Patent Publication Number: US-2016245297-A1

Title: Impeller comprising variably-dimensioned fillet to secure blades and compressor comprised thereof

Description:
BACKGROUND 
     The subject matter disclosed herein relates to compressors and, generally, to machines that use rotating elements to act on working fluids, with particular discussion about geometry in the region where one or more blades couple to the body of the rotating element. 
     As used herein, the term “compressor” describes machinery that acts on a working fluid, for example, to distribute the working fluid under pressure to a process line. This machinery can embody compressors (e.g., centrifugal compressors) and blowers, with artisans understanding that the difference between the two resides in the operating pressures of the fluid at the discharge. Examples of process lines may be found in various applications including chemical, water-treatment, petro-chemical, resource recovery and delivery, refinery, and like sectors and industries. 
     Compressors typically include a drive unit that is configured to rotate a rotating element (also “impeller”). Examples of the drive unit include steam turbines, gas turbines, and electric motors. The impeller may have a central body with a plurality of blades disposed thereon. In certain configurations, the blades are exposed. Other configurations enclose the blades on the impeller with a shroud or cover. This shroud secures to the impeller at the top of the blades. 
     In operation, rotation of the impeller draws a working fluid into the compressor. The blades are configured to accelerate the working fluid outwardly from the center of rotation, ejecting the working fluid from the impeller under pressure. The compressor directs the working fluid to a discharge. In most configurations, the discharge couples with a pipe that connects the compressor to the process line. 
     Engineers and designers expend great efforts to develop impeller designs to improve performance of the compressor. Structure for the blades is known among their design considerations to dramatically affect flow of the working fluid across the blades and the impeller in general. However, while this structure needs to be configured to maximize fluid dynamic concerns (aerodynamic for gasses and hydrodynamics for liquid) in order to benefit operation of the compressor, structural concerns including vibrations and loading often stand in tension with fluid dynamics because such structural concerns can lead to damage that reduces compressor efficiency and, ultimately, may lead to costly repair and maintenance on the compressor. 
     In the compressor industry, impellers for compressors undergo rigorous testing to confirm, inter alia, various mechanical and fluidic properties of the blades. It is often standard to employ computer modeling (including finite element analysis) to calculate resonant frequencies and to confirm fluid dynamics of the impeller design. It is also standard to implement physical tests on actual hardware. These physical tests may utilize accelerometers that mount to the blades to measure vibrations (and other physical phenomenon) that occur, for example, in response to one or more strikes to the blade from an impact hammer. 
     Analysis of these models and tests confirms that “open” impellers, or those that forego the shroud about the blades, are particularly susceptible to vibration. Without the shroud, the blades are effectively configured as tapered beams that are secured at only one end (to the impeller body). This structure provides little, if any, means to dampen vibration that propagates at the unsecured end. Aerodynamic demands on the blades, however, frustrate attempts to increase the physical dimensions (or other physical aspects) of the blades in a manner that could dampen vibration and improve mechanical performance. 
     BRIEF DESCRIPTION OF THE INVENTION 
     This disclosure describes improvements to impellers and, generally, rotating elements, to address the competing interests between fluid dynamics and structural integrity of the blades. As noted herein, the embodiments below define geometry for a joint region at the root of the blade where the blade secures to the impeller body. This geometry includes a profile that is configured to enhance mechanical properties of the blade and to improve flow of the working fluid outwardly from the impeller. The profile can comprise an arc or fillet that forms a concave surface between the root of the blade and the impeller body. This fillet has a radius that varies along the chord length of the blade. In one implementation, the radius decreases from the leading edge of the blade to the trailing edge of the blade. 
     The improvements find use across various types and styles of impellers. As discussed below, use of the profile in accordance with the concepts herein is particularly beneficial to improve performance on “open” impellers and/or those impellers that have exposed blades. One particular type of open impeller, known as a splitter-type impeller, is configured with blades of different dimensions that populate the outer surface of the impeller. These configurations typically include one set of “main blades” that extend substantially along the axial length of the impeller body and one set of “splitter blades” that are shorter than the “main blades.” In conventional practice, one of the splitter blades is disposed between an adjacent pair of the main blades. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       Reference is now made briefly to the accompanying drawings, in which: 
         FIG. 1  depicts a schematic diagram of a side view of an exemplary embodiment of an impeller in a first annular position, the impeller including an impeller body and a blade that couples with the impeller body at a joint region that configures the impeller to improve operation of a compressor; 
         FIG. 2  depicts a front, cross-section view of the impeller of  FIG. 1 ; 
         FIG. 3  depicts a side view of the impeller of  FIG. 1  in a second annular position that is rotationally offset from the first annular position; 
         FIG. 4  depicts a perspective view of an exemplary embodiment of an impeller with a plurality of blades including main blades and splitter blades, wherein the impeller has a variably-dimensioned fillet in the joint region that couples the main blades with the impeller body; 
         FIG. 5  depicts a schematic view of a cross-section of the impeller of  FIG. 4 ; 
         FIG. 6  depicts a perspective view of a compressor that implements the impeller of one or more of  FIGS. 1, 2, 3, 4, and 5 ; 
         FIG. 7  depicts a Campbell diagram that compares the resonant frequency of a blade on an exemplary embodiment of an impeller with the operating frequency of a compressor, the embodiment having a variably-dimensioned fillet in the joint region that couples the main blades with the impeller body; 
         FIG. 8  depicts a diagram of computated flow over an impeller with blades that secure to the impeller body using conventional practices; and 
         FIG. 9  depicts a diagram of computated flow over an exemplary embodiment of an impeller that has a variably-dimensioned fillet in the joint region that couples the main blades with the impeller body. 
     
