WO2016055744A1

WO2016055744A1 - Method for modeling a blade of unducted propeller

Info

Publication number: WO2016055744A1
Application number: PCT/FR2015/052715
Authority: WO
Inventors: Cyril VERBRUGGE; Clément Marcel Maurice DEJEU; Anthony Pascal Eloi LOUET; Jonathan Evert VLASTUIN
Original assignee: Snecma
Priority date: 2014-10-08
Filing date: 2015-10-08
Publication date: 2016-04-14
Also published as: FR3027132A1; FR3027132B1

Abstract

The present invention relates to a method for modeling at least one portion of a blade (2) of a non-ducted propeller (1), wherein the blade portion (2) is offset (3). The method is characterized in that it comprises the implementation, by data processing means (11) of a device (10), of the steps of: (a) Parametrizing at least one auxiliary curve representing the value of a deformation parameter (x₀, Y_max, dy_max) according to a section height in the blade (2), wherein said parametrization is implemented according to at least one additional parameter, (b) Parametrizing a main curve representing a deformation of said blade (2) characterizing the offset (3), according to a position along a section at a given height in the blade (2), wherein said parametrization is implemented according to at least the deformation parameter (x₀, y_max, dy_max) and said section height in the blade (2), (c) Optimizing at least one of the additional parameters; (d) Plotting the values of the optimized parameters on one interface (13) of said device (10).

Description

Method for modeling a blade of a non-faired propeller

GENERAL TECHNICAL FIELD The present invention relates to computer-aided design.

More specifically, it relates to a method of modeling a propeller blade. STATE OF THE ART

"Unfilled" fan motors (or "Propfan" or "Open rotor" type turboprop engines) are a type of turbomachine whose fan is fixed outside the casing, unlike conventional turbojet engines (of the "Turbofan" type) in which the fan is streamlined.

In particular, the "Contra-Rotating Open Rotor" (CROR), represented by FIG. 1, is known which is equipped with two propellers rotating in opposite directions. It is of great interest because of its particularly high propulsive performance.

The purpose of this type of engine is to keep the speed and performance of a turbojet engine while maintaining fuel consumption similar to that of a turboprop engine. The fact that the fan is no longer faired makes it possible to increase the diameter and the flow of air useful to the thrust.

However, the absence of fairing causes problems of compliance with specifications. In particular in terms of acoustics since this type of engine generates more noise than a conventional engine. Indeed, the production of traction on each propeller blade depends on the presence of a distribution of circulation on the wingspan of the propellers. And this circulation escapes naturally at the head of the blade (instead of being channeled by the casing), creating a tourbillon called "marginal". The interaction of this marginal swirl of upstream blade head on the rotating surfaces of the downstream propeller poses a real challenge in terms of acoustics, in that the loud noise generated is not blocked by any casing.

The current standards impose a maximum threshold of noise in near-ground zones, that is to say during take-off and approach, that the current geometries do not allow to reach.

It would be desirable to improve these geometries, particularly at the heads of the blades, so as to reduce the noise generated without significantly impacting the efficiency of the engine or its consumption.

Numerous computer tools for modeling blades or other aeronautical parts are known for this purpose, which make it possible to help design these parts by automatically optimizing some of their characteristics. The principle is to determine an aeromechanical geometrical optimum of the laws of the blade, in other words of one or more curves describing the value of a physical quantity (such as the yield, the pressure rise, the capacity of flow or the pumping margin) along a section or height of the blade, in a given environment, by performing a large number of simulation calculations.

However, the same methods are now used to draw the ducted blowers as the unducted propellers, that is to say the modeling of 2D profiles which are subsequently wound on current lines (in respect of the angles of the ducts). profile) and stacked according to a chosen and optimized stacking law.

Such solutions have proved suitable for many physical quantities of unducted propellers, but it remains very difficult to obtain a significant improvement in noise levels.

Alternatively, it would be possible to use mesh deformation algorithms. Such methods are still considered because they offer a lot of advantages in terms of surface cleanliness and ease of drawing. However, they still require a lot of development work before being used in industrial design

It would therefore be desirable to find an innovative method of modeling a non-faired propeller that allows a significant improvement in their aero-acoustic performance while being economical in terms of use of computing resources.

PRESENTATION OF THE INVENTION According to a first aspect, the present invention proposes a method of modeling at least part of a blade of a non-faired propeller, the blade portion having an offset, the method being characterized in that it comprises the implementation, by data processing means of an equipment, of steps of:

(a) parametrizing at least one auxiliary curve of at least class C ¹ representing the value of a deformation parameter as a function of a cutting height in the blade, the auxiliary curve being defined by at least a first and a second extreme control point defining the extent of said blade height,

the parameterization being implemented according to at least one complementary parameter, according to which the ordinate of the second extremal point of the auxiliary curve is expressed;

(b) Parameterization of a main curve of at least class

C ¹ representing a deformation of said blade characterizing the offset, as a function of a position along a section at a given height in the blade, the main curve being defined by at least a first and a second extremal control point defining the extent of said cut of the blade, the parameterization being implemented according to at least the deformation parameter and said height of the section in the blade, according to which the ordinate of the second extremal point of the main curve is expressed;

