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1

Turbine wheel reduced modal model for self-excited vibration suppression by inter-blade dry-friction damping

Pešek Luděk, Šnábl Pavel, Prasad Chandra Shekhar

Bulletin of the Polish Academy of Sciences. Technical Sciences

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2023

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Vol. 71, nr 6

art. no. e148250

EN

A new approach to calculations based on the modal synthesis method is proposed for the evaluation of structural and dry-friction damping effects on self-excited vibrations due to aeroelastic instability in bladed turbine wheels. The method described herein is used to study dry-friction damping of self-excited vibration of an industrial turbine wheel with 66 blades. For evaluating damping effects, the blade couplings are applied to this particular turbine wheel. Therefore, neighbouring blades are interconnected by rigid arms that are fixed on one side to one blade and are in frictional contact on their free side with the other blade. Due to relatively normal motions in contacts, the prescribed contact forces vary over time. The aerodynamic excitation arises from the spatially periodical flow of steam through the stator blade cascade. In this paper, we attempt to model flow-induced instabilities with the Van der Pol model linked to relative motion between neighbouring blades. The proposed modal synthesis method as ROM is a computationally efficient solution allowing substantial parametrization. The effect of the angles of contact surfaces on the wheel dynamics and on the level of the self-excitation suppression will be discussed herein.

2

Influence of the specific load on stability and vibrations of the multimember column with internal cracks

Sokół Krzysztof, Kuliński Krzysztof

Bulletin of the Polish Academy of Sciences. Technical Sciences

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2023

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Vol. 71, nr 4

art. no. e146408

EN

Slender systems are mostly studied when Euler’s load or follower load is considered. The use of those types of external loads results in well-known divergence or flutter shape of the characteristic curve. In this study, one takes into account the specific load which allows one to obtain an interesting divergence – pseudo flutter shape of characteristic curves on the external load–vibration frequency plane. The curves can change inclination angle as well as one can observe the change in vibration modes along them. The shape of those curves depends not only on the parameters of the slender system but also on loading heads that induce the specific load. In this study, one considers the slender multimember system in which cracks are present and weaken the host structure. The results of theoretical as well as numerical simulations are focused on the influence of the parameters of the loading heads on vibrations, stability, and loading capacity of the investigated system as well as on the possibility of partial reduction of unwanted crack effect.

3

Analytical solutions of supersonic flutter problems for laminated multilayered composite plates and cylindrical shells

Flis Justyna, Muc Aleksander

Vibrations in Physical Systems

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2020

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Vol. 31, nr 3

art. no. 2020305

EN

For laminated rectangular plates and cylindrical shells the analytical, closed form solution is found using classical and first order transverse shear formulations of kinematical hypothesis. The analysis is carried out for a specific boundary conditions dealing with two opposite edges being simply supported. The evaluated method of solution can be treated as the benchmark for numerical analysis since analytical results can be obtained directly with the use of the symbolic packages, such as Mathematica, Maple or Matlab.

4

Stability and bifurcation analysis of an overhung rotor with electromagnetic actuators

Przybyłowicz Piotr M., Kurnik Włodzimierz

Journal of Theoretical and Applied Mechanics

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2020

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Vol. 58 nr 2

525--539

EN

A rotating system consisting of a slender massless viscoelastic shaft simply supported in rolling bearings and a rigid massive disc mounted to the overhung end of the shaft is considered to study its stabilization against flutter. Instability and transverse vibration occurs due to the internal friction in the shaft. It is shown in the paper that the disc can be stabilized and its bifurcating self-excited vibration can be effectively reduced and modified by contactless radial magnetic actuators, using two alternative control strategies – semi-active utilizing constant or rotation-dependent actuator voltage or fully active with closed-loop state-dependent feedback. The near-critical transverse disc vibration is analyzed using the theory of Hopf bifurcation. Smooth, soft-type self-excitation is presented after activation of the dynamic vibration control which prevents the system from sudden jumps of vibration amplitude near the critical point.

5

Methods of modern aircraft aeroelastic analyses in the institute of aviation

Chajec W.

