Boundary Lyer Theory

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Fig. 1.6. Firld of flow of oil nho~~t n cirr~~lnr rylintlor at wrying IZrynolcln n~c~nbnrs nltcr Homnnn 171: Irnnnition from lnrninnr flow t,o n vortrx ntrrt-t, ill I:~n~innr fhv. Tl~r R = 65 t.o R - 281 I)c tnltrn from Fig. 2.9 freqrwnry rnngr for e. Principle of 8irnilnrit.y; t,he Itcynolds ntld Mac11 nlt~r~bcrs 19 \V. Jonm, J. J. Cillotta and 12. \V. \Val. krr [a]
20 I. Outlinc of fluid rnolim with frict.iot~ f. Comparison hrtween thc theory of pcrfcct 11r;itls anti cxpcrin~cnt 21 f. Compnrison between tl~c theory of pcrfcct fluids ntd rxperi~nrt~t In the cases of t,hc motion of water ant1 air, wllich arc the most ilnport.ant ones in engineering applications, the Itcynoltls nurnl)crs arc vcry Inrgc l)rml~sc of thc very low viscositics of thcsc fluids. 1.t wor~ld, thorcforc, apl)c:tr rcasonal)lc t,o c-xpccL very good :tgrecrncnt 1)clwccn cxperin~cnt, and a 1,hcory in which tl~c itlllllcncc of viscosity is ncglcctcd alt,ogcthcr, i. c. with the thcory of pcrfcct fluitls. In any case it secms uscful to bcgin thc comparison with experiment by rcfcrcnce to thory of perfcct fluids, if only on ncconnt of tho large num1)er of cxist,ing explicit mnthematical solnt,ions. In fact, for certain clnsscs of problems, st~clr as wave formation and tidal motion, exccllent results werc obtained wit01 t,hc aid of this theoryt. Most problems to bc rliscusscd in this book consist in I,hc study of the motion of solid 9odics through fluids at rcst, or of lluitls flowing through pipes a.nd channels. In such cascs t,hc use of the theory of pcrfcct fluids is limited because it,s solutions do not satisfy thc con- I tliLion of no slip at the solid surfacc which is always the case! with rcal fluids even at very small viscositics. In a pcrfcct tluitl thcro is slip at a yall, and tJlis circamst,ance inLroduccs, cvcn for slndl viscositics, such funtl:~.mc:~t.al tliKcrcnccs that it I is rather surprising to find in somc cascs (e. g. in the case of vcry slender, stream-linc bodies) that thc two solutions display a good measure of agreement. The greatest tliscrepancy betwccn the theory of a perfcct fluid and experiment exists in the consitlcration of drag. The perfcct-fluid theory leads to the conclusion that when an n.rhit,mry solid body movcs through an infinitely extended fluid at rcst it expericnccs no forcc acting in the clircction of motion, i. e. that its drag is zero (dlAlembcrt's paradox). This rcsult is in glaring cont.radiction to observed fact, as drag is mcnsurod on all bodics, evcn if it can bccome vcry smaU in the case of a streamline body in stcady flow parallcl to its axis. By way of ill~~stration we now propose to make some remarks concernirlg tlhe flow about a circular cylinder. The arrangcmmt of streamlines for a perfcct fluid is given in Fig. 1.9. It follows at once from considerations of symmetry that the resultant forcc in the direction of motiorl (drag) is equal to zero. The pressure clistributiou according to the theory of frictionless motion is given in Fig. 1.10, togcther with the results of measurements at three values of the Reynolds numbcr. At the leading edge, all measured pressure distributions agree, to a certain extent, with that for a perfcct fluid. At, the trailing end, the discrepancy between theory and measurement becomcs large because of the large drag of a circular cylinder. The pressure distribution at, the lowest, sobcritical Reynolds numbcr R = 1.0 x 105 diffcrs most from that given by potential theory. The measurements corresponding to the two largest Rcynolds numbers, R = 6.7 x 105 and R = 8.4 x 106, are closer to the potential curve t,han those performed at t,hc lowest Reynolds number. The large variation of pressure distril)ution wit,l~ Rcynolcls numbcr will be discussed in detail in the next cl~apt~er. A