WO2023031411A1

WO2023031411A1 - Centrifugal compressor impeller with a particular blade tip shape

Info

Publication number: WO2023031411A1
Application number: PCT/EP2022/074469
Authority: WO
Inventors: Tejas GARGE; Bharath Harish SEETHARAMAN
Original assignee: Cummins Ltd
Priority date: 2021-09-03
Filing date: 2022-09-02
Publication date: 2023-03-09
Also published as: GB202112576D0; GB202404141D0; GB2626095A

Abstract

An impeller element for a compressor is formed with an upstream region in which the radial extent of each impeller blade decreases in the downstream axial direction. At positions axially in register with this region, the radial position of the shroud surface is constant or increasing in the downstream axial direction, so the spacing between the free edge of the blade and the shroud surface increases in the downstream axial direction. This is found to lead to surprising increases in the efficiency of the compressor, particularly for low rotational speeds.

Description

CENTRIFUGAL COMPRESSOR IMPELLER WITH A PARTICULAR BLADE TIP SHAPE

FIELD OF THE INVENTION

The present invention relates to a turbomachine, and in particular to a turbomachine having a compressor including an impeller element. The turbomachine may be a turbocharger, e- booster (in which the compressor is electrically assisted) and/or e-compressor (in which the compressor is powered by an electric motor). The invention further relates to an impeller element for use in the turbomachine.

BACKGROUND OF THE INVENTION

Turbomachines are machines that transfer energy between a rotor and a fluid. For example, a turbomachine may transfer energy from a fluid to a rotor or may transfer energy from a rotor to a fluid. Two examples of turbomachines are a power turbine, which uses the rotational energy of a rotor driven by a fluid to do useful work, for example, generating electrical power; and a compressor which uses the rotational energy of the rotor to compress a fluid.

Turbochargers are well-known turbomachines for supplying air to an inlet of an internal combustion engine at pressures above atmospheric pressure (boost pressures). A conventional turbocharger essentially comprises an exhaust gas driven turbine wheel mounted on a rotatable shaft within a turbine housing connected downstream of an engine outlet manifold. Rotation of the turbine wheel rotates an impeller element (here, an “impeller”) mounted on the other end of the shaft within a compressor housing. The impeller delivers compressed air to an engine inlet manifold. The turbocharger shaft is conventionally supported by journal and thrust bearings, including appropriate lubricating systems, located within a central bearing housing connected between the turbine and compressor housings.

Figure 1 shows a schematic cross-section through a known turbocharger. The turbocharger comprises a turbine 1 joined to a compressor 2 via a central bearing housing 3. The turbine 1 comprises a turbine wheel 4 for rotation within a turbine housing 5. Similarly, the compressor 2 comprises an impeller 6 which can rotate within a compressor housing 7. The compressor housing 7 defines a compressor chamber within which the compressor wheel 6 can rotate. The turbine wheel 4 and compressor wheel 6 are mounted on opposite ends of a common turbocharger shaft 8 which extends through the central bearing housing 3. The turbine housing 5 has at least one exhaust gas inlet volute 9 (in Fig. 1 two volutes are shown) located annularly around the turbine wheel 4, and an axial exhaust gas outlet 10. The compressor housing 7 has an axial air intake passage (compressor inlet) 11 and a volute 12 arranged annularly around the compressor chamber. The volute 12 is in gas flow communication with a compressor outlet 13.

The bearing housing 3 defines a bearing chamber 22 through which the turbocharger shaft 8 passes. The shaft 8 is rotatably supported by a bearing assembly which comprises two journal bearings 14 and 15 housed towards the turbine end and compressor end respectively of the bearing housing 3. Oil is supplied to the bearing assembly from the oil system of the internal combustion engine via oil inlet 18 and is fed to the bearings 14, 15 by oil passageways 19. The oil fed to the bearings 14, 15 may be used to both lubricate the bearings and to remove heat from the bearings.

