Patent Publication Number: US-10760587-B2

Title: Extended sculpted twisted return channel vane arrangement

Description:
BACKGROUND OF THE INVENTION 
     Field of the Invention 
     The present disclosure generally relates to turbomachines and other fluid transport machinery and, more particularly, to vane arrangements for return channels within a turbomachine. 
     Description of Related Art 
     Turbomachines, such as centrifugal, axial, or mixed-flow compressors, pumps, fans, blowers, and turbines including hot gas expanders, are widely used throughout the energy industry worldwide. These machines interact with working fluid, which could be liquid or gas or multi-phase with single or multiple components to either provide energy to the fluid to increase its pressure or head, as in the case of compressors, or extract energy from a working fluid, as in the case of turbines (including expanders). These turbomachines find global and widespread applications in industries like ethylene production, refineries, process industries, air separation units, and power generation. 
     With reference to  FIG. 1 , a multi-stage, centrifugal-flow turbomachine  10 , such as a compressor, is illustrated in accordance with a conventional design. In some applications, a single stage may be utilized. In each stage of the turbomachine  10 , the fluid supplied to the turbomachine  10  is partially compressed and directed to the next stage, which further compresses the fluid. Using this arrangement, the fluid is compressed in stages through the turbomachine  10 . Such turbomachine  10  generally includes a shaft  20  supported within a housing  30  by a pair of bearings  40 . Turbomachine  10  shown in  FIG. 1  includes a plurality of stages to progressively increase the fluid pressure of the working fluid. Each stage is successively arranged along the longitudinal axis of turbomachine  10  and all stages may or may not have similar components operating on the same or similar principle. 
     With continuing reference to  FIG. 1 , an impeller  50  includes a plurality of rotating blades  60  circumferentially arranged and attached to an impeller hub  70  which is in turn attached to shaft  20 . Blades  60  may be optionally attached to a cover disk  65 . A plurality of impellers  50  may be spaced apart in multiple stages along the axial length of shaft  20 . Rotating blades  60  are fixedly coupled to impeller hub  70  such that rotating blades  60  along with impeller hub  70  rotate with the rotation of shaft  20 . Rotating blades  60  rotate downstream of a plurality of stationary vanes or stators  80  attached to a stationary tubular casing. The working fluid, such as a gas mixture, generally enters and exits turbomachine  10  in a perpendicular direction relative to the shaft  20 . Energy from the working fluid causes a relative motion of rotating blades  60  with respect to stators  80 . In a centrifugal compressor, the cross-sectional area between rotating blades  60  within impeller  50  decreases from an inlet end to a discharge end along the axis of rotation, such that the working fluid is compressed as it passes across impeller  50 . 
     Referring to  FIG. 2 , working fluid, such as a gas mixture, moves from an inlet end  90  to an outlet end  100  of turbomachine  10 . A row of stators  80  provided at inlet end  90  channels the working fluid into a row of rotating blades  60 . Stators  80  extend within the casing for channeling the working fluid to rotating blades  60 . Stators  80  are spaced apart circumferentially with equal spacing between individual struts around the perimeter of the casing. A diffuser  110  is provided at the outlet of rotating blades  60  for guiding the fluid flow coming off rotating blades  60 , while diffusing the flow, i.e., converting kinetic energy into static pressure rise. Diffuser  110  optionally has a plurality of diffuser vanes  120  extending within a casing. Diffuser blades  120  are spaced apart circumferentially typically with equal spacing between individual diffuser blades  120  around the perimeter of the diffuser casing. In a multi-stage turbomachine  10 , a plurality of return channel vanes  125  are provided at outlet end  100  of a fluid compression stage for channeling the working fluid to rotating blades  60  of the next successive stage. In such an embodiment, the return channel vanes  125  provide the function of stators  80  from the first stage of turbomachine  10 . The last impeller in a multi-stage turbomachine typically only has a diffuser, which may be provided with or without the diffuser vanes. The last diffuser channels the flow of working fluid to a discharge casing (volute) having an exit flange for connecting to the discharge pipe. In a single-stage embodiment, turbomachine  10  includes stators  80  at inlet end  90  and diffuser  110  at outlet end  100 . In another embodiment of the single-stage embodiment, the return channel vanes  125  may also be provided. 
