凝并与沉降共存的直接蒙特卡罗模拟及其验证
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摘要
气溶胶动力学方程是描述气溶胶动力学变化的主要方程,凝并与沉降共存问题是相关领域的常见的问题。建立了对该类问题的分段算法和直接蒙特卡罗模拟(Direct Simulation Monte Carlo method,DSMC)计算方法,对DSMC中事件后系统参数的更新方法进行了改进,并提出了用纳入解析解的分段算法的结果对DSMC模拟结果进行验证的方法。结果表明,改进的DSMC算法显著提高了计算效率,模拟结果与其它算法的结果一致。
The Direct Simulation Monte Carlo method(DSMC) is one of the popular numerical simulation methods for solving the General Dynamic Equation(GDE),a description of aerosol dynamics.Coagulation and Settling are usually the most important mechanisms in the GDE. A modified DSMC for simulation of simultaneous coagulation and settling is proposed to save the computation time.Its evaluation method based on the sectional method and self-preserved distribution is proposed in this paper.The results of simulations show that the time consumption of the DSMC method could be reduced by a factor of 100 and 1000 while running 1000 and 10000 particles respectively.And the results of the DSMC method are consistent with those of the sectional method.
The Direct Simulation Monte Carlo method(DSMC) is one of the popular numerical simulation methods for solving the General Dynamic Equation(GDE),a description of aerosol dynamics.Coagulation and Settling are usually the most important mechanisms in the GDE. A modified DSMC for simulation of simultaneous coagulation and settling is proposed to save the computation time.Its evaluation method based on the sectional method and self-preserved distribution is proposed in this paper.The results of simulations show that the time consumption of the DSMC method could be reduced by a factor of 100 and 1000 while running 1000 and 10000 particles respectively.And the results of the DSMC method are consistent with those of the sectional method.
引文
1 Prakash A,Bapat A P and Zachariah M R.A simple numerical algorithm and software for solution of nucleation,surface growth, and coagulation problems.Aerosol Science and Technology.2003, 37(11):892-898.
2 Liffman K.A direct simulation Monte-Carlo method for cluster coagulation.Journal of Computational Physics.1992, 100:116-127.
3 Smith M and Matsoukas T.Constant-number Monte Carlo simulation of population balances.Chemical Engineering Science. 1998,53(9):1777-1786.
8 Zhao H,Maisels A,Matsoukas T,et al.Analysis of four Monte Carlo methods for the solution of population balances in dispersed systems.Powder Technology.2007,173(1 ):38-50.
9 Palaniswaamy G and Loyalka S K.Direct simulation,Monte Carlo,aerosol dynamics:Coagulation and condensation.Annals of Nuclear Energy.2008,35(3):485-494.
10 Sun Z,Axelbaum R and Huertas J.Monte Carlo simulation of multicomponent aerosols undergoing simultaneous coagulation and condensation.Aerosol Science and Technology.2004, 38(10):963-971.
11 Wemury S,Kusters K A and Pratsinis S E.Timelag for attainment of the self-preserving particle size distribution by coagulation. Journal of Colloid and Interface Science.1994,165:53-59.
12 Friedlander S K and Wang C S.The self-preserving distribution for coagulation by Brownian motion.Journal of Colloid and Interface Science.1966,22:126-132.
13 Dekkers P J and Friedlander S K.The self-preserving size distribution theory:I.Effects of the Knudsen number on aerosol agglomerate Growth.Journal of Colloid and Interface Science. 2002,248(2):295-305.
14 Kruis F E,Maisels A and Fissan H.Direct simulation Monte Carlo method for particle coagulation and aggregation.AIChE J.2000, 46(9):1735-1742.
15 Sheng C and Shen X.Simulation of acoustic agglomeration processes of poly-disperse solid particles.Aerosol Science and Technology.2007,41(1):1-13.
4徐珊姝,吴子牛,等.一般超音速过渡区气动特性的桥函数方法[J].计算物理,2009,26(3):362-370.
5张根烜,王璐,张先锋,刘明侯,等微喷管流的连续介质模型及其适应性[J].计算物理,2007,24(5):598-604.
6赵海波,郑楚光,徐明厚,等.处理多分散颗粒凝并和冷凝/蒸发问题的多重.Monte Carlo算法[J].化工学报,2005, 56(5):796-802.
7杜敏,郝英立,刘向东,等.DSMC方法在大规模气固两相撞击流中的应用[J].化工学报,2009,60(8):1950-1958.
2 Liffman K.A direct simulation Monte-Carlo method for cluster coagulation.Journal of Computational Physics.1992, 100:116-127.
3 Smith M and Matsoukas T.Constant-number Monte Carlo simulation of population balances.Chemical Engineering Science. 1998,53(9):1777-1786.
8 Zhao H,Maisels A,Matsoukas T,et al.Analysis of four Monte Carlo methods for the solution of population balances in dispersed systems.Powder Technology.2007,173(1 ):38-50.
9 Palaniswaamy G and Loyalka S K.Direct simulation,Monte Carlo,aerosol dynamics:Coagulation and condensation.Annals of Nuclear Energy.2008,35(3):485-494.
10 Sun Z,Axelbaum R and Huertas J.Monte Carlo simulation of multicomponent aerosols undergoing simultaneous coagulation and condensation.Aerosol Science and Technology.2004, 38(10):963-971.
11 Wemury S,Kusters K A and Pratsinis S E.Timelag for attainment of the self-preserving particle size distribution by coagulation. Journal of Colloid and Interface Science.1994,165:53-59.
12 Friedlander S K and Wang C S.The self-preserving distribution for coagulation by Brownian motion.Journal of Colloid and Interface Science.1966,22:126-132.
13 Dekkers P J and Friedlander S K.The self-preserving size distribution theory:I.Effects of the Knudsen number on aerosol agglomerate Growth.Journal of Colloid and Interface Science. 2002,248(2):295-305.
14 Kruis F E,Maisels A and Fissan H.Direct simulation Monte Carlo method for particle coagulation and aggregation.AIChE J.2000, 46(9):1735-1742.
15 Sheng C and Shen X.Simulation of acoustic agglomeration processes of poly-disperse solid particles.Aerosol Science and Technology.2007,41(1):1-13.
4徐珊姝,吴子牛,等.一般超音速过渡区气动特性的桥函数方法[J].计算物理,2009,26(3):362-370.
5张根烜,王璐,张先锋,刘明侯,等微喷管流的连续介质模型及其适应性[J].计算物理,2007,24(5):598-604.
6赵海波,郑楚光,徐明厚,等.处理多分散颗粒凝并和冷凝/蒸发问题的多重.Monte Carlo算法[J].化工学报,2005, 56(5):796-802.
7杜敏,郝英立,刘向东,等.DSMC方法在大规模气固两相撞击流中的应用[J].化工学报,2009,60(8):1950-1958.