Boundary Lyer Theory

More documents

Recommendations

Info

VIII. General propertien of the boundary-layer equations Hct,z, A. : Zur Bcrccl~nung des Uhcrgnnges Intninnrer ~renzschichtm in die Auxsen~trijmrrng. Ii'ifty yorrs of boundnry-lnyer rcscarch (CV. Tolltnicn and 11. Giirtler, ed.). Brnunscl~wcig, 1955, 03-70. Fnlkncr, V.M., and Skan, S.W.: Some npproxitnntc solutiono of the houndnry Inyer equntiono. I'hil. Mag. 12, 865-896 (1031); AltC RM. 1314 (11130). (his, Th.: Kl~n~icho Crenzscl~ichten an Jtot.etio~~nlriirporn. Fifty years of bountlnry lnyer resenrcl~ (W. Tolln~icn nnd II. Cvrtler, cd.), Urnunschweig. 1955, 294-303. Goldstcin, S.: A note on the boundnry - lnyer cquntions. Yroc. Cnrnlr. Phil. Soc. 35, 338-340 ~ (1039). Grusohwit,z, I
1 64 IX. Exact solutions of the shady-state boundary-layer equations a. Flow past n wedge 165 a. Flow paat a wedge Thc: 'sirnilar' solutions discussed in Chap. VlIl consLit.utc a particularly sirnplo class of solutions u(x, y) which have the property that the velocity profiles at different distnnccs, x, can be made congruent with suitablc scale factors for u and y. The systcr.~ of p;mt,ial differential equations (9.1) and (9.2) is now rednced to onc ordinary rliffcrcntial cquation. It was proved in Chap. VlIl that such similar solutions exist when the velocity of t,hc potential flow is proportional to a power of tho length coordinate, 2, rneasurcd from the stagnetiot~ point,, i. e. for Jrrorn cqn. (8.24) it rollows that thc transformat.ion of thc int1ol)endcnt. v;l.riablc ?I, which lends to an ordinary tlifl'crcnt,inl equation, is: 'J'hr r~uation of ~ontinuit~y is intrgratcd by the introduction of a stream function, as S(~PII from cqns. (8.1 I) ant1 (8.23). 'l'hus the vrlocity romponel~ts become u = u1 2" /'(r]) = u / '(r]), 1 1 nt.rotluc:ing t,l~osc vnluos into tt~c nnrl put,t,ing, as in cqn. (8.21), we ol)Inin the following differential equallion for /(I)) /"' -t / /" -1- p (1 - 1'2) = 0 equation of motion (9.l), dividing by ni. IL~ zZ"'--I, It. will IN: roc::tllrtl t.li:tt it, was ;drcady given as eilrl. (8.15), antl that its I)OIIII(IR~Y f contlil ions a.re Y] 7 0 : / = 0 , 1' --= 0 ; /l=1. the velocity profiles have no point of inflexion, whereas in tho case of decolcrat.rti flow (m < 0, p < 0) they exhibit a point of inflexion. Sepxrat,ion occurs for = - 0.199, i. e. for nt = - 0.091. This result sl~ows tht the laminar horl~\tlnry layer is able t.o support only a very small dccelcration witl~o~lt separat,iorl occurir~n. by IJxrtmr. The additional solution leads to a velocity profile with baclz-flow (cl. Chap. Xf). Tl~c potential flow given by U(Z) = 1 ~ xm , exists in thc ricigllbourllootl of the stagnation poil~t on a wedge, Fig. 8.1, whosc included anglc 8, is given by eqn. (0.7). Two-dimensional stagnation flow, as well as thc boundary layer on n llat. plate at zero incidencc, constitut,~ particular cases of the present solutions, the former for p = 1 and in = 1, the latter for = 0 antl m = 0. Fig. 9. I. Velocit.y distri- bution in the 1:~tninar boundary layer in tile flow past a wedge given by U (x) = a, zm. Tllc exponent m and the wedge anglc P (Fig. 8.1) arc connecbd tlirongll cqn. (9.7) ,, lhc o:~.sc fl :- &, m 2- .j is worL11y of att.c~nI.io~r. 111 I,llis cnac I.llo tlillrc!t~l,i:~l equation for /(q) hccomcs: /"' .I- / /" 1- 4 (1 = 0; it, t,rnnsforn~s irlt,o ~.II(* tlifi:rcnt.inl c!qunt.ion ofroL:~(.iordIy symrnct.ric~~l flow with slngn:~l.io~t poit~l,, ocltl. (5.47), i. e., 4"' -1- 2 4 4" + 1 - 4" = 0 for $(C), if we put r] = 5 1/2 and d//dsj = d+/d