In use, the turbine wheel 4 is rotated about an axis 25 by the passage of exhaust gas from the exhaust gas inlet 9 to the exhaust gas outlet 10. Exhaust gas is provided to exhaust gas inlet 9 from an exhaust manifold (also referred to as an outlet manifold) of the engine (not shown) to which the turbocharger is attached. The turbine wheel 4 in turn rotates the impeller 6 which thereby draws intake air through the compressor inlet 11 and delivers boost air to an inlet manifold of the engine via the volute 12 and then the outlet 13.

The compressor chamber is defined between a shroud portion 17 of the compressor housing 7 and a hub portion 20 of the bearing housing 3. Note that the compressor housing may be formed as a one-piece (i.e. integral) unit including the shroud portion 17, although it may alternatively comprise multiple mutually-attached components. The shroud portion 17 has an inwardly facing shroud surface 21 which is circularly symmetric about the rotational axis 25.

T urning to Fig. 2, which is an enlarged view of part of the turbocharger of Fig. 1 , the impeller 6 includes a central portion 22 positioned on the rotational axis 25. The impeller also includes a number of blades 23 circumferentially spaced about the rotational axis 25 and extending radially outwardly from the central portion 22. The shroud surface 21 has a spacing from the rotational axis 25 which is non-decreasing in the downstream axial direction (left to right in Fig. 2). The central portion 22 of the impeller 6 has a central axis which coincides with the rotational axis 25.

The blades 23 are substantially laminar (i.e. each blade is a curved sheet) but curved in a three-dimensional shape. For simplicity, the shape of a blade 23 is conventionally represented by a “meridional view”, in which the blade 23 is projected into the z-r plane, where z represents distance along the rotational axis 25, and r is distance from the radial axis 25. Thus, this view neglects the circumferential position of the portion of the blade 23 at any given position in the z-direction (axial direction), and, at any position in the z-direction, just indicates the maximum extent of the blade 23 from the rotational axis 25 (i.e. the radial distance of the edge of the blade from the rotational axis 25). The leading edge of the blade 26 terminates in a corner 27 where the blade has a small clearance with the shroud surface 21 , typically of about 0.60mm. Proximate the corner 27, the free edge 28 of the blade 22 may have substantially equal maximum radial extent at a range of axial positions. That is, this portion of the free edge 28 lies on a ideal cylindrical surface with a central axis coincident with the rotational axis 25. The free edge 28 is made to a high precision (e.g. with departures from the ideal cylindrical surface being at most 0.05mm, and typically much lower). The inwardly-facing shroud surface 21 is also circularly cylindrical in this axial position, so the spacing of the free edge 28 of the blade 23 and the shroud surface 21 is typically substantially constant for an axial range of positions near the corner 27.

In axial positions which are successively further in the direction z along the axis, the edge 28 of the blade 23 has an increasing radial extent approaching a trailing edge 29 of the blade 23. In some designs, the clearance between the blade and the shroud surface decreases to 0.20mm near the trailing edge. In other designs, the spacing is approximately constant along the blade.

The radial spacing of the edge 28 and the shroud surface 21 is conventionally minimised, so far as is possible given production tolerances, subject to the requirement that the shroud surface 21 and the blade 23 are spaced apart along the whole edge 28 to avoid collisions as the impeller 6 rotates. Minimizing this spacing minimizes gas leakage in the passage between the edge 28 and the shroud surface 21 , and is conventionally believed to maximise the efficiency of the impeller 6.

