Needle Valve (IL)

Needle valve in an isothermal liquid system

Since R2020a

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Libraries:
Simscape / Fluids / Isothermal Liquid / Valves & Orifices / Flow Control Valves

Description

The Needle Valve (IL) block models flow reductions by a needle valve. The valve comprises a conical needle and a round, sharp-edged seat. The needle opens or closes according to the displacement signal at port S. A positive signal retracts the needle and opens the valve.

Opening Area

Needle Valve Schematic

Needle Valve Top View

The opening area of the valve is calculated as:

$$A_{open}=\pi h\sin \left(\frac{\theta }{2}\right)\left[d_0-\frac{h}{2}\sin \left(\theta \right)\right]+A_{leak},$$

where:

• h is the vertical distance between the outer edge of the needle and the seat, as indicated in the schematic above.

• θ is the seat cone angle, which always matches the Needle cone angle.

• d₀ is the Seat orifice diameter.

• A_leak is the Leakage area.

The opening area is bounded by the maximum displacement h_max:

$$h_{\max }=\frac{d_0\left[1-\sqrt{1-\cos \left(\frac{\theta }{2}\right)}\right]}{\sin \left(\theta \right)}.$$

For any needle displacement larger than h_max, A_open is the sum of the maximum orifice area and the Leakage area:

$$A_{open}=\frac{\pi }{4}{d}_0^2+A_{leak}.$$

For any combination of the signal at port S and the needle offset that is less than 0, the minimum valve area is the Leakage area.

If the Smoothing factor parameter is nonzero, the block smoothly saturates the displacement between 0 and h_max. For more information, see Numerical Smoothing.

Mass Flow Rate Equation

Mass is conserved through the valve:

$${\dot{m}}_A+{\dot{m}}_B=0.$$

The mass flow rate through the valve is calculated as:

$$\dot{m}=\frac{C_d{A}_{valve}\sqrt{2\overline{\rho }}}{\sqrt{P{R}_{loss}\left(1-{\left(\frac{A_{valve}}{A_{port}}\right)}^2\right)}}\frac{\Delta p}{{\left[\Delta p^2+\Delta p_{crit}^2\right]}^{1/4}},$$

where:

• C_d is the Discharge coefficient.

• A_valve is the instantaneous valve open area.

• A_port is the Cross-sectional area at ports A and B.

• $$\overline{\rho }$$ is the average fluid density.

• Δp is the valve pressure difference p_A – p_B.

The critical pressure difference, Δp_crit, is the pressure differential associated with the Critical Reynolds number, Re_crit, the flow regime transition point between laminar and turbulent flow:

$$\Delta p_{crit}=\frac{\pi \overline{\rho }}{8A_{valve}}{\left(\frac{\nu {\mathrm{Re}}_{crit}}{C_d}\right)}^2.$$

Pressure loss describes the reduction of pressure in the valve due to a decrease in area. PR_loss is calculated as:

$$P{R}_{loss}=\frac{\sqrt{1-{\left(\frac{A_{valve}}{A_{port}}\right)}^2\left(1-C_d^2\right)}-C_d\frac{A_{valve}}{A_{port}}}{\sqrt{1-{\left(\frac{A_{valve}}{A_{port}}\right)}^2\left(1-C_d^2\right)}+C_d\frac{A_{valve}}{A_{port}}}.$$

Pressure recovery describes the positive pressure change in the valve due to an increase in area. If you do not wish to capture this increase in pressure, clear the Pressure recovery check box. In this case, PR_loss is 1.

Examples

Diesel Engine In-Line Injection System

An in-line multi-element diesel injection system. It consists of a cam shaft, a lift pump, four in-line injection pumps, and four injectors.

• Open Model

Ports

Conserving

A — Liquid port

isothermal liquid

Liquid entry or exit port to the valve.

B — Liquid port

isothermal liquid

Liquid entry or exit port to the valve.

Input

S — Needle displacement, m

physical signal

Control member displacement in m, specified as a physical signal. A positive signal retracts the needle and opens the valve.

Parameters

Seat orifice diameter — Diameter of seat

5e-3 m (default) | positive scalar

Diameter of the seat orifice.

Needle cone angle — Control member geometry angle

90 deg (default) | positive scalar

Control member geometry angle. Refer to the Needle Valve Schematic in the valve description.

Needle position when in the seat — Needle offset

0 m (default) | scalar

Needle offset when the valve is closed. A positive, nonzero value indicates a partially open valve. A negative, nonzero value indicates an overlapped valve that remains closed for an initial displacement set by the physical signal at port S.

Leakage area — Gap area when in fully closed position

1e-10 m^2 (default) | positive scalar

Sum of all gaps when the valve is in the fully closed position. Any area smaller than this value is saturated to the specified leakage area. This contributes to numerical stability by maintaining continuity in the flow.

Cross-sectional area at ports A and B — Area at conserving ports

inf m^2 (default) | positive scalar

Areas at the entry and exit ports A and B, which are used in the pressure-flow rate equation that determines the mass flow rate through the valve.

Discharge coefficient — Discharge coefficient

0.64 (default) | positive scalar

Correction factor accounting for discharge losses in theoretical flows.

Critical Reynolds number — Upper Reynolds number limit for laminar flow

150 (default) | positive scalar

Upper Reynolds number limit for laminar flow through the orifice.

Smoothing factor — Numerical smoothing factor

0.01 (default) | positive scalar in the range [0,1]

Continuous smoothing factor that introduces a layer of gradual change to the flow response when the valve is in near-open or near-closed positions. Set this value to a nonzero value less than one to increase the stability of your simulation in these regimes.

Pressure recovery — Whether to account for pressure increase in area expansions

off (default) | on

Whether to account for pressure increase when fluid flows from a region of smaller cross-sectional area to a region of larger cross-sectional area.

Extended Capabilities

C/C++ Code Generation
Generate C and C++ code using Simulink® Coder™.

Version History

Introduced in R2020a