Wyniki wyszukiwania - Biblioteka Nauki

1

Comparison of the linear and nonlinear cumulative damage theories in transient analysis of a tuned and mistuned turbine blades

100%

Rządkowski R.

|

tom nr 112

155-170

EN

Mechanical vibrations in turbine stages are one of the most significant reasons for a failure of bladed discs assemblies in turbines and compressors. A numerical example of a transient analysis during a run-up and a run-down process and the estimated fatigue life of the tuned and the mistuned bladed discs are presented. Life estimates are made using the linear and nonlinear cumulative damage theories and a comparison of the results is presented. It is done in order to show the importance of the consideration of the detuned system and the differences between the tuned bladed disc analysis. The blade is modelled on a basis of extended beam theory including a bending-bending-torsional vibration. The disc modelled by the moderately thick plate theory. The equation of motion is obtained by using the extended Hamiltons principle and the Ritz method.

2

O projektowaniu komór filtracyjnych odpylaczy tkaninowych

100%

Rządkowski R.

|

tom R. 58, nr 8

433-435

PL

Omówiono podstawowe zasady technologii działania odpylaczy tkaninowych z regeneracją filtrów impulsem sprężonego powietrza. W odniesieniu do konstrukcji odpylaczy podano zalecenia doboru gatunków stali i ustalania naddatków grubości ścianek. Przedstawiono obciążenia działające na te konstrukcje oraz propozycję obliczania ugięć ścianek komór.

EN

Basic technological principles of operation of dust collector with regeneration of the filters by an impulse of compressed air are presented. For the dust collector structures are matching grades of steel and allowances of chamber wall thickness are adivised. Loads of that structures and proposition of walls' deflection calculation are advised.

3

Vibration of plate with beams in the 2D compressible flow

100%

Rządkowski R.

Archives of Civil Engineering

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1999

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tom Vol. 45, nr 2

331-344

EN

In the dynamic analysis of the turbine, the bladed disc is modelled by the plate with the beam placed on the outer disc radius. The bladed disc interact with passing flow through the forced vibration or flutter. In the present studies the flutter of a palisade will be considered. The partially integrated method of the time domain method is used to determine the aeroelastic stability of a bladed disc. This method involves the solution of the fluid and structural equations separately, but information is exchanged at each time step. The blades are allowed to move independently, and the motion of all blades is analyzed to determine the aeroelastic stability of a palisade. The flow model is capable of representing 2D-flows over a wide Mach number range from Iow subsonic to supersonic, including transonic flows. The aerodynamic model fully accounts for blade thickness and camber and the angle-of-attack effects. The unsteady Euler 2D equations are integrated using an explicit monotonous second-order accuracy Godunov's type difference scheme. The blade model applied here is a one-dimensional beam described by an extended beam-theory including all important effects on a rotating blade. The disc is modelled by a moderately thick plate theory. Assuming rigidly fixed blades on the disk rim, the displacements of any particle of the bladed disc are found. In the time domain method, the equation of motion was integrated in time, by a method of constant average acceleration (Wilson method). The initial conditions are the steady flowfield and an assumed unsteady forces applied to the blades. In order to verified the numerical program written on the basis of algorithms presented above numerical results were compared to experimental and theoretical results presented by Bolcs and Fransson. The First and Fourth Standard Configurations were used. The good agreement between the experimental and numerical results was observed.

