Three-dimensional flow structure in an axisymmetric separated/reattaching supersonic flow

Branden M. Kirchner, Gregory S. Elliott, J. Craig Dutton

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The three-dimensionality of turbulent motions in a massively separated Mach 2.49 longitudinal cylinder wake is investigated using tomographic particle image velocimetry (TPIV). Measurements were acquired within six volumetric subregions of the flow, including the separated shear layer, the recirculation region, the shear layer reattachment region, and the trailing wake, with a large ensemble of measurement volumes (between 2100 and 3300) acquired and processed per region to allow for adequate statistical convergence in the various analyses used. Large streamwise-elongated turbulent structures with a quasiaxial orientation were commonly observed to exist in regions of the flow encountering the adverse pressure gradient associated with shear layer reattachment. The statistical geometry and orientation of these structures within this region of the flow are demonstrated using linear stochastic estimation. The snapshot proper orthogonal decomposition method was also used to decompose the TPIV data into mode shapes. Both an energy-based and an enstrophy-based decomposition were performed, as the three-dimensional TPIV data allow for calculation of all components of the vorticity vector. It is demonstrated that the highest energy-containing modes for many of the TPIV subregions are associated with coherent turbulent structures, such as hairpin vortices or the aforementioned quasiaxial structures. The highest energy-containing mode from the recirculation region data represented 30% of the turbulent kinetic energy within a single mode, and appears to indicate a large-scale global flow interaction between the recirculation region and the separated shear layer with a helical orientation. This large-scale behavior appears consistent with past computational simulations of this flow that also predicted that low-order azimuthal and helical instability modes within the recirculation region play a significant role in the generation of large-scale structures and the production of pressure drag.

Original languageEnglish (US)
Article number024604
JournalPhysical Review Fluids
Issue number2
StatePublished - Feb 2021

ASJC Scopus subject areas

  • Computational Mechanics
  • Modeling and Simulation
  • Fluid Flow and Transfer Processes


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