# 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.

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

$${p}_{A}-{p}_{B}=\frac{\dot{m}\sqrt{{\dot{m}}^{2}+{\dot{m}}_{cr}^{2}}}{2{\rho}_{Avg}{C}_{d}^{2}{S}^{2}}\left[1-{\left(\frac{{S}_{R}}{S}\right)}^{2}\right]P{R}_{Loss},$$

where:

*p*_{A}and*p*_{B}are the pressures at port**A**and port**B**.$$\dot{m}$$ is the mass flow rate.

$${\dot{m}}_{cr}$$ is the critical mass flow rate:

$${\dot{m}}_{cr}={\mathrm{Re}}_{cr}{\mu}_{Avg}\sqrt{\frac{\pi}{4}{S}_{R}}.$$

*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:$$P{R}_{Loss}=\frac{\sqrt{1-{\left({S}_{R}/S\right)}^{2}\left(1-{C}_{d}^{2}\right)}-{C}_{d}\left({S}_{R}/S\right)}{\sqrt{1-{\left({S}_{R}/S\right)}^{2}\left(1-{C}_{d}^{2}\right)}+{C}_{d}\left({S}_{R}/S\right)}.$$

### Energy Balance

The energy conservation equation in the valve is

$${\varphi}_{A}+{\varphi}_{B}=0,$$

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

$$A=\frac{\pi {d}_{0}^{2}}{4}-{A}_{Covered}+{A}_{leak},$$

where:

*A*is the valve opening area.*A*is the value of the_{leak}**Leakage area**parameter.*d*_{0}is the valve orifice diameter.*A*_{Covered}is the portion of the valve orifice area covered by the gate:$${A}_{Covered}=\frac{{d}_{0}^{2}}{2}\text{acos}\left(\frac{\Delta l}{{d}_{0}}\right)-\frac{\Delta l}{2}\sqrt{{d}_{0}^{2}-{\left(\Delta l\right)}^{2}}.$$

*Δl*is the net displacement of the gate center relative to the orifice center.$$\Delta l=\{\begin{array}{ll}0,\hfill & \left({S}_{d}-{S}_{\mathrm{min}}\right)\le 0\hfill \\ {d}_{0},\hfill & \left({S}_{d}-{S}_{\mathrm{min}}\right)\ge {d}_{0}\hfill \\ \left({S}_{d}-{S}_{\mathrm{min}}\right),\hfill & \text{Else}\hfill \end{array}$$

*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

### Conserving

## Parameters

## Extended Capabilities

## Version History

**Introduced in R2016a**