Stochastic modeling of the multiple rebound effects for particle–rough wall collisions

The statistical behavior of colliding spherical particles onto rough walls is investigated by simulating deterministic rebounds onto two geometric rough walls with different collision angles. The first wall is generated from Gaussian distribution of wall roughness angles, whereas the other consists in a Gaussian distribution of the wall roughness heights and positions. The distribution of wall roughness angles experienced by the incident particles at the first rebound matches the effective probability distribution function (PDF) given by Sommerfeld and Huber [Sommerfeld, M., Huber, N., 1999. Experimental analysis and modelling of particle–wall collisions. Int. J. Multiphase Flow 25, 1457–1489]. The probability of the particles to make multiple rebounds according to the first rebound angle is characterized. As shown by the probability distribution function of the effective particle rebound angles, the multiple rebounds appear to be crucial for the global behavior of the particles moving away from the near-wall region, especially for the particles hitting the wall with primary collision angles very close to zero (referred to as grazing incident angles or particles). The multiple rebound effects lead to a zero probability for the particles to rebound with a grazing angle after the final collision onto the rough wall, contrary to the results obtained with the “Shadow Effect Model”. With a special emphasis on the description of the rebound mechanisms shown by the simulation results obtained with deterministic rebounds, a new Lagrangian stochastic model based on only one rebound but incorporating the effects of multiple rebounds, is proposed for the particle–rough wall interaction. The model is validated by comparing the PDF of the effective rebound angle with available measurements.