U.S. patent application number 12/018994 was filed with the patent office on 2009-03-19 for airfoil with cooling hole having a flared section.
This patent application is currently assigned to SIEMENS POWER GENERATION, INC.. Invention is credited to Robert K. Scott.
Application Number | 20090074588 12/018994 |
Document ID | / |
Family ID | 40454666 |
Filed Date | 2009-03-19 |
United States Patent
Application |
20090074588 |
Kind Code |
A1 |
Scott; Robert K. |
March 19, 2009 |
AIRFOIL WITH COOLING HOLE HAVING A FLARED SECTION
Abstract
An airfoil is provided for a gas turbine engine. The airfoil may
comprise a main body comprising a leading edge having a leading
edge outer surface, a trailing edge having a trailing edge outer
surface, a suction side having a suction side outer surface and a
pressure side having a pressure side outer surface. The main body
may further comprise at least one interior cooling passage and a
plurality of cooling holes extending from the cooling passage to at
least one of the leading edge outer surface, the trailing edge
outer surface, the suction side outer surface and the pressure side
outer surface. Preferably, at least one of the cooling holes
includes a proximal metering section having a first dimension
extending transverse to an axis extending in a flow direction of a
cooling fluid passing through the one cooling hole, a flared
section and an exit opening having a second dimension transverse to
the axis which is larger than the first dimension. The flared
section is preferably curvilinear as it extends from the proximal
metering section towards the exit opening.
Inventors: |
Scott; Robert K.; (Geneva,
FL) |
Correspondence
Address: |
SIEMENS CORPORATION;INTELLECTUAL PROPERTY DEPARTMENT
170 WOOD AVENUE SOUTH
ISELIN
NJ
08830
US
|
Assignee: |
SIEMENS POWER GENERATION,
INC.
Orlando
FL
|
Family ID: |
40454666 |
Appl. No.: |
12/018994 |
Filed: |
January 24, 2008 |
Related U.S. Patent Documents
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Application
Number |
Filing Date |
Patent Number |
|
|
60973573 |
Sep 19, 2007 |
|
|
|
Current U.S.
Class: |
416/96R ;
415/115 |
Current CPC
Class: |
F01D 5/186 20130101 |
Class at
Publication: |
416/96.R ;
415/115 |
International
Class: |
F01D 5/18 20060101
F01D005/18; F01D 5/08 20060101 F01D005/08 |
Claims
1. An airfoil for a gas turbine engine comprising: a main body
comprising a leading edge having a leading edge outer surface, a
trailing edge having a trailing edge outer surface, a suction side
having a suction side outer surface and a pressure side having a
pressure side outer surface, said main body further comprising at
least one interior cooling passage and a plurality of cooling holes
extending from said cooling passage to at least one of said leading
edge outer surface, said trailing edge outer surface, said suction
side outer surface and said pressure side outer surface; at least
one of said cooling holes including a proximal metering section
having a first dimension extending transverse to an axis extending
in a flow direction of a cooling fluid passing through said one
cooling hole, a flared section and an exit opening having a second
dimension transverse to the axis which is larger than said first
dimension, wherein said flared section is curvilinear as it extends
from said proximal metering section towards said exit opening.
2. An airfoil as set out in claim 1, wherein said one cooling hole
further comprises a distal section extending from at least a
portion of said flared section to at least a portion of said exit
opening.
3. An airfoil as set out in claim 2, wherein said one cooling hole
further comprises a concave interface section located between said
flared section and said distal section.
4. An airfoil as set out in claim 2, wherein said flared section
meets directly with said distal section.
5. An airfoil as set out in claim 1, wherein said proximal metering
section has a diameter D and a length between about 1.0D and about
5.0D.
6. An airfoil as set out in claim 5, wherein said one cooling hole
extends at an angle .theta. of from about 20 degrees to about 90
degrees to said one outer surface.
7. An airfoil as set out in claim 6, wherein said one outer surface
has a thickness T and said one cooling hole has an overall length L
determined from the following equation: length L=thickness T/Sin
.theta.
8. An airfoil as set out in claim 5, wherein said diameter D of
said proximal metering section is from about 0.5 mm to about 5.0
mm.
