17:
1328:
78:
processes are much faster than the physical processes such as vortex motion in the flow and, hence, the inner structure of a laminar flame remains intact in most circumstances. The constitutive layers of the inner structure correspond to specified intervals over which the temperature increases from the specified unburned mixture up to as high as the
930:
64:(or burning velocity) which depends on the convection-diffusion-reaction balance within the flame, i.e. on its inner chemical structure. The premixed flame is characterised as laminar or turbulent depending on the velocity distribution in the unburned pre-mixture (which provides the medium of propagation for the flame).
2086:. If the flow rate is equal to the flame speed, we would expect a stationary flat flame front normal to the flow direction. If the flow rate is above the flame speed, the flame front will become conical such that the component of the velocity vector normal to the flame front is equal to the flame speed.
1617:
Variations in local propagation speed of a laminar flame arise due to what is called flame stretch. Flame stretch can happen due to the straining by outer flow velocity field or the curvature of flame; the difference in the propagation speed from the corresponding laminar speed is a function of these
59:
premixed charge, the combustion process once initiated sustains itself by way of its own heat release. The majority of the chemical transformation in such a combustion process occurs primarily in a thin interfacial region which separates the unburned and the burned gases. The premixed flame interface
2064:
Under contrasting conditions, however, the inner structure of the premixed flame may be entirely disrupted causing the flame to extinguish either locally (known as local extinction) or globally (known as global extinction or blow-off). Such opposing cases govern the operation of practical combustion
1916:
A turbulent premixed flame can be assumed to propagate as a surface composed of an ensemble of laminar flames so long as the processes that determine the inner structure of the flame are not affected. Under such conditions, the flame surface is wrinkled by virtue of turbulent motion in the premixed
77:
Under controlled conditions (typically in a laboratory) a laminar flame may be formed in one of several possible flame configurations. The inner structure of a laminar premixed flame is composed of layers over which the decomposition, reaction and complete oxidation of fuel occurs. These chemical
1750:
1912:
In practical scenarios, turbulence is inevitable and, under moderate conditions, turbulence aids the premixed burning process as it enhances the mixing process of fuel and oxidiser. If the premixed charge of gases is not homogeneously mixed, the variations on equivalence ratio may affect the
2102:
In this configuration, the flame is typically initiated by way of a spark within a homogeneous pre-mixture. The subsequent propagation of the developed premixed flame occurs as a spherical front until the mixture is transformed entirely or the walls of the combustion vessel are reached.
410:
1323:{\displaystyle S_{L}=\left\{{\frac {2B\lambda _{b}\rho _{b}^{m+n}\nu _{F}^{m}Y_{O_{2},u}^{m+n-1}G(n,m,a)}{c_{p,b}\rho _{u}^{2}\nu _{O_{2}}W_{O_{2}}^{m+n-1}\beta ^{m+n+1}\mathrm {Le} _{O_{2}}^{-n}\mathrm {Le} _{F}^{-m}}}\right\}^{1/2}e^{-E_{a}/2RT_{b}}+O(\beta ^{-1}),}
892:
2081:
In a Bunsen flame, a steady flow rate is provided which matches the flame speed so as to stabilize the flame. If the flow rate is below the flame speed, the flame will move upstream until the fuel is consumed or until it encounters a
2028:
188:
2061:. This, however, is typically not the case as the propagation speed of the interface (with resect to unburned mixture) varies from point to point due to the aerodynamic stretch induced due to gradients in the velocity field.
1624:
1898:
1434:
253:
2227:
Chelliah, H. K., & Williams, F. A. (1987). Asymptotic analysis of two-reactant flames with variable properties and Stefan-Maxwell transport. Combustion science and technology, 51(4-6), 129-144.
2065:
devices such as SI engines as well as aero-engine afterburners. The prediction of the extent to which the inner structure of flame is affected in turbulent flow is a topic of extensive research.
1498:
662:
2218:
Rogg, B., & Williams, F. A. (1985). Asymptotic analysis of laminar flame propagation with variable transport coefficients. Combustion science and technology, 42(5-6), 301-316.
