Coefficient of heterogeneity in turbulent mixing zone

Abstract

The paper considers the equation for heterogeneity coefficient within the turbulent mixing area in the approximation of big Reynolds numbers and small Mach numbers. A mechanism is studied of the heterogeneity coefficient dissipation due to molecular diffusion. The Kolmogorov's hypothesis on developed turbulence is used to calculate a dissipative term. The model presented allows us to take into account the heterogeneity degree in LV- and KE-models of turbulent mixing. A system of equations allowing us to calculate directly the heterogeneity degree is derived for the case of the LV-model with the turbulent diffusion coefficient which is constant over the turbulent mixing area. A self-similar solution is derived for the heterogeneity coefficient which is in good agreement with the results of experiments and direct numerical simulations. The heterogeneity coefficient averaged over the mixing area is shown to depend weakly on the density drop between the mixing materials. Thus, it is kH = 0.25 at the drop n = 1–3, and at the drop n = 20 − kH = 0.23.

Measurement of spectral characteristics of the turbulent mixing zone

“…It is seen that the heterogeneity coefficient averaged over the mixing zone for both pairs of gases considered reaches the limiting value rather rapidly; this limiting value is Γ lim = 0.13 for A = 0.21 and Γ lim = 0.18 for A = 0.83. The limiting values Γ lim correspond to the range of the heterogeneity coefficient 0.15-0.25 obtained in model calculations [8,[11][12][13]. Figure 7 shows the spectral density of the mean square of fluctuations of the normalized concentration of the heavy gas as a function of the spatial frequency G(f ) for two pairs of gases at different time instants.…”