# Needle Valve

(To be removed) Hydraulic needle valve

**The Hydraulics (Isothermal) library will be removed in a
future release. Use the Isothermal Liquid library instead. (since R2020a)**

**For more information on updating your models, see Upgrading Hydraulic Models to Use Isothermal Liquid Blocks.**

## Library

Flow Control Valves

## Description

The Needle Valve block models a variable orifice created by a conical needle and a round sharp-edged orifice in thin material.

The flow rate through the valve is proportional to the valve opening and to the pressure differential across the valve. The flow rate is determined according to the following equations:

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

$$\Delta p={p}_{\text{A}}-{p}_{\text{B}},$$

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

$${h}_{\mathrm{max}}={d}_{s}\frac{1-\sqrt{1-\mathrm{cos}\frac{\alpha}{2}}}{\mathrm{sin}\alpha}$$

$$A(h)=\{\begin{array}{ll}{A}_{leak}\hfill & \text{for}h=0\hfill \\ \pi \cdot \left({d}_{s}-h\cdot \mathrm{sin}\frac{\alpha}{2}\cdot \mathrm{cos}\frac{\alpha}{2}\right)\cdot h\cdot \mathrm{sin}\frac{\alpha}{2}+{A}_{leak}\hfill & \text{for}0h{h}_{\mathrm{max}}\hfill \\ {A}_{\mathrm{max}}+{A}_{leak}\hfill & \text{for}h={h}_{\mathrm{max}}\hfill \end{array}$$

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

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 |

x_{0} | Initial opening |

x | Needle displacement from initial position |

h | Valve opening |

h_{max} | Maximum needle stroke |

d_{s} | Orifice diameter |

α | Needle angle |

ρ | Fluid density |

A_{leak} | Closed valve leakage area |

A_{max} | Maximum valve open area |

p_{cr} | Minimum pressure for turbulent flow |

The minimum pressure for turbulent flow,
*p*_{cr}, is calculated according to the laminar
transition specification method:

By pressure ratio — The transition from laminar to turbulent regime is defined by the following equations:

*p*_{cr}= (*p*_{avg}+*p*_{atm})(1 –*B*_{lam})*p*_{avg}= (*p*_{A}+*p*_{B})/2where

*p*_{avg}Average pressure between the block terminals *p*_{atm}Atmospheric pressure, 101325 Pa *B*_{lam}Pressure ratio at the transition between laminar and turbulent regimes ( **Laminar flow pressure ratio**parameter value)By Reynolds number — The transition from laminar to turbulent regime is defined by the following equations:

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

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

where

*D*_{H}Valve instantaneous hydraulic diameter *ν*Fluid kinematic viscosity *Re*_{cr}Critical Reynolds number ( **Critical Reynolds number**parameter value)

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`

opens the valve.

## Basic Assumptions and Limitations

Fluid inertia is not taken into account.

The flow passage area is assumed to be equal to the frustum side surface area.

## Parameters

**Valve orifice diameter**The diameter of the orifice of the valve. The default value is

`0.005`

m.**Needle cone angle**The angle of the valve conical needle. The parameter value must be in the range between 0 and 180 degrees. The default value is

`90`

degrees.**Initial opening**The initial opening of the valve. You can specify both positive and negative values. The default value is

`0`

.**Flow discharge coefficient**Semi-empirical parameter for valve 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

`0.65`

.**Laminar transition specification**Select how the block transitions between the laminar and turbulent regimes:

`Pressure ratio`

— The transition from laminar to turbulent regime is smooth and depends on the value of the**Laminar flow pressure ratio**parameter. This method provides better simulation robustness.`Reynolds number`

— The transition from laminar to turbulent regime is assumed to take place when the Reynolds number reaches the value specified by the**Critical Reynolds number**parameter.

**Laminar flow pressure ratio**Pressure ratio at which the flow transitions between laminar and turbulent regimes. The default value is

`0.999`

. This parameter is visible only if the**Laminar transition specification**parameter is set to`Pressure ratio`

.**Critical Reynolds number**The maximum Reynolds number for laminar flow. 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`

. This parameter is visible only if the**Laminar transition specification**parameter is set to`Reynolds number`

.**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. The parameter value must be greater than 0. The default value is

`1e-12`

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 valve inlet.

`B`

Hydraulic conserving port associated with the valve outlet.

`S`

Physical signal port to control spool displacement.

## Extended Capabilities

## Version History

**Introduced in R2006a**