Particle Velocity Fluctuations in Viscous Gas with Random Velocity as the Sum of Two Correlated Color Noises

Abstract

The article focuses on methods for studying the phenomenon of two-phase turbulent flows. The turbulence effect on the movement of solid particles in a viscous gas is under study. Dynamics of particles movement in a gas is written in the Stokes approximation, which allows us to suppose the dynamic relaxation time to be a constant value.The random gas velocity is modeled by the sum of two correlated random noises. It is shown that this approach makes it possible to model noise of any structural complexity. The paper describes two research methods based on fundamentally different Euler and Lagrange approaches to the description of a continuous medium. The first approach uses a well-known generalization of the spectral analysis technique for random processes, a popular method for studying turbulence. The second approach implementation is based on the modern generalizations of the theory of numerical algorithms for solving stochastic ordinary differential equations. The spectral method is used to obtain analytical expressions of correlation functions and variance of random processes describing the velocity of gas and solid particles. The qualitative difference between the correlation of fluctuations of modulated random velocities and the behavior of correlations in the case of a single-component gas velocity composition is analyzed. A method of direct numerical simulation for studied processes based on the numerical solution of a stochastic ordinary differential equations system is proposed and analyzed in detail. An array of statistical data obtained as a result of direct numerical modeling is collected and processed. Analytical results are compared qualitatively with numerical results. The influence of input parameters on the character of turbulent flow is studied. The dynamic relaxation time has a significant effect on the complexity of the autocorrelation function of the particle velocity and the response function of particles to gas velocity fluctuations. It is shown that the obtained functions tend to the known results of the standard theory. The considered methods for describing two-phase turbulent flows hold promise for further research.