FORM 2
THE PATENTS ACT, 1970
(39 of 1970)
&
THE PATENTS RULES, 2003
COMPLETE SPECIFICATION
(See section 10, rule 13)
1. Title of the invention: TURBINE BLADE AND STEAM TURBINE INCLUDING THE
SAME
2. Applicant(s)
NAME NATIONALITY ADDRESS
MITSUBISHI POWER, LTD. Japanese 3-1, Minatomirai 3-Chome, Nishi-ku,
Yokohama-shi, Kanagawa 2208401,
Japan
3. Preamble to the description
COMPLETE SPECIFICATION
The following specification particularly describes the invention and the manner in which it
is to be performed.
1
TECHNICAL FIELD
[0001] The present disclosure relates to a turbine blade and a steam turbine
including the same.
5
BACKGROUND
[0002] In a turbine such as a steam turbine or a gas turbine, a loss may be caused
by a fluid flow in a blade row. Thus, it is proposed that a concave portion and a
convex portion are disposed in an end wall (side wall) of a platform to which an
airfoil portion of a turbine blade is connected, 10 thereby suppressing the fluid loss in
the turbine.
[0003] For example, Patent Document 1 discloses a turbine blade which includes
a concave portion (passagethrough) disposed in the vicinity of a convex portion on
suction surface and a convex portion (bump) disposed in the vicinity of a leading
15 edge on a pressure surface of an airfoil portion, in a region of suction surface of the
airfoil portion of an end wall of a platform.
Citation List
Patent Literature
20 [0004]
Patent Document 1: US Patent Application Publication No. 2017/0226863
SUMMARY
Technical Problem
25 [0005] In general, a static pressure tends to be low in the vicinity of a convex
portion on a suction surface in operation of a turbine, and thus it is considered that
2
disposing the concave portion in the vicinity of the convex portion on the suction
surface in the vicinity of the end wall of the platform, it is possible to increase the
static pressure in the above-described portion to reduce a blade loading.
[0006] Meanwhile, a leakage flow from the upstream side of a turbine blade may
flow into the turbine blade in accordance with, 5 for example, the type of turbine. In
this case, a loss owing to the above-described leakage flow may be caused.
Conventionally, however, an end wall shape for reducing such loss owing
to the leakage flow has not been proposed, and Patent Document 1 does not mention
the end wall shape for reducing the loss owing to the leakage flow, either.
10 [0007] In view of the above, an object of at least one embodiment of the present
invention is to provide a turbine blade capable of reducing a loss which may be
caused by a leakage flow, and a steam turbine including the same.
Solution to Problem
15 [0008] (1) A turbine blade according to at least some embodiments of the present
invention includes an airfoil portion having a pressure surface and a suction surface
each of which extends between a leading edge and a trailing edge, and a platform
including an end wall to which a base-end portion of the airfoil portion is connected.
The end wall includes a concave portion on suction surface disposed at least in a
20 region of suction surface of the end wall, and a convex portion on pressure surface
disposed at least in a region of pressure surface of the end wall. The concave
portion on suction surface has a bottom point located on an axially upstream side
of a tangent point on the suction surface, the suction surface having a tangential line
extending in an axial direction through the tangent point. The end wall has at least
25 one contour line on the concave portion on suction surface, the at least one contour
line having a normal line on an intersection point between the at least one contour
3
line and the suction surface such that a normal vector having a negative gradient
along the normal line is directed toward the airfoil portion. The convex portion
on pressure surface has a peak point located on an axially downstream side of the
tangent point.
[0009] A leakage flow without a circumferential 5 component may flow into the
vicinity of the end wall of the turbine blade from the upstream side of the turbine
blade. The leakage flow flows into the rotating turbine blade and then heads for
the suction surface of the turbine blade, which may cause a collision (back hit) of
the leakage flow against the suction surface, or due to an interaction between the
10 leakage flow and a flow (main flow) including the circumferential component, may
cause circumferential non-uniformity of a static pressure distribution.
[0010] In this regard, in the above configuration (1), the bottom point of the
concave portion on suction surface is located on the axially upstream side of the
above-described tangent point, and the above-described normal vector is directed
15 toward the airfoil portion. That is, the bottom point of the concave portion on
suction surface is located close to the suction surface on the axially upstream side
of a position where the suction surface protrudes the most (a position of the abovedescribed
tangent point), and the concave portion on suction surface has an
obliquity descending toward the suction surface in the vicinity of the suction surface.
20 Thus, it is possible to increase the static pressure in the vicinity of the abovedescribed
position, making it possible to alleviate the circumferential nonuniformity
of the static pressure distribution in the vicinity of the end wall in the
axially upstream portion of the turbine blade, or to reduce the collision (back hit)
of the leakage flow from the upstream side of the turbine blade against the suction
25 surface. Thus, it is possible to reduce the circumferential non-uniformity of the
static pressure distribution and a loss owing to the back hit of the leakage flow.
4
Moreover, in the above configuration (1), the peak point of the convex
portion on pressure surface is located on the axially downstream side of the abovedescribed
tangent point. That is, the peak point of the convex portion on pressure
surface is located on the axially downstream side of the bottom point of the concave
portion on suction surface. Thus, it is possible 5 to reduce the static pressure in the
vicinity of the above-described position, making it possible to reduce a secondary
flow from the pressure surface toward the suction surface of the adjacent turbine
blade, and to prevent, for example, a leakage flow avoiding a collision against the
suction surface by the above-described concave portion on suction surface from
10 becoming the secondary flow in the vicinity of the pressure surface. Thus, it is
possible to reduce a secondary flow loss in the turbine blade.
In view of the foregoing, with the above configuration (1), it is possible to
effectively reduce the loss which may be caused by the leakage flow in the turbine.
[0011] (2) In some embodiments, in the above configuration (1), the convex
15 portion on pressure surface has at least one contour line having a normal line on an
intersection point between the at least one contour line and the pressure surface such
that a normal vector having a positive gradient along the normal line is directed
toward the airfoil portion.
[0012] With the above configuration (2), the above-described normal vector is
20 directed toward the airfoil portion. That is, the peak point of the convex portion
on pressure surface is located close to the pressure surface, and the convex portion
on pressure surface has an obliquity ascending toward the pressure surface in the
vicinity of the pressure surface. Thus, it is possible to reduce the static pressure in
the vicinity of the above-described position, making to possible to effectively
25 reduce the secondary flow in the turbine blade and to reduce the loss by the
secondary flow more effectively.
