A sizing model for a tube in tube sensible thermal energy storage heat exchanger with solid storage material

Sensible thermal energy storage (STES) systems are generally the most affordable and least complex type of thermal energy storage systems available. The main question when modeling STES systems is the outlet state of the heat transfer fluid for a given inlet condition. Traditional heat exchanger design methods such as the logarithmic mean temperature difference method do not apply to TES systems since these systems do not operate in steady state. Other design methods are only applicable to specific cases such as packed bed systems with a thermocline. The present paper proposes a novel framework for STES system design with solid, stationary storage material. The framework is validated based on the case of a tube in tube STES system. The novel design model characterizes the local conductive heat transfer in the Laplace domain. This local behavior is integrated over the surface of the heat exchanger using three methods: a height split, a height lumped and a fully lumped approach. Each method corresponds to a different assumption regarding the temperature gradient in the storage material and will therefore be applicable to different cases. By numerically inverting the Laplace transform, a prediction is obtained of the outlet temperature of the HTF in the time domain. The solution is compared to the result of a computational fluid dynamics (CFD) reference model for five selected cases, with the CFD requiring calculation times in the order of days on a dedicated server while the novel model requires seconds on a laptop. This difference in calculation time is the result of the need of the CFD model to discretize the domain in space and apply a time stepping algorithm. The transfer function approach requires neither discretization nor time stepping but it does require a numerical inverse Laplace transform. The transfer function approach has a good fit with the CFD predictions. Furthermore, the quality of the fit and the behavior of the system is predicted based on the Biot number, the thermocline width ratio and the cross conduction number where the latter two numbers are derived in the present paper. The novel approach can provide a method to obtain sizing models for STES systems with a solid storage material.