Surface pressure fluctuations in a separating turbulent boundary layer

Abstract

Measurements of surface pressure-fluctuation spectra and wave speeds are reported for a well-documented separating turbulent boundary layer. Two sensitive instrumentation microphones were used in a new technique to measure pressure fluctuations through pinhole apertures in the flow surface. Because a portion of the acoustic pressure fluctuations is the same across the nominally two-dimensional turbulent flow, it is possible to decompose the two microphone signals and obtain the turbulent flow contributions to the surface pressure spectra. In addition, data from several earlier attached-flow surface-pressure-fluctuation studies are re-examined and compared with the present measurements.The r.m.s. of the surface pressure fluctuation p′ increases monotonically through the adverse-pressure-gradient attached-flow region and the detached-flow zone. Apparently p′ is proportional to the ratio α of streamwise lengthscale to lengthscales in other directions. For non-equilibrium separating turbulent boundary layers, α is as much as 2.5, causing p′ to be higher than equilibrium layers with lower values of α.The maximum turbulent shearing stress τM appears to be the proper stress on which to scale p′; p′/τM from available data shows much less variation than when p′ is scaled on the wall shear stress. In the present measurements p′/τM increases to the detachment location and decreases downstream. This decrease is apparently due to the rapid movement of the pressure-fluctuation-producing motions away from the wall after the beginning of intermittent backflow. A correlation of the detached-flow data is given that is derived from velocity- and lengthscales of the separated flow.Spectra Φ (ω) for ωδ*/U∞ > 0.001 are presented and correlate well when normalized on the maximum shearing stress τM. At lower frequencies, for the attached flow Φ (ω) ∼ ω−0.7 while Φ(ω) ∼ (ω)−3 at higher frequencies in the strong adverse-pressuregradient region. After the beginning of intermittent backflow, Φ(ω) varies with ω at low frequencies and ω−3 at high frequencies; farther downstream the lower-frequency range varies with ω1.4.The celerity of the surface pressure fluctuations for the attached flow increases with frequency to a maximum; at higher frequencies it decreases and agrees with the semi-logarithmic overlap equation of Panton & Linebarger. After the beginning of the separation process, the wave speed decreases because of the oscillation of the instantaneous wave speed direction. The streamwise coherence decreases drastically after the beginning of flow reversal.