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Validation of Lagrangian Two-Way Coupled Point-Particle Models in Large-Eddy Simulations

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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

  1. 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)

    Article  Google Scholar 

  2. 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)

    Article  Google Scholar 

  3. 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)

    Article  Google Scholar 

  4. Squires, K.D., Eaton, J.K.: Particle response and turbulence modification in isotropic turbulence. Phys. Fluids A 2(7), 1191–1203 (1990)

    Article  Google Scholar 

  5. Sundaram, S., Collins, L. R.: Numerical considerations in simulating a turbulent suspension of finite-volume particles. J. Comput. Phys. 124(2), 337–350 (1996)

    Article  Google Scholar 

  6. 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)

    Article  MathSciNet  Google Scholar 

  7. 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)

    Article  MathSciNet  Google Scholar 

  8. Ireland, P.J., Desjardins, O.: Improving particle drag predictions in euler–Lagrange simulations with two-way coupling. J. Comput. Phys. 338, 405–430 (2017)

    Article  MathSciNet  Google Scholar 

  9. Bagchi, P., Balachandar, S.: Effect of turbulence on the drag and lift of a particle. Phys. Fluids 15(11), 3496–3513 (2003)

    Article  Google Scholar 

  10. Bagchi, P., Balachandar, S.: Response of the wake of an isolated particle to an isotropic turbulent flow. J. Fluid Mech. 518, 95–123 (2004)

    Article  Google Scholar 

  11. Burton, T.M., Eaton, J.K.: Fully resolved simulations of particle-turbulence interaction. J. Fluid Mech. 545, 67–111 (2005)

    Article  Google Scholar 

  12. 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)

    Article  Google Scholar 

  13. Vreman, A.W.: Particle-resolved direct numerical simulation of homogeneous isotropic turbulence modified by small fixed spheres. J. Fluid Mech. 796, 40–85 (2016)

    Article  MathSciNet  Google Scholar 

  14. 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)

    Article  Google Scholar 

  15. Hwang, W., Eaton, J. K.: Homogeneous and isotropic turbulence modulation by small heavy (St 50) particles. J. Fluid Mech. 564, 361–393 (2006)

    Article  Google Scholar 

  16. 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)

    Article  Google Scholar 

  17. Shotorban, B., Mashayek, F.: A stochastic model for particle motion in large-eddy simulation. J. Turbul. 7, N18 (2006)

    Article  Google Scholar 

  18. Kuerten, J.: Subgrid modeling in particle-laden channel flow. Phys. Fluids 18 (2), 025,108 (2006)

    Article  Google Scholar 

  19. Kuerten, J., Vreman, A.: Can turbophoresis be predicted by large-eddy simulation?. Phys. Fluids 17(1), 011,701–011,701 (2005)

    Article  Google Scholar 

  20. 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

    Article  Google Scholar 

  21. 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)

    Article  Google Scholar 

  22. 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)

    Article  Google Scholar 

  23. 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)

    Article  MathSciNet  Google Scholar 

  24. 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)

    Article  Google Scholar 

  25. White, F.M.: Viscous fluid flow. McGraw-Hill, New York (1991)

    Google Scholar 

  26. Siewert, C., Kunnen, R., Meinke, M., Schröder, W.: Orientation statistics and settling velocity of ellipsoids in decaying turbulence. Atmos. Res. 142, 45–56 (2014)

    Article  Google Scholar 

  27. 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)

    Article  MathSciNet  Google Scholar 

  28. 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)

    Article  MathSciNet  Google Scholar 

  29. Schneiders, L., Hartmann, D., Meinke, M., Schröder, W.: An accurate moving boundary formulation in cut-cell methods. J. Comput. Phys. 235, 786–809 (2013)

    Article  MathSciNet  Google Scholar 

  30. Liou, M.S., Steffen, C.J.: A new flux splitting scheme. J. Comput. Phys. 107(1), 23–39 (1993)

    Article  MathSciNet  Google Scholar 

  31. 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)

    Article  Google Scholar 

  32. 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)

    Article  Google Scholar 

  33. 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)

    Article  MathSciNet  Google Scholar 

  34. 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)

    Article  Google Scholar 

  35. 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)

    Article  Google Scholar 

  36. Turkel, E.: Preconditioning techniques in computational fluid dynamics. Annu. Rev. Fluid Mech. 31(1), 385–416 (1999)

    Article  MathSciNet  Google Scholar 

  37. 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)

    Article  MathSciNet  Google Scholar 

  38. 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)

    Article  MathSciNet  Google Scholar 

  39. 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)

    Article  MathSciNet  Google Scholar 

  40. 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)