PL

W analizie dynamicznej turbiny tarcza z łopatkami jest zamodelowana przez okrągłą płytę z belkami zamocowanymi sztywno na jej zewnętrznym promieniu. Płyta z łopatkami drga na skutek przepływającego czynnika. Są to drgania wymuszone lub flatter. W opracowaniu analizowany będzie flatter palisady. Do analizy stabilności układu wykorzystano metodę częściowego całkowania równań przepływu i dynamiki. W tej metodzie zagadnienia dynamiczne i przepływowe w każdym kroku czasowym są rozwiązywane niezależnie, a przekazuje się tylko między programami przemieszczenia siatek i siły niestacjonarne. W przedstawionym modelu każda belka może poruszać się niezależnie, a jej ruch w czasie określa stabilność. Model przepływowy opisuje dwuwymiarowy ściśliwy przepływ poddźwiękowy, transoniczny i naddźwiękowy. W modelu tym uwzględniono grubość łopatki, jej zakrzywienie oraz wpływ kąta natarcia. Niestacjonarne równania Eulera scałkowano, używając metodę objętości skończonych — schemat Godunova-Kołgana. Łopatka zamodelowana jest za pomocą jednowymiarowej obracającej się belki skręconej w stanie naturalnym, o zmiennych wzdłuż długości przekrojach poprzecznych. Tarcza zamodelowana jest za pomocą płyty o umiarkowanej grubości. Zakładając sztywne zamocowanie łopatek na tarczy, otrzymano przemieszczenia dowolnego elementu układu. Równania opisujące drgania układu rozwiązano, stosując metodę bezpośredniego całkowania Wilsona. Jako warunki początkowe przyjęto parametry przepływu stacjonarnego przez palisadę oraz założono określone siły wymuszające ruch łopatek. W celu zweryfikowania napisanego programu numerycznego porównano wyniki obliczeń numerycznych i wyniki badań eksperymentalnych dostępnych w literaturze (pierwsza i czwarta konfiguracja). Otrzymano dobrą zgodność z wynikami obliczeń numerycznych i eksperymentalnych.

4

Self-excited vibration of a palisade in 2D subsonic, transonic and supersonic flow

63%

Rządkowski R. , Kovalyov A.

TASK Quarterly : scientific bulletin of Academic Computer Centre in Gdansk

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2000

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tom Vol. 4, No 1

49-80

EN

In recent years coupled fluid-structure problems have appeared. The computational method used to solve this problem was based on a time-marching algorithm, so it was natural to consider a time domain flutter analysis method. The time domain method of flutter analysis is based on the simultaneous integration in time of the equation of motion for the structure and the fluid. The flow model is capable of representing 2D flows over a wide Mach number range from low subsonic to supersonic, including transonic flows. The aerodynamic model fully accounts for blade thickness and camber and the angle-of-attack effects. The unsteady Euler equations are integrated by using the explicit monotonous second-order accurate Godunov scheme. The blade is modelled on the basis of extended beam theory including a bending-bending-torsional vibration and also by the simple two-degree of freedom model. The equation of motion is obtained by using the extended Hamilton's principle and the Ritz method. The direct integration method is used to find a solution of the coupled fluid-structure problem. In this work the comparison of numerical and experimental results is presented for the first and fourth standard configurations.

5

3D inviscid flutter of IV Standard Configuration. Part II. Coupled fluid-structure oscilstions

63%

Rządkowski R. , Gnesin V.

|

tom nr 111

51-71

EN

A three-dimensional nonlinear time-marching method and numerical analysis for aerolastic behaviour of oscillating blade of the IV Standard Configuration has been presented. The approach is based on the solution of the coupled fluid-structure problem in which the aerodynamic and structural equations are integrated simultaneously in time. In this formulation of a coupled problem, the interblade phase angle at which stability (or instability) would occur, is a part of the solution. The ideal gas flow through multiple interblade passage (with periodicity on the whole annulus) is described by the unsteady Euler equations in the form of conservative laws, which are integrated by use of the explicit monotonous second order accurate Godunov-Kolgan finite volume scheme and moving hybrid H-H (or H-O) grid. The structure analysis uses the modal approach and 3D finite element model of the blade. The blade motion is assumed to be a linear combination of mode shapes with the modal coefficients depending on time. The influence of the natural frequencies on the aerolastic coupled oscillations for the Fourth Standard Configuration is shown. It has been shown that interaction between modes plays an important role in the aerolastic blade response. This interaction has essentially nonlinear character and leads to blade limit cycle oscillations. The sign of the aerodamping coefficient calculated for the harmonic oscillations, may be considered only as a necessary, but not a sufficient condition for self-exited oscillations.

