I'm planning on building a small model turbofan engine for a bit of fun but I thought I'd better get a better understanding of how they work first. I understand the majority of it at the moment but I'm struggling to see what the bypass air actually does, to my mind it seems like a waste of air and energy if its just going straight out of the engine without compression...could someone explain this to me?
On modern turbojets the bypass air provides (at least) two things
The air does bypass the engine core, but it is accelerated by the N1 fan and provides thrust as it is expelled rearward out of the engine. Thrust from the bypass air can contribute more than half of the total thrust produced by the engine (upwards of 80% of the total thrust for some engines in certain phases of flight). Part of the reason the bypass air is so efficient is that much energy is extracted from the core exhaust to spin the high and low pressure turbines (dual spool) that drive the N1 fan and the N2 compressor stages.
Engine cooling and noise reduction
Cool bypass air can be mixed with the hot air that went through the core at the rear of the engine. This mixing cools the engine exhaust and reduces the jet engine noise resulting from the rapid expansion of that air once it leaves the engine. The cool bypass air flowing around the engine core can also be used for general engine cooling.
An airplane engine provides thrust by accelerating air (plus some combustion products) backwards. As air is accelerated backwards the plane is accelerated forward thanks to conservation of momentum.
Momentum is proportional to velocity but kinetic energy is proportional to velocity squared. The result of this is that it is notionally more efficient to accelerate a larger amount of air to a low speed than a smaller amount to a higher speed.
In practice this is complicated by the fact that the air is already moving relative to the airplane. It is difficult to efficently add a small ammount of extra speed to already fast-moving air. So the best exhaust velocity depends on the speed at which the airplane will fly.
The exhaust velocity of a gas turbine core is higher than is desirable for most airplanes. So a turbine and fan are used to capture energy from the exhaust gasses and use them to accelerate bypass air resulting in a turbofan.
For planes that spend a lot of time at low speeds, designers may use a gearbox and propeller instead of the fan resulting in a turboprop.
The bypass air is actually what gives the jet engine most of its thrust. As the air enters the engine, some of it goes to the turbine core and runs the whole engine. But most of the air goes through and is sped up by the large fan giving it the thrust. Doing it this way increases the efficiency because the engine moves more air, although at a slightly lower velocity, than just a low-bypass engine which moves some air with high velocity.
Essentially, it is more efficient from a propulsion point of view.
Let me explain this with a very simple example. Imagine that you are over a skateboard and you would like to propulse yourself using your hands to give yourself the boost.
You have 2 options, either you use your hands over another person over an skateboard or you impulse yourself using a heavy desk?
As you will imagine, if you use the other guy with the skateboard he will go in the other direction with a similar speed, and the desk will be moved slightly.
But... it is clear in your mind that is more efficient to use the desk, moreover, you will prefer to use a wall.
What is happening?
When you are trying to impulse yourself (third Newton's law) you create the same force on the other side, but when using a bigger and heavier body that body will go slower. Essentially is more efficient to "propulse" using a heavier mass at lower speed that a lighter mass at higher speed.
Is exactly the same principle that you use in water, when you use diving fins you get faster speeds as you are moving your legs slower but moving a bigger amount of water, exactly like the skateboard.
The same principle applies to turbofans instead of water they use air. Instead of diving fins they use blades.
By creating a bypass they use also the air going through the bypass to get propulsion. Is more efficient than having a single core at very high speed.
Jet planes like fighter planes have their geometry designed for supersonic speed which is usually achieved with high velocity combusted jet exhaust from the jet engine. This consumes a lot of fuels in the high pressure compressor section.
Passenger planes on other hand are not designed to fly at supersonic speed so high velocity jet exhaust with high fuel consumption rate are not desired. The fuel optimal way to achieve this is to extract the kinetic energy from the combusted jet exhaust and transform it back into mechanical energy. This energy is used to drive the turbo fan which only compresses bypass air through the bypass section of the engine to the exhaust to achieve all the benefits of bypass jet engine as described in many other comments or articles. Note there is no fuel consumption here in the bypass section but only the excess kinetic energy of the hot exhaust is extracted and is used to run the bypass fan(s).
It is possible to design different engine mechanism to do the same thing as (high) bypass jet engine here, but it may be more complicated and has the penalty of heavier engine; therefore, less efficient than the current implementation.