Compressible pressure-based Lattice-Boltzmann applied to humid air with phase change

Abstract

A new compressible pressure-based Lattice Boltzmann Method is proposed to simulate humid air flows with phase change. The variable density and compressible effects are fully resolved, effectively lifting the Boussinesq approximation commonly used, e.g. for meteorological flows. Previous studies indicate that the Boussinesq assumption can lead to errors up to 25%, but the model remains common, for compressible models often suffer from a lack of stability. In order to overcome this issue, a new pressure-based solver is proposed, exhibiting excellent stability properties. Mass and momentum conservation equations are solved by a hybrid recursive regularized Lattice-Boltzmann approach, whereas the enthalpy and species conservation equations are solved using a finite volume method. The solver is based on a pressure-based method coupled with a predictor-corrector algorithm, and incorporates a humid equation of state, as well as a specific boundary condition treatment for phase change. In particular, boundary conditions that handle mass leakage are also proposed and validated. Three test cases are investigated in order to validate this new approach: the Rayleigh-Bénard instability applied to humid air, the atmospheric rising of a condensing moist bubble, and finally the evaporation of a thin liquid film in a vertical channel. Results indicate that the proposed pressure-based Lattice-Boltzmann model is stable and accurate on all cases.

A unified hybrid lattice-Boltzmann method for compressible flows: Bridging between pressure-based and density-based methods

“…A way to improve the stability of the methods while keeping an expression of the collision kernel close to the classical density-based one is to switch to pressure-based methods, in which the zeroth-order moment of the density functions is the pressure instead of the density = / 2 . These methods have been proposed initially for low-Mach reactive flows 9,10 and rapidly extended to low-Mach multiphase flows 11,12 , but only very recently to high-speed compressible 13 and reactive flows 14,15 and to humid air thermodynamics 16 . A possible explanation for their efficiency has been very recently proposed 17 through theoretical analysis.…”

Lattice-Boltzmann modeling of buoyancy-driven turbulent flows

“…It focuses on two gravity-driven configurations: the Rayleigh-Benard and Rayleigh-Taylor instabilities, since the properties of the flow solver are already validated in a large number of compressible flow configurations in the absence of gravity 2,16,17,19,24,25,70 .…”

“…This second option was found attractive, as it allows, for a reasonable cost 2 , to include an arbitrary number of additional scalar equations. Following recent successful applications to compressible [12][13][14][15][16][17] , atmospheric [18][19][20][21][22] or reactive flows [23][24][25] , the second option, often referred to as hybrid LBM is retained for this study. This works aims at investigating their applicability to buoyancy driven flows, such as those encountered in fire-related problems 26 .…”

Large eddy simulation of fire-induced flows using Lattice-Boltzmann methods

“…On the other hand, Lattice Boltzmann Methods (LBM) appear as an attractive alternative to the classical Navier-Stokes solvers due to their lower computational cost, their capacities for massively parallel computing and the ease to deal with complex geometries using multi-level Cartesian grids [24]. These methods have been successfully applied to different classes of problems, including compressible flows [25][26][27][28][29][30], atmospheric flows [31][32][33][34][35], reactive flows [36][37][38][39] and, recently, to buoyancydriven flows encountered in the far field of plumes [40].…”