Rayleigh–Taylor and Kelvin–Helmholtz hydrodynamic instabilities are frequent in many natural and industrial processes, but their numerical simulation is not an easy challenge. This work simulates both instabilities by using a lattice Boltzmann model on multiphase fluids at a liquid-vapour interface, instead of multicomponent systems like the oil–water one. The model, proposed by He, Chen and Zhang (1999) [1] was modified to increase the precision by computing the pressure gradients with a higher order, as proposed by McCracken and Abraham (2005) [2]. The resulting model correctly simulates both instabilities by using almost the same parameter set. It also reproduces the relation $\gamma \propto \sqrt{A}$ between the growing rate γ of the Rayleigh–Taylor instability and the relative density difference between the fluids (known as the Atwood number A), but including also deviations observed in experiments at low density differences. The results show that the implemented model is a useful tool for the study of hydrodynamic instabilities, drawing a sharp interface and exhibiting numerical stability for moderately high Reynolds numbers.

Accepted:

Published online:

Ali Mauricio Velasco ^{1};
José Daniel Muñoz ^{1}

@article{CRMECA_2015__343_10-11_571_0, author = {Ali Mauricio Velasco and Jos\'e Daniel Mu\~noz}, title = {Study of hydrodynamic instabilities with a multiphase lattice {Boltzmann} model}, journal = {Comptes Rendus. M\'ecanique}, pages = {571--579}, publisher = {Elsevier}, volume = {343}, number = {10-11}, year = {2015}, doi = {10.1016/j.crme.2015.07.014}, language = {en}, }

TY - JOUR AU - Ali Mauricio Velasco AU - José Daniel Muñoz TI - Study of hydrodynamic instabilities with a multiphase lattice Boltzmann model JO - Comptes Rendus. Mécanique PY - 2015 SP - 571 EP - 579 VL - 343 IS - 10-11 PB - Elsevier DO - 10.1016/j.crme.2015.07.014 LA - en ID - CRMECA_2015__343_10-11_571_0 ER -

Ali Mauricio Velasco; José Daniel Muñoz. Study of hydrodynamic instabilities with a multiphase lattice Boltzmann model. Comptes Rendus. Mécanique, Volume 343 (2015) no. 10-11, pp. 571-579. doi : 10.1016/j.crme.2015.07.014. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2015.07.014/

[1] A lattice Boltzmann scheme for incompressible multiphase flow and its application in simulation of Rayleigh–Taylor instability, J. Comput. Phys., Volume 152 (1999), p. 642

[2] Multiple-relaxation-time lattice-Boltzmann model for multiphase flow, Phys. Rev. E, Volume 71 (2005)

[3] Lattice Boltzmann model for simulating flows with multiple phases and components, Phys. Rev. E, Volume 47 (1993), p. 1815

[4] Discrete Boltzmann equation model for nonideal gases, Phys. Rev. E, Volume 57 (1998)

[5] Thermodynamic foundations of kinetic theory and lattice Boltzmann models for multiphase flows, J. Stat. Phys., Volume 107 (2002), p. 309

[6] Lattice Boltzmann modeling and simulation of compressible flows, Front. Phys., Volume 7 (2012) no. 5, p. 582

[7] A model for collision process in gases. I. Small amplitude processes in charged an neutral one component system, Phys. Rev., Volume 94 (1954), p. 511

[8] From the continuous to the lattice Boltzmann equation: the discretization problem and thermal models, Phys. Rev. E, Volume 73 (2006)

[9] A BBGKY-based density gradient approximation of interparticle forces: application for discrete Boltzmann methods, Physica A, Volume 362 (2006), p. 57

[10] Entropic lattice Boltzmann methods, Proc. R. Soc. Lond. A, Volume 457 (2001), p. 717

[11] Thermodynamic consistency of liquid-gas lattice Boltzmann simulations, Phys. Rev. E, Volume 74 (2006)

[12] Consistent lattice Boltzmann equations for phase transitions, Phys. Rev. E, Volume 90 (2014)

[13]

, Oxford University Press, Oxford, UK (1961), p. 445[14] (Cambridge Text in Applied Mathematics) (2002), p. 51

[15] Effect of shear on Rayleigh–Taylor mixing at small Atwood number, Phys. Rev. E, Volume 87 (2013)

*Cited by Sources: *

Comments - Policy