# Analysis of Fan Curves and Fan Laws in Thermal Management of Electronics

This is the second installment in a two-part series examining the use of fans in the thermal management of electronics. Part one, which can be found at https://www.qats.com/cms/2017/03/06/utilizing-fans-thermal-management-electronics-systems, took a closer look at the common types of fans and blowers and the factors that engineers should consider when picking a fan.

In part two, basic fan laws will be explored, as well as using fan curves to analyze fan performance in a system. These standard calculations can help engineers establish boundary conditions for air velocity and pressure drop and ensure that these will meet the thermal requirements (e.g. ambient and junction temperature) of the system.

CFD simulations of air velocity in a system with fans drawing air across high-powered components. Utilizing fan curves and fan laws enabled ATS engineers to establish the parameters for a successful use of fans for cooling this system. (Advanced Thermal Solutions, Inc.)

FAN LAWS

As noted by Mike Turner of Comair Rotron in “All You Need to Know About Fans,” the primary principle for determining whether or not a fan work within a particular system is that “any given fan can only deliver one flow at one pressure in a particular system.” Each fan has a specific operating point that can be discovered on the fan curve at the intersection of fan static pressure curve and the system pressure curve. Turner advises, “It is best to select a fan that will give an operating point being toward the high flow, low pressure end of the performance curve to maintain propeller efficiency and to avoid propeller stall.”

Before getting to the fan curve though, engineers must run through basic calculations to understand the conditions of the systems in which the fans will be placed. The three basic fan laws, according to Eldridge USA, are as follows:

While those fan laws will tell you about the specific fans, it is also critical to examine the system in which the fans will be operating. Among the equations that can be used to characterize a system are Volumetric Flow Rate, Mass Flow Rate, Pressure, Power, and Sound (equations are listed below).

A Qpedia Thermal eMagazine article entitled, “How to Use Fan Curves and Laws in Thermal Design,” added:

“Published fan laws apply to applications where a fan’s air flow rate and pressure are independent of the Reynolds number. In some applications, however, fan performance is not independent and thus the change in Reynolds number should be incorporated into the equation. To determine if the Reynolds number needs to be considered, it must first be calculated.

“According to AMCA specifications, an axial fan’s minimum Reynolds number is 2.0×106. When the calculated Reynolds number is above this value, its effects can be ignored.”

The equation to calculate the Reynolds number is as follows:

In an “Engineering Letter” from The New York Blower Company, it was explained that fan laws only work “within a fixed system with no change in the aerodynamics or airflow characteristics of the system.” In the case of electronics cooling, in which the system requirements will be mostly consistent (with margins for error in case of max power usage), these laws will govern the capabilities of the fans to provide the necessary forced convection cooling for the components in the system.

The Engineering Letter continued, “During the process of system design, the fan laws can be helpful in determining the alternate performance criteria or in developing a maximum/minimum range.” A Qpedia article entitled, “Designing Efficient Fans for Electronics Cooling Applications,” added, “As a general rule, fan efficiency increases with blade diameter and rotational speed.”

There are tools that can assist engineers in the calculation of these basic fan laws, including fan calculators, such as the one provided by Twin City Fans & Blowers.

ANALYZING FAN CURVES AND FAN PERFORMANCE

The aerodynamics of a fan can be charted in a fan curve, which displays the static pressure of the system dependent on the amount of air flow. As Turner noted, fan curves are read from right to left, beginning “with healthy aerodynamic flow and follow it through to aerodynamic stall.” Turner continued, “It is best to select a fan that will give an operating point being toward the high flow, low pressure end of the performance curve to maintain propeller efficiency and to avoid propeller stall.”

An example of a basic fan curve with static pressure on the Y-axis and airflow on the X-axis. Fan curves are read from right to left beginning with healthy airflow.

There are means for testing fan curves, such as the FCM-100 Fan Characterization Module (pictured below) from Advanced Thermal Solutions, Inc. (ATS). The FCM-100 is specially designed with flow restriction plates that allow the user to control pressure drop across the system during testing. Used in conjunction with pressure and velocity measurement equipment, it verifies manufacturer performance data.

The ATS FCM-100 Fan Characterization Module is a specialized unit designed to test and characterize fans of various sizes and performance outputs. (Advanced Thermal Solutions, Inc.)

The Qpedia article on fan curves explained, “During a typical fan test, a dozen or more operating points are plotted for pressure and flow rate, and from this data a fan curve is constructed.”

Once a fan curve is determined, it is possible to examine the data and find the operating range for the fans that will meet the thermal requirements of a system. It is also important to note a section in the fan curve, often referred to as the knee of the curve in which the relationship between flow rate and static pressure is no longer easy to predict. There is no longer an easily recognizable, calculable relationship between how a change in one will affect the other.

ATS field application engineer Vineet Barot explained how he analyzed fan curve data, particularly the knee of the curve, in a recent project:

“This is flow rate versus pressure. The more pressure you have in front of a fan, the slower it can pump out the air and this is the curve that determines that.

Fan operating points on the board, determined by CFD simulations. (Advanced Thermal Solutions, Inc.)

“This little area here is sometime called the knee of the fan curve. Let’s say we’re in this area, the flow rate and pressure is relatively linear, so if I increase my pressure, if I put my hand in front of the fan, the flow rate goes down. If I have no pressure, I have my maximum flow rate. If I increase my pressure then the flow rate goes down. What happens in this part? The same thing. In the knee, a slight increase in pressure, so from .59 to .63, reduces the flow rate quite a bit.

CFD simulations showed that the fans were operating in the “knee” where it is hard to judge the impact of pressure changes on flow rate and vice versa. (Advanced Thermal Solutions, Inc.)

“So, for a 0.1 difference in flow rate (in cubic meters per second) it took 0.4 inches of water pressure difference, whereas here for a 0.1 difference in flow rate it only took a .04 increase in pressure. That’s why there’s a circle there. It’s a danger area because if you’re in that range it gets harder to predict what the flow will be because any pressure-change, any dust build-up, any change in estimated open area might change your flow rate.

CFD analysis of flow vectors across high-powered components on a PCB. This simulation was part of an examination of fan performance in a system. (Advanced Thermal Solutions, Inc.)

CONCLUSION

While it is important to know the types of fans on the market and manufacturers provide data about the power and operating ranges of each product, it is important for there to be a basic understanding of the laws that govern how fans operate in a system and an ability to examine fan curve data in order to optimize performance.

“Bulk testing of electronics chassis provides the relationship between air flow and pressure drop and determines the fan performance needed to cool a given power load. The fan rating is often a misunderstood issue and published ratings can be somewhat misleading. Knowledge of fan performance curves, and how they are obtained, allows for a more informed decision when selecting a fan. Continued and ever shortening product design cycles demand a ‘get it right the first time’ approach. The upfront use of system curves, fan curves and fan laws can help meet this goal.”

Read more and see examples of fan laws and curves in practice at https://www.qats.com/cms/2013/07/24/how-to-use-fan-curves-and-laws-in-thermal-design.