This thesis investigates how surface deformations can delay the transition from laminar to turbulent flow in aircraft boundary layers, thereby reducing drag and improving fuel efficiency. This is important because aviation contributes significantly to greenhouse gas emissions, an
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This thesis investigates how surface deformations can delay the transition from laminar to turbulent flow in aircraft boundary layers, thereby reducing drag and improving fuel efficiency. This is important because aviation contributes significantly to greenhouse gas emissions, and improving the lift-to-drag ratio is one of the most effective ways to make aircraft more sustainable.
The focus is on the early stages of boundary layer transition, particularly the growth of stationary crossflow instabilities in swept-wing boundary layers. These instabilities play a major role in triggering turbulence on swept wings. While experiments and Direct Numerical Simulations (DNS) can study this process accurately, they are computationally expensive. Therefore, this thesis uses flow stability analysis methods, which are much faster.
Three stability-analysis approaches are discussed. The classical Orr–Sommerfeld method is computationally efficient but assumes a locally parallel flow and only works for small perturbations. The Parabolized Stability Equations (PSE) improve on this by including streamwise development and nonlinear interactions, but they are only valid for slowly varying flows. The Harmonic Navier–Stokes (HNS) equations retain all streamwise derivatives and can therefore handle strongly non-parallel flows, although at a higher computational cost than PSE.
To exploit these advantages, a new computational framework, the Delft Harmonic Navier–Stokes Solver (DeHNSSo), is developed. DeHNSSo can analyse the effect of both smooth and sharp surface deformations, such as humps and steps, on boundary layer instabilities. The solver uses a Fourier-based representation of perturbations, spectral discretisation in the wall-normal direction, and finite differences in the streamwise direction. Nonlinear interactions between perturbation modes are included iteratively.
The framework is validated using several standard instability cases, including Tollmien–Schlichting waves in a Blasius boundary layer and stationary crossflow instabilities in a swept-wing boundary layer. In all cases, DeHNSSo agrees closely with DNS and with other stability methods such as PSE and Adaptive Harmonic Linearised Navier–Stokes.
The main application of the solver is to investigate the effect of a shallow smooth surface hump on crossflow instabilities. The hump creates a local region of reversed crossflow without causing flow separation. Away from the hump, the boundary layer quickly returns to its original state.
For small perturbation amplitudes, the hump reduces the growth of crossflow instabilities over a large downstream region. Although there is some local destabilisation near the hump, the overall effect is stabilising because the perturbation shape is altered in a way that weakens the lift-up mechanism responsible for instability growth.
At larger perturbation amplitudes, however, the hump becomes less effective. A second unstable mode appears near the wall and transfers energy to the main instability. This can lead to locally increased disturbance amplitudes and earlier quasi-saturation, potentially accelerating transition.
The results suggest that smooth surface humps are most effective when the incoming disturbances are still small and approximately linear. Under those conditions, they can delay transition and reduce drag. The study therefore provides a promising basis for using optimised surface humps on aircraft wings. Future work could further optimise hump shape and arrangement and improve computational efficiency by coupling the HNS approach with faster methods such as nonlinear PSE.