Flow Characterization in Triply-Periodic-Minimal-Surface (TPMS) based Porous Geometries: Part 2 – Heat Transfer

Abstract

A complex heat transfer takes place between the solid matrix and the fluid within its pores and generally two types of assumptions are widely used for macro-scale modelling of heat transfer: local thermal equilibrium (LTE) when the solid and fluid phases are at the same temperature, and local thermal non-equilibrium (LTNE) when the solid and fluid phases are at different temperatures. A direct numerical simulation has been performed for heat transfer in Triply-Periodic-Minimal-Surface (TPMS) lattices, with identical void fraction and unit-cell size, but different geometrical shape, namely Diamond, I-WP, Primitive, and Gyroid. Further, each lattice derived into three different types of porous structures by designing second sub-volume as solid (Type 1), fluid (Type 2), and microporous zones (Type 3). The heat transfer in the hydrodynamically and thermally developed flow in a square mini-channel filled with these porous inserts for a range of Reynolds number \(0.01<Re<100\) and \(Pr=7\) is investigated. The temperature distributions, solid and fluid Nusselt numbers on the external walls and also heat transfer coefficient (pore-scale) in the internal walls, and quantitative departure from local thermal equilibrium (LTE) assumption for twelve different porous media are compared, and the effect of porous morphology, effective porosity, and flow rate on them are examined. Out of twelve porous media, the maximum and minimum effective Nusselt number on the external walls are obtained for Primitive lattice of Type 3 and Type 2 as 407.7 and 6.2, respectively. Similarly, pore-scale Nusselt number (on the internal walls) has maximum and minimum lattice of Type 1 and Type 3 as 64.2 and 7.6, respectively. As a general observation, the percentage deviation from LTE assumption is found to be maximum for Type 1 and 3 lattices, and minimum for Type 2 lattices throughout the range of flow rate. Primitive lattice with Type 1 treatment shows maximum deviation from LTE assumption, whereas Gyroid lattice of Type 2 treatment shows the minimum deviation.

Validation of Local Thermal Equilibrium (LTE) in Porous Media for Variation in Flow rate and Permeability: Transient Analysis

“…The more accurate model is the usage of two -phase energy equation, also known as heterogeneous energy equation , which considers the solid phase and the fluid phase at thermal non-equilibrium, and which is close to the actual situations, however, it is typically complex and computationally expensive to solve. Some researchers have also compared the extent of thermal equilibrium between the solid and fluid phases for variation in parameters , such as flow rate, porosity, permeability [13]. The numerical simulation of forced convection incompressible flow through porous media using two-phase equation model for local thermal non-equilibrium (LTNE) is used for the energy equation to solve the temperature field s [11,12].…”