    
    
     Where applicable like reference characters designate identical or corresponding components and units throughout the several views, which are not to scale unless otherwise indicated. Moreover, the embodiments disclosed herein may include elements that appear in one or more of the several views or in combinations of the several views. 
     DETAILED DESCRIPTION 
     The embodiments below address vibration of blades in open impellers. These embodiments introduce a variably-dimensioned feature at the bottom, or root, of the blade to raise the resonant frequency of the blade. The variably-dimensioned feature has a profile exemplified, in one embodiment, by an arc or a fillet with a radius that decreases from the leading edge to the trailing edge of the blade. The fillet modifies the structure of the blade in a manner that raises the resonant frequency at the leading edge above the frequency that results from operation of the compressor at speeds within its normal operating range. During modeling and testing, an unexpected result of use of the fillet was to improve aerodynamic performance of the impeller by reducing the wake zone at the trailing edge of the blade. 
       FIGS. 1, 2, and 3  depict various schematic views of an exemplary embodiment of a rotating element  100  (also, “impeller  100 ”) that can be configured for use on a compressor.  FIG. 1  shows a side view of the impeller  100  in a first annular position.  FIG. 2  depicts a front, cross-section of the impeller  100  taken at line  2 - 2  in  FIG. 1 .  FIG. 3  shows the side view of the impeller  100  in a second annular position that is rotationally offset from the first annular position of  FIG. 1 . 
     Turning first to  FIGS. 1 and 2 , the impeller  100  has an annular body  102  with a blade  104  disposed thereon. The annular body  102  has a first end  106 , a second end  108 , and an outer surface  110  that circumscribes a longitudinal axis  112  to give the annular body  102  its conical or frusto-conical shape. At the first end  106 , the annular body  102  has a first diameter D 1 . The second end  108  of the annular body  102  has an outer peripheral edge  114  with a second diameter D 2 . In most configurations, the second diameter D 2  is larger than the first diameter D 1 . 
     The blade  104  has a blade body  116  that extends axially along the longitudinal axis  112 . The blade body  116  has a root  118  (also “base  118 ”) proximate the annular body  102  and a top  120  disposed radially outwardly of the root  118 . In “open” impellers, the top  120  is exposed and, thus, likely to vibrate during operation of a compressor. The blade body  116  also has a first edge  122  and a second edge  124 , one each disposed proximate the first end  106  and the second end  108  of the annular body  102 . In one example, the profile extends annularly around one of the first edge and the second edge of the blade. The blade body  116  may terminate at the outer peripheral edge  114  with the second edge  124  terminating and/or formed integrally with the outer peripheral edge  114  of the annular body  102 . The edges  122 ,  124  area also referred to as the “leading edge  122 ” and as the “trailing edge  124 ” of the blade body  116 , the determination of which is based on the direction of flow of a working fluid F across the impeller  100 . In one embodiment, the first or leading edge  122  is spaced apart from the first end  106  of the annular body  102 . 
     As also shown in  FIG. 1 , the impeller  100  includes a joint region, shown generally as the hatched area enumerated by the numeral  126 , wherein the joint region  126  extends along the root  118  of the blade body  116 . Broadly, the joint region  126  defines geometry for structure of the impeller  100  that couples the blade body  116  (at the root  118 ) to the annular body  102 . This structure may be integral to both the annular body  102  and the blade body  116  because the impeller is often machined from a single piece (also, “block” or “billet”) of material, typically aluminum, steel, stainless steel, and the like. However, the geometry of the joint region  126  may also apply to welds and other suitably-fashioned structural elements that can secure the blade body  116  to the annular body  102 . 
