非结构网格FVM在复杂几何结构的湍流反应流计算中的应用研究
|
摘要
非结构网格有限体积法适合应用于复杂几何结构的流场计算,而SIMPLE系列算法适合应用于工业上广泛存在的低速流、不可压流计算,欧拉-拉格朗日方法适合应用于含稀疏颗粒相的流场计算。本文正是以这些理论为基础展开工作,包括CGNS网格前后处理,压力修正算法的实现和拓展,化学组分源项模型,颗粒相与气相之间的相互作用等。分述如下:
本文提出了两种将CGNS非结构网格点数据结构转化为非结构网格面数据结构的快速算法,以作为本文操作非结构网格的基础:内部网格面的整数hash表算法和内部双面壁边界网格面的实数hash表算法。由于CGNS非结构网格存储的是网格结点数据,例如网格结点坐标、每一个网格由哪些结点构成等数据信息;而有限体积法离散过程中,需要用到大量的面积分,所以更多的需要网格面数据结构。内部网格面的构造根据网格面两侧的网格在这个公共网格面上的结点序号相同的特点设计算法,双面壁网格面则根据重合在一起的两个边界网格面中心距离接近于零,或者说小于某一个特征小量,比如该网格面面积的算术平方根来设计算法。两种hash表算法具有快速,内存消耗量小于后续有限体积求解器内存峰值的特点,使前处理算法不会成为整个计算的瓶颈。
在压力修正方程的构造过程中,考虑温度修正量对密度修正量的影响,通过静焓方程构造温度修正量与压力修正量的关系,而这种做法的实际效果相当于增强了压力修正量方程线性代数方程组的主对角线。对于可压缩流计算,在流量计算时,在线性插值和迎风格式的基础上,网格面上的密度值采用低阶和高阶的混合格式,动量方程中的压力项处理为滞后的压力梯度项,即线性插值计算方法,和网格面上的压力积分之和,网格面上的压力值则可以采用低阶和高阶混合格式。这些做法兼顾了分辨率和计算的稳定性。
在喷雾燃烧数值模拟中考虑了湍流反应组分源项模型如EBU模型、ED模型、Arrinius/EBU/ED模型和Presumed PDF模型。对于颗粒相和气相之间的相互作用,本文一是将颗粒相对气相的反作用阻力中的部分阻力系数剥离,由拉格朗日系统转入欧拉系统,加入到气相动量方程线性代数方程组的主对角线上,这一系数为正实数,增强了主对角线的系数,也增强了含颗粒流的气相迭代计算稳定性;二是在采用时间推进方法计算稳态流场过程中,对耦合的颗粒相与连续相之间计算采用显式和隐式的计算方法进行了研究,这样做的目的在于相对传统的显式时间计算方式,可以采用一个较大的时间步长值进行迭代,从而减少时间推进时的计算量,使得喷雾燃烧数值模拟的计算稳定性得以增强同时减少计算量。
在课题组研制的自主知识产权流体力学软件开发过程中,本文作者承担了部分功能模块的研发工作,取得了上述研究成果。并就一些算例与商用软件和经典计算结果予以对比,验证了本文算法的正确性。
The unstructured FVM is fit for the complex flow field calculation, and the SIMPLE series algorithms are fit for the low march number, or incompressible flow field calculation, Euler-Largrange method is fit for the sparse spray flow field calculation. Based on these above, the preprocessing and postprocessing with CGNS system, the implementation and modification of SIMPLE series algorithms, the models of the species source term, the ineraction between the particle phase and the gas phase, and so on are carried out. The details are below:
Two hash methods forming the face structure from the node structure of the unstructured CGNS mesh are the bases to operate the unstructured mesh in this paper: the integer number hash method for the inner faces formation and the real number hash method for the two-side wall boundary faces formation. Because the node data is stored by the unstructured CGNS mesh, for example, the node coordinates, the node index list of every grid. The face intigral is very usual in Finite Volume method, so the shifting from node to face is needed. The same node index list in the interface of two neighbour cells is employed to formate the inner face, and the distance between the centers of two faces in a two-side wall boundary is approximate to zero, or else less than a specified real number for example the square root of the area of the faces, and this is the key point to formate faces in this kind of boundarys. The two method make the faces formation is very quick, and the computer memory consumed is less than the FVM solver, so the CGNS preprocessing is not the bottle neck of the whole computation.
In the formation of the pressure correction equation, the influence of the temperature correction to the density correction is considered, the relationship between the temperature correction and the pressure correction is based on the static enthalpy equation. This method enhanced the primary diagonal coefficient of the pressure correction equation. To the compressible flow calculation, some hybrid methods of low order and high order blending interpolation are employed, such as the hybrid method to get the density of the face mass flux, the hybrid method for the pressure term in the momentum equations, the transient term calculation. These methods compromise btween the resolution and stability.
The turbulent combustion species models such as EBU, Eddy Dissipation, Arrinius/EBU/ED, presumed PDF are employed to simulate the spray combustion. In this paper, the momentunm interaction between particle phase and gas phase is modeled by splitting the drag force coefficients, shifting to the Euler system from the Largrange system, adding these coeffients to the diagonal coefficients of the gas phase momentum equation linear algebraic matrix, and the added coefficients are positive, so the diagonal coefficients are enhanced and the calculation stability is enhanced. With the time marching method calculating the steady fields, the explicit and implicit methods of the coupling particulate flow are researched in this paper. With this method a larger time step can be used to reduce the calculation of the time marching progress.
In the in-house CFD software developing of our team, some tasks are finished by the writer of this paper. Some calculation cases compared to the commercial software prove the correctness of the methods in this paper.
