EP1965024A1 - Method of reducing levels of vibration in a turbomachine bladed wheel - Google Patents

Abstract

Initial configuration of the blades is defined. Synchronous forced response on one bladed wheel is calculated as a function of harmonic excitation force produced by another bladed wheel expressed in the form of a linear function of the generalized aerodynamic force for the mode considered. Geometric tangential shift value is determined for the stacked cross sections of one wheel to reduce the corresponding term to the generalized aerodynamic force. Set of cross sections with the tangential shifts defines a new configuration of the blades to be applied to one wheel.

Description

The present invention relates to the field of turbomachines and aims a method for reducing the vibrations on the blades of a bladed wheel subject to periodic excitation resulting from disturbances in the gas flow through the turbomachine, produced by a bladed wheel or an obstacle near said wheel, one being generally mobile and the other fixed.

A turbomachine comprises one or more rotors formed of bladed wheels, that is to say of blades mounted on a mobile disc rotated about an axis, and one or more grids formed of fixed bladed wheels, that is to say not movable in rotation with respect to the axis above. The vanes of the fixed and moving wheels are traversed by a gaseous fluid in a general direction parallel to the axis. One of the main sources of excitation of the fixed or mobile vanes is wakes and pressure fluctuations generated by the obstacles adjacent to the vane. These various obstacles, namely the blades of the upstream and downstream stages or the casing arms induce disturbances in the flow of fluid through the blades. The scrolling of the vanes in these disturbances creates a synchronous harmonic excitation of the rotational speed of the rotor and generates an unsteady pressure field on the surface of the blade.

In the field of aerospace turbomachines, the blades are particularly sensitive parts because they must meet in terms of dimensioning requirements of aerodynamic performance, aeroacoustics and mechanical resistance to rotation, temperature and aerodynamic load. All of these aspects mean that these structures are sufficiently charged statically and that, given the requirements of service life, the amplitudes of vibrations that they undergo must remain low. In addition, the aeroelastic coupling, ie the coupling between the dynamics of the bladed wheels and the fluid flow, conditions the vibratory stability of the structure.

As part of the design of a turbomachine, and taking into account the multidisciplinarity of stakeholders, the sizing process is iterative. Vibration sizing is done to avoid the presence critical resonances in the operating range of the machine. The assembly is validated at the end of the design cycle by a motor test on which the vibration amplitudes are measured. It sometimes appears high vibratory levels related to either resonances or vibratory instabilities. The development of the rotor concerned must then be redone which is particularly long and expensive.

The object of the present invention is to control, already during the design or development phase of the machine, the levels of vibratory response of the bladed wheels in a turbomachine structure comprising at least one mobile bladed wheel and one fixed bladed wheel traversed by a gas flow.

The invention thus aims at the treatment of the vibrations produced by the disturbances generated for example by one of the wheels in the gas flow on the other bladed wheel. It is aimed in a particular case disturbances generated on the gas flow by the wake of a fixed bladed wheel or an obstacle such as crank arms; these disturbances produce vibrations on the mobile downstream wheel.

The objective of the present invention is not limited to the control of vibration levels in a configuration where the bladed wheels are adjacent, it aims to control the vibratory responses on a bladed wheel for disturbances originating from upstream or downstream of the bladed wheel without being limited to adjacent wheels.

The invention also relates to aerodynamic vein-type excitation excitations generated by one or more samplings in the gas vein or by a distortion of the engine inlet sleeve, when the engine is a turbojet engine, in the event of crosswind or flight in incidence. These distortions are included in the term obstacle, afterwards.

Another object of the invention is the realization of a method that makes it possible to take the corrective measures that are required as early or as far upstream as possible in the process of designing and developing turbomachine bladed wheels.

It is particularly intended to reduce the synchronous vibration levels of the rotational speed of the rotor on a bladed wheel, mobile or fixed, generated by the relative scrolling of the wakes or the distortion induced by a bladed wheel adjacent or distant one or two stages, upstream or downstream.

