×

Propagation of wrinkled turbulent flames in the context of hydrodynamic theory. (English) Zbl 1241.76437

Summary: We study the propagation of premixed flames in two-dimensional homogeneous isotropic turbulence using a Navier-Stokes/front-capturing methodology within the context of hydrodynamic theory. The flame is treated as a thin layer separating burnt and unburnt gases, of vanishingly small thickness, smaller than the smallest fluid scales. The method is thus suitable to investigate the flame propagation in the wrinkled flamelet regime of turbulent combustion. A flow-control system regulates the mean position of the flame and the incident turbulence intensity. In this context we study the individual effects of turbulence intensity, turbulence scale, thermal expansion, hydrodynamic strain and hydrodynamic instability on the propagation characteristics of the flame. Results are obtained assuming positive Markstein length, corresponding to lean hydrocarbon-air or rich hydrogen-air mixtures. For stable planar flames we find a quadratic dependence of turbulent speed on turbulence intensity. Upon onset of hydrodynamic instability, corrugated structures replace the planar conformation and we observe a greater resilience to turbulence, the quadratic scaling being replaced by scaling exponents less than one. Such resilience is also confirmed by the observation of a threshold turbulence intensity below which the propagation speed of corrugated flames is indistinguishable from the laminar speed. Turbulent speed is found to increase and later plateau with increasing thermal expansion, this affecting the average flame displacement but not the mean flame curvature. In addition, turbulence integral scale is also observed to affect the propagation of the flame with the existence of an intermediate scale maximizing the turbulent speed. This maximizing scale is smaller for corrugated flames than it is for planar flames, implying that small eddies that will be unable to significantly perturb a planar front could be rather effective in perturbing a corrugated flame. Turbulent planar flames, and more so corrugated flames, were observed to experience a positive mean hydrodynamic strain, which was explained in terms of the overwhelming mean contribution of the normal component of strain. The positive straining causes a decrease in the mean laminar propagation speed which in turn can decrease the turbulent speed. The effect of the flame on the incident turbulent field was examined in terms of loss of isotropy and vorticity destruction by thermal expansion. The latter can be mitigated by a baroclinic vorticity generation which is enhanced for corrugated flames.

MSC:

76V05 Reaction effects in flows
76F05 Isotropic turbulence; homogeneous turbulence
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] DOI: 10.1017/S0022112082002481 · Zbl 0545.76133 · doi:10.1017/S0022112082002481
[2] DOI: 10.1016/0010-2180(91)90126-V · doi:10.1016/0010-2180(91)90126-V
[3] Bray, Proc. Combust. Inst. 26 pp 1– (1996) · doi:10.1016/S0082-0784(96)80195-0
[4] Markstein, Nonsteady Flame Propagation (1964)
[5] Bray, Turbulent Reacting Flows pp 115– (1980) · doi:10.1007/3540101926_10
[6] DOI: 10.1016/0010-2180(94)90011-6 · doi:10.1016/0010-2180(94)90011-6
[7] DOI: 10.1016/S0360-1285(01)00007-7 · doi:10.1016/S0360-1285(01)00007-7
[8] Borghi, Recent Advances in the Aerospace Sciences pp 117– (1985) · doi:10.1007/978-1-4684-4298-4_7
[9] DOI: 10.1080/00102209208951848 · doi:10.1080/00102209208951848
[10] DOI: 10.1017/S0022112009991388 · Zbl 1183.76925 · doi:10.1017/S0022112009991388
[11] DOI: 10.1017/S0022112094003010 · doi:10.1017/S0022112094003010
[12] DOI: 10.1017/S0022112075001814 · Zbl 0301.76030 · doi:10.1017/S0022112075001814
[13] Williams, Combustion Theory (1985)
[14] DOI: 10.1016/0094-5765(74)90110-6 · doi:10.1016/0094-5765(74)90110-6
[15] Landau, Acta Physicochim. USSR 19 pp 77– (1944)
[16] DOI: 10.1063/1.868693 · Zbl 1026.76568 · doi:10.1063/1.868693
[17] DOI: 10.1006/jcph.1998.5890 · Zbl 0933.76055 · doi:10.1006/jcph.1998.5890
[18] Kobayashi, Proc. Combust. Inst. 26 pp 389– (1996) · doi:10.1016/S0082-0784(96)80240-2
[19] DOI: 10.1137/S0036139998346440 · Zbl 1061.76024 · doi:10.1137/S0036139998346440
[20] Aldredge, J. Fluid Mech. 228 pp 487– (1991)
[21] DOI: 10.1016/j.proci.2004.08.098 · doi:10.1016/j.proci.2004.08.098
[22] DOI: 10.1137/S0036139998346439 · Zbl 1061.76023 · doi:10.1137/S0036139998346439
[23] DOI: 10.1098/rspa.1987.0150 · doi:10.1098/rspa.1987.0150
[24] Kobayashi, Proc. Combust. Inst. 27 pp 941– (1998) · doi:10.1016/S0082-0784(98)80492-X
[25] DOI: 10.1051/jphys:019850046090148500 · doi:10.1051/jphys:019850046090148500
[26] DOI: 10.1016/0094-5765(77)90096-0 · Zbl 0427.76047 · doi:10.1016/0094-5765(77)90096-0
[27] DOI: 10.1016/S0360-1285(99)00006-4 · doi:10.1016/S0360-1285(99)00006-4
[28] DOI: 10.1103/PhysRevA.37.2728 · doi:10.1103/PhysRevA.37.2728
[29] Karlin, Phys. Rev. 73 pp 016305– (2006)
[30] DOI: 10.1103/PhysRevLett.56.889 · Zbl 1101.82329 · doi:10.1103/PhysRevLett.56.889
[31] Ronney, Modeling in Combustion Science pp 3– (1994)
[32] DOI: 10.1016/S0010-2180(02)00405-4 · doi:10.1016/S0010-2180(02)00405-4
[33] DOI: 10.1017/S0022112005008098 · Zbl 1156.76464 · doi:10.1017/S0022112005008098
[34] Hinze, Turbulence (1975)
[35] DOI: 10.1080/13647830500463502 · Zbl 1115.80315 · doi:10.1080/13647830500463502
[36] DOI: 10.1017/S0022112092003124 · doi:10.1017/S0022112092003124
[37] DOI: 10.1146/annurev.fl.19.010187.001321 · doi:10.1146/annurev.fl.19.010187.001321
[38] DOI: 10.1017/S0022112092000776 · Zbl 0744.76063 · doi:10.1017/S0022112092000776
[39] DOI: 10.1016/0360-1285(85)90002-4 · doi:10.1016/0360-1285(85)90002-4
[40] Ghenai, Proc. Combust. Inst. 27 pp 979– (1998) · doi:10.1016/S0082-0784(98)80497-9
[41] DOI: 10.1016/j.combustflame.2009.11.018 · doi:10.1016/j.combustflame.2009.11.018
[42] DOI: 10.1016/j.combustflame.2004.07.010 · doi:10.1016/j.combustflame.2004.07.010
[43] Poinsot, J. Fluid Mech. 228 pp 561– (1991)
[44] DOI: 10.1016/S0082-0784(00)80231-3 · doi:10.1016/S0082-0784(00)80231-3
[45] DOI: 10.1016/j.pecs.2007.04.002 · doi:10.1016/j.pecs.2007.04.002
[46] DOI: 10.1016/S1540-7489(02)80244-9 · doi:10.1016/S1540-7489(02)80244-9
[47] Damköhler, Z. Elektrochem. 46 pp 601– (1940)
[48] DOI: 10.1016/S0082-0784(00)80216-7 · doi:10.1016/S0082-0784(00)80216-7
[49] DOI: 10.1016/j.proci.2010.06.029 · doi:10.1016/j.proci.2010.06.029
[50] DOI: 10.1017/CBO9780511612701 · Zbl 0955.76002 · doi:10.1017/CBO9780511612701
[51] DOI: 10.1080/13647830.2010.538722 · Zbl 1219.80118 · doi:10.1080/13647830.2010.538722
[52] DOI: 10.1017/S0022112098004212 · Zbl 0948.76087 · doi:10.1017/S0022112098004212
[53] DOI: 10.1017/S0022112082000457 · Zbl 0511.76074 · doi:10.1017/S0022112082000457
[54] DOI: 10.1017/S0022112092002519 · Zbl 0779.76100 · doi:10.1017/S0022112092002519
[55] DOI: 10.1017/S002211207900241X · Zbl 0434.76052 · doi:10.1017/S002211207900241X
[56] Peters, Proc. Combust. Inst. 21 pp 1231– (1986) · doi:10.1016/S0082-0784(88)80355-2
[57] DOI: 10.1016/S1540-7489(02)80222-X · doi:10.1016/S1540-7489(02)80222-X
[58] DOI: 10.1016/S0082-0784(00)80213-1 · doi:10.1016/S0082-0784(00)80213-1
[59] DOI: 10.1103/PhysRevLett.28.76 · doi:10.1103/PhysRevLett.28.76
[60] DOI: 10.1016/j.combustflame.2005.09.017 · doi:10.1016/j.combustflame.2005.09.017
[61] DOI: 10.1016/S0010-2180(97)00122-3 · doi:10.1016/S0010-2180(97)00122-3
[62] Cambray, Proc. Combust. Inst. 24 pp 61– (1992) · doi:10.1016/S0082-0784(06)80012-3
[63] DOI: 10.1016/0094-5765(77)90097-2 · Zbl 0427.76048 · doi:10.1016/0094-5765(77)90097-2
[64] DOI: 10.1017/S0022112003004683 · Zbl 1071.76066 · doi:10.1017/S0022112003004683
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.