颗粒团聚对稀相气固流动脉动关联项的影响
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摘要
研究了颗粒团聚对描述稀相气固两相流的气固相宏观控制方程中待封闭气固脉动关联项的影响规律并建立关键待封闭项代数模型。根据气相速度脉动与固相浓度关联项(漂移速度)控制方程,将漂移速度表达为固相非均匀程度和气固平均滑移速度的代数模型。分别采用两种基于颗粒动理学的欧拉-欧拉框架介尺度方法模拟三维周期条件且固相平均浓度为1%的稀相气固两相流动,第1种方法假设固相速度分布函数f为各项同性的双流体方法(TFM);第2种方法假设f服从各向异性高斯分布的积分矩法(AG)。网格分辨率为颗粒直径dp的1.75倍,气固间动量交换采用Stokes曳力模型,并与文献中采用相同参数设置的欧拉-拉格朗日(E-L)方法模拟结果进行对比。结果表明,AG方法的准确度优于TFM方法,气固平均滑移速度、气固脉动能等更接近E-L方法模拟结果。颗粒聚团的积分尺度小于气相脉动速度的积分尺度,两者均呈各向异性,竖直分量高于水平分量。模拟得到了气固速度脉动关联系数和漂移速度系数。
The effect of particle clusters on gas-solids fluctuation coupling terms in Reynolds stresses transport equations was investigated in this work. Based on its transport equation, covariance of solids phase volume fraction and gas phase fluctuating velocity, namely drift velocity was closured by an algebraic model, which was a function of both degree of segregation and mean slip velocity. Thereby two different kinetic-based Euler-Euler mesoscale methods were applied to simulate a dilute gas-particle flow in a triple periodic domain where solids phase averaged volume fraction was 1%. Stokes drag law was applied for inter-phase momentum transfer. Inter-particle collisions were approximated byBhatnagar-Gross-Krook model. Mesh resolution in this study was as 1.75 times as particle diameter dp. The difference between these two approaches was the way to solve solids phase kinetic equation. The first approach was an Anisotropic Gaussian(AG) Quadrature based moment method of which particle phase velocity density function f was assumed to follow a multivariate anisotropic Gaussian. The second approach was a typical two-fluid model(TFM) of which assumed f to follow isotropic distribution. To validate these two methods, results were compared with results given by a Euler-Lagrange(E-L) method in the literature. It demonstrated that AG method was able to produce better comparable results than TFM. For instance, the flow field properties given by AG method were closer to results given by E-L method, including mean slip velocity, gas and solids phase turbulent kinetic energy. Results showed that the integral scale of particle clusters was smaller than that of gas-phase fluctuation velocities. And the integral scale of both particle clusters and gas-phase fluctuation velocities turned out to be anisotropic that vertical components were larger than lateral components. The falling of particle clusters was mainly suppressed by form drag(i.e. gas pressure between front and tail). In the end, the coefficients of both gas-solids fluctuation velocity covariance and drift velocity were identified.
The effect of particle clusters on gas-solids fluctuation coupling terms in Reynolds stresses transport equations was investigated in this work. Based on its transport equation, covariance of solids phase volume fraction and gas phase fluctuating velocity, namely drift velocity was closured by an algebraic model, which was a function of both degree of segregation and mean slip velocity. Thereby two different kinetic-based Euler-Euler mesoscale methods were applied to simulate a dilute gas-particle flow in a triple periodic domain where solids phase averaged volume fraction was 1%. Stokes drag law was applied for inter-phase momentum transfer. Inter-particle collisions were approximated byBhatnagar-Gross-Krook model. Mesh resolution in this study was as 1.75 times as particle diameter dp. The difference between these two approaches was the way to solve solids phase kinetic equation. The first approach was an Anisotropic Gaussian(AG) Quadrature based moment method of which particle phase velocity density function f was assumed to follow a multivariate anisotropic Gaussian. The second approach was a typical two-fluid model(TFM) of which assumed f to follow isotropic distribution. To validate these two methods, results were compared with results given by a Euler-Lagrange(E-L) method in the literature. It demonstrated that AG method was able to produce better comparable results than TFM. For instance, the flow field properties given by AG method were closer to results given by E-L method, including mean slip velocity, gas and solids phase turbulent kinetic energy. Results showed that the integral scale of particle clusters was smaller than that of gas-phase fluctuation velocities. And the integral scale of both particle clusters and gas-phase fluctuation velocities turned out to be anisotropic that vertical components were larger than lateral components. The falling of particle clusters was mainly suppressed by form drag(i.e. gas pressure between front and tail). In the end, the coefficients of both gas-solids fluctuation velocity covariance and drift velocity were identified.
