Multiphase flow simulation by the cascaded lattice Boltzmann method_Daniel Lycett-Brown_University of Southampton参考.pptVIP
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Multiphase flow simulation by the cascaded lattice Boltzmann method_Daniel Lycett-Brown_University of Southampton参考
* Multiphase flow simulation by the cascaded lattice Boltzmann method Energy Technology Research Group Daniel Lycett-Brown and Kai H. LuoICMMES Taipei, 23-27 July 2012 Outline Cascaded LBM Single phase results Extension to multiphase Multiphase validation High Reynolds and Weber number droplet collisions Conclusions K.-L. Pan, P.-C. Chou Y.-J. Tseng, Phys Rev E 80, 036301 (2009) * * 1-D Start from the 1-D Maxwell distribution function: 3 discrete velocities, v(i). Complete moment set: Solving for φ(i): Temperature from the closure relation: I. Karlin P. Asinari, Physica A 389, 1530 (2010) * D2Q9 Constructed as a product of the D1Q3 lattice. This gives: * Central Moments Introduce central moments And identity M. Geier, A. Greiner J.G. Korvink, Phys. Rev. E 73, 066705 (2006) * Central Moments Taking f(0,0) as an example Collision can be written as: * Shear layer Roll-up of perturbed double periodic shear layer. Initial condition: Vorticity at t = 1.0: Reynolds number: On a 128x128 grid, highest stable Re: LBGK: Re ~ 20,000 Cascaded (at ω3 = ω4 = 1.98): Re ~ 1,000,000 * Spurious vortices On a 256x256 grid, Re = 30,000. LBGK: Spurious vortices Cascaded, ωB = ω3 = ω, ω4 = 1.99: Minimum grid size for no spurious vortices: LBGK: 288 x 288 Cascaded: ω3 = 1.8, ω4 = 1.95 192 x192 ω3 = 1.0, ω4 = 1.0 100 x100 * Spurious vortices On a 64x64 grid, Re = 10,000. Cascaded, ωB = ω, ω3 = ω4 = 1.0: * Accuracy and Convergence Cascaded LBGK on 240x240 grid, compared to LBGK solution on 1440x1440 grid. Re = 20,000. e.g. Varying ω3: LBGK error, 0.32% Convergence, ωB = ω, ω3 = ω4 = 1.0: * Viscosity Viscosity measured from decay of sinusoidal shear wave ω = 0.5 ω = 1.7 O(u2) O(u4) X. Shan S. Chen, Phys. Rev. E: 47, 1815 (1993) * Multiphase Calculate the force as in Shan-Chen, nearest neighbours: Carnahan-Starling equation of state: P. Yuan and L. Schaefer. Phys. Fluids,
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