Transition in Particle-laden Flows
Sammanfattning: This thesis presents the study of laminar to turbulent transition of particle laden flows. When a flow becomes turbulent, the drag increases one order of magnitude compared to a laminar flow, therefore, much research is devoted to understand and influence the transition. Previous research at the Linne Flow Centre at KTH has concentrated on the understanding of the bypass transition process of single-phase fluids. Though there are still questions, the principles of this process are now, more or less, known. However, little is known of the influence of particles on transition. While experiments in the 1960s already showed that particles can reduce the friction in turbulent channel flows significantly. The question explored in this thesis is whether this can be attributed to their influence on transition.The initial onset of transition has been investigated with both modal and non-modal linear stability analysis in a Poiseuille flow between two parallel plates. Particles are introduced as a second fluid and they are considered to be solid, spherical and homogeneously distributed. When the fluid density is much smaller than the particle density, ξ (≡ ρf/ρp) << 1, an increase of the critical Reynolds number is observed. However, transient growth of streamwise vortices resulting in streaks is not affected by inclusion of particles. Particles with ξ ∼ 1 hardly seem to have an effect on stability.Although linear analysis shows that particles hardly influence the transient growth of disturbances, they might affect other (non-linear) stages of transition. To investigate such effects, the full Navier-Stokes equations for 3D Poiseuille flow between two parallel plates are numerically solved and particles are introduced as points with two-way coupling. For particles in a channel flow with ξ<<1, results show that the transition to turbulence is delayed for mass fractions ƒ (=mp N / ρf) larger than 0.1. For a mass fraction of ƒ=0.4 the initial disturbance energy needed to get a turbulent flow increases with a factor of four.Even if lower particle mass fractions ƒ are used, locally there could be large particle mass fractions. Therefore, the next step is to investigate the generation of local large particle mass fractions ƒ. Such particle clusters can be as large as the typical flow structures in the flow, like streak width and vortex size. Then they might change the flow field and (in)stability mechanisms. Numerical simulations of bypass transition in a boundary layer flow are used to determine whether particles cluster and where they tend to cluster. It is found that point particles with ξ<<1 and a large particle relaxation time tend to move in the low speed regions of the flow. In case of streaks, the low speed streaks are most favourable. For smaller particle relaxation times, particles act as tracers and do not have a preferential position and are homogeneously distributed.For particles with ξ∼1 the linear stability analysis showed no transition effect at any ƒ. However, one effect neglected until now is that of particle size. For particles with dimensions of the same order of magnitude of the flow disturbance, particles might influence the flow field. To investigate whether such particles migrate towards positions where they can affect transition some exploratory numerical simulations and experiments are performed.Numerically, the lateral migration of large particles (H/d=5) with ξ=1 in a 3D Poiseuille flow between two parallel plates is investigated. In laminar channel flow, large particles tend to move laterally due to shear to an equilibrium position. For a single large particle some key parameters for migration are identified: the size of the particle and the velocity of the fluid. When multiple particles are present, they tend to form particle trains. If particles are close, they influence each other and the equilibrium position shifts towards the wall, where the final position is dependent on the inter particle spacing. Also, not one steady equilibrium position is present, but particles move around an equilibrium position.Experimentally, migration of particles in bypass transition with ξ=1 is investigated to find out whether neutrally buoyant particles have a preferential position within streaks. The first results with tracer particles (d∼50μm) and few large particles (d∼200μm) do not show detectable preferential positioning.
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