Change of k_min

[tobiasreischl]

• changed min value to Modelica.Constants.eps of k_min in PartialValve.mo

• Tested with existing test models and espresso machine

Closes #277

[CorentinLepais]

BasicControlValve test model failed when simulating with k_min<1e-10. I did not check the other valve models but the min value for k_min should definitely be higher than Modelica.Constant.eps

[tobiasreischl]

The problem is triggered by the dynamic closing process, not by the steady-state closed valve.
If the valve should close completely we need to include different dynamic behavior - or include a sperate case distinction.
For now the formulas don´t allow for quick shutting the valve without (relevant) leakage.

In the current PartialValve formulation,

[
dp \propto \left(\frac{m_\mathrm{flow}}{k_u}\right)^2
]

With inertance enabled, m_flow cannot decay as quickly as k_u during closing. Therefore, reducing k_min by one decade can increase the transient pressure-loss term by roughly two decades.

Adding a first-order actuator only shifts the problem to smaller values of k_min; it does not remove the underlying (1/k_u^2) scaling.

Possible improvements

• Regularize the zero-flow region in PartialValve, for example with Modelica.Fluid.Utilities.regSquare.
• In SpecificValveType, interpolate k_u directly or interpolate log(zeta) instead of zeta, since the current curve spans several orders of magnitude close to the closed position.
• Do not simply change the lower bound to Modelica.Constants.eps. This only allows numerically ill-conditioned parameter values without changing the underlying equations.
• Keep a validated finite lower bound for k_min for the current valve implementation.
• If ideal shut-off is required, implement it as a separate closed mode or dedicated shut-off valve model.

Conclusion

Regularization and improved curve scaling may reduce the practical lower limit of k_min, but arbitrarily small values are not numerically robust with the current pressure-loss formulation.