Efficient Implementation of Short Fundamental Equations of State for the Numerical Simulation of Dense Gas Flows P. Cinnella * and S.J. Hercus † Arts et M´ etiers ParisTech, Paris 75013, France 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 ρ and the internal energy per unit volume ρe. The resulting relationship, of the form T = T (ρ, ρe), 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. Nomenclature f Physical flux vector v Velocity vector w Conservative variable vector δ Reduced density, ρ/ρ c Δ sat Saturation curve error [%], 100(T sat Aux. − T sat SW )/T sat SW Δ i Local error [%], 100(T Aux.,i − T SW,i )/T SW,i , over the i =1,...,N points of the validation mesh ˙ m 2D Mass flow rate per unit depth ǫ Error [%], 100(ν Aux. − ν SW )/ν SW , for the turbine performance parameters ν =[η s ,˙ m 2D , P 2D ] η s Isentropic turbine efficiency, Δh real /Δh is µ Mean value, calculated over the 15 fluids considered in this work ω Acentric factor Φ Gibbs free energy φ Reduction [%] in calculation time, 100(t SW − t Aux. )/t SW Ψ Helmholtz free energy ψ Reduced Helmholtz energy ρe Internal energy per unit volume ρ Density σ Modeling uncertainty, % * Professor, Laboratoire DynFluid, 151 Bd de l’Hˆ opital, Paris 75013, France † Research Engineer, Laboratoire DynFluid, 151 Bd de l’Hˆ opital, Paris 75013, France 1 of 27 American Institute of Aeronautics and Astronautics 42nd AIAA Thermophysics Conference 27 - 30 June 2011, Honolulu, Hawaii AIAA 2011-3947 Copyright © 2011 by Paola Cinnella and Samuel Hercus. Published by the American Institute of Aeronautics and Astronautics, Inc., with permission.