Abstract
Unsteady flow characteristics of a normal shock wave, a lambda foot, and a separated turbulent boundary layer are investigated within a unique test section with supersonic inlet flow. The supersonic wind tunnel facility, containing this test section, provides a Mach number of approximately 1.54 at the test section entrance. Digitized shadowgraph flow visualization data are employed to visualize shock wave structure within the test section. These data are analyzed to determine shock wave unsteadiness characteristics, including grayscale spectral energy variations with frequency, as well as time and space correlations, which give coherence and time lag properties associated with perturbations associated with different flow regions. Results illustrate the complexity and unsteadiness of shock-wave-boundary-layer-interactions, including event frequencies from grayscale spectral energy distributions determined using a Lagrangian approach applied to shock wave location, and by grayscale spectral energy distributions determined using ensemble-averaging applied to multiple closely-located stationary pixel locations. Auto-correlation function results and two-point correlation functions (in the form of magnitude squared coherence) quantify the time-scales of periodic events, as well as the coherence of flow perturbations associated with different locations, over a range of frequencies. Associated time lag data provide information on the originating location of perturbation events, as well as the propagation direction and event sequence associated with different flow locations. Additional insight into spatial variations of time lag and flow coherence is provided by application of magnitude squared coherence analysis to multiple locations, relative to a single location associated with the normal shock wave.
Highlights
Shock wave boundary layer interactions occur in many aerospace applications
3.3 Shock wave Streamwise position grayscale spectral energy result A Lagrangian approach is used to determine the spectral energy distribution associated with the streamwise location of the normal shock wave, as discussed earlier
A Lagrangian approach is used to determine the spectral energy distribution associated with the streamwise location of the normal shock wave, The resulting grayscale energy spectrum is compared with an ensemble-averaged grayscale spectral energy distribution, which shows that both results evidence peaks at similar frequencies at approximately 40 Hz and between 2 Hz and 9 Hz
Summary
Shock wave boundary layer interactions occur in many aerospace applications. Some examples include ramjet isolator ducts, turbine blade tip gaps, and transonic wings. Low frequency unsteadiness associated with shock wave boundary layer interactions is not well understood and continues to be a debated topic This is because different studies concluded different and contradicting results. Power spectral densities and cross correlations were often used, especially for wall pressure signal data Many of these investigations employed Schlieren and shadowgraph imaging to determine unsteady and spatially-varying shock wave structure. Ganapathisubramani et al [7] and Humble et al [8] computed cross correlations between turbulent structures in the upstream boundary layer and the shock wave from particle image velocimetry data. The present investigation differs from many previous studies by providing greater detail of the analysis techniques used, and by using digitized shadowgraph data to visualize shock wave structure. The current investigation is aimed at improved analysis techniques for shock-wave-boundary-layer-interactions, for better physical understanding of these flows, and for development of improved techniques for control and management of flow unsteadiness associated with particular shock wave arrangements
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