气固两相自由剪切流动的直接数值模拟和实验研究
摘要
众所周知,湍流问题是个世纪难题。经过众多科学家百余年来的艰辛探索,迄今为止这一问题尚未得到彻底解决。对于更加复杂和广泛存在的气固两相流动问题,人类势必需要付出更多的辛勤耕耘。传统上,对湍流和气固两相流的数值模拟研究主要采用的是基于雷诺平均的湍流模型和气固两相流模型。这样得到的数值解是一种近似的平均解,无法了解流动的瞬时特性,更无从深入探索气固两相流动的内在物理机制。另一方面,现代高性能计算机的出现和应用,为湍流和气固两相流的研究提供了一个新的思路—直接数值模拟(DNS)。它不引入任何湍流模型,而是通过数值求解完整的Naviver—Stokes方程组,能得到包括Kolmogorov微尺度脉动运动在内的所有湍流瞬时流动量在三维空间中的演变。从而为湍流和气固两相流的研究注入新的活力,带来新的发展机遇。
在自然界和实际的工程应用中,气固两相自由剪切流动比较典型。对它的研究既有助于对湍流的根本机理和气固两相间相互作用机理的理解,又可以为相关的工程应用提供指导,还可以为更加复杂的气固两相流的理论发展和实验研究提供参考。因此,开展对气固两相自由剪切流动的研究不仅具有重要的学术理论意义,也有广泛的工程应用价值。在这样的背景下,本学位论文集中开展对气固两相自由剪切流动进行直接数值模拟的研究。具体涉及到对三维气固两相平面混合层、二维气固两相平面射流和三维气固两相平面射流的研究。着重考察自由剪切流动中气相流体拟序结构的演化规律、不同Stokes数颗粒的扩散特性和扩散机理、以及颗粒对气相流动特性的影响所造成的湍流变动。
在对三维气固两相平面混合层的研究中,假定流动为时间发展模式的、不可压缩的流动,颗粒初始时刻仅布置在流场上半侧的高速区。流场控制方程的求解采用拟谱算法,颗粒的跟踪分别采用单向、双向耦合的拉格朗日方法。结果发现,初始时刻位于流场上半侧的颗粒向下半侧的扩散程度跟颗粒的Stokes数成反比。颗粒的Stokes数越小,向流场下半侧的扩散越多,意味着颗粒跟流体的混合越充分。流场大涡结构对Stokes数为1的量级的中等颗粒的影响最强,使得这种颗粒大量聚集在涡结构的外围,浓度分布最不均匀;而其它颗粒在流场中的分布都比较均匀。双向耦合的模拟中,不仅观测到跟以往研究结果相似的现象,而且有新的发现。以往的研究大都认为,小尺寸颗粒由于耗散会衰减湍流,大尺寸颗粒由于尾迹作用会增强湍流。而本部分的DNS结果则表明,在混合层大涡结构的卷起和配对过程中,Stokes数为5的同一种颗粒对气相湍流特性的影响是完全不同的。在大涡结构的卷起过程中,颗粒削弱了流体基波、亚偕波能量、总的湍动能和湍流强度等;而在大涡结构配对过程中,趋势则相反,颗粒都增强了这些量。颗粒的这种削弱和增强作用跟颗粒的质量携带率成正比关系。
It is well-known that turbulence is a difficult problem over centuries. So far, this problem has not been thoroughly solved yet even if after more than one hundred years of hard exploring by lots of scientists. As to the gas-solid two-phase flow problems which are even more complicated and widely existent, Mankind has to pay more efforts. Traditionally, the numerical simulation studies of the turbulence and gas-solid two-phase flows are all based on the Reynolds-Averaged turbulence and gas-solid two-phase flow models. The numerical solution obtained by this method is an approximate mean result. It can not tell the instantaneous characteristics of the flows, and not to mention being used to deeply explore the inner physical mechanism in the gas-solid two-phase flows. On the other hand, the appearance and application of the modern high-performance computers offer a new way to study the turbulence and gas-solid two-phase flows—Direct Numerical Simulation(DNS). It doesn't introduce any turbulence model, but numerically solve the full Navier-Stokes equations, and can obtain the evolutions of all the instantaneous flow variables including the Kolmogorov micro scale fluctuation in the three-dimensional space. Therefore, DNS adds the new energy and brings new developing opportunity to the studies of turbulence and gas-solid two-phase flows.In the nature and practical engineering applications, the gas-solid two-phase free shear flows are typical. Studies on them are helpful to understand the turbulence mechanism and the interaction mechanism between the gas and the solid particles, are directive to the associated engineering applications, and can provide references to the theory-developing and experiment-investigating of the more complicated gas-solid two-phase flows. So, it is not only of academic theoretical significance but also has the extensive engineering application value to carry out the study on the gas-solid two-phase free shear flows. Under these backgrounds, this dissertation focuses on the study of the DNS of the gas-solid two-phase free shear flows, including DNS of the three-dimensional gas-solid two-phase plane mixing layer, the two-dimensional gas-solid two-phase plane jet and the three-dimensional gas-solid two-phase plane jet. The main objective is to investigate the evolution of the gas-phase coherent structures, the dispersion characteristics and dispersion mechanism of the particles with different Stokes numbers, as well as the turbulence modulation by the effects of the particles on the gas-phase flow characteristics.In the DNS of the three-dimensionally gas-solid two-phase plane mixing layer, the flow is assumed to be temporally evolving and incompressible. The particles are initially arranged in the upper region of the higher speed of the flow field. The governing equations of the gas-phase are directly solved by using the pseudo-spectral method. The particle trajectories are traced by using the one-way and two-way
coupled Lagrangian method, respectively. The results show that the dispersion extent to the nether region of the particles placed initially in the upper region of the flow field is in inverse proportion to the particle Stokes number. The smaller the Stokes number of the particles is, the more the dispersion to the nether region is, meaning that the mixing between particles and fluid is more sufficient. Due to the strongest effects by the large-scale vortex structures, the particles at the Stokes numbers of the order of unity concentrate largely in the outer boundaries, thus the particle concentration distribution is the most un-uniform. But the particles at other Stokes numbers distribute evenly in the How field. In the two-way coupling simulation, besides the similar phenomena to those of the previous studies, there are some new findings. In previous studies, it is usually thought that the particles with smaller scale can attenuate turbulence due to the dissipation, but the particles with the larger scale will enhance turbulence due to its wake effect. However, the present DNS results show that the same particles at the Stokes number of 5 have thoroughly different effects on the gas-phase flow characteristics during the rolling up and the pairing courses of the large-scale vortex structures in the mixing layer. In the rolling up of the large-scale vortex structures, the particles reduce the encrpy at fundamental wavenumber and subharmonic wavenumber, the total turbulent kinetic energy and the turbulence intensity of the fluid; but in the pairing course, the trends are opposite and the particles increase all the above variables. This reducing and increasing effects by the particles are direct proportion to the particle mass loading.In the DNS of the two-dimensionally gas-solid two-phase plane jet, the flow is spatially developing and weakly compressible. The fourth-order compact finite difference schemes are used to discretize the space derivatives in the governing equations of the gas-phase. The efficient fractional-step integration scheme is adopted to integrate time. The boundary conditions are also elaborately treated. In the two-way coupling, the momentum effect on the fluid by a particle is described by a point force. The results of the one-way coupling DNS display the transition of the flow field from a symmetric mode to an asymmetric mode in the near field of the jet, capture the consecutive pairing between two or three vortex structures, find the local-focusing phenomena of the dispersion of the particles at the intermediate Stokes numbers, and reveal the dispersion mechanism of particles at different Stokes numbers. These outcomes reinforce the conclusions of the previous researchers. As to the turbulence modulation by the effects of the particles on the gas-phase jet, the study of the two-way coupling DNS shows that the particles at the Stokes number of 0.01 and 50 promote the evolving of the coherent structures in the flow field and make the profiles of the turbulence intensity wider and lower, but the particles at the Stokes number of 1 delay the developing of the coherent structures and reduce the turbulence intensity, making the profiles of the turbulence intensity narrower and lower. Under the same mass loading, the influences on the coherent structures and the jet velocity half-width
在自然界和实际的工程应用中,气固两相自由剪切流动比较典型。对它的研究既有助于对湍流的根本机理和气固两相间相互作用机理的理解,又可以为相关的工程应用提供指导,还可以为更加复杂的气固两相流的理论发展和实验研究提供参考。因此,开展对气固两相自由剪切流动的研究不仅具有重要的学术理论意义,也有广泛的工程应用价值。在这样的背景下,本学位论文集中开展对气固两相自由剪切流动进行直接数值模拟的研究。具体涉及到对三维气固两相平面混合层、二维气固两相平面射流和三维气固两相平面射流的研究。着重考察自由剪切流动中气相流体拟序结构的演化规律、不同Stokes数颗粒的扩散特性和扩散机理、以及颗粒对气相流动特性的影响所造成的湍流变动。
在对三维气固两相平面混合层的研究中,假定流动为时间发展模式的、不可压缩的流动,颗粒初始时刻仅布置在流场上半侧的高速区。流场控制方程的求解采用拟谱算法,颗粒的跟踪分别采用单向、双向耦合的拉格朗日方法。结果发现,初始时刻位于流场上半侧的颗粒向下半侧的扩散程度跟颗粒的Stokes数成反比。颗粒的Stokes数越小,向流场下半侧的扩散越多,意味着颗粒跟流体的混合越充分。流场大涡结构对Stokes数为1的量级的中等颗粒的影响最强,使得这种颗粒大量聚集在涡结构的外围,浓度分布最不均匀;而其它颗粒在流场中的分布都比较均匀。双向耦合的模拟中,不仅观测到跟以往研究结果相似的现象,而且有新的发现。以往的研究大都认为,小尺寸颗粒由于耗散会衰减湍流,大尺寸颗粒由于尾迹作用会增强湍流。而本部分的DNS结果则表明,在混合层大涡结构的卷起和配对过程中,Stokes数为5的同一种颗粒对气相湍流特性的影响是完全不同的。在大涡结构的卷起过程中,颗粒削弱了流体基波、亚偕波能量、总的湍动能和湍流强度等;而在大涡结构配对过程中,趋势则相反,颗粒都增强了这些量。颗粒的这种削弱和增强作用跟颗粒的质量携带率成正比关系。
It is well-known that turbulence is a difficult problem over centuries. So far, this problem has not been thoroughly solved yet even if after more than one hundred years of hard exploring by lots of scientists. As to the gas-solid two-phase flow problems which are even more complicated and widely existent, Mankind has to pay more efforts. Traditionally, the numerical simulation studies of the turbulence and gas-solid two-phase flows are all based on the Reynolds-Averaged turbulence and gas-solid two-phase flow models. The numerical solution obtained by this method is an approximate mean result. It can not tell the instantaneous characteristics of the flows, and not to mention being used to deeply explore the inner physical mechanism in the gas-solid two-phase flows. On the other hand, the appearance and application of the modern high-performance computers offer a new way to study the turbulence and gas-solid two-phase flows—Direct Numerical Simulation(DNS). It doesn't introduce any turbulence model, but numerically solve the full Navier-Stokes equations, and can obtain the evolutions of all the instantaneous flow variables including the Kolmogorov micro scale fluctuation in the three-dimensional space. Therefore, DNS adds the new energy and brings new developing opportunity to the studies of turbulence and gas-solid two-phase flows.In the nature and practical engineering applications, the gas-solid two-phase free shear flows are typical. Studies on them are helpful to understand the turbulence mechanism and the interaction mechanism between the gas and the solid particles, are directive to the associated engineering applications, and can provide references to the theory-developing and experiment-investigating of the more complicated gas-solid two-phase flows. So, it is not only of academic theoretical significance but also has the extensive engineering application value to carry out the study on the gas-solid two-phase free shear flows. Under these backgrounds, this dissertation focuses on the study of the DNS of the gas-solid two-phase free shear flows, including DNS of the three-dimensional gas-solid two-phase plane mixing layer, the two-dimensional gas-solid two-phase plane jet and the three-dimensional gas-solid two-phase plane jet. The main objective is to investigate the evolution of the gas-phase coherent structures, the dispersion characteristics and dispersion mechanism of the particles with different Stokes numbers, as well as the turbulence modulation by the effects of the particles on the gas-phase flow characteristics.In the DNS of the three-dimensionally gas-solid two-phase plane mixing layer, the flow is assumed to be temporally evolving and incompressible. The particles are initially arranged in the upper region of the higher speed of the flow field. The governing equations of the gas-phase are directly solved by using the pseudo-spectral method. The particle trajectories are traced by using the one-way and two-way
