A Spectral Element Discontinuous Galerkin Thermal lattice Boltzmann method for Conjugate Heat Transfer applications

We present a spectral-element discontinuous Galerkin thermal lattice Boltzmann method (SEDG-TLBM) for fluid-solid conjugate heat transfer applications. In this work, we revisit the discrete Boltzmann equation (DBE) for nearly incompressible flows and propose a numerical scheme for conjugate heat transfer applications on unstructured, non-uniform mesh distributions. We employ a double-distribution function thermal lattice Boltzmann model to resolve flows with variable Prandtl (Pr) number. Based upon it’s finite element heritage ̋, the SEDG discretization provides an effective means to model and investigate thermal transport in applications with complex geometries. In particular, we numerically investigate the effect of Reynolds (Re) number on the conjugate heat transfer around a circular cylinder with ∗Corresponding Author Email addresses: [email protected] (Saumil S. Patel), [email protected] (Misun Min), [email protected] (Kalu Chibueze Uga), [email protected] (Taehun Lee ) Preprint submitted to Elsevier January 22, 2015 volumetric heat source. 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 (GLL) quadrature nodes. Thermal and hydrodynamic bounce-back boundary conditions are imposed via the numerical flux formulation which arises due to the discontinuous Galerkin approach. As a result, our scheme does not require tedious extrapolation at the boundaries which may cause loss of mass conservation. Steady-state results are presented for Re = 5− 40. In each case, we discuss the effect of Re on the heat flux (i.e. Nusselt number Nu) at the cylinder surface (i.e. fluid-solid interface). In addition, the influence of the Re number on the variation of the temperature distribution within the cylinder is studied. Our results are validated against the Navier-Stokes spectral-element based computational fluid dynamics (CFD) solver known as Nek5000.