EP2090788A1 - Rotor et turbocompresseur - Google Patents

Rotor et turbocompresseur Download PDF

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Publication number
EP2090788A1
EP2090788A1 EP08002766A EP08002766A EP2090788A1 EP 2090788 A1 EP2090788 A1 EP 2090788A1 EP 08002766 A EP08002766 A EP 08002766A EP 08002766 A EP08002766 A EP 08002766A EP 2090788 A1 EP2090788 A1 EP 2090788A1
Authority
EP
European Patent Office
Prior art keywords
impeller
backplate
downstream side
vane
radial direction
Prior art date
Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
Withdrawn
Application number
EP08002766A
Other languages
German (de)
English (en)
Inventor
Ian Brown
Francis Heyes
Geoffrey Ngao
Paul Roach
Current Assignee (The listed assignees may be inaccurate. Google has not performed a legal analysis and makes no representation or warranty as to the accuracy of the list.)
Napier Turbochargers Ltd
Original Assignee
Napier Turbochargers Ltd
Priority date (The priority date is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the date listed.)
Filing date
Publication date
Application filed by Napier Turbochargers Ltd filed Critical Napier Turbochargers Ltd
Priority to EP08002766A priority Critical patent/EP2090788A1/fr
Priority to KR1020107020435A priority patent/KR20100121515A/ko
Priority to EP08872443.0A priority patent/EP2252798B1/fr
Priority to US12/867,816 priority patent/US20100322781A1/en
Priority to JP2010546388A priority patent/JP5538240B2/ja
Priority to PCT/GB2008/004190 priority patent/WO2009101376A1/fr
Priority to CN2008801267703A priority patent/CN101952603B/zh
Publication of EP2090788A1 publication Critical patent/EP2090788A1/fr
Withdrawn legal-status Critical Current

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Classifications

    • F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
    • F04—POSITIVE - DISPLACEMENT MACHINES FOR LIQUIDS; PUMPS FOR LIQUIDS OR ELASTIC FLUIDS
    • F04D—NON-POSITIVE-DISPLACEMENT PUMPS
    • F04D29/00—Details, component parts, or accessories
    • F04D29/26—Rotors specially for elastic fluids
    • F04D29/28—Rotors specially for elastic fluids for centrifugal or helico-centrifugal pumps for radial-flow or helico-centrifugal pumps
    • F04D29/30—Vanes
    • F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
    • F04—POSITIVE - DISPLACEMENT MACHINES FOR LIQUIDS; PUMPS FOR LIQUIDS OR ELASTIC FLUIDS
    • F04D—NON-POSITIVE-DISPLACEMENT PUMPS
    • F04D29/00—Details, component parts, or accessories
    • F04D29/26—Rotors specially for elastic fluids
    • F04D29/28—Rotors specially for elastic fluids for centrifugal or helico-centrifugal pumps for radial-flow or helico-centrifugal pumps
    • F04D29/284—Rotors specially for elastic fluids for centrifugal or helico-centrifugal pumps for radial-flow or helico-centrifugal pumps for compressors
    • F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
    • F05—INDEXING SCHEMES RELATING TO ENGINES OR PUMPS IN VARIOUS SUBCLASSES OF CLASSES F01-F04
    • F05D—INDEXING SCHEME FOR ASPECTS RELATING TO NON-POSITIVE-DISPLACEMENT MACHINES OR ENGINES, GAS-TURBINES OR JET-PROPULSION PLANTS
    • F05D2240/00—Components
    • F05D2240/20—Rotors
    • F05D2240/30—Characteristics of rotor blades, i.e. of any element transforming dynamic fluid energy to or from rotational energy and being attached to a rotor
    • F05D2240/304—Characteristics of rotor blades, i.e. of any element transforming dynamic fluid energy to or from rotational energy and being attached to a rotor related to the trailing edge of a rotor blade

