基于格子Boltzmann方法的地下巷道热流态仿真研究
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摘要
近年来,地下矿山巷道火灾安全事故频发,给国家和人民生命财产造成了重大损失,因而对于巷道火灾蔓延规律的研究具有重大意义。然而近年来对于地下巷道热流模拟仿真研究主要局限在有限元法和有限体积法,该方法为得到Navier-Stokes方程需要求解复杂的偏微分方程,其计算过程复杂,且模拟仿真效果都不理想。此外也可采用实验方法来确定,但由于实际地下巷道条件复杂多变,因而不能完整模拟火灾发生后地下巷道的热流蔓延真实情况。故设计新的模型对地下巷道热流进行模拟仿真成为一个重要问题。
格子Boltzmann方法是近年来兴起的一种模拟流体流动的新方法,因其具有计算过程简单,无需求解复杂的偏微分方程,边界易处理等优点而得到众多学者的研究。本文以格子Boltzmann理论为基础,结合流体力学和热力学中关于热流动方面的知识,以某地下矿山巷道某处发生火灾为主要研究对象,采用速度-温度双分布格子Boltzmann模型,利用分块耦合算法,将不规则的地下矿巷道分为若干规则块,在规则块内部并行计算,各块分界处进行耦合,从而有效模拟仿真地下巷道热流蔓延规律。首先,以热格子Boltzmann模型为基础提出地下矿巷道热流模型,分析各种模型及边界处理方式,并模拟简单平直巷道热流蔓延情况。其次,提出基于耦合算法的速度和温度双分布格子Boltzmann模型,提出分块耦合算法原理,并得到巷道拓扑结构与分块方法,在此基础上将地下巷道分为若干规则块,随后对其温度和速度进行模拟,得出模拟仿真结果及规避火灾热流的有效方法。再次,由于地下巷道多存在可燃物和障碍物可能对巷道热流产生影响。故提出地下巷道易燃物引燃处理模型及热流阻滞模型,对实际巷道热流进行模拟,得出全巷道热流蔓延及阻滞规律。接着,针对实际生产中存在的反风方式进行深入分析,并在无风道反风的基础上提出采用备用风机进行反风模型。在热流温度达到一定限度时开启备用风机进行反风,在实际的模拟仿真中取得很好的效果。最后,针对实际巷道结构,在二维模型的基础上提出三维速度温度双分布热流模型,在实际巷道的热流模拟仿真中取得很好的效果。
本文将风流速度和热流温度一起考虑,提出了多个针对复杂地下巷道热流蔓延及仿真模型并对实际巷道进行不同情况的模拟仿真,并对三维热流蔓延模拟仿真进行探索研究,有利于以后进一步研究。
In recent years,because there are more and more underground mine tunnel fire accidents which bring heavy losses to our country's property and people's lives,thus it is of great significance to research the heat flow on underground tunnel.However,in recent years the heat flow research on underground runnel is confined to the finite element and the finite volume method which solve complicated partial differential equations to deduce the Navier-Stokes equations and have poor satisfied simulating effect.In addition,experimental methods can be adopted.Yet it can not simulate the fire flow completely because there are complex and changeable actual conditions in underground tunnel.Therefore it becomes an important issue to design new model to simulate heat flow on underground tunnel.
