System Operation with a System Resistance Curve

Introduction
This article is a continuation of the newsletter article dealing with the System Resistance Curve.  As discussed in the last installment we saw how a system curve was created by calculating the head loss for each pipeline in the system under a variety of flow rates. Once this is done then you can sum the head losses for the pipelines in series for a variety of flow rates.

Then by superimposing the pump curve on the system curve, the flow rate through the system occurs at the intersection of the pump curve and system curve. A centrifugal pump will only operate on its pump curve; this makes it helpful in understanding the operation of the pump in the piping system.

If you would like to change the flow rate through the system, this can only be accomplished by changing the shape of the pump curve or changing the shape of the system curve. In this article, we will see how we can change the flow rate through the system by:

• Installing a control valve
• Varying the pump speed
• Changing the impeller diameter
• Running multiple pumps in the system

Looking at the pump / system curve (Figure 1) you can see the intersection occurs at a flow rate of 400 gpm resulting in a total pump head of 70 ft. As a result, the balanced flow rate through the system occurs at 400 gpm.



Figure 1.

Controlling Flow with a Control Valve
As previously mentioned to achieve a flow rate other than 400 gpm thru this system, either the pump curve or the system curve must be changed.  By inserting a control valve in the piping system we can change the shape of the system curve. This example will demonstrate the change in the system curve by installing a control valve.

Much of the literature discussing a system curve with throttle valve installed shows the system curve steeper with the intersection occurring at the desired flow rate in this case 300 gpm (Figure 2). To limit the flow rate to a set value in this type of curve, head loss has been added across the control valve at a fixed position. Upon reviewing the literature showing the system curve in this form, it appears all the authors have a pump background.


Figure 2.

If you look at a reference published by authors with control valve backgrounds, the system curves appear like Figure 3. In this curve image you can still see the pump curve, along with the piping system curve with the control valve in its fully open position. The vertical line on the system curve represents the difference between what the pump produces, and what the system requires. As a result the vertical line on the curve represents the head loss needed across the control valve to limit the flow rate to the desired value, in this case 300 gpm. 


Figure 3.

Both Figure 2 and Figure 3 show a balanced flow rate at 300 gpm, but Figure 3 provides much more information about what is happening in the control valve. As a result in all of our training classes and publications we use the format outlined in Figure 3 when describing a system with a control valve.

In looking at both Figure 2 and 3 you can that when the system flow rate is limited to 200 gpm the pump will deliver 91 ft of total head. Using Figure 3, you can see the system experiences 17.5 ft of head loss with a 200 gpm flow rate. As a result the differential head across the control valve is the difference (91 – 17.5 = 73.5 ft) or 73.5 ft. Knowing the head loss across the control valve along with the valve’s Cv characteristics vs. valve position (provided by the valve manufacturer) one can calculate the valve position needed to limit the flow rate to 200 gpm.

Controlling Flow by Varying Pump Speed
Another way to change the flow rate through the system is by changing the pump curve. This can be accomplished by changing the speed of the pump impeller. 

In most pumping application, a Variable Speed Drive (VSD) is installed upstream of the electric motor.  The VSD varies the frequency of the power to the motor, resulting in varying the motors rotational speed to the pump. The pump affinity rules describe how a pumps performance varies with speed and  is outlined in Knowledge Base Article entitled VFD Pumps Can Cut Energy Cost but Static Head Reduces Savings.   


Figure 4.

By changing the rotational speed of the pump, the pump’s flow rate, head and power consumption are changed based on the pump affinity rules. As you can see in Figure 3, with our pump operating at 1800 rpm, the system curve and pump curve intersects at 70 ft. resulting in a flow rate through the system of 400 gpm. By slowing the speed down to 1365 rpm the pump develops 40 ft and intersects our system curve with a flow rate of 300 gpm. By further slowing down the pump to 905 rpm the pump develops 17.5 ft of head which intersects the system curve at 200 gpm.
 
The way the pump speeds are determined is by adjusting speed on the known pump curve (in this case the curve running at 1800 rpm), using the pump affinity rules until the speed adjusted pump curve intersects the system curve at the desired flow rate. Doing these calculations by hand requires many sets of iterative calculations but the PUMP-FLO Select program can perform these calculations and automatically intersect the users entered system curve.

Changing Flow by Changing Impeller Diameter
Another way of changing the shape of the pump curve is by adjusting the impeller diameter. Centrifugal pump manufactures allow some of their pump impellers to be trimmed (cut down in a lathe) to reduce the impeller diameter. This reduction of the impeller diameter changes the shape of the pump curve. Some literature says the pump affinity rules can be used to determine the performance at other impeller diameters. At Engineered Software we do not recommend this practice for three reasons:

1. Pump manufactures provide pump curves with multiple impeller diameters (See Figure 5). 
2. The manufacturer may not allow the pump to be trimmed, or may only allowed it to be trimmed to specific diameters.  Using the pump affinity rules you may specify an impeller diameter that may not be available.
3. Finally the pump affinity rules have a tendency to over state the head, flow, and efficiency values. 

Figure 5.

Looking at Figure 5, you can see a typical manufacturers pump curve for given pump. For this specific pump the impeller diameter ranges from 10.19 inches to 8 inches. An impeller diameter greater that 10.19 inches will cause the impeller to rub on the pump case, and diameters less than 8 inches are not recommended by the manufacturer. Looking at the system resistance curve you can see that the pump with an 8 inch diameter intersect the system curve at 315 gpm, and the pump with a 9 inch impeller diameter intersects the system curve at 360 gpm. 

Multiple Pump Operation
Running multiple pumps either in series or parallel will change the shape of the pump curve as well. In Figure 6, you can see two pumps operating (these are not the same pump curves used in the previous examples) in parallel on the same system curve as the previous examples. The single pump curve on the left show it intersecting the system curve at 310 gpm. By turning on the second pump configured for parallel operation the combined curve intersect the system curve at 400 gpm.


Figure 6.

Conclusion
As you can see in simple piping system, the system resistance curve provides a good indication of how the system will operate under a variety of operating conditions. To demonstrate the value of the system curve, we looked at a variety pump system curves under a variety of operating conditions. 

The system resistance curve comes up short for more complicated systems such as closed-loop cooling systems with multiple parallel paths, or systems with multiple destination tanks. These types of systems cannot be adequately described using a system resistance curve. In the next article, we will look at two ways in which we can evaluate a system without the limitations of a system resistance curve.