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1 Research Bulletin / Warsaw University of Technology, Institute of Aeronautics and Applied Mechanics
1 Zeszyty Naukowe. Cieplne Maszyny Przepływowe - Turbomachinery / Politechnika Łódzka

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The numerical study of 3D flutter in a transonic blade row

Gnesin V., Rządkowski R., Kolodyazhnaya L

Zeszyty Naukowe. Cieplne Maszyny Przepływowe - Turbomachinery / Politechnika Łódzka

1999

nr 115

149--158

A three - dimensional nonlinear time - marching method and numerical analysis of 3D flutter for oscillating blade row has been presented. 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, as the interblade phase angle at which a stability (instability) would occur is 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 monotonous second - order accurate Godunov - Kolgan finite - volume scheme and moving grids. In he structure analysis the modal approach is used. The natural frequencies and modal shapes of the blade were calculated by using the different models: 3D finite element model; 1D blade model is of a one-dimensional beam described by an extended beam-theory including all important effects on a rotating blade.

The general parallel algorithm for a time-domain aeroelastic analysis

Dul F.

Research Bulletin / Warsaw University of Technology, Institute of Aeronautics and Applied Mechanics

1998

nr 8

145-152

The time-domain aeroelastic analysis (TDA) consists in direct integration the coupled structural and aerodynamic equations and analyzing the evolution of the solutions to obtain either the critical values of parameters (e.g., the flutter speed) or domains of different types of motion. This approach is quite different comparing with the frequency domain analysis (FDA), in which an assumed harmonic motion of a construction is investigated by inspecting eigenvalues of a matrix problem. The main disadvantage of TDA lies in its high computational costs, which comes from a necessity of repeating of integration of fluid dynamics (CFD) and structure dynamics (CSD) equations of motion. Since each of those repeated steps is independent of another, there is a natural possibility of parallelization of computations which should lead to an essential reduction of computational cost. It is shown in this paper that the above idea may be applied directly to the TDA resulting in a very efficient and sufficiently accurate parallel algorithm. The searching for the critical flutter velocity is accomplished by finding the root of a polynomial being an approximation of the coefficients of energy growth of a relative elastic motion of construction. This polynomial approximation is on a set of coefficients computed for the set of an undisturbed velocities of flow by the identification procedure based on the assumed exponential form of the energy. The energy for a given flow velocity is computed by a direct integration of the CFD and CSD equations. The parallelization of the above idea in carrying on the computation of the coefficients independently for each assumed of velocity, without transfer of data processors. It has been verified in tests performed on the CRAY Superserver 6400 machine, that the proposed parallel TDA algorithm enables one to compute the critical speed with accuracy than 1%, which is sufficient for the purposes. This accuracy depends on the assumption of exponential of the energy of the system. The proposed algorithm is suited well to the machines having moderate number of processors (about ten).