**How you modulate or vary the flow of your fan systems may be hurting your bottom line. This author runs you through important calculations.**

Fans are designed to be capable of meeting the maximum demand of the system in which they are installed. Quite often, though, the actual demand varies and may be much less than the designed capacity.

The centrifugal fan imparts energy into air by centrifugal force. This results in an increase in pressure and produces airflow at the outlet of the fan. An example of what a typical centrifugal fan can produce at its outlet at a given speed is shown by the curve in Fig. 1. This curve is a plot of outlet pressure in static inches of water versus the flow of air in cubic feet per minute (CFM). Standard fan curves usually will show a number of curves for different fan speeds and include fan efficiency and power requirements. These are useful for selecting the optimum fan for any application, and are required to predict fan operation and other parameters when the fan operation is changed.

The system curve in Fig. 2 shows requirements of the vent system on which the fan is used. A plot of “load” requirement independent of the fan, it indicates the pressure required from the fan to overcome system losses and produce airflow. The intersection of the fan and the system curve is the natural operating point. It is the actual pressure and flow that will occur at the fan outlet when this system is operated. Without external influences, the fan will operate at this point.

Many systems require operation at a wide variety of points. There are several methods used to modulate or vary the flow (or CFM) of a system to achieve the optimum points. These include:

—This produces erratic airflow and is unacceptable for commercial or industrial uses.**Cycling**(as done in home heating systems)**Outlet dampers***(control louvers or dampers installed at the outlet of the fan)*—To control airflow, they are turned to restrict the outlet, thus reducing airflow.—By modifying the physical characteristics of the air inlet, the fan’s operating curve is modified, which, in turn, changes airflow.**Variable inlet vanes**—By changing the actual fan speed, the performance of the fan changes, thus producing a different airflow.**Variable frequency drives (VFDs)**

By changing the airflow or the fan speed, the system or fan curves are affected, resulting in a different natural operating point—*and, possibly, a change in the fan’s efficiency and power requirements*.

**Outlet dampers**

The outlet dampers affect the system curve by increasing the resistance to airflow. The system curve can be stated as:

**P = Kx (CFM) ^{2}**

*Where: P is pressure required to produce a given flow in the system K is a function of the system that represents the resistance to airflow CFM is the airflow desired *

The outlet dampers affect the K portion of this formula. The diagram in Fig. 3 depicts several different system curves indicating different outlet damper positions. Note that the power requirements for the type of system shown in Fig. 3 gradually decrease as flow is decreased (as shown in the Fig. 4).

**Variable inlet vanes **

This method modifies the fan curve so that it intersects the system curve at a different point. A representation of the changes in the fan curve for different inlet vane settings is shown in Fig. 5. The power requirements for this method decrease as airflow decreases, and to a greater extent than the outlet damper (as shown in Fig. 6). Variable frequency drives (VFDs) The VFD method takes advantage of the change in the fan curve that occurs when the speed of the fan is changed. These changes can be quantified in a set of formulas called the affinity laws.

*Where: N = Fan speed Q = Flow (CFM) P = Pressure (Static Inches of Water) HP = Horsepower *

Note that when the flow and pressure laws are combined, the result is a formula that matches the system curve formula – P = K x (CFM)^{2}.

Substituting (Q_{2}/Q_{1})^{2} for (N_{2}/N_{1})^{2} in the first equation gives us:

The quantity P_{1}/(Q_{1})^{2} coincides with the system constant, K. As depicted in Fig. 7, this means that the fan will follow the system curve when its speed is changed. As the fan speed is reduced, a significant reduction in power requirement is achieved (as shown in Fig. 8).

The variable speed method achieves flow control in a way that closely matches the system or load curve. This allows the fan to produce the desired results with the minimum of input power.

**Energy savings**

Clearly, not all methods for modulating or varying flow are appropriate for a given fan system. How can you be sure that the method you are using is the right one? More importantly, how can you be sure it is the most efficient? Whatever your chosen method is for modulating or varying flow, it may be easier than you thought to estimate its power consumption and associate a cost of operation with it. To accomplish this, an actual load profile and a fan curve are required (as shown in Figs. 9 and 10).

The following simple analysis of the variable speed method compared to the outlet damper method shows how energy savings are calculated.

Using the fan curve in Fig. 10, assume the selected fan is to be run at 300 RPM and that 100% CFM is to equal 100,000 CFM as shown on the chart. Assume the following load profile.

For each operating point, we can obtain a required horsepower from the fan curve. This horsepower is multiplied by the percent of time (divided by 100%) that the fan operates at this point. As shown in the following table for the outlet damper method, these calculations are then summed to produce a “weighted horsepower” that represents the average energy consumption of the fan.

Similar calculations are done to obtain a weighted horsepower for variable speed operation. However, the fan curve does not have enough information to read all the horsepower values for our operating points. To overcome this problem, we can use the formulas from the affinity laws.

The first point is obtained from the fan curve. 100% flow equals 100% speed equals 35 HP. The flow formula Q_{2}/Q_{1} = N_{2}/N_{1} can be substituted into the horsepower formula, HP_{2}/HP_{1} = (N_{2}/N_{1})^{3} to give us:

When Q_{1} = 100% and HP_{1} = 35 HP, Q_{2} and HP_{2} will have the following values:

As shown in the following variable speed method table, we now have sufficient information to calculate the weighted horsepower. Comparing the results of the two methods of control indicates the difference in power consumption.

In order to obtain a dollar value of savings, the kilowatt-hours used must be known. To calculate this, multiply the horsepower by 0.746 and then multiply the result by the hours that the fan will operate in a period of time. This would typically be for a month. Your results would look like the following example table at the bottom of the page.

This simple example shows a cost saving of more than $700 per month by using a variable speed method. Note that the example is very basic and does not consider motor and drive efficiency. Still, many organizations would consider that amount of monthly energy savings on a single fan system—*or anything close to it*—to be significant. Would yours? **UM**

*Sharon James is an application engineer with Rockwell Automation. E-mail him directly at: sjames@ra.rockwell.com*