Mathematical model of turbulence based on the dynamics of two fluids

Abstract

The paper presents an elaboration of a well-known two-fluid model for the description of turbulence. The idea that a turbulent flow can be modeled by considering a heterogeneous mixture of two fluids that make a relative motion is proven mathematically in the paper. It is shown that the fluctuating nature of the turbulent flow is due to relative motion of these fluids. Therefore, the proposed mathematical model is based on the theory of the dynamics of two fluids. For each fluid its own equation of motion is written, that leads to a closed system of equations. To calibrate the unknown constants of a new model, a problem of turbulent flow around a flat plate is considered. It is shown that the model is a low-Reynolds-number model. To verify the calibrated model, numerical studies of round and plane turbulent jets for various flow sections are conducted. It is shown that the model is not affected by the well-known problem of “round jet anomaly”. Another problem is investigated - an abrupt expansion of a strongly swirling flow - to study the possibility of the proposed model to describe anisotropic turbulent flows. The derived model is validated by comparing the results of numerical calculations with existing experimental data.