Edouard Boujo

École Polytechnique Fédérale de Lausanne | EPFL · School of Engineering

We study the stability of laminar wakes past three-dimensional rectangular prisms. The width-to-height ratio is set to $W/H=1.2$ , while the length-to-height ratio $1/6< L/H<3$ covers a wide range of geometries from thin plates to elongated Ahmed bodies. First, global linear stability analysis yields a series of pitchfork and Hopf bifurcations: (i)...

We study numerically and theoretically the gravity-driven flow of a viscous liquid film coating the inner side of a horizontal cylindrical tube and surrounding a shear-free dynamically inert gaseous core. The liquid-gas interface is prone to the Rayleigh-Plateau and Rayleigh-Taylor instabilities. Here we focus on the limit of low and intermediate B...

We study a gravity-driven viscous flow coating a vertical cylindrical fibre. The destabilisation of a draining liquid column into a downward moving train of beads has been linked to the conjunction of the Rayleigh–Plateau and Kapitza instabilities in the limit of small Bond numbers $Bo$ . Here, we focus on quasi-inertialess flows (large Ohnesorge n...

We study numerically and theoretically the gravity-driven flow of a viscous liquid film coating the inner side of a horizontal cylindrical tube and surrounding a shear-free dynamically inert gaseous core. The liquid-gas interface is prone to the Rayleigh-Plateau and Rayleigh-Taylor instabilities. Here, we focus on the limit of low and intermediate...

We consider nonlinear dynamical systems driven by stochastic forcing. It has been largely evidenced in the literature that the linear response of non-normal systems (e.g. fluid flows) may exhibit a large variance amplification, even in a linearly stable regime. This linear response, however, is relevant only in the limit of vanishing forcing intens...

We study the stability of laminar wakes past three-dimensional rectangular prisms. The width-to-height ratio is set to $W/H=1.2$, while the length-to-height ratio $1/6<L/H<3$ covers a wide range of geometries from thin plates to elongated Ahmed bodies. First, global linear stability analysis yields a series of pitchfork and Hopf bifurcations: (i) a...

We propose a theoretical approach to derive amplitude equations governing the weakly nonlinear evolution of non-normal dynamical systems, when they experience transient growth or respond to harmonic forcing. This approach reconciles the non-modal nature of these growth mechanisms and the need for a centre manifold to project the leading-order dynam...

We study a gravity-driven viscous flow coating a vertical cylindrical fiber. The destabilization of a draining liquid column into a downward moving train of beads has been linked to the conjunction of the Rayleigh-Plateau and Kapitza instabilities in the limit of small Bond numbers, Bo. Here, we focus on quasi-inertialess flows (large Ohnesorge num...

A formal framework to characterize and control/optimize the flow past permeable membranes by means of a homogenization approach is proposed and applied to the wake flow past a permeable cylindrical shell. From a macroscopic viewpoint, a Navier-like effective stress jump condition is employed to model the presence of the membrane, in which the norma...

We propose a theoretical approach to derive amplitude equations governing the weakly nonlinear evolution of nonnormal systems, when they experience transient growth or respond to harmonic forcing. This approach reconciles the non-modal nature of these growth mechanisms and the need for a center manifold to project the leading-order dynamics. Under...

The present work explores the impact of rotation on the dynamics of a thin liquid layer deposited on a spheroid (bi-axial ellipsoid) rotating around its vertical axis. An evolution equation based on the lubrication approximation was derived, which takes into account the combined effects of the non-uniform curvature, capillarity, gravity, and rotati...

Adjoint-based sensitivity analysis is routinely used today to assess efficiently the effect of open-loop control on the linear stability properties of unstable flows. Sensitivity maps identify regions where small-amplitude control is the most effective, i.e. yields the largest first-order (linear) eigenvalue variation. In this study an adjoint meth...

Three-dimensional control is considered in the flow past a backward-facing step (BFS). The BFS flow at Reynolds number Re=500 (defined with the step height and the maximum inlet velocity) is two-dimensional and linearly stable but increasingly receptive to disturbances, with a potential for amplification as the recirculation length increases. We co...

Adjoint-based sensitivity analysis is routinely used today to assess efficiently the effect of open-loop control on the linear stability properties of unstable flows. Sensitivity maps identify regions where small-amplitude control is the most effective, i.e. yields the largest first-order (linear) eigenvalue variation. In this study an adjoint meth...

The fluid–structure interaction between a thin circular disk and its turbulent wake is investigated experimentally and described with a low-order stochastic model. The disk faces a uniform flow at Reynolds number Re=133 000 and can rotate around one of its diameters. It is equipped with instantaneous pressure measurements to give the aerodynamic lo...