本文提出了两种将CGNS非结构网格点数据结构转化为非结构网格面数据结构的快速算法,以作为本文操作非结构网格的基础:内部网格面的整数hash表算法和内部双面壁边界网格面的实数hash表算法。由于CGNS非结构网格存储的是网格结点数据,例如网格结点坐标、每一个网格由哪些结点构成等数据信息;而有限体积法离散过程中,需要用到大量的面积分,所以更多的需要网格面数据结构。内部网格面的构造根据网格面两侧的网格在这个公共网格面上的结点序号相同的特点设计算法,双面壁网格面则根据重合在一起的两个边界网格面中心距离接近于零,或者说小于某一个特征小量,比如该网格面面积的算术平方根来设计算法。两种hash表算法具有快速,内存消耗量小于后续有限体积求解器内存峰值的特点,使前处理算法不会成为整个计算的瓶颈。
在压力修正方程的构造过程中,考虑温度修正量对密度修正量的影响,通过静焓方程构造温度修正量与压力修正量的关系,而这种做法的实际效果相当于增强了压力修正量方程线性代数方程组的主对角线。对于可压缩流计算,在流量计算时,在线性插值和迎风格式的基础上,网格面上的密度值采用低阶和高阶的混合格式,动量方程中的压力项处理为滞后的压力梯度项,即线性插值计算方法,和网格面上的压力积分之和,网格面上的压力值则可以采用低阶和高阶混合格式。这些做法兼顾了分辨率和计算的稳定性。
在喷雾燃烧数值模拟中考虑了湍流反应组分源项模型如EBU模型、ED模型、Arrinius/EBU/ED模型和Presumed PDF模型。对于颗粒相和气相之间的相互作用,本文一是将颗粒相对气相的反作用阻力中的部分阻力系数剥离,由拉格朗日系统转入欧拉系统,加入到气相动量方程线性代数方程组的主对角线上,这一系数为正实数,增强了主对角线的系数,也增强了含颗粒流的气相迭代计算稳定性;二是在采用时间推进方法计算稳态流场过程中,对耦合的颗粒相与连续相之间计算采用显式和隐式的计算方法进行了研究,这样做的目的在于相对传统的显式时间计算方式,可以采用一个较大的时间步长值进行迭代,从而减少时间推进时的计算量,使得喷雾燃烧数值模拟的计算稳定性得以增强同时减少计算量。
在课题组研制的自主知识产权流体力学软件开发过程中,本文作者承担了部分功能模块的研发工作,取得了上述研究成果。并就一些算例与商用软件和经典计算结果予以对比,验证了本文算法的正确性。
The unstructured FVM is fit for the complex flow field calculation, and the SIMPLE series algorithms are fit for the low march number, or incompressible flow field calculation, Euler-Largrange method is fit for the sparse spray flow field calculation. Based on these above, the preprocessing and postprocessing with CGNS system, the implementation and modification of SIMPLE series algorithms, the models of the species source term, the ineraction between the particle phase and the gas phase, and so on are carried out. The details are below:
Two hash methods forming the face structure from the node structure of the unstructured CGNS mesh are the bases to operate the unstructured mesh in this paper: the integer number hash method for the inner faces formation and the real number hash method for the two-side wall boundary faces formation. Because the node data is stored by the unstructured CGNS mesh, for example, the node coordinates, the node index list of every grid. The face intigral is very usual in Finite Volume method, so the shifting from node to face is needed. The same node index list in the interface of two neighbour cells is employed to formate the inner face, and the distance between the centers of two faces in a two-side wall boundary is approximate to zero, or else less than a specified real number for example the square root of the area of the faces, and this is the key point to formate faces in this kind of boundarys. The two method make the faces formation is very quick, and the computer memory consumed is less than the FVM solver, so the CGNS preprocessing is not the bottle neck of the whole computation.
In the formation of the pressure correction equation, the influence of the temperature correction to the density correction is considered, the relationship between the temperature correction and the pressure correction is based on the static enthalpy equation. This method enhanced the primary diagonal coefficient of the pressure correction equation. To the compressible flow calculation, some hybrid methods of low order and high order blending interpolation are employed, such as the hybrid method to get the density of the face mass flux, the hybrid method for the pressure term in the momentum equations, the transient term calculation. These methods compromise btween the resolution and stability.
The turbulent combustion species models such as EBU, Eddy Dissipation, Arrinius/EBU/ED, presumed PDF are employed to simulate the spray combustion. In this paper, the momentunm interaction between particle phase and gas phase is modeled by splitting the drag force coefficients, shifting to the Euler system from the Largrange system, adding these coeffients to the diagonal coefficients of the gas phase momentum equation linear algebraic matrix, and the added coefficients are positive, so the diagonal coefficients are enhanced and the calculation stability is enhanced. With the time marching method calculating the steady fields, the explicit and implicit methods of the coupling particulate flow are researched in this paper. With this method a larger time step can be used to reduce the calculation of the time marching progress.
In the in-house CFD software developing of our team, some tasks are finished by the writer of this paper. Some calculation cases compared to the commercial software prove the correctness of the methods in this paper.
