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

Abstract

International audienceA 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

Progress in Direct Noise Computation

“…The switching between the symmetrical and asymmetrical flow patterns as well as the predicted values for the base pressure have been accurately reproduced by the simulations. A case of strong coupling between shock oscillations and a longitudinal acoustic mode is also reported by Emmert et al [19] The simulation of such configurations involving turbulence, boundary layers, shocks and coupling through acoustic resonances is currently challenging. The hysteresis cycle described in figure 9 and the symmetric or asymmetrical state taken by the shock pattern is strongly dependent on the correct description of the turbulent boundary layers as well as of the impedance conditions at the boundaries of the computational domain.…”

“…This flow has been carefully studied in Emmert et al [19] by compressible largeeddy simulations based on a high-order algorithm and an additional non-linear adaptive filtering combined with high-order overlapping grid technique. Schlieren pictures of two computed regimes among others, are displayed in figure 10.…”

“…Schlieren pictures of two computed regimes among others, are displayed in figure 10. [19] for details.…”

Estimation of Automotive Wind Noise by Coupling Direct Noise Computation to Statistical Energy Analysis

“…The ability of Code_Safari to correctly reproduce the turbulent features and the sound sources of flows around academic geometries has been demonstrated by Daude et al 11 and Emmert et al 13 . The more complex geometry of a side car mirror over a flat plate has also been recently successfully tackled.…”

“…An emerging method for the numerical prediction of the aerodynamic noise inside a car is the coupling of an unsteady Computational Fluid Dynamics (CFD) solver to a vibro-acoustic Statistical Energy Analysis (SEA) solver 17,18 . The flow was simulated in this study using Code_Safari 11,13 Direct Noise Computation (DNC). Although this type of calculation is limited so far to simplified geometry, it is able to predict simultaneously the aerodynamic flow and the acoustic field by solving the full compressible three dimensional Navier-Stokes equations.…”