Basic properties of fluid

The domain used for the different phases must be defined by a medium characterized by one or more fluid subdomains of different properties. This composite environment is defined by Milieu_composite. The models give the basic properties of fluids: kinematic viscosity \(\mu\), density \(\rho\), thermal diffusivity \(\alpha\), conductivity \(\lambda\), heat capacity \(Cp\) and thermal dilatation coefficient \(\beta_{co}\). The base class Fluide_reel_base (reading T_ref, P_ref) fills the property tables rho_, h_, cp_, beta_, mu_, lambda_ and their pressure/temperature derivatives.

Incompressible fluid (Fluide_Incompressible, from TRUST): gives the properties above (or 0), but the density is mandatory; neither the density nor the specific heat can be a Champ_Uniforme.

Sodium gas / liquid (Fluide_sodium_gaz, Fluide_sodium_liquide): read Lois_sodium.h, valid from the solidification temperature to the tri-critical point (371 K to 2503.7 K, pressure \(4.127\times10^{-6}\) to \(260\times10^5\) Pa).

Stiffened gas (Fluide_stiffened_gas, params gamma, pinf, mu, lambda, Cv, q, q_prim; \(Cv=R/(\gamma-1)\) by default):

\[\rho=\frac{p+\texttt{pinf}}{(\gamma-1)(T+273.15)\,Cv}, \quad h=\gamma\,Cv\,(T+273.15)+q, \quad cp=\gamma\,Cv, \quad \beta=\frac{1}{T+273.15} \]

with \(\partial_P\rho=\frac{1}{(\gamma-1)(T+273.15)Cv}\), \(\partial_T\rho=-\frac{p+\texttt{pinf}}{(\gamma-1)(T+273.15)^2 Cv}\), \(\partial_P h=0\), \(\partial_T h=cp\), \(\mu\) and \(\lambda\) constant.

R12_C1 and Eau_c3 (Fluide_R12_c1_*, Fluide_eau_c3_*): the low-boiling refrigerant R12 (dichlorodifluoromethane) mimics pressurized-water-reactor dimensionless numbers (values from the Cathare code). For example [98] :

Property	Water	R12
Pressure [bar]	155	26
\(T_{sat}\) [°C]	344.9	86.5
\(\rho_{liquid}\) [kg/m³]	594.4	1019.3
\(Cp_{liquid}\) [kJ/kg]	8.950	1.413
\(\lambda_{liquid}\) [W/m/K]	0.472	0.0458
\(\mu_{liquid}\) [Pa·s]	\(6.82\times10^{-5}\)	\(9.23\times10^{-5}\)
\(\rho_{steam}\) [kg/m³]	101.9	170.7
\(Cp_{steam}\) [kJ/kg]	14.0	1.281
\(\lambda_{steam}\) [W/m/K]	0.126	0.0175
\(\mu_{steam}\) [Pa·s]	\(2.30\times10^{-5}\)	\(1.57\times10^{-5}\)
\(\sigma\) [J/m²]	\(4.65\times10^{-3}\)	\(1.80\times10^{-3}\)
\(L_{vap}\) [kJ/kg]	966.2	86.48

MUSIG fluid and medium (Fluide_MUSIG, Milieu_MUSIG): in the homogeneous MUlti-SIze Group (MUSIG) approach, a distribution of bubbles/droplets between \(r_{min}\) and \(r_{max}\) is characterized by a statistical law (linear LIN, exponential EXP or log LOG) discretized into \(n\) sub-groups with the same velocity [19].

Standard MUSIG and i-MUSIG models. In MUSIG all size groups move with the same velocity field, whereas i-MUSIG displays an arbitrary number of velocity groups.

All bubbles from the sub-groups share the velocity of the mean Sauter diameter \(D_{sm}\) of the distribution, so a single common set of (mass, momentum, energy) equations is solved, with new source terms linked to changes in the distribution (dilatability, coalescence, break-up). Example dataset:

Milieu_MUSIG
{
    gaz_helium FLUIDE_MUSIG
    {
        fluide StiffenedGas { gamma 1.4 pinf 0.0 }
        nbPhases 4
        diametres { rmin 0.01 rmax 0.1 lin }
    }
    liquide_sodium FLUIDE_MUSIG
    {
        fluide StiffenedGas { gamma 4.4 pinf 6e8 }
        nbPhases 8
    }
}

Interfacial properties

The liquid-gas interface is characterized by the surface tension \(\sigma\) (Interface_base, which fills sigma_). The simplest model is a constant surface tension (Interface_sigma_constant).

Saturation properties

The saturation models give the thermal properties at saturation conditions (Saturation_base, inheriting from Interface); they fill Tsat, Psat, Lvap, Hls (liquid enthalpy at saturation), Hvs (steam enthalpy at saturation) and their pressure/temperature derivatives. A unique pressure field is assumed.

Constant saturation properties (Saturation_constant, params Tsat, Psat, Lvap, Hlsat, Hvsat, tension_superficielle): exactly two of {Lvap, Hlsat, Hvsat} must be given (the third is deduced, \(H_{vs}=H_{ls}+L_{vap}\)); all derivatives with respect to pressure/temperature are zero. Sodium saturation properties are given by Saturation_sodium.

Fluid properties from external software

Fluid properties can be managed through an external software: EOS (the CEA-EDF software for state-equation management, which can use a user-defined equation through a plugin) or CoolProp (an open-source alternative). Both can call the NIST state-equation software Refprop. The generic TPPI tables are implemented in Fluide_generique_TPPI_base (validity domain tmin_, tmax_, pmin_, pmax_).

CoolProp (Fluide_generique_CoolProp, params model, fluid): provides free state equations for a selected list of fluids.

EOS (Fluide_generique_EOS, params model, fluid, optional phase): Refprop offers 147 pure fluids, 5 pseudo-pure fluids (such as air) and mixtures with up to 20 components. For example, a boiling flow using refprop10:

liquide_eau Fluide_generique_EOS { model refprop10 fluid waterliquid }

gaz_eau Fluide_generique_EOS { model refprop10 fluid watervapor }

The corresponding saturation properties use Saturation_generique_TPPI_base (CoolProp/EOS), e.g. saturation_eau saturation_generique_EOS { model refprop10 fluid waterliquid }. A sigma_mano parameter is available to input the surface tension manually when the TTSE surface-tension call in CoolProp fails.