Abstract:
A nozzle of a turbomachine is provided with chevrons with a non-axisymmetric inner face. A cover for the nozzle of longitudinal axis L-L includes an internal wall having a section with a predetermined abscissa on the L-L axis defining, on the wall, a neck line. The cover has, downstream from the abscissa, indentations in the trailing edge of the cover delimiting chevrons distributed in the circumferential direction, in which, on the cover, from the abscissa the internal wall moves away radially towards the outside of the upstream tangent, to the top of an indentation, the outer wall of the cover moves towards the upstream tangent to the top of an indentation, and the internal wall moves away radially towards the inside of the upstream tangent, to the tip of a chevron.

Description:
TECHNICAL FIELD 
       [0001]    The present invention relates to the general field of reduction of the jet noise at the outlet of a turbine engine nozzle. 
         [0002]    In particular, the present invention concerns the definition of the shape of a turbine engine nozzle which has, at its downstream end, a trailing edge comprising chevrons in order to reduce the jet noise. 
       PRIOR ART 
       [0003]    It is known that the jet at the outlet of a turbine engine nozzle encounters at least one other gaseous flow. Thus:
       when the turbine engine has a single flow, this flow comes into contact with the external air bypassing the nozzle; and   when the turbine engine has a double flow, the primary flow (or hot flow) and the secondary flow (or cold flow) come into contact with one another, but also with the external air.       
 
         [0006]    The speed difference between the jet at the nozzle outlet and the other gaseous flow or flows which it encounters creates fluid shears penetrating between these gaseous flows, which causes noise, commonly designated as “jet noise”. This “jet noise” is a broadband noise which is particularly inconvenient during the aeroplane take-off phase. 
         [0007]    The use of chevrons placed in a ring at the outlet of the nozzle is a known means for substantially reducing the low-frequency components of this noise. The patent application EP1873389A1 describes chevrons which make it possible to reduce the turbulent intensity of large vortices constituting the major sources of noise. The low-frequency noise is then substantially decreased. 
         [0008]    However, the incorporation of anti-noise chevrons in the region of the trailing edge of the nozzle is not entirely satisfactory. In fact, a pronounced inclination of the chevrons towards the outlet jet is generally necessary in order to obtain an acceptable reduction of the jet noise, which leads to a deterioration of performance levels, in particular the thrust, of the turbine engine at its different operating speeds. In addition, by decreasing the effective discharge cross-section of the internal gaseous flow of the nozzle, the inclination of the chevrons reduces the thrust ratio of the turbine engine between the take-off speed and the cruising speed. This results in a loss of operability of the turbine engine. This problem is particularly significant in the case of a convergent-divergent nozzle designed to optimise this operability. 
         [0009]    In the patent application FR1351152, the applicant has proposed an arrangement where the cross-section of the nozzle after the neck, whilst remaining circular, forms a divergent part into which the indentations of the cowl open, the chevrons retaining a convergent part relative to the neck in order to retain their effectiveness in terms of noise reduction. Moreover, the divergent part, which is open in certain sectors due to the indentations, makes it possible to obtain an effective discharge cross-section which is sufficient for maintaining the operational performance levels of the nozzle. However, this design does not allow sufficient degrees of freedom in order to treat all cases and has drawbacks for the internal flow, creating a possible recirculation zone in the zone where the chevrons curve in order to become convergent again. 
         [0010]    The present invention proposes an alternative in order to remedy these drawbacks and, in particular, to define the shape of a nozzle which makes it possible to achieve a greater effectiveness over all of the three criteria of performance levels, operability, and acoustics. 
       DESCRIPTION OF THE INVENTION 
       [0011]    The invention relates to a cowl for a nozzle having a longitudinal axis L-L delimited radially towards the exterior by its external wall and radially towards the interior by its internal wall, the internal wall of the cowl having a cross-section with a determined abscissa X 0  on the axis L-L defining a neck line on the wall, the upstream internal wall approaching the axis L-L by moving towards said cross-section, and said internal wall converging towards the axis L-L upstream of said cross-section and having, in any axial half-plane, a defined upstream tangent at its intersection with the neck line. 
         [0012]    Said cowl has, downstream of said determined abscissa X 0 , indentations in the trailing edge of the cowl which delimit chevrons distributed in the circumferential direction, and is characterised in that, in the downstream direction from said determined abscissa X 0 :
       the internal wall of the cowl diverges radially towards the exterior, in a first axial half-plane passing through the top of an indentation, from the upstream tangent on the point of the neck line in this half-plane,   the external wall of the cowl moves closer, in said first axial half-plane, to the upstream tangent on the point of the neck line in said first axial half-plane, and   the internal wall of the cowl diverges radially towards the interior, in a second axial half-plane passing through the tip of a chevron, from the upstream tangent on the point of the neck line in said second axial half-plane.       
 