(c) optimizing at least one of the complementary parameters;

(d) Restitution on an interface of said equipment of the values of the optimized parameters. According to other advantageous and nonlimiting features:

The inclination of the tangent to the auxiliary curve at the second extremal point is also expressed as a function of the at least one complementary parameter;

Said auxiliary curve passes successively through the first extremal control point, a central control point and the second extremal control point, the abscissa of the central control point being also expressed as a function of the at least one complementary parameter;

Said auxiliary curve comprises a non-uniform rational B-spline (NURBS) extending between the central control point and the second extremal point;

• at least one intermediate control point of the auxiliary curve is located between the central control point and the second extremal control point, the NURBS being defined by the central control point, the intermediate control points and the second control point extremal;

· The ordinate of the central control point and each intermediate control point of the auxiliary curve is equal to zero;

Said auxiliary curve is zero between the first extremal control point and the central control point;

• the tangent to the auxiliary curve at the central control point is horizontal; The parameterization of the main curve of step (b) is implemented according to a plurality of deformation parameters, an auxiliary curve being parameterized in step (a) for each deformation parameter;

Said main curve successively passes through the first extremal control point, a central control point and the second extreme control point of the main curve, the parameterization of the main curve of step (b) being implemented according to a first deformation parameter defining the abscissa of the central control point of the main curve, a second deformation parameter defining the ordinate of the second extremal point of the main curve, and a third deformation parameter defining the inclination of the tangent to the main curve at the second extremal control point of the main curve;

The complementary parameters comprise a relative height of beginning of deformation (h ₀ ) and / or a maximum offset (d _max ) at the end of the blade, the at least one main curve being associated with a relative height h of cutting in the blade, h G [h ₀ , 1];

A plurality of main curves corresponding to sections at different heights in the blade is parameterized in step (b).

The optimized values determined in step (c) are the values of the parameters for which the intensity of a marginal vortex generated by the blade is minimal. According to a second and a third aspect, the invention relates to a method of manufacturing a blade of a non-faired propeller, the blade having an offset, the method comprising steps of:

- Implementation of the method according to the first aspect so as to model at least a portion of the blade;

- Manufacture of said blade according to the modeling of the at least a portion of the blade obtained; As well as a non-faired propeller comprising a plurality of blades obtained via the method according to the second aspect.

According to a fourth aspect, the invention relates to equipment for modeling at least a portion of a blade of a non-faired propeller, the blade portion having an offset, characterized in that it comprises means for processing Data configured to implement:

A parametrization module of at least one auxiliary curve of at least C ^{1 class} representing the value of a deformation parameter as a function of a cutting height in the blade, the auxiliary curve being defined by at least a first and a second extreme control point defining the extent of said height of the blade, the parameterization being implemented according to at least one complementary parameter, according to which the ordinate of the second extreme point of the auxiliary curve is expressed;

a parametrization module of a main curve of at least class C ¹ representing a deformation of said blade characterizing the offset, as a function of a position along a section at a given height in the blade, the main curve being defined by at least a first and a second extremal control point defining the extent of said section of the blade,

the parameterization being implemented according to at least the deformation parameter and said height of the section in the blade, according to which the ordinate of the second extremal point of the main curve is expressed;

A module for determining optimized values of the deformation parameter or parameters;

- A rendering module on an interface of said equipment of the determined values. According to a fifth and a sixth aspect, the invention relates respectively to a computer program product comprising code instructions for the execution of a method according to the first aspect of the invention for modeling at least a part of a blade of a non-faired propeller; and computer-readable storage means on which a computer program product comprises code instructions for executing a method according to the first aspect of the invention for modeling at least a portion of a blade of a non-faired propeller.

PRESENTATION OF FIGURES

Other features and advantages of the present invention will appear on reading the following description of a preferred embodiment. This description will be given with reference to the appended drawings in which:

FIG. 1 previously described represents an example of a counter-rotating open rotor on the blades of which the method according to the invention is implemented;

- Figures 2a-2b are two views of the end of a blade of a non-faired propeller of such a rotor;

FIG. 3 represents a system for implementing the method according to the invention;

FIG. 4 illustrates the implementation of the method on a blade of a non-ducted propeller;

FIG. 5 is an example of a graph showing an auxiliary curve obtained by virtue of an embodiment of the method according to the invention;

FIGS. 6a-6b make it possible to compare the aero-acoustic performances of a known blade and of a modeled blade by means of the method according to the invention. DETAILED DESCRIPTION

Blade Offset In FIG. 1, the open-rotor shown comprises a turbine 4, and two non-keeled propellers 1. These propellers 1 are, in this example, counter-rotating. Each propeller 1 has a plurality of blades 2 extending radially from the rotor housing.

Figures 2a and 2b show a detail of the head of a blade 2. This head is equipped with an offset 3, in other words "Winglet" type system. It is a strong curvature, which sometimes takes the form of an orthogonal fin (Winglet winglet case). The advantage of such a system is to draw at the head of the blade 2 unloaded profiles (Cz = 0) or negatively charged by inverting the upper and lower surfaces.

