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_p^k) is then formulated in order to overcome the above limitations. Closure of the transport equation of k_p^k requires a model of the turbulence modulation term. Two simple turbulence modulation models are selected for the demonstration of k_p^k computations through two well-defined problems. Modifications to these two models are also made by introducing k_p^k variable into the models. It is found that the modified models yield more satisfactory k_p^k predictions than the original models in the test problems.