Direct Numerical Simulation of a particle-laden channel flow is performed, with particles assumed solid, spherical and heavy. Two-way coupling between fluidand particles is modeled with Stokes drag. The equations describing the fluid flow are solved with an Eulerian mesh and those describing particles are solved in a Lagrangian frame. The numerical code is validated with results from linear optimal growth from previous studies; the optimal growth of streamwise vortices resulting in streamwise streaks is still the most efficient mechanism for disturbance amplification at subcritical conditions as for the case of a single phase fluid.
We consider transition initiated by two initial disturbances well-known in literature, streamwise vortices and oblique waves. The threshold energy for transition is computed for both cases. It is observed that streamwise vortices in combination with an oblique wave as additional initial disturbance, result ina small increase of threshold energy compared to a clean fluid. In addition, the time at which transition occurs clearly increases for disturbances of equal initial energy. The threshold energy in the case of the so-called oblique scenario, increases by a factor about 4 in the presence of particles. The results are explained by considering the reduced amplification of oblique modes in the presence of particles.
The results from these two classical scenarios indicate that, although stability analysis shows hardly any effect on optimal growth, particles do influence secondary instabilities and streak breakdown, thus the non-linear stages of transition, in two different ways. The presence of particles introduced threedimensional, streamwise-dependent modulations, especially at low concentrations, that may trigger and enhance secondary instabilities of streamwiseindependent streaks. On the other hand, particles decrease the amplitude ofoblique modes thus delaying transition initiated by their nonlinear interactions as in the oblique scenario.
Stockholm: KTH Royal Institute of Technology , 2011. , 15 p.