arXiv subjects

Spencer J. Sherwin

Publications and source records attributed to Spencer J. Sherwin.

22 records · Page 2Linked to original sources

arXiv2016

Influence of localised smooth steps on the instability of a boundary layer

We consider a smooth forward facing step defined by the Gauss error function of height 4-30\% and four times the width of the local boundary layer thickness $δ_{99}$. The boundary layer flow over a smooth forward-facing stepped plate is studied with particular emphasis on stabilisation and destabilisation of the Tollmien-Schlichting (TS) waves and subsequently on transition. The interaction between TS waves at a range of frequencies and a base flow over a single/two forward facing smooth steps is conducted by linear analysis. The results indicate that for a high frequency TS wave, the amplitude of the TS wave is attenuated in the unstable regime of the neutral stability curve corresponding to a flat plate boundary layer. Furthermore, it is observed that two smooth forward facing steps lead to a more acute reduction of the amplitude of the TS wave. When the height of a step is increased to more than 20\% of the local boundary layer thickness for a fixed width parameter, the TS wave is amplified and thereby a destabilisation effect is introduced. Therefore, stabilisation or destabilisation effect of a smooth step is typically dependent on its shape parameters. To validate the results of the linear stability analysis, where a high-frequency TS wave is damped by the forward facing smooth steps direct numerical simulation (DNS) is performed. The results of the DNS correlate favorably with the linear analysis and show that for the investigated high frequency TS wave, the K-type transition process is altered whereas the onset of the H-type transition is postponed. The results of the DNS suggest that for a high-frequency perturbation $\mathcal{F}=150$ and in the absence of other external perturbations, two forward facing steps of height 5\% and 12\% of the boundary layer thickness delayed H-type transition scenario and completely suppresses it for the K-type transition.

physics.flu-dyn↗

arXiv2015

Implicit Large Eddy Simulation of a wingtip vortex at $Re_c = 1.2\cdot 10^6$

In this article we present recent developments in numerical methods for performing a Large Eddy Simulation (LES) of the formation and evolution of a wingtip vortex. The development of these vortices in the near wake, in combination with the large Reynolds numbers present in these cases, make these types of test cases particularly challenging to investigate numerically. We first give an overview of the Spectral Vanishing Viscosity--implicit LES (SVV-iLES) solver that is used to perform the simulations, and highlight techniques that have been adopted to solve various numerical issues that arise when studying such cases. To demonstrate the method's viability, we present results from numerical simulations of flow over a NACA 0012 profile wingtip at $Re_c = 1.2\cdot 10^6$ and compare them against experimental data, which is to date the highest Reynolds number achieved for a LES that has been correlated with experiments for this test case. Our model correlates favorably with experiment, both for the characteristic jetting in the primary vortex and pressure distribution on the wing surface. The proposed method is of general interest for the modeling of transitioning vortex dominated flows over complex geometries.

physics.flu-dyn↗

arXiv2014

An adaptive selective frequency damping method

The selective frequency damping (SFD) method is an alternative to classical Newton's method to obtain unstable steady-state solutions of dynamical systems. However this method has two main limitations: it does not converge for arbitrary control parameters; and when it does converge, the time necessary to reach the steady-state solution may be very long. In this paper we present an adaptive algorithm to address these two issues. We show that by evaluating the dominant eigenvalue of a "partially converged" steady flow, we can select a control coefficient and a filter width that ensure an optimum convergence of the SFD method. We apply this adaptive method to several classical test cases of computational fluid dynamics and we show that a steady-state solution can be obtained without any a priori knowledge of the flow stability properties.

physics.flu-dyn↗

arXiv2013

Encapsulated formulation of the Selective Frequency Damping method

We present an alternative "encapsulated" formulation of the Selective Frequency Damping method for finding unstable equilibria of dynamical systems, which is particularly useful when analysing the stability of fluid flows. The formulation makes use of splitting methods, which means that it can be wrapped around an existing time-stepping code as a "black box". The method is first applied to a scalar problem in order to analyse its stability and highlight the roles of the control coefficient $χ$ and the filter width $Δ$ in the convergence (or not) towards the steady-state. Then the steady-state of the incompressible flow past a two-dimensional cylinder at $Re=100$, obtained with a code which implements the spectral/hp element method, is presented.

physics.flu-dyn↗