引文
[1]周力行著.多相流湍流反应流体力学.北京:国防工业出版社,2002:17-174页
[2]Thierry Poinsot.Theoretical and Numerical Combustion.R.T.Edwards,Inc,2001:125-308P
[3]Bjorn F.Magnussen.On the Structure of turbulence and A generalized Eddy Dissipation Concept for Chemical Reaction in Turbulent Flow.19~(th) AIAA Aerospace Science Meeting.1981:1-7P
[4]Bjorn F.Magnussen.The Eddy Dissipation Turbulence Energy Cascade Model.Combustion Science and Technology.1989:1-24P
[5]Bjorn F.Magnussen.Modeling of NOx and soot Formation by the Eddy Dissipation Concept.CIMAC conference Tianjing,China,1989:1-21P
[6]Fluent 6.2.26帮助文件
[7]Vivek Saxena and Stephen B.Pope.PDF Simulation of Turbulent Combustion Incorporating Detailed Chemistry.Combustion and Flame,1999:117-350P
[8]Metin Muradoglu,Stephen B.Pope,and David A.Caughey.The Hybrid Method for the PDF Equations of Turbulent Reactive Flows:Consistency Conditions and Correction Algorithms.Journal of Computational Physics 172,2001:841 -878P
[9]范宝春,姜孝海,谢波.障碍物导致甲烷-氧气爆炸的三维数值模拟.煤炭学报,27(4):2002:1-3页
[10]李志强,魏飞,周力行.湍流燃烧NO生成反应率数值模拟的现状与进展.燃烧科学与技术,2004,10(5):1-7页
[11]周力行.湍流气粒两相流动和燃烧的理论和数值模拟.北京:科学出版 社,1994:1-245页
[12]郭治民,张会强.简化的联合PDF模型模拟湍流燃烧中NO生成.清华大学学报:自然科学版,2002:1504-1507P
[13]葛海文,朱雯明,胡国辉,李艺,董刚,王海峰,陈义良.基于无结构网格和颗粒方法相结合求解湍流的联合PDF方程.中国科学技术大学学报,2002,32(5):1-11页
[14]王锡斌,蒋德明,周龙保,潘克煜.二甲醚发动机湍流燃烧模型的研究.西安交通大学学报,2003,37(11):1-5页
[15]杜德方,解茂昭.层流小火焰模型在柴油机湍流燃烧中的应用.热科学与技术,2005,4(4):1-6页
[16]芩可法.高等燃烧学.杭州:浙江大学出版社,2000:170-193页
[17]严传俊,范玮.燃烧学.西安:西北工业大学出版社,2005:174-19页
[18]顾欣,臧述升,葛冰,周见广.加湿湍流燃烧火焰稳定的速度场特征分析.燃气轮机技术,2006,19(2):1-4页
[19]Diane M.A.Poirier.Advances in the CGNS database for erodynamics And CFD.ICEM CFD Engineering,Berkeley,CA,2000:1-11P
[20]Steve M.Legensky and David E.Edvards.CFD General Notation System(CGNS):Status And Future Directions.40~(th) AIAA Aerospace and Exhibit 14-17 RenD NV.January 2002:1-13P
[21]Diane Poirier.THE CGNS SYSTEM.NASA Ames Research Center,Moffett Field,CA,1998:1-16P
[22]Armin Wulf.The CGNS system Standard for Aerodynamic data.ICEM CFD Engineering,1999:1-30P
[23]Christopher L.Rumsey.AUser' s Guide to CGNS.Document Version 1.1.5 CGNS Version 2.3.NASA Langley Research center,2OO3:1-81P
[24]CFD General Notation System:Advanced Data Format(ADF) User's Guide.Document Version 1.1.1,2003:1-128P
[25]CFD General Notation System:Mid-Level Library.Document Version 2.3.7 CGNS Version 2.3,2003:1-69P
[26]CFD General Notation System:Overview and Entry-level document.Document Version 2.0.8,2003:1-31P
[27]CFD General Notation System:SIDS-to-ADF File Mapping Manual.Document Version 2.3 CGNS Version 2.3,2003:1-99P
[28]CFD General Notation System:Steering Committee Charter.Document Version 1.1,2003:1-22P
[29]The CFD General Notation System:Standard Interface Data Structures.The CGNS Steering Sub-committee of the AIAA CFD Committee on Standards,2003:1-171P
[30]马瑞民.Fortran 90程序设计.哈尔滨:哈尔滨工程大学出版社,1998:1-269页
[31]严蔚敏,吴伟民.数据结构.北京:清华大学出版社,2000:256-262页
[32]雷国东,柳贡民,张文平,朱明刚.CGNS API和FVM在非结构网格计算中的应用.计算物理,2007,24(3):277-281页
[33]ClaudioMattiussi.An Analysis of Finite Volume,Finite Element,and Finite Difference Methods Using Some Concepts from Algebraic Topology.JOURNAL OF COMPUTATIONAL PHYSICS 133,289-309,1997:1-21P
[34]M.D.Tidriri.Analysis of the hybrid fnite element/fnite volume methods for linear hyperbolic and convection-dominated convection-di&usion problems.Journal of Computational and Applied Mathematics 139,2002:323 -350P
[35]Joel H.Ferziger and Milovan Peric.Computational Method for Fluid Dynamics.Published by springer,Berlin.3~(rd)version:1-431P
[36]Jean-Michel Ghidaglia.The normal flux method at the boundary for multidimensional finite volume approximations in CFD.European Journal of Mechanics B/Fluids 24,2005):1-17P
[37]曾敏,陶文铨.密网格下SIMPLE等四种算法的收敛性与健壮性的比较.热科学与技术,2003,2(1):1-4页
[38]王志东,汪德灌.非正交同位网格中的SIMPLE算法.河海大学学报(自然科学版),2003,31(5):1-4页
[39]刘顺隆,郑群.计算流体力学.哈尔滨:哈尔滨工程大学出版社,1997:1-172页
[40]Jinn-Liang Liu.Object-Oriented Programming of adaptive finite element and finite volume methods.Applied Numerical Mathematics 21,1996:439-467P
[41]H.Jasak a,A.D.Gosman.Element residual error estimate for the finite volume method.Computers & Fluids 32(2003) 223-248P
[42]Michael Dumbser,Martin Kaser.Arbitrary high order non-oscillatory finite volume schemes on unstructured meshes for linear hyperbolic systems.Journal of Computational Physics 221,2007:693 -723P
[43]David Apsley.Introduction to CFD.Springer 2005:1-7P
[44]David Apsley.The fluid-flow equations.Springer 2005:1-15P
[45]David Apsley.Common Approximations.Springer 2005:1-7P
[46]David Apsley.The scalar transport equation.Springer 2005:1-22P