     The geometry includes a profile that varies in a direction along the longitudinal axis  112 . At a high level, the profile forms a curved or concave surface between the root  118  of the blade body  116  and the outer surface  110  of the annular body  102 . The dimensions of the profile, and in one example the concave surface, may decrease, for example, along the longitudinal axis  112  in a direction along the longitudinal axis  112  from the first end  106  of the annular body to the second end  108  of the annular body  102 . This configuration can result in higher operating efficiencies for a compressor that uses the impeller  100  because the blade body  116  exhibits a higher resonant frequency with the variably-dimensioned feature that forms the concave surface with the larger dimensions found at the leading edge  122 . The profile also configures the blade body  116  to meet other structural and aerodynamic requirements necessary for use in a compressor. In practice, these requirements often conflict with one another. Structural concerns, for example, need the blade body  116  to be of stout geometry to minimize vibration and tolerate high stresses. On the other hand, aerodynamic concerns favor geometry that reduces the “footprint” of the blade body  116  in the flow of the working fluid F to minimize drag and/or to optimize other fluid dynamics of the working fluid F that passes across the blade body  116  during operation of a compressor. 
       FIGS. 7, 8, and 9  serve to illustrate some of the benefits the geometry of the joint region  126  as relates to operation of the impeller  100 . Briefly,  FIG. 7  shows that the geometry of the joint region  126  increases the resonant frequency of the blade body  116  above the operating frequencies a compressor will generate at its preferred running speeds. This feature can prevent the blade body  116  from resonating at the operating frequencies to avoid mechanical failure and/or to prevent damage to the blade body  116 .  FIGS. 8 and 9  illustrate that the geometry in the joint region  126  can enhance flow dynamics of the impeller  100 . Notably, by comparing the diagrams of  FIGS. 8 and 9 , it can be seen that the geometry of the joint region  126  can reduce the size of the wake zone at the trailing edge  124  of the blade body  116 , which in turn reduces losses that can lower the operating efficiency of a compressor. This disclosure provides additional details of these diagrams in the EXPERIMENTAL SECTION further below. 
     Referring now to  FIG. 2 , the profile can form an fillet  128  (also, “arc  128 ”). The fillet  128  forms the concave surface at the root  118  of the blade body  116  and the outer surface  110  of the annular body  102 . The fillet  128  has a center  130  and a radius R. The center  130  is located relative to a reference plane  132  that is tangent to at least one point on the outer surface  110  of the impeller body  102 . The reference plane  132  is also parallel to a center plane  134  that bisects the annular body  102  through the longitudinal axis  112 . 
     Values for the radius R of the fillet  128  change (or vary) along the blade body  116  between the leading edge  122  ( FIG. 1 ) and the trailing edge  124  ( FIG. 1 ). As noted more below, the value of the radius R decreases along the longitudinal axis  112  in the direction from the first end  106  ( FIG. 1 ) to the second end  108  ( FIG. 1 ) of the annular body  102 . In one embodiment, the value of the radius R changes from a first value proximate the leading edge  122  ( FIG. 1 ) to a second value proximate the trailing edge  124  ( FIG. 1 ). Preferably, the first value is larger than the second value to configure the blade body  116  with the appropriate mechanical properties to withstand mechanical stimuli that are typically larger at the leading edge  122  than at the trailing edge  124 . 
     The radius R may decrease linearly, or in near linear manner, from the first value to the second value. However, this disclosure does contemplate step-wise changes that apply an increment to decrease the value of the radius R from the leading edge  122  ( FIG. 1 ) to the trailing edge  124  ( FIG. 1 ). This step-wise configuration can result in the joint region  126  having distinct sections (e.g., a first section, a second section, etc.) that correspond with the incremental decrease of the radius R when moving from the leading edge  122  to the trailing edge  124  of the blade body  116 . 
     In practical implementation, values for the radius R of the fillet  128  may satisfy an aspect ratio (also, “fillet ratio”) and a thickness ratio. The fillet ratio relates the values for the radius R in accordance with Equation (1) below: 
     
