三维气固两相混合层中相间耦合作用的直接数值模拟
|
摘要
为了分析考察气固两相流动中流体与颗粒相互作用,本文对三维平面混合层流动进行了直接数值模拟。混合层流动所涉及的传质问题在理论研究和生产实践中都比较常见。但因为受制于计算条件,关于气固两相混合层流动中两相相互作用的研究,尤其是直接数值模拟研究收效甚微。
在上述背景下,笔者对时间、空间两种模式的混合层模型进行了直接数值模拟,研究的重点在于流体与颗粒之间的相互作用。其中颗粒与流体之间可实现单向耦合、双向耦合不同工况。颗粒之间的碰撞采用硬球碰撞描述。对于空间模式模型的混合层模拟在并行计算条件下完成。
在时间模式气固两相三维平面混合层直接数值模拟的单向耦合模拟过程中,笔者展示了混合层流动中发生的St=3中等颗粒间的碰撞现象,结合混合层流场大涡演化结构分析颗粒碰撞发生的时间、位置,以及论述颗粒碰撞对颗粒扩散产生的影响。通过分析发现颗粒碰撞的发生与颗粒在混合层流动的聚集情况密切相关,因为颗粒碰撞的发生,颗粒的扩散有所增强。
在时间模式气固两相三维平面混合层直接数值模拟双向耦合工况下,因颗粒碰撞导致的扩散开的颗粒会在更广的范围内影响其他颗粒,并通过颗粒对流体的耦合作用影响流体。本章展示了如下的影响结果：考虑了颗粒间的碰撞后,流体相相互混合程度有所提高,雷诺应力会被增大。在流场发展末期,颗粒相、流体相平均流向速度降低,湍动能增强。
在并行条件下的空间模式气相三维平面混合层流场发展初期,笔者定量分析了流场中出现的多涡合并现象,并将统计模拟结果与经典实验数据作对比,取得了比较好的吻合效果,证明该模型的正确性。本章还展示了不同初始扰动幅值工况下流场涡结构的演化规律,由此发现在空间模式混合层流动中添加有效的扰动,在相同计算区域内有助于使涡卷起的位置更靠近上游,同时使涡的形态也更加复杂,于是可以捕捉到更多的流场信息。
硬球颗粒碰撞算法在空间模式气固两相三维平面混合层直接数值模拟过程中实现了并行。空间模式的气固两相混合层流动在考虑了颗粒与流体间的双向耦合和颗粒与颗粒间的相互碰撞后,颗粒相、流体相统计量模拟结果与经典实验数据吻合较好。因为颗粒碰撞的发生,颗粒相的分布更加均匀。不同St数的颗粒在空间模式混合层流动中展示了不同的扩散特性。在St=100工况下随着颗粒相质量携带率的有效提高,流场的涡结构被逐渐破坏,流体混合程度提高,流体相湍流增强。
With regard to the fluid-particle interaction and inter-particle collision in gas-solid turbulence, the direct numerical simulation of a three-dimensional gas-solid two-phase plane mixing layer is conducted. Researches on the plane mixing layer include the theories of heat transfer, mass transfer and flow dynamics of two parallel streams with different velocities. These researches are important both for scientists and engineers, but numerical studies of inter-phase coupling interaction between fluid and particles are few, especially for numerical researches using direct numerical simulation for the enormous calculated amount.
Under the above background, the present paper uses direct numerical simulation to investigate three-dimensional gas-solid two-phase plane mixing layer, focusing on the inter-phase interactions. The two flow models: temporally evolving mixing layer and spatially evolving mixing layer are both conducted. The particle motion is based on the one-way and two-way coupling method respectively, and inter-particle collision is simulated by using the hard-sphere model. Additionally, a large scale parallel computing is presented to simulate spatially evolving mixing layer for the requirement of calculated amount.
Calculations are performed for a bunch of particles Stokes numbers of3when investigating temporally evolving mixing layer under one-way coupling method. The results show that the preferential concentration phenomenon of particles is found after the beginning of the rolling up of the large-scale vortex structures due to the influence of the vortex. It is also found that the inter-particle collision occurs frequently in the local regions with higher particle concentration of the flow field. The evolution of inter-particle collision can be divided into3stages under the influence of the growth of the vortex and the particle dispersion. The results under the two-way coupling show that the particle distribution is more uniform.
In the two-way coupling case of temporally evolving mixing layer, the results show that the inter-particle collision influence on the mixing process of fluid positively, and the Reynolds stresses and turbulence kinetic energy of the flow field and particles are strengthened, but the mean stream-wise velocity of fluid phase and particle phase decrease due to the inter-particle collision. We reveal the rolling-up of span-wise vortexes, the mixing progress of vortexes, and the fully developed status in the gas-phase spatially evolving mixing layer without forcing, in the parallel computing environment. The flow field statistical results, include the stream-wise velocity and the Reynolds stress are compared match well with the experimental data. The inflow forcing is exert on three-dimensional plane mixing layer. Because of inflow forcing on the mixing layer, the positions of rolling-up vortexes is shifted upward.
Two-way interactions are considered in parallel computing, and the particles collisions are solved by the hard-sphere model in the parallel computing when simulating gas-solid two-phase spatially evolving mixing layer. The particle distribution is more uniform after considering collision. Particles in different sizes exhibit diverse dispersion behaviors and the statistics of the stream-wise velocity are matched well with the experimental data. Particles Stokes numbers of100under different mass loading is injected into fluid field.Particle phase breaks the large-scale vortex strucrures and strengthen the mixing of fluid and the turbilence kinetic energy of the flow field.
在上述背景下,笔者对时间、空间两种模式的混合层模型进行了直接数值模拟,研究的重点在于流体与颗粒之间的相互作用。其中颗粒与流体之间可实现单向耦合、双向耦合不同工况。颗粒之间的碰撞采用硬球碰撞描述。对于空间模式模型的混合层模拟在并行计算条件下完成。
在时间模式气固两相三维平面混合层直接数值模拟的单向耦合模拟过程中,笔者展示了混合层流动中发生的St=3中等颗粒间的碰撞现象,结合混合层流场大涡演化结构分析颗粒碰撞发生的时间、位置,以及论述颗粒碰撞对颗粒扩散产生的影响。通过分析发现颗粒碰撞的发生与颗粒在混合层流动的聚集情况密切相关,因为颗粒碰撞的发生,颗粒的扩散有所增强。
在时间模式气固两相三维平面混合层直接数值模拟双向耦合工况下,因颗粒碰撞导致的扩散开的颗粒会在更广的范围内影响其他颗粒,并通过颗粒对流体的耦合作用影响流体。本章展示了如下的影响结果：考虑了颗粒间的碰撞后,流体相相互混合程度有所提高,雷诺应力会被增大。在流场发展末期,颗粒相、流体相平均流向速度降低,湍动能增强。
在并行条件下的空间模式气相三维平面混合层流场发展初期,笔者定量分析了流场中出现的多涡合并现象,并将统计模拟结果与经典实验数据作对比,取得了比较好的吻合效果,证明该模型的正确性。本章还展示了不同初始扰动幅值工况下流场涡结构的演化规律,由此发现在空间模式混合层流动中添加有效的扰动,在相同计算区域内有助于使涡卷起的位置更靠近上游,同时使涡的形态也更加复杂,于是可以捕捉到更多的流场信息。
硬球颗粒碰撞算法在空间模式气固两相三维平面混合层直接数值模拟过程中实现了并行。空间模式的气固两相混合层流动在考虑了颗粒与流体间的双向耦合和颗粒与颗粒间的相互碰撞后,颗粒相、流体相统计量模拟结果与经典实验数据吻合较好。因为颗粒碰撞的发生,颗粒相的分布更加均匀。不同St数的颗粒在空间模式混合层流动中展示了不同的扩散特性。在St=100工况下随着颗粒相质量携带率的有效提高,流场的涡结构被逐渐破坏,流体混合程度提高,流体相湍流增强。
With regard to the fluid-particle interaction and inter-particle collision in gas-solid turbulence, the direct numerical simulation of a three-dimensional gas-solid two-phase plane mixing layer is conducted. Researches on the plane mixing layer include the theories of heat transfer, mass transfer and flow dynamics of two parallel streams with different velocities. These researches are important both for scientists and engineers, but numerical studies of inter-phase coupling interaction between fluid and particles are few, especially for numerical researches using direct numerical simulation for the enormous calculated amount.