         [0016]    In the present application, the terms “upstream” and “downstream” refer to the direction of the gaseous flows in a turbine engine or the nozzle thereof. A nozzle is defined as comprising a cowl of which the internal wall delimits a conduit into which an internal gaseous flow passes. A central body can be placed inside the cowl. In this case the conduit has an annular shape. A nozzle is said to be convergent (or divergent respectively) when the distance of the internal wall of the cowl from the central body or from the axis of the nozzle decreases (or increases respectively) in the downstream direction. An axial plane is understood to be a plane passing through the axis of revolution L-L, and an axial half-plane is the part of the axial plane extending on only one side of the axis L-L. 
         [0017]    In addition, in the present application the cowl has a thickness, and is therefore of the double-wall type and comprises an external wall around which flows an external gaseous flow, in the same direction as the internal gaseous flow. This external gaseous flow may be a secondary flow of the turbine engine, or the ambient air in which the aircraft moves. 
         [0018]    The neck cross-section serves for reference. In addition, at this location of minimal cross-section the mean direction of the gaseous flow in the nozzle is substantially parallel to the walls. Therefore, the tangent of the internal wall of the cowl to the neck gives an approximation of this direction of the gaseous flow at this cross-section. The three conditions defined in the invention therefore perform the following functions:
       constructing indentations which cause the internal flow to diverge,   guiding the external flow in the region of the indentations in order to promote the mixing of the flows,   constructing re-entrant chevrons in the internal flow,   and guiding the external Flow in the region of the tips in order to promote the mixing of the flows.       
 
         [0023]    On the one hand, the convergent design of the chevrons makes it possible to optimise them for reduction of the noise. On the other hand, the tops of the indentations can diverge from the axis regardless of the shape of the cross-section in the region of the chevrons, without taking account for example of the structural stresses of thickness of the cowl in the region of the chevrons. This makes it possible to obtain a larger equivalent discharge cross-section than in the previous solutions. This discharge cross-section is an important parameter in order to ensure the performance levels of the nozzle in various operating conditions, for example in order not to restrict the flow rate coefficient. In a way, the invention makes it possible to separate the geometric design parameters of the nozzle between those governing the acoustic performance levels and those governing the operational performance levels. The fact that the divergence of the external wall decreases constantly towards the top of the indentations makes it possible to decrease the separation of the external flow in this zone and thus contributes to the operational effectiveness of the nozzle. Another advantage of the invention is that it makes it possible to eliminate the part of maximum internal cross-section of the nozzle in the chevrons, corresponding to a possible separation zone. 
         [0024]    The lines defining the internal wall of the cowl upstream and downstream of the neck line in any axial half-plane preferably have the same tangent on this neck line. This avoids disruptions in the internal flow. 
         [0025]    The line defining the internal wall of the cowl downstream of said determined abscissa X 0  in an axial half-plane passing through the tip of a chevron is preferably concave when viewed from the axis L-L, with a view to improving the re-entrant nature of the chevron and avoiding recirculation zones in the internal flow. 
         [0026]    The line defining the internal wall of the cowl downstream of said determined abscissa X 0  in an axial half-plane passing through the top of an indentation is preferably convex when viewed from the axis L-L. This accords with the fact that the internal shape of the cowl forces the internal flow to diverge in this zone and to meet the external flow opposite a confluence where the two flows would be substantially parallel. 
         [0027]    The line defining the external wall of the cowl downstream of said determined abscissa X 0  in an axial half-plane passing through the top of an indentation is also preferably concave when viewed from the axis L-L. This condition reinforces the condition on the overall convergence of the external wall in an indentation in order to indicate that the direction imposed by the external wall at the top of the indentation on the external flow is re-entrant with respect to the mean direction of the internal flow. 
         [0028]    Advantageously, the lines defining the external wall of the cowl in any axial half-plane do not have a turning point downstream of said determined abscissa X 0  of the neck line, in order to limit the risks of separation in the external flow. 
         [0029]    Advantageously, the lines defining the internal wall of the cowl in any axial half-plane do not have a turning point downstream of the abscissa X 0  of the neck line. This condition, in a similar manner to that of the external wall, limits the separation of the flow inside the nozzle. 
         [0030]    Advantageously, the thickness of the cowl on its trailing edge is substantially constant. In fact, the thickness of the cowl is advantageously reduced to the minimum permitted by structural considerations at the tip of the chevrons in order to ensure the confluence of the two flows. It is useful to maintain this minimum thickness over all of the trailing edge in order to avoid recirculation zones due to a truncated trailing edge effect. In this way, convergent sectors can be defined around chevrons and divergent sectors can be defined around indentations, thereby organising the confluence between the external and internal gaseous flows to the cowl of the nozzle. 
         [0031]    The invention also relates to a nozzle for a turbine engine having a longitudinal axis L-L and comprising a cowl as defined previously. 
         [0032]    The invention also relates to a nozzle for a turbine engine having a longitudinal axis L-L and comprising a cowl as defined previously and a central body of revolution about the axis L-L. 
         [0033]    The features of the cowl advantageously make it possible to obtain properties which are remarkable in terms of the passage cross-section of the gaseous flow. Thus it is possible to obtain such a nozzle which has a central body and in which the radial passage cross-section at a point on a wall of the cowl is defined as the square of the radial distance of said point from the axis L-L minus the square of the radial distance of the axis L-L from the point of the wall of the central body situated on the same radius when said central body is present at the abscissa on the axis L-L of said point, and by the square of the radial distance of said point from the axis L-L when this is not the case, said nozzle being characterised in that, in the downstream direction from said determined abscissa of the neck line, the radial passage cross-section of the internal wall of the cowl increases in an axial half-plane passing through the top of an indentation. 
         [0034]    Thiscondition corresponds to the fact that the enlargement of the radial passage cross-section in the region of the indentations aims to increase the effective passage cross-section of the nozzle, or at the very least to preserve this effective passage cross-section, in spite of the constriction in the region of chevrons, with a view to increasing the operational performance levels of the nozzle. 
         [0035]    More generally, it is also possible to define a nozzle comprising a cowl which is delimited radially towards the exterior by its external wall and, radially towards the interior, by its internal wall,
       the internal wall of the cowl having a cross-section with a determined abscissa X 0  on the axis L-L defining on the wall a neck line upstream of which the nozzle is convergent, said internal wall approaching the axis L-L by moving upstream towards said cross-section and having, in any axial half-plane, a defined upstream tangent at its intersection with the neck line,   said cowl downstream of said determined abscissa X 0  having indentations in the trailing edge of the cowl which delimit chevrons distributed in the circumferential direction;   said nozzle optionally comprising a central body of revolution about the axis L-L and surrounded by the cowl, and the radial passage cross-section at a point on a wall of the cowl being defined as previously.       
 