6

2D inviscid flutter of the mistuned Fourth and First Standard Configuration

63%

Rządkowski R. , Kovalyov A.

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tom nr 112

139--154

EN

The trend in aviation engines with high specific power and, correspondingly, high aerodynamic loads leads to the problem of aeroelastic behaviour of blades not only in compressors and fans, but also in turbines. Investigations of aeroelastic of the blades in dependence of structural mistuning are presented. A numerical calculation method for unsteady aerodynamic characteristics of oscillating blade cascades under the action of unstable loads is based on solution of the coupled fluid-structure problem, in which the aerodynamic and structural dynamic equations are integrated simultaneously in time, thus providing the correct formulation of a coupled problem, as the interblade phase angle, at which a stability (instability) would occur, is a part of solution. The ideal gas flow around multiple stage passages (with periodicity on the whole annulus) is described by the unsteady 2D Euler equations in conservative form, which are integrated by using the explicit monotonous second order accurate Godunov-Kolgan finite-volume scheme on the moving grid. The blade is modelled by a very simple two degrees of freedom discrete model. In this model cascade performs the torsional and the bending oscillations under the given law. The aeroelastic behaviour of the blades in the unsteady aerodynamic flow is calculated for the mistuned blades assemblies of the Fourth and First Standard Configurations. The computational domain of the unsteady flow can not be restricted to the single blade passage. The results in the time domain analysis show the beneficial influence of the mistuning of the bending mode in comparison to the torsional mode. The dynamic properties of the mistuned systems are dependent on the way of coupling of the blades, whether it is either aerodynamic or mechanical.

7

3D inviscid flutter of IV Standard Configuration. Part.I. Harmonic oscillations

63%

Gnesin V. , Rządkowski R.

|

tom nr 111

37-50

EN

A three-dimensional nonlinear time-marching method and numerical analysis for aerolastic behaviour of oscillating blade row of the IV Standard Configuration has been presented. The approach is based on the solution of the coupled fluid-structure problem in which the aerodynamic and structural equations are integrated simultaneously in time. In this formulation of a coupled problem, the interblade phase angle at which stability (or instability) would occur, is a part of the solution. The ideal gas flow through multiple interblade passage (with periodicity on the whole annulus) is described by the unsteady Euler equations in the form of conservative laws, which are integrated by use of the explicit monotonous second order accurate Godunov-Kolgan finite volume scheme and a moving hybrid H-H (or H-O) grid. The structure analysis uses the modal approach and 3D finite element model of the blade. The blade motion is assumed to be a linear combination of modes shapes with the modal coefficients depending on time. The influence of the natural frequencies on the aerodynamic for the Fourth Standard Configuration is shown. The instability regions for the first two modes shapes and the distribution of the aerodamping coefficient along blade length were shown for a harmonic oscillation with the assumed interblade phase angle.

8

Aeroelastic behaviour of the last stage steam turbine blades. Part II. Coupled fluid-structure oscillations

63%

Gnesin V. , Rządkowski R.

Transactions of the Institute of Fluid-Flow Machinery

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2001

|

tom nr 108

73-94

EN

This paper presents the partial integrated method which has been employed for aeroelasticity predictions of the long steam turbine blades. The approach is based on the solution of the coupled fluid - structure problem in which the aerodynamic and structural dynamic equations are integrated simultaneously in time, thus providing the correct formulation of a problem. The ideal gas flow around the blade row is described by the unsteady 3D Euler equations in conservative form, which are integrated by using the explicit monotonous second-order accurate Godunov-Kolgan, finite volume scheme and moving grids. In the structural analysis the modal approach is used. The natural frequencies and modal shapes of the blade were calculated by using 3D finite element model. The coupled fluid-structure oscillations were shown for 5 modes shapes separately and with taking into account the interaction of five natural modes.

