Hydraulic variable orifice shaped as set of round holes drilled in sleeve

Orifices

The block models a variable orifice created by a cylindrical spool and a set of round holes drilled in the sleeve. All the holes are of the same diameter, evenly spread along the sleeve perimeter, and their center lines are located in the same plane. The flow rate through the orifice is proportional to the orifice opening and to the pressure differential across the orifice. The following schematic shows the cross section of an orifice with variable round holes, where

q | Flow rate |

h | Orifice opening |

x | Spool displacement from initial position |

d_{0} | Orifice hole diameter |

The flow rate is determined according to the following equations:

$$q={C}_{D}\cdot A(h)\sqrt{\frac{2}{\rho}}\cdot \frac{p}{{\left({p}^{2}+{p}_{cr}^{2}\right)}^{1/4}}$$

$$p={p}_{A}-{p}_{B}$$

$${p}_{cr}=\frac{\rho}{2}{\left(\frac{{\mathrm{Re}}_{cr}\cdot \nu}{{C}_{D}\cdot {D}_{H}}\right)}^{2}$$

$$h={x}_{0}+x\xb7or$$

$$A(h)=\{\begin{array}{ll}{A}_{leak}\hfill & \text{for}h=0\hfill \\ \left(\frac{1}{8}z\xb7{d}_{0}^{2}\left(2\mathrm{arccos}\left(1-\frac{2h}{{d}_{0}}\right)-\mathrm{sin}\left(2\mathrm{arccos}\left(1-\frac{2h}{{d}_{0}}\right)\right)\right)\right)+{A}_{leak}\hfill & \text{for}0h{d}_{0}\hfill \\ {A}_{\mathrm{max}}+{A}_{leak}\hfill & \text{for}h={d}_{0}\hfill \end{array}$$

$${D}_{H}=\sqrt{\frac{4A(h)}{\pi}}$$

$${A}_{\mathrm{max}}=\frac{\pi {d}_{0}^{2}}{4}$$

where

q | Flow rate |

p | Pressure differential |

p_{A}, p_{B} | Gauge pressures at the block terminals |

C_{D} | Flow discharge coefficient |

A(h) | Instantaneous orifice passage area |

d_{0} | Hole diameter |

z | Number of holes |

x_{0} | Initial opening |

x | Spool displacement from initial position |

h | Orifice opening |

or | Orifice orientation indicator. The variable assumes +1 value if a spool displacement in the globally assigned positive direction opens the orifice, and –1 if positive motion decreases the opening. |

ρ | Fluid density |

ν | Fluid kinematic viscosity |

p_{cr} | Minimum pressure for turbulent flow |

Re_{cr} | Critical Reynolds number |

D_{H} | Instantaneous orifice hydraulic diameter |

A_{leak} | Closed orifice leakage area |

A_{max} | Fully open orifice passage area |

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 $$p={p}_{A}-{p}_{B}$$. Positive signal at the physical
signal port `S`

opens or closes the orifice depending
on the value of the parameter **Orifice orientation**.

Fluid inertia is not taken into account.

**Diameter of round holes**Diameter of the orifice holes. The default value is

`5e-3`

m.**Number of round holes**Number of holes. The default value is

`6`

.**Flow discharge coefficient**Semi-empirical parameter for orifice capacity characterization. Its value depends on the geometrical properties of the orifice, and usually is provided in textbooks or manufacturer data sheets. The default value is

`0.6`

.**Initial opening**Orifice initial opening. The parameter can be positive (underlapped orifice), negative (overlapped orifice), or equal to zero for zero lap configuration. The value of initial opening does not depend on the orifice orientation. The default value is

`0`

.**Orifice orientation**The parameter is introduced to specify the effect of the orifice control member motion on the valve opening. The parameter can be set to one of two options:

`Opens in positive direction`

or`Opens in negative direction`

. The value`Opens in positive direction`

specifies an orifice whose control member opens the valve when it is shifted in the globally assigned positive direction. The parameter is extremely useful for building a multi-orifice valve with all the orifices being controlled by the same spool. The default value is`Opens in positive direction`

.**Critical Reynolds number**The maximum Reynolds number for laminar flow. The transition from laminar to turbulent regime is assumed to take place when the Reynolds number reaches this value. The value of the parameter depends on the orifice geometrical profile. You can find recommendations on the parameter value in hydraulics textbooks. The default value is

`10`

.**Leakage area**The total area of possible leaks in the completely closed valve. The main purpose of the parameter is to maintain numerical integrity of the circuit by preventing a portion of the system from getting isolated after the valve is completely closed. An isolated or "hanging" part of the system could affect computational efficiency and even cause simulation to fail. Therefore, MathWorks recommends that you do not set this parameter to 0. The default value is

`1e-15`

m^2.

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 to control spool displacement.

The flow rate is positive if fluid flows from port `A`

to
port `B`

. Positive signal at the physical signal
port `S`

opens or closes the orifice depending on
the value of the parameter **Orifice orientation**.

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