Modeling pseudo-turbulent heat flux in gas-solid heat transfer

Abstract

Flow past disperse solid particles or bubbles induces fluctuations in carrier fluid velocity, which correlate with temperature fluctuations in non-isothermal flows resulting in the pseudo-turbulent heat flux (PTHF). In the Eulerian-Eulerian (EE) two-fluid (TF) model, the transport of PTHF is shown to be an important contributor to the overall energy budget, and is modeled using a pseudo-turbulent thermal diffusivity (PTTD). The PTHF and PTTD were originally quantified using particle-resolved direct numerical simulation (PR-DNS) data, and correlations were developed over a range of solid volume fraction (0.1≤εs≤0.5) and mean slip Reynolds number (1≤Rem≤100) for a Prandtl number of 0.7. However, the original PTTD correlation diverges to infinity as the solid volume fraction goes to zero, which is physically unrealistic. This singular behavior is problematic for EE TF simulations at particle material fronts where solid volume fraction values can fall below the lower limit of existing data (εs=0.1) to zero in the pure carrier phase. In this work, additional PR-DNS data are reported for εs<0.1, and improved correlations are developed for the PTHF and PTTD. The new PTTD correlation is non-singular, and both the PTHF and PTTD decay exponentially to zero as the solid volume fraction approaches zero, which is physically reasonable. This improves prediction of PTHF transport in dilute flow using EE TF heat transfer simulations.