       
         
           
             
               
                 
                   
                     
                       R 
                       f 
                     
                     = 
                     
                       
                         V 
                         1 
                       
                       
                         V 
                         2 
                       
                     
                   
                   , 
                 
               
               
                 
                   Equation 
                    
                   
                       
                   
                    
                   
                     ( 
                     1 
                     ) 
                   
                 
               
             
           
         
       
     
     where R f  is the aspect ratio, V 1  is the first value of the radius R at the leading edge  122  ( FIG. 1 ), and V 2  is the second value of the radius R at the trailing edge  124  ( FIG. 1 ). In one example, the aspect ratio is in a range of approximately 1.5 to approximately 3. The thickness ratio relates the first value of the radius R with the thickness of the blade in accordance with the Equation (2) below: 
     
       
         
           
             
               
                 
                   
                     
                       R 
                       t 
                     
                     = 
                     
                       
                         V 
                         1 
                       
                       
                         T 
                         LE 
                       
                     
                   
                   , 
                 
               
               
                 
                   Equation 
                    
                   
                       
                   
                    
                   
                     ( 
                     2 
                     ) 
                   
                 
               
             
           
         
       
     
     where R t  is the thickness ratio, V 1  is the first value of the radius R at the leading edge  122  ( FIG. 1 ), and T LE  is the thickness of the blade body  116  ( FIG. 1 ) at the root  118  ( FIG. 1 ) proximate the leading edge  122  ( FIG. 1 ). In one example, the thickness ratio is at least approximately 1 or greater, and sometimes in a range of approximately 1 to approximately 2. In terms of actual values, the radius R depends on other design considerations (e.g., size, shape, etc.) for the blade and the impeller. 
     The thickness of the blade body  116  can also correspond with the values for the radius R. In general, the thickness of the blade body  116  decreases radially from the root  118  to the top  120 . This construction forms the blade body  116  in a manner that minimizes drag of the working fluid F ( FIG. 1 ) that traverses across the blade body  116  (from the leading edge  122  ( FIG. 1 ) to the trailing edge  124  ( FIG. 1 )). Notably, use of geometry (e.g., the fillet  128 ) with the variable radius R also reduces the thickness of the blade body  116  at the root  118  from the leading edge  122  to the trailing edge  124 . This construction may serve to align the geometry and mechanical properties of blade body  116  with the forces, stresses, vibrations, and like mechanical stimuli that occur at the leading edge  122  ( FIG. 1 ), the trailing edge  124  ( FIG. 1 ), and generally across the blade body  116  during operation of a compressor. 
       FIG. 3  illustrates the impeller  100  in a second annular position to show a planar view of the top  118  of the blade body  116 . The blade body  116  has a first side  136  and a second side  138  disposed annularly apart from the first side  136 . The blade body  116  also has a camber line  140  that defines a locus of points found midway between the surfaces of the sides  136 ,  138 . The camber line  140  follows the contour of the blade body  116 . In one example, variations in the radius R can be defined in relation to and/or along the camber line  140  of the blade body  116 . Each of the sides  136 ,  138  feature a surface that extends radially from the root  118  ( FIG. 2 ) to the top  120  ( FIG. 2 ) of the blade body  116 . The surface of the sides  136 ,  138  is also referred to as the “pressure surface” and the “suction surface” depending on the direction the impeller  100  rotates in a compressor. 
