Abstract
We present a system of analytical equations for computation of all thermodynamic properties of dry steam and liquid water (undesaturated, saturated and metastable supersaturated) and properties of the liquid- vapor phase interface. The form of the equations is such that it enables computation of all thermodynamic properties for independent variables directly related to the balanced quantities - total mass, liquid mass, energy, momenta. This makes it suitable for the solvers of fluid dynamics equations in the conservative form. Thermodynamic properties of dry steam and liquid water are formulated in terms of special thermodynamic potentials and all properties are obtained as analytical derivatives. For the surface tension, the IAPWS formula is used. The interfacial internal energy is derived from the surface tension and it is used in the energy balance. Unlike common models, the present one provides real (contrary to perfect gas approximation) properties of steam and water and reflects the energetic effects due to the surface tension. The equations are based on re- fitting the reference formulation IAPWS-95 and selected experimental data. The mathematical structure of the equations is optimized for fast computation.
Highlights
The need of enhancing the efficiency of steam turbines and lowering the costs of experimental development provides a driving force to the improvement of mathematical models of condensing steam flow
As we discuss bellow, neither IAPWS-95 nor IAPWS-IF97 are suitable for computational fluid dynamics (CFD) because their use requires millions of evaluations of lengthy formulas and, even more importantly, iterations are necessary to convert from the original set of variables to the required one
The model assumes that separate balance equations are written for the total energy of the liquid phase and for the internal energy of the phase interface
Summary
The need of enhancing the efficiency of steam turbines and lowering the costs of experimental development provides a driving force to the improvement of mathematical models of condensing steam flow. All needed thermodynamic properties of condensing steam are described most accurately by the so-called scientific formulation IAPWS-95 [1,2]. This formulation is based on all experimental data available. All properties needed will be derived from the IAPWS-adopted surface tension formula [5,6] This completes the set of relations needed for the computation of thermodynamic properties in a condensing steam flow simulation. The phase interface can be assumed to be at the temperature of the liquid phase ( g 0 ), because the heat transport inside the droplet is more efficient than the heat transport in the gaseous neighborhood. Including a distribution of droplet sizes, temperatures, and velocities is possible at the price of increasing the number of conserved quantities
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