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The DSpace digital repository system captures, stores, indexes, preserves, and distributes digital research material.Fri, 18 Jan 2019 18:24:01 GMT2019-01-18T18:24:01ZA domain decomposition matrix-free method for global linear stability
http://hdl.handle.net/10985/8644
A domain decomposition matrix-free method for global linear stability
ALIZARD, Frédéric; ROBINET, Jean-Christophe; GLOERFELT, Xavier
This work is dedicated to the presentation of a matrix-free method for global linear stability analysis in geometries composed of multi-connected rectangular subdomains. An Arnoldi technique using snapshots in subdomains of the entire geometry combined with a multidomain linearized Direct Numerical Finite difference simulations based on an influence matrix for partitioning are adopted. The method is illustrated by three benchmark problems: the lid-driven cavity, the square cylinder and the open cavity flow. The efficiency of the method to extract large-scale structures in a multidomain framework is emphasized. The possibility to use subset of the full domain to recover the perturbation associated with the entire flow field is also highlighted. Such a method appears thus a promising tool to deal with large computational domains and three-dimensionality within a parallel architecture.
Sun, 01 Jan 2012 00:00:00 GMThttp://hdl.handle.net/10985/86442012-01-01T00:00:00ZALIZARD, FrédéricROBINET, Jean-ChristopheGLOERFELT, XavierThis work is dedicated to the presentation of a matrix-free method for global linear stability analysis in geometries composed of multi-connected rectangular subdomains. An Arnoldi technique using snapshots in subdomains of the entire geometry combined with a multidomain linearized Direct Numerical Finite difference simulations based on an influence matrix for partitioning are adopted. The method is illustrated by three benchmark problems: the lid-driven cavity, the square cylinder and the open cavity flow. The efficiency of the method to extract large-scale structures in a multidomain framework is emphasized. The possibility to use subset of the full domain to recover the perturbation associated with the entire flow field is also highlighted. Such a method appears thus a promising tool to deal with large computational domains and three-dimensionality within a parallel architecture.Optimal wave packets in a boundary layer and initial phases of a turbulent spot
http://hdl.handle.net/10985/6717
Optimal wave packets in a boundary layer and initial phases of a turbulent spot
CHERUBINI, Stefania; ROBINET, Jean-Christophe; BOTTARO, Alessandro; DE PALMA, Pietro
The three-dimensional global optimal dynamics of a flat-plate boundary layer is studied by means of an adjoint-based optimization in a spatial domain of long – but finite – streamwise dimension. The localized optimal initial perturbation is characterized by a pair of streamwise-modulated counter-rotating vortices, tilted upstream, yielding at the optimal time elongated streaks of alternating sign in the streamwise direction. This indicates that perturbations with non-zero streamwise wavenumber have a role in the transient dynamics of a boundary layer. A scaling law is provided, describing the variation of the streamwise modulation of the optimal initial perturbation with respect to the streamwise domain length and to the Reynolds number. For spanwise-extended domains, a near-optimal three-dimensional perturbation is extracted during the optimization process; it is localized also in the spanwise direction, resulting in a wave packet of elongated disturbances modulated in the spanwise and streamwise directions. The nonlinear evolution of the optimal and near-optimal perturbations is investigated by means of direct numerical simulations. Both perturbations are found to induce transition at lower levels of the initial energy than local optimal and suboptimal perturbations. Moreover, it is observed that transition occurs in a well-defined region of the convected wave packet, close to its centre, via a mechanism including at the same time oscillations of the streaks of both quasi-sinuous and quasi-varicose nature. Hairpin vortices are observed before transition; they have an active role in the breakdown of the streaks and result in a turbulent spot which spreads out in the boundary layer.
