Channel flow induced by wall injection of fluid and particles

Abstract

The Taylor flow is the laminar single-phase flow induced by gas injection through porous walls, and is assumed to represent the flow inside solid propellant motors. Such a flow is intrinsically unstable, and the generated instabilities are probably responsible for the thrust oscillations observed in the aforesaid motors. However particles are embedded in the propellants usually used, and are released in the fluid by the lateral walls during the combustion, so that there are two heterogeneous phases in the flow. The purpose of this paper is to study the influence of these particles on stability by comparison with stability results from the single-phase studies, in a plane two-dimensional configuration. The particles are supposed to be chemically inert and of a uniform size. In order to carry out a linear stability study for this flow modified by the presence of particles, the mean particle velocity field is first determined, assuming that only the gas exerts forces on the particles. This field is sought in a self-similar form, which imposes a limit on the size of the particles. However, the particle mass concentration cannot be obtained in a self-similar form, but can only be described by a partial differential equation. The mean flow characteristics being determined, the spectrum of the discretized linear stability operator shows first that particle addition does not trigger any new ''dangerous'' modes compared with the single-phase flow case. It also shows that the most amplified mode in the case of the single-phase flow remains the most amplified mode in the case of the two-phase flow. Moreover, the addition of particles acts continuously upon stability results, behaving linearly with respect to the particle mass concentration when the latter is small. The linear correction to the monophasic mode, as well as the evolution of the modes with weak values of the particle mass concentration at the wall, are shown to be proportional to the ejection velocity of the particles. Then, the evolution of the eigenmodes from a given injection speed of the particles to another one is deduced by affinity, all other parameters being fixed. With a fixed Stokes number, stability results for a finite Reynolds number and results for the inviscid flow bring together when augmenting the particle mass concentration at the wall. Therefore, by knowing single-phase flow results and the evolution of stability characteristics of the two-phase flow in the inviscid case, it is easy to determine whether particle-laden Taylor flow is more or less stable than the monophasic Taylor flow for large particle mass concentration.

Boundary layers in a dilute particle suspension

“…In those circumstances, the irrotational assumption may not, in fact, be proper. It should be pointed out that the basic equation set (2.1), (2.2a) and (2.2b) falls into the same class as that taken in a number of recent successful studies by other authors, including Slater & Young (2001), Hernández (2001), Narayanan & Lakehal (2002) and Féraille & Casalis (2003).…”

Viscous Mean Flow Approximations for Porous Tubes with Radially Regressing Walls

“…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.…”

On the Lagrangian optimization of wall-injected flows: from the Hart–McClure potential to the Taylor–Culick rotational motion

“…For example, in the study of aeroacoustic instability (Griffond et al 2000;Chedevergne et al 2006), the Taylor-Culick model has provided a mean-flow approximation about which fluctuations may be induced (Majdalani 2001a;. In studying the effect of particle addition and particle mean-flow interactions, it has fallen at the epicentre of hydrodynamic instability theory (Féraille & Casalis 2003). In large-scale numerical simulations that involve particle burning and agglomeration, average speeds and accelerations within the chamber have routinely been estimated directly from the Taylor-Culick solution.…”

“…This is especially true in applications that require an analytical mean-flow formulation. Among the relevant examples, one may cite those studies concerned with vorticoacoustic wave propagation Majdalani 2001b) and hydrodynamic instability treatment in porous chambers with (Féraille & Casalis 2003) and without particle interactions (Ugurtas et al 2000;Fabignon et al 2003;Chedevergne et al 2006).…”