• A - on définit une configuration initiale des aubes, en fonction des performances attendues de la turbomachine, avec les profils aérodynamiques individuels de p coupes empilées radialement entre le pied et la tête desdites aubes ;
• B - on calcule la réponse forcée synchrone y(ω) sur la première roue aubagée en fonction de l'effort f(ω) d'excitation harmonique produite par la deuxième roue aubagée ou l'obstacle à partir de la relation y(ω) = F(^τy_υ*f(ω)), où F est une fonction linéaire de la force aérodynamique généralisée ^τy_υ*f(ω) pour le mode υ considéré;
• C - on définit un coefficient (α<1) de réduction de la réponse forcée synchrone y(ω) ;
• D - on détermine pour chacune desdites p coupes empilées de l'une des deux roues une valeur de décalage géométrique tangentiel de l'axe d'empilage θ de manière à réduire le terme correspondant à la force aérodynamique généralisée |^τy*f(ω)|, le déphasage temporel ϕ de la pression d'excitation f(ω) étant relié au décalage géométrique tangentiel par la relation θ= N_excit *ϕ où N_excit est le nombre de sources excitatrices; l'ensemble des p coupes avec les décalages tangentiels définit ainsi une nouvelle configuration des aubes de la dite une des deux roues.
• E - on calcule la réponse forcée synchrone y (ω) sur la première roue aubagée ;
• F - si | y'(ω) | > α* | y(ω) on reprend le calcul en D avec de nouvelles valeurs de décalage géométrique tangentiel à appliquer sur l'axe d'empilage.
• G - si |y'(ω)| < α* |y(ω)|, on applique la nouvelle configuration à au moins une partie, et plus particulièrement à l'ensemble des aubes de ladite une des deux roues.

According to the invention, the method for reducing vibratory levels that may occur in a turbomachine comprising at least a first bladed wheel and a second bladed wheel, when the two wheels are in relative motion relative to each other around an axis of rotation and traversed by a gaseous fluid, due to disturbances of aerodynamic origin produced by the second bladed wheel or an obstacle on the first bladed wheel, is characterized in that it comprises the following steps when of the design of said two bladed wheels:

• A - an initial configuration of the blades is defined, according to the expected performance of the turbomachine, with the individual aerodynamic profiles of p cuts piled radially between the foot and the head of said vanes;
• B - the synchronous forced response y (ω) is calculated on the first bladed wheel as a function of the harmonic excitation effort f (ω) produced by the second bladed wheel or the obstacle from the relation y (ω) = F ( ^τ y _υ * f (ω)), where F is a linear function of the generalized aerodynamic force ^τ y _υ * f (ω) for the υ mode considered;
• C - a coefficient (α <1) of reduction of the synchronous forced response y (ω) is defined;
• D - for each of said p stacked sections of one of the two wheels is determined a tangential geometric offset value of the stacking axis θ so as to reduce the term corresponding to the generalized aerodynamic force | ^τ y * f (ω) |, the temporal phase shift φ of the excitation pressure f (ω) being connected to the tangential geometric offset by the relation θ = N _excit * φ where N _excit is the number of excitatory sources; the set of p cuts with tangential offsets thus defines a new configuration of the blades of said one of the two wheels.
• E - the synchronous forced response y (ω) is calculated on the first bladed wheel;
• F - if | y '(ω) | > α * | y (ω) the calculation in D is repeated with new tangential geometric offset values to be applied on the stacking axis.
• G - if | y '(ω) | <α * | y (ω) |, the new configuration is applied to at least one part, and more particularly to all the vanes of said one of the two wheels.

Preferably, the initial configuration on the fixed wheel is modified, whether this is the exciter wheel or the wheel undergoing excitation.

• La première roue est une roue aubagée mobile et la deuxième roue aubagée est une roue fixe, la roue aubagée mobile étant dans le sillage de la roue aubagée fixe.
• La première roue aubagée est une roue mobile et la deuxième roue aubagée est une roue fixe, la roue mobile étant en amont de la roue fixe.
• La première roue aubagée est une roue fixe et la deuxième roue aubagée est une roue mobile, la roue fixe étant dans le sillage de la roue mobile.
• La première roue aubagée est une roue fixe et la deuxième roue aubagée est une roue mobile, la roue fixe étant en amont de la roue mobile.

The invention allows, more particularly, the treatment of different cases:

• The first wheel is a moving bladed wheel and the second bladed wheel is a fixed wheel, the bladed wheel being in the wake of the fixed bladed wheel.
• The first bladed wheel is a moving wheel and the second bladed wheel is a fixed wheel, the moving wheel being upstream of the fixed wheel.
• The first bladed wheel is a fixed wheel and the second bladed wheel is a moving wheel, the fixed wheel being in the wake of the moving wheel.
• The first bladed wheel is a fixed wheel and the second bladed wheel is a moving wheel, the fixed wheel being upstream of the moving wheel.