Under the above background, the present paper uses direct numerical simulation to investigate three-dimensional gas-solid two-phase plane mixing layer, focusing on the inter-phase interactions. The two flow models: temporally evolving mixing layer and spatially evolving mixing layer are both conducted. The particle motion is based on the one-way and two-way coupling method respectively, and inter-particle collision is simulated by using the hard-sphere model. Additionally, a large scale parallel computing is presented to simulate spatially evolving mixing layer for the requirement of calculated amount.
Calculations are performed for a bunch of particles Stokes numbers of3when investigating temporally evolving mixing layer under one-way coupling method. The results show that the preferential concentration phenomenon of particles is found after the beginning of the rolling up of the large-scale vortex structures due to the influence of the vortex. It is also found that the inter-particle collision occurs frequently in the local regions with higher particle concentration of the flow field. The evolution of inter-particle collision can be divided into3stages under the influence of the growth of the vortex and the particle dispersion. The results under the two-way coupling show that the particle distribution is more uniform.
In the two-way coupling case of temporally evolving mixing layer, the results show that the inter-particle collision influence on the mixing process of fluid positively, and the Reynolds stresses and turbulence kinetic energy of the flow field and particles are strengthened, but the mean stream-wise velocity of fluid phase and particle phase decrease due to the inter-particle collision. We reveal the rolling-up of span-wise vortexes, the mixing progress of vortexes, and the fully developed status in the gas-phase spatially evolving mixing layer without forcing, in the parallel computing environment. The flow field statistical results, include the stream-wise velocity and the Reynolds stress are compared match well with the experimental data. The inflow forcing is exert on three-dimensional plane mixing layer. Because of inflow forcing on the mixing layer, the positions of rolling-up vortexes is shifted upward.
Two-way interactions are considered in parallel computing, and the particles collisions are solved by the hard-sphere model in the parallel computing when simulating gas-solid two-phase spatially evolving mixing layer. The particle distribution is more uniform after considering collision. Particles in different sizes exhibit diverse dispersion behaviors and the statistics of the stream-wise velocity are matched well with the experimental data. Particles Stokes numbers of100under different mass loading is injected into fluid field.Particle phase breaks the large-scale vortex strucrures and strengthen the mixing of fluid and the turbilence kinetic energy of the flow field.
引文
Acton E. The modeling of large eddies in a two-dimensional shear layer. J Fluid Mech., 1976,76:561-592.
Alder B. J. and Wainwright T. E. Phase transition for a hard sphere system. J. Chem. Phys., 1957,27, 1208-1209.
Aref H. and Sigga E. D. Vortex dynamics of the two dimensional mixing layer. J. Fluid Mech., 1980. 100: 705-737. Ashurst W. T. In: Durst F., et al, eds. Turbulent Shear Flows 1, The First international Symposinm on Turbulent Shear Flows, 1977, The Pennsylvania State University, Berlin: Springer-Verlag, 1979,402-413.
Basu Sunanda and Basu S. Correlated measurements of scintillations and in-situ F-region irregularities from OGO-6. Geophys. Res. Lett., 1976, 3(11): 681-684.
Bell J. H. and Mehta R. D. Instabilities and bifurcations of interfacial water waves. Phys. Fluids A, 1991,4(6): 1428-1433.
Bell J. H. and Mehta R. D. Three-dimensional structures of a plane mixing layers. AIAA Paper, 1989a, 89-0124
Bernal L. P. and Roshko A. Streamwise vortex structure in plane mixing layers. J. Fluid Mech., 1986, 170:499-525.
Bird G. A. Molecular Gas Dynamics: Oxford:Oxford University Press, 1976.
Boivin M., Simonin. and Squires K D. Direct numerical simulation of turbulence modulation by particles in isotropic turbulence, J. Fluid Mech., 1998, 375: 235-263.
Browand F. K. An experimental investigation of the instability of an incompressible, separated shear layer. J. Fluid Mech. 1966, 26: 281-307.
Browand F. K. and Troutl T. R. A note on spanwise structure in two-dimensional mixing layer. J. Fluid Mech., 1980, 97: 771-781.
Browand F. K. and Weidman P. D. Large scales in developing mixing layer. J. Fluid Mech., 1976,76: 127-144.
Brown G. L. and Roshko A. On Density Effects and Large Structures in Turbulent Mixing Layers. J. Fluid Mech., 1974, 64: 775-816.
Cain A. B. and Reynolds W. C. and Ferziger J. H. Inter Rep No TF-14. Stanford University, Calif, 1981,231-256. Chein R. and Chung J. N. Simulation of particle dispersion in a two-dimension mixing layer AIChE J., 1998, 34: 946-954.
ChristoPher, K. W. Tarn, and Chen K C. J. Fluid Mech., 1979, 92:303-326.
Chung J. N. and Troutt, T. R. Simulation of particle dispersion in an axisymmetric jet. J. Fluid Mech., 1988, 186, 199-222.
Chung M. K. and Troutt T. R. Simulation of particle dispersion in an axisymmetric jet. J. Fluid Mech., 1988, 186: 199-222.
Churilov S. M., Shukhman I. G. Three-dimensional disturbances to a mixing layer in the nonlinear critical-layer regime. J. Fluid Mech., 1995, 291:57-81.
Corcos G. M. and Sherman F. S. Vorticity concentration and the dynamics of unstable free shear layers J. Fluid Mech., 1976, 73: 241-264.
Crowe C. T. On models for turbulence modulation in fluid-particle flows. Int. J. Multiphase Flow, 2000, 26:719-727.
Crowe C. T., Chung T. N. and Troutt T R. Particle mixing in free shear flows. Progress in Energy and Combustion Science, 1988, 14(3): 171-194.
Crowe C. T., Gore R. A. and Troutt T. R. Particle dispersion by coherent structures in free shear flows. Particulate Science and Technology, 1985, 3: 149-158.
Cundall P. A. and Strack O. D. L. Modeling of microscopic mechanisms in mechanics of granular materials: New Models and Constitutive Relations. 1983,137-149.
