Ball Valve (G)

Ball valve in the gas network.

blockType: EngeeFluids.Gas.Valves.FlowControl.Ball

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/Physical Modeling/Fluids/Gas/Valves & Orifices/Flow Control Valves/Ball Valve (G)

Description

The Ball Valve (G) unit is a ball valve in a gas network. A ball valve consists of a ball with an orifice that can rotate inside the valve body. When the valve is open, the orifice is completely aligned with the inlet and outlet of the valve. When the valve is closed, the ball rotates and reduces the amount of overlap, thereby reducing the effective orifice area. Ball valves are often used for flow shut-off applications because they can reliably shut off flow over many cycles. Ball valves are less common in applications where precise throttling is required. The physical signal on the S port controls the rotation of the ball.

Port parameterization

The calculation of local resistance capacity depends on the value of the Valve parametrization parameter:

Cv flow coefficient - flow coefficient determines the dependence of the flow capacity on the pressure drop;
Kv flow coefficient - flow coefficient determines the dependence of flow capacity on pressure drop, ;
Sonic conductance - steady-state acoustic conductance determines the flow capacity at critical flow, the condition at which the flow velocity is equal to the local speed of sound. Flow becomes critical when the ratio of outlet pressure to inlet pressure reaches a value called the critical pressure ratio;
Orifice area - the orifice area determines the flow capacity.

Opening area

The block calculates the opening area of the ball valve during the simulation based on the S port input data. The calculation of the opening area depends on the Opening characteristic parameter.

Area of overlapping circles

When the Opening characteristic parameter is set to Area of overlapping circles', the block calculates the valve opening area assuming that the valve orifice and ball channel are overlapping circles. The opening area is saturated when the input signal from port S falls outside the range of `0 rad to π/2 rad.

The block calculates the opening area as:

where

and are the radii of the valve port and ball port, respectively;
- displacement of the centre of the orifice relative to the centre of the valve port;
- rotation of the ball valve set by the signal from the S port. The valve is fully closed at 0 rad and fully open at π/2 rad.

Tabulated area

If you set the Opening characteristic parameter to Tabulated, the block interpolates the valve opening from the Area vector, Cv flow coefficient vector, Kv flow coefficient vector, or Sonic conductance vector parameters. The elements in these vectors correspond to the elements in the Ball rotation vector parameter. The block interpolates between data points using linear interpolation and uses nearest extrapolation for points outside the table boundaries.

Mass flow equation

The block equations depend on the Valve parametrization parameter.

If the Valve parametrization parameter is set to Cv flow coefficient, the mass flow rate, will be defined as

where

- is the value of the parameter Maximum Cv flow coefficient;
- valve opening area;
- is the maximum valve area when the valve is fully open;
- a constant equal to 27.3 for mass flow rate in kg/hour, pressure in bar and density in kg/m³;
- expansion coefficient;
- inlet pressure;
- outlet pressure;
- inlet density.

The expansion ratio is defined as:

where

- is the ratio of adiabatic index to 1.4;
- value of the parameter xT pressure differential ratio factor at choked flow.

When the pressure ratio exceeds the value of the Laminar flow pressure ratio parameter, , there is a smooth transition to the use of the linearised equation

where

When the pressure ratio falls below , the flow becomes critical and the equation is used

When the Valve parametrization is set to Kv flow coefficient, the unit uses the same equations but replaces with using the ratio . For more information on the mass flow equations when the Valve parametrization is set to Kv flow coefficient or Cv flow coefficient, see [2] and [3].

If the Valve parametrization is set to `Sonic conductance', the mass flow rate is defined as

where

- is the value of the parameter Maximum sonic conductance;
- is the critical pressure ratio;
- Subsonic index parameter value;
- parameter value ISO reference temperature;
- ISO reference density parameter value;
- inlet temperature.

When the pressure ratio exceeds the value of the Laminar flow pressure ratio parameter, , there is a smooth transition to the use of the linearised equation

When the pressure ratio falls below the critical pressure ratio , the flow becomes critical and the equation is used.

For more information on mass flow equations when the Valve parametrization parameter is set to `Sonic conductance', see [1].

When the Valve parametrization is set to Orifice area based on geometry, the mass flow rate is defined as

where

- is the opening area of the valve;
- is the value of Cross-sectional area at ports A and B;
- the value of the Discharge coefficient;
- adiabatic coefficient.

When the pressure ratio exceeds the Laminar flow pressure ratio, , there is a smooth transition to the linearised equation.

When the pressure ratio falls below , the flow becomes critical and the equation is used

For more information on mass flow equations when the Valve parametrization parameter is set to `Orifice area based on geometry', see [4].

