Lagrangian Transport Equation of Fluctuating Kinetic Energy in the Dispersed Phase

Limitations of the conventional stochastic approach which is widely used in the study of two-phase turbulent flows are addressed. The Lagrangian transport equation of the fluctuating kinetic energy in the dispersed phase (k^k_p) is then formulated in order to overcome the above limitations. Closure of the transport equation of k^k_p requires a model of the turbulence modulation term. Two simple turbulence modulation models are selected for the demonstration of k^k_p computations through two well-defined problems. Modifications to these two models are also made by introducing k variable into the models. It is found that the modified models yield more satisfactory k^k_p predictions than the original models in the test problems.