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http://hdl.handle.net/10985/23062
System Identification of Two-Dimensional Transonic Buffet
SANSICA, Andrea; KANAMORI, Masashi; HASHIMOTO, Atsushi; LOISEAU, Jean-Christophe; ROBINET, Jean-Christophe
When modeled within the unsteady Reynolds-Averaged Navier-Stokes framework, the
shock-wave dynamics on a two-dimensional aerofoil at transonic buffet conditions is char-
acterized by time-periodic oscillations. Given the time series of the lift coefficient at different
angles of attack for the OAT15A supercritical profile, the sparse identification of nonlinear dy-
namics (SINDy) technique is used to extract a parametrized, interpretable and minimal-order
description of this dynamics. For all of the operating conditions considered, SINDy infers
that the dynamics in the lift coefficient time series can be modeled by a simple parametrized
Stuart-Landau oscillator, reducing the computation time from hundreds of core hours to sec-
onds. The identified models are then supplemented with equally parametrized measurement
equations and low-rank DMD representation of the instantaneous state vector to reconstruct
the true lift signal and enable real-time estimation of the whole flow field. Simplicity, accuracy
and interpretability make the identified model a very attractive tool towards the construction
of real-time systems to be used during the design, certification and operational phases of the
aircraft life cycle.
Tue, 01 Feb 2022 00:00:00 GMThttp://hdl.handle.net/10985/230622022-02-01T00:00:00ZSANSICA, AndreaKANAMORI, MasashiHASHIMOTO, AtsushiLOISEAU, Jean-ChristopheROBINET, Jean-ChristopheWhen modeled within the unsteady Reynolds-Averaged Navier-Stokes framework, the
shock-wave dynamics on a two-dimensional aerofoil at transonic buffet conditions is char-
acterized by time-periodic oscillations. Given the time series of the lift coefficient at different
angles of attack for the OAT15A supercritical profile, the sparse identification of nonlinear dy-
namics (SINDy) technique is used to extract a parametrized, interpretable and minimal-order
description of this dynamics. For all of the operating conditions considered, SINDy infers
that the dynamics in the lift coefficient time series can be modeled by a simple parametrized
Stuart-Landau oscillator, reducing the computation time from hundreds of core hours to sec-
onds. The identified models are then supplemented with equally parametrized measurement
equations and low-rank DMD representation of the instantaneous state vector to reconstruct
the true lift signal and enable real-time estimation of the whole flow field. Simplicity, accuracy
and interpretability make the identified model a very attractive tool towards the construction
of real-time systems to be used during the design, certification and operational phases of the
aircraft life cycle.Global stability, sensitivity and passive control of low-Reynolds-number flows around NACA 4412 swept wings
http://hdl.handle.net/10985/23404
Global stability, sensitivity and passive control of low-Reynolds-number flows around NACA 4412 swept wings
NASTRO, Gabriele; ROBINET, Jean-Christophe; LOISEAU, Jean-Christophe; PASSAGGIA, Pierre-Yves; MAZELLIER, Nicolas
The stability and sensitivity of two- and three-dimensional global modes developing on steady spanwise-homogeneous laminar separated flows around NACA 4412 swept wings are numerically investigated for different Reynolds numbers Re and angles of
attack α. The wake dynamics is driven by the two-dimensional von Kármán mode whose emergence threshold in the α–Re plane is computed with that of the three-dimensional centrifugal mode. At the critical Reynolds number, the Strouhal number, the streamwise wavenumber of the von Kármán mode and the spanwise wavenumber of the leading three-dimensional centrifugal mode scale as a power law of α. The introduction of a sweep angle attenuates the growth of all unstable modes and entails a Doppler effect in the leading modes’ dynamics and a shift towards non-zero frequencies of the three-dimensional centrifugal modes. These are found to be non-dispersive as opposed to the von Kármán modes. The sensitivity of the leading global modes is investigated in the vicinity of the critical conditions through adjoint-based methods. The growth-rate sensitivity map displays a region on the suction side of the wing, wherein a streamwise-oriented force has a net stabilising effect, comparable to what could have been obtained inside the recirculation bubble. In agreement with the predictions of the sensitivity analysis, a spanwise-homogeneous force suppresses the Hopf bifurcation and stabilises the entire branch of von Kármán modes. In the limit of small amplitudes, passive control via spanwise-wavy forcing produces a stabilising effect similar to that of a
spanwise-homogeneous control and is more effective than localised spherical forces.
