Abstract
The accuracy of point-particle models with two-way coupling for particles of Kolmogorov-length-scale size is assessed. Turbulent kinetic energy budgets are analyzed in physical and in spectral space. It is shown that the force projection of the two-way coupling consistently models the direct transfer of kinetic energy on the particle surfaces and the enhanced viscous dissipation in the vicinity of the particles. Direct and large-eddy simulations of particle-laden flows in isotropic decaying turbulence are conducted and compared with direct-particle fluid simulations, where the particle-fluid interaction is fully resolved. An analysis in spectral space shows that turbulence modulation by particles mainly occurs at larger scales, although the momentum transfer takes place at the smallest scales. Therefore, the turbulent kinetic energy cascade of the single phase dominates in particle-laden flows. It is shown that point-particle models do not interfere with subgrid scale models, which usually act on the smallest scale. Consequently, point-particle models predict sufficiently accurate the turbulence modulation in direct numerical simulations and even when a subgrid scale model is used. The resolution of the LES does not affect the accuracy of the point-particle model, when the subgrid kinetic energy is negligible.
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References
Garg, R., Narayanan, C., Lakehal, D., Subramaniam, S.: Accurate numerical estimation of interphase momentum transfer in lagrangian–Eulerian simulations of dispersed two-phase flows. Int. J. Multiphase Flow 33(12), 1337–1364 (2007)
Boivin, M., Simonin, O., Squires, K.D.: Direct numerical simulation of turbulence modulation by particles in isotropic turbulence. J. Fluid Mech. 375, 235–263 (1998)
Elghobashi, S., Truesdell, G.: On the two-way interaction between homogeneous turbulence and dispersed solid particles. I: Turbulence modification. Phys. Fluids A 5 (7), 1790–1801 (1993)
Squires, K.D., Eaton, J.K.: Particle response and turbulence modification in isotropic turbulence. Phys. Fluids A 2(7), 1191–1203 (1990)
Sundaram, S., Collins, L. R.: Numerical considerations in simulating a turbulent suspension of finite-volume particles. J. Comput. Phys. 124(2), 337–350 (1996)
Gualtieri, P., Picano, F., Sardina, G., Casciola, C.M.: Exact regularized point particle method for multiphase flows in the two-way coupling regime. J. Fluid Mech. 773, 520–561 (2015)
Horwitz, J., Mani, A.: Accurate calculation of Stokes drag for point–particle tracking in two-way coupled flows. J. Comput. Phys. 318, 85–109 (2016)
Ireland, P.J., Desjardins, O.: Improving particle drag predictions in euler–Lagrange simulations with two-way coupling. J. Comput. Phys. 338, 405–430 (2017)
Bagchi, P., Balachandar, S.: Effect of turbulence on the drag and lift of a particle. Phys. Fluids 15(11), 3496–3513 (2003)
Bagchi, P., Balachandar, S.: Response of the wake of an isolated particle to an isotropic turbulent flow. J. Fluid Mech. 518, 95–123 (2004)
Burton, T.M., Eaton, J.K.: Fully resolved simulations of particle-turbulence interaction. J. Fluid Mech. 545, 67–111 (2005)
Zeng, L., Balachandar, S., Fischer, P., Najjar, F.: Interactions of a stationary finite-sized particle with wall turbulence. J. Fluid Mech. 594, 271–305 (2008)
Vreman, A.W.: Particle-resolved direct numerical simulation of homogeneous isotropic turbulence modified by small fixed spheres. J. Fluid Mech. 796, 40–85 (2016)
Eaton, J.K.: Two-way coupled turbulence simulations of gas-particle flows using point-particle tracking. Int. J. Multiphase Flow 35(9), 792–800 (2009)
Hwang, W., Eaton, J. K.: Homogeneous and isotropic turbulence modulation by small heavy (St 50) particles. J. Fluid Mech. 564, 361–393 (2006)
Geurts, B., Kuerten, J.: Ideal stochastic forcing for the motion of particles in large-eddy simulation extracted from direct numerical simulation of turbulent channel flow. Phys. Fluids 24(8), 081,702 (2012)
Shotorban, B., Mashayek, F.: A stochastic model for particle motion in large-eddy simulation. J. Turbul. 7, N18 (2006)
Kuerten, J.: Subgrid modeling in particle-laden channel flow. Phys. Fluids 18 (2), 025,108 (2006)
Kuerten, J., Vreman, A.: Can turbophoresis be predicted by large-eddy simulation?. Phys. Fluids 17(1), 011,701–011,701 (2005)
