittee for Aeronautic Headquarters, 1724 F treet TT'., 'Washington 25, D. C. roated by act of Congre approved March 3, 1915, for the upervl ion and direction of the cientific tudy of the problems of fligh t (U. Code, title 50, ec. 15 1). It member hip wa increa ed from 12 to 15 by act approved March 2, 1929, and to 17 by act approved May 25, 194 The member are appointed by the Pre ident, and serve a uch without compensation. J EHOME C. Hu. SAKE H, Sc. D., 1\Jas achu tts Institute of Technology, Chairman LEXANDEU WETMOHE, Sc. D ., Secretary, mith!;lonian In titution, 1fice Chairman DETLEV W. BRONK, PH. D., Pre ident, John Hopkin Diver- HON. DO NALD 'vV. Nyuop, Chairman, Civil Aeronautic Board. sity. Do ALD L. P UTT, lIajor General, nited tates Air Force, J OHN I-I. ASSADY, Vice Admiral, United 'tates 1 avy, D eputy Acting Deputy hief of Staff (Development). Chief of Naval Operation RTHUU E. RAY 10 'D , Sc. D ., Vice President, Engineering, EDWARD U. CONDON, PH. D., Director, National Bureau of Douglas Aircraft Co., Inc. tandard . FUANCIS VlT. REI UELDE RFEU, . D., Chief, United tates HON. THOMA W. S. DAVI , A istant Secretary of Commerce. VlTe ather Bureau. JAMES II. DOOLI1."l'LE, c. D., Vice P re ident, hell Oil o. R. 1\1. HAZEN, B. S., Director of Engineering, Alii on Division, G OUDON P. SA VILLE, Major G nerai, United tat S Air Force, General Motor Corp. D eputy Chief of taff-Dev 1 pment. WILLIAM L ITTLEWOOD , 1\1. E., Vice Presid ent, Engineering, HON. WALTEU G. WIIl'l'MAN, Chairman, R esear ch and Develop­ American Airlines, Inc. ment Board, D epar t ment of D efen e. THEODOUE . LON ' QUE '1', Rear Admiral, United tates Javy, THEODORE P . WUIGfI'l', C. D., Vice Pre ident for R esearch, D eputy and A i tant Chief of the Bureau of Aeronautics. Cornell University. HUGH L. DRYDE " PH. D., Director JOH F. VIC'l'OHY, LL. D., Executive ecretary JOH . W. HOWLEY, JR., B. ., Associate Director for Research E. H. H A~ I BERLIN , Executive Officer I'll" UY J. E. RI~ lD, D. Eng., Director, Langley Aeronautical Laboratory, Langley Field, Va. ll'I'H J . DEli'UA 'CE, B. ., Director, Ames Aeronautical Laboratory, Moffett Field, alif. EDWAUD R . HARP, C. D., Director , Lewis Flight Propul ion Laboratory, Cleveland Airport, Cleveland, Ohio TECHNICAL COMMITTEE AERODYN AAIJC OPEUA'l'IN G PROBLEMS POWER P LAN'l'S FOR ArnCRA FT TND STRY 0 SULTI G ATRCRAFT ONSTRUCTIO ' Coordination oj Reseal'e lL Needs oj l1Jilitary and ivil Aviation Prepamtion of Hesea1'ch Progmms A llocation of P roblems Prevention oj Duplication Consideration of Inventions LANGLEY AEUONAU1'ICA L LABORATORY, AAIES AERO.NA 'rICA !J LABORATOUY, LEWI FLIGHT PROJ'UL ION LABOUATORY, Langley Field, Va. Moffett Field, alif. Cleveland Airport, Cleveland, Ohio Conduct, under unified control, for aU agencies, of scientific resem'ch on the fundamental problems of flight OFFICE OF AEuo AunCAL I 1'ELLIGENCE, Washington, D. Collection, classification, compilation, and dissemination of scientific and technical information on aeronautics II l ----------------------/ REPORT 1040 SPECTRA AND DIFFUSION IN A ROUND TURBULENT JET 1 By TANLEY CORRSI N and 1JAHINDER . UBEROI SUMMARY (a) An aLtempt to e Labli h Lhe pre ence or absence of local . In a round tubulent j et at room tempemture, measurement isoLropy, (b) a compari on of velocity- and temperature­ oj the hear correlation coefficient as a junction oj jrequency £luctuation field when the over-all boundary condiLion on (through band-pa s jilters) has given a mther direct verijication mean velocity and LemperaLul"e arc effeeLively the allie, and oj Kolmogoroif'slocal-isotropy hypothesis. (c) a tudy of the diffusion of heat from a local (line) ouree On e -~imensional power spectm oj velocity and tempemture in Lhe turbulent flow. fluctuatwns, mpa ured in unheated and heated jets , re pectively, . The only specific experimental verification of local isotropy have been contrasted. Under the same condition the two Cor­ III a turbulent hear flow to date wa bv Town end in tbe responding tran vel' e correlation j1tnction have b ~en measured plane wake behind a circular rod (refere~ce 3 and 4). H e and compal'ed. found Lhat the skewnc and 11attening factor of the prob­ Finally, measurements have been made oj the mean thermal ability density of au/at in the hear flow ar