Sun, 01 Jan 2023 00:00:00 GMThttp://hdl.handle.net/10985/234042023-01-01T00:00:00ZNASTRO, GabrieleROBINET, Jean-ChristopheLOISEAU, Jean-ChristophePASSAGGIA, Pierre-YvesMAZELLIER, NicolasThe stability and sensitivity of two- and three-dimensional global modes developing on steady spanwise-homogeneous laminar separated flows around NACA 4412 swept wings are numerically investigated for different Reynolds numbers Re and angles of
attack α. The wake dynamics is driven by the two-dimensional von Kármán mode whose emergence threshold in the α–Re plane is computed with that of the three-dimensional centrifugal mode. At the critical Reynolds number, the Strouhal number, the streamwise wavenumber of the von Kármán mode and the spanwise wavenumber of the leading three-dimensional centrifugal mode scale as a power law of α. The introduction of a sweep angle attenuates the growth of all unstable modes and entails a Doppler effect in the leading modes’ dynamics and a shift towards non-zero frequencies of the three-dimensional centrifugal modes. These are found to be non-dispersive as opposed to the von Kármán modes. The sensitivity of the leading global modes is investigated in the vicinity of the critical conditions through adjoint-based methods. The growth-rate sensitivity map displays a region on the suction side of the wing, wherein a streamwise-oriented force has a net stabilising effect, comparable to what could have been obtained inside the recirculation bubble. In agreement with the predictions of the sensitivity analysis, a spanwise-homogeneous force suppresses the Hopf bifurcation and stabilises the entire branch of von Kármán modes. In the limit of small amplitudes, passive control via spanwise-wavy forcing produces a stabilising effect similar to that of a
spanwise-homogeneous control and is more effective than localised spherical forces.Numerical investigation of sheet cavitation over a 3-D venturi configuration
http://hdl.handle.net/10985/23682
Numerical investigation of sheet cavitation over a 3-D venturi configuration
GOUIN, Camille; JUNQUEIRA JUNIOR, Carlos; GONCALVES, Eric; ROBINET, Jean-Christophe
Sheet cavitation appears in many hydraulic applications and can lead to technical issues. Numerical simulation is a pertinent way to study the phenomenon. A numerical tool based on 1-fluid compressible RANS equations with a cavitation model is used to compute a flow within a 3-D venturi geometry with a 4° divergent angle. In the present work, a detailed study of this cavitating flow, which presents a quasi-stable vapour pocket, is carried out using tools such as Power Spectral Densities or Spectral Proper Orthogonal Decompositions. An oblique oscillation of the cavity is then identified and discussed.
Sat, 01 May 2021 00:00:00 GMThttp://hdl.handle.net/10985/236822021-05-01T00:00:00ZGOUIN, CamilleJUNQUEIRA JUNIOR, CarlosGONCALVES, EricROBINET, Jean-ChristopheSheet cavitation appears in many hydraulic applications and can lead to technical issues. Numerical simulation is a pertinent way to study the phenomenon. A numerical tool based on 1-fluid compressible RANS equations with a cavitation model is used to compute a flow within a 3-D venturi geometry with a 4° divergent angle. In the present work, a detailed study of this cavitating flow, which presents a quasi-stable vapour pocket, is carried out using tools such as Power Spectral Densities or Spectral Proper Orthogonal Decompositions. An oblique oscillation of the cavity is then identified and discussed.On the influence of the modelling of superhydrophobic surfaces on laminar–turbulent transition
http://hdl.handle.net/10985/23783
On the influence of the modelling of superhydrophobic surfaces on laminar–turbulent transition
PICELLA, Francesco; ROBINET, Jean-Christophe; CHERUBINI, Stefania
Superhydrophobic surfaces dramatically reduce the skin friction of overlying liquid flows, providing a lubricating layer of gas bubbles trapped within their surface nano-sculptures. Under wetting-stable conditions, different models can be used to numerically simulate their effect on the overlying flow, ranging from spatially homogeneous slip conditions at the wall, to spatially heterogeneous slip–no-slip conditions taking into account or not the displacement of the gas–water interfaces. These models provide similar results in both laminar and turbulent regimes, but their effect on transitional flows has not been investigated yet. In this work we study, by means of numerical simulations and global stability analyses, the influence of the modelling of superhydrophobic surfaces on laminar–turbulent transition in a channel flow. For the K-type scenario, a strong transition
delay is found using spatially homogeneous or heterogeneous slippery boundaries with flat, rigid liquid–gas interfaces. Whereas, when the interface dynamics is taken into account, the time to transition is reduced, approaching that of a no-slip channel flow. It is found that the interface deformation promotes ejection events creating hairpin heads that are prone to breakdown, reducing the transition delay effect with respect to flat slippery surfaces. Thus, in the case of modal transition, the interface dynamics must be taken into account for accurately estimating transition delay. Contrariwise, non-modal transition
triggered by a broadband forcing is unaffected by the presence of these surfaces, no matter the surface modelling. Thus, superhydrophobic surfaces may or not influence transition to turbulence depending on the interface dynamics and on the considered transition process.
