Linear Stability Analysis of the Quasi-One-Dimensional Flow in a Scramjet Engine
| This study presents a linear stability analysis of the flow within a dual-mode scramjet engine. The flow is assumed to be compressible, inviscid and quasi-one-dimensional, and the effects of area variation, wall friction, and distributed heat addition are considered. Unlike previous models that rely on asymptotic expansions about zero perturbation frequency, in this work the full linearized quasi-one-dimensional Euler equations are solved. Consequently, the spatial distributions of the flow disturbances throughout the entire scramjet domain are obtained and examined. Both modes of scramjet operation are analyzed – scram (supersonic throughout) and ram (thermally choked with an upstream shock wave), in contrast to the traditionally investigated choking due to geometric constraint. The nonlinear base flow, including the locations of the shock and the effective throat, is solved using a multi-domain spectral collocation method in conjunction with the shock-fitting approach, which is also applied to the linear perturbation equations. The analysis reveals that the energy of entropy, fast acoustic, and slow acoustic disturbances may grow downstream, particularly in regions of high heat release. Perturbations in the shock position and effective throat location are also quantified. |
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