corresponding pressure-distrih~t~ion curbe around a meridian section of o, spl~cre is rcproduccd in Fig. 1.11. Here, t,oo, measurements show large differences for the two Reynolds numbers, and, again, the smaller Reynolds numbcr lies in the range Fig. 1.0. Frictionlcss flow about a circular cylinder Pig. 1.10 Pig. 1.10. Pre~strre distribution on a circular cylinder in the suhcrit.icnl and er~pcrcriLic~ll range of Reynolds nnnihers after t,he ~neasurements of 0. Flncl~sbnrt [4] and A. Roahko [13]. qm - - 1 e 1'' is the stagnntion pressure of the oncoming flows - frlctionlerur flow Flacl,s,,nrl --- R = 1.9 x 10' . . . . . R - 8.4 x 10' Itonlikn (1001) Fig. 1.1 1. Pressure distribution around n sphere in the suhcri- tical and supercriticnl range of . Reynolds numbers, aa measured by 0. Flachsbart [3] 1 i:G of largc clrng cocfficicnl,~, whrrcas tho Irwgcr valuc lics in lhc rmgo of srnnll clrq coefficients, Pig. 1.5. In this case the n,czsnrcd prcssltre-cli~t~ributior~ curve for tho largo Reynolds number approximat,es the theorct~cai di:rvo of frictionless flow very well over the greatest part of the circumfcrcnce. , Considerably better agrcemcnt between the theo~etical and measured pressure distribution is obtained for a streamline body in a flow parallel bo its axis [5], Fig. 1.12. Good agreement exists here over almost the whole length of the body, with the exception of a small region near its trailing end. As will be shown later this circumstance is a consequence of the gradual pressurc increash in the downstream direction. Although, generally speaking, the theory of perfect fluids does not lead to useful results as far as drag calculations are concerned, the lift can be calculated from it v~ry successfully. Fig. 1.13 represents the relation between the lift cocfficicnt and angle of inritlcncc, as nteasurctl hy A. Bctx [2] in thc caso of a Zhukovsltii :iwofoil
Page 1 and 2: McGRAW-I4ILL SERIES IN MECHANICAL E
Page 3 and 4: vi Contents CIIAPTEII V. Exnct ~olu
Page 5: Y Contents A " I XI X 'I'lirorrt.ir
Page 8 and 9: xvi I'orcworcI Thc result was t.11~
Page 10 and 11: From Author's Preface to the First
Page 12 and 13: the aid of thorctical considcmtioti
Page 14 and 15: even in fluitls wit,lt vcry srnall
Page 16 and 17: 10 I. Or~llinr of lluicl rnot,ion w
Page 18 and 19: The vclwil y IL at some point i11 t
Page 22 and 23: 22 I. Outliric of fluid motion with
Page 24 and 25: 2 (i TI. O~~tlittr of Imun~lnry-lsy
Page 26 and 27: Fie. 2.511 Fig. 2 .5~ Fig. 2.5b Fig
Page 28 and 29: S - point orscpnrnt.ion T'ig. 2.12.
Page 30 and 31: 3 8 \ Y?\ If. 011tli11e of boundary
Page 32 and 33: 42 11. 011tli11e of Iw~~ntlnry-Inyr
Page 34 and 35: [:j2a] I?o~cilhrntl, I,.: Thr forn~
Page 36 and 37: 50 111. l)crivnt,ion of thc cquntio
Page 38 and 39: Fig. 3.3. Tmcd clintor1,ion of flui
Page 40 and 41: of flltitl is strcsscd in thrcc nlu
Page 42 and 43: 1:i~ 3.8. Qltnsintzt.ia cotnprrssio
Page 44 and 45: 66 111. 1)wivntion of the eqnntions
Page 46 and 47: CHAPTER I V General properties of t
Page 48 and 49: 74 TV. Gencrol proprtic~ of tho Nov
Page 50 and 51: Ilcre v, c, :tntl k tlrnol,c 1.I1t:
Page 52 and 53: conclil.ion (4.14) plays n part wl~
Page 54 and 55: 86 V. 1':xact solul ions of tlir N:
Page 56 and 57: 90 V. ICxnct sol~ttion~ of tho Nnvi
Page 58 and 59: 94 V. Exnct sohltiono ol' tho Nnvic
Page 60 and 61: Table 5.1. Functions occrtrring in
Page 62 and 63: 11. Flow taenr n rotnting disk. A f
Page 64 and 65: 106 V. JCxact solutions of the Navi
Page 66 and 67: cnu bo npplirtl nt mont, nn fnr RS
Page 68 and 69: 114 VI. Vcry slow motion where r2 =
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1 I8 VT. Very slow motion r. 'l'l~o
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122 VI. Very rrlow motion ext.endcd
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126 VT. \'cry slow rnot.ion Part B.
