Incorrect definition of isentropicExponent for moist air near saturation

Modelica.Media.Air.MoistAir.isentropicExponent (MSL 4.1.0) is currently defined as

gamma := specificHeatCapacityCp(state) / specificHeatCapacityCv(state);

This definition is only valid for ideal gases.
For real media, the correct thermodynamic definition is

gamma := rho / p * a^2

where rho is the density, p the pressure, and a the speed of sound.

Unfortunately, in Modelica.Media.Air.MoistAir, this dependency is circular: the speed of sound is itself computed based on the isentropic exponent. As a result, the formulation becomes invalid close to saturation.

Observed behavior

Model: MoistAirIsentropicExponent.zip
Tested with MSL 4.0.0 (as far as i know, no change in 4.1.0)

Figure 1a (top left) shows the isentropic exponent kappa (gamma) for "humidity" values from 99.8% to 100.2% (phi = p_H2O/p_H2O_sat = relative humidity, psi = x/x_sat = normalized humidity ratio; see Fig. 1c bottom left). In this narrow range, kappa changes dramatically from approximately 1.4 to 4.5.

Figure 1b illustrates the effect on an exemplary isentropic compression from 1 bar to 2 bar, with an inlet temperature of 20 °C:

• T_is: outlet temperature computed using Medium.specificEntropy
• T_kappa: outlet temperature computed using the isentropic exponent from
  Fig. 1a

The resulting outlet temperature varies from roughly 80 °C to 230 °C.

Practical impact

In climate and HVAC system modeling, it is common to set ambient conditions to saturated air ( phi = psi = 1). With the current implementation, this can lead to severe modeling errors.

Possible solutions

1. Documentation update
   Clearly state that isentropicExponent() is only valid for approximately
   phi, psi < 0.999.

2. Runtime warning
   Trigger a warning in isentropicExponent() for phi, psi > 0.999.

3. Use unsaturated kappa beyond saturation
   Apply the unsaturated isentropic exponent also for kappa >= 1.
   While not physically exact, this is far more accurate than the current
   behavior. The isentropic exponent changes only slightly for oversaturated
   air. The model would still be incorrect for large amount of liquid or solid water, but MoistAir
   does not properly support Xi = 1 anyway.

4. Full model correction
   Update the model formulation to be valid for psi, phi >= 1.

Recommendation

From a cost–benefit perspective, (3) + (1) appears to be the most practical solution to me.
Option (2) would also be useful, provided it does not generate an excessive number of warnings.

Remark

The definition of specificEntropy() does likewise not take liquid water and solid water into account, which is also noted in the documentation. Its defintion is however likely to cause only minor errors for slightly oversaturated air, comparably with option (3).