Efficient Implementation of Short Fundamental Equations of State for the Numerical Simulation of Dense Gas Flows

An artificial neural network (ANN) of the multi-layer perceptron (MLP) type is used to generate an explicit auxiliary thermodynamic equation, whose mathematical form is particularly well suited for implementation within Computational Fluid Dynamics (CFD) solvers. This equation directly relates the thermodynamic quantity of interest (tempera- ture) to the conservative variables (density, momentum per unit volume, total energy per unit volume), via the density and the internal energy per unit volume e. The resulting relationship, of the form T = T(, e), is added to the usual thermal and caloric equations of state, in order to avoid expensive iterative computations of the temperature. We select 15 dense gases of industrial interest, whose thermodynamic properties can be described by the 12-parameter Span-Wagner fundamental equation. The accuracy and computa- tional cost of the proposed formulation are verified a priori, via detailed comparisons with data provided by the baseline thermodynamic model, and a posteriori, by propagating the approximated thermodynamic model through a numerical flow simulation. Results are shown for transonic dense gas flows through a two-dimensional turbine cascade, for sample thermodynamic conditions close to the saturated vapor line. A 53% average reduction in computation time is observed, and the convergence and numerical stability of the numerical solution is greatly enhanced, while deviations less than 3% are observed on the computed quantities of interest with respect to the baseline solver.