WO2011055085A2

WO2011055085A2 - Method and tool for simulating the aerodynamic behaviour of an aerodynamic element of an aircraft having a variable sweep angle

Info

Publication number: WO2011055085A2
Application number: PCT/FR2010/052371
Authority: WO
Inventors: Benoît Calmels
Original assignee: Airbus Operations
Priority date: 2009-11-06
Filing date: 2010-11-04
Publication date: 2011-05-12
Also published as: FR2952454A1; FR2952454B1; WO2011055085A3

Abstract

The invention relates to a computer simulation method suitable for obtaining the aerodynamic behaviour of an aerodynamic element of an aircraft in a flow, said aerodynamic element having, between the leading edge and the trailing edge thereof, a local sweep angle with a value that varies between a value of the leading edge and a value of the trailing edge.

Description

METHOD AND TOOL FOR SIMULATION OF BEHAVIOR

AERODYNAMICS OF AERODYNAMIC ELEMENT OF AN AIRCRAFT

HAVING A VARIABLE ANGLE ANGLE

DESCRIPTION

TECHNICAL AREA

The present invention relates to the general field of aerodynamics and relates to the numerical simulation of the aerodynamic behavior of an aerodynamic element of an aircraft having a variable deflection angle.

It finds an application in the field of aeronautics in which the design of an aircraft requires precise knowledge of the aerodynamic coefficients associated, for example, with its type of wing.

STATE OF THE PRIOR ART

During the design of an aircraft and in particular the wing of the latter, it is sought to determine the overall aerodynamic coefficients associated with said wing, such as lift, drag and pitch moment.

These coefficients can be determined in various ways, in particular by analyzing an incident flow around a two - dimensional wing profile of said wing. The wing profile is generally obtained from a section along a plane of one of the wings of said wing, said plane of the profile being parallel to the plane of symmetry of the aircraft.

The aircraft may comprise a wing having a constant angle of deflection φ. FIG. 1 schematically illustrates, in plan view, an aircraft wing with a constant deflection angle in the reference frame linked to the aircraft. Figure 2 is a perspective view of the wing shown in Figure 1.

We define a first direct orthonormal reference Ra (Xa, Ya, Za), said landmark of the aircraft, whose plane (Xa, Za) coincides with the plane of symmetry of the aircraft, and whose axis Ya is orthogonal to the plane of symmetry of the aircraft. For the sake of clarity and without being limiting, we consider here that the wing extends in the plane (Xa, Ya).

Each of the generatrices of the wing forms a substantially constant angle with respect to the axis Ya. This angle is called the angle of the arrow. Thus, the generatrix of the wing forming the leading edge has a leading edge deflection angle φ _Β Α · The trailing edge angle <P _BF is defined in the same way, from the generator of the wing forming the trailing edge. The angle of the arrow is said to be constant when the leading edge arrow angles φ _Β Α and the trailing edge φ _Β ρ are equal. In other words, the generatrices of the wing are parallel to each other.

One can define a second reference direct orthogonal Rv (Xv, Yv, Zv), called reference ^local to the wing, associated with each of the wing-generating. The plan (Χν, Υν) coincides with the plane (Xa, Ya), and the Yv axis is parallel to the axis of the generatrix considered of the wing. Thus, the axis Xv of the local reference of the wing forms a local angle with said plane (Xa, Za) equal to the arrow angle φ. It should be noted that we go from the reference of the aircraft Ra to the local reference of the wing Rv by an elementary rotation angle -φ around the axis Za.

It should be noted that the definition of the angle of deflection is not limited to the wing, but can also be applied to other aerodynamic elements of the aircraft likely to present an angle of deflection, as, for example , empennages. The deflection angle of a tail is then defined from the generatrices thereof, according to the same principle as previously presented.

In the reference linked to the aircraft, the aircraft is located in a three-dimensional flow incident upstream velocity, noted V _∞ . Said upstream speed V _∞ can then be decomposed, in the local coordinate system of the airfoil Rv, into a first component V _∞ .coscp oriented in the plane (Xv, Zv) and a second component V _∞ .sincp oriented in the plane (Yv , Zv).

It is known that the first component V _∞ .coscp determines the field of overspeeds and therefore the lift, while the second component V _M .sin (p does not generate any overspeed (P. Rebuffet, Aerodynamique expérimentale, 1950, p 432 -433).

To determine the aerodynamic coefficients, the second component is usually neglected to remember that the first component oriented in the plane (Xv, Zv).

A two-dimensional incident flow around a defined wing profile in the plane of the profile P is then considered, the flow having a two-dimensional upstream speed of intensity V _∞ .cosp.

However, to take account of the fact that the wing profile is defined by a plane of the profile P parallel to the plane (Xa, Za) while the component V _∞ .cos (p of the three-dimensional upstream velocity V _∞ is oriented in the plan (Xv, Zv), the wing profile under consideration is modified: the component V _œ .cos (p of the three-dimensional upstream velocity V _∞ "sees", because of its orientation, a wing profile of relative thickness greater than that of the profile defined in the plane of the profile P.

Indeed, the relative thickness e _max / c of the profile defined in the plane (Xv, Zv) is related to the relative thickness of the profile defined in the plane of the profile P by the following relation:

where e _max and c are respectively the maximum thickness and the chord of the profile in the plane considered, and φ is the constant angle of deflection associated with said sails. The chord is defined as the distance, in the plane considered, between the leading edge and the trailing edge.

