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Hydraulic variable orifice created by circular tube and round insert

Orifices

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]):

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

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

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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