引文
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[14]Zeng Z X,Zhou L X.A two-scale second-order moment particle turbulence model and simulation of dense gas-particle flows in a riser[J].Powder Technology,2006,162(1):27-32.
[15]Jesse C,Desjardins O,Fox R O.Strongly coupled fluid-particle flows in vertical channels:II.turbulence modeling[J].Physics of Fluids,2016,28(3):033306.
[16]Fox R O.On multiphase turbulence models for collisional fluid-particle flows[J].Journal of Fluid Mechanics,2014,742:368-424.
[17]王维,洪坤,鲁波娜,等.流态化模拟:基于介尺度结构的多尺度CFD[J].化工学报,2013,64(1):95-106.Wang W,Hong K,Lu B N,et al.Fluidized bed simulation:structure-dependent multiscale CFD[J].CIESC Journal,2013,64(01):95-106.
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[19]Zhou L X.Advances in studies on turbulent dispersed multiphase flows[J].Chinese Journal of Chemical Engineering,2010,18(6):889-898.
[20]Tenneti S,Subramaniam S.Particle-resolved direct numerical simulation for gas-solid flow model development[J].Annual Review of Fluid Mechanics,2014,46:199-230.
[21]Igci Y,Sundaresan S.Constitutive models for filtered two-fluid models of fluidized gas-particle flows[J].Industrial&Engineering Chemistry Research,2011,50(23):13190-13201.
[22]Ozel A,Fede P,Simonin O.Development of filtered Euler-Euler two-phase model for circulating fluidized bed:high resolution simulation,formulation and a priori analyses[J].International Journal of Multiphase Flow,2013,55:43-63.
[23]Van M A,Sint A M,Deen N G,et al.Numerical simulation of dense gas-solid fluidized beds:a multiscale modeling strategy[J].Annual Review of Fluid Mechanics,2008,40:47-70.
[24]Jenkins J T,Savage S B.A theory for the rapid flow of identical,smooth,nearly elastic,spherical particles[J].Journal of Fluid Mechanics,1983,130:187-202.
[25]Desjardins O,Fox R O,Villedieu P.A quadrature-based moment method for dilute fluid-particle flows[J].Journal of Computational Physics,2008,227(4):2514-2539.
[26]Koch D L.Kinetic theory for a monodisperse gas-solid suspension[J].Physics of Fluids A,1990,10(2):1711-1723.
[27]Gidaspow D.Multiphase flow and fluidization:continuum and kinetic theory descriptions[M].Pittsburgh:Academic Press,1994:145-150.
[28]Rubinstein G J,Derksen J J,Sundaresan S.Lattice Boltzmann simulations of low-Reynolds-number flow past fluidized spheres:effect of Stokes number on drag force[J].Journal of Fluid Mechanics,2016,788:576-601.
[29]Cody G D,Johri J,Goldfarb D.Dependence of particle fluctuation velocity on gas flow,and particle diameter in gas fluidized beds for monodispersed spheres in the Geldart B and A fluidization regimes[J].Powder Technology,2008,182(2):146-170.
[30]Wang W,Chen Y P.Mesoscale modeling:beyond local equilibrium assumption for multiphase flow[M]//Advances in Chemical Engineering.Pittsburgh:Academic Press,2015:193-277.
[31]Wang J W.Effect of granular temperature and solid concentration fluctuation on the gas-solid drag force:a CFD test[J].Chemical Engineering Science,2017,168:11-14.
[32]Gopalan B,Shaffer F.Higher order statistical analysis of Eulerian particle velocity data in CFB risers as measured with high speed particle imaging[J].Powder Technology,2013,242:13-26.
