Derivation of a pdf kinetic equation for the transport of particles in turbulent flows

A transport equation for the particle phase space density (probability dens ity function (pdf) kinetic equation) is derived for the motion of a dilute suspension of particles in a turbulent flow. The underlying particle equati on of motion is based upon a Langevin equation but with a non-white noise d riving force derived from an Eulerian aerodynamic force field whose statist ics are assumed known. Specifically both the particle position and velocity are considered to be functionals of the driving force and an application o f a more general form of the Furutsu-Novikov theorem leads to closed expres sions for the phase space diffusion current (i.e. the net force due to the turbulence acting on the particles per unit volume of phase space). In the case of a Gaussian random driving force the closed expressions reduce to a simple Boussinesq form in gradients of the pdf with respect to particle vel ocity and position. As a practical application solutions of the equation ar e compared with results obtained from particle tracking in a developing sim ple shear generated by large eddy simulation.