Oscillations of the Supersonic Flow Downstream of an Abrupt Increase in Duct Cross Section

Abstract

T HE flow in a duct following a sudden change in section is described herein. Sonic flow through a convergent nozzle expands into a larger cross section to produce a mixed supersonic flow, and a low base pressure in the upstream corners. Under certain pressure conditions, oscillations occur in the duct and excessive externally generated noise results. These self-excited oscillations are caused by a boundarylayer/shock-wave interaction, and can exist in both circular and rectangular ducts. Many types of oscillations have been observed in different test arrangements, and a complete description of the flow may be found in the full paper.] Contents Most of the tests were carried out in a duct through which atmospheric air was induced by means of a downstream vacuum. A schematic diagram, characteristic of all the ducts tested, is shown in Fig. 1. Figure 2 shows typical interferograms for the different flow regimes obtained with a Mach-Zehnder interferometer in a rectangular duct, as the downstream receiver pressure pe increased. The base pressure typically varies with the ratio of pe to input stagnation pressure pa, as shown in Fig. 3. The flow structure can either be dominated by a series of reflected oblique shock waves or, when the base pressure pw increases, a single normal shock wave (Mach disk) close to the nozzle exit. For very low values of pe/pa, the reflected oblique shock waves are repeated in the stable structure shown in Fig. 2a. With higher values of pe/pa, flow separation occurs in the presence of oblique shock waves, as is shown in Figs. 2b and 2c, where the flow separates in the region of the third and second oblique reflections, respectively. In both cases the separation points oscillate through a small distance. The oscillations represented by Figs. 2b and 2c may be called the downstream and midstream oscillations, respectively. A further oscillation type occurs with the higher pe lpa values when the main flow structure changes from an oblique to a normal shock during a cycle. Figure 2d shows an instant during the oscillations which are of large amplitude and have been called the shock-pattern oscillations.2 As the pressure ratio pe/pa increases further the flow becomes stable with a normal shock wave in the duct (e.g., Fig. 2e for a pressure ratio pe/pa of 0.314). After a pressure range of stable flow an instability occurs in which the normal