9

Flutter and 3D unsteady forces acting on the last stage rotor blades with non-uniform pressure distribution behind the rotor blades of the steam turbine 13K215.

63%

Rządkowski R. , Gnesin V.

|

tom Vol. 27, nr 3

55-63

EN

A three-dimensional numerical analysis for aerodynamic unsteady forces and flutter parameters acting on the last stage steam turbine 13K215 rotor blades and total unsteady forces acting on the shaft have been presented. The low frequency excitation was simulated for a 94 rotating blades with 54 nozzles, it was assumed that the pressure behind tha rotor blades is changing in the circumferential direction. The flutter parameters of this stage were calculated.

PL

Przeprowadzono trójwymiarową analizę numeryczną niestacjonarnych sił aerodynamicznych i parametrów flateru łopatek wirnikowych ostatniego stopnia turbiny 13k215. Przeanalizowano wymuszenia niskoczęstotliwościowe dla 94 łopatek wirnikowych i 54 kierowniczych, zakładając równomierny rozkład ciśnienia za łopatkami wirnikowymi.

10

The numerical and experimental verification of the 3D inviscid flutter code

63%

Rządkowski R. , Gnesin V.

Transactions of the Institute of Fluid-Flow Machinery

|

2000

|

tom Nr 106

69-95

EN

In this study the numerical calculations were performed to compare the theoretical results of 3D inviscid flutter code with experimental results due to Bolcs and Fransson. The calculations were carried out for the torsional oscillations of the compressor cascade known as the First Standard Configuration, and the bending oscillations of the steam turbine cascade which has become the Fourth Standard Configuration. The developed numerical algorithm solves the Euler equation in conservative form, which is integrated by using the explicit monotonous second - order accurate Godunov - Kolgan finite - volume scheme and the moving hybrid grid. The structural model is based on the 3D and 1D models. The comparision of calculated and experimental results for the 1st and 4th Standard Configurations has shown the good quantitative and qualitative agreement for both integral performances (aerodamping coefficient) and local performances (unsteady pressure amplitude and phase distribution).

PL

Weryfiakacja numeryczna i eksperymentalna trójwymiarowego kodu obliczeniowego do obliczeń nielepkich drgań samowzbudnych. W pracy przedstawiono obliczenia numeryczne wykonane przy pomocy trójwymiarowego kodu obliczeniowego do obliczeń nielepkich drgań samowzbudnych, które porównano z danymi eksperymentalnymi Bolcs'a i Frasson'a. Obliczenia przeprowadzono dla drgań skrętnych kaskady sprężarki, znanej pod nazwą Pierwszej Konfiguracji Standardowej, oraz dla drgań giętych kaskady turbinowej parowej, którą nazwano Czwartą Konfiguracją Standardową. Opracowany algorytm numeryczny umożliwia rozwiązanie równania Eulera w formie zachowawczej, jest ono całkowane przy użyciu jawnego schematu Godunova - Kolgana drugiego rzędu dla objętościskończonych oraz przemieszczającej się siatki hybrydowej. Model strukturalny oparty jest na modelach 3D i 1D. Porównanie obliczeń z danymi eksperymentalnymi dla przypadków Pierwszej i Czwartej Konfiguracji Standardowej pokazuje dobrą zgodność ilościową oraz jakościową dla obu charakterystyk integralnych (tj. współczynnik tłumienia aerodynamicznego) oraz charakterystyk lokalnych (niestacjonarna amplituda ciśnienia i rozkład fazowy).

11

A theoretical model of 3D flutter in subsonic, transonic and supersonic inviscid flow

63%

Gnesin V. , Rządkowski R.

