A Discrete Lagrangian Particle Equation of Motion for Significant Reynolds Numbers and Diameters

It is often important to consider significant Reynolds numbers (e.g. up to 50) with respect to the drag, lift, torque, and history forces. Herein, an equation of motion is developed for solid spherical particles based on theoretical analysis, experimental data, and surfaceresolved simulations. Some comments are made with respect to the numerical implementation of this equation, especially with respect to the history force. The extension to significant particle sizes can be accomplished through spatial-averaging (both volumebased and surface-based) of the continuous flow properties. This averaging is consistent with the Faxen limit for solid spheres at small Reynolds numbers and added mass and fluid stress forces at inviscid limits. A discrete version of these corrections is generally an order of magnitude more accurate than point-force expressions.