Matthieu Marquillie

On the onset of nonlinear oscillations in a separating boundary-layer flow

The stability of a separating boundary-layer flow at the rear of a two-dimensional bump mounted on a flat plate is numerically investigated. Above a critical Reynolds number, the flow field is shown to undergo self-sustained two-dimensional low-frequency fluctuations in the upstream region of the separation bubble, evolving into aperiodic vortex shedding further downstream. The computed steady flow states below the critical Reynolds number are shown to be convectively unstable. On extrapolating the flow field to Reynolds numbers above criticality, some evidence is found that the onset of the oscillatory behaviour coincides with topological flow changes near the reattachment point leading to the rupture of the (elongated) recirculation bubble. The structural changes near reattachment are shown to trigger an abrupt local transition from convective to absolute instability, at low frequencies. On preventing the separation bubble from bursting by reaccelerating the flow by means of a second bump further downstream, the separated flow remains steady for increasing Reynolds numbers, until a local region of absolute instability in the upper part of the geometrically controlled recirculation bubble is produced. The resulting global instability consists of self-sustained nonlinear saturated perturbations oscillating at a well-defined frequency, very distinct from the the low-frequency motion of the elongated recirculation bubble in the single-bump geometry. A frequency selection criterion based on local absolute frequencies, which has been successfully applied to wake flows, is shown to accurately predict the global frequency.

Three-dimensional transverse instabilities in detached boundary layers

The direct numerical simulation of the incompressible Navier-Stokes equations of the flow above a bump shows a stationary longitudinal instability at a Reynolds number of Re=400. A three-dimensional global mode linear analysis is used to interpret these results and shows that the most unstable eigenmode is steady and localized in the recirculation bubble, with spanwise wavelength of approximatively ten bump heights. An inviscid geometrical optics analysis along closed streamlines is then proposed and modified accordingly to account for viscous effects. This motivates a final discussion regarding the physical origin of the observed instability.

Direct numerical simulation of a separated channel flow with a smooth profile

A direct numerical simulation (DNS) of a channel flow with one curved surface was performed at moderate Reynolds number (Re τ = 395 at the inlet). The adverse pressure gradient was obtained by a wall curvature through a mathematical mapping from physical coordinates to Cartesian ones. The code, using spectral spanwise and normal discretization, combines the advantage of a good accuracy with a fast integration procedure compared to standard numerical procedures for complex geometries. The turbulent flow slightly separates on the profile at the lower curved wall and is at the onset of separation at the opposite flat wall. The thin separation bubble is characterized with a reversal flow fraction. Intense vortices are generated not only near the separation line on the lower wall but also at the upper wall. Turbulent normal stresses and kinetic energy budget are investigated along the channel.

LES modeling of converging-diverging turbulent channel flow

The paper presents the results of the application of large-eddy simulation (LES) to turbulent channel flow with a varying pressure gradient obtained by an appropriately specified shape of one of the walls. The main objective of the paper is to assess various subgrid scale (SGS) models implemented in two different codes as well as to assess the sensitivity of the predictive accuracy to grid resolution. Additionally, the role of SGS viscosity, controlled by a constant parameter of the SGS model, was investigated. The simulations were performed with inlet conditions corresponding to two Reynolds numbers: and . The consistency and the accuracy of simulations are evaluated using direct numerical simulation (DNS) results. It is demonstrated that all SGS models require a comparable minimum grid refinement in order to capture accurately the recirculation region. Such a test case with a reversal flow, where the turbulence transport is dictated by the dynamics of the large-scale eddies, is well suited to demonstrat...

On the relation between kinetic energy production in adverse-pressure gradient wall turbulence and streak instability

A direct numerical simulation (DNS) of a turbulent channel flow with a lower curved wall is performed at Reynolds number Re τ≃617 at inlet. This adverse-pressure gradient turbulent flow is characterized by strong peaks of turbulent kinetic energy at both walls, as a consequence of the breakdown of more organized flow structures. To elucidate the underlying instability scenario, low-speed streak structures are extracted from the turbulent flow field and base flows formed with conditional streak averages, superimposing the mean streamwise velocity profile, are used for linear stability analyses. The size and shape of the counter-rotating streamwise vortices associated with the instability modes are shown to be reminiscent of the coherent vortices emerging from the streak skeletons in the direct numerical simulation. The distance of the streaks centre from the wall is used as a criterion for the conditional averages and the corresponding streak base flows are characterised by more or less pronounced contour...

