U.S. patent application number 11/505129 was filed with the patent office on 2008-02-21 for turbomachine with reduced leakage penalties in pressure change and efficiency.
Invention is credited to Syed Arif Khalid.
Application Number | 20080044273 11/505129 |
Document ID | / |
Family ID | 39101550 |
Filed Date | 2008-02-21 |
United States Patent
Application |
20080044273 |
Kind Code |
A1 |
Khalid; Syed Arif |
February 21, 2008 |
Turbomachine with reduced leakage penalties in pressure change and
efficiency
Abstract
A turbomachine is provided having at least one row of blades
oriented at a predetermined stagger. Casing grooves are provided
proximate to at least a portion of the tip of the blades. The
grooves are oriented substantially normal to the stagger of the
blades. The normal of the blade is determined from a chord of the
blade. The chord may be taken across a pair of corresponding points
one the upstream and downstream end of the blade, hence across the
extent of the cross-sectional shape of the blade. Alternatively, a
blade chord may be determined over only a portion of the blade, for
instance, from a point along the centerline of the upstream end of
the blade to a second point on the centerline midway down the blade
from the upstream end. Optimally, the grooves are positioned
adjacent to the upstream half of the blades, but may continue
across the axial extent of the blades. The spacing between grooves
can be optimized for blade stagger in order to find an optimal
number of grooves that concurrently cross the blade. Additionally,
obtaining an optimal groove depth for a particular turbomachine
requires knowing only the tip clearance gap as groove depth is
directly related to the tip clearance. Furthermore, since the
groove may be substantially smaller than prior art casing
treatments, fluid recirculation is reduced. The blade-normal groove
may take a variety of cross-sectional shapes. Optimally, the aft
surface of the groove will have less than a 45.degree. incline to
the radial at that point.
Inventors: |
Khalid; Syed Arif;
(Indianapolis, IN) |
Correspondence
Address: |
RUDOLPH J. BUCHEL JR., LAW OFFICE OF
P. O. BOX 702526
DALLAS
TX
75370-2526
US
|
Family ID: |
39101550 |
Appl. No.: |
11/505129 |
Filed: |
August 15, 2006 |
Current U.S.
Class: |
415/57.4 |
Current CPC
Class: |
F04D 29/321 20130101;
F04D 29/164 20130101; F04D 29/685 20130101; F04D 29/526
20130101 |
Class at
Publication: |
415/57.4 |
International
Class: |
F01D 1/02 20060101
F01D001/02 |
Claims
1. A turbomachine with reduced leakage penalties in pressure change
and efficiency comprising: a plurality of blades, each of said
plurality of blades extending substantially radially from a
rotational axis and terminating in a blade tip and having a forward
facing surface and an opposite facing surface which join together
at an upstream extent of the blade and at a downstream extent of
the blade, and each said plurality of blades having a
cross-sectional shape defined between the forward facing surface
and the opposite facing surface; and a casing, said casing having
an inner surface surrounding the plurality of blades, and a
plurality of casing grooves in said inner surface, said plurality
of casing grooves being oriented in a direction normal to an
orientation of the plurality of blades.
2. The turbomachine recited in claim 1, wherein the direction
normal to an orientation of the plurality of blades further
comprises, a direction normal to a point on one of the forward
facing surface and the opposite facing surface.
3. The turbomachine recited in claim 1, wherein the direction
normal to an orientation of the plurality of blades further
comprises, a direction normal to a point on a mean line between the
forward facing surface and the opposite facing surface.
4. The turbomachine recited in claim 1, wherein the direction
normal to an orientation of the plurality of blades further
comprises, a direction normal to a point on a chord line which
intersects a mean line defined between the forward facing surface
and the opposite facing surface.
5. The turbomachine recited in claim 2, wherein the plurality of
casing grooves being substantially linear.
6. The turbomachine recited in claim 2, wherein the plurality of
casing grooves being curvilinear.
7. The turbomachine recited in claim 2, wherein each of the
plurality of casing grooves is defined by a first groove wall and a
second groove wall.
8. The turbomachine recited in claim 2, wherein a cross-sectional
shape of each of the plurality of casing grooves is triangular.
9. The turbomachine recited in claim 2, wherein a cross-sectional
shape of each of the plurality of casing grooves is
rectangular.
10. The turbomachine recited in claim 2, wherein a cross-sectional
shape of each of the plurality of casing grooves is
trapezoidal.
11. The turbomachine recited in claim 2, wherein each of the
plurality of grooves being defined by an upstream extent and a
downstream extent.
12. The turbomachine recited in claim 11, wherein said upstream
extent of the plurality of grooves is downstream from the upstream
extent of the plurality of blades.
13. The turbomachine recited in claim 12, wherein said downstream
extent of the plurality of grooves is upstream from the downstream
extent of the plurality of blades.
14. The turbomachine recited in claim 1, wherein the direction
normal to an orientation of the plurality of blades being between a
minimum tangential angle at any point on said forward facing and
opposite surfaces, and a maximum tangential angle at any other
point on said forward facing and opposite facing surfaces.
15. The turbomachine recited in claim 14, wherein each of said
plurality of blades having a camber line defining blade
orientation, and each of said plurality of casing grooves having a
shape defined by at least a portion of said camber line.
16. The turbomachine recited in claim 8, said casing further
comprises a surface portion between each of the plurality of
grooves.
17. The turbomachine recited in claim 8, said casing further
comprises a peak between each of the plurality of grooves.
18. The turbomachine recited in claim 1 further comprises: a
plurality of vanes, each of said plurality of vanes extending
substantially radially from the casing and terminating in a vane
tip and having a forward facing surface and an opposite facing
surface which join together at an upstream extent of the blade and
at a downstream extent of the vane, and each said plurality of
vanes having a cross-sectional shape defined by the forward facing
surface and the opposite facing surface; a hub, said hub having an
outer surface, said outer surface adjoining the plurality of
blades; and a plurality of hub grooves within the hub surface, said
plurality of hub grooves being oriented in a direction normal to
the plurality of vanes.
19. The turbomachine recited in claim 1, wherein the turbomachine
is one of an axial flow machine and a non axial flow machine.
20. The turbomachine recited in claim 1, wherein the turbomachine
is one of a turbine, compressor, fan, blower and pump.
Description
BACKGROUND OF THE INVENTION
[0001] 1. Field of the Invention
[0002] The present invention relates generally to turbomachinery.
More particularly, the present invention relates to casing
treatments for increasing the efficiency of fluid flow in a
turbomachine.
