Turbulent flows on curved walls - insights from DNS

Turbulent flows on curved walls arise in many aerospace applications and combine curvature-driven centrifugal instabilities, non-uniform pressure gradients and – at high Mach number – shock-boundary layer interactions, producing complex and unsteady flow fields. In this context we present FLEW, a high-fidelity Direct Numerical Simu- lation (DNS) solver for compressible flows on body-fitted curvilinear meshes, based on high-order finite-difference discretisations 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 via DNS three canonical problems: 1. turbulent flow in curved channels under mild and strong curvature conditions across a wide range of Reynolds numbers; 2. transonic buffet over a supercritical aerofoil up to chord-based Reynolds number 6 ×10^5 with increasing angle of attack to span stable and fully-buffet flow conditions; 3. supersonic turbulent flow on a compression ramp at Mach number 2.9 with imposed crossflow to simulate Shock Wave-Boundary Layer Interactions (SBLI) with separation under cylindrical symmetry. The curved channel simulations show that concave wall curvature systematically reor- ganises the flow generating streamwise-aligned large-scale structures, which influences significantly flow transition and wall shear stress. Strong convex curvature suppresses the near-wall regeneration cycle while promoting spanwise-coherent motions. 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 scattering 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.