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# Temperature Control Valve (G)

Temperature control valve in a gas network

Libraries:
Simscape / Fluids / Gas / Valves & Orifices / Flow Control Valves

## Description

The Temperature Control Valve (G) block represents an orifice with a thermostat as a flow control mechanism. The thermostat contains a temperature sensor and an opening mechanism. The sensor is at the inlet and 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 actuates and the valve begins to open or close, depending on the operation mode specified by the Valve operation parameter. The change in opening area continues up to the limit of the temperature range of the valve, beyond which the opening area is a constant. Within the temperature range, the opening area is a linear function of temperature.

The flow can be laminar or turbulent, and it can reach up to sonic speeds. The maximum velocity happens at the throat of the valve where the flow is narrowest and fastest. The flow chokes and the velocity saturates when a drop in downstream pressure can no longer increase the velocity. Choking occurs when the back-pressure ratio reaches the critical value characteristic of the valve. The block does not capture supersonic flow.

### Control Temperature

The temperature reading at the inlet is the control signal for the valve. The more the temperature reading rises over the activation temperature, the more the opening area diverges from maximally closed when Valve operation is `Opens above activation temperature`, or from fully open when Valve operation is ```Closes above activation temperature```.

The difference between the sensor temperature reading and the activation temperature is the temperature overshoot. The block normalizes this variable against the temperature regulation range of the valve. The fraction of valve opening is

`$\stackrel{^}{T}=\frac{{T}_{S}-{T}_{Act}}{\Delta T},$`

where:

• TAct is the value of the Activation temperature parameter.

• TS is the sensor temperature reading.

• When Temperature sensing is `Valve inlet temperature`, TS is the upstream temperature of the valve.

• When Temperature sensing is `Gas sensing port`, TS is the temperature of the gas network where it connects to port T.

• When Temperature sensing is `Thermal sensing port`, TS is the temperature of the thermal network where it connects to port T.

• ΔT is the value of the Temperature regulation range parameter.

Numerical Smoothing

When the Smoothing factor parameter is nonzero, the block applies numerical smoothing to the fraction of valve opening, $\stackrel{^}{T}$. Enabling smoothing helps maintain numerical robustness in your simulation.

For more information, see Numerical Smoothing.

Sensor Dynamics

To emulate a real temperature sensor, which can only register a shift in temperature gradually, the block adds a first-order time lag to the temperature reading, TS. The lag gives the sensor a transient response to variations in temperature. This expression for TS is

`$\frac{d}{dt}{T}_{\text{S}}=\frac{{T}_{\text{In}}-{T}_{\text{S}}}{\tau },$`

where TIn is the actual inlet temperature at the current time step of the simulation and τ is the value of the Sensor time constant parameter. The smaller this parameter is, the faster the sensor responds.

### Valve Parameterizations

The block behavior depends on the Valve parametrization parameter:

• `Cv flow coefficient` — The flow coefficient Cv determines the block parameterization. The flow coefficient measures the ease with which a gas can flow when driven by a certain pressure differential.

• `Kv flow coefficient` — The flow coefficient Kv, where ${K}_{v}=0.865{C}_{v}$, determines the block parameterization. The flow coefficient measures the ease with which a gas can flow when driven by a certain pressure differential.

• `Sonic conductance` — The sonic conductance of the resistive element at steady state determines the block parameterization. The sonic conductance measures the ease with which a gas can flow when choked, which is a condition in which the flow velocity is at the local speed of sound. Choking occurs when the ratio between downstream and upstream pressures reaches a critical value known as the critical pressure ratio.

• `Orifice area` — The size of the flow restriction determines the block parametrization.

The block scales the specified flow capacity by the fraction of valve opening. As the fraction of valve opening rises from `0` to `1`, the measure of flow capacity scales from its specified minimum to its specified maximum.

### Momentum Balance

The block equations depend on the Orifice parametrization parameter. When you set Orifice parametrization to `Cv flow coefficient parameterization`, the mass flow rate, $\stackrel{˙}{m}$, is

`$\stackrel{˙}{m}={C}_{v}{N}_{6}Y\sqrt{\left({p}_{in}-{p}_{out}\right){\rho }_{in}},$`

where:

• Cv is the flow coefficient.

• N6 is a constant equal to 27.3 for mass flow rate in kg/hr, pressure in bar, and density in kg/m3.

• Y is the expansion factor.

• pin is the inlet pressure.

• pout is the outlet pressure.

• ρin is the inlet density.

