Boundary Lyer Theory

[40] fioffninnn, E.: Ikr WRrmciibrrgeng bei drr Stromung im Itohr. X. Ges. K5ltr-Ind. 44,
nn -107 - II!I:~I \- .,.
[41] Johnson, 1).S.: Vclocsity, temprmtl~rc, and hmt transfer mcnsuren~cnts in a t~~rbulcnt
bountlnry lnyrr do~~r~trrxtn of n ntepwise d~scontinuity in wall tempcrntc~rc. J. Appl. Mcch.
24 ..' 2 - X .. 1 ,-..,.,. lOTr7I
(421 .Johnnori, D.S. : Vclocit,y and l~niperat~urc fluctuation rncnaurcmei~ts in a t~~rbl~lcnt houndary
laycr downntrcnrn of a step\visc discontinuity in wall tenlporat~tre. Trn~ls. ASME ,I.
Appl. Mecdi. 26, 32.5--33G (I 9.59).
[43] von KB.rn16.n. Th.: '1'hc ptoblctn of rcsi~tancc in cotnprc~niblc fluirls. Volta Congress Rome
19JR. 222 -277; see also Coll. Works Ill, 17!)-221.
1441 von Khnhn, '1'11.: 'rho analogy bet.wccw lluid friction and hcnt t,ranafcr. Trnns. ASME 61,
70R--7 10 (I!):)!)); RCP 111~0 (:011. Work8 111, 3.56-X7.
14.51 Koatin, .I., and Hicltartlson, P.D.: Heat tmnufer ncrom turbnlent incompressible boundary
Inyera. Int.. J. Ilcat anti Mnun 'I'rnnufor 6, 147-189 (1963).
1461 Kcstin, J., nnd Ricl~arclson, 1'.1).: Wiirmeiibcrbrngung in turbulenten (:ren7*lcllichten.
Foruchp;. 1ng.-WCR. 29, 93-- 104 (1963).
[46a] Kcstin, J., and Perscn. L.N.: The Imnafer of hcnt across a turbulent boundary layer at
very high l'riindtl numbera. lnt. .J. I-lmt and Mass Transfer 5, 355-371 (1962).
1471 KistJer, A.L.:' Fluct.unt.ion rneasnrctiicti~ in a supcrsonic tnrbulcnt boundary layer. Phys.
@ Iui& 2, 2!)0 - 296 (1969).
1481 Klobnnoff, Y.S.: Chnrackristic8of turbulence in n boundary layerwith zeropressurcgmtlient.
NACA TN 3178 (1954); TR 1247, 1135-1163 (1955).
[49] Kovnuenny, L.S.O.: The hot-wire nncmometer in ~npersonic flow. JAS 17,565-673 (1950).
[50] Kutateladze, S.S., and Leont'ev, A.I.: Turbulent boundary layer in compressible gesee.
I'ransl. by D.U. Spnlding. Edward Arnold Publishera Ltd., London, 1904.
[6l] Lilley, G.M.: An npproximation solution of the turbulent boundary lnycr equation in incompressible
and compressible flow. Coll. Aero. Cranfield Rep. 134 (1960).
1621 Licpmann, H.W., and Goddard, F.E.: Note on the Mach number effect upon the skin
friction of rough sitrfncca. JAS 24, 7R4 (1957).
[R3] Lohb, R.K., Winklcr, EM., and Porsh, J.: ICxpcrirncntnl invratigntionoftr~rbr~lettt bormdary
layern in hypcrnonic flow. NAVOJtD Rep. 3880 (1955).
[54] Ludwieg, li.: Ein Gerat zur Measnng der Wandschubspannung turbulcnter Reibungsschichten.
1ng.-Arch. 17, 207-218 (1949).
[65] Ludwicg, 11.: 13cntiminung des Verhrilt.niaaea der A~tstauachkoeffizienten fiir Warme and
Inipula bci tnr1)ulenten Grcn7achichten. ZFW 4, 73-81 (1966).
[RO] Mack, L.M.: An experimental investigntion of the temperature recovery-factor. Jet Propuluion
Laboratnry, Calif. IIIRL. TCCIIII., Ynundcnn, Rep. 20-80 (1054).
1571 Mnger, 8.: Trnnalbrmntion of tlic compresuible turbulent boundary layer. JAS 25,305-31 1
(1958).