Journal of KONES

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2018

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Vol. 25, No. 4

33--42

EN

The aeroelastic phenomena analysis methods used in the Institute of Aviation for aircraft, excluding helicopters, are presented in the article. In industrial practice, a typical approach to those analyses is a linear approach and flutter computation in the frequency domain based on normal modes, including rigid body modes and control system modes. They are determined by means of the finite element method (FEM) model of structure or a result of ground vibration test (GVT). In the GVT case, relatively great vibration amplitudes are applied for a good examination of a not truly linear structure. Instead or apart from the measure of generalized masses, a very theoretical model is used for mode shapes cross orthogonality inspection and improvement. The computed or measured normal mode sets are the basis for flutter analysis by means of several tools and methods, like MSC.Nastran and ZONA commercial software as well as our own low-cost software named JG2 for the flutter analysis of low speed aeroplanes and for a preliminary analyses of other aircraft. The differences between the methods lie in determining normal mode set, unsteady aerodynamic model, flutter equation formulation, time of analysis, costs, etc. Examples with results comparison obtained by means of distinguished methods are presented. Some works in the field of aeroelastic analysis with nonlinear unsteady aerodynamic in the time domain using Tau-code and ANSYS Fluent software were also performed. Aeroelastic properties of deformed structures, like a sailplane with deflected wings, can be also analysed. The simplest way of this analysis is the semi-linear approach in which the deflections modify the aircraft geometry for normal modes determination.

6

3D flutter analysis of 11th standard configuration using ANSYS CFX

Kubitz L., Rzadkowski R., Kunicka Z.

Zeszyty Naukowe. Cieplne Maszyny Przepływowe - Turbomachinery / Politechnika Łódzka

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2014

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nr 146

119--140

EN

In this study, numerical simulations of 3D viscous flutter were performed and compared with the available experimental results using ANSYS CFX. The calculations were carried out for bending oscillations of the cascade known as the Eleventh Standard Configuration. The developed numerical algorithm solves the 3D Reynolds-averaged Navier-Stokes equation together with k-ω, SST, S-A models using the explicit monotonous second-order accurate finite-volume scheme and moving hybrid H-O structured grid. Comparison of the calculated and the experimental results for the Eleventh Standard Configurations has shown good quantitative and qualitative agreement for local performances (unsteady pressure amplitude and phase distribution) at off-design conditions, benchmark solutions are provided for various values of the inter-blade phase angle 0, 180, -90, 90 deg.

7

Ziegler Problem Revisited : Flutter and Divergence Interactions in a Generalized System

Kurnik W., Bogacz R.

Machine Dynamics Research

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2013

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Vol. 37, No. 4

71-84

EN

The classic Ziegler column under compressive follower force is considered now in a generalized form including a stabilizing spring acting at the end of the column. Damping in the joints is neglected. With increasing spring stiffness from zero to infinity one can observe evolution of the dynamic properties of the column from the original free-end form to the limit configuration with the end simply supported. Attention is focused not only on the stability of the straight-form equilibrium of the column but also on the eigen-frequencies, eigen-values and eigen-forms of motion of the column near the equilibrium. The follower force is responsible for loss of stability but the stabilizing spring considerably affects the stability boundary. The most interesting phenomena occur in the low zone of the spring stiffness where quite complicated interactions between flatter and divergence is observed under increasing follower force. Detailed analysis of the eigen-values is presented in the four regions of the parameter space to demonstrate new phenomena not reported in the literature.

8

Critical flow velocity in a pipe with electromagnetic actuators

Szmidt T., Przybyłowicz P.

Journal of Theoretical and Applied Mechanics

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2013

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Vol. 51 nr 2

487--496

EN

We study the influence of electromagnetic damping on the dynamics of a pipe conveying fluid. Pipes supported at both ends as well as cantilever ones (both discharging and aspirating the fluid) are considered. We assume physical parameters of the systems which allow an experimental verification of results. We develop simple methods of calculation of the internal and external damping coefficients which are based on known models, and do not require experiments. The governing partial equation of the pipe is discretised with Galerkin’s procedure, and the stability of the resultant dynamical system is determined with eigenvalues of its linearization. The actuators destabilise the pipe supported at both ends, but can remarkably improve stability of cantilever ones. The effect of magnetic damping strongly depends on the position at which actuators are attached to the pipe.