Dimotakis P. E. and Brown G. L. The mixing layer at high Reynolds number: Large-structure dynamics and entrainment. J. Fluid Mech., 1976, 78: 535-560.
Eaton J. K. and Fessler J. R. Preferential concentration of particles by turbulence. Int. J. Multiphase Flow, 1994, 20: 169-209.
Elghobashi S. E. and Truesdell G. C. On the two-way interaction between homogeneous turbulence and dispersed solid particles. I: Turbulence modification. Phys. Fluids, 1993, 5: 1790-1796.
Elghobashi S. E. On predicting particle-laden turbulent flows. Appl. Sci. Res, 1994, 52: 309-329.
Fan J. R. Zheng Y. Q., Yao J. and Cen K. F. Direct simulation of particle dispersion in a three-dimensional temporal mixing layer. Proc. R. Soc. Lond.A , 2001, 457:2151.
Fan J. R., Luo K., Zheng Y. Q., Jin H. H. and Cen K. F., Modulation on coherent vortex structures by dispersed solid particles in a three-dimensional mixing layer. Physical Review E., 2003, 68(3), 036309.
Fan J. R., Luo K., Zheng Y. Q., Man Y. H. and Cen K. F. Direct numerical simulation of a near-field particle-laden plane turbulent jet. Physical Review E., 2004, 70, 026303.
Fessler J. R., Kulick J. D. and Eaton J. K. Preferential concentration of heavy particles in a turbulent channel flow. Phys. Fluids, 1994, 6: 3742-3749
Gaster M., Kit E. and Wygnanski I. J. Fluid Mech., 1985,150: 149-190.
Gore R. A. and Crowe C T. Effect of particle size on modulating turbulent intensity. Int. J. Multiphase Flow, 1989,15: 279-285.
Hardalupas Y., Taylor A. M. K. P. and Whitelaw J. H. Velocity and particle-flux characteristics of turbulent particle-laden jets. Proc. R. Soc. London A, 1989,426: 31-78.
Heman M. A. and Jimenez J. Computer analysis of a high-speed film of the plane turbulent mixinglayer. J. Fluid Mech., 1982,119: 323-345.
Hetsroni G. Particle-turbulence interaction. Int. J. Multiphase Flow, 1989, 15: 735-746.
Ho C. M. Huerre P. Perturbed free shear layers. Annu. Rev. Fluid Mech., 1984,16, 365-424.
Ho C. M., Huang L. S., Subharmonics and vortex merging in mixing layers. J. Fluid Mech., 1982, 119:443-473.
Hopkins M. A. Constitutive relations for rapidly sheared granular flows: a Monte Carlo form based on the kinetic theory of dense gases. PhD dissertation, Clarkson University Potsdam, New York, 1987.
Hosokawa S., Tomiyama A., Morimura M., Fujiwara S. and 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.
Hussain F., Moser R., et al. In: Adrian R. J., et al., eds. Proceeding of Summer Program, 1988, London: Academic, 1988: 49-55.
Hussaini M. Y., Zang T. A. Spectral methods in fluid dynamics. Ann. Rev. Fluid Mech., 1985, 19:339-367.
Jiang Peijun; Luo Xukun; Lin Tsao-Jen and Fan Liang-Shih. High temperature and high pressure three-phase fluidization-bed expansion phenomena. Powder Technology, 1997, Vol. 90, no. 2.
Jimenez J. and Mattel C. Fractal interfaces and product generation in the two. dimensional mixing layer. Phys. Fluids A, 1991, 3(5): 1261-1268.
Jimenez J., Cogotlos M. and Bemal L. E. A perspective of the plane mixing layer. J. Fluid Mech., 1985, 152: 125-143.
Kelly R. E. The stability of an unsteady Kelvin-Helmhotz flow. J. Fluid Mech., 1965, 22: 547-560.
Kenning V M. and 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.
Kiger K. T. and Lasheras J. C. Dissipation due to particle/turbulence interaction in a two-phase, turbulent, shear layer. Phys. Fluids, 1997, 9(10): 3005-3019.
Konrad J. H. Ph. D. thesis. Calif. Inst. of Tech., 1976.
Koochesfahani M. M. and MacKinnon. Influence of forcing on the composition of mixed fluid in a two-stream shear layer. Phys Fluids. Phys. Fluids A, 1991, 3(5): 1135-1142.
Lain S. and 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.
Lain S., Sommerfeld M. and 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.
Larsheras J. C. and Chor H. Three-dimensionai instability of a plane free shear layer: an experimental study. J. Fluid Mech., 1988,189: 53-86.
Lasheras J. C, Cho J. S. and Maxworthy T. On the origin and evolution of stream-wise vortical structures in a plane, free shear layer. J. Fluid Mech., 1986, 172, 231-258.
Lazaro B. J. and Lasheras, J. C. Particle dispersion in the developing free shear layer. Part 1. Unforced flow. J. Fluid Mech., 1992a, 235: 143-178.
Lazaro B. J. and Lasheras, J. C. Particle dispersion in the developing free shear layer. Part 2. Forced flow. J. Fluid Mech., 1992b, 235: 179-221.
Lee S. L. and Durst F. On the motion of particles in turbulent duct flows. Int. J. Multiphase Flow, 1982, 8:125-146.
Levy Y. and Lockwood F. C. Velocity measurements in a particle laden turbulent free jet. Combustion and Flame, 1981,40: 333-339.
Liegmann H. W. and Laufer J. NACA Technical Note., 1947(unpublished), 1257.
Ling W., Chung J. N. and Crowe C. T., Direct numerical simulation of the two-way coupled interaction between particles and mixing layer. Proc. R. Soc. Lond. A., 2000, 456: 2931-2955.
Ling W., Chung J. N., Troutt T. R. and Crowe C. T. Direct numerical simulation of a three-dimensional temporal mixing layer with particle dispersion. J. Fluid Mech., 1998, 358: 61-85.
Ling W., Liu J., Chung J. N. and 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.
Longmire E. K. and Eaton J. K. Structure of a particle-laden round jet. J. Fluid Mech., 1992, 236:217-257.
Lopez J. M. and Bulbeck C. J. Behavior of streamwise rib vortices in a three-dimensional mixing layer. Phys. Fluids A, 1993, 5(7): 1694-1702.
Lun C, K. K. and Liu H.S. Numerical simulation of dilute turbulent gas-solid flows in horizontal channels. Int. J. Multiphase Flow., 1997, 23: 575-605.
Luo K., Fan J. R., Jin H. H. and Cen K. F. Direct numerical simulation dispersion by the vortex structures in a three-dimensional mixing layer: The roll-up. Powder Technology., 2004, 146: 102-110.
Mansour N. N., Moin P, et al In: Durst F., et al, Eds. Turbulent Shear Flows I, The First International Symposium on Turbulent Shear Flows, 1977, The Pennsylvania State University, Berlin: Spring-Verlag, 1979: 386-401.
Marcu B. and Meiburg E. Three-dimensional features of particle dispersion in a plane mixing layer. Phys. Fluids., 1996, 8: 2266-2268.
Metcalfe R. W., Orszag S. A., et al. Secondary instability of a temporally growing mixing layer. J. Fluid Mech., 1987, 184: 207-244.
