Abstract
Pseudopotential lattice Boltzmann (LB) models have been recognized as efficient numerical tools to simulate complex fluid systems, including those at thermodynamic equilibrium states and with phase transitions. However, when the equation of state (EOS) of real fluids is implemented, the existing pseudopotential LB models suffer from thermodynamic inconsistency. This study presents a multipseudopotential interparticle interaction (MPI) scheme, which is fully consistent with thermodynamics and applicable to engineering applications. In this framework, multiple pseudopotentials are employed to represent dominant interaction potentials at different extents of the mean free path of particles. By simulating van der Waals and Carnahan-Starling fluids, it is demonstrated that the MPI scheme can correctly simulate the physical nature of two-phase systems on the lattice including the continuum predictions of liquid-vapor coexistence states and the sound speeds in liquid and vapor phases. It is also shown that the lattice interactions of the MPI scheme represent underlying molecular interactions as they vary in a broad range from strong short-distance repulsions to weak long-distance attractions during phase transitions. Consequently, the MPI is proved to be a reliable LB scheme as it avoids generating unphysical potentials in implementing the EOSs of real fluids and limiting the spurious velocities at the interface of two-phase systems. Additionally, a straightforward procedure is suggested and discussed to preset the MPI system with the two-phase properties of a selected fluid.
Highlights
The lattice Boltzmann equation (LBE) was originally developed for ideal gases
To overcome the above mentioned shortcoming, here we introduce the concept of the multipseudopotential interparticle interaction (MPI), in comparison with the single pseudopotential interaction (SPI), as the pair interactions scheme to describe the hydrodynamic properties of real fluids, under the condition that each potential satisfies the thermodynamic requirement (5), Ftotal = F(1) + F(2) + · · · + F(n)
The MPI capability in reproducing the van der Waals (VW) and CS equation of state (EOS) is thoroughly investigated in comparison with another common scheme
Summary
Further efforts have been made to describe the nonideal gases (i.e., real fluids) and model the interfacial interactions of multiphase or multicomponent flows Among these proposed approaches [1,2,3,4,5,6,7,8], Shan and Chen’s (SC) model [2,3] has been extensively used to study two-phase flows, largely due to its straightforward definition and simple implementation [9,10,11,12,13,14,15,16]. The deviation indicates a lack of energy conservation in the SC model [17]
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