Fri, 01 Jan 2010 00:00:00 GMThttp://hdl.handle.net/10985/67172010-01-01T00:00:00ZCHERUBINI, StefaniaROBINET, Jean-ChristopheBOTTARO, AlessandroDE PALMA, PietroThe three-dimensional global optimal dynamics of a flat-plate boundary layer is studied by means of an adjoint-based optimization in a spatial domain of long – but finite – streamwise dimension. The localized optimal initial perturbation is characterized by a pair of streamwise-modulated counter-rotating vortices, tilted upstream, yielding at the optimal time elongated streaks of alternating sign in the streamwise direction. This indicates that perturbations with non-zero streamwise wavenumber have a role in the transient dynamics of a boundary layer. A scaling law is provided, describing the variation of the streamwise modulation of the optimal initial perturbation with respect to the streamwise domain length and to the Reynolds number. For spanwise-extended domains, a near-optimal three-dimensional perturbation is extracted during the optimization process; it is localized also in the spanwise direction, resulting in a wave packet of elongated disturbances modulated in the spanwise and streamwise directions. The nonlinear evolution of the optimal and near-optimal perturbations is investigated by means of direct numerical simulations. Both perturbations are found to induce transition at lower levels of the initial energy than local optimal and suboptimal perturbations. Moreover, it is observed that transition occurs in a well-defined region of the convected wave packet, close to its centre, via a mechanism including at the same time oscillations of the streaks of both quasi-sinuous and quasi-varicose nature. Hairpin vortices are observed before transition; they have an active role in the breakdown of the streaks and result in a turbulent spot which spreads out in the boundary layer.Numerical Study of the Effect of Freestream Turbulence on by-pass Transition in a Boundary Layer
http://hdl.handle.net/10985/9011
Numerical Study of the Effect of Freestream Turbulence on by-pass Transition in a Boundary Layer
CHERUBINI, Stefania; ROBINET, Jean-Christophe; DE PALMA, Pietro
We use direct numerical simulations in the presence of free-stream turbulence having different values of intensity, T u, and integral length scale, L, in order to determine which kind of structures are involved in the path to transition of a boundary-layer flow. The main aim is to determine under which conditions the path to transition involves structures similar to the linear or non-linear optimal perturbations. For high values of T u and L, we observe a large-amplitude path to transition characterized by localized vortical structures and patches of high- and low-momentum fluctuations. Such a scenario is found to correlate well with the L and hairpin structures resulting from the time evolution of non-linear optimal perturbations, whereas, for lower T u and L, a larger correlation is found with respect to linear optimal disturbances. This indicates that a large-amplitude path to transition exists, different from the one characterized by elongated streaks undergoing secondary instability. To distinguish between the two transition scenarios, a simple parameter linked to the streamwise localisation of high- and low-momentum zones is introduced. Finally, an accurate law to predict the transition location is provided, taking into account both T u and L, valid for both the transition scenarios.
