Analytical and numerical sizing of phase change material thickness for rectangular encapsulations in hybrid thermal storage tanks for residential heat pump systems

Thermal energy storage is essential to the operation of many systems. It plays a vital role in many renewable and CO2-reducing technologies which have a mismatch in time between when thermal energy is available and required. Water is the most commonly used thermal storage medium in many applications, however, for systems with a small temperature operating range, large storage volumes may be required since the energy storage capacity of water is proportional to the temperature range. In contrast, phase change materials (PCMs) can maintain high energy capacity under limited temperature conditions, but they typically have low thermal conductivities which results in slow melting/solidification rates. As such, careful design of the encapsulation geometry is required to take advantage of phase change thermal storage. Systems using phase change materials must ensure complete melting, and the encapsulation thickness must be designed according the system needs. Models of hybrid storage tanks employing both water and PCM are investigated, with PCM encapsulations embedded in water. This study uses a novel application of analytical formulations of 1-D melting to size rectangular PCM encapsulation to match the requirements of a residential heat pump system. With boundary conditions that reflect the heat pump and storage characteristics, the proposed analytical solution links encapsulation thickness to system requirements. The analytical formulation is derived for encapsulation thickness in terms of heat pump rating, temperature differential, storage material, and storage volume. The solution was verified through system-level numerical simulations using TRNSYS and an in-house enthalpy-porosity modeling tools detailed in the paper. The verifications have shown a good agreement, and the melt thickness predictions were within 4% between both models. The study proposes using the methodology as a standard for designing hybrid water-phase change material thermal storage for heat pumps, which can be expanded to various PCM geometries and thermal systems.