US20080044273A1 - Turbomachine with reduced leakage penalties in pressure change and efficiency - Google Patents

Turbomachine with reduced leakage penalties in pressure change and efficiency Download PDF

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Publication number
US20080044273A1
US20080044273A1 US11505129 US50512906A US2008044273A1 US 20080044273 A1 US20080044273 A1 US 20080044273A1 US 11505129 US11505129 US 11505129 US 50512906 A US50512906 A US 50512906A US 2008044273 A1 US2008044273 A1 US 2008044273A1
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blade
plurality
grooves
turbomachine
casing
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US11505129
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Syed Arif Khalid
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Syed Arif Khalid
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    • FMECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
    • F04POSITIVE DISPLACEMENT MACHINES FOR LIQUIDS; PUMPS FOR LIQUIDS OR ELASTIC FLUIDS
    • F04DNON-POSITIVE DISPLACEMENT PUMPS
    • F04D29/00Details, component parts, or accessories
    • F04D29/08Sealings
    • F04D29/16Sealings between pressure and suction sides
    • F04D29/161Sealings between pressure and suction sides especially adapted for elastic fluid pumps
    • F04D29/164Sealings between pressure and suction sides especially adapted for elastic fluid pumps of an axial flow wheel
    • FMECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
    • F04POSITIVE DISPLACEMENT MACHINES FOR LIQUIDS; PUMPS FOR LIQUIDS OR ELASTIC FLUIDS
    • F04DNON-POSITIVE DISPLACEMENT PUMPS
    • F04D29/00Details, component parts, or accessories
    • F04D29/26Rotors specially for elastic fluids
    • F04D29/32Rotors specially for elastic fluids for axial flow pumps
    • F04D29/321Rotors specially for elastic fluids for axial flow pumps for axial flow compressors
    • FMECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
    • F04POSITIVE DISPLACEMENT MACHINES FOR LIQUIDS; PUMPS FOR LIQUIDS OR ELASTIC FLUIDS
    • F04DNON-POSITIVE DISPLACEMENT PUMPS
    • F04D29/00Details, component parts, or accessories
    • F04D29/40Casings; Connections of working fluid
    • F04D29/52Casings; Connections of working fluid for axial pumps
    • F04D29/522Casings; Connections of working fluid for axial pumps especially adapted for elastic fluid pumps
    • F04D29/526Details of the casing section radially opposing blade tips
    • FMECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
    • F04POSITIVE DISPLACEMENT MACHINES FOR LIQUIDS; PUMPS FOR LIQUIDS OR ELASTIC FLUIDS
    • F04DNON-POSITIVE DISPLACEMENT PUMPS
    • F04D29/00Details, component parts, or accessories
    • F04D29/66Combating cavitation, whirls, noise, vibration or the like; Balancing
    • F04D29/68Combating cavitation, whirls, noise, vibration or the like; Balancing by influencing boundary layers
    • F04D29/681Combating cavitation, whirls, noise, vibration or the like; Balancing by influencing boundary layers especially adapted for elastic fluid pumps
    • F04D29/685Inducing localised fluid recirculation in the stator-rotor interface

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° incline to the radial at that point.

