Comptes rendus de l'Académie des sciences. Série II, Mécanique, physique, chimie, sciences de l'univers, sciences de la terre
Académie des sciences (France). Auteur du texte. Comptes rendus de l'Académie des sciences. Série... more Académie des sciences (France). Auteur du texte. Comptes rendus de l'Académie des sciences. Série 2, Mécanique, physique, chimie, sciences de l'univers, sciences de la terre. 1993-07-01.
Nowadays, frequency-domain time-linearized flow solvers are widely employed for aerospace enginee... more Nowadays, frequency-domain time-linearized flow solvers are widely employed for aerospace engineering applications like turbomachinery or wing aeroelacticity. Due to substantial savings in the computational costs compared to the classical time-nonlinear methods, these methods are promising in the context of industrial design process in aeronautics. Nevertheless, the timelinearized solution is often relying on the assumption of frozen turbulence which can lead to significant discrepancies in the unsteady flow prediction, especially when the steady flow exhibits strong shock-wave boundary layer interactions. In the present paper, we propose to account for effects of the turbulence on the unsteady field by linearizing the k-ω turbulence closure of Wilcox. To this end, an Automatic Derivation Tool is applied to the discretized Reynolds Average Navier-Stokes solver Turb'Flow TM. The resulting time-linearized LRANS solver Turb'Lin TM is used to computed the unsteady response of forced shock-wave motion in a transonic nozzle due to harmonic back pressure fluctuations. The accuracy of the present methodology is assessed by comparison with time-nonlinear and harmonic-balance solutions for both weak and strong shock-wave turbulent boundary layer interactions forced by an excitation frequency equal to 500 Hz.
Notes on numerical fluid mechanics and multidisciplinary design, 2021
HAL is a multidisciplinary open access archive for the deposit and dissemination of scientific re... more HAL is a multidisciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L'archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.
The flutter corresponds to an aerodynamic loading of the structure which amplifies the natural bl... more The flutter corresponds to an aerodynamic loading of the structure which amplifies the natural blade vibration. In this paper, a modern design of a high pressure compressor is investigated using a time-linearized RANS solver on 2D blade to blade channel. Two operating points at part speed have been selected, the first with only small supersonic pockets and the second with the interblade channel blocked. Two vibration modes are investigated, the first torsion mode (with a nodal diameter at 2) and the first flexion mode (with a nodal diameter at 2, 4 and 6). Two different two equations turbulence models, k-l and k-ω have been used to resolve the steady state. The unsteady resolution is based on the previous steady state field. Turbulent variables are calculated over time based on a k-ω turbulence model. It was found that for some mode shapes, but not for all, the work exchange between the flow and the blade presents a large disparity depending on the turbulence model used primarily in the steady calculation. This paper proposes a parametric study in terms of rotor velocities, nodal diameters and vibration mode shapes to determine which flow phenomena are sensitive to the turbulence modelling. Main results point to the effect of the shockwave motion, and its interaction with the boundary layer and its separation.
HAL (Le Centre pour la Communication Scientifique Directe), Mar 26, 2018
HAL is a multidisciplinary open access archive for the deposit and dissemination of scientific re... more HAL is a multidisciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L'archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.
A prerequisite for aeroelastic stability investigations in internal and external aerodynamics is ... more A prerequisite for aeroelastic stability investigations in internal and external aerodynamics is the understanding of the fluctuating forces acting on the structure. Unsteady transonic flows are complex because of mutual interactions between traveling acoustic waves, shock motion, and fluctuating turbulent boundary layers. This paper is concerned with the understanding of phenomena associated with pressure waves in non-uniform transonic flows and how they affect the unsteady pressure distribution as well as the shock motion. More precisely, the unsteady interaction of upstream propagating acoustic waves with a shock in a three dimensional transonic convergent-divergent nozzle is presented. Both numerical and experimental studies are carried out and compared with each other. Results show, at high frequency, the emergence of a high pressure amplification zone immediately downstream of the shock as an effect of the acoustic blockage theory. Furthermore, a systematic jump of the phase angle of the unsteady pressure perturbations is observed underneath the shock location. Interestingly, this phase shift varies both linearly with the perturbation frequency, and transversally with the strength of the shock. Numerical simulations also reveals a highly non linear behaviour of the shock motion through the appearance of a second sonic pocket during part of the unsteady cycle. In particular, the transversal propagation of the second sonic pocket is believed to correlate transversal and longitudinal acoustic modes within the channel.