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130 VII. Boundnry-layor cquntionzl
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'1. Skin friction \VlIat1 t.11~ I)o
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138 VII. no~~ndnry-layer cqnntions
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142 VII. Hor~nclnry-lnyrr rq~~ntii~
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146 VII. I~o~~ntlnr~ Inyrr cq~~ntio
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CIIAFTER VIII Gencral propertiee of
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164 VIII. Ccnernl propertic8 of Lhe
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158 VIII. General ppropcrtics of th
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VIII. General propertien of the bou
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'I'his c.quat,ion Lmnsforms into t1
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170 TX. 1Sxact uolutions of t.ho st
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174 TX. Exnct ~olut,ionu of tho sto
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178 IX, Exact solutions of tlrc ste
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and t,llc? clnsh now clet~otos tlil
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1 86 10 0.8 0.6 0.4 0.2 0 -0.2 -0.4
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ccnt,rred nt, (m -1- 1, n). 1'110 t
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194 IX. Jqxnct eolutions of thc stc
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O~l:cr ehnpw: Second-order cITcetls
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202 X. Approximate rncl.hoda for st
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206 X. Approxitnnte rnct.l~otls for
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210 X. Approximate mcthod~ for shad
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214 X. Approximato mothotls for sha
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218 X. Approximntn met,hods for shn
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222 X. Approximate methods for stea
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220 XI. Axinlly symniobricnl nnd th
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230 XI. Axinlly symmctricnl and thr
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23.1- XI. Axially uynimet.rira1 nnc
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the two wries expnnsicws for sin (%
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242 XI. Axially nymmct.riral and tl
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in cross-flow, tlrprntls only on lh
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250 XI. Axinlly nyrnmet,rirnl nntl
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XI. Axinlly ~,vn~n~et.rir;~l nnrl I
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258 XI. AxhIly syn~rnrtrirnl nncl t
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. . lit 1 h1:lgt.r. '1.: 'l'l~idc I
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206 XIT. l'l~rr~nnl bo1111r11iry ln
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270 XIT. 'I'l~rrtnal boundary layer
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can I)r rct.ni~rrvl in inrotnl~rrss
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if wc: pillf - - 'I1, - (A7'),. 11,
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Rotntirig rli~k: (:II:I~I. V, in pn
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286 X11. 'IY~rrrr~al bo~~ndnry laye
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290 XlI. Tl~rrnmal boundary layers
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with 0,' -. () at, r] - 0 and 0, =
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2!)H XI[. Thcrn~al bor~nrlnry Inyrr
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302 XJI. Therninl boundary layers i
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306 XII. Tllcrrnal hor~ndary layers
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310 XJI. 'I'hcrmnl boundnry layers
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314 X11. Thermal boundary laycrs in
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318 XIT. Tl~crnial bonndnry layers
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322 XII. Tl~or~nnl I)onndnry lnyers
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326 X l I. 'l'l~crn~nl hounrlnry ln
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330 X[[1. lmninar bor~ndnry lnyers
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334 XIIT. Lnrninnr 1)oundary laycra
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338 XI I I. Im~linnr I>orirtclt~ry
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342 XI11. Tmninnr Imlndary layeru i
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346 XI 11. T,ntninar I~or~nrjary hy
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350 XIII. 1,mninnr honnclxry lnycrn
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354 XI 11. 1,nminnr h~nrlnry 1:ryrm
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Fig.. l3.16. In 13.18. lain~innr ho
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a Intninn.r l)out~rlary I:~.ycr, bu
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1 I Itc vnriolts c4Twl.s ol'sl~oclt
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370 XIIJ. I~tminar boundary layers
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\'all I)rirst., 15.11..: 'l'hr prol
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CIIAPTER XIV Boundary-layer control
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5. J'rrvrntion of trauaitinn by the
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frorii th; 1c;ulitig rxlge! (l3l:wi
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390 XIV. Ilo~~n~lnry-lnycr contml F
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. - v, (x) =cons/ Fig. 14.14. 1,ant
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invc?st.igai.ctl. In this msc too,
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402 XIV. Dounclery-layer control 1.
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Ni\('A 'rM !I74 (1!)41). 1861 Sinli
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110 XV. Non-~teldy bortndnry layers
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414 XV. Non-st.cncly hour~tlnry Iny
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418 XV. Non-slmrly l~orrnclnry Inyr
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422 XV. Non-st,cndy hoixnd~ry Inycr
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420 XV. Non-nl,mdy Fig. 15.58 Fig.
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XV. Non-utcncly boouclary lnyers wh
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434 XV. Non-stcxcly boundary layers
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438 XV. Non-atcndy boundnry inyer~
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442 XV. Norl-st,aady boundary Isycr
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440 XV. Non-st,rndy ho~~nclnry laye
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450 XVI. Origin of tnrhulence I pyi
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XVT. Origin of turbulcncc I n. Some
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458 XVI. Origin of turbulence I b.
