SURGE
In the figure you can see the map curve for a given number of rpm for a compressor.
If you consider the pressure ratio of project the compressor can work in 2 point of the curve,
the one on the right is stable (B)
the one on the left is unstable(A)
If your compressor is working in B and an inconvenience make the flow of mass increase the pressure ratio go down,
this means that the pressure of the air flow, going out the compressor, is lower than p2=const.
So the flow decelerates because there is gradient of pressure opposing
and the flow of mass decrease and consequently the compressor return to work in B.
In a similar way if the flow of mass decrease a positive gradient of pressure accelerates the air flow and the compressor return to work in B.
If we are in A every little variation of the flow of mass is amplified, so a compressor mustn't work on the left of the surge line.
If a compressor work on the left of the surge line the air is pumped instead of being aspirated.
And the compressor can crash.
Usually the surge line interpolate the maximum of the map curves (but this is not a rule).
In axial compressor the field of stability is restricted if there are a lot of stages.
STALL
when the laminar air flow become tubolent there is stall. This situation can happen over the casing or over the blading.
the stall is favoured by a positive gradient of pressure (delta_p/delta_x > 0) and it is delayed by negative gradient of pressure (delta_p/delta_x < 0),
for this reason it's really difficult to have stall in a turbine (delta_p/delta_x in a turbine is negative).
Blading:
Over a blade we can have stall by the suction side or by the pressure side, it depends on the angle between tangential velocity (U) and relative velocity (W).
If this angle differs too much from the angle of project there is stall. If there is stall it means that a part of the flow of mass can't pass through two consecutive blade.
So the exceeding flow of mass must pass through the nearest vanes(Z-A & B-C in the figure); in this way the direction of the relative velocity of the nearest blades changes and after a short time the stall is passed in the next blade (from B to A).
We have a rotating stall.
By experimental tests we know that if the Lieblein coefficient is < 0.4 there isn't stall on blading. (c is the blade chord, s is the step between two blades, Wu is the component of W directed like U and Wa is the axial component of W).
(in the figure number 1 indicates the entrance of rotor and number 2 the exit of rotor)
Casing:
there isn't stall in the casing if the pressure coefficient in the rotor and the the pressure coefficient in the stator are < 0.5
the most critical point is the hub of stator blade.
It's usual to project with simmetric triangles of velocity (modulus of W2 = modulus of c1 and modulus of W1 = modulus of C2).
So the gap of pressure (delta_p) is the same for rotor and stator.
Besides is usual to have the absolute velocity in entrance of the stage-disc equal in modulus of abslolute velocity at the exit. (modulus of c1 = modulus of c3).
(in the figure p3 is the pressure at the exit of stator, c2 is the absolute velocity - c2= W2 + U, it's a vectorial sum).
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excuse me for my english, but I'm italian.