Features of a~turbulent mixing model based on the two-component model with different velocities of each component. Separation addition to diffusion models

V. Y. Neuvazhaev

Matematičeskoe modelirovanie, Tome 7 (1995) no. 7, pp. 3-18.

Résumé

Features of D. Youngs well-known turbulent mixing model have been studied in the simplest case of two incompressible fluids. The model is based on using its own velocity for each component and allows to take components separation into account. It was shown that in the considered case the initial system of equations is reduced to two quasi-linear equations for mixture density $\rho$ and length scale $L$. On some assumptions these equations have been integrated, and the solution has been built in an analytical form. The analysis of its features leads to the recommendation with respect to the choice of exchange terms as well as to suggestions for improving the model. Within the limits of the known diffusion $k$ and $k\varepsilon$ models the method taking the separation into account by adding an appropriate transposed term was suggested. Here the analytical solutions for acceleration changing a sign and specified by a stepwise manner have been built. The transposed term role has been studied and it was shown that the term should be taken into account only in a stable (separation) section of acceleration action. The obtained solutions allowed to carry out processing Yu. A. Kucherenko and A. P. Pylaev experiments, to substantiate the self-similar character of separation and to determine the constant as characterizing the intensity of separation.