Patent Publication Number: US-11391296-B1

Title: Diffuser pipe with curved cross-sectional shapes

Description:
TECHNICAL FIELD 
     The application relates generally to centrifugal compressors, and more particularly to diffuser pipes for such centrifugal compressors. 
     BACKGROUND 
     Diffuser pipes are provided in certain engines for diffusing a flow of high speed air received from an impeller of a centrifugal compressor and directing the flow to a downstream component, such as an annular chamber containing the combustor. The diffuser pipes are typically circumferentially arranged at a periphery of the impeller, and are designed to transform kinetic energy of the flow into pressure energy. Diffuser pipes seek to provide a uniform exit flow with minimal distortion, as it is preferable for flame stability, low combustor loss, reduced hot spots etc. 
     SUMMARY 
     There is disclosed a compressor diffuser for an aircraft engine, the compressor diffuser comprising: a plurality of diffuser pipes disposed circumferentially about a center axis of the compressor diffuser, the center axis extending in an axial direction, each diffuser pipe of the plurality of diffuser pipes: extending from an inlet of that diffuser pipe to an outlet of that diffuser pipe and increasing in cross-sectional area from the inlet toward the outlet, the outlet opening in the axial direction, at least the outlet defined by a radially inner wall, a radially outer wall, and side walls joining the radially inner wall to the radially outer wall, and both the radially inner wall and the radially outer wall being curved, a radius of curvature of the radially outer wall being different from a radius of curvature of the radially inner wall. 
     There is disclosed a diffuser pipe, comprising: a tubular body extending from an inlet to an outlet and increasing in cross-sectional area from the inlet toward the outlet, the outlet having a radially inner wall, a radially outer wall, and side walls joining the radially inner wall to the radially outer wall, the outlet having an elliptigon shape in which both the radially inner wall and the radially outer wall are curved, a radius of curvature of the radially outer wall being different from a radius of curvature of the radially inner wall. 
    
    
     
       DESCRIPTION OF THE DRAWINGS 
       Reference is now made to the accompanying figures in which: 
         FIG. 1  is a schematic cross-sectional view of an engine; 
         FIG. 2  is a perspective view of an impeller and diffuser pipes of a centrifugal compressor of the engine of  FIG. 1 ; 
         FIG. 3A  is a perspective view of a possible configuration for one of the diffuser pipes of  FIG. 2 ; 
         FIG. 3B  is a view of a cross-sectional profile of the diffuser pipe of  FIG. 3A , taken along the line IIIB-IIIB; 
         FIG. 3C  is a view of another cross-sectional profile of another diffuser pipe; 
         FIG. 4A  is a perspective view of another possible configuration for one of the diffuser pipes of  FIG. 2 ; 
         FIG. 4B  is a view of a cross-sectional profile of the diffuser pipe of  FIG. 4A , taken along the line IVB-IVB; 
         FIG. 5A  shows Mach number contours at different cross-sections of a diffuser pipe having a first cross-sectional shape; 
         FIG. 5B  shows Mach number contours at different cross-sections of a diffuser pipe having a second cross-sectional shape; and 
         FIG. 5C  shows Mach number contours at different cross-sections of a diffuser pipe having a third cross-sectional shape. 
     
    
    
     DETAILED DESCRIPTION 
       FIG. 1  illustrates a gas turbine engine  10  of a type preferably provided for use in subsonic flight, generally comprising in serial flow communication along an engine center axis  11  a fan  12  through which ambient air is propelled, a compressor section  14  for pressurizing the air, a combustor  16  in which the compressed air is mixed with fuel and ignited for generating an annular stream of hot combustion gases, and a turbine section  18  for extracting energy from the combustion gases. The compressor section  14  may include a plurality of stators  13  and rotors  15  (only one stator  13  and rotor  15  being shown in  FIG. 1 ), and it may include a centrifugal compressor  19 . 
     The centrifugal compressor  19  of the compressor section  14  includes an impeller  17  and a plurality of diffuser pipes  20 , which are located downstream of the impeller  17  and circumferentially disposed about a periphery of a radial outlet  17 A of the impeller  17 . The diffuser pipes  20  convert high kinetic energy at the impeller  17  exit to static pressure by slowing down fluid flow exiting the impeller. The diffuser pipes  20  may also redirect the air flow from a radial orientation to an axial orientation (i.e. aligned with the engine axis  11 ). In most cases, the Mach number of the flow entering the diffuser pipe  20  may be at or near sonic, while the Mach number exiting the diffuser pipe  20  may be less than 0.25 to enable stable air/fuel mixing, and light/re-light in the combustor  16 . 
       FIG. 2  shows the impeller  17  and the plurality of diffuser pipes  20 , also referred to as “fishtail diffuser pipes”, of the centrifugal compressor  19 . Each of the diffuser pipes  20  includes a diverging (in a downstream direction) tubular body  22 , formed, in one embodiment, of sheet metal. The enclosed tubular body  22  defines a flow passage  29  (see  FIG. 3A ) extending through the diffuser pipe  20  through which the compressed fluid flow is conveyed. The tubular body  22  includes a first portion  24  extending generally tangentially from the periphery and radial outlet  17 A of the impeller  17 . An open end is provided at an upstream end of the tubular body  22  and forms an inlet  23  (see  FIG. 3A ) of the diffuser pipe  20 . The first portion  24  may be inclined at an angle  81  relative to a radial axis R extending from the engine axis  11 . The angle  81  may be at least partially tangential, or even substantially tangentially, and may further correspond to a direction of fluid flow at the exit of the blades of the impeller  17 , such as to facilitate transition of the flow from the impeller  17  to the diffuser pipes  20 . The first portion  24  of the tubular body  22  can alternatively extend more substantially along the radial axis R. 
