Lattice Boltzmann kinetic modeling and simulation of thermal liquid–vapor system

Gan, Yanbiao; Xu, Aiguo; Zhang, Guangcai; Wang, Junqi; Yu, Xijun; Yang, Yang

doi:10.1142/s0129183114410022

Cited by 3 publications

(2 citation statements)

References 29 publications

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“…Moreover, the right column of Figure 17 revealed that the local maxima in the temperature profiles are located in the liquid-vapour interface regions. In these regions, where large density gradients are present, there is an unphysical heat generation process, due to the spurious velocity, a numerical effect that plagues the LB models [5,88,89,90,91,92,93,94,95,96,97]. This numerical effect has been succesfully reduced in this paper by using the fifth order weighted essentially non-oscillatory (WENO-5) numerical scheme.…”

Section: Phase Separation Dynamics Between Heat Extracting Parallel P...mentioning

confidence: 99%

Two-dimensional off-lattice Boltzmann model for van der Waals fluids with variable temperature

Busuioc

Ambruş

Biciusca

et al. 2020

Computers & Mathematics with Applications

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We develop a two-dimensional Lattice Boltzmann model for liquid-vapour systems with variable temperature. Our model is based on a single particle distribution function expanded with respect to the full-range Hermite polynomials. In order to ensure the recovery of the hydrodynamic equations for thermal flows, we use a fourth order expansion together with a set of momentum vectors with 25 elements whose Cartesian projections are the roots of the Hermite polynomial of order Q = 5. Since these vectors are off-lattice, a fifth-order projection scheme is used to evolve the corresponding set of distribution functions. A fourth order scheme employing a 49 point stencil is used to compute the gradient operators in the force term that ensures the liquid-vapour phase separation and diffuse reflection boundary conditions are used on the walls. We demonstrate at least fourth order convergence with respect to the lattice spacing in the contexts of shear and longitudinal wave propagation through the van der Waals fluid. For the planar interface, fourth order convergence can be seen at small enough lattice spacings, while the effect of the spurious velocity on the temperature profile is found to be smaller than 1.0%, even when T w 0.7 T c . We further validate our scheme by considering the Laplace pressure test. Galilean invariance is shown to be preserved up to second order with respect to the background velocity. We further investigate the liquid-vapour phase separation between two parallel walls kept at a constant temperature T w smaller than the critical temperature T c and discuss the main features of this process.

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Section: Phase Separation Dynamics Between Heat Extracting Parallel P...mentioning

confidence: 99%

Two-dimensional off-lattice Boltzmann model for van der Waals fluids with variable temperature

Busuioc

Ambruş

Biciusca

et al. 2020

Computers & Mathematics with Applications

View full text Add to dashboard Cite

show abstract

“…Distance concepts in the phase space or its sub-spaces are used to describe the difference and similarity of behavior. Up to now, DBM has been used in various multiphase flow systems, such as hydrodynamic instabilities [36,[40][41][42][43][44], compressible flows under impact [35][36][37][38], non-equilibrium combustion [45][46][47], non-equilibrium phase separation [48][49][50][51], and droplets collision [52]. For example, Gan, et al [48] used a DBM to study the Hydrodynamic Non-Equilibrium (HNE) and TNE effects in phase separation process.…”

Section: Introductionmentioning

confidence: 99%

Thermodynamic non-equilibrium effects in bubble coalescence: A discrete Boltzmann study

Sun,

Gan,

et al. 2022

Preprint

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The Thermodynamic Non-Equilibrium (TNE) effects in the coalescing process of two initially static bubbles under thermal conditions are investigated by a Discrete Boltzmann Model (DBM).The spatial distributions of the typical none-quilibrium quantity, i.e., the Non-Organized Momentum Fluxes (NOMF) during evolutions are investigated in detail. The density-weighted statistical method is used to highlight the relationship between the TNE effects and the morphological or kinetics characteristics of bubble coalescence. It is found that the xx-component and yy-component of NOMF are anti-symmetrical; the xy-component changes from an anti-symmetric internal and external double quadrupole structure to an outer octupole structure during the coalescing process.More importantly, the evolution of the averaged xx-component of NOMF provides two characteristic instants, which divide the non-equilibrium process into three stages. The first instant corresponds to the moment when the mean coalescing speed gets the maximum and at this time the ratio of minor and major axes is about 1/2. The second instant corresponds to the moment when the ratio of minor and major axes gets 1 for the first time. It is interesting to find that the three quantities, TNE intensity, acceleration of coalescence and negative slope of boundary length, show a high degree of correlation and attain their maxima simultaneously. Surface tension and heat conduction accelerate the process of bubble coalescence while viscosity delays it. Both surface tension and viscosity enhance the global non-equilibrium intensity, whereas heat conduction restrains it. These TNE features and findings present some new insights into the kinetics of bubble coalescence.

