Fanjet efficiency questions.

[PETTIFOGGER]

1. It's a known fact that the bigger you make a propeller/impeller/fan, the less horsepower it needs to move a set amount of air. This is why we see high-bypass fanjets getting bigger and bigger fans in the front. At some point, this fan is going to be too big to shroud in a housing and would have to be un-shrouded. Why, in the name of fuel efficiency hasn't this happened yet?

Answers seriatim: It is the relative speed of the air that is important for thrust. Higher bypass ratios are getting bigger because they use or ‘recover’ more energy produced by the gas generator, or core. A fan without a housing is a propeller, and different laws of fluid mechanics apply. Simply put, the air (flow field), when it reaches the ducted fan, slows down or hesitates at the face of the fan. This is part of the reason that the fan remains more efficient as speed increases. The lateral swirl, which is lost energy (slip) from a propeller, is contained by the ducting. It has happened. Apart from being noisy there was a return to the inefficiency of propellers at the air speed required.

3....Why don't fanjets have variable pitch blades like the turboprop has?

Because it is unnecessary, as the engines’ 'sweet-spot' is designed to coincide with the normal cruise speed required for a range of commercial aircraft.

4. Many blades in a fan or prop adds solidity and will require less power to shift air. The reasons turboprops rarely have more than 5-6 blades is that they have variable pitch hubs. A fanjet doesn't have VP, so they can have more blades. But there's a disparity here - if more blades are more efficient (as they keep telling us), then how come fixed pitch aircraft don't have more blades? Or reversed - why don't fanjets have fewer but variable pitch blades? You can't have your cake and eat it too - something has to be better than the other.

You can to a certain extent and that is the thinking behind it: a fan jet is a compound engine.The thrust physics of propellers and ducted fans are different. As a general rule for propellers, fewer blades are more efficient. More blades are generally used when the optimum disc size cannot be accommodated on the wing, but there are other considerations, such as nvh, weight, balance and proportionality.

5. If a bigger fan increases fuel efficiency is taken to its logical conclusion, soon the fans will be so big as they will be hard to hang under wings without scraping the ground. Would it therefore be beneficial and fuel efficient to add more engines with higher bypass ratios so as to shift more air? Example: instead of having 2x engines rated at 10kN (in the core turbine, I'm not talking total thurst from the fan part) each and with a 100sq.ft fan area - would it be more beneficial to have 4x 5kN engines with 200 sq.ft fan in instead?

Again, it is a question of aerodynamics and proportionality. From the viewpoint of efficient thrust per lb of fuel, the fewer fanjet engines the better.
I hope that this helps. I am happy to be corrected by others. These are un-researched answers and should not therefore be used for an academic paper or talk. That would need citations e.g. from Newton, Reynolds, Navier-Stokes to name but a few. As well as giving the mathematics, this site also gives various animated displays: http://www.grc.nasa.gov/WWW/K-12/airplane/aturbf.html.