Fan (G)

Fan in a gas network

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• Simscape / Fluids / Gas / Turbomachinery

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Description

The Fan (G) block models a rotor mounted on a drive shaft in a gas network. Normal operation occurs when the gas flows from port A to B. Port R is associated with the fan shaft, and port C is associated with the fan casing. The shaft rotational velocity is reported relative to port C.

You can specify the rotational orientation of the fan that generates flow from port A to port B in the Mechanical orientation parameter. Rotation of the fan counter to this setting will not generate any flow.

Parameterization by Flow Rate

When Fan specification is set to 1D tabulated data - static pressure and total efficiency table vs. flow rate, the static pressure differential is linearly interpolated from the Volumetric flow rate vector based on the reference volumetric flow rate, q_ref, which is a function of the Reference shaft speed, ω_ref. The static pressure differential is calculated as:

$$\Delta p=\frac{{\omega }^2}{{\omega }_{ref}^2}\frac{{\rho }_{in}}{{\rho }_{ref}}\Delta p_{ref}\left(q_{ref}\right),$$

where:

• ρ_ref is the Reference density associated with the tabulated data measurements.

• ω is the rotor shaft speed, ω_R - ω_C.

• ρ_in is the inlet gas density.

• Δp_ref is the Static pressure rise vector, which depends on the reference Volumetric flow rate vector, q_ref:

  $$q_{ref}=\frac{{\dot{m}}_{in}}{{\rho }_{in}}\frac{{\omega }_{ref}}{\omega }.$$

The total efficiency is interpolated from the Total efficiency vector based on the reference volumetric flow rate:

$${\eta }_{\text{T}}={\eta }_{\text{T}}(q_{ref}).$$

Parameterization by Angular Velocity and Flow Rate

When Fan specification is set to 2D tabulated data - static pressure and total efficiency vs. angular speed and flow rate, the static pressure differential is linearly interpolated from the Static pressure rise table, Dp(omega,q), as a function of the volumetric flow rate, q, and the Shaft speed vector, omega, ω. The static pressure differential is calculated as:

$$\Delta p=\frac{{\rho }_{in}}{{\rho }_{ref}}\Delta p_{ref}\left(q,\omega \right),$$

where the Flow rate vector, q, q, is calculated as $$q=\frac{\dot{m}}{{\rho }_{in}}.$$

The total fan efficiency is linearly interpolated from the Total efficiency table, Eta(omega,q) based on the volumetric flow rate and shaft angular velocity:

$${\eta }_{\text{T}}={\eta }_{\text{T}}(\omega ,q).$$

Parameterization by Angular Velocity and Pressure Differential

When Fan specification is set to 2D tabulated data - flow rate and total efficiency vs. angular speed and static pressure, the volumetric flow rate is linearly interpolated from the Flow rate table, q(omega,Dp), as a function of the shaft speed, ω, and the reference Static pressure rise vector, Dp, Δp_ref. The mass flow rate is calculated as:

$$\dot{m}={\rho }_{ref}{q}_{ref}(\omega ,\Delta p_{ref}),$$

where the reference static pressure rise is calculated as:

$$\Delta p_{ref}=\left(\frac{{\rho }_{ref}}{{\rho }_{in}}\right)\Delta p.$$

and where Δp is the static pressure differential over the fan, p_B- p_A.

The total efficiency is interpolated from the Total efficiency table, Eta(omega,Dp) based on the shaft speed and reference static pressure differential:

$${\eta }_{\text{T}}={\eta }_{\text{T}}(\omega ,\Delta p_{ref}).$$

When the operating region on your fan map is not rectangular, you can parameterize fan performance by the ratio of the operational to the maximum pressure rise over the fan. When Fan specification is set to 2D tabulated data - flow rate and total efficiency vs. angular speed and static pressure ratio, the volumetric flow rate is linearly interpolated from the Flow rate table, q(omega,Dp/DpMax), as a function of the Shaft speed vector omega, ω, and the Static pressure rise ratio vector, Dp/DpMax, $$\frac{\Delta p_{ref}}{\Delta p_{\max }}$$.

The mass flow rate is calculated as:

$$\dot{m}={\rho }_{ref}\Delta q_{ref}\left(\omega ,\frac{\Delta p_{ref}}{\Delta p_{\max }}\right),$$

where:

• Δp_max is the maximum pressure differential over the fan at a given shaft speed, or the Maximum pressure rise vector. It depends on the Shaft speed vector for maximum pressure rise vector, ω_max.