         [0039]    Such a nozzle is remarkable in that, in the downstream direction from said determined abscissa (X 0 ) of the neck line:
       the radial passage cross-section of the internal wall of the cowl increases in an axial half-plane passing through the top of an indentation,   the radial passage cross-section of the external wall of the cowl decreases in an axial half-plane passing through the top of an indentation, and   the radial passage cross-section of the internal wall of the cowl decreases in an axial half-plane passing through the tip of a chevron.       
 
         [0043]    The three conditions verified by the cowl in this nozzle, expressed in radial passage cross-section, refer to the progression of the passage cross-section transversely with respect to the axis L-L, as a function of the difference between the squares of the radii (R exterior   2 −R interior   2 ). They are easier to implement and to verify in the design of the nozzle than the conditions expressed at a distance relative to the tangent to the neck for the cowl alone. Although they are less representative of the development of the shapes with respect to the mean flow in the event of pronounced variations in the inclination of the walls around the axis L-L, they perform similar functions to the conditions defined in the first characterisation of the nozzle, in particular if the inclination of the walls is not too pronounced. 
     
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         [0044]    The invention will be better understood, and other details, features and advantages of the present invention will be more clearly apparent from the following description given by way of non-limiting example and with reference to the accompanying drawings, in which: 
           [0045]      FIG. 1  is a schematic axial section of a convergent-divergent nozzle of a turbine engine, devoid of anti-noise chevrons; 
           [0046]      FIG. 2  is a schematic profile view of the rear of a nozzle cowl defined in accordance with the present invention, which comprises anti-noise chevrons; 
           [0047]      FIG. 3  is a superimposition of the schematic cross-sections of the rear of the cowl of  FIG. 2 , along the axial half-planes passing through the tip of a chevron and through the top of an indentation; 
           [0048]      FIG. 4  is an enlarged schematic perspective view of the construction by lines in the axial half-planes of the external and internal surfaces of the cowl, in the region of the chevrons and of the indentations; 
           [0049]      FIG. 5  is an enlarged schematic perspective view of a cowl thus defined in the region of the chevrons and of the indentations; 
           [0050]      FIG. 6  is a superimposition of the schematic cross-sections of the rear of a nozzle according to the invention in the case where the cowl surrounds a central body of the turbine engine, along the axial half-planes passing through the tip of a chevron and through the top of an indentation, referencing the distances with respect to an axis parallel to the tangent to the neck; 
           [0051]      FIG. 7  shows the same geometric configuration as  FIG. 6 , but referencing the distances with respect to the axis of the nozzle. 
       
