AFT Fathom is a versatile tool for modeling incompressible fluid flow in pipe systems. Whether you’re working with open or closed systems, AFT Fathom provides engineers with powerful analysis capabilities. In this blog, we’ll explore the differences between open and closed systems and provide a step-by-step guide to modeling closed loop systems in AFT Fathom.
Open vs. Closed Systems:
An open system typically has inflows and outflows, where fluid enters at one point and exits at another, with no return path for the fluid. For example, an open system might take fluid from a reservoir, pass it through pipes and pumps, and discharge it elsewhere.
Modeling a Closed Loop System in AFT Fathom
Modeling a closed loop system in AFT Fathom is straightforward. Here’s a guide to get you started:
- Use a Reservoir Junction: Even in a closed system, you can use a Reservoir junction to act as a reference pressure. This will serve as a boundary condition, against which all other pressures in the system are compared. Simply locate the Reservoir junction anywhere in the system and set it to the known pressure at that point.
- Connect Inflow and Outflow Pipes: Since there are no inlets or outlets, the flow delivered by the Reservoir junction will be fully recirculated by other pipes in the system, achieving a net-zero flow.
- Balance Energy: When using a Reservoir junction in a closed system, selecting the “Balance Energy in Reservoir” option ensures that the reservoir temperature adjusts dynamically. This feature accounts for the overall energy balance in the system by varying the reservoir temperature based on heat transfer throughout the system.
Mass and Energy Balance in Closed system
Mass and Energy Balance in Closed system
Balancing Mass
In order to model a closed system, only one pressure junction is used in the model. Typically this would be either a Reservoir or Assigned Pressure. Pressure type junctions are an infinite source of fluid and do not balance flow. How then can one be used to balance flow in a closed system?
To answer this question, it is worth considering how AFT Fathom views a closed system model. AFT Fathom does not directly model closed systems, and in fact does not even realize a closed system is being modeled.
Consider the system shown in Figure 1. This is an open system. Fluid is taken from J1 and delivered to J4 and J5. Because AFT Fathom's solution engine solves for a mass balance in the system, all flow out of J1 must be delivered to J4 and J5. Because the flow is steady-state, no fluid can be stored in the system; what goes in must go out.
Now consider the systems in Figure 2. The first system appears to be closed, while the second appears to be open. If the same boundary condition (i.e., surface elevation and pressure) is used for J1, J11 and J12 in the second system, it will appear to AFT Fathom as an identical system to the first system. The reason is that AFT Fathom takes the first system and applies the J1 reservoir pressure as a boundary condition to pipes P4, P9 and P10. The second system uses three reservoirs to apply boundary conditions to P4, P9 and P10. But if the reservoirs all have the same elevation and pressure, the boundary conditions are the same as J1 in the first system. Thus the same boundary condition is used for P4, P9 and P10 in both models, and they appear identical to AFT Fathom.
But how is the flow balanced at J1 in the first system? Looking at the first system, one sees that to obtain a system balance, whatever flows into P10 must come back through P4 and P9. Because there is overall system balance by the solver, it will give the appearance of a balanced flow at the pressure junction J1. If there is only one boundary (i.e., junction) where flow can enter or leave the pipe system, then no flow will enter or leave because there isn't anywhere for it to go. Thus the net flow rate will be zero at J1 (i.e., it will be balanced). But recognize that AFT Fathom is not applying a mass balance to J1 directly. It is merely the result of an overall system balance.
Balancing Energy
Here the thermal aspects of open and closed systems are discussed.
Consider the system shown in Figure 3 .The flows are balanced at J1, but how can the energy be balanced? For example, assume the user sets a temperature of 100° F at J1. This temperature will be the inlet pipe temperature for all pipes that flow out of J1. In this case, the 100° F will apply only to pipe P10.
The pipes flowing into the reservoir (P4 and P9) will have their own temperatures that are obtained by balancing energy along their individual flow paths. This could include heat exchanger input and heat transfer to or from pipes, as well as any heat added to the fluid from pumps.
The only way to obtain an overall system energy balance is for the J1 reservoir temperature to adjust to the mixture temperature of all inflowing pipes. This is the function of the "Balance Energy At Junction" feature in the reservoir and assigned pressure junctions. The junction temperature (input as maybe 100° F) is allowed to "float" and find its own equilibrium. Each iteration the floating reservoir temperature is passed into pipe P10 until convergence. When passed into P10, this will affect the return temperatures of P4 and P9. There is a unique "mixture temperature" (or mixture enthalpy) that will yield an energy balance at J1. This will be the temperature/enthalpy from Equation 3 in the Network Implementation topic.
AFT Fathom allows engineers to model both open and closed systems with ease. The use of Reservoir junctions for pressure referencing and energy balancing ensures accurate simulation results, even in complex closed-loop designs. By understanding the differences between open and closed systems and applying the right techniques in AFT Fathom, engineers can confidently model a wide range of scenarios, from basic piping systems to intricate recirculating networks.