coupled Lagrangian method, respectively. The results show that the dispersion extent to the nether region of the particles placed initially in the upper region of the flow field is in inverse proportion to the particle Stokes number. The smaller the Stokes number of the particles is, the more the dispersion to the nether region is, meaning that the mixing between particles and fluid is more sufficient. Due to the strongest effects by the large-scale vortex structures, the particles at the Stokes numbers of the order of unity concentrate largely in the outer boundaries, thus the particle concentration distribution is the most un-uniform. But the particles at other Stokes numbers distribute evenly in the How field. In the two-way coupling simulation, besides the similar phenomena to those of the previous studies, there are some new findings. In previous studies, it is usually thought that the particles with smaller scale can attenuate turbulence due to the dissipation, but the particles with the larger scale will enhance turbulence due to its wake effect. However, the present DNS results show that the same particles at the Stokes number of 5 have thoroughly different effects on the gas-phase flow characteristics during the rolling up and the pairing courses of the large-scale vortex structures in the mixing layer. In the rolling up of the large-scale vortex structures, the particles reduce the encrpy at fundamental wavenumber and subharmonic wavenumber, the total turbulent kinetic energy and the turbulence intensity of the fluid; but in the pairing course, the trends are opposite and the particles increase all the above variables. This reducing and increasing effects by the particles are direct proportion to the particle mass loading.In the DNS of the two-dimensionally gas-solid two-phase plane jet, the flow is spatially developing and weakly compressible. The fourth-order compact finite difference schemes are used to discretize the space derivatives in the governing equations of the gas-phase. The efficient fractional-step integration scheme is adopted to integrate time. The boundary conditions are also elaborately treated. In the two-way coupling, the momentum effect on the fluid by a particle is described by a point force. The results of the one-way coupling DNS display the transition of the flow field from a symmetric mode to an asymmetric mode in the near field of the jet, capture the consecutive pairing between two or three vortex structures, find the local-focusing phenomena of the dispersion of the particles at the intermediate Stokes numbers, and reveal the dispersion mechanism of particles at different Stokes numbers. These outcomes reinforce the conclusions of the previous researchers. As to the turbulence modulation by the effects of the particles on the gas-phase jet, the study of the two-way coupling DNS shows that the particles at the Stokes number of 0.01 and 50 promote the evolving of the coherent structures in the flow field and make the profiles of the turbulence intensity wider and lower, but the particles at the Stokes number of 1 delay the developing of the coherent structures and reduce the turbulence intensity, making the profiles of the turbulence intensity narrower and lower. Under the same mass loading, the influences on the coherent structures and the jet velocity half-width
引文
1. Corrsin S. Investigation of flow in an axially symmetric heated jet of air. NACA Advis, 1943
2. Townsend. Measurement in the turbulent wake of a cylinder. Proc. R. Soc. London Ser. A, 1947, 190: 551-561
3. Corrsin S, Kistler A L. NACA Rep., 1955
4. Townsend A A. The structure of turbulent shear flow. Cambridge Univ. Press, 1956
5. Grant H L. The large eddied of turbulent motion. J. Fluid Mech., 1958, 4: 149-190
6. Kline S J, Rundstadler P W. Visual studies of the wall layers in the turbulent boundary layer. J. Appl. Mech., 1959, 26: 166
7. Kline S J, Reynolds W C, Schraub F A, Rundstadler P W. The structure of turbulent boundary layer. J. Fluid Mech., 1967, 30: 741-773
8. Crow S C, Champagne. Orderly structure in jet turbulence. J. Fluid Mech., 1971, 48: 567
9. Brown G L, Roshko A. On density effects and large structure in turbulent mixing layers. J. Fluid Mech., 1974, 64: 775-816
10.林建忠.湍流的拟序结构.北京:机械工业出版社,1995
11. Crowe C T, Gore R A, Troutt T R. Particle dispersion by coherent structures in free shear flows. Particulate Science and Technology, 1985, 3: 149-158
12. Crowe C T, Chung T N, Troutt T R. Particle mixing in free shear flows. Progress in Energy and Combustion Science, 1988, 14(3): 171-194
13. Wen F, Kamalu N, Chung J N, Crowe C T, Troutt T R. Particle dispersion by vortex structures in plane mixing layers. J Fluids Engng., 1992, 114: 657-666
14. Longmire E K, Eaton J K. Structure of a particle-laden round jet. J. Fluid Mech., 1992, 236: 217-257
15. Longmire E K. Active open-loop control of particle dispersion of round jets. AIAA Journal, 1994, 32(3): 555-563
16. Wicker R B, Eaton J K. Structure of a swirling, recirculating coaxial free jet and its effect on particle motion. Int. J. Multiphase Flow, 2001, 27: 949-970
17. Yang Y, Crowe C T, Chung J N, Troutt T R. Experiments on particle dispersion in a plane wake. Int. J. Multiphase Flow, 2000, 26: 1583-1607
18. Chein R, Chung J N. Simulation of particle dispersion in a two-dimension mixing layer. AIChE J., 1988, 34: 946-954
19. (?) T R. Simulation of particle dispersion in an axisymmetric jet. J. Fluid Mech., 1988, 186: 199-222
20. Tang L, Wen F, Yang Y, Crowe C T, Chung J N, Troutt T R. Self-organizing particle dispersion mechanism in free shear flows. Phys. Fluids A, 1992, 4: 2244-2251
21. Ling W, Chung J N, Troutt T R, Crowe C T. Direct numerical simulation of a three-dimensional temporal mixing layer with particle dispersion. J. Fluid Mech., 1998, 358: 61-85
22. Fan J R, Zheng Y Q, Yao J, Cen K F. Direct simulation of particle dispersion in a three-dimensional temporal mixing layer. Proc. R. Soc. Lond A, 2001, 457: 2151-2166
23. Tsuji Y, Morikawa Y. LDV measurements in air-solid two-phase flow in a vertical pipe. J. Fluid Mech., 1982, 139: 417—434
24. Lee S L, Durst F. On the motion of particles in turbulent duct flows. Int. J. Multiphase Flow, 1982, 8: 125-146
25. Parthasarathy R N, Faeth G M. Turbulence modulation in homogeneous dilute particle-laden flows. J. Fluid Mech., 1990, 220: 485-537
26. Modarress D, Tan H, Elghobashi S E. Two-component LDA measurement in a two-phase turbulent jet. AIAA Journal, 1984, 22: 624-630
27. Modarress D, Wuerer J, Elghobashi S E. An experimental study of a turbulent round two-phase jet. Chemical Engineering Communications, 1984, 28: 341-354
28. Schreck S, Kleis S J. Modification of grid-generated turbulence by solid particles. J. Fluid Mech., 1993, 249: 665-688
29. Levy Y, Lockwood F C. Velocity measurements in a particle laden turbulent free jet. Combustion and Flame, 1981, 40: 333-339
30. Tsuji Y, Morikawa Y, Shiomi H. LDV measurements of an air-solid two-phase flow in a vertical pipe. J. Fluid Mech., 1984, 139: 417-434
31. Gore R A, Crowe C T. Effect of particle size on modulating turbulent intensity. Int. J. Multiphase Flow, 1989, 15: 279-285
32. Hetsroni G. Particle-turbulence interaction. Int. J. Multiphase Flow, 1989, 15: 735-746
33. Yuan Z, Michaelides E E. Turbulence modulation in particulate flows-a theoretical approach. Int. J. Multiphase Flow, 1992, 18: 779-785
34. Yarin L P, Hetsroni G. Turbulence intensity in dilute two-phase flows-3. Int. J. Multiphase Flow, 1994, 20: 27-44
35. Elghobashi S E, Truesdell G C. On the two-way interaction between homogeneous turbulence and dispersed solid particles. Ⅰ: Turbulence modification. Phys. Fluids, 1993, 5: 1790-1796
36. Hardalupas Y, Taylor A M K P, Whitelaw J H. Velocity and particle-flux characteristics of turbulent particle-laden jets. Proc. R. Soc. London A, 1989, 426: 31-78
37. Eaton J K, Fessler J R. Preferential concentration of particles by turbulence. Int. J. Multiphase Flow, 1994, 20: 169-209
38. Boivin M, Simonin O, Squires K D. Direct numerical simulation of turbulence modulation by particles in isotropic turbulence. J. Fluid Mech., 1998, 375: 235-263
39. Elghobashi S E. On predicting particle-laden turbulent flows. Appl. Sci. Res, 1994, 52: 309-329
40. Hosokawa S, Tomiyama A, Morimura M, Fujiwara S, Sakaguchi T. Influences of relative velocity on turbulent intensity in gas-solid two-phase flow in a vertical pipe. In: Third International Conference on Multiphase Flow, ICMF'98, 1998, Lyon, France.
