Efficient simulation of non-classical liquid–vapour phase-transition flows: a method of fundamental solutions

Rana, Anirudh Singh; Saini, Sonu; Chakraborty, Suman; Lockerby, Duncan A.; Sprittles, James E.

doi:10.1017/jfm.2021.405

Cited by 13 publications

(12 citation statements)

References 80 publications

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“…Besides, the coupled constitutive relations theory was developed to capture the remarkable rarefaction effects at small scales in the liquid–vapour phase transition processes (Rana et al. 2021). Meanwhile, the rarefaction effects in a head-on collision of two identical droplets are investigated via various lattice Boltzmann models with different degrees of precision (Chen et al.…”

Section: Numerical Simulations and Analysismentioning

confidence: 99%

“…How to overcome these limitations is a core problem in physical modelling (Gurtin & Voorhees 1996; Vilar & Rubi 2001; Schweizer, Öttinger & Savin 2016; Rana et al. 2021).…”

Section: Numerical Simulations and Analysismentioning

confidence: 99%

“…More recently, in Struchtrup & Frezzotti (2022), a set of 26 moment equations for the Enskog-Vlasov equation has been derived by using the Grad moment method, which provides a computationally efficient and functionally unified approach for ideal and non-ideal fluid flows far from equilibrium. Besides, the coupled constitutive relations theory was developed to capture the remarkable rarefaction effects at small scales in the liquid-vapour phase transition processes (Rana et al 2021). Meanwhile, the rarefaction effects in a head-on collision of two identical droplets are investigated via various lattice Boltzmann models with different degrees of precision (Chen et al 2022b).…”

Section: Multi-scale Model and Trans-scale Abilitymentioning

confidence: 99%

“…Theoretical analysis is usually limited to cases with numerous simplifying assumptions and generalizations, such as the local equilibrium assumption, given small deviations from the equilibrium state and linear relationship between fluxes and forces. How to overcome these limitations is a core problem in physical modelling (Gurtin & Voorhees 1996;Vilar & Rubi 2001;Schweizer, Öttinger & Savin 2016;Rana et al 2021).…”

Section: Multi-scale Model and Trans-scale Abilitymentioning

confidence: 99%

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Discrete Boltzmann multi-scale modelling of non-equilibrium multiphase flows

Gan

Xu²,

Lai³

et al. 2022

J. Fluid Mech.

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The aim of this paper is twofold: the first aim is to formulate and validate a multi-scale discrete Boltzmann method (DBM) based on density functional kinetic theory for thermal multiphase flow systems, ranging from continuum to transition flow regime; the second aim is to present some new insights into the thermo-hydrodynamic non-equilibrium (THNE) effects in the phase separation process. Methodologically, for bulk flow, DBM includes three main pillars: (i) the determination of the fewest kinetic moment relations, which are required by the description of significant THNE effects beyond the realm of continuum fluid mechanics; (ii) the construction of an appropriate discrete equilibrium distribution function recovering all the desired kinetic moments; (iii) the detection, description, presentation and analysis of THNE based on the moments of the non-equilibrium distribution ( $f-f^{(eq)}$ ). The incorporation of appropriate additional higher-order thermodynamic kinetic moments considerably extends the DBM's capability of handling larger values of the liquid–vapour density ratio, curbing spurious currents, and ensuring mass/momentum/energy conservation. Compared with the DBM with only first-order THNE (Gan et al., Soft Matt., vol. 11 (26), 2015, pp. 5336–5345), the model retrieves kinetic moments beyond the third-order super-Burnett level, and is accurate for weak, moderate and strong THNE cases even when the local Knudsen number exceeds $1/3$ . Physically, the ending point of the linear relation between THNE and the concerned physical parameter provides a distinct criterion to identify whether the system is near or far from equilibrium. Besides, the surface tension suppresses the local THNE around the interface, but expands the THNE range and strengthens the THNE intensity away from the interface through interface smoothing and widening.

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Section: Numerical Simulations and Analysismentioning

confidence: 99%

“…How to overcome these limitations is a core problem in physical modelling (Gurtin & Voorhees 1996; Vilar & Rubi 2001; Schweizer, Öttinger & Savin 2016; Rana et al. 2021).…”

Section: Numerical Simulations and Analysismentioning

confidence: 99%

Section: Multi-scale Model and Trans-scale Abilitymentioning

confidence: 99%

Section: Multi-scale Model and Trans-scale Abilitymentioning

confidence: 99%

See 2 more Smart Citations

Discrete Boltzmann multi-scale modelling of non-equilibrium multiphase flows

Gan

Xu²,

Lai³

et al. 2022

J. Fluid Mech.

View full text Add to dashboard Cite

show abstract

“…If the boundary conditions are on a closed surface and the domain external to it (e.g. when calculating the evaporation from a drop [2], or the drag on a particle [3,4,5]), the origins of the fundamental solutions are located inside the enclosed volume; see Fig. 1.…”

Section: Introductionmentioning

confidence: 99%

Integration over discrete closed surfaces using the Method of Fundamental Solutions

Lockerby

2022

Engineering Analysis with Boundary Elements

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A second-order constitutive theory for polyatomic gases: theory and applications

Rana

Barve

2023

J. Fluid Mech.

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In the classical irreversible thermodynamics (CIT) framework, the Navier–Stokes–Fourier constitutive equations are obtained so as to satisfy the entropy inequality, by and large assuming that the entropy flux is equal to the heat flux over the temperature. This article is focused on the derivation of second-order constitutive equations for polyatomic gases; it takes the basis of CIT, but most importantly, allows up to quadratic nonlinearities in the entropy flux. Mathematical similarities between the proposed model and the classic Stokes–Laplace equations are exploited so as to construct analytic/semi-analytic solutions for the slow rarefied gas flow over different shapes. A set of second-order boundary conditions are formulated such that the model's prediction for the drag force is in excellent agreement with the experimental data over the whole range of Knudsen numbers. We have also computed the normal shock structure in nitrogen for Mach ${Ma} \lesssim 4$ . A very good agreement was observed with the kinetic theory, as well as with the experimental data.

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Efficient simulation of non-classical liquid–vapour phase-transition flows: a method of fundamental solutions

Abstract: Abstract

Cited by 13 publications

References 80 publications

Discrete Boltzmann multi-scale modelling of non-equilibrium multiphase flows

Discrete Boltzmann multi-scale modelling of non-equilibrium multiphase flows

Integration over discrete closed surfaces using the Method of Fundamental Solutions

A second-order constitutive theory for polyatomic gases: theory and applications

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