60th Annual Report on Research 2015

Report

In this year, we studied slip flow in porous media geometry models made up by overlapped spheres and randomly connected 2D channel networks, characterized the effect of finite Reynolds number on the drag coefficient of periodic arrays of spheres with slip boundaries, and compared DSMC simulations with lattice Boltzmann simulations in the slip flow regime in a 2D channel.

For geometry of overlapped spheres, we noted that the scheme of computing the surface normal has an influence over the stability of the numerical simulation, and the scheme that uses the local configuration of fluid and solid nodes to compute the surface normal provides a solution. In these geometries, as hypothesized, the contrast between pore body and pore throats, which increases with decreasing porosity, intensifies the degree of slip. Dimensionless permeability, defined as k_app / k where k_app is the apparent permeability and k is the Darcy permeability, increases with increasing Knudsen number and increases with decreasing porosity. Nonlinearity is observed in the dependence of k_app / k on the Knudsen number and it is attributed to the curvature of the solid surface. Indeed, in slip flows through 2D channel networks, very little nonlinear dependence of k_app / k on the Knudsen number was observed.

We extended the previously reported study of drag / permeability of periodic arrays of spheres by increasing the Reynolds number of the flow from zero (Stokes flow) to 5-8. Slip is usually associated with low Reynolds number; however, in certain processes such as combustion and dust transport in rarefied conditions, slip can be associated with finite Reynolds number, yet the flow still has a low Mach number and can be treated as nearly incompressible. We characterized the drag on periodic arrays of spheres with low Knudsen number and finite Reynolds number, as the first attempt to understand the effect of hydrodynamic interaction on drag under rarefied conditions, and established correlations.

To compare with lattice Boltzmann simulations with slip, we conducted preliminary DSMC simulations of rarefied flow through a 2D channel. Agreement between DSMC and lattice Boltzmann simulation agreed until Knudsen number reached about 0.2. We will continue to compare DSMC and lattice Boltzmann simulations in more complex geometries, to establish the respective ranges of Knudsen numbers for the two direct simulation methods.

This grant has been used to fund a PhD student, co-fund an undergraduate student, and co-fund a postdoctoral researcher’s position, which was held by the PhD student for six months after his graduation.

Figures

Figure 1 – Comparison between DSMC simulation (dots) and lattice Boltzmann simulation with surface slip (line) at Kn = 0.171. The tangential momentum accommodation equals 1.0.

Figure 2 – Distribution of x-velocity in a 2D porous medium model with random channel network. Flow direction is from left to right. The porosity of the model is 49%, Kn = 0.05 and the tangential momentum accommodation coefficient is 0.8. All units are in lattice units (unit grid spacing and time step).