(407g) Heat Transfer in Gas-Solid Flow: Model Development Using Particle-Resolved Direct Numerical Simulation

Heat transfer is important in many gas-solid flow applications such as fluidized beds that are used for biomass fast pyrolysis or CO2 capture using dry sorbents. Current computational fluid dynamics models solve evolution equations for the mean fluid and solid temperature that contain unclosed terms such as the average gas-solid heat transfer rate that require modeling.
We use particle-resolved direct numerical simulations (PR-DNS) of gas-solid heat transfer in thermally fully developed steady flow past fixed particle assemblies to quantify the average gas-solid heat flux and other unclosed terms in homogeneous gas-solid flows, and to propose models for them. Existing computational fluid dynamics models represent only the mean fluid temperature even when solving reacting gas-solid flow problems with Arrhenius-type gas-phase reactions. However, it is well known from single-phase turbulent reactive flow studies that the reaction rate evaluated at the mean temperature is a poor model for the average reaction rate in Arrhenius-type reactions due to the high level of temperature fluctuations resulting from turbulence. Therefore, the transport equation for the probability density function of composition (species mass fractions and temperature) is used to model such turbulent reacting flows (Pope, PECS 1985, Haworth, PECS, 2010). Recently, Tenneti & Subramaniam (Annu Rev Fluid Mechanics 2014) have shown using PR-DNS of gas-solid flow that high levels of pseudo-turbulent velocity fluctuations are also found in gas-solid flows where the particles and gas have a non-zero mean slip velocity. This recent finding motivates us to develop a transport equation for the probability density function of temperature in gas-solid flow. Starting from the transport equation for the velocity-temperature PDF in gas-solid flow, we identify the unclosed terms in this equation. We use PR-DNS data from thermally fully developed flow simulations of gas-solid heat transfer in steady flow past fixed particle assemblies to quantify the probability density function of temperature in gas-solid flow.