[47]David Apsley.The momentum equation.Springer 2005:1-22P
[48]David Apsley.Time-dependent methods.Springer 2005:1-7P
[49]David Apsley.Turbuience modeling in CFD.Springer 2005:1-21P
[50]David Apsley.The CFD process.Springer 2005:1-13P
[51]David Apsley.Turbulence.Springer 2004:1-20P
[52]Milovan Peric.Numerical methods for computing turbulent flows,part Ⅰ.Fluid Dynamics and Ship Theory Section Technical University of Hamburg-Harburg and ICCM Institute of Computational Continuum Mechanics GmbH, Hamburg. 2001:1-18P
[53] Milovan Peric. Numerical methods for computing turbulent flows, part II. Fluid Dynamics and Ship Theory Section Technical University of Hamburg-Harburg and ICCM Institute of Computational Continuum Mechanics GmbH, Hamburg. 2001:1-23P
[54] Milovan Peric. Numerical methods for computing turbulent flows, part III. Fluid Dynamics and Ship Theory Section Technical University of Hamburg-Harburg and ICCM Institute of Computational Continuum Mechanics GmbH, Hamburg. 2001:1-42P
[55] Milovan Peric. Numerical methods for computing turbulent flows, part IV. Fluid Dynamics and Ship Theory Section Technical University of Hamburg-Harburg and ICCM Institute of Computational Continuum Mechanics GmbH, Hamburg. 2001:1-33P
[56] Guo-dong Lei, Gong-min Liu, Wen-ping Zhang, Ming-gang Zhu. CGNS Data Format Used for A 2D/3D Finite Volume Unstructured Grid Flow Solver. Proceedings of the First International Multi-Symposiums on Computer and Computational Sciences.China, 2006(2):792-799P
[57] Samir Muzaferijal and David Gosman. Finite-Volume CFD Procedure and Adaptive Error Control Strategy for Grids of Arbitrary Topology. JOURNAL OF COMPUTATIONAL PHYSICS 138, 1997:766-787P
[58] Jinglian J. Liu and Bharat K. Soni. 2D Groundwater Contaminant Transport Modeling by using the Finite Volume Method on an Unstructured Grid System. Applied Mathematics and computation 89:1999-211, 1998:1-13P
[59] Sebastien Perron. A finite volume method to solve the 3D Navier- Stokes equations on unstructured collocated meshes. Computers& Fluids 33, 2004:1305-1333P
[60]Sylvain Boivin.A finite volume method to solve the Navier-Stokes equations for incompressible flows on unstructured meshes.Int.J.Therm.Sci.2000:806-825P
[61]Sebastien Perron.A new finite volume discretization scheme to solve 3D incompressible thermal flows on unstructured meshes.International Journal of Thermal Sciences 43,2004:833-848P
[62]Dongjoo Kim and Haecheon Choi.A Second-Order Time-Accurate Finite Volume Method for Unsteady Incompressible Flow on Hybrid Unstructured Grids.Journal of Computational Physics 162,411-428,2000:1-18P
[63]Marcelo H.Kobayashi,Jose M.C.Pereiray and Jose C.F.Pereiraz.A Conservative Finite-Volume Second-Order-Accurate ProjectionMethod on Hybrid Unstructured Grids.Journal of Computational Physics 150,40-75,1999:1-36P
[64]吴德铭,郜冶.实用计算流体力学基础.哈尔滨:哈尔滨工程大学出版社,2006:1-360页
[65]王福军.计算流体动力学分析CFD软件原理与应用.北京:清华大学出版社,2004:1-158页
[66]C.M.Rhie.Numerical Study of the Turbulent Flow Past An airfoil with Trailing Edge Separation.Journal of Computational Physics vol.21No.11 1983:1-8P
[67]D.Braess,R.Sarazin.An efficient smoother for the stokes problem.Applied Numerical Mathematics 23,1997:3-19P
[68]柏威,鄂学全.基于非结构化同位网格的SIMPLE算法.计算力学学报,2003,20(6):1-9页
[69]赖锡军,汪德歆,傅源方.非结构同位网格SIMPLE类算法收敛性能比较.空气动力学学报,2004,22(3):1-6页
[70]屈治国,何雅玲,陶文铨.求解流动和传热问题的一种新的全隐算法-CLEAR(上).工程热物理学报,2005,26(1):1-3页
[71]李斌,陈听宽,崔凝.SIMPLEX算法与其它算法收敛性的比较.华北电力大学学报,2004,31(3):1-5页
[72]范宝春.两相系统的燃烧、爆炸和爆轰.北京:国防工业出版社,1998:41-134页
[73]David Apsley.Turbulence Modeling in CFD.Springer 2007:1-21P
[74]David C.Wilcox.Turbulence Modeling for CFD.DCW industries,inc 1994:83-89P
[75]Anders Brink,Christian Mueller.Possibilities and Limitations of the Eddy Break-Up Model.COMBUSTION AND FLAME 123:275-279(200O):1-5P
[76]Lene K.Hjertager,Jorgen Osenbroch.Validation of the Eddy Dissipation Concept for fast chemical reactions in turbulent flows.Chemical Reaction Engineering Ⅶ:CFD.Quebec City,Canada,August 2000:6-11P
[77]AVL corporation.Fire help file Version 8.vol2:spray,2005:(2-2)-(2-6) P
[78]Sara Dailey Bauman.A Spray Model for an Adaptive Mesh Refinement Code.Doctor degree Paper of University of Wisconsin Madison,2001:30-38P,174-178P
[79]王燕军,王建昕.GDI汽油机喷雾模型的改进和数值模拟.北京:清华大学学报(自然科学版),2002:1-3页
[80]蔡文祥,胡好生,赵坚行.涡流器燃烧室头部两相反应流数值模拟.航空动力学报,2006,21(5):1-6页
[81]解茂昭.内燃机计算燃烧学.大连:大连理工大学出版社,2005:77-82页
[82]刘金武.直喷式发动机燃油喷射过程的多维模型仿真.系统仿真学报,2004,16(3):1-5页
[83]Ravindra Aglave,M.Chem.Engg.CFD Simulation of Combustion Using Automatically Reduced Reaction Mechanisms:A Case for Diesel Engine. Doctor degree paper of University of Heidelberg,2007:1-48P
