Abstract
This work relies on a compressible biglobal stability approach to describe the wave dynamics in a planar rocket chamber modeled as a porous channel. At first, the effectiveness of the compressible formulation is demonstrated by reproducing, in the absence of a mean flow, the Helmholtz frequencies and mode shapes. Next, the unsteady vorticity fluctuations, which intensify near the walls, are shown to be consistent with those associated with parietal vortex shedding. In this context, the penetration depth of vorticoacoustic waves is found to be strongly dependent on the penetration number. The latter gauges the cubic power of the injection speed to the product of kinematic viscosity, chamber half-height, and frequency squared. As for the strictly hydrodynamic modes, they seem to develop at the porous walls and grow in the core region, where the mean flow velocity is most appreciable. The ensuing modal analysis enables us to predict both longitudinal and transverse modes for several test cases, thus illustrating the tendency of hydrodynamic modes to intensify at higher injection speeds and longer chambers. Furthermore, by repeating the analysis with an active mean flow, one finds that successive increases in the injection speed gradually reduce the predicted frequencies relative to the eigenmodes obtained in a quiescent medium. Finally, recognizing that the spectral analysis is capable of recovering both longitudinal and transverse modes induced by acoustic and hydrodynamic disturbances, their coupled interactions, which often lead to specifically amplified frequencies in static tests, are robustly captured, namely, without resorting to any particular wave decomposition.
Highlights
Flow instability is commonly observed in various combustors, rockets, and gas turbine engines, where it is often referred to as “resonant combustion” or “combustion instability.” Characterized by internal pressure oscillations that appear at characteristic chamber frequencies, combustion instability is not exclusively associated with the instability of the combustion process itself
Their work is followed by several notable studies that may be worth enumerating. These include Sviridenkov and Yagodkin[4] and Beddini,[5] who explore the mean flow breakdown and turbularization in an idealized rocket chamber configuration; it is followed by the works of Casalis et al.,[6] who introduce the local-non-parallel (LNP) approach using a primitive variable formulation (PVF); Griffond et al.,[7] who focus on the incompressible Taylor–Culick flow stability in a semi-infinitely long porous cylinder;[8] and Griffond and Casalis,[9,10] who consider the planar counterpart, namely, the stability of the incompressible Taylor motion in a semi-infinitely long porous channel.[11]
Complementary studies include those by Feraille and Casalis,[12] who take into account the effect of particle entrainment on the porous channel flow stability, Phys
Summary
Flow instability is commonly observed in various combustors, rockets, and gas turbine engines, where it is often referred to as “resonant combustion” or “combustion instability.” Characterized by internal pressure oscillations that appear at characteristic chamber frequencies, combustion instability is not exclusively associated with the instability of the combustion process itself. Kovacic et al.[59] have managed to extract the acoustic transverse modes numerically, extending the validity of previous approaches to include high injection speeds and arbitrary chamber configurations Their results have compared favorably with the limited asymptotic solutions developed by Haddad and Majdalani.[57,58]. The resulting eigenvalue problem will be shown to provide accurate predictions of the oscillatory frequencies and mode shapes associated with the two-dimensional Taylor motion, helping to reconcile between hydrodynamic stability projections and other findings in the literature These include the ability to reproduce “in one swoop” the rich structures that accompany vorticoacoustic wave motion, with no need for unsteady flow decomposition and later reconstruction.
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