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:

$p_{B} - p_{A} = Δ p_{r e f} {(\frac{ω}{ω_{r e f}})}^{2} {(\frac{D}{D_{r e f}})}^{2},$

where:

Δp_ref 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, ω_R – ω_C.
ω_ref is the Reference shaft speed parameter.
$\frac{D}{D_{r e f}}$ is the Fan diameter scale factor parameter.

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

$τ = Φ_{r e f} \frac{ω^{2}}{ω_{r e f}^{3}} {(\frac{D}{D_{r e f}})}^{5} .$

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

$Φ_{r e f} = \frac{q_{r e f} Δ p_{r e f}}{η_{r e f}} .$

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_nom 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, Φ_nom, at peak or nominal conditions:

$η_{n o m} = \frac{q_{n o m} Δ p_{n o m}}{Φ_{n o m}} .$

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:

$q_{r e f} = q \frac{ω_{r e f}}{ω} {(\frac{D_{r e f}}{D})}^{3} .$

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):

$p_{B} - p_{A} = Δ p_{r e f} (q_{r e f}) (\frac{ρ}{ρ_{r e f}}) {(\frac{ω}{ω_{r e f}})}^{2} {(\frac{D}{D_{r e f}})}^{2} .$

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:

$τ = Φ_{r e f} (q_{r e f}) \frac{ω^{2}}{ω_{r e f}^{3}} (\frac{ρ}{ρ_{r e f}}) {(\frac{D}{D_{r e f}})}^{5},$

where ρ_ref is the Reference density.

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

$q_{r e f} = q \frac{ω_{r e f}}{ω} {(\frac{D_{r e f}}{D})}^{3} .$

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

$p_{B} - p_{A} = Δ p_{r e f} (q_{r e f}, ω) (\frac{ρ}{ρ_{r e f}}) {(\frac{D}{D_{r e f}})}^{2} .$

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

$τ = \frac{Φ_{r e f} (q_{r e f}, ω)}{ω} (\frac{ρ}{ρ_{r e f}}) {(\frac{D}{D_{r e f}})}^{5},$

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:

$q_{r e f} = q {(\frac{D_{r e f}}{D})}^{3} .$

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_ref, and the current shaft speed, ω:

$q = q_{r e f} (Δ p_{r e f}, ω) {(\frac{D}{D_{r e f}})}^{3},$

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

$Δ p_{r e f} = (p_{B} - p_{A}) (\frac{ρ_{r e f}}{ρ}) {(\frac{D_{r e f}}{D})}^{2} .$

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

$τ = \frac{Φ_{r e f} (Δ p_{r e f}, ω)}{ω} (\frac{ρ}{ρ_{r e f}}) {(\frac{D}{D_{r e f}})}^{5},$

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

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

$η = \frac{Φ_{f l u i d}}{Φ_{b r a k e}},$

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

$Φ_{b r a k e} = τ ω .$

The block calculates fluid power as

$Φ_{f l u i d} = q (p_{B} - p_{A}) .$

The block calculates torque as

$τ = \frac{Φ_{b r a k e}}{ω} .$

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:

Plot of fan characteristic curves

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

Simple CPU Cooling System

A simple CPU cooling system consists of a heat sink, a CPU fan, and fan controllers. The heat generated by the CPU is transferred to the heat sink by conduction and it is dissipated to the cooling air by forced convection mechanism. The heat sink is a parallel plate fin with rectangular fins between the plate fins. The CPU fan moves air across the heat sink by drawing air into the case grille from the outside and ejecting warm air from inside. The fan controller unit includes three control levels, representing a 3-speed switch, according to the CPU temperature. For lower CPU temperature, the fan speed is decreased and for higher temperature it is increased.

Open Model

Ports

Conserving

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A — Fluid entry
gas

Gas conserving port associated with the fluid.

B — Fluid exit
gas

Gas conserving port associated with the fluid.

R — Shaft
mechanical rotational

Mechanical rotational conserving port associated with the shaft.

C — Casing
mechanical rotational

Mechanical rotational conserving port associated with the casing.

Parameters

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Fan parameterization — Fan performance model
`Static pressure and flow rate at reference shaft speed` (default) | `1D tabulated data - static pressure vs. flow rate at reference shaft speed` | `2D tabulated data - static pressure vs. shaft speed and flow rate` | `2D tabulated data - flow rate vs. shaft speed and static pressure`

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.

Shaft power specification — Power definition
`Fan efficiency` (default) | `Brake power`

Fan power specification, specified as:

Fan efficiency: Derive the mechanical power from the fan efficiency.
Mechanical power: Specify the mechanical power directly.