Lattice Boltzmann Method(LBM) is emerging in recent years and is studied by many scholars because it calculates without solving complicated partial differential equations and deals with the border easily.Based on Lattice Boltzmann Method and combined with fluid dynamics and thermodynamics,the paper mainly researches on fire accident which occurred on underground mine tunnel.Adopted velocity and temperature dual-distributed Lattice Boltzmann Method,it separated irregular underground tunnel into some regular blocks with Separated & Coupled Algorithm.It can simulate the spreading laws of heat flow on underground tunnel because the lattice is calculated simultaneously in the regular blocks and coupled in borders between each blocks.First,the heat flow model on underground tunnel based on Thermal Lattice Boltzmann Method is proposed.Various models and boundary treatment patterns are analyzed,then the heat spreading on straight tunnel are simulated.Secondly,the principle of Separated & Coupled Algorithm and based on it Dual-distributed Lattice Boltzmann Model is proposed.Tunnel construction and the method of separated block is adopted.Based on it,the underground tunnel is separated some regular blocks. Following,its temperature and velocity are simulated.Then,an effective way to evading heat flow and simulated result are adopted.Thirdly,the Spreading & Hindering Model is proposed because there are many combustibles and obstacles which may have an impact on heat flow in underground tunnel.Through simulating heat flow of actual tunnel,the spreading & hindering laws on heat flow of entire tunnel can be adopted. Next,based on analyzing the anti-wind means which existed in actual production and on anti-wind without wind tunnel,Anti-Wind Models with backup fan is proposed.The backup fan which can carry out anti-wind when the heat temperature reaches certain limit is turned on,which achieve good results in actual simulating.Finally,in the view of actual tunnel structure,the 3-Dimension Model on temperature and velocity dual-distributed Lattice Boltzmann Method is proposed which achieve better effect on simulating heat flow on actual tunnel.
Considering with wind velocity and heat temperature,a number of spreading & hindering models in view of complex underground tunnel are proposed and actual tunnel can be simulated in various situations.And the heat flow spreading models on 3-dimension is explored and researched,which conducive to further study in depth.
格子Boltzmann方法是近年来兴起的一种模拟流体流动的新方法,因其具有计算过程简单,无需求解复杂的偏微分方程,边界易处理等优点而得到众多学者的研究。本文以格子Boltzmann理论为基础,结合流体力学和热力学中关于热流动方面的知识,以某地下矿山巷道某处发生火灾为主要研究对象,采用速度-温度双分布格子Boltzmann模型,利用分块耦合算法,将不规则的地下矿巷道分为若干规则块,在规则块内部并行计算,各块分界处进行耦合,从而有效模拟仿真地下巷道热流蔓延规律。首先,以热格子Boltzmann模型为基础提出地下矿巷道热流模型,分析各种模型及边界处理方式,并模拟简单平直巷道热流蔓延情况。其次,提出基于耦合算法的速度和温度双分布格子Boltzmann模型,提出分块耦合算法原理,并得到巷道拓扑结构与分块方法,在此基础上将地下巷道分为若干规则块,随后对其温度和速度进行模拟,得出模拟仿真结果及规避火灾热流的有效方法。再次,由于地下巷道多存在可燃物和障碍物可能对巷道热流产生影响。故提出地下巷道易燃物引燃处理模型及热流阻滞模型,对实际巷道热流进行模拟,得出全巷道热流蔓延及阻滞规律。接着,针对实际生产中存在的反风方式进行深入分析,并在无风道反风的基础上提出采用备用风机进行反风模型。在热流温度达到一定限度时开启备用风机进行反风,在实际的模拟仿真中取得很好的效果。最后,针对实际巷道结构,在二维模型的基础上提出三维速度温度双分布热流模型,在实际巷道的热流模拟仿真中取得很好的效果。
本文将风流速度和热流温度一起考虑,提出了多个针对复杂地下巷道热流蔓延及仿真模型并对实际巷道进行不同情况的模拟仿真,并对三维热流蔓延模拟仿真进行探索研究,有利于以后进一步研究。
In recent years,because there are more and more underground mine tunnel fire accidents which bring heavy losses to our country's property and people's lives,thus it is of great significance to research the heat flow on underground tunnel.However,in recent years the heat flow research on underground runnel is confined to the finite element and the finite volume method which solve complicated partial differential equations to deduce the Navier-Stokes equations and have poor satisfied simulating effect.In addition,experimental methods can be adopted.Yet it can not simulate the fire flow completely because there are complex and changeable actual conditions in underground tunnel.Therefore it becomes an important issue to design new model to simulate heat flow on underground tunnel.
