Gate Valve (TL)

Gate valve in a thermal liquid system

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

Description

The Gate Valve (TL) block represents a gate valve in a thermal 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 lifts the gate to open the valve. The diagram shows the relationship between the opening area and the net displacement of the gate.

Diagram showing the relationship between the opening area and the net displacement of the gate.

A smoothing function allows the valve opening area to change smoothly between the fully closed and fully open positions. The smoothing function reduces the abrupt opening area changes at the zero and maximum gate positions.

Mass Balance

The mass conservation equation in the valve is

${\dot{m}}_{A} + {\dot{m}}_{B} = 0,$

where:

${\dot{m}}_{A}$ is the mass flow rate into the valve through port A.
${\dot{m}}_{B}$ is the mass flow rate into the valve through port B.

Momentum Balance

The momentum conservation equation in the valve is

$p_{A} - p_{B} = \frac{\dot{m} \sqrt{{\dot{m}}^{2} + {\dot{m}}_{c r}^{2}}}{2 ρ_{A v g} C_{d}^{2} S^{2}} [1 - {(\frac{S_{R}}{S})}^{2}] P R_{L o s s},$

where:

p_A and p_B are the pressures at port A and port B.
$\dot{m}$ is the mass flow rate.
${\dot{m}}_{c r}$ is the critical mass flow rate:

${\dot{m}}_{c r} = {Re}_{c r} μ_{A v g} \sqrt{\frac{π}{4} S_{R}} .$
ρ_Avg is the average liquid density.
C_d is the discharge coefficient.
S is the valve inlet area.
PR_Loss is the pressure ratio:

$P R_{L o s s} = \frac{\sqrt{1 - {(S_{R} / S)}^{2} (1 - C_{d}^{2})} - C_{d} (S_{R} / S)}{\sqrt{1 - {(S_{R} / S)}^{2} (1 - C_{d}^{2})} + C_{d} (S_{R} / S)} .$

Energy Balance

The energy conservation equation in the valve is

$ϕ_{A} + ϕ_{B} = 0,$

where:

ϕ_A is the energy flow rate into the valve through port A.
ϕ_B is the energy flow rate into the valve through port B.

Valve Opening Area

The block computes the valve opening area by using the expression

$A = \frac{π d_{0}^{2}}{4} - A_{C o v e r e d} + A_{l e a k},$

where:

A is the valve opening area.
A_leak is the value of the Leakage area parameter.
d₀ is the valve orifice diameter.
A_Covered is the portion of the valve orifice area covered by the gate:

$A_{C o v e r e d} = \frac{d_{0}^{2}}{2} acos (\frac{Δ l}{d_{0}}) - \frac{Δ l}{2} \sqrt{d_{0}^{2} - {(Δ l)}^{2}} .$
Δl is the net displacement of the gate center relative to the orifice center.

$Δ l = {\begin{array}{l} 0, & (S_{d} - S_{\min}) \leq 0 \\ d_{0}, & (S_{d} - S_{\min}) \geq d_{0} \\ (S_{d} - S_{\min}), & Else \end{array}$
S_min is value of the Gate position when fully covering orifice parameter specified in the block dialog box.
S_d is the gate displacement specified through physical signal input port S.

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.

Ports

Input

expand all

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

expand all

A — Liquid port
thermal liquid

Thermal liquid conserving port associated with valve inlet A.

B — Liquid port
thermal liquid

Thermal liquid conserving port associated with valve inlet B.

Parameters

expand all

Orifice diameter — Orifice diameter
`0.01` `m` (default) | positive scalar

Valve open-area diameter.

Gate position when fully covering orifice — Gate offset
`0` `m` (default) | nonnegative 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 shut position
`1e-10` `m^2` (default) | positive scalar

Sum of all gaps when the valve is in the fully shut position. The block saturates smaller numbers to this value. This parameter contributes to numerical stability by maintaining continuity in the flow.

Smoothing factor — Numerical smoothing factor
`0.01` (default) | 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.

Cross-sectional area at ports A and B — Orifice area at conserving ports
`0.01` `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 that accounts for discharge losses in theoretical flows.

Gate Valve (TL)

Description

Mass Balance

Momentum Balance

Energy Balance

Valve Opening Area

Numerically Smoothed Displacement

Ports

Input

S — Gate displacement, m
physical signal

Conserving

A — Liquid port
thermal liquid

B — Liquid port
thermal liquid

Parameters

Orifice diameter — Orifice diameter
`0.01` `m` (default) | positive scalar

Gate position when fully covering orifice — Gate offset
`0` `m` (default) | nonnegative scalar

Leakage area — Gap area when in fully shut position
`1e-10` `m^2` (default) | positive scalar

Smoothing factor — Numerical smoothing factor
`0.01` (default) | scalar in the range [0,1]

Cross-sectional area at ports A and B — Orifice area at conserving ports
`0.01` `m^2` (default) | positive scalar

Discharge coefficient — Discharge coefficient
`0.64` (default) | positive scalar

Critical Reynolds number — Upper Reynolds number limit for laminar flow
`150` (default) | positive scalar

Extended Capabilities

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

Version History

See Also

Gate Valve (TL)

Description

Mass Balance

Momentum Balance

Energy Balance

Valve Opening Area

Numerically Smoothed Displacement

Ports

Input

S — Gate displacement, m physical signal

Conserving

A — Liquid port thermal liquid

B — Liquid port thermal liquid

Parameters

Orifice diameter — Orifice diameter 0.01 m (default) | positive scalar

Gate position when fully covering orifice — Gate offset 0 m (default) | nonnegative scalar

Leakage area — Gap area when in fully shut position 1e-10 m^2 (default) | positive scalar

Smoothing factor — Numerical smoothing factor 0.01 (default) | scalar in the range [0,1]

Cross-sectional area at ports A and B — Orifice area at conserving ports 0.01 m^2 (default) | positive scalar

Discharge coefficient — Discharge coefficient 0.64 (default) | positive scalar

Critical Reynolds number — Upper Reynolds number limit for laminar flow 150 (default) | positive scalar

Extended Capabilities

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

Version History

See Also

S — Gate displacement, m
physical signal

A — Liquid port
thermal liquid

B — Liquid port
thermal liquid

Orifice diameter — Orifice diameter
`0.01` `m` (default) | positive scalar

Gate position when fully covering orifice — Gate offset
`0` `m` (default) | nonnegative scalar

Leakage area — Gap area when in fully shut position
`1e-10` `m^2` (default) | positive scalar

Smoothing factor — Numerical smoothing factor
`0.01` (default) | scalar in the range [0,1]

Cross-sectional area at ports A and B — Orifice area at conserving ports
`0.01` `m^2` (default) | positive scalar

Discharge coefficient — Discharge coefficient
`0.64` (default) | positive scalar

Critical Reynolds number — Upper Reynolds number limit for laminar flow
`150` (default) | positive scalar

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