Definitions

  • the present invention relates to an impeller and a turbocharger.
  • An industrial turbocharger compressor impeller is typically made from aluminium. This material is relatively cheap, is easy to machine and is light enough so that turbo lag is not a major problem.
  • Current turbocharger impellers for medium speed diesel engines tend not to have a through bore since this minimises the stress in the impeller material and reduces the likelihood of the impeller failing due to fatigue during a typical 50,000 hour life.
  • Impeller creep failure is associated with areas of high stress and high temperature.
  • the area of highest temperature, and consequently the area which determines the creep life, is on the back of the impeller near the outer diameter. This is an area where typically a labyrinth seal is located to reduce the leakage of compressed air towards the bearings.
  • the high temperature is associated with windage heating in that area.
  • the impeller life must typically achieve 50,000 hours. This is achieved traditionally by limiting the operating speed of the turbocharger in line with calculations of the creep life. At lower operating speeds the impeller stresses are lower, the compressed air at the downstream side of the impeller is cooler, and the windage heating is less than at higher operating speed.
  • a combination of direct and indirect cooling of the flow in radial gaps formed between rotors and stators of turbine-type machines is disclosed, wherein a first cooling fluid, preferably water, is used for indirect cooling and a second gaseous cooling fluid, preferably air, is used for direct cooling.
  • a first cooling fluid preferably water
  • a second gaseous cooling fluid preferably air
  • the cooled air is typically taken from the diesel engine air manifold, after the compressed air has been cooled by the charge air cooler.
  • the introduction of this cooled air is a parasitic loss on the turbocharger efficiency, since the turbocharger has to compress the coolant air but the air is not used in the diesel engine.
  • this cooled air leaks into the main stream of the compressor flow between impeller and diffuser and will cause a disturbance to the flow which reduces the compressor efficiency. Nevertheless, by cooling the impeller the compressor is allowed to operate at higher speed while still achieving the required 50,000 hours life.
  • an additional 0.2 bar of boost pressure can be achieved with this system and this typically allows the engine rate power to increase by around 5%.
  • the first objective is solved by an impeller as claimed in claim 1.
  • the second objective is solved by a compressor as claimed in claim 11.
  • the third objective is solved by a turbocharger as claimed in claim 12.
  • the depending claims define further developments of the invention.
  • An inventive impeller comprises a rotation axis, a radial direction, a backplate and a number of vanes which are connected to the backplate at a line of connection.
  • Each vane comprises an upstream side, a downstream side and an outer side.
  • the downstream side of each vane comprises an edge portion which is located near the outer side.
  • the vanes project radially over the backplate and the downstream side further comprises a connecting portion connecting the edge portion to the line of connection between the respective vane and the backplate and including an angle with the radial direction.
  • the edge portion may be orientated perpendicular to the radial direction.
  • the connecting portion may have a convex rounded portion which is located near the connection line.
  • the backplate can comprise a radially outer peripheral surface and the connecting portion can be adjacent to the radially outer peripheral surface of the backplate.
  • the radially outer peripheral surface of the backplate may be located in a plane with a normal being locally parallel to the radial direction. This means, that the radially outer surface may run parallel to the rotation axis.
  • the radially outer peripheral surface of the backplate can be located in a plane with a normal which includes an angle between 0° and 45° with the radial direction.
  • the angle may have a value between 15° and 25°. This further reduces stress and temperature on the surface of the backplate.
  • the radially outer surface of the inventive impeller may especially be located at a radial position closer to the rotation axis than the radially outer surface of a conventional impeller.
  • the distance between the radially outer surface and the rotation axis of an inventive impeller is smaller than the distance between the radially outer surface and the rotation axis of a conventional impeller.
