Biglobal linear stability analysis of the flow induced by wall injection

Abstract

The hydrodynamic stability of the flow in a solid rocket motor is revisited using a general linear stability approach. A harmonic perturbation is introduced into the linearized Navier-Stokes equations leading to an eigenvalue problem posed as a system of partial differential equations with respect to the spatial coordinates. The system is discretized by a spectral collocation method applied to each spatial coordinate and the eigenvalues are determined using Arnoldi’s procedure. A special emphasis is placed on the boundary conditions. The main result is the discrete nature of the eigenvalue set. According to the present theory and the obtained results, only some discrete frequencies may exist in the motor (as eigenmodes). These frequencies only depend on the Reynolds number based on the injection velocity and the radius of the pipe flow. They are compared to measurements that have been performed at ONERA in one case with a cold-gas setup and in another case with a reduced scale live motor. Due to the agreement obtained with both experiments, the biglobal stability approach seems to offer new insight into the unresolved thrust oscillations problem.

A first step to Fluid-Structure interaction inside Solid Propellant Rocket Motors

“…[10], • and the shear layer instability. Jet tones are produced when unstable jet flow induced by an orifice is amplified by feedback generated as the jet impinges on a downstream surface.…”

“…During the past five decades, many studies on this topic have been conducted either analytically [10], numerically [11] or experimentally with more realistic cold flow apparatus (see [12][13][14]). In addition, for quantifying the effect of the obstacle deflection on flow, some numerical attempts to simulate inhibitors were conducted in a quasi-steady approach [15], but never been compared to experimental data.…”

Viscous Mean Flow Approximations for Porous Tubes with Radially Regressing Walls

“…(14)]. In reality, a small, rather negligible viscous layer develops at the headwall, whose analysis is described by Chedevergne et al [24].…”

“…This may be owed to its association with several studies involving hydrodynamic instability [23][24][25][26][27][28], acoustic instability [29][30][31][32][33][34][35], wave propagation [36][37][38][39], particle-mean flow interactions [40], and rocket performance measurements [41][42][43]. The Taylor-Culick solution was originally verified to be an adequate representation of the expected flowfield in SRMs both numerically by Sabnis et al [44] and experimentally by Dunlap et al [45,46], thereby confirming its character in a nonreactive chamber environment.…”

Internal Flows Driven by Wall-Normal Injection

“…It is usually referred to as the Taylor-Culick profile and remains one of the most cited models in rocket motor analysis. For example, Chedevergne et al (2006), Abu-Irshaid et al (2007), Griffond et al (2000), Beddini (1986) and Flandro & Majdalani (2003) made extensive use of the Taylor-Culick model as a basis for their instability work.…”