Closed-Loop Control of Fluid Flow: a Review of Linear Approaches and Tools for the Stabilization of Transitional Flows

International audienceFlow control is concerned with the targeted manipulation of intrinsic flow behavior to optimally satisfy prescribed objectives. This article will give an overview of the most common tools for the design of control strategies. We focus on linear control that is aimed at stabilizing fixed points of the Navier-Stokes equations, such as those existing in the case of transitional flows. Key steps to build a Galerkin-based and a data-based model will be presented and illustrated on two generic flow configurations: flow over an open cavity and over a backward-facing step. In the former case, a feedback configuration will result and particular attention will be paid to performance measures and robustness analyses. For the latter case, a feedforward setup has been chosen and a system-identification method will be employed to extract the fluid behavior from data sequences, via statistical learning techniques

Self-adaptation and viscous selection in concentrated two-dimensional vortex dipoles

International audienceIn this Letter we deal with 2D direct numerical simulations of concentrated vortex dipoles. We show that various initial dipolar vorticity distributions evolve towards a specific family of dipoles parametrized by the dipole aspect ratio a/b, where a is the radius of the vortices based on the vorticity polar moment in half a plane and b is the separation between the vortex centroids. This convergence is achieved through viscous effects. The considered Reynolds numbers Re= G/v are Re= 3000 and Re= 15000. Moreover, all the dipoles of this family are quasi-steady solutions of the Euler equations. Their scatter plots and drift velocities are given for a/b<03. © 2000 American Institute of Physics

Absolute instability in axisymmetric wakes: Compressible and density variation effects

International audienceLesshafft & Huerre (Phys. Fluids, 2007; vol. 19, 024102) have recently studied the transition from convective to absolute instability in hot round jets, for which absolute instability is led by axisymmetric perturbations and enhanced when lowering the jet density. The present paper analyses similarly the counterpart problem of wake flows, and establishes that absolute instability is then led by a large-scale helical wake mode favoured when the wake is denser than the surrounding fluid. This generalizes to variable density and compressible wakes the results of Monkewitz (J. Fluid Mech. vol 192, 1988, p. 561). Furthermore, we show that in a particular range of density ratios, the large-scale helical wake mode can become absolutely unstable by increasing only the Mach number up to high subsonic values. This possibility of an absolute instability triggered by an increase of the Mach number is opposite to the behaviour previously described in shear flows such as plane mixing layers and axisymmetric jets. A physical interpretation based on the action of the baroclinic torque is proposed. An axisymmetric short-scale mode, similar to that observed in plane mixing layers, leads the transition in light wakes, but the corresponding configurations require large counterflow for the instability to be absolute. These results suggest that the low-frequency oscillation present in afterbody wakes may be due to a nonlinear global mode triggered by a local absolute instability, since the azimuthal wavenumber and absolute frequency of the helical wake mode agree qualitatively with observations. © 2008 Cambridge University Press

Elephant modes and low frequency unsteadiness in a high Reynolds number, transonic afterbody wake

International audienceExperiments and large eddy numerical simulation of a fully turbulent afterbody flow in the high subsonic regime, typical of that developing in the wake of a space launcher, exhibit a large-scale low frequency oscillation of the wake. In the present paper, we investigate to what extent the existence of the synchronized oscillations can be interpreted, at the high Reynolds numbers prevailing in this class of flows, by a local stability analysis of the mean flow, as measured in experiments or computed in numerical simulations. This analysis shows the presence of a pocket of absolute instability in the near wake, slightly detached from the body. The global frequency is strikingly well predicted by the absolute frequency at the upstream station of marginal absolute instability, this frequency selection being in agreement with the theory of nonlinear global modes. This result strongly suggests that a so-called elephant mode is responsible for the intense oscillations observed in the lee of space launcher configurations. © 2009 American Institute of Physics

