Verifying consistency of boundary conditions with integral characteristics of mass conservation for particulates in flow

The mass conservation equation of the particulate phase, in the form of Euler-type transport equation for particle-number density, is integrated to investigate issues related to its boundary condition consistency. For each of the effects of convection, diffusion and particle settling, the provided boundary conditions need to meet the requirement for well-posed problems physically and mathematically for particulate phase simulation. The integration of the conservative form of the transport equation yields the relations between the rate of change of the total particle number and the boundary conditions. Results of these relations are compared with numerical solutions using a finite-volume solver, of which the numerical formulation is also based on the conservative form of the transport equation. Cases for particulate flow in a room-scale chamber with various combinations of convection, diffusion and settling processes are used as examples for boundary-condition consistency verification.