Wed, 01 Jan 2014 00:00:00 GMThttp://hdl.handle.net/10985/90112014-01-01T00:00:00ZCHERUBINI, StefaniaROBINET, Jean-ChristopheDE PALMA, PietroWe use direct numerical simulations in the presence of free-stream turbulence having different values of intensity, T u, and integral length scale, L, in order to determine which kind of structures are involved in the path to transition of a boundary-layer flow. The main aim is to determine under which conditions the path to transition involves structures similar to the linear or non-linear optimal perturbations. For high values of T u and L, we observe a large-amplitude path to transition characterized by localized vortical structures and patches of high- and low-momentum fluctuations. Such a scenario is found to correlate well with the L and hairpin structures resulting from the time evolution of non-linear optimal perturbations, whereas, for lower T u and L, a larger correlation is found with respect to linear optimal disturbances. This indicates that a large-amplitude path to transition exists, different from the one characterized by elongated streaks undergoing secondary instability. To distinguish between the two transition scenarios, a simple parameter linked to the streamwise localisation of high- and low-momentum zones is introduced. Finally, an accurate law to predict the transition location is provided, taking into account both T u and L, valid for both the transition scenarios.Investigation of the roughness-induced transition: global stability analyses and direct numerical simulations
http://hdl.handle.net/10985/8974
Investigation of the roughness-induced transition: global stability analyses and direct numerical simulations
LOISEAU, Jean-Christophe; ROBINET, Jean-Christophe; CHERUBINI, Stefania; LERICHE, Emmanuel
The linear global instability and resulting transition to turbulence induced by an isolated cylindrical roughness element of height h and diameter d immersed within an incompressible boundary layer flow along a flat plate is investigated using the joint application of direct numerical simulations and fully three-dimensional global stability analyses. For the range of parameters investigated, base flow computations show that the roughness element induces a wake composed of a central low-speed region surrounded by a three-dimensional shear layer and a pair of low- and high-speed streaks on each of its sides. Results from the global stability analyses highlight the unstable nature of the central low-speed region and its crucial importance in the laminar–turbulent transition process. It is able to sustain two different global instabilities: a sinuous and a varicose one. Each of these globally unstable modes is related to a different physical mechanism. While the varicose mode has its root in the instability of the whole three-dimensional shear layer surrounding the central low-speed region, the sinuous instability turns out to be similar to the von Kármán instability in the two-dimensional cylinder wake and has its root in the lateral shear layers of the separated zone. The aspect ratio of the roughness element plays a key role on the selection of the dominant instability: whereas the flow over thin cylindrical roughness elements transitions due to a sinuous instability of the near-wake region, for larger roughness elements the varicose instability of the central low-speed region turns out to be the dominant one. Direct numerical simulations of the flow past an aspect ratio 1 roughness element sustaining only the sinuous instability have revealed that the bifurcation occurring in this particular case is supercritical. Finally, comparison of the transition thresholds predicted by global linear stability analyses with the von Doenhoff–Braslow transition diagram provides qualitatively good agreement
Wed, 01 Jan 2014 00:00:00 GMThttp://hdl.handle.net/10985/89742014-01-01T00:00:00ZLOISEAU, Jean-ChristopheROBINET, Jean-ChristopheCHERUBINI, StefaniaLERICHE, EmmanuelThe linear global instability and resulting transition to turbulence induced by an isolated cylindrical roughness element of height h and diameter d immersed within an incompressible boundary layer flow along a flat plate is investigated using the joint application of direct numerical simulations and fully three-dimensional global stability analyses. For the range of parameters investigated, base flow computations show that the roughness element induces a wake composed of a central low-speed region surrounded by a three-dimensional shear layer and a pair of low- and high-speed streaks on each of its sides. Results from the global stability analyses highlight the unstable nature of the central low-speed region and its crucial importance in the laminar–turbulent transition process. It is able to sustain two different global instabilities: a sinuous and a varicose one. Each of these globally unstable modes is related to a different