Michałek, W., Kuerten, J.G., Zeegers, J., Liew, R., Pozorski, J., Geurts, B.J.: A hybrid stochastic-deconvolution model for large-eddy simulation of particle-laden flow. Phys. Fluids 25, 123,302 (2013). 12
Boivin, M., Simonin, O., Squires, K.D.: On the prediction of gas–solid flows with two-way coupling using large eddy simulation. Phys. Fluids 12(8), 2080–2090 (2000)
Kuerten, J.: Point-particle DNS and LES of particle-laden turbulent flow - a state-of-the-art review. Flow Turb. and Comb. 97(3), 689–713 (2016)
Schneiders, L., Meinke, M., Schröder, W.: Direct particle-fluid simulation of Kolmogorov-length-scale size particles in decaying isotropic turbulence. J. Fluid Mech. 819, 188–227 (2017)
Schneiders, L., Meinke, M., Schröder, W.: On the accuracy of Lagrangian point-mass models for heavy non-spherical particles in isotropic turbulence. Fuel 201, 2–14 (2017)
White, F.M.: Viscous fluid flow. McGraw-Hill, New York (1991)
Siewert, C., Kunnen, R., Meinke, M., Schröder, W.: Orientation statistics and settling velocity of ellipsoids in decaying turbulence. Atmos. Res. 142, 45–56 (2014)
Schneiders, L., Günther, C., Meinke, M., Schröder, W.: An efficient conservative cut-cell method for rigid bodies interacting with viscous compressible flows. J. Comput. Phys. 311, 62–86 (2016)
Hartmann, D., Meinke, M., Schröder, W.: A strictly conservative cartesian cut-cell method for compressible viscous flows on adaptive grids. Comput. Meth. Appl. Mech. Eng. 200(9), 1038–1052 (2011)
Schneiders, L., Hartmann, D., Meinke, M., Schröder, W.: An accurate moving boundary formulation in cut-cell methods. J. Comput. Phys. 235, 786–809 (2013)
Liou, M.S., Steffen, C.J.: A new flux splitting scheme. J. Comput. Phys. 107(1), 23–39 (1993)
Meinke, M., Schröder, W., Krause, E., Rister, T.: A comparison of second-and sixth-order methods for large-eddy simulations. Comput. Fluids 31(4), 695–718 (2002)
van Leer, B.: Towards the ultimate conservative difference scheme. V. A second-order sequel to Godunov’s method. J. Comput. Phys. 32(1), 101–136 (1979)
Meysonnat, P.S., Roggenkamp, D., Li, W., Roidl, B., Schröder, W.: Experimental and numerical investigation of transversal traveling surface waves for drag reduction. Eur. J. Mech. B / Fluids 55, 313–323 (2016)
Renze, P., Schröder, W., Meinke, M.: Large-eddy simulation of film cooling flows at density gradients. Int. J. Heat Fluid Flow 29(1), 18–34 (2008)
Rütten, F., Schröder, W., Meinke, M.: Large-eddy simulation of low frequency oscillations of the Dean vortices in turbulent pipe bend flows. Phys. Fluids 17(3), 035,107 (2005)
Turkel, E.: Preconditioning techniques in computational fluid dynamics. Annu. Rev. Fluid Mech. 31(1), 385–416 (1999)
Thornber, B., Drikakis, D., Williams, R.J., Youngs, D.: On entropy generation and dissipation of kinetic energy in high-resolution shock-capturing schemes. J. Comput. Phys. 227(10), 4853–4872 (2008)
Thornber, B., Mosedale, A., Drikakis, D., Youngs, D., Williams, R.J.: An improved reconstruction method for compressible flows with low mach number features. J. Comput. Phys. 227(10), 4873–4894 (2008)
Glowinski, R., Pan, T., Hesla, T., Joseph, D., Periaux, J.: A fictitious domain approach to the direct numerical simulation of incompressible viscous flow past moving rigid bodies: application to particulate flow. J. Comput. Phys. 169(2), 363–426 (2001)
Maxey, M.R., Riley, J.J.: Equation of motion for a small rigid sphere in a nonuniform flow. Phys. Fluids 26(4), 883–889 (1983)
Clift, R., Grace, J.R., Weber, M. E.: Bubbles, drops, and particles. Courier Corporation (2005)
Armenio, V., Fiorotto, V.: The importance of the forces acting on particles in turbulent flows. Phys. Fluids 13(8), 2437–2440 (2001)
Andersson, H.I., Zhao, L., Barri, M.: Torque-coupling and particle–turbulence interactions. J. Fluid Mech. 696, 319–329 (2012)
Armenio, V., Piomelli, U., Fiorotto, V.: Effect of the subgrid scales on particle motion. Phys. Fluids 11(10), 3030–3042 (1999)
Fede, P., Simonin, O.: Numerical study of the subgrid fluid turbulence effects on the statistics of heavy colliding particles. Phys. Fluids 18(4), 045,103 (2006)
Wang, Q., Squires, K.D.: Large eddy simulation of particle-laden turbulent channel flow. Phys. Fluids 8(5), 1207–1223 (1996)