• $$\frac{\Delta p_{ref}}{\Delta p_{\max }}$$ is the Static pressure rise ratio vector, Dp/DpMax, where Δp_ref is the pressure differential over the fan adjusted for density:

  $$\Delta p_{ref}=\frac{{\rho }_{ref}}{{\rho }_{in}}\Delta p.$$

The total fan efficiency is linearly interpolated from the Total efficiency table, Eta(omega,Dp/DpMax) based on the shaft angular velocity and pressure ratio:

$${\eta }_{\text{T}}={\eta }_{\text{T}}\left(\omega ,\frac{\Delta p_{ref}}{\Delta p_{\max }}\right).$$

Shaft Torque

The torque is calculated from the fan total efficiency, η_T:

$$\tau =\frac{W_{\text{F}}}{\omega {\eta }_{\text{T}}},$$

where η_T is the ratio of the fluid work to the mechanical work, $$\frac{W_F}{W_M}.$$

Note that this is an isentropic definition, and the network gas is assumed to be ideal.

The fluid work is calculated from the change in enthalpy over the fan:

$$W_{\text{F}}=\dot{m}\left(h_{\text{T,B}}-h_{\text{T,A}}\right),$$

where:

• h_T,B is the total enthalpy at port B, or the sum of the enthalpy at B due to the static pressure rise and the enthalpy due to the moving fluid:

  $$h_{\text{T,B}}=h_B+\frac{v_B^2}{2},$$

  where v_B is the gas velocity at port B.

• h_T,A is the total enthalpy at port A,

  $$h_{\text{T,A}}=h_A+\frac{v_A^2}{2},$$

  where v_A is the gas velocity at port A.

Numerical Smoothing

To maintain the simulation robustness during flow reversal, numerical smoothing is applied to the fluid density and shaft velocity when the shaft angular velocity falls below a specified value.

Inlet Density

When the shaft speed falls below the Shaft speed threshold for flow reversal, the gas density is calculated as a blend of the density at both ports:

$$\rho ={\rho }_{\text{A}}\left(\frac{1+\alpha }{2}\right)+{\rho }_{\text{B}}\left(\frac{1-\alpha }{2}\right),$$

where:

• ρ_A is the density at port A.

• ρ_B is the density at port B.

• α is a smoothing factor:

$$\alpha =\text{tanh}\left(\frac{4\dot{m}}{{\dot{m}}_{\text{Th}}}\right),$$

where $$\dot{m}$$_Th is the threshold mass flow rate:

$${\dot{m}}_{Th}={\omega }_{Th}\epsilon F_{\omega },$$

where:

• ω_Th is the Shaft speed threshold for flow reversal.

• ε is the Mechanical orientation, which is +1 when set to Positive and -1 when set to Negative.

• F_ω is a fraction of the Shaft speed threshold for flow reversal value at which the gas density is calculated.

Shaft Rotation Near Flow Reversal

When the calculated shaft speed falls below the Shaft speed threshold for flow reversal, the shaft angular velocity is smoothed. If the calculated shaft speed falls below 0, the value of the Shaft speed threshold for flow reversal, ω_Th, is applied instead:

$${\omega }^{*}=\{\begin{array}{ll}{w}_{\text{Th}},\hfill & \omega <0\hfill \\ \left(1-\lambda \right){\omega }_{\text{Th}}+\lambda \omega ,\hfill & \omega <{\omega }_{\text{Th}}\hfill \\ \omega ,\hfill & \omega \ge {\omega }_{\text{Th}}\hfill \end{array},$$

where λ, the smoothing function, is a cubic polynomial:

$$\lambda =3{\left(\frac{\omega }{{\omega }_{\text{Th}}}\right)}^2-2{\left(\frac{\omega }{{\omega }_{\text{Th}}}\right)}^3.$$

Mass Balance

Mass is conserved through the fan:

$${\dot{m}}_{\text{A}}+{\dot{m}}_{\text{B}}=0,$$

where:

• $$\dot{m}$$_A is the inlet mass flow rate at port A.

• $$\dot{m}$$_B is the outlet mass flow rate at port B.

Energy Balance

The energy balance over the block is:

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

where:

• ϕ_A is the energy flow rate at port A.

• ϕ_B is the energy flow rate at port B.

• W_F is the fluid power.

Assumptions and Limitations

• The fan is assumed to be quasi-steady.

• The fan performance is modeled in terms of static pressure rise, and not total fan pressure.

• The network gas is assumed to be ideal.

Ports

Conserving

A — Fluid port

gas

Fluid inlet port.

