均匀湍流内有限惯性颗粒碰撞率的直接模拟
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摘要
燃烧源可吸入颗粒物对于人体健康和自然环境有严重的危害作用,了解其在燃烧过程中生成和长大过程的机理是在燃烧过程中控制颗粒物生成的前提,其核心问题之一是颗粒-颗粒的碰撞和凝并过程。而由于湍流对细微颗粒具有复杂的输运作用和局部聚集效应,细颗粒的碰撞率将不同于常规的几何碰撞率。研究具有有限惯性、并有局部富集条件下颗粒的碰撞率是目前两相流体力学和气溶胶动力学的研究热点之一。
本文在系统总结有关颗粒平均碰撞率模型的研究进展和相关数学模型、算法的基础上,基于后溯算法,构建了能够模拟三维空间内具105~106个颗粒碰撞的直接模拟程序,其中颗粒动量方程采用二阶预估-校正格式,颗粒位移采用二阶Adams积分,气相湍流场采用拟谱方法求解,颗粒位置上流体的速度由气相场用四阶拉格朗日插值得到,通过采用相邻网格、网格排除和颗粒排序等方法对程序进行优化,程序计算量较常规方法可低2个数量级,满足了在微机上模拟巨量颗粒碰撞需要。使用该程序,首先对均匀剪切流内St<<1的颗粒(轻颗粒流)和St>1且速度呈高斯分布颗粒(重颗粒流)两种工况进行数值验证,其结果和文献中的解析解一致,证明了算法和程序的可靠性,并讨论了计算参数的选取原则。进一步的,本文对各向均匀同性湍流内有限惯性颗粒的聚集现象及其对碰撞率的影响进行了模拟计算,采用径向分布函数、归一化的条件颗粒浓度等参数定量表征了不同St数颗粒的局部聚集程度;对St=1的颗粒,受局部聚集的影响,其颗粒碰撞率可为零惯性颗粒的20~30倍。
Inhaled particulate matter originating from combustion does serious harm to human health and environment. Mechanism of formation and growth of inhaled particulate matter in combustion is the precondition of its control during combustion process, where the controlling process is inter-particle collision and coagulation. Because turbulence imposes complex transport and accumulation effects on fine particle, the collision rate of fine particles there may different from those predicted by the custom model. Research on collision rate of finite inertial particle with preferential concentration is one of hotspots in gas-particle flow mechanism and aerosol dynamics.
After a brief summary of the research developments in particle average collision rate model, correlated mathematic models and numerical simulation algorithms, a retroactive algorithm-based program was built for direct numerical simulation (DNS) the collisions between particles in 3-dimenional space, with particle number up to 105~106. The second-order forecast-correction method was applied in solution of particle’s momentum equation, where the fluid velocity at the particle location is determined using a fourth-order Lagrangian interpolation. The particle position was advanced by a second-order Adams integral method. The fluid velocity field was generated by a pseudo spectral method. By optimizing algorithms such as cell index, exclusive search and particle sequence et al., the program can fit the requirements of simulating collisions between huge numbers of particles on personal computer, whose computation load is two orders of magnitude less than that of custom algorithm. Verifications of the code were done by two cases: St<<1 particle in uniform shear flow and St>1 particle whose velocity distribution was Gaussian. The results were consistent with analytical solutions in literatures,which proved reliability of retroactive algorithm and the program. The principle of computational parameter selection was also discussed. Moreover, DNS study of finite inertial particle with preferential concentration in isotropic turbulence and its influence on collision rate were performed. The accumulation level of various St number particle was quantified by parameters such as radial distribution function, and conditional expectation of normalized particle number density et al.; It showed that collision rate of St =1 particle was 20~30 times larger than that of zero-inertial particle because of local preferential concentration.