     The tubular body  22  of the diffuser pipes  20  also includes a second portion  26 , which is disposed generally axially and is connected to the first portion  24  by an out-of-plane curved or bend portion  28 . An open end at the downstream end of the second portion  26  forms a pipe outlet  25  (see  FIG. 3A ) of the diffuser pipe  20 . Preferably, but not necessarily, the first portion  24  and the second portion  26  of the diffuser pipes  20  are integrally formed together and extend substantially uninterrupted between each other, via the curved, bend portion  28 . 
     The large radial velocity component of the flow exiting the impeller  17 , and therefore entering the first portion  24  of each of the diffuser pipes  20 , may be removed by shaping the diffuser pipe  20  with the bend portion  28 , such that the flow is redirected axially through the second portion  26  before exiting via the pipe outlet  25  to the combustor  16 . It will thus be appreciated that the flow exiting the impeller  17  enters the inlet  23  and the upstream first portion  24  and flows along a generally radial first direction. At the outlet of the first portion  24 , the flow enters the bend portion  28  which functions to turn the flow from a substantially radial direction to a substantially axial direction. The bend portion  28  may form a 90 degree bend. At the outlet of the bend portion  28 , the flow enters the downstream second portion  26  and flows along a substantially axial second direction different from the generally radial first direction. By “generally radial”, it is understood that the flow may have axial, radial, and/or circumferential velocity components, but that the axial and circumferential velocity components are much smaller in magnitude than the radial velocity component. Similarly, by “generally axial”, it is understood that the flow may have axial, radial, and/or circumferential velocity components, but that the radial and circumferential velocity components are much smaller in magnitude than the axial velocity component. 
     Referring to  FIG. 3A , the tubular body  22  of each diffuser pipe  20  has a radially inner wall  22 A and a radially outer wall  22 B. The radially outer wall  22 B is spaced further from the center axis  11  than the radially inner wall  22 A. The tubular body  22  also has a first side wall  22 C spaced circumferentially apart across the flow passage  29  from a second side wall  22 D. The first and second side walls  22 C, 22 D are curved. The first and second side walls  22 C, 22 D have a non-zero curvature value. The first and second side walls  22 C, 22 D are concave when viewed from the center axis  11  or from within the tubular body  22 , and are convex when viewed from outside the diffuser pipe  20 . The radially inner and outer walls  22 A, 22 B and the first and second side walls  22 C, 22 D meet and are connected to form the enclosed flow passage  29  extending through the tubular body  22 . The radially inner and outer walls  22 A, 22 B and the first and second side walls  22 C, 22 D meet and are connected to form a peripheral edge of the tubular body  22  which circumscribes the pipe outlet  25 . The radially inner wall  22 A may correspond to the wall of the tubular body  22  that has the smallest turning radius at the bend portion  28 , and the radially outer wall  22 B may correspond to the wall of the tubular body  22  that has the largest turning radius at the bend portion  28 . 
     The tubular body  22  diverges in the direction of fluid flow F therethrough, in that the internal flow passage  29  defined within the tubular body  22  increases in cross-sectional area between the inlet  23  and the pipe outlet  25  of the tubular body  22 . This increase in cross-sectional area of the flow passage  29  through each diffuser pipe  20  may be continuous along the complete length of the tubular body  22 , or the cross-sectional area of the flow passage  29  may increase in gradual increments along the length of the tubular body  22 . In the depicted embodiment, the cross-sectional area of the flow passage  29  defined within the tubular body  22  increases gradually and continuously along its length, from the inlet  23  to the outlet  25 . The direction of fluid flow F is along a pipe center axis  21  of the tubular body  22 . The pipe center axis  21  extends through each of the first, second, and bend portions  24 , 26 , 28  and has the same orientation as these portions. The pipe center axis  21  is thus curved. In the depicted embodiment, the pipe center axis  21  is equidistantly spaced from the radially inner and outer walls  22 A, 22 B of the tubular body  22 , and from the first and second side walls  22 C, 22 D, through the tubular body  22 . 
     Referring to  FIG. 3A , the tubular body  22  has a length L defined from the inlet  23  to the pipe outlet  25 . The length L of the tubular body  22  may be measured as desired. For example, in  FIG. 3A , the length L is the length of the pipe center axis  21  from the inlet  23  to the pipe outlet  25 . In an alternate embodiment, the length L is measured along one of the walls  22 A, 22 B, 22 C, 22 D of the tubular body  22 , from the inlet  23  to the pipe outlet  25 . Reference may be made herein to positions on the tubular body  22  along its length L. For example, a position on the tubular body  22  that is along a last 10% of the length L is anywhere in the segment of the tubular body  22  that is upstream of the pipe outlet  25  a distance equal to 10% of the length L. This same segment is also downstream of the inlet  23  a distance equal to 90% of the length L. Similarly, a position on the tubular body  22  that is along a first 90% of the length L is anywhere in the segment of the tubular body  22  that is downstream of the inlet  23  a distance equal to 90% of the length L. This same segment is also upstream of the pipe outlet  25  a distance equal to 10% of the length L. 