5
[0013] (3) In some embodiments, in the above configuration (1) or (2), the convex
portion on pressure surface expands along the pressure surface at least from a
position of the peak point to a position of the bottom point of the concave portion
on suction surface in the axial direction.
[0014] With the above configuration 5 (3), since the convex portion on pressure
surface extends along the pressure surface over a wide range at least from the
position of the peak point of the convex portion on pressure surface to the position
of the bottom point of the concave portion on suction surface in the axial direction,
it is possible to reduce the static pressure over the wide range in the vicinity of the
10 pressure surface. Thus, it is possible to effectively prevent the leakage flow
avoiding the collision against the suction surface by the concave portion on suction
surface from becoming the secondary flow in the vicinity of the pressure surface of
the adjacent turbine blade. Thus, it is possible to effectively reduce the secondary
flow loss in the turbine blade.
15 [0015] (4) In some embodiments, in any one of the above configurations (1) to (3),
a ratio L1/L0 of an axial distance L1 between the bottom point of the concave
portion on suction surface and the peak point of the convex portion on pressure
surface to an axial length L0 of the airfoil portion on the end wall is at least 0.1 and
at most 0.9.
20 [0016] With the above configuration (4), since the ratio L1/L0 of the distance L1
between the bottom point of the concave portion on suction surface and the peak
point of the convex portion on pressure surface to the axial length L0 of the airfoil
portion on the end wall is at least 0.1 and at most 0.9, the leakage flow avoiding the
collision against the suction surface by the concave portion on suction surface is
25 easily introduced to the vicinity of the convex portion on pressure surface. Thus,
it is possible to effectively prevent the leakage flow from becoming the secondary
6
flow in the vicinity of the pressure surface and to effectively reduce the secondary
flow loss in the turbine blade.
[0017] (5) In some embodiments, in any one of the above configurations (1) to (4),
an angle between an axial straight line, and a straight line that connects the bottom
point of the concave portion on suction surface 5 and the peak point of the convex
portion on pressure surface of an adjacent turbine blade is not less than 10 degrees
and not greater than 80 degrees.
[0018] With the above configuration (5), since the angle between the axial straight
line, and the straight line that connects the bottom point of the concave portion on
10 suction surface and the peak point of the convex portion on pressure surface of the
adjacent turbine blade is not less than 10 degrees and not greater than 80 degrees,
the leakage flow avoiding the collision against the suction surface by the concave
portion on suction surface is easily introduced to the vicinity of the convex portion
on pressure surface. Thus, it is possible to effectively prevent the leakage flow
15 from becoming the secondary flow in the vicinity of the pressure surface and to
effectively reduce the secondary flow loss in the turbine blade.
[0019] (6) In some embodiments, in any one of the above configurations (1) to (5),
the convex portion on pressure surface extends along the pressure surface over not
less than 90% of an axial length L0 of the airfoil portion on the end wall.
20 [0020] With the above configuration (6), since the convex portion on pressure
surface extends along the pressure surface over not less than 90% of the axial length
L0 of the airfoil portion on the end wall in the axial direction, it is possible to reduce
the static pressure over the wide range in the vicinity of the pressure surface. Thus,
it is possible to effectively prevent the leakage flow avoiding the collision against
25 the suction surface by the concave portion on suction surface from becoming the
secondary flow in the vicinity of the pressure surface of the adjacent turbine blade.
7
Thus, it is possible to effectively reduce the secondary flow loss in the turbine blade.
[0021] (7) In some embodiments, in any one of the above configurations (1) to (6),
the turbine blade is configured such that the concave portion on suction surface and
the convex portion on pressure surface of an adjacent turbine blade form a smooth
slope from the bottom point of the concave 5 portion on suction surface to the peak
point of the convex portion on pressure surface.
[0022] With the above configuration (7), since the concave portion on suction
surface and the convex portion on pressure surface of the adjacent turbine blade
form the smooth slope from the bottom point of the concave portion on suction
10 surface to the peak point of the convex portion on pressure surface, it is possible to
smoothly introduce the leakage flow avoiding the collision against the suction
surface by the concave portion on suction surface to the vicinity of the convex
portion on pressure surface. Thus, it is possible to effectively prevent the leakage
flow from becoming the secondary flow in the vicinity of the pressure surface and
15 to effectively reduce the secondary flow loss in the turbine blade.
[0023] (8) In some embodiments, in any one of the above configurations (1) to (7),
the end wall further includes a convex portion on suction surface disposed at least
in the region of suction surface, and the convex portion on suction surface expands
along the suction surface over a range that includes a throat forming position located
20 on the axially downstream side of the tangent point on the suction surface.
[0024] With the above configuration (8), since the above-described convex
portion on suction surface is disposed in the end wall, it is possible to reduce the
static pressure in the vicinity of the convex portion on suction surface, making it
possible to make the contour line on the suction surface more parallel to the blade
25 height direction in the range including the throat forming position in the vicinity of
the end wall. Moreover, since the concave portion on suction surface has the
8
obliquity ascending downstream from the bottom point along the suction surface, it
is possible to make the contour line on the suction surface described above much
more parallel to the blade height direction at an axial position of the concave portion
on suction surface. Thus, it is possible to suppress curl-up of a secondary flow
swirl that may be caused in the vicinity of the 5 base-end portion of the airfoil portion,
and to reduce the secondary flow loss more effectively.
[0025] (9) In some embodiments, in the above configuration (8), the convex
portion on pressure surface and the convex portion on suction surface of an adjacent
turbine blade share at least one contour line.
10 [0026] With the above configuration (9), since the convex portion on pressure
surface and the convex portion on suction surface of the adjacent turbine blade share
at least one contour, between the turbine blades adjacent to each other, the end wall
has a shape formed by smoothly connecting the convex portion on pressure surface
and the convex portion on suction surface. Thus, blocking of a fluid flow between
15 the turbine blades is suppressed, making it possible to suppress a decrease in turbine
efficiency.
[0027] (10) In some embodiments, in any one of the above configurations (1) to
(9), a ratio L2/L0 of an axial distance L2 between the leading edge and a front end
of the platform to an axial length L0 of the airfoil portion on the end wall is at most
20 0.1.