Nominal volumetric flow rate — Flow rate at reference shaft speed
`0.12` m^3/s (default) | positive scalar

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.

Nominal static pressure gain — Pressure gain at reference shaft speed
`5400` Pa (default) | positive scalar

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.

Nominal efficiency — Efficiency at reference shaft speed
`0.40` (default) | positive scalar

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.

Nominal mechanical power — Power at nominal efficiency
`1620` `W` (default) | positive scalar

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.

Maximum static pressure gain at zero flow — Maximum pressure at reference shaft speed
`6400` `Pa` (default) | positive scalar

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.

Maximum volumetric flow rate at zero pressure — Maximum flow rate at reference shaft speed
`0.24` `m^3/s` (default) | positive scalar

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 speed — Fan curve reference speed
`3000` `rpm` (default) | positive scalar

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.

Minimum shaft speed threshold as fraction of reference — Threshold for minimum shaft speed
`1e-2` (default) | positive scalar

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 q_ref.

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.

Volumetric flow rate vector — Fan curve flow rate vector
`[.0278, .0556, .0833, .111, .139, .167]` `m^3/s` (default) | vector

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.

Static pressure gain vector — Pressure gain for given volumetric flow rate
`[6410, 6375, 6018, 5366, 4501, 3609]` `Pa` (default) | vector

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.

Efficiency vector — Efficiency for given volumetric flow rate
`[.257, .394, .453, .47, .459, .415]` (default) | vector

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.

Mechanical power vector — Power for parameterization of torque
`[693, 900, 1107, 1267, 1363, 1452]` W (default) | 1-by-n vector

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.

Reference density — Density associated with fan curve data
`1.2` kg/m^3 (default) | positive scalar

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.

Shaft speed vector, w — Shaft angular velocity for given
`[2400; 3000; 3600]` rpm (default) | vector

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.

Volumetric flow rate vector, q — Flow rate for parameterization of pressure gain
`[.0278, .0556, .0833, .111, .139, .167]` m^3/s (default) | 1-by-n vector

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.

Static pressure gain table, dp(w,q) — Pressure for parameterization of pressure
`[4111, 4010, 3551, 2881, 2167, 1453; 6410, 6375, 6018, 5366, 4501, 3609; 9217, 9285, 9022, 8428, 7552, 6482]` `Pa` (default) | M-by-N matrix

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.

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.

Dependencies

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

Efficiency table, eta(w,q) — Efficiency for parameterization of torque
`[.3, .434, .468, .459, .4, .3; .257, .394, .453, .47, .459, .415; .225, .359, .434, .461, .47, .459]` 1 (default) | M-by-N matrix

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.

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.

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.

Mechanical power table, W(w,q) — Mechanical power for parameterization of torque
`[381, 514, 632, 697, 753, 809; 693, 900, 1107, 1267, 1363, 1452; 1139, 1438, 1732, 2029, 2233, 2358]` W (default) | M-by-N matrix

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.

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.

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.

Static pressure gain vector, dp — Pressure for parameterization of flow rate
`[31, 62, 93, 124]` Pa (default) | 1-by-N vector

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.

Volumetric flow rate table, q(w,dp) — Flow rate for parameterization of flow rate
`[.802, .759, .703, .611; .936, .902, .862, .81; 1.056, 1.027, .994, .956]` m^3/s (default) | M-by-N matrix

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.

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.

Dependencies

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

Efficiency table, eta(w,dp) — Efficiency for parameterization of torque
`[.088, .162, .22, .261; .068, .128, .18, .222; .055, .105, .148, .188]` (default) | M-by-N matrix

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.

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.

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.

Mechanical power table, W(w,dp) — Mechanical power for parameterization of torque
`[283, 290, 297, 290; 427, 437, 445, 452; 595, 606, 625, 631]` `W` (default) | M-by-N matrix

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.

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.

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.

Fan diameter scale factor — Model-to-reference scale factor
`1` (default) | positive scalar

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.

Mechanical orientation — Rotational orientation
`Positive angular velocity of port R relative to port C corresponds to normal fan operation` (default) | `Negative angular velocity of port R relative to port C corresponds to normal fan operation`

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

Inlet flow area (port A) — Port A area
`0.01` `m^2` (default) | positive scalar

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

Outlet flow area (port B) — Port B area
`0.01` `m^2` (default) | positive scalar

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

Extended Capabilities

C/C++ Code Generation
Generate C and C++ code using Simulink® Coder™.

