Consistent data-driven models

Abstract

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.