Thread: Discussion The Truth about ducted fans
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Old Jul 05, 2006, 07:03 PM
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Hi

In post 101 I included two pictures which only got scant recognition by the readers, so that I must assume that they were not properly explained. The “pressure development through ducted fan” graph was drawn quite some time ago, when I was mainly interested in coming to grips with the intricacies of ducted fan design and still thought of less powerful (but more efficient) fans than we are used to by now. Looking at the figures the graph represents an 80mm fan with a power input of about 300W.
In the static case (black lines) it creates a slight (-1200Pa) depression of the atmospheric pressure in front of the fan, which sucks air into the intake from all sides. Mainly for this reason and to fill the throat completely and as uniform as possible the intake lip must be nicely rounded. In comparison to the similar picture in post 111 (MINI fan in engine pod) the rotor is set a little distance back from the entry leaving a short straight duct piece in front of the rotor. This serves to even out minor eddies in the flow and helps also to fill out the area in case of small flow detachments. In full size we often find a divergence of this duct, but for models this should be avoided – it costs drag.
As we can see in the development of the pressures towards the entry the sum of dynamic(velocity) and the static pressures are zero, which shows that there is no energy added to the air of the stream tube up to the front face of the rotor. Rotor and stator, the fan stage, increase the energy level of the airflow by around 2000 Pa static pressure, which is totally converted into velocity (pressure) in the nozzle. There the static pressure is again down to atmospheric level.
Under flying conditions the picture changes. Now the air approaches the nacelle face already with the flying velocity, but still the fan produces a pressure depression which causes the air to further accelerate into the duct.
Ideally this air velocity increase should be just of the same magnitude as the area ratio decrease between the highlight and the throat. Pressure developments for the flying case are depicted in red. We see that the oncoming air has already some velocity pressure (in respect of the engine pod) and the total pressure stays the same up to the rotor face, exactly as in the static case; the velocity through the whole fan is higher than before. This also indicates a higher flow rate (for equal cross section areas) and a larger mass flow. In the fan stage energy again is transferred to the air, but this time already starting from an elevated level. We can assume that the motor still supplies the same power than before in the static case, so the total energy level of the air after it passed the fan stage is higher as well.
The only comment we can make here is, that obviously we must be able to utilise the velocity pressure (energy) of the free air stream. This is the main job of good intake design.
The situation as described for the flying case above is a very special one: for a given model and EDF with intake and fixed power there is only a narrow flying speed margin where the best overall system efficiency can be achieved.
In the design phase this situation should be considered, it does not mean however that this is necessarily also the maximum flying velocity.

Very often the question arises for the best size of the exit nozzle area (mostly diameter, since they are usually circular) for a particular EDF. In most cases this can be answered because there is sufficient experience available with that fan.
In a more general way this can be answered for any fan by some calculations. I don’t want to do those calculations here, but show in general terms the underlying principles, which also show some interesting underlying principles and connections.
We have already seen that the fan stage (rotor and stator) in an EDF must produce some pressure and air flow. It has to be seen as an air mover rather than a compressor. An axial fan is eminently suitable for this purpose.
The same criteria are used for ventilation fans which are used in the air conditioning industry and I have seen and also tried several of those in the past.
The industrial fans are selected normally with reference to the duties and manufacturer supplied graphs which show their characteristics. Furthermore all fans work to the same physical principles and obey the fan laws. The fan curves are well known in the industry and usually show the pressure and flow rates in respect of each other and the required power and rotational speed (rpm).
There are no comparable graphs available for EDFs. And there are no thrust curves available for industrial fans either. There are however useful interrelations to be expected.
I have measured the performance of my WM600 quite extensively and accurately and having done some calculations constructed a diagram which is included here below.
All air leaving a fan with higher velocity than at the entry carries an increased momentum (energy) which is basically lost, unless it feeds the fan again as in many industrial applications. This loss is made up from the mass flow times velocity differential squared. We can also express it as pressure per flow rate.
The diagram shows this as a curve (red line) called “Loss due to momentum in air jet from nozzle”. The horizontal scale is calibrated in litres per second (because that unit gives memorable figures) and the vertical scale shows the pressure in Pascal. (I have the same problems with Pascals as you, because I have been brought up with bar and mbar; I always memorise Pa by the nice term HectoPascal – used by “the weather” which gives the same numbers as the more familiar mbar, 1000 hectoPa = 1000mbar). The maximum pressure on the scale is 10,000Pa = 100mbar ~ 1.4psi, and the highest pressure produced by the fan with a shaft power input of 1.5kW is just 7500Pa ~ 1.05psi, not really very much considering.
The slightly higher red line shows the sum of the momentum loss plus the pipe loss of the short duct, the pink area is the duct loss itself.
The fan performance curves are the green lines as indicated for the various power levels. Where they cross the total loss line is the operating point , and for those interesting ones I have also drawn the fan rpm and the static thrust.

The next instalment is in the making, please be patient.

Have fun with fans

Klaus
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