The expansion factor is

`$Y=1-\frac{{p}_{in}-{p}_{out}}{3{p}_{in}{F}_{\gamma }{x}_{T}},$`

where:

• Fγ is the ratio of the isentropic exponent to 1.4.

• xT is the value of the xT pressure differential ratio factor at choked flow parameter.

The block smoothly transitions to a linearized form of the equation when the pressure ratio, ${p}_{out}/{p}_{in}$, rises above the value of the Laminar flow pressure ratio parameter, Blam,

`$\stackrel{˙}{m}={C}_{v}{N}_{6}{Y}_{lam}\sqrt{\frac{{\rho }_{avg}}{{p}_{avg}\left(1-{B}_{lam}\right)}}\left({p}_{in}-{p}_{out}\right),$`

where:

`${Y}_{lam}=1-\frac{1-{B}_{lam}}{3{F}_{\gamma }{x}_{T}}.$`

When the pressure ratio, ${p}_{out}/{p}_{in}$, falls below $1-{F}_{\gamma }{x}_{T}$, the orifice becomes choked and the block switches to the equation

`$\stackrel{˙}{m}=\frac{2}{3}{C}_{v}{N}_{6}\sqrt{{F}_{\gamma }{x}_{T}{p}_{in}{\rho }_{in}}.$`

When you set Orifice parametrization to ```Kv flow coefficient parameterization```, the block uses these same equations, but replaces Cv with Kv by using the relation ${K}_{v}=0.865{C}_{v}$. For more information on the mass flow equations when the Orifice parametrization parameter is ```Kv flow coefficient parameterization``` or ```Cv flow coefficient parameterization```, see [2][3].

When you set Orifice parametrization to `Sonic conductance parameterization`, the mass flow rate, $\stackrel{˙}{m}$, is

`$\stackrel{˙}{m}=C{\rho }_{ref}{p}_{in}\sqrt{\frac{{T}_{ref}}{{T}_{in}}}{\left[1-{\left(\frac{\frac{{p}_{out}}{{p}_{in}}-{B}_{crit}}{1-{B}_{crit}}\right)}^{2}\right]}^{m},$`

where:

• C is the sonic conductance.

• Bcrit is the critical pressure ratio.

• m is the value of the Subsonic index parameter.

• Tref is the value of the ISO reference temperature parameter.

• ρref is the value of the ISO reference density parameter.

• Tin is the inlet temperature.

The block smoothly transitions to a linearized form of the equation when the pressure ratio, ${p}_{out}/{p}_{in}$, rises above the value of the Laminar flow pressure ratio parameter Blam,

`$\stackrel{˙}{m}=C{\rho }_{ref}\sqrt{\frac{{T}_{ref}}{{T}_{avg}}}{\left[1-{\left(\frac{{B}_{lam}-{B}_{crit}}{1-{B}_{crit}}\right)}^{2}\right]}^{m}\left(\frac{{p}_{in}-{p}_{out}}{1-{B}_{lam}}\right).$`

When the pressure ratio, ${p}_{out}/{p}_{in}$, falls below the critical pressure ratio, Bcrit, the orifice becomes choked and the block switches to the equation

`$\stackrel{˙}{m}=C{\rho }_{ref}{p}_{in}\sqrt{\frac{{T}_{ref}}{{T}_{in}}}.$`

For more information on the mass flow equations when the Orifice parametrization parameter is ```Sonic conductance parameterization```, see [1].

When you set Orifice parametrization to `Orifice area parameterization`, the mass flow rate, $\stackrel{˙}{m}$, is

`$\stackrel{˙}{m}={C}_{d}{S}_{r}\sqrt{\frac{2\gamma }{\gamma -1}{p}_{in}{\rho }_{in}{\left(\frac{{p}_{out}}{{p}_{in}}\right)}^{\frac{2}{\gamma }}\left[\frac{1-{\left(\frac{{p}_{out}}{{p}_{in}}\right)}^{\frac{\gamma -1}{\gamma }}}{1-{\left(\frac{{S}_{R}}{S}\right)}^{2}{\left(\frac{{p}_{out}}{{p}_{in}}\right)}^{\frac{2}{\gamma }}}\right]},$`

where:

• Sr is the orifice or valve area.

• S is the value of the Cross-sectional area at ports A and B parameter.

• Cd is the value of the Discharge coefficient parameter.

• γ is the isentropic exponent.