9. An airfoil as set out in claim 1, wherein the shape of said
flared section is defined by the following equation: y = y 1 4
.times. 1 + [ ( y 1 / y 0 ) 4 - 1 ] [ 1 - x 1 d ] ##EQU00005##
wherein: y.sub.1=an exit radius or dimension for a largest portion
of said flared section; y.sub.0=a radius of said proximal metering
section; I.sub.d=a length of a longest portion of said flared
section; x=independent coordinate extending along the axis with an
origin at a beginning of said flared section; and y=dependent
coordinate perpendicular to the axis with an origin at a central
axis of said one cooling hole.
10. An airfoil as set out in claim 9, wherein said exit opening is
square or circular in shape as viewed along the axis of said one
cooling hole.
11. An airfoil as set out in claim 1, wherein the shape of said
flared section is defined by the following equation: y = y 1 1 + [
( y 1 / y 0 ) 2 - 1 ] [ 1 - x 1 d ] ##EQU00006## wherein:
y.sub.1=an exit radius or dimension for a curvilinear portion of
said flared section; y.sub.0=a radius of said proximal metering
section; I.sub.d=a length of a longest portion of said flared
section; x=independent coordinate extending along the axis with an
origin at a beginning of said flared section; and y=dependent
coordinate perpendicular to the axis with an origin at a central
axis of said one cooling hole.
Description
CROSS REFERENCE TO RELATED APPLICATION
[0001] This application claims priority from U.S. Provisional
Application Ser. No. 60/973,573, which was filed on Sep. 19, 2007,
the disclosure of which is incorporated by reference in its
entirety herein.
FIELD OF THE INVENTION
[0002] The present invention relates to an airfoil for a gas
turbine engine having at least one cooling hole extending from an
interior cooling passage to an outer surface of the airfoil and
wherein the cooling hole has a flared section.
BACKGROUND OF THE INVENTION
[0003] A conventional combustion gas turbine engine includes a
compressor, a combustor, and a turbine. The compressor compresses
ambient air. The combustor combines the compressed air with a fuel
and ignites the mixture creating combustion products defining a
working gas. The working gases travel to the turbine. Within the
turbine are a series of rows of stationary vanes and rotating
blades. Each pair of rows of vanes and blades is called a stage.
Typically, there are four stages in a turbine. The rotating blades
are coupled to a shaft and disc assembly. As the working gases
expand through the turbine, the working gases cause the blades, and
therefore the shaft and disc assembly, to rotate.
[0004] Combustors often operate at very high temperatures. Typical
combustor configurations expose turbine vanes and blades to these
high temperatures. As a result, turbine vanes and blades must be
made of materials capable of withstanding such high temperatures.
In addition, turbine vanes and blades often contain cooling systems
for prolonging the life of the vanes and blades and reducing the
likelihood of failure as a result of excessive temperatures.
[0005] Conventional turbine blades and vanes have many different
designs of internal cooling systems. For example, a plurality of
cooling holes may extend from an interior cooling passage to an
outer surface of an airfoil of a turbine vane or blade. It is
preferred that the wall of the vane or blade be as thin as
possible. It is also preferred that the cooling openings be shaped
and sized such that the cooling fluid moving through each cooling
opening does not separate from a wall defining the cooling
opening.
SUMMARY OF THE INVENTION
[0006] In accordance with an aspect of the present invention, an
airfoil is provided for a gas turbine engine. The airfoil may
comprise a main body comprising a leading edge having a leading
edge outer surface, a trailing edge having a trailing edge outer
surface, a suction side having a suction side outer surface and a
pressure side having a pressure side outer surface. The main body
may further comprise at least one interior cooling passage and a
plurality of cooling holes extending from the cooling passage to at
least one of the leading edge outer surface, the trailing edge
outer surface, the suction side outer surface and the pressure side
outer surface. Preferably, at least one of the cooling holes
includes a proximal metering section having a first dimension
extending transverse to an axis extending in a flow direction of a
cooling fluid passing through the one cooling hole, a flared
section and an exit opening having a second dimension transverse to
the axis which is larger than the first dimension. The flared
section is preferably curvilinear as it extends from the proximal
metering section towards the exit opening.
[0007] The one cooling hole may further comprise a distal section
extending from at least a portion of the flared section to at least
a portion of the exit opening.
[0008] In accordance with a first embodiment of the present
invention, the one cooling hole may further comprise a concave
interface section located between the flared section and the distal
section. In accordance with a second embodiment of the present
invention, the flared section meets directly with the distal
section.
[0009] The proximal metering section may have a diameter D and a
length between about 1.0D and about 5.0D. The diameter D of the
proximal metering section may be from about 0.5 mm to about 5.0
mm.