[0003] 2. Description of Related Art
[0004] In general, turbomachines utilize rows of blades on a hub
(axle or wheel) that spin with respect to a stationary casing that
encloses the hub and blades. Interleaved between the rows of
rotating blades are rows of stationary vanes (or blades) disposed
on the casing wall. As used herein internally, the terms blade,
vane and airfoil will be used synonymously, although it is
generally understood in the art that a blade is attached to the
rotating hub or axle, while a vane is affixed to the stationary
housing. The airfoil configuration of the blades is oriented on the
hub at a precise angle, or stagger, with respect to the axis of
rotation of the machine; similarly, the vanes are also oriented on
the casing wall at a precise stagger angle. A gap (clearance gap)
is required between the tips of the blades and the stationary
casing wall to avoid friction and prevent a catastrophic failure of
the machine. A blade or airfoil is generally considered to consist
of two surfaces that bound the blade passage. One surface largely
faces the direction of rotation while the other faces the opposite
direction. The two surfaces may be called "low" and "high" pressure
surfaces of the airfoil, but which one corresponds surface facing
the direction of rotation depends on whether the device is being
used to increase the pressure of the fluid (compressor or pump) or
being used to extract work from the fluid (turbine).
[0005] The following three directional definitions are commonly
used when discussing turbomachinery. (1) Axial refers to the
direction parallel to the axis of rotation, pointing in the
downstream direction. (2) Radial refers to the direction orthogonal
to the axis of rotation pointing outward from the axis. (3)
Tangential (also called circumferential) points in the direction of
blade rotation.
[0006] The clearance gap is a source of tip leakage of fluid (gas
for a compressor, liquid for a pump) between the high pressure side
of the blades and the lower pressure side, i.e., in the relative
frame of reference of the blade passage fluid leaks
circumferentially over the tips of the blades from the high to low
pressure side of the airfoils. Viewed in the relative frame of the
blade passage, it is widely known that the interaction between the
tip leakage and main passage flow results in loss (reduced
efficiency) and reduced effective flow area (reduced pressure rise
for compressor or pump) at the exit of the passage. The main
passage flow orientation that is largely parallel to the airfoil
surface in the relative frame of reference of the blade is
henceforth called the streamwise direction.
[0007] Historically, the focus of designers has been to minimize
gap clearance in an effort to reduce the amount of leakage and
thereby increase the efficiency of the turbomachine. These
clearance-based approaches have primarily concentrated on
mollifying two independent factors: dynamic structural deformity
and thermal expansion. For instance, the shape of rotating blades
deform as a result of the dynamic forces on the blades. The primary
phenomena that dynamically affect the clearance are the
"centrifugal" forces, thermal expansion, and frictional forces that
interact on the blades. Centrifugal forces cause the rotor and
blades to elongate, resulting in the blade tips being displaced
radially outward, thereby reducing the clearance across
substantially all of the blade tip. Fluid dynamic forces on the
airfoil, on the other hand, cause the blades to deform axially and
twist, thereby reducing the clearance of the blade tips away from
the rotational axis of the airfoils. The extreme operating
conditions of a turbomachine in terms of pressure and temperature
also affect the shape of the casing wall.
[0008] Changes in temperature cause the rotor and blades to expand
and contract, but thermal expansion is generally unrelated to the
dynamic forces. Some aircraft turbines experience temperature
variations in the incoming air stream of over 150.degree. F.
(65.60.degree. C.), for instance, between the hot air on the tarmac
and subfreezing air at cruising altitude and these variations get
magnified due to engine compression.
[0009] Many of the clearance-based approaches directed to
counteracting dynamic structural deformation of the rotor blades
are devoted to decreasing the density (and weight) of the blades
while simultaneously increasing their stiffness. Thus, the
magnitude of the centrifugal forces on the blades is reduced
resulting in a corresponding reduction in the resulting elongation
of the blades caused by the centrifugal forces at higher operating
speeds. A myriad of techniques have been employed to achieve this
result, such as adopting less dense, but stronger materials and
construction techniques, including, but not limited to high
performance alloys and innovative structural design. Innovative
techniques are employed to achieve favorable thermal expansions of
the rotor, blades, and case.
[0010] Another technique used by designers for reducing leakages
has been in the area of abradable seal elements, which are
designed, in general, to allow for minimal wear without
experiencing a catastrophic failure. Some examples of abradable
seal elements are found in, for instance, U.S. Pat. No. 3,365,172
to McDonald, Jan. 23, 1968; U.S. Pat. No. 3,411,794 to Allen, Nov.
19, 1968; U.S. Pat. No. 3,529,905 to Meginnis, Sep. 22, 1970; U.S.
Pat. No. 3,719,365 to Emmerson, Mar. 6, 1973; U.S. Pat. No.
6,203,021 to Wolfla, Mar. 20, 2001; U.S. Pat. No. 6,830,428 to Le
Biez, Dec. 14, 2004; U.S. Pat. No. 6,887,528 to Lau, May 3, 2005;
and U.S. Pat. No. 7,029,232 to Tuffs, Apr. 18, 2006, which are
incorporated by reference herein in their entireties. While the
design concepts vary between the specific applications, in general
the sealing element provides an abradable sealing material on or in
the casing surface region and/or the blade tips. This material is
sufficiently abradable or crushable so that contact with the other
parts, including blades, tips, ridges, or knives on the other
members of the seal, will provide the clearance for rotation
without damaging the other member of the seal or destroying the
effectiveness of the abradable part.
[0011] Still other techniques have been devoted to casing (or
shroud) treatments which modify the flow in the tip region without
using an abradate material. Typically, an air channel is formed in
the casing wall proximate to at least a portion of the blade tip
which disrupts the tip leakage or provides a path for energized
downstream fluid (in the case of a pump or compressor) to enter
further upstream thereby energizing the flow near the tip. The
channel is generally oriented with respect to the axis of rotation
of the turbomachine, casing (or shroud) or hub without regard to
the stagger of the blade. The geometry of prior art channels takes
one of three general configurations: circumferential; axial; and
recessed (passages). FIGS. 1A, 1B and 1C are diagrams of a portion
of blade and casing wall with circumferential, axial and recessed
casing treatments as known in the prior art. In each diagram,
rotating blade 104 is affixed to a rotating hub (not shown) with
blade tip 106 proximate to and separated from stationary casing
body 113 by gap (clearance) 110. Surfaces facing opposite rotation
direction 109 and surfaces facing rotation direction (not shown) of
blade 104 are optimally configured as airfoils, and the blades are
oriented at a predetermined stagger for moving air in direction 122
through the passage formed by two adjacent blades 104 as they
rotate in the direction 124 indicated by the curved black arrow.
Within each casing body 113 shown, channel 130A is formed in
respective casing walls 112.
[0012] More specifically with regard to FIG. 1A, multiple
circumferential channels 130A are formed in casing wall 112A.
Circumferential casing treatment channels are suggested in at least
U.S. Pat. No. 4,239,452 to Roberts, Dec. 16, 1980; U.S. Pat. No.