Lattice Boltzmann Method(LBM) is emerging in recent years and is studied by many scholars because it calculates without solving complicated partial differential equations and deals with the border easily.Based on Lattice Boltzmann Method and combined with fluid dynamics and thermodynamics,the paper mainly researches on fire accident which occurred on underground mine tunnel.Adopted velocity and temperature dual-distributed Lattice Boltzmann Method,it separated irregular underground tunnel into some regular blocks with Separated & Coupled Algorithm.It can simulate the spreading laws of heat flow on underground tunnel because the lattice is calculated simultaneously in the regular blocks and coupled in borders between each blocks.First,the heat flow model on underground tunnel based on Thermal Lattice Boltzmann Method is proposed.Various models and boundary treatment patterns are analyzed,then the heat spreading on straight tunnel are simulated.Secondly,the principle of Separated & Coupled Algorithm and based on it Dual-distributed Lattice Boltzmann Model is proposed.Tunnel construction and the method of separated block is adopted.Based on it,the underground tunnel is separated some regular blocks. Following,its temperature and velocity are simulated.Then,an effective way to evading heat flow and simulated result are adopted.Thirdly,the Spreading & Hindering Model is proposed because there are many combustibles and obstacles which may have an impact on heat flow in underground tunnel.Through simulating heat flow of actual tunnel,the spreading & hindering laws on heat flow of entire tunnel can be adopted. Next,based on analyzing the anti-wind means which existed in actual production and on anti-wind without wind tunnel,Anti-Wind Models with backup fan is proposed.The backup fan which can carry out anti-wind when the heat temperature reaches certain limit is turned on,which achieve good results in actual simulating.Finally,in the view of actual tunnel structure,the 3-Dimension Model on temperature and velocity dual-distributed Lattice Boltzmann Method is proposed which achieve better effect on simulating heat flow on actual tunnel.
Considering with wind velocity and heat temperature,a number of spreading & hindering models in view of complex underground tunnel are proposed and actual tunnel can be simulated in various situations.And the heat flow spreading models on 3-dimension is explored and researched,which conducive to further study in depth.
引文
[1]王广超,流体流动的格子Boltzmann方法,华中科技大学,2004年版
[2]陶文铨,数值传热学(第2版),西安:西安交通大学出版社,2001年5月出版
[3]Chen S,Doolen GD.Lattice Boltzmann methods for fluid flows.Annu.Rev.Fluid.Mech.,1998,30:229-364.
[4]郭照立,郑楚光,李青等.流体动力学的格子Boltzmann方法.湖北科学技术出版社.第1版.2002.1-166.
[5]Hardy J,Pomeau Y,Pazzis O De.Molecular Dynamics of a classical lattice gas:Transport properties and time correlation functions[J].Physics Review A,1976,13:1 94921 960.
[6]U.Frish,B.Hasslacher,and Y.Pomeau,Lattice-Gas Automata for the Navier-Stokes Equation,Phys.Rev.E,1986,Vol.56:1505-1508
[7]Higuera F,J imenez J,Succi S.Boltzmann app roach to lattice gas simulations[J].Europhysics Letters,1989,9:663.
[8]McNamara G G,Zanetti G.Use of the Boltzmann equation to siulate lattice gas automata[J].Physical Review Letters,1988,61:2 332-335.