[0010] The one cooling hole may extend at an angle .theta. of from
about 20 degrees to about 90 degrees to the one outer surface.
[0011] The one outer surface may have a thickness T and the one
cooling hole may have an overall length L determined from the
following equation:
length L=thickness T/Sin .theta.
[0012] The exit opening may be substantially square or
substantially circular in shape as viewed along the axis of the one
cooling hole. With the exit opening square or circular in shape,
the shape of the flared section may be defined by the following
equation:
y = y 1 4 .times. 1 + [ ( y 1 / y 0 ) 4 - 1 ] [ 1 - x 1 d ]
##EQU00001##
[0013] wherein: [0014] y.sub.1=an exit radius or dimension for a
largest portion of the flared section;
[0015] y.sub.0=a radius of the proximal metering section;
[0016] I.sub.d=a length of a longest portion of the flared
section;
[0017] x=independent coordinate extending along the axis with an
origin at a beginning point of the flared section; and
[0018] y=dependent coordinate perpendicular to the axis with an
origin at a central axis of the one cooling hole.
[0019] Alternatively, the shape of the flared section may be
defined by the following equation:
y = y 1 1 + [ ( y 1 / y 0 ) 2 - 1 ] [ 1 - x 1 d ] ##EQU00002##
[0020] wherein: [0021] y.sub.1=an exit radius or dimension for a
largest portion of a curvilinear portion of the flared section;
[0022] y.sub.0=a radius of the proximal metering section; [0023]
I.sub.d=a length of a longest portion of the flared section; [0024]
x=independent coordinate extending along the axis with an origin at
a beginning of the flared section; and [0025] y=dependent
coordinate perpendicular to the axis with an origin at a center
axis of the one cooling hole.
BRIEF DESCRIPTION OF THE DRAWINGS
[0026] FIGS. 1, 2 and 2A illustrate a cooling hole constructed in
accordance with a first embodiment of the present invention;
[0027] FIG. 3 is a perspective view, partially in cross section, of
a blade in which the cooling holes of the present invention may be
incorporated;
[0028] FIGS. 4, 5 and 5A illustrate a cooling hole constructed in
accordance with a second embodiment of the present invention;
[0029] FIG. 6 is an enlarged view of the circled portion labeled 6
in FIG. 4 with a concave section of an alternative embodiment
illustrated in dotted line;
[0030] FIG. 7 is an enlarged view of the circled portion labeled 7
in FIG. 5 with a concave section of an alternative embodiment
illustrated in dotted line; and
[0031] FIGS. 8, 9 and 9A illustrate a cooling hole constructed in
accordance with a third embodiment of the present invention.
DETAILED DESCRIPTION OF THE INVENTION
[0032] Referring now to FIG. 3, a blade 10 constructed in
accordance with the present invention is illustrated. The blade 10
is adapted to be used in a gas turbine (not shown) of a gas turbine
engine (not shown). Within the gas turbine are a series of rows of
stationary vanes and rotating blades. Typically, there are four
rows of blades in a gas turbine.
[0033] The blades are coupled to a shaft and disc assembly. Hot
working gases from a combustor (not shown) in the gas turbine
engine travel to the rows of blades. As the working gases expand
through the turbine, the working gases cause the blades, and
therefore the shaft and disc assembly, to rotate.
[0034] The blade 10 comprises an attachment portion or a root 12, a
platform 14 integral with the root 12 and an airfoil 20 formed
integral with the platform 14, see FIG. 3. The root 12 functions to
couple the blade 10 to the shaft and disc assembly (not shown) in
the gas turbine (not shown). The airfoil 20 is defined by a main
body 100 comprising a tip (not shown), a root section or a base
110, a leading edge 120, a trailing edge 130, a concave-shaped
pressure side 140, and a convex-shaped suction side 150. The
airfoil leading edge 120 has a leading edge outer surface 122, the
airfoil trailing edge 130 has a trailing edge outer surface 132,
the airfoil pressure side 140 has a pressure side outer surface 142
and the airfoil suction side 150 has a suction side outer surface
152. The main body 100 may be formed as a single integral unit from
a material such as a metal alloy 247 via a conventional casting
operation.
[0035] A conventional thermal barrier coating (not shown) is
provided on an outer surface 102 of the main body 100. The outer
surface 102 of the main body 100 is defined by the leading edge
outer surface 122, the trailing edge outer surface 132, the
pressure side outer surface 142 and the suction side outer surface
152.
