S.H.J. Westerbeek
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8 records found
1
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.
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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.
This work explores the use of a shallow surface hump for passive control and stabilisation of stationary crossflow (CF) instabilities. Wind tunnel experiments are conducted on a spanwise-invariant swept-wing model. The influence of the hump on the boundary layer stability and laminar-turbulent transition is assessed through infrared thermography and particle image velocimetry measurements. The results reveal a strong dependence of the stabilisation effect on the amplitude of the incoming CF disturbances, which is conditioned via discrete roughness elements at the wing leading edge. At a high forcing amplitude, weakly nonlinear stationary CF vortices interact with the hump and result in an abrupt anticipation of transition, essentially tripping the flow. In contrast, at a lower forcing amplitude, CF vortices interact with the hump during linear growth. Notable stabilisation of the primary CF disturbance and considerable transition delay with respect to the reference case (i.e. without hump) is then observed. The spatial region just downstream of the hump apex is shown to be key to the stabilisation mechanism. In this region, the primary CF disturbances rapidly change spanwise orientation and shape, possibly driven by the pressure gradient change-over caused by the hump and the development of CF reversal. The amplitude and shape deformation of the primary CF instabilities are found to contribute to a long-lasting suboptimal growth downstream of the hump, eventually leading to transition delay.
Stationary velocity-perturbation streaks have recently been identified in laminar swept-wing boundary-layer flow interacting with a surface forward-facing step. Streaky structures at the step promote early laminar-turbulent transition under certain conditions. This work utilizes direct numerical simulations to explore the mechanisms of growth of stationary streaks at the step and provides insight into their origin, nature, and spatial organization. The analysis is mainly focused on, but not restricted to, incoming perturbations in the form of stationary crossflow instability. Stationary streaky structures are found to be universal to swept forward-facing-step flow subjected to three-dimensional perturbations in the incoming boundary layer. The streaks at the step are primarily ascribed to the lift-up effect. They appear as a linear perturbation response of the highly sheared step flow to the cross-stream pattern of incoming perturbations. A mechanism of base-flow deceleration additionally contributes to feeding growth to the streaks. Linear stability analysis carried out through the harmonic Navier-Stokes method confirms that the streaks are a linear perturbation phenomenon. Effects of spanwise perturbation wavelength and effective sweep angle on the mechanisms of the streaks are also assessed.
DeHNSSo
The Delft Harmonic Navier-Stokes Solver for Nonlinear Stability Problems with Complex Geometric Features
The interaction between forward-facing steps of several heights and a pre-existing critical stationary crossflow instability of a swept-wing boundary layer is analysed. Direct numerical simulations (DNS) are performed of the incompressible three-dimensional laminar base flow and the stationary distorted flow that arise from the interaction between an imposed primary stationary crossflow perturbation and the steps. These DNS are complemented with solutions of the linear and the nonlinear parabolised stability equations, used towards identifying the influence of linearity and non-parallelism near the step. A fully stationary solution of the Navier-Stokes equations is enforced numerically, in order to isolate the mechanisms pertaining to the interaction of the stationary disturbance with the step. Results provide insight into the salient modifications of the base laminar boundary layer due to the step, and the response of the incoming crossflow instability to these changes. The fundamental spanwise Fourier mode of the disturbance field gradually lifts up as it approaches the step and passes over it. The flow environment around the step is characterised by a sudden spanwise modulation of the base-flow streamlines. Additional stationary perturbation structures are induced at the step, which manifest in the form of spanwise-aligned velocity streaks near the wall. Shortly downstream of the step, the fundamental component of the crossflow perturbation maintains a rather constant amplification for the smallest steps studied. For the largest step, however, the fundamental crossflow perturbation is stabilised significantly shortly downstream of the largest step. This surprising result is ascribed to a modulation of the kinetic energy transfer between the base flow and the fundamental perturbation field, which is brought forward as a new step interaction mechanism. Possible non-modal growth effects at the step are discussed. Furthermore, the results from DNS indicate significant amplification of the high-order harmonic crossflow components downstream of the step.
The nonlinear stability of three-dimensional boundary layers over various undulated surfaces was calculated using the generalized Nonlinear Parabolized Stability Equations (NPSE). The results are compared with a flat plate configuration to assess the effect of the undulation shape on the stability of the boundary layer. It was found that the effect of surface undulations is significant and should not be ignored when performing stability analysis. All undulation shapes considered in this work showed a destabilization of the primary mode and the associated harmonics. The stability of the boundary layer was directly affected by the amplitude of the undulations, while their respective shape did not meaningfully affect the evolution of the crossflow instabilities within the parameter range considered in this work.
The effect of discrete roughness elements on the development and breakdown of stationary crossflow instability on a swept wing is explored. Receptivity to various element heights and chordwise locations is explored using a combination of experimental and theoretical tools. Forcing configurations, determined based on linear stability predictions, are manufactured and applied on the wing in a low turbulence facility. Measurements are performed using infrared thermography, quantifying the transition front location, and planar particle image velocimetry, providing a reconstruction of stationary crossflow instabilities and their associated growth. Measurements are corroborated with simulations based on nonlinear parabolised stability equations. Results confirm the efficacy of discrete roughness elements in introducing and conditioning stationary crossflow instabilities. Primary instability amplitudes and resulting laminar-turbulent transition location are found to strongly depend on both roughness amplitude and chordwise location. The Reynolds number based on element height is found to satisfactorily approximate the initial forcing amplitude, revealing the importance of local velocity effects in non-zero-pressure gradient flows. Direct estimation of initial perturbation amplitudes from nonlinear simulations suggests the existence of pertinent flow mechanisms in the element vicinity, active in conditioning the onset of modal instabilities. Dedicated velocimetry planes, elucidate the development of a momentum deficit wake which rapidly decays downstream of the element followed by mild growth, representing the first experimental evidence of transient behaviour in swept wing boundary layers. The outcome of this work identifies a strong scalability of the transition dynamics to roughness amplitude and location, warranting the upscaling of roughness elements to more accessible, measurable and spatially resolved configurations in future experiments.