1
AN AIRFOIL AND PLATFORM ASSEMBLY FOR SUBSONIC FLOW
The invention relates to an assembly comprising an
airfoil for a turbine engine bladed wheel together with a
platform on which the airfoil is to be mounted, the
5 assembly as formed in this way being arranged in such a
manner that a plurality of airfoils fastened on the
platform or on a plurality of assembled-together
platforms can form a bladed wheel. The term "platform"
is used herein to designate a part that defines the
10 radially inner side of an interblade passage formed
between two adjacent airfoils of a bladed wheel. The
term "platform surface" is used to designate the platform
surface that faces the interblade passage. The platform
surface may also designate the assembly of the platform
15 surfaces of a bladed wheel considered collectively.
In known manner, the airfoils of a bladed wheel may
be made integrally with the rotor disk in order to
constitute a bladed wheel. The part made in this way
that combines both airfoils and their platforms is
20 referred to as a one-piece bladed wheel. In another
embodiment, the airfoils are made independently from the
rotor disk (i.e. they constitute distinct parts). Under
such circumstances, the airfoils are formed with
respective roots enabling them to be fastened to the
25 rotor disk, thereby constituting blades. The assembly
comprising blades on the rotor disk thus constitutes a
bladed wheel.
The invention seeks an advantageous arrangement of
an airfoil relative to the platform surface; such an
30 arrangement may be provided in the various constructions
described above, independently of whether the platform
and the airfoil do or do not constitute distinct parts.
The invention seeks more particularly to make
assemblies as described above for making bladed wheels of
35 (high pressure or low pressure) compressors, and in
particular of multistage compressors that are to be found
in turbine engines or in helicopter turboshaft engines.
2
The invention may also be used for making blades or
bladed wheels for the turbines of turbine engines (which
turbines may be high pressure or low pressure turbines).
The aerodynamic efficiency of a compressor stage
5 (equal to the ratio of the ideal work (i.e. the work
associated with an isentropic transformation) and the
work generally delivered to the fluid in order to obtain
a given pressure increase between the upstream and
downstream ends of the compressor stage) in a turbine
10 engine depends not only on the shape of the airfoils, but
also on the shape of the platforms. In order to improve
this efficiency, it is known to modify the platform
surface in one or more bladed wheels so as to locally
increase or decrease the flow section for the fluid
15 stream through the bladed wheel(s). For this purpose,
and in known manner, the platform is modified by
arranging a circumferential depression and/or a
circumferential bulging area in its surface level with
the airfoils. (The term "circumferential" is used herein
20 with respect to a depression or a bulging area to
designate a depression or a bulging area that is
substantially a surface of revolution, naturally with the
exception of the immediate vicinity of the airfoils.)
Such a modification, known as "contouring" serves to
25 improve the aerodynamic efficiency of the bladed wheel
and more generally of the compressor stage. The terms
"depression" and "bulging area" should be understood with
reference to a theoretical surface radially defining the
inside of the passage and varying linearly from upstream
30 to downstream of the bladed wheel.
Nevertheless, in spite of the increase in efficiency
as obtained in this way for the bladed wheel, such a
modification generally also gives rise to certain
undesirable effects on the fluid stream. Specifically:
35 • it may give rise to high pressure gradients at the
outlet from the bladed wheel; such gradients are harmful
to the operation of the bladed wheel, and in particular
3
to the overall efficiency of the turbine engine, in
particular in multistage compressors;
• it may give rise to non-uniformities in speed
distributions around the airfoils, in particular in the
5 vicinity of their roots; and
• finally, it may lead to a modification in the
compression ratio of the wheel (where the compression
ratio is equal to the ratio of the pressures upstream and
downstream of the bladed wheel).
10 When such undesirable side effects are observed,
they are generally remedied by modifying the shape of the
bladed wheels situated in the fluid passage downstream
from the bladed wheel under consideration. Nevertheless,
such modifications cannot conserve the improvement in
15 efficiency made possible by modifying the platform
surface of the bladed wheel under consideration; in
addition, it is not always possible to make such
modifications.