Mass conservation

The volume and mass of the fluid inside the component are assumed to be very small and these values are not considered. According to the principle of conservation of mass, the mass flow rate of fluid entering through one port is equal to the flow rate of fluid leaving through the other port:

where is defined as the mass flow rate entering the valve through the port designated by the subscript A or B.

Energy Conservation

The component being modelled is adiabatic. There is no heat transfer between the fluid and the wall that surrounds it. The fluid does not do any work as it moves from the inlet to the outlet. Energy can only be transferred by convection through ports A and B. According to the principle of conservation of energy, the sum of energy fluxes in the ports is always zero:

where is the energy flow into the valve via ports A or B.

Assumptions and limitations

The Sonic conductance value of the Valve parameterization parameter is intended for pneumatic systems. If this parameter is used for gases other than air, it may be necessary to correct the acoustic conductance value by the square root of the relative density.
The equation for the `Orifice area based on geometry' parameterization has less accuracy for gases that are far from ideal.
This block does not model supersonic flow.

Ports

Conserving

# A — gas inlet
gas

Details

Non-directional port, corresponds to valve port A.

Program usage name

port_a

# B — gas outlet
gas

Details

Non-directional port, corresponds to valve port B.

Program usage name

port_b

Input

# S — valve position, rad
scalar

Details

An input port that determines the degree of opening. The port is fully closed at 0 and fully open at π/2.

Data types	`Float64`.
Complex numbers support	No

Parameters

# Valve parameterization — ball valve parameterization
Orifice area based on geometry | Cv flow coefficient | Kv flow coefficient | Sonic conductance

Details

The mass flow calculation method is based on:

Cv flow coefficient - flow coefficient ;
Kv flow coefficient - flow coefficient , which is defined as ;
Sonic conductance - steady-state acoustic conductance;
Orifice area based on geometry - orifice area.

Values	`Orifice area based on geometry` \| `Cv flow coefficient` \| `Kv flow coefficient` \| `Sonic conductance`
Default value	`Orifice area based on geometry`
Program usage name	`valve_parameterization`
Evaluatable	No

# Opening characteristic — type of capacity characteristic
Area of overlapping circles | Tabulated data

Details

Method of converting the control signal on the S port to the selected bandwidth measure.

Values	`Area of overlapping circles` \| `Tabulated data`
Default value	`Area of overlapping circles`
Program usage name	`opening_characteristic`
Evaluatable	No

# Discharge coefficient (Cd) — flow coefficient

Details

The correction factor is the ratio of the actual mass flow rate to the theoretical mass flow rate through the valve.

Dependencies

To use this parameter, set the Valve parameterization parameter to `Orifice area based on geometry'.

Default value	`0.64`
Program usage name	`C_d`
Evaluatable	Yes

# Area vector — vector of area values for a given ball rotation
m^2 | cm^2 | ft^2 | in^2 | km^2 | mi^2 | mm^2 | um^2 | yd^2

Details

The flow area for a given ball rotation. Each element of the vector is related to the elements of the vector from the Ball rotation vector parameter. The first element corresponds to valve leakage and must be non-zero.

Dependencies

To use this parameter, set Valve parameterization to `Orifice area based on geometry' and Opening characteristic to `Tabulated data'.

Units	`m^2` \| `cm^2` \| `ft^2` \| `in^2` \| `km^2` \| `mi^2` \| `mm^2` \| `um^2` \| `yd^2`
Default value	`[1e-10, 45.0, 90.0, 135.0, 180.0, 225.0, 270.0, 315.0, 360.0, 405.0, 450.0] mm^2`
Program usage name	`area_vector`
Evaluatable	Yes

# Maximum Cv flow coefficient — flow coefficient corresponding to the maximum orifice area

Details

Flow coefficient value , when the value of the control signal at port S is 1 and the orifice area is maximum.

Dependencies

To use this parameter, specify Cv flow coefficient for Valve parameterization and Area of overlapping circles for Opening characteristic.

Default value	`4.0`
Program usage name	`C_v_max`
Evaluatable	Yes

# Cv flow coefficient vector — vector of flow coefficient values

Details

Flow coefficient vector . Each coefficient corresponds to an element in the Ball rotation vector. This parameter measures the degree to which the gas passes through the resistive element under the effect of the pressure difference. The size of the vector must be the same as the Ball rotation vector.

Dependencies

To use this parameter, set the Valve parameterization to `Cv flow coefficient' and the Opening characteristic to `Tabulated data'.

Default value	`[1e-6, 0.0725, 0.1437, 0.2375, 0.35, 0.5375, 0.875, 1.3125, 2.125, 3.25, 4.00]`
Program usage name	`C_v_vector`
Evaluatable	Yes

# Ball rotation vector — ball rotation
deg | rad | rev | mrad

Details

The ball rotation for a given flow capacity or area. The elements of this vector must relate to the elements of the Valve flow coefficient (Cv) vector, the Valve flow factor (Kv) vector, or the Area vector.