[BR] Matting. P.W., Chapman, D.R., Nyholtn, J.R., and tho me^, A.G.: Turbulent skin friction
at high Mach nnmbcrr and Reynold~ numbers in air and helium. NASA TI2 R-82 (1961).
[59] Mchffcrty, O.11.. irntl Hehbor, RE.: 'rho cffect of ndverae proasure gradienb on the characteristic~
of turhulcnt honndary lnyers in supcrsonic atrcams. JASS 29, 1-10, 18 (1962).
[60] Meier, H.U.: Experirncntellc und thcorctische Unterauchungen von turbulenten Grenzschichten
bei Uherschnlistrii~n~~ng. Mitt. MPI Stromungsfonchg. u. Aerodyn. Vernuchsanat.
Nr. 49, 1 - 136, (1070); Dim. Brnrtnschweig 1970. .
[61] Mcier, H.U., Lee, R.E., and Voisinet, I2.L.P.: Vergleichsmessungen mit einer Danberg-
Teniperaturaonde und einer kombinierten Druck-Tempcraturaonde in turbulenten Grenzachichtcn
bci Obcrsclinllotro~n~tng. ZPW. 22, 1-10 (1974).
[62] Moicr, H.U., Voiainct, R.L.P.; and Gatea, D.P.: Temperature diatributiona using the law
of the wall for cornprcauible flow with variable turbulent Prandtl numbers. AIAA 7th Fluid
and Plnnma Dynamics Conf.. Palo Alto, Calif. 1974, AIAA Paper No. 74-696 (1974).
16.31 Mcicr, H.11., and Jtotta, J.C.: Tempcrature di~tfibntions in supersonic turbulent boundary
Inyers. AIAA J. 9, 2149-21R6 (1971).
I641 Meior. H.U.: 1nvcstignt.ion of the hcat tranafcr tncclianism in auperuonic turbulent boundary
Inycrs. Wiirme- und Sbffiihcrtragnng 8, 169-165 (1975).
[c,:',] Morkovin, M. V.: Effect* of comprraaibility on turbulent flows. Colloqucs Jnt. CNRS No.
IOR, 3fi7- 3R0, MCcirniquo dc In turbulcn~~, Marseille, 1962.
[66] N~tnncr, W.: Wiirtneiibergang und I)rnckabfalI in rauhen Rohrcn. VDI-Porxcli. 455 (1956).
1671 Owrn, P.R., and Thomaon, W.R.: Hcnt trnn~fcr across rongh surfnccs. JPM 1.5, 321 --Xi4
- -
(1943).
[68] I'nppns, C.C.: Mcasnrcnwnt of beat trnnufcr in the tnrbulorit Iiornltlnry layer on n flat. plate
in supcrsonic (low and comparison wilh skin friction rcsulta. NACA TN :12'2!! (l!)h4).
[69] Perscn, L.N.: A note on the bnnic cquntions of tr~rbulcnt, boundary laycn nntl tho hcat
transfer throng11 such laycrs. ZFW 15, 31 1-314 (1967).
[70] Prandtl, L.: Eine Beziehung zwischen Wiirtncaltstnusrh nnd Striin~ungswiclerstntlcl (lor
Fliissigkciten. Phya. Z. 11, 1072- 1078 (1910); see also Coll. Works II, 585--5!M.
[71] Reichardt, H.: Dio Wiirmciihcrtragnng it1 Cnrb~~lonbn Rcil~~tngsscllicl~te~l. ZAMM 20, 297.-
328 (1!)40); NACA TM 1047 (1943).
172) - - Jloic:hnrtlt,, 11.: 11111)nla- rind Wiir~t~o~ir~nI.nr~sc.II bci froior 'I'1n~11111c~nz. ZAhlM 2.i. 21% 272
(1944).
[73] Reichnrdt, 11.: Ocr Eilifluu~ der wnndnahcn St,rijmung nt~f tlcn trrrbnlcnten Wiirmciibcrnng.
Rcp. Max-Plnnck-Inst, fiir St~riit~tungsforscl~~~ng No. 3, 1---li3 (1!)60).
[74] fZeichardt, H.: Die Grundlngen des turbulctrten Wiirmeiibcrgn~lges. Arch. Wiirtnotc!chn. 2,
129- 142 (1061).
[75] Reahotko, E., and Tucker, M.: Approxirnate calculation of the compre~~ihle tllrbulent
boundary layer with heat transfer and arbitrary preaanre grdicnt. NACA TN 4164 (19.571.
