Mathematical modeling of turbulent flow with homogeneous condensation in the supersonic nozzle

The flow of water vapor in a supersonic nozzle is examined. A mathematical model of homogeneous condensation process, which takes into account in the expression for the rate of formation of supercritical clusters influence of turbulence, is proposed. The formation rate of supercritical clusters is determined in accordance with the Smoluchowski coagulation equation $J = K n_{g-1} n_{g-2}$ as the multiplication of the concentrations of the colliding components, where $K = 8 \pi R D$ rate constant depends on the size of the colliding particles and it's diffusion rate in the gas mixture. Accounting turbulence provided by introducing into the expression for the rate constant of diffusion formation of supercritical clusters a values of the coefficient of turbulent diffusion $D_t$. In the simulation of turbulent flows by analogy with the molecular transport the turbulent diffusion coefficient associated with the turbulent viscosity through the turbulent Schmidt number — $D_t = \varepsilon / Sc_t$. Numerical simulation of two-dimensional axisymmetric and one-dimensional flows has been done. For modeling of turbulence in a two-dimensional axisymmetric flows used Nut-92 model, and in one-dimensional flows — Prandtl mixing length model. The good qualitative and quantitative agreement between the results of calculations by presented mathematical model with experimental data are shown.