    
    
     FIRST EMBODIMENT: CIRCULAR CONVERGENT-DIVERGENT REFERENCE NOZZLE 
       [0052]    When the cowl does not surround a central body, the rotationally symmetric cross-section of the nozzle around an axis L-L is defined by a cross-section perpendicular to the axis L-L. The surface area of a cross-section is defined solely by the radius of the internal wall of the cowl in this plane. Since the walls of the cowl are of circular cross-section, they are convergent or divergent here if the radius decreases or increases respectively in the downstream direction. 
         [0053]      FIG. 1  shows a known convergent-divergent reference nozzle  1   i  of a single-flow turbine engine. The reference nozzle  1   i  comprises an annular reference cowl  2   i  having a longitudinal axis L-L and a certain thickness which decreases close to its trailing edge  5   i.  The internal wall  3   i  of the cowl  2   i  defines a nozzle through which an internal gaseous flow F 1  passes. The external wall  4   i  of this cowl  2   i  is in contact with an external gaseous flow F 2 . 
         [0054]    The internal  3   i  and external  4   i  walls are connected to one another at their downstream end, with respect to the flow direction of the flows, in order to define the trailing edge  5   i  of the reference nozzle  1   i  which delimits its outlet cross-section  6   i.  The internal wall of the cowl  2   i  of the reference nozzle  1   i  has a convergent part as far as an abscissa X 0  on the axis L-L, connected to a divergent part downstream, which defines a neck  7   i  at X 0 . The external wall  4   i  of the cowl is, however, simply convergent towards the axis L-L. 
         [0055]    The reference nozzle  1   i  is devoid of anti-noise chevrons but it is suitable for a turbine engine (not shown) upstream of the convergent-divergent part shown in  FIG. 1 . As a function of the conditions on the internal flow which are imposed by this turbine engine upstream of the nozzle and are different according to the flight conditions, the nozzle is designed to correspond in particular to:
       a thrust coefficient at cruising speed CT RC , which gives the ratio between the thrust and the conditions which generate the internal flow F 1  and are created by the turbine engine;   a difference CV_DV , between the flow rate coefficient at take-off speed CD CTO  and that at cruising speed CD CC , which is required to be positive in order to increase the operability of the engine (passing on the good flow in order to avoid pumping, flotation or overheating).       
 
         [0058]    A cowl  2  defined according to the invention is designed in order to obtain an optimised nozzle  1  which has the same thrust coefficient CT RC , the same difference of flow rate coefficient CV_DV, and which additionally supplies a gain ΔEPNdB with respect to the intensity of the jet noise of the reference nozzle  1   i.  The jet noise can for example be measured and/or estimated at a predefined distance from the outlet cross-section  6  or  6   i  of the relevant nozzle, respectively the optimised nozzle  1  or the reference nozzle  1   i.    
         [0059]      FIG. 2  shows an example of a cowl  2  to the rear of an optimised nozzle  1  defined in accordance with the present invention. The shape of the internal wall  3  of the cowl  2  is identical to that of the internal wall  3   i  of the cowl  2   i  up to the abscissa X 0  on the axis L-L, corresponding to the cross-section of neck  7 . This cross-section defines a circular neck line  71  on the internal wall  3 , as shown on  FIG. 4 . Moreover, the tangent of the internal wall  3 , upstream, in an axial half-plane passing through any point on the neck line  71  is substantially parallel to the axis L-L. By way of example, the shape of the external wall  4  of the cowl  2  is identical to that of the external wall  4   i  of the cowl  2   i  up to an abscissa X 1  on the axis L-L, corresponding to a sectional plane  8  upstream of the abscissa X 0  of the neck  7 . In another embodiment, it is possible for the zone in which the external wall  4  of the cowl  2  is modified to be defined differently. 
         [0060]    Downstream of the abscissa X 0  of the neck  7 , the trailing edge  5  of the cowl  2  of the optimised nozzle  1  describes indentations  9  of substantially triangular shape having a rounded top  11 . Thus the indentations  9  define anti-noise chevrons  10  also of substantially triangular shape and having a rounded tip  13 , in the extension of the wall of the cowl  2 . Of course, the indentations and the chevrons could have any other appropriate shape (for example trapezoidal). 
         [0061]    The indentations  9 , regularly spaced from one another in the circumferential direction (although this could be different), are defined by a base situated on a circular  6  cross-section, limiting the downstream extension of the cowl, and by a top  11 , situated on a sectional plane  12  of the abscissa X 2 , downstream of the neck  7 . In the same way, the chevrons  10  defined by a tip  13  situated on the end circular cross-section  6  and by a base situated on the intermediate sectional plane  12 , are regularly spaced from one another. Furthermore, although it could be otherwise, in the example of  FIG. 2 , the indentations  9  are identical to one another. Therefore the same applies to the chevrons  10 . Finally, in the example shown, the abscissa X 3  of the circular cross-section  6  on which the tips  13  of the chevrons are located is offset from that of the outlet cross-section  6   i  of the reference nozzle  1   i.  However, this abscissa forms part of the adjustable parameters in the design of the new nozzle according to the invention. Therefore an embodiment may be provided in which the circular cross-section  6  would be placed differently. 
         [0062]    As  FIG. 3  shows, the shape of the cowl  2  according to the invention is defined so as to:
       firstly, obtain chevrons  10  of which the internal wall is convergent from the neck  7  and which chevrons re-enter the flux F 1  leaving the nozzle in order to optimise the anti-noise performance thereof;   secondly, on the contrary, allow the possibility for the nozzle to diverge at the top  11  of the indentations  9  in order to offer a wider equivalent outlet cross-section to the internal flow F 1  and to maintain the operational performance levels of the nozzle;   thirdly, retain a convergent shape of the external wall  4  of the cowl  2  towards the trailing edge  5  in order to convey the external flow F 2  into the internal flow F 1  and promote the mixing thereof.       
 