41. Varaksin A Yu, Kurosaki Y, Satoh I, Polezhaev Yu V, Polyakov A F. Experimental study of the direct influence of the small particles on the cartier air turbulence intensity for pipe flow. In: Third International Conference on Multiphase Flow, ICMF'98, 1998, Lyon, France.
42. Savolainen K, Karvinen R. The effect of particles on gas turbulence in a vertical upward pipe flow. In: Third International Conference on Multiphase Flow, ICMF'98, 1998, Lyon, France.
43. Kenning V M, Crowe C T. On the effect of particles on carrier phase turbulence in gas-particle flows. Int. J. Multiphase Flow, 1997, 23(2): 403-408
44. Crowe C T. On models for turbulence modulation in fluid-particle flows. Int. J. Multiphase Flow, 2000, 26: 719-727
45. Ling W, Liu J, Chung J N, Crowe C T. Parallel Algorithms for Particles-Turbulence Two-Way Interaction Direct Numerical Simulation. Journal of Parallel and Distributed Computing, 2002, 62(1): 38-60
46. Lain S, Sommerfeld M, Kussin J. Experimental studies and modelling of four-way coupling in particle-laden horizontal channel flow. Int. J. Heat Fluid Flow, 2002, 23: 647-656
47. Lain S, Sommerfeld M. Turbulence modulation in dispersed two-phase flow laden with solids from a Lagrangian perspective. Int. J. Heat and Fluid Flow, 2003, 24: 616-625
48.陶文铨.数值传热学.西安:西安交通大学出版社,1988
49.岑可法,樊建人.工程气固多相流动的理论及计算.杭州:浙江大学出版社,1990
50. Bradshaw P. Understanding and prediction of turbulent flow-1996. Int. J. Heat and Fluid Flow, 1997, 18: 45-54
51. Rodi W. Influence of buoyancy and rotation on equations for the turbulent length scale. In: 2nd Int. Symp. on Turbulent shear flows, Imperial College, London. 1979, 10: 37-42
52. Launder B E, Priddin C H, Sharma B I. The calculation of turbulent boundary layers on spinning and curved surfaces. J. Fluids Engineering, 1979, 99: 363-374
53. Leschziner M A, Rodi W. Computation of strongly swirling axisymmetric free jets. AIAA Journal, 1984, 22(12): 1742-1749
54. Speziale C G. On nonlinear k-l and k-ε models of turbulence. J. Fluid Mech., 1987, 178: 450-475
55. Wilcox. Multiscale model for turbulent flows. AIAA Journal, 1988, 26: 1311-1320
56. Yakhot V, Orszag S A. Renormalization group analysis of turbulence. J. Sci. Compt., 1988, 1: 3-51
57. Leseur M, Metais O. New trends in large-eddy simulation of turbulence. Annu. Rev. Fluid Mech., 1996, 28: 45-82
58. Smagorinsky J. General circulation experiments with the primitive equation. Mon. Weather Rev., 1963, 91(3): 99-164
59. Deardoff J W. A numerical study of three-dimensional turbulence channel flow at large Reynolds number. J. Fluid Mech., 1970, 41: 453-380
60. Schumann U. Sub-grid scale model for finite difference simulation of turbulent flows in plane channel and annuli. J. Comput. Phys., 1975, 18: 376-404
61. Schumann U. Large-eddy simulation of turbulent diffusion with chemical reactions in the convective boundary layer. Atmospheric Environment, 1989, 23(8): 1713-1727
62. Zhou Y, Murshed Hossain George Vahala. A critical look at the use of filters in large eddy simulation. Physics Letters A, 1989, 139(7): 330-332
63. Orszag S, Steven A, Staroselsky I. CFD: progress and problem. Computer physics Communications, 2000, 127: 165-171
64.苏铭德.大涡模拟的代数模型及其应用.中国科学A辑,1989,7:715—723
65. Germano M, Piomelli U, Moin P, Cabot W H. A dynamic subgrid-scale eddy viscosity model. Phys. Fluids A, 1991, 3: 1760
66. Moin P, Squires K, Cabot W, Lee S. A dynamic subgrid-scale model for compressible turbulence and scalar transport. Phys. Fluids A, 1991, 3(11): 2746-2757
67. Lilly D K. A proposed modification of the Germano subgrid-scale closure method. Phys. Fluids A, 1991, 4: 633-635
68. Germano M. Turbulence: the filtering approach. J. Fluid Mech., 1992, 238: 325-336
69. Breuer M. A challenging test case for large eddy simulation: high Reynolds number circular cylinder flow. Int. J. Heat and Fluid Flow, 2000, 21(5): 648-654
70. Akira Murata, Sadanari Mochizuki. Large eddy simulation with a dynamic subgrid-scale model of turbulent heat transfer in an orthogonally rotating rectangular duct with transverse rib turbulators. Int. J. Heat and Mass Transfer, 2000, 43(7): 1243-1259
71. Horng Wen Wu, Shiang Wuu Perng. LES analysis of turbulent flow and heat transfer in motored engines with various SGS models. Int. J. Heat and Mass Transfer, 2002, 45(11): 2315-2328
72. Chollet J P, Lesieur M. Parameterization of small scales of three-dimensional isotropic turbulence utilizing spectral closure. J. Atmos. Sci., 1981, 38: 2747-2757
73. MeTais O, Lesieur M. Statistical predictability of decaying turbulence. J. Atmos. Sci., 1986, 43: 857-870
74. Liu S, Meneveau C, Katz J. On the properties of similarity subgrid-seale models as deduced from measurements in turbulent jet. J. Fluid Mech., 1994, 275: 83-119
75. Lesieur M, Metais O. New trends in large-eddy simulation of turbulence. Annu. Rev. Fluid Mech., 1996, 28: 45-82
76. Meneveau C, Katz J. Scale-invariance and turbulence models for large-eddy simulation. Annu. Rev. Fluid Mech., 2000, 32: 1-32.
77. Thomas T G, Wiliams J J R. Simulation of Skewed turbulent flow past a surface mounted cube. Journal of W'md Engineering and Industrial Aerodynamics, 1999, 81: 347-360
78. Conway S, Caraeni D, Fuchs L. Large eddy simulation of the flow through the blades of a swirl generator. Int. J. Heat and Mass Transfer, 2000, 21: 664-673
79. Boris D, Bergeles G. 2D LES of vortex shedding from a square cylinder. Journal of Wind Engineering and Industrial Aerodynamics, 1999, 80: 31-46
80. Breuer M. A challenging test ease for large eddy simulation: high Reynolds number circular cylinder flow. Int J. Heat and Fluid Flow, 2000, 21: 648-654
81. Lubcke H, Schmidt S, Rung T, Thiele F. Comparison of LES and RANS in bluff-body flows. Journal of Wind Engineering and Industrial Aerodynamics, 2001, 89: 1471-1485
82.樊洪明,何钟怡,李先庭.洁净室流场大涡模拟.空气动力学学报,2001,19(3):302-309
83.王兵,张会强,王希麟,郭印诚,林文漪.不同亚格子模式后台阶湍流流动大涡模拟中的应用.工程热物理学报,2003,24(1):157-160
84. Fan J R, Luo K, Zhang X Y, Cen K F. Large Eddy Simulation of the Anti-Erosion Characteristics of the Ribbed-Bend in Gas-Solid Flows. ASME Journal of Engineering for Gas Turbines and Power, 2004, 126(3): 672-679.
85. Luo K, Fan J R, Jin H H, Cen K F. LES of the turbulent coherent structures and particle dispersion in the gas-solid wake flows. Powder Technology, 2004, 147: 49-58.
86. Jin H H, Luo K, Fan J R, Cen K F. Large eddy simulation of a particle-laden turbulent plane jet. Journal of Zhejiang University, 2003, 4(2): 175-180
87. Luo K, Jin H H, Fan J R, Cen K F. Two-way coupled interaction between coherent structures and particles in plane turbulent jet. Journal of Xi'An Jiaotong University, 2003, 37(3), 302-305
88. Moin P. Progress in large eddy simulation of turbulent flows. AIAA Paper, 1997-0749
89.居江宁,吴文权.圆柱绕流远场涡对的数值模拟.上海理工大学学报.2000, 22(3):194
90.郭少为,吴文权.离散涡法模拟建筑物绕流流场.华东工业大学学报.1997,19(1):25—32
91. Leonard A. Vortex method for flow simulation. J. Comput. Phys., 1980, 37: 289-335
92. Mirta Perlman. On the accuracy of vortex methods J. Comput. Phys., 1985, 59(2): 200-223
93. Ahmed F Ghoniem, Yves Cagnon. Vortex simulation of laminar recirculating flow. J. Comput. Phys.,1987, 68(2): 346-377
94. Masaru Kiya, Hajime Ishii. Vortex dynamics simulation of interacting vortex rings and filaments. Fluid Dynamics Research, 1988, 3: 197-202
95. Taehyeung Kima, Michael R Flynnb. Numerical simulation of air flow around multiple objects using the discrete vortex method. Journal of Wind Engineering and Industrial Aerodynamics, 1995, 56: 213-234
96. Ploumhans P, Winckelmans G. S. Vortex Methods for High-Resolution Simulations of Viscous Flow Past Bluff Bodies of General Geometry. J. Comput. Phys., 2000, 165: 354-406
97. Marshall J S, Grant J R. A Lagrangian vortex method for viscous axisymmetric fluid flows, with and without swirl. J. Comput. Phys. 1997, 138: 302
98. Akbari M H, Price S J. Simulation of dynamic stall for a NACA 0012 airfoil using a vortex method. Journal of Fluids and Structures, 2003, 17(6): 855-874
99.吴文权.旋涡的场特征与物质性—离散涡方法基础.工程热物理学报,1996,17(3):301-304
100.叶春明,吴文权.数值模拟圆柱流旋涡运动及尾流不稳定性分析.工程热物理学报,1997,18(2):169-172
101.吴文权,居江宁.可压缩流动离散涡方法工程热物理学报,2001,22(2):163-166
102.王东耀,童秉纲,马晖扬.确定性涡方法的精确度研究,空气动力学学报 1994,12(3):262-268
103.刘晶晶,Kit Lam,徐建中.粘性涡方法在多圆柱绕流数值模拟中的应用.工程热物理学报,1998,19(2):164-169
104. Frish U, Hasslacher B, Pomeau Y. Lattice-gas automata for Navier-Stokes equation. Phys. Rev. Lett., 1986, 56: 1505-1508
105. Wolfram S. Cellular automaton fluids. 1: Basic theory. J. Stat. Phys. 1986, 45: 471-526
106. d'Humi'eres D, Lallemand P, Frisch U. Lattice gas model for 3D hydrodynamics. Europhys. Lett., 1986, 2: 291-297
107. McNamara G., Zanetti G.. Use of the Boltzmann equation to simulate Lattice-Gas automata. Phys. Rev. Lett., 1988, 61: 2332
108. Higuera F J, Jim'enez J. Boltzmann approach to lattice gas simulations. Europhys. Lett. , 1989, 9: 663-68
109. Higuera F J, Succi S. Simulating the flow around a circular cylinder with a lattice Boltzmann equation. Europhys. Lett. , 1989, 8: 517-21
110. Higuera F J, Succi S, Benzi R. Lattice gas dynamics with enhanced collisions. Europhys. Lett. , 1989, 9: 345-49
111. Qian Y H, d'Humiers D, Lallenmand P. Lattice BGK models for Navier-Stokes equation. Earophys. Lett. , 1992, 17: 479
112. Chen S, Chen H, Martimez D. Lattice Blotzmann model for simulation of magnetohydrodynamic. Phys. Rev. Lett. , 1991, 67: 3776
113. Jin S, Xin Z P. The relaxation schemes for systems of conservation laws in arbitrary space dimensions. Comm. Pure Appl. Math. , 1995, 48: 235-76.
