# Temperature Control Valve (TL)

Flow control valve with temperature-based actuation

## Library

Thermal Liquid/Valves/Flow Control Valves

## Description

The Temperature Control Valve (TL) block models a valve capable of regulating flow rates based on fluid temperature. The valve begins to open at the activation temperature. It is fully opened at the peak of the temperature regulation range. The block approximates the sensor dynamics with a first-order time lag.

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. The figure shows the effect of smoothing on the valve opening area curve.

Opening-Area Curve Smoothing

### 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:

• SLinear is the linear valve opening area.

• SStart is the valve opening area at the beginning of the temperature actuation range. This area depends on the Valve operation parameter setting:

• SEnd is the valve opening area at the end of the temperature actuation range. This area depends on the Valve operation parameter setting:

• SMax is the valve opening area in the fully open position.

• SLeak is the valve opening area in the fully closed position. Only leakage flow remains in this position.

• TRange is the temperature regulation range.

• TActivation is the minimum temperature required to operate the valve.

• TSensor 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:

• TAvg is the arithmetic average of the valve port temperatures,

`${T}_{Avg}=\frac{{T}_{A}-{T}_{B}}{2},$`
where TA and TB are the temperatures at ports A and B.

• τ is the Sensor time constant value specified in the block dialog box.

The valve opening expressions introduce undesirable discontinuities at the fully open and fully closed positions. The block eliminates these discontinuities using polynomial expressions that smooth the transitions to and from the fully open and fully closed positions. The valve smoothing expressions are

`${\lambda }_{L}=3{\overline{T}}_{L}^{2}-2{\overline{T}}_{L}^{3}$`
and
`${\lambda }_{R}=3{\overline{T}}_{R}^{2}-2{\overline{T}}_{R}^{3}$`
where:
`${\overline{T}}_{L}=\frac{{T}_{Sensor}-{T}_{Activation}}{\Delta {T}_{smooth}}$`
and
`${\overline{T}}_{R}=\frac{{T}_{Sensor}-\left({T}_{Activation}+{T}_{Range}-\Delta {T}_{smooth}\right)}{\Delta {T}_{smooth}}.$`
In the equations:

• λL is the smoothing expression for the fully closed portion of the valve opening curve.

• λR is the smoothing expression applied to the fully open portion of the valve opening curve.

• ΔTsmooth is the temperature smoothing region:

`$\Delta {T}_{smooth}={f}_{smooth}\frac{{T}_{Range}}{2},$`
where fsmooth is a smoothing factor between 0 and 1.

The smoothed valve opening area is given by the piecewise conditional expression

`${S}_{R}=\left\{\begin{array}{ll}{S}_{Start},\hfill & {T}_{Sensor}\le {T}_{Activation}\hfill \\ {S}_{Start}\left(1-{\lambda }_{L}\right)+{S}_{Linear}{\lambda }_{L},\hfill & {T}_{Sensor}<{T}_{Activation}+\Delta {T}_{smooth}\hfill \\ {S}_{Linear},\hfill & {T}_{Sensor}<{T}_{Activation}+{T}_{Range}-\Delta {T}_{smooth}\hfill \\ {S}_{Linear}\left(1-{\lambda }_{R}\right)+{S}_{End}{\lambda }_{R},\hfill & {T}_{Sensor}<{T}_{Activation}+{T}_{Range}\hfill \\ {S}_{End},\hfill & {T}_{Sensor}\ge {T}_{Activation}+{T}_{Range}\hfill \end{array},\text{\hspace{0.17em}}$`
where:

• SR is the smoothed valve opening area.

### Mass Balance

The mass conservation equation in the valve is

`${\stackrel{˙}{m}}_{A}+{\stackrel{˙}{m}}_{B}=0,$`
where:

• ${\stackrel{˙}{m}}_{A}$ is the mass flow rate into the valve through port A.

• ${\stackrel{˙}{m}}_{B}$ is the mass flow rate into the valve through port B.

### Energy Balance

The energy conservation equation in the valve is

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

• ϕA is the energy flow rate into the valve through port A.

• ϕB is the energy flow rate into the valve through port B.

### Momentum Balance

The momentum conservation equation in the valve is

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

• pA and pB are the pressures at port A and port B.

• $\stackrel{˙}{m}$ is the mass flow rate.

• ${\stackrel{˙}{m}}_{cr}$ is the critical mass flow rate:

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

• ρAvg is the average liquid density.

• Cd is the discharge coefficient.

• S is the valve inlet area.

• PRLoss is the pressure ratio:

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

## Parameters

### Parameters Tab

Valve operation

Effect of fluid temperature on valve operation. Options include ```Opens above activation temperature``` and ```Closes above activation temperature```. The default setting is ```Opens above activation temperature```.

Activation temperature

Temperature required to actuate the valve. If the Valve operation parameter is set to ```Opens above activation temperature```, the valve begins to open at the activation temperature. If the Valve operation parameter is set to `Closes above activation temperature`, the valve begins to close at the activation temperature. The default value is `330` K.

Temperature regulation range

Temperature change from the activation temperature required to fully open the valve. The default value is `8` K, corresponding to a fully open valve at a temperature of `338` K.

Sensor time constant

Time constant in the first-order equation used to approximate the temperature sensor dynamics. The default value is `1.5` s.

Maximum opening area

Valve flow area in the fully open position. The default value is `1e-4` m^2.

Leakage area

Area through which fluid can flow in the fully closed valve position. This area accounts for leakage between the valve inlets. The default value is `1e-12` m^2.

Smoothing factor

Portion of the opening-area curve to smooth expressed as a fraction. Smoothing eliminates discontinuities at the minimum and maximum flow valve positions. The smoothing factor must be between `0` and `1`.

Opening-Area Curve Smoothing

A value of `0` corresponds to a linear expression with zero smoothing. A value of `1` corresponds to a nonlinear expression with maximum smoothing. The default value is `0.01`, corresponding to a nonlinear region spanning 1% the size of the full curve..

Cross-sectional area at ports A and B

Area normal to the direction of flow at the valve inlets. This area is assumed the same for all the inlets. The default value is `0.01` m^2.

Characteristic longitudinal length

Approximate length of the valve. This parameter provides a measure of the longitudinal scale of the valve. The default value is `0.1` m^2.

Discharge coefficient

Semi-empirical parameter commonly used as a measure of valve performance. The discharge coefficient is defined as the ratio of the actual mass flow rate through the valve to its theoretical value.

The block uses this parameter to account for the effects of valve geometry on mass flow rates. Textbooks and valve data sheets are common sources of discharge coefficient values. By definition, all values must be greater than 0 and smaller than 1. The default value is `0.7`.

Critical Reynolds number

Reynolds number corresponding to the transition between laminar and turbulent flow regimes. The flow through the valve is assumed laminar below this value and turbulent above it. The appropriate values to use depend on the specific valve geometry. The default value is `12`.

### Variables Tab

Sensor temperature

Fluid temperature at the start of simulation. The default value is `293.15` K, corresponding to room temperature.

Mass flow rate into port A

Mass flow rate into the component through port A at the start of simulation. The default value is ```1 kg/s```.

## Ports

• A — Thermal liquid conserving port representing valve inlet A

• B — Thermal liquid conserving port representing valve inlet B