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The structure of a separating turbulent boundary layer. Part 4. Effects of periodic free-stream unsteadiness

  • Roger L. Simpson (a1), B. G. Shivaprasad (a1) and Y.-T. Chew (a1) (a2)

Abstract

Unsteady separating turbulent boundary layers are of practical interest because of unsteady aerodynamic phenomena associated with blades in compressors and with helicopter rotors in translating motion during high-loading conditions. Extensive measurements of a steady free-stream, nominally two-dimensional, separating turbulent boundary layer have been reported by Simpson, Chew & Shivaprasad (1981a, b) and Shiloh, Shivaprasad & Simpson (1981). Here measurements are reported that show the effects of sinusoidal unsteadiness of the free-stream velocity on this separating turbulent boundary layer at a practical reduced frequency of 0·61. The ratio of oscillation amplitude to mean velocity is about 0·3.

Upstream of flow detachment, single- and cross-wire, hot-wire anemometer measurements were obtained. A surface hot-wire anemometer was used to measure the phase-averaged skin friction. Measurements in the detached-flow zone of phase-averaged velocities and turbulence quantities were obtained with a directionally sensitive laser anemometer. The fraction of time that the flow moves downstream was measured by the LDV and by a thermal flow-direction probe.

Upstream of any flow reversal or backflow, the flow behaves in a quasisteady manner, i.e. the phase-averaged flow is described by the steady free-stream flow structure. The semilogarithmic law-of-the-wall velocity profile applies at each phase of the cycle. The Perry & Schofield (1973) velocity-profile correlations fit the mean and ensemble-averaged velocity profiles near detachment.

After the beginning of detachment, large amplitude and phase variations develop through the flow. Unsteady effects produce hysteresis in relationships between flow parameters. As the free-stream velocity during a cycle begins to increase, the Reynolds shearing stresses increase, the detached shear layer decreases in thickness, and the fraction of time $\hat{\gamma}_{{\rm p}u}$ that the flow moves downstream increases as backflow fluid is washed downstream. As the free-stream velocity nears the maximum value in a cycle, the increasingly adverse pressure gradient causes progressively greater near-wall backflow at downstream locations, while $\hat{\gamma}_{{\rm p}u}$ remains high at the upstream part of the detached flow. After the free-stream velocity begins to decelerate, the detached shear layer grows in thickness and the location where flow reversal begins moves upstream. This cycle is repeated as the free-stream velocity again increases.

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References

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The structure of a separating turbulent boundary layer. Part 4. Effects of periodic free-stream unsteadiness

  • Roger L. Simpson (a1), B. G. Shivaprasad (a1) and Y.-T. Chew (a1) (a2)

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