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462 XVI. Origin of tnrb~rlmcc 1 num
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466 XVi. Origin of t.r~rhr~lrncc 1
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470 XVI. Origin of h~rlwlcnce T I R
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474 XVI. Origin of l,t~rl~~tlct~rr
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478 XVI. Origin of I.rtrb~tlmcr 1 t
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482 XVT. Origin of tmbulcncc I c. E
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486 XVI. Origin of k~rbulenre I 148
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490 XVII. Origin ol t,urbulencc 11
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404 XVII. Oriein of tnrbnlencc TI F
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498 XVII. Origin of turbnlmco II t,
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Tlw tlisl.nr~cc Iwt,wccn the point,
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c. Efict of ~urtintl on trnt~nition
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510 XVl I. Origin of Idmlrnro I I '
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514 , XVII. Origin of turbulence 11
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518 XVI I. Origin of turhr~lcncc 11
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on the bnsis of t.hc tl~corct,ical
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626 XVII. Origin oI t.11r011lonco I
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630 XVII. Origin ot t.~~rhr~lrncc J
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XVII. Origin of t.urh~~lencc TI 7 !
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638 XVII. Origin of t~~~rbnlc~~rr I
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\vi(,l~ a (-ylit~(lw envcrv(1 wiI.1
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646 XVII. Origin of turbulence TI F
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550 X\'ll. Origin of t,11rh111rnrc
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554 XVII. Origin of t,rlrbuloncc TI
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558 XVITI. Fundamentals of tr~rbule
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562 XVlI1. R~nclnmont.nIu of tur1)u
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The corrrlnt,ion co~ffiricnt~ y~ ra
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670 XV111. I'nntlntnrt~t~nlrr of tt
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574 XVIII. 1'undnnient.alu of tnrl~
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CHAPTER XIX Theoretical assumptions
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682 XIX. Thcoroticnl wsltmptionu fo
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586 XIX. Throretical aaotin~ptiona
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5l)O XIX. Tl~rorrt,icnl nmumptions
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594 XIX. 'rheoreticnl nssornptions
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698 XX. 'I'~~rl~ulrnt flow f,lrro~~
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602 XX. T~rrbulcnt flow thro~tgh pi
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606 XX. 'l't~rhl~lc~rit flow thro~~
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GI0 XX. Turbulent flow throngh pip
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Icror~~ ()I(, phj.sic*:~l ~)oint. o
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620 XX. Tnrbnlcnt flow tlvough pipe
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dimensions Fig. 20.26. 1tc.sist.anc
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628 XX. T~lrbnlmt flow through pipe
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632 XX. Turhulcnt flow through pipc
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636 XXI. Td~nlcnt houndnry layers a
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610 XXI. Ttrrbulent bor~ndnry layer
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644 XXI. Turbulent boundary laycrs
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048 XXI. Turbulent boundary layers
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652 XXI. Turt)~~lcnt houndnry layer
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656 XXI. Turbulent boundnry layers
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660 XX I. Tl~rhlent bo~~ndary layer
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664 XXI. Turbulent boundary layers
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CHAPTER XXII The incompreesible tur
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672 XXll. 'l'llc incon~prcssiblc tu
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070 XXII. Tlic incompreaaibto lnrl)
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FRO XXII. Tho incornprcs~iblo turbu
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684 XXII. 'Yhc incon~prcssible Lnrb
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688 XXJI. The incon~prcssible t,urb
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002 XXI1. Tho inro~nprc~sil~lo tt~r
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is prol)nt~t,iot~nl to the rnclius.
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lf$8] Mucsm:tnn, 11.: Z~~snrntncnhn
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70-t XX I1 I. 'Ihrbulcnt bonrwlnry
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708 XXIII. Turbulent bonndnry Iaycr
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712 XXI 11. 'I'~~rl~~~lemt bo~~ntln
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716 XXIII. 'I'urbr~lcnt bor~ntlnry
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720 XXIII. Turbulent boundary layer
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724 XXlll. 'rur1)ulcnt boundnry Iny
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[04] Smith, P.D.: An integral predi
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732 XXIV. Frcc trtrbt~lent flows; j
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700 XXIV. Prrc tr~rb~tlent flowa; j
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Neglecting u12, we obtain XXIV. Prc
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744 XXIV. lhc L~trl)ulcnt Ilow~; jo
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748 XXIV. Free turbulent flowa; jet
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762 XXIV. Frcc td)ulcnt flows; jcta
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756 XXIV. Prrc torbulent flows; jet
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760 XXV. DotcrminnLion of profilo d
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764 XXV. I)ot.crtninntiotl of profi
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768 XXV. Determination of profile d
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XXV. 1)obrlninalion of proRlo drag
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776 XXV. 1)ctormination of profile
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A. Reviews organized in serial publ
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784 Bibliography Sherman, I?. S., I
Page 405 and 406:
Clementa, lt.R., and Mad, D.J.: The
Page 407 and 408:
792 Bihliography 13ird, R.R., Slewn
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Oswatitach, I
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H:I:IR, 11. 776, 777 Ilnnsr. 1). 62
Page 413 and 414:
Scl~crb:trl,l~, I
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805 811bjrct lntlrx 209, 354, 385,
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812 Snhjcct lntlcx - vorl.irrs 526,
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List of most commonly used synibola
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Boundary Lyer Theory

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