[33]Grad H.Thermodynamik der gase/thermodynamics of gases[M].Heidelberg:Springer Press,1958:205-294.
[34]Fox R O.A quadrature-based third-order moment method for dilute gas-particle flows[J].Journal of Computational Physics,2008,227(12):6313-6350.
[35]Chalons C,Fox R O,Massot M.A multi-Gaussian quadrature method of moments for gas-particle flows in a LES framework[C]//Proceedings of the Summer Program.2010:76.
[36]孙丹,陈巨辉,刘国栋,等.稠密气固两相流各向异性颗粒相矩方法[J].力学学报,2010,42(6):1034-1041.Sun D,Chen J H,Liu G D,et al.Anisotropic second-order moment method of particles for dense gas-solid flow[J].Chinese Journal of Theoretical and Applied Mechanics,2010,42(6):1034-1041.
[37]蔡振宁.气体动理学中数值矩方法的算法研究与应用[D].北京:北京大学,2013:10.Cai Z N.Investigations and applications of the numerical moment method in the kinetic theory of gases[D].Beijing:Peking University,2013:10.
[38]ViéA,Doisneau F,Massot M.On the anisotropic Gaussian velocity closure for inertial-particle laden flows[J].Communications in Computational Physics,2015,17(1):1-46.
[39]Zhao B D,Li S Y,Wang J W.Generalized Boltzmann kinetic theory for EMMS-based two-fluid model[J].Chemical Engineering Science,2016,156:44-55.
[40]Capecelatro J,Desjardins O,Fox R O.On fluid-particle dynamics in fully developed cluster-induced turbulence[J].Journal of Fluid Mechanics,2015,780:578-635.
[41]Bhatnagar P L,Gross E P,Krook M.A model for collision processes in gases:I.small amplitude processes in charged and neutral one-component systems[J].Physical Review,1954,94(3):511.
[42]Marchisio D L,Fox R O.Computational models for polydisperse particulate and multiphase systems[M].Cambridge:Cambridge University Press,2013:250-253.
[43]GarzóV,Tenneti S,Subramaniam S,et al.Enskog kinetic theory for monodisperse gas-solid flows[J].Journal of Fluid Mechanics,2012,712:129-168.
[44]Capecelatro J,Desjardins O,Fox R O.Numerical study of collisional particle dynamics in cluster-induced turbulence[J].Journal of Fluid Mechanics,2014,747:R2.
[45]Kong B,Fox R O,Feng H,et al.Euler-Euler anisotropic Gaussian mesoscale simulation of homogeneous cluster-induced gas-particle turbulence[J].AIChE Journal,2017,63(7):2630-2643.
[46]Abbott M B,Minns A W.Computational hydraulics[M].London:Routledge,2017:256-257.
[2]Kasbaoui M H,Koch D L,Subramanian G,et al.Preferential concentration driven instability of sheared gas-solid suspensions[J].Journal of Fluid Mechanics,2015,770:85-123.
[3]Fullmer W D,Hrenya C M.The clustering instability in rapid granular and gas-solid flows[J].Annual Review of Fluid Mechanics,2017,49:485-510.
[4]Couto N,Silva V B,Bispo C,et al.From laboratorial to pilot fluidized bed reactors:analysis of the scale-up phenomenon[J].Energy Conversion and Management,2016,119:177-186.
[5]Fox R O.Large-eddy-simulation tools for multiphase flows[J].Annual Review of Fluid Mechanics,2012,44:47-76.
[6]祁海鹰,戴群特,陈程.大型流态化多相流数值模拟的关键科学问题-曳力模型的理论分析[J].力学与实践,2014,36(3):269-277.Qi H Y,Dai Q T,Chen C.The key scientific problems in the Eulerian modeling of large scale multi-phase flows-drag model[J].Mechanics in Engineering,2014,36(3):269-277.
[7]O’Brien T J,Syamlal M.Particle cluster effects in the numerical simulation of a circulating fluidized bed[C]//Proceedings of the Fourth International Conference on Circulating Fluidized Bed.1993:367-372.
