Flow control valve with temperature-based actuation

Thermal Liquid/Valves/Flow Control Valves

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**

The valve opening area calculation is based on the linear expression

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

*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:

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

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

*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.

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

$${\lambda}_{L}=3{\overline{T}}_{L}^{2}-2{\overline{T}}_{L}^{3}$$

$${\lambda}_{R}=3{\overline{T}}_{R}^{2}-2{\overline{T}}_{R}^{3}$$

$${\overline{T}}_{L}=\frac{{T}_{Sensor}-{T}_{Activation}}{\Delta {T}_{smooth}}$$

$${\overline{T}}_{R}=\frac{{T}_{Sensor}-\left({T}_{Activation}+{T}_{Range}-\Delta {T}_{smooth}\right)}{\Delta {T}_{smooth}}.$$

*λ*_{L}is the smoothing expression for the fully closed portion of the valve opening curve.*λ*_{R}is the smoothing expression applied to the fully open portion of the valve opening curve.*ΔT*_{smooth}is the temperature smoothing region:where$$\Delta {T}_{smooth}={f}_{smooth}\frac{{T}_{Range}}{2},$$

*f*_{smooth}is a smoothing factor between 0 and 1.

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

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

*S*_{R}is the smoothed valve opening area.

The mass conservation equation in the valve is

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

$${\dot{m}}_{A}$$ 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.

The energy conservation equation in the valve is

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

*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.

The momentum conservation equation in the valve is

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

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

**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`

.

**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`

.

A — Thermal liquid conserving port representing valve inlet A

B — Thermal liquid conserving port representing valve inlet B

Was this topic helpful?