     The tubular body  22  is composed of many cross-sectional profiles  27  which are arranged or stacked one against another along the length L of the tubular body  22 . Each cross-sectional profile  27  is a planar contour that lies in its own plane that is transverse or normal to the pipe center axis  21 .  FIG. 3A  shows multiple cross-sectional profiles  27  in every portion  24 , 26 , 28  of the tubular body  22 , and it will be appreciated that many more cross-sectional profiles  27  may be defined at other locations along the pipe center axis  21 . In the depicted embodiment, the orientation of the cross-sectional profiles  27  in the frame of reference of the diffuser pipe  20  may vary over the length L of the tubular body  22 , depending on where the cross-sectional profiles  27  are located along the pipe center axis  21 . Each cross-sectional profile  27  defines the shape, contour, or outline of the tubular body  22  at a specific location along the pipe center axis  21 . Each cross-sectional profile  27  shows the shape, contour, or outline of the tubular body  22 , as defined by its interconnected walls  22 A, 22 B, 22 C, 22 D, at a specific location along the pipe center axis  21 . 
     Referring to  FIG. 3A , and as described in greater detail below, the cross-sectional profiles  27  may vary over the length L of the tubular body  22 . The cross-sectional profiles  27  are different over the length L of the tubular body  22 . Each cross-sectional profile  27  may be unique, and thus different from the other cross-sectional profiles  27 . An area of the cross-sectional profiles  27  varies along the length L of the tubular body  22 . The area of a given cross-sectional profile  27  is defined between the inner, outer, first side, and second side walls  22 A, 22 B, 22 C, 22 D in the cross-sectional profile  27 . The area of the cross-sectional profiles  27  increases over the length L of the tubular body  22  in the direction of the pipe outlet  25 . This is consistent with the diverging flow passage  29  defined by the tubular body  22 . 
       FIG. 3B  shows one such cross-sectional profile  27  taken along the line IIIB-IIIB in  FIG. 3A , which is at the pipe outlet  25 . Referring to  FIG. 3B , both the radially outer wall  22 B and the radially inner wall  22 A are curved at the pipe outlet  25 . The radially inner and outer walls  22 A, 22 B have a curvature greater than zero. The radially inner and outer walls  22 A, 22 B have a radius of curvature that is less than infinity. The radially outer wall  22 B curves in a direction toward the center axis  11 , such that it is concave when viewed from the center axis  11  and convex when viewed from outside the diffuser pipe  20 . The pipe outlet  25  in  FIG. 3B  is thus free of planar portions. The radially inner and outer walls  22 A, 22 B and the side walls  22 D are curved along all or substantially all of their lengths. The radially inner and outer walls  22 A, 22 B and the side walls  22 D have curvatures greater than zero along all or substantially all of their lengths. The radially inner and outer walls  22 A, 22 B and the side walls  22 D are free of straight lines along all or substantially all of their lengths. 
     Referring to  FIG. 3B , the pipe outlet  25  is symmetric about a line H defining a height of the tubular body  22 . The pipe outlet  25  thus has the same shape or contour on each side of the line H. When one half of the pipe outlet  25  is folded about the line H, it will have the same shape as the other half of the pipe outlet  25 . Referring to  FIG. 3B , the line H extends between the radially inner and outer walls  22 A, 22 B. The line H extends generally radially to the center axis  11 , where “generally radially” is understood to mean that the line H may have axial, radial, and/or circumferential directional components, but that the axial and circumferential directional components are much smaller in magnitude than the radial directional component. Referring to  FIG. 3B , the line H defines the maximum height of the tubular body  22  between an apex point AP on the radially outer wall  22 B and the furthest point from the apex point AP on the radially inner wall  22 A, defined along a generally radial direction. Referring to  FIG. 3B , the line H is defined between radially spaced-apart maxima and minima on the radially outer wall  22 B and the radially inner wall  22 A, respectively. Referring to  FIG. 3B , the line H is a generally radial line relative to the center axis  11  that extends from an inflection point on the curved, radially outer wall  22 B to a point on the radially inner wall  22 A. Referring to  FIG. 3B , the line H extends through the pipe center axis  21 . 
     The diffuser pipe  20  disclosed herein therefore has, for one or more locations along its length L, a cross-sectional profile  27  that is curved along both of its radially inner and outer walls  22 A, 22 B, and which is symmetrical about a generally radial line through the cross-sectional profile  27 . This shape for the cross-sectional profile  27  may be referred to as an elliptical polygon (or “elliptogon”). As described in greater detail below, other similar shapes for the cross-sectional profiles  27  of the diffuser pipe  20  are also possible, such that the present disclosure presents different diffuser pipe  20  cross sectional shapes that may improve the stiffness of the diffuser pipe  20  stiffness by increasing its moment of inertia while maintaining its performance. 
