Application of a New Mathematical Tool (1d Spectral Portraits of Matrices) to the Problem of Aeroelasticity Vibrations of Turbine Blade Cascades

Годунов, С. К.; Kurzin, V. B.; Bunkov, V. G.; Sadkane, M.

doi:10.1615/tsagiscij.v40.i6.20

Cited by 3 publications

(3 citation statements)

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“…В этой связи отметим лекцию "Приложения нового математического аппарата одномерных спектральных портретов матриц к задачам об аэроупругих колебаниях", которую С. К. Годунов прочитал на Международном симпозиуме по нестационарной аэродинамике, аэроакустике и аэроупругости турбомашин (Москва, 2006 г.) [96], [97].…”

Section: математическая жизньunclassified

Сергею Константиновичу Годунову 85 Лет

Белых¹,

Brushlinskii²,

Vaskevich³

et al. 2015

Uspekhi Mat. Nauk

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Section: математическая жизньunclassified

Сергею Константиновичу Годунову 85 Лет

Белых¹,

Brushlinskii²,

Vaskevich³

et al. 2015

Uspekhi Mat. Nauk

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“…This method is rather common and can be applied to the flutter prediction of any aeroelastic structure. However, there are mathematical issues with finding the eigenvalues of complex nonsymmetric matrices [8]; also, computational resources comparable with the first method are necessary.…”

Section: Introductionmentioning

confidence: 99%

Experimental Validation of Numerical Blade Flutter Prediction

Vedeneev

Kolotnikov

Макаров³

2015

Journal of Propulsion and Power

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Blade flutter of modern gas-turbine engines is one of the main issues that engine designers have to face. The most used numerical method that is employed for flutter prediction is the energy method. Although a lot of papers are devoted to the analysis of different blade wheels, this method was rarely validated by experiments. Typical mesh size, time step, and various modeling approaches that guarantee reliable flutter prediction are not commonly known, whereas some examples show that predictions obtained through nonvalidated codes can be inaccurate. In this paper, we describe our implementation of the energy method. Analysis of convergence and sensitivity to various modeling abstractions are carefully investigated. Numerical results are verified by compressor and full engine flutter test data. It is shown that the prediction of flutter onset is rather reliable so that the modeling approaches presented in this paper can be used by other researchers for the flutter analysis of industrial compressor blades. Nomenclature f = natural frequency m = number of nodal diameters N = number of blades n = rotor speed W = work done by the unsteady pressure over one cycle of blade oscillation α = inlet angle of attack φ = 2π m∕N, interblade phase shift ω = 2πf, circular frequency

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“…An example of using such portraits for analysis of vibrations of mechanical systems was considered in [5].…”

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confidence: 99%

Determining dynamic characteristics of mechanical systems by the method of constructing one-dimensional spectral portraits of matrices

Kurzin

2008

J Appl Mech Tech Phys

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A number of important properties of vibrations of linear systems (the quality of stability of the systems, their conditionality with respect to the eigenvalues of the matrices, and the possibility of modeling systems with a large number of degrees of freedom by their subsystems with a smaller number of degrees of freedom), which can be determined by a new mathematical tool called "One-dimensional spectral portraits of matrices" developed under the guidance of S. K. Godunov, are considered. An example is given on constructing one-dimensional spectral portraits for matrices that describe aeroelastic vibrations of hydrodynamic cascades.

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Application of a New Mathematical Tool (1d Spectral Portraits of Matrices) to the Problem of Aeroelasticity Vibrations of Turbine Blade Cascades

Cited by 3 publications

References 0 publications

Сергею Константиновичу Годунову 85 Лет

Сергею Константиновичу Годунову 85 Лет

Experimental Validation of Numerical Blade Flutter Prediction

Determining dynamic characteristics of mechanical systems by the method of constructing one-dimensional spectral portraits of matrices

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