本文在系统总结有关颗粒平均碰撞率模型的研究进展和相关数学模型、算法的基础上,基于后溯算法,构建了能够模拟三维空间内具105~106个颗粒碰撞的直接模拟程序,其中颗粒动量方程采用二阶预估-校正格式,颗粒位移采用二阶Adams积分,气相湍流场采用拟谱方法求解,颗粒位置上流体的速度由气相场用四阶拉格朗日插值得到,通过采用相邻网格、网格排除和颗粒排序等方法对程序进行优化,程序计算量较常规方法可低2个数量级,满足了在微机上模拟巨量颗粒碰撞需要。使用该程序,首先对均匀剪切流内St<<1的颗粒(轻颗粒流)和St>1且速度呈高斯分布颗粒(重颗粒流)两种工况进行数值验证,其结果和文献中的解析解一致,证明了算法和程序的可靠性,并讨论了计算参数的选取原则。进一步的,本文对各向均匀同性湍流内有限惯性颗粒的聚集现象及其对碰撞率的影响进行了模拟计算,采用径向分布函数、归一化的条件颗粒浓度等参数定量表征了不同St数颗粒的局部聚集程度;对St=1的颗粒,受局部聚集的影响,其颗粒碰撞率可为零惯性颗粒的20~30倍。
Inhaled particulate matter originating from combustion does serious harm to human health and environment. Mechanism of formation and growth of inhaled particulate matter in combustion is the precondition of its control during combustion process, where the controlling process is inter-particle collision and coagulation. Because turbulence imposes complex transport and accumulation effects on fine particle, the collision rate of fine particles there may different from those predicted by the custom model. Research on collision rate of finite inertial particle with preferential concentration is one of hotspots in gas-particle flow mechanism and aerosol dynamics.
After a brief summary of the research developments in particle average collision rate model, correlated mathematic models and numerical simulation algorithms, a retroactive algorithm-based program was built for direct numerical simulation (DNS) the collisions between particles in 3-dimenional space, with particle number up to 105~106. The second-order forecast-correction method was applied in solution of particle’s momentum equation, where the fluid velocity at the particle location is determined using a fourth-order Lagrangian interpolation. The particle position was advanced by a second-order Adams integral method. The fluid velocity field was generated by a pseudo spectral method. By optimizing algorithms such as cell index, exclusive search and particle sequence et al., the program can fit the requirements of simulating collisions between huge numbers of particles on personal computer, whose computation load is two orders of magnitude less than that of custom algorithm. Verifications of the code were done by two cases: St<<1 particle in uniform shear flow and St>1 particle whose velocity distribution was Gaussian. The results were consistent with analytical solutions in literatures,which proved reliability of retroactive algorithm and the program. The principle of computational parameter selection was also discussed. Moreover, DNS study of finite inertial particle with preferential concentration in isotropic turbulence and its influence on collision rate were performed. The accumulation level of various St number particle was quantified by parameters such as radial distribution function, and conditional expectation of normalized particle number density et al.; It showed that collision rate of St =1 particle was 20~30 times larger than that of zero-inertial particle because of local preferential concentration.
引文
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Majerowicz, A., and Wagner, P. E. Brownian coagulation of atmospheric aerosols in the presence of nucleation mode aerosol sources. J. Aerosol Sci., 1986, 17:463-465
Gelbard, F., and Seinfeld, J.H. Numerical solutions of the dynamic equation for particle systems. J. Comput. Phys., 1978, 28:357-375
Landgrebe, J. D., and Pratsinis, S. E. A discrete-sectional model for powder production by gas phase chemical reaction and aerosol coagulation in the free-molecular regime. J. Colloid Interface Sci., 1990, 139:63-86
Mick, H. J., Hospital, A., and Roth, P. Computer simulations of soot particle coagulation in low-pressure flames. J. Aerosol Sci. 1991, 22:831-841
Otto, E., Stratmann, F., Fissan, H., Vemury, S., and Protsinis, S. E. Brownian coagulation in the transition regime 2: a comparision of two modeling approaches. J. Aerosol Sci., 1993:24:535-536
Otto, E., Stratmann, F., Fissan, H., Vemury, S., and Protsinis, S. E. Quasi-self-preserving log-normal size distribution in the transition regime. Part. Part. Systems. Charact. 1994, 11:359-366
Lee, K. W. Change of particle size distribution during Brownian coagulation. J. Colloid Interface Sci. 1983, 92:315-325
Lee, K. W., Curtis, L. A., and Chen, H. An analytic solution to free-molecule aerosol coagulation. Aerosol Sci. Technol., 1990, 12:457-462
Lee, K. W., Lee, Y. J. and Han, D. S. The log-normal size distribution theory for Brownian coagulation in the low Knudsen number regime. J. Colloid Interface Sci.