physical mechanism. While the varicose mode has its root in the instability of the whole three-dimensional shear layer surrounding the central low-speed region, the sinuous instability turns out to be similar to the von Kármán instability in the two-dimensional cylinder wake and has its root in the lateral shear layers of the separated zone. The aspect ratio of the roughness element plays a key role on the selection of the dominant instability: whereas the flow over thin cylindrical roughness elements transitions due to a sinuous instability of the near-wake region, for larger roughness elements the varicose instability of the central low-speed region turns out to be the dominant one. Direct numerical simulations of the flow past an aspect ratio 1 roughness element sustaining only the sinuous instability have revealed that the bifurcation occurring in this particular case is supercritical. Finally, comparison of the transition thresholds predicted by global linear stability analyses with the von Doenhoff–Braslow transition diagram provides qualitatively good agreementOptimal bursts in turbulent channel flow
http://hdl.handle.net/10985/11634
Optimal bursts in turbulent channel flow
FARANO, Mirko; CHERUBINI, Stefania; ROBINET, Jean-Christophe; DE PALMA, Pietro
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, StefaniaROBINET, Jean-ChristopheDE PALMA, PietroBursts 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.The onset of three-dimensional centrifugal global modes and their nonlinear development in a recirculating flow over a flat surface
http://hdl.handle.net/10985/6867
The onset of three-dimensional centrifugal global modes and their nonlinear development in a recirculating flow over a flat surface
CHERUBINI, Stefania; ROBINET, Jean-Christophe; DE PALMA, Pietro; ALIZARD, Frédéric
The three-dimensional stability dynamics of a separation bubble over a flat plate has been studied in both linear and nonlinear conditions. Using a global eigenvalue analysis, two centrifugal global modes are identified: an asymptotically unstable three-dimensional weakly growing mode which appears to be originated by a Rayleigh instability; a marginally stable three-dimensional steady mode which is originated by a convective Gortler instability. Direct numerical simulations show that both modes play a role in the route to transition toward the turbulent flow. A structural sensitivity analysis is used to investigate the mechanism of selection of the path toward transition when small perturbations are considered. Finally, a scenario of transition via Gortler modes breakdown is studied in detail, revealing the formation of trains of hairpin vortices in streamwise succession.
Publisher version : http://pof.aip.org/resource/1/phfle6/v22/i11/p114102_s1?isAuthorized=no
Fri, 01 Jan 2010 00:00:00 GMThttp://hdl.handle.net/10985/68672010-01-01T00:00:00ZCHERUBINI, StefaniaROBINET, Jean-ChristopheDE PALMA, PietroALIZARD, FrédéricThe three-dimensional stability dynamics of a separation bubble over a flat plate has been studied in both linear and nonlinear conditions. Using a global eigenvalue analysis, two centrifugal global modes are identified: an asymptotically unstable three-dimensional weakly growing mode which appears to be originated by a Rayleigh instability; a marginally stable three-dimensional steady mode which is originated by a convective Gortler instability. Direct numerical simulations show that both modes play a role in the route to transition toward the turbulent flow. A structural sensitivity analysis is used to investigate the mechanism of selection of the path toward transition when small perturbations are considered. Finally, a scenario of transition via Gortler modes breakdown is studied in detail, revealing the formation of trains of hairpin vortices in streamwise succession.Rapid path to transition via nonlinear localized optimal perturbations in a boundary-layer flow
http://hdl.handle.net/10985/6861
Rapid path to transition via nonlinear localized optimal perturbations in a boundary-layer flow
CHERUBINI, Stefania; DE PALMA, Pietro; ROBINET, Jean-Christophe; BOTTARO, Alessandro
Recent studies have suggested that in some cases transition can be triggered by some purely nonlinear mechanisms. Here we aim at verifying such an hypothesis, looking for a localized perturbation able to lead a boundary-layer flow to a chaotic state, following a nonlinear route. Nonlinear optimal localized perturbations have been computed by means of an energy optimization which includes the nonlinear terms of the Navier- Stokes equations. Such perturbations lie on the turbulent side of the laminar-turbulent boundary, whereas, for the same value of the initial energy, their linear counterparts do not. The evolution of these perturbations toward a turbulent flow involves the presence of streamwise-inclined vortices at short times and of hairpin structures prior to breakdown.