The object of the invention is to remedy such
20 drawbacks by proposing an assembly comprising an airfoil
for a turbine engine bladed wheel and a platform on which
the airfoil is suitable for being mounted;
a plurality of said airfoils being suitable for
being fastened to said platform or to a plurality of said
25 platforms assembled together so as to form a bladed wheel
having a wheel axis and defining upstream and downstream
directions along that axis, the airfoils being arranged
radially in the wheel;
in said wheel, the platform or the assembled-
30 together platforms present a surface between the airfoils
that is referred to as a platform surface and that
radially defines the inside of gas-passing passages
formed between the airfoils;
the platform surface presenting a circumferential
35 depression extending axially substantially between a
leading edge of an airfoil at its upstream end and up to
4
no more than 60% of an axial extent of the airfoil at its
downstream end,
which assembly gives good aerodynamic efficiency to
the bladed wheel, provides pressure gradients downstream
5 from the bladed wheel similar to those that would be
found in the absence of the circumferential depression in
the platform surface, and makes it possible to obtain
speed distributions of the fluid that are relatively
uniform, in particular in the vicinity of a blade root.
10 In order to present the solution provided by the
invention, the following elements are defined:
The "vicinity" of the platform relates to the
portion of the airfoil situated at a short distance (e.g.
less than 20% of the height of the airfoil) above the
15 fillets connecting the airfoil to the platform. The
skeleton angle is the angle formed by the neutral fiber
of the airfoil relative to the axis of the bladed wheel
in a plane perpendicular to the longitudinal direction of
the airfoil, the sign of the skeleton angle being
20 selected in such a manner that the upstream skeleton
angle (the skeleton angle at the leading edge of the
airfoil) is positive. The skeleton curve is the curve
plotting variations in a skeleton angle of an airfoil in
a section plane that is substantially parallel to the
25 platform surface, as a function of position along the
axis of the wheel. The linearized skeleton curve is the
curve representing variations of an angle as a function
of position along the axis of the wheel, which angle
makes a straight line connection between the points
30 representing the skeleton angle respectively at 10% and
at 90% of the axial extent of the airfoil from its
leading edge. The linearized skeleton angle, represented
by the linearized skeleton curve, is thus equal to the
skeleton angle at 10% and at 90% of the axial extent of
35 the airfoil from the leading edge (the upstream and
downstream ends of the airfoil, which may be subjected to
specific arrangements, are not taken into account).
I
[
5
The above-specified object is achieved according to
the invention by the fact that, in an assembly as
specified above, in a vicinity of the platform, a lowered
portion of the skeleton curve which lies under the
5 linearized skeleton curve extends axially over at least
half of the axial extent of said depression.
Thus, the invention consists in locally modifying
the shape of the airfoil so as to enable the skeleton
curve to be lowered (which amounts to "opening" the
10 skeleton angle, in the sense that the skeleton angle in
the section under consideration diminishes in absolute
value compared with the linearized skeleton curve) in
association with at least half of the circumferential
depression (and thus over a range axially overlapping
15 it), so as to adapt the airfoil to the modification of
the stream that is induced by the circumferential
depression provided in the platform. The alterations
made to the airfoil in the vicinity of the platform
enable the bladed wheel to operate optimally, taking
20 account of the modification to the platform surface
constituted by the circumferential depression.
The axial extent of the airfoil designates the
distance measured at the airfoil root and along the axis
of the bladed wheel between the leading edge and the
25 trailing edge of the airfoil. The circumferential
depression does not extend axially beyond 60% of the
axial extent of the airfoil.
In an assembly of the invention, because of the
lowered portion presented by the curve plotting variation
30 in the skeleton angle, i.e. the "skeleton" curve, over a
radially lower portion of the airfoil, the air or gas
stream is deflected so as to slow down in a frame of
reference relative to the blade in the vicinity of the
circumferential depression. The opening of the passage
35 provided by the circumferential depression facilitates
diffusion in the vicinity of the blade root, thus making
6
it possible, while resetting this diffusion to its value
prior to arranging the circumferential depression:
• in the upstream portion of the airfoil, to limit
i
the increase m the speed of the fluid stream, and thus
5 reduce Shockwave losses (as a result of the opening of
the skeleton angle, in particular in the range extending
from 0% to 40% of the axial extent of the airfoil); and
• in the downstream portion of the airfoil, to
reduce the profile stream offset (the offset between the
10 direction of the stream in the vicinity of the trailing
edge and the downstream skeleton angle) by locally
limiting the deflection that is imposed on the fluid.
