Closed cylindrical shell in a supersonic gas flow in the presence of a non-uniform temperature field

Аuthors

Baghdasaryan G. Y.^1*, Mikilyan M. A.^1**, Vardanyan I. A.^1***, Panteleyev A. V.^2****

1. Russian-Armenian University, 123, Hovsep Emin str., Yerevan, 0051, Armenia
2. ,

*e-mail: gevorg.baghdasaryan@rau.am
**e-mail: marine.mikilyan@rau.am
***e-mail: irena_123@bk.ru
****e-mail: avpanteleev@inbox.ru

Abstract

The article considers the problem of stability of a closed cylindrical shell under the action of an inhomogeneous temperature field and a supersonic gas flow, flowing around the shell. The authors obtained stability conditions for the unperturbed state of the aerothermoelastic system under consideration. It is shown, that the combined action of the temperature field and the ambient flow can control the process of stability, and change significantly the value of the flutter critical velocity by means of the temperature field.

The study is based on the following well-known assumptions:

a) Kirchhoff-Love's hypothesis on undeformable normals;

b) “The law of flat sections” in determining the aerodynamic pressure;

c) The linear law of temperature variation over the thickness of the shell;

d) The Neumann hypothesis on the absence of the temperature changes.

For simplicity and clarity, it is assumed that the heat exchange with the environment from the shell front surfaces proceeds according to the Newton – Richman law (the temperature remains constant on the surfaces), and the side surfaces are thermally insulated.

Under the action of a stationary temperature field, non-uniform in thickness, the shell bulges (with deflection and longitudinal movement) and, as a result, the aeroelastic pressure occurs. The above said bulging state is presumed unperturbed, and its stability is being studied under the action of the temperature field and the pressure of the flowing gas flow. Stability regions are plotted, and the the critical velocity values are obtained. Numerical computations revealed that accounting for the effect of thermoelastic stresses of the unperturbed state on the stability region is essential. The computational results of the critical velocity for the combined effect of the temperature field parameters and various values of geometric parameters are presented.

Keywords:

stability, temperature field, supersonic flow, flutter

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