John B. McLaughlin

INERTIAL MIGRATION OF A SMALL SPHERE IN LINEAR SHEAR FLOWS

The motion of a small, rigid sphere in a linear shear flow is considered. Saffmans analysis is extended to other asymptotic cases in which the particle Reynolds number based on its slip velocity is comparable with or larger than the square root of the particle Reynolds number based on the velocity gradient. In all cases, both particle Reynolds numbers are assumed to be small compared to unity. It is shown that, as the Reynolds number based on particle slip velocity becomes larger than the square root of the Reynolds number based on particle shear rate, the magnitude of the inertial migration velocity rapidly decreases to very small values. The latter behaviour suggests that contributions that are higher order in the particle radius may become important in some situations of interest.

Aerosol particle deposition in numerically simulated channel flow

The trajectories of rigid spherical particles in a turbulent channel flow are computed using a pseudospectral computer program to simulate the three‐dimensional, time‐dependent flow field. It is assumed that the channel is vertical so that gravity cannot directly cause the deposition of particles on the walls. The particles are assumed to be sufficiently small and widely separated so that their influence on the fluid velocity field can be ignored. It is found that when the particles are assigned random initial locations with initial velocities that are equal to the local fluid velocity, the particles tend to accumulate in the viscous sublayer. At the edge of the viscous sublayer, the particles that deposit on the wall typically possess normal components of velocity that are comparable in magnitude to the intensity of the normal component of the velocity in the core of the channel (i.e., of the order of magnitude of the friction velocity). A shear‐induced lift force having the form derived by Saffman for laminar flow is found to have virtually no effect on particle trajectories, except within the viscous sublayer where it plays a significant role both in the inertial deposition of particles and in the accumulation of trapped particles. The Reynolds number of the particles that deposit does not remain small compared with unity.

The inertial lift on a rigid sphere in a linear shear flow field near a flat wall

An expression which predicts the inertial lift, to lowest order, on a rigid sphere translating in a linear shear flow field near a flat infinite wall has been derived. This expression may be used when the wall lies within the inner region of the spheres disturbance flow. It is valid even when the gap is small compared to the radius of the sphere. When the sphere is far from the wall, the lift force predicted by the present analysis converges to the value predicted by earlier analyses which consider the sphere as a point force or a force doublet singularity. The effect of rotation of the sphere on the lift has also been analysed.

Brownian diffusion of submicrometer particles in the viscous sublayer

Diffusion of Brownian submicrometer particles from a point source in the vicous sublayer of a turbulent shear flow near a solid smooth wall is considered in this paper. The equation of motion of particles including the Brownian effect is considered. Ensembles of 500 particle trajectories are evaluated, compiled, and statistically analyzed. Effects of particle size, density ratio, and source distance from the wall on particle concentration profile and wall deposition rate are studied. The results are compared with those obtained from the exact solution to the corresponding convective diffusion equation in the absence of turbulent fluctuations. The effect of turbulence near a wall is also considered. The results show that the Brownian effects play a significant role in the diffusion of submicrometer particles at distances less than 2 wall units from the solid surface. The effect of turbulence, however, could become significant during the ejection/inrush process.

The lift on a small sphere in wall-bounded linear shear flows

This paper presents a closed-form solution for the inertial lift force acting on a small rigid sphere that translates parallel to a flat wall in a linear shear flow. The results provide connections between results derived by other workers for various limiting cases. An analytical form for the lift force is derived in the limit of large separations. Some new results are presented for the disturbance flow created by a small rigid sphere translating through an unbounded linear shear flow.