Fri, 01 Jan 2010 00:00:00 GMThttp://hdl.handle.net/10985/68612010-01-01T00:00:00ZCHERUBINI, StefaniaDE PALMA, PietroROBINET, Jean-ChristopheBOTTARO, AlessandroRecent studies have suggested that in some cases transition can be triggered by some purely nonlinear mechanisms. Here we aim at verifying such an hypothesis, looking for a localized perturbation able to lead a boundary-layer flow to a chaotic state, following a nonlinear route. Nonlinear optimal localized perturbations have been computed by means of an energy optimization which includes the nonlinear terms of the Navier- Stokes equations. Such perturbations lie on the turbulent side of the laminar-turbulent boundary, whereas, for the same value of the initial energy, their linear counterparts do not. The evolution of these perturbations toward a turbulent flow involves the presence of streamwise-inclined vortices at short times and of hairpin structures prior to breakdown.A purely nonlinear route to transition approaching the edge of chaos in a boundary layer
http://hdl.handle.net/10985/6864
A purely nonlinear route to transition approaching the edge of chaos in a boundary layer
CHERUBINI, Stefania; DE PALMA, Pietro; ROBINET, Jean-Christophe; BOTTARO, Alessandro
The understanding of transition in shear flows has recently progressed along new paradigms based on the central role of coherent flow structures and their nonlinear interactions. We follow such paradigms to identify, by means of a nonlinear optimization of the energy growth at short time, the initial perturbation which most easily induces transition in a boundary layer. Moreover, a bisection procedure has been used to identify localized flow structures living on the edge of chaos, found to be populated by hairpin vortices and streaks. Such an edge structure appears to act as a relative attractor for the trajectory of the laminar base state perturbed by the initial finite-amplitude disturbances, mediating the route to turbulence of the flow, via the triggering of a regeneration cycle of Lambda and hairpin structures at different space and time scales. These findings introduce a new, purely nonlinear scenario of transition in a boundary-layer flow.
Publisher version : http://iopscience.iop.org/1873-7005/44/3/031404
Sun, 01 Jan 2012 00:00:00 GMThttp://hdl.handle.net/10985/68642012-01-01T00:00:00ZCHERUBINI, StefaniaDE PALMA, PietroROBINET, Jean-ChristopheBOTTARO, AlessandroThe understanding of transition in shear flows has recently progressed along new paradigms based on the central role of coherent flow structures and their nonlinear interactions. We follow such paradigms to identify, by means of a nonlinear optimization of the energy growth at short time, the initial perturbation which most easily induces transition in a boundary layer. Moreover, a bisection procedure has been used to identify localized flow structures living on the edge of chaos, found to be populated by hairpin vortices and streaks. Such an edge structure appears to act as a relative attractor for the trajectory of the laminar base state perturbed by the initial finite-amplitude disturbances, mediating the route to turbulence of the flow, via the triggering of a regeneration cycle of Lambda and hairpin structures at different space and time scales. These findings introduce a new, purely nonlinear scenario of transition in a boundary-layer flow.Edge states in a boundary layer
http://hdl.handle.net/10985/6868
Edge states in a boundary layer
CHERUBINI, Stefania; DE PALMA, Pietro; ROBINET, Jean-Christophe; BOTTARO, Alessandro
The understanding of laminar-turbulent transition in shear flows has recently progressed along new paradigms based on the central role of nonlinear exact coherent states. We follow such paradigms to identify, for the first time in a spatially developing flow, localized flow structures living on the edge of chaos, which are the precursors of turbulence. These coherent structures are constituted by hairpin vortices and streamwise streaks. The results reported here extend the dynamical systems description of transition to spatially developing flows.
