湍流两相流的脉动速度联合PDF输运方程

A JOINT FLUCTUATION VELOCITY PDF TRANSPORT EQUATION OF TWO-PHASE FLOWS

概率密度函数（PDF）的方法是构造两相湍流模型的一种重要的方法.构建气体-颗粒速度联合PDF输运方程的关键是颗粒所见气体微团速度的Langevin方程.首先由N-S方程出发,精确推导出颗粒所见气体微团脉动速度的Langevin方程,进而通过理论分析表明,对比通常采用的颗粒所见气体微团瞬时速度的Langevin方程而言,采用前者能有效地减少关联量的统计偏差.最后,给出了颗粒-气体脉动速度的联合PDF输运方程.

The probability density distribution function (PDF) is one of important methods for developing the two-phase turbulence model. In the PDF method, for developing the joint PDF equation of two-phase velocity correlation, the key point is to propose a Langevin-type equation of the fluid velocity seen by particles, as a closure assumption of the PDF transport equation. In this paper, at first the Langevin equation of fluid fluctuation velocity seen by particles is exactly derived on the basis of the Navier-Stokes equations and the continuity equation of the gas phase with the help of Reynolds averaging scheme. This equation includes the increment due to the particle displacement relative to the fluid element path, and thus it is more accurate than the equations suggested by other researchers. Then, analysis on the error of bias associated with the Langevin equation for the instantaneous velocity seen and our derived Langevin equation is carried out. The results indicate the superiority of the Langevin equation for the fluid-particle fluctuation velocity compared with that for the instantaneous fluid-particle velocity in the following three aspects: All the interested correlations as well as their corresponding biases are independent of the number N of the samples representing the fluid field; Our equation does not require the time-averaging technique, so it will reduce the cost of computation; And the numerical solution of the equations is convergent regardless of the values of a, which is very important to the numerical simulation. Finally, a joint PDF transport equation for the fluid-particle fluctuation velocities is obtained.