# Orifice with Variable Area Round Holes

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

Orifices

## Description

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 d0 Orifice hole diameter

The flow rate is determined according to the following equations:

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

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

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

$h={x}_{0}+x·or$

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

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

where

 q Flow rate p Pressure differential pA, pB Gauge pressures at the block terminals CD Flow discharge coefficient A(h) Instantaneous orifice passage area d0 Hole diameter z Number of holes x0 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 pcr Minimum pressure for turbulent flow Recr Critical Reynolds number DH Instantaneous orifice hydraulic diameter Aleak Closed orifice leakage area Amax 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.

## Basic Assumptions and Limitations

• Fluid inertia is not taken into account.

## Dialog Box and Parameters

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.

## Global Parameters

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.

## Ports

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.