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# Important Parameters for Optimizing DC Fan Operation

By Bruce Rose, CUI Devices

DC fans are a staple of any engineer’s thermal management solution, designed to remove heat from an application via efficient forced air cooling. Although a well-known and easily-recognized component, DC fans still require a basic understanding of airflow and other key parameters to ensure the selected fan is optimized for a system’s needs. To aid in this understanding, this article will discuss proper airflow and air pressure calculations, aligning those parameters with a fan’s operating curve, the impact of designing in multiple fans, and more.

## An overview of airflow parameters

Before specifying a fan, it is important to understand various airflow and heat transfer parameters. Forced air works by absorbing heat from an object and then transferring it elsewhere to be dissipated, where the amount of energy transferred is reliant upon the mass, specific heat, and temperature change of the forced air.

The mass of forced air is calculated from the volume and density of the air being moved.

Inserting the second equation into the first relates the energy dissipated to the air volume.

Next, divide both sides by time to generate the following equation.

In general, the excess power is known and airflow (volume/time) is unknown, meaning the equation can be reformulated as follows:

This equation is more commonly written as:

Where
Q = airflow
q = heat to be dissipated
ρ = density of the air
Cp = specific heat of the air
ΔT = the temperature the air will rise when absorbing the heat to be dissipated
k = a constant value, dependent upon the units used in the other parameters

The density of dry air at sea level at 68°F (20°C) is 0.075 lbs/ft3 (1.20 kg/m3), while the specific heat of dry air is 0.24 Btu/lb °F (1 kJ/kg °C). Inserting these values simplifies the above equation to:

Where
Qf = airflow in Cubic Feet per Minute (CFM)
Qm = airflow in Cubic Meters per Minute (CMM)
q = heat to be dissipated in Watts
ΔTF = the temperature the air will rise when absorbing the heat to be dissipated in °F
ΔTC = the temperature the air will rise when absorbing the heat to be dissipated in °C

## Air pressure requirements

While the equations above solved for the airflow rate needed for sufficient cooling, one also needs to calculate the air pressure delivered by the fan. The path of airflow through a system creates an airflow resistance, which means that fans must be able to produce enough pressure to force the specified air volume through the system to achieve the required cooling. However, each system creates a unique pressure requirement, so it cannot be simplified into equations like with the airflow rate. Thankfully, modeling air pressure and airflow characteristics is made possible with many CAD products during the design phase. After the design is complete, anemometers and manometers can be used to further measure these characteristics.

Figure 1: Modeling airflow and air pressure (Image source: CUI Devices)

## Producing airflow and air pressure requirements

As outlined in the previous sections, a certain airflow rate and air pressure need to be produced by a fan (or fans) to achieve the required cooling. On manufacturers’ datasheets the following will be provided: airflow rate with no back pressure, maximum pressure with no airflow rate, and the fan’s airflow versus pressure performance curve.

In this example, a product was calculated to need an airflow rate of 10 CFM or more based on the heat to be removed and the air temperature limits, while the product’s mechanical design produced the airflow versus pressure graph below (Figure 2). The dashed line represents the minimum airflow required, whereas the orange curve denotes the relationship between airflow and pressure.

Figure 2: Minimum airflow plotted on airflow versus pressure curve (Image source: CUI Devices)

Utilizing the graph above, CUI Devices’ CFM-6025V-131-167 DC axial fan has been chosen, whose datasheet specifies an airflow rate of 16 CFM with no back pressure, static pressure of 0.1 inH2O with no airflow, and provides the performance graph below (Figure 3).

Figure 3: CUI Devices' CFM-6025V-131-167 performance graph (Image source: CUI Devices)

The Figure 3 graph can then be overlaid on the Figure 2 graph to produce the graph shown in Figure 4, which highlights the operating point of the selected fan. It is important to note that while the operating point of 11.5 CFM exceeds the airflow requirement of 10 CFM in this example, some applications will require a larger thermal operating margin. Therefore, a fan with different performance specifications would need to be selected.

Figure 4: Operating point of the fan denoted by the red circle (Image source: CUI Devices)

## Designing in and operating multiple fans

Larger or faster fans will generally offer greater maximum airflow and pressure. However, when a single fan is not up to the task, multiple fans can be operated either in parallel or series to boost certain performance parameters. For instance, operating fans in parallel increases the maximum airflow, but not the maximum pressure, whereas operating fans in series increases the maximum pressure, but not the maximum airflow.

Figure 5: Single versus parallel versus series fan operation. (Image source: CUI Devices)

The airflow versus pressure performance curve for a parallel or series orientation of fans is identical to a single fan curve, except the airflow or pressure values are multiplied by the number of fans operated in parallel or series, respectively. This is shown in practice below (Figure 6) with the airflow values multiplied by the number of fans in parallel.

Figure 6: Multiply airflow by number of fans in a parallel orientation or pressure by number of fans in a series orientation. (Image source: CUI Devices)

Overall, parallel fan operation is ideal for high-airflow and low-pressure applications, while series fan operation is better suited for high-pressure and low-airflow applications.

Figure 7: Comparing fan performance in high and low airflow resistance (Image source:  CUI Devices)

## Fan speed and fan affinity laws

Fan speed (RPM) affects air volume, air pressure, power consumed, and acoustic noise outputted by a fan. These relationships are outlined further by the “fan affinity laws”:

• The air volume moved by the fan is proportional to the fan speed.
• CFM α RPM
• Example: 4 x RPM produces 4 x CFM
• The air pressure from the fan is proportional to the square of the fan speed.
• Air pressure α RPM2
• Example: 2 x RPM produces 4 x pressure
• The power required to operate a fan increases by the cube of the fan speed.
• Power α RPM3
• Example: 4 x RPM requires 64 x power
• The acoustic noise produced by a fan will increase by 15 dB when the fan speed is doubled.
• Example: A 10 dB increase in acoustic noise is typically perceived by human hearing as a doubling of the noise level.

Figure 8: Fan affinity laws (Image source: CUI Devices)

## Conclusion

A basic understanding of airflow and pressure requirements as outlined in this article can aid designers in selecting the proper fan (or fans) to meet the forced air cooling needs of their application. When a single fan is not able to meet the calculated airflow or pressure parameters, orienting fans in parallel or series affords engineers additional options. With multiple airflow, pressure, and performance ratings, CUI Devices’ diverse portfolio of DC fans and blowers makes finding a suitable fan solution simple.

Disclaimer: The opinions, beliefs, and viewpoints expressed by the various authors and/or forum participants on this website do not necessarily reflect the opinions, beliefs, and viewpoints of Digi-Key Electronics or official policies of Digi-Key Electronics.

### About this author

Bruce Rose, CUI Devices

Article Authored by Bruce Rose, Principal Applications Engineer, CUI Devices.