Modeling Self-Oscillations of an Elastic Wing in the Transonic Flow

Аuthors

Kuz’mina S. I.

Central Aerohydrodynamic Institute named after N.E. Zhukovsky (TsAGI), 1, Zhukovsky str., Zhukovsky, Moscow Region, 140180, Russia

e-mail: kuzmina@tsagi.ru

Abstract

The article deals with the study of complex phenomena of dynamic aeroelasticity associated with the motion of the shock waves, such as flutter and limit cycles oscillation (LCO) in transonic flow.
Under conditions of mixed subsonic/supersonic flow-around, the energy method based on the analysis of the work of unsteady aerodynamic forces produced by the flow on the structure is being applied to solve the coupled problems of interaction between the structure and the flow. Numerical modeling of limit cycles oscillation was performed with the AIRTRAN program developed at TsAGI for solving aeroelasticity problems. The unsteady aerodynamic forces in transonic flow were being computed by the Godunov finite-difference method of integrating nonlinear Euler equations for an ideal gas. The problem of transonic LCO and their relationship with the specifics of pressure distribution and motion of shock waves over the wing surface were studied on the example of the CAST wing compartment. The self-oscillations modeling was performed to determine the effect on the aeroelastic characteristics of such parameters as excitation frequency, pitch oscillation amplitude and Mach number. Computational results were compared with the experimental data obtained from the research model with the supercritical CAST profile, which was tested in the TWG transonic wind tunnel. Computations were performed in a wide range of Mach numbers, including both subsonic (M = 0.7), transonic (M = 0.77 and M=0.8), and supersonic (M=1.02) flow-around modes of the wing.
The article presents computational results, including two types of distribution over the chord:
– operation of aerodynamic forces, produced by the flow, on the structure;
– the phase shift between the wing oscillations and the in dynamic pressure changing at the profile point.
The obtained results demonstrate that with transonic flow behind the oscillating shock front, an unsteady pressure component originates, which outruns the deflection angle. This leads to aerodynamic damping in the rear part of the wing. At the points of the profile that are ahead of the shock wave in the local supersonic zone, the phase lags are being realized, which leads to the negative damping occurrence. In this area of the wing, the aerodynamic forces perform positive work. Analysis of the presented dependencies of the work distribution on two parameters, namely the amplitude and frequency of oscillations, allows identifying the mechanism of the transonic LCO occurrence. The results of the numerical studies demonstrate that at a certain frequency (35 Hz), the work of the aerodynamic forces is positive at a small amplitude, but then it changes sign with the amplitude increase. Thus, it allows determining the limit cycle amplitude, at which the work of the aerodynamic forces during the oscillation period becomes equal to zero. The interval of the shock displacement along the chord herewith can be considered as a sort of a regulator of the self-oscillations amplitude. Indeed, since the increase of the shock oscillation interval occurs at the amplitude increase, the damping areas redistribute due to the positive damping area growth. This will lead automatically to the corresponding amplitude decrease. The reverse process will take place with the amplitude decrease.
The conducted studies demonstrate that the developed approach allows studying the LCO mechanism occurrence during the moving shock waves interaction with the elastic structure deformations.

Keywords:

transonic flutter, shock wave, amplitude of limit cycle oscillations, aerodynamic damping, elastic structure

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