90:
738:
912:(1944). Theory of Combustion and Detonation of Gases. In R. Sunyaev (Ed.), Selected Works of Yakov Borisovich Zeldovich, Volume I: Chemical Physics and Hydrodynanics (pp. 162-232). Princeton: Princeton University Press.
175:
379:
437:
851:
486:
204:
816:
586:
993:
Clavin, P., & Searby, G. (2016). Combustion waves and fronts in flows: flames, shocks, detonations, ablation fronts and explosion of stars. Cambridge
University Press.
246:
105:
etc., the analysis usually neglects effects due to the thermal expansion of the gas mixture by assuming a constant density model. Such an approximation is referred to as
966:
Kim, J. S., & Lee, S. R. (1999). Diffusional-thermal instability in strained diffusion flames with unequal Lewis numbers. Combustion Theory and
Modelling, 3(1), 123.
295:
939:
Kim, J. S. (1997). Linear analysis of diffusional-thermal instability in diffusion flames with Lewis numbers close to unity. Combustion Theory and
Modelling, 1(1), 13.
557:
266:
533:
509:
781:
761:
224:
957:
Kim, J. S. (1996). Diffusional-thermal instability of diffusion flames in the premixed-flame regime. Combustion science and technology, 118(1-3), 27-48.
975:
Barenblatt, G. I., Zeldovich Ya. B., Istratov, A. G. (1962). On diffusional-thermal stability of a laminar flame. J. Appl. Mech. Tech. Phys., 4, 21-26.
948:
Kim, J. S., Williams, F. A., & Ronney, P. D. (1996). Diffusional-thermal instability of diffusion flames. Journal of Fluid mechanics, 327, 273-301.
594:
930:
Joulin, G., & Clavin, P. (1979). Linear stability analysis of nonadiabatic flames: diffusional-thermal model. Combustion and Flame, 35, 139-153.
49:
and arises because of the difference in the diffusion coefficient values for the fuel and heat transport, characterized by non-unity values of
1018:
124:
884:
303:
879:
121:
and A. G. Istratov in 1962. With a one-step chemistry model and assuming the perturbations to a steady planar flame in the form
102:
98:
921:
Sivashinsky, G. I. (1977). Diffusional-thermal theory of cellular flames. Combustion
Science and Technology, 15(3-4), 137-145.
387:
894:
889:
1008:
821:
442:
180:
38:
786:
562:
588:
would determine the stability character. The stability margins are given by the following equations
1013:
70:
229:
114:
78:
57:
explaining chemical morphogenesis, although the mechanism was first discovered in the context of
271:
89:
542:
251:
17:
536:
518:
118:
62:
46:
491:
874:
766:
746:
209:
54:
42:
1002:
853:
The first curve separates the region of stable mode from the region corresponding to
512:
50:
733:{\displaystyle 8k^{2}+l+2=0,\quad 256k^{4}+(-6l^{2}+32l+256)k^{2}-l^{2}+8l+32=0}
74:
58:
69:
flames. Quantitative stability theory for premixed flames were developed by
66:
268:
is the temporal growth rate of the disturbance, the dispersion relation
170:{\displaystyle e^{i\mathbf {k} \cdot \mathbf {x} _{\bot }+\omega t}}
88:
97:
To neglect the influences by hydrodynamic instabilities such as
374:{\displaystyle 2\Gamma ^{2}(\Gamma -1)+l(\Gamma -1-2\omega )=0}
53:. The instability mechanism that arises here is the same as in
65:
in 1944 to explain the cellular structures appearing in lean
206:
is the transverse coordinate system perpendicular to flame,
857:, whereas the second condition indicates the presence of
984:
Williams, F. A. (2018). Combustion theory. CRC Press.
