On the modeling of scalar diffusion in isotropic turbulence
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The objectives of this paper are (i) to establish analytically some important features of the scalar diffusion process in turbulence and (ii) to derive a closure model for this process in terms of the scalar probability density function (pdf). The present analysis shows that hi isotropic turbulence the conditional scalar dissipation [χ(ψ)=D〈∂ø/ ∂xi∂ø/∂xi|ø=ψ〉], its derivative (∂χ/∂χ), and the conditional scalar diffusion [Θ(ψ)=D〈∂2ø/∂xi∂xi|ø=ψ〉] are zero at the extreme values of scalar concentration. Models for conditional-dissipation ratio (χ/∈s) and conditional-diffusion ratio (Θ/∈s) are derived from the observation [Girimaji, Combust. Sei. Technol. 78, 177 (1991); NASA Contract. Rep. CR 4446 (1992)] that the scalar pdf can be characterized by the β pdf at all stages of non-premixed mixing. The conditional-dissipation model is compared with the DNS data of Eswaran and Pope [Phys. Fluids 31, 506 (1988)] and the mapping-closure-based model [O'Brien and Jiang, Phys. Fluids A 3, 3121 (1991)]. The application of the model to multiscalar mixing is also briefly discussed.
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