With such an offset 3, it is possible to hope for a better dissipation of the marginal vortices generated at the end of the blade 2. However, it has not been possible so far to obtain a blade head geometry 2 that achieves sufficient clearance for this purpose. reduce noise. The present method is designed for the specific modeling of at least a portion of a blade 2 (in particular its head) of a non-faired propeller 1, the blade portion 2 having a tangential offset 3. The idea is to for this, define the offset 3 as a deformation of the "skeleton" of the blade 2 with respect to a reference plane, this advantageously from certain very specific parameters which will be described later.

The skeleton is, in a section (i.e. a cross-section) of the blade 2, a median line extending from a leading edge BA to a trailing edge BF. FIG. 4 represents a same blade 2 in two configurations: initial (that is to say without offset 3, the skeleton takes the form of a straight line) and deformed (that is to say with a displacement of the trailing edge so as to give a curved shape to the skeleton characterizing the offset 3). This figure 4 will be described in more detail further. The skeleton should not be confused with the rope, which also connects the leading and trailing edges in a section, but passing through the envelope of the blade 2.

Orthogonally to a section, we find the "height" of the blade 2, that is to say the position along a longitudinal axis. Each section of the blade 2 is at a given height in the blade 2. In the height, the skeleton is a median line that extends from a proximal edge of the blade (at the platform) to a distal edge ( at the summit level). It is important not to confuse the offset 3 with a "hump", that is to say a possible widening of the blade in its central part. Considering a hump as a deformation, it is in the axis of the skeleton of the blade 2 (the leading edge and the trailing edge are spaced apart), whereas the offset 3 is a deformation in an orthogonal direction. to the axis of the skeleton.

The blade portion 2 is modeled, during its design, via computer equipment 10 of the type shown in FIG. 3. It comprises data processing means 11 (one or more processors), storage means data 12 (for example one or more hard disks), interface means 13 (composed of input means such as a keyboard and a mouse or a touch interface, and playback means such as a screen for displaying results). Advantageously, the equipment 10 is a supercomputer, but it will be understood that an implementation on various platforms is quite possible.

Even if the dissipation of the vortices is the main criterion chosen to be optimized during the modeling of the blade, it will be understood that other criteria can be chosen. By way of example, it will be possible to try to maximize mechanical properties such as resistance to mechanical stresses, frequency responses of the blade, blade displacements, aerodynamic properties such as the yield, pressure rise, flow capacity or pumping margin, etc.

parameterization

It is necessary to parameterize the skeleton deformation law that one seeks to optimize, that is to say to make it a function of N input parameters. The optimization then consists in varying (generally randomly) these different parameters under stress, until they determine their optimal values for the predetermined criterion of dissipation of the vortices. A "smoothed" curve is then obtained by interpolation from the determined crossing points.

The number of necessary calculations is then directly linked (linearly or even exponentially) to the number of input parameters of the problem.

Many methods of parametrization of a law exist, and one can distinguish in particular two broad categories:

- Discrete model: the law is defined by the position of a plurality of points (in practice 5 to 10 for a law on the height, and 50 to 200 for a section), moved one by one during the optimization;

- Parametric model: the law is defined via mathematical curves known in the literature, such as Bézier curves or NURBS curves (non-uniform rational B-splines).

It is desirable to use a large number of parameters to improve all the quality of the shape of a law (this is a major issue for blade designs), but such an approach is quickly limited by the capacity and the resources of the current processors.

Even using expensive supercomputers, the time required to model a single law is substantial. Another problem is that in the presence of a large number of parameters of the problems appear: the determined laws indeed have too many crossing points to respect, and the first curves obtained are abnormally "wavy" (c ') is what is called the Runge phenomenon) and unusable in the state. They need to be reworked until they are smooth enough, which further increases the time needed to get the results

As will be seen, the present method allows excellent modeling quality of a blade head 2 which allows with a surprisingly small number of parameters to obtain a significant improvement in the dissipation of marginal vortices (and therefore the level of noise).

A close method is described in the patent application FR1357449.

In a step (a), implemented by the data processing means 11 under the control of an operator, at least one auxiliary curve (as opposed to a "main" curve which will be described shortly after) is parameterized. the value of a deformation parameter xo, ymax, dy _max (there may be more than the three that will be described) as a function of a cutting height in the blade 2. By "cutting" is also meant "part "cutting", that is to say all or part of the space extending from the leading edge BA to the trailing edge BF. Advantageously, there are several deformation parameters x ₀ , y _ma x, _max dy (we will see further examples) and an auxiliary curve is parameterized for each of them.

The deformation parameter (s) x ₀ , y _ma x, dy _max will be used to parameterize the main curve, which in turn represents the value of a deformation of the blade 2 (characterizing as explained the offset 3) in function of a position along a section of the blade 2 of the non-faired propeller 1, at a given height in the blade 2.

In other words, a double parametrization is carried out via parameterized curves, the parameters used for parametrization main (the deformation parameters x ₀ , y _ma x, dy _max ) being themselves parameterized by complementary parameters such as a relative height of deformation start h ₀ and / or a maximum offset d _max at the end of deformation the blade 2 (as will be seen, preferably three complementary parameters are used).