Blade vibration may trigger a self-induced aeroelastic instability (flutter). In turbomachinery c... more Blade vibration may trigger a self-induced aeroelastic instability (flutter). In turbomachinery choke flutter appears when a strong shock-wave chokes the blade passage. The aim of this study is to identify mechanisms responsible for the instability. An innovative methodology relying on the splitting of the emitter and receiver role of the blade is presented. It is successfully applied to 2D linearized RANS computations of choke flutter. The emission splitting shows that the vibration of the blades downstream of the shockwave generates a backward traveling pressure wave triggering the aeroelastic instability. The reception splitting demonstrates the destabilising contribution of the shock-wave / separated boundary layer interaction. The source of flutter is finally a combination of inviscid (regressive waves) and viscous (unsteady separation) mechanisms.
A prerequisite for aeroelastic stability investigations in turbomachines is the understanding of ... more A prerequisite for aeroelastic stability investigations in turbomachines is the understanding of the fluctuating aerodynamic forces acting on the blades. Unsteady transonic flows are naturally complex due to wave reflections and mutual interaction between flow disturbances, shock motion, and boundary layer behaviour. Complex phenomena appear in the shock/boundary layer region and produce phase lags and high time harmonics that can give a significant contribution to the overall unsteady lift and moment. Despite remarkable progress in computational and measurement capabilities, there are still important quantities which cannot be predicted very accurately (ie. peak heating in strong interaction region) or cannot be predicted at all (ie. unsteady pressure loads), observations which cannot be satisfactory explained, and physical processes which are not well understood. This paper is concerned with the understanding of phenomena associated with waves in non-uniform transonic flows and how they affect the unsteady surface pressure distribution and the far field radiated sound. More precisely, the unsteady interaction of upstream propagating acoustic waves with a shock in two dimensional transonic convergent-divergent nozzle is presented.
HAL (Le Centre pour la Communication Scientifique Directe), Aug 26, 2019
HAL is a multidisciplinary open access archive for the deposit and dissemination of scientific re... more HAL is a multidisciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L'archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés. Copyright
HAL (Le Centre pour la Communication Scientifique Directe), Sep 1, 2010
The design of new geometries for one aerodynamic conception leads to difficulties of CPU costs wh... more The design of new geometries for one aerodynamic conception leads to difficulties of CPU costs when discrete methods are used (one run per configuration). Strategies of simplification must be chosen either to restrict the number of calculations, or to limit the CPU time associated with each run. The approach proposed here consists in associating two strategies: using a meta-model and adjusting the limits of the parameters domain. A continuous database is so built of which size varies according to the number of parameters. The meta-model is based on high-order derivatives of flow variables (Turb'Opty TM solver). These are obtained by automatic differentiation of the discretized averaged Navier-Stokes 3D equations around a reference solution. The equations are therefore like those of conventional solvers (like SC/Tetra, Fluent, Star CD), but the unknown factors are here the derivatives of order 1, 2, ..., N of the field with respect to the parameters of operation or shape. These successive derivatives are stored in a database and their exploitation makes it possible to instantaneously obtain the new solution fields corresponding to the configurations sought by the user. The limits of the exploration domain depend on the derivatives order, the possible evaluation of the coupled terms, imposed constraints and physical high non-linearities. A continuous database can then be explored directly or coupled with other physics solvers, as well as with optimization tools. Some simplified applications show the validity of this approach. As an illustration, the database is coupled with a multi-objective Genetic Algorithm (GA) in order to solve large scale global optimization problems.
HAL (Le Centre pour la Communication Scientifique Directe), Sep 24, 2018
HAL is a multidisciplinary open access archive for the deposit and dissemination of scientific re... more HAL is a multidisciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L'archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.
