Developing theory of probability density function for stochastic modeling of turbulent gas-particle flows

doi:10.1007/s10483-018-2344-8

Abstract

Abstract: Turbulent gas-particle flows are studied by a kinetic description using a probability density function (PDF). Unlike other investigators deriving the particle Reynolds stress equations using the PDF equations, the particle PDF transport equations are directly solved either using a finite-difference method for two-dimensional (2D) problems or using a Monte-Carlo (MC) method for three-dimensional (3D) problems. The proposed differential stress model together with the PDF (DSM-PDF) is used to simulate turbulent swirling gas-particle flows. The simulation results are compared with the experimental results and the second-order moment (SOM) two-phase modeling results. All of these simulation results are in agreement with the experimental results, implying that the PDF approach validates the SOM two-phase turbulence modeling. The PDF model with the SOM-MC method is used to simulate evaporating gas-droplet flows, and the simulation results are in good agreement with the experimental results.

Key words: highly viscoelastic flow, lubricating approximation, varying thick slit channel, numerical simulation, turbulent flow, gas-particle flow, probability density function(PDF) modeling

2010 MSC Number:

76T99

Lixing ZHOU. Developing theory of probability density function for stochastic modeling of turbulent gas-particle flows. Applied Mathematics and Mechanics (English Edition), 2018, 39(7): 1019-1030.

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References

[1] WILLIAMS, F. A. Combustion Theory, Addison-Wesley, New York, 472-473(1965)
[2] ZHOU, L. X. Combustion Theory and Reacting Fluid Dynamics (in Chinese), Science Press, Beijing, 465-466(1986)
[3] POPE, S. B. PDF methods for turbulent reactive flows. Progress in Energy and Combustion Sciences, 11, 119-192(1985)
[4] DEREVICH, I. V. and ZAICHIK, L. I. The equations for the probability density of the particle velocity and temperature in a turbulent flow simulated by the Gauss stochastic field (in Russian). Journal of Applied Mathematics and Mechanics, 54, 767-780(1990)
[5] REEKS, M. W. On a kinetic equation for the transport of particles in turbulent flows. Physics of Fluids, A3, 446-456(1991)
[6] SIMONIN, O. Continuum modeling of dispersed turbulent two-phase flows. Combustion and Turbulence in Two-Phase Flows, The von Karman Institute For Fluid Dynamics, Belgium (1996)
[7] ZHOU, L. X., LIN, W. Y., and LI, Y. New statistical theory and a k-ε-PDF model for simulating gas-particle flows. Tsinghua Science and Technology, 2, 628-632(1997)
[8] LI, Y. and ZHOU, L. X. A k-ε-PDF two-phase turbulence model for simulating sudden-expansion particle-laden flows. Journal of Thermal Science, 5, 34-38(1996)
[9] ZHOU, L. X. and LI, Y. Simulation of strongly swirling gas-particle flows using a DSM-PDF two-phase turbulence model. Powder Technology, 113, 70-79(2000)
[10] ZHOU, L. X. and CHEN, T. Simulation of strongly swirling flows using USM and k-ε-kp two-phase turbulence models. Powder Technology, 114, 1-11(2001)
[11] LIU, Z. H., ZHENG, C. G., and ZHOU, L. X. A second-order-moment-Monte-Carlo (SOM-MC) model for simulating swirling gas-particle flows. Powder Technology, 120, 216-222(2001)
[12] LIU, Z. H., ZHENG, C. G., and ZHOU, L. X. A joint PDF model for turbulent spray evaporation/combustion. Proceedings of the Combustion Institute, 29, 561-568(2002)

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