114. Nadiga B T, Pullin D I. A method for near-equilibrium discrete-velocity gas flows. J. Comp. Phys. , 1994, 112: 162-72
115. Chen S, Wang Z, Shan X W, Doolen G D. Lattice Boltzmarm computational fluid dynamics in three dimensions. J. Stat. Phys. , 1992, 68: 379-400
116. Qian Y H, d'Humi'eres D, Lall(?)and P. Lattice BGK models for Navier-Stokes equation. Europhys. Lett. , 1992, 17: 479-84
117. Amati G, Succi S, Benzi R. Turbulent method by means of the discrete ordinate method for the Boltzmann equation. J channel flow simulation using a coarsegrained extension of the lattice Boltzmann method. Fluid Dyn. Res. 1997, 19: 289-302
118. Cao N, Chen S, Jin S, Martinez D. Physical symmetry and lattice symmetry in lattice Boltzmann method. Phys. Rev. E. , 1997, 55: R21-24
119. Chen H, Chen S, Mathaeus W H. Recovery of the Navier-Stokes equations using a lattice-gas Boltzmann method. Phys. Rev. A. , 1992, 45: R5339-42
120. Chen S, Chen H D, Martinez D, Matthaeus W. Lattice Boltzmann model for simulation of magnetohydrodynamics. Phys Rev. Lett. , 1991, 67: 3776-79
121. Chen S, Dawson S P, Doolen G D, Janecky D R, Lawniczak A. Lattice methods and their applications to reacting systems. Comp. Chem. Eng. , 1995, 19: 617-46
122. Chen S, Lookman T. Growth kinetics in multicomponent fluids. J. Stat. Phys. , 1995, 81: 223-235
123. Chen S, Martinez D, Mei R. On boundary conditions in lattice Boltzmann methods. Phys. Fluids, 1992, 8: 2527-36
124. Qian Y H. Lattice gas and lattice kinetic theory applied to the Navier-Stokes equations. PhD thesis, Universit'e Pierre et Marie Curie, 1990, Paris
125. Qian Y H. Simulating thermohydrodynamics with lattice BGK models. J. Sci. Comp. , 1993, 8: 231-41
126. Qian Y H, Orszag S A. Lattice BGK models for the Navier-Stokes equation: nonlinear deviation in compressible regimes. Europhys. Lett. , 1993, 21: 255-59
127. Qian Y H, Succi S, Massaioli F, Orszag S A. A benchmark for lattice BGK model: flowover a backward-facing step. Fields Inst. Comm. , 1996, 6: 207-15
128. Chen S Y, Doolen G D. Lattice Boltzmann method for fluid flows. Annu. Rev. Fluid Mech. , 1998, 30: 329-64
129. Qian Y H, Succi S, Orszag S A. Recent advances in lattice Boltzmann computing. Annu. Rev. Comp. Phys. , 1995, 3: 195-242
130. Hou S. Lattice Boltzmann method for incompressible viscous flow. PhD thesis, Kansas State Univ. , Manhattan, 1995, Kansas
131. Hou S, Zou Q, Chen S, Doolen G, Cogley A C. Simulation of cavity flow by the lattice Boltzmann method. J. Comp. Phys. , 1995, 118: 329-347
132. He X, Doolen G D. Lattice Boltzrnann method on curvilinear coordinates system: vortex shedding behind a circular cylinder. Phys. Rev. E. , 1997
133. Martinez D O, Matthaeus W H, Chen S, Montgomery D C. Comparison of spectralmethod and lattice Boltzmann simulations of two-dimensional hydrodynamics. Phys. Fluids, 1994, 6: 1285-98
134. Somers J A. Direct simulation of fluid flow with cellular automata and the lattice-Boltzmann equation. Applied Sci. Res. , 1993, 51: 127-33
135. Hou S, Sterling J, Chen S, Doolen G D. A lattice Boltzmarm subgrid model for high Reynolds number flows. Fields Inst. Comm. , 1996, 6: 151-66
136. Bekri S, Adler P M. Dispersion in multiphase flow through porous media. Int. J. Multiphase flow, 2002, 28: 665-697
137.阮剑,吴波,郑楚光.复杂流动的LBGK模拟.工程热物理学报,1992,20(6):764
138.徐辉,阮剑,郑楚光.二维卡门涡街的格子Boltzmann仿真.工程热物理学报,1997,18(3):381
139.吴波,郑楚光.十三点格子Boltzmann模型仿真.工程热物理学报,2000,21(4):520-524
140.吴一光,吴波,郑楚光.三维十五点格子Boltzmann模型仿真.工程热物理学报,2001,22 (4):503-506
141. Crowe C T, Sharma M P, Stock D E. The particle-Source-in-Cell(PSI-CELL) for gas-droplet flows. J. Fluid Engr. , 1977, 99: 325-331
142. Yuu S, Yasukouchi M, Hirosawa Y, Jotaki T. Particle turbulent diffusion in a duct laden jet. AIChE J. , 1978, 24: 509-519
143. Gosman A D, Ioannides E. Aspects of computer simulation of liquid-fulled combustors. AIAA Paper, 1981: 81-0323
144. Berlemont A, Desjonqueres P, Gouesbet G. . Particle Lagrangian simulation in turbulent flows. Int. J. Multiphase Flow, 1990, 14: 679-699
145. Sommerfeld M. Particle dispersion in turbulent flow: the effect of particle size distribution. Part. Syst. Charact. , 1990, 7: 209-220
146. Shuen J S, Chen L D, Faeth G M. Evaluation of a stochastic model of particle dispersion in a turbulent round jet. AIChE J. , 1983, 29: 167-170
147. Cen K F, Fan J R. A numerical model for the turbulent fluctuation and diffusion of gas-particle flows and its application in the freeboard of a fluidized bed. Particle Science and Technology, 1989, 6 (1)
148. Spalding D B. A general purpose computer program for multidimensional oneand two-phase flows. J. Math Comput. Simul. , 1981, 23: 267-276
149.周力行,黄晓晴.三维湍流气粒两相流的k—ε—kp模型.工程热物理学报,1991,12(4):428-433
150.周力行.湍流两相流动及燃烧的统一关联矩封闭模型.工程热物理学报,1991,12(2):203-209
151.周力行,林文漪.k—ε—kp两相湍流模型用于模拟有旋突扩气粒两相流动.工程热物理学报,1995,16(4):481-485
152.周力行,陈涛.统一二阶矩模型用于模拟旋流湍流两相流动.力学学报,1998,30(4):385-390
153.周力行.湍流两相流动和燃烧的统一关联矩封闭模型.工程热物理学报,1991,12(2):203-209
154. Reeks M W. PDF modeling of gas-particle flows. In: 2nd Int. Symp. On Multiphase Fluid, Non-Newtonian Fluid and Physicochemical Fluid Flows'97, 1997, Beijing
155. Zaichik L I, Alipchenkov V M. Simulation of transport of colliding particles suspended in turbulent shear flows. In: 2nd Int. Symp. On Turbulence, Heat and Mass Transfer, 1997, Delft University
156. Simonin O. Continuum modeling of dispersed turbulent two-phase flows. VKI Lectures "Combustion in Two Phase Flow" , 1996
157.李勇,周力行.k—ε—PDI两相湍流模型和台阶后方气粒两相流动的模拟.工程热物理学报,1996,17(2):234-238
158.周力行,李勇.旋流两相流动的DSM—PDF两相湍流模型.工程热物理学报,1999,20(2):252-257
159. Loth E. Numerical approaches for motion of dispersed particles, droplets and bubbles. Progress in Energy and Combustion Science, 2000, 26: 161-223
160. Martin J, Meiburg E. The accumulation of dispersion of heavy particles in forced two-dimensional mixing layer, Part Ⅰ: The fundamental and harmonic cases. Phys. Fluids A. , 1994, 7: 1116-1132
161. Walther J H, Koumoutsakos P. Three-Dimensional Vortex Methods for Particle-Laden Flows with Two-Way Coupling. J. Comput. Phys. , 2001, 167, 39-71
162. Tomomi Uchiyama, Masaaki Naruse. A numerical method for gas-solid two phase free turbulent flow using a vortex method. Powder Technology, 2001, 119: 206-214
163. Tomomi Uchiyama, Masaaki Naruse. Numerical simulation of gas-particle two-phase mixing layer by vortex method. Powder Technology, 2002, 125: 111-121
164. Deutsch E, Simonin O. Large eddy simulation applied to the modeling of particulate transport in turbulent two-phase flows. In: Eighth Symp. on Turbul. Shear Flows, Tech. Univ. Munich, 1991, 10.1.1-10.1.6.
