Bonpon,
Although previous posts have shed a good deal of light on this subject, I'm not entirely sure that they have answered your original question "what is the fan duct on a turbo-fan engine for?". I will attempt to do so and as usual, will go for simplicity rather than completeness.
The fan serves two functions. Firstly, it is the low pressure compressor. The air passing through the fan is compressed, then some of it is passed into the engine core, where it is compressed again and used for combustion, cooling and thrust. The second and arguably more important function of the fan is to provide additional thrust.
The relative proportions of total thrust produced by the hot gas flow and the fan, are generally equal to the ratios of airflow through each. A modern high by-pass engine for example, might have a by-pass ratio of 10:1 This means that for every eleven pounds of air going through the fan, 1 pound goes through the engine core, and the other 10 pounds by-passes the core. But this 10 pounds produces about 90% of the total thrust. So in one sense we can consider the fan to be simply a propeller. To understand the function of the duct we must consider the problems affecting propellers.
Propellers are simply a means of converting the rotating power of the engine into thrust. Their blades are aerofoils, which, by rotating at high speed, generate a total reaction. The forward-facing component of this is thrust and the majority of the remainder is the propeller torque. This is wasted in opposing rotation.
Like wings, propeller blades produce tip vortices which in turn produce induced drag. The magnitude of these tip vortices increases, as the total reaction of the blades increases. So if we produce a lot of thrust, we can expect strong tip vortices and lots of (energy wasting) induced drag. This problem can be greatly reduced by placing a duct around the tips, to reduce the tip vortices. Because tip losses increase with thrust, ducts are most beneficial in highly loaded, high thrust systems. So our modern turbo-fan producing 80000 or 90000 pounds of thrust will gain a lot from a duct, whereas a small piston/prop creating perhaps 2000 or 3000 will not.
The second problem affecting a propeller is that its angle of attack is proportional to the relative magnitudes of RPM and TAS. So as airspeed increases, the angle of attack decreases. This reduces aerodynamic efficiency, thereby causing thrust to reduce rapidly as speed increases. This limits the maximum speed that can be attained by propeller aircraft. Variable pitch props reduce this effect by increasing blade angle as TAS increases. Although this maintains a more or less constant angle of attack, it also tilts the total reaction away from the direction of flight. This increases the proportion of the total reaction that is wasted in the form of propeller torque. So the variable pitch prop system is not entirely successful. But by controlling the TAS of the incoming airflow, a fan duct can provide much greater control of angle of attack without the need to vary blade angle.
Ducts designed for subsonic flight commonly form a slightly divergent passage ahead of the fan. This slows down the incoming air, and increases its static pressure. This in turn increases the airspeeds at which turbo-fans can be operated efficiently. Also by producing a slightly convergent passage behind the fan, the duct accelerates the air, to increase the thrust produced.
The third problem is that of tip speed. The airspeed over the tip of a propeller blade is made up of rotational speed and aircraft TAS. Rotational speed is proportional to blade length and RPM. So if we use long blades and high RPM to create lots of thrust, the tip speeds will soon become very high, as TAS increases. When tip speed approaches the speed of sound, the blades create shock waves and just like wings, generate a great deal of extra drag. In a turbo-fan this problem is addressed into two ways. Firstly, by using lots of short blades rather than a few long ones. And secondly by using the duct to reduce the speed of the incoming airflow as described above.
So in a turbo-fan the duct reduces tip losses, controls incoming airflow speeds, and reduces the rate at which thrust drops with increasing TAS. In a sense it could do all the same things for a propeller but the benefits would be much less. . .These must then be balanced against the additional weight and drag costs described above by John.
. .TF,
Although your suggestion that the rear inlet duct in a Tristar might produce lift, appears logical, we need to consider the entire duct. At the front end it curves from horizontal to downward pointing. This will indeed accelerate the air downwards, and hence produce an upward force on the aircraft. But the rear end of the duct curves from downward pointing to horizontal. So the vertical velocity given to the air by the forward end is reduced to zero by the rear end. The overall vertical acceleration and hence upward force is therefore zero.
It is true however that long, contorted ducts reduce efficiency. That is why most designers use the minimum duct length necessary to achieve their objectives. A high engine as in the DC10 will produce a nose-down pitching moment, which needs to be balanced by the nose-up moments from the lower, wing mounted engines and (probably) a bit of trimming. The Tristar designers' decision to go for a low engine was probably aimed at eliminating this nose-down pitching moment. Having made this decision they were then stuck with the need for a long curved duct. The use of reverse flow combustion chambers in engines is a similar balance between costs and benefits. Reverse flow reduces efficiency slightly, but this is usually outweighed by the benefit of having shorter and hence lighter engines.