[8]Li J H,Ge W,Wang W,et al.Focusing on mesoscales:from the energy-minimization multiscale model to mesoscience[J].Current Opinion in Chemical Engineering,2016,13:10-23.
[9]周力行.多相湍流反应流体力学[M].北京:国防工业出版社,2002:50.Zhou L X.Dynamics of multiphase turbulent reacting fluid flows[M].Beijing:National Defence Industry Press,2002:50.
[10]Agrawal K,Loezos P N,Syamlal M,et al.The role of meso-scale structures in rapid gas-solid flows[J].Journal of Fluid Mechanics,2001,445:151-185.
[11]王淑彦,房建宇,邵宝力,等.基于不同亚格子尺度过滤模型下提升管内颗粒流动的数值模拟[J].高校化学工程学报,2016,30(2):325-331.Wang S Y,Fang J Y,Shao B L,et al.Numerical simulation of flow behavior of particles based on two-fluid model with different filtered drag models in riser[J].Journal of Chemical Engineering of Chinese Universities,2016,30(2):325-331.
[12]Cheng Y,Guo Y C,Wei F,et al.Modeling the hydrodynamics of downer reactors based on kinetic theory[J].Chemical Engineering Science,1999,54(13):2019-2027.
[13]于勇,蔡飞鹏,周力行,等.下降管中稠密两相湍流的数值模拟[J].工程热物理学报,2005,26(增刊1):117-120.Yu Y,Cai F P,Zhou L X,et al.Simulation of dense gas-particle flows in downer[J].Journal of Engineering Thermophysics,2005,26(S1):117-120.
[14]Zeng Z X,Zhou L X.A two-scale second-order moment particle turbulence model and simulation of dense gas-particle flows in a riser[J].Powder Technology,2006,162(1):27-32.
[15]Jesse C,Desjardins O,Fox R O.Strongly coupled fluid-particle flows in vertical channels:II.turbulence modeling[J].Physics of Fluids,2016,28(3):033306.
[16]Fox R O.On multiphase turbulence models for collisional fluid-particle flows[J].Journal of Fluid Mechanics,2014,742:368-424.
[17]王维,洪坤,鲁波娜,等.流态化模拟:基于介尺度结构的多尺度CFD[J].化工学报,2013,64(1):95-106.Wang W,Hong K,Lu B N,et al.Fluidized bed simulation:structure-dependent multiscale CFD[J].CIESC Journal,2013,64(01):95-106.
[18]杨宁,李静海.化学工程中的介尺度科学与虚拟过程工程:分析与展望[J].化工学报,2014,65(7):2403-2409.Yang N,Li J H.Mesoscience in chemical engineering and virtual process engineering:analysis and perspective[J].Journal of Chemical Industry and Engineering(China),2014,65(7):2403-2409.
[19]Zhou L X.Advances in studies on turbulent dispersed multiphase flows[J].Chinese Journal of Chemical Engineering,2010,18(6):889-898.
[20]Tenneti S,Subramaniam S.Particle-resolved direct numerical simulation for gas-solid flow model development[J].Annual Review of Fluid Mechanics,2014,46:199-230.
[21]Igci Y,Sundaresan S.Constitutive models for filtered two-fluid models of fluidized gas-particle flows[J].Industrial&Engineering Chemistry Research,2011,50(23):13190-13201.
[22]Ozel A,Fede P,Simonin O.Development of filtered Euler-Euler two-phase model for circulating fluidized bed:high resolution simulation,formulation and a priori analyses[J].International Journal of Multiphase Flow,2013,55:43-63.
[23]Van M A,Sint A M,Deen N G,et al.Numerical simulation of dense gas-solid fluidized beds:a multiscale modeling strategy[J].Annual Review of Fluid Mechanics,2008,40:47-70.
[24]Jenkins J T,Savage S B.A theory for the rapid flow of identical,smooth,nearly elastic,spherical particles[J].Journal of Fluid Mechanics,1983,130:187-202.
[25]Desjardins O,Fox R O,Villedieu P.A quadrature-based moment method for dilute fluid-particle flows[J].Journal of Computational Physics,2008,227(4):2514-2539.