[0028] In accordance with, for example, the type of turbine, the turbine blade in
which the ratio L2/L0 of the axial distance L2 between the leading edge of the
airfoil portion and the front end of the platform to the axial length L0 of the airfoil
portion on the end wall is at most 0.1 as in the above configuration (10), that is, a
25 turbine blade having the relatively short axial distance L2 between the front end of
the platform and the leading edge of the airfoil portion may be used. In this regard,
9
with the above configuration (10), when the above-described turbine blade having
the relatively short axial distance L2 between the front end of the platform and the
leading edge of the airfoil portion is adopted, as described in the above
configuration (1), it is possible to effectively reduce the loss which may be caused
5 by the leakage flow in the turbine.
[0029] (11) In some embodiments, in any one of the above configurations (1) to
(10), the base-end portion of the airfoil portion includes a fillet portion disposed in
a connection portion to the platform, and an axial distance L2 between the leading
edge and a front end of the platform is not less than 50% and not greater than 100%
10 of a width of the fillet portion in a planar view.
[0030] With the above configuration (11), in accordance with, for example, the
type of turbine, the turbine blade in which the axial distance L2 between the leading
edge of the airfoil portion and the front end of the platform is not less than 50% and
not greater than 100% of the width of the fillet portion disposed in the base-end
15 portion of the airfoil portion as in the above configuration (11), that is, the turbine
blade having the relatively short axial distance L2 between the front end of the
platform and the leading edge of the airfoil portion may be used. In this regard,
with the above configuration (11), when the above-described turbine blade having
the relatively short axial distance L2 between the front end of the platform and the
20 leading edge of the airfoil portion is adopted, as described in the above
configuration (1), it is possible to effectively reduce the loss which may be caused
by the leakage flow in the turbine.
[0031] (12) In some embodiments, in any one of the above configurations (1) to
(11), the concave portion on suction surface extends without crossing a dividing
25 line forming a boundary with an adjacent turbine blade.
[0032] With the above configuration (12), since the concave portion on suction
10
surface extends without crossing the dividing line forming the boundary with the
adjacent turbine blade and does not stride over the dividing line, productivity of the
turbine blade is good.
[0033] (13) A steam turbine according to at least some embodiments of the present
invention includes the turbine blade according 5 to any one of the above
configurations (1) to (12).
[0034] In the steam turbine, the leakage flow without the circumferential
component may flow into the vicinity of the end wall of the turbine blade from the
upstream side of the turbine blade. The leakage flow flows into the rotating
10 turbine blade and then heads for the suction surface of the turbine blade, which may
cause a collision (back hit) of the leakage flow against the suction surface, or due
to an interaction between the leakage flow and a flow (main flow) including the
circumferential component, may cause circumferential non-uniformity of a static
pressure distribution.
15 [0035] In this regard, in the above configuration (13), the bottom point of the
concave portion on suction surface is located on the axially upstream side of the
above-described tangent point, and the above-described normal vector is directed
toward the airfoil portion. That is, the bottom point of the concave portion on
suction surface is located close to the suction surface on the axially upstream side
20 of a position where the suction surface protrudes the most (a position of the abovedescribed
tangent point), and the concave portion on suction surface has an
obliquity descending toward the suction surface in the vicinity of the suction surface.
Thus, it is possible to increase the static pressure in the vicinity of the abovedescribed
position, making it possible to alleviate the circumferential non25
uniformity of the static pressure distribution in the vicinity of the end wall in the
axially upstream portion of the turbine blade, or to reduce the collision (back hit)
11
of the leakage flow from the upstream side of the turbine blade against the suction
surface. Thus, it is possible to reduce the circumferential non-uniformity of the
static pressure distribution and a loss owing to the back hit of the leakage flow.
Moreover, in the above configuration (13), the peak point of the convex
portion on pressure surface is located on 5 the axially downstream side of the abovedescribed
tangent point. That is, the peak point of the convex portion on pressure
surface is located on the axially downstream side of the bottom point of the concave
portion on suction surface. Thus, it is possible to reduce the static pressure in the
vicinity of the above-described position, making it possible to reduce a secondary
10 flow from the pressure surface toward the suction surface of the adjacent turbine
blade, and to prevent, for example, a leakage flow avoiding a collision against the
suction surface by the above-described concave portion on suction surface from
becoming the secondary flow in the vicinity of the pressure surface. Thus, it is
possible to reduce a secondary flow loss in the turbine blade.
15 In view of the foregoing, with the above configuration (13), it is possible
to effectively reduce the loss which may be caused by the leakage flow in the turbine.
[0036] (14) In some embodiments, in the above configuration (13), the steam
turbine includes a rotor blade which is the turbine blade, and a stator vane disposed
adjacent to the rotor blade on an upstream side of the rotor blade in an axial direction
20 of the steam turbine, and a ratio L3/L0 of an axial width L3 of a cavity formed
between the rotor blade and the stator vane to an axial length L0 of the airfoil
portion on the end wall is at least 0.15.
[0037] In the steam turbine in which the ratio L3/L0 of the axial width L3 of the
cavity to the axial length L0 of the airfoil portion is at least 0.15 as in the above
25 configuration (14), that is, in the steam turbine including the relatively wide cavity,
an influence by the leakage flow from the cavity may be prominent, and a collision
12
of the above-described leakage flow against the suction surface and the
circumferential non-uniformity of the static pressure distribution are likely to occur.
In this regard, with the above configuration (14), as described in the above
configuration (13), it is possible to reduce the circumferential non-uniformity of the
static pressure distribution and the loss owing to back 5 hit of the leakage flow, or to
reduce the secondary flow loss in the turbine blade. Thus, with the above
configuration (13), it is possible to effectively reduce the loss which may be caused
by the leakage flow in the turbine.
10 Advantageous Effects
[0038] An object of at least one embodiment of the present invention is to provide
a turbine blade capable of reducing a loss which may be caused by a leakage flow,
and a steam turbine including the same.
15 BRIEF DESCRIPTION OF DRAWINGS
[0039] FIG. 1 is a schematic cross-sectional view of a steam turbine according to
an embodiment, taken along its axial direction.
FIG. 2 is a schematic enlarged view including a stator vane and a rotor
blade of the turbine according to an embodiment.
20 FIG. 3 is a schematic view of rotor blades installed on the steam turbine
according to an embodiment.
FIG. 4A is a schematic view of the rotor blade according to an embodiment.
FIG. 4B is a schematic view of the rotor blade according to an embodiment.
FIG. 5 is a contour map of an end wall of rotor blades according to an
25 embodiment.
FIG. 6 is a contour map of the end wall of the rotor blades according to an
13
embodiment.
FIG. 7 is a contour map of the end wall of rotor blades according to an
embodiment.
