Smooth Body Flow Separation Investigations Using RBVMS Formulation

Overview

Accurately predicting smooth-body flow separation is a critical but computationally demanding challenge in aerodynamic and hydrodynamic engineering. In this research, conducted during my PhD with Dr. Artem Korobenko at the University of Calgary, we investigated the performance of the residual-based variational multiscale (RBVMS) method for predicting category III turbulent flow separation over a rearward-facing ramp. We employed linear finite element discretizations on a sequence of systematically refined meshes and applied a synthetic turbulence generation (STG) method at the inflow to ensure consistent boundary-layer development. To improve numerical stability and computational efficiency near the wall without relying on empirical turbulence concepts, we utilized the weak imposition of Dirichlet boundary conditions.

Results

  • The RBVMS formulation, combined with linear finite elements and weakly imposed boundary conditions, demonstrated robust capability in capturing key features of smooth-body turbulent separation.
  • We accurately predicted the onset of flow separation near \(\hat{x} \approx 0.425\), showing strong agreement with reference direct numerical simulation (DNS) and wall-resolved large-eddy simulation (LES) data.
  • Systematic mesh refinement successfully eliminated nonphysical jumps in the skin friction coefficient (\(C_{f}\)) over the ramp surface, indicating improved numerical convergence and wall resolution.
  • Our analysis revealed a high sensitivity to the spanwise domain width. A narrow domain of \(4\delta_{BL}\) artificially constrained the turbulence and negatively impacted skin friction distributions in the ramp region.
  • Expanding the spanwise domain to \(8\delta_{BL}\) significantly smoothed the separation bubble and improved physical accuracy. Further domain expansion to \(16\delta_{BL}\) yielded minimal differences, establishing \(8\delta_{BL}\) as a sufficient width to achieve statistical convergence for this configuration.