1997, 188:486-492
Park, S. H., Lee, K. W., Otto, E., and Fissan, H. The log-normal size distribution theory of Brownian aerosol coagulation for the entire particle size range: Part I: analytical solution using the harmonic mean coagulation kernel. J. Aerosol Sci., 1999, 30(1): 3-16
Debry, E., Sportisse, B., and Jourdain, B. A stochastic approach for the numerical simulation of the general dynamics equation for aerosols. J. Comput. Phys., 2003, 184:649-669
Fuchs, N. A. The Mechanics of Aesosols. New York: Pergamon Press, 1964.
Hidy, G. M., and Brock, J. R. Dynamics of Aerocolloidal Systems. New York: Pergamon,1970
Otto, E., Fissan, H., Park, S. H., and Lee, K. W. The log-normal size distribution theory of Brownian aerosol coagulation for the entire particle size range: Part II-analytical solution using Dahneke’s coagulation kernel. J. Aerosol Sci., 1999, 30(1): 17-34
Saffman, P.G., and Turner, J.S. On the collision of drops in turbulent clouds. J. Fluid Mech., 1956, (1): 16-30
Wang, L. P., Wexler, A. S., and Zhou, Y. Statistical mechanical descriptions of turbulent coagulation. Phys. Fluids, 1998, 10:2647-2651
Abrahamson, J. Collision rates of small particles in a vigorously turbulent fluid. Chem. Eng. Sci., 1975, 30:1371-1379
Williams, J.J.E., and Crane, R.I. Particle collision rate in turbulent flow. International Journal of Multiphase Flow, 1983, 9(4): 421-435
Yuu, S. Collision rate of small particles in a homogeneous and isotropic turbulence. AIChE J., 1984, 30: 802-807
Kruis, F.E., and Kusters, K.A. The collision rate of particles in turbulent flow. Chem. Eng. Comm., 1997, 158: 201-230
Zhou, Y., Wexler, A.S., Wang, L.-P. On the collision rate of small particles in isotropic turbulence. II. Finite-inertia case. Phys. Fluids, 1998, 10:1206-1216
Wang, L.P., Wexler, A.S., and Zhou, Y. Statistical mechanical description and modeling of turbulent collision of inertial particles. J. Fluid Mech. 2000, 415:117-153
Alipchenkov, V. M., and Zaichik, L. I. Particle collision rate in turbulent flow. Fluid Dynamics, 2001, 36(4): 608-618
Maxey, M.R. The gravitational settling of aerosol particles in homogeneous turbulence and random flow fields. J. Fluid Mech., 1987, 174: 441-465
Squires, K.D., and Eaton, J.K. Preferential concentration of particle by tubulentce. Phys. Fluids A, 1991, 3: 1169-1179.
Wang, L. P., and Maxey, M. R. Settling velocity and concentration distribution of heavy particles in homogeneous isotropic turbulence. J. Fluid Mech., 1993, 256: 27-68.
Fessler, J. R., Kulick, J.D., and Eaton, J.K. Preferential concentration of heavy particles in a turbulent channel flow. Phys. Fluids A, 1994, 6:3742-3749
Sundaram, S., and Collins, L.R. Collision statistics in an isotropic particle-laden turbulent suspension. Part 1. Direct numerical simulations. J. Fluid Mech., 1997, 335:75-109
Reade, W. C., and Collins, L.R. Effect of preferential concentration on turbulent collision rates, Physics of Fluids. 2000,12(10): 2530-2540
Kuboi, R., Komasawa, I., and Otake, T. Collision and coalescence of dispersed drops in turbulent liquid flow. J. Chem. Engng Japan, 1972, 5:423-424
Delichatsios, M.A., and Probstein, R. F. Coagulation in turbulent flows: theory and experiment. J. Colloid Interface Sci. 1975, 51:394-405
Higashitani, K., Yamauchi, K., Matsuno, Y., and Hosokawa, G. Turbulent coagulation of particle dispersed in a viscous fluid. J. Chem. Engng Japan, 1983, 16:299-304
De Boer, G. B. J., Hoedemakers, G. F. M., and Thoenes, D. Coagulation in turbulent flow: Part I and Part II. Chem. Engng Res. Des. 1989, 67:301-307,308-315
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