FIG. 8 is a contour map of the end wall of the rotor blades according to an
5 embodiment.
DETAILED DESCRIPTION
[0040] Some embodiments of the present invention will be described below with
reference to the accompanying drawings. It is intended, however, that unless
10 particularly identified, dimensions, materials, shapes, relative positions and the like
of components described or shown in the drawings as the embodiments shall be
interpreted as illustrative only and not intended to limit the scope of the present
invention.
[0041] First, the overall configuration of a steam turbine as an example of a
15 turbine to which a turbine blade is applied according to some embodiments will be
described with reference to FIGs. 1 and 2. The turbine in the present invention is
not limited to the steam turbine, but may be, for example, a gas turbine.
[0042] FIG. 1 is a schematic cross-sectional view of the steam turbine according
to an embodiment, taken along its axial direction. FIG. 2 is a schematic enlarged
20 view including a stator vane and a rotor blade of the turbine according to an
embodiment.
As shown in FIG. 1, a steam turbine 1 includes a rotor 2 rotatably supported
by a bearing portion 6, a plurality of stages of rotor blades 8 and stator vanes 9, an
inner casing 10, and an outer casing 12. The plurality of rotor blades 8 and a
25 plurality of stator vanes 9 are arranged in the circumferential direction to form rows,
respectively. The rows of the rotor blades 8 and the rows of the stator vanes 9 are
14
arranged alternately in the axial direction.
[0043] As shown in FIGs. 1 and 2, the rotor blade 8 includes an airfoil portion 30
and a platform 40 to which the airfoil portion 30 is connected, and is mounted to a
rotor disc 4 of the rotor 2 via the platform 40. The rotor 2 and the rotor blade 8
5 are housed in the inner casing 10.
Moreover, the stator vane 9 includes an airfoil portion 50, and an outer ring
52 and an inner ring 54 disposed on the radially outer side and the radially inner
side of the airfoil portion 50, respectively. The stator vane 9 is supported by the
inner casing 10 via the outer ring 52 and the inner ring 54.
10 [0044] In such a steam turbine 1, if steam is introduced from a steam inlet 3 to the
inner casing 10, the steam expands and increases in speed when passing through
the stator vane 9, performs work on the rotor blades 8, and rotates the rotor 2.
[0045] In addition, the steam turbine 1 includes an exhaust hood 14. Steam
(steam flows S) having passed through the rotor blades 8 and the stator vanes 9 in
15 the inner casing 10 flows into the exhaust hood 14, and is discharged to the outside
of the steam turbine 1 from an exhaust hood outlet 13 disposed on a lower side of
the exhaust hood 14 through the inside of the exhaust hood 14.
A condenser (not shown) is disposed below the exhaust hood 14. The
steam having finished working on the rotor blades 8 in the steam turbine 1 is
20 discharged from the exhaust hood 14 via the exhaust hood outlet 13 and flows into
the condenser.
[0046] The turbine blade according to some embodiments may be the rotor blade
8 of the steam turbine 1.
As an example of the turbine blade according to some embodiments, the
25 rotor blade 8 of the steam turbine 1 described above will be described below in
more detail.
15
[0047] FIG. 3 is a schematic view of rotor blades installed on the steam turbine 1
according to an embodiment. Each of FIGs. 4A and 4B is a schematic view of the
rotor blade according to an embodiment. FIGs. 3 to 4B are views for describing
the basic configuration of the turbine blade, and thus FIGs. 3 to 4B do not show a
“concave portion on suction surface, a “5 convex portion on pressure surface”, and
the like to be described later.
[0048] As shown in FIGs. 3 and 4, the rotor blade 8 (turbine blade) includes the
airfoil portion 30, the platform 40 to which the airfoil portion 30 is connected, and
a blade root portion 44.
10 [0049] The airfoil portion 30 includes a leading edge 31 and a trailing edge 32
each of which extends along a blade height direction, and a pressure surface 33 and
a suction surface 34 each of which extends between the leading edge 31 and the
trailing edge 32. The airfoil portion 30 has a base-end portion 35 connected to an
end wall 42 (side wall) of the platform 40. On a connection portion of the base15
end portion 35 and the platform 40, a fillet portion 36 for relaxing a stress
concentration in the connection portion is disposed.
[0050] The blade root portion 44 is connected to the platform 40 on an opposite
side to the airfoil portion 30. As shown in FIG. 3, the blade root portion 44
engages with a groove 4A formed in the rotor disc 4, thereby mounting the rotor
20 blade 8 to the rotor 2 (see FIG. 1).
[0051] As shown in FIG. 3, in the steam turbine 1, the plurality of rotor blades 8
are circumferentially arranged around a center axis, thereby forming an annular
blade row. FIG. 3 shows a pair of adjacent rotor blades 8, 8’ of the plurality of
rotor blades 8 forming the annular blade row. The axial direction which is the
25 direction of the center axis described above is a direction orthogonal to the abovedescribed
circumferential direction, and is the same direction as a center axis O (see
16
FIG. 1) of the rotor 2 for the steam turbine 1.
[0052] In the airfoil portion 30 of the rotor blade 8, the leading edge 31 is located
on the axially upstream side, and the trailing edge 32 is located on the axially
downstream side. Moreover, the platform 40 has a front end 40a and a rear end
40b, and extends between the front end 40a and 5 the rear end 40b in the axial
direction. That is, the front end 40a of the platform 40 is an upstream end in the
axial direction, and the rear end 40b of the platform 40 is a downstream end in the
axial direction.
[0053] The platform 40 of the rotor blade 8 shown in FIG. 4A extends along the
10 axial direction. In this case, the platform 40 of the plurality of rotor blades 8
arranged adjacent to each other in the circumferential direction has a shape of a
columnar side surface. A surface S1 forming the columnar side surface will be
referred to as a reference surface of the end wall 42 of the rotor blade 8 shown in
FIG. 4A.
15 [0054] On the other hand, the platform 40 of the rotor blade 8 shown in FIG. 4B
extends obliquely with respect to the axial direction. In this case, the platform 40
of the plurality of rotor blades 8 arranged adjacent to each other in the
circumferential direction has a shape of a conical side surface. The platform 40 in
FIG. 4B is oblique with respect to the axial direction by an angle φ. A surface S2
20 forming the conical side surface will be referred to as a reference surface of the end
wall 42 of the rotor blade 8 shown in FIG. 4B.