[84] A. Datta , S. K. Som. Combustion and emission characteristics in a gas turbine combustor at different pressure and swirl conditions. Applied Thermal Engineering 19 (1999) 949-967:1-19P
[85] Chrys Correa, M.S. (Chem. Eng.). Combustion Simulations in Diesel Engines using Reduced Reaction Mechanisms. Doctor Paper of University of Heidelberg, 2000:1-27P
[86] V. I. Golovitchev, N. Nordin. Detailed Chemistry Spray Combustion Model for the KIVA code. International Engine Modeling User's Group Meeting at the SAE congress, Detroit, 2001:1-7P
[87] N. Sterno, G. Greeves and S. Tullis. Improvements of the KIVA Dense Spray Modeling for HSDI Diesel Engines. SAE technical paper series 2007-01-0001:7-11P
[88] Haiyun Su, Sebastian Mosbach, Amit Bhave, Markus Kraft.Two-stage Fuel Direct Injection in a Diesel Fuelled HCCI Engine.Cambridge Centre for Computational Chemical Engineering, 2007:1-26P
[89] Christopher J. Rutland and Yunliang Wang. Turbulent liquid spray mixing and combustion - fundamental simulations. Journal of Physics: Conference Series 46, 2006: 28 - 37P
[90] David J. Torres a, Mario F. Trujillo. KIVA-4: An unstructured ALE code for compressible gas flow with sprays. Journal of Computational Physics 219, 2006:943 - 975P
[91] A. A. Amsden. KIVA-II A Computer Program for Chemically Reactive Flows with Sprays. Los Alamos National Laboratory, 1989:107-113P
[92] D. M. Snider. An Incompressible Three-Dimensional Multiphase Particle-in-Cell Model for Dense Particle Flows. Journal of Computational Physics 170, 2001:523-549P
[93]N.A.Patankar,D.D.Joseph.Lagrangian numerical simulation of particulate flows.International Journal of Multiphase Flow27,2001:1685-1706P
[94]N.A.Patankar,D.D.Joseph.Modeling and numerical simulation of particulate flow by the Eulerian-Lagrangian approach.International joural of multiphase flow.27,2001:1659-1684P
[95]D.M.Snider,P.J.O'Rourkeb,M.J.Andrews.Sediment flow in inclined vessels calculated using a multiphase particle-in-cell model for dense particle flows.International Journal of Multiphase Flow 24,1998:1359-1382P
[96]M.J.Andrews and P.J.O'Rouke.The multiphase particle in cell(MP-PIC) model for density particle flows.International Journal of Multiphase Flow.Vol 22,No.2,1996:379-402P
[97]D.Howard,W.M.Connolly and J.S.Rollet.Unsymmetric conjugate gradient methods and sparse direct methods in finite element flow simulation.International Journal for Numerical methods in Fluids,Vol.10,1990:925-945P
[98]Robert Beauwens.Iterative solution methods.Applied Numerical Mathematics 51,2004:437-450P
[99]I.Arany.The preconditioned Conjugate Gradient Method with Incomplete Factorization Preconditioners.Computer math and applications.Vol.31 No.4/5 1996:1-5P
[100]解惠青.共轭梯度法的一个计算公式.南京:南京航空航天大学学报,2000,31(6):1-5页
[101]谭欣星,席光.共轭梯度法在三维复杂流动数值分析中的应用.水动力学研究与进展,2002,17(1):1-8页
[102]沈阳黎明航空发动机(集团)有限责任公司.燃气轮机原理,结构与应用.北京:科学出版社,2000:286-362页
[103]彭泽琰,刘刚.航空燃气轮机原理.北京:国防工业出版社,2000: 301-311页.
[104]刘淡儿,任玉新,张涵信.非交错网格上不可压流动中的近似投影方法.空气动力学学报,2005,23(3):1-6页
[105]N.Y.Sharma,S.K Som.Influence of fuel volatility and spray parameters on combustion characteristics and NOx emission in a gas turbine combustor.Applied Thermal Engineering 24,2004:885-903P
[106]N.Y.Sharma,f.Datta,S.K.Som.Influence of spray and operating parameters on penetration of vaporizing fuel droplets in a gas turbine combustor.Applied Thermal Engineering 21,2001:1755-1768P
[107]M.R Halder 1,S.K.Dash,S.K Som.Initiation of air core in a simplex nozzle and the effects of operating and geometrical parameters on its shape and size.Experimental Thermal and Fluid Science 26,2002:871 -878P
[108]S.S.Sazhinl,T.Kristyadi,W.A.Abdelghaffar and M.R.Heikal.Models for fuel droplet heating and evaporation:comparative analysis,University of Brighton,2006:1-39P
[109]D.M.Wang.Three-Dimensional Diesel Engine Combustion Simulation with a Modified EPISO procedure,Numerical Heat Transfer,part A,vol.24,pp.249-272,1993:1-13P
[110]Yuri Martin Wright.Numerical investigation of turbulent spray combustion with Conditional Moment Closure.Doctor degree paper of University of Cambridge,UK,2005:7-39P
[111]Fumiteru AKAMATSU,Hiroyasu SAITOH,and Masashi KATSUKI.Proceedings of the 4th JSME-KSME Thermal Engineering Conference October 1-6,Kobe,Japan,2000:1-4P
[112]Hirotatsu Watanabe,Yoshikazu Suwa,Yohsuke Matsushita,Yoshio Morozumi.Spray combustion simulation including soot and NO formation.Energy Conversion and Management 48,2007:2077-2089P
[113]Pieter Wessling.Principles of computational fluid dynamics,Springer 2000:227-293P
[114]阎超.计算流体力学方法及应用.北京:北京航空航天大学出版社,2006:182-183页
