Hydraulic variable orifice created by circular tube and round insert

Orifices

The Annular Orifice block models a variable orifice created by a circular tube and a round insert, which may be eccentrically located with respect to the tube. The radial gap between the tube and the insert and its axial length are assumed to be essentially smaller than the insert diameter, causing the flow regime to be laminar all the time. A schematic representation of the annular orifice is shown in the following illustration.

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

$$q=\frac{\pi R{(R-r)}^{3}}{6\nu \rho L}\xb7\left(1+\frac{3}{2}{\epsilon}^{2}\right)\xb7p$$

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

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**.

Fluid inertia is not taken into account.

**Orifice radius**The radius of the tube. The default value is

`0.01`

m.**Insert radius**The radius of the insert. The default value is

`0.0098`

m.**Eccentricity**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. The default value is

`0`

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

`0.003`

m.**Orifice orientation**The parameter is introduced to specify the effect of the control signal on the orifice overlap. The parameter can be set to one of two options:

`Positive signal increases overlap`

or`Negative signal increases overlap`

. The default value is`Positive signal increases overlap`

.

Parameters determined by the type of working fluid:

**Fluid density****Fluid kinematic viscosity**

Use the Hydraulic Fluid block or the Custom Hydraulic Fluid block to specify the fluid properties.

The block has the following ports:

`A`

Hydraulic conserving port associated with the orifice inlet.

`B`

Hydraulic conserving port associated with the orifice outlet.

`S`

Physical signal port that controls the insert displacement.

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

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