Eugene Vogel
EASA Pump and Vibration Specialist
When working with pumps, you are sure to encounter instances where the pump curve is referenced, along with a number of parameters associated with it. A key parameter of the pump curve is the Best Efficiency Point (BEP). This simple concept of an operating point that yields the most efficient operation is not difficult to visualize. For electric motors, efficiency varies with load; the best efficiency being at about 75% load. However, with rotodynamic pumps – which include centrifugal and axial flow pumps – there are four key parameters to be considered, one of which is efficiency. These four parameters are head, flow (aka capacity or volume), power and efficiency.
They are related to each other by the simple formula:
Of course power is inversely proportional to efficiency: greater efficiency means less power is needed. Notice also that power is directly proportional to Flow x Head (QxH). Now, for a rotodynamic pump, the flow and head vary depending on the demand of the system. If the system restricts the discharge of the pump, as when a discharge throttle valve is closed, the head increases and the flow decreases.
Conversely, less restriction from the system means less head and greater flow. This relationship is illustrated by a pump curve, which is specific to each pump. See Figure 1. To understand BEP, it is essential to know that the flow through a rotodynamic pump varies from zero flow at “dead head” (discharge valve closed), to maximum flow at “run out” condition (no discharge restriction). Efficiency, it turns out, is a function of flow through the pump. See Figure 2.
Compare it to traffic flow
A good analogy is the flow of traffic on a highway, with efficiency measured as cars per minute. Early in the morning, traffic is moving fast, but there aren’t many cars, so efficiency in cars per minute is low. Just before rush hour, traffic is still moving fast and there are lots of cars, so efficiency is high. But at rush hour, the volume of cars increases greatly and traffic slows way down, so now there are lots of cars moving really slow and efficiency of the highway drops. There is one period, just before rush hour, when the efficiency of the highway in cars per minute is greatest – what you might describe as the best efficiency point for the highway.
And so it is for the pump BEP. See Figure 3. At zero flow (discharge valve closed), there is zero efficiency. As the discharge valve opens, flow increases and therefore so does efficiency. As discharge restriction is further reduced and flow increases, efficiency increases up to some point. Past that point, flow through the pump becomes more turbulent and efficiency decreases as the pump approaches run out condition where efficiency is very low (but not zero). So somewhere between dead head and run out condition, there is a flow rate at which the efficiency is maximum – that’s the BEP. Note that the BEP is indicated in Figure 3 at a flow rate of about 1600 units; that flow rate coincided with the maximum value on the efficiency curve. That flow rate also intersects the pump curve at a point equal to head of about 220 units.
Effects of flow rate
It is useful to look more closely at why the efficiency of the pump changes with flow rate. As mentioned above, turbulent flow through the pump plays a central role in determining pump efficiency: The greater the turbulence, the lower the efficiency. So it makes sense that the BEP is the point where turbulence is minimized. The impeller is what imparts the power to the liquid being pumped (“pumpage”). Impeller design is the most significant factor in determining the BEP of a pump.
To understand how impeller design affects efficiency, focus on how the pumpage exits the impeller, relative to the angle of the impeller vane at that point. The pumpage is swirling around in the impeller housing outside of the impeller, but at a slower speed than the tip of the impeller vane. The pumpage is being directed through the impeller and out of the impeller by the impeller vane.
So if the angle of the impeller vane directs the pumpage into the impeller housing at just the right angle to merge smoothly with the pumpage swirling there, turbulence is minimized and efficiency is maximized, yielding the BEP for that impeller.
Design engineers use a series of vectors to calculate the impeller vane angle for a certain flow rate. As seen in Figure 4, one vector (Vt) represents the speed of the vane tip, tangent to the impeller. A second vector (Vr) represents the velocity of the flow of the pumpage out of the impeller. The discharge angle of the flow is the sum of those two vectors and it should match the impeller vane angle at the discharge (Vm). The length of vector (Vr) changes with flow rate: greater flow through the pump means the pumpage must move faster as it exits the impeller.
So flow rate changes the discharge angle, and of course the impeller vane angle remains constant. The BEP is the flow rate where discharge angle matches the vane angle. A similar analysis is applied to the impeller intake.
The characteristics of the impeller housing also play a role, but the impeller design is the primary factor that determines at what flow rate the BEP occurs. So any change to the impeller will also change the BEP. Trimming an impeller outside diameter (OD), replacing an impeller with one of different diameter or number of vanes, or changing the rotating speed will all alter the BEP for the pump.
For any impeller modifications, an analysis of the impact on the pump curve, the efficiency curve and the BEP should be conducted.
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