  • An angle between a tangent located at the connecting portion adjacent to the connection line and the radial direction may have a value between 10° and 45°, preferably between 15° and 25°. This reduces vane leakage losses.
  • the edge portion of the downstream side can have a length in the direction of the rotation axis of more than 50% of the length of the downstream side in the direction of the rotation axis. This means, that only the part of the vane closest to the backplate is removed, so that the part of the vane that is working most efficiently on the working fluid remains.
  • the vane shape can be modified in the area of the downstream side so that the design conforms closely to the so-called "radial element” design. This ensures that the vane stresses are kept to an acceptable low level.
  • the inventive compressor comprises an inventive impeller, as previously described and an inventive turbocharger comprises an inventive compressor.
  • the inventive compressor and the inventive turbocharger have the same advantages as the inventive impeller has.
  • the inventive impeller has an increased impeller creep life compared to a conventional impeller. Moreover, the necessity for coolant flow is kept to a minimum.
  • Fig. 1 schematically shows a turbocharger in a sectional view.
  • Fig. 2 schematically shows part of a conventional turbocharger compressor impeller in a sectional view.
  • Fig. 3 schematically shows part of an embodiment of the inventive turbocharger compressor impeller in a sectional view.
  • Fig. 4 schematically shows part of an alternative embodiment of the inventive turbocharger compressor impeller in a sectional view.
  • FIG. 1 schematically shows a turbocharger in a sectional view.
  • the turbocharger comprises a turbine 11 and a compressor 10.
  • the turbine 11 and the compressor 10 are connected by a shaft 20.
  • the turbine 11 includes a rotor 4 which is located inside a turbine casing 3.
  • the turbine casing 3 has an exhaust inlet 5 which leads to the rotor 4 so that the exhaust entering the exhaust inlet 5 activates the rotor 4.
  • the turbine casing 3 has an exhaust outlet 6 through which the exhaust coming from the rotor 4 leaves the turbine casing 3.
  • the arrows 18 indicate the exhaust stream entering the turbine casing 3 through the exhaust inlet 5, activating the rotor 4 and leaving the turbine casing 3 through the exhaust outlet 6.
  • the compressor 10 includes an impeller 12 which is located inside a compressor casing 1. Moreover, the compressor 10 has an air inlet 7 which air leads to the impeller 12 and an air outlet 8 through which the air coming from the impeller 12 leaves the compressor casing 1.
  • the arrows 19 indicate the air stream entering the compressor casing 1 through the air inlet 7, being compressed by the impeller 12 and leaving the compressor casing 1 through the air outlet 8.
  • the impeller 12 comprises a backplate 2 and vanes 9.
  • the backplate 2 is connected to the shaft 20. Further, the backplate 2 is generally conical in shape and a plurality of circumferentially spaced arcuate vanes 9 are formed about its periphery.
  • the back surface 16 of the impeller 12 has radially spaced and axially extended ribs 17.
  • Labyrinth seals 13 are mounted to the compressor casing 1 opposite to the back surface 16 of the impeller 12 so as to mesh with the ribs 17. The labyrinth seals 13 engage the annular ribs 17 to reduce the leakage of compressed air towards the bearings along the back surface 16 of the impeller 12.
  • the rotor 4 of the turbine 11 is connected to the shaft 20 so that the activated rotor 4 activates the shaft 20.
  • the shaft 20 is further connected to the impeller 12 inside the compressor 10. Hence, the rotor 4 activates the impeller 12 by means of the shaft 20.
  • the rotation axis is indicated by reference numeral 21.
  • the exhaust stream 18 entering the exhaust inlet 5 activates the rotor 4 and leaves the turbine through the exhaust outlet 6.
  • the arrows 18 indicate the direction of the exhaust stream.
  • the impeller 12 in the compressor 10 driven by the rotor 4 sucks atmospherically fresh air into the air inlet 7 and compresses it to precompressed fresh air, which enters the air outlet 8.
  • the compressed air is then used for example in a reciprocating engine like e.g. a diesel engine.
  • the arrows 19 indicate the air stream direction.
  • FIG 2 schematically shows part of a conventional turbocharger compressor impeller 12 in a sectional view.
  • the impeller 12 is, for example, made from aluminium.
  • the impeller 12 comprises a backplate 2 and a vane 9.
