Temperature Control Valve (TL)

Flow control valve with temperature-based actuation

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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:

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

• 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.

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_Max. For more information, see Numerical Smoothing.

Examples

Engine Cooling System

Model an engine cooling system with an oil cooling circuit.

Open Model

Ports

Conserving

A — Liquid port

thermal liquid

Thermal liquid conserving port representing valve inlet A.

B — Liquid port

thermal liquid

Thermal liquid conserving port representing valve inlet B.

Parameters

Valve operation — Sign of the change in opening area induced by warming

Opens above activation temperature (default) | Closes above activation temperature

Sign of the change in opening area induced by warming. The opening area can expand with a rise in temperature or it can contract. The change begins at an activation temperature and continues with warming conditions throughout the temperature regulation range of the valve.

The default setting corresponds to a normally closed valve that opens with rising temperature; the alternative setting corresponds to a normally open valve that closes with the same.

Activation temperature — Temperature at which the opening mechanism triggers

330 K (default) | positive scalar

Temperature at which the opening mechanism triggers. Warming above this temperature will either open or close the valve, depending on the setting of the Valve operation parameter. The opening area remains variable throughout the temperature regulation range of the valve.

Temperature regulation range — Valve temperature range

8 K (default) | positive scalar

Temperature interval over which the valve opening area varies. The interval begins at the value of the Activation temperature parameter.

Sensor time constant — Time for a temperature change to register at the inlet sensor

1.5 s (default) | nonnegative scalar

Characteristic time for a temperature change to register at the inlet sensor. This parameter determines the delay between the onset of a change and a stable measurement of the change. A value of 0 means that the sensor responds instantaneously to a temperature change.

Maximum opening area — Opening area in the fully open position due to sealing imperfections

1e-4 m^2 (default) | positive scalar

Opening area of the valve in the fully open position, when the valve is at the upper limit of the pressure regulation range. The block uses this parameter to scale the valve opening throughout the pressure regulation range.

Leakage area — Opening area in the maximally closed position due to sealing imperfections

1e-10 m^2 (default) | positive scalar

Sum of all gaps when the valve is in the fully closed position. Any area smaller than this value is saturated to the specified leakage area. This contributes to numerical stability by maintaining continuity in the flow.

Smoothing factor — Numerical smoothing factor

0.01 (default) | scalar in the range [0,1]

Continuous smoothing factor that introduces a layer of gradual change to the flow response when the valve is in near-open or near-closed positions.

Cross-sectional area at ports A and B — Orifice area at conserving ports

0.01 m^2 (default) | positive scalar

Areas at the entry and exit ports A and B, which are used in the pressure-flow rate equation that determines the mass flow rate through the orifice.

Discharge coefficient — Discharge coefficient

0.64 (default) | positive scalar

Correction factor accounting for discharge losses in theoretical flows.

Critical Reynolds number — Upper Reynolds number limit for laminar flow

150 (default) | positive scalar

Upper Reynolds number limit for laminar flow through the valve.

Extended Capabilities

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

Version History

Introduced in R2016a