On the role of the lift force in turbulence simulations of particle deposition

Abstract Most calculations of particle deposition in turbulent boundary layers have been performed using an equation of motion in which the form for the lift force is that in a linear shear flow for a particle far from any boundaries, the so-called Saffman formula. Both direct and large eddy simulations of particle deposition in turbulent channel flow have shown that the dependence of the deposition velocity on particle relaxation time is over-predicted using the Saffman force. Since the derivation of the Saffman force there have been more general derivations of the lift on a particle in a shear flow. In this paper an ‘optimum’ lift force is formulated which represents the most accurate available description of the force acting on a particle in a wall-bounded shear flow. The effect of the force was examined through large eddy simulation (LES) of particle deposition in vertical turbulent channel flow. The optimum force for depositing particles is approximately three times smaller than the lift obtained using the Saffman formula. LES results also show that use of the optimum force yields a dependence of the deposition velocity on particle relaxation time less than that obtained using the Saffman form and in better agreement with experimental measurements. Neglecting the lift force altogether leads to an even smaller dependence of the deposition velocity on particle relaxation time and is in better agreement with empirical relations, although the deposition rates are smaller than experimental measurements for particles with intermediate relaxation times.

Turbulent deposition and trapping of aerosols at a wall

The trajectories of aerosols are computed in a high‐resolution direct numerical simulation of turbulent flow in a vertical channel. The aerosol equation of motion includes only a Stokes drag force and the influence of the aerosols on the gas flow is assumed to be negligible. Since the flow is vertical, aerosols deposit as a consequence of the turbulent fluctuations and their own inertia. It is shown that the eddies which are responsible for aerosol deposition are the same eddies that control turbulence production. Typical aerosol trajectories are shown and related to eddy structure. A free‐flight theory suggested by Friedlander and Johnstone [Ind. Eng. Chem. 49, 1151 (1957)] is found to be based on reasonable assumptions about typical velocities of depositing aerosols as they pass through the viscous sublayer, but the theory is shown to be deficient in other respects. The distribution of normal velocities of the aerosols that deposit is compared to the distribution of fluid particle velocities in the visc...

Numerical simulation of particle-laden turbulent channel flow

This paper presents results for the behavior of particle-laden gases in a small Reynolds number vertical channel down flow. Results will be presented for the effects of particle feedback on the gas-phase turbulence and for the concentration profile of the particles. The effects of density ratio, mass loading, and particle inertia will be discussed. The results were obtained from a numerical simulation that included the effects of particle feedback on the gas phase and particle–particle collisions. The resolution of the simulation was comparable to the smallest scales in the particle-free flow, but the grid spacings were larger than the particle size. Particle mass loadings up to 2 and both elastic and inelastic collisions were considered. Particle feedback causes the turbulent intensities to become more anisotropic as the particle loading is increased. For small mass loadings, the particles cause an increase in the gas flow rate. It will be shown that the particles tend to increase the characteristic length scales of the fluctuations in the streamwise component of velocity and that this reduces the transfer of turbulent energy between the streamwise component of velocity and the components transverse to the flow. Particle–particle collisions greatly reduce the tendency of particles to accumulate at the wall for the range of mass loadings considered. This was true even when the collisions were inelastic.

Ellipsoidal particles transport and deposition in turbulent channel flows

Abstract Ellipsoidal particle transport and deposition in dilute turbulent channel flows are studied. The instantaneous fluid velocity field is generated by the direct numerical simulation (DNS) of the Navier–Stokes equation via a pseudospectral method. The particle equations of motion used include the hydrodynamic forces and torques, the shear-induced lift and the gravitational forces. Eulers four parameters (quaternions) are used for describing the time evolution of particle orientations. Ensembles of ellipsoidal particle trajectories in turbulent channel flows are generated and statistically analyzed. The results are compared with those for spherical particles and their differences are discussed. Effects of particle size and aspect ratio, turbulence near wall eddies, and the gravitational and hydrodynamic forces are studied. The DNS predictions are compared with the available experimental data and earlier sublayer model simulation results and reasonable agreements are observed.

Direct numerical simulation of passive heat transfer in a turbulent channel flow

Abstract A direct numerical simulation of fully developed turbulent channel flow is used to study fully developed passive heat transfer between the channel walls. The time-dependent, three-dimensional Navier-Stokes equation and the advection-diffusion equation are solved numerically with 1064960 grid points. No subgrid point modeling is used since all the important turbulence scales are resolved. The Reynolds number, based on the channel half-width and the bulk velocity, is 2262, and the Prandtl number is 1.