AFT Fathom has long included the ability to model multi-stage pumps by representing them with an overall effective pump curve. New in AFT Fathom 10 is the ability to model "Interstage Bleed" or "Takeoff Flow" in these multi-stage pumps.

It is well known that arranging pumps in series has the effect of increasing the available head at a given flow. Large multi-stage pumps can be thought of as a series of smaller pumps - the impellers - all working together to increase the overall available head. Each impeller - stage - increases the pressure of the working fluid some incremental amount. This equivalency is demonstrated in the below AFT Fathom 10 model. Keep in mind that the connector pipes between stages are frictionless.

Figure 1 - Equivalent Representations of a Multistage Pump
Figure 1 - Equivalent Representations of a Multistage Pump

What happens if we extract some flow at some interstage point? In some applications, particularly in the power industry, it is more efficient to "tap in" between stages of an existing pump and extract flow at the intermediate pressure. This alleviates the need to install an entirely new pump for a relatively small secondary process.

We are adding a branching flow to our model in between the stages. Again, note that there are no pipes between stages in reality - the extraction takes place directly from the pump casing.

Figure 2 - Interstage Flow
Figure 2 - Interstage Flow
Figure 3 - Simplified Interstage Pump Schematic
Figure 3 - Simplified Interstage Pump Schematic

AFT Fathom has no issues solving this model - the appropriate flows and pressures will be found for all of the stages and piping connections. Unfortunately, this model assumes that the user knows the Pump Curves for each individual stage in the pump - information that is very unlikely to be readily available.

Instead, a manufacturer of such a pump is likely to provide only two curves:

  1. Overall Pump Curve - the head developed across the entire pump when the Takeoff Flow is zero.
  2. Upstream Stages Pump Curve - the head developed across all of the stages upstream of the Takeoff point.

Note that the Upstream Stages Pump Curve is not directly affected by the amount of Takeoff Flow - it can be thought of as an entirely independent pump. In order to model the Interstage Pump as two separate pumps, we need to know the Downstream Stages Pump Curve.

We can calculate this curve by subtracting the Upstream Stages Pump Curve from the Overall Pump Curve. The Upstream Stages and Downstream Stages Pump Curves are constant curves for a fixed speed. Neither curve changes with a varying Takeoff Flow.

However, if there is a non-zero Takeoff Flow, each curve will be operating at a different flow. The Upstream Stages Pump Curve will contribute head according to the point on the curve at the Suction Flow amount. The Downstream Stages Pump Curve will contribute head according to the Discharge  Flow. The total head contributed from Suction to Discharge is the sum of these two values.

There is one more Pump Curve that we can define for the device - an Overall Effective Pump Curve. This curve relates the actual head generated from Suction to Discharge at a given Discharge Flow. The actual head generated at any given Discharge Flow will be less than that indicated by the Overall Pump Curve if there is any Takeoff Flow. Some energy is being lost to the intermediate bleed.

Figure 4 - Pump Curves and Takeoff Flow
Figure 4 - Pump Curves and Takeoff Flow

How can we represent this in AFT Fathom 10? Thankfully, it is easy with the new Interstage Bleed feature.

Two Pump Junctions can be linked to one another, allowing AFT Fathom to determine the Downstream Stages Pump Curve, and only requiring manufacturer data from the user.

First, lay out your model with two Pump Junctions. The pumps must be connected with Pipes - by default, Pipes in AFT Fathom have pressure losses associated with them. Because there are not truly "pipes" connecting the two halves of the pump, these pipes should be very short in length, or preferably modeled as frictionless.

Figure 5 - Interstage Pump in AFT Fathom
Figure 5 - Interstage Pump in AFT Fathom

To tell AFT Fathom that these two pumps are in fact connected, check the "Interstage Bleed/Takeoff Flow" option in one of the two Pump property windows and select the Pump that it is linked to.

Figure 6 - Defining the Pump
Figure 6 - Defining the Pump

 The corresponding Pump is automatically updated.

Figure 7 - Connected Pump
Figure 7 - Connected Pump

That's it! The system is now defined and can be solved. Any configuration of pipes can be connected to the Suction, Discharge, or Takeoff points of the Interstage Pump. AFT Fathom's powerful network solver will account for the pressure losses throughout the system to determine what the actual flows and pressure are.