     As also shown in  FIG. 3 , the joint region  126  is formed on both the first side  136  and the second side  138  of the blade body  116 . The joint region  126  has an outer boundary  142  with a dimension B. Moving from the leading edge  122  to the trailing edge  124  on the blade body  116 , narrowing of the dimension B reflects a decrease (e.g., a linear decrease) in the value for the radius R of the fillet  128  ( FIG. 2 ). The profile in the joint region  126  may extend annularly around one of the leading edge  120  and the trailing edge  122 . In the present example, the outer boundary  142  extends from the trailing edge  124  on each side  136 ,  138  of the blade body  116  and about the leading edge  122 . This configuration is consistent the fillet  128  ( FIG. 2 ) formed substantially contiguously about the periphery of the blade body  116  and terminating at the outer peripheral edge  114  ( FIG. 1 ) of the annular body  102 . In one example, the camber line  140  bisects the joint region  126  so that the perpendicular distance from a point on the camber line  140  to a point on the outer boundary  142  is the same on both the first side  136  and the second side  138 . This distance may be equal to one-half the dimension B. 
       FIG. 3  also shows that the joint region  126  has a leading edge section  144  that extends annularly around the leading edge  122 . The structure in the leading edge section  142  rounds the leading edge  122 , at least at the root  118 , to address aerodynamic and fluid dynamic concerns. In one embodiment, the leading edge section  144  has a first boundary  146  on the first side  136  and a second boundary  148  on the second side  138 . The radius R ( FIG. 2 ) may have a value (e.g., the first value) that remains constant throughout the leading edge section  144  from the first boundary  146  to the second boundary  148 . 
       FIG. 4  depicts a perspective view of an exemplary embodiment of an impeller  200 . This embodiment has a central bore  250  that is configured to receive a shaft that is part of a mechanical drive assembly on the compressor. The embodiment also has a plurality of blades coupled with the outer surface  210  of the annular body  202 . The blades are disposed circumferentially around the longitudinal axis  212 . In one embodiment, the plurality of blades can include one or more main blades (e.g., a first main blade  252  and a second main blade  254 ) that are spaced annularly apart from one another to form a flow path  256 . Inside of the flow path  256 , the plurality of blades can also include one or more splitter blades (e.g., a splitter blade  258 ) that are annularly adjacent to both the first main blade  252  and the second main blade  254 . When in use in a compressor, the mechanical drive assembly rotates the impeller  200  about the longitudinal axis  212  to raise the energy of the working gas F that passes through the flow path  256  from the leading edge  222  to the trailing edge  224 . Use of the splitter blade  258  in the flow path  256 , and adjacent to the main blades  252 ,  254 , is known to improve overall performance including pressure ratio and efficiency of the impeller  200 . 
     The blades  252 ,  254 ,  258  can have an axial length, typically measured as the straight line distance between the leading edge  222  and the trailing edge  224  of the blade body  216 . This distance is often referred to as the “chord length” or the “meridional length” of the blades  252 ,  254 ,  258 . As noted above, in splitter-type impellers, the axial length of the first main blade  252  (the “first axial length”) and the second main blade  254  (“the second axial length”) are the same. In some embodiments, the axial length of the third blade  258  (“the third axial length”) is often axially shorter than the first axial length and the second axial length. 
