An Advection-Diffusion-Reaction (ADR) Equation For Correcting The Self-Induced Velocity and Temperature Disturbances in Euler-Lagrange Point-Particle Methods

In two-way coupled particle-laden Euler-Lagrange simulations, the particles are assumed subgrid and their momentum and energy exchange with the surrounding fluid are modeled as point sources. For particles on the order of the grid resolution, this exchange introduces a local disturbance in the fluid flow that can substantially alter their undisturbed values needed for closure models, resulting in significant errors in the particle dynamics. To correct for this disturbance, advection-diffusion-reaction (ADR) equations are derived for the momentum and heat transfer and solved in addition to the standard conservation equations in two-way coupling. An embedded voxel based approach is used in a small region of influence surrounding each particle to solve these equations and to correct for their self-disturbance. Tests are performed to show that the approach is applicable to arbitrary shaped grids, range of Reynolds and Pectlet numbers, different Euler-Lagrange interpolation kernels, and catpturing hydrodynamic effects of neighboring particles in multiple-particle systems. The newly developed approach is accurate, easy to implement in any flow solver, and affordable.