     Due to recent market demands for turbomachines that are capable of efficiently handling higher flow rates combined with reduced stage size, a high flow coefficient stage has been developed. Current designs include a 3D mixed-flow shrouded impeller aerodynamically matched with a low vane count (˜12) return channel. It has been discovered that the residual swirl angle and its spanwise variance at the stage exit are higher than desired for a multi-stage application. The higher the levels of residual swirl at the exit of the stage the greater the chance the swirl can compromise the overall head rise in a downstream impeller, which may not have been specifically designed to accommodate the increased swirl. In addition, the spanwise variance of the swirl angle can have an impact on the useable operating range of the downstream stage. A counter-rotating swirling flow near the shroud  65  at the return channel exit can adversely impact the aerodynamic stability of a downstream impeller. For high flow coefficient stages, return channels can be responsible for a large portion of overall stage inefficiency. 
     SUMMARY OF THE INVENTION 
     In view of the foregoing deficiencies, it is an object of this disclosure to achieve a useful reduction in the return channel exit residual average swirl angle and its spanwise variance. It is another object of this disclosure to maintain or improve the total pressure loss characteristics of the return channel system, while adhering to stage spacing and mechanical design constraints. In one example of the present disclosure, stage spacing is understood to be a distance between the diffuser hub of a given stage of the turbomachine to the same diffuser hub location on the previous stage. 
     In one example of the disclosure, a return channel vane for a return channel hub of a turbomachine including a body including a leading edge and a trailing edge provided on an opposite end of the body, wherein the leading edge is twisted relative to a meridional line of the body, and wherein the trailing edge is bowed outwardly relative to the meridional line of the body. 
     In another example of the disclosure, the return channel vane is comprised of at least three sections stacked on top of one another when viewed along a longitudinal axis of the return channel vane. At least two sections of the return channel vane have a leading edge with different blade angles relative to the meridional line of the body. At least two sections of the return channel vane have a trailing edge with different blade angles relative to the meridional line of the body. The trailing edge of one of the at least two sections is angled to one side of the meridional line of the body and the trailing edge of the other of the at least two sections is angled to an opposing side of the meridional line of the body. The blade angles range between +10° and −20° relative to the meridional line of the body. A leading edge of at least one section of the return channel vane extends further from the body than leading edges of the remaining sections of the return channel vane. A trailing edge of at least one section of the return channel vane extends further from the body than trailing edges of the remaining sections of the return channel vane. Each section has a curvature relative to a longitudinal axis of the return channel vane. The curvature of at least one section is different from the curvature of the remaining sections. The body of the return channel vane is curved relative to a longitudinal axis of the return channel vane. 
     In one example of the disclosure, a turbomachine including a housing having an inlet end opposite and outlet end along a longitudinal axis of the housing, a shaft assembly provided within the housing, the shaft assembly extending from the inlet end to the outlet end, a rotor having at least one impeller extending radially outward from the shaft assembly, and a return channel vane hub extending radially outward from the shaft assembly, the return channel vane hub includes at least one return channel vane extend therefrom, the at least one return channel vane comprising a body having a leading edge and a trailing edge, the leading edge is twisted and extended past an outer edge of the return channel vane hub, and the trailing edge is bowed outwardly. 
     In another example of the disclosure, the at least one return channel vane is comprised of at least three sections stacked on top of one another when viewed along a longitudinal axis of the return channel vane. At least two sections of the at least one return channel vane have a leading edge with different blade angles relative to the meridional line of the body. At least two sections of the at least one return channel vane have a trailing edge with different blade angles relative to the meridional line of the body. The trailing edge of one of the at least two sections is angled to one side of the meridional line of the body and the trailing edge of the other of the at least two sections is angled to an opposing side of the meridional line of the body. The blade angles range between +10° and −20° relative to the meridional line of the body. A leading edge of at least one section of the at least one return channel vane extends further from the body than leading edges of the remaining sections of the at least one return channel vane. A trailing edge of at least one section of the at least one return channel vane extends further from the body than trailing edges of the remaining sections of the at least one return channel vane. Each section has a curvature relative to a longitudinal axis of the at least one return channel vane. The curvature of at least one section is different from the curvature of the remaining sections. The body of the at least one return channel vane is curved relative to a longitudinal axis of the at least one return channel vane. 