Michael M. R. and Robert D. M. Direct simulation of a self-similar turbulent mixing layer. Phys Fluids, 1994, 6(2): 903-908.
Michalke A. On the inviscid instability of the hyperbolictangent velocity profile. J. Fluid Mech., 1964, 19: 543-556.
Michalke A. Vortex formation in a free boundary layer according to stability theory. J. Fluid Mech., 1965, 22: 371-383.
Miksad R. W. Experimental on the nonlinear stages of free-shear layer transition. J. Fluid Mech., 1972,56:695-719.
Miyauchi, Toshio, Tanahashi and Mamoru. Nippon Kikai Gakkai Ronbunshu B Hen, 1991, 57(540): 2577-2582.
Modarress D., Tan H. and Elghobashi S. E. Two-component LDA measurement in atwo-phase turbulent jet. AIAA Journal, 1984, 22: 624-630.
Modarress D., Wuerer J. and Elghobashi S. E. An experimental study of a turbulent round two-phase jet. Chemical Engineering Communications, 1984, 28: 341-354.
Moin P. and Mahesh K. Direct numerical simulation: a tool in turbulence research. Annu. Rev. Fluid Mech., 1998, 30: 539-578.
Monkewitz P. A. and Huerre R. Influence of the velocity ratio on the spatial instability of mixing layers. Phys Fluid, 1982, 25(7): 1137-1143.
Monkewitz P. A. Subharmonic resonance, pairing and shredding in the mixing layer. J. Fluid Mech., 1988, 188: 223-252.
Moore D. W. and Saffman P. G. The density of organized vortices in a turbulent mixing layer. J. Fluid Mech., 1975, 69: 465-473.
Moser R. D. and Rogers M. M. Mixing transition and the cascade to small scales in a plane mixing layer. Phys. Fluids A, 1991, 3(5): 1128-1134.
Moser R. D. and Rogers M. M. The three-dimensional evolution of a plane mixing layer: paring and transition to turbulence. J. Fluid Mech, 1993, 247: 275-320.
Oesterle B. and Petitjean A. Simulation of particle-to-particle interactions, gas-solid flows. Int. J. Multiphase Flow, 1993, 19: 199-211.
Overman E. A. I. and Zabusky N. On the pairing process in an excited plane turbulent mixing layer. J. Fluid Mech., 1982, 25(8): 1297-1305.
Park K. H., Metcalf W. and Hussain F. Role of coherent structures in an isothermally reacting mixing layer. Phys Fluids, 1994, 6(2): 885-888.
Parthasarathy R. N. and Faeth G. M. Turbulence modulation in homogeneous dilute particle-laden flows. J. Fluid Mech., 1990, 220: 485-537.
Pierrehumber R. T. and Widnall S. E. The structure of organized vortices in a shear layer. J. Fluid Mech., 1981, 102: 301-313.
Pierrehumber R. T. and Widnall S. E. The two-and three-dimensional instablities of a spatially periodic shear layer. J. Fluid Mech., 1982, 114: 59-82.
Plesniak M. W., Bell J. H. and Mehta R. D. Effects of small changes in initial conditions on mixing layer three-dimensionality. Exp Fluids, 1993,14(3): 286-288.
Poinsot T. and Veynante D. Theoretical and Numerical combustion, Second edition, Edwards, 2005, 41-466,1-25.
Pui N. K. and Gartshore I. S. Measurements of the growth rate and structure jn plane turbulent mixing layers. J. Fluid Mech., 1978, 91: 111-130.
Rayleigh, ord. Sci. Papers, Cambridge University Press, 1880, 1: 474-87.
Rilley J. J. and Metealf R.W. AIAA. Paper, No.80-0274,1980.
Saffman P. G. Corrigendum to "The lift on a small sphere in a slow shear flow". J. Fluid Mech., 1968, 31:624.
Saffman P. G. The lift on a small sphere in a slow shear flow. J. Fluid Mech., 1965, 22: 385-400.
Sakiz M. and Simonin O. Continuum modelling and Lagrangian simulation of massive frictional colliding particles in a vertical gas-solid channel flow. In: Michaelides, E. (Ed.), Proc. 4th Int. Conf. on Multiphase Flow. New Orleans, USA, (CD-ROM Proc. ICMF_2001, Paper 186), 2001.
Samimy M., Reeder M. F. and Elliott G. S. Compressibility effects on large structures in free shear flows. Phys. Fluids A, 1991, 4(6): 1251-1258.
SatoH. Journal of the Physical Society of japan, 1956, ll(6):702-709.
Schiller L. and Naumann A. Uber die grundlegenden Berechnungen bei der Schwerkraftaufbereitung, Ver. Deut. Ing., 1933, vol. 77: 318-320.
Schreck S. and Kleis S. J. Modification of grid-generated turbulence by solid particles. J. Fluid Mech., 1993, 249: 665-688.
Sommerfeld M. Analysis of collisions effects for turbulent gas-particle flow in a horizontal channel: Part I. Particle transport. Int. J. Multiphase Flow, 2003, 29: 675-699.
Sommerfeld M. and Zivkovic G. Recent advances in the numerical simulation of pneumatic conveying through pipe systems. In: Hirsch, Ch., Periaux, J., Onate, E. (Eds.), Computational Methods in Applied Science. In: Invited Lectures and Special Technological Sessions of the First European Computational Fluid Dynamics Conference and the First European Conference on Numerical Methods. Engineering, Brussels., 1992, 201-212.
Sommerfeld M. The importance of inter-particle collisions in horizontal gas-solid channel flows. In: Stock, D.E.et al. (Eds.), Gas-Particle Flows. In: ASME Fluids Engineering Conference, Hiltons Head, USA, FED-Vol. 228. ASME, 1995, 335-345.
Sommerfeld M. Validation of a stochastic Lagrangian modelling approach for inter-particle collisions in homogeneous isotropic turbulence. Int. J. Multiphase Flow, 2001, 27: 1829-1858.
Soria J. and Sondergaard R., et al. Phys. Fluids, 1994, 6(2): 871-876.
Spencer B. W. Statistical investigation of turbulent velocity and pressure fields in a two-stream mixing layer. Ph. D. Thesis, University of Illinois at Urbana Champaign, 1970.
Strikwerda J. C. Initial boundary value problem for incompletely parabolic systems, Commun. Pure Appl. Math, 1977, 30:797.
Sundaram S. and Collins L. R. Numerical considerations in simulating a turbulent suspension of finite-volume panicles. J. Comput Phys., 1996, 124: 337-350.
Sutherland J. C. and Kennedy A. Improved boundary conditions for viscous, reacting, compressible flows. J. Comput. Phys., 2003, 191: 502-524.
Tageldin M. S. and Cetegen B. M. Development of mixing and dispersion in an isothermal droplet-laden, confined turbulent mixing layer. Combust. Sci. Tech, 1997, 130, 131-169.
Takaki Ryuji. Phys. Fluids, 1978, 21(2):153-156.
Tanaka T. and Tsuji Y. Numerical simulation of gas-solid two-phase flow in a vertical pipe: On the effect of inter-particle collision. Gas-Solid Flows, 1991, FED-Vol. 121 ASME, 123-128.
