Nonlinear relationships of two-phase Reynolds stresses with the strain rates together with the transport equations of gas and particle turbulent kinetic energy and the two-phase correlation turbulent kinetic energy are proposed as the nonlinear k-ε-$kp$ turbulence model. The proposed model is applied to simulate swirling gas-particle flows. The predicted two-phase time-averaged velocities and Reynolds stresses are compared with the PDPA measurements and those predicted using the second-order moment model. The results indicate that the nonlinear k-ε-$kp$ model has the modeling capability near to that of the second-order moment model, but the former can save much computation time than the latter.

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