     These and other features and characteristics of the turbomachine, as well as the methods of operation and functions of the related elements of structures and the combination of parts and economies of manufacture, will become more apparent upon consideration of the following description and the appended claims with reference to the accompanying drawings, all of which form a part of this specification, wherein like reference numerals designate corresponding parts in the various figures. It is to be expressly understood, however, that the drawings are for the purpose of illustration and description only and are not intended as a definition of the limits of the invention. As used in the specification and the claims, the singular form of “a”, “an”, and “the” include plural referents unless the context clearly dictates otherwise. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG. 1  is a perspective view of a turbomachine according to the prior art; 
         FIG. 2  is a schematic cross-sectional view of one stage of the turbomachine shown in  FIG. 1 ; 
         FIG. 3( a )  is a perspective view of a turbomachine according to one example of the present disclosure; 
         FIG. 3( b )  is a perspective cross-sectional view of the turbomachine of  FIG. 3( a ) ; 
         FIG. 3( c )  is a cross-sectional view of the turbomachine of  FIG. 3( a ) ; 
         FIG. 4( a )  is perspective view of a return channel hub according to one example of the present disclosure; 
         FIG. 4( b )  is a rear view of the return channel hub of  FIG. 4( a ) ; 
         FIG. 4( c )  is a side view of the return channel hub of  FIG. 4( a ) ; 
         FIG. 4( d )  is a cross-sectional view of the return channel hub of  FIG. 4( a ) ; 
         FIG. 5( a )  is a side view of a return channel vane according to one aspect of the present disclosure; 
         FIG. 5( b )  is a perspective view of the return channel vane of  FIG. 5( a ) ; 
         FIG. 5( c )  is another perspective view of the return channel vane of  FIG. 5( a ) ; 
         FIG. 5( d )  is another perspective view of the return channel vane of  FIG. 5( a ) ; 
         FIG. 5( e )  is another perspective view of the return channel vane of  FIG. 5( a ) ; 
         FIG. 6( a )  is a meridional view of a return channel vane according to the prior art; 
         FIG. 6( b )  is a meridional view of a return channel vane having an extended leading edge according to the present disclosure; 
         FIG. 6( c )  is a meridional view of a return channel vane having an extended trailing edge according to the present disclosure; 
         FIG. 7  is an illustration of the return channel vane of  FIG. 5( a ) ; 
         FIG. 8  is a schematic illustration of a return channel vane according to the present disclosure; 
         FIG. 9  is an illustration of the return channel vane of  FIG. 5( a ) ; 
         FIG. 10  is a schematic illustration of the different stages of a turbomachine according to one aspect of the present disclosure; 
         FIG. 11  is a graphical representation of spanwise swirl distribution of a return channel vane according to the prior art and a return channel vane according to one aspect of the present disclosure; 
         FIG. 12  is another graphical representation of spanwise swirl distribution of a return channel vane according to the prior art and a return channel vane according to one aspect of the present disclosure; 
         FIG. 13  is a graphical representation of the blade angle distribution of a return channel vane according to one aspect of the present disclosure; 
         FIG. 14  is a schematic representation of the different sections that comprise the return channel vane of the present disclosure; 
         FIG. 15  is a perspective view of a return hub including multiple rows of return channel vanes according to another example of the present disclosure; 
         FIG. 16  is a meridional view of a return channel vane according to another example of the present disclosure; 
         FIG. 17  is a perspective view of the return channel vane of  FIG. 16 ; 
         FIG. 18  is a meridional view of a leading edge of a return channel vane according to another example of the present disclosure; 
         FIG. 19  is a perspective view of the return channel vane of  FIG. 18 ; and 
         FIG. 20  is a meridional view of a return channel vane according to another example of the present disclosure. 