Où

• Le signe Σ signifie que la réponse forcée y(ω) est la somme des réponses forcées de chacun des modes propres υ à la pulsation ω. La réponse forcée pour un mode propre déterminé est donnée par la relation entre crochets. La somme prend en compte l'ensemble des n modes propres υ pris en considération et qu'il s'agit de traiter, c'est à dire du mode propre υ=1 au mode propre υ = n.
• y_υ correspond à la déformée modale du mode υ sous l'hypothèse d'une norme unité des vecteurs propres par rapport à la masse
• ^Ty_υ correspond à la transposée du vecteur précédent,
• ω_υ correspond à la pulsation du mode propre υ
• ω correspond à la pulsation de l'excitation
• j²= -1
• β_υ correspond à l'amortissement modal généralisé pour le mode propre υ ...
• et f(ω) est la force d'excitation harmonique ; elle même de la forme f*cos(ω*t + ϕ) avec t le temps et ϕ le déphasage temporel.

The invention results from the theoretical analysis of vibratory phenomena. We show that the forced response y (ω), of a linear structure subjected to a harmonic excitation force f (ω), is linked to the latter by a relation which can be formulated with complex terms in the way expressed here. below under the assumption of a standard unit of the eigenvectors with respect to the mass: $$\mathrm{there}\left(\mathrm{\omega }\right)\mathrm{=}\mathrm{F}\left({}^{\mathrm{\tau }}{\mathrm{there}}_{\mathrm{\upsilon }\mathrm{*}}\mathrm{f}\left(\mathrm{\omega }\right)\right)\mathrm{=}{\displaystyle \underset{\mathrm{\upsilon }\mathrm{=}\mathrm{1}}{\overset{\mathrm{not}}{\mathrm{\Sigma }}}}\left[{\mathrm{there}}_{\mathrm{\upsilon }\mathrm{*}}{}^{\mathrm{T}}{\mathrm{there}}_{\mathrm{\upsilon }}\mathrm{/}\left({{\mathrm{\omega }}_{\mathrm{\upsilon }}}^{\mathrm{2}}-{\mathrm{<figure-callout\; id="2"\; label="\omega "\; filenames="imgf0002.png,imgf0003.png"\; state="\{\{state\}\}">\omega </figure-callout>}}^{\mathrm{2}}\mathrm{+}\mathrm{j}\mathrm{*}\mathrm{\omega }\mathrm{*}{\mathrm{\beta }}_{\mathrm{\upsilon }}\right)\right]\mathrm{*}\mathrm{f}\left(\mathrm{\omega }\right)$$

Or

• The sign Σ means that the forced response y (ω) is the sum of the forced responses of each of the eigen modes υ to the pulsation ω. The forced response for a specific eigenmode is given by the relationship between square brackets. The sum takes into account all the n eigen modes υ taken into consideration and that it is a question of treating, that is to say of the eigenmode υ = 1 to the eigenmode υ = n.
• y _υ corresponds to the modal deformed mode υ under the assumption of a norm unity of the eigenvectors with respect to the mass
• ^T y _υ corresponds to the transpose of the previous vector,
• ω _υ corresponds to the pulsation of the own mode υ
• ω corresponds to the pulsation of the excitation
• j ² = -1
• β _υ corresponds to the generalized modal damping for the eigen mode υ ...
• and f (ω) is the harmonic excitation force; it itself has the form f * cos (ω * t + φ) with t the time and φ the temporal phase shift.

In the case of an aerodynamic excitation applied on a bladed wheel, the term ^T y _υ * f (ω) represents the generalized aerodynamic force for the eigenmode υ.

The treatment of vibration phenomena comprises within the scope of the invention the implementation of means for reducing the modulus | y (ω) |.

While to minimize the module | y (ω) | of the forced response subjected to the excitation force f (ω), it is usually sought to increase the factor β _υ related to damping for the eigenmode υ, in accordance with the present invention, efforts have been made to reduction of the modulus of the term corresponding to the generalized aerodynamic force of each of the eigen modes υ.

A procedure to achieve this is to change the stacking axis of the studied blades in the direction tangential to the axis of rotation. The profile of the blade of a blade is geometrically defined from the profiles of each of the parallel sections made between the root of the blade and its top. The sections thus form a stack along a curve that is called the stacking axis. The profiles are determined aeromechanically.

