The proposed project advances the design of packed‑bed thermal energy storage (TES) using liquid metals as low Prandtl number heat transfer fluid. We will focus on determining the heat transport mechanisms in such TES – through analytical and numerical models, validated with own experimental data –, as they are not sufficiently understood in the literature yet. The experimental and numerical work of the proposed project are based on the results from the first funding period, summarized in the first part. The project focussed on the adaptation or development of a heat transport correlation for forced convection of low-Prandtl number fluids in packed beds based on own high-quality experimental data, complemented by further developing a numerical model. We obtained the following results so far: (1) We found that the axial heat transport (molecular and convective heat transfer), described by the effective thermal conductivity, dominates. For low Péclet numbers, where molecular conduction prevails, it can be calculated with known correlations for conventional (high Pr-number) fluids. (2) To test this hypothesis, a 1-D heterogeneous continuum model was successfully validated against experimental data for Péclet numbers below 0.32. However, for higher Péclet numbers relevant for industrial-scale TES, it is not sufficiently understood how to calculate the effective thermal conductivity. (3) To close this research gap, thermal step response measurements have been identified as a suitable concept and the design of a new test section has been completed. It is planned for the upcoming third year of the project to complete the construction and perform the experiments to determine the effective thermal conductivity for Péclet numbers of up to 10. (4) In parallel, the simulation tool and results for the packed-bed TES have been incorporated into two collaborations with project partners of the Priority Programme from groups of Areas A, B, and C‑machines. In the second part, our project proposal for the second funding period is given. We will focus on developing efficient models for multi‑parameter optimization of packed‑bed TES using liquid metals as heat transfer fluids, enabling the inverse design of optimal configurations and operating strategies for these TES in Carnot batteries. For this purpose, we will focus on fast (semi‑)analytical models capable of handling transient operation and realistic load profiles. Building on results from the first funding period, in which a heat transport correlation for liquid metals was validated up to Péclet numbers of 0.32 (and expected up to 10), the second phase aims to extend this correlation for a broad parameter space. For this purpose, the test section built in the first funding period will be used and adapted. The new models will be exchanged and tested with partners from Area A and B.

Dr.-Ing. Klarissa Niedermeier
Karlsruher Institut für Technologie (KIT)
Institut für Thermische Energietechnik und Sicherheit (ITES)

A Carnot Battery is an energy storage system that involves a heat pump cycle to convert electric energy to thermal energy at charge, stores thermal internal energy and converts it back to electricity at discharge, relying on a heat engine. It enables better utilization of intermittent renewable energy sources. Packed-bed thermal storage is the mostly chosen sensible thermal storage type for Carnot Batteries due to its low cost and simplicity. However, accurately predicting the charge/hold/discharge process is difficult; it is related to multiple areas of physics, including fluid dynamics, heat transfer, transport in porous media, and is affected by many parameters, including fluid properties, porous medium and tank geometries, particle sizes, and dynamic operating conditions, impeding design and optimisation. Packed-bed thermal storage systems are usually designed based on the first law of thermodynamics; a key parameter is the energy storage efficiency relating the discharged to the charged heat for a certain storage period. This project proposes analysing the charge/hold/discharge process of packed-bed storage systems with the second law of thermodynamics (SLA) to optimize their designs. The corresponding efficiency relates the discharged and charged exergy, respectively. By directly calculating the entropy generation rate, we are able to know the location, strength and cause of irreversibilities during a charge/hold/discharge process. The thermal storage systems will be optimized based on a better understanding of these losses in the storage systems. To perform an SLA of a thermal storage system, it is necessary to calculate the transient charge/discharge process accurately. This is a challenging task due to the wide ranges of length and time scales in a thermal storage system. It is planned to use two methods, a system simulation method (using Modelica) and a computational fluid dynamics (CFD) method (using OpenFOAM), in the simulations. The CFD results will be used to validate system simulation models of different granularity. In addition, a dimension study will be conducted to find the key dimensionless parameters that affect the transient process and can be used to quantify the uncertainty of the different model granularities. An inverse design model will be developed based on this dimension study and the developed models in order to quickly chose among suitable material combinations and designs. The simulation and inverse design models will be validated collaboratively in the small-scale Carnot battery laboratory and provided to partners within the priority program; the integration of a packed bed storage into a Carnot Battery will be tested in experiment and simulation in further collaborations within the priority program.

Prof. Dr.-Ing. Arne Speerforck
Institut für Technische Thermodynamik
Technische Universität Hamburg 

The Carnot battery serves as sustainable storage for electrical energy of fluctuating renewable energy sources and consists of different energy conversion processes, the electrical energy is converted in heat by a heat pump, to transfer the heat into a storage converted to inner energy. In the case of requirement of electrical energy, the heat is transferred from the thermal storage to a heat engine to receive the electrical energy by a turbine. In consequence, the Carnot battery itself is a time-varying system and all components are exposed to a strongly transient behaviour. This is particularly important for the heat exchangers, because they are more or less "inertial" depending of various influence parameters. According to the hypothesis of the priority programme – starting from the target variable (energy market, Subject area A) via the Carnot battery (Subject area B) to their component as machines, apparatus, storage and fluid (Subject area C) – the heat exchanger as main coupling component between heat pump, storage and heat engine has to be investigated to the specification of the demands of Subject area B and at least A. The most efficient heat exchangers are those with phase change of the heat pump and the heat engine with the largest potential for improvement in the evaporator. The thermal storage concept and material (sensible heat or latent heat) leads to strongly time-dependent heat flows which affect the design of the heat exchanger. The theoretical total efficiency for an ideal Carnot Battery is 100 %, if there are no exergy losses at all. The efficiency of the heat exchanger depends strongly from the driving temperature difference as function of the heat transfer mechanisms. Therefore, the knowledge of the real boiling mechanisms in heat transfer are essential for the design of the evaporator. For low superheat, convective boiling is expected, as well as for high superheat nucleate boiling. Nucleate boiling results in significantly smaller size and lower operating costs as well as procurement costs (material and fluids) than convective boiling. Low operating as well as procurement costs of the heat exchangers are essential to achieve the project goals of efficient Carnot battery (Subject area B and A). Consistent experimental and theoretical analysis of the charging and discharging of the Carnot Battery, the influence of the transient behaviour of the thermal storages and the boiling mechanisms within the evaporator will be investigated. Their effect on convective and nucleate boiling, the activation criteria of nucleation and bubble formation and finally in heat transfer during boiling is analysed. The deeper understanding of the complex transport processes in the evaporator lead to establish correlations for the design of evaporator at one side (Subject area C) and for the thermodynamic and thermo-economic modelling of the Carnot battery on the other side (Subject area B).

Professorin Dr.-Ing. Andrea Luke
Institut für Thermische Energietechnik
Fachgebiet Technische Thermodynamik
Universität Kassel