4,466,772 to Okapuu, Aug. 21, 1984; U.S. Pat. No. 6,527,509 to
Kurokawa, Mar. 4, 2003; and U.S. Pat. No. 6,582,189 to Irie, Jun.
24, 2003, which are incorporated by reference herein in their
entireties. As depicted, each of circumferential channels 130A
forms a continuous curvilinear cross-sectional channel about inner
casing wall 112A. However, the cross-sectional shape may also be
square, triangular, rectangular, trapezoidal or some combination of
the above (not shown). Generally, the channels are equally spaced
across the axial dimension of casing 113. Often, circumferential
channels 130A are positioned in the forward portion of blade tip
106 and terminate before reaching the rear (downstream) portion of
blade tip 106. Because the cross-section is invariant with the
direction of rotation, circumferential grooves appear stationary to
a moving blade and provide an increased leakage path over the blade
tip. Due to the complexity of the interaction of the flow through
the grooves and the tip leakage, some benefit in pressure rise may
be obtained for compressors, although this is generally associated
with a decrease in efficiency.
[0013] FIG. 1B show multiple axial channels 130B fashioned radially
within casing wall 112B. Axial casing treatment channels are
suggested in at least U.S. Pat. No. 4,239,452 to Roberts, Dec. 16,
1980; U.S. Pat. No. 6,540,482 to Irie, Apr. 1, 2003; and U.S. Pat.
No. 6,582,189 to Irie, Jun. 24, 2003, which are incorporated by
reference herein in their entireties. Channels 130B are depicted as
being square, or trapezoidal, but may instead have a curvilinear or
triangular cross-sectional shape (not shown). Trapezoidal shaped
channels may be highly exaggerated, wherein a portion of the depth
of the channel lies radially behind the casing wall 112B (not
shown). As in the example above, axial channels 130B are often
positioned in the forward portion of blade tip 106 (the upstream
side) and terminate before reaching the rear portion of blade tip
106 (the downstream side). An effect of the cross-section changing
abruptly with the direction of rotation is to impart high
tangential momentum in the fluid in the frame of reference of the
blade. The grooves also provide a pathway to recirculate flow from
downstream to upstream which reduces the overall efficiency of the
machine.
[0014] FIG. 1C shows multiple recessed channels (or passages) 130C
formed within casing body 113B with only ports 131C being exposed
in casing wall 112B. Recessed channel casing treatment (and exposed
port configurations) is suggested in at least U.S. Pat. No.
5,282,718 to Koff, Feb. 1, 1994; U.S. Pat. No. 5,308,225 to Koff,
May 3, 1994; and U.S. Pat. No. 6,231,301 to Barnett, May 15, 2001;
U.S. Pat. No. 6,585,479 to Torrance Jul. 1, 2003; U.S. Pat. No.
6,736,594 to Irie May 18, 2004; and U.S. Pat. No. 6,742,983,
Schmuecker, Jun. 1, 2004, which are incorporated by reference
herein in their entireties. Recessed channels 130C typically have
curvilinear or oval cross-sectional shape, but may instead have a
rectangular cross-sectional shape (not shown). As depicted, each of
ports 131C are positioned radially within casing wall 112C and
equally spaced from each other. Port ends 131C for a particular
recess channel are generally aligned axially. However, recessed
channels 130C are not always aligned axially. Passages, channels
and cavities (with or without turning vanes) recirculate flow from
downstream, which results in a corresponding loss in
efficiency.
[0015] Additionally, and not shown, a honeycomb structure may be
formed into the casing wall proximate to the blade tips as suggest
by is suggested in at least U.S. Pat. No. 5,520,508 to Khalid, Dec.
5, 1994. However, the honeycomb configuration time-varies
pressurizing and aspirating of cells imparts undesirable radial
fluid momentum.
BRIEF SUMMARY OF THE INVENTION
[0016] The present invention is directed to a casing treatment for
reducing the adverse effects of tip leakage over a blade in a
turbomachine. A turbomachine is provided having at least one row of
blades oriented at a predetermined stagger. Casing grooves are
provided proximate to at least a portion of the tip of the blades.
The grooves are orientated substantially normal to the stagger of
the blades. The normal of the blade is determined from a chord of
the blade. The chord may be taken across a pair of corresponding
points, one toward the upstream end and the other toward the
downstream end of the blade, hence across the extent of the
cross-sectional shape of the blade. Alternatively, a blade chord
may be determined over only a portion of the blade, for instance
from a point along the centerline of the upstream end of the blade
to a second point on the centerline midway down the blade from the
upstream end. The spacing between grooves can be optimized for
blade stagger in order to find an optimal number of grooves that
concurrently cross the blade. Additionally, obtaining an optimal
groove depth for a particular turbomachine requires knowing only
the tip clearance gap as groove depth is directly related to the
tip clearance. Furthermore, since the groove may be substantially
smaller than prior art casing treatments, flow recirculation within
the groove is reduced. The blade-normal groove may take a variety
of cross-sectional shapes. Optimally, the aft-facing surface of the
groove will have less than a 45.degree. incline to the radial at
that point.
BRIEF DESCRIPTION OF THE SEVERAL VIEWS OF THE DRAWINGS
[0017] The novel features believed characteristic of the present
invention are set forth in the appended claims. The invention
itself, however, as well as a preferred mode of use, further
objectives and advantages thereof, will be best understood by
reference to the following detailed description of an illustrative
embodiment when read in conjunction with the accompanying drawings
wherein:
[0018] FIGS. 1A, 1B and 1C are diagrams of a portion of blade and
casing wall with circumferential, axial and recessed casing
treatments as known in the prior art;
[0019] FIG. 2A is a cross-sectional view of an exemplary
turbomachine as understood in the prior art;
[0020] FIG. 2B is an oblique view of a typical hub and a partial
blade assembly as known in the prior art;
[0021] FIG. 3A is a diagram depicting a blade-normal groove with
respect to the chord of the blade in accordance with an exemplary
embodiment of the present invention;
[0022] FIG. 3B is a diagram depicting a blade-normal groove with
respect to the centerline of the blade in accordance with another
exemplary embodiment of the present invention;
[0023] FIGS. 4A-4D are views of a turbomachine with blade-normal
casing treatments in accordance with an exemplary embodiment of the
present invention;
[0024] FIG. 5 is a diagram depicting the ends of a blade-normal
grooves as being tapered in accordance with an exemplary embodiment
of the present invention;
[0025] FIGS. 6A-6E are diagrams of various cross-sectional shapes
in accordance with exemplary embodiments of the present
invention;
[0026] FIG. 7 is a cross-sectional view of a saw-toothed shape
embodiment with momentum components;
[0027] FIGS. 8A and 8B are diagrams depicting a blade-normal groove
with respect to the chord of the blade in a highly cambered turbine
blade application in accordance with an exemplary embodiment of the
present invention;
[0028] FIG. 9 is a cross-sectional view of an exemplary
turbomachine having multiple sets of casing groove and multiple
sets of vane normal hub grooves in accordance with an exemplary
embodiment of the present invention; and
[0029] FIGS. 10A and 10B illustrate the application of the present
blade-normal groove on a mixed flow (both axial and radial flow) or
radial flow turbomachine in accordance with an exemplary embodiment
of the present invention.