165. Aggarwal S K, Xiao Y. Effects of external forcing on droplet dispersion in a developing shear layer. J. Prop. Power, 1994, 10: 395-401
166. Wang Q, Squires K D, Simonin O. Large eddy simulation of turbulent gas solid flows in a vertical channel and evaluation of second-order models. Int. J. Heat and Fluid Transfer, 1998, 19: 505-511
167. Wang Q, Squires K D, Chen M, McLaughlin J B. On the role of the lift force in turbulence simulation of particle deposition. Int. J. Multiphase Flow, 1997, 23 (4) : 749-763
168. Glaze D J, Frandel S H. Effect of dispersion characteristics on particle temperature in an idealized nonpremixed reacting jet. Int. J. Multiphase Flow, 2000, 26: 609-633
169. Nadaoka K, Nihei Y, Yagi H. Grid-averaged Lagrangian LES model for multiphase turbulent flow. Int. J. Multiphase Flow, 1999, 25: 1619-1643
170. Apte SV, Mahesh K, Moin P, Oefelein J C. Large-eddy simulation of swirling particle-laden flows in a coaxial-jet combustor. Int. J. Multiphase Flow, 2003, 29 (8) : 1311-1331
171. Yuu S, Ueno T, Umekage T. Numerical simulation of the high Reynolds number slit nozzle gas-particle jet using subgrid-seale coupling large eddy simulation. Chemical Engineering Science, 2001, 56: 4293-4307
172. Sankaranarayanan K, Shan X, Kevrekidis I G, Sundaresan S. Bubble flow simulation with the lattice Boltzmann method. Chemical Engineering Science, 1999, 54 (21) : 4817-4823
173. Aidun CK, Lu Y-N. 1995. Lattice Boltzmann simulation of solid particles suspended in fluid. J. Stat. Phys. 81: 49-61
174. Jasberg A, Koponen A, Kataja M, Timonen J. Hydrodynamical forces acting on particles in a two-dimensional flow near a solid wall. Computer Physics Communications, 2000, 129 (1) : 196-206.
175. Raiskinmaki P, Shakib Manesh A, Koponen A. Simulation of non-spherical particles suspended in a shear flow. Computer Physics Communication, 2000, 129 (1) : 185-195
176. Ladd A J C. Short-time motion of colloidal particles: numerical simulation via a fluctuating lattice-Boltzmann equation Phys. Rev. Lett. , 1993, 70: 1339-42
177. Ladd A J C. Numerical simulations of particulate suspensions via a discretized Boltzmann equation. Part. 1. theoretical foundation. J. Fluid Mech. , 1994, 271: 285-309
178. Ladd A J C. Numerical simulations of particulate suspensions via a discretized Boltzmann equation. Part 2: Numerical results. J. Fluid Mech. , 1994, 271: 311-39
179. Ladd A J C. Sedimentation of homogeneous suspensions of non-Brownian spheres. Phys. Fluids, 1997, 9: 491-99
180. Behrend O. Solid-fluid boundaries in particle suspension simulations via the lattice Boltzmarm method. Phys. Rev. E, 1995, 52: 1164-75
181. Filippova O, Hand D. Lattice-Boltzmarm simulation of gas-particle flow in filters. Computers & Fluids, 1997, 26 (7) : 697-712
182. Bekri S, Adler P M. Dispersion in multiphase flow through porous media. Int. J. of Multiphase flow, 2002, 28: 665-697
183. Crowe C T, Troutt T R, Chung J N. Numerical models for two-phase turbulent flows. Annual Rev. Fluid Mech. , 1996, 28: 11-43
184. Mashayek F, Pandya R V R. Analytical description of particle/droplet-laden turbulent flows. Progress in Energy and Combustion Science, 2003, 29: 329-378
185.由长福,祁海鹰,徐旭常.Basset力研究进展与应用分析.应用力学学报,2002,19(2):31-33
186.由长福,祁海鹰,徐旭常.煤粉颗粒所受Magnus力的数值模拟.工程热物理学报,2001,22(5):625-628
187.由长福,祁海鹰,徐旭常.稠密气固两相流中单颗粒所受气动力的数值模拟.工程热物理学报,2002,23(1):103-106
188.由长福,祁海鹰,徐旭常.气固两相流动中非球形颗粒所受曳力的数值研究.化工学报,2003,54(2):188-191
189.肖海涛,祁海鹰,由长福,徐旭常.一个气固两相流动阻力的新模型.化工学报,2003,54(3):311-315
190.肖海涛,祁海鹰,由长福,徐旭常.循环流化床气固曳力模型.计算物理,2003,20(1):25-30
191.赵海波,柳朝晖,郑楚光.颗粒扩散的三个效应分析及其数值模拟.热科学与技术,2003,2(4):347-351
192.张会强,王赫阳,王希麟,郭印诚,林文漪.两相混合层中颗粒运动的数值模拟.工程热物理学报,2000,21(1):115-119
193.王赫阳,张会强,王希麟,郭印诚,林文漪.混台层流动的格子涡方法数值模拟.工程热物理学报,2002,23(5):576-578
194.林建忠,林江.气固两相固射流场涡结构影响固粒扩散的研究.应用数学和力学,1999,20(5):470-476
195.范全林,张会强,郭印诚,王希麟,林文漪.气粒两相平面湍射流拟序结构的大涡模拟.燃烧科学与技术,2001,7(1):21-25
196.范全林,张会强,郭印诚,王希麟,林文漪.重力对水平两相湍射流中颗粒行为的影响.燃烧科学与技术,2002,8(3):211-215
197.金晗辉,金涛,罗坤,樊建人,岑可法.大涡模拟二维气固两相平面射流.动力工程,2003,23(5):2676-2679
198. Jin H H, Luo K, Fan J R, Cen K F. Large eddy simulation of a particle-laden turbulent plane jet. Journal of Zhejiang University, 2003, 4 (2) : 175-180.
199.王兵,张会强,虞建丰,王希麟,郭印诚,林文漪.气粒两相二维后台阶突扩流动的大涡模拟.燃烧科学与技术,2003,9(5):447-452
200.王兵,张会强,王希麟,郭印诚,林文漪.湍流分离流动中的颗粒弥散机制清华大学学报:自然科学版,2003,43(11):1507-1510
201.柳朝晖,周向阳,郑楚光.空间发展湍流气粒两相平面混合层的大涡模拟与统计.工程热物理学报,2002,23(4):495-498
202.吴锤结,周菊光.悬浮颗粒运动的格子Boltzmann数值模拟.力学学报,2004,36(2):151-162
203.刘向军,徐旭常.循环流化床内颗粒团运动的数值模拟.工程热物理学报,2002,23(5):649-652
204.刘向军,徐旭常.循环流化床内稠密气固两相流动的数值模拟.中国电机工程学报,2003,23(5):161-165
205.刘向军,徐旭常.稠密气固两相流中颗粒密集效应的研究与应用.燃烧科学与技术,2004,10(2):120-124
206.刘向军,徐旭常.稠密气固两相流动过程模拟的改进模型与应用.动力工程,2004,24(2):234-239
207.陆慧林,刘文铁,孙永立,李文健,杨励丹.稠密气固两相湍流流动的实验和数值模拟.力学学报,2000,32(4):385-391
208.陆慧林,刘文铁,赵广播,Dimitri Gidaspow.管内稠密气固两相流数值模拟计算:颗粒动力学方法.化工学报,2000,51(1):31-38
209.陆慧林,何玉荣,刘阳,别如山,刘文铁.多组分颗粒稠密气固两相流动的数值模拟.工程热物理学报,2002,23(3):369-371
210.刘阳,陆慧林,刘文铁,赵云华.循环流化床多组分颗粒气固两相流动模型和数值模拟.化工学报,2003,54(8):1065-1071
211.刘阳,陆慧林,刘文铁,赵云华.气固流化床的离散颗粒运动—碰撞解耦模型与模拟.燃烧科学与技术,2003,9(6):551-555
212.郭印诚,陈志兵,陈新国,徐春明,高金森.颗粒动力学与湍动能耦合的稠密两相流动数学模型.计算机与应用化学,2003,20(1):186-190
2. Townsend. Measurement in the turbulent wake of a cylinder. Proc. R. Soc. London Ser. A, 1947, 190: 551-561
3. Corrsin S, Kistler A L. NACA Rep., 1955
4. Townsend A A. The structure of turbulent shear flow. Cambridge Univ. Press, 1956
5. Grant H L. The large eddied of turbulent motion. J. Fluid Mech., 1958, 4: 149-190
6. Kline S J, Rundstadler P W. Visual studies of the wall layers in the turbulent boundary layer. J. Appl. Mech., 1959, 26: 166
7. Kline S J, Reynolds W C, Schraub F A, Rundstadler P W. The structure of turbulent boundary layer. J. Fluid Mech., 1967, 30: 741-773
8. Crow S C, Champagne. Orderly structure in jet turbulence. J. Fluid Mech., 1971, 48: 567
9. Brown G L, Roshko A. On density effects and large structure in turbulent mixing layers. J. Fluid Mech., 1974, 64: 775-816
10.林建忠.湍流的拟序结构.北京:机械工业出版社,1995
11. Crowe C T, Gore R A, Troutt T R. Particle dispersion by coherent structures in free shear flows. Particulate Science and Technology, 1985, 3: 149-158
12. Crowe C T, Chung T N, Troutt T R. Particle mixing in free shear flows. Progress in Energy and Combustion Science, 1988, 14(3): 171-194
13. Wen F, Kamalu N, Chung J N, Crowe C T, Troutt T R. Particle dispersion by vortex structures in plane mixing layers. J Fluids Engng., 1992, 114: 657-666
14. Longmire E K, Eaton J K. Structure of a particle-laden round jet. J. Fluid Mech., 1992, 236: 217-257
15. Longmire E K. Active open-loop control of particle dispersion of round jets. AIAA Journal, 1994, 32(3): 555-563
16. Wicker R B, Eaton J K. Structure of a swirling, recirculating coaxial free jet and its effect on particle motion. Int. J. Multiphase Flow, 2001, 27: 949-970
17. Yang Y, Crowe C T, Chung J N, Troutt T R. Experiments on particle dispersion in a plane wake. Int. J. Multiphase Flow, 2000, 26: 1583-1607
18. Chein R, Chung J N. Simulation of particle dispersion in a two-dimension mixing layer. AIChE J., 1988, 34: 946-954
19. (?) T R. Simulation of particle dispersion in an axisymmetric jet. J. Fluid Mech., 1988, 186: 199-222
20. Tang L, Wen F, Yang Y, Crowe C T, Chung J N, Troutt T R. Self-organizing particle dispersion mechanism in free shear flows. Phys. Fluids A, 1992, 4: 2244-2251
21. Ling W, Chung J N, Troutt T R, Crowe C T. Direct numerical simulation of a three-dimensional temporal mixing layer with particle dispersion. J. Fluid Mech., 1998, 358: 61-85
22. Fan J R, Zheng Y Q, Yao J, Cen K F. Direct simulation of particle dispersion in a three-dimensional temporal mixing layer. Proc. R. Soc. Lond A, 2001, 457: 2151-2166
23. Tsuji Y, Morikawa Y. LDV measurements in air-solid two-phase flow in a vertical pipe. J. Fluid Mech., 1982, 139: 417—434
24. Lee S L, Durst F. On the motion of particles in turbulent duct flows. Int. J. Multiphase Flow, 1982, 8: 125-146
25. Parthasarathy R N, Faeth G M. Turbulence modulation in homogeneous dilute particle-laden flows. J. Fluid Mech., 1990, 220: 485-537
26. Modarress D, Tan H, Elghobashi S E. Two-component LDA measurement in a two-phase turbulent jet. AIAA Journal, 1984, 22: 624-630
27. Modarress D, Wuerer J, Elghobashi S E. An experimental study of a turbulent round two-phase jet. Chemical Engineering Communications, 1984, 28: 341-354
28. Schreck S, Kleis S J. Modification of grid-generated turbulence by solid particles. J. Fluid Mech., 1993, 249: 665-688
29. Levy Y, Lockwood F C. Velocity measurements in a particle laden turbulent free jet. Combustion and Flame, 1981, 40: 333-339
30. Tsuji Y, Morikawa Y, Shiomi H. LDV measurements of an air-solid two-phase flow in a vertical pipe. J. Fluid Mech., 1984, 139: 417-434
31. Gore R A, Crowe C T. Effect of particle size on modulating turbulent intensity. Int. J. Multiphase Flow, 1989, 15: 279-285
32. Hetsroni G. Particle-turbulence interaction. Int. J. Multiphase Flow, 1989, 15: 735-746
33. Yuan Z, Michaelides E E. Turbulence modulation in particulate flows-a theoretical approach. Int. J. Multiphase Flow, 1992, 18: 779-785
34. Yarin L P, Hetsroni G. Turbulence intensity in dilute two-phase flows-3. Int. J. Multiphase Flow, 1994, 20: 27-44
35. Elghobashi S E, Truesdell G C. On the two-way interaction between homogeneous turbulence and dispersed solid particles. Ⅰ: Turbulence modification. Phys. Fluids, 1993, 5: 1790-1796
36. Hardalupas Y, Taylor A M K P, Whitelaw J H. Velocity and particle-flux characteristics of turbulent particle-laden jets. Proc. R. Soc. London A, 1989, 426: 31-78
37. Eaton J K, Fessler J R. Preferential concentration of particles by turbulence. Int. J. Multiphase Flow, 1994, 20: 169-209
38. Boivin M, Simonin O, Squires K D. Direct numerical simulation of turbulence modulation by particles in isotropic turbulence. J. Fluid Mech., 1998, 375: 235-263
39. Elghobashi S E. On predicting particle-laden turbulent flows. Appl. Sci. Res, 1994, 52: 309-329
40. Hosokawa S, Tomiyama A, Morimura M, Fujiwara S, Sakaguchi T. Influences of relative velocity on turbulent intensity in gas-solid two-phase flow in a vertical pipe. In: Third International Conference on Multiphase Flow, ICMF'98, 1998, Lyon, France.
