Temperature Control Valve (TL)

Flow control valve with temperature-based actuation

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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. 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:

• 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:

  $$S_{Start}=\{\begin{array}{ll}{S}_{Leak},\hfill & \text{Valve opens above activation temperature}\hfill \\ S_{Max},\hfill & \text{Valve closes above activation temperature}\hfill \end{array}$$

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

  $$S_{End}=\{\begin{array}{ll}{S}_{Max},\hfill & \text{Valve opens above activation temperature}\hfill \\ S_{Leak},\hfill & \text{Valve closes above activation temperature}\hfill \end{array}$$

• 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.

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:

• 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:

  $$\Delta T_{smooth}=f_{smooth}\frac{T_{Range}}{2},$$

  where f_smooth is a smoothing factor between 0 and 1.

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

$$S_R=\{\begin{array}{ll}{S}_{Start},\hfill & T_{Sensor}\le T_{Activation}\hfill \\ S_{Start}\left(1-{\lambda }_L\right)+S_{Linear}{\lambda }_L,\hfill & T_{Sensor}<T_{Activation}+\Delta T_{smooth}\hfill \\ S_{Linear},\hfill & T_{Sensor}<T_{Activation}+T_{Range}-\Delta T_{smooth}\hfill \\ S_{Linear}\left(1-{\lambda }_R\right)+S_{End}{\lambda }_R,\hfill & T_{Sensor}<T_{Activation}+T_{Range}\hfill \\ S_{End},\hfill & T_{Sensor}\ge T_{Activation}+T_{Range}\hfill \end{array},$$

where:

• S_R is the smoothed valve opening area.

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.

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.

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:

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

Ports

• A — Thermal liquid conserving port representing valve inlet A

• B — Thermal liquid conserving port representing valve inlet B

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.

Model Examples

Engine Cooling System

Model an engine cooling system with an oil cooling circuit using Simscape™ Fluids™ Thermal Liquid blocks. The system includes a coolant circuit and an oil cooling circuit. A fixed-displacement pump drives coolant through the cooling circuit. The main portion of heat from the engine is absorbed by the coolant and dissipated through the radiator. The system temperature is regulated by the thermostat, which diverts flow to the radiator only when the temperature is above a threshold. The oil cooling circuit also absorbs some of the heat from the engine. The heat added to the oil is transferred to the coolant by the oil-coolant heat exchanger. The Radiator is the E-NTU Heat Exchanger (TL) block with the air-side flow controlled by physical signal inputs. The oil-coolant heat exchanger is the E-NTU Heat Exchanger (TL-TL) block. Both coolant pump and oil pump are driven by the engine speed.

Extended Capabilities

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