Transactions of the Institute of Fluid-Flow Machinery

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2000

|

tom Nr 106

45-68

EN

A three - dimensional nonlinear time - marching method for aeroelastic behaviour of oscilating turbine blade row has been presented. The approach is based on the solution of the coupled fluid - structure problem, where the aerodynamic and structural dynamics equations are integrated simultaneously in time, thus providing the correct formulation of a coupled problem as the interblade phase angle at which stability (instability) would occur is also a part of solution. The ideal gas flow around multiple interblade passages (with periodicity on the whole annulus) is described by the unsteady Euler equations in conservative form, which are integrated by using the explicit monotouns second - order accurate Godunov - Kolgan finite - volume scheme and moving hybrid H-O (or H-H) grid. The structural model is bades on the 3D and 1D models. In 3D model the mode shapes and natural frequencies have been obtained via standard FE analysis techniques. The 1D blade model applied here is a one - dimensional beam described by an extended beam - theory including all important effects on a rotating blade. The fluid and the structural equations are solved using the direct integration method or the modal superposition method. The fluid - structure model is also presented for a very simple two degree of freedom blade model.

PL

Teoretyczny model trójwymiarowego flatteru nielepkiego przepływu poddźwiękowego, transonicznego i ponaddźwiękowego. Przedstawiono trójwymiarową, nieliniową metodę kroczącą w czasie do badań zachowań aeroelastycznych drgającego szeregu łopatek turbiny. Metoda jest oparta na rozwiązaniu zagadnienia sprężonego płyn - wieniec turbiny, gdzie równania opisujące aerodynamikę i dynamikę konstrukcji całkowane są równocześnie w czasie i dlatego przedstawiają właściwy opis zagadnienia sprzężonego, gdyż międzyłopatkowy kąt fazowy, dla którego obserwujemy stabilność (niestabilność) jest także częścią rozwiązania. Przepływ kanałami międzyłopatkowymi gazu doskonałego (z określoną okresowością na całym pierścieniu) jest opisany niestacjonarnymi równaniami Euela, w formie zachowawczej, które są całkowane przy użyciu jawnego schematu drugiego rzędu w formie objętości skończonych Godunowa - Kolgana oraz przemieszczającej się siatki hybrydowej H-O (lub H-H). Model strukturalny jest oparty na modelach 3D i 1D. W przypadku modelu 3D częstości własne oraz postacie drgań własnych otrzymywane są przy pomocy standardowych technik elementów skończonych. Jednowymiarowy model łopatki, zastosowany w pracy, jest jednowymiarową belką opisaną przy pomocy rozszerzonej teorii belek, która umożliwia opis wszystkich ważnych efektów wirującej łopatki. Równania płynu oraz konstrukcji rozwiazywane są przy użyciu metody bezpośredniego całkowania lub superpozycji modalnej. Model płyn - konstrukcja jest także pokazany na przypadku bardzo prostego modelu łopatki o dwóch stopniach swobody.

12

The influence of steam extraction parameters on unsteady rotor forces

63%

Rządkowski R. , Gnesin V.

TASK Quarterly : scientific bulletin of Academic Computer Centre in Gdansk

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2007

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tom Vol. 11, No 3

253-261

EN

Aerodynamic unsteady forces of rotor blades in a turbine stage with steam extraction were calculated and blade failure was reported. A numerical calculation of the 3D transonic flow of an ideal gas through turbomachinery blade rows moving one in relation to another is presented. An ideal gas flow through mutually moving stator and rotor blades with periodicity on the whole annulus is described with unsteady Euler conservation equations, integrated using the explicit monotonous finite-volume difference scheme of Godunov-Kolgan and a moving hybrid H-H grid. In order to find the pressure distribution of steam parameters behind the rotor blades, calculations were performed for a steady flow through the stage and the steam extraction channels using the SPARC program and the unsteady forces of the rotor blade were calculated for four steam extraction conditions. For the maximal steam extraction the 10th harmonic of the axial force and moment was found to be close to the first natural frequency of the bladed disc with one nodal diameter. Thus, steam extraction can be the cause of the blade's failure.

13

Aeroelastic behaviour of the last stage steam turbine blades. Part I. Harmonic oscillations

63%

Rządkowski R. , Gnesin V.