41. Varaksin A Yu, Kurosaki Y, Satoh I, Polezhaev Yu V, Polyakov A F. Experimental study of the direct influence of the small particles on the cartier air turbulence intensity for pipe flow. In: Third International Conference on Multiphase Flow, ICMF'98, 1998, Lyon, France.
42. Savolainen K, Karvinen R. The effect of particles on gas turbulence in a vertical upward pipe flow. In: Third International Conference on Multiphase Flow, ICMF'98, 1998, Lyon, France.
43. Kenning V M, Crowe C T. On the effect of particles on carrier phase turbulence in gas-particle flows. Int. J. Multiphase Flow, 1997, 23(2): 403-408
44. Crowe C T. On models for turbulence modulation in fluid-particle flows. Int. J. Multiphase Flow, 2000, 26: 719-727
45. Ling W, Liu J, Chung J N, Crowe C T. Parallel Algorithms for Particles-Turbulence Two-Way Interaction Direct Numerical Simulation. Journal of Parallel and Distributed Computing, 2002, 62(1): 38-60
46. Lain S, Sommerfeld M, Kussin J. Experimental studies and modelling of four-way coupling in particle-laden horizontal channel flow. Int. J. Heat Fluid Flow, 2002, 23: 647-656
47. Lain S, Sommerfeld M. Turbulence modulation in dispersed two-phase flow laden with solids from a Lagrangian perspective. Int. J. Heat and Fluid Flow, 2003, 24: 616-625
48.陶文铨.数值传热学.西安:西安交通大学出版社,1988
49.岑可法,樊建人.工程气固多相流动的理论及计算.杭州:浙江大学出版社,1990
50. Bradshaw P. Understanding and prediction of turbulent flow-1996. Int. J. Heat and Fluid Flow, 1997, 18: 45-54
51. Rodi W. Influence of buoyancy and rotation on equations for the turbulent length scale. In: 2nd Int. Symp. on Turbulent shear flows, Imperial College, London. 1979, 10: 37-42
52. Launder B E, Priddin C H, Sharma B I. The calculation of turbulent boundary layers on spinning and curved surfaces. J. Fluids Engineering, 1979, 99: 363-374
53. Leschziner M A, Rodi W. Computation of strongly swirling axisymmetric free jets. AIAA Journal, 1984, 22(12): 1742-1749
54. Speziale C G. On nonlinear k-l and k-ε models of turbulence. J. Fluid Mech., 1987, 178: 450-475
55. Wilcox. Multiscale model for turbulent flows. AIAA Journal, 1988, 26: 1311-1320
56. Yakhot V, Orszag S A. Renormalization group analysis of turbulence. J. Sci. Compt., 1988, 1: 3-51
57. Leseur M, Metais O. New trends in large-eddy simulation of turbulence. Annu. Rev. Fluid Mech., 1996, 28: 45-82
58. Smagorinsky J. General circulation experiments with the primitive equation. Mon. Weather Rev., 1963, 91(3): 99-164
59. Deardoff J W. A numerical study of three-dimensional turbulence channel flow at large Reynolds number. J. Fluid Mech., 1970, 41: 453-380
60. Schumann U. Sub-grid scale model for finite difference simulation of turbulent flows in plane channel and annuli. J. Comput. Phys., 1975, 18: 376-404
61. Schumann U. Large-eddy simulation of turbulent diffusion with chemical reactions in the convective boundary layer. Atmospheric Environment, 1989, 23(8): 1713-1727
62. Zhou Y, Murshed Hossain George Vahala. A critical look at the use of filters in large eddy simulation. Physics Letters A, 1989, 139(7): 330-332
63. Orszag S, Steven A, Staroselsky I. CFD: progress and problem. Computer physics Communications, 2000, 127: 165-171
64.苏铭德.大涡模拟的代数模型及其应用.中国科学A辑,1989,7:715—723
65. Germano M, Piomelli U, Moin P, Cabot W H. A dynamic subgrid-scale eddy viscosity model. Phys. Fluids A, 1991, 3: 1760
66. Moin P, Squires K, Cabot W, Lee S. A dynamic subgrid-scale model for compressible turbulence and scalar transport. Phys. Fluids A, 1991, 3(11): 2746-2757
67. Lilly D K. A proposed modification of the Germano subgrid-scale closure method. Phys. Fluids A, 1991, 4: 633-635
68. Germano M. Turbulence: the filtering approach. J. Fluid Mech., 1992, 238: 325-336
69. Breuer M. A challenging test case for large eddy simulation: high Reynolds number circular cylinder flow. Int. J. Heat and Fluid Flow, 2000, 21(5): 648-654
70. Akira Murata, Sadanari Mochizuki. Large eddy simulation with a dynamic subgrid-scale model of turbulent heat transfer in an orthogonally rotating rectangular duct with transverse rib turbulators. Int. J. Heat and Mass Transfer, 2000, 43(7): 1243-1259
71. Horng Wen Wu, Shiang Wuu Perng. LES analysis of turbulent flow and heat transfer in motored engines with various SGS models. Int. J. Heat and Mass Transfer, 2002, 45(11): 2315-2328
72. Chollet J P, Lesieur M. Parameterization of small scales of three-dimensional isotropic turbulence utilizing spectral closure. J. Atmos. Sci., 1981, 38: 2747-2757
73. MeTais O, Lesieur M. Statistical predictability of decaying turbulence. J. Atmos. Sci., 1986, 43: 857-870
74. Liu S, Meneveau C, Katz J. On the properties of similarity subgrid-seale models as deduced from measurements in turbulent jet. J. Fluid Mech., 1994, 275: 83-119
75. Lesieur M, Metais O. New trends in large-eddy simulation of turbulence. Annu. Rev. Fluid Mech., 1996, 28: 45-82
76. Meneveau C, Katz J. Scale-invariance and turbulence models for large-eddy simulation. Annu. Rev. Fluid Mech., 2000, 32: 1-32.
77. Thomas T G, Wiliams J J R. Simulation of Skewed turbulent flow past a surface mounted cube. Journal of W'md Engineering and Industrial Aerodynamics, 1999, 81: 347-360
78. Conway S, Caraeni D, Fuchs L. Large eddy simulation of the flow through the blades of a swirl generator. Int. J. Heat and Mass Transfer, 2000, 21: 664-673
79. Boris D, Bergeles G. 2D LES of vortex shedding from a square cylinder. Journal of Wind Engineering and Industrial Aerodynamics, 1999, 80: 31-46
80. Breuer M. A challenging test ease for large eddy simulation: high Reynolds number circular cylinder flow. Int J. Heat and Fluid Flow, 2000, 21: 648-654
81. Lubcke H, Schmidt S, Rung T, Thiele F. Comparison of LES and RANS in bluff-body flows. Journal of Wind Engineering and Industrial Aerodynamics, 2001, 89: 1471-1485
82.樊洪明,何钟怡,李先庭.洁净室流场大涡模拟.空气动力学学报,2001,19(3):302-309
83.王兵,张会强,王希麟,郭印诚,林文漪.不同亚格子模式后台阶湍流流动大涡模拟中的应用.工程热物理学报,2003,24(1):157-160
84. Fan J R, Luo K, Zhang X Y, Cen K F. Large Eddy Simulation of the Anti-Erosion Characteristics of the Ribbed-Bend in Gas-Solid Flows. ASME Journal of Engineering for Gas Turbines and Power, 2004, 126(3): 672-679.