[0030] Other features of the present invention will be apparent
from the accompanying drawings and from the following detailed
description.
DETAILED DESCRIPTION OF THE INVENTION
Element Reference Number Designations
[0031] 02: Hub surface [0032] 03: Hub body [0033] 04:
Blade-rotating hub-mounted blade [0034] 06: Tip of rotating blade
[0035] 08: Blade surface facing rotation direction [0036] 09: Blade
surface facing opposite rotation direction [0037] 10: Gap
(clearance) between tip of rotating hub-mounted blade [0038] 12:
Casing wall [0039] 13: Casing body [0040] 14: Vane
(blade)--stationary casing mounted [0041] 16: Tip of stationary
vane [0042] 18: Forward facing surface of stationary vane [0043]
19: Aft facing surface of stationary vane [0044] 20: Leakage flow
over blade tip from high pressure side (pressure surface) to low
pressure side (suction [0045] 22: Direction of incoming flow [0046]
24: Rotation direction [0047] 26: Upstream limit of blade [0048]
28: Downstream limit of blade [0049] 30: Groove in stationary
casing wall [0050] 31: Groove start [0051] 32: Groove peak [0052]
33: Groove end [0053] 40: Groove in rotating hub surface [0054] 50:
Normal to blade [0055] 52: Chord line of airfoil [0056] 54:
Centerline of blade cross-section [0057] 56: Axis of rotation
[0058] 58: Radial axis [0059] 59: Aft-facing surface [0060]
.gamma.: Inclination angle of aft-facing surface with respect to
radial direction [0061] .alpha.: Orientation of groove respect to
the axle angle (blade-angle) [0062] g: Groove spacing [0063] s:
Non-groove spacing between grooves [0064] g-s: Groove width [0065]
A.sub.w: Width of airfoil [0066] A.sub.s: Axial span of airfoil
[0067] G.sub.s: Axial span of grooves
[0068] Tip leakage occurs when fluid (gas or liquid) from the high
pressure sides of blades leak circumferentially around the tips of
the blades to the low pressure sides, resulting in a corresponding
decrease in efficiency of the turbomachine. The phenomena may be
better understood with reference to FIGS. 2A and 2B. FIG. 2A is a
cross-sectional view of an exemplary turbomachine, while FIG. 2B is
an oblique view of a typical hub and a partial blade assembly.
FIGS. 2A and 2B depict an exemplary axial flow machine, but leakage
occurs on non-axial turbomachinery in a similar manner. Hub body
203 is shown as having rows of rotating blades 204 affixed to hub
surface 202, each of which rotate on hub 203 within casing body (or
shroud) 213. Clearance gap 210 is formed between blade tips 206 and
casing wall 212. In a similar configuration, stationary vanes 214
are affixed to casing wall 212 and extend toward hub surface 202,
forming clearance gap 210 between vane tips 216 and hub surface
202.
[0069] Leakage flow 220 escapes from high pressure sides 228 of the
airfoils, circumferentially around blade tips 206 (of blades 204),
to suction sides 226 of the airfoils, or alternatively,
circumferentially around vane tips 216 (of vanes 214). The amount
of leakage 220 depends on several design factors for the
turbomachine including airfoil design (comprising blade surfaces
facing rotation direction 208, surfaces facing opposite rotation
direction 209 and vane surfaces) and the magnitude of clearance gap
220, but also depends on other operating parameters for the machine
such as the recitation speed of the hub and temperature. Common
fluid dynamic casing treatment to ameliorate detrimental effects of
tip leakage include casing treatments for recirculating fluid from
the downstream part of the blade passage to upstream to energize
the flow near the casing and casing treatments for breaking up (mix
out) leakage flow. Often, these improve one aspect, e.g., pressure
rise, at expense of another, e.g., efficiency. For instance,
recirculation of the fluid results in losses and reduced
efficiency. Relative motion of axial grooves does not impart an
axial momentum component to the fluid and hence omits an important
component of the streamwise momentum. Injected radial momentum is
not recovered and therefore reduces efficiency of the turbomachine.
Moreover, many of these solutions involve substantial casing
modification, design work and added weight to the turbomachine;
deep slots, cavities and channels add weight and complexity to the
casing. What is needed is a mechanism for imparting streamwise
momentum component to the fluid with sufficient radial momentum to
induce mixing with the leakage flow, but with primarily streamwise
momentum (as defined previously) to reduce the penalties associated
with the leakage.
[0070] Traditionally, as discussed elsewhere above, casing
treatments have concentrated on, and been referenced to the axial
direction of the casing and/or the axis of rotation. This approach
has yielded moderate success in solutions to other shortcomings of
turbomachine design, but has met with less success in the area of
preventing tip leakage loss. What is needed is a new paradigm for
approaching casing treatments for reducing the adverse effects of
tip leakage.
[0071] In accordance with one exemplary embodiment of the present
invention a casing treatment is presented which relates to the
directional orientation (stagger) of the rotating blades rather
than being related to the axis of rotation of the turbomachine.
Grooves are disposed within the casing wall that are oriented
substantially normal (perpendicular) to the blade. Thus, the
application of the present invention represents a new paradigm in
casing treatments, that is, treating the casing with regard to the
stagger of the rotating blades without regard to the axis of
rotation.
[0072] Hereinafter, the terms "blade-normal" and "blade-normal
direction" should be understood as the direction that is
perpendicular to the normal direction from the casing wall and
simultaneously perpendicular to any contour line which lies on or
between the contour of forward facing surface of blade tip (i.e.,
the surface of the airfoil facing rotation direction) and the
contour of the opposite facing surface of blade tip (i.e., the
surface of the airfoil facing opposite rotation direction). As may
be appreciated, the normal to a constant radius casing (cylindrical
casing) points radially inwardly or outwardly. For a casing having
a radial variation with axial location, the casing normal direction
would point in both radial and axial directions (but never
tangential). For example, the downward normal direction from an
upwardly sloping casing (increasing in radius with axial location)
would point both radially down and axially downstream. Thus, the
above definition for blade-normal defines that direction as
parallel to the casing wall and could never be interpreted as the
direction normal to the tip (i.e., upward).
[0073] For instance, the blade-normal for a particular application
may be taken as perpendicular to the normal direction from the
casing wall and simultaneously perpendicular to the mean line of
the blade tip, i.e., a contour line defines the midline between
forward facing and the opposite facing surfaces of blade tip.