SUMMARY OF THE INVENTION

In general terms, the present invention proposes that the impeller is formed with an upstream region (i.e. proximate the leading edge and distal from the trailing edge) in which the maximum radial extent of each impeller blade decreases in the downstream axial direction. At positions axially in register with this region, the radial position of the shroud surface is typically constant or increasing in the downstream axial direction, so the radial spacing between the free edge of the blade and the shroud surface increases in the downstream axial direction in the region. This is found to lead to surprising increases in the efficiency of the compressor, particularly for low rotational speeds. Specifically, a first expression of the invention is an impeller element for a compressor of a turbomachine, the impeller element including: a central portion; and a plurality of impeller blades extending from the central portion away from the central axis, each impeller blade having, at each point along the central axis, a corresponding maximum extent from the central axis, each impeller blade having a leading edge and a trailing edge, wherein in use gas is driven, by rotation of the impeller element about the central axis, along the blade from the leading edge to the trailing edge, a downstream axial direction being defined as a direction along the central axis in which the trailing edge of each impeller blade is spaced from the leading edge of the impeller blade; the central axis including a narrowing portion within which, for points on the central axis which are successively further in the downstream axial direction, the corresponding maximum extent of the blades from the central axis is successively smaller.

In use, the central axis of the impeller element is positioned in a compressor chamber of the turbomachine, with a central axis of the central portion located on a rotational axis of the turbomachine and with the central portion of the impeller element connected to a drive shaft of the turbomachine.

If, as in a conventional system, the shroud surface has a spacing from the rotational axis of the turbo-machine which, in use (i.e. with the impeller element installed in the compressor chamber, with the central axis of the impeller element coinciding with the rotational axis), is non-decreasing in the downstream axial direction, at least in the narrowing portion of the central axis of the impeller element, then the spacing of the shroud surface and the shroud surface increases in the downstream axial direction. This reverses the conventional way of designing these elements, because it would be expected to cause gas leakage near the shroud surface. However, it has been discovered that this reversal of the conventional approach leads to a surprising improvement of the efficiency of the compressor, in certain regimes, though at the expense of slightly reduced efficiency in others.

Specifically, the increase in efficiency is apparent for relatively low rotational speeds, such as rotational speeds below the design point of the compressor (i.e. rotational speeds which are less commonly used in designing compressors, but which are encountered in use of the turbomachines). Furthermore, the increase in efficiency is most apparent for low values of the mass flow parameter (MFP; a conventional parameter indicating the mass flow rate of gas through the compressor). In other words, the improvement is most noticeable for off- peak, low flow conditions, and leads to improved off-peak, low flow efficiencies.

Flow simulations suggest that this is due to a reduction at low flow of an increase in entropy at portions of the blade near the leading edge, leading to fewer losses. Furthermore, it is observed in simulations that the wall shear stress, which in conventional systems is concentrated at the leading edge of the blade, is, in embodiments of the invention, spread out through the narrowing portion of the blade, indicating that there is better alignment of the flow with the surface of the blade (“flow alignment”).

This increase of efficiency may be at the cost of a slight choke flow decrease, leading to slightly reduced efficiency at high flow rates, particularly at high rotation speeds. These flow rates and rotation speeds are conventionally used as the design point, but considering also the lower rotations speeds and flow rates which are encountered when the compressor is in use, overall the efficiency of an embodiment of the invention may be higher than that of a conventional system, contrary to prior expectations.

BRIEF DESCRIPTION OF THE DRAWINGS

A non-limiting embodiment of the invention will now be described, for the sake of example only, with reference to the following figures, in which:

Fig. 1 is a cross-sectional drawing of a known turbocharger;

Fig. 2 is a meridional view of a portion of a compressor of a known turbocharger;

Fig. 3 is a meridional view of a portion of a compressor of a turbocharger which is an embodiment of the invention;

Fig. 4 is an enlarged view of a portion of first realisation of an impeller blade in the embodiment of Fig. 3;

Fig. 5 is an enlarged view of a portion of second realisation of an impeller blade in the embodiment of Fig. 3;

Fig. 6 compares the calculated impeller efficiency of a known turbocharger and an example of a turbocharger as shown in Figs. 3 and 4; and

Fig 7 is composed Figs. 7(a)-(d), and is a schematic comparison of losses and wall shear in a conventional impeller blade (Fig. 7(a) and Fig. 7(c) respectively), and in an embodiment of the invention (Figs. 7(b) and Fig. 7(d) respectively).

