673:
Williams, F. A. (1975). " A Review of Some
Theoretical Considerations of Turbulent Flame Structure." in analytical Numerical Methods for Investigation of Flow Fields with Chemical Reactions, Especially Related Fields to Combustion. In AGARD Conference Proceedings, 1975 (Vol.
379:
452:
138:
319:
202:
611:
576:
486:
578:, the flame thickness is smaller than the Kolmogorov scale, thus the flame burning velocity is not affected by the turbulence field. Here, the burning velocity is given by the
541:
488:, the premixed turbulent flame falls into the category of corrugated flamelets and wrinkled flamelets, otherwise into the thin reaction zone or broken reaction zone flames.
699:
79:
402:
260:
229:
49:
613:, the turbulent transport penetrates into the preheat zone of the flame (thin reaction zone) or even into the reactive-diffusive zone (distributed flames).
714:
327:
664:
Klimov, A. M. (1988). Laminar flame in a turbulent flow (No. FTD-ID (RS) T-0642-88). FOREIGN TECHNOLOGY DIV WRIGHT-PATTERSON AFB OH.
582:
and these laminar flamelets are called as wrinkled flamelets or corrugated flamelets, depending on the turbulence intensity. When
414:
91:
709:
689:
269:
704:
147:
52:
585:
550:
460:
515:
405:
694:
232:
509:
505:
655:
Klimov, A. M. (1963). Laminar flame in a turbulent flow. Zhur. Prikl. Mekh. Tekh. Fiz, 3, 4958.
637:
Libby, P. A., & Williams, F. A. (1980). Turbulent reacting flows. Turbulent reacting flows.
57:
82:
387:
238:
207:
27:
579:
544:
263:
683:
17:
144:
In premixed turbulent combustion, the chemical time scale can be defined as
628:
Peters, N. (2000). Turbulent combustion. Cambridge university press.
374:{\displaystyle \mathrm {Ka} ={\frac {\delta _{L}^{2}}{\eta ^{2}}}}
457:
if the Damköhler number is defined with
Kolmogorov scale. If
404:
is the
Kolmogorov scale. The Karlovitz number is related to
447:{\displaystyle \mathrm {Ka} ={\frac {1}{\mathrm {Da} }}}
133:{\displaystyle \mathrm {Ka} ={\frac {t_{F}}{t_{\eta }}}}
646:
Williams, F. A. (2018). Combustion theory. CRC Press.
588:
553:
518:
463:
417:
390:
330:
272:
241:
210:
150:
94:
60:
30:
605:
570:
535:
480:
446:
396:
373:
313:
254:
223:
196:
132:
73:
43:
24:is defined as the ratio of chemical time scale
8:
589:
587:
554:
552:
519:
517:
464:
462:
434:
429:
418:
416:
389:
363:
353:
348:
342:
331:
329:
305:
296:
290:
277:
271:
246:
240:
215:
209:
188:
183:
174:
168:
155:
149:
122:
112:
106:
95:
93:
65:
59:
35:
29:
700:Dimensionless numbers of fluid mechanics
621:
314:{\displaystyle \delta _{L}=D_{T}/S_{L}}
496:In premixed turbulent combustion, the
197:{\displaystyle t_{F}=D_{T}/S_{L}^{2}}
7:
266:and the flame thickness is given by
715:Dimensionless numbers of chemistry
606:{\displaystyle \mathrm {Ka} >1}
593:
590:
571:{\displaystyle \mathrm {Ka} <1}
558:
555:
523:
520:
481:{\displaystyle \mathrm {Ka} <1}
468:
465:
438:
435:
422:
419:
335:
332:
99:
96:
14:
536:{\displaystyle \mathrm {Ka} =1}
1:
731:
512:, is the condition where
498:Klimov–Williams criterion
492:Klimov–Williams criterion
74:{\displaystyle t_{\eta }}
607:
572:
537:
482:
448:
398:
375:
315:
256:
225:
198:
134:
85:. The number reads as
75:
45:
710:Dimensionless numbers
608:
573:
538:
502:Klimov–Williams limit