     
    
    
     DESCRIPTION OF THE DISCLOSURE 
     For purposes of the description hereinafter, the terms “upper”, “lower”, “right”, “left”, “vertical”, “horizontal”, “top”, “bottom”, “lateral”, “longitudinal”, and derivatives thereof shall relate to the invention as it is oriented in the drawing figures. However, it is to be understood that the invention may assume alternative variations and step sequences, except where expressly specified to the contrary. It is also to be understood that the specific devices and processes illustrated in the attached drawings, and described in the following specification, are simply exemplary embodiments of the invention. Hence, specific dimensions and other physical characteristics related to the embodiments disclosed herein are not to be considered as limiting. 
     With reference to  FIGS. 3( a )-3( c ) , a turbomachine  200  according to one example of the present disclosure is shown. In one example, the turbomachine  200  is a multi-stage, centrifugal-flow turbomachine. In some applications, a single stage may be utilized. Such turbomachine  200  generally includes a shaft  210  supported within a housing  220  by a pair of bearings. Turbomachine  200  shown in  FIG. 3( a )  may include a plurality of stages to progressively increase the fluid pressure of the working fluid. Each stage is successively arranged along the longitudinal axis of turbomachine  200  and all stages may or may not have similar components operating on the same or similar principle. In one aspect, the turbomachine  200  has a high flow coefficient compressor stage. In one example, the impeller  240  has a design ϕ of 0.237. In another aspect, the impeller  240  has a design ϕ of 0.18-0.28. It is also contemplated the present disclosure can be used with the turbomachine  10  of  FIG. 1 . 
     With continuing reference to  FIGS. 3( a )-3( c ) , an impeller  240  includes a plurality of rotating blades  250  circumferentially arranged and attached to an impeller hub  260  which is in turn attached to the shaft  210 . The blades  250  may be optionally attached to a cover disk. A plurality of impellers  240  may be spaced apart in multiple stages along the axial length of shaft  210 . The rotating blades  250  are fixedly coupled to impeller hub  260  such that the rotating blades  250 , along with the impeller hub  260 , rotate with the rotation of the shaft  210 . The rotating blades  250  rotate downstream of a plurality of stationary vanes or stators  270  attached to a stationary tubular casing. The working fluid, such as a gas mixture, enters and exits turbomachine  200  in the axial direction of shaft  210 . The rotating blades  250  are rotated using an external energy source, such as a motor. The rotating blades  250  in turn work on the fluid to compress the fluid and increase its energy content. The rotating blades  250  are attached to both the impeller hub  260  and an impeller shroud. The rotating blades  250  rotate with reference to stator  270  and return channel vanes  330  (described below). In a centrifugal compressor, the cross-sectional area between the rotating blades  250  within the impeller  240  decreases from an inlet end to a discharge end, such that the working fluid is compressed as it passes across impeller  240 . 
     The working fluid, such as a gas mixture, moves from an inlet end  280  to an outlet end  290  of the turbomachine  200 . A row of stators  270  provided at the inlet end  280  channels the working fluid into a row of the rotating blades  250 . The stators  270  extend within the casing for channeling the working fluid to the rotating blades  250 . The stators  270  are spaced apart circumferentially with equal spacing between individual struts around the perimeter of the casing. A diffuser  300  is provided at the outlet of the rotating blades  250  for guiding the fluid flow coming off the rotating blades  250 , while diffusing the flow, i.e., converting kinetic energy into static pressure rise. The diffuser  300  optionally has a plurality of diffuser vanes extending within a casing. In one example, the diffuser blades are spaced apart circumferentially typically with equal spacing between individual diffuser blades around the perimeter of the diffuser casing. In a multi-stage turbomachine  200 , a plurality of return channel vanes  310  are provided at in the flow path after the fluid compression phase for channeling the working fluid to the rotating blades  250  of the next successive stage. In such an embodiment, the return channel vanes  310  provide the function of stators from the first stage of turbomachine  200 . The last impeller in a multi-stage turbomachine typically only has a diffuser, which may be provided with or without the diffuser vanes. The last diffuser channels the flow of working fluid to a discharge casing (volute) having an exit flange for connecting to the discharge pipe. In one example of a single-stage embodiment, the turbomachine  200  includes stators  270  at the inlet end  280  and the diffuser  300  at the outlet end  290 . The working fluid flows along a flow path  320  through the turbomachine  200  such that the working fluid is compressed from the inlet end  280  to the outlet end  290  of the turbomachine  200 . 