DETAILED DESCRIPTION OF THE EMBODIMENT

Referring Fig. 3, a meridional view is shown of a portion of an impeller element (“impeller”)

36 compressor of a turbomachine which is an embodiment of the present invention. The turbomachine may be a turbocharger which is identical to the known turbocharger shown in Fig. 1 , except that the impeller 36 of the compressor is replaced by the one illustrated in Fig. 3. Elements having the same meaning as in Fig. 2 are given the same reference numerals.

The impeller element 36 includes a central portion 22 which is substantially circularly symmetric about a central axis. The horizontal direction in Fig. 3 is parallel to the central axis. The impeller element 36 is installed in the turbomachine such that the central axis of the impeller element 36 coincides with the rotational axis 25 of the turbomachine. The impeller element further includes a plurality of laminar (sheet-like) blades 30 which extend away from the central axis 35. If the number of blades is denoted /, where /V is an integer, the impeller element 36 has /V-fold rotational symmetry about the central axis 25. In general, each blade 30 may have a curved three-dimensional shape, but the meridional view of Fig. 3 does not indicate the circumferential position of any part of the blade 30, so it appears as a two-dimensional area.

The impeller blade 30 has a leading edge 26 which extends away from the rotational axis 25, to a point 32 which is the point on the leading edge 26 which is furthest from the central axis 25. That is, in the meridional view, the radial distance of the free edge of the blade from the central axis 25 is locally maximal at the point 32. Although as shown in Fig. 3, the radially- outermost point 32 of the leading edge is shown having a sharp corner, in practice this corner may be rounded to some extent, and may have a significant rounding. The radially- outermost point 32 of the leading edge 26 is a point on the free edge of the blade 30 which is furthermost in the direction opposite to downstream axial direction and for which the tangent to the edge of the blade 36 when viewed in the meridional plane, is parallel to the central axis 25.

The radial distance of the point 32 from the central axis 25 is denoted R. R may be in the range 20mm to 80mm, more preferably in the range 25mm to 50mm. For example, it may be substantially 37.5mm. Note that R, like all the distances referred to in this document, is measured at room temperature. The impeller blade 30 also has a trailing edge 29 which is further from the central axis 25 than the leading edge 26. In use, gas is driven, by rotation of the impeller element 36 about the central axis 25, along the blade 30 from the leading edge 26 to the trailing edge 29. A “downstream” axial direction, defined as a direction along the central axis 25 in which the trailing edge 29 of each impeller blade is spaced from the leading edge 26 of the impeller blade, is the left-to-right direction in Fig. 3.

At the radially-outer end point 32 of the leading edge 26, the blade edge includes a corner.

Consider points within a portion 31 of the central axis 25 (this portion is referred to here as a “narrowing portion”). Each of the points in the narrowing portion 31 of the central axis 25 is in axial register with a corresponding location on the edge of the blade 30, which is at a corresponding distance in the radial direction (i.e. the upward direction in Fig. 3) from the central axis 25. This distance is the maximum extent of the blade 30 for the corresponding point in the narrowing portion 31 of the central axis 25. The narrowing portion 31 of the central axis is in axial register with a portion 33 of the free edge of the blade. For points in the narrowing portion 31 of the central axis 25 which are successively further in the downstream axial direction (i.e. points which are successively further to the right in Fig. 3), the corresponding maximum extents of the blade 30 from the central axis are successively smaller. That is, throughout the narrowing portion 31 of the axis 25, the corresponding portion 33 of the edge of the blade 30 slopes downwardly in the left-to-right direction on Fig. 3. The narrowing portion 31 thus defines an upstream portion 33 of the free edge of the blade 30, in axial register with the narrowing portion 31 , where the radial extent of the impeller blade 30 decreases in the downstream axial direction.

