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Ch J Robinet - One of the best experts on this subject based on the ideXlab platform.
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bifurcations in shock wave laminar Boundary Layer interaction global instability approach
Journal of Fluid Mechanics, 2007Co-Authors: Ch J RobinetAbstract:The principal objective of this paper is to study some unsteady characteristics of an interaction between an incident oblique shock wave impinging on a laminar Boundary Layer developing on a flat plate. More precisely, this paper shows that some unsteadiness, in particular the low-frequency unsteadiness, originates in a supercritical Hopf bifurcation related to the dynamics of the Separated Boundary Layer. Various direct numerical simulations were carried out of a shock-wave/laminar-Boundary-Layer interaction (SWBLI). Three-dimensional unsteady Navier-Stokes equations are numerically solved with an implicit dual time stepping for the temporal algorithm and high-order AUSMPW+ scheme for the spatial discretization. A parametric study on the oblique shock-wave angle has been performed to characterize the unsteady behaviour onset. These numerical simulations have shown that starting from the incident shock angle and the spanwise extension, the flow becomes three-dimensional and unsteady. A linearized global stability analysis is carried out in order to specify and to find some characteristics observed in the direct numerical simulation. This stability analysis permits us to show that the physical origin generating the three-dimensional characters of the flow results from the existence of a three-dimensional stationary global instability.
Uwe Ehrenstein - One of the best experts on this subject based on the ideXlab platform.
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optimal control of a Separated Boundary Layer flow over a bump
Journal of Fluid Mechanics, 2018Co-Authors: Pierre-yves Passaggia, Uwe EhrensteinAbstract:The optimal control of a globally unstable two-dimensional Separated Boundary Layer over a bump is considered using augmented Lagrangian optimization procedures. The present strategy allows for controlling of the flow from a fully developed nonlinear state back to the steady state using a single actuator. The method makes use of a decomposition between the slow dynamics associated with the base flow modification and the fast dynamics, known as flapping, characterized by a large scale oscillation of the recirculation region. Starting from a steady state forced by a suction actuator located near the separation point, the base flow modification is shown to be controlled by a vanishing suction strategy. For weakly unstable flow regimes, this control law can be further optimized by means of direct–adjoint iterations of the nonlinear Navier–Stokes equations. In the absence of external noise, this novel approach proves to be capable of controlling the transient dynamics and the base flow modification simultaneously.
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Open-loop control of a Separated Boundary Layer
Comptes Rendus Mecanique, 2014Co-Authors: Edouard Boujo, François Gallaire, Uwe EhrensteinAbstract:Abstract Linear optimal gains G opt ( ω ) 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 ( ω ) to steady control (volume force in the flow, or blowing/suction at the wall). The bump summit is identified as the region the most sensitive to wall control. Based on these (linear) sensitivity results, a simple open-loop control strategy is designed, with steady wall suction at the bump summit. Calculations on non-linear base flows confirm that optimal gains can be significantly reduced at all frequencies using this control. Finally, sensitivity analysis is applied to the length of the recirculation region l c and reveals that the above control configuration is also the most efficient to shorten the recirculation region. This suggests that l c is a relevant macroscopic parameter to characterize wall-bounded Separated flows, which could be used as a proxy for energy amplification when designing steady open-loop control.
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open loop control of noise amplification in a Separated Boundary Layer flow
Physics of Fluids, 2013Co-Authors: Edouard Boujo, Uwe Ehrenstein, François GallaireAbstract: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 the largest in the shear Layer. The largest amplification occurs at frequencies corresponding to eigenvalues which first become unstable at higher Reynolds number. Nonlinear direct numerical simulations show that a low level of noise is indeed sufficient to trigger random flow unsteadiness, characterized here by large-scale vortex shedding. Next, a variational technique is used to compute efficiently the sensitivity of optimal gains to steady control (through source of momentum in the flow, or blowing/suction at the wall). A systematic analysis at several frequencies identifies the bump summit as the most sensitive region for control with wall actuation. Based on ...
