Stability analysis of channel flow laden with small particles.

This thesis deals with the stability of particle laden flows. Both modal and non-modal linear analyses have been performed on two-way coupled particleladen flows, where particles are considered spherical, solid and either heavy or light. When heavy particles are considered, only Stokes drag is used as interaction term. Light particles cannot be modeled with Stokes drag alone, therefore added mass and fluid acceleration are used as additional interaction forces. The modal analysis investigates the asymptotic behavior of disturbances on a base flow, in this thesis a pressure-driven plane channel flow. A critical Reynolds number is found for particle laden flows: heavy particles increase the critical Reynolds number compared to a clean fluid, when particles are not too small or too large. Neutrally buoyant particles, on the other hand, have no influence on the critical Reynolds number. Non-modal analysis investigates the transient growth of disturbances, before the subsequent exponential behavior takes over. We investigate the kinetic energy growth of a disturbance, which can grow two to three orders of magnitude for clean fluid channel flows. This transient growth is usually the phenomenon that causes transition to turbulence: the energy can grow such that secondary instabilities and turbulence occurs. The total kinetic energy of a flow increases when particles are added to the flow as a function of the particle mass fraction. But instead of only investigating the total energy growth, the non-modal analysis is expanded such that we can differentiate between fluid and particle energy growth. When only the fluid is considered in a particle-laden flow, the transient growth is equal to the transient growth of a clean fluid. Besides thes Stokes drag, added mass and fluid acceleration, this thesis also discusses the influence of the Basset history term. This term is often neglected in stability analyses due to its arguably weak effect, but also due to difficulties in implementation. To implement the term correctly, the history of the particle has to be known. To overcome this and obtain a tractable problem, the square root in the history term is approximated by an exponential. It is found that the history force as a small effect on the transient growth. Finally, Direct numerical simulations are performed for flows with heavy particles to investigate the influence of particles on secondary instabilities. The threshold energy for two routes to turbulence is considered to investigate whether the threshold energy changes when particles are included. We show that particles influence secondary instabilities and particles may delay transition.QC 2011101