Also, the modified wing profile is obtained by correcting the local thickness of the initial wing profile by the relation: e ₂ (x ') = - ^ (χ') (2)

COS (j9

where βι (χ ') and θ2 (χ') are the local thicknesses, respectively, of the initial profile and the modified profile, at the distance 'to the leading edge along said chord defined in the plane of the P-profile.

FIG. 3 illustrates, in dotted lines, the initial wing profile along the plane of the profile P parallel to (Xa, Za), and in full line, the modified wing profile.

The study of the VOo.coscp two-dimensional upstream velocity incident flow around the modified wing profile is usually performed by wind tunnel or numerical simulation tests.

From the velocity and pressure fields around the profile obtained by experimental measurements or by the numerical solution, one can calculate the local coefficients, such as the coefficients of pressure and parietal friction, to deduce the global aerodynamic coefficients mentioned previously. The aerodynamic behavior of the aircraft is then determined by said aerodynamic coefficients.

It should be noted that, in the case of wind tunnel tests, the global aerodynamic coefficients can be measured directly using force measuring devices, such as, for example, three or six-axis scales.

However, the approach described above can not simply be extended to the case of aircraft whose wings have a variable angle of deflection. Figure 4 schematically illustrates in plan view a wing portion having a variable deflection angle.

The leading edge arrow angle φ _ΒΑ is then different from the trailing edge arrow angle cp _BF . In addition, for each of the generatrices of the wing between the leading edge and the trailing edge, a local deflection angle is associated which has a different value. Thus, along the chord defined in a plane of any profile P parallel to the plane (Xa, Za), the angle of deflection is defined locally and its value varies between a leading edge value and a trailing edge value according to a law of variation given.

By way of illustration, in the case of a trapezoidal wing such as that represented in FIG. 4, the law of variation of the local deflection angle is:

tan φ (χ ') = tan <p _B4 . (l-x') + tan <p _BF .x '(3)

It should be noted that the local reference of the wing Rv depends here on the value of the local deflection angle φ (χ ').

The wind tunnel and numerical simulation studies carried out in the case of a wing with a constant deflection angle are difficult to extend to the case of the wing with variable deflection angle, since the two-dimensional flow in the latter situation is accelerated. or slowed down.

Indeed, the leading edge deflection angle φ _Β Α is usually greater than the trailing edge deflection angle (p _B F- Also, the bidimensional two-dimensional upstream velocity incident flow V _∞ .cos ( p around the wing profile has a speed at the leading edge whose intensity Vco.cosc _BA is lower than that Voo.coscps _F of the speed at the trailing edge. The two-dimensional flow is accelerated along the wing profile. Otherwise, the flow is slowed down.

However, two-dimensional studies carried out in the wind tunnel or by numerical simulations do not currently make it possible to reproduce this acceleration or this slowdown, which affects the precision of the results.

Of course, this characteristic of the flow is only present for the two-dimensional velocity flow V _∞ c os (p L'L'L'L'L'L'L'L'L'L'L'L'L'L'L'L'L'L'L'L'L'L'L'L'L'L'L'L'L'L'L'.

It is therefore possible to carry out studies concerning not only a two-dimensional simplified flow around a wing profile, but a three-dimensional upstream three-dimensional flow V _∞ around a three-dimensional wing as shown in FIG. three-dimensional can be realized in wind tunnel or by numerical simulation. However, because of their three-dimensional aspect, the implementation of these studies, both experimentally and numerically, is made particularly cumbersome and complex. For the same reason, the analysis of the data obtained in these studies (for example, velocity and pressure fields) is particularly long and difficult. STATEMENT OF THE INVENTION

The main purpose of the invention is to present a computer simulation method for obtaining the aerodynamic behavior of an aerodynamic element of an aircraft, said aerodynamic element having, between the leading edge and the trailing edge of that here, a local arrow angle whose value varies between a leading edge value and a trailing edge value.

According to the invention, said method comprises the steps according to which:

a two-dimensional profile is obtained from a section along a plane of a three-dimensional geometric model of said aerodynamic element;

a mesh of a two-dimensional geometric domain delimited at least in part by said profile is produced, said mesh defining a computational domain;

each mesh of said mesh is associated with a local three-dimensional coordinate system R (X, Y, Z) for which the axis X forms a local angle with said plane of the profile, and the axis Z is included in said plane of the profile and orthogonal to the chord of the profile, so that for any mesh between the leading edge and the trailing edge of the profile, the local angle is equal to said value of the locally defined deflection angle;

a discrete numerical model of the Navier-Stokes equations is solved by computer, on said mesh, so as to obtain the numerical solution of a flow of fluid within said computational domain, said resolution of said digital model comprising, at each time step, a step of calculating the speed in each of the meshes of said mesh to obtain a velocity field in the computation domain, said velocity in a given cell, expressed in the plane ( X, Z) of said corresponding local three-dimensional coordinate system, being calculated from the speed of at least one adjacent mesh upstream or downstream along the axis of said rope, said speed of said neighboring mesh being previously expressed in the plane (X, Z) of the local three-dimensional coordinate system of the mesh in question.

Said plane of the profile may be chosen parallel to the plane of symmetry of said aircraft.

