Stochastic description of premixed turbulent combustion in terms of a coarse-grained flame surface density
✍ Scribed by Sergei P. Fedotov
- Publisher
- Elsevier Science
- Year
- 1996
- Tongue
- English
- Weight
- 528 KB
- Volume
- 106
- Category
- Article
- ISSN
- 0010-2180
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✦ Synopsis
The problem of premixed turbulent combustion has been formulated in terms of a stochastic differential equation for a coarse-grained flame surface density (FSD). A closed equation for the one-point probability density function (PDF) for FSD has been derived, using the functional derivative technique, together with the assumption that the convection velocity and flame stretch are homogeneous, isotropic, Gaussian random fields with many spatial scales and rapid oscillations in time. It has been shown that in the homogeneous case, the stationary PDF can be obtained analytically. It has been demonstrated that the most probable value of FSD that is preferentially observed in an experiment might be considerably different from its ensemble mean value. This observation suggests that the turbulent combustion cannot be generally characterized by the mean values of relevant parameters. 6), ( 9) see Eqs. ( 6), ( 10) three-dimensional spectrum of n(t, x) nonlinear term in Eq. (1) gamma function wave number random flame stretch parameter integral scale of turbulence see Eq. (7) one-point probability density function (PDF) of E steady PDF of E coarse-grained scale time random velocity field components of v(t, x) root mean square velocity coordinate components of x coordinate see Eq. (12) Greek Symbols a mean value of the flame stretch parameter k(t, x) /3 see nonlinear term in Eq. (1): f(~) =/3X 2 8(x) delta function
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