         [0066]    In order to achieve this object, first of all the profile of the walls of the cowl  2  is defined in the axial half-planes passing through the ends of the chevrons and of the indentations. These lines are defined with the aid of splines or any other means known to a person skilled in the art by imposing a certain number of conditions on said lines. 
         [0067]    In an axial half-plane passing through the top  11  of an indentation  9 :
       The internal wall  3  of the cowl  2 , illustrated in  FIG. 4 , forms, between the sectional point  72  of the neck  7  and the internal point  11 A at the top  11  of the indentation, a line  39  determined by the internal radius R 0  of the neck  7 , the abscissas X 0  of the point  72  on the neck and X 2  of the internal point  11 A, the radius R 2  defining the distance of the axis L-L from the point  11 A, and an angle a with the axis L-L, imposed on the tangent of the line  39  at the point  11 A.       
 
         [0069]    The external wall  4  of the cowl  2 , illustrated in  FIG. 4 , forms, between the point  82  on the abscissa X 1  and the external point  11 B at the top  11  of the indentation, a line  49  determined by the abscissa X 1 , the radius R 1  of the external wall at the point  82 , the abscissa X 2  of the external point  11 B (identical to that of the point  11 A on the example shown), by the thickness e of the cowl at the trailing edge  5  (indicated in  FIGS. 4 and 5 ), radially separating the points  11 A and  11 B, and an angle β with the axis L-L, imposed on the tangent of the line  49  at the point  11 B. 
         [0070]    In an axial half-plane passing through the tip  13  of a chevron  10 :
       The internal wall  3  of the cowl  2  forms, between the sectional point  73  of the neck  7  and the internal point  13 A at the tip  13  of the chevron  10 , a line  30  determined by the internal radius R 0  of the neck  7 , the abscissas X 0  of the point  73  on the neck and X 3  of the internal point  13 A, the radius R 3  defining the distance of the axis L-L from the point  13 A, and an angle θ with the axis L-L, imposed on the tangent of the line  30  at the point  13 A.   The external wall  4  of the cowl  2  forms, between the point  83  on the abscissa X 1  and the external point  13 B at the tip  13  of the chevron  10 , a line  40  determined by the abscissa X 1 , the radius R 1  of the external wall at the point  83 , the abscissa X 3  of the external point  13 B at the tip of the chevron (equal to that of the internal point  13 A on the example shown), by the thickness e of the cowl at the trailing edge  5 , radially separating the points  13 A and  13 B, and an angle y with the axis L-L, imposed on the tangent of the line  40  at the point  13 B.       
 
         [0073]    Furthermore, the internal radius R 2  at the internal point  11 A of the top of the indentation  9  is required to be greater than the internal radius R 0  at the neck  7 , and the internal radius R 3  at the internal point  13 A on the tip of chevrons is required to be less than the same internal radius R 0  at the neck  7 . 
         [0074]    Moreover, the lines  30 ,  39 ,  40  and  49  are required to be connected tangentially to the upstream surfaces of the initial cowl. This implies in particular that the tangents  70  and  79  of the lines  30  and  39  respectively, at the points  73  and  72  on the neck line  71 , form an angle of substantially zero with the axis L-L. Furthermore, as  FIG. 3  shows, in the axial half-plane these lines are required not to have turning points. In particular, the line  30  defining the internal wall  3  between the neck  7  and the tip  13 A of a chevron must be constantly convergent, that is to say that its distance from the axis L-L decreases towards the tip  13 A. Likewise the angles β and γ are required to be negative, that is to say that the external face  4  of the cowl converges towards the axis L-L at the corresponding ends. 
         [0075]    These conditions can be reformulated with respect to the mean direction of the internal flow F 1  at the neck  7  which is substantially parallel to the axis L-L, and therefore to the tangent of the internal wall  3  to the neck line  71 : 
         [0076]    In the downstream direction,
       the re-entrant chevron  10  in the internal flow F 1 , the sectional line  30  in the axial half-plane passing through the tip  13  diverges radially towards the interior of the tangent  70  to the neck,   as the indentation  9  is divergent for the internal flow F 1 , the sectional line  39  in the axial half-plane passing through the top  11  diverges radially towards the exterior of the tangent  79  to the neck, and   the sectional line  49  in the axial half-plane passing through the top  11  moves radially closer to the tangent  79  to the neck, directing the external flow F 2  towards the flow F 1 .       
 
