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Entropic multi-relaxation time lattice Boltzmann model for complex flows

Published online by Cambridge University Press:  26 July 2016

B. Dorschner ,
F. Bösch ,
S. S. Chikatamarla ,
K. Boulouchos  and
I. V. Karlin
B. Dorschner
Affiliation:
Aerothermochemistry and Combustion Systems Laboratory, Institute of Energy Technology, Department of Mechanical and Process Engineering, ETH Zurich, 8092 Zürich, Switzerland
F. Bösch
Affiliation:
Aerothermochemistry and Combustion Systems Laboratory, Institute of Energy Technology, Department of Mechanical and Process Engineering, ETH Zurich, 8092 Zürich, Switzerland
S. S. Chikatamarla
Affiliation:
Aerothermochemistry and Combustion Systems Laboratory, Institute of Energy Technology, Department of Mechanical and Process Engineering, ETH Zurich, 8092 Zürich, Switzerland
K. Boulouchos
Affiliation:
Aerothermochemistry and Combustion Systems Laboratory, Institute of Energy Technology, Department of Mechanical and Process Engineering, ETH Zurich, 8092 Zürich, Switzerland
I. V. Karlin*
Affiliation:
Aerothermochemistry and Combustion Systems Laboratory, Institute of Energy Technology, Department of Mechanical and Process Engineering, ETH Zurich, 8092 Zürich, Switzerland
*
†Email address for correspondence: karlin@lav.mavt.ethz.ch
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Abstract

Entropic lattice Boltzmann methods were introduced to overcome the stability issues of lattice Boltzmann models for high Reynolds number turbulent flows. However, to date their validity has been investigated only for simple flows due to the lack of appropriate boundary conditions. We present here an extension of these models to complex flows involving curved and moving boundaries in three dimensions. Apart from a thorough investigation of resolved and under-resolved simulations for periodic flow and turbulent flow in a round pipe, we study in detail the set-up of a simplified internal combustion engine with a valve/piston arrangement. This arrangement allows us to probe the non-trivial interactions between various flow features such as jet breakup, jet–wall interaction, and formation and breakup of large vortical structures, among others. Besides an order of magnitude reduction in computational costs, when compared to state-of-the-art direct numerical simulations (DNS), these methods come with the additional advantage of using static Cartesian meshes also for moving objects, which reduces the complexity of the scheme. Going beyond first-order statistics, a detailed comparison of mean and root-mean-square velocity profiles with high-order spectral element DNS simulations and experimental data shows excellent agreement, highlighting the accuracy and reliability of the method for resolved simulations. Moreover, we show that the implicit subgrid features of the entropic lattice Boltzmann method can be utilized to further reduce the grid sizes and the computational costs, providing an alternative to modern modelling approaches such as large-eddy simulations for complex flows.

JFM classification

Mathematical Foundations: Computational methods Turbulent Flows: Turbulence simulation
Type
Papers
Information
Journal of Fluid Mechanics , Volume 801 , 25 August 2016 , pp. 623 - 651
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Copyright
© 2016 Cambridge University Press 