The assembly of the invention may be subjected to
the following improvements:
15 • the circumferential depression may extend axially
substantially between the leading edge at its upstream
end and only 40% of the axial extent of the airfoil at
its downstream end;
I • the deepest section of said depression may be
20 situated axially in the range 15% to 35% of the axial
extent of the airfoil from the leading edge of the
airfoil;
• the platform surface may present a circumferential
bulging area situated axially in the downstream half of
25 the airfoil;
• a most projecting section of the bulging area may
be situated axially in the range 50% to 70% of the axial
i
extent of the airfoil from the leading edge of the
I airfoil;
I 30 'in said vicinity, the skeleton curve may present a
I raised portion lying above the linearized skeleton angle
j
curve and situated axially downstream from said lowered
portion. This raised portion may be located axially
substantially level with said bulging area, and may
35 possibly extend axially over the entire axial extent of
the bulging area. The fact that the raised portion is
axially substantially level with the bulging portion
7
means that the difference between the limits of the
raised portion and the bulging portion (along the axis of
the bladed wheel) is less than 10%, whether upstream or
downstream;
5 • the skeleton curve may present a slope of absolute
value that is less than that of the linearized skeleton
curve in the range 80% to 100%, and preferably in the
range 60% to 100% of the axial extent of the airfoil from
its leading edge. This arrangement makes it possible to
10 reduce the profile stream difference at the trailing edge
of the airfoil. In an embodiment, the skeleton curve may
in particular be situated under the linearized skeleton
curve between 10% and 90% of the axial extent of the
airfoil;
15 • an upstream skeleton angle may be the skeleton
angle at the leading edge of the airfoil; in a radially
lower fourth of the airfoil, the upstream skeleton angle
may increase in absolute value (the upstream angle of the
airfoil is said to close) on approaching the airfoil
20 root. This configuration of the leading edge of the
airfoil contributes to reducing or eliminating the
negative effects induced by the circumferential
depression in the platform surface.
A second object of the invention is to provide a
25 turbine engine blade that imparts good aerodynamic
efficiency to a bladed wheel made up with the help of
such blades, that provides pressure gradients downstream,
from the bladed wheel similar to those that would be
observed in the absence of the circumferential depression
30 in the platform surface, and that makes it possible to
obtain relatively uniform speed distributions, in
particular in the vicinity of the blade root.
This object is achieved by the fact that the turbine
engine blade is constituted by an assembly as defined
35 above, comprising a platform formed integrally with at
least one airfoil. The platforms of such blades are
generally arranged in such a manner that they define the
8
entire interblade surface radially defining the inside of
the gas flow passages that exist between the airfoils.
A third object of the invention is to provide a
turbine engine bladed wheel that presents good
5 aerodynamic efficiency, pressure gradients downstream
from the bladed wheel similar to those that would be
observed in the absence of a circumferential depression
in the platform surface, and speed distributions that are
relatively uniform, in particular in the vicinity of the
I 10 blade root.
This object is achieved by the fact that the bladed
wheel is made using assemblies as defined above, and in
particular with blades each comprising a platform made
I integrally with at least one airfoil. A one-piece bladed
15 wheel constitutes an example of such a bladed wheel.
Finally, the invention may advantageously be
incorporated in a turbine engine including at least one
bladed wheel as defined above.
