SodiumSaturationFluidProperties

Description

The SodiumSaturationFluidProperties class provides fluid properties for _saturated_ liquid sodium based on correlations used in the SAS4A/SASSYS-1 reactor dynamics and safety analysis code developed at Argonne National Laboratory for liquid metal reactors Dunn (2017). These property models are obtained as fits to experimental data, with computational efficiency motivating the use of a simpler functional fits than proposed in the original references upon which the SAS4a/SASSYS-1 implementation is based, namely Fink and Leibowitz (1979). Only for and are the original correlations/data used, since the SAS4A/SASSYS-1 implementation does not differentiate between and for the saturated liquid.

Density is calculated as an empirical fit to two saturated liquid density correlations recommended by Fink and Leibowitz that cover the range :

This equation fits the Fink and Leibowitz models to within 9.5%.

The speed of sound used for compressible-flow wave speeds is the Fink and Leibowitz correlation fit to sodium measurements over the range :

Here, is in m/s. This independent correlation is used because the saturated-liquid density fit neglects pressure dependence and therefore cannot supply a physical sound speed through its pressure derivative.

The thermal conductivity is a fit to experimental data by Fink and Leibowitz below 1500 K, and extrapolated values above 1500 K based on a method described by Grosse Dunn (2017):

This equation fits the Fink and Leibowitz data to within 0.5%.

The dynamic viscosity is given as a fit to experimental data by Fink and Leibowitz below 1200 K and extrapolated values about 1200 K based on a method described by Grosse Dunn (2017):

This equation fits the Fink and Leibowitz data to within 0.5%.

The baseline isobaric and isochoric specific heats are obtained as fits to the saturated-liquid experimental data in Fink and Leibowitz over the range :

The values for both fits are 0.997. The fit matches the experimental data to within 0.5%, while the fit matches the data to within 1.5%. For the pressure extension described below, the implementation assigns the curve to the reference pressure Pa. Thus, the subscript 0 identifies the model baseline; it does not indicate that the original data were measured along a separate constant-pressure isobar. The fit is used directly without a pressure correction.

At the reference pressure, the baseline enthalpy is defined by

and is therefore computed by integrating the empirical fit:

In the implementation this integral is written as

where is an antiderivative of . The integration constant is selected to match the Fink and Leibowitz enthalpy correlation at 371 K. This construction enforces exactly and agrees with the Fink and Leibowitz enthalpy correlation to within 0.2% over the valid range of the fit.

A pressure extension is then derived from this baseline enthalpy and the temperature-only specific-volume correlation . For a simple compressible system, the Gibbs free-energy and enthalpy differentials are

and

Callen (1985).

Equality of the mixed partial derivatives of gives the Maxwell relation

.

At , the entropy baseline follows from :

The entropy datum is chosen as . Because depends only on temperature in this model, integration of the Maxwell relation with respect to pressure from then gives

.

At constant temperature, the enthalpy form of the Gibbs relation then gives

,

which integrates to

.

Finally, applying the definition to this pressure-extended enthalpy gives

Therefore, the polynomial above supplies the empirical baseline, while the second term is not another empirical fit: it follows from differentiating the Gibbs-consistent pressure extension. At , this correction vanishes and .

These expressions satisfy the Gibbs relation exactly within the assumed model. They are only a first-order pressure extension of the original saturated-liquid correlations because pressure dependence of and other higher-order pressure effects are neglected; they do not constitute a full subcooled-sodium equation of state. In particular, the independent correlation is retained rather than derived from this pressure extension. The inverse temperature relation is obtained by Newton inversion of this pressure-extended enthalpy correlation.

Range of Validity

The underlying empirical correlations describe saturated liquid sodium. Values away from use the first-order pressure extension described above and should not be interpreted as a validated subcooled-sodium equation of state.

Input Parameters

References