Description

The computation is based on the parameters provided by the technical report R7-97.

Structure of the formulation

The R7-97 report consists of a set of equations for different regions which cover the following range of validity:

• $273.15K < T < 1073.15K$ and $p < 100MPa$
• $1073.15K < T < 2273.15K$ and $p < 50MPa$

Reference constants

The specific gas constant of ordinary water used for this formulation is

• $R = 0.461 526\ kJ.kg^{-1}.K^{-1}$

This value results from the recommended values of the molar gas constant, and the molar mass of ordinary water (Wagner et al., Harvey et al.). The values of the critical parameters

• $T_c = 647.096 K$
• $p_c = 22.064 MPa$
• $\rho _c = 322 kg.m^{-3}$

are from the corresponding IAPWS release.

Auxiliary Equation for the Boundary between Regions 2 and 3

$$\pi = n_1 + n_2 \theta + n_3 \theta ^2$$

$$\theta = n_4 + \left( \frac{\pi - n_5}{n_3} \right)^{1/2}$$

Region 4: Saturation line

The equation for describing the saturation line is an implicit quadratic equation which can be directly solved with regard to both saturation pressure $p_s$ and saturation temperature $T_s$. The details are largely described in the literature IAPWS R797, IAPWS R695.

$$\beta ^2 \theta ^2 + n_1 \beta ^2 \theta + n_2 \beta ^2 + n_3 \beta \theta ^2 +n_4 \beta \theta +n_5 \beta + n_6 \theta ^2 + n_7 \theta + n_8 = 0$$

where

$$\beta = \left( p_s/p^* \right)^{1/4}$$

and

$$\theta = \frac{T_s}{T^*} + \frac{n_9}{\left( T_s/T^* \right) + n_{10}}$$

with $p^*=1MPa$ and $T^*=1K$ and $n_i$ are coefficients.

The saturation-pressure equation (Basic Equation): psat

The solution of the quadratic equation with regard to saturation pressure is as follows:

$$\frac{p_s}{p^*} = \left[ \frac{2C}{-B + \left( B^2 - 4AC \right)} \right]^4$$

with $p^*=1MPa$ and

$$A = \theta ^2 + n_1 \theta + n_2$$

$$B = n_3 \theta ^2 + n_4 \theta + n_5$$

$$C = n_6 \theta ^2 + n_7 \theta + n_8$$

Range of validity: $273.15 K \leq T \leq 647.096 K$.

The saturation-temperature equation (Backward Equation): Tsat

The saturation-temperature solution of the quadratic equation reads

$$\frac{T_s}{T^*} = \frac{n_{10} + D - \left[ \left(n_{10} + D\right)^2 - 4\left( n_9+n_{10}D \right) \right]^{1/2}}{2}$$

where $T^*=1K$ and

$$D = \frac{2G}{-F - \left( F^2 - 4EG \right)^{1/2}}$$

$$E = \theta ^2 + n_3\beta + n_6$$

$$F = n_1 \beta ^2 +n_4 \beta + n_7$$

$$G = n_2 \beta ^2 + n_5 \beta + n_8$$

Range of validity: $611.213Pa \leq p \leq 22.064MPa$

Plot