US20140369827A1 - Rotor for a turbomachine - Google Patents

Rotor for a turbomachine Download PDF

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Publication number
US20140369827A1
US20140369827A1 US14/373,287 US201214373287A US2014369827A1 US 20140369827 A1 US20140369827 A1 US 20140369827A1 US 201214373287 A US201214373287 A US 201214373287A US 2014369827 A1 US2014369827 A1 US 2014369827A1
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US
United States
Prior art keywords
rotor
rotor blade
section
blade row
blades
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.)
Abandoned
Application number
US14/373,287
Inventor
Benjamin Kumm
Norbert Surken
Xiaoping Zhou
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.)
Siemens AG
Original Assignee
Siemens AG
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 Siemens AG filed Critical Siemens AG
Assigned to SIEMENS AKTIENGESELLSCHAFT reassignment SIEMENS AKTIENGESELLSCHAFT ASSIGNMENT OF ASSIGNORS INTEREST (SEE DOCUMENT FOR DETAILS). Assignors: Sürken, Norbert, ZHOU, XIAOPING, Kumm, Benjamin
Publication of US20140369827A1 publication Critical patent/US20140369827A1/en
Abandoned legal-status Critical Current

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Classifications

    • FMECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
    • F01MACHINES OR ENGINES IN GENERAL; ENGINE PLANTS IN GENERAL; STEAM ENGINES
    • F01DNON-POSITIVE DISPLACEMENT MACHINES OR ENGINES, e.g. STEAM TURBINES
    • F01D3/00Machines or engines with axial-thrust balancing effected by working-fluid
    • F01D3/02Machines or engines with axial-thrust balancing effected by working-fluid characterised by having one fluid flow in one axial direction and another fluid flow in the opposite direction
    • FMECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
    • F04POSITIVE - DISPLACEMENT MACHINES FOR LIQUIDS; PUMPS FOR LIQUIDS OR ELASTIC FLUIDS
    • F04DNON-POSITIVE-DISPLACEMENT PUMPS
    • F04D19/00Axial-flow pumps
    • FMECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
    • F01MACHINES OR ENGINES IN GENERAL; ENGINE PLANTS IN GENERAL; STEAM ENGINES
    • F01DNON-POSITIVE DISPLACEMENT MACHINES OR ENGINES, e.g. STEAM TURBINES
    • F01D25/00Component parts, details, or accessories, not provided for in, or of interest apart from, other groups
    • F01D25/04Antivibration arrangements
    • FMECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
    • F01MACHINES OR ENGINES IN GENERAL; ENGINE PLANTS IN GENERAL; STEAM ENGINES
    • F01DNON-POSITIVE DISPLACEMENT MACHINES OR ENGINES, e.g. STEAM TURBINES
    • F01D5/00Blades; Blade-carrying members; Heating, heat-insulating, cooling or antivibration means on the blades or the members
    • F01D5/02Blade-carrying members, e.g. rotors
    • F01D5/06Rotors for more than one axial stage, e.g. of drum or multiple disc type; Details thereof, e.g. shafts, shaft connections
    • FMECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
    • F01MACHINES OR ENGINES IN GENERAL; ENGINE PLANTS IN GENERAL; STEAM ENGINES
    • F01DNON-POSITIVE DISPLACEMENT MACHINES OR ENGINES, e.g. STEAM TURBINES
    • F01D5/00Blades; Blade-carrying members; Heating, heat-insulating, cooling or antivibration means on the blades or the members
    • F01D5/02Blade-carrying members, e.g. rotors
    • F01D5/10Anti- vibration means
    • FMECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
    • F05INDEXING SCHEMES RELATING TO ENGINES OR PUMPS IN VARIOUS SUBCLASSES OF CLASSES F01-F04
    • F05DINDEXING SCHEME FOR ASPECTS RELATING TO NON-POSITIVE-DISPLACEMENT MACHINES OR ENGINES, GAS-TURBINES OR JET-PROPULSION PLANTS
    • F05D2220/00Application
    • F05D2220/30Application in turbines
    • F05D2220/31Application in turbines in steam turbines
    • FMECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
    • F05INDEXING SCHEMES RELATING TO ENGINES OR PUMPS IN VARIOUS SUBCLASSES OF CLASSES F01-F04
    • F05DINDEXING SCHEME FOR ASPECTS RELATING TO NON-POSITIVE-DISPLACEMENT MACHINES OR ENGINES, GAS-TURBINES OR JET-PROPULSION PLANTS
    • F05D2250/00Geometry
    • F05D2250/30Arrangement of components
    • FMECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
    • F05INDEXING SCHEMES RELATING TO ENGINES OR PUMPS IN VARIOUS SUBCLASSES OF CLASSES F01-F04
    • F05DINDEXING SCHEME FOR ASPECTS RELATING TO NON-POSITIVE-DISPLACEMENT MACHINES OR ENGINES, GAS-TURBINES OR JET-PROPULSION PLANTS
    • F05D2260/00Function
    • F05D2260/96Preventing, counteracting or reducing vibration or noise
    • F05D2260/961Preventing, counteracting or reducing vibration or noise by mistuning rotor blades or stator vanes with irregular interblade spacing, airfoil shape