Transactions of the Institute of Fluid-Flow Machinery

|

2001

|

tom nr 108

59-72

EN

This paper presents an integrated non-linear numerical model for aeroelasticity predictions of the long steam turbine blade. The approach is based on the solution of the coupled fluid - structure problem in which the aerodynamic and structural dynamic equations are integrated simultaneously in time, thus providing the correct formulation of a problem. The ideal gas flow around multiple interblade possages (with periodicity on the whole annulus) is described by the unsteady 3D Euler equations in conservative form, which are integrated by using the explicit monotonous second - order accurate Godunov-Kolgan, finite volume scheme and moving grids. In the structural analysis the modal approach is used. The natural frequencies and modal shapes of the blade were calculated using 3D finite element model. The instability regions for 5 models shapes and the distribution of the aerodamping coefficient along the blade length were shown for a harmonic oscillation with the assumed interblade phase angle.

14

Analysis of 3D flutter of long steam turbine blades - harmonic oscillations

63%

Rządkowski R. , Gnesin V.

Zeszyty Naukowe. Cieplne Maszyny Przepływowe - Turbomachinery / Politechnika Łódzka

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2000

|

tom nr 117, vol. 1

239-248

EN

This paper presents an integrated non-linear numerical model for aeroelasticity predictions of the long steam turbine blades. The approach is based on the solution of the coupled fluid - structure problem in which the aerodynamic and structural dynamic equations are integrated simultaneously in time, thus providing the correct formulation of a problem. The ideal gas flow around multiple interblade passages (with periodicity on the whole annulus) is described by the unsteady 3D Euler equations in conservative form, which are integrated by using the explicit monotonous second - order accurate Godunov - Kolgan finite - volume scheme and moving grids. In the structure analysis the modal approach is used. The natural frequencies and modal shapes of the blade were calculated by using 3D finite element model. The instability regions for 5 modes shapes were shown for a harmonic oscillation with the assumed interblade phase angle.

15

Vibrations of disc with twisted blades in 3D compressible flow

63%

Rządkowski R. , Gnesin V.

Archives of Civil Engineering

|

2003

|

tom Vol. 49, nr 3

355-373

EN

Numerical calculations of the 3D transonic flow of an ideal gas through turbomachinery rotor blade row and stator, rotor blades moving relatively one to another with taking into account the blades oscillations are presented. The approach is based on the solution of the coupled aerodynamic-structure problem for the 3D flow through the turbine stage in which fluid and dynamic equations are integrated simultaneously in time. An ideal gas flow through the mutually moving stator and rotor blades with periodicity on the whole annulus is described by the unsteady Euler conservation equations, which are integrated using the explicit monotonous finite-volume difference scheme of Godunov-Kolgan and moving hybrid H-H grid. The structure analysis uses the modal approach and 3D finite element model of a blade. There has been performed the calculation for the last stage of the steam turbine with rotor blades of 0,765 m.

PL

Przedstawiono obliczenia numeryczne w 3D transonicznym przepływie gazu doskonałego poprzez łopatki wirnikowe i kierownicze, gdzie drgające łopatki wirnikowe poruszają się względem siebie. Model jest oparty na rozwiązaniu sprzężonego zagadnienia 3D mechaniczno-przepływowego poprzez stopień turbinowy. W modelu równania przepływu i dynamiki są całkowane z krokiem czasowym. Przepływ gazu doskonałego przez nieruchome łopatki kierownicze i obracające i drgające łopatki wirnikowe, z założeniem periodyczności na części obwodu, został opisany niestacjonarnymi równaniami Eulera, które zostały scałkowane przy pomocy metody objętości skończonych — Godunowa-Kolgana na ruchomych siatkach typu H-H. W modelu mechanicznym wykorzystano metodę superpozycji modalnej i 3D model MES dla łopatki. Obliczenia przeprowadzono dla ostatniego stopnia parowej turbiny o długości łopatek wirnikowych równej 0.765 [m].