B — Fluid port

gas

Fluid outlet port.

R — Fan shaft

gas

Port associated with the rotor shaft torque and angular velocity.

C — Case

gas

Port associated with fan casing torque and angular velocity.

Parameters

Fan specification — Parameterization type

1D tabulated data - static pressure and total efficiency vs. flow rate (default) | 2D tabulated data - static pressure and total efficiency vs. angular speed and flow rate | 2D tabulated data - flow rate and total efficiency vs. angular speed and static pressure | 2D tabulated data - flow rate and total efficiency vs. angular speed and static pressure ratio

Fan parameterization type. You can choose from four tabulated data options:

• 1D tabulated data - static pressure and total efficiency vs. flow rate: Model fan performance as a 1D look-up table based on volumetric flow rate.

• 2D tabulated data - static pressure and total efficiency vs. angular speed and flow rate: Model fan performance as a 2D look-up table based on shaft velocity and static pressure rise.

• 2D tabulated data - flow rate and total efficiency vs. angular speed and static pressure: Model fan performance as a 2D look-up table based on shaft velocity and static pressure rise.

• 2D tabulated data - flow rate and total efficiency vs. angular speed and pressure ratio: Model fan performance as a 2D look-up table based on shaft velocity and the pressure ratio between the fan static pressure rise and the maximum static pressure rise.

Mechanical orientation — Fan rotational direction in normal operation

Positive (default) | Negative

Rotational direction of the fan in normal operation. Flow is generated from port A to B in this setting. If the fan rotates counter to this direction, no flow is generated.

Volumetric flow rate vector — Volumetric flow rate for 1D tabulated parameterization of pressure and efficiency

[4.7, 5.2, 5.7, 6.1, 6.6] m^3/s (default) | vector of 2 or more elements

Volumetric flow rate for 1D tabulated parameterization of pressure and efficiency. The vector must have the same elements as the Static pressure rise vector and the Total efficiency vector parameters. The vector elements are listed in ascending order and must be greater than 0.

Dependencies

To enable this parameter, set Fan specification to 1D tabulated data - static pressure and total efficiency vs. flow rate.

Static pressure rise vector — Differential pressure for 1D tabulated parameterization of pressure

[1120, 995.36, 870.94, 746.52, 622.1] (default) | vector of 2 or more elements

Differential pressure for 1D tabulated parameterization of pressure. The vector must have the same elements as the Volumetric flow rate vector parameter. The vector elements are listed in descending order and must be greater than 0.

Dependencies

To enable this parameter, set Fan specification to 1D tabulated data - static pressure and total efficiency vs. flow rate.

Total efficiency vector — Total efficiency for 1D tabulated parameterization of efficiency

[.1, .2, .25, .15, .1] (default) | vector of elements in the range of (0,1]

Total efficiency for 1D tabulated parameterization of efficiency. The vector must have the same elements as the Volumetric flow rate vector parameter. The vector elements must be greater than 0.

Dependencies

To enable this parameter, set Fan specification to 1D tabulated data - static pressure and total efficiency vs. flow rate.

Reference shaft speed — Rotor shaft speed at which 1D tabulated data is specified

910 rpm (default) | positive scalar

Rotor shaft speed that corresponds to the values of the Volumetric flow rate vector.

Dependencies

To enable this parameter, set Fan specification to 1D tabulated data - static pressure and total efficiency vs. flow rate.

Shaft speed vector, omega — Fan angular velocity for 2D tabulated parameterization of pressure and efficiency

[450, 500, 550, 600, 650] rpm (default) | vector of 2 or more elements

Fan angular velocity for 2D tabulated parameterization of pressure and efficiency. The vector must have the same number of elements as the rows of the Static pressure rise table, Dp(omega,q) and Total efficiency table, Eta(omega,q) tables. The vector elements are listed in ascending order and must be greater than 0.

Dependencies

To enable this parameter, set Fan specification to 2D tabulated data - static pressure and total efficiency vs. angular speed and flow rate.

Flow rate vector, q — Volumetric flow rate for 2D tabulated parameterization of pressure and efficiency

[450, 500, 550, 600, 650] rpm (default) | vector of 2 or more elements

Volumetric flow rate for 2D tabulated parameterization of pressure and efficiency. The vector must have the same number of elements as the columns of the Static pressure rise table, Dp(omega,q) and Total efficiency table, Eta(omega,q) tables. The vector elements are listed in ascending order and must be greater than 0.