Version History

Introduced in R2018b

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R2023a: Expose threshold for low shaft speed

Use the Minimum shaft speed threshold as fraction of reference parameter to control the minimum shaft speed threshold as a fraction of the reference shaft speed. The Minimum shaft speed threshold as fraction of reference parameter is available in the block when the Fan parameterization parameter is Static pressure and flow rate at reference shaft speed or 1D tabulated data – static pressure vs flow rate at reference shaft speed.

R2022b: Extend performance beyond normal operating conditions

Both the 1-D and 2-D parameterizations now allow negative values. When simulation is outside the range of the provided table, block extrapolates the pressure based on the average slope of the fan curves.

You can now use NaN elements where data is unavailable. These 2-D tabulated fan parameters support contiguous NaN elements in the upper-right portion of the table:

Static pressure gain table, dp(w,q)
Efficiency table, eta(w,q)
Mechanical power table, W(w,q)
Volumetric flow rate table, q(w,dp)
Efficiency table, eta(w,dp)
Mechanical power table, W(w,dp)

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

R2021b: 2-D Tabulated Data Parameterization: Flow Rate as a Function of Shaft Speed and Pressure Ratio

In R2021b, the block no longer supports the 2-D Tabulated Data Parameterization: Flow Rate as a Function of Shaft Speed and Pressure Ratio parameterization. In R2021b and later, if you open models created in a prior release that include the Fan (G) block, Simscape™ Fluids™ replaces the block with the Fan (MA) - Legacy block. This block supports the 2-D Tabulated Data Parameterization: Flow Rate as a Function of Shaft Speed and Pressure Ratio setting.

You can preserve the functionality of a model using this parameterization by setting Fan parameterization to 2D tabulated data - flow rate vs. shaft speed and static pressure¹ and converting the ratios to absolute values. An example script that performs this conversion takes in the legacy parameters omega_DpMax_TLU, DpMax_TLU, omega_flow_TLU, Dp_DpMax_TLU, flow_rate_TLU, and eta_flow_TLU and returns the converted parameters omega_g_TLU, pressure_g_TLU, pressure_g_TLU, and eta_g_TLU:

% Shaft speed vector for maximum pressure rise vector 
omega_DpMax_TLU = [1800, 2400, 3000]; 

% Maximum pressure rise vector
DpMax_TLU       = [400, 1200, 2000]; 

% Shaft speed vector, omega 
omega_flow_TLU  = [1800, 2400, 3000]; 

% Static pressure rise ratio vector, Dp/DpMax 
Dp_DpMax_TLU    = linspace(0, 1, 4); 

% Flow rate table, q(omega,Dp/DpMax) 
flow_rate_TLU   = [ 
    0.33    0.26    0.18    0.07 
    1.20    0.91    0.64    0.26 
    1.84    1.61    1.13    0.46]; 

% Total efficiency table, Eta(omega,Dp/DpMax) 
eta_flow_TLU    = [ 
    0.22    0.25    0.27    0.28 
    0.48    0.52    0.55    0.53 
    0.42    0.45    0.49    0.44]; 

% Create interpolants of the tables 
DpMax_TLU_interp = griddedInterpolant(omega_DpMax_TLU, DpMax_TLU, ... 
    'linear', 'linear'); 

flow_rate_TLU_interp = griddedInterpolant({omega_flow_TLU, Dp_DpMax_TLU}, flow_rate_TLU, ... 
    'linear', 'linear'); 

eta_flow_TLU_interp = griddedInterpolant({omega_flow_TLU, Dp_DpMax_TLU}, eta_flow_TLU, ... 
    'linear', 'nearest'); 

% Maximum pressure rise 
DpMax = DpMax_TLU_interp(max(omega_flow_TLU, omega_DpMax_TLU(1)));  

% Shaft speed vector, w 
omega_q_TLU = omega_flow_TLU; 

% Static pressure gain vector, Dp 
pressure_q_TLU = unique(DpMax(:)*Dp_DpMax_TLU(:)'); 

% Interpolation query points as full grid arrays 
omega_grid = omega_q_TLU(:)*ones(1, length(pressure_q_TLU)); 

Dp_DpMax_grid = pressure_q_TLU(:)' ./ DpMax(:); 

% Volumetric flow rate table, q(w,Dp) 
flow_rate_q_TLU = flow_rate_TLU_interp(omega_grid, Dp_DpMax_grid); 

flow_rate_q_TLU = max(flow_rate_q_TLU, 1e-4*flow_rate_TLU(1,1)); % keep it > 0 

% Efficiency table, eta(w,Dp) 
eta_q_TLU = eta_flow_TLU_interp(omega_grid, Dp_DpMax_grid);

Fan (G)