The invention can be well understood and its
20 advantages appear better on reading the following
detailed description of embodiments given as non-limiting
examples. The description refers to the accompanying
drawings, in which:
• Figure 1 is a diagrammatic perspective view of a
25 compressor stage of a turbine engine of the invention;
j • Figure 2 is a diagrammatic perspective view of
three assemblies of the invention, forming a part of the
wheel shown in Figure 1;
• Figures 3A and 3B are figures showing an assembly
30 comprising a platform associated with an airfoil and
comprising:
a) a diagrammatic view of the assembly as seen
in the circumferential direction; and
b) a graph showing the skeleton curve of the
35 airfoil of said assembly;
9
where Figure 3A shows a prior art assembly and Figure 3B
shows an assembly constituting a first embodiment of the
invention;
• Figure-4 is a graph showing two variants for the
5 skeleton curve of an airfoil of an assembly of the
invention, corresponding respectively to the first
embodiment and to a second embodiment;
• Figure 5 is a section of an airfoil of an assembly
of the invention; and
10 • Figure 6 is a graph plotting the curve showing
variations in the skeleton angle upstream from an airfoil
in an embodiment of the invention.
In the various figures, elements that are identical
or similar are given the same references.
15 Figure 1 shows a portion of an axial-flow compressor
10 in a turbine engine 100. The compressor 10 comprises
a casing 12 having a bladed wheel 14 mounted therein.
The bladed wheel 14 itself comprises a rotor disk 16
having radial blades 18 fastened thereon in conventional
20 manner in an axisymmetric configuration. The bladed
wheel is arranged to be capable of turning about an axis
of rotation A inside the casing 12.
The arrangement of the blades 18 on the bladed
wheels 14 is shown in greater detail by Figure 2, which
25 shows a fragment of the wheel 14.
In the wheel 14, each blade 18 forms an assembly 1
associating an airfoil 20, a platform 22, and a blade
root 24. The blade platforms 22 are thus made integrally
with the airfoils 20. Naturally, the invention may be
30 implemented in other types of bladed wheel, in which the
airfoils and the platform(s) constitute distinct parts.
The roots 24 serve to fasten the blades 18 to the
rotor disk 16.
The platforms 22 associated within the bladed wheel
35 14 make up a platform surface 30 that defines the
radially inner side of the inter-blade passages that
allow gas to pass between the blades. This platform
10
surface is approximately a surface of revolution - or at
least it may be approximated by a surface of revolution.
The blades 18 are arranged in such a manner that
when they are assembled together so as to make up the
5 wheel 14, the platforms of the blades define the entire
platform surface 30 formed between the airfoils 20.
Thus, no additional portion forms a portion of or shapes
the platform surface 30. In order to enable the blades
18 to be assembled together, the edges 32 on one of the
10 sides in the circumferential direction of the bladed
wheel of a platform are complementary in shape to the
edges 34 of the platforms situated on the opposite sides
relative to the circumferential direction C.
Each airfoil 20 has a leading edge 26 and a trailing
15 edge 28, and it extends radially in a radial direction B
that is specific to each airfoil.
In Figure 2, there can be seen a section plane V
that constitutes a section plane substantially parallel
to the platform surface 30, and it is situated in the
20 vicinity of the root of the airfoil 20.
Figure 5 is a section of an airfoil 120 of a turbine
engine blade in a plane perpendicular to the longitudinal
axis of the airfoil.
This section shows the neutral fiber 122 of the
25 airfoil for the plane in question. The neutral fiber is
the set of points of the airfoil that are equidistant
from the two side faces of the airfoil (its pressure side
and its suction side). For example, the point M shown is
I at the same distance d from the pressure side and from
30 the suction side. The skeleton angle a at the point M is
the angle between the tangent 124 to the neutral fiber at
the point M and the axis A of the wheel. The skeleton
angle ttg or upstream skeleton angle is the skeleton angle
at the leading of the airfoil 120.
35 Figures 3A and 3B show respectively an assembly 1
(combining a platform 22 and an airfoil 20) in a prior
art embodiment and in an embodiment of the invention.
11
Figure 3A:
The platform surface 30 shown in Figure 3Aa) has not
been subjected to any specific alteration along the axis
of the airfoil 20 (i.e. along the axis A), This platform
5 surface is thus a reference platform surface 30j.gf that is
substantially conical.
