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Nonlinear wave propagation in Rayleigh line base flow
M. Tyagi,
Published in
2006
Volume: 21
   
Pages: 15849 - 15879
Abstract
The goal of present work is to analytically investigate the process of nonlinear wave steepening, which leads to the shock formation, in a flow with heat addition or removal (Rayleigh line flow). The methodology used is the tracking of a propagating wave front in a hyperbolic system, whose evolution is governed by a first order nonlinear ordinary differential equation (Riccati's equation). The evolution equation can be exactly solved for the first derivative of an unsteady flow variable as function of Mach number of the base flow. This solution is used to develop the criteria of the shock formation in case of a compressive disturbance and quenching in case of an expansive disturbance. The expressions for the time and location of shock formation are derived In the Rayleigh line flow, two kinds of flow fields are identified: converging field and diverging field. According to the linear ray theory of wave propagation, the strength of the disturbance scales up in the converging field and scales down in the diverging field. The propagation of finite amplitude waves in the Rayleigh line flow exhibit many interesting behavior. In a diverging field, it is possible to prevent the steepening of a compression wave into shock. In a converging field, an expansion wave may quench or steepen into shock. However, these expansion shocks are unstable. Various regions are identified where shock formation is opposed or favored. It is found that there are regions in the base flow, where linear ray theory will predict the local amplification/attenuation of wave; however, shock formation in the flow may be opposed/favored.
About the journal
JournalCollection of Technical Papers - 44th AIAA Aerospace Sciences Meeting