Italia458
Would it be correct to say that the flow outside the boundary layer does not have energy added or subtracted (and it's incompressible and inviscid) so Bernoulli applies to it?
Yes, Bernouilli's equation is, for all practical purposes, valid outside the boundary layer - but note ft's comment that strictly speaking you have to define the limits of the boundary layer.That can be done in several ways but the fine differences only matter to aerodynamic pedants (I'm not one I hope)
Is the boundary layer then responsible for the induced and parasitic drag?
The boundary layer is not "responsible" for drag in any direct sense of course. It is the viscous forces associated with the velocity shear inside the boundary layer that produce skin friction drag.
If you are looking at a 2D wing then there will be no induced drag in the classic sense since you have an infinite aspect ratio. For sensible finite wings then there will be drag due to lift - for a wing in inviscid flow and with an elliptical loading that will be Prandtl's classic CL^2/(Pi*A.Ratio). For non-elliptic loading and the effect of fuselage Europeans usually put an induced drag factor 'k' in front of that. In the USA it is more common to use the Oswald efficiency e = 1/k. This bit of drag due to lift has nothing to do with the boundary layer.
In real life viscosity and the effect of pressure gradients on the upper surface mean that as AoA (CL) is increased the boundary layer flow will start to separate and the drag will increase. In practical measurements this shows up as an increase in 'k'.
So boundary layer flow is involved in both skin friction drag and part of the induced drag. If there are any separations around at zero lift it can also be involved in the pressure drag.
Regarding the loss of total pressure behind the TE, where does that energy go?
Never really thought about it deeply, but since the energy loss comes from frictional forces why doesn't it (eventually) show up where friction effects always do show up - heat! [That isn't taken into account by Bernouilli either].
Going to be offline next week, but parting thought - if you want a
quantitative explanation of lift generation then you have no choice but the circulation explanation L = rho * circulation* airspeed, but if you are happy with a
qualitative explanation you can opt for the Newtonian L = mass flow rate * downwash. Neither of those two parameters can be defined numerically (see below) so it doesn't satisfy me, but if you can live with that well "Chacun a son gout" BTW, Bernouilli's equation doesn't figure in either of those explanations
[We don't know the depth of the region affected by the wing or even its shape; downwash is not uniform over this region, in fact it varies with distance below the wing]