It has been assumed that for a given section a change in the tangential direction leaves the modules of unsteady pressures unchanged for small variations (for example, of the order of one degree for a wheel of 150 sectors: cf figure 10 )

• avec ϕ = déphasage temporel ;
• θ = déphasage géométrique ;
• N_excit = nombre d'aubes excitatrices.

This therefore makes it possible to directly connect the temporal phase φ of the pressures to the tangential distance θ relative to the stacking axis by cutting the blade. With the following relation one establishes the equivalence between the temporal phase shift on the pressures and the geometrical phase shift, ie the tangential displacement to be applied on the dawn $$\mathrm{\phi }\mathrm{=}\mathrm{\theta }\mathrm{*}{\mathrm{NOT}}_{\mathrm{excited}}$$

• with φ = temporal phase shift;
• θ = geometric phase shift;
• N _excit = number of exciter blades.

• La figure 1 représente de façon schématique une structure de turbomachine.
• Les figures 2 à 5 montrent différents cas qu'il est possible de traiter conformément à l'invention.
• La figure 6 montre une aube d'une roue aubagée fixe de configuration initiale.
• La figure 7 est un organigramme des différentes étapes de la méthode selon l'invention.
• La figure 8 montre la définition de l'angle θ de décalage tangentiel d'une coupe défini par rapport à l'axe de rotation
• La figure 9 montre une aube de roue aubagée fixe dont la configuration a été modifiée conformément à l'invention afin de réduire les niveaux vibratoires.
• La figure 10 est un graphique illustrant un exemple pour un profil d'aube des valeurs de l'angle de décalage tangentiel.

The procedure according to the invention is described in more detail below in relation to the figures in which:

• The figure 1 schematically represents a turbomachine structure.
• The Figures 2 to 5 show different cases that can be treated according to the invention.
• The figure 6 shows a dawn of a fixed bladed wheel of initial configuration.
• The figure 7 is a flowchart of the different steps of the method according to the invention.
• The figure 8 shows the definition of the tangential offset angle θ of a section defined with respect to the axis of rotation
• The figure 9 shows a fixed bladed wheel blade whose configuration has been modified in accordance with the invention to reduce vibration levels.
• The figure 10 is a graph illustrating an example for a blade profile of tangential offset angle values.

As we see on the figure 1 a turbomachine structure 1, here a compressor, comprises at least one bladed wheel 3 movable about an axis of rotation adjacent to at least one fixed bladed wheel 2 or 4. Generally the structure comprises a plurality of movable wheels separated by wheels fixed.

As has been reported above, the relative movement of one wheel relative to the other within an axial gas flow, represented by the arrow F is a source of disturbances. For example with reference to the figure 2 a first movable wheel 11 is influenced by a second fixed bladed wheel 12 while in its wake. This wake is the source of disturbances on the first moving wheel 11.

Other cases are possible within the scope of the invention; on the figure 3 a first movable bladed wheel 11 'is considered in its position upstream with respect to a second fixed wheel 12' and which undergoes the excitatory forces generated by the second downstream wheel 12 '.

In the case of figure 4 the disturbances generated on a first fixed bladed wheel 21 are considered by the gas flow passing through an upstream moving bladed wheel 22.

In the case of figure 5 , the disturbances generated on a first fixed wheel 21 'by the gas flow passing through a second downstream bladed wheel 22' are considered.

Other cases are covered by the present invention, it is not limited to adjacent wheels.

The profile of a blade and its blade in particular is generally determined by a plurality of cuts made in the radial direction between the foot and the top. The figure 6 shows a fixed blade 30 of a stationary turbomachine stage with a foot 31 and its platform, a top 32 and its platform, and in between, a blade 33 swept by the gas flow. The blade 33 in position in the turbomachine is radially oriented relative to the axis of the latter. The blade is geometrically defined by the individual profile of a plurality of sections C ₁ , C ₂ , C ₃ ,... C _p (p being of the order of 20) by planes p1, p2, ... pp tangents to this radial direction. For a moving wheel the profile of the blade swept by the gas flow is defined in the same way by cuts made in the tangent planes.

According to the invention, the module of the forced response y (ω) of the blades of a first bladed wheel is reduced by searching for an adequate distribution of the components of the pressures to minimize the modulus of the generalized aerodynamic force associated with each of the eigen modes υ . As it follows from the formula (1) reported above, the generalized aerodynamic force associated with an eigenmode is a multiplying factor that appears in each of the terms of the sum Σ.