A second point 34 on the blade edge is in axial register with the point on the central axis 35 which is furthermost (within the narrowing portion 31 of the central axis 25) in the axial downstream direction. Thus, at the point 34, the corresponding maximum extent of the blade 30 from the central axis 25 is the smallest, out of all the points on the free edge of the blade 30 which are in axial register with the narrowing portion 31.

In the embodiment shown in Fig. 3, the radially-outmost point 32 of the leading edge 26 is illustrated as being in axial register with the end of the narrowing portion 31 of the central axis 25 which is least far in the downstream axial direction (i.e. the left-hand edge of the narrowing portion 31), which is referred to below as a “first point” on the central axis 25. Although this feature is preferable, and is assumed in the explanation below, the free edge of the blade 36 may alternatively be formed with a short portion, extending in the downstream axial direction from the point 37, in which the free edge has a constant maximum extent. Thus, in this case, the point 32 would be axially spaced from the narrowing portion 31.

The central axis 25 also includes a “widening portion” 39. For points in the widening portion 39 of the central axis 25 which are successively further in the downstream axial direction (i.e. points on the central axis 25 which are successively further to the right in Fig. 3), the corresponding maximum extents of the blade 30 from the central axis are successively greater. That is, throughout the widening portion 39 of the axis 25, the corresponding portion of the edge of the blade 25 slopes upwardly in the left-to-right direction on Fig. 4. At a third point 37, the blade 36 has the same maximum extent R from the central axis 25 as that at the first point 32. As illustrated in Fig. 3, the point 34 is in axial register with the downstream end of the widening portion 39. Furthermore, as illustrated in Fig. 3, the downstream end of the narrowing portion 31 and the upstream end of the widening portion 39 touch, at a location on the central axis 25 which in axial register with the point 34. However, in variants of the embodiment, the narrowing portion 31 and widening portion 39 may be axially spaced apart, e.g. such that in axial positions between the portions 31, 39 pf the central axis 25, the blade 36 has a constant maximum extent from the central axis 25.

The impeller shroud 17 has an inwardly-facing surface 21 which is rotationally-symmetric about the axis 25, and has a radial distance from the central axis 25 which may be substantially constant in the narrowing portion 31 (and optionally also in the widening portion 39). That is, the inwardly-facing surface 21 forms a circular cylinder in the narrowing portion (and optionally also the widening portion 39). Thus, the spacing of the impeller shroud 17 and the impeller blades 30 is successively greater in the narrowing portion 31 for points on the central axis which are successively further in the downstream axial direction. Specifically, when the impeller blades 30 are not rotating, the radial spacing between the impeller shroud 17 and each impeller blade 30 may be at least 2% of R at at least one axial position (e.g. the axial position in axial register with the second point 34). Note that the spacing (like all the spacings referred to in this document) is measured at a time when the impeller element 36 is not rotating, because when it is rotating vibrations may cause the spacing to vary with time.

Figs. 4 and 5 show a portion of the edge of the blade 30 of the embodiment of Fig. 3 in two possible detailed realisations of the embodiment. In both realisations, the distance of the point 34 from the central axis 35 is denoted R_±. This is less than the distance R of the points 32, 37 from the central axis 25. Specifically, the maximum extent R of the blade from the central axis 25 at the first point 32 is preferably at least 0.1mm greater than the maximum extent R_± of the blades from the central axis at the second point 34, i.e. R - R_± is at least 0.1mm, which is significantly greater than the conventional manufacturing tolerance of an impeller blade. Furthermore, R - R_± may be at least 0.2mm, at least 0.3, or at least 0.4mm.

