On the thermal entrance length of moderately dense gas-particle flows

TL;DR

This study investigates how particle clustering in moderately dense gas-particle flows affects the thermal entrance length, revealing that clustering can significantly increase it due to covariance effects, with a new closure model developed.

Contribution

The paper introduces a novel analysis of particle clustering effects on thermal entrance length and develops a closure model using Gene Expression Programming.

Findings

Clustering doubles or triples the thermal entrance length.

Covariance between volume fraction and temperature fluctuations is key.

Closure model accurately predicts effects across various conditions.

Abstract

The dissipative nature of heat transfer relaxes thermal flows to an equilibrium state that is devoid of temperature gradients. The distance to reach an equilibrium temperature -- the thermal entrance length -- is a consequence of diffusion and mixing by convection. The presence of particles can modify the thermal entrance length due to interphase heat transfer and turbulence modulation by momentum coupling. In this work, Eulerian--Lagrangian simulations are utilized to probe the effect of solids heterogeneity (e.g., clustering) on the thermal entrance length. For the moderately dense systems considered here, clustering leads to a factor of 2--3 increase in the thermal entrance length, as compared to an uncorrelated (perfectly mixed) distribution of particles. 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, closure is obtained for this term in a one-dimensional averaged two-fluid equation and is shown to be accurate under a wide range of flow conditions.