In Figure 3Ab), there is plotted the curve showing
the variations in the skeleton angle of the Figure 3Aa)
airfoil in the plane A-A (the plane marked in chain-
10 dotted lines in Figure 3Aa)), as a function of axial
position along the axis of the wheel 14. Axial position
is marked in percentage as a function of position
relative to the axial extent E of the airfoil 20. The
axial extent E is the distance along the axis A between
15 the leading edge 26 and the trailing edge 28 at the root
of the airfoils 20 (Figures 3Aa)). The airfoil 20 of the
assembly shown in Figure 3A is an airfoil of the type in
which the skeleton curves and the linearized skeleton
coincide, as shown in Figures 3Ab).
20 Figure 3B:
Figure 3B shows an embodiment of the invention. In
this embodiment, the platform surface 30 has been altered
I along the airfoil 20.
The alterations made are defined radially in
25 relative manner relative to the reference platform
surface 30j.gf. This surface 30j.gf is defined as the
substantially conical surface approximating the platform
surface 30, this reference surface 30j.gf being determined
while ignoring both the circumferential depression and
I 30 also any other localized alterations (if any and whether
circumferential or otherwise) that might project from or
be set back in the platform surface at various axial
locations along the airfoils 20.
The surface alterations of the platform 30 and of
35 the airfoils 20 are also defined axially relative to the
axial extent E of the airfoils 20.
•
12
The platform surface 30 is altered to have a
circumferential depression 40 (Figure 3Ba)). The term
depression (or conversely superconvergent or bulging
surface) is used to mean a portion of the platform
5 surface that lies radially inside (or respectively
outside) the reference platform surface 30j,gf and
corresponds to the airflow passage locally being enlarged
(or respectively reduced).
The circumferential depression 40 extends axially
10 from the leading edges 26 of the airfoils 20 up to 60% of
the axial extent E of the airfoils (along the axis A ).
In fact, the depression 40 extends nearly up to 60% of
the axial extent E. The axial section 41 (perpendicular
to the axis of the wheel 14) where this depression 40 is
j 15 the deepest is situated axially in the range 15% to 35%
i of the axial extent E, and specifically at 30% of the
i
axial extent E. In the sentence above, the "deepest"
section means the section of the depression 40 where the •
distance d2 relative to the reference platform surface
20 SO^gf is the greatest (see Figure 3Ba) ) .
Furthermore, the platform surface presents a
I circumferential bulging area 42, that may be referred to
as "superconvergent", that is situated axially in the
i downstream half of the airfoil. The most projecting
25 section 43 of this bulging area 42 is situated axially in
the range 50% to 70% of the axial extent of the airfoil
i
i from the leading edge of the axrfoil, and specifically at
70% of the axial extent E. In the sentence above, the
; "most projecting" section means the section of the
30 circumferential area 42 for which the distance d3 from the
reference platform surface 30j.gf is the greatest.
The above-described alterations 40 and 42 improve
the efficiency of the bladed wheel 14. However they
disturb the flow of fluid in the vicinity of the platform
35 surface compared with the flow made possible by the
theoretical platform surface 30^.^^. In the invention, in
order to compensate for these disturbances, the shape of
13
the airfoils 20 is modified in the manner shown in
Figures 3Bb) and 4.
This modification affects (in general manner) mainly
the radially inner half of an airfoil 20. This
5 modification can be seen in particular in a section plane
of the airfoil (plane V, Figure 2) that is parallel to
the platform surface and that is situated in the vicinity
of the platform.
This modification is shown in Figure 4 in which
10 there can be seen:
• as a bold dashed line, the skeleton curve 4 6
representing variations in the skeleton angle a of the
airfoil 20 for the first embodiment of the invention
(Figure 3B);
i
15 • as a fine dashed line, the skeleton curve 47
representing the variations in the skeleton angle a of an
airfoil in a second embodiment of the invention; and
• as a continuous line, the linearized skeleton
I curve 45 of the airfoil 20, representing the variations
I 20 in the linearized skeleton angle, which is the same for
both embodiments.
In these various curves, the variations in the
skeleton angle a are plotted as a function of axial
position along the airfoil, this axial position being
25 given as a percentage relative to the axial extent E of
the airfoil 20.
I In both embodiments, the shape of the platform
surface is the same and is as shown in Figure 3B.