[0036] In the illustrated embodiment, the airfoil main body 100
further comprises an interior cooling passage 160 and a plurality
of cooling holes 170 extending from the cooling passage 160 to at
least one of the leading edge outer surface 122, the trailing edge
outer surface 132, the pressure side outer surface 142 and the
suction side outer surface 152, see FIG. 3. While only a single
interior cooling passage 160 is illustrated in the FIG. 3
embodiment, two or more interior cooling passages may be provided
in the airfoil main body 100. Also, while only three cooling holes
170 are illustrated in the pressure side 140 of the embodiment of
FIG. 3, one, two or four or more cooling holes 170 may be provided
in the pressure side 140 and one or more cooling holes 170 may be
provided in the leading edge 120, the trailing edge 130, and/or the
convex-shaped suction side 150.
[0037] A cooling fluid, such as air or steam, is supplied under
pressure in the direction of arrow A in FIG. 3 to a cooling fluid
entrance (not shown) provided in the root 12. The cooling fluid may
be supplied by the compressor (not shown) of the gas turbine engine
via conventional supply structure (not shown) extending to the
cooling fluid entrance channel.
[0038] The cooling fluid moves through the cooling fluid entrance,
through the platform 14 and into the interior cooling passage 160
of the airfoil main body 100. From the airfoil cooling passage 160,
the cooling fluid passes through the cooling holes 170 and, after
exiting the cooling holes 170, provides film cooling for a
downstream portion, i.e., in a direction away from the leading edge
120 toward the trailing edge 130, of the outer surface 102 of the
main body 100.
[0039] Each of the cooling holes 170 may be formed so as to have
substantially the same shape and size. Hence, only a single cooling
hole, for each embodiment of cooling holes, will be discussed
herein.
[0040] Referring now to FIGS. 1 and 2, a cooling hole 170 formed in
accordance with a first embodiment of the present invention may
extend to the outer surface 102 of the main body 100 at an angle
.theta. of from about 20 degrees to about 90 degrees. The cooling
hole 170 may comprise a proximal metering section 172 having a
diameter D.sub.172 extending transverse to a central axis A.sub.170
of the cooling hole 170, wherein the central axis A.sub.170 extends
in a flow direction FD of a cooling fluid passing through the
cooling hole 170. The diameter D.sub.172 of the proximal metering
section 172 may be from about 0.5 mm to about 5.0 mm. An entrance
172A of the proximal metering section 172 defines an entrance for
the cooling hole 170 and communicates with the interior cooling
passage 160. The cooling hole 170 further comprises a flared
section 174 connected with and extending away from the proximal
metering section 172; a distal section 176 connected with and
extending away from a portion of the flared section 174; and an
exit opening 178 connected to the distal section 176 and a portion
of the flared section 174.
[0041] In the embodiment illustrated in FIGS. 1 and 2, the flared
section 174 has a curvilinear shape as it extends away from the
proximal metering section 172 towards the distal section 176 and
the exit opening 178 in an X direction, see FIGS. 2 and 2A. In a
Y-Z plane, the flared section 174 has a generally circular shape.
Because the cooling hole 170 is positioned at an angle .theta. less
than 90 degrees relative to the outer surface 102 of the main body
100, a length of a first portion 174A of the flared section 174 in
the X direction is greater than a length of a second portion 174B
of the flared section 174, see FIG. 2. If the second portion 174B
had a length equal to the length of the first portion 174A, it
would have an additional section 174C, shown in dotted line in FIG.
2. The shape of the flared section 174 may be defined by the
following equation:
y = y 1 4 .times. 1 + [ ( y 1 / y 0 ) 4 - 1 ] [ 1 - x 1 d ] (
Equation 1 ) ##EQU00003##
[0042] wherein: [0043] y.sub.1=an exit radius for the largest
portion, i.e., the first portion 174A, of the flared section 174;
[0044] y.sub.0=a radius of the proximal metering section 172;
[0045] I.sub.d=a length of the longest portion, i.e., the first
portion 174A, of the flared section 174; [0046] x=independent
coordinate extending along the central axis A.sub.170 of the
cooling hole 170 with an origin at a beginning point P.sub.B174 of
the flared section 174; and [0047] y=dependent coordinate
perpendicular to the central axis A.sub.170 of the cooling hole 170
with an origin at the central axis A.sub.170.
[0048] The radius y.sub.0 (also referred to herein as "a first
dimension") of the proximal metering section 172 is less than a
largest dimension (also referred to herein as "a second dimension")
of the exit opening 178.