         [0080]    Moreover, a three-dimensional tip-depression line defining the trailing edge  5  is calculated by known means in order to pass through the tops  11  of the indentations  9  at the tips  13  of the chevrons  10  according to the chosen shape, the distance of said line from the axis L-L varying monotonically, always in the same direction, from the top  11  of an indentation to the tip  13  of a neighbouring chevron  10 . In fact, an internal line  5 A and an external line  5 B, separated by the thickness e, define this trailing edge respectively for the internal  3  and external  4  walls of the cowl. As indicated in  FIGS. 4 and 5 , in the embodiment the radial thickness of the contour of each indentation  9 —defined between trailing edge lines  5 A and  5 B—is kept constant along said trailing edge. Said thickness is preferably equal to the thickness of the trailing edge of the cowl  2  of the reference nozzle  1 , that is to say for example 3.5 mm. 
         [0081]    As shown in  FIG. 4 , the surface defining the external wall  4  of the cowl towards the trailing edge  5  is determined by known computer-assisted design means, by portions between the indentations and the chevrons between the following curves:
       the line  81  defining the external wall of the cowl on the sectional plane of the abscissa X 1 , between the points  82  and  83 ,   the trailing edge line  5 B between the points  11 B and  13 B,   the line  40  connecting the points  83  and  13 B in the axial half-plane of the chevrons,   the line  49  connecting the points  82  and  11 B in the axial half-plane of the indentations.       
 
         [0086]    In addition, it is preferably required that the sectional lines of this surface through any axial half-plane do not have any turning points. Moreover, a tangent continuity of the connection surfaces with the surface  4  of the cowl is preferably required upstream of the line  81  at the connection point. Thus disruptions to the external flow F 2  are avoided. Preferably, the tangent of the sectional line of the surface defining the external wall in any axial half-plane is required to be always oriented towards the axis, whilst maintaining the fact that this external surface has no turning point. 
         [0087]    As can be seen in  FIG. 3 , it should be noted that in this surface construction the axial sectional line  40  passing through the tip  13 B of the chevron is approximately in the extension of the profile of the initial nozzle and that the axial sectional line  49  passing through the top of the indentation corresponds to a recess with respect to this profile. In this configuration, the external wall  4  of the cowl remains entirely inside the surface created by the revolution about the axis L-L of the line  40  defining its trace in the axial half-plane passing through the tip of the chevrons. Thus, the modified cowl does not have, radially, overall dimensions greater than that of the reference nozzle. 
         [0088]    The surface defining the internal wall  3  of the cowl  2  towards the trailing edge  5  is determined between the chevrons and the indentations in the same way as the external wall  4 , by:
       the curve  71  of the cross-section of the internal wall  3  in the plane of the abscissa X 1  between the points  72  and  73 ,   the internal trailing edge line  5 A between the points  11 A and  13 A,   the line  30  connecting the points  73  and  13 A in the axial half-plane of the chevrons,   the line  39  connecting the points  72  and  11 A in the axial half-plane of the indentations.       
 
         [0093]    Moreover, a tangent continuity, in any axial half-plane, of the connection surfaces with the internal wall  3  of the cowl is preferably required upstream of the line  71  at the connection point. 
         [0094]    It should be noted, as can be seen from  FIG. 3, 4 or 5 , and from the conditions imposed, that from the tip  13 A of the chevron towards the top  11 A of the indentation, the axial lines of the surfaces defining the internal wall  3  progressively change orientation: they converge constantly without a turning point in the region of the chevron, they diverge in the region of the indentation. Advantageously, these lines are convex when viewed from the axis L-L around the top  11 A of the indentation  9  and their tangent in the region of the trailing edge line  5 A is divergent. The angle a of the tangent of the axial line  39  is positive, as is indicated in  FIG. 3 . 
         [0095]    Moreover, as can be seen in  FIG. 5 , the cowl obtained by assembling these surfaces has an azimuthal alternation between convergent angular sectors centred around axial half-planes passing through the tips  13 A of the chevrons  10 , and divergent sectors centred around axial half-planes passing through the tops  11 A of the indentations  9 . 
         [0096]    A brief description of the different steps enabling the definition of the optimised nozzle equipped with chevrons  10  is given below. 
         [0097]    In a preliminary phase, an initial value is attributed to the dimensional parameters defining the chevrons  10  and the indentations  9  towards the trailing edge  5  of the cowl  2 , namely the parameters e, X 0 , X 1 , X 2 , X 3 , R 0 , R 1 , R 2 , R 3 , θ, γ, β and α. 
         [0098]    Then, by any means accessible to a person skilled in the art, performance criteria which are associated with the optimised nozzle equipped with chevrons  10  and designed with the aid of the aforementioned dimensional parameters are calculated. These criteria are for example the three criteria introduced previously, namely the thrust coefficient at cruising speed CT CC , the difference CV_DV between the flow rate coefficient at take-off speed CD CTO  and the flow rate coefficient at cruising speed CD CC , the difference ΔEPNdB between the intensity of the jet noise of the reference nozzle  1   i  and that of the nozzle equipped with chevrons according to the invention. 
         [0099]    Predefined performance conditions to be satisfied are also associated with each criterion, in particular:
       the performance condition associated with the difference between the thrust coefficients ΔCT is satisfied when this difference ΔCT is less than a second predefined threshold. Said threshold is, for example, equal to 0.001 (that is to say ΔCT&lt;0.001);   the performance condition associated with the difference between the flow rate coefficients CV_DV is satisfied when this difference CV_DV is at least equal to a first predefined threshold. Said threshold is, for example, equal to 0.015 (that is to say CV_DV≧0.015); and   the performance condition associated with the difference between intensities of the jet noise ΔEPNdB is satisfied when this difference ΔEPNdB is positive (that is to say ΔEPNdB&gt;0) and, preferably, at least equal to a third predefined threshold.       
 