We present a model-based, output-only parameter identification method for self-sustained oscillators forced by dynamic noise, which we illustrate experimentally with a simple aeroacoustic setup: a turbulent jet impinging a beer bottle and producing a distinct whistling tone in a finite range of jet angles and jet velocities. Given a low-order model...

Three-dimensional control is considered in the flow past a backward-facing step (BFS). The BFS flow at Reynolds number $Re=500$ (defined with the step height and the maximum inlet velocity) is two-dimensional and linearly stable but increasingly receptive to disturbances, with a potential for amplification as the recirculation length increases. We...

This paper investigates the flow of a solidifying liquid film on a solid surface subject to a complex kinematics, a process relevant to pancake making and surface coating. The flow is modeled using the lubrication approximation, with a gravity force whose magnitude and direction depend on the time-dependent orientation of the surface. Solidificatio...

Two-dimensional (2D) flows can be controlled efficiently using spanwise “waviness,” i.e., a control (e.g., wall blowing and suction or wall deformation) that is periodic in the spanwise direction. This study tackles the global linear stability of 2D flows subject to small-amplitude three-dimensional (3D) spanwise-periodic control. Building on previ...

The fluid–structure interaction between a thin circular disk and its turbulent wake is investigated experimentally and described with a low-order stochastic model. The disk faces a uniform flow at Reynolds number Re = 133 000 and can rotate around one of its diameters. It is equipped with instantaneous pressure measurements to give the aerodynamic...

The fluid–structure interaction between a thin circular disk and its turbulent wake is investigated experimentally and described with a low-order stochastic model. The disk faces a uniform flow at Reynolds number Re = 133 000 and can rotate around one of its diameters. It is equipped with instantaneous pressure measurements to give the aerodynamic...

This paper investigates the flow of a solidifying liquid film on a solid surface subject to a complex kinematics, a process relevant to pancake making and surface coating. The flow is modeled using the lubrication approximation with a temperature-dependent viscosity and a gravity force whose magnitude and direction depend on the time-dependent orie...

Blowing across the opening of a bottle to produce sound is an entertaining and yet intriguing activity. We investigate experimentally this phenomenon, and quantify the common observation that a distinct tone is obtained for a large enough blowing velocity and for a finite range of blowing angles. We extract the spatio-temporal evolution of the acou...

Two-dimensional (2D) flows are efficiently controlled with spanwise waviness, i.e. spanwise-periodic (SP) wall blowing/suction/deformation. We tackle the global linear stability of 2D flows subject to small-amplitude 3D SP control. Building on previous work for parallel flows (Boujo et al. 2015), an adjoint method is proposed for computing the 2nd-...

We report experimental evidence of thermoacoustic bistability in a lab-scale turbulent combustor over a well-defined range of fuel–air equivalence ratios. Pressure oscillations are characterized by an intermittent behavior with “bursts,” i.e., sudden jumps between low and high amplitudes occurring at random time instants. The corresponding probabil...

Complex systems exhibiting critical transitions when one of their governing parameters varies are ubiquitous in nature and in engineering applications. Despite a vast literature focusing on this topic, there are few studies dealing with the effect of the rate of change of the bifurcation parameter on the tipping points. In this work, we consider a...

This study assesses the ability of a sensitivity-based, span-wise homogeneous control velocity distributed at the surface of a circular cylinder to cut down the cost of reducing drag by more classical techniques, e.g., base bleed and lateral suction. At Reynolds number Re=100, achieving the linear optimal reduction requires a time-dependent control...

Turbulent mixing layers over cavities can couple with acoustic waves and lead to undesired oscillations. To understand the nonlinear aspects of this phenomenon, a turbulent mixing layer over a deep cavity at Reynolds number 150 000 is considered and its response to harmonic forcing is analysed with large-eddy simulations (LES) and linearised Navier...

We report experimental evidence of thermoacoustic bi-stability in a lab-scale turbulent combustor over a well-defined range of fuel-air equivalence ratios. Pressure oscillations are characterized by an intermittent behavior with “bursts”, i.e. sudden jumps between low and high amplitudes occurring at random time instants. The corresponding probabil...

The problem of output-only parameter identification for nonlinear oscillators forced by colored noise is considered. In this context, it is often assumed that the forcing noise is white, since its actual spectral content is unknown. The impact of this white noise forcing assumption upon parameter identification is quantitatively analyzed. First, a...

Flow around a square cylinder controlled using plasma actuators (PAs) is numerically investigated by direct numerical simulation in order to clarify the most effective location of actuator installation and to elucidate the mechanism of control effect. The Reynolds number based on the cylinder diameter and the free-stream velocity is set to be 100 t...