     With reference to  FIGS. 4( a )-4( d ) , a return channel vane hub  330  (hereinafter referred to as “return hub  330 ”) is described. In one example, the return hub  330  is held stationary with reference to the shaft  210 . The return hub  330  includes a plurality of return channel vanes  310  that extend therefrom. In one example, shown in  FIG. 15 , multiple rows of return channel vanes may be provided on the return hub  330 . In one example, a first row of return channel vanes  310  according to the present disclosure may be provided and a second row of conventional return channel vanes  311  may be provided. In another example, two rows of return channel vanes  310  according to the present disclosure can be provided. The rows of return channel vanes  310  may extend radially from the center of the return hub  330 . The return channel vanes  310  extend perpendicular to the return hub  330  towards the outlet end  290  of the turbomachine  200  to deflect the flow of the working fluid through the return channel. The return channel vanes  310  may be fastened to the return hub  330 . In another example, the return channel vanes  310  are formed integral with the return hub  330 . In one example, the plurality of return channel vanes  310  are spread at equal distances around the center of the return hub  330 . For example, a plurality of twelve (12) return channel vanes  310  are spaced apart from one another. In another example, 16-24 return channel vanes  310  are spaced apart from one another. In another example, the return channel vanes  310  are spaced at predetermined varied distances from one another to minimize the average exit bulk swirl from the return channel. Each return channel vane  310  includes a body  340  with a leading edge  350  and a trailing edge  360 . In one example, the leading edge  350  should be understood to be the edge of the body  340  provided on an outer portion of the return hub  330  or the portion of the body  340  that first comes in contact with the fluid. In one example, the trailing edge  360  is understood to be the edge of the body  340  provided on an inner portion of the return hub  330  or the portion of the body  340  where the body  340  ends in the stage and is farthest from the leading edge  350  along the general direction of the flow. The leading edge  350  is provided further from a center axis of the return hub  330  than is the trailing edge  360 . Optimal results for the use of these return channel vanes  310  are in applications with a reduced vane count and high flow coefficients. It is contemplated, however, that these return channel vanes  310  can be used in any type of application. 
     With reference to  FIGS. 5( a )-5( e ) , the return channel vanes  310  are described in detail. These forms of return channel vanes  310  differ from conventional return channel vanes. The conventional return channel vanes have a constant cross section vane shape, which is extruded span-wise from the return hub  330  to a shroud of the flow path. The disclosed return channel vanes  310  assist in controlling aerodynamic loading and local flow structure, thereby resulting in a more uniform exit swirl angle distribution, as well as a low level average exit bulk swirl from the return channel. As shown in  FIG. 11 , the curve A corresponds to an extruded vane according to the prior art. The curve A shows a swirl angle that varies from −24° to +24°. The curve B corresponds to a return channel vane  310  according to the present disclosure. The curve B shows a reduced swirl angle that varies from −14° to +5°. The zero (0) position on the Y-axis of  FIG. 11  corresponds to the hub location and the 1.0 position on the Y-axis corresponds to the shroud location. Using the arrangement of the return channel vanes  310  described in the present disclosure provides low bulk residual swirl angle with a small or no increase of total pressure losses for a relatively lower vane count. The form of these return channel vanes  310  can be adjusted based on 3D computational fluid dynamics simulations that take into account specific operating parameters of the turbomachine  200 . The return channel vanes  310  provide a higher quality conveyance of flow between stages of the turbomachine  200 . In the example shown in  FIG. 5( a ) , the return channel vane  310  includes an extruded shape in the body  340  of the return channel vane  310 . In one example, the body  340  is bent at its center to create a U-shape. It is also contemplated that the body  340  may be extruded into other shapes. 
     An increased vane passing frequency margin from a downstream impeller resonant frequency is also achieved using the arrangement of the return channel vanes  310  of the present disclosure. The increased vane passing frequency margin reduces the risk of high cycle fatigue in which a component fails due to extended usage. In a multi-stage arrangement, as shown in  FIG. 10 , as the leading edges of the downstream impeller rotate around the rotational axis of the turbomachine  100 , the leading edges of the impeller pass the stationary trailing edge  360  of the return channel vanes  310  of the upstream stage. Using the present return channel vanes  310  allows for use of less return channel vanes (i.e., fewer number of trailing edges). By using a lower number of return channel vanes  310 , the vane passing frequency margin is increased. 