It should be noted that it does not necessarily change the dawn excited. It suffices to act on one of the vanes either forming the excitation source or being excited by the excitation source.

The procedure is developed below in relation to the organization chart of the figure 7

The first two steps are to define the specifications in terms of aerodynamic performance of the structure comprising the two bladed wheels, and then to calculate the initial configuration of the bladed wheels. This configuration includes the profiles of sections c ₁ ,... C _p and their stacking. It is generally carried out by aerodynamic iterations as is known to those skilled in the art.

• L'excitation est déterminée à l'aide calcul aérodynamique instationnaire,
• Un calcul de réponse forcée aéroélastique (définie par la relation (1)) est ensuite réalisé afin de déterminer les niveaux vibratoires ;
• La criticité de ces niveaux vibratoires est déterminée à l'aide d'un diagramme de Haig. Ce diagramme défini pour un matériau donné permet de définir pour une contrainte statique donnée la contrainte dynamique admissible pour avoir une durée de vie infinie en vibratoire.

Step 3: calculate the aeroelastic forced response y (ω) on the vane with the initial configuration excited with a synchronous aerodynamic f (ω) excitation:

• The excitation is determined using unsteady aerodynamic calculation,
• A computation of aeroelastic forced response (defined by the relation (1)) is then carried out in order to determine the vibratory levels;
• The criticality of these vibratory levels is determined using a Haig diagram. This diagram defined for a given material makes it possible to define for a given static stress the admissible dynamic stress to have an infinite lifetime in vibratory.

If the predicted vibratory levels (or measured in test) are important compared to the experiment, we define a target α * | y (ω) | (with 0 <α <1) in terms of maximum vibration level.

It must be ensured that alpha is the smallest possible value given the manufacturing tolerances.

Step 4: The procedure according to the invention is applied with the maximum vibratory level above as target.

The modulus of the aeroelastic forced response is minimized for a given mode knowing that it can be extended to any mode.

The method consists in determining the geometric offset θ, illustrated on the figure 8 applied on the tangential stacking axis so as to minimize the vibratory response due to the disturbance, such as the wake. We adopt a tangential offset setting to be applied to the blade profile to be modified. On the figure 8 we took over the blade 30 of the figure 6 , and the calculation performed on the section c2. We determine the value of θ which leads to angularly shift the cut in c'2.

For this, spline / poles or any discrete bases or chosen to project the stacking law are used for example.
The optimization method can be any. As an example, we quote some classical methods: gradient method, so-called "simulated annealing" method, genetic method ... (The quantity to be minimized is the modulus | ^T y _υ * f (ω) | or the sum modules in the case of multimode optimization).

Step 5: Perform a calculation of aeroelastic forced response y '(ω) on the modified blade to verify that the target in terms of maximum vibration level is reached. If this is not the case, a new profile definition is defined.

Step 6: once the target has been reached, it is verified that the aerodynamic performances are preserved by modifying the stacking axis of the blade concerned.

Step 7: the new definition of vane is retained; it meets the aerodynamic criteria in terms of performance and the mechanical criteria in terms of vibration levels.

The figure 9 shows an example of aspect that takes the dawn 30 of the figure 6 after application of the method of the invention. The cuts c1, c2 ... cp are not aerodynamically modified. They have each undergone a tangential shift around the axis of the turbomachine.

We have shown on the figure 10 a graph showing an example of an optimized blade profile; each point represents the value of the angle θ for each of the cuts C ₁ to C _p over the entire height of the blade of the blade. It can be seen that this value remains relatively low, lower in this example than 1 degree with respect to the position corresponding to the initial configuration.

Insofar as the correction values are greater than the blade manufacturing tolerances, there is a means for reducing the vibration levels without adding mass or modifying both the aerodynamic performance of the turbomachine and the technological interfaces of the blades. .

We reduce the levels generated by wakes: wake of rectifier / distributor or mobile bladed wheel trail; as previously stated, the levels generated by aerodynamic vein distortions generated by one or more samplings in the gas vein or by distortion of the engine inlet sleeve. We do not take into account other types of excitation. Although it is aimed at the rectifier / distributor wheels and the moving wheels, it acts preferably on the excitation source which is a bladed stator / distributor wheel.