Tang L., Wen F., Yang Y., Crowe C. T., Chung J. N. and Troutt T. R. Self-organizing particle dispersion mechanism in free shear flows. Phys. Fluids A, 1992, 4: 2244-2251
Tong X. L. and Wang L. P. Two-way coupled particle-laden mixing layer. Part 1: Linear instability. Int. J. Multiphase Flow, 1999, 25: 575-598.
Tsuji Y. and Morikawa Y. LDV measurements in air-solid two-phase flow in a vertical pipe. J. Fluid Mech., 1982, 139: 417-434.
Tsuji Y., Morikawa Y. and Shiomi H. LDV measurements of an air-solid two-phase flow in a vertical pipe. J. Fluid Mech., 1984, 139: 417-434.
Upender K. and Kaul. Do large structure control their own growth in a mixing layer An assessemnt. J. Fluid Mech., 190: 427-450.
Varaksin A. Yu, Kurosaki Y., Satoh I., Polezhaev Yu V. and Polyakov A. F. Experimental study of the direct influence of the small particles on the carrier air turbulence intensity for pipe flow. In: Third International Conference on Multiphase Flow, ICMF'98, 1998, Lyon, France.
Wang L. P., Wexler A. S. and Zhou Y. On the collision rate of small particles in isotropic turbulence I. zero-inertia case. Phys. Fluids, 1998,10: 266-276.
Wang L. P., Wexler, A.S. and Zhou, Y. On the collision rate of small particles in isotropic turbulence II. finite inertia case. Phys. Fluids, 1998, 10: 1206-1216.
Weibrot I. and Wygnanski I. On coherent structure s in highly excited mixing layer. J. Fluid Mech., 1988, 195: 137-159.
Wen F., Kamalu N., Chung J. N., Crowe C. T. and Troutt T. R. Particle dispersion by vortex structures in plane mixing layers. J. Fluid Engng., 1992,114: 657-666.
Wicker R. B. and 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.
Williams D. R. and Hama F. P. Streaklines in a shear layer perturbed by two waves. Phys. Fluids, 1980,23:442-447.
Winant C. D., Browand F. K., The mechanism of turbulent mixing-layer growth at moderate Reynolds number. J. Fluid Mech., 1974, 63: 237-255.
Winker C. M., Rani Sarma L. and Vanka S.P. Preferential concentration of particles in a fully developed turbulent square duct flow. International Journal of Multiphase Flow, 2004, 30: 27-50.
Wygnanski I.,Oster D.,et al .On the perseverance of a quasi-two-dimensional eddy-structure in a turbulent mixing layer J. Fluid Mech.,1979.93:325-335.
Wygnanski I.,Weisbrot I.J.Fluid Mech.,1988,195:161-173.
Yarin L.P,and Hetsroni G. Turbulence intensity in dilute two-phase flows-3.Int. J. Multiphase Flow, 1994,20:27-44.
Yuan Z. and Michaelides E. E. Turbulence modulation in particulate flows-a theoretical approach. Int. J. Multiphase Flow, 1992,18:779-785.
Zhang H. and Ahmadi G. Aerosol particle transport and deposition in vertical and horizontal turbulent duct flow. J. Fluid Mech.,2000,406:55-80.
Zhiwei Hu, Xiaoyu Luo and Kai H.Luo.Numerical Simulation of Particle Dispersion in a Spatially Deveoping Mixing Kayer.Theoretical and Computational Fluid Fluid Dynamics,2002, 15:403-420.
Zhongmin Yang and Sture K. F. Karlsson. Evolution of coherent structures in a plane mixing layer. Phys. Fluids A, 1991,3(9):2207-2219.
陈景兵.时间及空间模式下的可压缩气固两相混合层数值模拟.国防科技大学硕士学位论文,2006.
陈玉华.气固两相流中基于碰撞的颗粒团聚的数值模拟.东南大学硕士学位论文,2002.
林建忠,范西俊.计算流体力学研究进展,北京：科学出版社,1994,510-515.
林建忠,沈利平,魏中磊.空气动力学报,1995,13(2)：232-237.
罗坤.气固两相自由剪切流动的直接数值模拟和实验研究.浙江大学博士学位论文,2005.
倪慧.具有展向曲率的可压缩混合层中扰动演化的数值模拟.天津大学硕士学位论文,2004.
万国新.二维可压缩单相及气固两相混合层流动数值模拟.国防科技大学硕士学位论文,2005.
王光谦,倪晋仁.颗粒流研究评述.力学与实践,1992.
王康健.气固两相平面混合层的直接数值模拟及扰动波对平面混合层的影响.浙江大学硕士学位论文,2004.
吴文渊.颗粒流体两相流中颗粒团聚物存在的临界条件.工程热物理学报,1992,13(3)：325-328.
徐晓磊.基于并行计算的三维可压混合层大涡模拟.南京理工大学硕士学位论文,2006.
闫洁.三维气固两相平板间射流中相间耦合作用的直接数值模拟.浙江大学博士学位论文,2009.
由长福.循环流化床内颗粒团运动的研究模型.清华大学学报,1998,38(5)：1-3
赵耕夫.应用数学与力学.1995,16(4)：359-365.郑友取.气固两相混合层湍流拟序结构的直接数值模拟和实验验证.浙江大学博士学位论文,2001.
周恒,马亮.中国科学.A辑,1995,25(3)：303-311.
周培源,林建忠,魏中磊.水动力学研究与进展,Ser A,1991,6(2)：1-9.
Alder B. J. and Wainwright T. E. Phase transition for a hard sphere system. J. Chem. Phys., 1957,27, 1208-1209.
Aref H. and Sigga E. D. Vortex dynamics of the two dimensional mixing layer. J. Fluid Mech., 1980. 100: 705-737. Ashurst W. T. In: Durst F., et al, eds. Turbulent Shear Flows 1, The First international Symposinm on Turbulent Shear Flows, 1977, The Pennsylvania State University, Berlin: Springer-Verlag, 1979,402-413.
Basu Sunanda and Basu S. Correlated measurements of scintillations and in-situ F-region irregularities from OGO-6. Geophys. Res. Lett., 1976, 3(11): 681-684.
Bell J. H. and Mehta R. D. Instabilities and bifurcations of interfacial water waves. Phys. Fluids A, 1991,4(6): 1428-1433.
Bell J. H. and Mehta R. D. Three-dimensional structures of a plane mixing layers. AIAA Paper, 1989a, 89-0124
Bernal L. P. and Roshko A. Streamwise vortex structure in plane mixing layers. J. Fluid Mech., 1986, 170:499-525.
Bird G. A. Molecular Gas Dynamics: Oxford:Oxford University Press, 1976.
Boivin M., Simonin. and Squires K D. Direct numerical simulation of turbulence modulation by particles in isotropic turbulence, J. Fluid Mech., 1998, 375: 235-263.
Browand F. K. An experimental investigation of the instability of an incompressible, separated shear layer. J. Fluid Mech. 1966, 26: 281-307.
Browand F. K. and Troutl T. R. A note on spanwise structure in two-dimensional mixing layer. J. Fluid Mech., 1980, 97: 771-781.
Browand F. K. and Weidman P. D. Large scales in developing mixing layer. J. Fluid Mech., 1976,76: 127-144.