[0055] The characteristics of the end wall 42 of the rotor blade 8 according to
some embodiments will be described below. The end wall 42 will be described
below with reference to a state in which the end wall 42 is viewed from a direction
25 orthogonal to the above-described reference surfaces S1, S2 toward the center axis.
For example, an axial straight line on the end wall 42 means the axial straight line
17
perpendicularly projected on the end wall 42 (see the “axial direction on the end
wall” in FIG. 4B).
[0056] Each of FIGs. 5 and 6 is a contour map of the end wall 42 of a rotor blade
8A (rotor blade 8) according to an embodiment. FIG. 5 shows heights of the end
wall 42 at respective positions by a plurality of contour lines 5 and a shade of color.
The above-described reference surface (S1 of FIG. 4A or S2 of FIG. 4B) is a surface
of zero height. FIG. 6 shows the same contour map as FIG. 5 without the shade
of color.
The contour lines in the present specification are contour lines on the end
10 wall 42 including the region of pressure surface and the region of suction surface to
be described later, and do not include a contour line of the airfoil portion 30
(including the fillet portion 36).
[0057] As shown in FIGs. 5 and 6, the end wall 42 of the rotor blade 8A includes
a concave portion on suction surface 102 disposed at least in a region of suction
15 surface RSS of the end wall 42 and a convex portion on pressure surface 104
disposed at least in a region of pressure surface RPS of the end wall 42. The end
wall 42 is divided into the region of suction surface RSS and the region of pressure
surface RPS by a region boundary line LB. The region boundary line LB is a line
that connects center positions of the suction surface 34 of the rotor blade 8A and a
20 pressure surface of the adjacent rotor blade. The region of suction surface RSS is
a region between the suction surface 34 and the region boundary line LB, and the
region of pressure surface RPS is a region between the pressure surface 33 and the
region boundary line LB. In FIGs. 5 and 6, on the side of the suction surface 34 of
the rotor blade 8A, a rotor blade 8A’ is disposed adjacent to the rotor blade 8A.
25 In some embodiments, a part of the concave portion on suction surface 102
may exist on the region of pressure surface RPS, or a part of the convex portion on
18
pressure surface 104 may exist on the region of suction surface RSS.
[0058] A bottom point P1, which is a point of a lowest height in the concave
portion on suction surface 102, is located on the axially upstream side of a tangent
point Ptan on the suction surface 34 which has a tangential line Ltan-ax extending
in the axial direction through the tangent point Ptan. 5 Then, the end wall 42 has a
contour line Lcon1 on the concave portion on suction surface 102. The contour
line Lcon1 has a shape such that a normal vector Vn1-A, Vn1-B, which has a
negative gradient along a normal line of the contour line Lcon1 on an intersection
point between the contour line Lcon1 and the suction surface 34, is directed toward
10 the airfoil portion 30.
[0059] Moreover, a peak point P2, which is a point of a highest height in the
convex portion on pressure surface 104, is located on the axially downstream side
of the above-described tangent point Ptan. Provided that an axial position of the
leading edge 31 is 0%Cax, and an axial position of the trailing edge is 100%Cax,
15 an axial position of the peak point P2 may be not less than 50%Cax and not greater
than 80%Cax.
[0060] A leakage flow 112 without a circumferential component from the
upstream side of the rotor blade 8 may flow into the vicinity of the end wall 42 of
the rotor blade 8 (turbine blade). For example, in the steam turbine 1 shown in
20 FIG. 2, in addition to inflow of the main flow 112 which is rectified by the stator
vane 9 disposed on the upstream side of the rotor blade 8, includes the
circumferential component, and heads for the pressure surface 33 of the rotor blade
8, a leakage flow 114 without the circumferential component from a cavity 60
between the rotor blade 8 and the stator vane 9 may flow into the rotor blade 8.
25 Since the rotor blade 8 (turbine blade) rotates, the leakage flow 114 without the
circumferential component heads for the suction surface 34 of the rotor blade 8.
19
Thus, a collision (back hit) of the leakage flow 114 against the suction surface 34
may be caused, or due to an interaction between the leakage flow 114 and the main
flow 112 including the circumferential component having passed through the stator
vane 9, circumferential non-uniformity of a static pressure distribution may be
caused in the vicinity of the front end 40a of the 5 platform 40 of the rotor blade 8.
[0061] In this regard, in the above-described rotor blade 8A, the bottom point P1
of the concave portion on suction surface 102 is located on the axially upstream
side of the above-described tangent point Ptan, and the above-described normal
vector Vn1-A, Vn1-B is directed toward the airfoil portion 30. That is, the bottom
10 point P1 of the concave portion on suction surface 102 is located close to the suction
surface 34 on the axially upstream side of a position where the suction surface 34
protrudes the most (a position of the above-described tangent point Ptan), and the
concave portion on suction surface 102 has an obliquity descending toward the
suction surface 34 in the vicinity of the suction surface 34. Thus, it is possible to
15 increase the static pressure in the vicinity of the above-described position, making
it possible to alleviate the circumferential non-uniformity of the static pressure
distribution in the vicinity of the end wall 42 in the axially upstream portion of the
rotor blade 8A, or to reduce the collision (back hit) of the leakage flow from the
upstream side of the rotor blade 8A against the suction surface 34. Thus, it is
20 possible to reduce the circumferential non-uniformity of the static pressure
distribution and a loss owing to the back hit of the leakage flow.
[0062] Moreover, in the above-described rotor blade 8A, the peak point P2 of the
convex portion on pressure surface 104 is located on the axially downstream side
of the above-described tangent point Ptan. That is, the peak point P2 of the convex
25 portion on pressure surface 104 is located on the axially downstream side of the
bottom point P1 of the concave portion on suction surface 102. Thus, it is possible
20
to reduce the static pressure in the vicinity of the above-described position, making
it possible to reduce a secondary flow from the pressure surface 33 toward the
suction surface 34 of the adjacent rotor blade 8A, and to prevent, for example, a
leakage flow avoiding a collision against the suction surface 34 by the abovedescribed
concave portion on suction surface 5 102 from becoming the secondary
flow in the vicinity of the pressure surface 33. Thus, it is possible to reduce a
secondary flow loss in the rotor blade 8A.
[0063] In view of the foregoing, with the above-described rotor blade 8A, it is
possible to effectively reduce the loss which may be caused by the leakage flow in
10 the steam turbine 1.
