Implementation of a hydraulic check valve. Note that small reverse flows can still occur with this model.
The basic flow function
ṁ = sign(Δp) k √ Δp ,
with regularization near the origin, is used to compute the mass
flow rate through the fully closed and fully open valve,
respectively. The valve is considered fully closed when subjected
to a negative pressure drop, and its flow coefficient k is
then equal to l * Kv_SI, where Kv_SI is
equal to Kv but in SI units. The valve is considered
fully open when the pressure drop exceeds
dpValve_closing, and its flow coefficient k is
then equal to Kv_SI. For valve positions between these
two extremes, a quintic spline interpolation is applied to
determine the mass flow rate as a function of the pressure drop
across the valve.
The parameters m_flow_nominal and
dpValve_nominal determine the flow coefficient of the
check valve when it is fully open. The leakage ratio l
determines the minimum flow coefficient, for negative pressure
differences. The parameter dpFixed_nominal allows to
include a series pressure drop with a fixed flow coefficient into
the model. The parameter dpValve_closing determines
when the flow coefficient starts to increase, which is typically in
the order of dpValve_nominal.
The check valve implementation approximates the physics where a
forward pressure difference opens the valve such that the valve
opening increases, causing a growing orifice area and thus
increasing the flow coefficient. Near
dp=dpValve_closing, the valve is fully open and the
flow coefficient saturates to the flow coefficient value determined
by dpValve_nominal and m_flow_nominal.
For typical valve diameters, the check valve is only fully open
near nominal mass flow rate. Therefore, the model sets
dpValve_closing=dpValve_nominal/2 by default.