2122:, soot formation is mitigated as well. Premixed combustion has therefore gained significance in recent times. The uses involve lean-premixed-prevaporized (LPP) gas turbines and
1917:
gases increasing the surface area of the flame. The wrinkling process increases the burning velocity of the turbulent premixed flame in comparison to its laminar counterpart.
2254:
Clavin, Paul, and Geoff Searby. Combustion Waves and Fronts in Flows: Flames, Shocks, Detonations, Ablation Fronts and
Explosion of Stars. Cambridge University Press, 2016.
1578:
1844:
1822:
698:
221:
1780:
1608:
922:
769:
526:
1518:
1800:
241:
2059:
1549:
761:
557:
488:
457:
1950:
1610:
mixtures. This result is first obtained by T. Mitani in 1980. Second order correction to this formula with more complicated transport properties were derived by
1942:
738:
718:
605:
581:
433:
97:
2166:
1745:{\displaystyle U_{L}=S_{L}-S_{L}{\mathcal {M}}_{c}\delta _{L}\kappa +{\mathcal {M}}_{a}\delta _{L}\mathbf {n} \cdot \nabla \mathbf {n} \cdot \mathbf {n} }
2111:
Since the equivalence ratio of the premixed gases may be controlled, premixed combustion offers a means to attain low temperatures and, thereby, reduce
2236:
Rogg, B. (1986). On the accuracy of asymptotic flame speed predictions for two-reactant flames. Combustion science and technology, 45(5-6), 317-329.
2245:
Clavin, P., & Graña-Otero, J. C. (2011). Curved and stretched flames: the two
Markstein numbers. Journal of Fluid Mechanics, 686, 187-217.
2296:
Williams, F. A. (1985). Turbulent combustion. In The mathematics of combustion (pp. 97-131). Society for
Industrial and Applied Mathematics.
2034:
which is defined such that the level-sets of G represent the various interfaces within the premixed flame propagating with a local velocity
405:{\displaystyle \omega =B\left({\frac {\rho Y_{F}}{W_{F}}}\right)^{m}\left({\frac {\rho Y_{O_{2}}}{W_{O_{2}}}}\right)^{n}e^{-E_{a}/RT},}
2094:
Here, the pre-mixed gases flow in such a way so as to form a region of stagnation (zero velocity) where the flame may be stabilized.
2273:
2176:
1849:
1339:
60:
propagates through the mixture until the entire charge is depleted. The propagation speed of a premixed flame is known as the
28:, and on the right a lean fully oxygen premixed flame produces no soot and the flame color is produced by molecular radical
191:
83:
1442:
2209:
MITANI, T. (1980). Propagation velocities of two-reactant flames. Combustion
Science and Technology, 21(3-4), 175-177.
2135:
79:
2306:
Kerstein, Alan R. (1988-01-01). "Field equation for interface propagation in an unsteady homogeneous flow field".
529:
1913:
propagation speed of the flame. In some cases, this is desirable as in stratified combustion of blended fuels.
614:
86:, the extent of reaction and, hence, the temperature attained across the flame may be different from the AFT.
584:
436:
24:
depend on oxygen supply. On the left a rich fuel mixture with no premixed oxygen produces a yellow sooty
2123:
82:(AFT). In the presence of volumetric heat transfer and/or aerodynamic stretch, or under the development
2073:
The flow configuration of premixed gases affects the stabilization and burning characteristics of the
1521:
700:
are the reaction orders. Let the unburnt conditions far ahead of the flame be denoted with subscript
195:
2349:
1558:
53:
1827:
1805:
887:{\displaystyle \phi ={\frac {\nu _{O_{2}}W_{O_{2}}}{\nu _{F}W_{F}}}{\frac {Y_{F,u}}{Y_{O_{2},u}}}}
671:
200:
52:. Since the fuel and oxidiser—the key chemical reactants of combustion—are available throughout a
1758:
1611:
491:
1587:
901:
497:
2325:
2308:
2279:
2269:
2172:
1503:
741:
665:
560:
1785:
226:
2317:
1920:
The propagation of such a premixed flame may be analysed using the field equation called as
1901:
190:, the planar, adiabatic flame has explicit expression for the burning velocity derived from
2037:
2023:{\displaystyle {\frac {\partial G}{\partial t}}+\mathbf {v} \cdot \nabla G=U_{L}|\nabla G|}
1527:
746:
535:
466:
442:
16:
2119:
25:
2140:
1927:
723:
703:
590:
566:
418:
183:{\displaystyle \nu _{F}{\rm {{F}+\nu _{O}{\rm {{O}_{2}\rightarrow {\rm {Products}}}}}}}
2354:
2343:
1552:
244:
56:
29:
21:
2083:
1581:
608:
243:(number of moles of fuel consumed per unit volume per unit time) is taken to be
61:
1824:
is the unit normal on the flame surface pointing towards the unburnt gas side,
1921:
41:
2321:
2283:
2200:
Linan, A., & Williams, F. A. (1993). Fundamental aspects of combustion.