PL

W pracy przeprowadzono badania wpływu tłumienia elektromagnetycznego na właściwości dynamiczne przewodu z przepływającym płynem. Rozważono przewody podparte obustronnie swobodnie oraz zamocowane wspornikowo (dla obydwu przypadków ruchu płynu, tj. rury wyrzucającej czynnik na zewnątrz oraz rury ssącej). Założono takie parametry fizyczne układu, które pozwalają na weryfikację eksperymentalną uzyskanych wyników. Zaproponowano proste metody pozwalające na oszacowanie wartości tłumienia zewnętrznego i wewnętrznego oparte na znanych modelach i nie wymagających przeprowadzania doświadczeń. Równanie różniczkowe cząstkowe ruchu przewodu z przepływem dyskretyzowano metodą Galerkina, a po wyznaczeniu wartości własnych układu zlinearyzowanego, określono jego stateczność. W wyniku przeprowadzonych analiz zaobserwowano, że aktuatory elektromagnetyczne destabilizują przewód obustronnie podparty, ale znacząco poprawiają stateczność rury wspornikowej, przy czym efekt tłumienia magnetycznego silnie zależy od położenia aktuatorów względem miejsca zamocowania takiego przewodu.

9

An active electromagnetic stabilization of the Leipholz column

Szmidt T., Przybyłowicz P.

Archives of Control Sciences

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2012

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Vol. 22, no. 2

161-174

EN

We study the application of electromagnetic actuators for the active stabilization of the Leipholz column. The cases of the compressive and tensional load of the column placed in air and in water are considered. The partial differential equation of the column is discretized by Galerkin's procedure, and the stability of the obtained control system is evaluated by the eigenvalues of its linearization. Four different methods of active stabilization are investigated. They incorporate control systems based on feedback proportional to the transverse displacement of the column, its velocity and the current in the electromagnets. Conditions in which these strategies are effective in securing safe operation of the column are discussed in detail.

10

Influence of mesh density on 2D viscous flutter in a turbomachinery cascade

Pająk A., Soliński M., Rządkowski R.

Zeszyty Naukowe. Cieplne Maszyny Przepływowe - Turbomachinery / Politechnika Łódzka

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2011

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nr 140

169-178

EN

In this study numerical simulations of 2D viscous flutter were performed and compared with available experimental results for various mesh densities and flow parameters. Calculations were carried out for the bending oscillations of an Eleventh Standard Configuration cascade. ANSYS CFX code was used for the SST, SA and k-ω turbulence model calculations.

11

Relation between shape and the phenomenon of flutter for bridge deck-like bluff bodies

Nowicki T., Flaga A.

Archives of Mechanics

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2011

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Vol. 63, nr 2

201-201

EN

The paper deals with experimental analysis of the influence of cross–section shape of a body on the phenomenon of flutter. The aeroelastic section model that was the object of study in a laboratory corresponded to a central section of a long bridge deck. Such structures are subjected to flutter like aeroplane wings or helicopter rotors. Unlike in aviation, bridge decks cross-sections can be designed much more freely. The analysis is concentrated on a problem how the cross-section shape of a deck can affect interaction with incoming air stream. The results obtained suggest that the influence is closely related to elastic characteristics of a deck.

12

Aeroelastic computation using the beddoes-leishman dynamic stall model

Dumitrescu H., Frunzulica F.

International Journal of Applied Mechanics and Engineering

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2008

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Vol. 13, no 1

63-73

EN

The application of the semi-empirical dynamic stall model by Beddoes and Leishman (B-L) on aeroelastic conditions is described. The approach is to couple the structural model to the nonlinear Beddoes-Leishman model and integrate through time. The nonlinear aerodynamic effects are included in the B-L model and thus, the behavior of the unstable system can be investigated after flutter has occurred, i.e., periodicity (limit cycle oscillations), chaos, etc., can be analyzed. The B-L time integration approach is applied to quickly decide test cases for the unsteady CFO computations, which are much more time consuming. Computations using a NavierStokes solver are compared to the present results.

13

Mechatronic approach towards flight flutter testing

Karpiel G., Petko M., Uhl T.