Because most airfoils have a generally curvilinear shape, the
contour lines, e.g., the mean line, will also have a curvilinear
shape. However, the blade-normal direction may be determined at any
one point along a contour, thereby resulting in a generally linear
casing groove. Alternatively, the magnitude of the blade-normal
direction may generally correspond with the curvilinear shape of
the contour, resulting in a curvilinear casing groove that mimics
the shape of the contour line it was taken from.
[0074] Therefore, and as should be well appreciated, the range
orientations that are blade-normal is bound by using any tangent
along either of the two airfoil surfaces.
[0075] As a practical matter and as used herein, the phrase normal
(or perpendicular) to the blade means the orientation for reducing
the adverse effects of leakage .+-.25.degree. from the
perpendicular of any tangent on the curves where the two airfoil
surfaces meet the tip. The casing grooves are axially aligned with
and proximate to at least a portion of the blades tips. In
accordance with another exemplary embodiment of the present
invention, a hub treatment is presented which relates to the
directional orientation of the stationary vanes. Here, grooves are
disposed within the hub surface that are oriented substantially
normal (perpendicular) to the vane chord or mean line of the
stationary vanes. The hub grooves are axially aligned with and
proximate to at least a portion of the vane tips. The concept of
blade-normal grooves may be better understood with respect to FIGS.
3A and 3B, both of which are radial inward views of the blade and
casing, i.e., viewed inward toward the axis of rotation.
[0076] FIG. 3A is a diagram depicting a blade-normal groove with
respect to the chord of the blade in accordance with an exemplary
embodiment of the present invention. Each of rotating blades 304 is
depicted in the figure as having a width A.sub.w and length
A.sub.l.; Length A.sub.l translates to a axial length of A.sub.s
due to the stagger of the airfoil. The tangential distance from
blade to blade is represented as p. Blades 304 rotate in direction
324 with flow parallel to the blade surface in the reference frame
of the blade passage 322, resulting in leakage 320 over the blade
tips (also viewed in the blade frame of reference). From the top
view it can be seen that each blade has surface facing rotation
direction 308 and surface facing opposite rotation direction 309
which together define the cross-sectional shape of the airfoil.
Using the cross-sectional shape, the centerline of the airfoil can
be visualized as mean or camber line 354. The camber line, as is
well known in the art, is a measure of the curvature of an airfoil
and as such is an imaginary line which lies halfway between the
forward facing surface and the opposite facing surface of the
airfoil. Generally, the camber line intersects the chord line at
the leading and trailing edges of the airfoil. Because most
airfoils are curvilinear, the resulting blade camber line 354 is
also nonlinear.
[0077] Blade chord line 352 is depicted as a line segment passing
through two center points of the blade along camber line 354. As
shown, the center points are located on the extreme upstream and
downstream ends of camber line 354 (i.e., having an axial spacing
of approximately A.sub.s). Blade-normal 350c is determined from
blade chord 352, which then approximates the blade-normal based on
the position of camber line 354 to the blade. This blade-normal is
the basis for determining the orientation angle, .alpha., of the
casing grooves measured with respect to a line parallel to the axis
of rotation, represented as line 356. In accordance with this
embodiment, one blade-normal is produced from the extent of the
entire cross-sectional shape of the blade resulting in and linear
casing groove treatment oriented at angle .alpha., with respect to
the axis of rotation of the turbomachine. As depicted in the
figure, plurality of blade-normal casing grooves 330A is disposed
within the casing wall, each oriented at blade-normal angle
.alpha.. Grooves 330A are spaced at a groove distance, g, with
non-groove distance, s, between grooves (resulting in a groove
width of g-s). Each of grooves 330A have an axial length of
G.sub.s, where 0.5 A.sub.s<G.sub.s.ltoreq.A.sub.s. Using the
blade to blade distance, p, optimal values for groove distance g,
non-groove distance s and groove width (g-s) may be determined as
will be discussed below with regard to FIG. 7.
[0078] The present casing groove design imparts streamwise (i.e.,
parallel to the blade surface) momentum to the leakage flow in the
relative frame of the blade, hence reducing the adverse effects of
leakage. In the blade frame of reference, the cross-section of
presently described casing grooves 330A "moves" downstream relative
to blades 304. By contrast, prior art circumferential grooves have
a cross-section that appears "stationary" relative to a moving
blade. The relative wall motion of casing grooves 330A imparts both
axial and tangential momentum in the fluid via relative wall
motion. Since the primary effect of a moving wall on neighboring
fluid is in the direction normal to its surface rather than
parallel to it, the "motion" of the substantially perpendicular
grooves 330A results in near-casing fluid being dragged with wall
motion and predominantly pushed normal to grooves 330A and along
(substantially parallel to) the blade stagger. Hence, the
blade-normal groove orientation of the present invention imparts
streamwise momentum to the flow.
[0079] In accordance with another exemplary embodiment of the
present invention, the blade chord used for determining the
blade-normal direction is computed over the axial portion of the
blade that is coextensive with the grooves. The portion of the
blade not coextensive with the groove is not used for chord
determination. For instance, if the axial length, G.sub.s, of
grooves 330A is shorter than the axial span, A.sub.s, of blade 304,
only the G.sub.s--long portion of blade 304 that is coextensive
with axial length span of grooves 330A is used for computing the
blade chord. In other words, a blade chord is defined as having
both endpoints within G.sub.s (not shown). That chord is used for
finding blade-normal 350-c. Blades-normal grooves 330A are then
limited to an axial length of G.sub.s.
[0080] By way of an another example, one chord endpoint is
positioned proximate to the upstream end of the blade, for instance
on camber line 354, while the second end of the blade chord line is
located at a point on the blade corresponding to
distance.gtoreq.0.5 A.sub.l from the first point. The second point
would then be positioned between the axial midpoint of blade 304
and the downstream end of blade 304 (i.e., having an axial spacing
of between 0.5 A.sub.s and A.sub.s), for instance also along camber
line 354. The normal of that chord line is assumed to be the
effective blade-normal for the portion of blade 304 between the
chord endpoints and blade-normal grooves 330A are aligned with that
blade chord.
[0081] In the preceding the blade chord was defined from endpoints
along the center line of blade 304, i.e., camber line 354. However,
in accordance with still another exemplary embodiment of the
present invention, the endpoints of a blade chord are positioned
along the blade surface facing rotation direction 308 (depicted as
line 308 from a radial view) or alternative along blade surface
facing opposite rotation direction 309 illustrated as line 309 from
the radial view. In so doing, a normal taken from this blade chord
more accurately represents the normal of an airfoil surface of the
blade, rather than a normal for the entire cross-sectional shape of
blade 304. As will be understood from the following description,
the optimal area for axial coverage area for the blade-normal
casing grooves of the present invention is coextensive with the
upstream half of the blades, i.e., between the upstream end of the
blades and the axial midpoint of the blades (i.e., approximately
0.5 A.sub.s from the upstream blade end). Therefore, for optimal
flow results the position of the blade chord should relate to only
that portion of the blade proximate to the casing grooves. For
example, if the axial length of blade-normal grooves is half of the
axial length of the blades, G.sub.s=0.5 A.sub.s, then the normal
angle .alpha. should be determined from a chord in the 0.5 A.sub.s
of the blade proximate to the intended position of the blade-normal
grooves. For a compressor or pump, by truncating the chord to the
upstream portion of the blade, the magnitude of angle .alpha. will
be somewhat higher. For a turbine blade (for which the camber angle
increases with axial distance), limiting the extent of the grooves
to the upstream portion of the passage would result in lower angle
.alpha..