     As also shown in  FIG. 4 , the impeller  200  incorporates multiple fillets  128  ( FIG. 2 ) including a first fillet  260  and a second fillet  262 , one each disposed at the root of the main blades  252 ,  254 , respectively. The fillets  260 ,  262  form a first concave surface and a second concave surface between root of the main blades  250 ,  252  and the outer surface  210  of the annular body  202 . The impeller  200  also includes a third fillet  264  disposed at the root of the splitter blade  258  that forms a third concave surface between the root of the splitter blade  258  and the outer surface  210  of the annular body  202 . The first fillet  260  can incorporate the geometry of the fillet  126  ( FIG. 2 ). As discussed above, this geometry enhances the mechanical properties of the main blades  252 ,  254  that populate the impeller  200 . In one embodiment, the first fillet  260  has a radius R with a value that decreases along the longitudinal axis  212  in a direction from the first end  206  to the second end  208  of the annular body  202 . The second fillet  262  can also incorporate a radius R with a value that is the same as the value of the radius of the first fillet  260 . In one embodiment, the third fillet  264  may also incorporate the geometry of the fillet  128  ( FIG. 2 ). However, the value of the radius of the third fillet  264  may vary or remain constant along the longitudinal axis  212  in the direction from the first end  206  to the second end  206  of the annular body  202 . This disclosure contemplates, for example, that the dimensions of the splitter blade  258  may not require the benefits the fillet  128  ( FIG. 2 ) affords because the dimensions (e.g., the third axial length) of the splitter blade  258  tend to afford the splitter blade  258  with suitable mechanical properties, namely, a higher resonant frequency than the main blades  252 ,  254 . 
       FIG. 5  depicts a schematic diagram of a cross-section of the impeller  200  taken at line  5 - 5  of  FIG. 4 . As shown, the blade body  216  varies in height as indicated by a first height dimension H 1  and a second height dimension H 2 . The dimensions H 1 , H 2  are measured from the outer surface  210  of the annular body  202  at the leading edge  222  and the trailing edge  224 , respectively. 
       FIG. 6  depicts a perspective view of the impeller  200  as part of an example of a compressor  266 . This example embodies a centrifugal compressor (shown without inlet guide blades at the inlet); however, the impeller  200  may find use in other types and/or configurations of the compressor  266 . Use of the compressor  266  is often associated with industrial processes as found in, for example, the automotive, electronics, aerospace, oil and gas, power generation, petrochemical, and like sectors and industries. 
     The compressor  266  has an inlet  268  with an inner wall  270  that defines a flow area  272 . The inner wall  270  can form part of a component commonly referred to as an “inlet guide blade housing cover” or “inlet housing” that has a first end and a second end. In the present example, the first end of the inlet housing forms an opening to receive working fluid during operation of the compressor  266 . At the second end, the inlet housing couples with a volute  274  that has an outlet  276  (also, “discharge  276 ”). Examples of the discharge  276  are configured to couple the compressor  266  with industrial piping, conduits, and like flow-related structures. As also shown in  FIG. 6 , the mechanical drive assembly of the compressor  266  includes a drive unit  278  that couples with the impeller  200 , typically through a gearbox and/or one or more like mechanical components. In use, the impeller  200  is disposed in the inlet housing. The drive unit  278  rotates the impeller  200  to draw working fluid (e.g., air) into the inlet  268 . The impeller  200  compresses the working fluid, which in turn flows through the volute  274  to form an exit flow that discharges from the compressor  266  at the discharge  276 . The exit flow can exhibit one or more flow properties (e.g., flow rate, pressure, etc.) that meet certain desired setpoints on a process line. 
     EXPERIMENTAL EXAMPLES 
     Use of the variably-dimensioned fillet  128  ( FIG. 2 ) is different from conventional practices that implement uniform dimension(s) for features, including rounded and/or arcuate corners, between the root  118  ( FIG. 1 ) of the blade  104  ( FIG. 1 ) and the impeller body  106  ( FIG. 1 ). As noted above, it has been found that variable dimensions for the fillet  128  ( FIG. 2 ) in accordance with the concepts herein can modify performance of an impeller to avoid potential problems that might develop during prolonged operation in a compressor. 
       FIG. 7  illustrates a Campbell diagram  300  that compares a first resonant frequency  302  for the main blades and/or splitter blades of an impeller with plots of engine order lines of varying multiples. The diagram  300  also includes a minimum operating speed  304  and a maximum operating speed  306 , which are consistent with the nominal operating range  308  for, e.g., a centrifugal compressor. Values for the plots are calculated in accordance with Equation (3) below, 
     