Sat, 01 Aug 2020 00:00:00 GMThttp://hdl.handle.net/10985/237832020-08-01T00:00:00ZPICELLA, FrancescoROBINET, Jean-ChristopheCHERUBINI, StefaniaSuperhydrophobic surfaces dramatically reduce the skin friction of overlying liquid flows, providing a lubricating layer of gas bubbles trapped within their surface nano-sculptures. Under wetting-stable conditions, different models can be used to numerically simulate their effect on the overlying flow, ranging from spatially homogeneous slip conditions at the wall, to spatially heterogeneous slip–no-slip conditions taking into account or not the displacement of the gas–water interfaces. These models provide similar results in both laminar and turbulent regimes, but their effect on transitional flows has not been investigated yet. In this work we study, by means of numerical simulations and global stability analyses, the influence of the modelling of superhydrophobic surfaces on laminar–turbulent transition in a channel flow. For the K-type scenario, a strong transition
delay is found using spatially homogeneous or heterogeneous slippery boundaries with flat, rigid liquid–gas interfaces. Whereas, when the interface dynamics is taken into account, the time to transition is reduced, approaching that of a no-slip channel flow. It is found that the interface deformation promotes ejection events creating hairpin heads that are prone to breakdown, reducing the transition delay effect with respect to flat slippery surfaces. Thus, in the case of modal transition, the interface dynamics must be taken into account for accurately estimating transition delay. Contrariwise, non-modal transition
triggered by a broadband forcing is unaffected by the presence of these surfaces, no matter the surface modelling. Thus, superhydrophobic surfaces may or not influence transition to turbulence depending on the interface dynamics and on the considered transition process.Instability mechanisms in meandering streamwise vortex pairs of upswept afterbody wakes
http://hdl.handle.net/10985/24023
Instability mechanisms in meandering streamwise vortex pairs of upswept afterbody wakes
RANJAN, Rajesh; ROBINET, Jean-Christophe; GAITONDE, Datta
Wakes of upswept afterbodies are often characterized by counter-rotating streamwise vortex pairs which meander in space. One application concerns aft regions of cargo aircraft, which are characterized by a relatively flat upswept base. Here we consider a canonical configuration comprised of a cylinder with upswept basal surface. The resulting longitudinal vortices, which are much closer to each other than wing-tip vortices, can adversely influence paratrooper and cargo drop operations as well as trailing aircraft. The unsteady dynamics of these vortices are examined using spatio-temporally resolved Large-Eddy Simulations (LES) and stability considerations. Emphasis is placed on understanding the potential instability dynamics responsible for meandering, which was observed, characterized and quantified at a representative location downstream of the body. The dynamics is then successfully mapped to a matched Batchelor vortex pair, and spatial and temporal stability analyses are performed with both counter-rotating vortices in the computational domain. Both spatial and temporal analyses
reveal dipole structures associated with |m| = 1 elliptic modes as dominant modes in afterbody vortices. A short-wave elliptic instability mode is found to dominate the meandering motion in the vortex pair; this mode was stable in the case of an isolated vortex. Further, the strain due to axial velocity plays a key role in the instability and therefore breakdown. The low frequency of the unstable mode (Strouhal number StD ≃ 0.3 based on cylinder diameter) is consistent with the spectral analysis of meandering in the LES. Stability analyses at very low-wavenumber do not exhibit any unstable mode suggesting an absence of the Crow instability.