Advantageously, for any mesh located upstream of the leading edge of the profile, said local angle is equal to said value of the arrow angle at the leading edge (ΦΒΑ) I and, for any mesh located downstream of the edge of the leakage of the profile, said local angle is equal to said value of the arrow angle at the trailing edge ((BF) ·

Preferably, said discrete numerical model of the Navier-Stokes equations comprises a condition imposed on the boundaries of said mesh comprising a defined local velocity, in each of the meshes of said limits, by the projection of the upstream incident velocity of said flow (V _∞ ) in the plane (X, Z) of said local three-dimensional coordinate system of the mesh in question. Advantageously, the step of calculating the speed in each of the cells of said mesh comprises the following sub-steps:

a three-dimensional velocity is defined in said mesh next to the mesh considered from, on the one hand, the two-dimensional velocity in said neighboring mesh, the latter being expressed in the plane (X, Z) of said corresponding local three-dimensional mark, and on the other hand, a third component defined by the projection of the upstream incident velocity of said flow along the Y axis of the corresponding local three-dimensional reference;

said three-dimensional velocity thus defined is expressed in the local three-dimensional coordinate system of the mesh in question;

said three-dimensional velocity thus expressed is projected in the plane (X, Z) of the local three-dimensional coordinate system of the mesh in question, so as to obtain the two-dimensional velocity in said adjacent mesh expressed in the plane (X, Z) of the local three-dimensional coordinate system of the mesh considered.

Preferably, the step of obtaining said profile comprises a modification of the thickness of the profile according to the relation: e ₂ (x ') = .e _x {x')

cos <p (x ')

where ei (x ') and e2 (') are the local thicknesses, respectively, of the initial profile and the modified profile, at the distance x 'at the leading edge following said rope, and φ (χ ') is the value of the local arrow angle at said distance x'.

Advantageously, said imposed speed limit condition further comprises a local velocity component resulting from a disturbance of the fluid surrounding the aircraft induced by said aircraft.

Said numerical solution obtained may comprise velocity and pressure fields defined within the computational domain.

Preferably, an additional step of displaying the resulting digital solution is provided.

The invention also relates to a method for estimating aerodynamic coefficients of an aerodynamic element of an aircraft in a flow, said aerodynamic element having, between the leading edge and the trailing edge thereof, an angle local arrow whose value varies between a leading edge value and a trailing edge value.

According to the invention, this method comprises the steps of:

implementing the computer simulation method of the aerodynamic behavior of said aerodynamic element according to any one of the preceding features; then

estimating the aerodynamic coefficients of said aircraft from said digital solution obtained.

Said step of estimating the aerodynamic coefficients may comprise an intermediate step of estimating the local pressure and wall friction coefficients from said solution obtained numerical and dynamic pressure defined from the incident upstream velocity of said flow.

Said local aerodynamic coefficients can be integrated according to said initial profile to the unmodified thickness, so as to obtain overall aerodynamic coefficients expressed in the reference linked to the aircraft.

Said global aerodynamic coefficients thus obtained can be projected in an aerodynamic reference oriented along said average speed upstream, so as to obtain the lift coefficients, drag and pitching moment.

Other advantages and features of the invention will become apparent in the detailed non-limiting description below.

BRIEF DESCRIPTION OF THE DRAWINGS

Embodiments of the invention will now be described, by way of nonlimiting examples, with reference to the accompanying drawings, in which:

Figure 1, already described, is a schematic top view of an aircraft wing having a constant deflection angle;

Figure 2, already described, is a schematic perspective view of the wing shown in Figure 1;

Figure 3, already described, is a schematic view of unmodified and modified wing profiles obtained from the wing shown in Figures 1 and 2; Figure 4, already described, is a schematic top view of a wing wing with a variable boom angle;

FIG. 5 is a schematic view of the two-dimensional geometrical domain corresponding to the computational domain;

Figure 6 is a schematic representation of some meshs belonging to the mesh, in the case of a regular Cartesian mesh; and

Figure 7 is a schematic top view of a wing portion on which are shown some local three-dimensional marks associated with different mesh of the mesh.

DETAILED PRESENTATION OF A PREFERRED EMBODIMENT

The embodiments of the invention which are presented hereinafter relate to a wing of an aircraft whose wings have a variable angle of deflection. However, the present invention is not limited to the wing wings of the aircraft. Any aerodynamic element of the aircraft can be studied, such as, for example, empennages.

Consider an aircraft whose wing, shown in Figure 4, has a variable deflection angle. More specifically, said wing comprises two wings each having, between its leading edge and its trailing edge, a local deflection angle whose value varies between a leading edge value and a trailing edge value according to a law of variation given. The leading edge and the trailing edge are defined by the corresponding generatrix of the wing.

The rope is the distance connecting the leading edge and the trailing edge along a cross sectional plane of the wing, preferably parallel to the plane of symmetry of the aircraft.

In the reference linked to the aircraft, a three-dimensional incident flow, of upstream velocity vector V _∞ , flows around the aircraft.

We consider a reference of the aircraft Ra and a local reference of the wing Rv as defined above.

We also define a direct orthonormal reference Re (Xe, Ye, Ze), called aerodynamic reference of the incident flow, whose Xe axis of the abscissa is oriented along the direction of the upstream velocity vector V _∞ of the incident flow and whose the axis Ye is orthogonal to the plane of symmetry of the aircraft.

The upstream speed vector V _∞ can form a non-zero angle, here called angle of incidence a, with the axis Xa of the reference mark of the aircraft. This angle is sometimes called angle of attack {AoA, in English).

Subsequently, and for the sake of clarity of the description without this being limiting, it is considered that the upstream velocity vector V _∞ of the incident flow is parallel to the plane of symmetry of the aircraft. In other words, the wing has a skid angle β substantially zero. The planes (Xe, Ze) and (Xa, Za) are then parallel.

It should be noted that the passage of the aerodynamic reference to the reference of the aircraft is made by rotation about the axis Ya of an angle equal to the angle incidence -a. The aerodynamic reference and the reference of the aircraft therefore coincide with each other when the angle of incidence is zero. Furthermore, the passage of the reference of the aircraft Ra to the local reference of the wing Rv is made by rotation around the axis Za by an angle equal to the local deflection angle - <p (x).