2329:
2145:
49:
460:
15:
898:
Then the planar laminar burning velocity for fuel-rich mixture (
45:
2112:
1893:{\displaystyle {\mathcal {M}}_{c}\ \&\ {\mathcal {M}}_{a}}
1429:{\displaystyle G(n,m,a)=\int _{0}^{\infty }y^{n}(y+a)^{m}\ dy}
1879:
1856:
1697:
1667:
40:
is a flame formed under certain conditions during the
2191:
Williams, F. A. (2018). Combustion theory. CRC Press.
2118:
emissions. Due to improved mixing in comparison with
2040:
1953:
1930:
1852:
1830:
1808:
1788:
1761:
1627:
1590:
1561:
1530:
1506:
1445:
1342:
933:
904:
772:
749:
726:
706:
674:
617:
593:
569:
538:
500:
469:
445:
421:
256:
229:
203:
100:
1493:{\displaystyle a=\beta (\phi -1)/\mathrm {Le} _{F}}
2053:
2022:
1936:
1892:
1838:
1816:
1794:
1774:
1744:
1602:
1572:
1543:
1512:
1492:
1428:
1322:
916:
886:
755:
732:
712:
692:
656:
599:
575:
551:
520:
482:
451:
427:
404:
235:
215:
182:
44:of a premixed charge (also called pre-mixture) of
1584:. Similarly one can write the formula for lean
94:For a one-step irreversible chemistry, i.e.,
8:
2165:Lewis, Bernard; Elbe, Guenther von (2012).
720:and similarly, the burnt gas conditions by
2168:Combustion, Flames and Explosions of Gases
2045:
2039:
2015:
2004:
1998:
1977:
1954:
1952:
1929:
1884:
1878:
1877:
1861:
1855:
1854:
1851:
1831:
1829:
1809:
1807:
1787:
1766:
1760:
1737:
1729:
1718:
1712:
1702:
1696:
1695:
1682:
1672:
1666:
1665:
1658:
1645:
1632:
1626:
1589:
1562:
1560:
1535:
1529:
1505:
1484:
1476:
1470:
1444:
1411:
1389:
1379:
1374:
1341:
1305:
1284:
1269:
1263:
1255:
1241:
1237:
1221:
1216:
1208:
1198:
1191:
1186:
1178:
1159:
1137:
1130:
1125:
1113:
1108:
1098:
1093:
1077:
1029:
1016:
1011:
1001:
996:
980:
975:
965:
952:
938:
932:
903:
868:
863:
847:
841:
832:
822:
808:
803:
791:
786:
779:
771:
748:
725:
705:
673:
646:
641:
622:
616:
592:
568:
543:
537:
510:
505:
499:
474:
468:
444:
420:
386:
380:
372:
362:
348:
343:
330:
325:
315:
304:
292:
281:
271:
255:
228:
202:
149:
148:
139:
134:
132:
131:
125:
113:
112:
111:
105:
99:
657:{\displaystyle W_{F}\ \&\ W_{O_{2}}}
2157:
668:of fuel and oxidizer, respectively and
7:
2009:
1985:
1965:
1957:
1870:
1726:
1566:
1563:
1480:
1477:
1380:
1212:
1209:
1182:
1179:
681:
631:
171:
168:
165:
162:
159:
156:
153:
150:
135:
126:
114:
14:
1978:
1832:
1810:
1782:is the laminar flame thickness,
1738:
1730:
1719:
1618:effects and may be written as:
2268:. Cambridge University Press.