    Article  Google Scholar 

  41. Clift, R., Grace, J.R., Weber, M. E.: Bubbles, drops, and particles. Courier Corporation (2005)

  42. Armenio, V., Fiorotto, V.: The importance of the forces acting on particles in turbulent flows. Phys. Fluids 13(8), 2437–2440 (2001)

    Article  Google Scholar 

  43. Andersson, H.I., Zhao, L., Barri, M.: Torque-coupling and particle–turbulence interactions. J. Fluid Mech. 696, 319–329 (2012)

    Article  MathSciNet  Google Scholar 

  44. Armenio, V., Piomelli, U., Fiorotto, V.: Effect of the subgrid scales on particle motion. Phys. Fluids 11(10), 3030–3042 (1999)

    Article  Google Scholar 

  45. 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)

    Article  Google Scholar 

  46. Wang, Q., Squires, K.D.: Large eddy simulation of particle-laden turbulent channel flow. Phys. Fluids 8(5), 1207–1223 (1996)

    Article  Google Scholar 

  47. Elghobashi, S.: On predicting particle-laden turbulent flows. Appl. Sci. Res. 52 (4), 309–329 (1994)

    Article  Google Scholar 

  48. Maxey, M., Patel, B., Chang, E., Wang, L.P.: Simulations of dispersed turbulent multiphase flow. Fluid Dyn. Res. 20(1), 143–156 (1997)

    Article  Google Scholar 

  49. Schumann, U., Patterson, G.: Numerical study of pressure and velocity fluctuations in nearly isotropic turbulence. J. Fluid Mech. 88(4), 685–709 (1978)

    Article  Google Scholar 

  50. Orszag, S.A.: Numerical methods for the simulation of turbulence, vol. 12 (1969)

    Google Scholar 

  51. Ferrante, A., Elghobashi, S.: On the physical mechanisms of two-way coupling in particle-laden isotropic turbulence. Phys. Fluids 15(2), 315–329 (2003)

    Article  Google Scholar 

  52. Lucci, F., Ferrante, A., Elghobashi, S.: Modulation of isotropic turbulence by particles of Taylor length-scale size. J. Fluid Mech. 650, 5–55 (2010)

    Article  Google Scholar 

  53. Strutt, H., Tullis, S., Lightstone, M.: Numerical methods for particle-laden DNS of homogeneous isotropic turbulence. Comp. Fluids 40(1), 210–220 (2011)

    Article  Google Scholar 

  54. Pope, S.: Turbulent flows. Cambridge University Press, Cambridge (2000)

    Book  Google Scholar 

  55. 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)

    Article  Google Scholar 

  56. 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)

    Article  MathSciNet  Google Scholar 

  57. Thornber, B., Mosedale, A., Drikakis, D.: On the implicit large eddy simulations of homogeneous decaying turbulence. J. Comput. Phys. 226(2), 1902–1929 (2007)

    Article  Google Scholar 

  58. Geurts, B.J., Fröhlich, J.: A framework for predicting accuracy limitations in large-eddy simulation. Phys. Fluids 14(6), L41–L44 (2002)

    Article  Google Scholar 

  59. Batchelor, G.: The theory of homogeneous turbulence. Cambridge University Press, Cambridge (1953)

    MATH  Google Scholar 

  60. 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)

    Article  MathSciNet  Google Scholar 

  61. Xu, Y., Subramaniam, S.: Consistent modeling of interphase turbulent kinetic energy transfer in particle-laden turbulent flows. Phys. Fluids 19(8), 085,101 (2007)

    Article  Google Scholar 

  62. Kim, S., Karrila, S.J.: Microhydrodynamics: principles and selected applications. Courier Corporation (2013)

  63. Cisse, M., Homann, H., Bec, J.: Slip** motion of large neutrally buoyant particles in turbulence. J. Fluid Mech 735 (2013)

  64. 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)

    Article  Google Scholar 

  65. Domaradzki, J.A., Rogallo, R.S.: Local energy transfer and nonlocal interactions in homogeneous, isotropic turbulence. Phys. Fluids A 2(3), 413–426 (1990)

    Article  Google Scholar 

  66. 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)

    Article  MathSciNet  Google Scholar 

  67. 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)

    Article  Google Scholar 

  68. 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)

    Article  Google Scholar 

  69. 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)

    Article  Google Scholar 

  70. Csanady, G.T.: Turbulent diffusion of heavy particles in the atmosphere. J. Atmospheric Sci. 20(3), 201–208 (1963)

    Article  Google Scholar 

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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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  1. Institute of Aerodynamics, RWTH Aachen University, Wüllnerstr. 5a, Aachen, 52062, Germany

    K. Fröhlich, L. Schneiders, M. Meinke & W. Schröder

  2. JARA-HPC, Forschungszentrum Jülich, Jülich, 52425, Germany

    M. Meinke & W. Schröder

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  1. K. Fröhlich
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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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