To put this another way (e.g. in the case that R is 37.5mm), R - R_± may be at least 0.3% of R, and may be at least 0.6% of R, at least 0.9% of R, or at least 1.2% of R. Alternatively, the maximum extent R of the blades from the central axis at the first point 32 may be in the range 0.8%-2.5% of R greater than the maximum extent R_± of the blades from the central axis at the second point. The axial spacing of the first point 32 and the third point 37 may be no more than 0.5R, or even no more than 0.4R.

The free edge of the blade extending from point 32 to point 37, and including point 34, forms a curve. The curve preferably has a radius of curvature at at least one point which is less than R, and optionally less than 0.5R.

In each figure, the maximum slope of the edge of the blade 30 (i.e. the angle between the central axis 25 and a tangent to the curve at least one point between the second and third points 34, 37) is denoted by a. It may be at least 5 degrees, and indeed may be at least 10 degrees, such as about 15 degrees. It may be less than 30 degrees. In the downstream axial direction from the point 37, the maximum extent of the blade 36 for each respective axial position continuously increases.

In the case of Fig. 4, the third point 37 is formed as a sharp corner. The maximum slope of the edge between points 34 and 37 is at, or proximate, point 37. In the meridional view of Fig. 4, the upper edge of the blade is concave at all points between the points 32 and 34, and at points in the downstream axial direction from the point 37, and changes discontinuously at the point 37.

In the case of Fig. 5, the third point 37 is a rounded corner. In this case, the maximum slope of the edge between points 34 and 37 is at a point 37a which is axially spaced from the point 37. In the meridional view of Fig. 4, the upper edge of the blade is concave between the points 32 and 37a, convex at points in the downstream axial direction from the point 37a to a point 37b, and concave again downstream of the point 37b.

Turning to Fig. 6, experimental simulation results are shown comparing the efficiency of an impeller a conventional impeller element as shown in Fig. 2 (solid lines), with an impeller element as shown in Figs 3 and 4 (dashed lines), for five different rotational speeds: 47000rpm, 62553rpm, 83404rpm, 104225rpm and 120000rpm. For each of these speeds, the total-to-total (T-T) isoentropic efficiency of the impeller element from the compressor inlet to the impeller output is plotted on the vertical axis, while the normalised flow rate is plotted on the horizontal axis. The normalized flow rate is the MFP divided by the inlet area of the impeller (the area of the inlet 11 to the impeller).

Surprisingly, despite the greater spacing between the impeller blade and the shroud surface in the embodiment, and thus the increased risk of gas leakage, it was found that for 47000rpm, 62553rpm, 83404rpm and 104225rpm the efficiency of the embodiment is at least as high as that of the conventional system for all flow rates. For the flow rates 47000rpm and 62553rpm the efficiency improvement is observed only at high flow rates. For 83404rpm and 104225rpm, the efficiency improvement is observed for all flow rates except the very highest.

For 120000rpm, which is a more conventional operating speed, the efficiency improvement is observed for the lowest flow rates, but there are rotational speeds at which the conventional system has higher efficiency, and overall there is no clear difference of efficiency. Note that this rotational speed has frequently been used as a design point in prior research, so the improvement possible for lower rotational speeds would not have been observable in this research.

Further computational simulations help to explain the observed efficiency improvement of the embodiment relative to conventional systems observed for lower speeds. First, it was observed that the impeller pressure ratio (i.e. the ratio of the pressure at the outlet of the impeller to the pressure at the input to the impeller) was almost the same as for the conventional impeller element and the embodiment, for all rotational speeds and all flow rates.

Figs. 7(a) and 7(b) represent schematically the results of computational flow experiments to determine where losses (increase in entropy) occur for a typical mass flow parameter (MFP) and rotational speed. Fig. 7(a) is a perspective view of a part of the conventional impeller element of Fig. 2. It was found that losses are principally found in the hashed region marked as 40 near the tip 27 of the leading edge 26 of the impeller blade 23. Fig. 7(b) is a perspective view of a part of the impeller element 36 of Fig. 3, and in this case increases in entropy were found to be lower, and confined to the smaller area marked as 41. The reduced increase in entropy is directly related to improved efficiency in the embodiment.

