A Theoretical Approach of Thrust Oscillations in Solid Rocket Motors
- Paper number
IAC-05-E2.2.08
- Author
Mr. François Chedevergne, Office National d’Etudes et de Recherches Aérospatiales (ONERA), France
- Coauthor
Mr. Grégoire Casalis, Office National d’Etudes et de Recherches Aérospatiales (ONERA), France
- Year
2005
- Abstract
Large solid rocket motors exhibit undesirable thrust oscillations during their firing. These oscillations are connected to inflow pressure fluctuations induced by flow instabilities. The intrinsic stability of the main flow is revisited thanks to a general linear stability approach. The main flow model is the flow induced by wall injection in a semi-infinite cylinder. An analytical solution was found by Taylor and then used successfully for motors flow calculations by Culick. This is the so-called Taylor-Culick flow. As the main flow is non-parallel, the classical stability theory based on a wave-like form decomposition for the perturbation field leads to a non-consistent approach. To avoid this problem, a harmonic perturbation, taking into account the non-parallel nature of the mean flow, is introduced into the linearized Navier-Stokes equations. A collocation method based on chebyschev polynomials is used to discretize the system of partial differential equations with respect to the spatial coordinates. This leads to an eigenvalue problem, solved using the Arnoldi's procedure. The main result is that the set of eigenvalues is revealed to be discrete. Thus, only some discrete frequencies may exist in the motor (as eigenmodes). On one hand, these modes are predicted to be temporally stable. On the other hand, the associated eigenfunctions are exponentially growing in the streamwise direction. The results are then compared to reduced scale motors measurements and also to cold gas set-up measurements that exhibit thrust oscillations. The observed good agreements allow to define the relevant parameter that governs the oscillations. This parameter is the ratio of the gas injection velocity (linked to the combustion velocity of the propellant) and the inflow radius (linked to the burned mass). Short-time Fourier transforms of unsteady fluctuating pressure signals highlight the coexistence of several modes in specific ranges of frequency linked to the longitudinal acoustic frequencies. As the theoretical results indicate that the calculated modes have to be damped in time, an exciting frequency is believed to interfere. For solid rocket motors, the longitudinal acoustic modes play a major role and are believed to be those sources of excitation. However, those sources can be from different origins as shown by cold-gas experiments. The pressure fluctuations, and consequently the thrust oscillations, only arise after a certain time. At the beginning of the firing, the aspect ratio of the motors (inflow radius / length) is very small and then the flow is expected to become turbulent soon in the streamwise direction. The turbulent dissipation prevents the growth of coherent vortex. As the inflow radius increases, due to the propellant combustion, the flow becomes laminar in the major part of the pipe. This allows the growth of some frequencies. According to that new approach, the thrust oscillations are thus linked to the hydrodynamic modes of the main flow, coupled themselves to an external source. This shed light in a new way on the understanding of the thrust oscillations arising. Further investigations may explain the complex interaction that seems to exist between the computational modes and the external source of excitation, like for instance the longitudinal acoustic modes.
- Abstract document
- Manuscript document
IAC-05-E2.2.08.pdf (🔒 authorized access only).
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