(658b) A GPU-Based Monte Carlo Technique for the Simulation of Simultaneous Nucleation, Coagulation and Growth Based on Weighted Simulation Particles

The synthesis and production of particles is usually modelled with the help of the population balance equation (PBE). The Monte Carlo (MC)-simulation is one method â?? among others - to solve this equation numerically. It has the advantage, that it can be easily adapted to particle populations described by several particle properties, it can render single particle events and track thus the history of single particles. The usage of weighted simulation particles allows simulations with higher accuracy (Zhao et al. 2009) and the simple incorporation of nucleation-processes into the simulation in the scope of a hybrid approach (Menz et al. 2014; Hao et al. 2013).

The MC-simulations require in general large computational times which arise due to the demanding coagulation process. MC simulations are therefore not well suited for the coupling to CFD- or compartmental models. Several techniques have been proposed to overcome this problem. One of those recent approaches made use of a GPU and a fast approximation of the mean coagulation rate (Wei, Kruis 2013). Speed ups of a factor of 200 were reported by the mere use of the GPU for the coagulation process (Wei 2014).

We present in the following an extension of the constant-number algorithm for the simulation of coagulation (Wei, Kruis 2013). The operator splitting technique (Celnik et al. 2007) is used to simulate in an hybrid approach the growth of the simulated particles and nucleation of new ones during one MC time step. The implementation of the nucleation process is based on a parallel merging algorithm, which keeps the number of the simulation-particles constant. The growth of single simulation particles is simulated by the parallel solution of the corresponding differential equations describing the growth rates. This makes the simulation of condensation and evaporation processes possible. We present in this context the fast parallel summation technique in order to account for the mass-balance (i.e. the coupling to the gaseous phase). This coupling influences in turn the nucleation and condensation (or evaporation) rates of the simulated particles.

We present the application of this algorithm to a simple case study: the simulation of particle synthesis in a hot wall reactor and discuss the dependency of the particle properties on the used temperature profile.

This work was supported by the Deutsche Forschungsgemeinschaft in the frame of the priority program SPP 1679: Dynsim.

Bibliography

Celnik, M.; Patterson, R.; Kraft, M.; Wagner, W. (2007): Coupling a stochastic soot population balance to gas-phase chemistry using operator splitting. In Combust. Flame 148 (3), pp. 158â??176.

Hao, X.; Zhao, H.; Xu, Z.; Zheng, C. (2013): Population balance-Monte Carlo simulation for gas-to-particle synthesis of nanoparticles. In Aerosol Sci. Technol. 47 (10), pp. 1125â??1133.

Menz, W. J.; Akroyd, J.; Kraft, M. (2014): Stochastic solution of population balance equations for reactor networks. In J. Comput. Phys. 256, pp. 615â??629.

Wei, Jianming (2014): Comparison of computational efficiency of inverse and acceptanceâ??rejection scheme by Monte Carlo methods for particle coagulation on CPU and GPU. In Powder Technol. 268, pp. 420â??423.

Wei, Jianming; Kruis, Frank Einar (2013): A GPU-based parallelized Monte-Carlo method for particle coagulation using an acceptanceâ??rejection strategy. In Chem. Eng. Sci. 104, pp. 451â??459.

Zhao, H.; Kruis, F. E.; Zheng, C. (2009): Reducing statistical noise and extending the size spectrum by applying weighted simulation particles in Monte Carlo simulation of coagulation. In Aerosol Sci. Technol. 43 (8), pp. 781â??793.