A three-dimensional fictitious domain method for direct numerical simulations of particle-laden flows with heat transfer

Abstract

In the present work, a three-dimensional fictitious domain method for particulate flows with heat transfer is proposed. For the case of fixed particle temperature, an iterative scheme for the temperature Lagrange multiplier is proposed, in order to determine its initial value and overcome the spurious oscillation of the explicit scheme at the initial time stage for different initial fluid and particle temperatures. Both explicit and implicit schemes are proposed for the solution of coupled fluid and solid temperature equations in the case of freely evolving particle temperature. The implicit scheme is suited to the case of large density ratios, specific heat ratios, or thermal conductivity ratios. Our method for the case of fixed particle temperature is verified via the test problems of a stationary hot sphere heating the surrounding quiescent fluid, a fixed sphere, and spheroid, respectively, in uniform flow, and sedimentation of a sphere and spheroid, respectively, in a vertical channel. We propose a new correlation of particle Nusselt number for an isolated sphere in a relatively small domain. Our code for the case of varying particle temperatures is verified via the effective thermal conductivity of a motionless sphere and the rising of a catalyst particle in an enclosure. Our method is applied to the sedimentation of a sphere at different Grashof numbers, specific heat ratios, and conductivity ratios. In addition, some preliminary results on heat transfer in turbulent channel flows laden with neutrally buoyant spherical and spheroidal particles, respectively, from fully resolved simulations with our method are reported.