[0082] FIG. 3B is a diagram depicting a blade-normal channel with
respect to the centerline of the blade in accordance with another
exemplary embodiment of the present invention. Here the
blade-normal is taken along the non-linear camber line 354 rather
than the linear blade chord 352. Because camber line 354 is
nonlinear, a plurality of blade-normal lines 350-1, 350-2 . . .
350-m result from tangential points along camber line 354. Thus,
rather than determining a single blade-normal angle .alpha., normal
lines 350-1, 350-2 . . . 350-m result in multiple blade-normal
angles .alpha..sub.1, .alpha..sub.2 . . . .alpha..sub.m.
Blade-normal casing grooves 330B constructed from normal lines
350-1, 350-2 . . . 350-m replicates the character of camber line
354 as depicted in the figure. Blade-normal casing grooves 330B
represent influences on the fluid flow attributable to both sides
of the airfoil equally, i.e., surface facing rotation direction 308
and surface facing opposite rotation direction 309 equally, because
centerline 354 is an unweighted average of both surfaces.
Alternatively, the line for computing the blade-normals may be
biased away from the centerline by weighting the average to shift
the line away from the center position of blade 304. In accordance
with still another exemplary embodiment of the present invention,
the orientation and non-linear character of blade-normal casing
grooves may be determined by the character of only one blade
surface, e.g., either surface facing rotation direction 308 or
surface facing opposite rotation direction 309, rather than the
centerline of blade 304.
[0083] FIGS. 4A-4D are views of a turbomachine with blade-normal
casing treatments in accordance with an exemplary embodiment of the
present invention. FIG. 4A is a cross-sectional view of the upper
portion of a turbomachine as seen from below and along the axis of
rotation in the downstream direction. Portions of blades 404 are
illustrated within casing body 413 wherein clearance gap 410 is
formed between the blade tips and casing wall 412. The direction of
rotation is shown by arrow 424. A plurality of blade-normal casing
grooves 430 are depicted oriented at an angle .alpha. from the axis
of rotation, represented as line 456. Casing grooves 430 are
oriented substantially normal (perpendicular) to blade chord or
mean line of blades 404 (shown as line 354 in FIGS. 3A and 3B).
[0084] FIG. 4B is a cross-sectional view of the upper portion of a
turbomachine along the axis of rotation. Casing grooves 430 are
radially disposed around the entire portion of casing wall 412
proximate to blades 404. Here, the cross-sectional shape of casing
grooves 430 is depicted as square or rectangular. An enlargement of
casing grooves 430 contained within cross-sectional box 401 is
depicted in FIG. 4C. Notice, however, cross-sectional box 401 is
oriented perpendicular (normal) to the direction of grooves 430. A
top view of the groove structure along section AA is depicted in
FIG. 4D (because segment line AA is curved, the resulting section
is substantially flattened with respect to the curvature of the
casing).
[0085] It should be mentioned that in comparison with prior art
casing channeling, the depth (d) and width (g-s) of the present
blade-normal casing grooves are small, but large in comparison to
the roughness of the casing wall. As such, the ingress and egress
ends of the blade-normal casing grooves have been depicted as an
abrupt termination. Optimally, however, rather than an abrupt
transition from casing wall 513 to depth d, according to one
exemplary embodiment, a gradual slope is fashioned at one or either
end of the grooves, as shown in FIG. 5. There, the ingress and
egress ends of blade-normal grooves 530 terminate to the casing
surface as a graduated relief, having a groove width (g-s) as
discussed above and with a groove depth d. Generally, the slope of
the relief may be determined by the groove width (g-s) such that
the groove depth d occurs at an approximate distance of 2(g-s) from
the groove end.
[0086] Furthermore, although the cross-sectional shape of the
present blade-normal grooves has been depicted as square or
rectangular, other geometric shapes are possible or even favorable.
FIGS. 6A-6E are diagrams of various cross-sectional shapes in
accordance with embodiments of the present invention. In each
figure, casing body 613 is depicted as being sectioned orthogonal
to the axis of rotation. Grooves 630A-630-E are formed in casing
surface 612 as a unique geometric shape. For instance, blade-normal
groove 630A is rectangular (or square), blade-normal groove 630B is
trapezoidal, blade-normal groove 630C is triangular with non-groove
spaces of casing surface between the grooves, blade-normal groove
630D is triangular without non-groove spaces of casing surface
between the grooves, i.e., saw-toothed, and blade-normal groove
630E is curvilinear, e.g., elliptical, parabolic, oval, etc.). One
consideration for optimizing flow results is the inclination angle,
.gamma., of aft-facing surface with respect to radial direction
discussed below with regard to FIG. 7. The cross-sectional shape of
grooves 630 should be designed such that angle
.gamma..gtoreq.0.degree..
[0087] As discussed elsewhere above, the turbomachine for which
grooves are applied is taken to be an axial flow type. The
blade-normal grooves of the present invention reduce the adverse
effects of leakage in other types of turbomachine that do not rely
on axial flow. It should be appreciated that although somewhat more
difficult, it is possible to determine the chord of blade on
non-axial turbomachinery. However, because the curvature of the
vanes of an impeller is usually more pronounced than that of axial
flow type turbomachinery, the blade-normal for determining groove
orientation is more accurately determined from the a line on the
vane rather than its chord, e.g., a centerline. As described above,
the term "blade-normal" rather than "chord-normal" to encompass
both axial and non-axial types of turbomachinery.
[0088] Below is a discussion of optimizing the blade-normal groove
configurations based on various design parameters for
turbomachines. The optimization will be discussed with respect to a
cross-sectional view oriented normal to the casing grooves as
illustrated in FIG. 7. It should be appreciated, however, that
although the shape is triangular, the discussion is valid for any
other shape. The principles described below also apply to
turbomachines with large radius changes, but the parametric
description of these machines is more complicated. Those of
ordinary skill in the art will understand the differences and
readily apply the necessary conversions. Also, it should be
understood that the parameters shown in FIG. 7 are viewed along the
groove (i.e., along the orientation angle .alpha.) and that for
simplicity of discussion the orientation angle .alpha. is taken to
be constant along the groove.