824:
789:
769:
749:
597:
565:
545:
521:
494:
445:
390:
306:
274:
254:
232:
212:
183:
127:
783:
plane. The first curve is associated with condition
539:. This relation provides in general three roots for
432:{\displaystyle \Gamma ={\sqrt {1+4\omega +4k^{2}}}}
77:(1979) and for diffusion flames by Jong S. Kim and
845:
810:
775:
755:
732:
580:
551:
527:
503:
480:
431:
373:
289:
260:
240:
218:
198:
169:
297:for one-reactant flames is given implicitly by
8:
834:
828:
799:
793:
575:
569:
823:
788:
768:
748:
703:
690:
662:
640:
605:
596:
564:
544:
520:
493:
470:
444:
421:
397:
389:
314:
305:
273:
253:
233:
231:
211:
190:
185:
182:
150:
145:
136:
132:
126:
905:
85:Dispersion relation for premixed flames
846:{\displaystyle \Im \{\omega \}\neq 0.}
481:{\displaystyle l\equiv (Le-1)/\beta }
93:Diffusive-thermal instability diagram
7:
199:{\displaystyle \mathbf {x} _{\bot }}
248:is the perturbation wavevector and
825:
790:
566:
391:
344:
323:
311:
191:
151:
25:
811:{\displaystyle \Im \{\omega \}=0}
234:
186:
146:
137:
632:
581:{\displaystyle \Re \{\omega \}}
107:diffusive-thermal approximation
818:, whereas on the second curve
683:
649:
559:in which the one with maximum
467:
452:
362:
341:
332:
320:
284:
278:
113:which was first introduced by
111:thermo-diffusive approximation
1:
885:Kuramoto–Sivashinsky equation
743:describing two curves in the
31:Diffusive–thermal instability
18:Diffusive-thermal instability
241:{\displaystyle \mathbf {k} }
35:thermo–diffusive instability
27:Instrinsic flame instability
1019:Fluid dynamic instabilities
895:Double diffusive convection
880:Darrieus–Landau instability
103:Rayleigh–Taylor instability
99:Darrieus–Landau instability
39:intrinsic flame instability
1035:
290:{\displaystyle \omega (k)}
552:{\displaystyle \omega }
261:{\displaystyle \omega }
73:(1977), Guy Joulin and
890:Clavin–Garcia equation
847:
812:
777:
757:
734:
582:
553:
529:
528:{\displaystyle \beta }
505:
482:
433:
375:
291:
262:
242:
220:
200:
171:
94:
863:pulsating instability
848:
813:
778:
758:
735:
583:
554:
530:
506:
483:
434:
376:
292:
263:
243:
221:
201:
172:
92:
855:cellular instability
822:
787:
767:
747:
595:
563:
543:
519:
492:
443:
388:
304:
272:
252:
230:
210:
181:
125:
41:that occurs both in
71:Gregory Sivashinsky
843:
808:
773:
753:
730:
578:
549:
525:
504:{\displaystyle Le}
501:
478:
429:
371:
287:
258:
238:
216:
196:
167:
115:Grigory Barenblatt
95:
79:Forman A. Williams
55:Turing instability
776:{\displaystyle k}
756:{\displaystyle l}
427:
219:{\displaystyle t}
16:(Redirected from
1026:
994:
991:
985:
982:
976:
973:
967:
964:
958:
955:
949:
946:
940:
937:
931:
928:
922:
919:
913:
910:
852:
850:
849:
844:
817:
815:
814:
809:
782:
780:
779:
774:
762:
760:
759:
754:
739:
737:
736:
731:
708:
707:
695:
694:
667:
666:
645:
644:
610:
609:
587:
585:
584:
579:
558:
556:
555:
550:
537:Zeldovich number
534:
532:
531:
526:
515:of the fuel and
510:
508:
507:
502:
487:
485:
484:
479:
474:
438:
436:
435:
430:
428:
426:
425:
398:
380:
378:
377:
372:
319:
318:
296:
294:
293:
288:
267:
265:
264:
259:
247:
245:
244:
239:
237:
225:
223:
222:
217:
205:
203:
202:
197:
195:
194:
189:
176:
174:
173:
168:
166:
165:
155:
154:
149:
140:
47:diffusion flames
21:
1034:
1033:
1029:
1028:
1027:
1025:
1024:
1023:
999:
998:
997:
992:
988:
983:
979:
974:
970:
965:
961:
956:
952:
947:
943:
938:
934:
929:
925:
920:
916:
911:
907:
903:
871:
820:
819:
785:
784:
765:
764:
745:
744:
699:
686:
658:
636:
601:
593:
592:
561:
560:
541:
540:
517:
516:
490:
489:
441:
440:
417:
386:
385:
310:
302:
301:
270:
269:
250:
249:
228:
227:
208:
207:
184:
179:
178:
144:
128:
123:
122:
119:Yakov Zeldovich
87:
63:Yakov Zeldovich
43:premixed flames
28:
23:
22:
15:
12:
11:
5:
1032:
1030:
1022:
1021:
1016:
1011:
1009:Fluid dynamics
1001:
1000:
996:
995:
986:
977:
968:
959:
950:
941:
932:
923:
914:
904:
902:
899:
898:
897:
892:
887:
882:
877:
875:Turing pattern
870:
867:
842:
839:
836:
833:
830:
827:
807:
804:
801:
798:
795:
792:
772:
752:
741:
740:
729:
726:
723:
720:
717:
714:
711:
706:
702:
698:
693:
689:
685:
682:
679:
676:
673:
670:
665:
661:
657:
654:
651:
648:
643:
639:
635:
631:
628:
625:
622:
619:
616:
613:
608:
604:
600:
577:
574:
571:
568:
548:
524:
500:
497:
477:
473:
469:
466:
463:
460:
457:
454:
451:
448:
424:
420:
416:
413:
410:
407:
404:
401:
396:
393:
382:
381:
370:
367:
364:
361:
358:
355:
352:
349:
346:
343:
340:
337:
334:
331:
328:
325:
322:
317:
313:
309:
286:
283:
280:
277:
257:
236:
215:
193:
188:
164:
161:
158:
153:
148:
143:
139:
135:
131:
86:
83:
26:
24:
14:
13:
10:
9:
6:
4:
3:
2:
1031:
1020:
1017:
1015:
1012:
1010:
1007:
1006:
1004:
990:
987:
981:
978:
972:
969:
963:
960:
954:
951:
945:
942:
936:
933:
927:
924:
918:
915:
909:
906:
900:
896:
893:
891:
888:
886:
883:
881:
878:
876:
873:
872:
868:
866:
864:
860:
856:
840:
837:
831:
805:
802:
796:
770:
750:
727:
724:
721:
718:
715:
712:
709:
704:
700:
696:
691:
687:
680:
677:
674:
671:
668:
663:
659:
655:
652:
646:
641:
637:
633:
629:
626:
623:
620:
617:
614:
611:
606:
602:
598:
591:
590:
589:
572:
546:
538:
522:
514:
498:
495:
475:
471:
464:
461:
458:
455:
449:
446:
422:
418:
414:
411:
408:
405:
402:
399:
394:
368:
365:
359:
356:
353:
350:
347:
338:
335:
329:
326:
315:
307:
300:
299:
298:
281:
275:
255:
226:is the time,
213:
162:
159:
156:
141:
133:
129:
120:
116:
112:
108:
104:
100:
91:
84:
82:
81:(1996,1997).
80:
76:
72:
68:
64:
60:
56:
52:
51:Lewis numbers
48:
44:
40:
36:
32:
19:
989:
980:
971:
962:
953:
944:
935:
926:
917:
908:
862:
858:
854:
742:
513:Lewis number
383:
110:
106:
96:
34:
30:
29:
75:Paul Clavin
1014:Combustion
1003:Categories
901:References
59:combustion
859:traveling
838:≠
832:ω
826:ℑ
797:ω
791:ℑ
697:−
653:−
573:ω
567:ℜ
547:ω
523:β
476:β
462:−
450:≡
409:ω
392:Γ
360:ω
354:−
348:−
345:Γ
327:−
324:Γ
312:Γ
276:ω
256:ω
192:⊥
160:ω
152:⊥
142:⋅
869:See also
177:, where
67:hydrogen
861:and/or
535:is the
511:is the
45:and in
384:where
37:is an
763:vs.
681:256
634:256
109:or
61:by
33:or
1005::
865:.
841:0.
722:32
672:32
488:,
439:,
117:,
101:,
835:}
829:{
806:0
803:=
800:}
794:{
771:k
751:l
728:0
725:=
719:+
716:l
713:8
710:+
705:2
701:l
692:2
688:k
684:)
678:+
675:l
669:+
664:2
660:l
656:6
650:(
647:+
642:4
638:k
630:,
627:0
624:=
621:2
618:+
615:l
612:+
607:2
603:k
599:8
576:}
570:{
499:e
496:L
472:/
468:)
465:1
459:e
456:L
453:(
447:l
423:2
419:k
415:4
412:+
406:4
403:+
400:1
395:=
369:0
366:=
363:)
357:2
351:1
342:(
339:l
336:+
333:)
330:1
321:(
316:2
308:2
285:)
282:k
279:(
235:k
214:t
187:x
163:t
157:+
147:x
138:k
134:i
130:e
20:)
Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.