Closed-loop control of an open cavity flow using reduced-order models

International audienceThe control of separated fluid flow by reduced-order models is studied using the two-dimensional incompressible flow over an open square cavity at Reynolds numbers where instabilities are present. Actuation and measurement locations are taken on the upstream and downstream edge of the cavity. A bi-orthogonal projection is introduced to arrive at reduced-order models for the compensated problem. Global modes, proper orthogonal decomposition (POD) modes and balanced modes are used as expansion bases for the model reduction. The open-loop behaviour of the full and the reduced systems is analysed by comparing the respective transfer functions. This analysis shows that global modes are inadequate to sufficiently represent the inputoutput behaviour whereas POD and balanced modes are capable of properly approximating the exact transfer function. Balanced modes are far more efficient in this process, but POD modes show superior robustness. The performance of the closed-loop system corroborates this finding: while reduced-order models based on POD are able to render the compensated system stable, balanced modes accomplish the same with far fewer degrees of freedom. © 2009 Cambridge University Press

Effect of compressibility on the global stability of axisymmetric wake flows

International audienceWe study the linear dynamics of global eigenmodes in compressible axisymmetric wake flows, up to the high subsonic regime. We consider both an afterbody flow at zero angle of attack and a sphere, and find that the sequence of bifurcations destabilizing the axisymmetric steady flow is independent of the Mach number and reminiscent of that documented in the incompressible wake past a sphere and a disk (Natarajan & Acrivos, J. Fluid Mech., vol. 254, 1993, p. 323), hence suggesting that the onset of unsteadiness in this class of flows results from a global instability. We determine the boundary separating the stable and unstable domains in the (M, Re) plane, and show that an increase in the Mach number yields a stabilization of the afterbody flow, but a destabilization of the sphere flow. These compressible effects are further investigated by means of adjoint-based sensitivity analyses relying on the computation of gradients or sensitivity functions. Using this theoretical formalism, we show that they do not act through specific compressibility effects at the disturbance level but mainly through implicit base flow modifications, an effect that had not been taken into consideration by previous studies based on prescribed parallel base flow profiles. We propose a physical interpretation for the observed compressible effects, based on the competition between advection and production of disturbances, and provide evidence linking the stabilizing/destabilizing effect observed when varying the Mach number to a strengthening/weakening of the disturbance advection mechanism. We show, in particular, that the destabilizing effect of compressibility observed in the case of the sphere results from a significant increase of the backflow velocity in the whole recirculating bubble, which opposes the downstream advection of disturbances. © 2010 Cambridge University Press

Amplifier and resonator dynamics of a low-Reynolds-number recirculation bubble in a global framework

International audienceThe stability behaviour of a low-Reynolds-number recirculation flow developing in a curved channel is investigated using a global formulation of hydrodynamic stability theory. Both the resonator and amplifier dynamics are investigated. The resonator dynamics, which results from the ability of the flow to self-sustain perturbations, is studied through a modal stability analysis. In agreement with the literature, the flow becomes globally unstable via a three-dimensional stationary mode. The amplifier dynamics, which is characterized by the ability of the flow to exhibit large transient amplifications of initial perturbations, is studied by looking for the two- and three-dimensional initial perturbations that maximize the energy gain over a given time horizon. The optimal initial two-dimensional perturbations have the form of wave packets localized in the upstream part of the recirculation bubble. It is shown that they are first amplified while travelling downstream along the shear layer of the recirculation bubble and then decay when leaving the recirculation bubble. Maximal energy gain is thus achieved for a time horizon approximately corresponding to the propagation of the wave packet along the whole recirculation bubble. The resonator and amplifier dynamics are associated with different types of structures in the flow: three-dimensional steady structures for the resonator dynamics and nearly two-dimensional unsteady structures for the amplifier dynamics. A comparison of the strength of the two dynamics is proposed. The transient energetic growth of the two-dimensional unsteady perturbations is large at moderate time, compared to the very weak exponential growth of the three-dimensional stationary mode. This suggests that, as soon as there is noise in the system, the amplifier dynamics dominates the resonator dynamics, thus explaining the appearance of unsteadiness rather than the emergence of stationary structures in similar experimental flows. © 2008 Cambridge University Press