Definitions

  • the invention relates to a rotor for a two-channel turbomachine, in particular a steam turbine, wherein the rotor has a first rotor section for a first channel and a second rotor section for a second channel, wherein the first rotor section has a first rotor blade row, a second rotor blade row and further rotor blade rows as well as a final rotor blade row, wherein the second rotor section has a first, second and further rotor blade rows, as well as a final rotor blade row.
  • Turbomachines such as steam turbines, comprise in general a rotor which is mounted such that it can rotate and a housing which is arranged about the rotor.
  • a rotor which is mounted such that it can rotate and a housing which is arranged about the rotor.
  • the rotors for turbomachines are configured for a certain range of operational frequencies, in which no torsional frequencies arise, wherein it is known that the rotor blades which are arranged on the rotors have an effect on the torsional frequencies.
  • a rotor for a two-channel turbomachine in particular a steam turbine
  • the rotor has a first rotor section for a first channel and a second rotor section for a second channel
  • the first rotor section has a first rotor blade row, a second rotor blade row and further rotor blade rows as well as a final rotor blade row
  • the second rotor section has a first, second and further rotor blade rows, as well as a final rotor blade row
  • the configuration of the rotor blades of a rotor blade row of the first rotor section is of different design to the configuration of the rotor blades of a rotor blade row of the second rotor section
  • the rotor blades of the corresponding rotor blade rows of the first rotor section and of the second rotor section are of substantially identical design.
  • the invention proceeds from the idea that, in the case of rotors of two-channel design, the rotor blade rows in the first channel and the associated corresponding rotor blade rows of the second channel are of identical design.
  • Rotors commonly have a first rotor blade row in the first channel and also in the second channel, which are of identical design. Also of identical design are the rotor blades of the second rotor blade row in the first and second channels. These rotor blade rows of the first and second channels are rotor blade rows which correspond to one another in the sense that they change the thermodynamic variables of the flow medium in a substantially identical manner.
  • the invention now proceeds from the idea that the corresponding rotor blade rows need not necessarily be of identical design. Rather, the invention proceeds from the idea of consciously forming the first channel and the second channel differently. To that end, the invention proposes making the configuration of the rotor blades of a rotor blade row of the first rotor section of different design to the configuration of the rotor blades of a rotor blade row of the second rotor section. This is to be understood as meaning that the mutually corresponding rotor blade rows are of different design to one another, the remaining mutually corresponding rotor blade rows being of substantially identical design.
  • the rotor blades of the final rotor blade row of the first rotor section are of different design to the rotor blades of the final rotor blade row of the second rotor section.
  • the rotor blades of the final rotor blade row are the longest.
  • the final rotor blade rows therefore have the greatest influence on the torsional vibrations of the rotor. Changing a rotor blade row therefore has a large effect on the entire rotor.
  • the rotor blades of the various rotor blade rows differ with respect to their dynamic properties.
  • the rotor blades of the various rotor blade rows differ with respect to their elastic properties.
  • elastic properties of the rotor blades also play an important part in influencing the torsional vibrations on a rotor. Changing the dynamic and/or elastic properties of the rotor blades would therefore lead to a large effect on the torsional vibrations.