     The shapes for the cross-sectional profile  27  may help to increase the dynamic stiffness of the diffuser pipe  20  while retaining its aerodynamic performance. The diffuser pipe  20  is joined to the casing of the impeller  17  such that the tubular body  22  is cantilevered from the point of attachment and is subjected to bending or flexion. The tubular body  22  at the inlet  23  may have a flange or other mounting member that may be fastened to the casing of the impeller  17  to fixedly attach the diffuser pipe  20  to the casing. The unattached remainder of the diffuser pipe  20 , and the pipe outlet  25 , “overhangs” and is free of other structural support, such that they are cantilevered from the casing. This may cause a movement of the pipe outlet  25  toward and away from the center axis  11 , a movement sometimes referred to as “flapping”, during operation of the engine  10 . Additionally, the shapes of the cross-sectional profile  27  as described herein (including the elliptogon, kidney and peanut shapes) may provide an increase in the area moment of inertia of the diffuser pipes  20  relative to typical, elliptically shaped, pipe such as that of the reference cross-sectional profile  27 R. The area moment of inertia of the cross-sectional profile  27  is a property which can be used to predict deflection and/or bending stress of the pipe having such a cross-sectional profile. Because the proposed shapes of the cross-sectional profile  27  have a greater area moment of inertia relative to a corresponding elliptical profile  27 R, the diffuser pipe  20  having such a cross-sectional profile  27  may be stiffer and thereby increasing its natural frequency. 
     By providing the cross-sectional profile  27  with the shapes, it may be more difficult for the pipe outlet  25  to displace radially during operation of the engine  10  such that the diffuser pipe  20  is stiffened. By providing the cross-sectional profile  27  with the shapes, it may be possible to increase an area moment of inertia (i.e. a property of a shape used to predict deflection and bending stress). Since the cross-sectional profile  27  with the shapes may increase the moment of inertia, the diffuser pipe  20  may be stiffer, thereby increasing a natural frequency of the diffuser pipe  20 . By providing the cross-sectional profile  27  with the shapes, it may thus be possible to change the natural frequency of the diffuser pipe  20 , such that the natural frequency is outside the range of certain vibratory frequencies which can exist within the engine operating envelope and can cause cracking and fatigue of the diffuser pipe  20 . By providing the cross-sectional profile  27  with the shapes, it may be possible to tune or select the natural frequency of the diffuser pipe  20  such that the natural frequency does not coincide with engine dynamics excitation frequencies over the entire engine operating range. Providing the cross-sectional profile  27  with the shapes may allow the length L of the diffuser pipe  20  to be increased without negatively impacting its vibrational response or its aerodynamic response, and thus make such a longer diffuser pipe  20  suitable for use in an engine  10  with increased power or size. Furthermore, providing the diffuser pipe  20  with the shapes of the cross-sectional profile  27  may not require expensive manufacturing techniques or retooling. By making the cross-sectional profile  27  “taller” by curving radially outwardly the radially outer wall  22 B, it may be possible to stiffen the diffuser pipe  20  against flexion or bending motions. 
     There are many possible shapes for the cross-sectional profiles  27  within the scope of the present disclosure. For example, and referring to  FIG. 3B , the shape of the cross-sectional profile  27  at the pipe outlet  25  is an elliptical polygon (sometimes referred to as an elliptogon). The shape of the cross-sectional profile  27  at the pipe outlet  25  is not oblong, where an oblong shape is an elongated rectangle or oval with parallel sides. The shape of the pipe outlet  25  is not oval. The shape of the pipe outlet  25  is different from a shape defined by two semi-circles with the same radius spaced apart and interconnected by parallel lines. The shape of the pipe outlet  25  has all curved lines represented by the radially inner and/or outer walls  22 A, 22 B and side walls  22 D. The shape of the pipe outlet  25  is free of parallel lines. Some conventional pipes, in contrast, have oblong, elliptical and symmetrical cross-sectional shapes along the downstream region of the diffuser pipe. Some non-limiting examples of specific shapes for the cross-sectional profiles  27  are now described in greater detail. 
     Referring to  FIG. 3B , the shape for the pipe outlet  25  may be referred to as an elliptical polygon (or “elliptogon”). A radius of curvature ROW of the curved radially outer wall  22 B is different from a radius of curvature RIW of the curved radially inner wall  22 A. The radii of curvature ROW,RIW have different values, such that the curvatures of the radially inner and outer walls  22 A, 22 B are different. In the shape of the pipe outlet  25  shown in  FIG. 3B , the curvature of the radially inner wall  22 A is much smaller than the curvature of the radially outer wall  22 B. The radius of curvature RIW for the radially inner wall  22 A is therefore much larger than the radius of curvature ROW of the radially outer wall  22 B. For example, the radially inner wall  22 A may have a curvature value of very small magnitude, particularly in comparison to the curvature value of the radially outer wall  22 B. For example, and referring to  FIG. 3B , a middle portion of the radially inner wall  22 A around the line H is slightly curved, but the magnitude of its curvature is small and orders of magnitude less than the curvature of the radially outer wall  22 B. In an embodiment, the radius of curvature RIW of the radially inner wall  22 A tends toward infinity, and the radially inner wall  22 A is represented in the cross-sectional profile  27  as an almost straight line being transverse to the line H. Referring to  FIG. 3B , the line H is perpendicular to the almost straight radially inner wall  22 A. 
