1. 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 N

2. 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

3. 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)

4. 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

5. 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

6. 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

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

8. 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

9. 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

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

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

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

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

14. 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

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