This dissertation aims to contribute to the knowledge of the effect of the addition of particles in the transition to turbulence of pipe flows. The following work studied, to this end, the linear stability of a particulate pipe flow where the solid phase is modelled with an Eulerian formulation and the system resolved using of an eigenvalue solver. This work has been extended to a linear transient growth analysis, with the same physical model and solid phase formulation. The transient growth analysis has been conducted with a linear Direct Numerical Simulation code. An iterative variational method has been used to obtain the flow transient growth. The last part of this work considers a point particle model using a mixed Eulerian-Lagrangian formulation, where the fluid phase is described with a standard Eulerian formulation while the solid phase behaviour is determined through particle Lagrangian tracking. This allows for a nonlinear analysis of the particulate flow, done with a DNS code. The linear stability analysis showed that the addition of particles can lead to linear instability at experimentally realistic parameters, as opposed to the single phase pipe flow which is linearly stable for all Reynolds numbers. This thesis also highlights the important role of the particles size on the flow stability. Smaller particles have a destabilising effect on the flow stability while the effect is inverted as particles become larger. Another critical parameter is the distribution of particles across the pipe, in particular across the particle radius. The effect of the particles on the flow stability is stronger when they are concentrated closer to the Segré-Silberberg radius. In particular, linear instability has only been observed when particles are concentrated in an annulus whose position is close to the Segré-Silberberg radius. The flow transient growth is also significantly increased by the addition of particles, in particular for, again, particles concentrated close to the Segré-Silberberg radius, for which the transient growth can be more than tripled compared to the case of the single phase flow. Moreover, we found with the point particle model a tendency for medium-sized particles to migrate and accumulate close to the wall, where their effect on the flow stability is larger.
|Date of Award||Aug 2019|
|Supervisor||Chris Pringle (Supervisor) & Alban Potherat (Supervisor)|