High Order Spectral Analysis of Laminar Hypersonic Boundary Layers and CVA Application

Abstract

Three high order spectral analysis techniques - the short-time Fourier transform (STFT), the Fourier bispectrum, and the STFT bispectrum - are developed and used to characterize the nonlinear dynamics of a transitioning hypersonic boundary layer flow. The measurement of a hot-wire operated with a constant voltage anemometer (CVA) in the NASA Langley Mach 6 quiet tunnel are analyzed, and the effects of wall cooling and adverse pressure gradient on the nonlinear dynamics are examined.

The STFT clearly identifies the modulation of the dominant second mode and its harmonic in the nonlinear region of the transition process. Phase modulation is observed to be the primary energy transfer mechanism, but in the latter nonlinear stages the role of amplitude modulation is increasingly important. The Fourier bispectrum quantifies the modulation as a low frequency phase coupled quadratic interaction. In addition, the Fourier bispectrum quantifies the dominant role of the second mode through its forcing of harmonic quadratic interactions. The STFT bispectrum identifies the transient stages of nonlinear interactions that are observed to be important in the nonlinear stages of transition. These nonharmonic, broadband interactions may offer new approaches for control of hypersonic transition.

In a final element of this work, a new capability for the CVA is developed and demonstrated. A rapid and automated stepping of the wire voltage is developed, and used to obtain calibrated measurements in a short duration wind tunnel.