We present a model-based output-only method for identifying from time series the parameters governing the dynamics of stochastically forced oscillators. In this context, suitable models of the oscillator's damping and stiffness properties are postulated, guided by physical understanding of the oscillatory phenomena. The temporal dynamics and the pr...

Flow around a square cylinder controlled using plasma actuators (PAs) is numerically investigated by direct numerical simulation in order to clarify the most effective location of actuator installation and to elucidate the mechanism of control effect. The Reynolds number based on the cylinder diameter and the free-stream velocity is set to be 100 t...

Thermoacoustic instabilities in gas turbines and aeroengine combustors fall within the category of complex systems. They can be described phenomenologically using nonlinear stochastic differential equations, which constitute the grounds for output-only model-based system identification. It has been shown recently that one can extract the governing...

The purpose of this review article is to push amplitude equations as far as possible from threshold. We focus on the Stuart–Landau amplitude equation describing the supercritical Hopf bifurcation of the flow in the wake of a cylinder for critical Reynolds number Re_c = 46. After having reviewed Stuartʼs weakly nonlinear multiple-scale expansion met...

We use the adjoint method to compute sensitivity maps for the limit-cycle frequency and amplitude of the Bénard–von Kármán vortex street in the wake of a circular cylinder. The sensitivity analysis is performed in the frame of the semi-linear self-consistent model recently introduced by Mantič et al. ( Phys. Rev. Lett. , vol. 113, 2014, 084501), wh...

Practical combustion systems are prone to thermoacoustic instabilities, which affect the mechanical integrity of the components. This paper investigates how the turbulence-induced-noise stochastically drives these thermoacoustic limit-cycles. A model of the constructive feedback between the flames and the combustor acoustics is proposed and include...

The question of optimal spanwise-periodic modification for the stabilisation of spanwise-invariant flows is addressed. A 2nd-order sensitivity analysis is conducted for the linear temporal stability of parallel flows U0 subject to small-amplitude spanwise-periodic modification e*U1, e<<1. Spanwise-periodic modifications have a quadratic effect on s...

The two-dimensional backward-facing step flow is a canonical example of noise amplifier flow: global linear stability analysis predicts that it is stable, but perturbations can undergo large amplification in space and time as a result of non-normal effects. This amplification potential is best captured by optimal transient growth analysis, optimal...

A variational technique is used to derive analytical expressions for the sensitivity of several geometric indicators of flow separation to steady actuation. Considering the boundary layer flow above a wall-mounted bump, the six following representative quantities are considered: the locations of the separation point and reattachment point connected...

We use adjoint-based gradients to analyze the sensitivity of the drag force on a square cylinder. At Re = 40, the flow settles down to a steady state. The quantity of interest in the adjoint formulation is the steady asymptotic value of drag reached after the initial transient, whose sensitivity is computed solving a steady adjoint problem from kno...

Flow separation is relevant to many industrial applications, since it is detrimental to the aerodynamic performance of vehicles, induces vibrations in mechanical structures, but can also contribute to improve mixing in combustion devices. In this thesis, the fundamental problem of separated flow control is addressed using adjoint-based methods appl...

Linear optimal gains $G_{opt}(\omega)$ are computed for the separated boundary-layer flow past a two-dimensional bump in the subcritical regime. Very large values are found, making it possible for small-amplitude noise to be strongly amplified and to destabilize the flow. Next, a variational technique is used to compute the sensitivity of $G_{opt}(...

A variational technique is used to derive analytical expressions for the sensitivity of recirculation length to steady forcing in separated flows. Linear sensitivity analysis is applied to the two-dimensional steady flow past a circular cylinder for Reynolds numbers 40≤Re≤120, in both the subcritical and supercritical regimes. Regions that are the...

Linear optimal gains are computed for the subcritical two-dimensional separated boundary-layer flow past a bump. Very large optimal gain values are found, making it possible for small-amplitude noise to be strongly amplified and to destabilize the flow. The optimal forcing is located close to the summit of the bump, while the optimal response is th...

A variational technique is used to derive analytical expressions for the sensitivity of recirculation length to steady forcing in separated flows. Linear sensitivity analysis is applied to the two-dimensional steady flow past a circular cylinder for Reynolds numbers $40 \leq Re \leq 120$, in both the subcritical and supercritical regimes. Regions t...

A numerical simulation was carried out in order to assess the hypothesis that arterial elongation and bending usually observed in the elderly may be related to exposure to high wall shear stress. A model of carotid artery with realistic mechanical properties was constructed and combined with a flow solver. The artery was made to grow in circumferen...