The use of a double level of curves is an important difference with the parameterization proposed in the application FR1357449, in which a deformation parameter is either a constant or is directly expressed as a function of the height h and one or more of the complementary parameters by a fixed formula. For example it is proposed to use a coefficient ί ^ - ^ q _U i varies quadratically between 0 and

\ 1-

1 when h goes through the interval [h ₀ , 1].

Compared to this known method, the present method allows a greater variety of profiles and a greater flexibility thanks to the intermediate parameterization, while simplifying the model. It will be understood that it is quite possible that one or more of the deformation parameters x ₀ , y _ma x and dy _max are moving parameters conforming to the prior art, that is to say that they are not expressed via an auxiliary curve.

In general, the main and auxiliary curves are here of the same type, and in the remainder of this description, the example of an auxiliary curve will essentially be described. The skilled person will transpose the teaching for the main curve.

The position along the height of the blade 2 is preferably expressed as a function of the skeleton length (in abscissa), and more precisely the "normalized" distance, that is to say, expressed between 0 and 1 when the blade 2 is passed from the proximal end to the distal end (from the platform to the top). This corresponds in other words to the coordinate h that would have a point of the skeleton in an orthonormal coordinate system in which the proximal end would have (0,0) as coordinates, and the distal end (1, 0). For example, a cut point associated with a standard skeleton length of "0.5" is on the skeleton mediator. Note that since the auxiliary curve can extend over only a part (continuous) of the height of the blade 2, the associated function is defined on a subinterval of [0, 1].

It will be understood, however, that the invention is in no way limited to the expression of an auxiliary curve representing the value of a deformation parameter as a function of a skeleton length, and that other references are possible (for example length of rope).

Each auxiliary curve representing the value of a deformation parameter x ₀ , y, dy _max must be understood as the modeling of the law this parameter, ie a law of distribution. The main curve (representing this time the value of a deformation) can be understood as the modeling of the deformation law, a strain law having the same format as the distribution law where h is replaced by x (the coordinate that would have, for a given section, a point of the skeleton in an orthonormal coordinate system in which the point BA would have (0,0) as coordinates, and the point BF (1, 0)), and the deformation parameter x ₀ , y _ma x, dymax by y (the value of the deformation).

These curves are at least C ¹ regularity of class, that is to say that they correspond to a continuous function and at least 1 ^ere continuous derivative on its definition space (the blade height 2). We will see later the importance of this condition. In practice, each curve obtained is C ^∞ by pieces (indefinitely differentiable functions on each interval), with continuity of the curve and the derivative at the connections (the intermediate control points). It will be understood that these are minimum conditions and that the curve can be, for example, C ⁿ over its entire definition space. From here will be described the example of an auxiliary curve, but it will be understood that the main curve is similar and may have any combination of the advantageous features that will be described for the auxiliary curve. An auxiliary curve is defined thanks to its control points. In a known manner, two extreme user control points PCE1 and PCE ₂ are fixed and define the extent of the section (ie the field of definition of the curve). Each auxiliary curve further preferably comprises at least one central user control point PCC disposed between these two extreme points PCE1 and PCE ₂ .

The present central point PCC is an "explicit" control point, since the auxiliary curve passes through it. Indeed, the latter preferably comprises two parts connected at said central point.

Alternatively, the auxiliary curve may be for example a curve for example of Bezier and include only control points "implicit" (by which it does not pass as will be seen later).

More particularly, the first part (which extends from the first extreme control point PCEi to a central control point PCC) preferably corresponds to the null function. In other words, the first extreme control point PCEi and the central control point PCC have a zero ordinate, just like any point on the auxiliary curve between them.

The second part of the auxiliary curve (which extends from the central control point PCC to the second extremal control point PCE ₂ ) is itself a parametric curve, preferably a non-uniform rational B-spline (NURBS) and / or a polynomial curve, in particular a so-called Bezier curve. The latter have the characteristic of being polynomial & NURBS type. They are defined as combinations of N + 1 elementary polynomials called Bernstein Polynomials: we define a Bézier curve by the set of points Σf _{= 0} £ f (t) - Pi, t G [0,1], the Bf (t) = ( ^N ) t ^N (1 - t) ^{N ~ 1} being the N + 1 Bernstein polynomials of degree N.

The points {Po, PI. .. PN} are called "implicit" control points of the curve and are the variables by which a law of a blade can be modeled by a Bezier curve (or another NURBS). These points are called "implicit" because a Bézier curve can be seen as the set of centroids of the N + 1 weighted control points of a weight equal to the value of the Bernstein polynomial associated with each control point. In other words, these points act as attractive localized weights the curve generally without it happening there (except the first and the last, respectively corresponding to t = 0 and t = 1, and some cases of alignment points).