Figs. 7(c) and 7(d) represent schematically the results of computational flow experiments to show the wall shear for a mass flow parameter of 39 and a rotational speed of 66000rpm. Fig. 7(c) is a perspective view of a part of the conventional impeller element of Fig. 2. It was found that wall shear is concentrated the hashed region marked as 42 along the leading edge 26 of the impeller blade 23. Fig. 7(d) is a perspective view of a part of the impeller element of Fig. 3, and in this case the wall shear is less concentrated; it is spread out through the hashed area marked as 43, demonstrating better alignment of the gas flow with the blades in the embodiment.

Claims

1. An impeller element for a compressor of a turbomachine, the impeller element including: a central portion; and a plurality of impeller blades extending from the central portion away from the central axis, each impeller blade having, at each point along the central axis, a corresponding maximum extent from the central axis, each impeller blade having a leading edge and a trailing edge, wherein in use gas is driven, by rotation of the impeller element about the central axis, along the blade from the leading edge to the trailing edge, a downstream axial direction being defined as a direction along the central axis in which the trailing edge of each impeller blade is spaced from the leading edge of the impeller blade; the central axis including a narrowing portion within which, for points on the central axis which are successively further in the downstream axial direction, the corresponding maximum extent of the blades from the central axis is successively smaller.

2. An impeller element according to claim 1 , wherein: the narrowing portion of the central axis comprises a first point and a second point; the second point is spaced in the downstream axial direction from the first point; and the maximum extent of the blades from the central axis at the first point is at least 0.1 mm greater than the maximum extent of the blades from the central axis at the second point.

3. An impeller element according to claim 1, wherein: the narrowing portion of the central axis comprises a first point and a second point; the second point is spaced in the downstream axial direction from the first point; and the maximum extent Ri of the blades from the central axis at the second point is at least 0.3% of R less than the maximum extent of the blades from the central axis at the second point, where R is the distance from the central axis of the point on the leading edge which is furthest from the central axis.

4. An impeller element according to claim 3 wherein the central axis further comprises a third point, the third point being spaced in the downstream axial direction from the second point, wherein the maximum extent of the blades from the central axis at the third point is that same as at the first point, and wherein the third point is located less than 0.5R from the first point along the central axis.

5. An impeller element according to claim 4 in which the second point is the point between the first point and the third point for which the maximum extent of the blades from the central axis is minimal, and the maximum extent Ri of the blades from the central axis at the second point is in the range 0.8%-2.5% of R less than the maximum extent of the blades from the central axis at the first point.

6. An impeller element according to claim 4 or 5, wherein, when plotted in a meridional view, the maximum extent of the blades from the central axis forms a curve passing through the first point, the second point, and the third point, and wherein the curve has a radius of curvature at at least one point which is less than R.

7. An impeller element according to claim 6, wherein, in the meridional view, the angle between the central axis and a tangent to the curve at least one point between the second and third points is at least 5 degrees.

8. A turbomachine, comprising an impeller element according to any preceding claim, wherein the turbomachine includes a compressor containing the impeller element, the central axis of the central portion of the impeller element is located on a rotational axis of the turbomachine, and the central portion of the impeller element is connected to a drive shaft of the turbomachine.

9. A turbomachine according to claim 8, in which the compressor further comprises an impeller shroud, wherein the spacing of the impeller shroud and the impeller blades is successively greater in the narrowing portion for points on the central axis which are successively further in the downstream axial direction.

10. A turbomachine according to claim 9 in which at at least one point of the narrowing portion, the spacing between the impeller shroud and the impeller blades is at least 2% of R when the impeller blades are not moving, where R is the distance from the central axis of the point on the leading edge which is furthest from the central axis.

11. A turbomachine according to claim 9 to 10 which is a turbocharger.

12. An engine comprising a turbocharger according to claim 11.