Elghobashi, S.: On predicting particle-laden turbulent flows. Appl. Sci. Res. 52 (4), 309–329 (1994)
Maxey, M., Patel, B., Chang, E., Wang, L.P.: Simulations of dispersed turbulent multiphase flow. Fluid Dyn. Res. 20(1), 143–156 (1997)
Schumann, U., Patterson, G.: Numerical study of pressure and velocity fluctuations in nearly isotropic turbulence. J. Fluid Mech. 88(4), 685–709 (1978)
Orszag, S.A.: Numerical methods for the simulation of turbulence, vol. 12 (1969)
Ferrante, A., Elghobashi, S.: On the physical mechanisms of two-way coupling in particle-laden isotropic turbulence. Phys. Fluids 15(2), 315–329 (2003)
Lucci, F., Ferrante, A., Elghobashi, S.: Modulation of isotropic turbulence by particles of Taylor length-scale size. J. Fluid Mech. 650, 5–55 (2010)
Strutt, H., Tullis, S., Lightstone, M.: Numerical methods for particle-laden DNS of homogeneous isotropic turbulence. Comp. Fluids 40(1), 210–220 (2011)
Pope, S.: Turbulent flows. Cambridge University Press, Cambridge (2000)
Van Atta, C., Antonia, R.: Reynolds number dependence of skewness and flatness factors of turbulent velocity derivatives. Phys. Fluids (1958-1988) 23(2), 252–257 (1980)
Geurts, B.J., Kuczaj, A.K., Titi, E.S.: Regularization modeling for large-eddy simulation of homogeneous isotropic decaying turbulence. J. Phys. A 41(34), 344,008 (2008)
Thornber, B., Mosedale, A., Drikakis, D.: On the implicit large eddy simulations of homogeneous decaying turbulence. J. Comput. Phys. 226(2), 1902–1929 (2007)
Geurts, B.J., Fröhlich, J.: A framework for predicting accuracy limitations in large-eddy simulation. Phys. Fluids 14(6), L41–L44 (2002)
Batchelor, G.: The theory of homogeneous turbulence. Cambridge University Press, Cambridge (1953)
Dairay, T., Lamballais, E., Laizet, S., Vassilicos, J.C.: Numerical dissipation vs. subgrid-scale modelling for large eddy simulation. J. Comput. Phys. 337, 252–274 (2017)
Xu, Y., Subramaniam, S.: Consistent modeling of interphase turbulent kinetic energy transfer in particle-laden turbulent flows. Phys. Fluids 19(8), 085,101 (2007)
Kim, S., Karrila, S.J.: Microhydrodynamics: principles and selected applications. Courier Corporation (2013)
Cisse, M., Homann, H., Bec, J.: Slip** motion of large neutrally buoyant particles in turbulence. J. Fluid Mech 735 (2013)
Kidanemariam, A.G., Chan-Braun, C., Doychev, T., Uhlmann, M.: Direct numerical simulation of horizontal open channel flow with finite-size, heavy particles at low solid volume fraction. New J. Phys. 15(2), 025,031 (2013)
Domaradzki, J.A., Rogallo, R.S.: Local energy transfer and nonlocal interactions in homogeneous, isotropic turbulence. Phys. Fluids A 2(3), 413–426 (1990)
Gao, H., Li, H., Wang, L.P.: Lattice Boltzmann simulation of turbulent flow laden with finite-size particles. Comput. Math. Appl. 65(2), 194–210 (2013)
Luo, K., Wang, Z., Li, D., Tan, J., Fan, J.: Fully resolved simulations of turbulence modulation by high-inertia particles in an isotropic turbulent flow. Phys. Fluids 29(11), 113,301 (2017)
Ten Cate, A., Derksen, J.J., Portela, L.M., Van Den Akker, H.E.: Fully resolved simulations of colliding monodisperse spheres in forced isotropic turbulence. J. Fluid Mech. 519, 233–271 (2004)
Lucci, F., L’vov, V., Ferrante, A., Rosso, M., Elghobashi, S.: Eulerian–Lagrangian bridge for the energy and dissipation spectra in isotropic turbulence. Theor. Comput. Fluid Dyn. 28(2), 197–213 (2014)
Csanady, G.T.: Turbulent diffusion of heavy particles in the atmosphere. J. Atmospheric Sci. 20(3), 201–208 (1963)
Acknowledgements
This work has been financed by the German Research Foundation (DFG) within the framework of the SFB/Transregio ’Oxyflame’ (subproject B2). The support is gratefully acknowledged. Computing resources were provided by the High Performance Computing Center Stuttgart (HLRS) and by the Jülich Supercomputing Center (JSC) within a Large-Scale Project of the Gauss Center for Supercomputing (GCS).
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Fröhlich, K., Schneiders, L., Meinke, M. et al. Validation of Lagrangian Two-Way Coupled Point-Particle Models in Large-Eddy Simulations. Flow Turbulence Combust 101, 317–341 (2018). https://doi.org/10.1007/s10494-018-9933-3
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DOI: https://doi.org/10.1007/s10494-018-9933-3