Dynamique des Fluides (DynFluid)
http://hdl.handle.net/10985/184
Thu, 08 Aug 2024 12:01:08 GMT2024-08-08T12:01:08ZDynamique des Fluides (DynFluid)https://sam.ensam.eu:443/bitstream/id/f6e10806-ce30-4948-b330-0d37453c2150/
http://hdl.handle.net/10985/184
On the miscibility of PVDF/PMMA polymer blends: Thermodynamics, experimental and numerical investigations
http://hdl.handle.net/10985/18008
On the miscibility of PVDF/PMMA polymer blends: Thermodynamics, experimental and numerical investigations
AID, Sara; EDDHAHAK, Anissa; ORTEGA, Zaida; CHAABANI, Sana; TCHARKHTCHI, Abbas; KHELLADI, Sofiane
In this paper the miscibility of PVDF/PMMA blends was studied using different approaches: experimental tests, thermodynamics and numerical simulation. The first part of this study is devoted to the experimental work and aims to investigate the miscibility of blends by different experimental techniques. First, blends of PVDF/PMMA at different ratios were compounded and characterized using physico-chemical and rheological methods. The effect of PMMA content on the crystallization behavior of PVDF in the blend was experimentally investigated. At a second stage, the thermodynamic interaction parameter of Flory-Huggins was evaluated as a function of the PMMA proportion in the blends based on the experimental data related to the PVDF melting point and enthalpy. Besides, a numerical method has been developed using Fluent Ansys software to describe the coalescence phenomenon under different scenarios of viscosity ratios and grain sizes of polymers. The confrontation of the code simulation results with the experimental and thermodynamic approaches has shown a good agreement for reproducing the behavior of miscible polymers as well as their aptitude to form a homogeneous blend.
Tue, 01 Jan 2019 00:00:00 GMThttp://hdl.handle.net/10985/180082019-01-01T00:00:00ZAID, SaraEDDHAHAK, AnissaORTEGA, ZaidaCHAABANI, SanaTCHARKHTCHI, AbbasKHELLADI, SofianeIn this paper the miscibility of PVDF/PMMA blends was studied using different approaches: experimental tests, thermodynamics and numerical simulation. The first part of this study is devoted to the experimental work and aims to investigate the miscibility of blends by different experimental techniques. First, blends of PVDF/PMMA at different ratios were compounded and characterized using physico-chemical and rheological methods. The effect of PMMA content on the crystallization behavior of PVDF in the blend was experimentally investigated. At a second stage, the thermodynamic interaction parameter of Flory-Huggins was evaluated as a function of the PMMA proportion in the blends based on the experimental data related to the PVDF melting point and enthalpy. Besides, a numerical method has been developed using Fluent Ansys software to describe the coalescence phenomenon under different scenarios of viscosity ratios and grain sizes of polymers. The confrontation of the code simulation results with the experimental and thermodynamic approaches has shown a good agreement for reproducing the behavior of miscible polymers as well as their aptitude to form a homogeneous blend.Efficiency of bio- and socio-inspired optimization algorithms for axial turbomachinery design
http://hdl.handle.net/10985/17836
Efficiency of bio- and socio-inspired optimization algorithms for axial turbomachinery design
AIT CHIKH, Mohamed Abdessamed; BELAIDI, Idir; PARIS, José; DELIGANT, Michael; BAKIR, Farid; KHELLADI, Sofiane
Turbomachinery design is a complex problem which requires a lot of experience. The procedure may be speed up by the development of new numerical tools and optimization techniques. The latter rely on the parameterization of the geometry, a model to assess the performance of a given geometry and the definition of an objective functions and constraints to compare solutions. In order to improve the reference machine performance, two formulations including the off-design have been developed. The first one is the maximization of the total nominal efficiency. The second one consists to maximize the operation area under the efficiency curve. In this paper five optimization methods have been assessed for axial pump design: Genetic Algorithm (GA), Particle Swarm Optimization (PSO), Cuckoo Search (CS), Teaching Learning Based Optimization (TLBO) and Sequential Linear Programming (SLP). Four non-intrusive methods and the latter intrusive. Given an identical design point and set of constraints, each method proposed an optimized geometry. Their computing time, the optimized geometry and its performances (flow rate, head (H), efficiency (η), net pressure suction head (NPSH) and power) are compared. Although all methods would converge to similar results and geometry, it is not the case when increasing the range and number of constraints. The discrepancy in geometries and the variety of results are presented and discussed. The computational fluid dynamics (CFD) is used to validate the reference and optimized machines performances in two main formulations. The most adapted approach is compared with some existing approaches in literature.