[2]Thierry Poinsot.Theoretical and Numerical Combustion.R.T.Edwards,Inc,2001:125-308P
[3]Bjorn F.Magnussen.On the Structure of turbulence and A generalized Eddy Dissipation Concept for Chemical Reaction in Turbulent Flow.19~(th) AIAA Aerospace Science Meeting.1981:1-7P
[4]Bjorn F.Magnussen.The Eddy Dissipation Turbulence Energy Cascade Model.Combustion Science and Technology.1989:1-24P
[5]Bjorn F.Magnussen.Modeling of NOx and soot Formation by the Eddy Dissipation Concept.CIMAC conference Tianjing,China,1989:1-21P
[6]Fluent 6.2.26帮助文件
[7]Vivek Saxena and Stephen B.Pope.PDF Simulation of Turbulent Combustion Incorporating Detailed Chemistry.Combustion and Flame,1999:117-350P
[8]Metin Muradoglu,Stephen B.Pope,and David A.Caughey.The Hybrid Method for the PDF Equations of Turbulent Reactive Flows:Consistency Conditions and Correction Algorithms.Journal of Computational Physics 172,2001:841 -878P
[9]范宝春,姜孝海,谢波.障碍物导致甲烷-氧气爆炸的三维数值模拟.煤炭学报,27(4):2002:1-3页
[10]李志强,魏飞,周力行.湍流燃烧NO生成反应率数值模拟的现状与进展.燃烧科学与技术,2004,10(5):1-7页
[11]周力行.湍流气粒两相流动和燃烧的理论和数值模拟.北京:科学出版 社,1994:1-245页
[12]郭治民,张会强.简化的联合PDF模型模拟湍流燃烧中NO生成.清华大学学报:自然科学版,2002:1504-1507P
[13]葛海文,朱雯明,胡国辉,李艺,董刚,王海峰,陈义良.基于无结构网格和颗粒方法相结合求解湍流的联合PDF方程.中国科学技术大学学报,2002,32(5):1-11页
[14]王锡斌,蒋德明,周龙保,潘克煜.二甲醚发动机湍流燃烧模型的研究.西安交通大学学报,2003,37(11):1-5页
[15]杜德方,解茂昭.层流小火焰模型在柴油机湍流燃烧中的应用.热科学与技术,2005,4(4):1-6页
[16]芩可法.高等燃烧学.杭州:浙江大学出版社,2000:170-193页
[17]严传俊,范玮.燃烧学.西安:西北工业大学出版社,2005:174-19页
[18]顾欣,臧述升,葛冰,周见广.加湿湍流燃烧火焰稳定的速度场特征分析.燃气轮机技术,2006,19(2):1-4页
[19]Diane M.A.Poirier.Advances in the CGNS database for erodynamics And CFD.ICEM CFD Engineering,Berkeley,CA,2000:1-11P
[20]Steve M.Legensky and David E.Edvards.CFD General Notation System(CGNS):Status And Future Directions.40~(th) AIAA Aerospace and Exhibit 14-17 RenD NV.January 2002:1-13P
[21]Diane Poirier.THE CGNS SYSTEM.NASA Ames Research Center,Moffett Field,CA,1998:1-16P
[22]Armin Wulf.The CGNS system Standard for Aerodynamic data.ICEM CFD Engineering,1999:1-30P
[23]Christopher L.Rumsey.AUser' s Guide to CGNS.Document Version 1.1.5 CGNS Version 2.3.NASA Langley Research center,2OO3:1-81P
[24]CFD General Notation System:Advanced Data Format(ADF) User's Guide.Document Version 1.1.1,2003:1-128P
[25]CFD General Notation System:Mid-Level Library.Document Version 2.3.7 CGNS Version 2.3,2003:1-69P
[26]CFD General Notation System:Overview and Entry-level document.Document Version 2.0.8,2003:1-31P
[27]CFD General Notation System:SIDS-to-ADF File Mapping Manual.Document Version 2.3 CGNS Version 2.3,2003:1-99P
[28]CFD General Notation System:Steering Committee Charter.Document Version 1.1,2003:1-22P
[29]The CFD General Notation System:Standard Interface Data Structures.The CGNS Steering Sub-committee of the AIAA CFD Committee on Standards,2003:1-171P
[30]马瑞民.Fortran 90程序设计.哈尔滨:哈尔滨工程大学出版社,1998:1-269页
[31]严蔚敏,吴伟民.数据结构.北京:清华大学出版社,2000:256-262页
[32]雷国东,柳贡民,张文平,朱明刚.CGNS API和FVM在非结构网格计算中的应用.计算物理,2007,24(3):277-281页
[33]ClaudioMattiussi.An Analysis of Finite Volume,Finite Element,and Finite Difference Methods Using Some Concepts from Algebraic Topology.JOURNAL OF COMPUTATIONAL PHYSICS 133,289-309,1997:1-21P
[34]M.D.Tidriri.Analysis of the hybrid fnite element/fnite volume methods for linear hyperbolic and convection-dominated convection-di&usion problems.Journal of Computational and Applied Mathematics 139,2002:323 -350P
[35]Joel H.Ferziger and Milovan Peric.Computational Method for Fluid Dynamics.Published by springer,Berlin.3~(rd)version:1-431P
[36]Jean-Michel Ghidaglia.The normal flux method at the boundary for multidimensional finite volume approximations in CFD.European Journal of Mechanics B/Fluids 24,2005):1-17P
[37]曾敏,陶文铨.密网格下SIMPLE等四种算法的收敛性与健壮性的比较.热科学与技术,2003,2(1):1-4页
[38]王志东,汪德灌.非正交同位网格中的SIMPLE算法.河海大学学报(自然科学版),2003,31(5):1-4页
[39]刘顺隆,郑群.计算流体力学.哈尔滨:哈尔滨工程大学出版社,1997:1-172页
[40]Jinn-Liang Liu.Object-Oriented Programming of adaptive finite element and finite volume methods.Applied Numerical Mathematics 21,1996:439-467P
[41]H.Jasak a,A.D.Gosman.Element residual error estimate for the finite volume method.Computers & Fluids 32(2003) 223-248P
[42]Michael Dumbser,Martin Kaser.Arbitrary high order non-oscillatory finite volume schemes on unstructured meshes for linear hyperbolic systems.Journal of Computational Physics 221,2007:693 -723P
[43]David Apsley.Introduction to CFD.Springer 2005:1-7P
[44]David Apsley.The fluid-flow equations.Springer 2005:1-15P
[45]David Apsley.Common Approximations.Springer 2005:1-7P
[46]David Apsley.The scalar transport equation.Springer 2005:1-22P
[47]David Apsley.The momentum equation.Springer 2005:1-22P