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Open-loop control of a Separated Boundary Layer
2013Co-Authors: Edouard Boujo, François Gallaire, Uwe EhrensteinAbstract: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 $G_opt(\omega)$ to steady control (volume force in the flow, or blowing/suction at the wall). The bump summit is identified as the region the most sensitive to wall control. Based on these (linear) sensitivity results, a simple open-loop control strategy is designed, with steady wall suction at the bump summit. Calculations on non-linear base flows confirm that optimal gains can be significantly reduced at all frequencies using this control. Finally, sensitivity analysis is applied to the length of the recirculation region $l_c$ and reveals that the above control configuration is also the most efficient to shorten the recirculation length. This suggests that $l_c$ is a relevant macroscopic parameter to characterize wall-bounded Separated flows, which could be used as a proxy for energy amplification when designing steady open-loop control.
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Instabilités bi-et tridimensionnelles dans une couche limite décollée compressible subsonique
2013Co-Authors: Matthieu Merle, Uwe Ehrenstein, Jeanchristophe RobinetAbstract:Flow separation is a common feature in wall-bounded flow, where it is generally induced by an adverse pressure gradient. Here we reconsider a bump-type geometry which has been used in previous numerical investigations of the stability of the laminar recirculation bubble for incompressible flow. It has been shown for low Reynolds number that the first bifurcation of the 2D stationnary flow is characterized by a zero-frequency 3D instability mode. For larger Reynolds number a second bifurcation appears (Hopfbifurcation) and Separated Boundary-Layer is then subject to a low frequency phenomenon known as'flapping'. The influence of compressibility for this type of flow is assessed.We first solve the compressible Navier-Stokes equations in order to obtain an equilibrium solution for increasing compressibility effects. Two-dimensional global stability of this solution is then investigatesand we assess the influence of Mach number on the critical Reynolds number for which the Separated flow becomes unstable with respect to oscillatory perturbations.Three-dimensional transverse instabilities are addressed as well and in particular the evolution of growth rate and transverse wave length of the most unstable mode for several Mach numbers.
Jeanchristophe Robinet - One of the best experts on this subject based on the ideXlab platform.
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Transonic buffet instability: From two-dimensional airfoils to three-dimensional swept wings
Physical Review Fluids, 2019Co-Authors: Edorado Paladini, Samir Beneddine, Julien Dandois, Denis Sipp, Jeanchristophe RobinetAbstract:The objective of the present study is to explain the evolution of the transonic buffet phenomenon from two-dimensional airfoils to three-dimensional swept wings by a global stability analysis. With respect to two-dimensional buffet, shock oscillation frequency increases by a factor of 4 to 7 in the case of a swept 30° wing and three-dimensional patterns in the detached Boundary Layer are convected outboard. Crouch et al. [J. Comput. Phys. 224, 924 (2007)] explained the two-dimensional transonic buffet phenomenon by the appearance of a real positive complex eigenvalue of the linearized Jacobian matrix. In the case of an infinite unswept wing, the present study shows that two unstable modes actually exist: The two-dimensional transonic buffet mode already identified by Crouch et al. [J. Fluid Mech. 628, 357 (2009)] and a strongly amplified three-dimensional zero-frequency mode. The latter exhibits regular patterns in the Separated Boundary Layer, which relates to the so-called buffet cells as named by Iovnovich et al. [AIAA J. 53, 449 (2015)]. The nonzero sweep angle generates a spanwise velocity component on the wing which convects the cells outboard. This impacts both modes identified in the unswept case: The two-dimensional mode is weakly damped by the sweep while the three-dimensional buffet cells mode, even if weakly damped, remains strongly unstable and now exhibits a nonzero frequency which increases with the sweep angle. The frequency and wavelength of the most unstable three-dimensional mode for a sweep angle of 30° agree well with numerical and experimental values of the three-dimensional transonic buffet on wings. The analysis of the wavemaker of the three-dimensional modes indicates that the core of the instability is nearly solely located in the Separated region, with a maximum along the separation line. In contrast, the wavemaker of the two-dimensional buffet mode exhibits stronger values all along the
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Instabilités bi-et tridimensionnelles dans une couche limite décollée compressible subsonique
2013Co-Authors: Matthieu Merle, Uwe Ehrenstein, Jeanchristophe RobinetAbstract:Flow separation is a common feature in wall-bounded flow, where it is generally induced by an adverse pressure gradient. Here we reconsider a bump-type geometry which has been used in previous numerical investigations of the stability of the laminar recirculation bubble for incompressible flow. It has been shown for low Reynolds number that the first bifurcation of the 2D stationnary flow is characterized by a zero-frequency 3D instability mode. For larger Reynolds number a second bifurcation appears (Hopfbifurcation) and Separated Boundary-Layer is then subject to a low frequency phenomenon known as'flapping'. The influence of compressibility for this type of flow is assessed.We first solve the compressible Navier-Stokes equations in order to obtain an equilibrium solution for increasing compressibility effects. Two-dimensional global stability of this solution is then investigatesand we assess the influence of Mach number on the critical Reynolds number for which the Separated flow becomes unstable with respect to oscillatory perturbations.Three-dimensional transverse instabilities are addressed as well and in particular the evolution of growth rate and transverse wave length of the most unstable mode for several Mach numbers.