Mon, 01 Jan 2018 00:00:00 GMThttp://hdl.handle.net/10985/178362018-01-01T00:00:00ZAIT CHIKH, Mohamed AbdessamedBELAIDI, IdirPARIS, JoséDELIGANT, MichaelBAKIR, FaridKHELLADI, SofianeTurbomachinery design is a complex problem which requires a lot of experience. The procedure may be speed up by the development of new numerical tools and optimization techniques. The latter rely on the parameterization of the geometry, a model to assess the performance of a given geometry and the definition of an objective functions and constraints to compare solutions. In order to improve the reference machine performance, two formulations including the off-design have been developed. The first one is the maximization of the total nominal efficiency. The second one consists to maximize the operation area under the efficiency curve. In this paper five optimization methods have been assessed for axial pump design: Genetic Algorithm (GA), Particle Swarm Optimization (PSO), Cuckoo Search (CS), Teaching Learning Based Optimization (TLBO) and Sequential Linear Programming (SLP). Four non-intrusive methods and the latter intrusive. Given an identical design point and set of constraints, each method proposed an optimized geometry. Their computing time, the optimized geometry and its performances (flow rate, head (H), efficiency (η), net pressure suction head (NPSH) and power) are compared. Although all methods would converge to similar results and geometry, it is not the case when increasing the range and number of constraints. The discrepancy in geometries and the variety of results are presented and discussed. The computational fluid dynamics (CFD) is used to validate the reference and optimized machines performances in two main formulations. The most adapted approach is compared with some existing approaches in literature.A Thin Film Fluid Structure Interaction Model for the Study of Flexible Structure Dynamics in Centrifugal Pumps
http://hdl.handle.net/10985/18057
A Thin Film Fluid Structure Interaction Model for the Study of Flexible Structure Dynamics in Centrifugal Pumps
ALBADAWI, Abdulaleem; SPECKLIN, Mathieu; CONNOLLY, Robert; DELAURÉ, Yan
This paper describes a fluid-structure interaction (FSI) model for the study of flexible cloth-like structures or the so-called rags in flows through centrifugal pumps. The structural model and its coupling to the flow solver are based on a Lagrangian formulation combining structural deformation and motion modeling coupled to a sharp interface immersed boundary model (IBM). The solution has been implemented in the open-source library OpenFOAM relying in particular on its PIMPLE segregated Navier–Stokes pressure–velocity coupling and its detached eddy simulation (DES) turbulence model. The FSI solver is assessed in terms of its capability to generate consistent deformations and transport of the immersed flexible structures. Two benchmark cases are covered and both involve experimental validation with three-dimensional (3D) structural deformations of the rag captured using a digital image correlation (DIC) technique. Simulations of a rag transported in a centrifugal pump confirm the suitability of the model to inform on the dynamic behavior of immersed structures under practical engineering conditions.
