Flow control valve with temperature-based actuation
Simscape / Fluids / Thermal Liquid / Valves & Orifices / Flow Control Valves
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
The valve opening area calculation is based on the linear expression
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:
TAvg is the arithmetic average of the valve port temperatures,
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
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:
where fsmooth is a smoothing factor between 0 and 1.
The smoothed valve opening area is given by the piecewise conditional expression
SR is the smoothed valve opening area.
The mass conservation equation in the valve is
is the mass flow rate into the valve through port A.
is the mass flow rate into the valve through port B.
The energy conservation equation in the valve is
ϕA is the energy flow rate into the valve through port A.
ϕB is the energy flow rate into the valve through port B.
The momentum conservation equation in the valve is
pA and pB are the pressures at port A and port B.
is the mass flow rate.
is the critical mass flow rate:
ρAvg is the average liquid density.
Cd is the discharge coefficient.
S is the valve inlet area.
PRLoss is the pressure ratio:
A — Thermal liquid conserving port representing valve inlet A
B — Thermal liquid conserving port representing valve inlet B
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 required to actuate the valve. If the Valve
operation parameter is set to
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
Temperature change from the activation temperature required to fully
open the valve. The default value is
corresponding to a fully open valve at a temperature of
Time constant in the first-order equation used to approximate the
temperature sensor dynamics. The default value is
Valve flow area in the fully open position. The default value is
Area through which fluid can flow in the fully closed valve position.
This area accounts for leakage between the valve inlets. The default
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
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..
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
Approximate length of the valve. This parameter provides a measure of the
longitudinal scale of the valve. The default value is
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
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
Fluid temperature at the start of simulation. The default value is
293.15 K, corresponding to room
Mass flow rate into the component through port A
at the start of simulation. The default value is