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Low order modeling of vortex driven self-sustained pressure pulsations in solid rocket motors - Lionel Hirschberg - Ph.D. Thesis - Free download

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VKI PHDT 2019-05, Lionel Hirschberg, Low order modeling of vortex driven self-sustained pressure pulsations in solid rocket motors, ISBN 978-2-87516-141-3, 217 pgs


Low order modeling of vortex driven self-sustained pressure pulsations in solid rocket motors - Lionel Hirschberg - Ph.D. Thesis - Free download

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Low order modeling of vortex driven self-sustained pressure pulsations in solid rocket motors
By Lionel Hirschberg

PhD Thesis from the von Karman Institute / Université Paris-Saclay, January 2019, ISBN 978-2-87516-141-3, 217 pgs



Solid Rocket Motors (SRMs) can display self-sustained acoustic oscillations driven by coupling between hydrodynamic instabilities of the internal flow and longitudinal acoustic standing waves. The hydrodynamic instabilities are triggered by the acoustic standing wave and results in the formation of coherent vortical structures. For nominal ranges of flow conditions the sound waves generated by the interaction between these vortices and the choked nozzle at the end of the combustion chamber reinforces the acoustic oscillation. Most available literature on this subject focuses on the threshold of instability using a linear model. The focus of this work is on the prediction of the limit-cycle amplitude. The limit cycle is reached due to nonlinear saturation of the source, as a consequence of the formation of large coherent vortical structures. In this case the vortex-nozzle interaction becomes insensitive to the amplitude of the acoustic standing wave. Hence, one can focus on the sound generation of a vortex with the nozzle. Sound production can be predicted from an analytical two-dimensional planar incompressible frictionless model using the so-called Vortex Sound Theory. In this model the vorticity is assumed to be concentrated in a line vortex. Experiments indicate that the volume of cavities around so-called “integrated nozzles” have a large influence on the pulsation amplitude for large SRMs. This is due to the acoustical field normal to the vortex trajectory, induced by the compressibility of the gas in this cavity. As an alternative to the incompressible analytical model a compressible frictionless model with an internal Euler Aeroacoustic (EIA) flow solver is used for simulations of vortex-nozzle interaction. A dedicated numerical simulation study focusing on elementary processes such as vortex-nozzle and entropy spot-nozzle interaction allows a systematic variation of relevant parameters and yields insight which would be difficult by means of limit cycle studies of the full engine. A systematic study of the vortex-nozzle interaction in the case of a choked nozzle has been undertaken by varying: the upstream Mach number, the vortex-core radius, the upstream point where the vortex is released and the vortex circulation. The results are summarized by using a lumped element model for plane wave propagation, which is based on theoretical scaling laws. This model provides physical insight and predicts the acoustic pulse amplitude due to vortex nozzle-interaction within 25%. Simulations are made for integrated nozzles with a surrounding cavity and nozzle inlets mounted flush in a wall normal to the combustion chamber wall. The Euler code is also used to explore the potential use of nozzle with a gradual ramp as an inlet. Such a nozzle could reduce the limit-cycle pulsation amplitude. From EIA simulations it appears that sound due to vortex-nozzle interaction is mainly generated during the approach phase and that for the relevant parameter range there is no impingement of the vortex on the nozzle wall as has been suggested in the literature. In the incompressible analytical model the effect of the nozzle cavity is represented by a fluctuating volume line source. Using an energy balance approach, a single fit-parameter model is formulated which qualitatively predicts limit-cycle observations in cold gas-scale experiments reported in the literature. Finally the Euler model is used to compare the sound production by vortex-nozzle interaction with that due to the ingestion of an entropy non-uniformity also called entropy spot. In addition to insight, this study provides a systematic procedure to develop a lumped element model for the sound source due to non-homogeneous flow-nozzle interactions in SRMs. Such lumped models based on experimental data or a limited number of flow simulations can be used to ease the design of SRMs.

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