[48]David Apsley.Time-dependent methods.Springer 2005:1-7P
[49]David Apsley.Turbuience modeling in CFD.Springer 2005:1-21P
[50]David Apsley.The CFD process.Springer 2005:1-13P
[51]David Apsley.Turbulence.Springer 2004:1-20P
[52]Milovan Peric.Numerical methods for computing turbulent flows,part Ⅰ.Fluid Dynamics and Ship Theory Section Technical University of Hamburg-Harburg and ICCM Institute of Computational Continuum Mechanics GmbH, Hamburg. 2001:1-18P
[53] Milovan Peric. Numerical methods for computing turbulent flows, part II. Fluid Dynamics and Ship Theory Section Technical University of Hamburg-Harburg and ICCM Institute of Computational Continuum Mechanics GmbH, Hamburg. 2001:1-23P
[54] Milovan Peric. Numerical methods for computing turbulent flows, part III. Fluid Dynamics and Ship Theory Section Technical University of Hamburg-Harburg and ICCM Institute of Computational Continuum Mechanics GmbH, Hamburg. 2001:1-42P
[55] Milovan Peric. Numerical methods for computing turbulent flows, part IV. Fluid Dynamics and Ship Theory Section Technical University of Hamburg-Harburg and ICCM Institute of Computational Continuum Mechanics GmbH, Hamburg. 2001:1-33P
[56] Guo-dong Lei, Gong-min Liu, Wen-ping Zhang, Ming-gang Zhu. CGNS Data Format Used for A 2D/3D Finite Volume Unstructured Grid Flow Solver. Proceedings of the First International Multi-Symposiums on Computer and Computational Sciences.China, 2006(2):792-799P
[57] Samir Muzaferijal and David Gosman. Finite-Volume CFD Procedure and Adaptive Error Control Strategy for Grids of Arbitrary Topology. JOURNAL OF COMPUTATIONAL PHYSICS 138, 1997:766-787P
[58] Jinglian J. Liu and Bharat K. Soni. 2D Groundwater Contaminant Transport Modeling by using the Finite Volume Method on an Unstructured Grid System. Applied Mathematics and computation 89:1999-211, 1998:1-13P
[59] Sebastien Perron. A finite volume method to solve the 3D Navier- Stokes equations on unstructured collocated meshes. Computers& Fluids 33, 2004:1305-1333P
[60]Sylvain Boivin.A finite volume method to solve the Navier-Stokes equations for incompressible flows on unstructured meshes.Int.J.Therm.Sci.2000:806-825P
[61]Sebastien Perron.A new finite volume discretization scheme to solve 3D incompressible thermal flows on unstructured meshes.International Journal of Thermal Sciences 43,2004:833-848P
[62]Dongjoo Kim and Haecheon Choi.A Second-Order Time-Accurate Finite Volume Method for Unsteady Incompressible Flow on Hybrid Unstructured Grids.Journal of Computational Physics 162,411-428,2000:1-18P
[63]Marcelo H.Kobayashi,Jose M.C.Pereiray and Jose C.F.Pereiraz.A Conservative Finite-Volume Second-Order-Accurate ProjectionMethod on Hybrid Unstructured Grids.Journal of Computational Physics 150,40-75,1999:1-36P
[64]吴德铭,郜冶.实用计算流体力学基础.哈尔滨:哈尔滨工程大学出版社,2006:1-360页
[65]王福军.计算流体动力学分析CFD软件原理与应用.北京:清华大学出版社,2004:1-158页
[66]C.M.Rhie.Numerical Study of the Turbulent Flow Past An airfoil with Trailing Edge Separation.Journal of Computational Physics vol.21No.11 1983:1-8P
[67]D.Braess,R.Sarazin.An efficient smoother for the stokes problem.Applied Numerical Mathematics 23,1997:3-19P
[68]柏威,鄂学全.基于非结构化同位网格的SIMPLE算法.计算力学学报,2003,20(6):1-9页
[69]赖锡军,汪德歆,傅源方.非结构同位网格SIMPLE类算法收敛性能比较.空气动力学学报,2004,22(3):1-6页
[70]屈治国,何雅玲,陶文铨.求解流动和传热问题的一种新的全隐算法-CLEAR(上).工程热物理学报,2005,26(1):1-3页
[71]李斌,陈听宽,崔凝.SIMPLEX算法与其它算法收敛性的比较.华北电力大学学报,2004,31(3):1-5页
[72]范宝春.两相系统的燃烧、爆炸和爆轰.北京:国防工业出版社,1998:41-134页
[73]David Apsley.Turbulence Modeling in CFD.Springer 2007:1-21P
[74]David C.Wilcox.Turbulence Modeling for CFD.DCW industries,inc 1994:83-89P
[75]Anders Brink,Christian Mueller.Possibilities and Limitations of the Eddy Break-Up Model.COMBUSTION AND FLAME 123:275-279(200O):1-5P
[76]Lene K.Hjertager,Jorgen Osenbroch.Validation of the Eddy Dissipation Concept for fast chemical reactions in turbulent flows.Chemical Reaction Engineering Ⅶ:CFD.Quebec City,Canada,August 2000:6-11P
[77]AVL corporation.Fire help file Version 8.vol2:spray,2005:(2-2)-(2-6) P
[78]Sara Dailey Bauman.A Spray Model for an Adaptive Mesh Refinement Code.Doctor degree Paper of University of Wisconsin Madison,2001:30-38P,174-178P
[79]王燕军,王建昕.GDI汽油机喷雾模型的改进和数值模拟.北京:清华大学学报(自然科学版),2002:1-3页
[80]蔡文祥,胡好生,赵坚行.涡流器燃烧室头部两相反应流数值模拟.航空动力学报,2006,21(5):1-6页
[81]解茂昭.内燃机计算燃烧学.大连:大连理工大学出版社,2005:77-82页
[82]刘金武.直喷式发动机燃油喷射过程的多维模型仿真.系统仿真学报,2004,16(3):1-5页
[83]Ravindra Aglave,M.Chem.Engg.CFD Simulation of Combustion Using Automatically Reduced Reaction Mechanisms:A Case for Diesel Engine. Doctor degree paper of University of Heidelberg,2007:1-48P
