Deposition of inertia-dominated particles inside a turbulent boundary layer

Abstract

Non-equilibrium mechanism in the transport of inertia-dominated particles was explained in the problem of particle deposition inside a turbulent boundary layer. Due to the finite inertia of particles and mean shearing of the carrier flows, the transport of inertia-dominated particles inside a turbulent boundary layer is seriously affected by a non-equilibrium memory effect, making the particle retain the memory of its earlier state after spending a characteristic time scale related with the turbulent deposition process. A non-equilibrium constitutive equation for the particle Reynolds stress was derived from the stochastic differential equation of motion of particles governed by the Stokes drag and shear-induced lift forces. This new constitutive model was then applied to the problem of particle deposition in the fully developed turbulent channel flows. It was theoretically predicted that for inertia-dominated particles with τ p +>10 the distribution of wallward drift velocity in the vicinity of the wall deviates considerably from the equilibrium profile due to an additional turbophoresis, which is generated by the non-equilibrium part of the wall-normal particle Reynolds stress depending on the particle inertia and mean shearing of the carrier flow. And it was also predicted that, when the shear-induced lift force induces a large discrepancy between the particle and fluid motions, the turbulent particle diffusivity might be considerably reduced by the effect of crossing trajectories, resulting in the decrease of diffusive deposition of particles. From this fact it could be postulated that although the shear-induced lift force reduces the diffusive flux of particles, the increase of non-equilibrium wallward drift due to the lift force overwhelms the reduction of diffusive flux and, eventually, enhances the particle deposition to the wall. The predicted deposition velocities as a function of particle relaxation time were in excellent agreement with existing numerical and experimental data.