# Fan (G)

Fan in gas network

Libraries:
Simscape / Fluids / Gas / Turbomachinery

## Description

The Fan (G) block represents a fan in a gas network. You can model the torque and pressure gain over the fan as a function of static pressure and flow rate or by using 1D or 2D tabulated reference pressure, shaft speed, and flow rate data.

By default, flow and pressure gain are from port A to port B. Port C represents the fan casing, and port R represents the fan shaft. You can specify the normal operating shaft direction in the Mechanical orientation parameter. If the shaft begins to spin in the opposite direction, the pressure difference across the fan drops to zero.

### Parameterization by Nominal Pressure, Flow Rate, and Shaft Speed

When you set the Fan parameterization parameter to ```Static pressure and flow rate at reference shaft speed```, the block uses the analytical fan affinity laws and reference pressure differential to calculate the pressure gain from port A to port B:

`${p}_{B}-{p}_{A}=\Delta {p}_{ref}{\left(\frac{\omega }{{\omega }_{ref}}\right)}^{2}{\left(\frac{D}{{D}_{ref}}\right)}^{2},$`

where:

• Δpref is the reference pressure differential. The block uses a quadratic fit of the fan pressure differential values at the Maximum static pressure gain at zero flow, Nominal static pressure gain, and Maximum volumetric flow rate at zero pressure parameters.

• ω is the shaft angular velocity, ωRωC.

• ωref is the Reference shaft speed parameter.

• $\frac{D}{{D}_{ref}}$ is the Fan diameter scale factor parameter.

The block calculates the shaft torque from the reference mechanical power and the fan affinity laws:

`$\tau ={\Phi }_{ref}\frac{{\omega }^{2}}{{\omega }_{ref}^{3}}{\left(\frac{D}{{D}_{ref}}\right)}^{5}.$`

Where Φref is the proportion of the pressure gain to the fan efficiency:

`${\Phi }_{ref}=\frac{{q}_{ref}\Delta {p}_{ref}}{{\eta }_{ref}}.$`

When you set the Shaft power specification parameter to `Fan efficiency`, the block uses a quadratic fit of efficiency between the fan peak performance, ηnom, and 0. ηnom is equivalent to the Nominal efficiency parameter, which the block interprets as the peak efficiency. If you set the Shaft power specification parameter to `Brake power`, the block derives the nominal fan efficiency from the nominal brake power, Φnom, at peak or nominal conditions:

`${\eta }_{nom}=\frac{{q}_{nom}\Delta {p}_{nom}}{{\Phi }_{nom}}.$`

The block assumes the efficiency is zero when there is no flow or when the flow reaches the maximum volumetric flow rate at zero pressure. The block uses the current flow q to compute the reference flow rate as:

`${q}_{ref}=q\frac{{\omega }_{ref}}{\omega }{\left(\frac{{D}_{ref}}{D}\right)}^{3}.$`

### 1-D Tabulated Data Parameterization: Pressure as a Function of Flow Rate at Reference Shaft Speed

When you set the Fan parameterization parameter to ```1D tabulated data - static pressure vs. flow rate at reference shaft speed```, you can model fan performance as a function of volumetric flow rate. The block interpolates the pressure gain from port A to port B from the 1-D Static pressure gain vector parameter, Δpref(qref):

`${p}_{B}-{p}_{A}=\Delta {p}_{ref}\left({q}_{ref}\right)\left(\frac{\rho }{{\rho }_{ref}}\right){\left(\frac{\omega }{{\omega }_{ref}}\right)}^{2}{\left(\frac{D}{{D}_{ref}}\right)}^{2}.$`

Here, ρ is the moist air density, and ρref is the reference density, which is equivalent to the Reference density parameter. The block calculates the shaft torque from the reference mechanical power and the fan affinity laws:

`$\tau ={\Phi }_{ref}\left({q}_{ref}\right)\frac{{\omega }^{2}}{{\omega }_{ref}^{3}}\left(\frac{\rho }{{\rho }_{ref}}\right){\left(\frac{D}{{D}_{ref}}\right)}^{5},$`

where ρref is the Reference density.

The block uses the current flow q to compute the reference flow rate:

`${q}_{ref}=q\frac{{\omega }_{ref}}{\omega }{\left(\frac{{D}_{ref}}{D}\right)}^{3}.$`

When the simulation is outside the range of the provided tables, the block extrapolates pressure based on the average slope of the fan curves and the reference torque to the nearest point.