Diagnostyka

|

2007

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nr 4(44)

99-104

EN

The paper presents an idea of identification of the flutter phenomena during a flight. The proposed flutter detection algorithm is based on the identification of natural frequencies and modal damping ratio for an airplane structure based on in-flight vibration measurements. The procedure can be realized during a flight using measured actual vibration. The algorithm is based on recursive identification of model parameters and wavelets based signal filtering. The real-time realization is implemented in hardware and tested during a flight. FPGA technology is used for the hardware design. The results of a test of the hardware system prototype are presented.

PL

W artykule przedstawiono implementację algorytmu identyfikacji flatteru podczas lotu. Przedstawiony algorytm bazuje na identyfikacji częstotliwości własnych oraz współczynnika tłumienia poprzez pomiar drgań struktury samolotu. Zaprezentowana procedura może być realizowana podczas lotu wykorzystując dostępne sygnały z czujników drgań. Algorytm wykorzystuje transformatę falkową jako filtr częstotliwościowo-czasowy dla izolacji pojedynczych postaci drgań o parametrach zmiennych w czasie. Realizację w czasie rzeczywistym wykonaną w postaci sprzętowej sprawdzono podczas testowego lotu. Do zaprojektowania struktury sprzętowej użyto technologii FPGA. Przedstawiono rezultat działania prototypowego urządzenia.

14

Identyfikacja aerosprężystych własności laminatowej konstrukcji nośnej na przykładzie koncepcyjnego samolotu szkolno-treningowego

Olejnik A., Kachel S., Rogólski R., Leszczyński P.

Biuletyn Wojskowej Akademii Technicznej

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2007

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Vol. 56, nr 3

73-110

PL

W opracowaniu przedstawiono rozwiązanie zagadnienia aerosprężystej niestateczności kompozytowej konstrukcji płatowcowej. Wdrożono wyznaczania krytycznej prędkości i postaci flatteru samolotu przy wspomaganiu komercyjnego pakietu obliczeniowego. W oparciu o dyskretny model struktury do analiz metodą elementów skończonych oraz model panelowy do aerodynamiki niestacjonarnej wyznaczono numerycznie prędkości wystąpienia drgań samowzbudnych. W ramach nadawania własności materiałowych elementom wirtualnej struktury zrealizowano koncepcję modelowania kompozytu warstwowego. Model obliczeniowy konstrukcji zweryfikowano na podstawie wyników doświadczalnych badań stoiskowych.

EN

The paper presents a solution of aeroelastic instability phenomena of composite airframe. A method of critical flutter airspeed evaluation was applied by support of professional software package. Numerical values of self-excited vibration velocities were determined on the basis of integrated aeroelastic model including a structural FEM model and a panel aero model for unsteady aerodynamics. A conception of laminate composite modelling was put into effect. The aircraft structure discreet model was verified then by equalling the results and the results from test-bed experiments.

15

Numeryczne badanie wpływu orientacji wzmocnienia na własności aerosprężyste laminatowych płyt wolnonośnych

Olejnik A., Kachel S., Rogólski R., Leszczyński P.

Biuletyn Wojskowej Akademii Technicznej

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2006

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Vol. 55, nr 4

45-70

PL

Niniejszy artykuł dotyczy zagadnienia optymalizacji aerosprężystego układu powierzchniowego w odniesieniu do struktury laminatowej. Przy wspomaganiu komercyjnego pakietu obliczeniowego wykonano serie analiz w zakresie statyki, dynamiki i flatteru wolnonośnych płyt wykonanych z laminatu węglowego. Próba znalezienia optymalnych cech aerosprężystych rozpatrywanych modeli polega na dobraniu najbardziej korzystnej orientacji ułożenia tkaniny względem kierunku odniesienia. Celem doboru różnych kątów ukierunkowania tkaniny jest wybranie konfiguracji o najlepszych własnościach ze względu na odkształcalność statyczną i niestateczność dynamiczną spowodowaną drganiami samowzbudnymi. Dla zaprezentowanych konfiguracji konstrukcyjnych wykonano cykl obliczeń w celu określenia wielkości odkształceń oraz krytycznych prędkości flatteru. Wyniki analiz przedstawiono na rysunkach oraz wykresach ilustrujących zmianę badanego parametru w obliczeniowym zakresie kątów orientacji wzmocnienia.