[26]Koch D L.Kinetic theory for a monodisperse gas-solid suspension[J].Physics of Fluids A,1990,10(2):1711-1723.
[27]Gidaspow D.Multiphase flow and fluidization:continuum and kinetic theory descriptions[M].Pittsburgh:Academic Press,1994:145-150.
[28]Rubinstein G J,Derksen J J,Sundaresan S.Lattice Boltzmann simulations of low-Reynolds-number flow past fluidized spheres:effect of Stokes number on drag force[J].Journal of Fluid Mechanics,2016,788:576-601.
[29]Cody G D,Johri J,Goldfarb D.Dependence of particle fluctuation velocity on gas flow,and particle diameter in gas fluidized beds for monodispersed spheres in the Geldart B and A fluidization regimes[J].Powder Technology,2008,182(2):146-170.
[30]Wang W,Chen Y P.Mesoscale modeling:beyond local equilibrium assumption for multiphase flow[M]//Advances in Chemical Engineering.Pittsburgh:Academic Press,2015:193-277.
[31]Wang J W.Effect of granular temperature and solid concentration fluctuation on the gas-solid drag force:a CFD test[J].Chemical Engineering Science,2017,168:11-14.
[32]Gopalan B,Shaffer F.Higher order statistical analysis of Eulerian particle velocity data in CFB risers as measured with high speed particle imaging[J].Powder Technology,2013,242:13-26.
[33]Grad H.Thermodynamik der gase/thermodynamics of gases[M].Heidelberg:Springer Press,1958:205-294.
[34]Fox R O.A quadrature-based third-order moment method for dilute gas-particle flows[J].Journal of Computational Physics,2008,227(12):6313-6350.
[35]Chalons C,Fox R O,Massot M.A multi-Gaussian quadrature method of moments for gas-particle flows in a LES framework[C]//Proceedings of the Summer Program.2010:76.
[36]孙丹,陈巨辉,刘国栋,等.稠密气固两相流各向异性颗粒相矩方法[J].力学学报,2010,42(6):1034-1041.Sun D,Chen J H,Liu G D,et al.Anisotropic second-order moment method of particles for dense gas-solid flow[J].Chinese Journal of Theoretical and Applied Mechanics,2010,42(6):1034-1041.
[37]蔡振宁.气体动理学中数值矩方法的算法研究与应用[D].北京:北京大学,2013:10.Cai Z N.Investigations and applications of the numerical moment method in the kinetic theory of gases[D].Beijing:Peking University,2013:10.
[38]ViéA,Doisneau F,Massot M.On the anisotropic Gaussian velocity closure for inertial-particle laden flows[J].Communications in Computational Physics,2015,17(1):1-46.
[39]Zhao B D,Li S Y,Wang J W.Generalized Boltzmann kinetic theory for EMMS-based two-fluid model[J].Chemical Engineering Science,2016,156:44-55.
[40]Capecelatro J,Desjardins O,Fox R O.On fluid-particle dynamics in fully developed cluster-induced turbulence[J].Journal of Fluid Mechanics,2015,780:578-635.
[41]Bhatnagar P L,Gross E P,Krook M.A model for collision processes in gases:I.small amplitude processes in charged and neutral one-component systems[J].Physical Review,1954,94(3):511.
[42]Marchisio D L,Fox R O.Computational models for polydisperse particulate and multiphase systems[M].Cambridge:Cambridge University Press,2013:250-253.
[43]GarzóV,Tenneti S,Subramaniam S,et al.Enskog kinetic theory for monodisperse gas-solid flows[J].Journal of Fluid Mechanics,2012,712:129-168.
[44]Capecelatro J,Desjardins O,Fox R O.Numerical study of collisional particle dynamics in cluster-induced turbulence[J].Journal of Fluid Mechanics,2014,747:R2.
[45]Kong B,Fox R O,Feng H,et al.Euler-Euler anisotropic Gaussian mesoscale simulation of homogeneous cluster-induced gas-particle turbulence[J].AIChE Journal,2017,63(7):2630-2643.
[46]Abbott M B,Minns A W.Computational hydraulics[M].London:Routledge,2017:256-257.