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Simulation of phase separation in a Van der Waals fluid under gravitational force with Lattice Boltzmann method

Ezequiel Oscar Fogliatto (Comisión Nacional de Energía Atómica, Buenos Aires, Argentina and Instituto Balseiro, Bariloche, Argentina)
Alejandro Clausse (Comisión Nacional de Energía Atómica, Buenos Aires, Argentina, National Council for Scientific and Technical Research, Buenos Aires, Argentina and Universidad Nacional del Centro de la Provincia de Buenos Aires, Tandil, Argentina)
Federico Eduardo Teruel (Comisión Nacional de Energía Atómica, Buenos Aires, Argentina, National Council for Scientific and Technical Research, Buenos Aires, Argentina and Instituto Balseiro, Bariloche, Argentina)

International Journal of Numerical Methods for Heat & Fluid Flow

ISSN: 0961-5539

Article publication date: 7 June 2019

Issue publication date: 11 September 2019

Abstract

Purpose

This paper aims to assess the accuracy of Lattice Boltzmann method (LBM) for numerical simulation of the stratification of a Van der Waals (VdW) fluid subjected to a gravity field and non-uniform temperature distribution. A sensitivity analysis of the influence of the pseudopotential parameters and the grid resolution is presented. The effect of gravity force on interface densities, density profiles and liquid volume fraction is studied.

Design/methodology/approach

The D2Q9 multiple-relaxation-time pseudopotential LBM for two-phase flow is proposed to simulate the phase separation. The analytical solution for density profiles in a one-dimensional problem is derived and used as a benchmark case to validate the numerical results.

Findings

The numerical results reproduce the analytical density profiles with great accuracy over a wide range of simulation conditions, including variations of the gravity and temperature fields. Particularly, the numerical simulations are able to represent the effect of gravity on the existence and position of the liquid–vapor boundary of an ideal pure substance in thermodynamic equilibrium. The sensitivity of the results to variations of the calibration parameters of the VdW pseudopotential was assessed.

Research limitations/implications

The numerical simulations were performed assuming a VdW fluid in a 2-D cavity with one periodic direction for which analytical solutions for benchmarking purposes are possible to obtain.

Originality/value

The following fundamental question is addressed: Is the pseudopotential LBM capable of simulating accurately the liquid–vapor equilibrium under gravity forces and temperature gradients? Moreover, regarding that the pseudopotential model requires the calibration of several internal parameters to achieve thermodynamic consistency, the sensitivity of the results to variations of these parameters is assessed.

Keywords

Acknowledgements

This work was supported by grants from Universidad Nacional de Cuyo (PB 2017-2019), from ANPCyT-FONCyT (PICT 201-0937 and 2016-0441), and from CONICET (PIP 112 201301-00829 CO).

Citation

Fogliatto, E.O., Clausse, A. and Teruel, F.E. (2019), "Simulation of phase separation in a Van der Waals fluid under gravitational force with Lattice Boltzmann method", International Journal of Numerical Methods for Heat & Fluid Flow, Vol. 29 No. 9, pp. 3095-3109. https://doi.org/10.1108/HFF-11-2018-0682

Publisher

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Emerald Publishing Limited

Copyright © 2019, Emerald Publishing Limited