Modelling the effect of step and roughness features on swept wing boundary layer instabilities
Creators: name: Cooke, Emma
Publisher: name: Imperial College London
Year: 2020

description: Destabilisation effects of forward facing steps, backward facing steps and bumps on stationary and travelling crossflow disturbances are investigated computationally for a 40 degree infinitely swept wing. Step and bump heights range from 18% to 82% of the boundary layer thickness and are located at 3%, 10% and 20% chord. The spectral/hp element solver, Nektar++, is used to compute base flow profiles with an embedded swept wing geometry. Parabolised Stability Equations (PSE) and Linearised Harmonic Navier-Stokes (LHNS) models are used to evaluate growth of convecting instabilities. The presence of surface step features impose an extremely rapidly varying flow field locally, which requires accurate resolution of the perturbed flow field. Derivations of these PSE and LHNS models incorporating the excrescence (PSEh, LHNSh) are elucidated. Unlike the PSE, which suffer from a stream-wise numerical step size restriction, the LHNS are a fully elliptic set of equations which may use an arbitrarily fine grid resolution. Unsurprisingly, the PSE codes fail to capture the effect of abrupt changes in surface geometry introduced by the step features. Results for the LHNS and roughness incorporating LHNSh are given for the varying vertical step and ramped type steps. Comparisons are made between the LHNSh model and direct numerical simulations involving the time-stepping linearised Navier-Stokes solver (NekLNS) in the Nektar++ software framework. Most previous work in the topic area has focused on Tollmien-Schlichting perturbations over two-dimensional flat plate flows or aerofoils, the novelty of this work lies with analysing crossflow instability over a swept wing boundary-layer flow with step features. PSEh and LHNSh models are tested with convecting Tollmien Schlichting instability over a dimple and randomly distributed roughness on an overall flat plate flow. The dimple case performs very well whereas it is more difficult to obtain converged results with the random roughness case, likely due to large stream-wise velocity gradient changes. A 45degree ramped shape roughness is investigated and remarkably good agreement between the LHNSh solution and NekLNS solution is found. Forward facing ramps and steps are found to act as greater amplifiers with increased height, whilst backward facing ramps and steps predict very weak changes in the disturbance development. This is contrary to the wider literature and an argument is made that backward facing steps and ramps initiate an immediate non-linear interaction which cannot be captured with linear theory. Vertical forward facing step cases also predict greater amplification with increased step height, which is not observed in the backward facing step cases. Again, this is believed to be due to non-linear mode interaction that is immediately triggered by the step. Bump roughness cases agree well qualitatively with experimental work on a 40 degree swept wing, the AERAST geometry. Good agreement locally to the roughness could not be drawn with the NekLNS solutions, likely due to the presence of strong stream-wise gradients and mesh limitations.