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References

Ansumali, S., Karlin, I. V. & Öttinger, H. C. 2003 Minimal entropic kinetic models for hydrodynamics. Europhys. Lett. 63 (6), 798–804.Google Scholar
Barenblatt, G. I., Chorin, A. J. & Prostokishin, V. M. 1997 Scaling laws for fully developed turbulent flow in pipes. Appl. Mech. Rev. 50 (7), 413–429.CrossRefGoogle Scholar
Batchelor, G. K. 2000 An Introduction to Fluid Dynamics. Cambridge University Press.Google Scholar
Bösch, F., Chikatamarla, S. S. & Karlin, I. V. 2015 Entropic multi-relaxation lattice Boltzmann scheme for turbulent flows. Phys. Rev. E 92 (4), 043309.Google Scholar
Celik, I., Yavuz, I. & Smirnov, A. 2001 Large eddy simulations of in-cylinder turbulence for internal combustion engines: a review. Intl J. Engine Res. 2 (2), 119–148.CrossRefGoogle Scholar
Chen, H., Kandasamy, S., Orszag, S., Shock, R., Succi, S. & Yakhot, V. 2003 Extended Boltzmann kinetic equation for turbulent flows. Science 301 (5633), 633–636.CrossRefGoogle ScholarPubMed
Chikatamarla, S. S., Frouzakis, C. E., Karlin, I. V., Tomboulides, A. G. & Boulouchos, K. B. 2010 Lattice Boltzmann method for direct numerical simulation of turbulent flows. J. Fluid Mech. 656, 298–308.Google Scholar
Chikatamarla, S. S. & Karlin, I. V. 2013 Entropic lattice Boltzmann method for turbulent flow simulations: boundary conditions. Physica A 392 (9), 1925–1930.Google Scholar
Dorschner, B., Chikatamarla, S. S., Bösch, F. & Karlin, I. V. 2015 Grad’s approximation for moving and stationary walls in entropic lattice Boltzmann simulations. J. Comput. Phys. 295, 340–354.Google Scholar
El Tahry, S. H. & Haworth, D. C. 1992 Directions in turbulence modeling for in-cylinder flows in reciprocating engines. J. Propulsion Power 8 (5), 1040–1048.Google Scholar
Falcucci, G., Jannelli, E., Ubertini, S. & Succi, S. 2013 Direct numerical evidence of stress-induced cavitation. J. Fluid Mech. 728, 362–375.Google Scholar
Falcucci, G., Ubertini, S., Bella, G., De Maio, A. & Palpacelli, S. 2010 Lattice Boltzmann modeling of diesel spray formation and break-up. SAE Intl J. Fuels Lubricants 3 (1), 582–593.Google Scholar
Frapolli, N., Chikatamarla, S. S. & Karlin, I. V. 2014 Multispeed entropic lattice Boltzmann model for thermal flows. Phys. Rev. E 90 (4), 043306.Google Scholar
Geier, M., Greiner, A. & Korvink, J. G. 2006 Cascaded digital lattice Boltzmann automata for high Reynolds number flow. Phys. Rev. E 73, 066705.Google Scholar
Gorban, A. N. & Karlin, I. V. 2004 Invariant Manifolds for Physical and Chemical Kinetics, Lecture Notes in Physics, vol. 660. Springer.Google Scholar
Guo, Z., Zheng, C. & Shi, B. 2002 An extrapolation method for boundary conditions in lattice Boltzmann method. Phys. Fluids 14 (6), 2007–2010.Google Scholar
Gutmark, E. & Wygnanski, I. 1976 The planar turbulent jet. J. Fluid Mech. 73 (03), 465–495.Google Scholar
Haworth, D. C. 1999 Large-eddy simulation of in-cylinder flows. Oil Gas Sci. Technol. 54 (2), 175–185.Google Scholar
Johnson, T. A. & Patel, V. C. 1999 Flow past a sphere up to a Reynolds number of 300. J. Fluid Mech. 378, 19–70.CrossRefGoogle Scholar
Kannepalli, C. & Piomelli, U. 2000 Large-eddy simulation of a three-dimensional shear-driven turbulent boundary layer. J. Fluid Mech. 423, 175–203.Google Scholar
