arXiv subjects

E. Boujo

Publications and source records attributed to E. Boujo.

9 recordsLinked to original sources

arXiv2025

On the symmetry-breaking instability of the flow past axisymmetric bluff bodies

The primary bifurcation of the flow past three-dimensional axisymmetric bodies is investigated. We show that the azimuthal vorticity generated at the body surface is at the root of the instability, and that the mechanism proposed by Magnaudet and Mougin (2007) in the context of spheroidal bubbles extends to axisymmetric bodies with a no-slip surface. The instability arises in a thin region of the flow in the near wake and is associated with the occurrence of strong vorticity gradients. We propose a simple yet effective scaling law for the prediction of the instability, based on a measure of the near-wake vorticity and of the radial extent of the separation bubble. At criticality, the resulting Reynolds number collapses approximately to a constant value for bodies with different geometries and aspect ratios, with a relative variation that is one order of magnitude smaller than that of the standard Reynolds number based on the free-stream velocity and body diameter. The new scaling can be useful to assess whether the steady flow past axisymmetric bodies is globally unstable, without the need for an additional stability analysis.

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arXiv2022

From thin plates to Ahmed bodies: linear and weakly non-linear stability of rectangular prisms

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) at lower Reynolds numbers $Re$, two stationary modes, $A$ and $B$, become unstable, breaking the top/bottom and left/right planar symmetries, respectively; (ii) at larger $Re$, two oscillatory modes become unstable and, again, each mode breaks one of the two symmetries. The critical $Re$ of these four modes increase with $L/H$, qualitatively reproducing the trend of stationary and oscillatory bifurcations in axisymmetric wakes (e.g. thin disk, sphere and bullet-shaped bodies). Next, a weakly non-linear analysis based on the two stationary modes $A$ and $B$ yields coupled amplitude equations. For Ahmed bodies, as $Re$ increases state $(A,0)$ appears first, followed by state $(0,B)$. While there is a range of bistability of those two states, only $(0,B)$ remains stable at larger $Re$, similar to the static wake deflection (across the larger base dimension) observed in the turbulent regime. The bifurcation sequence, including bistability and hysteresis, is validated with fully non-linear direct numerical simulations, and is shown to be robust to variations in $W$ and $L$ in the range of common Ahmed bodies.

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arXiv2020

Optimal spanwise-periodic control for recirculation length in a backward-facing step flow

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 compute optimal spanwise-periodic control (steady wall blowing/suction or wall deformation) for decreasing the recirculation length, based on a second-order sensitivity analysis. Results show that wall-normal velocity control is always more efficient than wall-tangential control. The most efficient spanwise wavelength for the optimal control depends on the location: $β=0.6$ on the upper wall and $β=1$ on the upstream part of the lower wall. The linear amplification of the optimal control resembles the maximum linear gain, which confirms the link between recirculation length and amplification potential in this flow. Sensitivity predictions for blowing/suction amplitudes up to $O(10^{-3})$ and wall deformation amplitudes up to $O(10^{-2})$ are in good agreement with three-dimensional direct numerical simulations. For larger wall deformation amplitudes, the flow becomes unsteady. This study illustrates how the concept of second-order sensitivity and the associated optimization method allow for a systematic exploration of the best candidates for spanwise-periodic control.

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arXiv2019

Second-order sensitivity in the cylinder wake: optimal spanwise-periodic wall actuation and wall deformation

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-order eigenvalue sensitivity. Such control has a zero 1st-order linear effect, so the 2nd-order quadratic effect prevails. The sensitivity operator allows one (i) to predict the effect of any control without computing the controlled flow, (ii) to compute the optimal control for growth rate/frequency modification. The method takes advantage of spanwise periodicity to reduce computational complexity (from a 3D problem to a 2D one). The approach is applied to the leading eigenvalue of the laminar flow around a circular cylinder. Two SP controls are explored: wall actuation (blowing/suction) and wall deformation. Decomposing the eigenvalue variation, we find that the 3D contribution (from the SP 1st-order flow modification) is generally larger than the 2D one from the mean flow correction (spanwise-invariant 2nd-order flow modification). The optimal control for stabilization is top-down symmetric, leading to varicose streaks in the wake. Analyzing the competition between amplification and stabilization shows that optimal varicose streaks are not significantly more amplified than sinuous ones but have a stronger stabilizing effect. The optimal wall deformation induces a flow modification similar to that of the optimal wall actuation. In general, spanwise and tangential actuation have a small contribution to the optimal control, so normal-only actuation is a good trade-off between simplicity and effectiveness. Our method opens the way to the systematic design of optimal SP control for a variety of control objectives other than linear stability.

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arXiv2019

Pancake making and surface coating: optimal control of a gravity-driven liquid film

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. Solidification is modeled with a temperature-dependent viscosity. Because the flow eventually ceases as the liquid film becomes very viscous, the key question this study aims to address is: what is the optimal surface kinematics for spreading the liquid layer uniformly? Two methods are proposed to tackle this problem. In the first one, the surface kinematics is assumed a priori to be harmonic and parameterized. The optimal parameters are inferred using the Monte-Carlo method. This ``brute-force'' approach leads to a moderate improvement of the film uniformity compared to the reference case when no motion is imposed to the surface. The second method is formulated as an optimal control problem, constrained by the governing partial differential equation, and solved with an adjoint equation. Key benefits of this method are that no assumption is made on the form of the control, and that significant improvement in thickness uniformity are achieved with a comparatively smaller number of evaluations of the objective function.