The block smoothly transitions to a linearized form of the equation when the pressure ratio, ${p}_{out}/{p}_{in}$, rises above the value of the Laminar flow pressure ratio parameter, Blam,

`$\stackrel{˙}{m}={C}_{d}{S}_{r}\sqrt{\frac{2\gamma }{\gamma -1}{p}_{avg}^{\frac{2-\gamma }{\gamma }}{\rho }_{avg}{B}_{lam}^{\frac{2}{\gamma }}\left[\frac{1-\text{\hspace{0.17em}}{B}_{lam}^{\frac{\gamma -1}{\gamma }}}{1-{\left(\frac{{S}_{R}}{S}\right)}^{2}{B}_{lam}^{\frac{2}{\gamma }}}\right]}\left(\frac{{p}_{in}^{\frac{\gamma -1}{\gamma }}-{p}_{out}^{\frac{\gamma -1}{\gamma }}}{1-{B}_{lam}^{\frac{\gamma -1}{\gamma }}}\right).$`

When the pressure ratio, ${p}_{out}/{p}_{in}$, falls below${\left(\frac{2}{\gamma +1}\right)}^{\frac{\gamma }{\gamma -1}}$ , the orifice becomes choked and the block switches to the equation

`$\stackrel{˙}{m}={C}_{d}{S}_{R}\sqrt{\frac{2\gamma }{\gamma +1}{p}_{in}{\rho }_{in}\frac{1}{{\left(\frac{\gamma +1}{2}\right)}^{\frac{2}{\gamma -1}}-{\left(\frac{{S}_{R}}{S}\right)}^{2}}}.$`

For more information on the mass flow equations when the Orifice parametrization parameter is ```Orifice area parameterization```, see [4].

### Mass Balance

The block assumes the volume and mass of fluid inside the valve is very small and ignores these values. As a result, no amount of fluid can accumulate in the valve. By the principle of conservation of mass, the mass flow rate into the valve through one port equals that out of the valve through the other port

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

where $\stackrel{˙}{m}$ is defined as the mass flow rate into the valve through the port indicated by the A or B subscript.

### Energy Balance

The resistive element of the block is an adiabatic component. No heat exchange can occur between the fluid and the wall that surrounds it. No work is done on or by the fluid as it traverses from inlet to outlet. Energy can flow only by advection, through ports A and B. By the principle of conservation of energy, the sum of the port energy flows is always equal to zero

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

where ϕ is the energy flow rate into the valve through ports A or B.

### Variables

To set the priority and initial target values for the block variables prior to simulation, use the Initial Targets section in the block dialog box or Property Inspector. For more information, see Set Priority and Initial Target for Block Variables.

Nominal values provide a way to specify the expected magnitude of a variable in a model. Using system scaling based on nominal values increases the simulation robustness. Nominal values can come from different sources, one of which is the Nominal Values section in the block dialog box or Property Inspector. For more information, see Modify Nominal Values for a Block Variable.

### Assumptions and Limitations

• The `Sonic conductance` setting of the Valve parameterization parameter is for pneumatic applications. If you use this setting for gases other than air, you may need to scale the sonic conductance by the square root of the specific gravity.

• The equation for the `Orifice area` parameterization is less accurate for gases that are far from ideal.

• This block does not model supersonic flow.

## Ports

### Conserving

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Gas conserving port associated with the opening through which the flow enters or exits the valve. The direction of flow depends on the pressure differential established across the valve. The block allows both forward and backward directions.

Opening through which the working fluid can enter or exit the valve. The direction of flow depends on the pressure differential established across the valve. The block allows both forward and backward directions.

Gas or thermal conserving port associated with temperature sensing. There is no mass or energy flow through this port. When Temperature sensing is `Gas sensing port`, port T is a gas sensing port. When Temperature sensing is ```Thermal sensing port```, port T is a thermal sensing port.

#### Dependencies

To enable this port, set Temperature sensing to ```Gas sensing port``` or ```Thermal sensing port```.

## Parameters

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Sign of the change in opening area that is 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.

Method the block uses to measure the temperature that controls the valve:

• When you set Temperature sensing to `Valve inlet temperature`, the valve uses the upstream temperature to control the valve.

• When you set Temperature sensing to `Gas sensing port`, the block enables port T, which is a gas sensing port. Connect this port to any part of a gas network to use that temperature to control the valve. Port T is only used for sensing and has no flow going in or out.

• When you set Temperature sensing to `Thermal sensing port`, the block enables the thermal sensing port T. Connect this port to any part of a thermal network to use that temperature to control the valve. Port T is only used for sensing and has no heat exchange with the environment.

