Development and validation of a local thermal non-equilibrium model for high-temperature thermal energy storage in packed beds

Abstract

High-temperature thermal energy storage (TES) in packed beds is gaining interest for industrial energy recovery. The wide range of temperature distributions causes significant variations in thermophysical properties of the fluid and solid phases, leading to inaccuracies of classical TES models and heat transfer correlations. The objective of this work is to develop and validate a detailed but pragmatic model accounting for high-temperature effects. Based on a literature survey spanning over several communities interested in high- temperature porous media, we propose a generic local thermal non-equilibrium model for granulate porous media accounting for conservation of mass, momentum and energy (two-equation temperature model). The effective parameters needed to inform the model are the effective thermal conductivities of the different phases and the heat transfer coefficient. An experimental-numerical inverse analysis method is employed to determine these parameters. A dedicated experimental facility has been designed and built to study a model granulate made of glass bead of 16 mm diameter. Experiments are conducted using the Transient Single-Blow Technique (TSBT) by passing hot air (ranging from 293 K to 630 K) through cold particles at various mass flow rates, covering a Reynolds number range of 58 to 252. The new model was implemented in the Porous material Analysis Toolbox based on OpenFoam (PATO) used to compute the transient temperature fields. Two optimization algorithms were employed to determine the parameters by minimizing the error between experimental and simulated temperatures: a Latin Hypercube Sampling (LHS) method, and a local optimization method Adaptive nonlinear least-squares algorithm (NL2SOL). The results indicate that the value of heat transfer coefficient ℎ�� in the two-equation model falls in the range of 1.0 × 104 ∼ 1.93× 104 W/(m3 K) under the given conditions. The axial dispersion gas thermal conductivity was found to be around 5.9 and 67.1 times higher than the gas thermal conductivity at Peclet numbers of around 55 and 165, respectively. Furthermore, two improved correlations of Nusselt number (���� = 2+1.54����(�� )0.6�� ��(�� )1∕3) and of axial dispersion gas thermal conductivity (��������,∥ = 0.00053����(�� )2.21�� ��(�� ) ⋅ ���� ) are proposed and validated for a range of Reynolds number from 58 to 252. The overall approach is therefore validated for the model granulate of the study, opening new perspectives towards more precise design and monitoring of high-temperature TES systems.