In general, in the known modeling techniques of a law using a spline, the extreme control points Po and P _N of the curve used are fixed (they define the extent of the part of a part on which the modeling will be implemented), but the other points {Pi ... P _N- i} have mobile coordinates constituting the input parameters for the optimization algorithm. FIG. 5 represents an example of an auxiliary curve obtained by the present method (in this case for modeling the parameter y _ma x), with its user control points. In Figure 4 previously introduced appears a main curve. It will be noted that the curve represented by FIG. 5 has been arranged vertically to illustrate the fact that the deformation parameter x ₀ , y _max , model dy _max varies with the height of the blade 2. In other words, the "low""Of the figure represents the" bottom "of the blade 2, that is to say its proximal end, while the" top "of the figure represents the" top "of the blade 2, that is to say say its proximal end. The fact that the curve has been arranged in this direction to facilitate comprehension does not change the fact that the height h is the abscissa, and the value of the deformation parameter x ₀ , y _ma x, dy _max the ordinate.

In the following description we will take the preferred example in which the second part of the auxiliary curve is NURBS type (the auxiliary curve comprising a central control point PCC), but it will be understood that the invention is limited to no parameterized curve. In particular, each NURBS can be entirely determined by the user control points defining its extremities (in this case the central control point PCC and the second extremal control point PCE ₂ ). In other words, the parameters of the control points (in terms of coordinates, and derivatives) serve as boundary conditions for the calculation by the data processing means 1 1 of the spline equation, which can be chosen minimum degree sufficient to meet these boundary conditions. This corresponds to a situation in which "K = 0" (see below).

The parameter (s) defining the NURBS endpoints

PCC and PCE ₂ are selected from an abscissa of the point, an ordinate of the point, a tangent orientation to the curve at the point and two voltage coefficients each associated with a half-tangent to the curve at the point. It will be seen later which parameterization is proposed by the present invention.

The fact that the auxiliary curve is of at least class C ¹ requires the central point PCC to provide continuity even on the derivative (even tangent). On the other hand, the "length" of the two half-tangents can be different on both sides of the central point (the latter is in particular zero to the left of the central point PCE ₂ since all the derivatives of the null function are null), length that reflects the propensity of the curve on either side of the point to "stick" to the tangent. This is modeled by the "voltage coefficients" mentioned above.

Alternatively K≥ 1, that is to say that at least one intermediate control point PCI ,, i G l, K} is disposed between the central control point PCC and the second extreme control point PCE ₂ . The intermediate control points PCI ,, i G 1, K} are implicit points as described above, whose abscissa and / or the ordinate can serve as a parameter for the parameterization. This case will be particularly described below.

In any case, the second extremal point PCE ₂ is here the main moving point. In particular, at least the ordinate of the second extremal point PCE ₂ is a function of the complementary parameter or parameters. In the presence of a central control point PCC, its abscissa (or as will be seen later, that of any intermediate control points PCI ,, i G Œl, Kl) is advantageously dependent on the additional parameter or parameters.

Deformation parameters and user control points

Preferably, up to three complementary parameters are chosen from among the following to parameterize an auxiliary curve:

the abscissa of the central control point PCC of the auxiliary curve (in particular the relative height of the beginning of deformation h ₀ );

the ordinate of the second extremal point PCE ₂ of the auxiliary curve (for example the maximum offset d _max at the end of the blade 2, used mainly for the expression of the second deformation parameter y _max , see below); and

the inclination of the tangent to the curve at the second extremal point PCE ₂ of the auxiliary curve (in other words the derivative of the auxiliary curve at this point). Three complementary parameters alone make it possible to parameterize all the user control points defining an auxiliary curve, and to express a deformation parameter x ₀ , y _ma x, dy _max as a function of the height h. It should be noted that certain complementary parameters may be common to two auxiliary curves, in particular the parameter h ₀ . Assuming that three deformation parameters x ₀ , y _ma x, _max dy are used, up to nine complementary parameters can thus be used (and seven if we consider that h ₀ is common).

As explained, in a step (b), implemented by the data processing means 11 under the control of an operator, is then parameterized according to the deformation parameter or parameters x ₀ , y _max , dy _max themselves. parameterized, a main curve of at least class C ¹ representing the value of a deformation of the blade 2 (characterizing as explained the offset 3) as a function of a position along a section of the blade 2 of the non-faired propeller 1, at a given height in the pale 2.

The main curve is similar to an auxiliary curve, i.e. it is defined by at least a first and a second extremal control point defining the extent of said section of the blade 2, and advantageously passes through a central point of control.

By analogy with the three complementary parameters, the deformation parameters that can be expressed are:

the abscissa of a central control point of the main curve which is the first deformation parameter x ₀ ;

the ordinate of a second extremal point of the main curve which is the second deformation parameter y _max ; and

- the inclination of the tangent to the curve at a second extremal point of the main curve (in other words the derivative of the main curve at this point), which is the third deformation parameter dy _max .

These auxiliary curves make it possible to increase in a controlled manner the value of the deformation parameters as one rises in the blade 2, and very substantially increases the variety of the offsets 3 which can be modeled while keeping the advantages in terms of modeling quality and efficiency of the general parameterization.

For the precise case of the parameter xo, preferably the auxiliary curve expresses not xo but 1 - xo (because x ₀ has an inverse variation of the other deformation parameters going up along the blade 2).