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sensitivity and optimal forcing response in Separated Boundary Layer flows
Physics of Fluids, 2009Co-Authors: Frederic Alizard, S Cherubini, Jeanchristophe RobinetAbstract:The optimal asymptotic response to time harmonic forcing of a convectively unstable two-dimensional Separated Boundary Layer on a flat plate is numerically revisited from a global point of view. By expanding the flow disturbance variables and the forcing term as a summation of temporal modes, the linear convective instability mechanism associated with the response leading to the maximum gain in energy is theoretically investigated. Such a response is driven by a pseudoresonance of temporal modes due to the non-normality of the underlying linearized evolution operator. In particular, the considered expansion on a limited number of modes is found able to accurately simulate the linear instability mechanism, as suggested by a comparison between the global linear stability analysis and a linearized direct numerical simulation. Furthermore, the dependence of such a mechanism on the Reynolds number and the adverse pressure gradient is investigated, outlining a physical description of the destabilization of the ...
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Sensitivity and optimal forcing response in Separated Boundary Layer flows
Physics of Fluids, 2009Co-Authors: Frederic Alizard, S Cherubini, Jeanchristophe RobinetAbstract:The optimal asymptotic response to time harmonic forcing of a convectively unstable two-dimensional Separated Boundary Layer on a flat plate is numerically revisited from a global point of view. By expanding the flow disturbance variables and the forcing term as a summation of temporal modes, the linear convective instability mechanism associated with the response leading to the maximum gain in energy is theoretically investigated. Such a response is driven by a pseudoresonance of temporal modes due to the non-normality of the underlying linearized evolution operator. In particular, the considered expansion on a limited number of modes is found able to accurately simulate the linear instability mechanism, as suggested by a comparison between the global linear stability analysis and a linearized direct numerical simulation. Furthermore, the dependence of such a mechanism on the Reynolds number and the adverse pressure gradient is investigated, outlining a physical description of the destabilization of the flow induced by the rolling up of the shear Layer. Therefore, the convective character of the problem suggests that the considered flat plate Separated flows may act as a selective noise amplifier. In order to verfy such a possibility, the responses of the flow to the optimal forcing and to a small level of noise are compared, and their connection to the onset of self-excited vortices observed in literature is investigated. For that purpose, a nonlinear direct numerical simulation is performed, which is initialized by a random noise superposed to the base flow at the inflow Boundary points. The band of excited frequencies as well as the associated peak match with the ones computed by the asymptotic global analysis. Finally, the connection between the onset of unsteadiness and the optimal response is further supported by a comparison between the optimal circular frequency and a typical Strouhal number predicted by numerical simulations of previous authors in similar cases.
Jeanfrancois Debieve - One of the best experts on this subject based on the ideXlab platform.
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space and time organization in a shock induced Separated Boundary Layer
Journal of Fluid Mechanics, 2006Co-Authors: Pierre Dupont, C Haddad, Jeanfrancois DebieveAbstract:The interaction of an oblique shock wave impinging on a turbulent Boundary Layer at Mach number 2.3 is experimentally investigated for a wide range of shock intensities. Characteristic time and length scales of the unsteady reflected shock and inside the downstream interaction region are obtained and compared with already existing results obtained in compression ramp experiments as well as in subsonic detached flows. Dimensionless characteristic frequencies are highlighted to characterize low-frequency shock unsteadiness as well as the different large scales which develop inside the initial part of the interaction. The possibility of describing the spatial development of the large scales inside the interaction zone using a mixing-Layer scheme including compressibility effects is tested for a wide range of Mach numbers, shock intensities and geometrical configurations. Moreover, strong evidence of a statistical link between low-frequency shock movements and the downstream interaction is given. Finally, the downstream evolution of the structures shed into the Boundary Layer is characterized and shows features specific of our configuration.
François Gallaire - One of the best experts on this subject based on the ideXlab platform.