[0089] Initially, it is possible to determine an optimal number of
grooves for a particular rotor blade configuration. The number of
grooves comes from first determining the groove cross-section
dimensions (i.e., groove shape viewed along the groove) and the
orientation angle of the grooves, .alpha.. The number of grooves
can be characterized by the number of grooves per blade passage
width p (tangential distance from one blade to the next),
represented below as n.
n = p cos .alpha. g ( 1 ) ##EQU00001## [0090] g=distance from
groove to groove viewed along groove; [0091] p=tangential distance
from blade to blade; [0092] n=number of grooves per blade passage
width; [0093] a=orientation angle of grooves
[0094] Thus, the optimal number of grooves for a given blade design
comes from obtaining optimal orientation angle .alpha. and groove
cross-section widthg.
[0095] The motion of the blades with respect to the casing can be
viewed from the rotating blade frame of reference as the casing
"moving" in the direction opposite blade rotation. For relatively
smooth groove surfaces, the motion imparted to nearby fluid is
predominantly normal, or orthogonal, to the groove surfaces. To
fully define the orientation of the groove aft-facing surface,
define another angle as the inclination angle of groove aft-facing
surface 759 with respect to a radial line 758. For rectangular
groove cross-section, .gamma.=0.degree.. For a saw-toothed
cross-section, .gamma.<45.degree..
[0096] As the groove moves at speed U (radius multiplied by blade
angular speed) in the tangential direction relative to the blade,
the cross-section viewed along the groove moves at speed U
cos(.alpha.) in the direction normal to the groove. Assuming that
the velocity imparted to the fluid attains a velocity normal to the
aft-facing surface, its velocity magnitude relative to the blade
can be represented as the following.
U cos.alpha.cos.gamma. (2)
[0097] This velocity has the following components: U
cos.alpha.cos.gamma.sin.gamma. in the radial direction; and U
cos.alpha.(cos.gamma.).sup.2 in the non-radial directions.
[0098] For an axial turbomachine envisioned in this discussion, the
radial component enhances mixing with the leakage flow, but does
not impart beneficial streamwise momentum. The non-radial component
has the benefit of improving the streamwise momentum of the leakage
flow. The direction considerations below reveal how .alpha. and
.gamma. should be set.
[0099] To favorably influence tip leakage flow, both the magnitude
and direction of the velocity from the grooves are important.
Setting angle .alpha. for blade-normal orientation provides the
optimal axial and tangential components, but some radial component
is also beneficial to encourage the groove flow to mix with the tip
leakage flow. Thus, even though inclining the aft-facing groove
surface will reduce the magnitude of streamwise velocity from the
grooves, aft-facing groove side inclination angle y should be set
large enough to direct the groove flow toward the blade tip.
[0100] To determine the number of grooves, the size of the grooves
should first be determined. Using d=groove depth and s=non-groove
distance between grooves, the dimension of remaining sides of the
cross-section parameters can be set by choosing a triangular
cross-section and setting the angle that the top groove surface
makes with the aft-facing surface to be 90.degree.. With such an
angle, the top wall is parallel to the flow from the aft-facing
surface.
[0101] From trigonometry, the length of the cross-section opening
to the blade passage can be determined as follows.
d cos .gamma. sin .gamma. ( 3 ) ##EQU00002##
[0102] In general, some non-grooved areas can be included between
grooves to improve robustness to blade rub. The groove-to-groove
distance (viewed along the groove) is then determined as
follows.,
g = s + d cos .gamma. sin .gamma. ( 4 ) ##EQU00003##
[0103] Substituting into Equation (1) above, n is determined as
follows.
n = p cos .alpha. s + ( d cos .gamma. sin .gamma. ) ( 5 )
##EQU00004##
[0104] The above expressions for g and n apply for a triangular
cross-section in which the angle between surfaces at the top of the
groove is 90.degree.. They illustrate how the number of grooves per
blade passage width depends on the orientation angle .alpha. and
the groove cross-section (including non-grooved space between
grooves).
[0105] Next, to reduce the adverse effects of leakage, the
streamwise momentum imparted to the leakage flow should be
optimized. A rear-facing step (.gamma. less than 45.degree.) with
respect to the flow relative to the blade is a reasonable choice
for groove cross-section. The length that primarily sets the amount
of leakage for a given blade design and operating point is the tip
clearance gap t. To influence the leakage flow, the grooves should
be of similar size. Thus, to provide sufficient momentum (velocity
multiplied by mass flow) to alter the leakage flow, the groove
depth d should approximately equal the tip clearance gap t. Using a
depth d>>t encourages recirculation of flow within
blade-normal groove 730 and contributes to unnecessary losses.
[0106] The following illustrates a groove design, including a
suitable number of grooves, for a saw-toothed (triangular)
cross-section, where d=t and .gamma.=30.degree..
[0107] Viewing the groove cross-section along the groove, the
length of the aft-facing surface of the groove is
d cos .gamma. = t 0.75 2 = 2 t 3 . ##EQU00005##
The angle that the other surface makes with respect to the
aft-facing surface should be 90.degree. so that it is parallel to
the desired relative flow direction. This results in a groove width
of 4t/ {square root over (3)}.
[0108] To maximize the effect to the cross-sectional shape on
leakage, a sharp "peak" should separate each groove. However, in an
effort to make the grooves more robust to blade rub, a non-grooved
distance can be inserted between grooves, where s>0, thereby
increasing the groove-to-groove distance
[0109] The number of grooves per blade passage would then be as
given by Equation 5.
n = p cos .alpha. g = p cos .alpha. s + ( 4 t 3 ) ##EQU00006##
For p=2, .alpha.=45.degree., t=0.1, and s=0 (p and t in arbitrary
length units), n would be approximately 6.1.
[0110] Thus, for grooves having depth equal to the clearance gap,
the optimum number of grooves decreases with increased clearance
height. For non-grooved space of zero, the number of grooves is
inversely proportional to clearance height.
[0111] A triangular cross-section with a non-grooved space (defined
by s) would therefore be more effective at imparting streamwise
momentum than a trapezoidal shape. This is because a triangular
shape provides an upper surface that can be set to be parallel to
the flow normal to the aft-facing surface. The trapezoidal
cross-section would likely interfere with the flow normal to the
aft-facing surface of the groove. Also, the added groove
cross-sectional area would increase the recirculation of flow
within the groove, thereby increasing loss.
[0112] It should be reiterated that the orientation of the casing
grooves may vary with the axial location of the grooves. Thus, the
local groove orientation may be optimized by axial location. The
optimal orientation angle of the groove may depart from normal to
the blade angle for two reasons: (1) blade angle variation with
axial location, and (2) behavior of leakage flow may justify a
somewhat different angle from blade-normal.