The modification made in accordance to the invention
30 to the airfoil 20 consists in the fact that the skeleton
angle curve presents a lowered portion extending axially
over less than half the axial extent of the
circumferential depression 40. (The term "lowered
portion" is used to mean a portion of a curve lying under
35 the linearized skeleton angle curve: in other words, in
the lowered portion, the skeleton angle is lower in
absolute value than the linearized skeleton angle and is
14
wider open.) This lowered portion is referenced 44 and
I 144 respectively for the first embodiment and for the
second embodiment.
In the embodiments shown, the depression 40 extends
5 over an area 40R occupying 0% to 60% of the axial extent
E. In the invention, the curve 4 6 presents a lowered
portion 44 extending axially over an area 44R covering at
least 30% of the axial extent of the area 40R (from 0% to
60%) of the depression 40. Thus, in the first
10 embodiment, the area 44R extends from 10% to 53%
approximately of the axial extent E.
The area 44R may be included axially within the area
40R covered by depression 40, or it may extend beyond
said area in a downstream direction. In an embodiment,
15 the entire lowered portion 44 lies within the depression
40, and the area 44R is included within the area 40R.
Conversely, in the second embodiment, the lowered portion
144 extends over nearly all of the axial extent of the
airfoil, in particular it extends from 10% to 90% of the
20 axial extent of the airfoil.
Furthermore, in addition to the lowered portion 44,
the skeleton curve 4 6 shown in Figure 4, which shows the
shape of the airfoil 20 in the vicinity of the platform,
also presents a raised portion 48. The term "raised
25 portion" is used herein to mean a portion of the curve
that lies above the linearized skeleton angle curve 45.
This raised portion 48 is situated axially downstream
from the lowered portion 44. In the example shown, the
area 42R over which the bulging portion 42 extends lies
30 in the range 60% to 100% of the axial extent E, and the
area 48R over which the raised portion 48 extends lies in
the range 53% to 90% of the axial extent E. Thus, the
bulging area 42 and the raised portion 48 of the airfoil
section are situated axially in substantially the same
35 location.
In general, depending on the embodiment (see
Figure 4), the raised portion 48 may begin at its
15
upstream end in the range 40% to 60% of the axial extent
\ of the airfoil. At its downstream end it may continue
substantially to about 90% of the axial extent E, at
which point the curves 45, 46, and 47 cross, by
5 construction. The presence of this raised portion 48
seeks to limit the possible effects on the offset to the
i
flow profile that is induced by the lowered portion 44.
The raised portion 48 preferably extends over at least
30% of the axial extent of the airfoil, and preferably
10 over at least 40%.
In the second embodiment, and unlike the first, the
skeleton curve 47 does not have a raised portion
downstream from the lowered portion. On the contrary,
the skeleton curve remains under the linearized skeleton
15 curve, with a lowered portion 144 occupying nearly all of
the axial extent of the airfoil (in the range 10% to
90%). It follows that the skeleton curve 47 presents a
slope of smaller absolute value than does the linearized
skeleton curve in the range 80% to 100%, and even in this
20 embodiment in the range 60% to 100% of the axial extent E
of the airfoil from its leading edge.
Figure 6 shows a potential additional alteration of
the airfoil suitable for compensating the undesirable
effects caused by the alterations to the surface of the
25 platform 30. Figure 6 shows variations in the upstream
I
skeleton angle ttg of an airfoil as a function of the
height h expressed as a percentage of the total height of
the airfoil and as measured from the root of the airfoil
to the end of the airfoil.
30 In this embodiment, in a radially lower half of the
airfoil, the upstream skeleton angle ttg (Figure 5)
differs from the upstream skeleton angles used in normal
manner. In the lower half of the airfoil, the variations
in the skeleton angle are represented by the curve 80 for
35 a typical upstream skeleton angle as used in known
manner, and by the curve 82 for the upstream skeleton
angle in an embodiment of the invention. In the upper
16
half of the blade, these two curves coincide to form a
curve 81.