Response analysis of a laminar premixed M-flame to flow perturbations using a linearized compressible Navier-Stokes solver

International audienceThe response of a laminar premixed methane-air flame subjected to flow perturbations around a steady state is examined experimentally and using a linearized compressible Navier-Stokes solver with a one-step chemistry mechanism to describe combustion. The unperturbed flame takes an M-shape stabilized both by a central bluff body and by the external rim of a cylindrical nozzle. This base flow is computed by a nonlinear direct simulation of the steady reacting flow, and the flame topology is shown to qualitatively correspond to experiments conducted under comparable conditions. The flame is then subjected to acoustic disturbances produced at different locations in the numerical domain, and its response is examined using the linearized solver. This linear numerical model then allows the componentwise investigation of the effects of flow disturbances on unsteady combustion and the feedback from the flame on the unsteady flow field. It is shown that a wrinkled reaction layer produces hydrodynamic disturbances in the fresh reactant flow field that superimpose on the acoustic field. This phenomenon, observed in several experiments, is fully interpreted here. The additional perturbations convected by the mean flow stem from the feedback of the perturbed flame sheet dynamics onto the flow field by a mechanism similar to that of a perturbed vortex sheet. The different regimes where this mechanism prevails are investigated by examining the phase and group velocities of flow disturbances along an axis oriented along the main direction of the flow in the fresh reactant flow field. It is shown that this mechanism dominates the low-frequency response of the wrinkled shape taken by the flame and, in particular, that it fully determines the dynamics of the flame tip from where the bulk of noise is radiated

Analysis and Comparison of Transonic Buffet Phenomenon over Several Three-Dimensional Wings

International audienceThe transonic buffet is a complex aerodynamic instability that appears on wings and airfoils at a high subsonic Mach number and/or angle of attack. It consists of a shock oscillation that induces pressure and notably lift fluctuations, thus limiting the flight envelope of civil aircraft. The aim of the present Paper is to improve the understanding of the flow physics of the three-dimensional transonic buffet over swept wings through the analysis and comparison of four different experimental databases. In particular, the objective is to identify characteristic values of the phenomenon such as Strouhal numbers, convection velocities, buffet onset, etc. It is shown that some dimensionless numbers are kept constant among the different databases and consequently can be considered as characteristics, whereas others change. The key factors in the understanding of the three-dimensional transonic buffet phenomenon lie in explaining common features but also the variability of transonic buffet characteristics in different configurations. In particular, it is shown that three-dimensional buffet is characterized by a Strouhal number in the range 0.2–0.3 and a spanwise convection velocity of 0.245 0.015 U∞, where U∞ denotes the freestream velocity. These characteristic ranges of frequencies are larger than those of the two-dimensional buffet phenomenon, which suggests different physical mechanisms

Global bionetworks and challenges in regulating autologous adult stem cells

Autologous adult stem cells (ASCs) are increasingly being administered to patients with limited evidence from clinical trials that they are safe and effective. The marketing of autologous ASCs predominantly over the Internet by companies based in low-to-middle income countries, such as the Bahamas, Mexico, India and China, is well documented.(1, 2) However, even in countries such as the United States, Japan, and Australia, physicians are prescribing autologous ASCs to patients outside the context of clinical trials. These doctors often form part of loose collaborative networks of clinicians, businesses, patients and researchers operating both domestically and across national boundaries. The emergence of these networks not only puts patients who seek out these interventions at risk: it threatens to undermine the very basis of ‘good medical practice’.funded by the Ministry of Education, Singapore, and the Humanities and Social Sciences (HSS) Division of the Office of the Deputy President (Research and Technology) at the National University of Singapore (NU