  • the rotor blades of the various rotor blade rows differ with respect to their external geometry.
  • the rotor blades of the various rotor blade rows are of different design with respect to their materials.
  • Rotor blades which are of different design with respect to their geometry have a different frequency spectrum, such that rotor blade rows which are of different design with respect to their geometry have an effect on the torsional vibrations of a rotor.
  • the density and further physical properties of the materials used have a great effect on the torsional vibrations.
  • individual rotor blades are of different design. It is equally possible to change a plurality of individual rotor blades in a rotor blade row, or in various rotor blade rows, in order to thereby achieve a change in the torsional vibrations.
  • a plurality of rotor blade rows of the first rotor section are of different design to the rotor blade rows of the second section.
  • the rotor blades of the various rotor blade rows may be of different design depending on which torsional vibrations are to be expected or damped.
  • FIGURE shows, schematically, a cross-sectional view of a rotor according to the invention.
  • FIG. 1 shows a cross-sectional view of a rotor 2 which is mounted such that it can rotate about an axis of rotation 1 .
  • the rotor 2 is distinguished by a diameter 3 , rotor blades being arranged on the surface 4 of the rotor 2 .
  • the rotor 2 shown in the FIGURE comprises a first rotor section 5 for a first channel.
  • This first rotor section 5 comprises a first rotor blade row 7 , a second rotor blade row 8 and a final rotor blade row 9 . Further rotor blade rows are not shown for the sake of clarity.
  • the second rotor section 6 also comprises a first rotor blade row 10 , corresponding to the first rotor blade row 7 of the first channel 14 , a second rotor blade row 11 and a final rotor blade row 12 .
  • the first rotor blade row 7 and the rotor blade row 10 are mutually corresponding rotor blade rows. This means that, in accordance with the prior art, these two rotor blade rows are of substantially identical configuration. Accordingly, the second rotor blade row 8 and the second rotor blade row 11 are also mutually corresponding rotor blade rows. This is also the case for the final rotor blade row 9 and the final rotor blade row 12 , i.e. both rotor blade rows are mutually corresponding rotor blade rows.
  • the individual rotor blade rows comprise a plurality of rotor blades which are arranged on the circumference of the rotor 2 .
  • the configuration of the rotor blades of the final rotor blade row 9 is, according to the invention, of different design to the configuration of the rotor blades of the final rotor blade row 12 of the second rotor section 6 .
  • the overall frequency behavior of the rotor 2 is different to the frequency behavior if the rotor blade rows had been of substantially identical design with respect to one another.
  • the remaining rotor blade rows i.e. the first rotor blade row 7 is correspondingly of substantially identical design to the rotor blade row 10 .
  • fresh steam flows via a supply (not represented in more detail) into an inflow region 13 and from there splits into a first flow duct in the first rotor section 5 of the first channel and into a second flow duct 15 in the second rotor section 6 in the second channel.
  • the rotor blades of the final rotor blade row 9 are of different design with respect to the rotor blades of the final rotor blade row 12 .
  • the rotor blades of the various rotor blade rows are of different design with respect to their external geometry and/or the materials.

Abstract

A rotor for a double-flow turbomachine is provided, wherein the first flow and the second flow have several rows of rotor blades, wherein at least one row of rotor blades is different from the corresponding row of rotor blades of the other flow.