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 20 and 21:
Fig. 1.6. Firld of flow of oil nho~
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 =
Page 70 and 71: 1 I8 VT. Very slow motion r. 'l'l~o
Page 72 and 73: 122 VI. Very rrlow motion ext.endcd
Page 74 and 75: 126 VT. \'cry slow rnot.ion Part B.
Page 76 and 77: 130 VII. Boundnry-layor cquntionzl
Page 78 and 79: '1. Skin friction \VlIat1 t.11~ I)o
Page 80 and 81: 138 VII. no~~ndnry-layer cqnntions
Page 82 and 83: 142 VII. Hor~nclnry-lnyrr rq~~ntii~
Page 84 and 85: 146 VII. I~o~~ntlnr~ Inyrr cq~~ntio
Page 86 and 87: CIIAFTER VIII Gencral propertiee of
Page 88 and 89: 164 VIII. Ccnernl propertic8 of Lhe
Page 90 and 91: 158 VIII. General ppropcrtics of th
Page 94 and 95: 'I'his c.quat,ion Lmnsforms into t1
Page 96 and 97: 170 TX. 1Sxact uolutions of t.ho st
Page 98 and 99: 174 TX. Exnct ~olut,ionu of tho sto
Page 100 and 101: 178 IX, Exact solutions of tlrc ste
Page 102 and 103: and t,llc? clnsh now clet~otos tlil
Page 104 and 105: 1 86 10 0.8 0.6 0.4 0.2 0 -0.2 -0.4
Page 106 and 107: ccnt,rred nt, (m -1- 1, n). 1'110 t
Page 108 and 109: 194 IX. Jqxnct eolutions of thc stc
Page 110 and 111: O~l:cr ehnpw: Second-order cITcetls
Page 112 and 113: 202 X. Approximate rncl.hoda for st
Page 114 and 115: 206 X. Approxitnnte rnct.l~otls for
Page 116 and 117: 210 X. Approximate mcthod~ for shad
Page 118 and 119: 214 X. Approximato mothotls for sha
Page 120 and 121: 218 X. Approximntn met,hods for shn
Page 122 and 123: 222 X. Approximate methods for stea
Page 124 and 125: 220 XI. Axinlly symniobricnl nnd th
Page 126 and 127: 230 XI. Axinlly symmctricnl and thr
Page 128 and 129: 23.1- XI. Axially uynimet.rira1 nnc
Page 130 and 131: the two wries expnnsicws for sin (%
Page 132 and 133: 242 XI. Axially nymmct.riral and tl
Page 134 and 135: in cross-flow, tlrprntls only on lh
Page 136 and 137: 250 XI. Axinlly nyrnmet,rirnl nntl
Page 138 and 139: XI. Axinlly ~,vn~n~et.rir;~l nnrl I
Page 140 and 141: 258 XI. AxhIly syn~rnrtrirnl nncl t
Page 142 and 143:
. . lit 1 h1:lgt.r. '1.: 'l'l~idc I
Page 144 and 145:
206 XIT. l'l~rr~nnl bo1111r11iry ln
Page 146 and 147:
270 XIT. 'I'l~rrtnal boundary layer
Page 148 and 149:
can I)r rct.ni~rrvl in inrotnl~rrss
Page 150 and 151:
if wc: pillf - - 'I1, - (A7'),. 11,
Page 152 and 153:
Rotntirig rli~k: (:II:I~I. V, in pn
Page 154 and 155:
286 X11. 'IY~rrrr~al bo~~ndnry laye
Page 156 and 157:
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 208 and 209:
. - v, (x) =cons/ Fig. 14.14. 1,ant
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
Page 258 and 259:
404 XVII. Oriein of tnrbnlencc TI F
Page 260 and 261:
498 XVII. Origin of turbnlmco II t,
Page 262 and 263:
Tlw tlisl.nr~cc Iwt,wccn the point,
Page 264 and 265:
c. Efict of ~urtintl on trnt~nition
Page 266 and 267:
510 XVl I. Origin of Idmlrnro I I '
Page 268 and 269:
514 , XVII. Origin of turbulence 11
Page 270 and 271:
518 XVI I. Origin of turhr~lcncc 11
Page 272 and 273:
on the bnsis of t.hc tl~corct,ical
Page 274 and 275:
626 XVII. Origin oI t.11r011lonco I
Page 276 and 277:
630 XVII. Origin ot t.~~rhr~lrncc J
Page 278 and 279:
XVII. Origin of t.urh~~lencc TI 7 !
Page 280 and 281:
638 XVII. Origin of t~~~rbnlc~~rr I
