Parametric Instability of Pressurized Propellant Tanks

Paper number

IAC-05-C2.1.A.02

Author

Dr. Jochen Albus, EADS Astrium GmbH, Germany

Coauthor

Dr. Stefan Dieker, Germany

Coauthor

Dr. Andreas Rittweger, EADS Astrium Space Transportation, Germany

Coauthor

Prof. Huba Öry, Aachen University of Technology, Germany

Year

2005

Abstract

Pressurized propellant tanks might become dynamically unstable with detrimental dynamic responses, when a dynamic excitation leads to a coupling of axis-symmetric modes and ovalization modes and when the damping in the responding mode is not sufficiently high. This phenomenon can be identified in most cases as a Parametric Instability. Such a Parametric Instability was observed during the dynamic qualification test campaign of the ARIANE 5 cryogenic upper stage ESC-A under certain test conditions. The Parametric instability was identified during the sine vibration test campaign, analytically predicted and finally the problem was solved successfully. 

This paper describes the phenomenon of the Parametric Instability of pressurized propellant tanks and presents an analytical methodology to assess the risk of the occurrence of a Parametric Instability. 

The phenomenon of the Parametric Instability will be first explained by an Euler beam analogy. Besides the Euler Beam Analogy, the phenomenon of the propellant tank Parametric Instability can be explained by an oscillating eigenfrequency of the shell ovalization modes.

When the propellant tank is excited with a sinusoidal base motion in its axis-symmetric modes, a dynamic pressure on the tank shell occurs. This dynamic pressure changes the stiffness of the tank (circumferential bending stiffness) too and by this shifts the eigenfrequencies of the ovalization modes periodically. As the dynamic pressure oscillates with the eigenfrequency of the excited axis-symmetric mode, also the eigenfrequency of the ovalization mode will oscillate with this frequency. By this a parameter of the governing differential equation is no more constant.

Both ways, describing the phenomenon of the Parametric Instability, lead to formulation of a Mathieu-type differential equation with the same parameters. 

The Mathieu Stability Chart will be determined analytically, including the damping of the responding mode as parameter. The Parametric Instability risk assessment is supported by experimental determination of the parameters of the Mathieu equation as well as by experimental determination of the damping of the responding modes.

Analytical methods enable to predict the growth-rate of the dynamic response in case of instability, taking into account the internal damping. Even in case of instability failure occurs only if the duration of the excitation and the actual growth-rate lead to detrimental response levels.

Moreover, the presented analysis methods enable to predict the risk of Parametric Instability and to avoid it by appropriate design of the propellant tank.

Abstract document

IAC-05-C2.1.A.02.pdf

Manuscript document

IAC-05-C2.1.A.02.pdf (🔒 authorized access only).

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