Annular Orifice

Hydraulic variable orifice created by circular tube and round insert

• Library:

• Simscape / Fluids / Hydraulics (Isothermal) / Orifices

• 

Description

The Annular Orifice block annular leakage in a fully-developed laminar flow created by a circular tube and a round insert in an isothermal liquid network. The insert can be located off-center from the tube by an eccentricity value.

The flow rate is computed using the Hagen-Poiseuille equation (see [1]):

$$q=\frac{\pi R{(R-r)}^3}{6\nu \rho L}·\left(1+\frac{3}{2}{\epsilon }^2\right)·p$$

$$\epsilon =\frac{e}{R-r}$$

where

q	Flow rate
p	Pressure differential
R	Orifice radius
r	Insert radius
L	Overlap length
ε	Eccentricity ratio
e	Eccentricity
ρ	Fluid density
ν	Fluid kinematic viscosity

Use this block to simulate leakage path in plungers, valves, and cylinders.

The block positive direction is from port A to port B. This means that the flow rate is positive if it flows from A to B and the pressure differential is determined as $$\Delta p=p_{\text{A}}-p_{\text{B}},$$. Positive signal at the physical signal port S increases or decreases the overlap, depending on the value of the parameter Orifice orientation.

Assumptions and Limitations

Fluid inertia is not taken into account.

Ports

Input

S — Physical signal port that controls the insert displacement, m

physical signal

Physical signal port that controls the insert displacement.

Conserving

A — Hydraulic conserving port associated with the orifice inlet

hydraulic

Hydraulic conserving port associated with the orifice inlet.

B — Hydraulic conserving port associated with the orifice outlet

hydraulic

Hydraulic conserving port associated with the orifice outlet.

Parameters

Orifice radius — Radius of the tube

0.01 m (default) | positive scalar

The radius of the tube.

Insert radius — Radius of the insert

0.0098 m (default) | positive scalar

The radius of the insert.

Eccentricity — Distance between the central axes of the insert and the tube

0 (default) | nonnegative scalar

The distance between the central axes of the insert and the tube. The parameter can be a positive value, smaller than the difference between the radius of the tube and the radius of the insert, or equal to zero for coaxial configuration.

Initial length — Initial overlap between the tube and the insert

0.003 m (default) | positive scalar

Initial overlap between the tube and the insert. The parameter must be positive. The value of the initial length does not depend on the orifice orientation.

Orifice orientation — Specifies the effect of the control signal on the orifice overlap

Positive signal increases overlap (default) | Negative signal increases overlap

Specifies the effect of the control signal on the orifice overlap.

References

[1] Noah D. Manring, Hydraulic Control Systems, John Wiley & Sons, 2005

Extended Capabilities

C/C++ Code Generation
Generate C and C++ code using Simulink® Coder™.

Version History

Introduced in R2006b