Fri, 01 Jul 2022 00:00:00 GMThttp://hdl.handle.net/10985/240232022-07-01T00:00:00ZRANJAN, RajeshROBINET, Jean-ChristopheGAITONDE, DattaWakes of upswept afterbodies are often characterized by counter-rotating streamwise vortex pairs which meander in space. One application concerns aft regions of cargo aircraft, which are characterized by a relatively flat upswept base. Here we consider a canonical configuration comprised of a cylinder with upswept basal surface. The resulting longitudinal vortices, which are much closer to each other than wing-tip vortices, can adversely influence paratrooper and cargo drop operations as well as trailing aircraft. The unsteady dynamics of these vortices are examined using spatio-temporally resolved Large-Eddy Simulations (LES) and stability considerations. Emphasis is placed on understanding the potential instability dynamics responsible for meandering, which was observed, characterized and quantified at a representative location downstream of the body. The dynamics is then successfully mapped to a matched Batchelor vortex pair, and spatial and temporal stability analyses are performed with both counter-rotating vortices in the computational domain. Both spatial and temporal analyses
reveal dipole structures associated with |m| = 1 elliptic modes as dominant modes in afterbody vortices. A short-wave elliptic instability mode is found to dominate the meandering motion in the vortex pair; this mode was stable in the case of an isolated vortex. Further, the strain due to axial velocity plays a key role in the instability and therefore breakdown. The low frequency of the unstable mode (Strouhal number StD ≃ 0.3 based on cylinder diameter) is consistent with the spectral analysis of meandering in the LES. Stability analyses at very low-wavenumber do not exhibit any unstable mode suggesting an absence of the Crow instability.Minimal energy thresholds for sustained turbulent bands in channel flow
http://hdl.handle.net/10985/24022
Minimal energy thresholds for sustained turbulent bands in channel flow
PARENTE, Enza; ROBINET, Jean-Christophe; DE PALMA, Paul; CHERUBINI, Stefania
In this work, nonlinear variational optimization is used for obtaining minimal seeds for the formation of turbulent bands in channel flow. Using nonlinear optimization together with energy bisection, we have found that the minimal energy threshold for obtaining spatially patterned turbulence scales with$Re^{-8.5}$for$Re>1000$. The minimal seed, which is different to that found in a much smaller domain, is characterized by a spot-like structure surrounded by a low-amplitude large-scale quadrupolar flow filling the whole domain. This minimal-energy perturbation of the laminar flow has dominant wavelengths close to$4$in the streamwise direction and$1$in the spanwise direction, and is characterized by a spatial localization increasing with the Reynolds number. At$Re \lesssim 1200$, the minimal seed evolves in time, creating an isolated oblique band, whereas for$Re\gtrsim 1200$, a quasi-spanwise-symmetric evolution is observed, giving rise to two distinct bands. A similar evolution is found also at low$Re$for non-minimal optimal perturbations. This highlights two different mechanisms of formation of turbulent bands in channel flow, depending on the Reynolds number and initial energy of the perturbation. The selection of one of these two mechanisms appears to be dependent on the probability of decay of the newly created stripe, which increases with time, but decreases with the Reynolds number.
