So lets consider that the stall angle (=Cl max) of a B747 is at 16° (in clean configuration). Does this mean, that, at whatever speed you are flying (i.e. 500 knots), you would stall if you go on a climb angle of more than 16°? So there is no need to always reduce the speed to the stall speed (which might lie at around 150 knots...). I am just wondering, since, if you fly in the microsoft flight simulator with a big jet, you can have an angle of attack of 30° and more, and not stall until you get to the stall speed.
Is there always a stall if you exceed a specific angle of attack?
Yes, stall depends only on angle of attack. However
Does this mean, that, at whatever speed you are flying (i.e. 500 knots), you would stall if you go on a climb angle of more than 16°?
No. Climb angle and angle of attack are completely different things.
This image from How It Flies shows the four different angles involved. Pitch is the angle between aircraft floor and horizontal, wing incidence is angle between aircraft floor and wing¹, angle of climb is angle between direction of flight (a.k.a “flight path” or “relative wind”) and horizontal and finally angle of attack is angle between direction of flight and wing.
The image shows that angle of attack + angle of climb = pitch + wing incidence.
Up to stall, lift depends approximately linearly on angle of attack and square of speed (and on air density). In straight flight the forces on the aircraft need to be balanced, so angle of attack will be such that they are. If you increase pitch, the angle of attack will increase, which will cause unbalanced force, which will cause upward acceleration and that will increase the climb angle at the expense of the angle of attack again.
So if you go on a climb more than 16°, the angle of attack will not significantly differ from what it is when you fly level at the same speed.
I am just wondering, since, if you fly in the microsoft flight simulator with a big jet, you can have an angle of attack of 30° and more, and not stall until you get to the stall speed.
No, you can't. You, however, can climb at 30° or more, for a while before you run out of speed. Which at low altitude is actually quite long; the jet engines are designed to have enough power at high altitudes where air is much thinner and to allow taking off when one engine fails late in the take-off roll. Therefore low with all engines operating at full power you have quite a bit of extra thrust available.
Also note, that stall does not mean loss of all lift. You only loose part of it. A significant part, but not all. Stalled aircraft is still controllable (though ailerons effect is reversed) and some aircraft (though this would be fighters, not airliners like 747) may even have enough lift and thrust to maintain altitude when stalled.
¹ Specifically, the zero-lift line of the wing. This coincides with the chord of symmetric wings, but cambered wings have it tilted up.
Short answer: No.
Long answer: The stall angle of attack varies with speed, altitude, Mach number and the rate of angle of attack increase, as discussed here and here. Since the lift curve slope of a wing does not change with the pitch rate, a high pitch rate will indeed increase the stall AoA by up to 50%.
Speed and altitude effects are expressed in the Reynolds number, and this will also shift the AoA up by several degrees when increased from, say, 200,000 to 5,000,000. The influence of the Mach number will really manifest itself above Mach 0.5, but if the leading edge radius is small, it can already make a difference of several degrees between incompressible conditions and Mach 0.3. Stall at higher Mach numbers is more complex, because before lift drops, the wing will experience increasing buffeting, which by itself will limit the operational AoA.
Next, pitch angle and angle of attack are not the same, but they differ by the flight path angle and the wind angle of attack, which is nonzero if you fly in an up- or downdraft. This is discussed in detail here.
If your engine or airspeed allows, you can fly a full loop without ever stalling the airplane.
For a given wing configuration eg leading/trailing flap, sweep etc, the stall will occur at the same AoA in incompressible flow (low speed, low alt flight) - that's assuming you can clearly define the stall as some fighter aircraft don't have a sudden classical lift break, rather their stall might be defined by rapid drag rise, controllability, handling issues.
For compressible flow, ie flight at high Mach number, the stall AoA will reduce: Stall AoA at 300KCAS/sea-level is greater than the stall AoA at 30,000ft/300KCAS.
Two effects at play here... Compressibility and Viscosity. The effect of compressibility is the predominant one.
Viscosity (Reynolds number). For a given wing design and configuration, as you go up in altitude, the density of the air decreases, while viscosity increases with lower temp. This has a small effect on Reynolds Number.
Compressibility: energy lost in compressing the air is significant at higher mach, which is why you see lower AoA for a given defined stall.
Incidentally, buffet onset is not always a defining attribute of the stall as some jet fighters will experience buffet at very low AoA eg 6-7 degrees, well before the defined stall.