[0064] In some embodiments, for example, as shown in FIGs. 5 and 6, a contour
line Lcon2 of the convex portion on pressure surface 104 has a shape such that a
normal vector Vn2-A, which has a positive gradient along a normal line of the
contour line Lcon2 on an intersection point between the contour line Lcon2 and the
15 pressure surface 33, is directed toward the airfoil portion 30.
[0065] In this case, the above-described normal vector Vn2-A is directed toward
the airfoil portion 30, that is, the peak point P2 of the convex portion on pressure
surface 104 is located close to the pressure surface 33, and the convex portion on
pressure surface 104 has an obliquity ascending toward the pressure surface 33 in
20 the vicinity of the pressure surface 33. Thus, it is possible to reduce the static
pressure in the vicinity of the above-described position, making to possible to
effectively reduce the secondary flow in the rotor blade 8A (turbine blade) and to
reduce the loss by the secondary flow more effectively.
[0066] In some embodiments, for example, as shown in FIGs. 5 and 6, the convex
25 portion on pressure surface 104 expands along the pressure surface 33 at least from
a position of the peak point P2 to a position of the bottom point P1 of the concave
21
portion on suction surface 102 in the axial direction.
For example, the convex portion on pressure surface 104 may extend along
the pressure surface 33 over not less than 90% of an axial length (that is, an axial
distance between a position of the leading edge 31 and a position of the trailing
edge 32) L0 of the airfoil portion 30 on the end 5 wall 42. In other words, an axial
length LPT of the convex portion on pressure surface 104 in an extension range along
the pressure surface 33 may be not less than 90% of the axial length L0 of the airfoil
portion 30 described above.
[0067] In this case, since the convex portion on pressure surface 104 extends along
10 the pressure surface 33 over a wide range at least from the position of the peak point
P2 of the convex portion on pressure surface 104 to the position of the bottom point
P1 of the concave portion on suction surface 102 in the axial direction, it is possible
to reduce the static pressure over the wide range in the vicinity of the pressure
surface 33. Thus, it is possible to effectively prevent the leakage flow avoiding
15 the collision against the suction surface 34 by the concave portion on suction
surface 102 of the rotor blade 8A from becoming the secondary flow in the vicinity
of the pressure surface 33 of the adjacent rotor blade 8A. Thus, it is possible to
effectively reduce the secondary flow loss in the rotor blade 8A.
[0068] In some embodiments, a ratio L1/L0 of an axial distance L1 (see FIG. 6)
20 between the bottom point P1 of the concave portion on suction surface 102 and the
peak point P2 of the convex portion on pressure surface 104 of the rotor blade 8A
to the axial length L0 (see FIG. 6) of the airfoil portion 30 on the end wall 42 may
be at least 0.1 and at most 0.9.
[0069] In this case, since the ratio L1/L0 of the distance L1 between the bottom
25 point of the concave portion on suction surface and the peak point of the convex
portion on pressure surface to the axial length L0 of the airfoil portion 30 on the
22
end wall 42 is at least 0.1 and at most 0.9, the leakage flow avoiding the collision
against the suction surface 34 by the concave portion on suction surface 102 is
easily introduced to the vicinity of the convex portion on pressure surface 104 of
the adjacent rotor blade 8A. Thus, it is possible to effectively prevent the leakage
flow from becoming the secondary flow in the vicinity 5 of the pressure surface 33
of the adjacent rotor blade 8A and to effectively reduce the secondary flow loss in
the rotor blade 8A.
[0070] Alternatively, in some embodiments, an angle θ (see FIG. 6) between an
axial straight line Lax, and a straight line LA that connects the bottom point P1 of
10 the concave portion on suction surface 102 of the rotor blade 8A and a peak point
P1’ of the convex portion on pressure surface 104 of the adjacent turbine blade 8A’
is not less than 10 degrees and not greater than 80 degrees.
[0071] In this case, since the angle between the axial straight line Lax, and the
straight line LA that connects the bottom point P1 of the concave portion on suction
15 surface 102 and a peak point P2’ of the convex portion on pressure surface 104 of
the adjacent turbine blade 8A’ is not less than 10 degrees and not greater than 80
degrees, the leakage flow avoiding the collision against the suction surface 34 by
the concave portion on suction surface 102 is easily introduced to the vicinity of the
convex portion on pressure surface 104 of the adjacent rotor blade 8A’. Thus, it is
20 possible to effectively prevent the leakage flow from becoming the secondary flow
in the vicinity of the pressure surface 33 and to effectively reduce the secondary
flow loss in the rotor blade 8A.
[0072] In some embodiments, for example, as shown in FIGs.5 and 6, the turbine
blade is configured such that the concave portion on suction surface 102 of the rotor
25 blade 8A and the convex portion on pressure surface 104 of the adjacent rotor blade
8A’ form a smooth slope from the bottom point P1 of the concave portion on suction
23
surface 102 to the peak point P2’ of the convex portion on pressure surface 104.
That is, in the embodiments shown in FIGs. 5 and 6, the height of the end wall 42
monotonically increases from the bottom point P1 of the concave portion on suction
surface 102 of the rotor blade 8A to the peak point P2' of the convex portion on
pressure surface 5 104 of the adjacent rotor blade 8A'.
[0073] In this case, since the concave portion on suction surface 102 of the rotor
blade 8A and the convex portion on pressure surface 104 of the adjacent rotor blade
8A’ form the smooth slope from the bottom point P1 of the concave portion on
suction surface 102 to the peak point P2’ of the convex portion on pressure surface
10 104, the leakage flow avoiding the collision against the suction surface 34 by the
concave portion on suction surface 102 can smoothly be introduced to the vicinity
of the convex portion on pressure surface 104 of the adjacent rotor blade 8A’.
Thus, it is possible to effectively prevent the leakage flow from becoming the
secondary flow in the vicinity of the pressure surface 33 of the adjacent rotor blade
15 8A’ and to effectively reduce the secondary flow loss in the rotor blade 8A.
[0074] In some embodiments, a ratio L2/L0 of an axial distance L2 (see FIG. 6)
between the front end 40a of the platform 40 and the leading edge 31 of the airfoil
portion 30 in the end wall 42 to the axial length L0 of the airfoil portion 30 on the
end wall 42 may be at most 0.1.
20 [0075] Alternatively, in some embodiments, the above-described distance L2 is
not less than 50% and not greater than 100% of a width WF (see FIG. 6) of the fillet
portion 36 disposed on the base-end portion 35 of the airfoil portion 30 in a planar
view (that is, the width of the fillet portion 36 as the end wall 42 is viewed from a
direction orthogonal to the above-described reference surface S1 or S2).
