Implementation of a hydraulic check valve. Note that the small reverse flows can still occur with this model.
The basic flow function
m = sign(Δp) k √ Δp ,
with regularization near the origin, is used to compute the pressure drop. The flow coefficient
k = m ⁄ √ 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.