On Mathematical Modeling of Swirling Turbulent Wakes with Varied Total Excess Momentum and Angular Momentum

Abstract

The flow in swirling turbulent wakes with varying total excess momentum and angular momentum is described using two second-order mathematical models. The first one includes averaged equations of momenta, turbulence energy balance, and dissipation rate in the far-wake approximation. The closure of the mathematical model relies on Rodi’s algebraic model for Reynolds stresses. The second model is based on simplified representations of the turbulent viscosity coefficients. For small distances, the calculated profiles of averaged motion velocities and turbulence energy are in good agreement with the experimental data of Lavrent’ev Institute of Hydrodynamics of SB RAS. At large distances, numerical experiments have yielded a self-similar solution of problems of dynamics of turbulent wake behind a self-propelled body and momentumless swirling turbulent wake. Group-theoretical analysis of the simplified mathematical model has been done. The model had been reduced to a system of ordinary differential equations, which was solved numerically using asymptotic expansions. The solution obtained was compared with the self-similar solution found by direct numerical integration of the differential equations of the model at large distances from the body, and good agreement was observed. In addition, the problem of asymptotic behavior of swirling turbulent wake behind a sphere with non-zero values of total excess momentum and angular momentum was considered. The group-theoretical analysis has shown the absence of physically meaningful self-similar solutions to the equations of the turbulence model under consideration.