In all cases, the control of the inclination of the tangent to the auxiliary curve at the second extremal point PCE ₂ is preferably via an intermediate control point as mentioned above (this implies that the second part of the curve is NURBS and there is at least one intermediate control point, ie K≥ 1). If there is more than one intermediate control point, this intermediate control point for controlling the tilt of the tangent is the K ^th PCIK intermediate control point, in other words the last intermediate control point. encountered by traversing the control points from the leading edge BA to the trailing edge BF.

In other words, in this preferred embodiment, step (a) consists of a parameterization of one, two or three auxiliary curves of class at least C ¹ each representing the value of a deformation parameter x ₀ , y _ma x, dy _max according to a cutting height in the blade 2, the auxiliary curve being defined by:

at. A first and a second extreme control point PCEi, PCE ₂ defining the extent of said height of the blade 2;

b. a central control point PCC, and at least one intermediate control point (in this case the "K ^eme ") PCIK _, arranged successively between the extreme points PCEi, PCE ₂ , the auxiliary curve passing through the central control point PCC (but in practice not through the PCIK intermediate checkpoint),

the parameterization being implemented according to a first complementary parameter defining the abscissa of the central control point PCC, a second complementary parameter defining the ordinate of the second extremal point PCE ₂ , and a third complementary parameter according to which (in particular in combination with the second complementary parameter) the abscissa of the PCIK intermediate control point is expressed. As seen in FIG. 5 previously introduced, the ordinate of the first extremal control point PCEi, of the central control point PCC and of each PCI intermediate control point, is advantageously chosen fixed and equal to zero. In other words, these K + 2 first control points are aligned and on the initial skeleton. Only the second extreme control point PCE ₂ departs from it.

And as explained above, the NURBS-type portion of the auxiliary curve does not pass through the PCI intermediate control points. This alignment does not create any angular points but on the contrary controls the progressivity of its curvature. As an additional condition (which is automatically the case when the first part of the curve, that is to say the interval (0, h ₀ ), in other words the section [PCEi - PCC], is the null function), the derivative of the curve is constrained as null (horizontal tangent) at the level of the first extremal control point PCEi and the central control point PCC, since the first two control points have the same ordinate equal to zero . In such a situation, the first complementary parameter h ₀ can be seen as the relative height of the beginning of deformation h ₀ : as long as h is less than h ₀ the skeleton is not deformed (since the curve is zero), and the deformation parameter x ₀ , y _ma x, modeled _max dy is non-zero in the interval [h ₀ , 1].

The intermediate control points PCI ,, iG l, K} and in particular the K ^th PCIK intermediate control point are "mobile" points, which in turn have a variable abscissa such that they are close to the second extremal control point. PCE ₂ when the inclination of the tangent increases, which digs the arch.

The abscissa of the K ^th PCIK intermediate control point is thus a function of the second and third complementary parameters, which makes it possible to control the orientation of the section [PCIK-PCE ₂ ], to which the curve is tangent by definition.

The abscissa h _K of the K ^th intermediate control point PCIK is in particular given by the formula

, ordinate PCE ₂ (second complementary parameter)

tangent tilt PCE ₂ (third additional parameter)

If K≥2, then at least one other (-7) intermediate control point exists between the central control point PCC and the K ^th point Intermediate Control PCIK-More precisely the one or ^more (i G

[1, ^ - 1]) PCI intermediate control points, are moving points whose abscissa h _t is a function of those (/, h _K ) of the central control point and the K ^th intermediate control point PCC, PCI _K.

These abscissas are preferably defined so that the mobile intermediate control points have regular gaps. The abscissa h _t of K-1 intermediate control points PCI, with i G H1, K - 1]) is thus given by the formula h ^^^ = h ₀ + i _K -) * ^ with (h _K ) the abscissa of the K ^th PCIK- intermediate control point

Thus, in general with K≥ 1 (case of FIG. 5), the coordinates of the 4 main points of an auxiliary curve are:

PCEi (0; 0) - derivative = 0

PCC (h ₀ ; 0) - derivative = 0

n ^ i second complementary parameter ~>

rUI | <(1;;;^' U)

third additional parameter

PCE2 (1; second complementary parameter) - derivative = third complementary parameter

Step (b) then preferably consists of a parametrization of at least one main curve of at least C ^{1 class} representing a deformation of said blade 2 characterizing the offset 3, as a function of a position along a cutting at a given height in the blade 2, the main curve being defined by:

at. A first and a second extremal control point defining the extent of said cut of the blade 2;

b. a central control point, and at least one intermediate control point (in this case the "K ^eme ") _, arranged successively between the extremal points, the main curve passing through the central control point (but in practice not by the intermediate point of control), the parameterization being implemented according to a first deformation parameter x ₀ defining the abscissa of the central control point of the main curve, a second deformation parameter y _max defining the ordinate of the second extremal point of the main curve, and a third deformation parameter dy _m ax according to which (in particular in combination with the second deformation parameter y _max ) the abscissa of the intermediate control point of the main curve is expressed.

Optimization and restitution

Each of the additional parameters may be a fixed parameter (for example input by the user) or a "variable" parameter, that is to say a parameter whose value will be able to be optimized.