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arXiv2019

Processing time-series of randomly forced self-oscillators: the example of beer bottle whistling

We present a model-based, output-only parameter identification method for self-sustained oscillators forced by dynamic noise, which we illustrate experimentally with an aeroacoustic setup: a turbulent jet impinging a beer bottle and producing a whistling tone in a finite range of jet angles and velocities. Given a low-order model of the system, the identification analyzes stationary time series of a single observable: acoustic pressure fluctuations in the bottle. As this observable exhibits the characteristics of weakly non-linear self-oscillations, we choose as a minimal model the Van der Pol (VdP) oscillator: a linear acoustic oscillator (bottle) subject to stochastic forcing and non-linear deterministic forcing (turbulent jet). Although very simple, the VdP oscillator driven by random noise proves to be a sufficient phenomenological description of the aeroacoustic limit cycle for model-based linear growth rate identification. The associated stochastic amplitude equation allows us to describe the stochastic fluctuations of the acoustic amplitude resulting from a competition between (i) linear growth rate from the coherent unsteady vortex force, (ii) random forcing from the turbulence, (iii) non-linear saturation of the coherent flapping of the jet. Finally, the associated adjoint Fokker-Planck equation reveals the deterministic potential well and the stochastic forcing intensity governing these random fluctuations. Additional experiments with an external control validate the identification results. We observe that different operating conditions can yield similar statistics but different dynamics, showing that the identification method can disentangle deterministic and stochastic effects in systems forced stochastically. This output-only identification approach can be used in a wide range of phenomena exhibiting stationary self-sustained oscillations in the presence of random forcing.

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arXiv2019

Stochastic modelling of a freely rotating disk facing a uniform flow

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 loading; moments and centre of pressure of the front and base sides. When the disk is fixed and aligned, symmetry-breaking vortex shedding is observed and all orientations are visited with equal probability, yielding axisymmetric long-term statistics. Very-low-frequency antisymmetric modes as recently observed by Rigas et al. (2014) are not observed unless the disk shape is modified into that of a bullet, showing the importance of the separation angle. It suggests that these modes are linearly stable for the disk while they are unstable for the bullet shape. When the disk is fixed and inclined, the base center of pressure (CoP) shifts preferentially towards one side of the rotation axis. Finally, when the disk is free to rotate, the front moment is proportional to the disk inclination (aerodynamic stiffness), while the base moment is well correlated with the disk inclination. From these observations, a low-order model is derived that couples (i) the CoP, forced stochastically by the turbulent flow, and (ii) the disk inclination, as a linear harmonic oscillator forced by the base moment. The model captures well the main statistic and dynamics features observed experimentally. One difference lies in the distribution of the disk inclination (which features exponential tails in the measurements but is Gaussian in the model), suggesting a possible refinement with non-linearities or time delays. The model is expected to capture coupled dynamics in other systems involving turbulent wakes behind freely rotating bluff bodies.

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arXiv2015

Second-order sensitivity of parallel shear flows and optimal spanwise-periodic flow modifications

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 stability, i.e. the 1st-order eigenvalue variation is zero. A 2nd-order sensitivity operator is computed from a 1D calculation, allowing one to predict how eigenvalues are affected by any U1, without actually solving for modified eigenvalues/eigenmodes. Comparisons with full 2D stability calculations in a plane channel flow and in a mixing layer show excellent agreement. Next, optimisation is performed on the 2nd-order sensitivity operator: for each eigenmode streamwise wavenumber and base flow modification spanwise wavenumber b, the most stabilising profiles U1 are computed, together with lower bounds for the variation in leading eigenvalue. These bounds increase like b^-2 as b goes to 0, yielding a large stabilising potential. However, 3D modes with wavenumbers |b0|=b and b/2 are destabilised, thus larger control wavenumbers should be preferred. The modification U1 optimised for the most unstable streamwise wavenumber has a stabilising effect on other streamwise wavenumbers too. Finally, the potential of transient growth to amplify perturbations and stabilise the flow is assessed. Combined optimal perturbations that achieve the best balance between transient linear amplification and flow stabilisation are determined. In the mixing layer with b<1.5, these combined optimal perturbations appear similar to transient growth-only optimal perturbations, and achieve a more efficient overall stabilisation than optimal 1D and 2D modifications computed for stabilisation only. This is consistent with the efficiency of streak-based control strategies.

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arXiv2014

Controlled reattachment in separated flows: a variational approach to recirculation length reduction

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 $40 \leq Re \leq 120$, both in the subcritical and supercritical regimes. Regions which are the most sensitive to volume forcing and wall blowing/suction are identified. Control configurations which reduce the recirculation length are designed based on the sensitivity information, in particular small cylinders used as control devices in the wake of the main cylinder, and fluid suction at the cylinder wall. Validation against full non-linear Navier-Stokes calculations shows excellent agreement for small-amplitude control. The linear stability properties of the controlled flow are systematically investigated. At moderate Reynolds numbers, we observe that regions where control reduces the recirculation length correspond to regions where it has a stabilising effect on the most unstable global mode associated to vortex shedding, while this property does not hold any more at larger Reynolds numbers.

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