[9]Qian YH,Simulating thermohydrodynamics with lattice BGK models,J.Sci.Comput.8(3):231-242(1993)
[10]Alexander FJ,Chen S,Sterling JD,Lattice Boltzmann thermohydrodynamics,Phys.Rev.E,47,R2249-2252(1993)
[11]Chen Y.Ohashi H,Akiyama M,Theremal lattice Bhatnagar-Gross-Kook Model without nonlinear deviations in Macrodynamic Equations,phys.Rev E,50,2776-2783(1994)
[12]He X Y,Chen S Y,Doolen G D,A novel thermal model for the lattice Boltzmann method incompressible limit[J].J Comput Phys,1998,146(1):282-300
[13]Guo Z L,Shi B C,Zheng C G,A coupled lattice BGK model for the Bouessinesq equation[J].Int J Num Fluids,2002,39(4):325-342
[14]Gang G H,Tao W Q,HE Y L,Simulation of the fluid flow and heat transfer in a plane channel using the lattice Boltzmann method[J].Int J Mod Phys:B,2003,17(1):183-187
[15]黄华国,张晓丽,王蕾,基于三维曲面元胞自动机模型的林火蔓延模型[J],北京林业大学报,2005,27(3):94-97
[16]黄光球,汪晓海,陈惠明,基于元胞自动机的地下矿火灾蔓延仿真方法[J],系统仿真学报,2007,19(1):201-205
[17]周西华,王继仁,梁栋,掘进巷道风流温度场分布规律的研究,辽宁工程技术大学学报,2003,22(1):1-3
[18]周西华,王继仁,单亚飞,王树刚,梁栋,掘进巷道风流温度分布规律的数值模拟,中国安全科学学报,2002,12(2):19-23
[19]邢书仁,吴兵,周心权,张莉聪,区域模拟与巷道火灾一维烟流流动模拟耦合方法初探,中国安全科学学报,2004,14(2):24-26
[20]王海燕,赵洪泽,基于数值模拟的矿井火灾虚拟再现方法研究,中国煤炭,2007,33(7):74-76
[21]蒋军成,王省身.矿井火灾巷道烟气流动场模型[J].矿冶工程,1997,17(2):6-10
[22]贾进章,马恒,刘剑.矿井火灾时期温度分布数值模拟[J].辽宁工程技术大学学报,2003,22(4):460-46
[23]周福宝,王德明,矿山通风网络火灾的计算机仿真模拟[J],金属矿山,2008,2:115-117
[24]高建良,魏平儒,掘进巷道分流热环境的数值模拟[J],煤炭学报,2006,31(2):201-205
[25]贾进章,马恒,刘剑,矿井火灾时期温度分布数值模拟[J],辽宁工程科技大学学报,2003,22(4):460-462
[27]李杰林,周科平,苏家红,唐谷修,自燃火灾巷道烟流的数字模拟及安全评价[J],中国安全科学学报,2006,16(4):37-41
[28]傅培舫,周怀春,俞启香,蒋时才,叶汝陵,巷道火灾节流过程及其影响因素的研究[J],煤炭学报,2005,30(2):146-150
[29]王德明,程远平,周福宝,季经纬,矿井火灾火源燃烧特性的实验研究[J],中国矿业大学学报,2002,31(1):30-33
[30]Zou Q,Hou S,Chen S,Doolen GD.An improved incompressible lattice Boltzmann model for time-independent flows.J.Stat.Phys.,1995,81:35-48
[31]Lin Z,Fang H,Tao R,Improved lattice Boltzmann model for incompressible two-independent flows,J.Stat.Phys.81:35-48(1995)
[32]Chen Y,Ohashi H,Lattice-BGK methods for simulating incompressible fluid flows,Int.J.Mod.Phys.C,8:793-803(1997)
[33]He X,Luo L-S,Lattice Boltzemann model for the incompressible Navier-Stokes equation J.Stat.Phys.,88:927-944(1997)
[34]Guo Z-L,Shi B-C,Wang N-C,Lattice BGK model for incompressible Navier-Stokes equation,J.Comput.Phys.165:288-306(2000)
[35]Guo ZL,Shi BC,Zheng CG,A coupled lattice BGK model for Bouessinesq equation,Int.J.Num.Fluids,39:325-342(2002)
[36]Guo ZL,Zheng CG,Shi BC,Non-equilibrium extrapolation method for velocity and pressure boundary conditions in the lattice Boltzmann method,Chinese Phys.,11(04):366-374(2002)
[37]王兴勇,Lattice Boltzmann方法的理论及其在水利计算中应用的研究,河海大学,2003年3月
[38]张桂茹,二维直角管道的LBM模拟,吉林大学,2007年4月
[39]李克平,刘慕仁,13速四方格子BGK模型热流体性质研究[J].广西师范大学学报(自然科学版),1997,15(4):7-13
[40]郑忠,高小强.13-Bit多速格子气自动机模型的理论分析与模拟[J],重庆大学学报(自然科学版),2000,23(6):82-86
[41]G.H.Tang,W.Q.Tao,Y.L.He,Simulation of fluid and heat transfer in a plane channel using the Lattice Boltzmann method[J],Int.Jou.Mod.Phys B,2003,17(2):183-187
[42]童长青,何雅玲,王勇,刘迎文,封闭方腔自然对流的格子-Boltzmann方法动态模拟[J],2007,41(1):32-36
[43]王勇,何雅玲,唐桂华,陶文铨,二位管道内交变流动的格子-Boltzmann方法模拟研究[J],西安交通大学学报,2006,40(1):14-17
[44]Zhaoli Guo,Chuguang Zheng,Baochang Shi,Thermal lattice Boltzmann equation for low Mach number flows:Decoupling model,Phy.Rev,2007,75:036704:1-14
[45]H.Chen,S.Chen,and W.H.Matthaeus,Recovery of the Navier-Stokes Equations Using a Lattice-Gas Boltzmann Method,Phys.Rev.A.,1992,Vol.45:R5339-R5342
[46]Chen S,Martinez D,Mei R.On boundary conditions in lattice Boltzmann methods.Phys.Fluids.,1996,8:2527-2536.
