The Finite Analytic/Grid Approach To Solve PDF Transport Equation Of Two-phase Flow

It is a difficult problem that how to solve the high-dimensional scalar particle PDF transport equation of two-phase flows in position-velocity phase space. An numerical method, Finite Analytic/Particle approach, was put forward in our previous work, and the particle high-dimensional scalar PDF transport equation reduced to velocity phase space and position space, in which the reduced PDF equation in velocity phase space can be solved analytically and the reduced PDF equation in position phase space can be solved by Monte Carlo techniques.In this paper, a new method named Finite Analytic/Grid approach is promoted in which the particle high-dimensional scalar PDF transport equation in position-velocity phase space is reduced to velocity phase space and position phase space too, and the particle velocity PDF and the particle position PDF are gained using different methods. On the one hand, an analytical solution of the particle velocity PDF is obtained by Fokker-Planck techniques; on the other hand, the particle position PDF is solved by finite difference method, which determines the distribution of particles in two-phase flow. As an example, an simple two-phase flow was simulated using present method, and it is shown that the Finite Analytic/Grid approach is succeed to simulate the two-phase flow by comparing the numerical simulation with the experimental results.At last, a wall-jet-flow loaded with solid particles is simulated both using the Finite Analytic/Grid method and the Finite Analytic/Particle approach. The numerical results of the two methods are analyzed and compared with the experimental results. It is concluded that the Finite Analytic/Grid method is much better to forecast the average velocity of particles than Finite Analytic/Particle approach, can improve the results of particle fluctuating velocity, calculate particles concentration easily and obtain smooth curve of particles concentration distribution.