Description

    CROSS REFERENCE TO RELATED APPLICATIONS
  • This application is the US National Stage of International Application No. PCT/EP2012/072096 filed Nov. 8, 2012, and claims the benefit thereof. The International Application claims the benefit of European Application No. EP12000481 filed Jan. 25, 2012. All of the applications are incorporated by reference herein in their entirety.
  • FIELD OF INVENTION
  • The invention relates to a rotor for a two-channel turbomachine, in particular a steam turbine, wherein the rotor has a first rotor section for a first channel and a second rotor section for a second channel, wherein the first rotor section has a first rotor blade row, a second rotor blade row and further rotor blade rows as well as a final rotor blade row, wherein the second rotor section has a first, second and further rotor blade rows, as well as a final rotor blade row.
  • BACKGROUND OF INVENTION
  • Turbomachines, such as steam turbines, comprise in general a rotor which is mounted such that it can rotate and a housing which is arranged about the rotor. There is a risk that certain torsional frequencies could lead to destruction of the rotor or of the rotor blades on the rotor. For this reason, the rotors for turbomachines are configured for a certain range of operational frequencies, in which no torsional frequencies arise, wherein it is known that the rotor blades which are arranged on the rotors have an effect on the torsional frequencies.
  • SUMMARY OF INVENTION
  • It is an object of the invention to propose a rotor for a turbomachine which has a lower tendency to torsional frequencies.
  • This object is achieved with a rotor for a two-channel turbomachine, in particular a steam turbine, wherein the rotor has a first rotor section for a first channel and a second rotor section for a second channel, wherein the first rotor section has a first rotor blade row, a second rotor blade row and further rotor blade rows as well as a final rotor blade row, wherein the second rotor section has a first, second and further rotor blade rows, as well as a final rotor blade row, wherein the configuration of the rotor blades of a rotor blade row of the first rotor section is of different design to the configuration of the rotor blades of a rotor blade row of the second rotor section, wherein the rotor blades of the corresponding rotor blade rows of the first rotor section and of the second rotor section are of substantially identical design.
  • The invention proceeds from the idea that, in the case of rotors of two-channel design, the rotor blade rows in the first channel and the associated corresponding rotor blade rows of the second channel are of identical design. Rotors commonly have a first rotor blade row in the first channel and also in the second channel, which are of identical design. Also of identical design are the rotor blades of the second rotor blade row in the first and second channels. These rotor blade rows of the first and second channels are rotor blade rows which correspond to one another in the sense that they change the thermodynamic variables of the flow medium in a substantially identical manner.
  • The invention now proceeds from the idea that the corresponding rotor blade rows need not necessarily be of identical design. Rather, the invention proceeds from the idea of consciously forming the first channel and the second channel differently. To that end, the invention proposes making the configuration of the rotor blades of a rotor blade row of the first rotor section of different design to the configuration of the rotor blades of a rotor blade row of the second rotor section. This is to be understood as meaning that the mutually corresponding rotor blade rows are of different design to one another, the remaining mutually corresponding rotor blade rows being of substantially identical design.
  • Further advantageous developments are provided in the subclaims.
  • Thus, in a first advantageous development, the rotor blades of the final rotor blade row of the first rotor section are of different design to the rotor blades of the final rotor blade row of the second rotor section. For thermodynamic reasons, both in the first channel and in the second channel, the rotor blades of the final rotor blade row are the longest. The final rotor blade rows therefore have the greatest influence on the torsional vibrations of the rotor. Changing a rotor blade row therefore has a large effect on the entire rotor.
  • In one advantageous development, the rotor blades of the various rotor blade rows differ with respect to their dynamic properties.