[47]Bouzidi M,Firdaouss M,Lallemand P.Monentum Transfer of a Lattice Boltzmann Fluid with Boundaries J.Phys.Fluids,2001,(13):3452-3459
[48]蔡增基,龙天渝,流体力学泵与风机,中国建筑工业出版社,1999年第4版:90-95
[49]冯士德,张琼,任荣彩,用格子Boltzmann模型模拟非等温流场,物理学报[J],2001,50(7):1207-1212
[50]宴一光,吴波,郑楚光,三维十五点格子Boltzmann模型仿真,工程热物理学报[J],2001,22(4):503-506
[51]康秀英,刘大禾,周静,金永娟,晶格Boltzmann方法模拟流体在三维圆管的流场,北京师范大学学报,2006,42(3):272-275
[52]赵以惠,矿井通风与空气调节M。北京:中国矿业大学出版社,1990.70-72.
[53]姬长发,徐炳坤,赵建余,多井口多风机矿井反风的非稳定流动模拟,西安科技学院学报,2003,23(3):241-244
[54]常心坦,矿井火灾通风的数学模型及计算机模拟M.美国矿业局,1987.80-120
[55]宋福海,常文杰,杨忠东,计算机模拟矿井反风的探讨,煤矿安全[J],2002,33(1):34-36
[56]王子邦,矿井反风技术分析与相关问题的探讨,应用技术[J],2006,11:59-61
[57]Shan X W,Chen H D.Lattice Boltzmann model for simulating flows with multiple phases and components.Phy Rev E,1993,47:1815-1819
[58]严薇薇,刘阳,许友生,用格子Boltzmann研究多孔介质内的自然对流患热问题,西安石油大学学报[J],2007,22(3):149-152
[59]陈胜,柳朝晖等,低Mach数反应流动的格子Boltzmann模型,中国科学E 辑 技术科学2006,36(9):1002-1015
[60]何雅玲,王勇,李庆,格子Boltzmann方法的理论及应用,2009年1月第一版:8-14
[2]陶文铨,数值传热学(第2版),西安:西安交通大学出版社,2001年5月出版
[3]Chen S,Doolen GD.Lattice Boltzmann methods for fluid flows.Annu.Rev.Fluid.Mech.,1998,30:229-364.
[4]郭照立,郑楚光,李青等.流体动力学的格子Boltzmann方法.湖北科学技术出版社.第1版.2002.1-166.
[5]Hardy J,Pomeau Y,Pazzis O De.Molecular Dynamics of a classical lattice gas:Transport properties and time correlation functions[J].Physics Review A,1976,13:1 94921 960.
[6]U.Frish,B.Hasslacher,and Y.Pomeau,Lattice-Gas Automata for the Navier-Stokes Equation,Phys.Rev.E,1986,Vol.56:1505-1508
[7]Higuera F,J imenez J,Succi S.Boltzmann app roach to lattice gas simulations[J].Europhysics Letters,1989,9:663.
[8]McNamara G G,Zanetti G.Use of the Boltzmann equation to siulate lattice gas automata[J].Physical Review Letters,1988,61:2 332-335.
