Stochastic modelling of three-dimensional particle rebound from isotropic rough wall surface

Abstract

This paper describes an extension of the two-dimensional approach to particle-rough wall collision modelling (Sommerfeld and Huber, 1999; Konan et al., 2009) to the case of three-dimensional particle rebound from an isotropic rough wall surface. The virtual three-dimensional rough wall is represented as a Gaussian correlated surface. Normal vector angle statistical distributions are investigated in detail for such virtual rough walls, and a statistical modelling approach for these angles is proposed and validated in the frame of the low roughness approximation. Next, deterministic simulations of fully elastic particle collisions with the three-dimensional virtual wall roughness structure are carried out for various particle incident angles. It is shown that the rebound angle, in the bouncing plane of the particle, obeys the distribution given by the two-dimensional modelling approach. However, the three-dimensional structure induces a transverse deviation bouncing angle that obeys a Gaussian distribution with a standard deviation that increases with increase in incident angle. A statistical modelling approach for the virtual wall normal vector seen by any particle for a given incident angle is proposed and validated from deterministic simulation results. The probability that particles make only one rebound is in agreement with the two-dimensional multiple-collision model assumption. A new stochastic procedure for particle-isotropic rough wall interactions in a Lagrangian framework is developed and verified by comparisons with deterministic simulations and available experimental results.