EN

This paper concerns optimization of aeroelastic surface-shaped system in relation to laminated structure. By the use of one commercial computing program, some analyses were performed on static displacement, dynamics and flutter of cantilevered plates made of carbon fiber laminate. The trial to estimate optimal aeroelastic properties of the considered models consists in matching the best carbon fabric orientation in respect of main reference direction. There could be many laminate orientations in range of 0-90° and the main task is to select the one that gives best properties in respect of static deformations and dynamic instability due to flutter. Some numerical computations were performed for the discussed structure configurations in order to determine displacement sizes and critical flutter airspeeds. The results were shown in the pictures and diagrams illustrating the change of the examined parameter in a computational range of reinforcement orientation angles.

16

The flutter effect in rotating machines

Kiciński J.

Bulletin of the Polish Academy of Sciences. Technical Sciences

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2004

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Vol. 52, nr 3

195-207

EN

The considerations presented in the paper relate to one of the most intriguing phenomena, which is the development of oil whirls and oil whips in rotors with journal bearings. This effect is sometimes referred to as flutter, as its origin is in some relation to self-exciting vibrations of the system. Despite the fact that the flutter has been an object of investigation in numerous research centres all over the world, its nature has not been sufficiently recognized yet. The present paper delivers a description of particular phases of development of the hydrodynamic instability and proposes diagnostic determinants for this state. The object of investigations also included bearings with hybrid lubrication and siphon pockets in the oil gaps. The answer has been received to the question whether the self-exciting vibrations in rotating machines can be avoided, or reduced by means of additional oil supply having the form of siphon oil.

17

High altitude long endurance unmanned aerial vehicle of a new generation - a design challenge for a low cost, reliable and high performance aircraft

Goraj Z., Frydrychewicz A., Świtkiewicz R., Hernik B., Gadomski J., Goetzendorf-Grabowski T., Figat M., Suchodolski S.

Bulletin of the Polish Academy of Sciences. Technical Sciences

|

2004

|

Vol. 52, nr 3

173-194

EN

This paper describes a design process of HALE PW-114 sensor-craft, developed for high altitude (20 km) long endurance (40 h) surveillance missions. Designed as a blended wing (BW) configuration, to be made of metal and composite materials. Wing control surfaces provide longitudinal balance. Fin in the rear fuselage section together with wingtips provide directional stability. Airplane is equipped with retractable landing gear with controlled front leg that allows operations from conventional airfields. According to the initial requirements it is twin engine configuration, typical payload consists of electro-optical/infra-red FLIR, big SAR (synthetic aperture radar) and SATCOM antenna required for the longest range. Tailless architecture was based on both Horten and Northrop design experience. Global Hawk was considered as a reference point - it was assumed that BW design has to possess efficiency, relative payload and other characteristics at least the same or even better than that of Global Hawk. FLIR, SAR and SATCOM containers were optimised for best visibility. All payload systems are put into separate modular containers of easy access and quickly to exchange, so this architecture can be consider as a "modular". An optimisation process started immediately when the so-called "zero configuration", called PW-l11 was ready. It was designed in the canard configuration. A canard was abandoned in HALE PW-113. Instead, new, larger outer wing was designed with smaller taper ratio. New configuration analysis revealed satisfactory longitudinal stability. Calculations suggested better lateral qualities for negative dihedral. These modifications, leading to aerodynamic improvement, gave HALE PW-114 as a result. The design process was an interdisciplinary approach, and included a selection of thick laminar wing section, aerodynamic optimisation of swept wing, stability analysis, weight balance, structural and flutter analysis, many on-board redundant systems, reliability and maintability analysis, safety improvement, cost and performance optimisation. Presented paper focuses mainly on aerodynamics, wing design, longitudinal control and safety issues. This activity is supported by European Union within V FR, in the area Aeronautics and Space.

18

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.

Rządkowski R., Gnesin V.

Advances in Manufacturing Science and Technology

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2003

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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.

19

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

Gnesin V., Rządkowski R.

Transactions of the Institute of Fluid-Flow Machinery

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2002

|

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.

20

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

Rządkowski R., Gnesin V.

Transactions of the Institute of Fluid-Flow Machinery

|

2002

|

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.