483:
449:
399:
397:{\displaystyle \eta }
376:
316:
257:
255:{\displaystyle S_{L}}
226:
224:{\displaystyle D_{T}}
199:
135:
76:
53:Kolmogorov time scale
46:
44:{\displaystyle t_{F}}
586:
551:
516:
461:
415:
388:
328:
270:
239:
208:
148:
92:
58:
28:
580:laminar flame speed
358:
264:laminar flame speed
233:thermal diffusivity
193:
603:
568:
533:
510:Forman A. Williams
478:
444:
394:
371:
344:
311:
252:
221:
194:
179:
130:
71:
41:
690:Chemical kinetics
442:
369:
321:, in which case,
128:
722:
675:
671:
665:
662:
656:
653:
647:
644:
638:
635:
629:
626:
612:
610:
609:
604:
596:
577:
575:
574:
569:
561:
547:of unity). When
542:
540:
539:
534:
526:
487:
485:
484:
479:
471:
453:
451:
450:
445:
443:
441:
430:
425:
406:Damköhler number
403:
401:
400:
395:
380:
378:
377:
372:
370:
368:
367:
357:
352:
343:
338:
320:
318:
317:
312:
310:
309:
300:
295:
294:
282:
281:
261:
259:
258:
253:
251:
250:
230:
228:
227:
222:
220:
219:
203:
201:
200:
195:
192:
187:
178:
173:
172:
160:
159:
139:
137:
136:
131:
129:
127:
126:
117:
116:
107:
102:
80:
78:
77:
72:
70:
69:
50:
48:
47:
42:
40:
39:
22:Karlovitz number
730:
729:
725:
724:
723:
721:
720:
719:
680:
679:
678:
672:
668:
663:
659:
654:
650:
645:
641:
636:
632:
627:
623:
619:
584:
583:
549:
548:
514:
513:
494:
459:
458:
413:
412:
386:
385:
359:
326:
325:
301:
286:
273:
268:
267:
242:
237:
236:
211:
206:
205:
164:
151:
146:
145:
118:
108:
90:
89:
61:
56:
55:
31:
26:
25:
12:
11:
5:
728:
726:
718:
717:
712:
707:
705:Fluid dynamics
702:
697:
692:
682:
681:
677:
676:
666:
657:
648:
639:
630:
620:
618:
615:
602:
599:
595:
592:
567:
564:
560:
557:
545:Schmidt number
532:
529:
525:
522:
504:, named after
493:
490:
477:
474:
470:
467:
455:
454:
440:
437:
433:
428:
424:
421:
393:
382:
381:
366:
362:
356:
351:
347:
341:
337:
334:
308:
304:
299:
293:
289:
285:
280:
276:
249:
245:
218:
214:
191:
186:
182:
177:
171:
167:
163:
158:
154:
142:
141:
125:
121:
115:
111:
105:
101:
98:
83:Béla Karlovitz
81:, named after
68:
64:
38:
34:
13:
10:
9:
6:
4:
3:
2:
727:
716:
713:
711:
708:
706:
703:
701:
698:
696:
693:
691:
688:
687:
685:
670:
667:
661:
658:
652:
649:
643:
640:
634:
631:
625:
622:
616:
614:
600:
597:
581:
565:
562:
546:
530:
527:
511:
507:
503:
499:
491:
489:
475:
472:
431:
426:
411:
410:
409:
407:
391:
364:
360:
354:
349:
345:
339:
324:
323:
322:
306:
302:
297:
291:
287:
283:
278:
274:
265:
247:
243:
234:
216:
212:
189:
184:
180:
175:
169:
165:
161:
156:
152:
123:
119:
113:
109:
103:
88:
87:
86:
84:
66:
62:
54:
36:
32:
23:
19:
669:
660:
651:
642:
633:
624:
543:(assuming a
501:
497:
495:
456:
383:
143:
21:
15:
506:A.M. Klimov
695:Combustion
684:Categories
617:References
18:combustion
392:η
361:η
346:δ
275:δ
124:η
67:η
204:, where
262:is the
231:is the
384:where
20:, the
674:164).
598:>
563:<
508:and
473:<
235:and
500:or
408:as
51:to
16:In
686::
601:1
594:a
591:K
566:1
559:a
556:K
531:1
528:=
524:a
521:K
476:1
469:a
466:K
439:a
436:D
432:1
427:=
423:a
420:K
365:2
355:2
350:L
340:=
336:a
333:K
307:L
303:S
298:/
292:T
288:D
284:=
279:L
248:L
244:S
217:T
213:D
190:2
185:L
181:S
176:/
170:T
166:D
162:=
157:F
153:t
140:.
120:t
114:F
110:t
104:=
100:a
97:K
63:t
37:F
33:t
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