[84] A. Datta , S. K. Som. Combustion and emission characteristics in a gas turbine combustor at different pressure and swirl conditions. Applied Thermal Engineering 19 (1999) 949-967:1-19P
[85] Chrys Correa, M.S. (Chem. Eng.). Combustion Simulations in Diesel Engines using Reduced Reaction Mechanisms. Doctor Paper of University of Heidelberg, 2000:1-27P
[86] V. I. Golovitchev, N. Nordin. Detailed Chemistry Spray Combustion Model for the KIVA code. International Engine Modeling User's Group Meeting at the SAE congress, Detroit, 2001:1-7P
[87] N. Sterno, G. Greeves and S. Tullis. Improvements of the KIVA Dense Spray Modeling for HSDI Diesel Engines. SAE technical paper series 2007-01-0001:7-11P
[88] Haiyun Su, Sebastian Mosbach, Amit Bhave, Markus Kraft.Two-stage Fuel Direct Injection in a Diesel Fuelled HCCI Engine.Cambridge Centre for Computational Chemical Engineering, 2007:1-26P
[89] Christopher J. Rutland and Yunliang Wang. Turbulent liquid spray mixing and combustion - fundamental simulations. Journal of Physics: Conference Series 46, 2006: 28 - 37P
[90] David J. Torres a, Mario F. Trujillo. KIVA-4: An unstructured ALE code for compressible gas flow with sprays. Journal of Computational Physics 219, 2006:943 - 975P
[91] A. A. Amsden. KIVA-II A Computer Program for Chemically Reactive Flows with Sprays. Los Alamos National Laboratory, 1989:107-113P
[92] D. M. Snider. An Incompressible Three-Dimensional Multiphase Particle-in-Cell Model for Dense Particle Flows. Journal of Computational Physics 170, 2001:523-549P
[93]N.A.Patankar,D.D.Joseph.Lagrangian numerical simulation of particulate flows.International Journal of Multiphase Flow27,2001:1685-1706P
[94]N.A.Patankar,D.D.Joseph.Modeling and numerical simulation of particulate flow by the Eulerian-Lagrangian approach.International joural of multiphase flow.27,2001:1659-1684P
[95]D.M.Snider,P.J.O'Rourkeb,M.J.Andrews.Sediment flow in inclined vessels calculated using a multiphase particle-in-cell model for dense particle flows.International Journal of Multiphase Flow 24,1998:1359-1382P
[96]M.J.Andrews and P.J.O'Rouke.The multiphase particle in cell(MP-PIC) model for density particle flows.International Journal of Multiphase Flow.Vol 22,No.2,1996:379-402P
[97]D.Howard,W.M.Connolly and J.S.Rollet.Unsymmetric conjugate gradient methods and sparse direct methods in finite element flow simulation.International Journal for Numerical methods in Fluids,Vol.10,1990:925-945P
[98]Robert Beauwens.Iterative solution methods.Applied Numerical Mathematics 51,2004:437-450P
[99]I.Arany.The preconditioned Conjugate Gradient Method with Incomplete Factorization Preconditioners.Computer math and applications.Vol.31 No.4/5 1996:1-5P
[100]解惠青.共轭梯度法的一个计算公式.南京:南京航空航天大学学报,2000,31(6):1-5页
[101]谭欣星,席光.共轭梯度法在三维复杂流动数值分析中的应用.水动力学研究与进展,2002,17(1):1-8页
[102]沈阳黎明航空发动机(集团)有限责任公司.燃气轮机原理,结构与应用.北京:科学出版社,2000:286-362页
[103]彭泽琰,刘刚.航空燃气轮机原理.北京:国防工业出版社,2000: 301-311页.
[104]刘淡儿,任玉新,张涵信.非交错网格上不可压流动中的近似投影方法.空气动力学学报,2005,23(3):1-6页
[105]N.Y.Sharma,S.K Som.Influence of fuel volatility and spray parameters on combustion characteristics and NOx emission in a gas turbine combustor.Applied Thermal Engineering 24,2004:885-903P
[106]N.Y.Sharma,f.Datta,S.K.Som.Influence of spray and operating parameters on penetration of vaporizing fuel droplets in a gas turbine combustor.Applied Thermal Engineering 21,2001:1755-1768P
[107]M.R Halder 1,S.K.Dash,S.K Som.Initiation of air core in a simplex nozzle and the effects of operating and geometrical parameters on its shape and size.Experimental Thermal and Fluid Science 26,2002:871 -878P
[108]S.S.Sazhinl,T.Kristyadi,W.A.Abdelghaffar and M.R.Heikal.Models for fuel droplet heating and evaporation:comparative analysis,University of Brighton,2006:1-39P
[109]D.M.Wang.Three-Dimensional Diesel Engine Combustion Simulation with a Modified EPISO procedure,Numerical Heat Transfer,part A,vol.24,pp.249-272,1993:1-13P
[110]Yuri Martin Wright.Numerical investigation of turbulent spray combustion with Conditional Moment Closure.Doctor degree paper of University of Cambridge,UK,2005:7-39P
[111]Fumiteru AKAMATSU,Hiroyasu SAITOH,and Masashi KATSUKI.Proceedings of the 4th JSME-KSME Thermal Engineering Conference October 1-6,Kobe,Japan,2000:1-4P
[112]Hirotatsu Watanabe,Yoshikazu Suwa,Yohsuke Matsushita,Yoshio Morozumi.Spray combustion simulation including soot and NO formation.Energy Conversion and Management 48,2007:2077-2089P
[113]Pieter Wessling.Principles of computational fluid dynamics,Springer 2000:227-293P
[114]阎超.计算流体力学方法及应用.北京:北京航空航天大学出版社,2006:182-183页