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.

Radial-Inflow Turbines are considered the most suited expanders for waste heat recovery via high-temperature mini-organic Rankine Cycle (ORC) turbogenerators thanks to high compactness, large expansion ratio handled by a single stage, and comparatively low weight. Reaching high efficiency in these machines is however a formidable challenge, as they are bounded to operate with expansion ratios exceeding 40. Although scarcely investigated in the published literature, the size of the stator-rotor radial gap is a key design parameter as it has a large influence on fluid-dynamic performance, manufacturing, and mechanical integrity. In addition, the working conditions of the turbine are such that the stator operates with highly supersonic flows in the non-ideal thermodynamic regime, making the flow pattern in stator-rotor radial gap, which can be regarded as an area-decreasing channel, very complex. Under these conditions, the radial gap size could impact the stage efficiency up to few percentage points. The paper presents a study aimed at investigating the impact of variable radial gap on the fluid-dynamic performance of radial-inflow turbines for high-temperature mini-ORC power systems. The reference turbine is a supersonic machine for laboratory experiments under realization at Delft University of Technology, referred to as ORCHID turbine. First, a theoretical analysis is carried out to identify the relevant non-dimensional parameters governing the flow physics in the gap. Then, the effect of the radial gap size on the fluid-dynamic performance of the ORCHID turbine is assessed by means of RANS and uRANS computations. The results show that the change in radial gap size leads to a redistribution of expansion ratio between vaned and vaneless part of stationary component via a substantial change of the stator trailing edge flow structures, which, in turn strongly affects stator loss and stage efficiency, leading to 8% points reduction.