Skin friction on a flapping plate in uniform flow.

To calculate the energy costs of swimming or flying, it is crucial to evaluate the drag force originating from skin friction. This topic seems not to have received a definite answer, given the difficulty in measuring accurately the friction drag along objects in movement. The incoming flow along a flat plate in a flapping normal motion has been considered, as limit case of a yawed cylinder in uniform flow, and applying the laminar boundary layer assumption it is demonstrated that the longitudinal drag scales as the square root of the normal velocity component. This lends credit to the assumption that a swimming-like motion may induce a drag increase because of the compression of the boundary layer, which is known as the ‘Bone–Lighthill boundary-layer thinning hypothesis’. The boundary-layer model however cannot predict the genuine three-dimensional flow dynamics and in particular the friction at the leeward side of the plate. A multi-domain, parallel, compact finite-differences Navier–Stokes solution procedure is considered, capable of solving the full problem. The time-dependent flow dynamics is analysed and the general trends predicted by the simplified model are confirmed, with however differences in the magnitude of the friction coefficient. A tentative skin friction formula is proposed for flow states along a plate moving at steady as well as periodic normal velocities.

Direct Numerical Simulations of Converging–Diverging Channel Flow

Two Direct Numerical Simulations (DNS) of a converging–diverging channel flows were performed at Re τ = 395 and Re τ =617. The present DNS of adverse pressure gradient flow were designed within the WALLTURB project to meet two main objectives. The first one was to gather three-dimensional fully resolved data in order to investigate statistics and coherent structures of turbulence under strong pressure gradient with and without curvature. The second one was to have a reference for the evaluation of RANS and LES models. The flow slightly separates at the lower curved wall and is at the onset of separation at the opposite flat wall. Intense vortices are generated at the location of the minimum friction velocity even without averaged recirculation. The full budget of the Reynolds stresses were computed along the channel at both walls. The occurrence of a well documented secondary peak of velocity fluctuations due to adverse pressure gradient is shown to be the consequence of a very strong production peak.

Low Speed Streaks Instability of Turbulent Boundary Layer Flows with Adverse Pressure Gradient

A Direct Numerical Simulation of turbulent flow subjected to an adverse pressure gradient (APG) was performed. As already noticed by many authors in such configurations, a second outer peak of turbulent kinetic energy is observed in the region of APG. In the present configuration, this peak is due to the production of intense vortices which are shown to be related to the instability of low speed streaks.

Low-speed streak instability in near wall turbulence with adverse pressure gradient

A direct numerical simulation of a turbulent channel flow with a lower curved wall is performed at Reynolds number Reτ ≈ 600. Low-speed streak structures are extracted from the turbulent flow field and base flows formed with conditional streaks averages, superimposing the mean streamwise velocity profile, are used for linear stability analyses. The instability in the presence of a strong pressure gradient at the lower wall is shown to be of varicose type, whereas at the upper wall (with weak pressure gradient) varicose and sinuous unstable modes can coexist. The onset of the dominant instability mechanism of varicose type is shown to coincide with the strong production peaks of turbulent kinetic energy near the maximum of pressure gradient on both the curved and the flat walls. The size and shape of the counter-rotating streamwise vortices associated with the instability modes are shown to be reminiscent of the coherent vortices emerging from the streak skeletons in the direct numerical simulation.

Low-frequency beating and transverse instability of a laminar separated boundary-layer flow behind a bump

The instability behavior of a separated laminar boundary-layer ow over a shallow bump is investigated experimentally. This geometry generates an elongated recirculation bubble subject to a low-frequency apping. Previous numerical simulations have shown that, for this con guration, two instabilities coexist. The centrifugal instability of the recirculation bubble is rst investigated, then the low-frequency beating is compared with the two-dimensional instability observed in numerical simulations.