Shock Wave/ Turbulent Boundary Layer Interactions on a Cylinder Stefen A. Lindörfer, Christopher S. Combs, Phillip A. Kreth, and John D. Schmisseur Department of Mechanical, Aerospace, and Biomedical Engineering The University of Tennessee Space Institute This material is based upon research supported by the U. S. Office of Naval Research under award number N00014-15-1-2269.

Background – SWTBLI Shock wave/turbulent boundary layer interactions (SWTBLIs) remain a limiting factor in the design of supersonic and hypersonic vehicles Extensive experimental research since 1950s Computational Fluid Dynamics (CFD) requires as many inputs from experiment as possible  Conduct complementary experimental & computational  experiments https://www.nasa.gov/centers/langley/images/content/142861main_x43a_intscramjet_550.gif

Geometry Studied – Cylinder Several canonical configurations exist to provide fundamental research Blunt single fin extends application to control surfaces Can be represented by a standing cylinder (Dolling and Bogdonoff, 1981) Canonical Configurations for SWBLIs (Gaitonde, 2013) Blunt Fin SWBLI (Hung and Buning, 1984) Cylinder SWBLI (Itoh and Mizoguchi, 2016)

Geometry Studied – Cylinder 3.175 mm Ø, 12.7 mm tall cylinder on a flat plate h > 2.4D requirement for semi-infinite consideration (Dolling and Bogdonoff, 1981) Flat plate angled at α = -2.9° x = 40D downstream of leading edge of flat plate How well do shock structures align with experiment? Can unsteady behavior be characterized? Do fluctuations exhibit particular frequencies? Strouhal number? Cylinder on Flat Plate

Computational Methods via CFD++ Steady & unsteady Reynolds-averaged Navier-Stokes (RANS) 2nd order implicit Target residual drop 10-8 Domain split into upstream 2D and downstream 3D section Saves cell count and provides inflow profile for multiple runs 2D: 4-eq Transition SST 3D: 2-eq SST

Upstream – Flat Plate Mesh Blunt leading edge with radius 127 μm 2D shock-aligned mesh via a priori method (1.2 M cells) y+ = 0.01, GR = 1.1

Upstream – Flat Plate Results 3D coarse mesh with cylinder added (38.5 M cells) Take vertical slices until flow conditions are matched

Upstream – Flat Plate Results CFD within 1% difference of experiment x/D = -12 will be used as inflow profile for downstream case Wind Tunnel Freestream Flat Plate CFD Flat Plate Experiment % diff P∞ [kPa] 26.4 31.1 30.9 0.836 T∞ [K] 159 167 166 0.805 u∞ [m/s] 507 490 493 0.543 M∞ 2.1 1.89 1.91 0.969

Downstream – Cylinder Mesh 2D base extruded along transverse direction (29.0 M cells) Radial grid extends r = 3D y+ = 0.01, GR = 1.2 r+ = 1, GR = 1.1 Top View of Base of 3D Cylinder Mesh

Downstream – Cylinder – RANS Centerline slices taken at z = 0 Flow features shift over steady-state iterations Mach Number Contour Pressure Contour (Inverted)

Downstream – Cylinder – RANS Triple point around 1.8 in CFD, 1.37 in experiment  ≈30% difference Density Gradient Magnitude Contour Pressure Gradient Magnitude Contour

Downstream – Cylinder – URANS Δt = δ/(50∙u∞) = 50 ns Equivalent to 400 kHz resolution at 50 points/step Preliminary solution over 23.3 μs

Downstream – Cylinder – URANS Average forward flow separation around 3 in CFD, 2.18 in experiment ≈30% difference, consistent with triple point error

Future Work Grid and time-step independence study for URANS Establish characteristic frequencies Strouhal number Bandwidth Perform surface heat transfer analysis Analyze shock wave/laminar boundary layer interaction Compare and contrast behaviors Easier to get accurate results with RANS

Questions? Acknowledgments: Ross Chaudhry – University of Minnesota Michael Adler – The Ohio State University Roshan Oberoi – CFD++ Support