Conjugate heat transfer with the entropic lattice Boltzmann method

Abstract

A conjugate heat-transfer model is presented based on the two-population entropic lattice Boltzmann method. The present approach relies on the extension of Grad's boundary conditions to the two-population model for thermal flows, as well as on the appropriate exact conjugate heat-transfer condition imposed at the fluid-solid interface. The simplicity and efficiency of the lattice Boltzmann method (LBM), and in particular of the entropic multirelaxation LBM, are retained in the present approach, thus enabling simulations of turbulent high Reynolds number flows and complex wall boundaries. The model is validated by means of two-dimensional parametric studies of various setups, including pure solid conduction, conjugate heat transfer with a backward-facing step flow, and conjugate heat transfer with the flow past a circular heated cylinder. Further validations are performed in three dimensions for the case of a turbulent flow around a heated mounted cube.

Lattice Boltzmann advection-diffusion model for conjugate heat transfer in heterogeneous media

“…20, one can observe a large recirculating zone right in front of the cube in the form of a horseshoe. This observation is in agreement with reported results from both LES [43] and ELBM [26] simulations. The turbulent velocity field is further assessed through the 295 average stream-wise velocity and the streamwise and spanwise diagonal components of the Reynolds stress tensor in Fig.…”

“…One approach to alleviate this restriction is to include an appropriate correction term at interfaces. This approach has been successfully applied to conjugate heat transfer in heterogeneous media [22,23,24,25,26]. The main shortcomings of this approach are practicality and limited applicability to more general cases.…”

Grid refinement for entropic lattice Boltzmann models

“…For the g-populations, however, this is no more valid, since the non-equilibrium part depends on two independent relaxation parameters. This can be verified by deriving an analytical expression for the nonequilibrium g-populations through Chapman-Enskog expansion, as in [25]. The non-equilibrium part of the gpopulation depends on the higher-order, non-conserved moments as…”

Semi-Lagrangian lattice Boltzmann model for compressible flows on unstructured meshes

“…where f eq i , g eq i are equilibrium parts computed from (10) and (14) to (17); f (1) i , g (1) i are nonequilibrium parts; and ρ tgt , u tgt , and T tgt are target values which need to be specified. The nonequilibrium parts are obtained based on the Grad's approximation and using the general formula (14) to (17) with the nonequilibrium moments given in Table II [14,30] P (1) αβ…”