2016:
2005:
1467:
1455:
1408:
1395:
1364:
1346:
1314:
1298:
1068:
1050:
145:
1:
1573:{\displaystyle \mathrm {Le} }
192:activation energy asymptotics
84:intrinsic flame instabilities
2069:Premixed flame configuration
1839:{\displaystyle \mathbf {v} }
1817:{\displaystyle \mathbf {n} }
693:{\displaystyle m\ \&\ n}
216:{\displaystyle \beta \gg 1.}
2136:Flamelet generated manifold
1775:{\displaystyle \delta _{L}}
1614:and co-workers in the 80s.
763:for the unburnt mixture as
80:adiabatic flame temperature
20:Different flame types of a
2371:
1603:{\displaystyle \phi <1}
917:{\displaystyle \phi >1}
68:Premixed flame propagation
1904:of curvature and strain.
1846:is the flow velocity and
1555:at constant pressure and
521:{\displaystyle Y_{O_{2}}}
2322:10.1103/PhysRevA.37.2728
2264:Peters, Norbert (2000).
1802:is the flame curvature,
1513:{\displaystyle \lambda }
740:, then we can define an
90:Laminar burning velocity
1795:{\displaystyle \kappa }
236:{\displaystyle \omega }
2055:
2024:
1938:
1894:
1840:
1818:
1796:
1776:
1746:
1604:
1574:
1545:
1514:
1494:
1430:
1324:
918:
888:
757:
734:
714:
694:
658:
601:
585:universal gas constant
577:
553:
522:
484:
453:
437:pre-exponential factor
429:
406:
237:
217:
184:
33:
2056:
2054:{\displaystyle U_{L}}
2025:
1939:
1895:
1841:
1819:
1797:
1777:
1747:
1605:
1575:
1546:
1544:{\displaystyle c_{p}}
1515:
1495:
1431:
1325:
919:
889:
758:
756:{\displaystyle \phi }
735:
715:
695:
659:
602:
578:
554:
552:{\displaystyle E_{a}}
523:
485:
483:{\displaystyle Y_{F}}
454:
452:{\displaystyle \rho }
430:
407:
238:
218:
185:
19:
2266:Turbulent combustion
2038:
1951:
1928:
1850:
1828:
1806:
1786:
1759:
1625:
1588:
1559:
1528:
1522:thermal conductivity
1504:
1443:
1340:
931:
902:
770:
747:
724:
704:
672:
615:
591:
567:
536:
498:
467:
443:
419:
254:
227:
201:
98:
1900:are the respective
1384:
1229:
1206:
1154:
1103:
1046:
1006:
991:
2051:
2020:
1934:
1890:
1836:
1814:
1792:
1772:
1742:
1612:Forman A. Williams
1600:
1570:
1541:
1510:
1490:
1426:
1370:
1320:
1207:
1177:
1121:
1089:
1007:
992:
971:
914:
884:
753:
730:
710:
690:
654:
597:
573:
549:
518:
492:fuel mass fraction
480:
449:
425:
402:
233:
223:The reaction rate
213:
180:
34:
2309:Physical Review A
1972:
1937:{\displaystyle G}
1902:Markstein numbers
1875:
1869:
1419:
1231:
882:
839:
742:equivalence ratio
733:{\displaystyle b}
713:{\displaystyle u}
686:
680:
666:molecular weights
636:
630:
600:{\displaystyle T}
576:{\displaystyle R}
561:activation energy
428:{\displaystyle B}
356:
298:
196:Zel'dovich number
2362:
2334:
2333:
2316:(7): 2728–2731.