         [0103]    Then an optimisation algorithm is applied to the set of dimensional parameters thus initialised in order to define the shape of the cowl  2  equipped with chevrons, such that the optimised nozzle  1  satisfies the predefined conditions on said performance criteria. 
         [0104]    For example, it is verified that the aforementioned three performance criteria CV_DV, ΔCT and ΔEPNdB calculated with the initial values of the dimensional parameters each satisfy predefined performance conditions which are respectively associated with them. 
         [0105]    In the case where at least one of said calculated performance criteria does not satisfy the performance condition associated therewith, a new initial value is attributed to at least one of the aforementioned dimensional parameters, and then the three performance criteria are calculated again. For example, the new initial value can correspond to the previous initial value incremented by one unit. 
         [0106]    As long as the conditions associated with the three performance criteria are not satisfied simultaneously, the aforementioned two steps from the preceding paragraph are repeated. 
         [0107]    When the three calculated performance criteria satisfy the associated performance conditions, the last values attributed to the dimensional parameters are validated in order to define the definitive shape of the walls  3  and  4  of the cowl  2  of the optimised nozzle  1 . 
       SECOND EMBODIMENT: CONVERGENT REFERENCE NOZZLE 
       [0108]    In this variant, the reference nozzle  1   i  is simply convergent. An attempt will then be made to reduce the effect of supplementary convergence introduced by chevrons. 
         [0109]    The cowl  2  of the nozzle obtained according to the present invention has, towards its trailing edge  5 , a shape comprising chevrons  10  and indentations  9 , which is defined by the same parameters as those of the first embodiment. 
         [0110]    In this case there is no predefined neck, since the reference nozzle is convergent. A preliminary step therefore consists in choosing a cross-section  7 , for an abscissa X 0  on the axis L-L upstream of the outlet  6 i of the reference nozzle  1 i, on the basis of which the shape of the internal wall  3  of the cowl  2  of the optimised nozzle is modified. Once this abscissa X 0  is determined, the construction of the surfaces defining the internal  3  and external  4  walls of the cowl  2  uses the same parameters and the same method as for the first embodiment. 
         [0111]    The method for defining the optimised nozzle therefore comprises a preliminary step compared with the first embodiment which consists in choosing the abscissa X 0  of the neck cross-section of the optimised nozzle. Since the reference nozzle  1   i  is convergent, the more this abscissa X 0  is raised in the upstream direction, the larger the neck cross-section  7  is and the more it is possible, as compensation, to make the chevrons  10  convergent. 
         [0112]    The method for defining the optimised nozzle then repeats the steps of the method used in the first embodiment. 
       THIRD EMBODIMENT: ANNULAR REFERENCE NOZZLE 
       [0113]    In the case of an exhaust nozzle for a double-flow turbojet engine for example, the nozzle corresponds to the air conduit defined between the internal wall of a cowl  2  and the wall  21  of a central body  20  of circular cross-section around the axis L-L shown in  FIG. 6 . 
         [0114]    The cross-section of the nozzle is no longer defined by the radius of the internal face of the cowl  2 . Known methods are used in this configuration and define, as the cross-section, a surface which is substantially perpendicular to the mean flow, which is no longer a plane perpendicular to the axis L-L. For example, the calculation method known as “rolling ball” consists in making a ball roll on one of the walls. When this ball touches the two walls, the line which joins the two points of contact defines the passage cross-section between these two points. By varying the diameter of the ball it is thus possible to define the passage cross-section over the length of the nozzle. Next, the convergent or divergent nature of the nozzle is characterised as a function of the evolution of the surface area of this surface as it progresses downstream. 
         [0115]    For the implementation of the invention, the shape of the wall  21  is not modified. Use is then made of the fact that the wall  21  of the central body is a determined surface area having a relatively regular shape, and that the aim is to characterise portions of wall  3  or  4  of the cowl  2  for which the nozzle cross-section is uniformly convergent or divergent. The object of the invention is also repeated, which is that of:
       constructing re-entrant chevrons  10  in the flow F 1  coming from the neck  7 ,   constructing indentations  9  causing divergence of this same flow F 1 , and   guiding the external flow F 2  towards the flow F 1  coming from the neck in the region of the indentations  9 .       
 