85. Luo K, Fan J R, Jin H H, Cen K F. LES of the turbulent coherent structures and particle dispersion in the gas-solid wake flows. Powder Technology, 2004, 147: 49-58.
86. Jin H H, Luo K, Fan J R, Cen K F. Large eddy simulation of a particle-laden turbulent plane jet. Journal of Zhejiang University, 2003, 4(2): 175-180
87. Luo K, Jin H H, Fan J R, Cen K F. Two-way coupled interaction between coherent structures and particles in plane turbulent jet. Journal of Xi'An Jiaotong University, 2003, 37(3), 302-305
88. Moin P. Progress in large eddy simulation of turbulent flows. AIAA Paper, 1997-0749
89.居江宁,吴文权.圆柱绕流远场涡对的数值模拟.上海理工大学学报.2000, 22(3):194
90.郭少为,吴文权.离散涡法模拟建筑物绕流流场.华东工业大学学报.1997,19(1):25—32
91. Leonard A. Vortex method for flow simulation. J. Comput. Phys., 1980, 37: 289-335
92. Mirta Perlman. On the accuracy of vortex methods J. Comput. Phys., 1985, 59(2): 200-223
93. Ahmed F Ghoniem, Yves Cagnon. Vortex simulation of laminar recirculating flow. J. Comput. Phys.,1987, 68(2): 346-377
94. Masaru Kiya, Hajime Ishii. Vortex dynamics simulation of interacting vortex rings and filaments. Fluid Dynamics Research, 1988, 3: 197-202
95. Taehyeung Kima, Michael R Flynnb. Numerical simulation of air flow around multiple objects using the discrete vortex method. Journal of Wind Engineering and Industrial Aerodynamics, 1995, 56: 213-234
96. Ploumhans P, Winckelmans G. S. Vortex Methods for High-Resolution Simulations of Viscous Flow Past Bluff Bodies of General Geometry. J. Comput. Phys., 2000, 165: 354-406
97. Marshall J S, Grant J R. A Lagrangian vortex method for viscous axisymmetric fluid flows, with and without swirl. J. Comput. Phys. 1997, 138: 302
98. Akbari M H, Price S J. Simulation of dynamic stall for a NACA 0012 airfoil using a vortex method. Journal of Fluids and Structures, 2003, 17(6): 855-874
99.吴文权.旋涡的场特征与物质性—离散涡方法基础.工程热物理学报,1996,17(3):301-304
100.叶春明,吴文权.数值模拟圆柱流旋涡运动及尾流不稳定性分析.工程热物理学报,1997,18(2):169-172
101.吴文权,居江宁.可压缩流动离散涡方法工程热物理学报,2001,22(2):163-166
102.王东耀,童秉纲,马晖扬.确定性涡方法的精确度研究,空气动力学学报 1994,12(3):262-268
103.刘晶晶,Kit Lam,徐建中.粘性涡方法在多圆柱绕流数值模拟中的应用.工程热物理学报,1998,19(2):164-169
104. Frish U, Hasslacher B, Pomeau Y. Lattice-gas automata for Navier-Stokes equation. Phys. Rev. Lett., 1986, 56: 1505-1508
105. Wolfram S. Cellular automaton fluids. 1: Basic theory. J. Stat. Phys. 1986, 45: 471-526
106. d'Humi'eres D, Lallemand P, Frisch U. Lattice gas model for 3D hydrodynamics. Europhys. Lett., 1986, 2: 291-297
107. McNamara G., Zanetti G.. Use of the Boltzmann equation to simulate Lattice-Gas automata. Phys. Rev. Lett., 1988, 61: 2332
108. Higuera F J, Jim'enez J. Boltzmann approach to lattice gas simulations. Europhys. Lett. , 1989, 9: 663-68
109. Higuera F J, Succi S. Simulating the flow around a circular cylinder with a lattice Boltzmann equation. Europhys. Lett. , 1989, 8: 517-21
110. Higuera F J, Succi S, Benzi R. Lattice gas dynamics with enhanced collisions. Europhys. Lett. , 1989, 9: 345-49
111. Qian Y H, d'Humiers D, Lallenmand P. Lattice BGK models for Navier-Stokes equation. Earophys. Lett. , 1992, 17: 479
112. Chen S, Chen H, Martimez D. Lattice Blotzmann model for simulation of magnetohydrodynamic. Phys. Rev. Lett. , 1991, 67: 3776
113. Jin S, Xin Z P. The relaxation schemes for systems of conservation laws in arbitrary space dimensions. Comm. Pure Appl. Math. , 1995, 48: 235-76.
114. Nadiga B T, Pullin D I. A method for near-equilibrium discrete-velocity gas flows. J. Comp. Phys. , 1994, 112: 162-72
115. Chen S, Wang Z, Shan X W, Doolen G D. Lattice Boltzmarm computational fluid dynamics in three dimensions. J. Stat. Phys. , 1992, 68: 379-400
116. Qian Y H, d'Humi'eres D, Lall(?)and P. Lattice BGK models for Navier-Stokes equation. Europhys. Lett. , 1992, 17: 479-84
117. Amati G, Succi S, Benzi R. Turbulent method by means of the discrete ordinate method for the Boltzmann equation. J channel flow simulation using a coarsegrained extension of the lattice Boltzmann method. Fluid Dyn. Res. 1997, 19: 289-302
118. Cao N, Chen S, Jin S, Martinez D. Physical symmetry and lattice symmetry in lattice Boltzmann method. Phys. Rev. E. , 1997, 55: R21-24
119. Chen H, Chen S, Mathaeus W H. Recovery of the Navier-Stokes equations using a lattice-gas Boltzmann method. Phys. Rev. A. , 1992, 45: R5339-42
120. Chen S, Chen H D, Martinez D, Matthaeus W. Lattice Boltzmann model for simulation of magnetohydrodynamics. Phys Rev. Lett. , 1991, 67: 3776-79
121. Chen S, Dawson S P, Doolen G D, Janecky D R, Lawniczak A. Lattice methods and their applications to reacting systems. Comp. Chem. Eng. , 1995, 19: 617-46
122. Chen S, Lookman T. Growth kinetics in multicomponent fluids. J. Stat. Phys. , 1995, 81: 223-235
123. Chen S, Martinez D, Mei R. On boundary conditions in lattice Boltzmann methods. Phys. Fluids, 1992, 8: 2527-36
124. Qian Y H. Lattice gas and lattice kinetic theory applied to the Navier-Stokes equations. PhD thesis, Universit'e Pierre et Marie Curie, 1990, Paris
125. Qian Y H. Simulating thermohydrodynamics with lattice BGK models. J. Sci. Comp. , 1993, 8: 231-41
126. Qian Y H, Orszag S A. Lattice BGK models for the Navier-Stokes equation: nonlinear deviation in compressible regimes. Europhys. Lett. , 1993, 21: 255-59
127. Qian Y H, Succi S, Massaioli F, Orszag S A. A benchmark for lattice BGK model: flowover a backward-facing step. Fields Inst. Comm. , 1996, 6: 207-15
128. Chen S Y, Doolen G D. Lattice Boltzmann method for fluid flows. Annu. Rev. Fluid Mech. , 1998, 30: 329-64
129. Qian Y H, Succi S, Orszag S A. Recent advances in lattice Boltzmann computing. Annu. Rev. Comp. Phys. , 1995, 3: 195-242
130. Hou S. Lattice Boltzmann method for incompressible viscous flow. PhD thesis, Kansas State Univ. , Manhattan, 1995, Kansas
131. Hou S, Zou Q, Chen S, Doolen G, Cogley A C. Simulation of cavity flow by the lattice Boltzmann method. J. Comp. Phys. , 1995, 118: 329-347
132. He X, Doolen G D. Lattice Boltzrnann method on curvilinear coordinates system: vortex shedding behind a circular cylinder. Phys. Rev. E. , 1997
133. Martinez D O, Matthaeus W H, Chen S, Montgomery D C. Comparison of spectralmethod and lattice Boltzmann simulations of two-dimensional hydrodynamics. Phys. Fluids, 1994, 6: 1285-98
134. Somers J A. Direct simulation of fluid flow with cellular automata and the lattice-Boltzmann equation. Applied Sci. Res. , 1993, 51: 127-33
135. Hou S, Sterling J, Chen S, Doolen G D. A lattice Boltzmarm subgrid model for high Reynolds number flows. Fields Inst. Comm. , 1996, 6: 151-66
136. Bekri S, Adler P M. Dispersion in multiphase flow through porous media. Int. J. Multiphase flow, 2002, 28: 665-697
137.阮剑,吴波,郑楚光.复杂流动的LBGK模拟.工程热物理学报,1992,20(6):764
138.徐辉,阮剑,郑楚光.二维卡门涡街的格子Boltzmann仿真.工程热物理学报,1997,18(3):381
139.吴波,郑楚光.十三点格子Boltzmann模型仿真.工程热物理学报,2000,21(4):520-524
140.吴一光,吴波,郑楚光.三维十五点格子Boltzmann模型仿真.工程热物理学报,2001,22 (4):503-506
141. Crowe C T, Sharma M P, Stock D E. The particle-Source-in-Cell(PSI-CELL) for gas-droplet flows. J. Fluid Engr. , 1977, 99: 325-331
142. Yuu S, Yasukouchi M, Hirosawa Y, Jotaki T. Particle turbulent diffusion in a duct laden jet. AIChE J. , 1978, 24: 509-519
143. Gosman A D, Ioannides E. Aspects of computer simulation of liquid-fulled combustors. AIAA Paper, 1981: 81-0323
144. Berlemont A, Desjonqueres P, Gouesbet G. . Particle Lagrangian simulation in turbulent flows. Int. J. Multiphase Flow, 1990, 14: 679-699
145. Sommerfeld M. Particle dispersion in turbulent flow: the effect of particle size distribution. Part. Syst. Charact. , 1990, 7: 209-220
146. Shuen J S, Chen L D, Faeth G M. Evaluation of a stochastic model of particle dispersion in a turbulent round jet. AIChE J. , 1983, 29: 167-170
147. Cen K F, Fan J R. A numerical model for the turbulent fluctuation and diffusion of gas-particle flows and its application in the freeboard of a fluidized bed. Particle Science and Technology, 1989, 6 (1)
148. Spalding D B. A general purpose computer program for multidimensional oneand two-phase flows. J. Math Comput. Simul. , 1981, 23: 267-276
149.周力行,黄晓晴.三维湍流气粒两相流的k—ε—kp模型.工程热物理学报,1991,12(4):428-433
150.周力行.湍流两相流动及燃烧的统一关联矩封闭模型.工程热物理学报,1991,12(2):203-209
151.周力行,林文漪.k—ε—kp两相湍流模型用于模拟有旋突扩气粒两相流动.工程热物理学报,1995,16(4):481-485
152.周力行,陈涛.统一二阶矩模型用于模拟旋流湍流两相流动.力学学报,1998,30(4):385-390
153.周力行.湍流两相流动和燃烧的统一关联矩封闭模型.工程热物理学报,1991,12(2):203-209
154. Reeks M W. PDF modeling of gas-particle flows. In: 2nd Int. Symp. On Multiphase Fluid, Non-Newtonian Fluid and Physicochemical Fluid Flows'97, 1997, Beijing
155. Zaichik L I, Alipchenkov V M. Simulation of transport of colliding particles suspended in turbulent shear flows. In: 2nd Int. Symp. On Turbulence, Heat and Mass Transfer, 1997, Delft University
156. Simonin O. Continuum modeling of dispersed turbulent two-phase flows. VKI Lectures "Combustion in Two Phase Flow" , 1996
157.李勇,周力行.k—ε—PDI两相湍流模型和台阶后方气粒两相流动的模拟.工程热物理学报,1996,17(2):234-238
158.周力行,李勇.旋流两相流动的DSM—PDF两相湍流模型.工程热物理学报,1999,20(2):252-257
159. Loth E. Numerical approaches for motion of dispersed particles, droplets and bubbles. Progress in Energy and Combustion Science, 2000, 26: 161-223
160. Martin J, Meiburg E. The accumulation of dispersion of heavy particles in forced two-dimensional mixing layer, Part Ⅰ: The fundamental and harmonic cases. Phys. Fluids A. , 1994, 7: 1116-1132
161. Walther J H, Koumoutsakos P. Three-Dimensional Vortex Methods for Particle-Laden Flows with Two-Way Coupling. J. Comput. Phys. , 2001, 167, 39-71
162. Tomomi Uchiyama, Masaaki Naruse. A numerical method for gas-solid two phase free turbulent flow using a vortex method. Powder Technology, 2001, 119: 206-214
163. Tomomi Uchiyama, Masaaki Naruse. Numerical simulation of gas-particle two-phase mixing layer by vortex method. Powder Technology, 2002, 125: 111-121
164. Deutsch E, Simonin O. Large eddy simulation applied to the modeling of particulate transport in turbulent two-phase flows. In: Eighth Symp. on Turbul. Shear Flows, Tech. Univ. Munich, 1991, 10.1.1-10.1.6.