[0049] The shape and size of the cooling hole 170 may be designed
as follows. Typically, the thickness T of the airfoil main body 100
is predefined. Also, the diameter D.sub.172 of the proximal
metering section 172 is predefined and typically selected to be as
small as possible, e.g., 1 mm, so as to minimize the risk that the
cooling hole 170 may be blocked by dirt and the like. With the
diameter D.sub.172 of the proximal metering section 172 equal to
about 1 mm, the main body thickness T may equal 3.8D.sub.172 or 3.8
mm. The angle .theta., the angle at which the cooling hole 170 is
positioned relative to the outer surface 102 of the main body 100,
is also predefined and is typically selected to be as small as
possible so as to be within manufacturing capabilities.
[0050] With the angle .theta. and the thickness T of the airfoil
main body 100 predefined, the overall length L.sub.170 of the
cooling hole 170 may be determined via the following equation:
length L.sub.170=thickness T/Sin .theta. (Equation 2)
[0051] With the angle .theta. and the thickness T of the airfoil
main body 100 predefined and the overall length L.sub.170 of the
cooling hole 170 predetermined, different values of y.sub.1/y.sub.0
and I.sub.d from Equation 1, above, are selected and tested to
determine the values for y.sub.1/y.sub.0 and I.sub.d which provide
a desired film cooling effectiveness for the outer surface 102 of
the airfoil main body 100. The length L.sub.172 of the proximal
metering section 172 is equal to the overall length L.sub.170 of
the cooling hole 170 minus the length I.sub.d of the longest
portion, i.e., the first portion 174A, of the flared section 174.
Equation 1, above, is then used to determine values for x and y,
i.e., the shape, of the flared section 174.
[0052] In prior art cooling holes, a transition section extending
away from the proximal metering section towards an exit opening had
a straight or linear shape as the transition section expanded away
from the metering section. If the metering section had a length
less than about 5.0D (where D=the diameter of the metering
section), there was risk that the cooling fluid would separate from
the wall defining the transition section, causing a reduction in
film cooling for a downstream portion of the outer surface of the
airfoil main body. Because the flared section 174 of the cooling
hole 170 of the present invention has a curvilinear shape as it
extends away from the proximal metering section 172 towards the
distal section 176 and exit opening 178 in a X direction, see FIGS.
2 and 2A, it is believed that a cooling fluid moving from the
proximal metering section 172, through the flared section 174 and
into the distal section 176 or exit opening 178 will have an
increased likelihood of not separating from a wall W.sub.174
defining the flared section 174, even if the metering section 172
has a length L.sub.172 less than about 5.0D.sub.172.
[0053] In the embodiment illustrated in FIGS. 1 and 2, the flared
section 174 meets directly with the distal section 176 or the exit
opening 178. However, it is also contemplated that a concave
interface section (not shown) may be provided between the flared
section 174 and the distal section 176.
[0054] In FIGS. 4 and 5, a cooling hole 270 formed in accordance
with a second embodiment of the present invention, where like
elements are referenced by like reference numerals, is illustrated.
The cooling hole 270 may extend to the outer surface 102 of the
main body 100 at an angle .theta. of from about 20 degrees to about
90 degrees. The cooling hole 270 may comprise a proximal metering
section 272 having a diameter D.sub.272 extending transverse to a
central axis A.sub.270 of the cooling hole 270, wherein the central
axis A.sub.270 extends in a flow direction FD of a cooling fluid
passing through the cooling hole 270. The diameter D.sub.272 of the
proximal metering section 272 may be from about 0.5 mm to about 5.0
mm. An entrance 272A of the proximal metering section 272 defines
an entrance for the cooling hole 270 and communicates with the
interior cooling passage 160. The cooling hole 270 further
comprises a flared section 274 connected with and extending away
from the proximal metering section 272; a distal section 276
connected with and extending away from a portion of the flared
section 274; and an exit opening 278 connected to the distal
section 276 and a portion of the flared section 274.
