Measurements, including the six components of the Reynolds-stress tensor, have been made along three generators of a centre-mounted circular cylinder with an elliptical nose cone. The pressure distribution was axisymmetric upstream and asymmetric downstream. The streamwise adverse pressure gradient led to almost zero skin friction in the direction of the limiting streamline, and the circumferential pressure gradient led to skew angles up to 30° in the vicinity of the wall. Special emphasis was laid on measurements in the wall region (y+ > 4), on the repeatability of these measurements and on an estimate of error bounds. The turbulence level encountered (up to 60% close to the wall) was much higher than in other threedimensional boundary-layer measurements. It has been shown that available measuring techniques have to be improved considerably or even abandoned if used under these conditions. Previous measurements of collateral velocity profiles in three-dimensional boundary layers will probably now have to be corrected for severe aerodynamic interference effects.It has been shown that the normal stresses , both characteristic of three-dimensional flow and caused by the circumferential pressure gradient, are influenced in different ways by the streamwise and circumferential pressure gradients. Spectra of u′-fluctuations are again similar to those obtained from two-dimensional boundary layers.Mean velocity profiles obey the linear and logarithmic law of the wall known from two-dimensional boundary layers both along a line of symmetry and in the threedimensional boundary layer. This may be because the streamwise pressure gradient dominates over the circumferential pressure gradient in this experiment.Finally it has been found that the skew angle γ of the Reynolds shear stress vector leads the skew angle ζ of the resultant velocity gradient or ‘mean shear’, both having the opposite sign of the skew angle β of the mean velocity vector except close to the wall. The ratio of Reynolds shear stress and turbulent kinetic energy is no longer ‘approximately’ constant as is assumed for two-dimensional boundary layers.

https://www.cambridge.org/core/services/aop-cambridge-core/content/view/S0022112081002371

Turbulence measurements in an adverse-pressure-gradient three-dimensional turbulent boundary layer along a circular cylinder

Flow-induced acoustic resonators are investigated as adaptive passive devices of separation control. Passive methods do not require an external energy input to manipulate the flow. In this case, fluid in a resonator oscillates by interaction with a cross-flow. Vortices generated at the orifice rearrange the flow downstream of the resonator so that additional momentum is transported into the near-wall region reducing or even eliminating reverse flow in the time-mean. The characteristic parameters of the control (fluctuating momentum flux in the orifice and frequency of the oscillation) can be adjusted to the flow conditions by changing the geometry of the resonator via an adaptive feed-back controller. To determine the natural frequencies and modes of resonators, analytical, numerical, and experimental methods were applied. A cross-flow can trigger resonance, if the frequency at which vortices form in the resonator orifice is close to one of these natural frequencies. The formation of vortices is conditioned by the geometry of the resonator neck. It was optimized such that vorticity production was enhanced resulting in a greater impact on a downstream separation region. Neighboring resonators exhibit a mode of anti-phase oscillation when arranged in spanwise direction. In the wake of the nodes of the oscillation, alternating longitudinal vortices form which increase the wall-shear stress in this region. Therefore, they contribute to a further reduction of a separation region. Compared with a single resonator, the radiated sound pressure is diminished by about an order of magnitude. The method was successfully applied to two flow configurations: the flow in a half diffuser with expansion angle 23◦ and the flow around an airfoil with FX 61-184 profile at high angle of attack (α = 23◦). In both cases, resonators were located just upstream of the separation line. Microphone measurements as well as phase-locked LDA and PIV measurements of the velocity fields in the resonator necks and in their wakes were performed. In the diffuser, a separating turbulent boundary layer was controlled by resonators of rectangular cross-section. The mode of oscillation was of the Helmholtz type. As a result, the extension of the closed reverse-flow region was reduced and the pressure recovery was increased by 13 % with one resonator, and by 18 % using two resonators that oscillated in anti-phase. To adapt the resonator to changing flow conditions, a closed-loop control concept based on an extremum seeking strategy was employed. Manipulated variables were the slit width and the height of the resonator cavity, while controlled variables were the sound pressure in the resonator and the pressure recovery in the diffuser. The global optimum of both parameters was found by the controller independent of the initial conditions. In the airfoil experiments, the laminar flow separating close to the leading edge of the wing section was manipulated by a resonator of circular cross-section oscillating in the first azimuthal cavity mode. The length of the separation region, which initially extended over the entire upper surface of the wing, was reduced. Velocity profiles measured downstream of the resonator showed an increase in momentum near the wall. Thereby, the suction peak in the pressure distribution was partially restored resulting in a lift gain of up to 36 % compared with the unforced case.

Separation Control by Flow-Induced Oscillations of a Resonator

Experimental techniques in three-dimensional turbulent boundary layers

Measurements of static pressure across the boundary layer on the wall of a circular cylinder with flow parallel to its axis display wall-interference effects which exceed corrections due to turbulence by almost an order of magnitude. Two different types of static pressure probe were investigated and gave different pressure distributions in the same boundary layer.

H. H. Fernholz

Papers

Wall interference effects of static pressure probes in an incompressible turbulent boundary layer