       
         
           
             
               
                 
                   
                     
                       f 
                       i 
                     
                     = 
                     
                       
                         n 
                         * 
                         Ω 
                       
                       60 
                     
                   
                   , 
                 
               
               
                 
                   Equation 
                    
                   
                       
                   
                    
                   
                     ( 
                     3 
                     ) 
                   
                 
               
             
           
         
       
     
     wherein f i  is the frequency, Ω is the operating speed (or “rotation speed”) of the compressor, and n is the Engine Order. The first resonant frequency  302  corresponds with blades (e.g., blades  252 ,  254  of  FIG. 4 ) on an impeller that uses the variably-dimensioned fillet (e.g., fillet  128  of  FIG. 2 ). In one example, the first resonant frequency  302  has a value of 1.898 KHz. As shown in the diagram, use of the variably-dimensioned fillet provides a structurally stable design for the blades because the new geometry of the fillet pushes the resonant frequency beyond and/or far removed from the maximum operating speed  306  for the compressor. 
       FIGS. 8 and 9  illustrate diagrams of computated flow at the trailing edge of blades on a conventional impeller  400  ( FIG. 8 ) and an exemplary embodiment of an impeller  500  ( FIG. 9 ) that uses the variably-dimensioned fillet (e.g., fillet  126  of  FIG. 2 ) of the present disclosure. The computated flow includes flow lines (identified as arrows on the diagram) that illustrate progression of a working fluid through the flow paths between main blades of the respective impeller. As shown, the computated flow forms a first wake zone  402  ( FIG. 8 ) on the conventional impeller  400  and a second wake zone  502  ( FIG. 9 ) on the embodiment  500  as the flow moves radially outwardly from the impellers  400 ,  500 . In general, a wake zone is defined as a volumetric void in the flow of the working fluid and is classified as an efficiency loss for overall operation of a compressor. The wake zones  402 ,  502  correspond to areas of separation of the working fluid from both sides of the blade. Notably, the second wake zone  502  is relatively smaller than the first wake zone  402 , which indicates smaller losses in flow on the embodiment  500  with the variably-dimensioned fillet. These smaller losses typically result in higher compressor efficiency. 
     In view of the foregoing, the embodiments of this disclosure may comprise one or more clauses alone or in any suitable combination. Examples of such clauses follow below: 
     A1. An impeller, comprising an annular body with a longitudinal axis, the annular body having a first end with a first diameter and a second end with a second diameter that is larger than the first diameter; a blade disposed on the annular body and extending axially along the longitudinal axis, the blade having a root proximate the annular body and a top disposed radially outwardly of the root, wherein the blade and the annular body form a joint region that extends along the root of the blade, the joint region having a profile that varies in a direction along the longitudinal axis from the first end of the annular body to the second end of the annular body. 
     A2. The impeller of claim A1, wherein the profile is configured in accordance with an aspect ratio between a first dimension of the profile proximate the first end of the annular body and a second dimension of the profile proximate the second end of the annular body, and wherein the aspect ratio is configured so that the profile increases from the first end to the second end. 
     A3. The impeller of claim A1, wherein the profile forms an arc with a radius, and wherein the radius has a first value proximate the first end and a second value proximate the second end, and wherein the first value is larger than the second value. 
     A4. The impeller of claim A1, wherein the blade has a first side and a second side disposed annularly apart from the first side, and wherein the joint region is formed on both the first side and the second side of the blade. 
     A5. The impeller of claim  1 , wherein the blade has a first edge and a second edge, one each disposed proximate the first end of the annular body and the second end of the annular body, and wherein the profile extends annularly around one of the first edge and the second edge of the blade. 
     A6. The impeller of claim  5 , wherein the annular body has an outer peripheral edge at the second end, and wherein the second edge of the blade terminates at the outer peripheral edge. 
     A7. An impeller, comprising an annular body having a frusto-conical shape with a longitudinal axis; a first blade disposed on the annular body, the first blade having a first blade body with a root proximate the annular body, the first blade body extending axially along the longitudinal axis; and a first fillet disposed at the root of first blade body and the annular body, the first fillet having a radius with a value that varies along the longitudinal axis. 