     The apex point AP is a point on the line H. The apex point AP is the location on the radially outer wall  22 B that is furthest from the center axis  11 . The apex point AP is the location on the radially outer wall  22 B at which there is an inflection point in the curve of the radially outer wall  22 B. The apex point AP is the location on the radially outer wall  22 B at which the tangent to the curve of the radially outer wall  22 B changes between a negative value for the slope of the tangent line and a positive value for the slope. From the apex point AP, the radially outer wall  22 B curves in a direction toward the radially inner wall  22 A (i.e. a radially inward direction) toward a radially outer end of each of the first and second side walls  22 C, 22 D. The radially outer wall  22 B has two curved segments on either side of the line H. From the apex point AP, each of the curved segments curves in a direction away from the apex point AP and toward the radially inner wall  22 A, and joins to a radially outer end of one of the first and second side walls  22 C, 22 D. 
     Referring to  FIG. 3B , the pipe outlet  25  includes a width line WL extending between points of the first and second side walls  22 C, 22 D that are disposed furthest from one another. The length of the width line WL corresponds to the largest width of the pipe outlet  25 , where the width is defined between the first and second side walls  22 C, 22 D. The width line WL may or may not extend through the pipe center axis  21 . The width line WL intersects the line H defining the height of the tubular body  22  and divides the line H into a first height portion HP 1  extending between the apex point AP on the radially outer wall  22 B and the width line WL, and a second height portion HP 2  extending between the radially inner wall  22 A and the width line WL. The length of the first and second height portions HP 1 ,HP 2  are parameters which can be selected by a designer of the diffuser pipe  20  to obtain the desired shape for the pipe outlet  25 . For the pipe outlet  25  disclosed herein, a ratio of the first height portion HP 1  over the second height portion HP 2  (i.e. HP 1 /HP 2 ) may be between about 1.1 and 4. The first height portion HP 1  is thus always greater than the second height portion HP 2 , by a factor ranging in value from 1.1 to 4. This range of ratios helps to ensure that the radially outer wall  22 B is curved, such that the shape of the pipe outlet  25  may be the desired elliptical polygon through the range of ratio values. 
     Referring to  FIG. 3B , the line H defining the height intersects the width line WL and divides the width line into a first width portion WP 1  extending between one of the first and second side walls  22 C, 22 D and the line H, and a second width portion WP 2  extending between the other of the first and second side walls  22 C, 22 D and the line H. The length of the first and second width portions WP 1 ,WP 2  are parameters which can be selected by a designer of the diffuser pipe  20  to obtain the desired shape for the pipe outlet  25 . For the pipe outlet  25  disclosed herein, a ratio of the first width portion WP 1  over the second width portion WP 2  (i.e. WP 1 /WP 2 ) may be approximately 1. The first width portion WP 1  is thus equal to the second width portion WP 2 . This helps to ensure that the pipe outlet  25  is symmetrical about the line H defining the height of the tubular body  22 , such that the shape of the pipe outlet  25  may be the desired elliptical polygon. Referring to  FIG. 3B , the ratio of the first width portion WP 1  over the second width portion WP 2  remains approximately 1 at all points along the line H, such that the first side wall  22 C and the second side wall  22 D are both symmetrical about the line H at all radial points thereon. The pipe outlet  25  in  FIG. 3B  is a symmetric elliptogon shape. In an alternative possible shape for the pipe outlet  25  that is asymmetrical about the line H, the ratio of the first width portion WP 1  over the second width portion WP 2  may be between 0.2 and 5, such that the asymmetry of the pipe outlet  25  may be on either side of the line H. Referring to  FIG. 3B , the pipe outlet  25  is asymmetric about the width line WL. The shape or contour of the pipe outlet  25  is different on each radially-opposite side of the width line WL. The radially outer wall  22 B and the radially inner wall  22 A are not symmetrical about the width line WL. 
     Although the cross-sectional profile  27  at the pipe outlet  25  has a shape different from the oblong or pure ellipse cross-sectional shape of a conventional pipe, the cross-sectional profile  27  may have the same area and/or same parameters as a conventional oblong or pure ellipse cross-sectional shape. Referring to  FIG. 3B , a reference cross-sectional profile  27 R is defined in the plane normal to the pipe center axis  21  at the same location along the pipe center axis  21  as the pipe outlet  25 . The reference cross-sectional profile  27 R is shaped as an ellipse and defines a reference width WR along a major axis and a reference height HR along a minor axis. The shape of the pipe outlet  25  is different than the ellipse shape of the reference cross-sectional profile  27 R. Despite the differences in shape, the reference width WR of the reference cross-sectional profile  27 R is equal to the width of the pipe outlet  25 , represented in  FIG. 3B  by the width line WL. In some designs for diffuser pipes  20 , the width of the flow passage  29  is an important design parameter affecting the aerodynamic performance of the diffuser pipe  20 . Therefore, by equating the width of the cross-sectional profile  27  to the width of a conventional elliptical cross-sectional shape for a pipe, the designer of the diffuser pipe  20  is able to better benchmark the aerodynamic performance of the diffuser pipe  20  against a conventional “elliptical” diffuser pipe. Furthermore, the circumferential envelope of the diffuser pipe  20  may be the same as that of a conventional “elliptical” diffuser pipe because their widths are the same, such that no reconfiguration or redesign of engine components near the diffuser pipes  20  may required. In an embodiment, the maximum height, measured along a general radial line to the center axis  11 , of the cross-sectional profile  27  is equal to the maximum height HR of the reference cross-sectional profile  27 R. 