The computer simulation method of the aerodynamic behavior of said aerodynamic element, here of the wing of the aircraft, according to the invention is now described with reference to FIGS. 5 to 7.

From a three-dimensional geometric model of the wing of said aircraft, a two-dimensional wing profile 1 is produced. The profile 1 is obtained from a section along a plane, called plane of the profile P, of the geometric model of the wing. The plane of the profile P is parallel to the plane of symmetry of the aircraft, and therefore to the plane (Xa, Za) of the reference mark of the aircraft.

As explained above, the local thickness of the wing profile 1 is changed. This modification comes from the fact that we consider, as explained above, along the profile 1 defined in the plane of the profile P, a two-dimensional flow whose velocity is the component V _∞ .cos (p in the plane (Xv, Zv ) of the three-dimensional upstream velocity V _∞ .

However, the plane (Xv, Zv) and the plane of the profile P do not coincide. As a result, the Voo.coscp component of the three-dimensional upstream velocity V _∞ "sees" a profile different from the profile 1 considered, namely the profile defined according to the plane (Xv, Zv). Also, the local thickness of the considered wing profile, namely the wing profile 1 defined according to the plane of the profile P, is modified according to the following relation:

where ei (x ') and θ2 (χ') are the local thicknesses, respectively, of the initial profile and the modified profile, at the distance x 'at the leading edge along the chord of the profile, and φ (χ') is the value of the local deflection angle at said distance x '.

It should be noted that the angle of deflection considered for making this modification of the local thickness is indeed the local deflection angle and not a value of the deflection angle which remains constant regardless of the distance x 'next the rope of the profile.

A two - dimensional geometrical domain 2 is defined, which corresponds to the area of space that surrounds the wing profile 1 and in which the flow of the air will be reproduced by simulation. This domain 2 is also called domain of calculation.

This geometric domain 2 preferably has a shape of rectangle, but may have any other shape, for example a rectangle whose face is convex when viewed from outside the rectangle.

The upstream face 3 of the geometrical domain is located opposite the nose of the wing profile and the downstream face 4 is disposed vis-à-vis the upstream face. Upstream faces 3 and downstream 4 are connected by two lower faces 5 and upper 6.

The wing profile 1 is disposed in this geometric area 2 so as to be sufficiently far from each of said faces.

The upstream and downstream faces 4 may be arranged at a distance from the wing profile 1 of the order of one to several tens of times the chord of the profile. The lower 5 and upper 6 faces may be located at a distance from the wing profile 1 of the order of one to several times the chord of the profile.

A mathematical model is chosen to reproduce the flow of air surrounding the wing profile.

This model is the model of compressible real fluids, called Navier-Stokes. The fluid is supposed to be viscous, Newtonian and compressible, and heat conducting.

This well-known physical model includes a set of partial differential equations called the continuity equation, the equation of dynamics and the energy equation and writing, respectively:

"DT _n U d ² T p C _v - = -P - + Φ .. + λ

dt dx. x _j dx _f

where p (x) the density of the fluid, U (x) the velocity field, P (x) the pressure field, T (x) the temperature field, F is an external force of volume, such as gravity, μ dynamic viscosity, C _v specific heat at constant volume, Φ _ν the viscosity dissipation rate, and λ thermal conductivity.

This physical model of Navier-Stokes can however be adapted to the description of turbulent flows.

The general Navier-Stokes equations given above can be reformulated into the known form of the averaged equations, called RANS for Reynolds Averaged Navier-Stokes, and then include a turbulence model.

Various known turbulence models can be used, such as, for example, two-equation turbulence models such as the k-ε and k-co models.

Among these models, the SST model as described in the Menter article entitled "Zonal Two Equation k-Turbulence Models for Aerodynamic Flows" and published in 1993 in AIAA Paper 93-2906 can be used.

The so-called Kato-Launder modification can be taken into account to correct the turbulent production term in the turbulent kinetic energy equation. This approach is described in the article by Kato and Launder titled "The Modeling of Turbulent Flow Around Stationary and Vibrating Square Cylinders" and published in 1993 in Proc. 9th Symposium on Turbulent Shear Flows, Kyoto, pages 10.4.1 to 10.4.6.

Moreover, it is also possible to take into account, in the SST model with the Kato-Launder modification, the so-called Kok TNT correction which reduces the turbulent overproduction in the heart of the whirlpools. This model is described in Kok's article "Resolving the dependence of the free stream of the k-co turbulence model" and published in 2000 in AIAA Journal 38, 1292-1295.

Of course, the invention is not limited to the use of these turbulence models. Other models can be used, such as the k-ω EARSM model developed by Hellsten.

The Navier-Stokes physical model also includes an initial condition and boundary conditions.

In order to reproduce the accelerated flow presented above, the three-dimensional local coordinate system Rv (Xv, Yv, Zv) of the canopy is extended at each point of the two-dimensional geometrical domain by defining a local three-dimensional coordinate system R (X, Y, Z). ), this being preferably orthogonal.

The X axis of the local three-dimensional coordinate system R forms a local angle φ (χ, ζ) with the plane of the profile P and the Z axis is included in said plane of the profile and is orthogonal to said string.