  • the vane 9 is connected to the backplate 2 at a line of connection 22.
  • Each vane 9 comprises an upstream side 14 and a downstream side 15.
  • the air which is sucked into the air inlet 7 arrives at the upstream side 14 of the vane 9, passes the vane 9 along the direction 19 and leaves it at the downstream side 15 towards the air outlet 8.
  • an outer side 23 Opposite to the line of connection 22 an outer side 23 is located.
  • the outer side 23 has a concave shape.
  • the upstream side 14 runs, perpendicular to the rotation axis 21. However, an angle may be present between the upstream side 14 and the rotation axis 21 may have a value between 0° and ⁇ 10°.
  • the downstream side 15 is orientated perpendicular to a radial direction which is defined by the rotation axis 21.
  • the backplate 2 comprises a radially outer peripheral surface 25.
  • the radially outer peripheral surface 25 is located in a plane with a normal being locally parallel to the radial direction.
  • the distance between the radially outer peripheral surface 25 and the rotation axis 21 is indicated by reference numeral 30.
  • FIG 3 schematically shows part of an inventive turbocharger compressor impeller 112 in a sectional view. Elements which correspond to elements of figure 1 or 2 are designated with the same reference numerals and will not be described again in detail.
  • the conventional impeller 12, as it is shown in figure 2 and the inventive impeller 112, which is shown in figure 3 , differ in the shape of the downstream side 15 of the vane 9 and in the radial location of the radially outer peripheral surface 25 of the backplate 2.
  • the downstream side 15 of the inventive impeller 112 comprises an edge portion 27 which is located near the outer side 23 and a connecting portion 24 which is located near the line of connection 22 and connects the line of connection 22 to the edge portion 27.
  • the connecting portion 24 in figure 3 has a convex rounded shape. However, it can also have an other shape, for example a linear shape or an S-shape.
  • the edge portion 27 which is located near the outer side 23 is further orientated perpendicular to a radial direction which is defined by the rotation axis 21. Furthermore, the edge portion 27 which is located near the outer side 23 may run parallel to the rotation axis 21. This is the case for the vane 9, which is shown in figure 3 .
  • the edge portion 27 of the downstream side 15 has a length in the direction of the rotation axis 21 of more than 50% of the length of the downstream side 15 in the direction of the rotation axis 21.
  • the edge portion 27 which is located near the outer side 23 adjoins to the connecting portion 24 which is located near the line of connection 22.
  • the connecting portion 24 adjoins to the radially outer peripheral surface 25, which has the same properties as the corresponding radially outer peripheral surface 25 in figure 2 .
  • the distance between the radially peripheral outer surface 25 and the rotation axis 21 in figure 3 is indicated by reference numeral 31 and is smaller than the corresponding distance 30 of the conventional impeller 12, which is shown in figure 2 .
  • the vane 9 of the inventive impeller 112 projects radially over the backplate 2.
  • Figure 3 further shows a tangent 26 of the connecting portion 24 at the point, where the connecting portion 24 is adjacent to the radially outer peripheral surface 25.
  • the angle 29 between the tangent 26 and a line 28 radial to the rotation axis 21 has a value between 10° and 45°, preferably between 15° and 25°.
  • FIG 4 schematically shows part of an alternative embodiment of the inventive turbocharger compressor impeller 212 in a sectional view. Elements which correspond to elements of figure 3 are designated with the same reference numerals and are not described again in detail.
  • the impeller 212 which is shown in figure 4 comprises a connecting portion 24 with an S-shape.
  • the radially outer peripheral surface 25 in figure 4 includes an angle 32 to the rotation axis 21.
  • the angle 32 has a value between 0° and 45°, preferably between 15° and 25°. This further reduces stress and temperature on the back surface 16.
  • the connecting portion has a s-shape in the present embodiment it could as well have other shapes like, e.g., the convex rounded shape of the connecting portion of the first embodiment, a linear shape.
  • the improved design of the inventive impeller 112, 212 reduces vane leakage losses and keeps vane stresses to an acceptable low level. This increases the impeller creep life and minimises the necessity for coolant flow.