Temperature at which the opening mechanism is triggered. 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.

Span of the temperature interval over which the valve opening area varies with temperature. The interval begins at the activation temperature of the valve. It ends at the sum of the same with the regulation range specified here.

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 same, taken as the sensor nears its new steady state. A value of `0` means that the sensor responds instantaneously to a temperature change.

Method to calculate the mass flow rate.

• `Cv flow coefficient` — The flow coefficient Cv determines the block parameterization.

• `Kv flow coefficient` — The flow coefficient Kv, where ${K}_{v}=0.865{C}_{v}$, determines the block parameterization.

• `Sonic conductance` — The sonic conductance of the resistive element at steady state determines the block parameterization.

• `Orifice area` — The size of the flow restriction determines the block parametrization.

Value of the Cv flow coefficient when the restriction area available for flow is at a maximum. This parameter measures the ease with which the gas traverses the resistive element when driven by a pressure differential.

#### Dependencies

To enable this parameter, set Valve parameterization to ```Cv flow coefficient```.

Ratio between the inlet pressure, pin, and the outlet pressure, pout, defined as $\left({p}_{in}-{p}_{out}\right)/{p}_{in}$ where choking first occurs. If you do not have this value, look it up in table 2 in ISA-75.01.01 [3]. Otherwise, the default value of 0.7 is reasonable for many valves.

#### Dependencies

To enable this parameter, set Valve parameterization to ```Cv flow coefficient``` or ```Kv flow coefficient```.

Maximum value of the Kv flow coefficient when the restriction area available for flow is at a maximum. This parameter measures the ease with which the gas traverses the resistive element when driven by a pressure differential.

#### Dependencies

To enable this parameter, set Valve parameterization to ```Kv flow coefficient```.

Value of the sonic conductance when the cross-sectional area available for flow is at a maximum.

#### Dependencies

To enable this parameter, set Valve parameterization to ```Sonic conductance```.

Pressure ratio at which flow first begins to choke and the flow velocity reaches its maximum, given by the local speed of sound. The pressure ratio is the outlet pressure divided by inlet pressure.

#### Dependencies

To enable this parameter, set Valve parameterization to ```Sonic conductance```.

Empirical value used to more accurately calculate the mass flow rate in the subsonic flow regime.

#### Dependencies

To enable this parameter, set Valve parameterization to ```Sonic conductance```.

Temperature at standard reference atmosphere, defined as 293.15 K in ISO 8778.

You only need to adjust the ISO reference parameter values if you are using sonic conductance values that are obtained at difference reference values.

#### Dependencies

To enable this parameter, set Valve parameterization to ```Sonic conductance```.

Density at standard reference atmosphere, defined as 1.185 kg/m3 in ISO 8778.

You only need to adjust the ISO reference parameter values if you are using sonic conductance values that are obtained at difference reference values.

#### Dependencies

To enable this parameter, set Valve parameterization to ```Sonic conductance```.

Cross-sectional area of the orifice opening when the cross-sectional area available for flow is at a maximum.

#### Dependencies

To enable this parameter, set Valve parameterization to ```Orifice area```.

Correction factor that accounts for discharge losses in theoretical flows.

#### Dependencies

To enable this parameter, set Valve parameterization to ```Orifice area```.

Ratio of the flow rate of the orifice when it is closed to when it is open.

Continuous smoothing factor that introduces a layer of gradual change to the flow response when the orifice is in near-open or near-closed positions. Set this parameter to a nonzero value less than one to increase the stability of your simulation in these regimes.

Pressure ratio at which flow transitions between laminar and turbulent flow regimes. The pressure ratio is the outlet pressure divided by inlet pressure. Typical values range from `0.995` to `0.999`.

Area normal to the flow path at each port. The ports are equal in size. The value of this parameter should match the inlet area of the components to which the resistive element connects.

## References

[1] ISO 6358-3. "Pneumatic fluid power – Determination of flow-rate characteristics of components using compressible fluids – Part 3: Method for calculating steady-state flow rate characteristics of systems". 2014.

[2] IEC 60534-2-3. "Industrial-process control valves – Part 2-3: Flow capacity – Test procedures". 2015.

[3] ANSI/ISA-75.01.01. "Industrial-Process Control Valves – Part 2-1: Flow capacity – Sizing equations for fluid flow underinstalled conditions". 2012.

[4] P. Beater. Pneumatic Drives. Springer-Verlag Berlin Heidelberg. 2007.

## Version History

Introduced in R2018b

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