Natural convection heat transfer modeling by the cascaded thermal lattice Boltzmann method

Sharma, Keerti Vardhan; Straka, Róbert; Tavares, Frederico W.

doi:10.1016/j.ijthermalsci.2018.08.033

Cited by 19 publications

(12 citation statements)

References 48 publications

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“…Discussion on the state of the art From an application point-of-view, there is a wide range of physical phenomena which can be described by a form of the advection-diffusion-reaction equation. Models based on the LBM were developed for processes such as multicomponent reaction [1], combustion [2], solid and fluid dissolution related to underground CO 2 storage [3,4], crystallization and melting [5,6], Joule heating in electro-osmotic flows [7] and heat transfer [8][9][10][11][12][13][14][15][16][17][18]. Selected studies involving the use of LBM are listed below to present both the scope of modelling approaches, and applicability of the concepts discussed in this work.…”

Section: Introductionmentioning

confidence: 99%

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Revisiting the second-order convergence of the lattice Boltzmann method with reaction-type source terms

Gruszczyński¹,

Dzikowski²,

Łaniewski-Wołłk³

2021

Preprint

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This study derives a method to consistently recover the second-order convergence of the lattice Boltzmann method (LBM), which is frequently degraded by the improper discretisation of required source terms. The work focuses on advection-diffusion models in which the source terms are dependent on the intensity of transported fields. Such terms can be observed in reaction-type equations used for example in heat and mass transfer problems or multiphase flows. The main findings are applicable to a wide range of formulations within the LBM framework. All considered source terms are interpreted as contributions to the zeroth-moment of the distribution function. These account for sources in a scalar field, such as density, concentration, temperature or a phase field. In addition to this, certain immersed boundary methods can be interpreted as a source term in their formulation, highlighting a further application for this work.This paper makes three primary contributions to the current state-of-the-art. Firstly, it identifies the differences observed between the ways source terms are included in the LBM schemes present in the literature. The algebraic manipulations are explicitly presented in this paper to clarify the differences observed, and identify their origin. Secondly, it derives in full detail, the implicit relation between the value of the transported macroscopic field, and the sum of the LBM densities. This relation is shown in the paper to be a crucial ingredient for preserving the second-order convergence in the case of complex source terms. Moreover, the derived relation is valid for any source term discretization scheme, and three equivalent forms of the second-order accurate collision operator are presented. Finally, closed form solutions of this implicit relation are shown for a variety of common models, including general linear and second order terms; population growth models, such as the Logistic or Gompertz model; and Allen-Cahn Equation.The second-order convergence of the proposed LBM schemes is verified on both linear and non-linear source terms. Commonly used diffusive and acoustic scalings are discussed, and their pitfalls are identified. Moreover, for a simplified case, the competing errors are shown visually with isolines of error in the space of spatial and temporal resolutions.

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Section: Introductionmentioning

confidence: 99%

“…Arguably, the most widely explored application of the advection-diffusion LBM is found in coupled flow-heat transfer problems [8][9][10][11][12][13][14][15][16][17][18]. To model the underlying physics, a two-population approach is frequently used.…”

Section: Introductionmentioning

confidence: 99%

Revisiting the second-order convergence of the lattice Boltzmann method with reaction-type source terms

Gruszczyński¹,

Dzikowski²,

Łaniewski-Wołłk³

2021

Preprint

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“…In a fully coupled double distribution function approach, a second distribution function evolving between the same lattice nodes, at the same timesteps as the hydrodynamic one, is introduced to simulate the evolution of the energy field [15]. Due to tight coupling, many benchmarks published for this type of LBM models are restricted to Pr ≤ 100 [16][17][18] or Pr 1 [15,[19][20][21][22][23][24][25][26][27][28][29][30][31][32][33]. Limits of this way of modelling, are explored in the current paper.…”

mentioning

confidence: 99%

“…To solve the advection-diffusion equations, a lower order lattices like D2Q H 5 [24][25][26]28] and D3Q H 7 [31,33,[44][45][46][47][48][49] are frequently used. However, to properly recover complex thermal flows (e.g.…”

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confidence: 99%

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A comparative study of 3D Cumulant and Central Moments lattice Boltzmann schemes with interpolated boundary conditions for the simulation of thermal flows in high Prandtl number regime

Gruszczyński,

Łaniewski-Wołłk

2022

Preprint

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Thermal flows characterized by high Prandtl number are numerically challenging as the transfer of momentum and heat occurs at different time scales. To account for very low thermal conductivity and obey the Courant-Friedrichs-Lewy condition, the numerical diffusion of the scheme has to be reduced. As a consequence, the numerical artefacts are dominated by the dispersion errors commonly known as wiggles. In this study, we explore possible remedies for these issues in the framework of lattice Boltzmann method by means of applying novel collision kernels, lattices with large number of discrete velocities, namely D3Q27, and a second-order boundary conditions.For the first time, the cumulant-based collision operator, is utilised to simulate both the hydrodynamic and the thermal field. Alternatively, the advected field is computed using the central moments' collision operator. Different relaxation strategies have been examined to account for additional degrees of freedom introduced by a higher order lattice.To validate the proposed kernels for a pure advection-diffusion problem, the numerical simulations are compared against analytical solution of a Gaussian hill. The structure of the numerical dispersion is shown by simulating advection and diffusion of a square indicator function. Next, the influence of the interpolated boundary conditions on the quality of the results is measured in the case of the heat conduction between two concentric cylinders. Finally, a study of steady forced heat convection from a confined cylinder is performed and compared against a Finite Element Method solution.It has been found, that the relaxation scheme of the advected field must be adjusted to profit from lattice with a larger number of discrete velocities, like D3Q27. Obtained results show clearly that it is not sufficient to assume that only the first-order central moments/cumulants contribute to solving the macroscopic advection-diffusion equation. In the case of central moments, the beneficial effect of the two relaxation time approach is presented.

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Experimental Studies of Heat Transfer Under Natural Convection in Heat Pipe Insulated with Vacuum Chamber

Rai

Pandey

Chaube

2021

Lecture Notes in Mechanical Engineering

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Natural convection heat transfer modeling by the cascaded thermal lattice Boltzmann method

Cited by 19 publications

References 48 publications

Revisiting the second-order convergence of the lattice Boltzmann method with reaction-type source terms

Revisiting the second-order convergence of the lattice Boltzmann method with reaction-type source terms

A comparative study of 3D Cumulant and Central Moments lattice Boltzmann schemes with interpolated boundary conditions for the simulation of thermal flows in high Prandtl number regime

Experimental Studies of Heat Transfer Under Natural Convection in Heat Pipe Insulated with Vacuum Chamber

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