[0055] In the embodiment illustrated in FIGS. 4 and 5, the flared
section 274 has a curvilinear shape as it extends away from the
proximal metering section 272 towards the distal section 276 and
exit opening 278 in an X direction, see FIGS. 5 and 5A. In a Y-Z
plane, the flared section 274 has a generally square shape. Because
the cooling hole 270 is positioned at an angle .theta. less than 90
degrees relative to the outer surface 102 of the main body 100, a
length of a first portion 274A of the flared section 274 in the X
direction is greater than a length of a second portion 274B of the
flared section 274, see FIG. 5. If the second portion 274B had a
length equal to the length of the first portion 274A, it would have
an additional section 274C, shown in dotted line in FIG. 5. The
shape of the flared section 274 may be defined by Equation 1 above,
wherein:
[0056] y.sub.1=an exit radius or dimension for the largest portion,
i.e., the first portion 274A, of the flared section 274;
[0057] y.sub.0=a radius of the proximal metering section 272;
[0058] I.sub.d=a length of the longest portion, i.e., the first
portion 274A, of the flared section 274;
[0059] x=independent coordinate extending along the central axis
A.sub.270 Of the cooling hole 270 with an origin at a beginning
point P.sub.B274 of the flared section 274; and
[0060] y=dependent coordinate perpendicular to the central axis
A.sub.270 of the cooling hole 270 with an origin at the central
axis A.sub.270. In this embodiment, values for z substantially
equal values for y, when both z and y have the same corresponding x
value.
[0061] The shape and size of the cooling hole 270 may be designed
using generally the same steps set out above for designing the
cooling hole 170 of the first embodiment.
[0062] In the embodiment illustrated in FIGS. 4 and 5, the flared
section 274 meets directly with the distal section 276. However, it
is also contemplated that a concave interface section 275 may be
provided between the flared section 274 and the distal section 276,
see FIGS. 6 and 7 wherein the concave section 275 is shown in
dotted line.
[0063] In FIGS. 8 and 9, a cooling hole 370 formed in accordance
with a third embodiment of the present invention, where like
elements are referenced by like reference numerals, is illustrated.
The cooling hole 370 may extend to the outer surface 102 of the
main body 100 at an angle .theta. of from about 20 degrees to about
90 degrees. The cooling hole 370 may comprise a proximal metering
section 372 having a diameter D.sub.372 extending transverse to a
central axis A.sub.370 of the cooling hole 370, wherein the central
axis A.sub.370 extends in a flow direction FD of a cooling fluid
passing through the cooling hole 370. The diameter D.sub.372 of the
proximal metering section 372 may be from about 0.5 mm to about 5.0
mm. An entrance 372A of the proximal metering section 372 defines
an entrance for the cooling hole 370 and communicates with the
interior cooling passage 160. The cooling hole 370 further
comprises a flared section 374 connected with and extending away
from the proximal metering section 372; a distal section 376
connected with and extending away from a portion of the flared
section 374; and an exit opening 378 connected to the distal
section 376 and a portion of the flared section 374.
[0064] In the embodiment illustrated in FIGS. 8 and 9, the flared
section 374 has a curvilinear shape in a Y direction as it extends
away from the proximal metering section 372 and towards the distal
section 376 and first sides 378A of the exit opening 378 in an X
direction, see FIGS. 9 and 9A. It is noted that the Y and Z axes
have been reversed in this embodiment from their respective
positions in the embodiments of FIGS. 2, 2A, 5 and 5A. The flared
section 374 has at least one planar wall 374A spaced away from the
central axis A.sub.370 by a distance equal to diameter D.sub.372/2
or y.sub.0. The shape of the flared section 374 in the Y direction
may be defined by Equation 3:
y = y 1 1 + [ ( y 1 / y 0 ) 2 - 1 ] [ 1 - x 1 d ] ##EQU00004##
[0065] wherein: [0066] y.sub.1=an exit radius or dimension for a
largest portion of a curvilinear portion of the flared section 374;
[0067] y.sub.0=a radius of the proximal metering section 372;
[0068] I.sub.d=a length of the longest portion of the flared
section 374; [0069] x=independent coordinate extending along the
central axis A.sub.370 of the cooling hole 370 with an origin at a
beginning point P.sub.B374 of the flared section 374; and [0070]
y=dependent coordinate perpendicular to the central axis A.sub.370
of the cooling hole 370 with an origin at the central axis
A.sub.370.
[0071] The shape and size of the cooling hole 370 may be designed
using generally the same steps set out above for designing the
cooling hole 170 of the first embodiment.
[0072] While a particular embodiment of the present invention has
been illustrated and described, it would be obvious to those
skilled in the art that various other changes and modifications can
be made without departing from the spirit and scope of the
invention. It is therefore intended to cover in the appended claims
all such changes and modifications that are within the scope of
this invention.
* * * * *