Modified k- ϵ model for two-phase turbulent jets

Abstract

A modified k- ϵ model is proposed for two-phase turbulent jets which takes into account the additional dissipation of turbulent kinetic energy by the dispersed phase. Within the context of the two-phase averaged equation for the turbulent kinetic energy of the continuous phase, a constitutive relation is proposed for the additional dissipation of turbulence. The additional dissipation effect was modeled using a transfer function, which relates the fluctuations of the dispersed phase with the fluctuations of the continuous phase, integrating over the turbulence energy spectrum. A further improvement to the theory considers that dissipation only occurs when the eddies are bigger than the particles. Therefore a cutoff frequency is proposed and for big particles or bubbles dissipation may become negligible. The model is inserted in an Eulerian computational fluid dynamics code. The results are compared with data available in the literature for an air-particle jet. The results agree with the data within the range of experimental error. Comparisons were also made without including dissipation effects and it was concluded that the dissipation due to eddy-particle interactions is significant and should be included in a general two-phase k- ϵ model.