Gábor Házi

Lattice Boltzmann methods for two-phase flow modeling

Abstract In this paper the most important properties of the lattice Boltzmann methods are reviewed with focus on two-phase flow modeling. The lattice methods are compared with the conventional computational fluid dynamics methods, their advantages and disadvantages are highlighted. Necessary improvements for practical applications are summarized.

Estimation of the liquid-vapor spinodal from interfacial properties obtained from molecular dynamics and lattice Boltzmann simulations

Interfacial pressure and density profiles are calculated from molecular dynamics and lattice Boltzmann simulations of a liquid film in equilibrium with its vapor. The set of local values of tangential pressure and density along an interface exhibits a van der Waals-type loop; starting from the stable vapor bulk phase one passes through metastable and unstable states to the stable liquid bulk phase. The minimum and maximum values of the profile of tangential pressure are related to the liquid and vapor spinodal states, respectively. The spinodal pressures turn out to be linearly related to the extreme values of the tangential pressure in the interface. The comparison with equations of state shows good agreement with the simulation results of the spinodals. In addition the properties of the metastable region are obtained. Based on this investigation a method is proposed for the estimation of the liquid spinodal from experimentally obtained interfacial properties. Estimations for water and helium are presented.

On the cubic velocity deviations in lattice Boltzmann methods

The macroscopic equations derived from the lattice Boltzmann equation are not exactly the Navier?Stokes equations. Here the cubic deviation terms and the methods proposed to eliminate them are studied. The most popular two- and three-dimensional models (D2Q9, D3Q15, D3Q19, D3Q27) are considered in the paper. It is demonstrated that the compensation methods provide only partial elimination of the deviations for these models. It is also shown that the compensation of Qian and Zhou (1998 Europhys. Lett. 42 359) using the compensation parameter K = 1 in a D2Q9 or D3Q27 model can eliminate all the cross terms perfectly, but the deviation terms ?x?u3x, ?y?u3y and ?z?u3z still survive the compensation.

LATTICE BOLTZMANN SIMULATION OF TWO-DIMENSIONAL WALL BOUNDED TURBULENT FLOW

This paper reports on a numerical study of two-dimensional decaying turbulence in a square domain with no-slip walls. The generation of strong small-scale vortices near the no-slip walls have been observed in the lattice Boltzmann simulations just like in earlier pseudospectral calculations. Due to these vortices the enstrophy is not a monotone decaying function of time. Considering a number of simulations and taking their ensemble average, we have found that the decay of enstrophy and that of the kinetic energy can be described well by power-laws. The exponents of these laws depend on the Reynolds number in a similar manner than was observed before in pseudospectral simulations. Considering the ensemble averaged 1D Fourier energy spectra calculated along the walls, we could not find a simple power-law, which fits well to the simulation data. These spectra change in time and reveal an exponent close to -3 in the intermediate and an exponent -5/3 at low wavenumbers. On the other hand, the two-dimensional energy spectra, which remain almost steady in the intermediate decay stage, show clear power-law behavior with exponent larger than -3 depending on the initial Reynolds number.

LATTICE BOLTZMANN SIMULATION OF VAPOR–LIQUID EQUILIBRIUM ON 3D FINITE LATTICE

Numerical calculations for three-dimensional vapor–liquid equilibria have been accomplished by lattice Boltzmann simulations. The aim of this investigation is to test the capability of the lattice Boltzmann method in comparison with solutions obtained by the underlying equation of state. As a result we have found a finite-size effect (just like the ones obtained in one and two dimensions) at small lattice sizes for all phase equilibrium properties and related constants such as the critical exponent β. Here, systems with up to 1003 lattice sites are investigated. Reasonable convergence has been obtained from about 323 lattice sites.

Negative pressure tail of a reflected pressure pulse: Comparison of a lattice Boltzmann study to the experimental results

A numerical pressure wave reflection experiment in a two-dimensional liquid and its comparison with experimental results are presented. The liquid is simulated by the pseudo-potential extension of the lattice-Boltzmann method. In the simulation a pressure pulse is produced by a point source and the resulting pressure wave is reflected back by a wettable rigid wall. Negative pressure tail can be observed at the vicinity of the wall/liquid interface. The resulted shape of the positive and the negative pressure wave is compared with experimental results obtained in an electromagnetic shock-wave generator. Good agreement has been found between the experimental and simulation results.

On the Pressure Dependency of Physical Parameters in Case of Heat Transfer Problems of Supercritical Water

Studying heat transfer problems of supercritical water, the pressure dependency of thermophysical parameters (density, specific heat, viscosity, and thermal conductivity) and the work done by pressure are often neglected. Here we show that the variations of some physical parameters as functions of pressure have the same order of magnitude than their variations as functions of temperature in supercritical water. Therefore, pressure dependency of physical parameters should be taken into account in heat transfer calculations of supercritical water. It is also pointed out that the work done by pressure should not be neglected in supercritical water since the pressure work term has the same order of magnitude than the convective term near the pseudocritical temperature.

ON THE SYSTEM SIZE OF LATTICE BOLTZMANN SIMULATIONS

In lattice Boltzmann simulations particle groups — represented by scalar velocity distributions — are moved on a finite lattice. The size of these particle groups is not well-defined although it is crucial to assume that they should be big enough for using a continuous distribution. Here we propose to use the liquid–vapor interface as an internal yardstick to scale the system. Comparison with existing experimental data and with molecular dynamics simulation of Lennard–Jones-argon shows that the number of atoms located on one lattice site is in the order of few atoms. This contradicts the initial assumption concerning the number of particles in the group, therefore seems to raise some doubts about the applicability of the lattice Boltzmann method in certain problems whenever interfaces play important role and ergodicity does not hold.

THE EFFECT OF FINITE LATTICE-SIZE IN LATTICE BOLTZMANN MODEL

In this paper, numerical results on two-dimensional vapor–liquid equilibrium calculated by lattice Boltzmann method have been presented. Artefacts resulted by the finite lattice-size have been reviewed. A set of criteria for minimal lattice-size to avoid lattice artefacts is given.

Merging of shielded Gaussian vortices and formation of a tripole at low Reynolds numbers

The interaction between two corotating shielded Gaussian vortices is studied by two-dimensional numerical simulations at low Reynolds numbers. It is shown that the outcome of the interactions can be a shielded monopole, a tripole, or dipolar breaking depending on the initial separation distance and Reynolds number. A flow regime map is given in the parameter space of initial separation distance and Reynolds number. Using formal decomposition for vorticity, we show that the tripole formation is due the same physical mechanism than merging of unshielded vortices, while in dipolar breaking both the symmetric and antisymmetric vorticity contributions play important role.