  • In a further advantageous development, the rotor blades of the various rotor blade rows differ with respect to their elastic properties. In addition to the dynamic properties, elastic properties of the rotor blades also play an important part in influencing the torsional vibrations on a rotor. Changing the dynamic and/or elastic properties of the rotor blades would therefore lead to a large effect on the torsional vibrations.
  • In a further advantageous development, the rotor blades of the various rotor blade rows differ with respect to their external geometry.
  • Equally, in one advantageous development, the rotor blades of the various rotor blade rows are of different design with respect to their materials. Rotor blades which are of different design with respect to their geometry have a different frequency spectrum, such that rotor blade rows which are of different design with respect to their geometry have an effect on the torsional vibrations of a rotor. The density and further physical properties of the materials used have a great effect on the torsional vibrations.
  • In advantageous developments, individual rotor blades are of different design. It is equally possible to change a plurality of individual rotor blades in a rotor blade row, or in various rotor blade rows, in order to thereby achieve a change in the torsional vibrations.
  • In a further advantageous development, a plurality of rotor blade rows of the first rotor section are of different design to the rotor blade rows of the second section. The rotor blades of the various rotor blade rows may be of different design depending on which torsional vibrations are to be expected or damped.
  • The invention will now be illustrated in more detail with reference to an exemplary embodiment.
  • BRIEF DESCRIPTION OF THE DRAWINGS
  • The FIGURE shows, schematically, a cross-sectional view of a rotor according to the invention.
  • DETAILED DESCRIPTION OF INVENTION
  • FIG. 1 shows a cross-sectional view of a rotor 2 which is mounted such that it can rotate about an axis of rotation 1. The rotor 2 is distinguished by a diameter 3, rotor blades being arranged on the surface 4 of the rotor 2. The rotor 2 shown in the FIGURE comprises a first rotor section 5 for a first channel. This first rotor section 5 comprises a first rotor blade row 7, a second rotor blade row 8 and a final rotor blade row 9. Further rotor blade rows are not shown for the sake of clarity.
  • The second rotor section 6 also comprises a first rotor blade row 10, corresponding to the first rotor blade row 7 of the first channel 14, a second rotor blade row 11 and a final rotor blade row 12. The first rotor blade row 7 and the rotor blade row 10 are mutually corresponding rotor blade rows. This means that, in accordance with the prior art, these two rotor blade rows are of substantially identical configuration. Accordingly, the second rotor blade row 8 and the second rotor blade row 11 are also mutually corresponding rotor blade rows. This is also the case for the final rotor blade row 9 and the final rotor blade row 12, i.e. both rotor blade rows are mutually corresponding rotor blade rows. The individual rotor blade rows comprise a plurality of rotor blades which are arranged on the circumference of the rotor 2.
  • The configuration of the rotor blades of the final rotor blade row 9 is, according to the invention, of different design to the configuration of the rotor blades of the final rotor blade row 12 of the second rotor section 6. By virtue of the fact that the configuration of the rotor blades in the rotor blade row 9 is of different design to the rotor blades of the rotor blade row 12, the overall frequency behavior of the rotor 2 is different to the frequency behavior if the rotor blade rows had been of substantially identical design with respect to one another.
  • The remaining rotor blade rows, i.e. the first rotor blade row 7 is correspondingly of substantially identical design to the rotor blade row 10.
  • In operation, fresh steam flows via a supply (not represented in more detail) into an inflow region 13 and from there splits into a first flow duct in the first rotor section 5 of the first channel and into a second flow duct 15 in the second rotor section 6 in the second channel.
  • With respect to their dynamic properties and/or elastic properties, the rotor blades of the final rotor blade row 9 are of different design with respect to the rotor blades of the final rotor blade row 12. To that end, the rotor blades of the various rotor blade rows are of different design with respect to their external geometry and/or the materials.
  • By means of the change, according to the invention, of the configuration of the rotor blades of a rotor blade row, an additional degree of freedom is gained in order to change the torsion frequencies in a rotor 2.