ABSTRACT The upwind schemes are well suited to inviscid transonic flow but not to viscous flow. I... more ABSTRACT The upwind schemes are well suited to inviscid transonic flow but not to viscous flow. It is the opposite for central schemes. This paper presents a new approach which combines the central scheme and the upwind scheme. Liou's flux splitting is selected to define this new mixed AUSM+ Liou scheme. The results, obtained on supersonic viscous configuration, are compared to other schemes' results and to semi-empirical results. These calculations show the benefit of the present approach.
ABSTRACT Within the framework of aerospace turbines, an isolated integral bladed disk is examined... more ABSTRACT Within the framework of aerospace turbines, an isolated integral bladed disk is examined. The blisk presents very high eigenfrequencies with complex deformations of the blades. A 3D steady RANS computation is at first performed with the aim of characterizing the subsonic flow. Then a simplified 2D approach is considered in order to study fluid-structure interaction and to evaluate the stability: the blades have been found stable. In addition, an original method to better understand the level of stability is presented: the blade vibration is decomposed into elementary geometric movements in order to dissociate the different mechanisms that participate to reach stability. With the assumption of first-order behaviors, the linearized RANS unsteady fields corresponding to both the full deformation and the elementary movements are calculated. Some elementary relative blade movements appear to be either stabilizing or destabilizing when looking at the aerodynamic damping coefficient. The coupling between these elementary movements has also been investigated. Either constructive or destructive interference have been observed. The conclusions that emerge from this study are in line with the results of the classical bending-torsion flutter theory and lead to the improvement of the structure in terms of stability by modifying its mode shape.
International audienceIn this paper, an Ultra High Bypass Ratio fan is analyzed using a time-line... more International audienceIn this paper, an Ultra High Bypass Ratio fan is analyzed using a time-linearized Reynolds-Averaged Navier-Stokes equation solver to investigate the choke flutter. Simulations have been performed on a 2D blade to blade extraction. The steady flow exhibits a strong shock-wave which chokes the blade to blade channel. A flow separation zone can be noticed near the shock-wave on the suction side. The inter blade phase angle (IBPA) and the reduced frequency have been set to obtain a case with a choke flutter instability. The blade is decomposed in 424 subsections to track the contribution of local vibration to the global damping. Results analysis point to a restricted number of excitation sources at the trailing edge which induce a large part of the work exchange on a limited region of the airfoil. Main phenomena suspected are the shock-wave motion and the shock-wave / boundary layer interaction
Comptes rendus de l'Académie des sciences. Série II, Mécanique, physique, chimie, sciences de l'univers, sciences de la terre
Académie des sciences (France). Auteur du texte. Comptes rendus de l'Académie des sciences. Série... more Académie des sciences (France). Auteur du texte. Comptes rendus de l'Académie des sciences. Série 2, Mécanique, physique, chimie, sciences de l'univers, sciences de la terre. 1993-07-01.
Nowadays, frequency-domain time-linearized flow solvers are widely employed for aerospace enginee... more Nowadays, frequency-domain time-linearized flow solvers are widely employed for aerospace engineering applications like turbomachinery or wing aeroelacticity. Due to substantial savings in the computational costs compared to the classical time-nonlinear methods, these methods are promising in the context of industrial design process in aeronautics. Nevertheless, the timelinearized solution is often relying on the assumption of frozen turbulence which can lead to significant discrepancies in the unsteady flow prediction, especially when the steady flow exhibits strong shock-wave boundary layer interactions. In the present paper, we propose to account for effects of the turbulence on the unsteady field by linearizing the k-ω turbulence closure of Wilcox. To this end, an Automatic Derivation Tool is applied to the discretized Reynolds Average Navier-Stokes solver Turb'Flow TM. The resulting time-linearized LRANS solver Turb'Lin TM is used to computed the unsteady response of forced shock-wave motion in a transonic nozzle due to harmonic back pressure fluctuations. The accuracy of the present methodology is assessed by comparison with time-nonlinear and harmonic-balance solutions for both weak and strong shock-wave turbulent boundary layer interactions forced by an excitation frequency equal to 500 Hz.