### 2-D Tabulated Data Parameterization: Pressure as a Function of Shaft Speed and Flow Rate

When you set the Fan parameterization parameter to ```2D tabulated data - static pressure vs. shaft speed and flow rate```, you can model fan performance as a 2-D function of volumetric flow rate and angular velocity. The block interpolates the pressure gain from port A to port B from the 2-D Static pressure gain table, dp(w,q) parameter. The block defines the reference pressure gain, Δpref(qref,ω), as

`${p}_{B}-{p}_{A}=\Delta {p}_{ref}\left({q}_{ref},\omega \right)\left(\frac{\rho }{{\rho }_{ref}}\right){\left(\frac{D}{{D}_{ref}}\right)}^{2}.$`

The block calculates shaft torque from the reference mechanical power and the fan affinity laws:

`$\tau =\frac{{\Phi }_{ref}\left({q}_{ref},\omega \right)}{\omega }\left(\frac{\rho }{{\rho }_{ref}}\right){\left(\frac{D}{{D}_{ref}}\right)}^{5},$`

where the reference mechanical power is a function of the reference flow rate and the current shaft speed.

The block uses the current flow q to compute the reference flow rate:

`${q}_{ref}=q{\left(\frac{{D}_{ref}}{D}\right)}^{3}.$`

When the simulation is outside the range of the provided tables, the block extrapolates pressure based on the average slope of the fan curves and the reference torque to the nearest point.

Missing Data

If your table has unknown data points, use `NaN` in place of these values. The block fills in the `NaN` elements by extrapolating based on the average slope of the fan curves. Do not use artificial numerical values because these values distort fan behavior when operating in that region. When using unknown data:

• The `NaN` elements in the table must be contiguous.

• The positions of the `NaN` elements in the , , and parameters must match each other.

• `NaN` elements must be located in the upper-right portion of the table, which corresponds to the highest volumetric flow rate and lowest shaft speed.

### 2-D Tabulated Data Parameterization: Flow Rate as a Function of Shaft Speed and Pressure

When you set the Fan parameterization parameter to ```2D tabulated data - flow rate vs. shaft speed and static pressure```, you can model the flow rate through the fan as a 2-D function of pressure and angular velocity. The volumetric flow rate is interpolated from the 2-D Volumetric flow rate table, q(w,dp) parameter, qref. The reference flow rate is a function of the reference pressure gain, Δpref, and the current shaft speed, ω:

`$q={q}_{ref}\left(\Delta {p}_{ref},\omega \right){\left(\frac{D}{{D}_{ref}}\right)}^{3},$`

where the reference pressure gain derives from the pressure differential over the fan:

`$\Delta {p}_{ref}=\left({p}_{B}-{p}_{A}\right)\left(\frac{{\rho }_{ref}}{\rho }\right){\left(\frac{{D}_{ref}}{D}\right)}^{2}.$`

The shaft torque derives from the reference mechanical power and the fan affinity laws:

`$\tau =\frac{{\Phi }_{ref}\left(\Delta {p}_{ref},\omega \right)}{\omega }\left(\frac{\rho }{{\rho }_{ref}}\right){\left(\frac{D}{{D}_{ref}}\right)}^{5},$`

where the reference mechanical power is a function of the reference flow rate and the current shaft speed.

When the simulation is outside the range of the provided tables, the block extrapolates pressure based on the average slope of the fan curves and the reference torque to the nearest point.

Missing Data

If your table has unknown data points, use `NaN` in place of these values. The block fills in the `NaN` elements by extrapolating based on the average slope of the fan curves. Do not use artificial numerical values because these values distort fan behavior when operating in that region. When using unknown data:

• The `NaN` elements in the table must be contiguous.

• The positions of the `NaN` elements in the , , and parameters must match each other.

• `NaN` elements must be located in the upper-right portion of the table, which corresponds to the highest volumetric flow rate and lowest shaft speed.

### Power and Efficiency

You can specify shaft power as either fan efficiency or brake power.

The block calculates efficiency as

`$\eta =\frac{{\Phi }_{fluid}}{{\Phi }_{brake}},$`

where the brake power, or mechanical power measured at the shaft, is

`${\Phi }_{brake}=\tau \omega .$`

The block calculates fluid power as

`${\Phi }_{fluid}=q\left({p}_{B}-{p}_{A}\right).$`

The block calculates torque as

`$\tau =\frac{{\Phi }_{brake}}{\omega }.$`

### Visualizing the Fan Curve

You can check the parameterized fan performance by plotting the pressure, power, efficiency, and torque as a function of the flow. To generate a plot of the current fan settings, right-click on the block and select Fluids > Plot Fan Characteristics. If you change settings or data, click Apply on the block parameters and click Reload Data on the fan curve figure.

