# Fan (MA)

**Libraries:**

Simscape /
Fluids /
Moist Air /
Turbomachinery

## Description

The Fan (MA) block represents a fan in a moist air 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:

*Δp*is the reference pressure differential. The block uses a quadratic fit of the fan pressure differential values at the_{ref}**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,*ω*–_{R}*ω*._{C}*ω*is the_{ref}**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 *Φ _{ref}* 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,
*η _{nom}*, and 0.

*η*is equivalent to the

_{nom}**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,
*Φ*, at peak or nominal conditions:

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

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,
*Δp _{ref}(q_{ref})*:

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

Here, *ρ* is the moist air density, and
*ρ _{ref}* 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:

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

where *ρ _{ref}* 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,
*Δp _{ref}(q_{ref},ω)*, as

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

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

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

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**Static pressure gain table, dp(w,q)**,**Efficiency table, eta(w,q)**, and**Mechanical power table, W(w,q)**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,
*q _{ref}*. The reference flow rate is a
function of the reference pressure gain,

*Δp*, and the current shaft speed,

_{ref}*ω*:

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

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:

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

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**Volumetric flow rate table, q(w,dp)**,**Efficiency table, eta(w,dp)**, and**Mechanical power table, W(w,dp)**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.

## Examples

## Ports

### Conserving

## Parameters

## Extended Capabilities

## Version History

**Introduced in R2021b**