25 [0076] For uniformity of the circumferential distribution of the static pressure in
the vicinity of the front end 40a of the platform 40, it is desirable that the above-
24
described concave portion on suction surface 102 is disposed close to the front end
40a as much as possible.
Meanwhile, in accordance with, for example, the type of turbine, a turbine
blade having the relatively short axial distance L2 between the front end 40a of the
platform 40 and the leading edge 31 of the 5 airfoil portion 30 may be used, as
described above. The above-described turbine blade is used in a case in which,
for example, a rotor length is requested to be short as much as possible in terms of
measures against a vibration in the turbine. In this case, it is difficult to dispose
the concave portion on suction surface on the upstream side of the leading edge 31
10 of the airfoil portion 30, due to limitations of space.
In this regard, with the rotor blade 8A according to the above-described
embodiment, as already described, it is possible to effectively reduce the loss which
may be caused by the leakage flow in the turbine, even if the axial distance L2
between the front end 40a of the platform 40 and the leading edge 31 of the airfoil
15 portion 30 is relatively short.
[0077] In some embodiments, for example, as shown in FIGs. 5 and 6, the concave
portion on suction surface 102 of the rotor blade 8A extends without crossing a
dividing line LS forming a boundary with an adjacent rotor blade 8A’.
Thus, since the concave portion on suction surface 102 of the rotor blade
20 8A extends without crossing the dividing line LS forming the boundary with an
adjacent rotor blade 8A’, that is, the concave portion on suction surface 102 does
not stride over the dividing line LS, productivity of the rotor blade 8A is good.
[0078] Each of FIGs. 7 and 8 is a contour map of the end wall 42 of a rotor blade
8B (rotor blade 8) according to an embodiment different from the embodiments
25 shown in FIGs. 5 and 6. FIG. 7 shows heights of the end wall 42 at respective
positions by a plurality of contour lines and a shade of color. The above-described
25
reference surface (S1 of FIG. 4A or S2 of FIG. 4B) is the surface of zero height.
FIG. 8 shows the same contour map as FIG. 7 without the shade of color.
[0079] The rotor blade 8B according to the present embodiment has the
characteristics of the rotor blade 8A that have already been described with reference
to FIGs. 5 and 6. That is, the end wall 42 of 5 the rotor blade 8B shown in FIGs. 7
and 8 includes the concave portion on suction surface 102 and the convex portion
on pressure surface 104 each having the above-described characteristics.
[0080] The end wall 42 of the rotor blade 8B shown in FIGs. 7 and 8 further
includes a convex portion on suction surface 106 disposed at least in the region of
10 suction surface RSS. Then, the convex portion on suction surface 106 expands
along the suction surface 34 over a range that includes a throat forming position PTH
located on the downward side of the tangent point Ptan on the suction surface 34.
The convex portion on suction surface 106 may partially extend to a region
other than the region of suction surface RSS.
15 [0081] In general, a fluid flows in a direction orthogonal to a contour line.
However, in the case of the turbine blade without the convex portion on suction
surface 106 described above, an obliquity of the contour line with respect to the
blade height direction (spanwise direction) increases on a base-end side of the
suction surface 34 (in the vicinity of the end wall 42) in particular, which may curl
20 up a secondary flow swirl in the vicinity of the suction surface and increase a loss.
In this regard, in the embodiments shown in FIGs. 7 and 8, respectively,
since the above-described convex portion on suction surface 106 is disposed in the
end wall 42, it is possible to reduce the static pressure in the vicinity of the convex
portion on suction surface 106, making it possible to make the contour line on the
25 suction surface 34 more parallel to the blade height direction in the range including
the throat forming position PTH in the vicinity of the end wall 42. Moreover, since
26
the concave portion on suction surface 102 has the obliquity ascending downstream
from the bottom point P1 along the suction surface 34, it is possible to make the
contour line on the suction surface 34 described above much more parallel to the
blade height direction at an axial position of the concave portion on suction surface
102. Thus, it is possible to suppress the curl-5 up of the secondary flow swirl that
may be caused in the vicinity of the base-end portion 35 of the airfoil portion 30,
and to reduce the secondary flow loss more effectively.
[0082] In some embodiments, for example, as shown in FIGs. 7 and 8, the convex
portion on pressure surface 104 of a rotor blade 8B’ and the convex portion on
10 suction surface 106 of the adjacent rotor blade 8B share at least one contour line (a
contour line Lcon3, Lcon4 in FIG. 8). That is, the convex portion on pressure
surface 104 of the rotor blade 8B’ and the convex portion on suction surface 106 of
the adjacent rotor blade 8B form one continuous ridge.
[0083] In this case, since the convex portion on pressure surface 104 of the rotor
15 blade 8B’ and the convex portion on suction surface 106 of the adjacent rotor blade
8B share at least one contour line (Lcon3, Lcon4), between the rotor blades 8B
adjacent to each other, the end wall 42 has a shape formed by smoothly connecting
the convex portion on pressure surface 104 and the convex portion on suction
surface 106. Thus, blocking of a fluid flow between the rotor blades 8B and 8B’
20 is suppressed, making it possible to suppress a decrease in turbine efficiency.
[0084] In some embodiments, in the steam turbine 1, a ratio L3/L0 of an axial
width L3 (see FIG. 2) of the cavity 60 formed between the rotor blade 8 and the
stator vane 9 disposed on the axially upstream side of the rotor blade 8 to the axial
length L0 (see FIG. 2, 6) of the airfoil portion 30 on the end wall 42 is at least 0.15.
25 [0085] As described above, the ratio L3/L0 of the axial width L3 of the cavity 60
to the axial length L0 of the airfoil portion 30 is at least 0.15, that is, in the steam
27
turbine 1 including the relatively wide cavity 60, an influence by the leakage flow
114 from the cavity 60 may be prominent, and a collision of the above-described
leakage flow against the suction surface 34 and the circumferential non-uniformity
of the static pressure distribution are likely to occur.
In this regard, according to the above-5 described embodiment, as already
described, it is possible to reduce the circumferential non-uniformity of the static
pressure distribution and the loss owing to back hit of the leakage flow, or to reduce
the secondary flow loss in the rotor blade 8, even under the above-described
circumference where the loss owing to the leakage flow 114 is likely to occur.
10 Thus, it is possible to effectively reduce the loss which may be caused by the
leakage flow in the steam turbine 1.