According to a second step (b), the method thus comprises an optimization step by the data processing means 11 of at least one complementary parameter (and, if appropriate, at least one deformation parameter x ₀ , y _ma x, dy _max if the latter is a simple parameter which is not itself expressed via an auxiliary curve).

It will be understood that this optimization step (b) consists in determining the optimized values of the complementary parameters of one or more of the deformation parameters x ₀ , y _max , d _max and / or the direct determination of the optimized values of a or more of the deformation parameters x ₀ , y _max , dy _max if they are not a function of the height h and complementary parameters.

Many techniques for the implementation of this step (b) are known to those skilled in the art, and it is possible for example simply to vary pseudo-randomly the selected variable parameters while performing simulations to determine these optimized values (c 'is, say for which the chosen criterion, in particular the decrease of the marginal vortices, is maximized) of the parameters of the control points. The invention is however not limited to this possibility.

In a last step (c), the determined values of the complementary parameter (s) (or the values of the deformation parameters obtained as a function of the values of the complementary parameters and the height h of the section) are restored by the interface means. equipment 10 for exploitation, for example by displaying the modeling curve in which the parameters are set to these optimized values.

Alternatively, the interface means 13 can only display these numerical values.

tests

Tests were carried out on blades 2 thus modeled, so as to verify the possibility of being able, for a given blade, to substantially increase the dissipation of the marginal vortices.

FIGS. 6a and 6b show, respectively for a conventional blade and for a blade 2 whose offset 3 has been optimized thanks to the present method, the vorticity (in other words the intensity of the marginal vortex) downstream of the propeller non-faired 1 upstream of the open-rotor of Figure 1.

There is a decrease in the intensity of the order of 30% to 40% of the maximum vorticity. Note also that the beginning of the vortex is at a slightly lower radius for the new blade 2.

The only optimization of the tangential offset 3 thus clearly shows a significant modification of the swirling vane head physics, both in high speed (trajectory modification, centrifugation), and in low speed (significant reduction in the swirling intensity and pitch shifted primer). Manufacturing process and propeller

Once its modeled head, the blade 2 can be manufactured. Is thus proposed a method of manufacturing a blade 2 of a non-faired propeller 1, the blade 2 having an offset 3, the method comprising steps of:

- Manufacture of said blade 2 according to the modeling of the at least a portion of the blade 2 obtained.

A non-faired propeller 1 comprising a plurality of blades 2 thus produced can be obtained. Each of its blades therefore has the offset 3 to improve the dissipation of marginal vortices, and thus the reduction of noise levels, without reducing its performance.

Equipment

The equipment 10 (shown in FIG. 3) for implementing the method of modeling at least a portion of a blade 2 comprises data processing means 11 configured to implement:

A parametrization module of at least one auxiliary curve of at least class C ¹ representing the value of a deformation parameter x ₀ , y _ma x, dy _max as a function of a cutting height in the blade 2, the auxiliary curve being defined by at least a first and a second extreme control point PCEi, PCE ₂ defining the extent of said height of the blade 2;

the parameterization being implemented according to at least one additional parameter, according to which the ordinate of the second extremal point PCE ₂ of the auxiliary curve is expressed;

a parametrization module of a main curve of at least class C ¹ representing a deformation of said blade 2 characterizing the offset 3, as a function of a position along a section at a given height in the blade (2) , the main curve being defined by at least a first and a second extremal control point defining the extent of said section of the blade 2,

the parameterization being implemented according to at least the deformation parameter x ₀ , y _ma x, dy _max and said height of the section in the blade 2, according to which the ordinate of the second extreme point of the main curve is expressed;

A module for optimizing at least one of the complementary parameters;

A rendering module on an interface 13 of said equipment 10 of the values of the optimized parameters. Computer program product

According to other aspects, the invention relates to a computer program product comprising code instructions for the execution (on data processing means 11, in particular those of the equipment 10) of a method according to the first aspect of the invention modeling at least a portion of a blade 2 of a non-faired propeller 1, and storage means readable by a computer equipment (for example a memory 12 of this equipment 10) on which we find this product computer program.

Claims

A method of modeling at least a portion of a blade (2) of a non-ducted propeller (1), the blade portion (2) having an offset (3), the method being characterized in that it comprises the implementation, by data processing means (1 1) of an equipment (10), of steps of:

(a) parametrizing at least one auxiliary curve of at least class C ¹ representing the value of a deformation parameter (x ₀ , y _ma x, _max dy) as a function of a cutting height in the blade (2 ), the auxiliary curve being defined by at least a first and a second extreme control point (PCE1, PCE ₂ ) defining the extent of said height of the blade (2),

the parameterization being implemented according to at least one complementary parameter, according to which the ordinate of the second extremal point (PCE ₂ ) of the auxiliary curve is expressed;

(b) Parametrisation of a main curve of at least class C ¹ representing a deformation of said blade (2) characterizing the offset (3), as a function of a position along a section at a given height in the blade (2), the main curve being defined by at least a first and a second extremal control point defining the extent of said section of the blade (2),

the parameterization being implemented according to at least the deformation parameter (x ₀ , y _ma x, _max dy) and said height of the cut in the blade (2), according to which the ordinate of the second extremal point of the curve principal is expressed; (c) optimizing at least one of the complementary parameters;

(d) rendering on an interface (13) of said equipment (10) optimized parameter values.

