The dependence of numerous industries on fossil fuels threatens the global ecosystem through the onset of irreversible climate change. Technologies such as organic Rankine cycle (ORC) systems can help reduce this dependence by harvesting electricity from waste heat. Similarly, hydrogen can be used as an alternative, carbon-free fuel for energy-intensive applications. ORC and hydrogen combustion technologies are designed with the help of computational fluid dynamics (CFD) simulations combined with fluid models that calculate thermophysical and chemical properties. Although highly accurate reference models are available, their high computational cost makes them impractical for design applications.

A promising alternative is the data-driven equation of state (DDEoS), in which fluid properties are calculated with artificial neural networks trained on data generated with reference models. Two DDEoS applications were considered: a flamelet-generated manifold (FGM) model for laminar hydrogen flames and a consistent equation of state model based on the entropy potential for nonideal compressible fluid dynamics (NICFD). Although conventional machine learning methods can achieve high accuracy, reliably satisfying known relations between fluid properties, such as the Maxwell relations and Gibbs free energy relation, remains challenging. Violating these relations can lead to nonphysical effects in flow simulations, reducing numerical robustness and accuracy.

The first objective was to investigate physics-informed machine learning (PIML) methods for integrating known relations between fluid properties into the training of DDEoS models for FGM and NICFD. For the hydrogen FGM model, several relations between the FGM controlling variables and fluid properties were derived and integrated into the training process as boundary conditions. This significantly improved the accuracy of fluid properties evaluated in chemical equilibrium compared with a data-fitting approach.

The second part of the research investigated the relationships between accuracy, computational cost, the definition of the progress variable, and network hyperparameters for FGM. The accuracy of fluid properties evaluated by the DDEoS was significantly affected by the definition of the progress variable, with the highest accuracy obtained when the progress variable was optimized to be monotonic throughout the flamelet manifold. Several relations between accuracy, complexity, and network hyperparameters were identified. Using optimized network parameters, the computational cost of hydrogen flame simulations was reduced by more than 60% while maintaining sufficient accuracy.

For NICFD, a PIML approach was developed to train a thermodynamically consistent equation of state model for evaluating fluid properties in the nonideal thermodynamic state. Compared with a data-fitting approach, the PIML model evaluated thermodynamic states less accurately. However, the CFD simulation converged faster because of the higher thermodynamic consistency achieved with the PIML approach.

Finally, the data-driven fluid models were evaluated for design applications. For an ORC stator vane, the search direction in the design space was accurately evaluated using the developed DDEoS model compared with a reference fluid model. For a partially premixed hydrogen burner, constrained optimization using the FGM model increased the discharge coefficient by 13% while maintaining a constant outflow temperature. Although the final design did not meet the definition of a true optimum, the improvement in performance indicates the effectiveness of the FGM method in design applications. The results demonstrate that physics-informed data-driven equations of state can reduce computational cost while maintaining sufficient accuracy and improving thermodynamic consistency in CFD-based design applications. ... Read more

This article presents a data-driven method to evaluate thermodynamic properties of pure fluids and mixtures of fixed composition in the ideal- and nonideal thermodynamic states. Thermodynamic consistency is ensured by computing the fluid properties on the basis of the entropy potential and its first- and second- order derivatives, calculated with a physics-informed neural network. The computational performance of the method was investigated by implementing the resulting data-driven model in the open-source SU2 CFD software and by performing RANS simulations of the nonideal compressible flows through an organic Rankine cycle turbine cascade. Compared to using a multiparameter equation of state through a thermodynamic library coupled with SU2, the method was found to be 60 % more computationally efficient while maintaining high accuracy. ... Read more

Modeling non-ideal compressible flows in the context of computational fluid-dynamics (CFD) requires the calculation of thermodynamic state properties at each step of the iterative solution process. To this purpose, the use of a built-in fundamental equation of state (EoS) in entropic form, i.e., s= s(e, ρ), can be particularly cost-effective, as all state properties can be explicitly calculated from the conservative variables of the flow solver. This approach can be especially advantageous for massively parallel computations, in which look-up table (LuT) methods can become prohibitively expensive in terms of memory usage. The goal of this research is to: i) develop a fundamental relation based on the entropy potential; ii) create a data-driven model of entropy and its first and second-order derivatives, expressed as a function of density and internal energy; iii) test the performance of the data-driven thermodynamic model on a CFD case study. Notably, two Multi-Layer Perceptron (MLP) models are trained on a synthetic dataset comprising 500k thermodynamic state points, obtained by means of the Span-Wagner EoS. The thermodynamic properties are calculated by differentiating the fundamental equation, thus ensuring thermodynamic consistency. Conversely, thermodynamic stability is properly enforced during the regression process. Albeit the method is applicable to the development of equation of state models for arbitrary fluids and thermodynamic conditions, the present work only considers siloxane MM in the single phase region. The MLP model is implemented in the open-source SU2 software [8] and is used for the numerical simulation of non-ideal compressible flows in a planar converging-diverging nozzle. Finally, the accuracy and the computational performance of the data-driven thermodynamic model are assessed by comparing the resulting flow field, the wall time and the memory requirements with those obtained with direct calls to a cubic EoS, and with a LuT method. ... Read more