The default block parameterization results in these plots:

### Assumptions and Limitations

• If the shaft rotates opposite to the specified mechanical orientation, pressure difference across the block drops to zero and the results may not be accurate.

• The block assumes that the fan is quasi-steady.

• The block simulates fan performance in terms of static pressure rise, and not total fan pressure.

## Ports

### Conserving

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Gas conserving port associated with the fluid.

Gas conserving port associated with the fluid.

Mechanical rotational conserving port associated with the shaft.

Mechanical rotational conserving port associated with the casing.

## Parameters

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Fan performance model, specified as:

• ```Static pressure and flow rate at reference shaft speed```: Specify fan performance based on typical, nominal, or rated pressure gain and volumetric flow rate.

• ```1D tabulated data – static pressure vs flow rate at reference shaft speed```: Specify fan performance based on interpolation of pressure gain data as a function of volumetric flow rate.

• ```2D tabulated data – static pressure vs shaft speed and flow rate```: Specify fan performance based on the interpolation of pressure gain data as a function of shaft speed and volumetric flow rate.

• ```2D tabulated data – flow rate vs shaft speed and static pressure```: Specify fan performance based on the interpolation of volumetric flow rate data as a function of shaft speed and pressure gain.

Fan power specification, specified as:

• `Fan efficiency`: Derive the mechanical power from the fan efficiency.

• `Mechanical power`: Specify the mechanical power directly.

Volumetric flow rate through the fan at the reference shaft speed under nominal, typical, or rated operating conditions.

#### Dependencies

To enable this parameter, set Fan parameterization to ```Static pressure and flow rate at reference shaft speed```.

Pressure increase from port A to port B at the reference shaft speed under nominal, typical, or rated operating conditions.

#### Dependencies

To enable this parameter, set Fan parameterization to ```Static pressure and flow rate at reference shaft speed```.

Efficiency of converting the shaft power to fluid power at the reference shaft speed under nominal, typical, or rated operating conditions.

#### Dependencies

To enable this parameter, set:

• Fan parameterization to ```Static pressure and flow rate at reference shaft speed```.

• Shaft power specification to `Fan efficiency`.

Mechanical power driving moist air flow at the reference shaft speed under nominal, typical, or rated operating conditions.

#### Dependencies

To enable this parameter, set:

• Fan parameterization to ```Static pressure and flow rate at reference shaft speed```.

• Shaft power specification to `Brake power`.

Pressure increase from port A to port B at the reference shaft speed when there is no flow through the fan.

#### Dependencies

To enable this parameter, set Fan parameterization to ```Static pressure and flow rate at reference shaft speed```.

Free-delivery volumetric flow rate at the reference shaft speed and constant pressure.

#### Dependencies

To enable this parameter, set Fan parameterization to ```Static pressure and flow rate at reference shaft speed```.

Reference shaft angular velocity corresponding to the fan characteristic curve data.

#### Dependencies

To enable this parameter, set Fan parameterization to ```Static pressure and flow rate at reference shaft speed``` or ```1D tabulated data - static pressure vs. flow rate at reference shaft speed```.

Threshold for the minimum shaft speed as a fraction of the reference shaft speed. The block uses this value to prevent the shaft speed from becoming zero and causing a division by zero error in the expression for qref.

#### Dependencies

To enable this parameter, set Fan parameterization to ```Static pressure and flow rate at reference shaft speed``` or ```1D tabulated data - static pressure vs. flow rate at reference shaft speed```.

Vector of volumetric flow rate grid points for the 1-D interpolation of the fan characteristic curve. When Shaft power specification is `Brake power`, the fan data can extend beyond the normal operating region, and these values can be negative.

#### Dependencies

To enable this parameter, set Fan parameterization to ```1D tabulated data - static pressure vs. flow rate at reference shaft speed```.

Vector of pressure gain data points. Each element in the vector corresponds to an element in the Volumetric flow rate vector parameter. The pressure gain is the increase in pressure from port A to port B at the reference shaft speed. When Shaft power specification is ```Brake power```, the fan data can extend beyond the normal operating region, and these values can be negative.

#### Dependencies

To enable this parameter, set Fan parameterization to ```1D tabulated data - static pressure vs. flow rate at reference shaft speed```.

