Boundary Lyer Theory

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. - v, (x) =cons/ Fig. 14.14. 1,antinar l)ou~lcl:try layer on n ~yt~~~ncLrie:~l Zltukovskii norofoil with uttiforttt s~~cl,iott; II,,(x) -- COIIRI~, t~ngle or it~c:idc~~w a - 0, ns cnlct~lah:d I)y I':.'l'ruckc~tbrodt [loll II'ltrr~ srtc.t,iort is :~pplirtl t,o n wing, it is ncccssary to discern two distinct problcn~s whir11 ntipltt~ : I I : ~ 1. 11. ~rl;ly I)(% (l(:sirrrI t.o incrcnsc t11c maximum lift hy dolaying scparnth~. 2. 11, nlny I)o (lnsil;rblo t,o m:~inl.nin 1:rminar flow and to avoid tmnsition in order lo 1.(~t1~~(~(~ sl
XIV. <strong>Boundary</strong>-lnycr control b. <strong>Boundary</strong>-lnyer suction 397 Fig. 14.16. Incrrascin thr ~nnxitnnrn lift, of n swept-I~n~~I~ wing by s~~ctio~~.Cornpariso~~ brtwern rontinuous suction and suction applied tl~rough slib, ns Inca- uured 11y 15. D. Popplct,on 1661 Ileynolds nurnbcr R =. 1-3 x 10'; rrlrlivc width ol slila rll = 0-004 :~c:rolhils. Sint-t: :11. high a.nglvs of inc:itlonc:c: thin acrofoils tlcvciop n s11:~rp ncg;~.I.ivc.prcss~~rc p(dc nc::~r I,hc IIOSV on t11c 11p1)t:r sitlt:, it, is nw~:ss:~.ry 1,o :~pply S I I ~ I ~ l,l~crt-. ~ I I In this t:onncxion it is important tlo know whctl~cr to apply suction t,hrough a porous wall (~~nifnrm surt.ion) or t.hrough a systcrn of slits. The diagram in Fig. 14.16 shows ;I, comprison l~t:l,wccn t,he results of cont,inuous suction and suction applied through slits on n swr,pf,-hack wing as measured by E. 1). Poppleton [66]; see also ref. [38]. 11, is dc:w that the snmc incmasc in tho lift coefficient can be ohtaincd with n much rccl~~cod mass flow when c:onl.inuous suc:tion is usctl. l'hc diagram in Fig. 14.17 c~on1,:iins informnl.ion on the most favonral~lc position of t,he suction zone at the nos(:. 'l'hc mcasummcnt.s carriccl out on an 8% thick symmet,rical aerofoil seem t.o intlio:~.t,c th:~.t continuous suction is most cfTcctivc when it is confined t.o the npper sitlt: or t,hc wing and when it cxtcnds over a region of 0.15 1 approximat,ely. 'I'he tni~~irn~~rn mass flow rtyuirrtl t,o avoid scpnrntion depends on the position antl thc I'ig. 14.17. MTcct, on in- c:rmsc ill lift, coefficient of c11:uiging tho position of the porons si~ction snrfacc for nn S :(, thick acrofoil at. an nnglc of incitlcncc ofa - 15" extent of the porous surface and, even more significantly, on the Ileynolds nunher. This, of course, is a very important consideration when results of model experiments are applied to full-scale arrangements. Some data on thc depentlcncc of t1he mass flow on the Reynolds number are shown in Fig. 14.18. 'J'hcy arc based on mensurcmcnts performed by N. Crcgory and W. S. Walker [32] on a thin symmetrical arrofoil. 'l'hc graph shows thc minimum volumc flow of suction rcqnirotl to avoid separation for a f xed anglc of incidence or a = 14O plotted in terms of tl~c Rcynoltis number. Several curves of cQ 0 = const, whicll were obtained from the theory of purely laminar flow, have also been plot,tcd for comparison. 2.2. Decrease in dmg. An exprrimcntal proof of the fact that it is possible to maintain lnrninar eontlitions in the bonntlary lnycr with the aid of sn(+or~ wns firsl, givcn by 11. Ilolst,cin [37], and shortly afterwards by .J. Acltcrct, M. ltas Fig. 14.18. Minimum suction volume required for the prevention of sc*pnrnt,ion ns n fnncbion of ll~o Reynolds 1111m1)er for an angle of incidence of u = 14", after Gregory antl Walltrr [32] and \IT. Pfenninger [3]. W. I'fenninger [el] cardcd out oxtensivc cxperimcnts on the problem of reducing dmg by the application of suc:t,ion tllrough which 1nn1in:~r Ilow is maintained. Figure 14.19 reproclnccs some of his results, ol)l.ninctl with a thin :wrofoil which was provitld with a largo n~~mbcr of sliction slit,s. 