Optimization of Packed-Bed Energy Storage Systems Based on a Second Law Analysis

TL;DR

The paper addresses optimizing packed-bed sensible heat storage systems by quantifying exergy destruction through a second-law (entropy/exergy) analysis. It develops a macroscopic entropy and exergy transport framework for flow and heat transfer in porous media, derived from pore-scale equations, and applies this SLA within CFD to a PROMES-CNRS lab-scale test bed. Key findings include dominant boundary losses (exit and wall leakage) and significant internal losses near the thermocline, with an optimal tank aspect ratio around 0.75 and a truncated-cone geometry combined with an 8 mm particle size yielding exergy loss reductions from about 4.9% to 4.1%. The work demonstrates that integrating SLA with energy analysis provides a practical, design-oriented tool for improving the efficiency of energy storage systems.

Abstract

Packed-bed sensible heat storage (SHS) is important for balancing energy supply and demand over time. To improve the efficiency of a packed-bed SHS system through second law analysis (SLA), we developed macroscopic entropy and exergy transport equations for fluid flow and heat transfer in porous media based on microscopic transport equations. These equations enable us to identify where and how much exergy is destroyed. Using a packed-bed SHS system developed at the PROMES-CNRS laboratory as a test case, we demonstrated how to apply SLA to optimize an SHS system. Our analysis revealed that, in addition to exit and heat leakage losses at tank surfaces, thermal and solid conduction losses inside the tank significantly contribute to total loss in the studied SHS system. These internal losses occur close to the thermocline. However, their slower transport causes a delay in their emergence. The SLA suggests an optimal tank aspect ratio of D/H = 0.75, at which the total exergy loss coefficient reaches its minimum value when exit loss is not considered. As particle size decreases, the exergy loss coefficient also decreases due to enhanced heat transfer between the fluid and solid phases. The pressure loss for the studied SHS system is negligible. The SLA favors a truncated cone-shaped tank with a slightly larger upper surface. Through the SLA, the exergy loss coefficient is reduced from 4.9% for the original design to 4.1% for the optimized design. This study demonstrates that, when used in conjunction with energy analysis, the SLA is an effective tool for optimizing energy storage systems.

Figures (20)

• Figure 1: Schematic illustration of a packed-bed thermal store (a) and the corresponding two-dimensional axisymmetric computational domain.
• Figure 2: Time evolution of the HTF temperature at the center line. The numerical results of mesh A($20\times180$), B($30\times270$) and C($40\times360$) are compared.
• Figure 3: Time evolution of the HTF temperature at the center line. The numerical results are compared with the experimental results in hoffmannThermoclineThermalEnergy2016.
• Figure 4: Time evolution of the averaged HTF temperature at the top and bottom of the storage tank.
• Figure 5: Fluid temperature $T_f$ fields during charge ($0\mathrm{h}$-$3\mathrm{h}$) and discharge ($3\mathrm{h}$-$6\mathrm{h}$). The iso-surfaces of $T=465 \mathrm{K}$ (black lines) and $T=455 \mathrm{K}$ (white lines) are shown to indicate the location of the thermocline. The axis of the tank is indicated at $T=1\, h$