Spatial Instability Analysis Of Two-dimensional Channel Flow In The Slots Of SRM

Under some conditions, the exhaust gas flow in solid rocket motor such as the boosters of the European launcher Ariane V may exhibit large fluctuations at a frequency tuned to that of an longitudinal acoustic mode. The origin of such a resonance is not yet fully clear and its fundamental research will be needed. Previous research mainly concentrated on the so-called vortex shedding which occur down-stream of the discontinuities and induced oscillations by some mutation of geometry. Whereas a less explored mechanism for this type of flow is related to a purely hydro-dynamical instability. With the development of large segmented solid rocket motors in our country, it is of much importance to study on the issues of vortex shedding and induced spatial instabilities.In this paper, the exhaust gas flow in the slots of SRM three-dimensional star grain is simplified to the two-dimensional planar channel flow with fluid injection through porous walls. The local linear spatial theory is applied to the spatial instability of two-dimensional solid rocket motor grain. Stability analysis is performed using the small perturbation method in normal mode mathematical form, the governing equation is discretized using the fourth order accurate two-point compact scheme, Block LU factorization is employed and the complex spatial eigenvalue a which is determined by trial and error with a Newton-Raphson convergence method and to realize the solving of the linearized equations finally. The primary research is the spatial instability of Taylor mean flow, and two instability modes are obtained.The main conclusions are as follows:1. The calculation results of the mean Poiseuille flow profile agree well with that in related literatures, the validity of the Fortran code is proved. The eigenvalue accuracy determined by the fourth order accurate compact scheme is much higher than that by second order accurate box scheme, while the computation cost in the latter case is twice that in the former.2. Two instability modes that obtained from the literature under typical conditions are investigated, the corresponding amplitude curves of the fluctuating velocity in the stream-wise and transverse direction as well as the fluctuating pressure are presented, besides, the critical values and neutral curves for each mode are given under the condition of Re=900. It can be observed that the considered steady flow becomes unstable at a given distance away from the front wall, and then the distance is fixed. In the case of ω=30and x=10, the relations of the wave number and growth rate versus Reynolds number are presented, in which it can be found that the wave number and growth rate increase rapidly with the growth of Reynolds number in the case of the Reynolds number is small, while the wave number and growth rate are gradually less influenced by the Reynolds number when the Reynolds number grows large enough.3. The impact of porous wall injection speed on eigenvalue and eigensolutions is researched, and the evolution of stream-wise perturbation is studied. It can be concluded that, the maximum fluctuation amplitude of the eigensolutions continuously decreases along the flow direction, the eigensolutions damps to varying degrees in different directions, and the fluctuating velocity in the normal direction damps most severe.