Implementation of a hydraulic check valve. Note that the 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 pressure drop. The flow coefficient
k = ṁ ⁄ √ Δp
is increased from l*KV_Si to KV_Si,
where KV_Si is equal to Kv but in SI units.
Therefore, the flow coefficient k is set to a value close to zero for negative pressure differences, thereby
restricting reverse flow to a small value.
The flow coefficient k saturates to its maximum value at the pressure dpValve_closing.
For larger pressure drops, the pressure drop is a quadratic function of the flow rate.
The parameters m_flow_nominal and dpValve_nominal
determine the flow coefficient of the check valve when it is fully opened.
A typical value for a nominal flow rate of 1 m/s is
dpValve_nominal = 3400 Pa.
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.