Sun, 01 May 2022 00:00:00 GMThttp://hdl.handle.net/10985/240222022-05-01T00:00:00ZPARENTE, EnzaROBINET, Jean-ChristopheDE PALMA, PaulCHERUBINI, StefaniaIn this work, nonlinear variational optimization is used for obtaining minimal seeds for the formation of turbulent bands in channel flow. Using nonlinear optimization together with energy bisection, we have found that the minimal energy threshold for obtaining spatially patterned turbulence scales with$Re^{-8.5}$for$Re>1000$. The minimal seed, which is different to that found in a much smaller domain, is characterized by a spot-like structure surrounded by a low-amplitude large-scale quadrupolar flow filling the whole domain. This minimal-energy perturbation of the laminar flow has dominant wavelengths close to$4$in the streamwise direction and$1$in the spanwise direction, and is characterized by a spatial localization increasing with the Reynolds number. At$Re \lesssim 1200$, the minimal seed evolves in time, creating an isolated oblique band, whereas for$Re\gtrsim 1200$, a quasi-spanwise-symmetric evolution is observed, giving rise to two distinct bands. A similar evolution is found also at low$Re$for non-minimal optimal perturbations. This highlights two different mechanisms of formation of turbulent bands in channel flow, depending on the Reynolds number and initial energy of the perturbation. The selection of one of these two mechanisms appears to be dependent on the probability of decay of the newly created stripe, which increases with time, but decreases with the Reynolds number.Variational Nonlinear Optimization in Fluid Dynamics: The Case of a Channel Flow with Superhydrophobic Walls
http://hdl.handle.net/10985/24021
Variational Nonlinear Optimization in Fluid Dynamics: The Case of a Channel Flow with Superhydrophobic Walls
CHERUBINI, Stefania; PICELLA, Francesco; ROBINET, Jean-Christophe
Variational optimization has been recently applied to nonlinear systems with many degrees of freedom such as shear flows undergoing transition to turbulence. This technique has unveiled powerful energy growth mechanisms able to produce typical coherent structures currently observed in transition and turbulence. However, it is still not clear the extent to which these nonlinear optimal energy growth mechanisms are robust with respect to external disturbances or wall imperfections. Within this framework, this work aims at investigating how nano-roughnesses such as those of superhydrophobic surfaces affect optimal energy growth mechanisms relying on nonlinearity. Nonlinear optimizations have been carried out in a channel flow with no-slip and slippery boundaries, mimicking the presence of superhydrophobic surfaces. For increasing slip length, the energy threshold for obtaining hairpin-like nonlinear optimal perturbations slightly rises, scaling approximately with Re−2.36 no matter the slip length. The corresponding energy gain increases with Re with a slope that reduces with the slip length, being almost halved for the largest slip and Reynolds number considered. This suggests a strong effect of boundary slip on the energy growth of these perturbations. While energy is considerably decreased, the shape of the optimal perturbation barely changes, indicating the robustness of optimal perturbations with respect to wall slip.
Tue, 01 Dec 2020 00:00:00 GMThttp://hdl.handle.net/10985/240212020-12-01T00:00:00ZCHERUBINI, StefaniaPICELLA, FrancescoROBINET, Jean-ChristopheVariational optimization has been recently applied to nonlinear systems with many degrees of freedom such as shear flows undergoing transition to turbulence. This technique has unveiled powerful energy growth mechanisms able to produce typical coherent structures currently observed in transition and turbulence. However, it is still not clear the extent to which these nonlinear optimal energy growth mechanisms are robust with respect to external disturbances or wall imperfections. Within this framework, this work aims at investigating how nano-roughnesses such as those of superhydrophobic surfaces affect optimal energy growth mechanisms relying on nonlinearity. Nonlinear optimizations have been carried out in a channel flow with no-slip and slippery boundaries, mimicking the presence of superhydrophobic surfaces. For increasing slip length, the energy threshold for obtaining hairpin-like nonlinear optimal perturbations slightly rises, scaling approximately with Re−2.36 no matter the slip length. The corresponding energy gain increases with Re with a slope that reduces with the slip length, being almost halved for the largest slip and Reynolds number considered. This suggests a strong effect of boundary slip on the energy growth of these perturbations. While energy is considerably decreased, the shape of the optimal perturbation barely changes, indicating the robustness of optimal perturbations with respect to wall slip.Nonlinear optimal perturbation of turbulent channel flow as a precursor of extreme events
http://hdl.handle.net/10985/24141
Nonlinear optimal perturbation of turbulent channel flow as a precursor of extreme events
CIOLA, Nicola; DE PALMA, Paul; ROBINET, Jean-Christophe; CHERUBINI, Stefania
This work aims at studying the mechanisms behind the occurrence of extreme dissipation events in a channel flow, identifying nonlinear optimal perturbations as potential precursors of these events. Nonlinear optimal perturbations with respect to a generic turbulent instantaneous snapshot are computed for the first time using a direct-adjoint algorithm in the channel flow at
$Re_{\tau }\approx 180$ . The resulting initial perturbation displays the upstream tilting characteristic of Orr's mechanism and is positioned along the interfaces between two opposite-sign velocity streaks of the pre-existing turbulent field. Such a perturbation induces a sudden breakdown of the pre-existing structures and a heavier tail in the dissipation probability density function distribution. Different mechanisms are at play during this process: the high shear present at the interface between coherent low- and high-momentum regions is exploited to break down the larger structures and drive energy to small scales. This energy cascade is fed by an enhanced lift-up effect that produces intense streaks near the wall. It is found that the optimal perturbation grows exponentially during the first phase of its evolution reflecting the existence of a secondary modal instability of the streaks. To corroborate the results, the conditional spatiotemporal proper orthogonal decomposition (POD) analysis of Hack & Schimdt (J. Fluid Mech., vol. 907, 2021, A9) is performed both in the perturbed and in the unperturbed flow, showing a clear agreement between the two cases and with the reference study. Thus, the optimal perturbation at initial time can be considered as a precursor of extreme events.