The local angle φ (χ, ζ) is defined at any coordinate point (x, z) of the two-dimensional geometric domain. This local angle φ (χ, ζ) can be defined as follows:

- For any point located upstream of the leading edge of the profile along the axis of the cord thereof, the local angle φ is equal to said value of the angle of arrow φ at the leading edge: VX <X _B A, VZ, φ (χ,

where X _B A is the abscissa of the leading edge.

- For any point situated between the leading edge and the trailing edge of the profile along the axis of the chord of the latter, the local angle φ is equal to the said local value of the deflection angle φ defined by said law of variation: Vxe [x _BA , BF], Vz, φ (χ, ζ) = φ (χ);

- For any point situated downstream from the trailing edge of the profile along the axis of the chord of the latter, the local angle φ is equal to the value of the arrow angle φ at the trailing edge: VX≥X _B F VZ, φ (χ,

x _BF is the abscissa of the trailing edge.

Thus, at each point of the two-dimensional geometrical domain 2, a local three-dimensional coordinate is defined which depends on the local arrow angle. The two-dimensional geometric domain 2 is thus formed of three parts A1, A2 and A3, as illustrated in FIG.

It should be noted that the local angle φ (χ, ζ) is constant in the upstream Al and downstream A3 portions. In part A2, it coincides with the local deflection angle and depends only on the position in x. Thus, in the part A2, the local three-dimensional coordinate system R coincides with the local coordinate system of the wing Rv.

The initial condition may include a velocity field imposed throughout the two-dimensional geometric domain.

The speed at the initial moment, in each of the points of the two-dimensional geometrical domain, can be projecting the upstream three-dimensional velocity V _∞ in the plane (X, Z) of the corresponding local three-dimensional coordinate system R.

As an illustration, in the case of an upstream speed V _∞ having an angle of incidence at zero, the projection of the upstream speed in the plane (X, Z) of the corresponding local three-dimensional reference is written: (V _∞ . cos [φ (x, z)], 0), where the local angle φ (χ, ζ) depends on the position of the considered point according to the three parts of the two-dimensional geometrical domain defined previously. Thus, the initial condition effectively corresponds to an accelerated flow when ΦΒΑ> 9BF since the two-dimensional velocity V _∞ . cos [φ (X≥ _B FÎ Z)] = V _∞ .cos (p _B F downstream of the wing profile is greater than the two-dimensional velocity V _∞ cos [φ (X <X _B A, Z)] = V _∞ .cos (p _B A upstream of the wing profile.

The boundary conditions of the different boundaries (domain faces and wing profile surface) of the geometric domain can be divided into several categories.

A first category of boundary conditions relates to the condition imposed on the surface of the wing profile.

The boundary condition imposed on the surface of the wing profile is a conventional "wall" type condition.

By conventional "wall" type of condition, it is understood that the velocity at the surface considered is zero, more particularly the tangential and normal components, and that any disturbance of the fluid surrounding the aircraft is reflected by said surface.

A second category of boundary conditions concerns the upstream 3, downstream 4, lower 5 and upper 6 faces of the geometric domain 2.

Concerning the upstream face 3, a speed condition is imposed which has a fixed component obtained by the projection of the upstream three-dimensional velocity V _∞ in the plane (X, Z) of the local three-dimensional coordinate system R at the considered point belonging to said upstream face 3 The imposed speed advantageously comprises an additional component V 'resulting from a disturbance of the fluid surrounding the aircraft induced by said aircraft. Thus, an air flow enters the geometric domain with an average speed corresponding to V _∞ .cos (p _B A when the angle of incidence is substantially zero.

A disturbance of the surrounding fluid may be any type of pressure wave such as a sound wave, a shock wave or more generally a discontinuity wave, or even a flow of air induced by the presence of the wing profile. The airflow type disturbance can come directly from the wing profile. In addition, any perturbation of the surrounding fluid induced by the aircraft can leave the geometrical domain 2 through the upstream face 3. The disturbance is then said to be outgoing.

The speed imposed on the upstream face 3 may be non-uniform and depends on the outgoing disturbance. Thus, the velocity component V _∞ .cos (p _B A is preferably constant regardless of the considered point of the face upstream 3, while the speed V 'is not necessarily constant, in intensity and orientation, and depends on the considered point of the upstream face 3.

It should be noted that said outgoing disturbance may be substantially zero or negligible in front of the flow of air entering through the upstream face. The imposed speed is then substantially equal to the component Voo.cos (p _B A.

As regards the other faces of the geometric domain, that is to say the downstream 4, lower 5 and upper 6 faces, the imposed boundary condition may be of the same type as for the upstream face.

At each of the downstream 4, lower 5 and upper 6 faces, the boundary condition has an imposed velocity which has a fixed component obtained by the projection of the upstream three-dimensional velocity in the (X, Z) plane of the local three-dimensional mark R at the point considered belonging to said considered face. The imposed speed advantageously comprises an additional component V 'resulting from a disturbance of the fluid surrounding the aircraft induced by said aircraft.

Any perturbation of the surrounding fluid induced by the aircraft can then leave the geometrical domain through said faces.

As before, the additional component of the speed imposed on these faces is not necessarily constant, in intensity and orientation, according to the point of the face considered. By way of illustration, in the case of a three-dimensional upstream velocity V _o having an angle of incidence equal to zero, the velocity imposed along the upstream face is (V _∞, cosq> _B A, 0) + V ', depending on the face downstream (VCO.COSÇBF 0) + V ', and following the lower and upper faces: (V _∞ cos [φ (x)], 0) + V'.