2303:
2297:
2294:
2288:
2287:
2261:
2255:
2252:
2246:
2243:
2237:
2234:
2228:
2225:
2219:
2216:
2210:
2207:
2201:
2198:
2192:
2189:
2183:
2182:
2162:
2120:diffusion flames
2090:Stagnation flame
2060:
2058:
2057:
2052:
2050:
2049:
2029:
2027:
2026:
2021:
2019:
2008:
2003:
2002:
1981:
1973:
1971:
1963:
1955:
1943:
1941:
1940:
1935:
1899:
1897:
1896:
1891:
1889:
1888:
1883:
1882:
1873:
1867:
1866:
1865:
1860:
1859:
1845:
1843:
1842:
1837:
1835:
1823:
1821:
1820:
1815:
1813:
1801:
1799:
1798:
1793:
1781:
1779:
1778:
1773:
1771:
1770:
1751:
1749:
1748:
1743:
1741:
1733:
1722:
1717:
1716:
1707:
1706:
1701:
1700:
1687:
1686:
1677:
1676:
1671:
1670:
1663:
1662:
1650:
1649:
1637:
1636:
1609:
1607:
1606:
1601:
1579:
1577:
1576:
1571:
1569:
1550:
1548:
1547:
1542:
1540:
1539:
1519:
1517:
1516:
1511:
1499:
1497:
1496:
1491:
1489:
1488:
1483:
1474:
1435:
1433:
1432:
1427:
1417:
1416:
1415:
1394:
1393:
1383:
1378:
1329:
1327:
1326:
1321:
1313:
1312:
1291:
1290:
1289:
1288:
1273:
1268:
1267:
1250:
1249:
1245:
1236:
1232:
1230:
1228:
1220:
1215:
1205:
1197:
1196:
1195:
1185:
1176:
1175:
1153:
1136:
1135:
1134:
1120:
1119:
1118:
1117:
1102:
1097:
1088:
1087:
1071:
1045:
1028:
1021:
1020:
1005:
1000:
990:
979:
970:
969:
953:
943:
942:
923:
921:
920:
915:
893:
891:
890:
885:
883:
881:
880:
873:
872:
858:
857:
842:
840:
838:
837:
836:
827:
826:
816:
815:
814:
813:
812:
798:
797:
796:
795:
780:
762:
760:
759:
754:
739:
737:
736:
731:
719:
717:
716:
711:
699:
697:
696:
691:
684:
678:
663:
661:
660:
655:
653:
652:
651:
650:
634:
628:
627:
626:
606:
604:
603:
598:
582:
580:
579:
574:
558:
556:
555:
550:
548:
547:
528:is the oxidizer
527:
525:
524:
519:
517:
516:
515:
514:
489:
487:
486:
481:
479:
478:
458:
456:
455:
450:
434:
432:
431:
426:
411:
409:
408:
403:
398:
397:
390:
385:
384:
367:
366:
361:
357:
355:
354:
353:
352:
338:
337:
336:
335:
334:
316:
309:
308:
303:
299:
297:
296:
287:
286:
285:
272:
242:
240:
239:
234:
222:
220:
219:
214:
189:
187:
186:
181:
179:
178:
177:
176:
175:
174:
144:
143:
138:
130:
129:
117:
110:
109:
2370:
2369:
2365:
2364:
2363:
2361:
2360:
2359:
2340:
2339:
2338:
2337:
2305:
2304:
2300:
2295:
2291:
2276:
2263:
2262:
2258:
2253:
2249:
2244:
2240:
2235:
2231:
2226:
2222:
2217:
2213:
2208:
2204:
2199:
2195:
2190:
2186:
2179:
2164:
2163:
2159:
2154:
2132:
2116:
2109:
2100:
2098:Spherical flame
2092:
2079:
2071:
2041:
2036:
2035:
1994:
1964:
1956:
1949:
1948:
1926:
1925:
1910:
1876:
1853:
1848:
1847:
1826:
1825:
1804:
1803:
1784:
1783:
1762:
1757:
1756:
1708:
1694:
1678:
1664:
1654:
1641:
1628:
1623:
1622:
1586:
1585:
1557:
1556:
1531:
1526:
1525:
1502:
1501:
1475:
1441:
1440:
1407:
1385:
1338:
1337:
1301:
1280:
1259:
1251:
1187:
1155:
1126:
1109:
1104:
1073:
1072:
1012:
961:
954:
948:
947:
934:
929:
928:
900:
899:
864:
859:
843:
828:
818:
817:
804:
799:
787:
782:
781:
768:
767:
745:
744:
722:
721:
702:
701:
670:
669:
642:
637:
618:
613:
612:
589:
588:
565:
564:
539:
534:
533:
506:
501:
496:
495:
470:
465:
464:
441:
440:
417:
416:
376:
368:
344:
339:
326:
321:
317:
311:
310:
288:
277:
273:
267:
266:
252:
251:
225:
224:
199:
198:
133:
121:
101:
96:
95:
92:
75:
70:
26:diffusion flame
12:
11:
5:
2368:
2366:
2358:
2357:
2352:
2342:
2341:
2336:
2335:
2298:
2289:
2274:
2256:
2247:
2238:
2229:
2220:
2211:
2202:
2193:
2184:
2177:
2156:
2155:
2153:
2150:
2149:
2148:
2143:
2141:Luminous flame
2138:
2131:
2128:
2114:
2108:
2105:
2099:
2096:
2091:
2088:
2078:
2075:
2070:
2067:
2048:
2044:
2032:
2031:
2018:
2014:
2011:
2007:
2001:
1997:
1993:
1990:
1987:
1984:
1980:
1976:
1970:
1967:
1962:
1959:
1933:
1909:
1906:
1887:
1881:
1872:
1864:
1858:
1834:
1812:
1791:
1769:
1765:
1753:
1752:
1740:
1736:
1732:
1728:
1725:
1721:
1715:
1711:
1705:
1699:
1693:
1690:
1685:
1681:
1675:
1669:
1661:
1657:
1653:
1648:
1644:
1640:
1635:
1631:
1599:
1596:
1593:
1568:
1565:
1538:
1534:
1509:
1487:
1482:
1479:
1473:
1469:
1466:
1463:
1460:
1457:
1454:
1451:
1448:
1437:
1436:
1425:
1422:
1414:
1410:
1406:
1403:
1400:
1397:
1392:
1388:
1382:
1377:
1373:
1369:
1366:
1363:
1360:
1357:
1354:
1351:
1348:
1345:
1331:
1330:
1319:
1316:
1311:
1308:
1304:
1300:
1297:
1294:
1287:
1283:
1279:
1276:
1272:
1266:
1262:
1258:
1254:
1248:
1244:
1240:
1235:
1227:
1224:
1219:
1214:
1211:
1204:
1201:
1194:
1190:
1184:
1181:
1174:
1171:
1168:
1165:
1162:
1158:
1152:
1149:
1146:
1143:
1140:
1133:
1129:
1124:
1116:
1112:
1107:
1101:
1096:
1092:
1086:
1083:
1080:
1076:
1070:
1067:
1064:
1061:
1058:
1055:
1052:
1049:
1044:
1041:
1038:
1035:
1032:
1027:
1024:
1019:
1015:
1010:
1004:
999:
995:
989:
986:
983:
978:
974:
968:
964:
960:
957:
951:
946:
941:
937:
924:) is given by
913:
910:
907:
896:
895:
879:
876:
871:
867:
862:
856:
853:
850:
846:
835:
831:
825:
821:
811:
807:
802:
794:
790:
785:
778:
775:
752:
729:
709:
689:
683:
677:
649:
645:
640:
633:
625:
621:
596:
572:
546:
542:
513:
509:
504:
477:
473:
448:
424:
413:
412:
401:
396:
393:
389:
383:
379:
375:
371:
365:
360:
351:
347:
342:
333:
329:
324:
320:
314:
307:
302:
295:
291:
284:
280:
276:
270:
265:
262:
259:
245:Arrhenius form
232:
212:
209:
206:
173:
170:
167:
164:
161:
158:
155:
152:
147:
142:
137:
128:
124:
120:
116:
108:
104:
91:
88:
74:
71:
69:
66:
57:stoichiometric
38:premixed flame
13:
10:
9:
6:
4:
3:
2:
2367:
2356:
2353:
2351:
2348:
2347:
2345:
2331:
2327:
2323:
2319:
2315:
2311:
2310:
2302:
2299:
2293:
2290:
2285:
2281:
2277:
2275:9780511612701
2271:
2267:
2260:
2257:
2251:
2248:
2242:
2239:
2233:
2230:
2224:
2221:
2215:
2212:
2206:
2203:
2197:
2194:
2188:
2185:
2180:
2178:9780323138024
2174:
2170:
2169:
2161:
2158:
2151:
2147:
2144:
2142:
2139:
2137:
2134:
2133:
2129:
2127:
2125:
2121:
2117:
2106:
2104:
2097:
2095:
2089:
2087:
2085:
2076:
2074:
2068:
2066:
2062:
2046:
2042:
2012:
1999:
1995:
1991:
1988:
1982:
1974:
1968:
1960:
1947:
1946:
1945:
1931:
1924:for a scalar
1923:
1918:
1914:
1907:
1905:
1903:
1885:
1862:
1789:
1767:
1763:
1734:
1723:
1713:
1709:
1703:
1691:
1688:
1683:
1679:
1673:
1659:
1655:
1651:
1646:
1642:
1638:
1633:
1629:
1621:
1620:
1619:
1615:
1613:
1597:
1594:
1591:
1583:
1554:
1553:specific heat
1536:
1532:
1523:
1507:
1485:
1471:
1464:
1461:
1458:
1452:
1449:
1446:
1423:
1420:
1412:
1404:
1401:
1398:
1390:
1386:
1375:
1371:
1367:
1361:
1358:
1355:
1352:
1349:
1343:
1336:
1335:
1334:
1317:
1309:
1306:
1302:
1295:
1292:
1285:
1281:
1277:
1274:
1270:
1264:
1260:
1256:
1252:
1246:
1242:
1238:
1233:
1225:
1222:
1217:
1202:
1199:
1192:
1188:
1172:
1169:
1166:
1163:
1160:
1156:
1150:
1147:
1144:
1141:
1138:
1131:
1127:
1122:
1114:
1110:
1105:
1099:
1094:
1090:
1084:
1081:
1078:
1074:
1065:
1062:
1059:
1056:
1053:
1047:
1042:
1039:
1036:
1033:
1030:
1025:
1022:
1017:
1013:
1008:
1002:
997:
993:
987:
984:
981:
976:
972:
966:
962:
958:
955:
949:
944:
939:
935:
927:
926:
925:
911:
908:
905:
877:
874:
869:
865:
860:
854:
851:
848:
844:
833:
829:
823:
819:
809:
805:
800:
792:
788:
783:
776:
773:
766:
765:
764:
750:
743:
727:
707:
687:
675:
667:
647:
643:
638:
623:
619:
610:
594:
586:
570:
562:
544:
540:
531:
530:mass fraction
511:
507:
502:
493:
475:
471:
462:
446:
438:
422:
399:
394:
391:
387:
381:
377:
373:
369:
363:
358:
349:
345:
340:
331:
327:
322:
318:
312:
305:
300:
293:
289:
282:
278:
274:
268:
263:
260:
257:
250:
249:
248:
246:
230:
210:
207:
204:
197:
193:
140:
122:
118:
106:
102:
89:
87:
85:
81:
72:
67:
65:
63:
58:
55:
51:
47:
43:
39:
31:
30:band emission
27:
23:
22:Bunsen burner
18:
2313:
2307:
2301:
2292:
2265:
2259:
2250:
2241:
2232:
2223:
2214:
2205:
2196:
2187:
2171:. Elsevier.
