Heat exchangers are key components within Rankine-based Carnot Batteries. One approach to improve the efficiency of these thermodynamic cycles involves the utilization of zeotropic refrigerant mixtures instead of pure working fluids. The prediction of heat transfer characteristics for boiling and condensation as well as monitoring of part load conditions, are of particular interest for system design and control. Non-intrusive sensors, combined with machine learning (ML) methods, offer promising opportunities for condition monitoring and optimisation of heat exchangers in application-oriented systems. Within this project, a tube bundle test rig is employed to measure boiling heat transfer. These experimental investigations determine heat transfer coefficients under varying pressure, heat flux and vapor quality. Furthermore, an existing condensation test section is expanded with a second test tube. By this measure, data at higher mass flux densities and corresponding annular flow regimes are collected. The heat transfer measurements are conducted simultaneously using non-intrusive sensors. Suitable instrumentation includes a fiber-optic temperature measurement system, an infrared thermography camera, a passive acoustic sensor, and active ultrasonic transducers. The measurement data enables conclusions regarding circumferential temperature distribution, boiling regime, flow conditions, and heat transfer coefficients. Moreover, these datasets are used to develop a model for monitoring and prediction of part load operation. The experimental data undergo in a first step an exploratory analysis, Data are cleaned concerning missing values and outliers, and statistical metrics are computed. The objective is to identify correlations between the signals from the non-invasive sensors and the heat transfer measurements. Subsequently, a modeling approach focusses ML techniques. These supervised learning methods enable the generalization of patterns from the measurement data and the characterization of component behavior under variable operating conditions. The data are subsequently splitted into training, validation, and test sets. The model training process consists of setting up the network structure through hyperparameter tuning. The optimised models are integrated into the experimental facility to evaluate and monitor system performance during a second measurement phase. Based on this, selected models undergo further refinement within an iterative process involving training and validation. Additionally, the developed models are intended to be tested at both the component and system levels in collaboration with cooperation partners of the priority programme.

Professor Dr.-Ing. Dieter Brüggemann
Dr.- Ing. Florian Heberle
Universität Bayreuth
Fakultät für Ingenieurwissenschaften
Lehrstuhl für Technische Thermodynamik und Transportprozesse

This project aims to improve the modelling of thermodynamic and transport properties of mixtures of carbon dioxide (CO₂) and alkanes and to establish a reliable data base for the optimization of Carnot-battery energy storage. Such mixtures are promising working fluids because their thermophysical properties can be tuned by changing the composition, enabling more efficient heat exchange and better adaptation to specific temperature profiles. However, reliable experimental data for these mixtures are scarce, and existing models are often not accurate enough for the demanding energetic and exergetic optimization of Carnot batteries. The project therefore focuses on developing new, physically consistent and highly-accurate equations of state and transport property models for CO₂–alkane and alkane–alkane mixtures. A reference model for the CO₂ + propane system will be established using advanced fitting methods and additional constraints that ensure realistic behaviour outside well-measured regions. This approach will then be extended to a wider range of mixtures, including systems with heavier alkanes and multicomponent mixtures – progress made in the first funding period forms the basis for this work. In parallel, a software tool will be developed to analyse how uncertainties in individual thermophysical properties (such as density or enthalpy) influence the results of process simulations while maintaining thermodynamic consistency. This will allow users to assess which properties require high accuracy for a given application and to select appropriate models accordingly. For mixtures containing long-chain alkanes, alternative modelling approaches and coupling strategies between different equation-of-state classes will be explored to overcome the lack of accurate reference models. Furthermore, an optimisation framework will be created to determine mixture compositions that lead to favourable temperature profiles in heat exchangers, supporting efficient Carnot-battery design. For selected binary and ternary CO₂/ethane/propane mixtures, highly accurate viscosity measurements will be performed to provide reliable experimental data for model development and validation. Overall, the project will deliver improved mixture property models, new experimental data, and practical tools for process simulation and optimisation, thereby supporting the development of efficient and economically viable Carnot-battery systems based on natural working fluids.

Professor Dr.-Ing. Roland Span
Ruhr-Universität Bochum
Fakultät für Maschinenbau
Lehrstuhl für Thermodynamik

Dr.-Ing. Monika Thol, Ph.D.
Ruhr-Universität Bochum
Fakultät für Maschinenbau
Lehrstuhl für Thermodynamik 

The identification of suitable working fluids for Carnot batteries (CB) is a key challenge in meeting their complex performance requirements. Mixtures are becoming increasingly important as working fluids, but their description via multiparameter Helmholtz equations of state incurs enormous computational costs in process optimization. At the same time, reference data for calibrating mixture models in equations of state are often lacking. The same holds true for the prediction of transport properties, which are indispensable for optimizing real processes. This proposal aims to model relevant mixtures with systematic uncertainty quantification. In addition to thermodynamic properties, we focus on viscosities, modelled by Residual Entropy Scaling (RES) approaches. Uncertainties in both the model parameters and the residual entropy as input into the RES approach will be quantified via novel variants of generalized Bayesian inference. To enable the generation of mixture data required for calibration by molecular simulation, we will advance the Bayesian parametrization of force‐field parameters. Thereby we focus on the sequential strategy to minimise the number of expensive molecular simulations and on enabling the simultaneous determination of numerous transferable parameters for an entire component family. Further challenges arise from incorporating both equilibrium data and transport properties into the parametrization. Using viscosity data from molecular simulations, both as targets in force‐field fitting and as reference in the Bayesian inference of RES models, also requires methods to reduce the statistical uncertainty of the simulation results. Building on our achievement from the first funding period, we will construct Gaussian process surrogates for thermodynamic properties, facilitating the embedding of our mixture models into process simulations and the inverse design workflows of our project partners. Together with robust viscosity models and comprehensive uncertainty quantification, these tools will enable the reliable selection of the optimal working‐fluid mixture and determination of its ideal composition from a CB process perspective.

Prof. Dr.-Ing. Gabriele Raabe
Technische Universität Braunschweig
Fakultät für Maschinenbau
Institut für Thermodynamik

Professor Dr.-Ing. Ulrich Römer
Technische Universität Braunschweig
Fakultät für Maschinenbau
Institut für Dynamik und Schwingungen