(761 Reynolds, 0.: 011 tho extent and nct,ion of tho heating surface for rtcaln hnilcrs. h"~.
Munchester Lit. Phil. Soc. 14, 7-12 (1874).
[77] Reynolds, W.C., Kays, Mr.M., and Kline, S. J.: Hcat trnnufcrin the turbulcnt inconlpr~~ible
boundary Iayor. I. Constant wall temperature. NASA Mcmo. 12-1-58 W (1968); 11. Stop
wnll tcmpernt,ure distribution. NASA Mcmo. 12 -2-68 W (1958); 111. Arbitrary wall
temperatnrc and heat flux. NASA Mcmo. 12-3-58 W (1958); IV. Effect or loc:ntion of
trnnsition nnd prcdiction of hont tmnafor in n known tran~ibion ragion. NASA Momo.
13-A--5R .- - -- W .. I , IORRI. - -. ..-,.
[78] Itotta, J.C.: Ober den Einfluaa der Mnchschen Zahl und dm Wiirmeiibergangs auf das
Wandgesctz turbulcnter Stramun en. ZFW 7, 264-274 (1959).
1701 Rotta, J.C.: Turbulent boundary!ayera with heat trnnsfer in comprcssible flow. AGARTI
t. . Rep, 281 (1900).
[80] Itotta, J.C.: llemerkung zum Einflnes dcr 1)ichtoschwank~ngcn in turbulcnlotl Urcns-
scliichten bei kom~reaaibler Stromung. 1ng.-Arch. 32, 187-190 (1963). - .. .
[81] Rotta, J.C.: ~entp~rnturvrrteilun~en in dei turbulenten Grenzschicht an der ebencn l'lntte.
lnt. J. Hcat Maaa Transfer 7, 216-228 (1964).
[82] Rotta, J.C.: Effect of streamwise wnll curvaturc on compr~lsiblc turbulent. bonndnry layers.
IUTAM Symp. Kyoto, Japan, 1966. Phys. Fluids 10, S 174-S 180 (1967).
[83] Rotta, J.C.: Eine Bcziehung zwischen den ortlichcn Ibib~rngsbciwerten turbulcnkr Grcnzachichten
hci kotnpressiblcr und inkomproasiblcr Stromong. ZFW 18, 195-201 (1!)70).
[84] Itott.~, J.C.: POICI'RAN IV - Hechrnprogmmm fiir ~rcnzachichtcn hoi kotnlirrsd~lon
ebenen untl achuensymmetrischen Strbmungcn. DLR FB 71 -51, 1-82 (1971).
1851 Rubeain. M.W.: A modified Reynolda analogy for the conlprcssible turbulrnt boundary
laycr on a flat plate. NACA TN 2917 (1963).
. 1861 Schubauer. G.U.. and Tchen, C.M.: Turbdent flow. High Spcocl Aorodyt~trtnics and Jot
>
Propulsion V, 75-196, Princeton (1959).
[87] Seiff, A.: Examination of the existing data on the hcat transfer of turbulent houndnry
lavera at su~enonic speeds from the point of view of Reynolds analogy. NACA TN 3284
Heat trnnsfer to a turbnlent stream from a surface with n step-wise tliscontinuity
in wall temperature. International dovcloptnents in hcat tranafcr (L'roc. Cod.
organized by ASME at Boulder, Coloredo, 1961), Part 11, 439-446.
[89] Spalding, D.B., and Chi, S.W.: The drag of n compressible turbulent boudary layer on
a smooth flat. plate wit.h and without hcat trnnsfer. JFM 18, 117-143 (1964).
[90] Spence, D.A.: Velocity and enthalpy distributions in the compr~lsible turbnlent boundary
layer on a flat plato. JFM 8, 368-387 (19GO).
[9l] Spcnce, D.A.: Some applicatione of Crocco'a integral for tho turbulent boundary Iayor.
Proc. 1960 Heat Transfer Fluid Mech. Inat., Stanford Univ. 62-76 (1960).
[92] Spmce, D.A.: The growth of comprwible turbulent boundary layers on isothermal and
adtubatic walls. ARC RM 3191 (1961).
[93] Stratford, B.S., and Beavers, G.S.: The calculation of tho con~prmaiblc tnrbulcnt bonndnry
layer in an arbitrary presaure gradient. A correlation of certain previous mclhods. ARC
RM 3207 (3959).