Claims (10)

1-8. (canceled)
9. A rotor for a two-channel turbomachine, comprising:
a first rotor section for a first channel and a second rotor section for a second channel,
wherein the first rotor section has a first rotor blade row, a second rotor blade row and further rotor blade rows as well as a final rotor blade row,
wherein the second rotor section has a first rotor blade row, second rotor blade row and further rotor blade rows, as well as a final rotor blade row,
wherein the configuration of the rotor blades of a rotor blade row of the first rotor section of the first channel is of different design to the configuration of the rotor blades of the corresponding rotor blade row of the second rotor section of the second channel, wherein the rotor blades of the rotor blade row of the first rotor section are made for the rotor blade row of the first rotor section of the first channel and wherein the rotor blades of the corresponding rotor blade row are made for the corresponding rotor blade row of the second rotor section,
wherein the rotor blades of the corresponding rotor blade rows of the first rotor section and of the second rotor section are of substantially identical design.
10. The rotor as claimed in claim 9,
wherein the rotor blades of the final rotor blade row of the first rotor section are of different design to the rotor blades of the final rotor blade row of the second rotor section.
11. The rotor as claimed in claim 9,
wherein the rotor blades of the various rotor blade rows differ with respect to their dynamic properties.
12. The rotor as claimed in claim 9,
wherein the rotor blades of the various rotor blade rows differ with respect to their elastic properties.
13. The rotor as claimed in claim 9,
wherein the rotor blades of the various rotor blade rows differ with respect to their external geometry.
14. The rotor as claimed in claim 9,
wherein the rotor blades of the various rotor blade rows differ with respect to the materials.
15. The rotor as claimed in claim 9,
wherein individual rotor blades in their rotor blade row are of different design.
16. The rotor as claimed in claim 9,
wherein a plurality of rotor blade rows of the first rotor section are of different design to the rotor blade rows of the second rotor section.
17. The rotor as claimed in claim 9, wherein the two-channel turbomachine is a steam turbine.
US14/373,287 2012-01-25 2012-11-08 Rotor for a turbomachine Abandoned US20140369827A1 (en)

Applications Claiming Priority (3)

Application Number Priority Date Filing Date Title
EP12000481 2012-01-25
EP12000481.7 2012-01-25
PCT/EP2012/072096 WO2013110367A1 (en) 2012-01-25 2012-11-08 Rotor for a turbomachine

Publications (1)

Publication Number Publication Date
US20140369827A1 true US20140369827A1 (en) 2014-12-18

Family

ID=47221328

Family Applications (1)

Application Number Title Priority Date Filing Date
US14/373,287 Abandoned US20140369827A1 (en) 2012-01-25 2012-11-08 Rotor for a turbomachine

Country Status (5)

Country Link
US (1) US20140369827A1 (en)
EP (1) EP2776679A1 (en)
JP (1) JP2015509161A (en)
CN (1) CN104093937B (en)
WO (1) WO2013110367A1 (en)

Families Citing this family (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN103821567B (en) * 2014-01-23 2015-11-18 西北工业大学 A kind of aircraft engine high pressure rotor Structural Design
CN106089307B (en) * 2016-07-29 2018-01-09 杭州汽轮机股份有限公司 A kind of low parameter big flow double split flow back pressure turbine

Family Cites Families (9)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US4108573A (en) * 1977-01-26 1978-08-22 Westinghouse Electric Corp. Vibratory tuning of rotatable blades for elastic fluid machines
JPS53104009A (en) * 1977-02-21 1978-09-09 Hitachi Ltd Shrink fit rotor for steam turbine
JPS5827503U (en) * 1981-08-19 1983-02-22 株式会社東芝 steam turbine
JPS59150903A (en) * 1983-02-09 1984-08-29 Toshiba Corp Blade arrangement of rotary machine
US4958985A (en) * 1989-03-01 1990-09-25 Westinghouse Electric Corp. Performance low pressure end blading
US6814543B2 (en) * 2002-12-30 2004-11-09 General Electric Company Method and apparatus for bucket natural frequency tuning
US7766625B2 (en) * 2006-03-31 2010-08-03 General Electric Company Methods and apparatus for reducing stress in turbine buckets
US8210796B2 (en) * 2008-04-15 2012-07-03 General Electric Company Low exhaust loss turbine and method of minimizing exhaust losses
US8100641B2 (en) * 2008-09-09 2012-01-24 General Electric Company Steam turbine having stage with buckets of different materials

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Publication number Publication date
CN104093937A (en) 2014-10-08
EP2776679A1 (en) 2014-09-17
JP2015509161A (en) 2015-03-26
CN104093937B (en) 2016-05-18
WO2013110367A1 (en) 2013-08-01

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Owner name: SIEMENS AKTIENGESELLSCHAFT, GERMANY

Free format text: ASSIGNMENT OF ASSIGNORS INTEREST;ASSIGNORS:KUMM, BENJAMIN;SUERKEN, NORBERT;ZHOU, XIAOPING;SIGNING DATES FROM 20140616 TO 20140625;REEL/FRAME:033345/0636

STCB Information on status: application discontinuation

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