Description

Parameterization by Nominal Pressure, Flow Rate, and Shaft Speed

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

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

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

Power and Efficiency

Visualizing the Fan Curve

Assumptions and Limitations

Examples

Simple CPU Cooling System

Ports

Conserving

A — Fluid entry gas

B — Fluid exit gas

R — Shaft mechanical rotational

C — Casing mechanical rotational

Parameters

Shaft power specification — Power definition Fan efficiency (default) | Brake power

Nominal volumetric flow rate — Flow rate at reference shaft speed 0.12 m^3/s (default) | positive scalar

Dependencies

Nominal static pressure gain — Pressure gain at reference shaft speed 5400 Pa (default) | positive scalar

Dependencies

Nominal efficiency — Efficiency at reference shaft speed 0.40 (default) | positive scalar

Dependencies

Nominal mechanical power — Power at nominal efficiency 1620 W (default) | positive scalar

Dependencies

Maximum static pressure gain at zero flow — Maximum pressure at reference shaft speed 6400 Pa (default) | positive scalar

Dependencies

Maximum volumetric flow rate at zero pressure — Maximum flow rate at reference shaft speed 0.24 m^3/s (default) | positive scalar

Dependencies

Reference shaft speed — Fan curve reference speed 3000 rpm (default) | positive scalar

Dependencies

Minimum shaft speed threshold as fraction of reference — Threshold for minimum shaft speed 1e-2 (default) | positive scalar

Dependencies

Volumetric flow rate vector — Fan curve flow rate vector [.0278, .0556, .0833, .111, .139, .167] m^3/s (default) | vector

Dependencies

Static pressure gain vector — Pressure gain for given volumetric flow rate [6410, 6375, 6018, 5366, 4501, 3609] Pa (default) | vector

Dependencies

Efficiency vector — Efficiency for given volumetric flow rate [.257, .394, .453, .47, .459, .415] (default) | vector

Dependencies

Mechanical power vector — Power for parameterization of torque [693, 900, 1107, 1267, 1363, 1452] W (default) | 1-by-n vector

Dependencies

Reference density — Density associated with fan curve data 1.2 kg/m^3 (default) | positive scalar

Dependencies

Shaft speed vector, w — Shaft angular velocity for given [2400; 3000; 3600] rpm (default) | vector

Dependencies

Volumetric flow rate vector, q — Flow rate for parameterization of pressure gain [.0278, .0556, .0833, .111, .139, .167] m^3/s (default) | 1-by-n vector

Dependencies

Static pressure gain table, dp(w,q) — Pressure for parameterization of pressure [4111, 4010, 3551, 2881, 2167, 1453; 6410, 6375, 6018, 5366, 4501, 3609; 9217, 9285, 9022, 8428, 7552, 6482] Pa (default) | M-by-N matrix

Dependencies

Efficiency table, eta(w,q) — Efficiency for parameterization of torque [.3, .434, .468, .459, .4, .3; .257, .394, .453, .47, .459, .415; .225, .359, .434, .461, .47, .459] 1 (default) | M-by-N matrix

Dependencies

Mechanical power table, W(w,q) — Mechanical power for parameterization of torque [381, 514, 632, 697, 753, 809; 693, 900, 1107, 1267, 1363, 1452; 1139, 1438, 1732, 2029, 2233, 2358] W (default) | M-by-N matrix

Dependencies

Static pressure gain vector, dp — Pressure for parameterization of flow rate [31, 62, 93, 124] Pa (default) | 1-by-N vector

Dependencies

Volumetric flow rate table, q(w,dp) — Flow rate for parameterization of flow rate [.802, .759, .703, .611; .936, .902, .862, .81; 1.056, 1.027, .994, .956] m^3/s (default) | M-by-N matrix

Dependencies

Efficiency table, eta(w,dp) — Efficiency for parameterization of torque [.088, .162, .22, .261; .068, .128, .18, .222; .055, .105, .148, .188] (default) | M-by-N matrix

Dependencies

Mechanical power table, W(w,dp) — Mechanical power for parameterization of torque [283, 290, 297, 290; 427, 437, 445, 452; 595, 606, 625, 631] W (default) | M-by-N matrix

Dependencies

Fan diameter scale factor — Model-to-reference scale factor 1 (default) | positive scalar

Mechanical orientation — Rotational orientation Positive angular velocity of port R relative to port C corresponds to normal fan operation (default) | Negative angular velocity of port R relative to port C corresponds to normal fan operation

Inlet flow area (port A) — Port A area 0.01 m^2 (default) | positive scalar

Outlet flow area (port B) — Port B area 0.01 m^2 (default) | positive scalar

Extended Capabilities

C/C++ Code Generation Generate C and C++ code using Simulink® Coder™.