Claims (7)

Process for reducing vibratory levels that may occur in a turbomachine (1) comprising at least a first bladed wheel (11; 11 ';21;21') and a second bladed wheel (12; 12 ';22;22') when the two wheels are in relative motion relative to each other about an axis of rotation and traversed by a gaseous fluid, due to aerodynamic disturbances produced by the second bladed wheel or an obstacle on the first bladed wheel, characterized in that it comprises the following steps when designing said two bladed wheels: A - an initial configuration of the blades is defined, according to the expected performances of the turbomachine, with the individual aerodynamic profiles of p cuts (c1, c2, ..cp) stacked radially between the foot and the head of said blades; B - the synchronous forced response y (ω) is calculated on the first bladed wheel as a function of the harmonic excitation effort f (ω) produced by the second bladed wheel or the obstacle from the relation y (ω) = F ( ^τ Y _υ * f (ω)), where F is a linear function of the generalized aerodynamic force ^τ Y _υ * f (ω) for the eigen mode υ considered; C - a coefficient (α <1) of reduction of the synchronous forced response y (ω) is defined; D - for each of said p sections (c1 c2, ... cp) stacked of one of the two wheels, a tangential geometric offset value θ is determined so as to reduce the term corresponding to the generalized aerodynamic force associated with the eigenmode υ. | ^τ y * f (ω) |, the temporal phase shift φ of the excitation pressure f (ω) being connected to the tangential geometric offset by the relation θ = N _excit * φ where N _excit is the number of excitatory sources; the set of p cuts with the tangential offsets thus defines a new configuration of the blades of said one of the two wheels. E - the synchronous forced response y '(ω) is calculated on the first bladed wheel; F - if | y '(ω) 1> α * | y (ω) |, the D calculation is repeated with new tangential geometric offset values. G - if 1 y '(ω) <α * | y (ω) |, the new configuration is applied to at least a portion of the blades of said one of the two wheels. Method according to the preceding claim according to $$\mathrm{there}\left(\mathrm{\omega }\right)\mathrm{=}\mathrm{F}\left({}^{\mathrm{\tau }}{\mathrm{there}}_{\mathrm{\upsilon }\mathrm{*}}\mathrm{f}\left(\mathrm{\omega }\right)\right)\mathrm{=}{\displaystyle \underset{\mathrm{\upsilon }\mathrm{=}\mathrm{1}}{\overset{\mathrm{not}}{\mathrm{\Sigma }}}}\left[{\mathrm{there}}_{\mathrm{\upsilon }\mathrm{*}}{}^{\mathrm{T}}{\mathrm{there}}_{\mathrm{\upsilon }*}1\mathrm{/}\left({{\mathrm{\omega }}_{\mathrm{\upsilon }}}^{\mathrm{2}}-{\mathrm{\omega }}^{\mathrm{2}}\mathrm{+}\mathrm{j}\mathrm{*}\mathrm{\omega }\mathrm{*}{\mathrm{\beta }}_{\mathrm{\upsilon }}\right)\right]\mathrm{*}\mathrm{f}\left(\mathrm{\omega }\right)$$

or The sign Σ means that the forced response y (ω) is the sum of the forced responses of each of the eigen modes υ to the pulsation ω, y _υ corresponds to the modal deformed mode υ under the assumption of a standard unit of the eigenvectors with respect to the mass ^T y _υ corresponds to the transpose of the previous vector, ω _υ corresponds to the pulsation associated with the mode υ, ω corresponds to the pulsation of the excitation, j ² = -1, β _υ corresponds to the generalized modal damping for the mode, and f (ω) is the harmonic excitation force; it itself of the form f * cos (ω * t) + φ) with t the time and φ the temporal phase shift. Method according to one of the preceding claims, wherein said one of the two wheels (12, 12 '; 22; 22') is a fixed bladed wheel. Method according to one of the preceding claims wherein the first bladed wheel (11) is a moving wheel and the second bladed wheel (12) is a fixed wheel, the bladed wheel being in the wake of the fixed bladed wheel. Method according to one of claims 1 and 2 wherein the first bladed wheel (11 ') is a moving wheel and the second bladed wheel (12') is a fixed wheel, the impeller being upstream of the fixed wheel. Method according to one of claims 1 and 2 wherein the first bladed wheel (21) is a fixed wheel and the second bladed wheel (22) is a moving wheel, the fixed wheel being in the wake of the moving wheel. Method according to one of claims 1 and 2 wherein the first bladed wheel (21 ') is a fixed wheel and the second bladed wheel (22') is a moving wheel, the fixed wheel being upstream of the moving wheel.

Images