[9]Qian YH,Simulating thermohydrodynamics with lattice BGK models,J.Sci.Comput.8(3):231-242(1993)
[10]Alexander FJ,Chen S,Sterling JD,Lattice Boltzmann thermohydrodynamics,Phys.Rev.E,47,R2249-2252(1993)
[11]Chen Y.Ohashi H,Akiyama M,Theremal lattice Bhatnagar-Gross-Kook Model without nonlinear deviations in Macrodynamic Equations,phys.Rev E,50,2776-2783(1994)
[12]He X Y,Chen S Y,Doolen G D,A novel thermal model for the lattice Boltzmann method incompressible limit[J].J Comput Phys,1998,146(1):282-300
[13]Guo Z L,Shi B C,Zheng C G,A coupled lattice BGK model for the Bouessinesq equation[J].Int J Num Fluids,2002,39(4):325-342
[14]Gang G H,Tao W Q,HE Y L,Simulation of the fluid flow and heat transfer in a plane channel using the lattice Boltzmann method[J].Int J Mod Phys:B,2003,17(1):183-187
[15]黄华国,张晓丽,王蕾,基于三维曲面元胞自动机模型的林火蔓延模型[J],北京林业大学报,2005,27(3):94-97
[16]黄光球,汪晓海,陈惠明,基于元胞自动机的地下矿火灾蔓延仿真方法[J],系统仿真学报,2007,19(1):201-205
[17]周西华,王继仁,梁栋,掘进巷道风流温度场分布规律的研究,辽宁工程技术大学学报,2003,22(1):1-3
[18]周西华,王继仁,单亚飞,王树刚,梁栋,掘进巷道风流温度分布规律的数值模拟,中国安全科学学报,2002,12(2):19-23
[19]邢书仁,吴兵,周心权,张莉聪,区域模拟与巷道火灾一维烟流流动模拟耦合方法初探,中国安全科学学报,2004,14(2):24-26
[20]王海燕,赵洪泽,基于数值模拟的矿井火灾虚拟再现方法研究,中国煤炭,2007,33(7):74-76
[21]蒋军成,王省身.矿井火灾巷道烟气流动场模型[J].矿冶工程,1997,17(2):6-10
[22]贾进章,马恒,刘剑.矿井火灾时期温度分布数值模拟[J].辽宁工程技术大学学报,2003,22(4):460-46
[23]周福宝,王德明,矿山通风网络火灾的计算机仿真模拟[J],金属矿山,2008,2:115-117
[24]高建良,魏平儒,掘进巷道分流热环境的数值模拟[J],煤炭学报,2006,31(2):201-205
[25]贾进章,马恒,刘剑,矿井火灾时期温度分布数值模拟[J],辽宁工程科技大学学报,2003,22(4):460-462
[27]李杰林,周科平,苏家红,唐谷修,自燃火灾巷道烟流的数字模拟及安全评价[J],中国安全科学学报,2006,16(4):37-41
[28]傅培舫,周怀春,俞启香,蒋时才,叶汝陵,巷道火灾节流过程及其影响因素的研究[J],煤炭学报,2005,30(2):146-150
[29]王德明,程远平,周福宝,季经纬,矿井火灾火源燃烧特性的实验研究[J],中国矿业大学学报,2002,31(1):30-33
[30]Zou Q,Hou S,Chen S,Doolen GD.An improved incompressible lattice Boltzmann model for time-independent flows.J.Stat.Phys.,1995,81:35-48
[31]Lin Z,Fang H,Tao R,Improved lattice Boltzmann model for incompressible two-independent flows,J.Stat.Phys.81:35-48(1995)
[32]Chen Y,Ohashi H,Lattice-BGK methods for simulating incompressible fluid flows,Int.J.Mod.Phys.C,8:793-803(1997)
[33]He X,Luo L-S,Lattice Boltzemann model for the incompressible Navier-Stokes equation J.Stat.Phys.,88:927-944(1997)
[34]Guo Z-L,Shi B-C,Wang N-C,Lattice BGK model for incompressible Navier-Stokes equation,J.Comput.Phys.165:288-306(2000)
