Numerical analysis of nonlinear stability of two-phase flow in the blasius boundary layer

Two mathematical models (i.e., perturbation and energy balance equations) are established to study the nonlinear stability of two-phase flow in the Blasius boundary layer based on the weakly nonlinear theory. The derived equations are discretized using the finite difference method. The results show that the averaged Reynolds stress is the fundamental consequence of the nonlinearity, and has a substantial effect on the mean flow. The distortion of the mean flow caused by the Reynolds stress modifies the rate of energy transfer from the mean flow to disturbance. The existence of particles alleviates the distortedness. The minimum critical Reynolds number is close to but less than the calculated value from the linear stability equation. The addition of fine and coarse particles to the Blasius boundary layer has destabilizing and stabilizing effects, respectively. The nonlinear interaction between mean flow and disturbance reduces the growth rate of the disturbance, while the nonlinear interaction between particle phase and gas phase increases the growth rate of the disturbance.