     Referring to  FIG. 3B , the area of the cross-sectional profile  27  at the pipe outlet  25  is equal to the area of the reference cross-sectional profile  27 R. Thus, despite the cross-sectional profile  27  at the pipe outlet  25  having a shape different from the oblong or pure ellipse cross-sectional shape of a conventional pipe, the aerodynamic performance of the diffuser pipe  20  may be compared or benchmarked against that of a conventional “elliptical” diffuser pipe because their cross-sectional areas are the same. Furthermore, the radial and circumferential envelope of the diffuser pipe  20  may be the same as that of a conventional “elliptical” diffuser pipe because their cross-sectional areas are the same, such that no reconfiguration or redesign of engine components near the diffuser pipes  20  may be required. It can thus be appreciated that the cross-sectional area of the diffuser pipe  20  is not changed compared to a conventional diffuser pipe, just its shape. The cross-sectional width of the diffuser pipe  20  may also remain the same as the cross-sectional width of a conventional diffuser pipe. Referring to  FIG. 3B , a center of area CA of the cross-sectional profile  27  at the pipe outlet  25  is closer to the radially inner wall  22 A than a center of the reference area CRA of the reference cross-sectional profile  27 R is closer to its radially inner wall. The cross-sectional profile  27  thus has a “lower” or “dropped” (i.e. disposed closer to the center axis  11 ) center of area CA than the center of the reference area CRA, despite both cross-sectional profiles  27 , 27 R having the same area. 
     Referring to  FIG. 3B , the radially inner wall  22 A has a compound curvature. The radially inner wall  22 A in the cross-sectional profile  27  shown is made up of two or more curves with different radii that bend the same way and are on the same side of a common tangent. Thus, the radius of curvature RIW of the radially inner wall  22 A varies, or does not remain constant, between the side walls  22 D. 
     Referring to  FIG. 3B , the compound curve of the radially inner wall  22 A has a first curved portion  22 ACP 1  joined to one of the side walls  22 D and having a first radius of curvature RC 1 , a second curved portion  22 ACP 2  joined to the other of the side walls  22 D and having a second radius of curvature RC 2 , and a third curved portion  22 A 1  between the first and second curved portions  22 ACP 1 , 22 ACP 2  having a third radius of curvature RC 3 . The first and second curved portions  22 ACP 1 , 22 ACP 2  are similarly curved, such that the first radius of curvature RC 1  is approximately equal to the second radius or curvature RC 2 . The third curved portion  22 A 1  is curved differently from the curvature of first and second curved portions  22 ACP 1 , 22 ACP 2 , such that the third radius of curvature RC 2  is different from the first and second radii of curvature RC 1 ,RC 2 . The third curved portion  22 A 1  defines an apex point of the radially inner wall  22 A, which is the point on the radially inner wall  22 A that is furthest from the center axis  11 . The first and second curved portion  22 ACP 1 , 22 ACP 2  each define proximal points of the radially inner wall  22 A, which are the points on the radially inner wall  22 A that are closest to the center axis  11 . At each of the apex and proximal points, tangents to the radially inner wall  22 A are define which are parallel to the width line WL. Thus, in the shape of the pipe outlet  25  shown in  FIG. 3B , at least the radially inner wall  22 A has multiple and different radii of curvature. Still referring to  FIG. 3 , the radius of curvature ROW of the radially outer wall  22 A remains substantially constant, or is a simple curve, throughout its length between the side walls  22 D. The radius of curvature ROW of the radially outer wall  22 B does not define a compound curve. 
     Other elliptical polygon shapes for the cross-sectional profile  27  are possible and within the scope of the present disclosure. For example, and referring to  FIG. 3C , the elliptical polygon shape of the cross-sectional profile  27  of  FIG. 3B  is flipped or inverted. In  FIG. 3C , the radially inner wall  22 A of the cross-sectional profile  27  has a curvature greater than the curvature of the radially outer wall  22 B. The disclosure above related to the curved radially inner and outer walls  22 A, 22 B of  FIG. 3B  applies mutatis mutandis to the curved radially inner and outer walls  22 A, 22 B of  FIG. 3C . Such an inverted shape for the cross-sectional profile  27  in  FIG. 3C  may provide the same stiffening structural benefits to the diffuser pipe  20  that are described above. Another possible elliptical polygon shape for the cross-sectional profile  27  is shown in  FIG. 3B , in which the radially inner wall  22 A is curved outwardly relative to the pipe center axis  21 . 