Karlin, I. V., Ansumali, S., De Angelis, E., Öttinger, H. C. & Succi, S.2003 Entropic lattice Boltzmann method for large scale turbulence simulation arXiv:cond-mat/0306003 [cond-mat.stat-mech] p. 11.Google Scholar
Karlin, I. V., Bösch, F. & Chikatamarla, S. S. 2014 Gibbs’ principle for the lattice-kinetic theory of fluid dynamics. Phys. Rev. E 90 (3), 031302.Google Scholar
Karlin, I. V., Ferrante, A. & Öttinger, H. C. 1999 Perfect entropy functions of the lattice Boltzmann method. Europhys. Lett. 47 (2), 182–188.CrossRefGoogle Scholar
Karlin, I. V., Succi, S. & Chikatamarla, S. S. 2011 Comment on ‘Numerics of the lattice Boltzmann method: effects of collision models on the lattice Boltzmann simulations’. Phys. Rev. E 84 (6), 068701.Google Scholar
Keating, B., Vahala, G., Yepez, J., Soe, M. & Vahala, L. 2007 Entropic lattice Boltzmann representations required to recover Navier–Stokes flows. Phys. Rev. E 75 (3), 036712.Google Scholar
Kida, S. 1985 Three-dimensional periodic flows with high-symmetry. J. Phys. Soc. Japan 54 (6), 2132–2136.CrossRefGoogle Scholar
Kida, S. & Murakami, Y. 1987 Kolmogorov similarity in freely decaying turbulence. Phys. Fluids 30 (7), 2030–2039.Google Scholar
Kim, J., Kim, D. & Choi, H. 2001 An immersed-boundary finite-volume method for simulations of flow in complex geometries. J. Comput. Phys. 171 (1), 132–150.CrossRefGoogle Scholar
Lallemand, P. & Luo, L.-S. 2000 Theory of the lattice Boltzmann method: dispersion, dissipation, isotropy, galilean invariance, and stability. Phys. Rev. E 61 (6), 6546–6562.Google Scholar
Lallemand, P. & Luo, L.-S. 2003 Lattice Boltzmann method for moving boundaries. J. Comput. Phys. 184 (2), 406–421.Google Scholar
Lamb, H. 1932 Hydrodynamics. Cambridge University Press.Google Scholar
Lammers, P., Beronov, K. N., Volkert, R., Brenner, G. & Durst, F. 2006 Lattice BGK direct numerical simulation of fully developed turbulence in incompressible plane channel flow. Comput. Fluids 35 (10), 1137–1153.Google Scholar
Liu, K. & Haworth, D. C. 2010 Large-eddy simulation for an axisymmetric piston-cylinder assembly with and without swirl. Flow, Turbul. Combustion 85 (3–4), 279–307.Google Scholar
Mahesh, K. 2013 The interaction of jets with crossflow. Annu. Rev. Fluid Mech. 45, 379–407.Google Scholar
Mazloomi, A. M., Chikatamarla, S. S. & Karlin, I. V. 2015 Entropic lattice Boltzmann method for multiphase flows. Phys. Rev. Lett. 114 (17), 174502.Google Scholar
McKeon, B. J., Swanson, C. J., Zagarola, M. V., Donnelly, R. J. & Smits, A. J. 2004 Friction factors for smooth pipe flow. J. Fluid Mech. 511, 41–44.CrossRefGoogle Scholar
Mei, R., Yu, D., Shyy, W. & Luo, L.-S. 2002 Force evaluation in the lattice Boltzmann method involving curved geometry. Phys. Rev. E 65 (4), 041203.Google Scholar
Mendoza, M., Boghosian, B. M., Herrmann, H. J. & Succi, S. 2010 Fast lattice Boltzmann solver for relativistic hydrodynamics. Phys. Rev. Lett. 105, 014502.Google Scholar
Morrison, J. F., McKeon, B. J., Jiang, W. & Smits, A. J. 2004 Scaling of the streamwise velocity component in turbulent pipe flow. J. Fluid Mech. 508, 99–131.Google Scholar
Morse, a. P., Whitelaw, J. H. & Yianneskis, M. 1979 Turbulent flow measurements by laser-doppler anemometry in motored piston-cylinder assemblies. J. Fluids Engng 101 (2), 208–216.Google Scholar
Perry, A. E., Hafez, S. & Chong, M. S. 2001 A possible reinterpretation of the Princeton superpipe data. J. Fluid Mech. 439, 395–401.Google Scholar