Thus, the physical model comprises, as previously described, the set of equations of the Navier-Stokes model, preferably adapted to the description of a turbulent flow, as well as an initial condition, and boundary conditions imposed on the boundaries of the geometric domain (faces of the domain and surface of the aircraft model). The geometric domain is discretized to obtain a two-dimensional mesh. The boundaries of the mesh coincide with those of the geometric domain. The mesh can be of the structured or unstructured type. The mesh is made using software, for example the CATIA V5 software.

In the general case, each cell is numbered in i, k and corresponds to a single position defined in x, z in the two-dimensional geometrical domain. Thus, the coordinates x and z are each functions of i and k: x (i, k) and z (i, k).

Figure 6 illustrates a portion of an example of non-orthogonal Cartesian grid with face-centered. It should be noted that the vector i_ is not necessarily collinear with the axis of the string.

The mesh comprises the three parts A1, A2 and A3 of the two-dimensional geometric domain. Also, the benchmark local three-dimensional R depends on the value of the local angle φ (i, k).

So :

For any mesh located upstream of the leading edge of the profile along the axis of the cord thereof, the local angle φ is preferably equal to said value of the arrow angle φ at the leading edge:

V (i, k) / x (i, k) <X _B A, φ (i, k) = φ _ΒΑ

- For any mesh between the leading edge and the trailing edge of the profile along the axis of the chord of the latter, the local angle φ is equal to the said local value of the deflection angle φ defined by said variation law: V (i, k) / x (i, k) e [XBA, XBF], φ (i, k) = φ [x (i, k)];

- For any mesh located downstream of the trailing edge of the profile along the axis of the chord of the latter, the local angle φ is preferably equal to said value of the arrow angle φ at the trailing edge:

V (i, k) / x (i, k)> X _B F, φ (i, k) = φ _Β ; - ·.

We can note R ^{(1, k)} the local three-dimensional coordinate system associated with any coordinate grid i, k.

A discrete numerical model is then obtained by the temporal and spatial discretization of the Navier-Stokes physical model described previously.

Different types of general numerical schemes can be used for spatial discretization, such as finite volumes, finite elements, or finite differences for spatial discretization.

Preferably, the finite volume technique is used, in particular the second-order face-centered, and time discretization is obtained by an explicit Runge-Kutta scheme. Time discretization can also be obtained by various schemes known to those skilled in the art.

Thus, we obtain a discrete numerical model of

Navier-Stokes including an initial condition imposed on the initial time at all meshes of the geometrical domain, and boundary conditions imposed on the borders of the mesh.

The resolution of the discrete digital model described above is carried out by computer, which makes it possible to simulate the flow of air around the modified wing profile of said aircraft.

According to the invention, said resolution of the digital model comprises, at each time step, a step of calculating the speed in each of the meshs of said mesh to obtain a speed field in the computation domain, said speed in a given mesh, expressed in the plane (X, Z) of said corresponding local three-dimensional coordinate system being calculated from the speed of at least one adjacent mesh upstream or downstream along the axis of said rope, said speed of said neighboring mesh being previously expressed in the plane (X, Z) of the local three-dimensional coordinate system of the mesh in question.

Meshes (i, k), (il, k) and (i + l, k) are associated, respectively, with the three-dimensional local reference marks R ⁽ⁱ ' ^k) , R * ^{1 "1} ' ^k) and R ^{(i + 1} ' ^k) .

As illustrated in FIG. 7, the velocity v ^{<1, k)} of the cell (i, k) is expressed in the plane (X ^{(1, k)} , Z ^{(1, k)} ) of the local three-dimensional reference R ^{(1, k>} . For the sake of clarity, the index k is not indicated in this FIG. 7. The velocities V ^{(1 ~ I, k)} of the neighboring cell (il, k) following the axis of the chord and the velocity V ^{<i + 1} ' ^k) of the neighboring mesh (i + 1, k) are expressed, respectively, in the planes (X ^(1-1 ' ^k) , _z ^{(1 "1 , k))} and (X ^{(i + 1} ^'k), Z ^{(i + 1'} ^k)) corresponding to the local three-dimensional marks R ^(1_1 ^'k) _e R t ^{(1 + 1 <k>,}

The velocity v ^{(1, k)} of the mesh (i, k) is calculated, for example, from the speeds v ^{(1 ~ 1, k>} and v ^{(1 + 1} ^'k). However, the velocities v ^{( 1_1} '^k> and v ^{(1 + 1} ' ^k) used for this calculation step are each previously projected in the local three-dimensional coordinate system R ⁽¹ ' ^k) associated with the mesh in question (i, k).

It should be noted that we go from the R mark ⁽¹ ' ^{, k>} , i' ≠ i, to the mark R ^{<1, k)} by a simple rotation around the Z axis of an angle [φ ^{(i '} '^k> -φ ⁽ⁱ ' ⁾ ].

Moreover, it should be noted that, by adjacent mesh upstream or downstream along the axis of the rope, is meant any mesh other than the mesh considered upstream or downstream thereof along the axis of the rope. The neighboring mesh may be a mesh adjacent to the mesh in question. It can also be arranged at a distance from said mesh considered.

Thus, to obtain the speed in a given mesh, all the speeds used corresponding to the adjacent meshes upstream or downstream along the axis of the chord are projected in the local three-dimensional coordinate system R ^{(1, k)} associated with the mesh in question (i, k).

Thus, without using sources or fluid wells, the flow is accelerated (in the case present where φ _Β Α><PBF) · Of course, in the case where ΦΒΑ <<BF? the flow is slowed down.

