## AFT Product Tips

# Closing the Loop on Modeling Closed Loop Systems in AFT software

For several users of AFT software, it goes pretty predictably: first you place a pressure junction, then maybe a pump, then some sources of pressure drop including valves and heat exchangers, and then the model is finished off with another pressure junction. Of course, this is greatly oversimplifying the process and the vast array of systems that are modeled with AFT software, but here’s my point: most users are more familiar with modeling open systems that include individual pressure junctions located both upstream and downstream of the system. But what about modeling closed systems? The truth is that modeling closed systems is no more difficult (or even all that different) than simulating their more-commonly modeled counterpart, but questions about the specifics of modeling closed systems come up occasionally, so here’s what you need to know to close the loop on modeling closed loop systems in AFT software.

In order to discuss how closed loop systems can be modeled, a solid understanding of how pressure junctions work is crucial. To aid us in our discussion, we will refer to AFT Fathom, but note that modeling closed loop systems applies in exactly the same way to AFT Arrow and AFT Impulse. It is necessary to elaborate on the fact that AFT Fathom does not balance flow around pressure-type junctions (those junctions that allow the user to define a fixed pressure at the point of the junction, and that act as an infinite source or sink of fluid). Because mass is not balanced around pressure-type junctions, in the system below, the mass flow rate in pipe P1 is completely disconnected from the mass flow rate in pipe P2. The pressure junction J2 acts as an infinite source and/or sink of fluid according to the hydraulics that result from the rest of the system.

When is the mass flow rate conserved? The mass flow rate is balanced around all other junction types (except for the volume balance junction in AFT Fathom). If we replace the junction J2 with a branch junction, the mass flow rate is balanced around this junction, and the mass flow rate in both pipes is now necessarily the same.

To further our understanding of the balancing of mass flow rate at non pressure-type junctions, let’s see how this is applied in the more complex, branched system shown in Figure 3.

In Figure 3, all interior junctions (J13, J8, J11, and J12) balance flow, but this is sufficient to achieve an overall mass flow rate balance because the flow into each of these junctions must equal the total flow out of each junction. The branch junction J8 is inarguably the most interesting from a mass balance perspective because the flow splits here. Because the downstream conditions in each branching path are identical, the flow distribution through each flow path is identical. Note that, because mass flow is not balanced at the pressure-type junctions, the system in Figure 3 could be equivalently modeled as that shown in both Figures 4 and 5.

Figure 4 appears to combine the downstream pressure junctions into one junction, but it is mathematically identical to the system shown in Figure 3 because the mass flow balance around all four non-pressure-type junctions is maintained. We know that the results are the same because the pressure and flow at each junction is equivalent in both models.

Because the pressure junctions J9 and J10 in Figure 3, and equivalently J16 in Figure 4, all contain the same hydraulic information, we discard these junctions entirely in Figure 5, giving the system the appearance of a closed system.

From the pressures reported in Figure 5, it is clear that the system is mathematically equivalent to those systems modeled in Figures 3 and 4. This allows us to arrive at a perhaps non-intuitive conclusion: it simply doesn’t matter to AFT Fathom whether a system is modeled explicitly as open OR closed…as long as the systems are mathematically equivalent, the results will not change.

There is a special case of a closed system that seems to cause users the most grief, and this involves those incompressible systems that have a known flow rate, but no explicitly known pressure, as the system shown in Figure 6.

In this system, the engineer knows the flow rate through the closed loop and sets the pump flow to this value, but because it is a closed loop, a pressure somewhere in the system isn’t immediately apparent to the engineer. When trying to run this model (with a fixed flow specified in the pump), a user will receive a message stating that a reference pressure has not been entered, and the model cannot, therefore, complete its calculations. “What pressure should I use?” is among the most common questions asked when a user finds himself/herself in this situation. My answer highlights both the importance (and sometimes unimportance, depending on the application and the purpose of the model) of the value entered as the reference pressure: No matter what pressure you enter, the flow rate and the pressure drop (dP) contributed by each component will be identical, but the absolute pressures in the model will be different. One caveat to this statement: this is only true of incompressible systems, as the density is constant and does not vary with velocity. See the AFT Fathom results in Figures 7 and 8 for a demonstration of this (note that a pressure of 25 psia has been used in Figure 7 and a pressure of 115 psia has been used in Figure 8).

And there you have it! Modeling closed systems in AFT software is not complicated or mysterious. With a solid grasp on the fundamentals of hydraulics modeling (especially when it comes to modeling pressure-type junctions), modeling closed systems becomes a rather open-and...."closed".... engineering case.

#### Comments 2

Really nice article! This greatly simplifies the thought process around closed systems.

I think it's worth noting that the absolute pressure doesn't impact pressure drop is only true for incompressible fluids. It can have a significant effect on compressible fluids since decreased pressure leads to greater velocity, and greater velocity causes greater loss. AFT Arrow is great for seeing the effect of absolute pressure on pressure losses in a gas system.