Fast Calculation of Thermodynamic Properties of Water and Steam in Process Modelling using Spline Interpolation
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Optimising heat cycles and calculating nonstationary processes require extremely fast algorithms for thermodynamic properties of working fluids because they are frequently used in the inner iteration cycles of the process calculations. The IAPWS-IF97 [1,2] contains very fast and accurate equations. For Computational Fluid Dynamics (CFD), however, even IAPWSIF97 is too slow. Therefore in CFD, fluid properties are often calculated with simple equations, for example with the ideal gas equation. Depending on the range of state this procedure leads to inaccuracies in the process calculation. IAPWS therefore established a task group in 2007 for developing fast property algorithms for water and steam. In the past, table look-up methods have been developed to calculate fluid properties faster and with reasonable accuracy. One of these methods, the Tabular Taylor Series Expansion Method (TTSE) [3], was adopted by IAPWS as a guideline in 2003 [4]. One disadvantage of this method is that it does not represent the property surfaces in a continuous form. In order to calculate fluid properties as fast as or faster as TTSE but with continuously represented property surfaces, two-dimensional splines can be used in a table look up method. In the first step a bi-quadratic spline surface for the function ( ) 2 , T p h SPL for region 2 of IAPWSIF97 was developed. Additionally, ( ) 2 , h p T INV was obtained by solving ( ) 2 , T p h SPL in terms of h. This paper gives a brief introduction into splinebased fluid property calculations and discusses its characteristics in comparison to IAPWS-IF97 and TTSE. The main focus of this work is the development of an extremely fast spline-based algorithm for calculating thermodynamic properties. An investigation to determine splineinterpolation algorithms for thermodynamic properties not only for water and steam but also for other pure fluids and mixtures is currently being conducted. Fast Calculation of Thermodynamic Properties of Water and Steam in Process Modelling using Spline Interpolation