Gate Valve (IL)

Gate valve in an isothermal liquid system

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

Description

The Gate Valve (IL) block represents flow control by a gate valve in an isothermal liquid network. The valve comprises a round, sharp-edged orifice and a round gate with the same diameter. The gate opens or closes according to the displacement signal at port S. A positive signal retracts the gate and opens the valve.

Opening Area

Gate Valve Opening Schematic

The area open to flow as the gate retracts is:

$$A_{open}=\frac{\pi d_0^2}{4}-A_{shielded},$$

where d₀ is the Valve orifice diameter. The area shielded by the gate in a partially open valve is:

$$A_{shielded}=\frac{d_0^2}{2}{\cos }^{-1}\left(\frac{\Delta l}{d_0}\right)-\frac{\Delta l}{2}\sqrt{d_0^2-{\left(\Delta l\right)}^2},$$

where Δl is the gate displacement, which is the sum of the signal at port S and the Gate position when fully covering orifice.

If displacement exceeds the Orifice diameter, the valve area 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 gate offset that is less than 0, the minimum valve area is the Leakage area.

Numerically Smoothed Displacement

When the valve is in a near-open or near-closed position, you can maintain numerical robustness in your simulation by adjusting the Smoothing factor parameter. If the Smoothing factor parameter is nonzero, the block smoothly saturates the gate displacement between 0 and the Valve orifice diameter parameter. 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 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, which is 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 want to capture this increase in pressure, clear the Pressure recovery check box. In this case, PR_loss is 1.

Examples

Compare Test Harnesses for Isothermal Liquid Flow Control Valves

This example uses test harnesses to compare the Ball Valve (IL), Gate Valve (IL), and Poppet Valve (IL) blocks. A test harness is a minimum viable model that you can use to parameterize blocks or isolate dynamics.

Model

Simulation Results from Scopes

This figure shows the mass flow rate through each of the valves. All three valves start closed and slowly open before reaching their maximum area. At the maximum area, the mass flow rate also reaches its maximum and cannot increase further. Each curve has a different profile while opening because each valve has a different area profile that depends on the valve geometry.

Ports

Input

S — Gate displacement, m

physical signal

Physical signal port associated with the valve gate displacement, in m. A positive signal retracts the gate and opens the valve.

Conserving

A — Liquid port

isothermal liquid

Isothermal liquid conserving port associated with valve inlet A.

B — Liquid port

isothermal liquid

Isothermal liquid conserving port associated with valve inlet B.

Parameters

Valve orifice diameter — Orifice diameter

5e-3 m^2 (default) | positive scalar

Valve open-area diameter.

Gate position when fully covering orifice — Gate offset

0 m (default) | positive scalar

Gate offset when the valve is closed. A positive, nonzero value indicates a partially open valve when the signal at port S is 0. A negative, nonzero value indicates an overlapped valve that remains closed for an initial positive 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 — Orifice 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 orifice.

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 valve.

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.

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