[0113] FIGS. 8A and 8B illustrates the application of the present
blade-normal groove casing treatment to an axial turbine. FIG. 8A
is a top view of the groove structure which further depict high
camber blades. The view is radially inward toward the axis of
rotation as in FIGS. 3A and 3B. Here, each of highly cambered
blades 804 is depicted in the figure as having a width A.sub.w and
length A.sub.l.; Length A.sub.l translates to a axial length of
A.sub.s due to the stagger of the airfoil. The tangential distance
from blade to blade is represented as p. Blades 804 rotate in
direction 824 with flow parallel to the blade surface in the
reference frame of the blade passage 822, resulting in leakage over
the blade tips. From the top view it can be seen that each blade
has surface facing rotation direction 808 and surface facing
opposite rotation direction 809 which together define the
cross-sectional shape of the airfoil. Using the cross-sectional
shape, camber line 854 can be seen. Casing grooves 830 are depicted
as being curvilinear that approximate or mimic the character of
camber line 854. Here, casing grooves 830 are depicted as being
triangular, with groove start 831, groove peak 832 and groove end
833, that is the groove start for the adjacent groove. Since a
turbine blade is typically more highly cambered (has more flow
turning) than an axial compressor used in previous illustrations,
an optimal groove design will have varying orientation angle with
axial location as shown. FIG. 8B is a cross-sectional view of the
upper portion of the axial turbine along the axis of rotation taken
at segment line AA. The triangular shape of grooves 830 is more
apparent in the cross-sectional view although, again, the
cross-sectional shape of the groove is predicated on the
orientation to the groove (this view is taken perpendicular to the
rotational axis and on any portion of the grooves). Here, groove
start 831, groove peak 832 and groove end 833 are clearly
distinguishable. Note that the variation in orientation angle
.alpha. with axial location implies a variation in groove-to-groove
distance (g-s) viewed along the groove. This is accomplished by
varying either g or s, or both (not shown).
[0114] Furthermore, it should be understood that the configuration
of the particular blade-normal grooves may depend on other factors
such as the dynamics of the particular stage of the turbomachine to
be considered, whether the application is on the case (static) or
the hub (rotation). This is graphically represented in FIG. 9. It
should be understood that the illustration is FIG. 9 is merely
exemplary and the particular casing and hub configurations are
depicted by way of example only. FIG. 9 is similar to FIG. 2B above
and as such is a cross-sectional view of an exemplary turbomachine.
Hub body 903 is shown as having rows of rotating blades 904 affixed
to hub surface 902, each of which rotate on hub 903 within casing
body 913. Blade-normal casing grooves 930A are depicted on the
first stage as having a rectangular cross-sectional shape, while in
the second stage blade-normal casing grooves 930D are shown as
having a triangular cross-sectional shape without a groove space,
i.e., s=0. Clearance gap 910 is shown between blade tips 906 and
casing wall 912.
[0115] In accordance with still another exemplary embodiment of the
present invention, blade (vane) normal grooves may also be disposed
on hub surface 902, such as for cantilevered stators. There,
stationary vanes (stator blades) 914 are affixed to casing wall 912
and extend toward hub surface 902, forming clearance gap 910
between vane tips 916 and hub surface 902. Leakage may also occur
across vane tips 916, as well as blade tip 906. Vane-normal hub
grooves 940A are depicted on the first stage as having a
rectangular cross-sectional shape, while in the second-stage vane
normal hub grooves 940D are shown as having a triangular
cross-sectional shape without a groove space, i.e., s=0.
[0116] In any case, the groove depth should be optimized for
streamwise flow in the tip region, while avoiding losses due to
recirculation. As a threshold proposition, the groove depth
approximately equals to the tip clearance height will satisfy both,
i.e., d.apprxeq.t).
[0117] As described immediately above, a good cross-sectional shape
provides the proper direction without excessive groove
cross-sectional area. The durability benefits of rectangular or
trapezoidal grooves could be obtained by adding non-grooved space s
between triangular grooves. As such, triangular cross-sections
exhibit the promise to be more effective and potentially just as
durable. When blade rub is not a concern (e.g., for large
clearances), sharp groove peaks (s=0) are an optimal choice.
[0118] Finally, and as mentioned elsewhere above, the orientation
of the blade-normal groove is an approximation of the blade-normal
and varies based on several factors such as which algorithm is used
for computing the normal. Additional, the orientation of the
grooves may vary from blade-normal without sacrificing efficiency.
Assuming it is desirous to maintain the relative streamwise
velocity component within 10% on an optimal value, the groove
orientation should be maintained within .+-.25.degree. of
blade-normal direction. It is reiterated that the inclination angle
.gamma. of the aft-facing surface of the groove should be less than
45.degree. (i.e., y<45.degree.) to achieve a balance of
streamwise and radial momentum components.
[0119] The illustrations and discussions above have largely
admitted an axial compressor, however the present invention is
equally applicable to all other types of turbomachinery with tip
clearance, for example fans, blowers, pumps, turbines.
[0120] FIGS. 10A and 10B illustrate the application of the present
blade-normal groove on a mixed flow (both axial and radial flow) or
radial flow turbomachine in accordance with another exemplary
embodiment of the present invention. FIG. 10A depicts an exploded
view of a radial machine while FIG. 10B show grooves 1030 from a
bottom view with an outline of rotor 1013 in position.
[0121] For mixed flow or radial flow pump impeller 1003, flow
starts axial and becomes largely radial in direction. Impeller
blades 1004, or vanes, form complex three-dimensional shape.
Grooves 1030 in casing 1013 are shown substantially perpendicular
to the blade edges parallel to casing. Thus, casing grooves 1030
form a swirl, or helical, pattern in casing 1013.
[0122] The corresponding structures, materials, acts, and
equivalents of all means or step plus function elements in the
claims below are intended to include any structure, material, or
act for performing the function in combination with other claimed
elements as specifically claimed. The description of the present
invention has been presented for purposes of illustration and
description, but is not intended to be exhaustive or limited to the
invention in the form disclosed. Many modifications and variations
will be apparent to those of ordinary skill in the art without
departing from the scope and spirit of the invention. The
embodiment was chosen and described in order to best explain the
principles of the invention and the practical application, and to
enable others of ordinary skill in the art to understand the
invention for various embodiments with various modifications as are
suited to the particular use contemplated.
[0123] The terminology used herein is for the purpose of describing
particular embodiments only and is not intended to be limiting of
the invention. As used herein, the singular forms "a", "an" and
"the" are intended to include the plural forms as well, unless the
context clearly indicates otherwise. It will be further understood
that the terms "comprises" and/or "comprising," when used in this
specification, specify the presence of stated features, integers,
steps, operations, elements, and/or components, but do not preclude
the presence or addition of one or more other features, integers,
steps, operations, elements, components, and/or groups thereof.
* * * * *