Vector of fan efficiency data points. Each element in the vector corresponds to an element in the Volumetric flow rate vector parameter. The efficiency is the ratio of fluid power to shaft mechanical power at the reference shaft speed.

#### Dependencies

To enable this parameter, set Fan parameterization to ```1D tabulated data - static pressure vs. flow rate at reference shaft speed``` and Shaft power specification to ```Fan efficiency```.

Vector of shaft mechanical power data points. Each element in the vector corresponds to an element in the Volumetric flow rate vector parameter. The mechanical power is the power that drives the fan at the reference shaft speed. These values can be negative if the fan data extends beyond the normal operating region.

#### Dependencies

To enable this parameter, set Fan parameterization to ```1D tabulated data - static pressure vs. flow rate at reference shaft speed``` and Shaft power specification to ```Brake power```.

Moist air density for a given characteristic fan curve.

#### Dependencies

To enable this parameter, set Fan parameterization to ```1D tabulated data - static pressure vs. flow rate at reference shaft speed```, ```2D tabulated data - static pressure vs. shaft speed and flow rate``` or ```2D tabulated data - flow rate vs. shaft speed and static pressure```.

Vector of shaft angular velocity grid points for the 2-D interpolation of the fan characteristic curves.

#### Dependencies

To enable this parameter, set Fan parameterization to ```2D tabulated data - static pressure vs. shaft speed and flow rate``` or ```2D tabulated data - flow rate vs. shaft speed and static pressure```.

Vector of volumetric flow rate grid points for the 2-D interpolation of the fan characteristic curves. When Shaft power specification is `Brake power`, the fan data can extend beyond the normal operating region, and these values can be negative.

#### Dependencies

To enable this parameter, set Fan parameterization to ```2D tabulated data - static pressure vs. shaft speed and flow rate```.

M-by-N matrix of pressure gain data points for the 2-D interpolation of the pressure gain. The pressure gain is the increase in pressure from port A to port B. When Shaft power specification is ```Brake power```, the fan data can extend beyond the normal operating region, and these values can be negative. M and N are the sizes of the corresponding vectors:

• M is the number of elements in the Shaft speed vector, w parameter. The elements corresponding to zero flow rate must be in strictly ascending order.

• N is the number of elements in the Volumetric flow rate vector, q parameter.

If your table has unknown data points, use `NaN` in place of these values. The block fills in the `NaN` elements by extrapolating based on the average slope of the fan curves. Do not use artificial numerical values because these values distort fan behavior when operating in that region. When using unknown data:

• The `NaN` elements in the table must be contiguous.

• The positions of the `NaN` elements in the , , and parameters must match each other.

• `NaN` elements must be located in the upper-right portion of the table, which corresponds to the highest volumetric flow rate and lowest shaft speed.

#### Dependencies

To enable this parameter, set Fan parameterization to ```2D tabulated data - static pressure vs. shaft speed and flow rate```.

M-by-N matrix of efficiency data points for the 2-D interpolation of torque. The efficiency is the ratio of fluid power to shaft mechanical power. M and N are the sizes of the corresponding vectors:

• M is the number of elements in the Shaft speed vector, w parameter.

• N is the number of elements in the Volumetric flow rate vector, q parameter.

If your table has unknown data points, use `NaN` in place of these values. The block fills in the `NaN` elements by extrapolating based on the average slope of the fan curves. Do not use artificial numerical values because these values distort fan behavior when operating in that region. When using unknown data:

• The `NaN` elements in the table must be contiguous.

• The positions of the `NaN` elements in the , , and parameters must match each other.

• `NaN` elements must be located in the upper-right portion of the table, which corresponds to the highest volumetric flow rate and lowest shaft speed.

#### Dependencies

To enable this parameter, set Fan parameterization to ```2D tabulated data - static pressure vs. shaft speed and flow rate``` and Shaft power specification to ```Fan efficiency```.

M-by-N table of mechanical power data points for the 2-D interpolation of torque. These values can be negative if the fan data extends beyond the normal operating region. The mechanical power is the power that drives the fan. M and N are the sizes of the corresponding vectors:

• M is the number of elements in the Shaft speed vector, w parameter. The elements corresponding to zero flow rate must be in strictly ascending order.

• N is the number of elements in the Volumetric flow rate vector, q parameter.

If your table has unknown data points, use `NaN` in place of these values. The block fills in the `NaN` elements by extrapolating based on the average slope of the fan curves. Do not use artificial numerical values because these values distort fan behavior when operating in that region. When using unknown data:

• The `NaN` elements in the table must be contiguous.