Tue, 01 Aug 2023 00:00:00 GMThttp://hdl.handle.net/10985/241412023-08-01T00:00:00ZCIOLA, NicolaDE PALMA, PaulROBINET, Jean-ChristopheCHERUBINI, StefaniaThis work aims at studying the mechanisms behind the occurrence of extreme dissipation events in a channel flow, identifying nonlinear optimal perturbations as potential precursors of these events. Nonlinear optimal perturbations with respect to a generic turbulent instantaneous snapshot are computed for the first time using a direct-adjoint algorithm in the channel flow at
$Re_{\tau }\approx 180$ . The resulting initial perturbation displays the upstream tilting characteristic of Orr's mechanism and is positioned along the interfaces between two opposite-sign velocity streaks of the pre-existing turbulent field. Such a perturbation induces a sudden breakdown of the pre-existing structures and a heavier tail in the dissipation probability density function distribution. Different mechanisms are at play during this process: the high shear present at the interface between coherent low- and high-momentum regions is exploited to break down the larger structures and drive energy to small scales. This energy cascade is fed by an enhanced lift-up effect that produces intense streaks near the wall. It is found that the optimal perturbation grows exponentially during the first phase of its evolution reflecting the existence of a secondary modal instability of the streaks. To corroborate the results, the conditional spatiotemporal proper orthogonal decomposition (POD) analysis of Hack & Schimdt (J. Fluid Mech., vol. 907, 2021, A9) is performed both in the perturbed and in the unperturbed flow, showing a clear agreement between the two cases and with the reference study. Thus, the optimal perturbation at initial time can be considered as a precursor of extreme events.Modal and nonmodal stability analysis of turbulent stratified channel flows
http://hdl.handle.net/10985/24881
Modal and nonmodal stability analysis of turbulent stratified channel flows
VARIALE, Donato; PARENTE, Enza; ROBINET, Jean-Christophe; CHERUBINI, Stefania
Unstable or optimally growing perturbations of turbulent flows are often representative of the energy-containing coherent structures populating the flow, as for streaks in a turbulent channel. Within this framework, this work aims at studying the modal and nonmodal stability of stably stratified turbulent channel flow, assessing the influence of stratification while changing the friction Richardson number, Riτ, at fixed friction Reynolds number, Reτ. When increasing the stratification of the flow, the energy gain for streamwise independent perturbations at the outer peak increases by two orders of magnitude, and the spanwise wavenumber for which the energy gain peaks reaches values comparable to those reported in the direct numerical simulations of Garcia-Villalba and Del Alamo. At the same time, the value of the optimal gain for the inner peak slightly changes, corroborating the observations made through direct numerical simulation (DNS) about the fact that the wall cycle is not altered by the presence of stratification. Moreover, for nonzero values of the streamwise and spanwise wavenumbers, α and β, the energy gain curve has two peaks, one for shorter target times and α > β, leading to a center-channel temperature peak, and another occurring for α < β at larger target times. In the former case, energy production is mostly linked to velocity production, whereas, in the latter case, the strongest term is that of temperature production, indicating that this mechanism is driven by the increase of the potential energy rather than the kinetic one, and it is intimately linked to the presence of stratification. For strong stratification, the optimal energy gain considerably extends towards higher values of α, leading to energy amplifications reaching three orders of magnitudes for values of α up to 2. The associated optimal perturbations are characterized by temperature patches at the center channel, phase lagged by π/2 with the wall-normal velocity, similarly to gravity waves recovered in the DNS for sufficiently large stratification. However, for large values of β, we observe an increasing asymmetry
in the optimal perturbations, probably due to the shielding effect of the core of the channel, as also observed in the DNS of Garcia-Villalba and Del Alamo.
