Effect of Helmholtz resonators on boundary-layer turbulence

Abstract

HELMHOLTZ resonators were investigated as a passive device for the purpose of modifying a turbulent boundary layer. Resonators, imbedded in a wall, also occur inadvertently when porous walls are used to reduce boundarylayer growth or as acoustic control devices in inlet ducts and combustors. In all cases it is of interest to know the effect of the resonators on the boundary layer. Helmholtz resonators are formed by cavities that are vented by a small orifice (see Fig. 1). They respond to excitation from the shear layer at the orifice as well as from incident acoustic waves. Previous experimental work '~4 has focused on the conditions for resonance in a single resonator. In the present study, a row of 10 resonators was positioned across the span of a wind-tunnel wall. Separate studies5'6 were conducted to determine the response of the resonator row to the boundary layer and the interaction that occurred between adjacent resonators. The relevant results are that peak response was achieved at a freestream velocity of 26.5 m/s, and the frequency and amplitude of the cavity pressure oscillations were 570 Hz and 143 dB (equivalent to 80% of the freestream dynamic pressure). In addition, adjacent resonators showed a strong antiphase locking with an average coherence coefficient of 70% and a phase lag of 150 to 180 deg. The phase locking between resonators was localized, and coherence decreased rapidly with resonators that were further away. Contents Experiments were conducted in a wind tunnel with a test section of 0.71 m x 1.0 m and 2.7 m long (28 in. x 40 in. x 9 ft). Ten resonators were formed with orifices of diameter D = 1.03 cm (0.406 in.) and 0.305 cm (0.120 in.) thickness. They were spaced 3.05 cm (1.20 in) on centers occupying the central 27.5 cm (10.8 in) of the 1.0 m (40 in.) span. At the location of the resonators, with flow parameters chosen to produce a resonant condition, the boundary layer had a thickness of d = 2.8 cm (1.1 in.), friction velocity UT = 1.0 m/s, and freestream speed of 26 m/s (58 mph). The corresponding Ret> was 5500. Measurement locations were chosen at the streamwise (X) positions X/D= -3,-0.5, 0.5, 3, 10,20,40, and 80 together with six spanwise (Z) positions, three directly in line with the resonator orifices and three half-way between the orifices. Laser velocimeter measurements of the streamwise and vertical velocity were obtained and processed to yield values of the