     An improved design-point and off-design point aerodynamic matching with a downstream impeller is achieved with the present disclosure. This improved aerodynamic matching leads to higher overall multistage compressor performance and operating range. With reference to  FIG. 12 , curve C denotes a conventional extruded return channel vane and curve D corresponds to a return channel vane  310  according to the present disclosure. The various line types of the curves C, D represent flow conditions (solid line=nominal (i.e., design flow), dashed line=lower than nominal, and dotted line=higher than nominal). The dashed line and the dotted line represent off-design or unintended flow conditions. The curve C has a high variation as it moves spanwise from 0 to 1 on the graph, while the curve D does not vary as much. At a lower than nominal flow, the curve D continues providing a uniform distribution of swirl, while the curve C is much more non-uniform. This condition is also experienced with flow that is higher than nominal. Since the curve D does not vary as much at off-design conditions, the downstream stage will continue to receive uniform flow and its performance will remain consistent as the flow is varied during compressor operation. Thus, an improved matching between any given stage with the return channel vane arrangement of the present disclosure and the downstream stage. The given stage with the return channel vane arrangement provides flow that matches well with the conditions that will provide optimum aerodynamic performance. The present return channel vane arrangement provides reduced aeromechanics stimulus on a downstream impeller, which reduces high cycle fatigue risk for components of the compressor. The non-uniformity in the flow exiting a return channel can act as a stimulus for a downstream impeller. The flow exiting the present return channel vane arrangement is more uniform. Further, since a lower number of return channel vanes  310  are provided in the present arrangement, the number of non-uniform sections per 360° exit will be reduced, thereby reducing the impact on the downstream impeller. 
     In one aspect, the return channel vane  310  has a sculpted and twisted body  340  shape. The body  340  has a bowed structure at the trailing edge  360  and a variable thickness along the longitudinal length of the body  340 . The bowed structure modifies the end-wall loadings of the return channel vane  310  and impacts the span-wise pressure gradients that redistribute flow through the return channel. The thickness of the leading edge  350  and the trailing edge  360  is less than the thickness of the center of the body  340 . The leading edge  350  of the body  340  is twisted about the longitudinal axis of the body  340  to induce bending in the return channel vane  310 . 
     In the example shown in  FIGS. 5( a )-5( e ) , the return channel vane  310  has an extended, sculpted, and twisted body  340  shape. The return channel vane  310  of  FIG. 5( c )  includes a body  340  with a bowed structure at the trailing edge  360  and a variable thickness along the longitudinal length L of the body  340 . The thickness of the leading edge  350  and the trailing edge  360  is less than the thickness of the center of the body  340 . The leading edge  350  of the body  340  is twisted about the longitudinal axis of the body  340  to induce bending in the return channel vane  310 . The trailing edge  360  is sculpted to include a curvature relative to the longitudinal length L of the body  340 . In one aspect, the twist angle β of the trailing edge  360  of each section  500 ,  505 ,  510 ,  515 ,  520  with respect to the meridional line  550  of the body  340  may be different. In one example, the twist angle β of the trailing edge  360  generally varies from +10° and −20° with respect to the meridional line  550  of the body  360 . The return channel vane  310  of  FIG. 5( c )  also includes an extended leading edge  350  that, when attached to the return hub  330 , extends past the edge of the return hub  330  and into the crossover portion of the return channel. Therefore, this example of the return channel vane  310  has a longer longitudinal length than the other examples of the return channel vane  310 . In one aspect, the trailing edge  360  is positioned away from the downstream impeller stage. By positioning the trailing edge  360  away from the downstream impeller stage, the aeromechanical interactions with the downstream stage are alleviated. As shown in  FIG. 10 , by having more space between the trailing edge  360  of an upstream stage and the leading edge of the rotating impeller downstream, the stimulus that the flow exiting from the given stage that may be provided to the rotating downstream impeller, i.e., the coupling between them, will be reduced. In one aspect, the body  340  of the return channel vane  310  is adjusted based on the blade angle distribution based on the blade loading or the flow characteristics and manufacturing considerations. 
