The top-down methodology ambitioned in the SPP 2403 requires accurate data on thermodynamic equilibrium and transport properties if high efficiencies are to be achieved. In inverse design, theoretically sound equations describing these properties are necessary to identify optimal working fluids and operating conditions. The development of predictive equations for transport properties has remained well behind that ofequilibrium properties, such that it is the objective of the proposed project. In fact, the better availability of equilibrium property data and predictive equations makes exploring the link between transport and equilibrium thermodynamics compelling. Entropy scaling and density scaling, having isomorph theory as a background, will be addressed for modeling the shear viscosity and thermal conductivity of pure fluids and mixtures. One of the goals of this project is the elaboration of a trustworthy methodology and recommendations for the application of entropy scaling to transport property modeling. A critical evaluation of the available modifications of Rosenfeld’s pioneering work on entropy scaling theory based on studies of the siloxanes and their mixtures will be performed. Rosenfeld suggested that transport properties, when scaled with the appropriate physical dimensions, are an univariate function of the residual entropy. This project also lays a focus on the theoretical and methodological development of density scaling, since it, contrary to entropy scaling, does not require the availability of a Helmholtz energy equation of state. Preparatory work of the applicant showed that the use of a constant effective density scaling exponent, related to the fluid’s effective hardness, can transform the unique variable of density scaling into a univariate function of residual entropy. In this sense, a study of density scaling and its relationship with entropy scaling is proposed. This will require the use of model fluids and mixtures, based on the Mie potential, which allows for variation of the repulsive interaction. As a class of real fluids, the siloxane chemical family, linear and cyclic, as well as mixtures thereof will be studied. The choice of a chemical family will offer the possibility to investigate the link between model parameters and molecular structure, which is required for inverse design. In case of mixtures, emphasis will be put to mixing rules and to highly asymmetric mixtures, where the univariate behavior is expected to break down. Generally, molecular simulation techniques will be employed to obtain evenly distributed hybrid transport property data sets as well as residual entropy data. This project, conceived as a part of SPP 2403, includes a high level of collaboration with other partners. It is not limited to the development of transport property scaling schemes, but also includes the supply of equilibrium properties and the study of other fluids according to the specific needs of other SPP 2403 project partners.

Professor Dr.-Ing. Jadran Vrabec
Technische Universität Berlin
Institut für Prozess- und Verfahrenstechnik

The selection of a suitable working fluid represents one of the most important factors in the design of a thermodynamic cycle. As the fluid has to meet manifold criteria, mixtures are gaining increasingly importance in order to obtain the most appropriate solution, i.e. the required combination of properties unattainable by pure compounds. Two different strategies are followed in the literature for the fluid design: 1. A computer-aided model (mixture) design approach in combination with the formulation of a mixedinter-nonlinear-programming (MINLP) problem – which though usually employs property models with limited accuracy or models, which do not include widely used refrigerants. 2. A screening approach, i.e. performing system simulations of the defined cycle for a large number of fluids described by highly accurate multiparameter Helmholtz equations of state (HEOS) that are considered state of the art for the calculation of thermophysical properties. HEOS though are too computationally demanding to allow for their use in the MINLP. Furthermore, potential working fluid mixtures whose mixing parameters or models for the HEOS are missing need to be excluded from screenings.

The aim of the proposed project is to overcome these two main restrictions when using HEOS is the working fluid selection. This will be achieved by the development of dedicated surrogate models based on Gaussian processes (GP) for HEOS of (binary) refrigerant mixtures to enable the efficient calculation of their thermodynamic properties in a MINLP based design approach. Additionally, molecular simulations on mixtures not yet described by optimized HEOS will allow to derive their mixing parameters so that they can also be included in the optimization process. To account for the mismatch between the HEOS and molecular simulations, we will introduce stochastic HEOS models, for which stochastic GP surrogates will be generated. These stochastic surrogate models will be employed in a MINLP to identify a suitable mixture for a specific application. The stochastic approach followed in this proposal will additionally allow for optimization considering uncertainties of the underlying property models. 

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