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  • Engineering & Computer Science (AREA)
  • Mechanical Engineering (AREA)
  • General Engineering & Computer Science (AREA)
  • Supercharger (AREA)
  • Structures Of Non-Positive Displacement Pumps (AREA)
EP08002766A 2008-02-14 2008-02-14 Rotor et turbocompresseur Withdrawn EP2090788A1 (fr)

Priority Applications (7)

Application Number Priority Date Filing Date Title
EP08002766A EP2090788A1 (fr) 2008-02-14 2008-02-14 Rotor et turbocompresseur
KR1020107020435A KR20100121515A (ko) 2008-02-14 2008-12-18 임펠러 및 터보과급기
EP08872443.0A EP2252798B1 (fr) 2008-02-14 2008-12-18 Rotor et turbocompresseur
US12/867,816 US20100322781A1 (en) 2008-02-14 2008-12-18 Impeller and turbocharger
JP2010546388A JP5538240B2 (ja) 2008-02-14 2008-12-18 羽根車およびターボチャージャー
PCT/GB2008/004190 WO2009101376A1 (fr) 2008-02-14 2008-12-18 Roue à aube et turbocompresseur
CN2008801267703A CN101952603B (zh) 2008-02-14 2008-12-18 叶轮及涡轮增压器

Applications Claiming Priority (1)

Application Number Priority Date Filing Date Title
EP08002766A EP2090788A1 (fr) 2008-02-14 2008-02-14 Rotor et turbocompresseur

Publications (1)

Publication Number Publication Date
EP2090788A1 true EP2090788A1 (fr) 2009-08-19

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ID=39597663

Family Applications (2)

Application Number Title Priority Date Filing Date
EP08002766A Withdrawn EP2090788A1 (fr) 2008-02-14 2008-02-14 Rotor et turbocompresseur
EP08872443.0A Not-in-force EP2252798B1 (fr) 2008-02-14 2008-12-18 Rotor et turbocompresseur

Family Applications After (1)

Application Number Title Priority Date Filing Date
EP08872443.0A Not-in-force EP2252798B1 (fr) 2008-02-14 2008-12-18 Rotor et turbocompresseur

Country Status (6)

Country Link
US (1) US20100322781A1 (fr)
EP (2) EP2090788A1 (fr)
JP (1) JP5538240B2 (fr)
KR (1) KR20100121515A (fr)
CN (1) CN101952603B (fr)
WO (1) WO2009101376A1 (fr)

Cited By (7)

* Cited by examiner, † Cited by third party
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WO2012160290A1 (fr) * 2011-05-23 2012-11-29 Turbomeca Rouet de compresseur centrifuge
CN104373376A (zh) * 2014-10-29 2015-02-25 湖南天雁机械有限责任公司 弧形斜流涡轮增压器压气机叶轮
CN104500440A (zh) * 2014-12-12 2015-04-08 常州环能涡轮动力股份有限公司 一种抗低周疲劳的涡轮增压器压气机叶轮
WO2016041789A1 (fr) * 2014-09-17 2016-03-24 Siemens Aktiengesellschaft Turbomachine à énergie fluidique radiale
US11041405B2 (en) 2019-09-18 2021-06-22 Garrett Transportation I Inc. Turbocharger turbine wheel
US11297989B2 (en) * 2016-09-01 2022-04-12 Samsung Electronics Co., Ltd. Cleaner
CN114729647A (zh) * 2019-12-09 2022-07-08 三菱重工发动机和增压器株式会社 离心压缩机的叶轮、离心压缩机以及涡轮增压器

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DE102011051650B4 (de) * 2011-07-07 2020-04-30 Atlas Copco Energas Gmbh Turbomaschine
JP5967966B2 (ja) * 2012-02-13 2016-08-10 三菱重工コンプレッサ株式会社 インペラ及びこれを備えた回転機械
US9624776B2 (en) * 2012-05-03 2017-04-18 Borgwarner Inc. Reduced stress superback wheel
CN102691527B (zh) * 2012-06-12 2014-06-04 中国科学院工程热物理研究所 一种开式向心涡轮叶片背部凹槽结构
CN103775198B (zh) * 2014-02-26 2016-05-18 岑溪市东正新泵业贸易有限公司 转叶轮增压器
JP6559401B2 (ja) * 2014-03-31 2019-08-14 株式会社Ihi 圧縮機インペラ、遠心圧縮機、及び過給機
JP6866019B2 (ja) * 2014-06-24 2021-04-28 コンセプツ エヌアールイーシー，エルエルシー ターボ機械の流動制御構造及びその設計方法
DE102014219107A1 (de) * 2014-09-23 2016-03-24 Siemens Aktiengesellschaft Radialverdichterlaufrad und zugehöriger Radialverdichter
CN104314863A (zh) * 2014-10-29 2015-01-28 湖南天雁机械有限责任公司 具有降低轴向载荷功能的压气机叶轮
CN104314864A (zh) * 2014-10-29 2015-01-28 湖南天雁机械有限责任公司 具有降低涡轮增压器轴向载荷的压气机斜流叶轮
DE102014224283A1 (de) * 2014-11-27 2016-06-02 Robert Bosch Gmbh Verdichter mit einem Dichtkanal
US9856886B2 (en) * 2015-01-08 2018-01-02 Honeywell International Inc. Multistage radial compressor baffle
EP3273065B1 (fr) * 2015-03-17 2021-06-16 Mitsubishi Heavy Industries Engine & Turbocharger, Ltd. Rotor de machine rotative, compresseur, turbocompresseur et procédé de fabrication de rotor de machine rotative
CN109306967A (zh) * 2017-07-28 2019-02-05 深圳市美好创亿医疗科技有限公司 风机
JP7461458B2 (ja) * 2020-03-24 2024-04-03 三菱重工エンジン＆ターボチャージャ株式会社 遠心圧縮機の羽根車を製造する方法
CN115989370A (zh) * 2020-08-05 2023-04-18 三菱重工发动机和增压器株式会社 离心压缩机的叶轮以及离心压缩机
CN112443359B (zh) * 2020-11-20 2022-12-27 蜂巢蔚领动力科技(江苏)有限公司 一种具有s型子午面出口边的向心透平叶轮
US11702937B2 (en) 2021-04-20 2023-07-18 Saudi Arabian Oil Company Integrated power pump

