A Two-order Moment Lagrange Model Based On PDF Theory And Large Eddy Numerical Simulation

PDF transport equation is a bond between the macro model and micro stochasticmodel of two-phase flow and an effective method to deal with the two-phase turbulentproblems. It is more reliable than the micro model and gets more information than themacro model. Meanwhile, large eddy numerical simulation is the most promising wayof simulating the turbulence at present. It needs fewer computational resources thandirect numerical simulation and gets more information than Reynolds average N—Sequations. Therefore, combining the PDF transport equation and large eddysimulation will be more effective to simulate the two-phase turbulence.This paper mainly studied the relationship between the Langevin equation ofparticle motion and the particle PDF transport equation. Firstly, the PDF transportequation was given which was based on the colored noise dimension expandingmethod. Then, the mean Lagrange equation and particle second-order momentequation were obtained based on PDF transport equation. Based on Langevin equation,the similar equation was also gained, and the two results with the different methodswere compared with each other. Finally, on the basis of this theory, a Two-OrderMoment Lagrange model was founded.A wall-jet-flow loaded with solid particles was simulated with the newTwo-Order Moment Lagrange model. Gas phase was simulated with large eddysimulation and particle phase was simulated with the Second-Order MomentLagrange model in this paper. Then the calculation values and experiment valueswere compared. It shows that new model in this paper can obtain more particlemotion information than previous method and improves the two-phase turbulencemodel in some extent. At the same time, this study can be viewed as a criterion tocompare with the PDF transport equation. It also lays a good foundation for solvingthe high-dimensional PDF equation.