[35]Guo ZL,Shi BC,Zheng CG,A coupled lattice BGK model for Bouessinesq equation,Int.J.Num.Fluids,39:325-342(2002)
[36]Guo ZL,Zheng CG,Shi BC,Non-equilibrium extrapolation method for velocity and pressure boundary conditions in the lattice Boltzmann method,Chinese Phys.,11(04):366-374(2002)
[37]王兴勇,Lattice Boltzmann方法的理论及其在水利计算中应用的研究,河海大学,2003年3月
[38]张桂茹,二维直角管道的LBM模拟,吉林大学,2007年4月
[39]李克平,刘慕仁,13速四方格子BGK模型热流体性质研究[J].广西师范大学学报(自然科学版),1997,15(4):7-13
[40]郑忠,高小强.13-Bit多速格子气自动机模型的理论分析与模拟[J],重庆大学学报(自然科学版),2000,23(6):82-86
[41]G.H.Tang,W.Q.Tao,Y.L.He,Simulation of fluid and heat transfer in a plane channel using the Lattice Boltzmann method[J],Int.Jou.Mod.Phys B,2003,17(2):183-187
[42]童长青,何雅玲,王勇,刘迎文,封闭方腔自然对流的格子-Boltzmann方法动态模拟[J],2007,41(1):32-36
[43]王勇,何雅玲,唐桂华,陶文铨,二位管道内交变流动的格子-Boltzmann方法模拟研究[J],西安交通大学学报,2006,40(1):14-17
[44]Zhaoli Guo,Chuguang Zheng,Baochang Shi,Thermal lattice Boltzmann equation for low Mach number flows:Decoupling model,Phy.Rev,2007,75:036704:1-14
[45]H.Chen,S.Chen,and W.H.Matthaeus,Recovery of the Navier-Stokes Equations Using a Lattice-Gas Boltzmann Method,Phys.Rev.A.,1992,Vol.45:R5339-R5342
[46]Chen S,Martinez D,Mei R.On boundary conditions in lattice Boltzmann methods.Phys.Fluids.,1996,8:2527-2536.
[47]Bouzidi M,Firdaouss M,Lallemand P.Monentum Transfer of a Lattice Boltzmann Fluid with Boundaries J.Phys.Fluids,2001,(13):3452-3459
[48]蔡增基,龙天渝,流体力学泵与风机,中国建筑工业出版社,1999年第4版:90-95
[49]冯士德,张琼,任荣彩,用格子Boltzmann模型模拟非等温流场,物理学报[J],2001,50(7):1207-1212
[50]宴一光,吴波,郑楚光,三维十五点格子Boltzmann模型仿真,工程热物理学报[J],2001,22(4):503-506
[51]康秀英,刘大禾,周静,金永娟,晶格Boltzmann方法模拟流体在三维圆管的流场,北京师范大学学报,2006,42(3):272-275
[52]赵以惠,矿井通风与空气调节M。北京:中国矿业大学出版社,1990.70-72.
[53]姬长发,徐炳坤,赵建余,多井口多风机矿井反风的非稳定流动模拟,西安科技学院学报,2003,23(3):241-244
[54]常心坦,矿井火灾通风的数学模型及计算机模拟M.美国矿业局,1987.80-120
[55]宋福海,常文杰,杨忠东,计算机模拟矿井反风的探讨,煤矿安全[J],2002,33(1):34-36
[56]王子邦,矿井反风技术分析与相关问题的探讨,应用技术[J],2006,11:59-61
[57]Shan X W,Chen H D.Lattice Boltzmann model for simulating flows with multiple phases and components.Phy Rev E,1993,47:1815-1819
[58]严薇薇,刘阳,许友生,用格子Boltzmann研究多孔介质内的自然对流患热问题,西安石油大学学报[J],2007,22(3):149-152
[59]陈胜,柳朝晖等,低Mach数反应流动的格子Boltzmann模型,中国科学E 辑 技术科学2006,36(9):1002-1015
[60]何雅玲,王勇,李庆,格子Boltzmann方法的理论及应用,2009年1月第一版:8-14
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