Does the flow get through? CFD answers with the pressure all along the duct.

All the CFD case studies

A fan in CFD is first the problem of every cooling system designer: a fan, a duct, a finned heat exchanger. The fan pushes, the exchanger brakes. Is the fan enough to get the wanted flow rate through the exchanger? No data sheet answers, since each sheet describes its component alone. This case study puts both in the same duct and lets the CFD (Computational Fluid Dynamics, numerical simulation of the flow) bench decide. The radiator is a simple STL file (the 3D surface format that every CAD software exports) dropped into the domain: any object from your CAD can take its place.

The pressure cut along the axis of the duct tells the whole story: the air arrives from the right (green), the fan compresses it (orange), the finned radiator relaxes it (back to green). The banner at the top recalls the speed, power, torque and thrust of the computation.

• Contents:

1. The installation
2. The CFD of a ducted fan: a heavier computation than a free propeller
3. The pressure along the duct
4. The fan flow rate in CFD, and the verdict
5. The velocity between the fins
6. Take-aways

1: The installation

The case as built in the bench: the duct (white wireframe), the fan in the centre, and on the left the blue fins of the inserted radiator. The object was positioned in the Insert tab, with the mouse or by giving its position in metres.

2: The CFD of a ducted fan: a heavier computation than a free propeller

A closed duct costs more than a rotor in open air: the air must be described everywhere between the fan and the wall, and the radiator fins multiply the surfaces. The Duct Level 3 preset produced 6.5 million cells in 4 h 35 on a 6-core desktop PC, and the first phase of the computation took 18 minutes. It is an overnight computation, not a coffee-break one; the bench announces it beforehand in its estimate, next to the preset list, and a Duct Level 1 would have given a first overview much faster: the estimate gives the duration before launching.

The results panel. Besides thrust and torque, a closed duct brings up two lines that do not exist for a free propeller: the pressure change between the inlet and the outlet of the duct, and the flow rate. The panel also recalls that the duct wall and the hub are treated without friction, a choice of the preset.

3: The pressure along the duct

Pressure coloured on all the walls, seen from downstream of the fan. The duct is green on the right (air being drawn in, slightly low pressure) and orange between the fan and the radiator (compressed air waiting to cross the fins). The radiator fins, on the left, are green: it is the radiator that has consumed the overpressure. The zone after the radiator is outside the frame of this image.

The reading is that of a pressure gauge walked along the duct. The fan raises the pressure; the radiator brings it back down. What CFD adds to the reasoning is the value, read on the results panel, and the distribution, read on the pressure section at the top of the page: the overpressure is not uniform over the section, it is stronger towards the wall than in the centre, behind the hub.

4: The fan flow rate in CFD, and the verdict

The flow rate is not a result of the computation: it is set by the velocity imposed at the duct inlet, 12.3 m/s. The bench computes what it costs, in pressure, to push this flow rate through the fan and the radiator, and it is the sign of this Δp (the pressure difference between the inlet and the outlet) that gives the verdict. Between the inlet and the outlet of the duct, the pressure drops by 22 Pa: the radiator holds back a little more than the fan pushes. The bench says it itself in its result note: "a negative Δp means that the object holds back more than the rotor pushes, not that the rotor lowers the pressure". Concretely, this fan, at this speed, is not quite enough to push 16 m³/s through this exchanger in a straight duct: either a little more speed, or a less dense exchanger, or a lower flow rate to accept. This is exactly the question a design office asks itself, and the answer is one signed number.

Two remarks to read this number correctly. The outlet pressure is the one imposed at the end of the duct, it is not measured: the Δp is therefore relative to that outlet. And since the duct wall is frictionless in this preset, the Δp does not contain the pressure loss of the shell itself, which a classical pipe calculation adds without difficulty.

The CFD thrust on the blades (270 N, 289 N with the hub) is well below the designer's (479 N, blades alone). The radiator downstream probably changes the operating point of the fan, which no longer works in the conditions it was drawn for; this single computation does not allow the share of this effect and that of the method to be separated.

5: The velocity between the fins

The same cut, coloured by speed. Between the radiator fins, on the left, the air accelerates (red streaks): the flow area is reduced. It is this acceleration, then the deceleration that follows, that costs pressure. At the blade tip, the blue and red patches are the fan jet seen in section. The green and cyan checkerboards on the right are a sampling effect of the cut, not a flow structure.

6: Take-aways

• An object from your CAD is dropped into the domain as STL, and CFD computes the complete system, not the separate components.
• The verdict is one signed number: the pressure change between the inlet and the outlet of the duct, here −22 Pa. Negative, the exchanger wins; positive, the fan has margin.
• The 16.3 m³/s flow rate is imposed at the inlet, and conserved to within 0.03 % up to the outlet: CFD does not lose air along the way. What it computes is the pressure needed to push it through.
• A closed duct is a heavy computation: 6.5 million cells and a night of meshing at Level 3. Start at Level 1, read the estimate before launching.

The CFD case studies

« Previous: Tidal turbine CFD: a 16 m rotor in the current  |  Next: Wing CFD and hydrofoil: lift and drag »

1. Understanding a CFD result in five pictures
2. Boat propeller CFD: thrust and pressure on the blades
3. Aircraft propeller CFD: cruise and static thrust
4. Drone propeller CFD: hover
5. Wind turbine CFD: power and wake
6. Tidal turbine CFD: a 16 m rotor in the current
7. Ducted fan CFD: duct and radiator (you are here)
8. Wing CFD and hydrofoil: lift and drag

These case studies complement the Heliciel design tutorials (in French), which cover the BEM side: blade design, choice of speed, performance curves. To go further into the method, the technical collection of twenty tutorials remains available.