         [0119]    In a first variant of the invention, the variations in cross-section which a method of the “rolling ball” type could provide are approximated by the procedure described below. Reference is made to the mean direction of flow F 1  at the neck  7 . The tangent of the internal wall  3  of the cowl  2  on the neck line  71  in an axial half-plane is no longer obligatorily parallel to this axis. 
         [0120]    On the contrary, this tangent substantially follows the mean flow around the central body  20  and its direction therefore represents approximately the direction of the internal flow F 1  close to the cowl in the axial half-plane, in the region of the cross-section of the neck. Therefore, in the definition of the lines  30  and  39  or  40  and  49  defining the internal  3  and external  4  walls of the cowl  2  in the relevant axial half-planes, the direction of the axis L-L is replaced by that of the tangent  70  or  79  defined in this half-plane by the internal wall upstream of the corresponding points  72  or  73  on the neck line  71 . 
         [0121]      FIG. 6  shows the rear of an optimised nozzle according to the invention, repeating the notations of the first embodiment. The different characteristic locations on the cowl  2 , the end of the chevrons  13 , the top  11  of the indentations, the line  71 , corresponding to the points  72  and  73 , of the neck cross-section on the internal wall  3  of the cowl, and the line  81 , corresponding to the points  82  and  83 , of the cross-section of the external wall of the cowl, are referenced by their respective abscissas on the axis L-L: X 3 , X 2 , X 0 , X 1 . 
         [0122]    In contrast, in each axial half-plane, a straight line L′L′ parallel to the tangents  70  and  79  respectively, and passing through the point X 0  of the neck  7  is defined. The conditions for the divergence of the characteristic points are then determined by their respective distances from this straight line L′L′: D 3 , D 2 , D 0 , D 1 . Moreover, the angles of the tangents are likewise calculated with respect to this straight line L′L′. 
         [0123]    Using these conventions, the same steps defining the walls of the cowl  2  as in the first embodiment are repeated but:
       the radius at a point on an internal  3  or external  4  wall of the cowl  2  is replaced by the divergence at this point from the straight line L′L′;   the angle formed by a tangent in an axial half-plane at a point on a wall of the cowl with the axis L-L is replaced by the angle which said tangent forms with the tangent of the internal wall  3  on the neck line  71 .       
 
         [0126]    In this way, the condition observed in the first embodiment is apparent in the downstream direction from the abscissa X 0 :
       the sectional line  30  in the axial half-plane passing through the tip  13  diverges radially towards the interior of the tangent  70  to the neck,   the sectional line  39  in the axial half-plane passing through the top  11  diverges radially towards the exterior of the tangent  79  to the neck, and   the sectional line  49  in the axial half-plane passing through the top  11  moves radially closer to the tangent  79  to the neck.       
 
         [0130]    The algorithm for defining the cowl then repeats the same steps as in the first embodiment in order to obtain a nozzle which meets the required performance criteria. 
         [0131]    A variant in this configuration, shown in  FIG. 7 , consists in referring to the surface area of cross-sections defined in the plane perpendicular to the central axis L-L, even if they are not actually perpendicular to the mean flow. In this case, the radial passage cross-section S′=(R extertior   2 −R interior   2 ) at a point on the walls of the cowl  2  is defined as the difference between the square, R exterior   2 , of the distance of this point from the axis L-L, and the square, R interior   2 , of the distance from the axis L-L of the point on the wall  21  of the central body  20  situated on the same radius perpendicular to the axis L-L, when the central body is present in the sectional plane transverse to the axis L-L containing this point. When the central body is not present in the sectional plane transverse to the axis L-L containing a point on a wall of the cowl, the radial passage cross-section is simply the square of the distance of this point from the axis L-L. 
         [0132]    By applying the convergence and divergence criteria to the radial passage cross-section, this variant is then transposed directly from the first embodiment by replacing the radii R 0 , R 1 , R 2  and R 3  by the corresponding radial passage cross-sections S′ 0 , S′ 2 , and S′ 3 . 
         [0133]    The method can be immediately transposed to the case where the reference nozzle is simply convergent as in the second embodiment. 
         [0134]    Finally, the invention also applies to a generalisation of the three examples presented, for a nozzle which is not necessarily circular around the axis L-L. In a variant of the method applied to this case, the surfaces of the cowl are defined by the sectional lines in the successive axial planes by turning azimuthally about a central axis L-L. The parameters defining the indentations  9  and the chevrons  10  in the different axial planes are then different according to the azimuth of the axial plane, as a function of the shape required for the transverse cross-section of the nozzle around this axis L-L. In contrast, the shape of the sectional lines of the internal  3  and external  4  walls of the cowl  2  in the axial planes passing through the tops  11  of the indentations  9  and through the tops  13  of chevrons  10  follow the conditions previously set out with respect to the points  72  and  73  of the neck line.