Continuous spline functions for the computation of thermodynamic properties of non-ideal fluids in advanced three-dimensional CFD applications

New technological constraints imposed by new energy production processes require more detailed understanding of the thermodynamic and fluid-dynamic phenomena realized in power plants. Use of experimental investigations is necessarily limited due to the extremely high costs involved. Therefore, computational fluid dynamics became an indispensable tool for the design and optimization of components for the energy industry, in particular steam and gas turbines. Whilst for the numerical simulation of the flow in the latter assuming ideal gas behavior of the working fluid constitutes an acceptable approximation, this not the case for the former, where phase changes and large departures of the thermodynamic properties from the ideal state must be accounted for. Fully-compressible, density-based flow solvers are perfectly suited to solve the system of the Euler/Navier-Stokes equations governing the flow in turbo-machines, however introducing non-ideal state relationships in existing CFD codes dramatically increases computational efforts. Non-ideal fluids possess generally highly non-linear caloric and thermally state relationships, hence expensive iterative solution methods are to be employed to obtain accurate updates of the primitive state variables which would render use of numerical simulation in realistic industrial configuration unfeasible. In this paper an innovative approach is described for the calculation of the thermodynamic state of steam for density-based fully compressible CFD applications. Continuous spline functions are used to describe the fundamental caloric and thermal relationships and the relevant thermodynamic differentials also across the saturation boundaries. The spline method has been embedded in a fully implicit, Roe-based turbo-machinery code and the new generalized formulation thus obtained applied to the simulation of the flow in a model turbine stage. The approach proposed has proved to allow a drastic reduction of the computational time whilst achieving very high accuracy