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

• An efficient algorithm was proposed for thermodynamic properties on p–h surface.
• The two-phase regime was modeled using curve extension approach.
• Non-uniform grids and bisection algorithm were applied to reduce memory loadings.
• New functions were 2.47–94.1 times faster in computation speed than IAPWS-IF97.
• New functions were 1–4 orders of magnitude higher consistency than IAPWS-IF97.

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 100 kJ/kg ≤ h ≤ 4180 kJ/kg and 0.001 MPa ≤ p ≤ 100 MPa was divided into single- and two-phase regions. The spline function zSPL(p,h) in two-phase regime was calculated using one-dimensional spline function hsatSPL(p) at the saturated p–h line and the corresponding spline function zSPL(p,h) in single-phase region. For zSPL(p,h) in the single-phase region, virtual two-phase region data evaluated through curve extension approach was adopted for increased accuracy of zSPL(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 TSPL(p,h), ρSPL(p,h) and sSPL(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.