An optimal path to transition in a duct

This paper is concerned with the transition of the laminar flow in a duct of square cross-section. Like in the similar case of the pipe flow, the motion is linearly stable for all Reynolds numbers, rendering this flow a suitable candidate for a study of the 'bypass' path to turbulence. It has already been shown \citep{Biau_JFM_2008} that the classical linear optimal perturbation problem, yielding optimal disturbances in the form of longitudinal vortices, fails to provide an 'optimal' path to turbulence, i.e. optimal perturbations do not elicit a significant nonlinear response from the flow. Previous simulations have also indicated that a pair of travelling waves generates immediately, by nonlinear quadratic interactions, an unstable mean flow distortion, responsible for rapid breakdown. By the use of functions quantifying the sensitivity of the motion to deviations in the base flow, the 'optimal' travelling wave associated to its specific defect is found by a variational approach. This optimal solution is then integrated in time and shown to display a qualitative similarity to the so-called 'minimal defect', for the same parameters. Finally, numerical simulations of a 'edge state' are conducted, to identify an unstable solution which mediates laminar-turbulent transition and relate it to results of the optimisation procedure

Transition to turbulence in duct flow

The transition of the flow in a duct of square cross-section is studied. Like in the similar case of the pipe flow, the motion is linearly stable for all Reynolds numbers; this flow is thus a good candidate to investigate the 'bypass' path to turbulence. Initially the so-called 'linear optimal perturbation problem' is formulated and solved, yielding optimal disturbances in the form of longitudinal vortices. Such optimals, however, fail to elicit a significant response from the system in the nonlinear regime. Thus, streamwise-inhomogeneous, sub-optimal disturbances are focussed upon; nonlinear quadratic interactions are immediately evoked by such initial perturbations and an unstable streamwise-homogeneous large amplitude mode rapidly emerges. The subsequent evolution of the flow, at a value of the Reynolds number at the edge between fully developed turbulence and relaminarization, shows the alternance of patterns with two pairs of large scale vortices near opposing parallel walls. Such edge states bear a resemblance to optimal disturbance

Rapid path to transition via nonlinear localized optimal perturbations in a boundary-layer flow

Recent studies have suggested that in some cases transition can be triggered by some purely nonlinear mechanisms. Here we aim at verifying such an hypothesis, looking for a localized perturbation able to lead a boundary-layer flow to a chaotic state, following a nonlinear route. Nonlinear optimal localized perturbations have been computed by means of an energy optimization which includes the nonlinear terms of the Navier- Stokes equations. Such perturbations lie on the turbulent side of the laminar-turbulent boundary, whereas, for the same value of the initial energy, their linear counterparts do not. The evolution of these perturbations toward a turbulent flow involves the presence of streamwise-inclined vortices at short times and of hairpin structures prior to breakdown

Drag-model sensitivity of Kelvin-Helmholtz waves in canopy flows

Two models of the flow over and through an immersed, vegetated layer are examined to study the onset of instability waves across the layer and to assess the effect of mild variations in the mean flow and in the drag force exerted by the canopy onto the frequency and growth rate of the monami instability. One of the two models, based on the use of Darcy’s equation, with a tensorial permeability, within the canopy is more robust than the other (which uses a scalar drag coefficient), i.e., it is less sensitive to the inevitable imperfections or approximations in the input data

Minimal Dark Matter bound states at future colliders

The hypothesis that Dark Matter is one electroweak multiplet leads to predictive candidates with multi-TeV masses that can form electroweak bound states. Bound states with the same quantum numbers as electroweak vectors are found to be especially interesting, as they can be produced resonantly with large cross sections at lepton colliders. Such bound states exist e.g. if DM is an automatically stable fermionic weak 5-plet with mass $M \approx$ 14 TeV such that the DM abundance is reproduced thermally. In this model, a muon collider could resolve three such bound states. Production rates are so large that details of DM spectroscopy can be probed with larger statistics: we compute the characteristic pattern of single and multiple $\gamma$ lines.Comment: v2, to appear on JHE

Effects of porosity and inertia on the apparent permeability tensor in fibrous media