Dependencies

To use this parameter, set the Opening characteristic parameter to `Tabulated' and the Valve parameterization parameter to `Cv flow coefficient'.

Units	`deg` \| `rad` \| `rev` \| `mrad`
Default value	`pi / 2.0 * [0.0:0.1:1.0…] rad`
Program usage name	`phi_vector_C_v`
Evaluatable	Yes

# Maximum Kv flow coefficient — flow coefficient corresponding to the maximum orifice area

Details

Flow coefficient value , when the value of the control signal at port S is 1 and the orifice area is maximum.

Dependencies

To use this parameter, specify Kv flow coefficient for Valve parameterization and Area of overlapping circles for Opening characteristic.

Default value	`3.6`
Program usage name	`K_v_max`
Evaluatable	Yes

# Kv flow coefficient vector — vector of flow coefficient values

Details

Dependencies

To use this parameter, specify Kv flow coefficient for Valve parameterization and Tabulated data for Opening characteristic.

Default value	`[1e-6, 0.0653, 0.1293, 0.2137, 0.3150, 0.4838, 0.7875, 1.1813, 1.8381, 2.8112, 3.6]`
Program usage name	`K_v_vector`
Evaluatable	Yes

# Ball rotation vector — ball rotation
deg | rad | rev | mrad

Details

Dependencies

To use this parameter, specify `Tabulated' for Opening characteristic and `Kv flow coefficient' for Valve parameterization.

Units	`deg` \| `rad` \| `rev` \| `mrad`
Default value	`pi / 2.0 * [0.0:0.1:1.0…] rad`
Program usage name	`phi_vector_K_v`
Evaluatable	Yes

# xT pressure differential ratio factor at choked flow — critical differential pressure ratio

Details

The ratio between the inlet pressure and the outlet pressure , defined as , at which the flow becomes critical. If this value is not known, it can be found in Table 2 in ISA-75.01.01 [3]. By default the value 0.7 is suitable for many valves.

Dependencies

To use this parameter, set the Valve parameterization parameter to Cv flow coefficient.

Default value	`0.7`
Program usage name	`delta_p_ratio_C_v`
Evaluatable	Yes

# xT pressure differential ratio factor at choked flow — critical differential pressure ratio

Details

The ratio between the inlet pressure and the outlet pressure , defined as , at which the flow becomes critical. If this value is not known, it can be found in Table 2 in ISA-75.01.01 3. By default the value 0.7 is suitable for many valves.

Dependencies

To use this parameter, set the Valve parameterization parameter to Kv flow coefficient.

Default value	`0.7`
Program usage name	`delta_p_ratio_K_v`
Evaluatable	Yes

# Maximum sonic conductance — acoustic conductivity corresponding to the maximum aperture area
l/(bar*s) | gal/(min*psi) | m^3/(Pa*s)

Details

The value of acoustic conductivity when the orifice cross-sectional area is maximised.

Dependencies

To use this parameter, set the Valve parameterization to Sonic conductance and the Opening characteristic to Area of overlapping circles.

Units	`l/(bars)` \| `gal/(minpsi)` \| `m^3/(Pa*s)`
Default value	`12.0 l/(bar*s)`
Program usage name	`C_max`
Evaluatable	Yes

# Critical pressure ratio — critical pressure ratio

Details

The ratio of pressures at which the flow becomes critical and the flow velocity reaches a maximum determined by the local speed of sound. The ratio between the outlet pressure and the inlet pressure : .

Dependencies

To use this parameter, set the Valve parameterization to Sonic conductance and the Opening characteristic to Area of overlapping circles.

Default value	`0.3`
Program usage name	`B_critical_linear`
Evaluatable	Yes

# Sonic conductance vector — vector of acoustic conductivity values
l/(bar*s) | gal/(min*psi) | m^3/(Pa*s)

Details

A vector of acoustic conductivity values within a resistive element. The values must be specified in ascending order. Each conductivity corresponds to an element in the Ball rotation vector parameter. The dimensionality of the vector corresponds to the dimensionality of the Ball rotation vector.

Dependencies

To use this parameter, set Valve parameterization to Sonic conductance and Opening characteristic to Tabulated data.

Units	`l/(bars)` \| `gal/(minpsi)` \| `m^3/(Pa*s)`
Default value	`[1e-5, 0.2175, 0.4312, 0.7125, 1.05, 1.6125, 2.625, 3.9375, 6.375, 9.75, 12.0] l/(bar*s)`
Program usage name	`C_vector`
Evaluatable	Yes

# Critical pressure ratio vector — vector of critical pressure ratio values

Details

Vector of critical pressure ratios. The critical pressure ratio is the ratio of the outlet pressure to the inlet pressure at which the flow becomes critical and the flow velocity reaches a maximum determined by the local speed of sound. The dimensionality of the vector corresponds to that of the Ball rotation vector.

