Thesis title: Turbulent flows on curved walls -- insights from DNS
Turbulent flows on curved walls occur in many aerospace applications and combine curvature-driven centrifugal instabilities, non-uniform pressure gradients, and -- at high Mach numbers -- shock wave - boundary layer interactions (SBLI), producing complex and unstable flow fields.
In this context, we present FLEW, a solver for high-fidelity direct numerical simulations (DNS) of compressible flows on body-fitted curvilinear grids, based on high-order accurate finite-difference discretizations in generalized curvilinear coordinates.
After verification on the inviscid Taylor–Green vortex and validation
against canonical benchmarks, we employ FLEW (and an additional incompressible solver)
to study three canonical problems via DNS:
1) turbulent flow in curved channels under mild and strong curvature conditions over a wide range of Reynolds numbers;
2) transonic buffet on a supercritical airfoil up to a Reynolds number based on the chord 6x10^5 with increasing angle of attack to cover stable and fully-buffet flow conditions;
3) supersonic turbulent flow on a compression ramp at Mach number of 2.9 with imposed cross-flow to simulate SBLI with separation under cylindrical symmetry.
Simulations of the curved channel show that the concave curvature of the wall systematically reorganizes the flow, generating large-scale streamwise-aligned structures,
which significantly influence the flow transition and wall shear stress. Strong convex curvature suppresses the near-wall regeneration cycle, while promoting coherent secondary motions along the transverse direction.
DNS of transonic buffet reproduce the experimentally observed inversion of shock motion with increasing angle of attack and the
onset of low-frequency shock oscillations past the critical condition. Modal analysis reveals a dominant coherent mode at Strouhal number 0.1 (based on the chord length and freestream velocity), which couples the shock motion with the unsteady shedding of large vortical structures from the separated shear layer. These structures travel downstream towards the trailing edge, where acoustic scatting generates upstream-traveling waves that perturb the shock wave, consistent with a feedback loop model.
Regarding the swept SBLI over compression ramp, increasing sweep enlarges the separation region, increases the coherence of pressure fluctuations and shifts the characteristic low-frequency
dynamics upward. These effects are explained by a coupling between breathing mode of the separation bubble and the spanwise convection of large-scale coherent structures.
We derive a scaling law for the low-frequency unsteadiness that is corroborated by DNS and experimental results.