The flow in three-dimensional fibrous porous media is studied in the inertial regime by first simulating for the motion in unit, periodic cells, and then solving successive closure problems leading – after applying an intrinsic averaging procedure – to the components of the apparent permeability tensor. The parameters varied include the orientation of the driving pressure gradient, its magnitude (which permits to define a microscopic Reynolds number), and the porosity of the medium. All cases tested refer to situations for which the microscopic flow is steady. When the driving force is oriented in a direction whichlies on the plane perpendicular to the fibers’ axis, the results found agree with those available the literature. The fact that the medium is composed by bundles of parallel fibers favours a deviation of the mean flow towards the fibers’ axis when the driving pressure gradient has even a small component along it, and this is enhanced by a decreasing porosity; this phenomenon is well quantified by the knowledge of the components of the permeability. Contrary to our initial expectations, for the over one hundred cases which we have simulated, the apparent permeability tensor remains, to a very good approximation, diagonal, a fact mainly related to the transversely isotropic nature of the medium. To obtain a complete,albeit approximate, database of the diagonal components of the apparent permeability tensor we have developed a metamodel, based on kriging interpolation, and carefully calibrated it. The resulting response surfaces can be invaluable in determining the force caused by the presence of inclusions in macroscopic simulations of the flow through bundles of fibers whose orientations and dimensions can vary in space and/or time

Natural convection heat transfer from a ribbed vertical plate: Effect of rib size, pitch, and truncation

Buoyancy-induced flows over ribbed vertical surfaces involve complex thermal and dynamic interactions between the mainstream and the surface texture, yielding contrasting effects on the heat transfer performance of the heated plate; proper analysis of the overall effect on the heat transfer rate is essential for efficient operation and optimization purposes. The present work pursues an insight into the different factors controlling this problem. Natural convection heat transfer from a vertical plate of 0.5 m height, regularly roughened with wooden transverse square ribs, is experimentally investigated. The surface temperature of the baseplate is varied so that a range of the plate Rayleigh number (Ra) from 3.4 × 108 to 4.9 × 108 is covered. The density of the roughness pattern and the rib pitch-to-height ratio (P/e) are varied by changing the number of ribs attached to the surface (from 10 to 40 rib rows) and using three different square cross-sections (of side lengths 2, 3, or 5 mm). The experimental work relies on the schlieren optical technique, through which the thermal boundary layer is visualized and the Nusselt number distribution is acquired. Analysis of the results reveals that enhancement of the local Nusselt number, relative to a corresponding smooth surface, may be attained only at the central part of the inter-rib region; this occurs exclusively for relatively large values of P/e. At a later stage, the effectiveness of rib truncation in enhancing the heat transfer from the baseplate is explored. Three staggered arrangements are considered, by varying the number of rib segments per row, and heat transfer enhancement, sensitive to the number of rib segments per row, is found. This paper also provides insight into the role of thermal-field disturbances close to turbulent transition, and sheds light on the potential of truncated ribs to amplify such perturbations

Flow of shear-thinning fluids through porous media

Pseudo-plastic fluids exhibit a non-linear stress-strain relationship which can provoke large, localized viscosity gradients. For the flow of such fluids in porous media the consequence is a strong variability of the effective permeability with porosity, angle of the macroscopic pressure gradient, and rheological parameters of the fluid. Such a variability is investigated on the basis of adjoint homogenization theory for a Carreau fluid in an idealized porous medium geometry, highlighting differences with respect to the Newtonian case. It is shown in particular that the more we depart from Newtonian conditions, the more the (often used) hypothesis of an effective viscosity in Darcy’s law is a poor approximation, for the effective permeability tensor becomes strongly anisotropic

Modeling waves in fluids flowing over and through poroelastic media

Multiscale homogenization represents a powerful tool to treat certain fluid-structure interaction problems involving porous, elastic, fibrous media. This is shown here for the case of the interaction between a Newtonian fluid and a poroelastic, microstructured material. Microscopic problems are set up to determine effective tensorial properties (elasticity, permeability, porosity, bulk compliance of the solid skeleton) of the homogenized medium, both in the interior and at its boundary with the fluid domain, and an extensive description is provided of such properties for varying porosity. The macroscopic equations which are derived by homogenization theory employ such effective properties thus permitting the computation of velocities and displacements within the poroelastic mixture for two representative configurations of standing and travelling waves

A penalization method to treat the interface between a free-fluid region and a fibrous porous medium

The coupling between the flow through a fibrous porous medium and that in a free-fluid region is studied. The flow dynamics inside the porous medium are described using the volume averaging method applied to the incompressible Navier−Stokes equations in the laminar regime. The two different flow domains are coupled via a penalization method that consists of varying the porous medium properties (porosity and permeability) continuously across the interface. This approach permits the use of the same set of the equations throughout the whole domain. The averaging method is validated against simulations which fully account for the presence of cylindrical fibers positioned at the bottom wall of a square driven cavity. Numerical experiments are carried out for two different Reynolds numbers, large enough to ensure that inertial effects inside the porous domain are not negligible. Good agreement is found when comparing the two approaches