Dynamique des Fluides (DynFluid)
http://hdl.handle.net/10985/184
Mon, 25 May 2020 14:21:02 GMT2020-05-25T14:21:02ZDynamique des Fluides (DynFluid)https://sam.ensam.eu:443/bitstream/id/64024902-df5a-4eb1-9dad-a3acf158ad2c/
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; KHELLADI, Sofiane; ORTEGA, Zaida; CHAABANI, Sana; TCHARKHTCHI, Abbas
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, AnissaKHELLADI, SofianeORTEGA, ZaidaCHAABANI, SanaTCHARKHTCHI, AbbasIn 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; KHELLADI, Sofiane; PARIS, José; DELIGANT, Michael; BAKIR, Farid
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, IdirKHELLADI, SofianePARIS, JoséDELIGANT, MichaelBAKIR, FaridTurbomachinery 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, A.; SPECKLIN, Mathieu; CONNOLLY, R.; DELAURÉ, Y.
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, A.SPECKLIN, MathieuCONNOLLY, R.DELAURÉ, Y.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.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.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.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.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.Sensitivity analysis of optimal transient growth for turbulent boundary layers
http://hdl.handle.net/10985/18609
Sensitivity analysis of optimal transient growth for turbulent boundary layers
ALIZARD, Frédéric; ROBINET, Jean-Christophe; FILLIARD, Guillaume
Structural approaches based on modal decomposition of the flow dynamics have gained acceptance for a wide variety of turbulent shear flows. In this context, a singular value decomposition associated with a governing operator, aiming to model the linear amplification of coherent structures, is used to reproduce some fundamental motions in a turbulent boundary layer. In particular, as already found by Cossu et al. (2009), elongated streaky structures scaled in inner and outer units are identified. The sensitivity of these singular values to a mean flow modification is analysed. It is illustrated that the linear amplification of very large-scales which populate the outer motion is not affected when the leading singular value associated with the inner layer is damped. Moreover, we notice that the resulting optimal mean flow deviation is consistent with findings of Xu et al. (2007) in which the active control of a turbulent boundary layer is studied through direct numerical simulations.
Thu, 01 Jan 2015 00:00:00 GMThttp://hdl.handle.net/10985/186092015-01-01T00:00:00ZALIZARD, FrédéricROBINET, Jean-ChristopheFILLIARD, GuillaumeStructural approaches based on modal decomposition of the flow dynamics have gained acceptance for a wide variety of turbulent shear flows. In this context, a singular value decomposition associated with a governing operator, aiming to model the linear amplification of coherent structures, is used to reproduce some fundamental motions in a turbulent boundary layer. In particular, as already found by Cossu et al. (2009), elongated streaky structures scaled in inner and outer units are identified. The sensitivity of these singular values to a mean flow modification is analysed. It is illustrated that the linear amplification of very large-scales which populate the outer motion is not affected when the leading singular value associated with the inner layer is damped. Moreover, we notice that the resulting optimal mean flow deviation is consistent with findings of Xu et al. (2007) in which the active control of a turbulent boundary layer is studied through direct numerical simulations.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.Optimal transient growth in compressible turbulent boundary layers
http://hdl.handle.net/10985/18612
Optimal transient growth in compressible turbulent boundary layers
ALIZARD, Frédéric; PIROZZOLI, Sergio; BERNARDINI, Matteo; GRASSO, Francesco
The structure of zero-pressure-gradient compressible turbulent boundary layers is analysed using the tools of optimal transient growth theory. The approach relies on the extension to compressible flows of the theoretical framework originally developed by Reynolds & Hussain (J. Fluid Mech., vol. 52, 1972, pp. 263–288) for incompressible flows. The model is based on a density-weighted triple decomposition of the instantaneous field into the contributions of the mean flow, the organized (coherent) motions and the disorganized background turbulent fluctuations. The mean field and the eddy viscosity characterizing the incoherent fluctuations are here obtained from a direct numerical simulation database. Most temporally amplified modes (optimal modes) are found to be consistent with scaling laws of turbulent boundary layers for both inner and outer layers, as well as in the logarithmic region, where they exhibit a self-similar spreading. Four free-stream Mach numbers are considered: $\mathit{Ma}_{\infty }=0.2$, 2, 3 and 4. Weak effects of compressibility on the characteristics length and the orientation angles are observed for both the inner- and the outer-layer modes. Furthermore, taking into account the effects of mean density variations, a universal behaviour is suggested for the optimal modes that populate the log layer, regardless of the Mach number. The relevance of the optimal modes in describing the near-wall layer dynamics and the eddies that populate the outer region is discussed.
Thu, 01 Jan 2015 00:00:00 GMThttp://hdl.handle.net/10985/186122015-01-01T00:00:00ZALIZARD, FrédéricPIROZZOLI, SergioBERNARDINI, MatteoGRASSO, FrancescoThe structure of zero-pressure-gradient compressible turbulent boundary layers is analysed using the tools of optimal transient growth theory. The approach relies on the extension to compressible flows of the theoretical framework originally developed by Reynolds & Hussain (J. Fluid Mech., vol. 52, 1972, pp. 263–288) for incompressible flows. The model is based on a density-weighted triple decomposition of the instantaneous field into the contributions of the mean flow, the organized (coherent) motions and the disorganized background turbulent fluctuations. The mean field and the eddy viscosity characterizing the incoherent fluctuations are here obtained from a direct numerical simulation database. Most temporally amplified modes (optimal modes) are found to be consistent with scaling laws of turbulent boundary layers for both inner and outer layers, as well as in the logarithmic region, where they exhibit a self-similar spreading. Four free-stream Mach numbers are considered: $\mathit{Ma}_{\infty }=0.2$, 2, 3 and 4. Weak effects of compressibility on the characteristics length and the orientation angles are observed for both the inner- and the outer-layer modes. Furthermore, taking into account the effects of mean density variations, a universal behaviour is suggested for the optimal modes that populate the log layer, regardless of the Mach number. The relevance of the optimal modes in describing the near-wall layer dynamics and the eddies that populate the outer region is discussed.