Progress in Energy and Combustion Science, Vol.21, No.2, 153-171, 1995
Microscales of Turbulent Combustion
A novel approach leading to the microscales of complex turbulent flows is reviewed. The approach is illustrated in terms of the classical microscales proposed by Taylor, Kolmogorov, Oboukhov-Corrsin and Batchelor. A thermal mesomicroscale between the Kolmogorov and Batchelor scales, eta(theta) = (eta eta(B)(2))(1/3) is introduced. Here eta and eta(B), respectively, denote the Kolmogorov and Batchelor scales, nu and alpha the kinematic and thermal diffusivities, and epsilon the rate of turbulent mechanical energy per unit mass. The foundations of the well-known correlation for forced convection over a flat plate, Nu(l) similar to Re-l(3/4) Pr-1/3, l being an integral scale, is interpreted in terms of l, eta and eta(theta). The approach is utilized to construct the microscales of forced and natural diffusion flames. In terms of a dame Batchelor scale eta B = (nu(beta)D(beta)(2)/epsilon)(1/4), the thermal scale is extended to a flame mesomicroscale, eta(beta). Here nu(beta) = nu (1 + B) and D-beta = D (1 + B), respectively, denote the flame momentum diffusivity and the b-property diffusivity, nu and D being the usual diffusivities and B the transfer number. A model for the fuel consumption in forced flames is proposed in terms of eta(beta). The model correlates well with the existing experimental data. For buoyancy driven flames, a Kolmogorov scale eta(beta) similar to (1 + sigma(beta))(1/4) (D-beta(3)/B)(1/4). is proposed. Here sigma(beta) = nu/D-beta denotes a flame Schmidt number, B being the rate of buoyant energy production. The limit of this scale for sigma(beta) --> 0 turns out to be a flame Oboukhov-Corrsin scale, eta(c) similar to (D-beta(3))(1/4)/B). A model for the fuel consumption in buoyancy-driven flames is proposed in terms of eta(beta). The model correlates well with the existing experimental data. For oscillating (on the mean) flows, a Kolmogorov scale, eta similar to (nu(3)/epsilon)(1/4)/[1 + omega(nu/epsilon)(1/2)](1/2) is proposed. Here omega denotes the frequency of externally imposed-internally induced flow. The two limits of this scale corresponding to omega --> 0 and omega --> infinity are the usual Kolmogorov and Stokes scales. A model for heat transfer in pulse combustor tailpipes is proposed in terms of eta. The model correlates well with the existing experimental data.