Mon, 01 Jan 2018 00:00:00 GMThttp://hdl.handle.net/10985/180572018-01-01T00:00:00ZALBADAWI, AbdulaleemSPECKLIN, MathieuCONNOLLY, RobertDELAURÉ, YanThis paper describes a fluid-structure interaction (FSI) model for the study of flexible cloth-like structures or the so-called rags in flows through centrifugal pumps. The structural model and its coupling to the flow solver are based on a Lagrangian formulation combining structural deformation and motion modeling coupled to a sharp interface immersed boundary model (IBM). The solution has been implemented in the open-source library OpenFOAM relying in particular on its PIMPLE segregated Navier–Stokes pressure–velocity coupling and its detached eddy simulation (DES) turbulence model. The FSI solver is assessed in terms of its capability to generate consistent deformations and transport of the immersed flexible structures. Two benchmark cases are covered and both involve experimental validation with three-dimensional (3D) structural deformations of the rag captured using a digital image correlation (DIC) technique. Simulations of a rag transported in a centrifugal pump confirm the suitability of the model to inform on the dynamic behavior of immersed structures under practical engineering conditions.Investigation on the mixture formation, combustion characteristics and performance of a Diesel engine fueled with Diesel, Biodiesel B20 and hydrogen addition
http://hdl.handle.net/10985/17847
Investigation on the mixture formation, combustion characteristics and performance of a Diesel engine fueled with Diesel, Biodiesel B20 and hydrogen addition
ALDHAIDHAWI, Mohanad; CHIRIAC, Radu; BĂDESCU, Viorel; DESCOMBES, Georges; PODEVIN, Pierre
An experimental and numerical study was performed to investigate the impact of Biodiesel B20 (blends 20% Rapeseed methyl ester with 80 % Diesel volumetric fraction) and different energetic fractions of hydrogen content (between 0 and 5%) on the mixture formation, combustion characteristics, engine performance and pollutant emissions formation. Experiments were carried out on a tractor Diesel engine, four-cylinders, four-stroke, 50 kW/2400 rpm, and direct injection. Simulations were conducted using the AVL codes (HYDSIM and BOOST 2013). Simulation results were validated against experimental data, by comparing the inline pressure, needle lift, in-cylinder pressure curves for Biodiesel B20 and pure Diesel fuels at 1400 rpm and 2400 rpm, respectively, under full load operating conditions. Good agreement with a maximum of 2.5% relative deviation on the peak results revealed that overall operation conditions Biodiesel B20 provides lower engine performance, efficiency, and emissions except the NOx which are slightly increased. The Biodiesel B20 has shorter ignition delay. By hydrogen addition to B20 with aspiration of the intake air flow the CO emissions, smoke, and total unburned hydrocarbon emissions THC decreased, while the NOx kept the same increasing trend for 1400 rpm and has not quite apparent trend for 2400 rpm. The enrichment by hydrogen of Diesel and B20 fuels has not a significant effect on ignition delay.
Sun, 01 Jan 2017 00:00:00 GMThttp://hdl.handle.net/10985/178472017-01-01T00:00:00ZALDHAIDHAWI, MohanadCHIRIAC, RaduBĂDESCU, ViorelDESCOMBES, GeorgesPODEVIN, PierreAn experimental and numerical study was performed to investigate the impact of Biodiesel B20 (blends 20% Rapeseed methyl ester with 80 % Diesel volumetric fraction) and different energetic fractions of hydrogen content (between 0 and 5%) on the mixture formation, combustion characteristics, engine performance and pollutant emissions formation. Experiments were carried out on a tractor Diesel engine, four-cylinders, four-stroke, 50 kW/2400 rpm, and direct injection. Simulations were conducted using the AVL codes (HYDSIM and BOOST 2013). Simulation results were validated against experimental data, by comparing the inline pressure, needle lift, in-cylinder pressure curves for Biodiesel B20 and pure Diesel fuels at 1400 rpm and 2400 rpm, respectively, under full load operating conditions. Good agreement with a maximum of 2.5% relative deviation on the peak results revealed that overall operation conditions Biodiesel B20 provides lower engine performance, efficiency, and emissions except the NOx which are slightly increased. The Biodiesel B20 has shorter ignition delay. By hydrogen addition to B20 with aspiration of the intake air flow the CO emissions, smoke, and total unburned hydrocarbon emissions THC decreased, while the NOx kept the same increasing trend for 1400 rpm and has not quite apparent trend for 2400 rpm. The enrichment by hydrogen of Diesel and B20 fuels has not a significant effect on ignition delay.Sensitivity and optimal forcing response in separated boundary layer flows
http://hdl.handle.net/10985/6862
Sensitivity and optimal forcing response in separated boundary layer flows
ALIZARD, Frédéric; CHERUBINI, Stefania; ROBINET, Jean-Christophe
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.
