Abstract
The dense solid-phase governing equations for two-phase flows are obtained by using the kinetic theory of gas molecules. Assuming that the solid-phase velocity distributions obey the Maxwell equations, the collision term for particles under dense two-phase flow conditions is also derived. In comparison with the governing equations of a dilute two-phase flow, the solid-particle's governing equations are developed for a dense turbulent solid-liquid flow by adopting some relevant terms from the dilute two-phase governing equations. Based on Cauchy-Helmholtz theorem and Smagorinsky model, a second-order dynamic sub-grid-scale (SGS) model, in which the sub-grid-scale stress is a function of both the strain-rate tensor and the rotation-rate tensor, is proposed to model the two-phase governing equations by applying dimension analyses. Applying the SIMPLEC algorithm and staggering grid system to the two-phase discretized governing equations and employing the slip boundary conditions on the walls, the velocity and pressure fields, and the volumetric concentration are calculated. The simulation results are in a fairly good agreement with experimental data in two operating cases in a conduit with a rectangular cross-section and these comparisons imply that these models are practical.
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References
Zhou LX. Theory and Modeling of Turbulent Two-Phase Flow and Combustion. Beijing: Tsinghua University Press, 1991 (in Chinese)
Enwald H, Perirano E, et al. Eulerian two-phase flow theory applied to fluidization.Int J Multiphase Flow, 1996, 22(Suppl.): 21–66
Zhang Y, Wilson JD, Lozowski EP. A trajectory simulation model for heavy particle motion in turbulent flow.ASME J Fluid Eng, 1989. 492–494
Tang XL, Tang HF, Wu YL. Silt abrasion of hydraulic runner with silt-laden two-phase flow analysis. In: Mei ZY et al. eds. The Second International Symposium on Fluid Machinery and Fluid Engineering (2nd ISFMFE), Beijing: China Science & Technology Press, 2000, 344–348
Wu YL, Oba R, Ikohagi T. Computation on turbulent dilute liquid-particle flows through a centrifugal impeller.Japanese J Multiphase Flow, 1994, 8(2): 118–125
Zhou LX, Chen T. Simulation of swirling gas-particle flows using USM andk-ε-k p two-phase turbulence models.Power Technology, 2001, 114: 1–11
Wang Q, Squires KD. Large eddy simulation of particle deposition in a vertical turbulent channel flow.Int J Multiphase Flow, 1996, 22(4): 667–683
Boivin M, Simonin O, Squire KD. On the prediction of gas-solid flows with two-way coupling using large eddy simulation.Physics of Fluids, 2000, 12(8): 2080–2090
Ni JR, Wang GQ, Borthwick AJL. Kinetic theory for particles in dilute and dense solid-liquid flows.Journal of Hydraulic Engineering, ASCE, 2000, 126(12): 893–903
Ishii M. Thermo-Fluid Dynamic Theory of Two-Phase Flow. Paris: Eyrolles, 1975
Pai S-I. Two-phase Flow. New York: Vieweg, 1977
Liu DY. Fluid Dynamics of Two-phase System. Beijing: Higher Education Press, 1993 (in Chinese)
Samuelsberg A, Hjertager BH. An experimental and numerical study of flow patterns in a circulating fluidized bed reactor.International Journal of Multiphase Flow, 2000, 22(3): 575–591
Mathiesen V, Solberg T, Hjertager TH. An experimental and computational study of multiphase flow behavior in a circulating fluidized bed.International Journal of Multiphase Flow, 2000, 26: 387–419
Mathiesen V, Solberg T, et al. Predictions of gas/particle flow with an Eulerian model including a realistic particle size distribution.Power Technology, 2000, 112: 34–45
Benyahia S, Arastoopour H, et al. Simulation of particles and gas flow behavior in the riser section of a circulating fluidized bed using the kinetic theory approach for the particulate phase.Power Technology, 2000, 112: 24–33
Filippova O, Hanel D. Lattice-Boltzmann simulation of gas-particle flow in filters.Computers & Fluid, 1997, 26(7): 697–712
Moser RD, Kim J, Mansour NN. Direct numerical simulation of turbulent channel flow up toRe τ=590.Phys Fluids, 1999, (11): 943
Smagrinsky J. General circulation experiments with the primitive equations I.Mon Weather Review, 1963, 91(3): 99–165
Deardorff JW. A numerical study of three-dimensional turbulent channel flow at large Reynolds numbers.J Fluid Mechanics, 1970, 41: 453–480
Leith CE, Backscatter S. In a subgrid-scale model: plane shear mixing layer.Phys Fluids, 1990, 2: 297
Germano M, Piomelli U, et al. A dynamic subgridscale eddy viscosity model.Phys Fluids, 1991, A3(7): 1760–1765
Lilly DK. A proposed modification of the Germano subgrid-scale closure method.Phys Fluids A, 1992, 4(3): 633–635
Zang Y, Street RL, Koseff JR. A dynamic mixed subgrid-scale model and its application to turbulent recirculating flows.Phys Fluids A, 1993, 5(12): 3186–3196
Ghosal S, Lund TS, et al. A dynamic localization model for large-eddy simulation of turbulent flows.J Fluid Mech, 1995, 286: 229–255
Bardina J, Ferziger JH, Reynolds WC. Improved subgrid-scale models for large-eddy simulation.AIAA Paper, 1980, (80): 1357
Chapman S, Cowling TG. The Mathematical Theory of Non-Uniform Cases. Third Edition, London: Cambridge University Press, 1970
Vincenti WG, Kruger GH Jr. Introduction to Physical Gas Dynamics, New York: John Wiley, 1965
Ding JX, Gidaspow D. A bubbling fluidization model using kinetic theory of granular flow.AIChE J, 1990, 36(4): 523–538
Soo SL. Particulated and Continuum: Multiphase Fluid Dynamics. New York: Hemisphere Publication Corp, 1989
Wang ZY, Ning C. Experimental study of two-phase turbulent flow with hyperconcentration of coarse particles.Science in China, Ser A, 1984, 27(12): 1317–1327
Wang ZY, Ning C. Experimental study of laminated load.Science in China, Ser A, 1985, 28(1): 102–112
Ferziger JH. Large eddy numerical simulation of turbulent flows.AIAA J, 1977, 15(9): 1261–1267
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The project supported by the National Natural Science Foundation of China (50176022)
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Xuelin, T., Zhongdong, Q. & Yulin, W. Improved subgrid scale model for dense turbulent solid-liquid two-phase flows. Acta Mech Sinica 20, 354–365 (2004). https://doi.org/10.1007/BF02489373
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DOI: https://doi.org/10.1007/BF02489373