The effect of particle clustering on the thermal entrance length in moderately dense gas-solid flows

We perform highly-resolved Eulerian--Lagrangian simulations of moderately dense, gas-solid flows to study the thermal entrance length. We show that strong momentum coupling between the phases results in the generation of dense particle clusters that leads to a 2–3 fold increase in the thermal entrance length, as compared to a uniform (perfectly mixed) distribution. The observed increase is found to be primarily due to the covariance between volume fraction and temperature fluctuations, referred to as the fluid drift temperature. Using scaling arguments and Gene Expression Programming, model closure is obtained in the context of a one-dimensional averaged two-fluid equation.