Efficient evaluation of thermodynamic properties of water and steam on p-h surface

An efficient algorithm for evaluating thermodynamic properties on p-h thermodynamic surface of water and steam is proposed based on bi-quadratic spline interpolation method. With focus on discontinuities of first- or second-order derivatives of thermodynamic property z(p,h) at the saturated p-h line, the p-h surface at 100kJ/kg≤h≤4180kJ/kg and 0.001MPa≤p≤100MPa was divided into single- and two-phase regions. The spline function z^SPL(p,h) in two-phase regime was calculated using one-dimensional spline function h_sat^SPL(p) at the saturated p-h line and the corresponding spline function z^SPL(p,h) in single-phase region. For z^SPL(p,h) in the single-phase region, virtual two-phase region data evaluated through curve extension approach was adopted for increased accuracy of z^SPL(p,h) near the saturated p-h line. Non-uniform grid lines and bisection algorithm were also introduced to reduce the memory loadings. Calculation results of T^SPL(p,h), ρ^SPL(p,h) and s^SPL(p,h) show with the spline functions developed in this paper were 2.47-94.1 times faster in computing speed and 1-4 orders of magnitude higher consistency with IAPWS-95 than IAPWS-IF97. We proposed that the currently developed spline algorithm and optimization algorithm are applicable to efficient evaluation of thermodynamic properties of water and steam on p-s, h-s or other state surfaces. © 2013 Taiwan Institute of Chemical Engineers.