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P. Colonna, S. Rebay, J. Harinck and A. Guardone has been designed for inlet conditions corresponding to a slightly superheated vapor at a reduced pressure P/Pc ≈ 0.6. Significant real gas effects are therefore present only in the initial phase of the expansion through the nozzle blade. Therefore the predicted performance of the nozzle blade is not expected to be heavily affected by the chosen thermodynamic model. Conclusions are drawn on the difference (magnitude and trends) in ORC turbine per- formance caused by the (in)accuracy of the adopted EoS model. The sensitivity of the turbine performance to the accuracy of the EoS model and the operating condition has important consequences for the design of ORC turbines. 2 THE EULER SOLVER AND THE ADVANCED THERMODYNAMIC MODELS 2.1 The Euler solver The numerical solution of the 2D inviscid Navier-Stokes (Euler) equations has been performed with the novel zFlow program.5 The main features characterizing the CFD code zFlow are briefly summarized. The spatial approximation of the inviscid Navier- Stokes (Euler) equations is constructed with an high resolution finite volume method suitable for general unstructured and hybrid grids. The method can be regarded as an hybrid between the Finite Element (FE) and Finite Volume (FV) methods in that the finite volume metric quantities are formulated on the basis of the langrangian polynomial shape functions typically used in finite element methods.6 The high resolution upwind discretization is constructed on the basis of the Roe approximate Riemann solver intro- duced in7 generalized to the case of fluids characterized by arbitrary equations of state according to the method of Vinokur and Montagn ́e.8 This class of discretization schemes is particularly well suited to the computation of high Mach number flows such as those occurring in an ORC turbine. The use of unstructured grids allows for the straightfor- ward treatment of domains of arbitrarily complex geometry. Another important feature of zFlow is represented by the adopted implicit time integration scheme, which allows for the computation of steady state solutions in a much more efficient way with respect to conventional explicit schemes. The gain in computational efficiency is crucial when complex equation of state are needed for an accurate flow simulation. The zFlow solver has been successfully validated for ideal gas simulations.5,9 A more detailed description of the numerical methods and models implemented in zFlow is given elsewhere.5 2.2 The advanced thermodynamic models The CFD code zFlow integrates a rich thermodynamic library for the calculation of properties of pure fluids and mixtures which has been extended to include the particular (secondary) thermodynamic functions required by the implicit upwind flow solver.10 The software library11 contains, amongst others, a cubic EoS (StanMix) and state-of-the-art multi-parameter EoS models (TPSI, RefProp). All the needed thermodynamic properties, 3PDF Image | REAL-GAS EFFECTS IN ORC TURBINE FLOW SIMULATIONS
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