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Intrinsic

The intrinsic constitutive relations are relations which are unique for a given fluid, for instance, steam. These relations include the transport properties and the equations of state. In our case we only need to consider the fluids water and steam.

In general we need the following quantities

.

Thermodynamic properties:

)

Water from subcooled to saturated state:

.

Density: $\rho_\ell(p,T)$.

.

Specific enthalpy: $h_\ell(p,T)$ and $T_\ell(h,p)$.

.

Specific heat: $C_{p,\ell}(p,T)$.

)

Steam in saturated state:

.

Density: $\rho_g(p_{\mbox{\protect\scriptsize sat}})$.

.

Specific enthalpy: $h_g(p_{\mbox{\protect\scriptsize sat}})$.

)

Saturation curve: $T_{\mbox{\protect\scriptsize sat}}(p)$ and $p_{\mbox{\protect\scriptsize sat}}(T)$.

.

Transport properties:

)

Water from slightly subcooled to saturated state:

.

Viscosity: $\mu_\ell$.

.

Thermal conductivity: $k_\ell$.

.

Surface tension: $\sigma(T)$.

)

Steam in saturated state: Viscosity: $\mu_g(p_{\mbox{\protect\scriptsize sat}})$.

The properties are given by steam tables in various books. One way to use these tables is to interpolate between the values in the table. When we have to use a computer the drawback is, however, firstly that we have to type in all these numbers (very error prone operation) and secondly we have to use a large amount of storage.

It is in general better to use a curve fit which interpolates the data. A source for such curve fit functions is the ASME steam tables [21]. These functions are, however, very complicated which implies a long evaluation time on a computer. Furthermore the very high accuracy that the functions processes is unnecessary in a thermal-hydraulic analysis where some of the external constitutive relations have mean errors of 10 percent (eg the two-phase shear stress relation).

This situation creates a need for simpler curve fitting functions which due to the simpler form probably have higher interpolation errors.

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