Publisher version : http://pof.aip.org/resource/1/phfle6/v21/i6/p064108_s1?isAuthorized=no
Thu, 01 Jan 2009 00:00:00 GMThttp://hdl.handle.net/10985/68622009-01-01T00:00:00ZALIZARD, FrédéricCHERUBINI, StefaniaROBINET, Jean-ChristopheThe 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.A 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.Restricted nonlinear model for high- and low-drag events in plane channel flow
http://hdl.handle.net/10985/18049
Restricted nonlinear model for high- and low-drag events in plane channel flow
ALIZARD, Frédéric; BIAU, Damien
A restricted nonlinear (RNL) model, obtained by partitioning the state variables into streamwise-averaged quantities and superimposed perturbations, is used in order to track the exact coherent state in plane channel flow investigated by Toh & Itano (J. Fluid Mech., vol. 481, 2003, pp. 67–76). When restricting nonlinearities to quadratic interaction of the fluctuating part into the streamwise-averaged component, it is shown that the coherent structure and its dynamics closely match results from direct numerical simulation (DNS), even if only a single streamwise Fourier mode is retained. In particular, both solutions exhibit long quiescent phases, spanwise shifts and bursting events. It is also shown that the dynamical trajectory passes close to equilibria that exhibit either low- or high-drag states. When statistics are collected at times where the friction velocity peaks, the mean flow and root-mean-square profiles show the essential features of wall turbulence obtained by DNS for the same friction Reynolds number. For low-drag events, the mean flow profiles are related to a universal asymptotic state called maximum drag reduction (Xi & Graham, Phys. Rev. Lett., vol. 108, 2012, 028301). Hence, the intermittent nature of self-sustaining processes in the buffer layer is contained in the dynamics of the RNL model, organized in two exact coherent states plus an asymptotic turbulent-like attractor. We also address how closely turbulent dynamics approaches these equilibria by exploiting a DNS database associated with a larger domain.
Tue, 01 Jan 2019 00:00:00 GMThttp://hdl.handle.net/10985/180492019-01-01T00:00:00ZALIZARD, FrédéricBIAU, DamienA restricted nonlinear (RNL) model, obtained by partitioning the state variables into streamwise-averaged quantities and superimposed perturbations, is used in order to track the exact coherent state in plane channel flow investigated by Toh & Itano (J. Fluid Mech., vol. 481, 2003, pp. 67–76). When restricting nonlinearities to quadratic interaction of the fluctuating part into the streamwise-averaged component, it is shown that the coherent structure and its dynamics closely match results from direct numerical simulation (DNS), even if only a single streamwise Fourier mode is retained. In particular, both solutions exhibit long quiescent phases, spanwise shifts and bursting events. It is also shown that the dynamical trajectory passes close to equilibria that exhibit either low- or high-drag states. When statistics are collected at times where the friction velocity peaks, the mean flow and root-mean-square profiles show the essential features of wall turbulence obtained by DNS for the same friction Reynolds number. For low-drag events, the mean flow profiles are related to a universal asymptotic state called maximum drag reduction (Xi & Graham, Phys. Rev. Lett., vol. 108, 2012, 028301). Hence, the intermittent nature of self-sustaining processes in the buffer layer is contained in the dynamics of the RNL model, organized in two exact coherent states plus an asymptotic turbulent-like attractor. We also address how closely turbulent dynamics approaches these equilibria by exploiting a DNS database associated with a larger domain.Linear stability of optimal streaks in the log-layer of turbulent channel flows
http://hdl.handle.net/10985/18611
Linear stability of optimal streaks in the log-layer of turbulent channel flows
ALIZARD, Frédéric
The importance of secondary instability of streaks for the generation of vortical struc-tures attached to the wall in the logarithmic region of turbulent channels is studied. Thestreaks and their linear instability are computed by solving equations associated withthe organized motion that include an eddy-viscosity modeling the effect of incoherentfluctuations. Three friction Reynolds numbers,Reτ=2000,3000, and 5000, areinvestigated. For all flow cases, optimal streamwise vortices (i.e., having the highestpotential for linear transient energy amplification) are used as initial conditions. Dueto the lift-up mechanism, these optimal perturbations lead to the nonlinear growthof streaks. Based on a Floquet theory along the spanwise direction, we observe theonset of streak secondary instability for a wide range of spanwise wavelengths whenthe streak amplitude exceeds a critical value. Under neutral conditions, it is shown thatstreak instability modes have their energy mainly concentrated in the overlap layer andpropagate with a phase velocity equal to the mean streamwise velocity of the log-layer.These neutral log-layer modes exhibit a sinuous pattern and have characteristic sizesthat are proportional to the wall distance in both streamwise and spanwise directions, inagreement with the Townsend’s attached eddy hypothesis (A. Townsend, the structureof turbulent shear flow, Cambridge university press, 1976 2nd edition). In particular,for a distance from the wall varying fromy+≈100 (in wall units) toy≈0.3h, wherehis half the height of the channel, the neutral log-layer modes are self-similar with aspanwise width ofλz≈y/0.3 and a streamwise length ofλx≈3λz, independently ofthe Reynolds number. Based on this observation, it is suggested that compact vorticalstructures attached to the wall can be ascribed to streak secondary instabilities. Inaddition, spatial distributions of fluctuating vorticity components show that the onsetof secondary instability is associated with the roll-up of the shear layer at the edgeof the low-speed streak, similarly to a three-dimensional mixing layer.