Brown G. L. and Roshko A. On Density Effects and Large Structures in Turbulent Mixing Layers. J. Fluid Mech., 1974, 64: 775-816.
Cain A. B. and Reynolds W. C. and Ferziger J. H. Inter Rep No TF-14. Stanford University, Calif, 1981,231-256. Chein R. and Chung J. N. Simulation of particle dispersion in a two-dimension mixing layer AIChE J., 1998, 34: 946-954.
ChristoPher, K. W. Tarn, and Chen K C. J. Fluid Mech., 1979, 92:303-326.
Chung J. N. and Troutt, T. R. Simulation of particle dispersion in an axisymmetric jet. J. Fluid Mech., 1988, 186, 199-222.
Chung M. K. and Troutt T. R. Simulation of particle dispersion in an axisymmetric jet. J. Fluid Mech., 1988, 186: 199-222.
Churilov S. M., Shukhman I. G. Three-dimensional disturbances to a mixing layer in the nonlinear critical-layer regime. J. Fluid Mech., 1995, 291:57-81.
Corcos G. M. and Sherman F. S. Vorticity concentration and the dynamics of unstable free shear layers J. Fluid Mech., 1976, 73: 241-264.
Crowe C. T. On models for turbulence modulation in fluid-particle flows. Int. J. Multiphase Flow, 2000, 26:719-727.
Crowe C. T., Chung T. N. and Troutt T R. Particle mixing in free shear flows. Progress in Energy and Combustion Science, 1988, 14(3): 171-194.
Crowe C. T., Gore R. A. and Troutt T. R. Particle dispersion by coherent structures in free shear flows. Particulate Science and Technology, 1985, 3: 149-158.
Cundall P. A. and Strack O. D. L. Modeling of microscopic mechanisms in mechanics of granular materials: New Models and Constitutive Relations. 1983,137-149.
Dimotakis P. E. and Brown G. L. The mixing layer at high Reynolds number: Large-structure dynamics and entrainment. J. Fluid Mech., 1976, 78: 535-560.
Eaton J. K. and Fessler J. R. Preferential concentration of particles by turbulence. Int. J. Multiphase Flow, 1994, 20: 169-209.
Elghobashi S. E. and Truesdell G. C. On the two-way interaction between homogeneous turbulence and dispersed solid particles. I: Turbulence modification. Phys. Fluids, 1993, 5: 1790-1796.
Elghobashi S. E. On predicting particle-laden turbulent flows. Appl. Sci. Res, 1994, 52: 309-329.
Fan J. R. Zheng Y. Q., Yao J. and Cen K. F. Direct simulation of particle dispersion in a three-dimensional temporal mixing layer. Proc. R. Soc. Lond.A , 2001, 457:2151.
Fan J. R., Luo K., Zheng Y. Q., Jin H. H. and Cen K. F., Modulation on coherent vortex structures by dispersed solid particles in a three-dimensional mixing layer. Physical Review E., 2003, 68(3), 036309.
Fan J. R., Luo K., Zheng Y. Q., Man Y. H. and Cen K. F. Direct numerical simulation of a near-field particle-laden plane turbulent jet. Physical Review E., 2004, 70, 026303.
Fessler J. R., Kulick J. D. and Eaton J. K. Preferential concentration of heavy particles in a turbulent channel flow. Phys. Fluids, 1994, 6: 3742-3749
Gaster M., Kit E. and Wygnanski I. J. Fluid Mech., 1985,150: 149-190.
Gore R. A. and Crowe C T. Effect of particle size on modulating turbulent intensity. Int. J. Multiphase Flow, 1989,15: 279-285.
Hardalupas Y., Taylor A. M. K. P. and Whitelaw J. H. Velocity and particle-flux characteristics of turbulent particle-laden jets. Proc. R. Soc. London A, 1989,426: 31-78.
Heman M. A. and Jimenez J. Computer analysis of a high-speed film of the plane turbulent mixinglayer. J. Fluid Mech., 1982,119: 323-345.
Hetsroni G. Particle-turbulence interaction. Int. J. Multiphase Flow, 1989, 15: 735-746.
Ho C. M. Huerre P. Perturbed free shear layers. Annu. Rev. Fluid Mech., 1984,16, 365-424.
Ho C. M., Huang L. S., Subharmonics and vortex merging in mixing layers. J. Fluid Mech., 1982, 119:443-473.
Hopkins M. A. Constitutive relations for rapidly sheared granular flows: a Monte Carlo form based on the kinetic theory of dense gases. PhD dissertation, Clarkson University Potsdam, New York, 1987.
Hosokawa S., Tomiyama A., Morimura M., Fujiwara S. and 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.
Hussain F., Moser R., et al. In: Adrian R. J., et al., eds. Proceeding of Summer Program, 1988, London: Academic, 1988: 49-55.
Hussaini M. Y., Zang T. A. Spectral methods in fluid dynamics. Ann. Rev. Fluid Mech., 1985, 19:339-367.
Jiang Peijun; Luo Xukun; Lin Tsao-Jen and Fan Liang-Shih. High temperature and high pressure three-phase fluidization-bed expansion phenomena. Powder Technology, 1997, Vol. 90, no. 2.
Jimenez J. and Mattel C. Fractal interfaces and product generation in the two. dimensional mixing layer. Phys. Fluids A, 1991, 3(5): 1261-1268.
Jimenez J., Cogotlos M. and Bemal L. E. A perspective of the plane mixing layer. J. Fluid Mech., 1985, 152: 125-143.
Kelly R. E. The stability of an unsteady Kelvin-Helmhotz flow. J. Fluid Mech., 1965, 22: 547-560.
Kenning V M. and 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.
Kiger K. T. and Lasheras J. C. Dissipation due to particle/turbulence interaction in a two-phase, turbulent, shear layer. Phys. Fluids, 1997, 9(10): 3005-3019.
Konrad J. H. Ph. D. thesis. Calif. Inst. of Tech., 1976.
Koochesfahani M. M. and MacKinnon. Influence of forcing on the composition of mixed fluid in a two-stream shear layer. Phys Fluids. Phys. Fluids A, 1991, 3(5): 1135-1142.
Lain S. and 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.
Lain S., Sommerfeld M. and 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.
Larsheras J. C. and Chor H. Three-dimensionai instability of a plane free shear layer: an experimental study. J. Fluid Mech., 1988,189: 53-86.
Lasheras J. C, Cho J. S. and Maxworthy T. On the origin and evolution of stream-wise vortical structures in a plane, free shear layer. J. Fluid Mech., 1986, 172, 231-258.
Lazaro B. J. and Lasheras, J. C. Particle dispersion in the developing free shear layer. Part 1. Unforced flow. J. Fluid Mech., 1992a, 235: 143-178.
Lazaro B. J. and Lasheras, J. C. Particle dispersion in the developing free shear layer. Part 2. Forced flow. J. Fluid Mech., 1992b, 235: 179-221.
Lee S. L. and Durst F. On the motion of particles in turbulent duct flows. Int. J. Multiphase Flow, 1982, 8:125-146.
Levy Y. and Lockwood F. C. Velocity measurements in a particle laden turbulent free jet. Combustion and Flame, 1981,40: 333-339.
