This is a model of a controlled restriction with lumped volumes. The opening area A is controlled with a signal sNorm, normalized between -1 and +1. The area remains at until sNorm has exceeded the overlap parameter. When sNorm reaches 1, the area A equals the parameter . When sNorm is between overlap and 1, the area A follows the equation below:



The flow through the orifice is proportional to the square root of the pressure drop:



where

A		:	Opening area
		:	Maximum opening area
		:	Minimum opening area
sNorm		:	Normalized control signal
overlap		:	The orifice does not start to open until sNorm has exceeded this value
		:	Mass flow rate
		:	Fluid density
		:	Discharge coefficient
		:	Pressure difference between ports a and b

Implementation

The flow equation is linearized for pressure differences near zero to increase numerical stability.

Reference

K. Gieck and R. Gieck, Engineering Formulas, 7th ed., Germering, Germany: Gieck Publishing, 1997 p. N7.

medium	Value: Oil() Type: Medium Description: Medium in the component
Gleak	Value: 1e-020 Type: PressureDependentLeakage (m³/(s⋅Pa)) Description: Conductance of closed valve
Aleak	Value: (Gleak * ReCr * medium.nu * medium.rho * sqrt(Modelica.Constants.pi) / (4 * Cd ^ 2)) ^ (2 / 3) Type: Area (m²) Description: Minimum opening area
AMax	Value: 0.001 Type: Area (m²) Description: Maximum opening area
Cd	Value: 0.62 Type: Real Description: Coefficient of discharge for the opening
ReCr	Value: 12 Type: Real Description: Critical Reynolds number
overlap	Value: 0 Type: Length (m) Description: Normalized position when the opening is closed
V	Value: 0.0001 Type: Volume (m³) Description: Volume of component