Effect of Submergence on Transonic Flow Around a Hemisphere

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Effect of Submergence on Transonic Flow Around a Hemisphere

Malkus, Mikala J. / Frede, Michael T. / Sherer, Scott E. / Garmann, Daniel J.

The effect of varying submergence on the transonic flow past canonical wall-mounted hemispheres is investigated at a freestream Mach number $M_{\infty} = 0.8$ using delayed detached eddy simulations. Four submergence levels are considered, ranging from a full hemisphere (100% exposed) to a highly submerged case where the equator is well below the waterline (40% exposed). Analysis of the mean and unsteady features indicates that the shock foot and line of surface separation move downstream with submergence. However, the frequency associated with the streamwise motion of the shock remains consistent between the cases in terms of a suitably nondimensionalized Strouhal number ${S t}_{D} \sim 0.26$ . Proper orthogonal decomposition is used to isolate and rank the different modes; as the hemisphere is submerged, there is an evident change in prominence from the asymmetric “shifting” to the symmetric “breathing” mode. Dynamic mode decomposition was used to investigate the spectral content of these modes; the results show that the breathing mode collapses at a frequency of ${S t}_{D} \sim 0.26$ for all cases, while the shifting mode extends over a broad frequency range of ${S t}_{D}$ between 0.13 and 0.21. Aero-optic analysis shows that the distortion for the more submerged hemisphere cases is associated primarily with the breathing mode, while for the fully exposed hemisphere the shifting mode is dominant.