Liegmann H. W. and Laufer J. NACA Technical Note., 1947(unpublished), 1257.
Ling W., Chung J. N. and Crowe C. T., Direct numerical simulation of the two-way coupled interaction between particles and mixing layer. Proc. R. Soc. Lond. A., 2000, 456: 2931-2955.
Ling W., Chung J. N., Troutt T. R. and Crowe C. T. Direct numerical simulation of a three-dimensional temporal mixing layer with particle dispersion. J. Fluid Mech., 1998, 358: 61-85.
Ling W., Liu J., Chung J. N. and 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.
Longmire E. K. and Eaton J. K. Structure of a particle-laden round jet. J. Fluid Mech., 1992, 236:217-257.
Lopez J. M. and Bulbeck C. J. Behavior of streamwise rib vortices in a three-dimensional mixing layer. Phys. Fluids A, 1993, 5(7): 1694-1702.
Lun C, K. K. and Liu H.S. Numerical simulation of dilute turbulent gas-solid flows in horizontal channels. Int. J. Multiphase Flow., 1997, 23: 575-605.
Luo K., Fan J. R., Jin H. H. and Cen K. F. Direct numerical simulation dispersion by the vortex structures in a three-dimensional mixing layer: The roll-up. Powder Technology., 2004, 146: 102-110.
Mansour N. N., Moin P, et al In: Durst F., et al, Eds. Turbulent Shear Flows I, The First International Symposium on Turbulent Shear Flows, 1977, The Pennsylvania State University, Berlin: Spring-Verlag, 1979: 386-401.
Marcu B. and Meiburg E. Three-dimensional features of particle dispersion in a plane mixing layer. Phys. Fluids., 1996, 8: 2266-2268.
Metcalfe R. W., Orszag S. A., et al. Secondary instability of a temporally growing mixing layer. J. Fluid Mech., 1987, 184: 207-244.
Michael M. R. and Robert D. M. Direct simulation of a self-similar turbulent mixing layer. Phys Fluids, 1994, 6(2): 903-908.
Michalke A. On the inviscid instability of the hyperbolictangent velocity profile. J. Fluid Mech., 1964, 19: 543-556.
Michalke A. Vortex formation in a free boundary layer according to stability theory. J. Fluid Mech., 1965, 22: 371-383.
Miksad R. W. Experimental on the nonlinear stages of free-shear layer transition. J. Fluid Mech., 1972,56:695-719.
Miyauchi, Toshio, Tanahashi and Mamoru. Nippon Kikai Gakkai Ronbunshu B Hen, 1991, 57(540): 2577-2582.
Modarress D., Tan H. and Elghobashi S. E. Two-component LDA measurement in atwo-phase turbulent jet. AIAA Journal, 1984, 22: 624-630.
Modarress D., Wuerer J. and Elghobashi S. E. An experimental study of a turbulent round two-phase jet. Chemical Engineering Communications, 1984, 28: 341-354.
Moin P. and Mahesh K. Direct numerical simulation: a tool in turbulence research. Annu. Rev. Fluid Mech., 1998, 30: 539-578.
Monkewitz P. A. and Huerre R. Influence of the velocity ratio on the spatial instability of mixing layers. Phys Fluid, 1982, 25(7): 1137-1143.
Monkewitz P. A. Subharmonic resonance, pairing and shredding in the mixing layer. J. Fluid Mech., 1988, 188: 223-252.
Moore D. W. and Saffman P. G. The density of organized vortices in a turbulent mixing layer. J. Fluid Mech., 1975, 69: 465-473.
Moser R. D. and Rogers M. M. Mixing transition and the cascade to small scales in a plane mixing layer. Phys. Fluids A, 1991, 3(5): 1128-1134.
Moser R. D. and Rogers M. M. The three-dimensional evolution of a plane mixing layer: paring and transition to turbulence. J. Fluid Mech, 1993, 247: 275-320.
Oesterle B. and Petitjean A. Simulation of particle-to-particle interactions, gas-solid flows. Int. J. Multiphase Flow, 1993, 19: 199-211.
Overman E. A. I. and Zabusky N. On the pairing process in an excited plane turbulent mixing layer. J. Fluid Mech., 1982, 25(8): 1297-1305.
Park K. H., Metcalf W. and Hussain F. Role of coherent structures in an isothermally reacting mixing layer. Phys Fluids, 1994, 6(2): 885-888.
Parthasarathy R. N. and Faeth G. M. Turbulence modulation in homogeneous dilute particle-laden flows. J. Fluid Mech., 1990, 220: 485-537.
Pierrehumber R. T. and Widnall S. E. The structure of organized vortices in a shear layer. J. Fluid Mech., 1981, 102: 301-313.
Pierrehumber R. T. and Widnall S. E. The two-and three-dimensional instablities of a spatially periodic shear layer. J. Fluid Mech., 1982, 114: 59-82.
Plesniak M. W., Bell J. H. and Mehta R. D. Effects of small changes in initial conditions on mixing layer three-dimensionality. Exp Fluids, 1993,14(3): 286-288.
Poinsot T. and Veynante D. Theoretical and Numerical combustion, Second edition, Edwards, 2005, 41-466,1-25.
Pui N. K. and Gartshore I. S. Measurements of the growth rate and structure jn plane turbulent mixing layers. J. Fluid Mech., 1978, 91: 111-130.
Rayleigh, ord. Sci. Papers, Cambridge University Press, 1880, 1: 474-87.
Rilley J. J. and Metealf R.W. AIAA. Paper, No.80-0274,1980.
Saffman P. G. Corrigendum to "The lift on a small sphere in a slow shear flow". J. Fluid Mech., 1968, 31:624.
Saffman P. G. The lift on a small sphere in a slow shear flow. J. Fluid Mech., 1965, 22: 385-400.
Sakiz M. and Simonin O. Continuum modelling and Lagrangian simulation of massive frictional colliding particles in a vertical gas-solid channel flow. In: Michaelides, E. (Ed.), Proc. 4th Int. Conf. on Multiphase Flow. New Orleans, USA, (CD-ROM Proc. ICMF_2001, Paper 186), 2001.
Samimy M., Reeder M. F. and Elliott G. S. Compressibility effects on large structures in free shear flows. Phys. Fluids A, 1991, 4(6): 1251-1258.
SatoH. Journal of the Physical Society of japan, 1956, ll(6):702-709.
Schiller L. and Naumann A. Uber die grundlegenden Berechnungen bei der Schwerkraftaufbereitung, Ver. Deut. Ing., 1933, vol. 77: 318-320.
Schreck S. and Kleis S. J. Modification of grid-generated turbulence by solid particles. J. Fluid Mech., 1993, 249: 665-688.
Sommerfeld M. Analysis of collisions effects for turbulent gas-particle flow in a horizontal channel: Part I. Particle transport. Int. J. Multiphase Flow, 2003, 29: 675-699.
Sommerfeld M. and Zivkovic G. Recent advances in the numerical simulation of pneumatic conveying through pipe systems. In: Hirsch, Ch., Periaux, J., Onate, E. (Eds.), Computational Methods in Applied Science. In: Invited Lectures and Special Technological Sessions of the First European Computational Fluid Dynamics Conference and the First European Conference on Numerical Methods. Engineering, Brussels., 1992, 201-212.
