Computational fluid dynamics based stochastic aerosol modeling: Combination of a cell-based weighted random walk method and a constant-number Monte-Carlo method for aerosol dynamics

No method is currently available to combine stochastic, particle-based PBE modeling by means of Monte-Carlo simulation of individual particles and CFD. CFD is based on solving numerically partial differential equations, whereas Monte-Carlo simulation of the PBE bases on converting kinetic rate equations into probabilities and selecting the relevant events by means of random numbers. A joint mathematical framework is thus missing. The goal of this work is to develop a method which allows combining Monte-Carlo based PBE modeling with a CFD model. As a first step towards this goal, a Weighted Random Walk (WRW) method to simulate the particle transport due to convection and diffusion is developed. The simulation particles have no exact position as in Lagrangian particle tracking methods but belong to a CFD cell. The movement of the simulation particles in space is performed by calculation of the transition probability into the neighboring cells and the use of random numbers to simulate the particle transport into these cells. As the particle number concentration can be very different in different regions of the simulated reactor volume, we introduce here also a weighting method which allows fixing the number of simulation particles per cell. The WRW method is combined with a relatively simple constant-number MC method allowing to simulate stochastically the dynamic evolution of the particle population. Four different validative case studies of increasing complexity are performed, comparing the simulation results with those of a CFD-based moment model.