     Yet another possible elliptical polygon shape for the cross-sectional profile  127  is described with reference to  FIGS. 4A and 4B . Both the radially outer wall  22 B and the radially inner wall  22 A of the cross-sectional profile  127  are curved. The cross-sectional profile  127  has a peanut or kidney shape, in that part of the radially inner wall  22 A protrudes toward the radially outer wall  22 B. More particularly, and referring to  FIG. 4B , the radially inner wall  22 A is a compound curve that has an indented portion  22 A 1  (corresponding to the third curved portion  22 A 1  described above) that extends toward the radially outer wall  22 B. The indented portion  22 A 1  is a local depression in the radially inner wall  22 A. The indented portion  22 A 1  is symmetrical about the line H defining the height of the tubular body  22 . The indented portion  22 A 1  includes a peak point PP that is on a radial line from the center axis  11  and on the line H. The indented portion  22 A 1  includes the portions of the radially inner wall  22 A that are positioned furthest from the center axis  11 . Referring to  FIG. 4B , the radially inner wall  22 A has two lateral portions  22 AL (corresponding to the first and second curved portions  22 ACP 1 , 22 ACP 2  described above) disposed on opposite circumferential sides of the indented portion  22 A 1 . The lateral portions  22 AL are positioned closer to the center axis  11  than the indented portion  22 A 1 . The lateral portions  22 AL are symmetrical about the line H. The disclosure above related to the compound curve of the radially inner wall  22 A and the radii of curvature ROW,RIW,RC 1 ,RC 2 ,RC 3  of  FIG. 3B  applies mutatis mutandis to the compound curve of the radially inner wall  22 A of  FIG. 3C . Referring to  FIG. 4B , the first and second side walls  22 C, 22 D are free of any indentations. As the fluid flow F separates on the radially inner side of the diffuser pipe  20  after the bend portion  28 , the peanut or kidney shape provided by the indented portion  22 A 1  of the radially inner wall  22 A may have positive aerodynamic effects on the fluid flow F by containing or confining low momentum flow in the “valleys” of the lateral portions  22 AL. 
     Referring to  FIGS. 4A and 4B , the shape of the cross-sectional profile  127  at the pipe outlet  25  is an elliptical polygon (sometimes referred to as an elliptogon), and more specifically is a kidney shape. The pipe outlet  25  is not oblong, where an oblong shape is an elongated rectangle or oval with parallel sides. The shape of the pipe outlet  25  is not oval. The shape of the pipe outlet  25  is different from a shape defined by two semi-circles with the same radius spaced apart and interconnected by parallel lines. The shape of the pipe outlet  25  has all curved lines represented by the radially inner and/or outer walls  22 A, 22 B and side walls  22 D. The shape of the pipe outlet  25  is free of parallel lines. Some conventional pipes, in contrast, have oblong, elliptical or symmetrical cross-sectional shapes along the downstream region of the diffuser pipe. 
     Referring to  FIG. 4B , the peanut or kidney shape may be governed by the ratio of a height HIP of the indented portion  22 A 1  over a height HCS of the cross-sectional profile  127 . The height HIP of the indented portion  22 A 1  is measured along a line being substantially radial to the center axis  11 . The line extends from a first tangent at an inflection point of the curved lateral portions  22 AL, to a second tangent at an inflection point of the curved indented portion  22 A 1 . The height HCS of the cross-sectional profile  127  extends between the second tangent and the apex point AP of the radially outer wall  22 B. For the cross-sectional profile  127  shown in  FIG. 4B , a ratio of the height HIP of the indented portion  22 A 1  over the height HCS of the cross-sectional profile  127  may be between 0 and 0.3. The height HCS of the cross-sectional profile  127  is thus always greater than the height HIP of the indented portion  22 A 1 . Where the value of the ratio is zero, the radially inner wall  22 A have very little curvature. Where the value of the ratio is greater than zero, the range of ratios helps to ensure that the radially inner wall  22 A is curved and contributing to the desired peanut or kidney shape of the cross-sectional profile  127 . The peanut or kidney shape of the cross-sectional profile  127  may take other forms as well. For example, in one non-limiting example, the radially outer wall  22 B also has an indented portion  22 A 1 . For example, in another non-limiting example, the cross-sectional profile  127  is inverted, such that only the radially outer wall  22 B has the indented portion  22 A 1 . 
     Referring to  FIG. 4B , the cross-sectional profile  127  is symmetric about the line H defining a height of the tubular body  22 . The outlet  25  in  FIG. 4B  is a symmetrical kidney shape. In an alternative possible shape for the cross-sectional profile  127  that is asymmetrical about the line H, the ratio of the first width portion WP 1  over the second width portion WP 2  may be such that the asymmetry of the cross-sectional profile  127  may be on either side of the line H. Referring to  FIG. 4B , the cross-sectional profile  127  is asymmetric about the width line WL. The shape or contour of the cross-sectional profile  127  is different on each side of the width line WL. The radially outer wall  22 B and the radially inner wall  22 A are not symmetrical about the width line WL. 