Thu, 01 Jan 2015 00:00:00 GMThttp://hdl.handle.net/10985/186112015-01-01T00:00:00ZALIZARD, FrédéricThe importance of secondary instability of streaks for the generation of vortical struc-tures attached to the wall in the logarithmic region of turbulent channels is studied. Thestreaks and their linear instability are computed by solving equations associated withthe organized motion that include an eddy-viscosity modeling the effect of incoherentfluctuations. Three friction Reynolds numbers,Reτ=2000,3000, and 5000, areinvestigated. For all flow cases, optimal streamwise vortices (i.e., having the highestpotential for linear transient energy amplification) are used as initial conditions. Dueto the lift-up mechanism, these optimal perturbations lead to the nonlinear growthof streaks. Based on a Floquet theory along the spanwise direction, we observe theonset of streak secondary instability for a wide range of spanwise wavelengths whenthe streak amplitude exceeds a critical value. Under neutral conditions, it is shown thatstreak instability modes have their energy mainly concentrated in the overlap layer andpropagate with a phase velocity equal to the mean streamwise velocity of the log-layer.These neutral log-layer modes exhibit a sinuous pattern and have characteristic sizesthat are proportional to the wall distance in both streamwise and spanwise directions, inagreement with the Townsend’s attached eddy hypothesis (A. Townsend, the structureof turbulent shear flow, Cambridge university press, 1976 2nd edition). In particular,for a distance from the wall varying fromy+≈100 (in wall units) toy≈0.3h, wherehis half the height of the channel, the neutral log-layer modes are self-similar with aspanwise width ofλz≈y/0.3 and a streamwise length ofλx≈3λz, independently ofthe Reynolds number. Based on this observation, it is suggested that compact vorticalstructures attached to the wall can be ascribed to streak secondary instabilities. Inaddition, spatial distributions of fluctuating vorticity components show that the onsetof secondary instability is associated with the roll-up of the shear layer at the edgeof the low-speed streak, similarly to a three-dimensional mixing layer.Invariant solutions in a channel flow using a minimal restricted nonlinear model
http://hdl.handle.net/10985/18606
Invariant solutions in a channel flow using a minimal restricted nonlinear model
ALIZARD, Frédéric
Simulations using a Restricted Nonlinear (RNL) system, where mean flow distortion resulting from Reynolds stress feedback regenerates rolls, is applied in a channel flow under subcritical conditions. This quasi-linear restriction of the dynamics is used to study invariant solutions located in the bulk of the flow found recently by Rawat et al. (2016) [14]. It is shown that the RNL system truncated to a single streamwise mode for the perturbation supports invariant solutions that are found to bifurcate from a relative periodic orbit into a travelling wave solution when the spanwise size is increasing. In particular, the travelling wave solution exhibits a spanwise localized structure that remains unchanged for large values of the spanwise extent as the invariant solution lying on the lower branch found by Rawat et al. (2016) [14]. In addition, travelling wave solutions provided by this minimal RNL system are self-similar with respect to the Reynolds number based on the centreline velocity, and the half-channel height varying from 2000 to 5000.