'I'hc gr:~1)11 in Vig. 14.19a sllows thc optimum vnlucs or Lhc skin-fricljion c:ooflicic:nt plothl ill I.c:r~ns ol tl~c Ilcynolds number. It is sccn that t.hcrc is a largo saving in tlr:rg, cvcn if the power consumption of the suction pump is debited against it. 'l'hc graph shows, I'urtl~cr, that, at moderatc values of the lift cocfficicnl,, cvcn at largc Itr~n01~Is ~~u~nl)c:rs, the values of the skin-friction coefficient arc not muc:h l~ighcr t.l~n~~ I.llosc for a flat ~)lat.c at zero incitlcncc. Moreover, Fig. 14.1!11) ticmonsl,rnl~cs t11:~t thcsc low vnlurs persist, over a ~onsi(lcr:~1)1c rangc of vnl~cs of t11c lift (:n(:fli(:ic~li,, c,,. J'III~IIC~, the expcrimc:nl.s tlo~~~o~rsi,r:~l.c:tl 1.11:~t l.I~t: tlcc:rc::rsc ill l,l~c tltxg t~fT~:ctc.tl I)y ~~~:lirlt:~ining a Iatni~~nr I)ol~ntl:~ry I:~,yc:r wiLh thc :~.itl of sucl,ion tlcpc~~tls I:trgrly on n rnrrfnl shaping of slits. If this proc:~nt,ion is not t,al
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McGRAW-I4ILL SERIES IN MECHANICAL E
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vi Contents CIIAPTEII V. Exnct ~olu
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Y Contents A " I XI X 'I'lirorrt.ir
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xvi I'orcworcI Thc result was t.11~
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From Author's Preface to the First
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the aid of thorctical considcmtioti
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even in fluitls wit,lt vcry srnall
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10 I. Or~llinr of lluicl rnot,ion w
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The vclwil y IL at some point i11 t
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Fig. 1.6. Firld of flow of oil nho~
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22 I. Outliric of fluid motion with
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2 (i TI. O~~tlittr of Imun~lnry-lsy
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Fie. 2.511 Fig. 2 .5~ Fig. 2.5b Fig
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S - point orscpnrnt.ion T'ig. 2.12.
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3 8 \ Y?\ If. 011tli11e of boundary
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42 11. 011tli11e of Iw~~ntlnry-Inyr
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[:j2a] I?o~cilhrntl, I,.: Thr forn~
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50 111. l)crivnt,ion of thc cquntio
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Fig. 3.3. Tmcd clintor1,ion of flui
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of flltitl is strcsscd in thrcc nlu
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1:i~ 3.8. Qltnsintzt.ia cotnprrssio
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66 111. 1)wivntion of the eqnntions
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CHAPTER I V General properties of t
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74 TV. Gencrol proprtic~ of tho Nov
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Ilcre v, c, :tntl k tlrnol,c 1.I1t:
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conclil.ion (4.14) plays n part wl~
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86 V. 1':xact solul ions of tlir N:
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90 V. ICxnct sol~ttion~ of tho Nnvi