Description

    BACKGROUND OF THE INVENTION
  • 1. Field of the Invention
  • 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.
  • 2. Description of Related Art
  • 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).
  • 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.
  • 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.
  • 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.
  • 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° F. (65.60° 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.
  • 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.
  • 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.
  • 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.
  • 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.
  • 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.
  • 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.
  • 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
  • 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° incline to the radial at that point.
  • BRIEF DESCRIPTION OF THE SEVERAL VIEWS OF THE DRAWINGS
  • 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:
  • 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;
  • FIG. 2A is a cross-sectional view of an exemplary turbomachine as understood in the prior art;
  • FIG. 2B is an oblique view of a typical hub and a partial blade assembly as known in the prior art;
  • 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;
  • 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;
  • FIGS. 4A-4D are views of a turbomachine with blade-normal casing treatments in accordance with an exemplary embodiment of the present invention;
  • 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;
  • FIGS. 6A-6E are diagrams of various cross-sectional shapes in accordance with exemplary embodiments of the present invention;
  • FIG. 7 is a cross-sectional view of a saw-toothed shape embodiment with momentum components;
  • 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;
  • 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
  • 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.
  • 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
    • 02: Hub surface
    • 03: Hub body
    • 04: Blade-rotating hub-mounted blade
    • 06: Tip of rotating blade
    • 08: Blade surface facing rotation direction
    • 09: Blade surface facing opposite rotation direction
    • 10: Gap (clearance) between tip of rotating hub-mounted blade
    • 12: Casing wall
    • 13: Casing body
    • 14: Vane (blade)—stationary casing mounted
    • 16: Tip of stationary vane
    • 18: Forward facing surface of stationary vane
    • 19: Aft facing surface of stationary vane
    • 20: Leakage flow over blade tip from high pressure side (pressure surface) to low pressure side (suction
    • 22: Direction of incoming flow
    • 24: Rotation direction
    • 26: Upstream limit of blade
    • 28: Downstream limit of blade
    • 30: Groove in stationary casing wall
    • 31: Groove start
    • 32: Groove peak
    • 33: Groove end
    • 40: Groove in rotating hub surface
    • 50: Normal to blade
    • 52: Chord line of airfoil
    • 54: Centerline of blade cross-section
    • 56: Axis of rotation
    • 58: Radial axis
    • 59: Aft-facing surface
    • γ: Inclination angle of aft-facing surface with respect to radial direction
    • α: Orientation of groove respect to the axle angle (blade-angle)
    • g: Groove spacing
    • s: Non-groove spacing between grooves
    • g-s: Groove width
    • Aw: Width of airfoil
    • As: Axial span of airfoil
    • Gs: Axial span of grooves
  • 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.
  • 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.
  • 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.
  • 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.
  • 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).
  • 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.
  • 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.
  • 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° 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.
  • 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 Aw and length Al.; Length Al translates to a axial length of As 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.
  • 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 As). Blade-normal 350 c 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, α, 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 α, 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 α. 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 Gs, where 0.5 As<Gs≦As. 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.
  • 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.
  • 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, Gs, of grooves 330A is shorter than the axial span, As, of blade 304, only the Gs—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 Gs (not shown). That chord is used for finding blade-normal 350-c. Blades-normal grooves 330A are then limited to an axial length of Gs.
  • 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≧0.5 Al 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 As and As), 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.
  • 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 As 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, Gs=0.5 As, then the normal angle α should be determined from a chord in the 0.5 As 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 α 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 α.
  • 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 α, normal lines 350-1, 350-2 . . . 350-m result in multiple blade-normal angles α1, α2 . . . αm. 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.
  • 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 α 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).
  • 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).
  • 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.
  • 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, γ, 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 γ≧0°.
  • 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.
  • 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 α) and that for simplicity of discussion the orientation angle α is taken to be constant along the groove.
  • 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, α. 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 α g ( 1 )
      • g=distance from groove to groove viewed along groove;
      • p=tangential distance from blade to blade;
      • n=number of grooves per blade passage width;
      • a=orientation angle of grooves
  • Thus, the optimal number of grooves for a given blade design comes from obtaining optimal orientation angle α and groove cross-section widthg.
  • 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, γ=0°. For a saw-toothed cross-section, γ<45°.
  • 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(α) 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 cosαcosγ  (2)
  • This velocity has the following components: U cosαcosγsinγ in the radial direction; and U cosα(cosγ)2 in the non-radial directions.
  • 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 α and γ should be set.
  • To favorably influence tip leakage flow, both the magnitude and direction of the velocity from the grooves are important. Setting angle α 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.
  • 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°. With such an angle, the top wall is parallel to the flow from the aft-facing surface.
  • From trigonometry, the length of the cross-section opening to the blade passage can be determined as follows.
  • d cos γ sin γ ( 3 )
  • 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 γ sin γ ( 4 )
  • Substituting into Equation (1) above, n is determined as follows.
  • n = p cos α s + ( d cos γ sin γ ) ( 5 )
  • 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°. They illustrate how the number of grooves per blade passage width depends on the orientation angle α and the groove cross-section (including non-grooved space between grooves).
  • Next, to reduce the adverse effects of leakage, the streamwise momentum imparted to the leakage flow should be optimized. A rear-facing step (γ less than 45°) 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.
  • The following illustrates a groove design, including a suitable number of grooves, for a saw-toothed (triangular) cross-section, where d=t and γ=30°.
  • Viewing the groove cross-section along the groove, the length of the aft-facing surface of the groove is
  • d cos γ = t 0.75 2 = 2 t 3 .
  • The angle that the other surface makes with respect to the aft-facing surface should be 90° so that it is parallel to the desired relative flow direction. This results in a groove width of 4t/√{square root over (3)}.
  • 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
  • The number of grooves per blade passage would then be as given by Equation 5.
  • n = p cos α g = p cos α s + ( 4 t 3 )
  • For p=2, α=45°, t=0.1, and s=0 (p and t in arbitrary length units), n would be approximately 6.1.
  • 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.
  • 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.
  • 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.
  • 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 Aw and length Al.; Length Al translates to a axial length of As 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 α 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).
  • 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.
  • 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.
  • 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≈t).
  • 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.
  • 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° of blade-normal direction. It is reiterated that the inclination angle γ of the aft-facing surface of the groove should be less than 45° (i.e., y<45°) to achieve a balance of streamwise and radial momentum components.
  • 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.
  • 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.
  • 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.
  • 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.
  • 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.

Claims (20)

  1. 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. 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. 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. 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. 5. The turbomachine recited in claim 2, wherein the plurality of casing grooves being substantially linear.
  6. 6. The turbomachine recited in claim 2, wherein the plurality of casing grooves being curvilinear.
  7. 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. 8. The turbomachine recited in claim 2, wherein a cross-sectional shape of each of the plurality of casing grooves is triangular.
  9. 9. The turbomachine recited in claim 2, wherein a cross-sectional shape of each of the plurality of casing grooves is rectangular.
  10. 10. The turbomachine recited in claim 2, wherein a cross-sectional shape of each of the plurality of casing grooves is trapezoidal.
  11. 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. 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. 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. 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. 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. 16. The turbomachine recited in claim 8, said casing further comprises a surface portion between each of the plurality of grooves.
  17. 17. The turbomachine recited in claim 8, said casing further comprises a peak between each of the plurality of grooves.
  18. 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. 19. The turbomachine recited in claim 1, wherein the turbomachine is one of an axial flow machine and a non axial flow machine.
  20. 20. The turbomachine recited in claim 1, wherein the turbomachine is one of a turbine, compressor, fan, blower and pump.
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