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US1796057A (en) * 1928-03-17 1931-03-10 Smith Frederick Robertson Supercharging fan for internal-combustion engines
GB347043A (en) * 1929-06-07 1931-04-23 Lucie Annie Jeanne Rateau Improvements in or relating to the blades of radial rotors of centrifugal blowers and compressors
DE2338718A1 (de) * 1973-07-31 1975-02-13 Motoren Turbinen Union Radialverdichterlaufrad fuer turbomaschinen
US5297928A (en) 1992-06-15 1994-03-29 Mitsubishi Jukogyo Kabushiki Kaisha Centrifugal compressor
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WO2001029425A1 (fr) 1999-10-20 2001-04-26 Abb Turbo Systems Ag Procede et dispositif de refroidissement de l'ecoulement dans les fentes radiales formees entre les rotors et les stators de turbomachines
US20040052644A1 (en) * 2001-06-06 2004-03-18 David Decker Method of making turbocharger including cast titanium compressor wheel

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* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
RU2583322C2 (ru) * 2011-05-23 2016-05-10 Турбомека Крыльчатка центробежного компрессора
FR2975733A1 (fr) * 2011-05-23 2012-11-30 Turbomeca Rouet de compresseur centrifuge
CN103562557A (zh) * 2011-05-23 2014-02-05 涡轮梅坎公司 离心式压缩机叶轮
WO2012160290A1 (fr) * 2011-05-23 2012-11-29 Turbomeca Rouet de compresseur centrifuge
US9683576B2 (en) 2011-05-23 2017-06-20 Turbomeca Centrifugal compressor impeller
CN103562557B (zh) * 2011-05-23 2016-05-04 涡轮梅坎公司 一种涡轮引擎、离心式压缩机和用于离心式压缩机的叶轮
WO2016041789A1 (fr) * 2014-09-17 2016-03-24 Siemens Aktiengesellschaft Turbomachine à énergie fluidique radiale
CN104373376A (zh) * 2014-10-29 2015-02-25 湖南天雁机械有限责任公司 弧形斜流涡轮增压器压气机叶轮
CN104500440A (zh) * 2014-12-12 2015-04-08 常州环能涡轮动力股份有限公司 一种抗低周疲劳的涡轮增压器压气机叶轮
US11297989B2 (en) * 2016-09-01 2022-04-12 Samsung Electronics Co., Ltd. Cleaner
US20220183522A1 (en) * 2016-09-01 2022-06-16 Samsung Electronics Co., Ltd. Cleaner
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CN101952603A (zh) 2011-01-19
EP2252798B1 (fr) 2018-09-05
WO2009101376A1 (fr) 2009-08-20
EP2252798A1 (fr) 2010-11-24
JP5538240B2 (ja) 2014-07-02
CN101952603B (zh) 2013-06-26
US20100322781A1 (en) 2010-12-23
KR20100121515A (ko) 2010-11-17
JP2011512479A (ja) 2011-04-21

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