• The positions of the `NaN` elements in the , , and parameters must match each other.

• `NaN` elements must be located in the upper-right portion of the table, which corresponds to the highest volumetric flow rate and lowest shaft speed.

#### Dependencies

To enable this parameter, set Fan parameterization to ```2D tabulated data - static pressure vs. shaft speed and flow rate``` and Shaft power specification to ```Brake power```.

Vector of pressure gain grid points for the 2-D interpolation of the fan characteristic curves. When Shaft power specification is `Brake power`, the fan data can extend beyond the normal operating region, and these values can be negative.

#### Dependencies

To enable this parameter, set Fan parameterization to ```2D tabulated data - flow rate vs. shaft speed and static pressure```.

M-by-N matrix of volumetric flow rate data points for the 2-D interpolation of volumetric flow rate. When Shaft power specification is ```Brake power```, the fan data can extend beyond the normal operating region, and these values can be negative. M and N are the sizes of the corresponding vectors:

• M is the number of elements in the Shaft speed vector, w parameter. The elements corresponding to zero flow rate must be in strictly ascending order.

• N is the number of elements in the Static pressure gain vector, Dp parameter.

If your table has unknown data points, use `NaN` in place of these values. The block fills in the `NaN` elements by extrapolating based on the average slope of the fan curves. Do not use artificial numerical values because these values distort fan behavior when operating in that region. When using unknown data:

• The `NaN` elements in the table must be contiguous.

• The positions of the `NaN` elements in the , , and parameters must match each other.

• `NaN` elements must be located in the upper-right portion of the table, which corresponds to the highest volumetric flow rate and lowest shaft speed.

#### Dependencies

To enable this parameter, set Fan parameterization to ```2D tabulated data - flow rate vs. shaft speed and static pressure```.

M-by-N matrix of efficiency data points for the 2-D interpolation of torque. The efficiency is the ratio of fluid power to shaft mechanical power. M and N are the sizes of the corresponding vectors:

• M is the number of elements in the Shaft speed vector, w parameter.

• N is the number of elements in the Static pressure gain vector, Dp parameter.

If your table has unknown data points, use `NaN` in place of these values. The block fills in the `NaN` elements by extrapolating based on the average slope of the fan curves. Do not use artificial numerical values because these values distort fan behavior when operating in that region. When using unknown data:

• The `NaN` elements in the table must be contiguous.

• The positions of the `NaN` elements in the , , and parameters must match each other.

• `NaN` elements must be located in the upper-right portion of the table, which corresponds to the highest volumetric flow rate and lowest shaft speed.

#### Dependencies

To enable this parameter, set Fan parameterization to ```2D tabulated data - flow rate vs. shaft speed and static pressure``` and Shaft power specification to ```Fan efficiency```.

M-by-N matrix of mechanical power data points for the 2-D interpolation of torque. These values can be negative if the fan data extends beyond the normal operating region. The mechanical power is the power that drives the fan. M and N are the sizes of the corresponding vectors:

• M is the number of elements in the Shaft speed vector, w parameter. The elements corresponding to zero flow rate must be in strictly ascending order.

• N is the number of elements in the Static pressure gain vector, Dp parameter.

If your table has unknown data points, use `NaN` in place of these values. The block fills in the `NaN` elements by extrapolating based on the average slope of the fan curves. Do not use artificial numerical values because these values distort fan behavior when operating in that region. When using unknown data:

• The `NaN` elements in the table must be contiguous.

• The positions of the `NaN` elements in the , , and parameters must match each other.

• `NaN` elements must be located in the upper-right portion of the table, which corresponds to the highest volumetric flow rate and lowest shaft speed.

#### Dependencies

To enable this parameter, set Fan parameterization to ```2D tabulated data - flow rate vs. shaft speed and static pressure``` and Shaft power specification to ```Brake power```.

Geometric scale factor to increase or decrease the size of the simulated fan from the given fan parameterization. The scaling may not be accurate for scale factors much larger or much smaller than 1.

Normal operating shaft direction. By default, flow and pressure gain are from port A to port B.

Cross-sectional area of the moist air flow at the fan inlet.

Cross-sectional area of the moist air flow at the fan outlet.

## Version History

Introduced in R2018b

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1 Prior to R2021b, this setting was called ```2D tabulated data - flow rate and total efficiency vs. angular speed and static pressure```.