Dependencies

To enable this parameter, set Fan specification to 2D tabulated data - static pressure and total efficiency vs. angular speed and flow rate.

Static pressure rise table, Dp(omega,q) — Differential pressure for 2D tabulated parameterization of pressure

[675, 650, 560, 420; 830, 800, 695, 520; 1008, 966, 840, 630; 1200, 1150, 1000, 750; 1370, 1300, 1250, 1000] Pa (default) | M-by-N matrix

M-by-N matrix of the static pressure rise at the specified shaft speed and volumetric flow rate. Linear interpolation is employed between table elements. M and N are the sizes of the corresponding vectors:

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

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

Dependencies

To enable this parameter, set Fan specification to 2D tabulated data - static pressure and total efficiency vs. angular speed and flow rate.

Total efficiency table, Eta(omega,q) — Total efficiency for 2D tabulated parameterization of efficiency

[.22, .23, .25, .24; .38, .39, .4, .34; .58, .6, .62, .6; .81, .82, .84, .8; .88, .91, .95, .9] (default) | vector of elements in the range (0,1]

M-by-N matrix of the total efficiency at the specified shaft speed and volumetric flow rate. Linear interpolation is employed between table elements. M and N are the sizes of the corresponding vectors:

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

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

Dependencies

To enable this parameter, set Fan specification to 2D tabulated data - static pressure and total efficiency vs. angular speed and flow rate.

Shaft speed vector, omega — Fan angular velocity for 2D tabulated parameterization of flow rate and efficiency

[450, 500, 550, 600, 650] rpm (default) | vector of 2 or more elements

Fan angular velocity for 2D tabulated parameterization of flow rate and efficiency. The vector must have the same number of elements as the rows of the Static pressure rise table, Dp(omega,Dp) and Total efficiency table, Eta(omega,Dp) tables. The vector elements are listed in ascending order and must be greater than 0.

Dependencies

To enable this parameter, set Fan specification to 2D tabulated data - flow rate and total efficiency vs. angular speed and static pressure.

Static pressure rise vector, Dp — Differential pressure for 2D tabulated parameterization of flow rate and efficiency

[1 / 8, 1 / 4, 3 / 8, 1 / 2] * 3386.4 Pa (default) | vector of 2 or more elements

Differential pressure for 2D tabulated parameterization of flow rate and efficiency. The vector must have the same number of elements as the columns of the Flow rate table, q(omega,Dp) and Total efficiency table, Eta(omega,Dp) tables. The vector elements are listed in ascending order and must be greater than 0.

Dependencies

To enable this parameter, set Fan specification to 2D tabulated data - flow rate and total efficiency vs. angular speed and static pressure.

Flow rate table, q(omega,Dp) — Volumetric flow rates for 2D tabulated parameterization of flow rate

[.3282, .2965, .2556, .1973; .8254, .71, .5876, .4545; 1.2018, 1.0829, .9083, .7034; 1.5065, 1.4098, 1.2722, .9844; 1.8368, 1.7507, 1.6055, 1.2417] m^3/s (default) | vector of 2 or more elements

M-by-N matrix of the volumetric flow rates at the specified shaft speed and differential pressure. Linear interpolation is employed between table elements. M and N are the sizes of the corresponding vectors:

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

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

Dependencies

To enable this parameter, set Fan specification to 2D tabulated data - flow rate and total efficiency vs. angular speed and static pressure.

Total efficiency table, Eta(omega,Dp) — Total efficiency for 2D tabulated parameterization of efficiency

[.22, .23, .25, .24; .38, .39, .4, .34; .58, .6, .62, .6; .81, .82, .84, .8; .88, .91, .95, .9] (default) | vector of elements in the range (0,1]

M-by-N matrix of the total efficiency at the specified shaft speed and differential pressure. Linear interpolation is employed between table elements. M and N are the sizes of the corresponding vectors:

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

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

Dependencies

To enable this parameter, set Fan specification to 2D tabulated data - flow rate and total efficiency vs. angular speed and static pressure.

Shaft speed vector for maximum pressure rise vector — Shaft speed associated with maximum pressure

[1800, 2000, 2400, 2800, 3000] rpm (default) | vector of 2 or more elements

Angular velocity associated with the fan maximum pressure differential. The vector must have the same number of elements as the Maximum pressure rise vector. The vector elements are listed in ascending order and must be greater than 0.

Dependencies

To enable this parameter, set Fan specification to 2D tabulated data - flow rate and total efficiency vs. angular speed and static pressure ratio.

