# Temperature Control Valve (TL)

Flow control valve with temperature-based actuation

**Libraries:**

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

## Description

The Temperature Control Valve (TL) block models an orifice with a thermostat as a flow control mechanism. The thermostat contains a temperature sensor and a black-box opening mechanism—one whose geometry and mechanics matter less than its effects. The sensor responds with a slight delay, captured by a first-order time lag, to variations in temperature.

When the sensor reads a temperature in excess of a preset activation value, the opening mechanism is actuated. The valve begins to open or close, depending on the chosen operation mode—the first case corresponding to a normally closed valve and the second to a normally open valve. The change in opening area continues up to the limit of the valve's temperature regulation range, beyond which the opening area is a constant.

A smoothing function allows the valve opening area to change smoothly between the fully closed and fully open positions. The smoothing function does this by removing the abrupt opening area changes at the zero and maximum ball 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 valve opening area calculation is based on the linear expression

$${S}_{Linear}=\left(\frac{{S}_{End}-{S}_{Start}}{{T}_{Range}}\right)\left({T}_{Sensor}-{T}_{Activation}\right)+{S}_{Start},$$

where:

*S*_{Linear}is the linear valve opening area.*S*_{Start}is the valve opening area at the beginning of the temperature actuation range. This area depends on the**Valve operation**parameter setting:$${S}_{Start}=\{\begin{array}{ll}{S}_{Leak},\hfill & \text{Valveopensaboveactivationtemperature}\hfill \\ {S}_{Max},\hfill & \text{Valveclosesaboveactivationtemperature}\hfill \end{array}$$

*S*_{End}is the valve opening area at the end of the temperature actuation range. This area depends on the**Valve operation**parameter setting:$${S}_{End}=\{\begin{array}{ll}{S}_{Max},\hfill & \text{Valveopensaboveactivationtemperature}\hfill \\ {S}_{Leak},\hfill & \text{Valveclosesaboveactivationtemperature}\hfill \end{array}$$

*S*_{Max}is the valve opening area in the fully open position.*S*_{Leak}is the valve opening area in the fully closed position. Only leakage flow remains in this position.*T*_{Range}is the temperature regulation range.*T*_{Activation}is the minimum temperature required to operate the valve.*T*_{Sensor}is the measured valve temperature.

The valve model accounts for a first-order lag in the measured valve temperature through the differential equation:

$$\frac{d}{dt}\left({T}_{Sensor}\right)=\frac{{T}_{Avg}-{T}_{Sensor}}{\tau},$$

where:

*T*_{Avg}is the arithmetic average of the valve port temperatures,$${T}_{Avg}=\frac{{T}_{A}+{T}_{B}}{2},$$

where

*T*_{A}and*T*_{B}are the temperatures at ports A and B.*τ*is the**Sensor time constant**value specified in the block dialog box.

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 valve
area between *S _{Leak}* and

*S*. For more information, see Numerical Smoothing.

_{Max}## Examples

## Ports

### Conserving

## Parameters

## Extended Capabilities

## Version History

**Introduced in R2016a**