Version History

R2023a: Expose threshold for low shaft speed

R2022b: Extend performance beyond normal operating conditions

R2021b: 2-D Tabulated Data Parameterization: Flow Rate as a Function of Shaft Speed and Pressure Ratio

See Also

A — Fluid entry
gas

B — Fluid exit
gas

R — Shaft
mechanical rotational

C — Casing
mechanical rotational

Shaft power specification — Power definition
`Fan efficiency` (default) | `Brake power`

Nominal volumetric flow rate — Flow rate at reference shaft speed
`0.12` m^3/s (default) | positive scalar

Nominal static pressure gain — Pressure gain at reference shaft speed
`5400` Pa (default) | positive scalar

Nominal efficiency — Efficiency at reference shaft speed
`0.40` (default) | positive scalar

Nominal mechanical power — Power at nominal efficiency
`1620` `W` (default) | positive scalar

Maximum static pressure gain at zero flow — Maximum pressure at reference shaft speed
`6400` `Pa` (default) | positive scalar

Maximum volumetric flow rate at zero pressure — Maximum flow rate at reference shaft speed
`0.24` `m^3/s` (default) | positive scalar

Reference shaft speed — Fan curve reference speed
`3000` `rpm` (default) | positive scalar

Minimum shaft speed threshold as fraction of reference — Threshold for minimum shaft speed
`1e-2` (default) | positive scalar

Volumetric flow rate vector — Fan curve flow rate vector
`[.0278, .0556, .0833, .111, .139, .167]` `m^3/s` (default) | vector

Static pressure gain vector — Pressure gain for given volumetric flow rate
`[6410, 6375, 6018, 5366, 4501, 3609]` `Pa` (default) | vector

Efficiency vector — Efficiency for given volumetric flow rate
`[.257, .394, .453, .47, .459, .415]` (default) | vector

Mechanical power vector — Power for parameterization of torque
`[693, 900, 1107, 1267, 1363, 1452]` W (default) | 1-by-n vector

Reference density — Density associated with fan curve data
`1.2` kg/m^3 (default) | positive scalar

Shaft speed vector, w — Shaft angular velocity for given
`[2400; 3000; 3600]` rpm (default) | vector

Volumetric flow rate vector, q — Flow rate for parameterization of pressure gain
`[.0278, .0556, .0833, .111, .139, .167]` m^3/s (default) | 1-by-n vector

Static pressure gain table, dp(w,q) — Pressure for parameterization of pressure
`[4111, 4010, 3551, 2881, 2167, 1453; 6410, 6375, 6018, 5366, 4501, 3609; 9217, 9285, 9022, 8428, 7552, 6482]` `Pa` (default) | M-by-N matrix

Efficiency table, eta(w,q) — Efficiency for parameterization of torque
`[.3, .434, .468, .459, .4, .3; .257, .394, .453, .47, .459, .415; .225, .359, .434, .461, .47, .459]` 1 (default) | M-by-N matrix

Mechanical power table, W(w,q) — Mechanical power for parameterization of torque
`[381, 514, 632, 697, 753, 809; 693, 900, 1107, 1267, 1363, 1452; 1139, 1438, 1732, 2029, 2233, 2358]` W (default) | M-by-N matrix

Static pressure gain vector, dp — Pressure for parameterization of flow rate
`[31, 62, 93, 124]` Pa (default) | 1-by-N vector

Volumetric flow rate table, q(w,dp) — Flow rate for parameterization of flow rate
`[.802, .759, .703, .611; .936, .902, .862, .81; 1.056, 1.027, .994, .956]` m^3/s (default) | M-by-N matrix

Efficiency table, eta(w,dp) — Efficiency for parameterization of torque
`[.088, .162, .22, .261; .068, .128, .18, .222; .055, .105, .148, .188]` (default) | M-by-N matrix

Mechanical power table, W(w,dp) — Mechanical power for parameterization of torque
`[283, 290, 297, 290; 427, 437, 445, 452; 595, 606, 625, 631]` `W` (default) | M-by-N matrix

Fan diameter scale factor — Model-to-reference scale factor
`1` (default) | positive scalar

Mechanical orientation — Rotational orientation
`Positive angular velocity of port R relative to port C corresponds to normal fan operation` (default) | `Negative angular velocity of port R relative to port C corresponds to normal fan operation`

Inlet flow area (port A) — Port A area
`0.01` `m^2` (default) | positive scalar

Outlet flow area (port B) — Port B area
`0.01` `m^2` (default) | positive scalar

C/C++ Code Generation
Generate C and C++ code using Simulink® Coder™.