Publisher version : http://pof.aip.org/resource/1/phfle6/v23/i5/p051705_s1?isAuthorized=no
Sat, 01 Jan 2011 00:00:00 GMThttp://hdl.handle.net/10985/68682011-01-01T00:00:00ZCHERUBINI, StefaniaDE PALMA, PietroROBINET, Jean-ChristopheBOTTARO, AlessandroThe understanding of laminar-turbulent transition in shear flows has recently progressed along new paradigms based on the central role of nonlinear exact coherent states. We follow such paradigms to identify, for the first time in a spatially developing flow, localized flow structures living on the edge of chaos, which are the precursors of turbulence. These coherent structures are constituted by hairpin vortices and streamwise streaks. The results reported here extend the dynamical systems description of transition to spatially developing flows.The minimal seed of turbulent transition in the boundary layer
http://hdl.handle.net/10985/6718
The minimal seed of turbulent transition in the boundary layer
CHERUBINI, Stefania; DE PALMA, Pietro; ROBINET, Jean-Christophe; BOTTARO, Alessandro
This paper describes a scenario of transition from laminar to turbulent flow in a spatially developing boundary layer over a flat plate. The base flow is the Blasius non-parallel flow solution; it is perturbed by optimal disturbances yielding the largest energy growth over a short time interval. Such perturbations are computed by a nonlinear global optimization approach based on a Lagrange multiplier technique. The results show that nonlinear optimal perturbations are characterized by a localized basic building block, called the minimal seed, defined as the smallest flow structure which maximizes the energy growth over short times. It is formed by vortices inclined in the streamwise direction surrounding a region of intense streamwise disturbance velocity. Such a basic structure appears to be a robust feature of the base flow since it is practically invariant with respect to the initial energy of the perturbation, the target time, the Reynolds number and the dimensions of the computational domain. The minimal seed grows very rapidly in time while spreading, and it triggers nonlinear effects which bring the flow to turbulence in a very efficient manner, through the formation of a turbulence spot. This evolution of the initial optimal disturbance has been studied in detail by direct numerical simulations. Using a perturbative formulation of the Navier–Stokes equations, each linear and nonlinear convective term of the equations has been analysed. The results show the fundamental role of the streamwise inclination of the vortices in the process. The nonlinear coupling of the finite amplitude disturbances is crucial to sustain such streamwise inclination, as well as to generate dislocations within the flow structures, and local inflectional velocity distributions. The analysis provides a picture of the transition process characterized by a sequence of structures appearing successively in the flow, namely, 3 vortices, hairpin vortices and streamwise streaks. Finally, a disturbance regeneration cycle is conceived, initiated by the fast nonlinear amplification of the minimal seed, providing a possible scenario for the continuous regeneration of the same fundamental flow structures at smaller space and time scales.
Sat, 01 Jan 2011 00:00:00 GMThttp://hdl.handle.net/10985/67182011-01-01T00:00:00ZCHERUBINI, StefaniaDE PALMA, PietroROBINET, Jean-ChristopheBOTTARO, AlessandroThis paper describes a scenario of transition from laminar to turbulent flow in a spatially developing boundary layer over a flat plate. The base flow is the Blasius non-parallel flow solution; it is perturbed by optimal disturbances yielding the largest energy growth over a short time interval. Such perturbations are computed by a nonlinear global optimization approach based on a Lagrange multiplier technique. The results show that nonlinear optimal perturbations are characterized by a localized basic building block, called the minimal seed, defined as the smallest flow structure which maximizes the energy growth over short times. It is formed by vortices inclined in the streamwise direction surrounding a region of intense streamwise disturbance velocity. Such a basic structure appears to be a robust feature of the base flow since it is practically invariant with respect to the initial energy of the perturbation, the target time, the Reynolds number and the dimensions of the computational domain. The minimal seed grows very rapidly in time while spreading, and it triggers nonlinear effects which bring the flow to turbulence in a very efficient manner, through the formation of a turbulence spot. This evolution of the initial optimal disturbance has been studied in detail by direct numerical simulations. Using a perturbative formulation of the Navier–Stokes equations, each linear and nonlinear convective term of the equations has been analysed. The results show the fundamental role of the streamwise inclination of the vortices in the process. The nonlinear coupling of the finite amplitude disturbances is crucial to sustain such streamwise inclination, as well as to generate dislocations within the flow structures, and local inflectional velocity distributions. The analysis provides a picture of the transition process characterized by a sequence of structures appearing successively in the flow, namely, 3 vortices, hairpin vortices and streamwise streaks. Finally, a disturbance regeneration cycle is conceived, initiated by the fast nonlinear amplification of the minimal seed, providing a possible scenario for the continuous regeneration of the same fundamental flow structures at smaller space and time scales.