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94 V. Exnct sohltiono ol' tho Nnvic
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Table 5.1. Functions occrtrring in
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11. Flow taenr n rotnting disk. A f
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106 V. JCxact solutions of the Navi
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cnu bo npplirtl nt mont, nn fnr RS
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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
Page 158 and 159: with 0,' -. () at, r] - 0 and 0, =
Page 160 and 161: 2!)H XI[. Thcrn~al bor~nrlnry Inyrr
Page 162 and 163: 302 XJI. Therninl boundary layers i
Page 164 and 165: 306 XII. Tllcrrnal hor~ndary layers
Page 166 and 167: 310 XJI. 'I'hcrmnl boundnry layers
Page 168 and 169: 314 X11. Thermal boundary laycrs in
Page 170 and 171: 318 XIT. Tl~crnial bonndnry layers
Page 172 and 173: 322 XII. Tl~or~nnl I)onndnry lnyers
Page 174 and 175: 326 X l I. 'l'l~crn~nl hounrlnry ln
Page 176 and 177: 330 X[[1. lmninar bor~ndnry lnyers
Page 178 and 179: 334 XIIT. Lnrninnr 1)oundary laycra
Page 180 and 181: 338 XI I I. Im~linnr I>orirtclt~ry
Page 182 and 183: 342 XI11. Tmninnr Imlndary layeru i
Page 184 and 185: 346 XI 11. T,ntninar I~or~nrjary hy
Page 186 and 187: 350 XIII. 1,mninnr honnclxry lnycrn
Page 188 and 189: 354 XI 11. 1,nminnr h~nrlnry 1:ryrm
Page 190 and 191: Fig.. l3.16. In 13.18. lain~innr ho
Page 192 and 193: a Intninn.r l)out~rlary I:~.ycr, bu
Page 194 and 195: 1 I Itc vnriolts c4Twl.s ol'sl~oclt
Page 196 and 197: 370 XIIJ. I~tminar boundary layers
Page 198 and 199: \'all I)rirst., 15.11..: 'l'hr prol
Page 200 and 201: CIIAPTER XIV Boundary-layer control
Page 202 and 203: 5. J'rrvrntion of trauaitinn by the
Page 204 and 205: frorii th; 1c;ulitig rxlge! (l3l:wi
Page 206 and 207: 390 XIV. Ilo~~n~lnry-lnycr contml F
Page 210 and 211: invc?st.igai.ctl. In this msc too,
Page 212 and 213: 402 XIV. Dounclery-layer control 1.
Page 214 and 215: Ni\('A 'rM !I74 (1!)41). 1861 Sinli
Page 216 and 217: 110 XV. Non-~teldy bortndnry layers
Page 218 and 219: 414 XV. Non-st.cncly hour~tlnry Iny
Page 220 and 221: 418 XV. Non-slmrly l~orrnclnry Inyr
Page 222 and 223: 422 XV. Non-st,cndy hoixnd~ry Inycr
Page 224 and 225: 420 XV. Non-nl,mdy Fig. 15.58 Fig.
Page 226 and 227: XV. Non-utcncly boouclary lnyers wh
Page 228 and 229: 434 XV. Non-stcxcly boundary layers
Page 230 and 231: 438 XV. Non-atcndy boundnry inyer~
Page 232 and 233: 442 XV. Norl-st,aady boundary Isycr
Page 234 and 235: 440 XV. Non-st,rndy ho~~nclnry laye
Page 236 and 237: 450 XVI. Origin of tnrhulence I pyi
Page 238 and 239: XVT. Origin of turbulcncc I n. Some
Page 240 and 241: 458 XVI. Origin of turbulence I b.
Page 242 and 243: 462 XVI. Origin of tnrb~rlmcc 1 num
Page 244 and 245: 466 XVi. Origin of t.r~rhr~lrncc 1
Page 246 and 247: 470 XVI. Origin of h~rlwlcnce T I R
Page 248 and 249: 474 XVI. Origin of l,t~rl~~tlct~rr
Page 250 and 251: 478 XVI. Origin of I.rtrb~tlmcr 1 t
Page 252 and 253: 482 XVT. Origin of tmbulcncc I c. E
Page 254 and 255: 486 XVI. Origin of k~rbulenre I 148
Page 256 and 257: 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
Page 409 and 410:
Oswatitach, I
Page 411 and 412:
H:I:IR, 11. 776, 777 Ilnnsr. 1). 62
Page 413 and 414:
Scl~crb:trl,l~, I
Page 415 and 416:
805 811bjrct lntlrx 209, 354, 385,
Page 417 and 418:
812 Snhjcct lntlcx - vorl.irrs 526,
Page 419:
List of most commonly used synibola
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Boundary Lyer Theory

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