Sun, 01 Jan 2017 00:00:00 GMThttp://hdl.handle.net/10985/186062017-01-01T00:00:00ZALIZARD, FrédéricSimulations using a Restricted Nonlinear (RNL) system, where mean flow distortion resulting from Reynolds stress feedback regenerates rolls, is applied in a channel flow under subcritical conditions. This quasi-linear restriction of the dynamics is used to study invariant solutions located in the bulk of the flow found recently by Rawat et al. (2016) [14]. It is shown that the RNL system truncated to a single streamwise mode for the perturbation supports invariant solutions that are found to bifurcate from a relative periodic orbit into a travelling wave solution when the spanwise size is increasing. In particular, the travelling wave solution exhibits a spanwise localized structure that remains unchanged for large values of the spanwise extent as the invariant solution lying on the lower branch found by Rawat et al. (2016) [14]. In addition, travelling wave solutions provided by this minimal RNL system are self-similar with respect to the Reynolds number based on the centreline velocity, and the half-channel height varying from 2000 to 5000.Space–time dynamics of optimal wavepackets for streaks in a channel entrance flow
http://hdl.handle.net/10985/18898
Space–time dynamics of optimal wavepackets for streaks in a channel entrance flow
ALIZARD, Frédéric; CADIOU, A.; LE PENVEN, L.; DI PIERRO, B.; BUFFAT, M.
The laminar–turbulent transition of a plane channel entrance flow is revisited using global linear optimization analyses and direct numerical simulations. The investigated case corresponds to uniform upstream velocity conditions and a moderate value of Reynolds number so that the two-dimensional developing flow is linearly stable under the parallel flow assumption. However, the boundary layers in the entry zone are capable of supporting the development of streaks, which may experience secondary instability and evolve to turbulence. In this study, global optimal linear perturbations are computed and studied in the nonlinear regime for different values of streak amplitude and optimization time. These optimal perturbations take the form of wavepackets having either varicose or sinuous symmetry. It is shown that, for short optimization times, varicose wavepackets grow through a combination of Orr and lift-up effects, whereas for longer target times, both sinuous and varicose wavepackets exhibit an instability mechanism driven by the presence of inflection points in the streaky flow. In addition, while the optimal varicose modes obtained for short optimization times are localized near the inlet, where the base flow is strongly three-dimensional, when the target time is increased, the sinuous and varicose optimal modes are displaced farther downstream, in the nearly parallel streaky flow. Finally, the optimal wavepackets are found to lead to turbulence for sufficiently high initial amplitudes. It is noticed that the resulting turbulent flows have the same wall-shear stress, whether the wavepackets have been obtained for short or for long time optimization.
Mon, 01 Jan 2018 00:00:00 GMThttp://hdl.handle.net/10985/188982018-01-01T00:00:00ZALIZARD, FrédéricCADIOU, A.LE PENVEN, L.DI PIERRO, B.BUFFAT, M.The laminar–turbulent transition of a plane channel entrance flow is revisited using global linear optimization analyses and direct numerical simulations. The investigated case corresponds to uniform upstream velocity conditions and a moderate value of Reynolds number so that the two-dimensional developing flow is linearly stable under the parallel flow assumption. However, the boundary layers in the entry zone are capable of supporting the development of streaks, which may experience secondary instability and evolve to turbulence. In this study, global optimal linear perturbations are computed and studied in the nonlinear regime for different values of streak amplitude and optimization time. These optimal perturbations take the form of wavepackets having either varicose or sinuous symmetry. It is shown that, for short optimization times, varicose wavepackets grow through a combination of Orr and lift-up effects, whereas for longer target times, both sinuous and varicose wavepackets exhibit an instability mechanism driven by the presence of inflection points in the streaky flow. In addition, while the optimal varicose modes obtained for short optimization times are localized near the inlet, where the base flow is strongly three-dimensional, when the target time is increased, the sinuous and varicose optimal modes are displaced farther downstream, in the nearly parallel streaky flow. Finally, the optimal wavepackets are found to lead to turbulence for sufficiently high initial amplitudes. It is noticed that the resulting turbulent flows have the same wall-shear stress, whether the wavepackets have been obtained for short or for long time optimization.