very closely wakes behind local (lin e) heat sources in the unheated turbulent equal to tho e in the (eff ecLively i otropic) turbulence far jet, and the order oj magnitude oj the temperature fluctuation behind a grid. incc difl'crenLiaLion empha ize the ilia-her has been determined. frequencie , hi mea urement how , in e ence, thaI, b the value of certain sLaLi Lical quantities related 1,0 th e smaller INTRODUCTION eddies in a shear flow are Lhe arne as the value for the smaller eddie in isotropic turbulence. H e al 0 found th e microscale At tbe present time there apparently exi ts no stati tical of u in Lhe tream direcLion Lo be nearly Lime Lhe micro- Lheory of Lurbulcnt heal' flow. On ignificant theoreLical -/2 cal of v in that direction, a relation which i exactly true consideraLion has been proposed: The hypoLhe i of local for i otr-opic turbulence. i otropy, originated by Kolmogoroff (reference 1 and 2). ntil recently, only mean-velociLy and mean-temperaLw·e Kolmogoroff ha ugge ted that the fine tructure in turbu­ eli tribution were mea ured 1,0 provide a compari on of the lent heal' now may be i otropic; recent experiment of tran fer rates of momentum an l of heat in Lmbulent hear Town end (ref rences 3 and 4) in a turbulent wake seem to flow wiLh over-all heal, tran fer. The previou reporL in this verify Lhi hypothesis. roun i-jeL inve Ligation (1' f l' nee 10) included a beginning on In view of Lhi situation, th variou experimental re- Lhe problem of diJ."ect comparison of the velocity and tempera­ earch~ in lh~ field follow two oour es: Fir t, they attempL Lure 11ueLuation a well a om mea urements of velociLy­ 1,0 ve~'ify or dIsprove local isotropy; seconel , they try in all temperaLw·e correIa lion. The flu cLuation in a warm conceIvable ,~ay to make mea urement that may hed light Lmbulent wake have b en ludied by TO"~1 end (reference upon the ba IC naLure of the turbulen hear llow 0 that the ll). foundation for a ucce ful theory can be laid. ' p to Lhe pre ent Lime , however, th re appeal' till Lo be no During recenL year iL bas become videnL that mea Ul" - , ucce ful hypothe j Lo account for lll(' well-known fact thaI, ment of th(' inten ity of turbulence alone cannot provide heat (and othcr calar quantilie , like material) i diffused suffi ciCI~t information about tb e taLi tical and dynamical more rapidly than momenLwn in a tmbulenL 11ow. Thus, propertlC of the flow field. Such quanLiLi a correlation more detailed tudy of Lhe f1u cLuaLion eerned in order . specLra, probability densities, th various term in the tUl"bu~ The fn." t real analy i on lhe liITusive proper y (for scalar lenL kinetic-energy balance, and so forLh may be expected 1,0 quan Litic ) of a homogeneous tmbulent field was Taylor' reveal many e enLial feaLme of the problem. well-known work " DiHu ion by onLinuou i\Iovcmcnt " The Lypc of turbulent shear fiow that .ha.v come lU1cler (referen e 12). do e exp('rimenLal Cl·uLiny are Lhe boundary layer (referenc(, The mean thermal wake behind a line OUl·ce of heal, in a 5 and 6), Lbe planc channel (reference 7), the plane wake flowing i oLropic tmbulence ha been carefully mea UT d by (references 3 and 4), the plane ingle free-mi.;'{ing region chubau I' (refer('nce 13) in the region clo e to the mce, and (referenc(, ), and the round jet (reference 9 and 10). Th by immon (mca memcn L l' ported in reference 14) over an pre ent work is a continuation of tha I, reported in referen ce extended range. Taylor' theory of diffusion by conLinuou 9 and ]0. movement i cLirectly applicabl to the diffu ion from a line The general objecLive of thi inve tigation have been to omce of heat in a homogen ou tmbulent field, and he ha learn omeLhing more about the £l ow in a fully developed round turbulenL jet and about Lhe heat tran fer in uch a I Supersedes :\'ACA T:\, 2124, " peclrums and DiITusioll in a Round T urbulent Jet" by flow. 1'he work reported here ha fallen into three phase : Stan l ~y Con·sin and IVfahinder s. Ubcroi, 1950. 1 I L 2 I {I~ POR'I' lO-lO- XATlONAL AD\'U:iO RY COt- l iVIiTTEE FOR AERONAU'I'l :-; made a generalization Lo pC'rmit application of th e m eth od in (J maz maximum m ean tempC'rature clift rence at a a dC'C<1ying iso lropic tmbulC']1 cC' (rdC'rC'llce ]4) .
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