Numerical study of self-induced transonic flow oscillations behind a sudden duct enlargement

A sonic flow in a plane duct passing an abrupt increase in cross section is studied using compressible large-eddy simulations. Different flow patterns are likely to appear in this configuration according to the ratio between the downstream ambient pressure and the upstream reservoir pressure. For low pressure ratios, the flow is entirely supersonic in the channel and a steady symmetrical shock pattern is observed. For higher pressure ratios, the flow can be attached to one side of the channel with a jet-like shock cell structure, or can be characterized by strong oscillations of a single normal shock located near the sudden expansion, known as base-pressure oscillations in literature. A hysteresis phenomenon is found experimentally and the state reached by the transonic flow depends on the path followed by the pressure ratio. Moreover, a coupling of these base-pressure oscillations with the quarter-wavelength resonance of the duct can occur. All these regimes are numerically investigated and the results are favorably compared to available experimental data. A case of frequency locking of this self-excited mechanism is also reproduced, in agreement with a modeling of the resonator. The governing equations are solved using high-order central finite differences combined with an overset grid approach. The large-eddy simulations are based on a relaxation filtering and a nonlinear shock-capturing scheme is also implemented for shock waves.

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