Mon, 01 Jan 2024 00:00:00 GMThttp://hdl.handle.net/10985/248812024-01-01T00:00:00ZVARIALE, DonatoPARENTE, EnzaROBINET, Jean-ChristopheCHERUBINI, StefaniaUnstable or optimally growing perturbations of turbulent flows are often representative of the energy-containing coherent structures populating the flow, as for streaks in a turbulent channel. Within this framework, this work aims at studying the modal and nonmodal stability of stably stratified turbulent channel flow, assessing the influence of stratification while changing the friction Richardson number, Riτ, at fixed friction Reynolds number, Reτ. When increasing the stratification of the flow, the energy gain for streamwise independent perturbations at the outer peak increases by two orders of magnitude, and the spanwise wavenumber for which the energy gain peaks reaches values comparable to those reported in the direct numerical simulations of Garcia-Villalba and Del Alamo. At the same time, the value of the optimal gain for the inner peak slightly changes, corroborating the observations made through direct numerical simulation (DNS) about the fact that the wall cycle is not altered by the presence of stratification. Moreover, for nonzero values of the streamwise and spanwise wavenumbers, α and β, the energy gain curve has two peaks, one for shorter target times and α > β, leading to a center-channel temperature peak, and another occurring for α < β at larger target times. In the former case, energy production is mostly linked to velocity production, whereas, in the latter case, the strongest term is that of temperature production, indicating that this mechanism is driven by the increase of the potential energy rather than the kinetic one, and it is intimately linked to the presence of stratification. For strong stratification, the optimal energy gain considerably extends towards higher values of α, leading to energy amplifications reaching three orders of magnitudes for values of α up to 2. The associated optimal perturbations are characterized by temperature patches at the center channel, phase lagged by π/2 with the wall-normal velocity, similarly to gravity waves recovered in the DNS for sufficiently large stratification. However, for large values of β, we observe an increasing asymmetry
in the optimal perturbations, probably due to the shielding effect of the core of the channel, as also observed in the DNS of Garcia-Villalba and Del Alamo.Optimal bursts in turbulent channel flow
http://hdl.handle.net/10985/11634
Optimal bursts in turbulent channel flow
FARANO, Mirko; CHERUBINI, Stefania; DE PALMA, Pietro; ROBINET, Jean-Christophe
Bursts are recurrent, transient, highly energetic events characterized by localized variations of velocity and vorticity in turbulent wall-bounded ﬂows. In this work, a nonlinear energy optimization strategy is employed to investigate whether the origin of such bursting events in a turbulent channel ﬂow can be related to the presence of high-amplitude coherent structures. The results show that bursting events correspond to optimal energy ﬂow structures embedded in the fully turbulent ﬂow. In particular, optimal structures inducing energy peaks at short time are initially composed of highly oscillating vortices and streaks near the wall. At moderate friction Reynolds numbers, through the bursts, energy is exchanged between the streaks and packets of hairpin vortices of different sizes reaching the outer scale. Such an optimal ﬂow conﬁguration reproduces well the spatial spectra as well as the probability density function typical of turbulent ﬂows, recovering the mechanism of direct-inverse energy cascade. These results represent an important step towards understanding the dynamics of turbulence at moderate Reynolds numbers and pave the way to new nonlinear techniques to manipulate and control the self-sustained turbulence dynamics.
Sun, 01 Jan 2017 00:00:00 GMThttp://hdl.handle.net/10985/116342017-01-01T00:00:00ZFARANO, MirkoCHERUBINI, StefaniaDE PALMA, PietroROBINET, Jean-ChristopheBursts are recurrent, transient, highly energetic events characterized by localized variations of velocity and vorticity in turbulent wall-bounded ﬂows. In this work, a nonlinear energy optimization strategy is employed to investigate whether the origin of such bursting events in a turbulent channel ﬂow can be related to the presence of high-amplitude coherent structures. The results show that bursting events correspond to optimal energy ﬂow structures embedded in the fully turbulent ﬂow. In particular, optimal structures inducing energy peaks at short time are initially composed of highly oscillating vortices and streaks near the wall. At moderate friction Reynolds numbers, through the bursts, energy is exchanged between the streaks and packets of hairpin vortices of different sizes reaching the outer scale. Such an optimal ﬂow conﬁguration reproduces well the spatial spectra as well as the probability density function typical of turbulent ﬂows, recovering the mechanism of direct-inverse energy cascade. These results represent an important step towards understanding the dynamics of turbulence at moderate Reynolds numbers and pave the way to new nonlinear techniques to manipulate and control the self-sustained turbulence dynamics.