一个三参数状态方程的改进

本文在分析了一个三参数状态方程的不足之处后,提出通过带约束条件的最小二乘法,用正交多项式拟合来确定方程的参数,使对比温度T_r在0.5～1范围内汽液两相饱和参数的计算精确度有较大幅度的提高。

Improvement on the State Equation with Three Parameters

The defects of the state equation with three parameters p =RT(1+X+X2-X3)/V(1-x)3are discussed. It is shown that the state equation is not in good agreement with what is obtained from the experimental data in the neighboring region of the critical point because parameters a and b of the equation do not satisfy the conditions at the critical point. For this reason, an orthogonal polynomial is used to fit these parameters by the least squares method with additional constraint. The constraint is that the fitting curve should pass through the critical point. Calculation results show that not only is the modified equation more accurate so far as the saturation properties in both liquid and vapour phases are concerned, but also it is easier to be used to predict the supercritical properties.