165. Aggarwal S K, Xiao Y. Effects of external forcing on droplet dispersion in a developing shear layer. J. Prop. Power, 1994, 10: 395-401
166. Wang Q, Squires K D, Simonin O. Large eddy simulation of turbulent gas solid flows in a vertical channel and evaluation of second-order models. Int. J. Heat and Fluid Transfer, 1998, 19: 505-511
167. Wang Q, Squires K D, Chen M, McLaughlin J B. On the role of the lift force in turbulence simulation of particle deposition. Int. J. Multiphase Flow, 1997, 23 (4) : 749-763
168. Glaze D J, Frandel S H. Effect of dispersion characteristics on particle temperature in an idealized nonpremixed reacting jet. Int. J. Multiphase Flow, 2000, 26: 609-633
169. Nadaoka K, Nihei Y, Yagi H. Grid-averaged Lagrangian LES model for multiphase turbulent flow. Int. J. Multiphase Flow, 1999, 25: 1619-1643
170. Apte SV, Mahesh K, Moin P, Oefelein J C. Large-eddy simulation of swirling particle-laden flows in a coaxial-jet combustor. Int. J. Multiphase Flow, 2003, 29 (8) : 1311-1331
171. Yuu S, Ueno T, Umekage T. Numerical simulation of the high Reynolds number slit nozzle gas-particle jet using subgrid-seale coupling large eddy simulation. Chemical Engineering Science, 2001, 56: 4293-4307
172. Sankaranarayanan K, Shan X, Kevrekidis I G, Sundaresan S. Bubble flow simulation with the lattice Boltzmann method. Chemical Engineering Science, 1999, 54 (21) : 4817-4823
173. Aidun CK, Lu Y-N. 1995. Lattice Boltzmann simulation of solid particles suspended in fluid. J. Stat. Phys. 81: 49-61
174. Jasberg A, Koponen A, Kataja M, Timonen J. Hydrodynamical forces acting on particles in a two-dimensional flow near a solid wall. Computer Physics Communications, 2000, 129 (1) : 196-206.
175. Raiskinmaki P, Shakib Manesh A, Koponen A. Simulation of non-spherical particles suspended in a shear flow. Computer Physics Communication, 2000, 129 (1) : 185-195
176. Ladd A J C. Short-time motion of colloidal particles: numerical simulation via a fluctuating lattice-Boltzmann equation Phys. Rev. Lett. , 1993, 70: 1339-42
177. Ladd A J C. Numerical simulations of particulate suspensions via a discretized Boltzmann equation. Part. 1. theoretical foundation. J. Fluid Mech. , 1994, 271: 285-309
178. Ladd A J C. Numerical simulations of particulate suspensions via a discretized Boltzmann equation. Part 2: Numerical results. J. Fluid Mech. , 1994, 271: 311-39
179. Ladd A J C. Sedimentation of homogeneous suspensions of non-Brownian spheres. Phys. Fluids, 1997, 9: 491-99
180. Behrend O. Solid-fluid boundaries in particle suspension simulations via the lattice Boltzmarm method. Phys. Rev. E, 1995, 52: 1164-75
181. Filippova O, Hand D. Lattice-Boltzmarm simulation of gas-particle flow in filters. Computers & Fluids, 1997, 26 (7) : 697-712
182. Bekri S, Adler P M. Dispersion in multiphase flow through porous media. Int. J. of Multiphase flow, 2002, 28: 665-697
183. Crowe C T, Troutt T R, Chung J N. Numerical models for two-phase turbulent flows. Annual Rev. Fluid Mech. , 1996, 28: 11-43
184. Mashayek F, Pandya R V R. Analytical description of particle/droplet-laden turbulent flows. Progress in Energy and Combustion Science, 2003, 29: 329-378
185.由长福,祁海鹰,徐旭常.Basset力研究进展与应用分析.应用力学学报,2002,19(2):31-33
186.由长福,祁海鹰,徐旭常.煤粉颗粒所受Magnus力的数值模拟.工程热物理学报,2001,22(5):625-628
187.由长福,祁海鹰,徐旭常.稠密气固两相流中单颗粒所受气动力的数值模拟.工程热物理学报,2002,23(1):103-106
188.由长福,祁海鹰,徐旭常.气固两相流动中非球形颗粒所受曳力的数值研究.化工学报,2003,54(2):188-191
189.肖海涛,祁海鹰,由长福,徐旭常.一个气固两相流动阻力的新模型.化工学报,2003,54(3):311-315
190.肖海涛,祁海鹰,由长福,徐旭常.循环流化床气固曳力模型.计算物理,2003,20(1):25-30
191.赵海波,柳朝晖,郑楚光.颗粒扩散的三个效应分析及其数值模拟.热科学与技术,2003,2(4):347-351
192.张会强,王赫阳,王希麟,郭印诚,林文漪.两相混合层中颗粒运动的数值模拟.工程热物理学报,2000,21(1):115-119
193.王赫阳,张会强,王希麟,郭印诚,林文漪.混台层流动的格子涡方法数值模拟.工程热物理学报,2002,23(5):576-578
194.林建忠,林江.气固两相固射流场涡结构影响固粒扩散的研究.应用数学和力学,1999,20(5):470-476
195.范全林,张会强,郭印诚,王希麟,林文漪.气粒两相平面湍射流拟序结构的大涡模拟.燃烧科学与技术,2001,7(1):21-25
196.范全林,张会强,郭印诚,王希麟,林文漪.重力对水平两相湍射流中颗粒行为的影响.燃烧科学与技术,2002,8(3):211-215
197.金晗辉,金涛,罗坤,樊建人,岑可法.大涡模拟二维气固两相平面射流.动力工程,2003,23(5):2676-2679
198. Jin H H, Luo K, Fan J R, Cen K F. Large eddy simulation of a particle-laden turbulent plane jet. Journal of Zhejiang University, 2003, 4 (2) : 175-180.
199.王兵,张会强,虞建丰,王希麟,郭印诚,林文漪.气粒两相二维后台阶突扩流动的大涡模拟.燃烧科学与技术,2003,9(5):447-452
200.王兵,张会强,王希麟,郭印诚,林文漪.湍流分离流动中的颗粒弥散机制清华大学学报:自然科学版,2003,43(11):1507-1510
201.柳朝晖,周向阳,郑楚光.空间发展湍流气粒两相平面混合层的大涡模拟与统计.工程热物理学报,2002,23(4):495-498
202.吴锤结,周菊光.悬浮颗粒运动的格子Boltzmann数值模拟.力学学报,2004,36(2):151-162
203.刘向军,徐旭常.循环流化床内颗粒团运动的数值模拟.工程热物理学报,2002,23(5):649-652
204.刘向军,徐旭常.循环流化床内稠密气固两相流动的数值模拟.中国电机工程学报,2003,23(5):161-165
205.刘向军,徐旭常.稠密气固两相流中颗粒密集效应的研究与应用.燃烧科学与技术,2004,10(2):120-124
206.刘向军,徐旭常.稠密气固两相流动过程模拟的改进模型与应用.动力工程,2004,24(2):234-239
207.陆慧林,刘文铁,孙永立,李文健,杨励丹.稠密气固两相湍流流动的实验和数值模拟.力学学报,2000,32(4):385-391
208.陆慧林,刘文铁,赵广播,Dimitri Gidaspow.管内稠密气固两相流数值模拟计算:颗粒动力学方法.化工学报,2000,51(1):31-38
209.陆慧林,何玉荣,刘阳,别如山,刘文铁.多组分颗粒稠密气固两相流动的数值模拟.工程热物理学报,2002,23(3):369-371
210.刘阳,陆慧林,刘文铁,赵云华.循环流化床多组分颗粒气固两相流动模型和数值模拟.化工学报,2003,54(8):1065-1071
211.刘阳,陆慧林,刘文铁,赵云华.气固流化床的离散颗粒运动—碰撞解耦模型与模拟.燃烧科学与技术,2003,9(6):551-555
212.郭印诚,陈志兵,陈新国,徐春明,高金森.颗粒动力学与湍动能耦合的稠密两相流动数学模型.计算机与应用化学,2003,20(1):186-190