Abstract
This paper focuses on the prediction of particle distributions in a flow field computed by large eddy simulation (LES). In an LES, small eddies are not resolved. This gives rise to the question in which cases these eddies need to be reconstructed (modeled) for tracing particles. Therefore the influence of eddies on the particles in dependence on eddy and particle time-scales is discussed. For the case where modeling is necessary, a stochastic model is presented. The model proposed is a model in physical space and not in velocity space, i.e. not the velocities of the unresolved eddies but the effects of these eddies on particle positions are reconstructed. The model is evaluated by an a priori analysis of particle dispersion in turbulent channel flow.
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References
V. Armenio, U. Piomelli, and V. Fiorotto. Effect of the subgrid scales on particle motion. Physics of Fluids, 11(10):3030–3042, 1999
A. J. Chorin. Numerical solution of the Navier Stokes equations. Math. Comput., 22:745–762, 1968
R. Clift, J. R. Grace, and M. E. Weber. Bubbles, Drops and Particles. Academic Press, New York, 1978
J.W. Deardorff. A numerical study of three-dimensional turbulent channel flow at large Reynolds numbers. J. Fluid Mech., 41:453–480, 1970
J. R. Fessler, J. D. Kulick, and J. K. Eaton. Preferential concentration of heavy particles in a turbulent channel flow. Phys. Fluids, 6:3742–3749, 1994
L. Y. M. Gicquel, P. Givi, F. A. Jabei, and S. B. Pope. Velocity filtered density function for large eddy simulation of turbulent flows. Phys. Fluids, 14:1196–1213, 2002
E. Hairer and G. Wanner. Solving Ordinary Differential Equations II. Stiff and Differential-Algebraic Problems. Springer Series in Computational Mathematics. Springer-Verlag, 1990
J. Kim, P. Moin, and R. Moser. Turbulence statistics in fully developed channel flow at low Reynolds number. J. Fluid Mech., 177:133–166, 1987
P. E. Kloeden and E. Platen. Numerical solution of stochastic differential equations. Applications of mathematics. Springer Verlag, Berlin, 3 edition, 1999
J. G. M. Kuerten. Subgrid modeling in particle-laden channel flow. Phys. Fluids, 18:025108, 2006
D. K. Lilly. The representation of small-scale turbulence in numerical simulation experiments. In Proceedings of the IBM Scientific Computing Symposium on Environmental Sciences, pages 195–210, 1967
M. Manhart. Rheology of suspensions of rigid-rod like particles in turbulent channel flow. Journal of Non-Newtonian Fluid Mechanics, 112(2–3):269–293, 2003
M. Manhart. A zonal grid algorithm for DNS of turbulent boundary layers. Computers and Fluids, 33(3):435–461, 2004
M. R. Maxey and J. J. Riley. Equation of motion for a small rigid sphere in a nonuniform flow. Phys. Fluids, 26:883–889, 1983
N. A. Okong’o and J. Bellan. A priori subgrid analysis of temporal mixing layers with evaporating droplets. Phys. Fluids, 12:1573–1591, 2000
N. A. Okong’o and J. Bellan. Consistent large-eddy simulation of a temporal mixing layer with evaporating drops. Part 1. Direct numerical simulation, formulation and a priori analysis. J. Fluid Mech., 499:1–47, 2004
S. B. Pope. Lagrangian pdf methods for turbulent flows. Annu. Rev. Fluid Mech., 26:23–63, 1994
D. W. I. Rouson and J. K. Eaton. On the preferential concentration of solid particles in turbulent channel flow. J. Fluid Mech., 428:149–169, 2001
B. Shotorban and F. Mashayek. A stochastic model for particle motion in large-eddy simulation. JoT, 7:N18, 2006
R. Temam. On an approximate solution of the Navier Stokes equations by the method of fractional steps (part 1). Arch. Ration. Mech. Anal, 32:135–153, 1969
Q. Wang and K. D. Squires. Large eddy simulation of particle-laden turbulent channel flow. Phys. Fluids, 8:1207–1223, 1996
J. H. Williamson. Low-storage Runge-Kutta schemes. Journal of Computational Physics, 35:48–56, 1980
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Gobert, C., Motzet, K., Manhart, M. (2007). A stochastic model for large eddy simulation of a particle-laden turbulent flow. In: Geurts, B.J., Clercx, H., Uijttewaal, W. (eds) Particle-Laden Flow. ERCOFTAC Series, vol 11. Springer, Dordrecht. https://doi.org/10.1007/978-1-4020-6218-6_27
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DOI: https://doi.org/10.1007/978-1-4020-6218-6_27
Publisher Name: Springer, Dordrecht
Print ISBN: 978-1-4020-6217-9
Online ISBN: 978-1-4020-6218-6
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