Maximum pressure rise vector — Maximum pressure for parameterization by pressure ratio

[1 / 8, 1 / 4, 3 / 8, 1 / 2, 5 / 8] * 3386.4 Pa (default) | vector of 2 or more elements

Maximum differential pressure for parameterization by pressure ratio. The vector must have the same number of elements as the Shaft speed vector for maximum pressure rise vector. The vector elements are listed in ascending order and must be greater than 0.

Dependencies

To enable this parameter, set Fan specification to 2D tabulated data - flow rate and total efficiency vs. angular speed and static pressure ratio.

Shaft speed vector, omega — Fan angular velocity for 2D tabulated parameterization of flow rate and efficiency

[1800, 2000, 2400, 2800, 3000] rpm (default) | vector of 2 or more elements

Fan angular velocity for 2D tabulated parameterization of flow rate and efficiency. The vector must have the same number of elements as the rows of the Flow rate table, q(omega,Dp/DpMax) and Total efficiency table, Eta(omega,Dp/DpMax) tables. The vector elements are listed in ascending order and must be greater than 0.

Dependencies

To enable this parameter, set Fan specification to 2D tabulated data - flow rate and total efficiency vs. angular speed and static pressure ratio.

Static pressure rise ratio vector, Dp/DpMax — Differential pressure ratio for 2D tabulated parameterization of flow rate and efficiency

linspace(0, 1, 7) (default) | vector of elements in the range of [0,1]

Differential pressure ratio for 2D tabulated parameterization of flow rate and efficiency. The vector must have the same number of elements as the columns of the Flow rate table, q(omega,Dp/DpMax) and Total efficiency table, Eta(omega,Dp/DpMax) tables. The vector elements are listed in ascending order. The vector does not need to be the same size as the Maximum pressure rise vector.

Dependencies

To enable this parameter, set Fan specification to 2D tabulated data - flow rate and total efficiency vs. angular speed and static pressure ratio.

Flow rate table, q(omega,Dp/DpMax) — Volumetric flow rates for 2D tabulated parameterization of flow rate

[.3282, .2965, .2556, .1973, .1799, .1288, .0736; .8254, .71, .5876, .4545, .4157, .2967, .1696; 1.2018, 1.0829, .9083, .7034, .6415, .4584, .2619; 1.5065, 1.4098, 1.2722, .9844, .8991, .6418, .3668; 1.8368, 1.7507, 1.6055, 1.2417, 1.1337, .8098, .464] m^3/s (default) | vector of 2 or more elements

M-by-N matrix of the volumetric flow rates at the specified shaft speed and differential pressure ratio. Linear interpolation is employed between table elements. M and N are the sizes of the corresponding vectors:

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

• N is the number of vector elements in the Static pressure rise ratio vector, Dp/DpMax parameter.

Dependencies

To enable this parameter, set Fan specification to 2D tabulated data - flow rate and total efficiency vs. angular speed and static pressure ratio.

Total efficiency table, Eta(omega,Dp/DpMax) — Total efficiency for 2D tabulated parameterization of efficiency

[.22, .23, .25, .26, .27, .275, .28; .38, .39, .4, .41, .42, .425, .43; .48, .5, .52, .54, .55, .54, .53; .4, .42, .44, .46, .48, .45, .44; .42, .43, .45, .47, .49, .46, .44] (default) | vector of elements in the range [0,1]

M-by-N matrix of the total efficiency at the specified shaft speed and differential pressure ratio. Linear interpolation is employed between table elements. M and N are the sizes of the corresponding vectors:

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

• N is the number of vector elements in the Static pressure rise ratio vector, Dp/DpMax parameter.

Dependencies

To enable this parameter, set Fan specification to 2D tabulated data - flow rate and total efficiency vs. angular speed and static pressure ratio.

Reference density — Gas density at tabulated data measurement

1.2 kg/m^3 (default) | positive scalar

Gas density at which the volumetric flow rate, differential pressure, and shaft speed data were collected.

Shaft speed threshold for flow reversal — Minimum rotor shaft speed

1 rpm (default) | positive scalar

Threshold value for flow reversal. Below this value, the shaft speed is maintained at the Shaft speed threshold for flow reversal and a smoothing function is applied to the flow rate. The shaft does not generate flow below this value.

Inlet gas flow area (port A) — Inlet area

0.01 m^2 (default) | positive scalar

Cross-sectional area of the fan inlet.

Outlet gas flow area (port B) — Outlet area

0.01 m^2 (default) | positive scalar

Cross-sectional area of the fan outlet.

Model 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.

Extended Capabilities

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