Power application is NOT stall recovery
"This shows that increasing the thrust at the SW in order to increase the speed and hence to decrease the AOA is not the proper reaction in many cases"
Sadly both FAA and JAR approved schools are training pilots in a flawed manner by the insistence on a minimum height loss instead of getting the wings flying again. How does a glider recover from a stall?
JAR 25 / FAR25 Test Pilots always pitch to reduce AoA long before adding power to recover from stall.
Reducing the Angle of Attack (AoA)/Aircraft Attitude to unload the wing and reattach the airflow is the key BEFORE applying power once speed is about 20% above stall speed.
Most Commercial Pilots are taught to operate safely and effectively within a flight regime of up to +/- 60 deg Angle of Bank and +/- 30 deg pitch. However, the majority of Flight schools on both sides of the Atlantic seem to teach Full Power as part of a Standard Stall Recovery (SSR). The Royal Air Force's Central Flying School also teaches SSR but the emphasis is on reducing AoA to remove buffet whilst simultaneously adding power - not holding the pitch attitude as suggested. Holding the pitch attitude whilst applying full power is a Low Level Windshear/Terrain avoidance manoeuvre not a stall recovery technique! The emphasis on minimum height loss at the stall by some Flight/Simulator examiners on check rides has exacerbated the issue.
Propellor Aircraft:
The idea that this technique worked for stall recovery on 1950s piston powered aircraft is inaccurate. As Sean Roberts of the National Test Pilot's School explained at the Bombardier Safety Standdown, all aeroplanes with tractor propellors will pitch up with application of power due to propellor normal forces. This is as true for WW2 fighters as for 2011 Turbo Prop Twins.
At high AoA, the propellor slipstream is deflected downwards. By Newton's laws, the opposite reaction is the propellor normal force which causes the nose to pitch up as full power is applied. At the same time, the local angle attack of the wing immediately behind the slipstream will be very slightly reduced (increased local dynamic pressure) but the rest of the wing will stall from the wing tips inwards. Without an increase in CLmax (eg: flaps), the stalling speed will not change significantly but the effect of power will increase the pitch attitude at which the stall occurs.
Asymmetric Blade Effect:
We now have a high nose attitude senario with further buffet onset and a greater likelihood of un-demanded roll or yaw. The latter caused by a combination of one wing tip stalling before the other and asymmetric propellor blade effect. Test Pilot, Sean Roberts, uses the helicopter rotor as an example (c.f. 90 deg AoA on propellor blade). Unless you are flying a machine with counter rotating propellors, the difference between the advancing and retreating blades creates asymmetric propellor disc loading which will yaw the aeroplane (For conventional US engined aircraft, Clockwise rotation to Pilot, will yaw left). What started as a basic stall recovery is now a more serious aircraft upset made worse by the pilot applying power at high AoA.
Buffet (stall) + un-demanded roll or yaw = SPIN !
Modern Jets:
Underslung engines on A320/B737/EMB175 all pitch up with power application without automatics in play. Rear Mounted Engined aircraft like the MD80/Citation XLS/Gulfstream VI are far less susceptible to power on pitch up unless the airflow has already separated from the wing and turbulent flow is ingested into the engines creating compressor stall /rollback.
Swept wings complicate stalling matters further. The downwash effect of trailing vorticity on a swept wing is quite different to a straight one. The overall result is less downwash at the wing tips than inboard. On a tapered swept wing there can even be upwash at the wing tips. This means a swept wing will stall at the tips first leading to a nose up pitching moment as the centre of lift moves forward thus increasing the stall in a runaway manner. Better wing design (wing fences, vortex generators, slat operation, etc), and advances in Control Systems have largely overcome these issues but a forewarned pilot is a safer one.
In summary, at the first symptom of a wing stall, reduce AoA (unload) and accelerate to 1.1 Vs before applying power. Better still (prevention being better than cure) stop the stall happening in the first place by monitoring flight path (AoA, lift vector, energy management) and the automatics. Prioritise by setting appropriate aircraft AoA/attitude and Power in the unlikely (but possible) even the computers do drop out.