     With reference to  FIGS. 6( a )-6( c ) , each example of the return channel vanes  310  is shown in the return channel of the turbomachine  200 . As shown in  FIG. 6( a ) , the conventional return channel vanes  311  extend along the return channel along the length of the return hub  330 . In one aspect shown in  FIG. 6( b ) , however, the return channel vane  310  includes a leading edge  350  that extends into the crossover portion of the return channel, but does not extend to the apex  400  of the return hub  330 . In one example, the crossover portion of the return channel is understood to be the portion of the return channel positioned between the impeller  240  and the return hub  330 . By providing an extended leading edge  350  (which provides a longer return channel vane for a fixed trailing edge), a longer path length is provided for flow turning (the flow entering the return channel is radial and has a spiral form, which needs to be formed axially as much as possible—parallel to the axis of rotation for entry into the downstream stage). As shown in  FIG. 6( c ) , the trailing edge  360  may be extended toward the next stage of the turbomachine  200 . 
     With reference to  FIGS. 7 and 8 , it is shown that each return channel vane  310  includes at least three sections  500 ,  505 ,  510 ,  515 ,  520 . In one aspect, each return channel vane  310  is made of five sections  500 ,  505 ,  510 ,  515 ,  520 . The sections  500 ,  505 ,  510 ,  515 ,  520  are formed together to form a monolithic structure for the return channel vane  310 . By using five sections  500 ,  505 ,  510 ,  515 ,  520  to form the return channel vanes  310 , an improved turning of the flow is achieved as soon as the flow approaches the return channel vane  310 . With reference to  FIG. 9 , each section  500 ,  505 ,  510 ,  515 ,  520  of the return channel vane  310  has a different starting and trailing blade angle β. The starting and trailing angle β is measured relative to the meridional line  550  of each return channel vane  310 . The different starting angles β assist in improving the blade loading in the entry section of the return channel. The leading edge  350  of each return channel vane  310  is tailored to achieve a good incidence, which requires a different starting angle β for each section  500 ,  505 ,  510 ,  515 ,  520 , resulting in a “swept” leading edge  350 . It is also contemplated that, due to the stacking of the sections  500 ,  505 ,  510 ,  515 ,  520 , the trailing edge  360  may also be “swept”. In contrast, conventional return channel vanes are flat or straight across from hub to shroud. The vane sections  500 ,  505 ,  510 ,  515 ,  520  may be offset circumferentially to obtain beneficial aerodynamic properties, such as recovery in static pressure. The multiple vane sections  500 ,  505 ,  510 ,  515 ,  520  are stacked (placed on top of one another) to satisfy the bulk (or average) stage exit swirl and its spanwise distribution, while maintaining or improving return channel loss characteristics. By arranging the vane sections  500 ,  505 ,  510 ,  515 ,  520  in this manner, a sculpted shape is achieved for the return channel vane  310 , especially the trailing edge  360  of the return channel vane  310 . As shown in  FIGS. 7 and 9 , each trailing edge of the vane sections  500 ,  505 ,  510 ,  515 ,  520  may have a different trailing angle β relative to the meridional line  550  of the return channel vane  310 . In one aspect, the trailing edge of at least one vane section  500 ,  505 ,  510 ,  515 ,  520  may extend to one side of the meridional line  550  and the trailing edge of at least another vane section  500 ,  505 ,  510 ,  515 ,  520  may extend to an opposite side of the meridional line  550 , which is also shown in  FIGS. 5( b )  and  7 . 