Page 282 and 283:
\vi(,l~ a (-ylit~(lw envcrv(1 wiI.1
Page 284 and 285:
646 XVII. Origin of turbulence TI F
Page 286 and 287:
550 X\'ll. Origin of t,11rh111rnrc
Page 288 and 289:
554 XVII. Origin of t,rlrbuloncc TI
Page 290 and 291:
558 XVITI. Fundamentals of tr~rbule
Page 292 and 293:
562 XVlI1. R~nclnmont.nIu of tur1)u
Page 294 and 295:
The corrrlnt,ion co~ffiricnt~ y~ ra
Page 296 and 297:
670 XV111. I'nntlntnrt~t~nlrr of tt
Page 298 and 299:
574 XVIII. 1'undnnient.alu of tnrl~
Page 300 and 301:
CHAPTER XIX Theoretical assumptions
Page 302 and 303:
682 XIX. Thcoroticnl wsltmptionu fo
Page 304 and 305:
586 XIX. Throretical aaotin~ptiona
Page 306 and 307:
5l)O XIX. Tl~rorrt,icnl nmumptions
Page 308 and 309:
594 XIX. 'rheoreticnl nssornptions
Page 310 and 311:
698 XX. 'I'~~rl~ulrnt flow f,lrro~~
Page 312 and 313:
602 XX. T~rrbulcnt flow thro~tgh pi
Page 314 and 315:
606 XX. 'l't~rhl~lc~rit flow thro~~
Page 316:
GI0 XX. Turbulent flow throngh pip
Page 319 and 320:
Icror~~ ()I(, phj.sic*:~l ~)oint. o
Page 321 and 322:
620 XX. Tnrbnlcnt flow tlvough pipe
Page 323 and 324:
dimensions Fig. 20.26. 1tc.sist.anc
Page 325 and 326:
628 XX. T~lrbnlmt flow through pipe
Page 327 and 328:
632 XX. Turhulcnt flow through pipc
Page 329 and 330:
636 XXI. Td~nlcnt houndnry layers a
Page 331 and 332:
610 XXI. Ttrrbulent bor~ndnry layer
Page 333 and 334:
644 XXI. Turbulent boundary laycrs
Page 335 and 336:
048 XXI. Turbulent boundary layers
Page 337 and 338:
652 XXI. Turt)~~lcnt houndnry layer
Page 339 and 340:
656 XXI. Turbulent boundnry layers
Page 341 and 342:
660 XX I. Tl~rhlent bo~~ndary layer
Page 343 and 344:
664 XXI. Turbulent boundary layers
Page 345 and 346:
CHAPTER XXII The incompreesible tur
Page 347 and 348:
672 XXll. 'l'llc incon~prcssiblc tu
Page 349 and 350:
070 XXII. Tlic incompreaaibto lnrl)
Page 351 and 352:
FRO XXII. Tho incornprcs~iblo turbu
Page 353 and 354:
684 XXII. 'Yhc incon~prcssible Lnrb
Page 355 and 356:
688 XXJI. The incon~prcssible t,urb
Page 357 and 358:
002 XXI1. Tho inro~nprc~sil~lo tt~r
Page 359 and 360:
is prol)nt~t,iot~nl to the rnclius.
Page 361 and 362:
lf$8] Mucsm:tnn, 11.: Z~~snrntncnhn
Page 363 and 364:
70-t XX I1 I. 'Ihrbulcnt bonrwlnry
Page 365 and 366:
708 XXIII. Turbulent bonndnry Iaycr
Page 367 and 368:
712 XXI 11. 'I'~~rl~~~lemt bo~~ntln
Page 369 and 370:
716 XXIII. 'I'urbr~lcnt bor~ntlnry
Page 371 and 372:
720 XXIII. Turbulent boundary layer
Page 373 and 374:
724 XXlll. 'rur1)ulcnt boundnry Iny
Page 375 and 376:
[04] Smith, P.D.: An integral predi
Page 377 and 378:
732 XXIV. Frcc trtrbt~lent flows; j
Page 379 and 380:
700 XXIV. Prrc tr~rb~tlent flowa; j
Page 381 and 382:
Neglecting u12, we obtain XXIV. Prc
Page 383 and 384:
744 XXIV. lhc L~trl)ulcnt Ilow~; jo
Page 385 and 386:
748 XXIV. Free turbulent flowa; jet
Page 387 and 388:
762 XXIV. Frcc td)ulcnt flows; jcta
Page 389 and 390:
756 XXIV. Prrc torbulent flows; jet
Page 391 and 392:
760 XXV. DotcrminnLion of profilo d
Page 393 and 394:
764 XXV. I)ot.crtninntiotl of profi
Page 395 and 396:
768 XXV. Determination of profile d
Page 397 and 398:
XXV. 1)obrlninalion of proRlo drag
Page 399 and 400:
776 XXV. 1)ctormination of profile
Page 401 and 402:
A. Reviews organized in serial publ
Page 403 and 404:
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
show all

Boundary Lyer Theory

Create successful ePaper yourself

Delete template?

Save as template?