Sommerfeld M. The importance of inter-particle collisions in horizontal gas-solid channel flows. In: Stock, D.E.et al. (Eds.), Gas-Particle Flows. In: ASME Fluids Engineering Conference, Hiltons Head, USA, FED-Vol. 228. ASME, 1995, 335-345.
Sommerfeld M. Validation of a stochastic Lagrangian modelling approach for inter-particle collisions in homogeneous isotropic turbulence. Int. J. Multiphase Flow, 2001, 27: 1829-1858.
Soria J. and Sondergaard R., et al. Phys. Fluids, 1994, 6(2): 871-876.
Spencer B. W. Statistical investigation of turbulent velocity and pressure fields in a two-stream mixing layer. Ph. D. Thesis, University of Illinois at Urbana Champaign, 1970.
Strikwerda J. C. Initial boundary value problem for incompletely parabolic systems, Commun. Pure Appl. Math, 1977, 30:797.
Sundaram S. and Collins L. R. Numerical considerations in simulating a turbulent suspension of finite-volume panicles. J. Comput Phys., 1996, 124: 337-350.
Sutherland J. C. and Kennedy A. Improved boundary conditions for viscous, reacting, compressible flows. J. Comput. Phys., 2003, 191: 502-524.
Tageldin M. S. and Cetegen B. M. Development of mixing and dispersion in an isothermal droplet-laden, confined turbulent mixing layer. Combust. Sci. Tech, 1997, 130, 131-169.
Takaki Ryuji. Phys. Fluids, 1978, 21(2):153-156.
Tanaka T. and Tsuji Y. Numerical simulation of gas-solid two-phase flow in a vertical pipe: On the effect of inter-particle collision. Gas-Solid Flows, 1991, FED-Vol. 121 ASME, 123-128.
Tang L., Wen F., Yang Y., Crowe C. T., Chung J. N. and Troutt T. R. Self-organizing particle dispersion mechanism in free shear flows. Phys. Fluids A, 1992, 4: 2244-2251
Tong X. L. and Wang L. P. Two-way coupled particle-laden mixing layer. Part 1: Linear instability. Int. J. Multiphase Flow, 1999, 25: 575-598.
Tsuji Y. and Morikawa Y. LDV measurements in air-solid two-phase flow in a vertical pipe. J. Fluid Mech., 1982, 139: 417-434.
Tsuji Y., Morikawa Y. and Shiomi H. LDV measurements of an air-solid two-phase flow in a vertical pipe. J. Fluid Mech., 1984, 139: 417-434.
Upender K. and Kaul. Do large structure control their own growth in a mixing layer An assessemnt. J. Fluid Mech., 190: 427-450.
Varaksin A. Yu, Kurosaki Y., Satoh I., Polezhaev Yu V. and Polyakov A. F. Experimental study of the direct influence of the small particles on the carrier air turbulence intensity for pipe flow. In: Third International Conference on Multiphase Flow, ICMF'98, 1998, Lyon, France.
Wang L. P., Wexler A. S. and Zhou Y. On the collision rate of small particles in isotropic turbulence I. zero-inertia case. Phys. Fluids, 1998,10: 266-276.
Wang L. P., Wexler, A.S. and Zhou, Y. On the collision rate of small particles in isotropic turbulence II. finite inertia case. Phys. Fluids, 1998, 10: 1206-1216.
Weibrot I. and Wygnanski I. On coherent structure s in highly excited mixing layer. J. Fluid Mech., 1988, 195: 137-159.
Wen F., Kamalu N., Chung J. N., Crowe C. T. and Troutt T. R. Particle dispersion by vortex structures in plane mixing layers. J. Fluid Engng., 1992,114: 657-666.
Wicker R. B. and 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.
Williams D. R. and Hama F. P. Streaklines in a shear layer perturbed by two waves. Phys. Fluids, 1980,23:442-447.
Winant C. D., Browand F. K., The mechanism of turbulent mixing-layer growth at moderate Reynolds number. J. Fluid Mech., 1974, 63: 237-255.
Winker C. M., Rani Sarma L. and Vanka S.P. Preferential concentration of particles in a fully developed turbulent square duct flow. International Journal of Multiphase Flow, 2004, 30: 27-50.
Wygnanski I.,Oster D.,et al .On the perseverance of a quasi-two-dimensional eddy-structure in a turbulent mixing layer J. Fluid Mech.,1979.93:325-335.
Wygnanski I.,Weisbrot I.J.Fluid Mech.,1988,195:161-173.
Yarin L.P,and Hetsroni G. Turbulence intensity in dilute two-phase flows-3.Int. J. Multiphase Flow, 1994,20:27-44.
Yuan Z. and Michaelides E. E. Turbulence modulation in particulate flows-a theoretical approach. Int. J. Multiphase Flow, 1992,18:779-785.
Zhang H. and Ahmadi G. Aerosol particle transport and deposition in vertical and horizontal turbulent duct flow. J. Fluid Mech.,2000,406:55-80.
Zhiwei Hu, Xiaoyu Luo and Kai H.Luo.Numerical Simulation of Particle Dispersion in a Spatially Deveoping Mixing Kayer.Theoretical and Computational Fluid Fluid Dynamics,2002, 15:403-420.
Zhongmin Yang and Sture K. F. Karlsson. Evolution of coherent structures in a plane mixing layer. Phys. Fluids A, 1991,3(9):2207-2219.
陈景兵.时间及空间模式下的可压缩气固两相混合层数值模拟.国防科技大学硕士学位论文,2006.
陈玉华.气固两相流中基于碰撞的颗粒团聚的数值模拟.东南大学硕士学位论文,2002.
林建忠,范西俊.计算流体力学研究进展,北京：科学出版社,1994,510-515.
林建忠,沈利平,魏中磊.空气动力学报,1995,13(2)：232-237.
罗坤.气固两相自由剪切流动的直接数值模拟和实验研究.浙江大学博士学位论文,2005.
倪慧.具有展向曲率的可压缩混合层中扰动演化的数值模拟.天津大学硕士学位论文,2004.
万国新.二维可压缩单相及气固两相混合层流动数值模拟.国防科技大学硕士学位论文,2005.
王光谦,倪晋仁.颗粒流研究评述.力学与实践,1992.
王康健.气固两相平面混合层的直接数值模拟及扰动波对平面混合层的影响.浙江大学硕士学位论文,2004.
吴文渊.颗粒流体两相流中颗粒团聚物存在的临界条件.工程热物理学报,1992,13(3)：325-328.
徐晓磊.基于并行计算的三维可压混合层大涡模拟.南京理工大学硕士学位论文,2006.
闫洁.三维气固两相平板间射流中相间耦合作用的直接数值模拟.浙江大学博士学位论文,2009.
由长福.循环流化床内颗粒团运动的研究模型.清华大学学报,1998,38(5)：1-3
赵耕夫.应用数学与力学.1995,16(4)：359-365.郑友取.气固两相混合层湍流拟序结构的直接数值模拟和实验验证.浙江大学博士学位论文,2001.
周恒,马亮.中国科学.A辑,1995,25(3)：303-311.
周培源,林建忠,魏中磊.水动力学研究与进展,Ser A,1991,6(2)：1-9.