2. Method according to claim 1, wherein the inclination of the tangent to the auxiliary curve at the second extremal point (PCE ₂ ) is also expressed as a function of the at least one complementary parameter.

3. Method according to one of claims 1 and 2, wherein said auxiliary curve successively passes through the first extremal control point (PCEi), a central control point (PCC) and the second extremal control point (PCE ₂ ). , the abscissa of the central control point (PCC) of the auxiliary curve being also expressed as a function of the at least one complementary parameter.

The method of claim 3, wherein said auxiliary curve comprises a non-uniform rational B-spline (NURBS) extending between the central control point (PCC) and the second extremal point (PCE ₂ ).

The method of claim 4, wherein at least one intermediate control point (PCI, i G 1, K 1, K 1) of the auxiliary curve is disposed between the central control point (PCC) and the second extreme control point (PCE ₂ ), the NURBS being defined by the central control point (PCC), the intermediate control points (PCI ,, i G II, Kl) and the second extremal control point (PCE ₂ ).

The method of claim 5, wherein the ordinate of the central control point (PCC) and each intermediate control point (PCI) of the auxiliary curve is zero.

7. Method according to one of claims 3 to 6, wherein said auxiliary curve is zero between the first extreme control point (PCEi) and the central control point (PCC).

The method according to one of claims 3 to 7, wherein the tangent to the auxiliary curve at the central control point (PCC) is horizontal.

9. Method according to one of claims 1 to 8, wherein the parameterization of the main curve of step (b) is implemented according to a plurality of deformation parameters (x ₀ , y _ma x, dy _max ) , an auxiliary curve being parameterized in step (a) for each deformation parameter (x ₀ , y _ma x, dy _max ).

10. The method of claim 9, wherein said main curve successively passes through the first extremal control point, a central control point and the second extremal control point of the main curve, the parameterization of the main curve of the step. (b) being implemented according to a first deformation parameter (x ₀ ) defining the abscissa of the central control point of the main curve, a second deformation parameter (y _ma x) defining the ordinate of the second extremal point of the main curve, and a third deformation parameter {dy _max ) defining the inclination of the tangent to the main curve at the second extreme control point of the main curve.

11. Method according to one of claims 1 to 10, wherein the complementary parameters comprise a relative height of beginning of deformation (h ₀ ) and / or a maximum offset (d _max ) at the end of the blade (2). the at least one main curve being associated with a relative height h of cutting in the blade (2), h G [h ₀ , 1].

12. Method according to one of claims 1 to 1 1, wherein a plurality of main curves corresponding to sections at different heights in the blade (2) is parameterized in step (b).

13. Method according to one of claims 1 to 12, wherein the optimized values determined in step (c) are the values of the complementary parameters for which the intensity of a marginal vortex generated by the blade (2) is minimal.

14. A method of manufacturing a blade (2) of a non-ducted propeller (1), the blade (2) having an offset (3), the method comprising steps of:

- Implementing the method according to one of claims 1 to 13 so as to model at least a portion of the blade (2); - Manufacture of said blade (2) according to the modeling of the at least a portion of the blade (2) obtained.

15. Non-faired propeller (1) comprising a plurality of blades (2) obtained via the process according to claim 14.

16. Equipment (10) for modeling at least a portion of a blade (2) of a non-faired propeller (1), the blade portion (2) having an offset (3), characterized in that it comprises data processing means (1 1) configured to implement:

A parametrization module of at least one auxiliary curve of at least class C ¹ representing the value of a deformation parameter (x ₀ , y _ma x, _max dy) as a function of a cutting height in the blade ( 2), the auxiliary curve being defined by at least a first and a second extreme control point (PCE1, PCE ₂ ) defining the extent of said height of the blade (2), the parameterization being implemented according to at least one complementary parameter, according to which the ordinate of the second extremal point (PCE ₂ ) of the auxiliary curve is expressed;

a parametrization module of a main curve of at least class C ¹ representing a deformation of said blade (2) characterizing the offset (3), as a function of a position along a section at a given height in the blade (2), the main curve being defined by at least a first and a second extremal control point defining the extent of said section of the blade (2),

the parameterization being implemented according to at least the deformation parameter (x ₀ , y _ma x, _max dy) and said height of the cut in the blade (2), according to which the ordinate of the second extremal point of the curve principal is expressed;

An optimization module of at least one of the complementary parameters;

A module for rendering on an interface (13) of said equipment (10) optimized parameter values.

17. Computer program product comprising code instructions for the execution of a method according to one of claims 1 to 13 for modeling at least a portion of a blade (2) of a non-faired propeller (1) when said program is run on a computer.

18. Storage medium readable by a computer equipment on which a computer program product comprises code instructions for the execution of a method according to one of claims 1 to 13 for modeling at least a part of a blade (2) of a non-faired propeller (1).