Study of Wall Effects on Thermal Charging Efficiency of a Packed Bed by Using a Data-Driven Darcy's Equation

Abstract

A packed bed of rocks using air as the heat transfer fluid is a promising large-scale thermal energy storage technology for low-cost pumped thermal electricity storage. When the gas seepage velocity is small, with the use of Darcy's equation, gas flow through porous media is a parabolic PDE problem, whose numerical solution is not computationally demanding. The Forchheimer or Ergun equations have to be used, when the form drag under increased velocity becomes comparable with the surface shears. The Forchheimer equation introduces nonlinear pressure–velocity coupling issue that needs to be iteratively solved and hence is computationally involving. To overcome the coupling issue, this paper proposes a data-driven tuning factor on the permeability parameter to account for the form drag, so that the Darcy's equation could still be employed and the problem maintains a parabolic PDE in the Forchheimer regime for efficient computational speed. It was found that the tuning factor only needs to correlate to the Reynolds number and has good extrapolation ability. Furthermore, wall effects on thermal charging efficiency were analyzed by employing the tuned Darcy's equation. It was found that there is linear relationship between the reduced pressure drops of a packed bed and increased charging time due to wall channeling effects.