Piomelli, U. & Elias, B. 2002 Wall-layer models for large-eddy simulations. Annu. Rev. Fluid Mech. 34 (1), 349–374.Google Scholar
Pope, S. B. 2000 Turbulent Flows. Cambridge University Press.Google Scholar
Roos, F. W. & Willmarth, W. W. 1971 Some experimental results on sphere and disk drag. AIAA J. 9 (2), 285–291.Google Scholar
Rutland, C. J. 2011 Large-eddy simulations for internal combustion engines: a review. Intl J. Engine Res. 12 (5), 421–451.Google Scholar
Schmitt, M., Frouzakis, C. E., Tomboulides, A. G., Wright, Y. M. & Boulouchos, K. 2014a Direct numerical simulation of multiple cycles in a valve/piston assembly. Phys. Fluids 26 (3), 035105.Google Scholar
Schmitt, M., Frouzakis, C. E., Wright, Y. M., Tomboulides, A. G. & Boulouchos, K. 2014b Investigation of cycle-to-cycle variations in an engine-like geometry. Phys. Fluids 26 (12), 125104.Google Scholar
Spasov, M., Rempfer, D. & Mokhasi, P. 2009 Simulation of a turbulent channel flow with an entropic lattice Boltzmann method. Intl J. Numer. Methods Fluids 60 (11), 1241–1258.CrossRefGoogle Scholar
Stanley, S. A., Sarkar, S. & Mellado, J. P. 2002 A study of the flow-field evolution and mixing in a planar turbulent jet using direct numerical simulation. J. Fluid Mech. 450, 377–407.Google Scholar
Succi, S. 2001 The Lattice Boltzmann Equation: For Fluid Dynamics and Beyond. Oxford University Press.Google Scholar
Thantanapally, C., Singh, S., Patil, D. V., Succi, S. & Ansumali, S. 2013 Quasiequilibrium lattice Boltzmann models with tunable prandtl number for incompressible hydrodynamics. Intl J. Modern Phys. C 24 (12), 1340004.Google Scholar
Towers, D. & Towers, C. 2008 High-speed PIV: applications in engines and future prospects. In Particle Image Velocimetry: New Developments and Recent Applications, pp. 345–361. Springer.Google Scholar
Wang, Y., Shu, C., Teo, C. J. & Wu, J. 2015 An immersed boundary-lattice Boltzmann flux solver and its applications to fluid structure interaction problems. J. Fluids Struct. 54, 440–465.Google Scholar
Weber, R., Visser, B. M. & Boysan, F. 1990 Assessment of turbulence modeling for engineering prediction of swirling vortices in the near burner zone. Intl J. Heat Fluid Flow 11 (3), 225–235.Google Scholar
Wei, T., Fife, P., Klewicki, J. & McMurtry, P. 2005 Properties of the mean momentum balance in turbulent boundary layer, pipe and channel flows. J. Fluid Mech. 522, 303–327.Google Scholar
Westerweel, J., Elsinga, G. E. & Adrian, R. J. 2013 Particle image velocimetry for complex and turbulent flows. Annu. Rev. Fluid Mech. 45 (1), 409–436.Google Scholar
Wosnik, M., Castillo, L. & George, W. K 2000 A theory for turbulent pipe and channel flows. J. Fluid Mech. 421, 115–145.Google Scholar
Wu, X. & Moin, P. 2008 A direct numerical simulation study on the mean velocity characteristics in turbulent pipe flow. J. Fluid Mech. 608, 81–112.Google Scholar
Zagarola, M. V., Perry, A. E. & Smits, A. J. 1997 Log laws or power laws: the scaling in the overlap region. Phys. Fluids 9 (7), 2094–2100.Google Scholar
Zagarola, M. V. & Smits, A. J. 1998 Mean-flow scaling of turbulent pipe flow. J. Fluid Mech. 373, 33–79.Google Scholar

Dorschner supplementary movie

Evolution of the velocity magnitude during 8 cycles in the valve/piston assembly.

Download Dorschner supplementary movie(Video)
Video 73.8 MB