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Whenever, I come across turboprop, the author always mentions that they have higher bypass ratio than turbofan but no one explains the reason for this.
So, is the bypass ratio higher due to higher disc radius of turboprop or is it due to less air flow through the core or the combination of both?
If it is only due to less air flow inside the core, then they can still have a higher bypass ratio in turbofan right? (Since advanced turbofan produce less noise due to the nacelle)
Bypass ratio is the ratio of the overall flow to the core flow (which goes eventually through the combustion chamber). Overall flow is either the flow captured by the intake or going through the propeller disc. Even for piston aircraft it is possible to define a bypass ratio if you interpret the air which flows through the cylinders as the core flow.
A turbofan essentially uses a shrouded propeller of high solidity (or activity ratio) which helps to accelerate the flow through it as much as possible. It needs to produce the most thrust from the limited air volume captured by the shroud's intake. The limitation is needed to limit the tip speed of the fan and the overall size and drag of the shroud.
Propellers, on the other hand, accelerate a bigger flow by less and need to cover less of the propeller disc for doing this. To keep thrust constant, a bigger mass flow needs to be involved into the acceleration.
Plot of the thrust specific fuel consumption in lb of fuel per lb of thrust per hour of different engines over the logarithm of their bypass ratio (picture source).
A comparison is only sensible if we look at the same core component: If a turbofan and a turboprop share the same high pressure components. One example would be the Rolls-Royce/Allison 2100 and the Rolls-Royce/Allison 3007. Wikipedia gives the mass flow of the 3007 as 109 - 127 kg/s but gives no information for the 2100. Using the maximum flight speed of the Alenia C-27J of 167 m/s and its propeller diameter of 4.15 m, we can find a lower bound for the mass flow through one of its propellers if we make the heroic assumption that the maximum speed is reached in 25000 ft (7620 m) where air density is 0.55 kg/m³.
Mass flow through the propeller of one 2100 is at least 1242.4 kg/s or about ten times of what it is for the 3007. The mass flow though the core is the same because both engines share the same hot section. The static thrust of the 2100 is higher than that of the 3007 but drops more quickly with speed, so at high speed the 3007 produces more thrust.
There is a limitation when designing a fan, the speed at the tip to not reach sonic conditions. Essentially, that means that is basically rotational speed times diameter of the blade. So... at same conditions the factor of rotational speed and diameter of the blade will be a design condition.
That is coming up with 2 different design solutions:
It is a simplification, but essentially the first is call turbofan and the second turboprop.
By design, the turboprop will have higher diameter and so higher bypass ratio but will carry a heavy reduction gear. So... we have a tradeof.
That is why some low subsonic airplanes prefer turboprop in comparison to turbojet.