In conventional manner, the airfoils are arranged in
such a manner that the upstream skeleton angle decreases
5 in absolute value from the tip of the airfoil (h=100%, h
being the radial distance from the root of the airfoil)
I to the root of the airfoil (h=0%). Conversely, in this
improvement of the invention, in the lower fourth of the
airfoil and possibly up to 40% of the height of the
10 airfoil extending from the root of the airfoil, the
absolute value of the upstream skeleton angle increases
(i.e. the skeleton angle becomes more closed) on
approaching the root of the airfoil. This modification
seeks to compensate the localized increase in flow rate
15 at the root of the airfoil caused by the contouring of
the passage. It also serves to protect the blade from
any loss of surge margin.
The invention is particularly suitable for blades
that are to operate in a subsonic flow.
20

17
CLAIMS
1. An assembly (1) comprising an airfoil (20) for a
turbine engine bladed wheel and a platform (22) on which
the airfoil is suitable for being mounted;
5 a plurality of said airfoils being suitable for
being fastened to said platform or to a plurality of said
platforms assembled together so as to form a bladed wheel
(14) having a wheel axis (A) and defining upstream and
downstream directions along that axis, the airfoils being
10 arranged radially in the wheel;
in said wheel, the platform (22) or the assembledi
together platforms present a surface (30) between the
airfoils that is referred to as a platform surface and
that radially defines the inside of gas-passing passages
15 formed between the airfoils;
said platform surface presenting a circumferential
depression (40) extending axially substantially between a
leading edge of an airfoil at its upstream end and up to
no more than 60% of an axial extent of the airfoil at its
20 downstream end,
the assembly being characterized in that:
where a "skeleton curve" is the curve representing
variations of a skeleton angle (a) of the airfoil in a
section plane substantially parallel to the platform
25 surface as a function of position along the axis of the
wheel;
and where a "linearized skeleton curve" (45) is the
curve representing variations of an angle as a function
of position along the axis of the wheel that connects
30 together in a straight line the points representing the
skeleton angle respectively at 10% and at 90% of the
axial extent of the airfoil from the leading edge;
in a vicinity of the platform, a lowered portion
(44) of the skeleton curve which lies under the
35 linearized skeleton curve (45) extends axially over at
least half of the axial extent (40R) of said depression.
i
18
2. An assembly according to claim 1, wherein the
circumferential depression extends axially substantially
between the leading edge at its upstream end and only 40%
of the axial extent of the airfoil at its downstream end.
5
3. An assembly according to claim 1 or claim 2, wherein
the deepest section of said depression (40) is situated
axially in the range 15% to 35% of the axial extent of
the airfoil from the leading edge of the airfoil.
10
4. An assembly according to any one of claims 1 to 3,
wherein said platform surface presents a circumferential
bulging area (42) situated axially in the downstream half
of the airfoil.
15
5. An assembly according to any one of claims 1 to 4,
wherein a most projecting section (43) of said bulging
area is situated axially in the range 50% to 70% of the
axial extent of the airfoil from the leading edge of the
20 airfoil.
5. An assembly according to any one of claims 1 to 5,
wherein, in said vicinity, the skeleton curve presents a
raised portion (48) lying above the linearized skeleton
25 angle curve and situated axially downstream from said
lowered portion.
7. An assembly according to claim 6, wherein said raised
portion (48) is located axially substantially at the
30 level of said bulging area.
8. An assembly according to any one of claims 1 to 5,
wherein the skeleton curve presents a slope of absolute
value that is less than that of the linearized skeleton
35 curve in the range 80% to 100%, and preferably in the
range 60% to 100% of the axial extent of the airfoil from
its leading edge.
19
m
9. An assembly according to any one of claims 1 to 8,
wherein an upstream skeleton angle is the skeleton angle
• at the leading edge of the airfoil; in a radially lower
5 fourth of the airfoil, said upstream skeleton angle
increases in absolute value on approaching the airfoil
root.
10. A turbine engine blade (18) constituted by an
10 assembly according to any one of claims 1 to 9 and having
a platform formed integrally with at least one airfoil.
11. A turbine engine bladed wheel (14) formed with blades
. according to claim 10.
15 . . •
12. A turbine engine bladed wheel (14) formed with at
least one assembly according to any one of claims 1 to 9.
13. A turbine -engine (100) including at least one bladed
^ 20 wheel according to claim 11 or claim 12.