     With reference to  FIG. 13 , the blade angle β distribution of the return channel vane  310  is described in further detail. The blade angle β is plotted against the percentage (%) meridional distance in which 0% corresponds to the leading edge  350  of the vane  310  and 100% corresponds to the trailing edge  360  of the vane  310 . The blade angle β is measured from the meridional line. This graph shows how the blade angle β is distributed in the meridional projection of the return channel vane  310 . At the leading edge  350  of the vane  310 , the blade angle β varies mildly from hub to shroud, while at the trailing edge  360  of the vane  310  the variation is increased. The leading edge blade angle β (0% m) for each section is determined based on the incoming flow such that the leading edge  350  aligns well with the flow to provide improved incidence. The entrance region blade angle β (approx. 0-7% m) is arranged to provide a good flow turning from the leading edge  350  to the mid-region of the return channel. The mid-region blade angle β (approx. 7-50% m) is arranged to continue providing good flow turning such that the flow does not (but may) separate. As flow travels through the return channel, the static pressure increases. The blade angle β distribution (along with thickness) provides a varying channel area to achieve good pressure recovery. Further, due to the need to place an anchoring bolt through this region, the freedom to arrange the blade angle β distribution is limited. The blade angle β distribution of the transition area to the trailing edge  360  (approx. 50-80% m) provide good flow turning. The blade angle β distribution for the trailing edge  360  (100% m) is arranged to impact the spanwise distribution of swirl exiting the stage. As shown in  FIG. 14 , each section  500 ,  505 ,  510 ,  515 ,  520  of the return channel vane  310  includes a varying shape and thickness. The arrangement of the blade angle β corresponds simultaneously with the thickness distribution of the return channel vane  310  since together they provide variable area passage that smoothly turns the flow to axial, while reducing the swirl as well as increasing the static pressure of the flow. The kinetic energy of the flow is converted into static pressure recovery, while the total pressure is always reduced. The total pressure, which includes dynamic pressure and static pressure, loses the dynamic component to gain an additional static component. 
     With reference to  FIGS. 16 and 17 , in another example of the return channel vane  310 , at least one of the leading edge  350  and the trailing edge  360  includes middle sections that extend further than the outer sections of the leading  350  or trailing edge  360 . In this example, the middle portion of the leading  350  or trailing edge  360  extend further upstream or downstream, respectively, than the outer edges of the leading  350  or trailing edge  360 . With reference to  FIGS. 18 and 19 , according to another example of the return channel vane  310 , the leading edge  350  includes at least one section with nominal extension upstream. In this example, the outer edges of the leading edge  350  extend upstream, while a middle portion of the leading edge  350  does not. With reference to  FIG. 20 , according to another example of the present disclosure, the lowermost section of the leading edge  350  of the return channel vane  310  extends away from the body  340  relative to the longitudinal axis of the body  340 . The uppermost section of the trailing edge  360  may also extend away from the body  340  relative to the longitudinal axis of the body  340 . 
     A method of developing and designing the present return channel vanes  310  is now described. Initially, a base compressor computational fluid dynamics (CFD) model is initiated to conduct flow diagnosis of the compressor, i.e., exit swirl distribution, average exit swirl distribution, total pressure loss characteristics, and blade loading, among other factors. An operator then assesses whether any undesirable flow features can be remedied by using the concepts of the return channel vane  310  of the present disclosure, i.e., extending the leading edge, adding more sections to the vanes, and adjusting the angles of the leading and trailing edges. In the event these concepts appear to be applicable, the baseline return channel vanes are converted to the return channel vanes  310  of the present disclosure. A CFD analysis is then again conducted to determine the flow diagnosis of the compressor. This CFD analysis and modification of the return channel vane is repeated until the desired flow diagnosis of the compressor is achieved. The return channel vane  310  can be modified to include an extended leading edge  350  that extends into the crossover of the return channel, where the swirl is generally low. The lean of the return channel vane  310  should also be kept in mind. The lean is the angle between the vane surface and the hub surface. The leading edge  350  could become more curved or swept as vane sections are added from the hub to the shroud. The body  340  of the return channel vane  310  can be adjusted based on the observed blade loading (or how well the vane turns the flow) of the return channel vane  310  through CFD. This adjustment can be restricted, however, due to the need to drill holes for anchoring bolts into the return channel vane  310 . 
     While several examples of the turbomachine  200  and return channel vanes  310  are shown in the accompanying figures and described in detail hereinabove, other examples will be apparent to, and readily made by, those skilled in the art without departing from the scope and spirit of the disclosure. Accordingly, the foregoing description is intended to be illustrative rather than restrictive. The invention described hereinabove is defined by the appended claims and all changes to the invention that fall within the meaning and range of equivalency of the claims are to be embraced within their scope.