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Progess of discrete Boltzmann modeling and simulation of combustion system

Xu¹,

Zhang²,

Ying³

2015

Acta Phys. Sin.

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Detonation is a kind of self-propagating supersonic combustion where the chemical reaction is rapid and violent under an extreme condition. The leading part of a detonation front is pre-shocked by a strong shock wave propagating into the explosive and triggering chemical reaction. The combustion system can be regarded as a kind of chemical reactive flow system. Therefore, the fluid modeling plays an important role in the studies on combustion and detonation phenomena. The discrete Boltzmann method (DBM) is a kind of new fluid modeling having quickly developed in recent thirty years. In this paper we review the progress of discrete Boltzmann modeling and simulation of combustion phenomena. Roughly speaking, the discrete Boltzmann models can be further classified into two categories. In the first category the DBM is regarded as a kind of new scheme to numerically solve partial differential equations, such as the Navier-Stokes equations, etc. In the second category the DBM works as a kind of novel mesoscopic and coarse-grained kinetic model for complex fluids. The second kind of DBM aims to probe the trans- and supercritical fluid behaviors or to study simultaneously the hydrodynamic non-equilibrium (HNE) and thermodynamic non-equilibrium (TNE) behaviors. It has brought significant new physical insights into the systems and promoted the development of new methods in the fields. For example, new observations on fine structures of shock and detonation waves have been obtained; The intensity of TNE has been used as a physical criterion to discriminate the two stages, spinodal decomposition and domain growth, in phase separation; Based on the feature of TNE, some new front-tracking schemes have been designed. Since the goals are different, the criteria used to formulate the two kinds of models are significantly different, even though there may be considerable overlaps between them. Correspondingly, works in discrete Boltzmann modeling and simulation of combustion systems can also be classified into two categories in terms of the two kinds of models. Up to now, most of existing works belong to the first category where the DBM is used as a kind of alternative numerical scheme. The first DBM for detonation [Yan, et al. 2013 Front. Phys. 8 94] appeared in 2013. It is also the first work aiming to investigate both the HNE and TNE in the combustion system via DBM. In this review we focus mainly on the development of the second kind of DBM for combustion, especially for detonation. A DBM for combustion in polar-coordinates [Lin, et al. 2014 Commun. Theor. Phys. 62 737] was designed in 2014. It aims to investigate the nonequilibrium behaviors in implosion and explosion processes. Recently, the multiple-relaxation-time version of DBM for combustion [Xu, et al. 2015 Phys. Rev. E 91 043306] was developed. As an initial application, various non-equilibrium behaviors around the detonation wave in one-dimensional detonation process were preliminarily probed. The following TNE behaviors, exchanges of internal kinetic energy between different displacement degrees of freedom and between displacement and internal degrees of freedom of molecules, have been observed. It was found that the system viscosity (or heat conductivity) decreases the local TNE, but increases the global TNE around the detonation wave. Even locally, the system viscosity (or heat conductivity) results in two competing trends, i.e. to increase and decrease the TNE effects. The physical reason is that the viscosity (or heat conductivity) takes part in both the thermodynamic and hydrodynamic responses to the corresponding driving forces. The ideas to formulate DBM with the smallest number of discrete velocities and DBM with flexible discrete velocity model are presented. As a kind of new modeling of combustion system, mathematically, the second kind of DBM is composed of the discrete Boltzmann equation(s) and a phenomenological reactive function; physically, it is equivalent to a hydrodynamic model supplemented by a coarse-grained model of the TNE behaviors. Being able to capture various non-equilibrium effects and being easy to parallelize are two features of the second kind of DBM. Some more realistic DBMs for combustion are in progress. Combustion process has an intrinsic multi-scale nature. Typical time scales cover a wide range from 10-13 to 10-3 second, and typical spatial scales cover a range from 10-10 to 1 meter. The hydrodynamic modeling and microscopic molecular dynamics have seen great achievements in combustion simulations. But for problems relevant to the mesoscopic scales, where the hydrodynamic modeling is not enough to capture the nonequilibrium behaviors and the molecular dynamics simulation is not affordable, the modeling and simulation are still keeping challenging. Roughly speaking, there are two research directions in accessing the mesoscopic behaviors. One direction is to start from the macroscopic scale to smaller ones, the other direction is to start from the microscopic scale to larger ones. The idea of second kind of DBM belongs to that of the first direction. It will contribute more to the studies on the nonequilibrium behaviors in combustion phenomena.

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Lattice Boltzmann kinetic modeling and simulation of thermal liquid–vapor system

Cited by 3 publications

References 29 publications

Two-dimensional off-lattice Boltzmann model for van der Waals fluids with variable temperature

Two-dimensional off-lattice Boltzmann model for van der Waals fluids with variable temperature

Thermodynamic non-equilibrium effects in bubble coalescence: A discrete Boltzmann study

Progess of discrete Boltzmann modeling and simulation of combustion system

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