The Nature of Oblique Instability Waves in Boundary Layer Transition

Author: Robey, Harry Francis, III

Year: 1986

Degree: Dissertation (Ph.D.)

Advisor: Liepmann, Hans Wolfgang

Committee Members: Liepmann, Hans Wolfgang; Coles, Donald Earl; Knowles, James K.; Babcock, Charles D.; Cohen, Donald S.

Option: Aeronautics

DOI: 10.7907/7VG8-Y513

Abstract

An experimental study of both the weakly non-linear as well as the three-dimensional nature of boundary layer transition is conducted using the active surface heating technique of Liepmann et al. In the present study, this technique is extended to provide a means for controllably and repeatably introducing three-dimensional disturbances into a laminar boundary layer. A review of the surface heating technique is presented along with a discussion of some peculiarities encountered in extending this technique to three-dimensional geometries. A thorough description of the design and operation of a programmable 32-element heater array and the supporting instrumentation are given as well.

The heater array is first used to study the effect of weak nonlinearity on boundary layer transition. By keeping the forced disturbances as two-dimensional as possible, it is shown that the effects of weak non-linearity are relatively benign. The growth rates are seen to follow the linear theory up to perturbation amplitudes (τ'wτ̅w) of nearly twelve percent. The only deviation from the linear theory arises in the form of non-linearly generated harmonics phase-locked to the fundamental. It is concluded that although these non-linearly generated harmonics do alter the wave behavior to some extent, they are by themselves not sufficient to explain the transition from small linear oscillations to the large amplitude, broad-band, three-dimensional oscillations characteristic of a fully turbulent boundary layer.

The effect of three-dimensionality on boundary layer transition is then investigated through an analytical and experimental study of single oblique instability waves. This subject has remained largely unexplored, as such disturbances were generally thought to be more stable and therefore less dangerous than their two-dimensional counterparts. Through a series of experiments, however, it is shown that certain conditions exist for which oblique waves are observed to be more unstable than any two-dimensional wave. It is shown that oblique waves exhibit a non-stationary period-doubling behavior that is not seen in two-dimensional disturbances. A vortex pairing mechanism is proposed to explain this behavior, and is shown to occur in a manner consistent with the Biot-Savart law for the induced velocity field.

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