2167:
2160:
2110:
2107:Applications
2101:
2093:
2084:flame holder
2080:
2077:Bunsen flame
2072:
2063:
2033:
1919:
1915:
1911:
1754:
1616:
1582:Lewis number
1438:
1332:
897:
414:
93:
76:
37:
35:
609:temperature
62:flame speed
54:homogeneous
2350:Combustion
2344:Categories
2152:References
2124:SI engines
1922:G equation
42:combustion
2010:∇
1986:∇
1983:⋅
1966:∂
1958:∂
1908:Turbulent
1871:&
1790:κ
1764:δ
1735:⋅
1727:∇
1724:⋅
1710:δ
1689:κ
1680:δ
1652:−
1592:ϕ
1508:λ
1462:−
1459:ϕ
1453:β
1381:∞
1372:∫
1307:−
1303:β
1257:−
1223:−
1200:−
1157:β
1148:−
1106:ν
1091:ρ
1040:−
994:ν
973:ρ
963:λ
906:ϕ
820:ν
784:ν
774:ϕ
751:ϕ
682:&
632:&
447:ρ
374:−
319:ρ
275:ρ
258:ω
231:ω
208:≫
205:β
194:when the
146:→
123:ν
103:ν
2284:56066895
2146:Oxy-fuel
2130:See also
664:are the
50:oxidiser
2330:9899999
1580:is the
1551:is the
1520:is the
1500:. Here
607:is the
583:is the
559:is the
490:is the
461:density
459:is the
435:is the
73:Laminar
2328:
2282:
2272:
2175:
1874:
1868:
1755:where
1418:
1333:where
685:
679:
635:
629:
415:where
2355:Fire
2326:PMID
2280:OCLC
2270:ISBN
2173:ISBN
1944:as:
1595:<
1439:and
909:>
48:and
46:fuel
2318:doi
2346::
2324:.
2314:37
2312:.
2278:.
2126:.
2113:NO
1524:,
611:,
587:,
563:,
532:,
494:,
463:,
439:,
247:,
211:1.
36:A
2332:.
2320::
2286:.
2181:.
2115:x
2047:L
2043:U
2030:,
2017:|
2013:G
2006:|
2000:L
1996:U
1992:=
1989:G
1979:v
1975:+
1969:t
1961:G
1932:G
1886:a
1880:M
1863:c
1857:M
1833:v
1811:n
1768:L
1739:n
1731:n
1720:n
1714:L
1704:a
1698:M
1692:+
1684:L
1674:c
1668:M
1660:L
1656:S
1647:L
1643:S
1639:=
1634:L
1630:U
1598:1
1567:e
1564:L
1537:p
1533:c
1486:F
1481:e
1478:L
1472:/
1468:)
1465:1
1456:(
1450:=
1447:a
1424:y
1421:d
1413:m
1409:)
1405:a
1402:+
1399:y
1396:(
1391:n
1387:y
1376:0
1368:=
1365:)
1362:a
1359:,
1356:m
1353:,
1350:n
1347:(
1344:G
1318:,
1315:)
1310:1
1299:(
1296:O
1293:+
1286:b
1282:T
1278:R
1275:2
1271:/
1265:a
1261:E
1253:e
1247:2
1243:/
1239:1
1234:}
1226:m
1218:F
1213:e
1210:L
1203:n
1193:2
1189:O
1183:e
1180:L
1173:1
1170:+
1167:n
1164:+
1161:m
1151:1
1145:n
1142:+
1139:m
1132:2
1128:O
1123:W
1115:2
1111:O
1100:2
1095:u
1085:b
1082:,
1079:p
1075:c
1069:)
1066:a
1063:,
1060:m
1057:,
1054:n
1051:(
1048:G
1043:1
1037:n
1034:+
1031:m
1026:u
1023:,
1018:2
1014:O
1009:Y
1003:m
998:F
988:n
985:+
982:m
977:b
967:b
959:B
956:2
950:{
945:=
940:L
936:S
912:1
894:.
878:u
875:,
870:2
866:O
861:Y
855:u
852:,
849:F
845:Y
834:F
830:W
824:F
810:2
806:O
801:W
793:2
789:O
777:=
728:b
708:u
688:n
676:m
648:2
644:O
639:W
624:F
620:W
595:T
571:R
545:a
541:E
512:2
508:O
503:Y
476:F
472:Y
423:B
400:,
395:T
392:R
388:/
382:a
378:E
370:e
364:n
359:)
350:2
346:O
341:W
332:2
328:O
323:Y
313:(
306:m
301:)
294:F
290:W
283:F
279:Y
269:(
264:B
261:=
172:s
169:t
166:c
163:u
160:d
157:o
154:r
151:P
141:2
136:O
127:O
119:+
115:F
107:F
32:.
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