On the hydrodynamic stability of a particle-laden flow in growing flat plate boundary layer

The parabolized stability equation (PSE) was derived to study the linear stability of particle-laden flow in growing Blasius boundary layer. The stability characteristics for various Stokes numbers and particle concentrations were analyzed after solving the equation numerically using the perturbation method and finite difference. The inclusion of the nonparallel terms produces a reduction in the values of the critical Reynolds number compared with the parallel flow. There is a critical value for the effect of Stokes number, and the critical Stokes number being about unit, and the most efficient instability suppression takes place when Stokes number is of order 10. But the presence of the nonparallel terms does not affect the role of the particles in gas. That is, the addition of fine particles ( Stokes number is much smaller than 1) reduces the critical Reynolds number while the addition of coarse particles ( Stokes number is much larger than 1) enhances it. Qualitatively the effect of nonparallel mean flow is the same as that for the case of plane parallel flows.