Dependencies

To use this parameter, set the Valve parameterization to `Sonic conductance' and the Opening characteristic to `Tabulated data'.

Default value	`0.3 * ones(11)`
Program usage name	`B_critical_vector`
Evaluatable	Yes

# Ball rotation vector — ball rotation
deg | rad | rev | mrad

Details

Dependencies

To use this parameter, specify `Tabulated data' for Opening characteristic and `Sonic conductance' for Valve parameterization.

Units	`deg` \| `rad` \| `rev` \| `mrad`
Default value	`pi / 2.0 * [0.0:0.1:1.0…] rad`
Program usage name	`phi_vector_C`
Evaluatable	Yes

# Ball rotation vector — ball rotation
deg | rad | rev | mrad

Details

Dependencies

To use this parameter, set the Opening characteristic parameter to `Tabulated' and the Valve parameterization parameter to `Orifice area based on geometry'.

Units	`deg` \| `rad` \| `rev` \| `mrad`
Default value	`pi / 2.0 * [0.0:0.1:1.0…] rad`
Program usage name	`phi_vector_area`
Evaluatable	Yes

# Subsonic index — degree value used to calculate the mass flow rate in subsonic flow regime

Details

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

Dependencies

To use this parameter, set the Valve parameterization parameter to `Sonic conductance'.

Default value	`0.5`
Program usage name	`m`
Evaluatable	Yes

Details

The temperature in the standard reference atmosphere in ISO 8778.

The values of the ISO reference parameters only need to be adjusted if acoustic conductivity values obtained with different reference values are used.

Dependencies

To use this parameter, set the Valve parameterization parameter to `Sonic conductance'.

Units	`K` \| `degC` \| `degF` \| `degR` \| `deltaK` \| `deltadegC` \| `deltadegF` \| `deltadegR`
Default value	`293.15 K`
Program usage name	`T_reference`
Evaluatable	Yes

# ISO reference density — reference density according to ISO 8778
g/cm^3 | kg/m^3 | lbm/gal

Details

Density in a standard reference atmosphere in ISO 8778.

The values of the ISO reference parameters need only be adjusted if acoustic conductivity values obtained with different reference values are used.

Dependencies

To use this parameter, set the Valve parameterization parameter to `Sonic conductance'.

Units	`g/cm^3` \| `kg/m^3` \| `lbm/gal`
Default value	`1.185 kg/m^3`
Program usage name	`rho_reference`
Evaluatable	Yes

# Cross-sectional area at ports A and B — inlet or outlet area
m^2 | cm^2 | ft^2 | in^2 | km^2 | mi^2 | mm^2 | um^2 | yd^2

Details

This area is used when calculating the mass flow rate through the ports.

The ports are all the same size. The value of this parameter must match the inlet port area of the component to which the unit is connected.

Units	`m^2` \| `cm^2` \| `ft^2` \| `in^2` \| `km^2` \| `mi^2` \| `mm^2` \| `um^2` \| `yd^2`
Default value	`pi * (0.025 ^ 2) / 4.0 m^2`
Program usage name	`port_area`
Evaluatable	Yes

# Ball bore area — ball bore area
m^2 | cm^2 | ft^2 | in^2 | km^2 | mi^2 | mm^2 | um^2 | yd^2

Details

Cross-sectional area of the valve ball bore.

Dependencies

To use this parameter, set the Valve parameterization to `Orifice area based on geometry' and the Opening characteristic to `Area of overlapping circles'.

Units	`m^2` \| `cm^2` \| `ft^2` \| `in^2` \| `km^2` \| `mi^2` \| `mm^2` \| `um^2` \| `yd^2`
Default value	`pi * (0.02 ^ 2) / 4.0 m^2`
Program usage name	`ball_bore_area`
Evaluatable	Yes

# Leakage flow fraction — cost ratio

Details

The ratio of the flow rate through a closed orifice to that through an open orifice.

Dependencies

To use this parameter, set the Valve parameterization to `Orifice area based on geometry' and the Opening characteristic to `Area of overlapping circles'.

Default value	`1e-6`
Program usage name	`leakage_fraction`
Evaluatable	Yes

# Laminar flow pressure ratio — pressure ratio at which the flow transitions between laminar and turbulent regimes

Details

The ratio of outlet pressure to inlet pressure at which the flow transitions between laminar and turbulent flow regimes.

Typical values range from 0.995 to 0.999.

Default value	`0.999`
Program usage name	`B_laminar`
Evaluatable	Yes

Ball Valve (G)

Description

Port parameterization

Opening area

Area of overlapping circles

Tabulated area

Mass flow equation

Mass conservation

Energy Conservation

Assumptions and limitations

Ports

Conserving

Input

Parameters

Parameters

See also