By placing a fan or propeller in a duct or shroud, as in Fig. 6.10, flow patterns can be obtained, that are significantly different from those produced by an unducted propeller or fan. The flow patterns depend on the relationship between the flight speed and the engine thrust. Figure 6.10 shows two sets of patterns, one corresponding to the low speed high-power take-off condition, and the other to the high speed cruise case. In this figure, the broken lines represent streamlines which divide the flow that goes round the outside of the duct, from that which flows through it. Again, in three dimensions, these would correspond to stream-tubes, which may be termed dividing stream-tubes.
To explain how the duct or shroud works, we shall look first, at a subsonic flow of air through a converging streamlined duct with no fan to assist it, as illustrated in Figure 6.11. Since no energy is being added, the device cannot produce a thrust, so the jet of air at C (where the pressure is at the free-stream value) cannot be moving faster than the free stream at A.
The dividing stream-tube diameter at A must, therefore, be no larger than at C, since the same amount of air is passing at about the same speed at both A
Fig. 6.11 Flow through a streamlined duct
If no energy is added, then the flow speed at C cannot be greater than at A, since the pressure is atmospheric at both positions. In the duct at B, the flow speed is lower, and the pressure is higher than the surrounding atmosphere
and C. As the flow enters the duct at B, however, the area is larger, so the speed must be lower there. If the speed falls, then the Bernoulli relationship tells us that the pressure will be higher.
A duct can, therefore, provide a means of reducing the air speed and increasing its pressure locally. If we place a fan in the duct, then the addition of energy to the flow can create a jet, and the streamline pattern can be as shown in Fig. 6.12. This is similar to the cruise case shown in Fig. 6.10.
As shown, there is still a reduction in speed, and an accompanying increase in pressure as the flow enters the duct. This is a very useful feature if the aircraft is flying at a high subsonic Mach number, because the air now enters the fan at a lower Mach number. The Mach number is lowered further, by the fact that the rise in pressure is accompanied by a rise in temperature, so that the local speed of sound is also increased.
In Fig. 6.12 we have shown the surrounding stream-tube for an unducted propeller, having the same diameter as the ducted fan, and producing the same amount of thrust. A fan operated in this way is less efficient than a free propeller of the same diameter, since the fan draws its air from a smaller area of the free stream, as shown in Fig. 6.12. The mass of air used per second, and the resulting (Froude) efficiency are, therefore, both smaller for the fan. The price is, however, worth paying, as the fan may be used at flight Mach numbers where conventional propellers suffer excessive losses due to compressibility effects.
It should be noted, that for high speed turbo-fan (fan-jet) propulsion, it is normal for the outer part of the blade to run with supersonic relative flow between the blade and the air, but with subsonic relative flow for the inner
Pressure greater than surrounding atmospheric
for an unducted propeller producing
the same amount of thrust
Fig. 6.12 Ducted fan at high speed
As with the simple unassisted flow through a duct, the flow slows down as it enters the duct, and the pressure rises. The surrounding stream-tube for a propeller of the same diameter producing the same amount of thrust, is shown by dashed lines part. We shall deal with the linking of such ducted fans to gas-turbine engines to provide turbo-fan propulsion later.