A Novel Interpolation-Based Method for Thermodynamic Properties Calculation in Dense-Gas Flow Simulations

The reliable modeling of real-gases is nowadays of great importance in many industrial applications, especially in the energy eld. The prediction of real-gas thermodynamic properties based on the direct use of an equation of state (EoS) and of its derivatives, implies a high computational cost in case of numerical studies, when a set of governing equations is iteratively solved (e.g. detailed CFD calculations, dynamic plant simula- tions). A dierent approach is represented by the use of look-up tables. In the thermodynamic regions of interest, a grid of nodal points (storing all thermodynamic and transport properties) is preliminary built. Within the discretized domain, the properties in any point are computed using fast interpolation methods, with a dramatic reduction in computational time [2, 3]. However, a proper technique has to be applied to guarantee the thermodynamic consistency, which is not automatically satised as in the case of direct EoS application. Finally the desired accuracy can be addressed by selecting the number of nodes and the interpolation scheme. This paper presents a novel interpolation method for property calculation of real gases using look-up tables. Herein, any grid has been built using accurate EoS implemented in the software FluidProp [4]. The method assigns a selected functional form to the internal energy e as a function of the specic volume v and of the specic entropy per unit mass s (e = e(v; s)). Within any cell of the thermodynamic domain, the coecients of the functional form are calculated referring to the local grid data; therefore, a fundamental relation is locally established, in such a way that any thermodynamic property of any internal point is intrinsically consistent. A similar approach has been adopted also for computing the transport properties. Two dierent functional forms are assigned to the dynamic viscosity and to the thermal conductivity k as a function of the specic volume and of the specic entropy per unit mass ( = (v; s), k = k(v; s)); the two sets of coecients are then computed at any cell on the basis of the transport properties stored within local grid points. The method is here presented for the siloxane MDM and for the carbon dioxide CO2. Both single and two-phase regions close to vapor saturation line have been explored, for reduced temperature ranging between Tr ' 0:6 and Tr ' 1:05. The accuracy and the computational cost of the method have been assessed in comparison with those resulting from direct EoS computation. As an example of application, the through ow calculation of a centrifugal turbine operating with MDM is also presented.