Nonlinear resonant interactions in internal cavity flows

Abstract

F the suggestion of Flandro and Jacobs that periodic vortex shedding from internal obstructions could produce significant oscillating pressure levels in turbulent duct flow, Culick and Magiawala, Dunlop and Brown, and Brown et at. presented a variety of results verifying the phenomenon of acoustic energy production by vortex shedding and interaction. In further investigation of some of the flow mechanisms involved in acoustic energy production by vortex shedding, Isaacson and Marshall presented measurements of oscillating velocity frequency spectra which indicated that in certain flow regimes, velocity'oscillations occur which satisfy the frequency resonant interaction. This Note presents results of bispectral cross-power measurements of trios of frequencies occurring in an internal cavity in a turbulent flow which provide additional evidence that these trios of frequencies are of quadratic interaction origin. These measurements were made in a subsonic wind tunnel which is driven by a centrifugal fan, driving air into a settling chamber which is 0.61 m on each side and 1.22 m long. The settling chamber is segmented and contains four damping screens, which act to reduce the turbulence of the flow into the test section. A converging section connects the settling chamber to the test section which is 0.178 m on each side and 2.44m long. The internal flow cavity is made up of four plexiglas restrictors, with the forward set of restrictors located 1.89 m downstream of the entrance to the test section. A schematic diagram of the flow cavity is shown in Fig. 1. For the measurements reported here, the gap between the forward pair of restrictors was 53.3 mm and the distance between the two pairs of restrictors was 101.6 mm. A TSI Model 1050 constant-temperature hot-film anemometer, together with a TSI Model 1055 linearizer, and a TSI Model 1057 signal conditioner were used for these measurements. The single sensor, located a distance of 16 mm behind the forward restrictor pair along .the flow axis of zero vertical velocity, was used to measure the velocity frequency spectrum presented in Fig. 2. The output of this sensor was also used to generate the bispectral measurements indicated in Fig. 3. The frequency spectra were obtained with a HewlettPackard Model 3590A wave analyzer and an HP Model 3594A sweeping local oscillator. The analog output of the analyzer was digitally processed with, a Hewlett-Packard Model 2240A measurement and control processor, with an HP-85 computer as the controller. The data were plotted on a Hewlett-Packard Model 7225A plotter. Note that the cavity configuration used in this experiment produces two converging, almost parallel, shear layers at the forward baffles. Kelly has shown that shear layers of this type produce instabilities of both subharmonic and superharmonic frequencies relative to the most unstable frequency determined by the Orr-Sommerfeld equations. Phillips has shown that waves of this type can be turned away from the critical region of the shear layer and