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Open-loop control of a Separated Boundary Layer
Comptes Rendus Mecanique, 2014Co-Authors: Edouard Boujo, François Gallaire, Uwe EhrensteinAbstract:Abstract Linear optimal gains G opt ( ω ) 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 ( ω ) to steady control (volume force in the flow, or blowing/suction at the wall). The bump summit is identified as the region the most sensitive to wall control. Based on these (linear) sensitivity results, a simple open-loop control strategy is designed, with steady wall suction at the bump summit. Calculations on non-linear base flows confirm that optimal gains can be significantly reduced at all frequencies using this control. Finally, sensitivity analysis is applied to the length of the recirculation region l c and reveals that the above control configuration is also the most efficient to shorten the recirculation region. This suggests that l c is a relevant macroscopic parameter to characterize wall-bounded Separated flows, which could be used as a proxy for energy amplification when designing steady open-loop control.
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open loop control of noise amplification in a Separated Boundary Layer flow
Physics of Fluids, 2013Co-Authors: Edouard Boujo, Uwe Ehrenstein, François GallaireAbstract: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 the largest in the shear Layer. The largest amplification occurs at frequencies corresponding to eigenvalues which first become unstable at higher Reynolds number. Nonlinear direct numerical simulations show that a low level of noise is indeed sufficient to trigger random flow unsteadiness, characterized here by large-scale vortex shedding. Next, a variational technique is used to compute efficiently the sensitivity of optimal gains to steady control (through source of momentum in the flow, or blowing/suction at the wall). A systematic analysis at several frequencies identifies the bump summit as the most sensitive region for control with wall actuation. Based on ...
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Open-loop control of a Separated Boundary Layer
2013Co-Authors: Edouard Boujo, François Gallaire, Uwe EhrensteinAbstract: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 $G_opt(\omega)$ to steady control (volume force in the flow, or blowing/suction at the wall). The bump summit is identified as the region the most sensitive to wall control. Based on these (linear) sensitivity results, a simple open-loop control strategy is designed, with steady wall suction at the bump summit. Calculations on non-linear base flows confirm that optimal gains can be significantly reduced at all frequencies using this control. Finally, sensitivity analysis is applied to the length of the recirculation region $l_c$ and reveals that the above control configuration is also the most efficient to shorten the recirculation length. This suggests that $l_c$ is a relevant macroscopic parameter to characterize wall-bounded Separated flows, which could be used as a proxy for energy amplification when designing steady open-loop control.
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Open-loop control of noise amplification in a Separated Boundary Layer flow
Physics of Fluids, 2013Co-Authors: Edouard Boujo, Uwe Ehrenstein, François GallaireAbstract: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 the largest in the shear Layer. The largest amplification occurs at frequencies corresponding to eigenvalues which first become unstable at higher Reynolds number. Nonlinear direct numerical simulations show that a low level of noise is indeed sufficient to trigger random flow unsteadiness, characterized here by large-scale vortex shedding. Next, a variational technique is used to compute efficiently the sensitivity of optimal gains to steady control (through source of momentum in the flow, or blowing/suction at the wall). A systematic analysis at several frequencies identifies the bump summit as the most sensitive region for control with wall actuation. Based on these results, a simple open-loop control strategy is designed, with steady wall suction at the bump summit. Linear calculations on controlled base flows confirm that optimal gains can be drastically reduced at all frequencies.Nonlinear direct numerical simulations also show that this control allows the flow to withstand a higher level of stochastic noise without becoming nonlinearly unstable, thereby postponing bypass transition. In the supercritical regime, sensitivity analysis of eigenvalues supports the choice of this control design. Full restabilization of the flow is obtained, as evidenced by direct numerical simulations and linear stability analysis.
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control of a Separated Boundary Layer reduced order modeling using global modes revisited
Theoretical and Computational Fluid Dynamics, 2011Co-Authors: Uwe Ehrenstein, Pierre-yves Passaggia, François GallaireAbstract:The possibility of model reduction using global modes is readdressed, aiming at the controlling of a globally unstable separation bubble induced by a bump geometry. A combined oblique and orthogonal projection approach is proposed to design an estimator and controller in a Riccati-type feedback setting. An input–output criterion is used to appropriately select the modes of the projection basis. The full-state linear instability dynamics is shown to be successfully controlled by the feedback coupling with controllers of moderate degrees of freedom.
