A spectral‐element discontinuous Galerkin thermal lattice Boltzmann method for conjugate heat transfer applications. (29th May 2016)

• Record Type: Journal Article
• Authors: Patel, Saumil; Min, Misun; Lee, Taehun
• Is Part Of: International journal for numerical methods in fluids. Volume 82:Number 12(2016)
• Page Start: 932
• Page End: 952
• Publication Date: 2016-05-29
• Subjects: conjugate heat transfer -- spectral‐element method -- discontinuous Galerkin method -- Lattice Boltzmann method; Fluid dynamics -- Mathematics -- Periodicals; 532
• DOI: 10.1002/fld.4250
• Languages: English
• ISSNs: 0271-2091

Abstract

Summary: We present a spectral‐element discontinuous Galerkin thermal lattice Boltzmann method for fluid–solid conjugate heat transfer applications. Using the discrete Boltzmann equation, we propose a numerical scheme for conjugate heat transfer applications on unstructured, non‐uniform grids. We employ a double‐distribution thermal lattice Boltzmann model to resolve flows with variable Prandtl ( P r ) number. Based upon its finite element heritage, the spectral‐element discontinuous Galerkin discretization provides an effective means to model and investigate thermal transport in applications with complex geometries. Our solutions are represented by the tensor product basis of the one‐dimensional Legendre–Lagrange interpolation polynomials. A high‐order discretization is employed on body‐conforming hexahedral elements with Gauss–Lobatto–Legendre quadrature nodes. Thermal and hydrodynamic bounce‐back boundary conditions are imposed via the numerical flux formulation that arises because of the discontinuous Galerkin approach. As a result, our scheme does not require tedious extrapolation at the boundaries, which may cause loss of mass conservation. We compare solutions of the proposed scheme with an analytical solution for a solid–solid conjugate heat transfer problem in a 2D annulus and illustrate the capture of temperature continuities across interfaces for conductivity ratio γ > 1. We also investigate the effect of Reynolds ( R e ) and Grashof ( G r ) number on the conjugate heat transfer between a heat‐generating solid and a surrounding fluid. Steady‐state results are presented for R e = 5−40 and G r = 10 5 −10 6 . In each case, we discuss the effect of R e and G r on the heat flux (i.e. Nusselt number N u ) at the fluid–solid interface. Our results are validated against previous studies that employ finite‐difference and continuous spectral‐element methods to solve the Navier–Stokes equations. Copyright © 2016 John Wiley & Sons, Ltd. Abstract : This graphic shows isotherms for Gr = 10 6 in a horizontal annulus using the proposed spectral‐element discontinuous Galerkin thermal lattice Boltzmann method. Using the discrete Boltzmann equations for nearly incompressible, thermal flows, the spectral‐element discontinuous Galerkin thermal lattice Boltzmann method is able to solve fluid–solid conjugate heat transfer applications on unstructured, non‐uniform grids. Bounce‐back boundary conditions are imposed via the numerical flux formulation that arises because of the discontinuous Galerkin approach. This scheme does not require tedious extrapolation at the boundaries that may cause loss of mass conservation.