16

Bump-type foil bearing, 2D finite element model

51%

Rządkowski R. , Kicinski J. , Drewczynski M. , Żywica G.

|

tom nr 133

309--316

EN

Gas foil bearing technology has made significant progress during the last 30 years. Foil bearings fulfill most of the requirements of novel oil-free turbomachinery. Numerical calculations were conducted to determine the structural stiffness of commercially available bump-type foil bearings. A 2D FE model of foil bearing was prepared. The top foil deflections versus applied force were calculated numerically. The numerical results were compared with experimental results.

17

Stator clocking in SO3 compressor first stage rotor blades

51%

Rządkowski R. , Gnesin V. , Kolodyazhnaya L. , Szczepanik R.

|

tom nr 133

299--308

EN

Numerical calculations of the 3D transonic flow of an ideal gas through three-row compressor stage including the clocking effects are presented. The approach is based on the solution of the coupled aerodynamic-structure problem for the 3D flow through the turbine stage in which fluid and dynamic equations are integrated simultaneously in time. There has been performed the calculation for the stage of the compressor with rotor blades of 0.163 m. The aeroelastic characteristics are obtained for different position of the stator rows. The clocking effect influence the stability region of the rotor blades.

18

Experimental investigation of palisade flutter for the harmonic oscillations

51%

Tsyimbalyuk V. , Zinkowskij A. , Rządkowski R.

Transactions of the Institute of Fluid-Flow Machinery

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2005

|

tom nr 116

3-26

EN

The experimental stand for the flutter analysis was described. In this stand one can measure simultaneously unsteady aerodynamic force and moment with arbitrary combinations of bending and torsion motions of airfoil cascades in the subsonic flow. The cascade is composed of nine blades, four of them are vibrating. Unsteady flow effects have been investigated for subsonic flow in a compressor cascade. Specifically, experimental forced bending and torsion vibration were performed. The aerodynamic work coefficient of bending and torsional cascade vibrations for different interblade phase angles, Strouhal Numbers, and the incidence angles were shown.

19

Vibration of turbomachine blading with damages

51%

Vorobiov I. , Rządkowski R. , Chugay M. , Romanenko V.

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tom nr 133

351--358

EN

The work presents analysis of vibrations of turbomachine blading with damages. 3D models and finite elements method are used. The influence of the different depth and locations of cracks on the natural frequencies, displacement forms and stress intensity is analyzed. The real turbomachine blading with damages is considerated. The validity of results obtained has been done by comparison with experimental data. The received results can be used at research of vibration stress localizations of turbomachine blading with damages.

20

Natural frequencies of tuned and mistuned bladed discs on a shaft

51%

Rządkowski R. , Drewczyński M. , Kubitz L.

TASK Quarterly : scientific bulletin of Academic Computer Centre in Gdansk

|

2006

|

tom Vol. 10, No 3

275-289

EN

The dynamic behaviour of a rotor consisting of two tuned and mistuned bladed discs on a solid shaft is considered. The effect of the shaft's flexibility on the dynamic characteristics of the bladed discs and the coupling effects between the shaft and bladed disc modes are investigated. Results show clearly the coupling effects in a bladed disc-shaft system. Interference diagrams are developed, from which the dynamic behaviour of a bladed disc can be predicted for varying flexibility relationships between solid shafts and bladed discs. The global rotating mode shapes of flexible tuned and mistuned bladed disc-shaft assemblies are calculated. Rotational effects, such as centrifugal stiffening, are accounted for and all the possible couplings between the flexible parts are allowed. Calculated natural frequencies obtained from the blade, the bladed disc and the shaft with two discs are checked to discover resonance conditions and coupling effects. It is shown that blade mistuning strongly affects the interaction between flexible bladed discs and a flexible shaft. This interaction affects the flexible bladed disc modes and is not restricted to the modes with zero, one and two nodal diameters. The torsional frequency of the shaft with two bladed discs is coupled with the zero nodal diameter modes of the single bladed discs. It is shown that including the shaft in the bladed discs model is important from the designer's point of view and may alter the spectrum of frequencies considerably.