     A8. The impeller of claim A7, wherein the frusto-conical shape finals a first end of the annular body with a first diameter and a second end of the annular body with a second diameter that is larger than the first diameter, wherein the value of the radius of the first fillet has a first value at the first end and a second value at the second end, and wherein the first value is larger than the first value. 
     A9. The impeller of claim A8, wherein the first fillet is configured in accordance with an aspect ratio between the first value and the second value, and wherein the aspect ratio is configured so that the value of the radius decreases from the first value to the second value. 
     A10. The impeller of claim A8, wherein the first fillet is configured in accordance with a thickness ratio between the first value of the radius and a thickness of the blade as measured at the root, and wherein the thickness ratio is configured so that the radius decreases from the first value to the second value. 
     A11. The impeller of claim A7, further comprising a second blade disposed on the annular body and annularly adjacent the first blade, the second blade having a second blade body with a root proximate the annular body, the second blade body extending axially along the longitudinal axis; and a second fillet disposed at the root of the second blade body and the annular body, the second fillet extending axially along the second blade. 
     A12. The impeller of claim A11, wherein the second fillet has a radius that is the same the radius of the first fillet. 
     A13. The impeller of claim A1, wherein the radius of the second fillet remains constant along the longitudinal axis in the direction from the first end to the second end of the annular body. 
     A14. The impeller of claim A13, wherein the first blade has a first axial length and the second blade has a second axial length, each of the first axial length and the second axial measured in a direction along the longitudinal axis, and wherein the second axial length is the same as the first axial length. 
     A15. The impeller of claim A11, further comprising a third blade disposed on the annular body and annularly adjacent to both the first blade and the second blade, the third blade extending axially along the longitudinal axis, wherein the third blade is axially shorter than the first blade and the second blade. 
     A16. A compressor to provide a working fluid to a process line, comprising an impeller comprising an annular body having a plurality of blades formed integrally therewith, wherein the plurality of blades comprises a first blade that forms a first concave surface with the annular body that extends along at least part of the first blade, and wherein the first concave surface has a radius that decreases along the first blade in a direction from the first end to the second end of the annular body. 
     A17. The compressor of claim A16, wherein the plurality of blades comprises a second blade that is annularly offset from the first blade, wherein the second blade forms a second concave surface with the annular body that extends along at least part of the second blade, and wherein the radius of the second concave surface is the same as the radius of the first concave surface. 
     A18. The compressor of claim A17, wherein the first concave surface and the second concave surface extend around the periphery of the first blade and the second blade, respectively. 
     A19. The compressor of claim A17, wherein the plurality of blades comprises a third blade disposed annularly between the first blade and the second blade, wherein the third blade forms a third concave surface with the annular body, and wherein the radius of the third concave surface is different from the first concave surface and the second concave surface. 
     A20. The compressor of claim A19, wherein the radius of the third concave surface remains constant along the third blade in the direction from the first end to the second end of the inlet housing. 
     As used herein, an element or function recited in the singular and proceeded with the word “a” or “an” should be understood as not excluding plural said elements or functions, unless such exclusion is explicitly recited. Furthermore, references to “one embodiment” of the claimed invention should not be interpreted as excluding the existence of additional embodiments that also incorporate the recited features. 
     This written description uses examples to disclose the invention, including the best mode, and also to enable any person skilled in the art to practice the invention, including making and using any devices or systems and performing any incorporated methods. The patentable scope of the invention is defined by the claims, and may include other examples that occur to those skilled in the art. Such other examples are intended to be within the scope of the claims if they have structural elements that do not differ from the literal language of the claims, or if they include equivalent structural elements with insubstantial differences from the literal language of the claims.