More precisely, said step of calculating the speed in each of the cells of said mesh preferably comprises the following substeps:

Firstly, a three-dimensional velocity is defined in said mesh adjacent to the mesh considered from, on the one hand, the two-dimensional velocity in said adjacent mesh, the latter being expressed in the plane (X, Z) of said three-dimensional mark. corresponding local, and secondly a third component defined by the projection of the average velocity upstream along the Y axis of the corresponding local three-dimensional reference.

Thus, in the case where the angle of incidence is zero, the two-dimensional velocity V ₂ D ⁺¹ ' ^k) in said adjacent cell (i + 1, k) is written (V _x ^{i + 1} ' ^k , V _z ^{i + 1} ' ^k ) in the plane (X ^{(1 + 1, k>} , Z ^{<1 + 1} ' ^k) ) of said corresponding three-dimensional local coordinate system R ^{(1 + 1} ' ^k > _ L _a third component is defined by the projection of the three-dimensional upstream velocity along the γ axis (ι ⁺ ι ^> ^ _u local three-dimensional coordinate system R ^{<1 + 1} ' ^k) and write Voo. sin [φ (i + 1, k)]. The 3D three-dimensional velocity ⁺¹ ' ^k) in said neighboring mesh is then written (V _x ^{i + 1} ' \ V _- sin [φ (i + 1, k)], V _z ^{i + 1} ' ^k ) in the local three-dimensional coordinate system corresponding to R < ^{1 + 1} ' ^k >.

Then, said three-dimensional velocity V3 _D ^{<1 + 1, k)} thus defined is expressed in the three-dimensional local coordinate system R ^{(1, k)} of the mesh considered.

We denote by V _3D ^{(1 + 1, k>} | RU + I, k) the three-dimensional velocity defined in the reference R ^{(1 + 1, k)} , and V _3D ^{(1 + 1} ' ^k) | R <i, k) the same three-dimensional velocity expressed in the reference R ' ^K) . We then have the relation of passage between the two marks:

(i + l, K) | _ p rp (i + l, k) p (i, k) ·, rr (1 + 1, k) i

^V 3D I R (i + 1, k) - t 'i H - KJ. V _3D IR (i, _k ) where P [R ^{(1 + 1, k>} - ÷ R ⁽¹ ' ^k) ] is the matrix of passage of the reference mark R ^{(1 + 1} '^K> to the mark R ⁽¹ ' ^{k )} .

Finally, said three-dimensional velocity V _3D ^{(1 + 1} ' ^k) I _R (i, k) thus expressed is projected in the plane (X' ^K) , Z ⁽¹ ' ^K) ) of the local three-dimensional coordinate system R ⁽¹ ' ^{k )} of the mesh in question, to obtain the two-dimensional velocity V ₂ D ^{! l + 1} '^k> Ι κα, ^ in the said adjacent cell (i + 1, k) expressed in the plane (X' ^k) , z ^{(1 , k>} ) of the local three-dimensional coordinate system R ' ¹ ^' ^ e the mesh in question.

This step of calculating the speed field is performed at each time step, for all meshes of the mesh.

Thus, without resorting to sources or fluid wells, the flow is accelerated (in this case where φ _ΒΑ > 9BF) · Of course, in the case where Φ _ΒΑ <9 _B F, the flow is slowed down .

Finally, to follow the evolution of the resolution of the discrete digital model, a convergence criterion is used which allows to stop the simulation when it is checked.

The convergence criterion may be a physical quantity such as a speed or a pressure measured at a given point of the mesh. When this data is stationary, it is considered that the flow of the fluid in the field of calculation is established. The simulation can then be stopped.

A numerical solution of the flow of the fluid surrounding the wing profile is obtained.

This numerical solution includes fields of speed, pressure, temperature at any point of the mesh.

It is stored in the memory of said computer, or in separate storage means.

The digital solution can be displayed on a computer screen.

By software means, the aerodynamic behavior of the aircraft is analyzed from the numerical solution obtained.

The local aerodynamic coefficients of the modified wing profile of the aircraft are then calculated from the velocity and pressure fields obtained.

The local aerodynamic coefficients include the pressure and friction coefficients. For the dimensioning, the reference pressure is preferably the three-dimensional dynamic pressure, and not the two-dimensional dynamic pressure. Indeed, this one is not defined in a unique way since it can vary in the field of computation.

To obtain the overall aerodynamic coefficients in the reference system of the aircraft, the local coefficients previously obtained along the wing profile are integrated. For the sizing of the lengths, it is possible to use the chord of the profile. We then obtain the global coefficients in the reference of the aircraft, namely the normal force, tangential force coefficients and the pitch moment coefficient.

Finally, the projection in an aerodynamic reference of the flow Re of the global coefficients previously calculated makes it possible to obtain the global aerodynamic coefficients in the said aerodynamic reference Re, ie the lift, drag and momentum coefficients. pitch.

The simulation can be repeated for different values of the speed V ", the law of variation of the angle of arrow φ (χ ') along the chord of the profile, as well as the angle a.

This analysis can also be performed for various geometric aircraft models, and therefore different wing profiles.

The analysis results can be classified as databases. Each database indicates the aerodynamic coefficients of the aircraft for a wide range of the flight range defined by, in particular, the speed of the aircraft, the law of variation of the deflection angle φ (χ '), the angle a and the aircraft model used.

Of course, various modifications may be made by those skilled in the art to the invention which has just been described, solely by way of non-limiting examples.

Regarding the physical model used, we can choose a simplified model of Navier-Stokes. By for example, the fluid surrounding the aircraft can be considered as non-viscous. The Navier-Stokes model is then reduced to the Euler equations for perfect fluids.