[0086] Embodiments of the present invention were described in detail above, but
the present invention is not limited thereto, and also includes an embodiment
obtained by modifying the above-described embodiments and an embodiment
15 obtained by combining these embodiments as appropriate.
[0087] Further, in the present specification, an expression of relative or absolute
arrangement such as “in a direction”, “along a direction”, “parallel”, “orthogonal”,
“centered”, “concentric” and “coaxial” shall not be construed as indicating only the
arrangement in a strict literal sense, but also includes a state where the arrangement
20 is relatively displaced by a tolerance, or by an angle or a distance whereby it is
possible to achieve the same function.
For instance, an expression of an equal state such as “same” “equal” and
“uniform” shall not be construed as indicating only the state in which the feature is
strictly equal, but also includes a state in which there is a tolerance or a difference
25 that can still achieve the same function.
Further, an expression of a shape such as a rectangular shape or a
28
cylindrical shape shall not be construed as only the geometrically strict shape, but
also includes a shape with unevenness or chamfered corners within the range in
which the same effect can be achieved.
As used herein, the expressions “comprising”, “including” or “having” one
constitutional element is not an exclusive expression 5 that excludes the presence of
other constitutional elements.
Reference Signs List
[0088]
10 1 Steam turbine
2 Rotor
3 Steam inlet
4 Rotor disc
4A Groove
15 6 Bearing portion
8, 8A, 8B Rotor blade
9 Stator vane
10 Inner casing
12 Outer casing
20 13 Exhaust hood outlet
14 Exhaust hood
30 Airfoil portion
31 Leading edge
32 Trailing edge
25 33 Pressure surface
34 Suction surface
29
35 Base-end portion
36 Fillet portion
40 Platform
40a Front end
5 40b Rear end
42 End wall
44 Blade root portion
50 Airfoil portion
52 Outer ring
10 54 Inner ring
60 Cavity
102 Concave portion on suction surface
104 Convex portion on pressure surface
106 Convex portion on suction surface
15 112 Main flow
LB Region boundary line
LS Dividing line
Lcon1 to Lcon4 Contour line
Ltan-ax Tangent line
20 O Center axis
P1 Bottom point
P2 Peak point
PTH Throat forming position
Ptan Tangent point
25 RPS Region of pressure surface
RSS Region of suction surface
30
S1 Reference surface
S2 Reference surface
Vn Normal vector
31
I/We Claim:
1. A turbine blade, comprising:
an airfoil portion having a pressure surface and a suction surface each of
which extends between a leading 5 edge and a trailing edge; and
a platform including an end wall to which a base-end portion of the airfoil
portion is connected,
wherein the end wall includes:
a concave portion on suction surface disposed at least in a region
10 of suction surface of the end wall; and
a convex portion on pressure surface disposed at least in a region
of pressure surface of the end wall,
wherein the concave portion on suction surface has a bottom point located
on an axially upstream side of a tangent point on the suction surface, the suction
15 surface having a tangential line extending in an axial direction through the tangent
point,
wherein the end wall has at least one contour line on the concave portion
on suction surface, the at least one contour line having a normal line on an
intersection point between the at least one contour line and the suction surface such
20 that a normal vector having a negative gradient along the normal line is directed
toward the airfoil portion, and
wherein the convex portion on pressure surface has a peak point located
on an axially downstream side of the tangent point.
25 2. The turbine blade according to claim 1,
wherein the convex portion on pressure surface has at least one contour
32
line having a normal line on an intersection point between the at least one contour
line and the pressure surface such that a normal vector having a positive gradient
along the normal line is directed toward the airfoil portion.
3. The turbine 5 blade according to claim 1 or 2,
wherein the convex portion on pressure surface expands along the pressure
surface at least from a position of the peak point to a position of the bottom point
of the concave portion on suction surface in the axial direction.
10 4. The turbine blade according to any one of claims 1 to 3,
wherein a ratio L1/L0 of an axial distance L1 between the bottom point of
the concave portion on suction surface and the peak point of the convex portion on
pressure surface to an axial length L0 of the airfoil portion on the end wall is at least
0.1 and at most 0.9.
15
5. The turbine blade according to any one of claims 1 to 4,
wherein an angle between an axial straight line, and a straight line that
connects the bottom point of the concave portion on suction surface and the peak
point of the convex portion on pressure surface of an adjacent turbine blade is not
20 less than 10 degrees and not greater than 80 degrees.
6. The turbine blade according to any one of claims 1 to 5,
wherein the convex portion on pressure surface extends along the pressure
surface over not less than 90% of an axial length L0 of the airfoil portion on the end
25 wall.
33
7. The turbine blade according to any one of claims 1 to 6,
wherein the turbine blade is configured such that the concave portion on
suction surface and the convex portion on pressure surface of an adjacent turbine
blade form a smooth slope from the bottom point of the concave portion on suction
surface to the peak 5 point of the convex portion on pressure surface.
8. The turbine blade according to any one of claims 1 to 7,
wherein the end wall further includes a convex portion on suction surface
disposed at least in the region of suction surface, and
10 wherein the convex portion on suction surface expands along the suction
surface over a range that includes a throat forming position located on the axially
downstream side of the tangent point on the suction surface.
9. The turbine blade according to claim 8,
15 wherein the convex portion on pressure surface and the convex portion on
suction surface of an adjacent turbine blade share at least one contour line.
10. The turbine blade according to any one of claims 1 to 9,
wherein a ratio L2/L0 of an axial distance L2 between the leading edge
20 and a front end of the platform to an axial length L0 of the airfoil portion on the end
wall is at most 0.1.
11. The turbine blade according to any one of claims 1 to 10,
wherein the base-end portion of the airfoil portion includes a fillet portion
25 disposed in a connection portion to the platform, and
wherein an axial distance L2 between the leading edge and a front end of
34
the platform is not less than 50% and not greater than 100% of a width of the fillet
portion in a planar view.
12. The turbine blade according to any one of claims 1 to 11,
wherein the concave portion on suction 5 surface extends without crossing a
dividing line forming a boundary with an adjacent turbine blade.
13. A steam turbine, comprising:
the turbine blade according to any one of claims 1 to 12.
10
14. The steam turbine according to claim 13, comprising:
a rotor blade which is the turbine blade; and
a stator vane disposed adjacent to the rotor blade on an upstream side of
the rotor blade in an axial direction of the steam turbine,
15 wherein a ratio L3/L0 of an axial width L3 of a cavity formed between the
rotor blade and the stator vane to an axial length L0 of the airfoil portion on the end
wall is at least 0.15.