     Referring to  FIG. 4B , the area of the cross-sectional profile  127  is equal to the area of the reference cross-sectional profile  127 R that is elliptical and which has the same width WL and the same height measured along the line H. Thus, despite the cross-sectional profile  127  having a shape different from the oblong or pure ellipse cross-sectional shape of a conventional pipe, the aerodynamic performance of the diffuser pipe  20  may be compared or benchmarked against that of a conventional “elliptical” diffuser pipe because their cross-sectional areas are the same. Furthermore, the radial and circumferential envelope of the diffuser pipe  20  may be the same as that of a conventional “elliptical” diffuser pipe because their cross-sectional areas are the same, such that no reconfiguration or redesign of engine components near the diffuser pipes  20  may be required. Referring to  FIG. 4B , a center of area CA of the cross-sectional profile  127  is closer to the radially inner wall  22 A than a center of the reference area CRA of the reference cross-sectional profile  127 R. The cross-sectional profile  127  thus has a “lower” or “dropped” (i.e. disposed closer to the center axis  11 ) center of area CA than the center of the reference area CRA, despite both cross-sectional profiles  127 , 127 R having the same area. 
     Although  FIGS. 3B and 4B  show a single cross-sectional profile  27 , 127  at a particular location along the diffuser pipe  20 , it will be appreciated that the cross-sectional profiles  27 , 127 , as well as any other cross-sectional shapes or contours disclosed herein, may also be present at other locations along the length L of the diffuser pipe  20 . Referring to  FIGS. 3A and 4A , the elliptogon and/or kidney or peanut cross-sectional profiles  27 , 127  are present at every point of the pipe center axis  21  from the bend portion  28  to the pipe outlet  25 . More particularly, the cross-sectional profiles  27 , 127  are present along all points of the length L of the tubular body  22  from an upstream end  28 A of the bend portion  28  to the pipe outlet  25 . The upstream end  28 A is the extremity of the bend portion  28  closest to the radially-extending first portion  24 . The cross-sectional profiles  27 , 127  thus extend along all of the length of the bend portion  28  and the second portion  26  to reinforce or stiffen these portions of the diffuser pipe  20 . The cross-sectional profiles  27 , 127  may start at the bend portion  28  and “blend” or become more pronounced (e.g. greater curvature to the radially outer wall  22 B, greater height HIP of the indented portion  22 A 1 , etc.) in the direction of the fluid flow F along the pipe center axis  21  toward the pipe outlet  25 . In an embodiment, the cross-sectional profiles  27 , 127  are not present in the radial, first portion  24  of the diffuser pipe  20  since there may be no bending or flexion moment acting on the first portion  24 . In an embodiment, the cross-sectional shape along the first portion  24  is elliptical. In an embodiment, the cross-sectional shape of the inlet  23  is circular. 
       FIGS. 5A to 5C  compare the Mach number of the fluid flow F through diffuser pipes  20  having different cross-sectional shapes. The cross-sectional shape of the diffuser pipe in  FIG. 5A  is elliptical, and thus resemble the shape of a conventional diffuser pipe. The cross-sectional shape of the diffuser pipe  20  in  FIG. 5B  is elliptical polygonal, and is defined by the cross-sectional profile  27 . The cross-sectional shape of the diffuser pipe  20  in  FIG. 5C  is elliptical polygonal with a peanut or kidney shape, and is defined by the cross-sectional profile  127 .  FIGS. 5A to 5C  show that the fluid flow F at various sections along the diffuser pipe is substantially the same for all three cross-sectional shapes, suggesting that the cross-sectional profiles  27 , 127  disclosed herein may stiffen the diffuser pipe  20  without negatively impacting its aerodynamic performance when compared to an “elliptical” diffuser pipe. 
     Referring to  FIGS. 3A and 4A , there is disclosed a method of stiffening (i.e. reducing the flexion) of the diffuser pipe  20  which is cantilevered at its inlet  23  to the casing of the impeller  17 . The method includes providing a cross-sectional profile  27 , 127  to the diffuser pipe  20  in its bend and/or axial portions  28 , 26 . The cross-sectional profile  27 , 127  is defined by a curved radially outer wall  22 B and has symmetry about the line H defining a height of the diffuser pipe  20 . 
     Referring to  FIGS. 3A and 4A , there is disclosed a method of stiffening (i.e. reducing the flexion) of the diffuser pipe  20  which is cantilevered at its inlet  23  to the casing of the impeller  17 . The method includes providing a cross-sectional profile  27 , 127  to the diffuser pipe  20  in its bend and/or axial portions  28 , 26 . The cross-sectional profile  27 , 127  is defined by a curved radially inner and outer walls  22 A, 22 B, where the radius of curvature ROW of the radially outer wall  22 B is different from the radius of curvature RIW of the radially inner wall  22 A. 
     The diffuser pipes  20  disclosed herein may have dimples, which are extrusions or impressions in one of the radially inner and outer walls  22 A, 22 B, in addition to the cross-sectional profiles  27 , 127  disclosed herein. Dimples may give the diffuser pipe  20  a different natural frequency such that it is out of the range of dynamic frequencies during operation of the engine  10 , thereby contributing to tuning the diffuser pipe  20  modes out of running range at high speeds. When employed with dimples, the cross-sectional shapes disclosed herein may help to reduce risks of the diffuser pipe  20  cracking due to high cycle fatigue (HCF). 
     The embodiments described in this document provide non-limiting examples of possible implementations of the present technology. Upon review of the present disclosure, a person of ordinary skill in the art will recognize that changes may be made to the embodiments described herein without departing from the scope of the present technology. Yet further modifications could be implemented by a person of ordinary skill in the art in view of the present disclosure, which modifications would be within the scope of the present technology.