Furthermore, the description of the turbulence by the Navier-Stokes model can be obtained, alternatively to the RANS model described above, by the LES (Large Eddy Simulation) type, hybrid RANS / LES, or DES (Detached Eddy) type models. Simulation) .

The present invention is not limited to the case of zero skid angle. In the case of a non-zero skid angle, the passage of the aerodynamic reference to the reference of the aircraft is effected by two elementary rotations, a first rotation about the axis Ya of an angle equal to the angle d incidence a and a second rotation about the axis Za of an angle equal to the angle of wiggle β. The process is then similar to that described above.

Claims

A method of computer simulation of the aerodynamic behavior of an aerodynamic element of an aircraft in a flow, said aerodynamic element having, between the leading edge and the trailing edge thereof, a local deflection angle ( φ) whose value varies between a leading edge value and a trailing edge value, characterized in that:

a two-dimensional profile is obtained from a section along a plane (P) of a three-dimensional geometric model of said aerodynamic element;

a mesh of a two-dimensional geometric domain delimited at least in part by said profile, said mesh defining a computational domain;

each mesh of said mesh is associated with a local three-dimensional coordinate system R (X, Y, Z) for which the axis X forms a local angle with said plane of the profile, and the axis Z is included in said plane of the profile and orthogonal to the chord of the profile, such that for any mesh between the leading edge and the trailing edge of the profile, the local angle is equal to said locally defined deflection angle (φ);

a discrete numerical model of the Navier-Stokes equations is solved by computer, on said mesh, so as to obtain the numerical solution of a flow of fluid within said computational domain, said resolution of said digital model comprising, at each time step, a step of calculating the speed in each of the meshes of said mesh to obtain a velocity field in the computation domain, said velocity in a given cell, expressed in the plane ( X, Z) of said corresponding local three - dimensional coordinate system, being calculated from the speed of at least one adjacent mesh upstream or downstream along the axis of said rope, said speed of said neighboring mesh being previously expressed in the plane (X, Z) of the local three-dimensional coordinate system of the mesh in question.

2. A method of computer simulation of the aerodynamic behavior of an aerodynamic element of an aircraft according to claim 1, characterized in that, for any mesh upstream of the leading edge of the profile, said local angle is equal to said value of the leading edge deflection angle (ΦΒΑ), and in that, for any mesh downstream of the trailing edge of the profile, said local angle is equal to said trailing edge deflection angle value.

3. A method of computer simulation of the aerodynamic behavior of an aerodynamic element of an aircraft according to claim 1 or 2, characterized in that said discrete numerical model of the Navier-Stokes equations comprises a condition imposed on the boundaries of said mesh comprising a speed defined local level, in each of the meshes of the said limits, by projecting the incident upstream velocity of said flow (V _∞ ) in the plane (X, Z) of said local three-dimensional coordinate system of the mesh in question.

4. A method of computer simulation of the aerodynamic behavior of an aerodynamic element of an aircraft according to claim 3, characterized in that said imposed speed limit condition further comprises a local velocity component resulting from a disturbance of the fluid. surrounding the aircraft induced by the aircraft.

5. A method of computer simulation of the aerodynamic behavior of an aerodynamic element of an aircraft according to any one of claims 1 to 4, characterized in that the step of calculating the speed in each of the meshes of said mesh comprises the Sub-steps:

a three-dimensional velocity is defined in said mesh next to the mesh considered from, on the one hand, the two-dimensional velocity in said neighboring mesh, the latter being expressed in the plane (X, Z) of said corresponding local three-dimensional mark, and of on the other hand, a third component defined by the projection of the upstream incident velocity of said flow along the Y axis of the corresponding local three - dimensional mark;

said three-dimensional velocity thus defined is expressed in the local three-dimensional coordinate system of the mesh in question; said three-dimensional velocity thus expressed is projected in the plane (X, Z) of the local three-dimensional coordinate system of the mesh in question, thereby obtaining the two-dimensional velocity in said adjacent mesh expressed in the plane (X, Z) of the local three-dimensional coordinate system of the mesh considered.

6. A method of computer simulation of the aerodynamic behavior of an aerodynamic element of an aircraft according to any one of claims 1 to 5, characterized in that the step of obtaining said profile comprises a modification of the thickness of the aircraft. profile following the relation: e ₂ (x ') = .e _x (x')

cos ^ (x ')

where ei (x ') and e ₂ (x') are the local thicknesses, respectively, of the initial profile and the modified profile, at the distance x 'at the leading edge along said chord, and φ (χ') is the value of the local arrow angle at said distance x '.

7. A method for estimating aerodynamic coefficients of an aerodynamic element of an aircraft in a flow, said aerodynamic element having, between the leading edge and the trailing edge thereof, a local deflection angle whose value varies between a leading edge value and a trailing edge value, characterized in that it comprises the steps of:

implementation of the computer simulation method of the aerodynamic behavior of said element aerodynamic apparatus according to one of claims 1 to 6; then

8. An estimation method according to claim 7, characterized in that said step of estimating the aerodynamic coefficients comprises an intermediate step of estimating the local pressure and wall friction coefficients from said digital solution obtained and the pressure dynamic defined from the incident upstream velocity of said flow.

9. An estimation method according to claim 8, characterized in that said local aerodynamic coefficients are integrated according to said initial profile to the unmodified thickness, so as to obtain overall aerodynamic coefficients expressed in the reference linked to the aircraft.

10. An estimation method according to claim 9, characterized in that said overall aerodynamic coefficients thus obtained are projected in an aerodynamic frame of reference oriented along said upstream speed, so as to obtain the lift, drag and pitch moment coefficients. .