Fast Calculation Of The Thermodynamic Properties Of Water And Steam On P-T And P-s Thermodynamic Plane

IAPWS-IF97is widely applied to current industrial calculations of thermodynamic properties of water and steam in a broad range. The basic formula for IAPWS-IF97are g(T,p) or f[p,T), which is usually in the form of a polynomial function of dozens. When using these formulas, most thermodynamic properties require iterative computations, resulting in the slow speed of calculation. In addition, the inconsistency of positive and negative function may lead to divergence after several iterations, which can not meet the power plant unit of dynamic monitoring and control. Therefore, it is important to develop new methods to achieve a rapid and accurate calculation for thermodynamic properties of water and steam.In industrial applications, the calculations of thermodynamic properties of water and steam on p-T and p-s thermodynamic surface are invoked by high frequency, and thus the establish of thermodynamic properties of water and steam on p-T and p-s thermodynamic plane is essential. In this paper, an efficient algorithm for evaluating thermodynamic properties of water and steam on p-T and p-s thermodynamic surface was proposed based on dual-grid and bi-quadratic spline interpolation model in view of Wang et al, and the calculating area included the1-4zones of IAPWS-IF97. The optimization algorithm embodied in the following four points:1) In the left and right sides of the p-T saturation line adopting the method of virtual surface extension respectively allows a smooth transition at the p-T thermodynamic surface. Generating two spline coefficients preserved and stored the spline coefficients in real data side. Such optimization algorithm not only greatly improved the accuracy of the region near the saturation line, but also reduced the workload of the grid search. What’more, it enhanced the speed of the spline interpolation model.2) Since property functions or their derivatives are not continuous crossing the saturation curves, the calculation of thermodynamic properties on two-phase area of p-s thermodynamic surface was simplized to the evaluation of thermal properties on saturation curves. Linear, quadratic, and Bessel curve extension methods were introduced to solve the derivative discontinuity problem of the thermodynamic properties on the saturated line. Among them, quadratic curve extension method is the best, which increased the consistency between the spline function and IAPWS-95by2-5orders of magnitude.3) Three nonuniform grid distributions (equidifferent, geometric and power-law) were prompted to improve the grid density of low pressure area and improved accuracy in the low pressure zone. The results show that the power-law distribution has the best performance, which simultaneously ensure the high and low pressure areas’s consistency with IAPWS-95.4) The bisection method was determined as the best search algorithm of the state-point of interest for the non-uniform grid.The calculation results showed that the optimized spline interpolation model developed in this paper can meet the requirements for industrial application of thermodynamic properties of water and steam on speed and accuracy. In the case of density, comparisons of computing speed made between spline function and IAPWS-IF97showed that the spline function pSPL(p, T) developed in this paper were34.96-126.97times faster than IAPWS-IF97in computing speed and2-3orders of magnitude higher consistency with IAPWS-95than IAPWS-IF97; and the spline function pSPL(p,s) developed in this paper were23.25-122.17times faster than IAPWS-IF97in computing speed and3-4orders of magnitude higher consistency with IAPWS-95than IAPWS-IF97. The bi-quadratic spline interpolation model for fast calculation of thermodynamic properties of water and steam can meet the demands of industrial applications, and is also applicable to other working fluids.