Needle Valve

Hydraulic needle valve

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Flow Control Valves

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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:

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

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

$$h=x_0+x$$

$$h_{\max }=d_s\frac{1-\sqrt{1-\cos \frac{\alpha }{2}}}{\sin \alpha }$$

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

$$A_{\max }=\frac{\pi d_s^2}{4}$$

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
x0	Initial opening
x	Needle displacement from initial position
h	Valve opening
hmax	Maximum needle stroke
ds	Orifice diameter
α	Needle angle
ρ	Fluid density
Aleak	Closed valve leakage area
Amax	Maximum valve open area
pcr	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)/2

  where

  pavg	Average pressure between the block terminals
  patm	Atmospheric pressure, 101325 Pa
  Blam	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

  DH	Valve instantaneous hydraulic diameter
  ν	Fluid kinematic viscosity
  Recr	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

C/C++ Code Generation
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