Method for profiling blades of an axial turbomachine

1. A method for profiling blades of an axial turbomachine comprising:

a) preparing a geometric model of a blade profile (R, −1, +1);

b) determining an oscillation mode of the geometric model;

c) calculating a time profile of a position-dependent disruptive pressure p({right arrow over (x)}, t)=p ges ({right arrow over (x)}, t)−p 0 ({right arrow over (x)} ) in a channel between two adjacent blade profiles over an oscillation period of an oscillation belonging to the oscillation mode,

wherein in order to calculate the profile it is assumed that the position-dependent disruptive pressure p({right arrow over (x)}, t) in the channel is proportional to a magnitude of a surface ({right arrow over (x)}, t) which extends in the channel and is arranged perpendicular to the flow lines between blade surfaces bounding the channel, and perpendicular to these blade surfaces,

wherein {right arrow over (x)} is a coordinate on one of the two blade surfaces,

t is time,

p 0 ({right arrow over (x)}) is a position-dependent pressure when the blade profile is stationary, and

p ges ({right arrow over (x)}, t) is a position-dependent total pressure;

d) determining a damping of an oscillation caused by the position-dependent disruptive;

e) changing the geometric model and determining a different oscillation mode for the changed geometric model, as well as carrying out step c) with the changed geometric model and the different oscillation mode; and

f) determining a damping of an oscillation using the disruptive pressure profile p({right arrow over (x)}, t) calculated in step e) and accepting the changed geometric model for the case that the damping of the oscillation turns out to be greater than damping of the oscillationin step d), otherwise repeating steps e) and f) with another changed geometric model.

2. The method as claimed in claim 1 ,

wherein an integration of the position-dependent disruptive pressure is performed in step d) along the complete channel.

3. The method as claimed in claim 1 , further comprising:

g) numerically calculating an oscillation, engendered by a flow, of the geometric model accepted in step f) and calculating the damping of an oscillation.

4. The method as claimed in claim 3 ,

wherein a convection and an inertia of the flow are taken into account in step g).

5. The method as claimed in claim 1 ,

wherein the oscillation mode is represented in complex form: {right arrow over ( 99 )}={right arrow over (a)} c +i{right arrow over (a)} s ,

wherein {right arrow over (ϕ)} is the oscillation mode, {right arrow over (a)} c and {right arrow over (a)} s are local deformations.

6. The method as claimed in claim 5 ,

wherein {right arrow over (a)} c and {right arrow over (a)} s are prepared by means of a finite element structure solver.

7. The method as claimed in claim 5 ,

wherein ({right arrow over (x)}, t) is illustrated according to ( {right arrow over (x)}, t )= 0 ({right arrow over ( x )})+ Re └( Â 1 e iβ 1 e iσ +Â R e iβ R ) e iωt ┘,

wherein 0 ({right arrow over (x)}) is the area ({right arrow over (x)}, t) when the blade profiles are stationary, R =|{right arrow over (n)} R ·{right arrow over (ϕ)}| R is a projection of the oscillation mode onto the normal {right arrow over (n)} R to the blade surface at the coordinate {right arrow over (x)} for the one blade profile, Â 1 =|{right arrow over (n)} 1 ·{right arrow over (ϕ)}| 1 is a projection of the oscillation mode onto the normal {right arrow over (n)} 1 to the blade surface at a point on the blade surface of the other blade profile, β 1 and β R are the relative phase offset between an imaginary component and a real component, σ is the phase offset of the oscillations of the two blade profiles, and ω is the angular frequency.

8. The method as claimed in claim 7 ,

wherein the damping of the oscillation is determined in step d) for different values of β 1 , β R and σ.

9. The method as claimed in claim 7 ,

wherein 0 ({right arrow over (x)}) is determined in that a circle is found on the blade surface of the one blade profile at the coordinate {right arrow over (x)} which is tangential to the blade surface of the one blade profile at the coordinate {right arrow over (x)} and the blade surface of the other blade profile at the point, and 0 ({right arrow over (x)}) is selected in such a way that 0 ({right arrow over (x)}) is tangential to the normal {right arrow over (n)} R at the coordinate {right arrow over (x)} and to the normal {right arrow over (n)} 1 at that point.

10. The method as claimed in claim 9 ,

wherein 0 ({right arrow over (x)}) determined through an interpolation of a function, or through a second-order polynomial, between the coordinate {right arrow over (x)} and the point.