Notes on numerical fluid mechanics and multidisciplinary design, 2021
HAL is a multidisciplinary open access archive for the deposit and dissemination of scientific re... more HAL is a multidisciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L'archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.
The flutter corresponds to an aerodynamic loading of the structure which amplifies the natural bl... more The flutter corresponds to an aerodynamic loading of the structure which amplifies the natural blade vibration. In this paper, a modern design of a high pressure compressor is investigated using a time-linearized RANS solver on 2D blade to blade channel. Two operating points at part speed have been selected, the first with only small supersonic pockets and the second with the interblade channel blocked. Two vibration modes are investigated, the first torsion mode (with a nodal diameter at 2) and the first flexion mode (with a nodal diameter at 2, 4 and 6). Two different two equations turbulence models, k-l and k-ω have been used to resolve the steady state. The unsteady resolution is based on the previous steady state field. Turbulent variables are calculated over time based on a k-ω turbulence model. It was found that for some mode shapes, but not for all, the work exchange between the flow and the blade presents a large disparity depending on the turbulence model used primarily in the steady calculation. This paper proposes a parametric study in terms of rotor velocities, nodal diameters and vibration mode shapes to determine which flow phenomena are sensitive to the turbulence modelling. Main results point to the effect of the shockwave motion, and its interaction with the boundary layer and its separation.
HAL (Le Centre pour la Communication Scientifique Directe), Mar 26, 2018
HAL is a multidisciplinary open access archive for the deposit and dissemination of scientific re... more HAL is a multidisciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L'archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.
A prerequisite for aeroelastic stability investigations in internal and external aerodynamics is ... more A prerequisite for aeroelastic stability investigations in internal and external aerodynamics is the understanding of the fluctuating forces acting on the structure. Unsteady transonic flows are complex because of mutual interactions between traveling acoustic waves, shock motion, and fluctuating turbulent boundary layers. This paper is concerned with the understanding of phenomena associated with pressure waves in non-uniform transonic flows and how they affect the unsteady pressure distribution as well as the shock motion. More precisely, the unsteady interaction of upstream propagating acoustic waves with a shock in a three dimensional transonic convergent-divergent nozzle is presented. Both numerical and experimental studies are carried out and compared with each other. Results show, at high frequency, the emergence of a high pressure amplification zone immediately downstream of the shock as an effect of the acoustic blockage theory. Furthermore, a systematic jump of the phase angle of the unsteady pressure perturbations is observed underneath the shock location. Interestingly, this phase shift varies both linearly with the perturbation frequency, and transversally with the strength of the shock. Numerical simulations also reveals a highly non linear behaviour of the shock motion through the appearance of a second sonic pocket during part of the unsteady cycle. In particular, the transversal propagation of the second sonic pocket is believed to correlate transversal and longitudinal acoustic modes within the channel.
Blade vibration may trigger a self-induced aeroelastic instability (flutter). In turbomachinery c... more Blade vibration may trigger a self-induced aeroelastic instability (flutter). In turbomachinery choke flutter appears when a strong shock-wave chokes the blade passage. The aim of this study is to identify mechanisms responsible for the instability. An innovative methodology relying on the splitting of the emitter and receiver role of the blade is presented. It is successfully applied to 2D linearized RANS computations of choke flutter. The emission splitting shows that the vibration of the blades downstream of the shockwave generates a backward traveling pressure wave triggering the aeroelastic instability. The reception splitting demonstrates the destabilising contribution of the shock-wave / separated boundary layer interaction. The source of flutter is finally a combination of inviscid (regressive waves) and viscous (unsteady separation) mechanisms.
A prerequisite for aeroelastic stability investigations in turbomachines is the understanding of ... more A prerequisite for aeroelastic stability investigations in turbomachines is the understanding of the fluctuating aerodynamic forces acting on the blades. Unsteady transonic flows are naturally complex due to wave reflections and mutual interaction between flow disturbances, shock motion, and boundary layer behaviour. Complex phenomena appear in the shock/boundary layer region and produce phase lags and high time harmonics that can give a significant contribution to the overall unsteady lift and moment. Despite remarkable progress in computational and measurement capabilities, there are still important quantities which cannot be predicted very accurately (ie. peak heating in strong interaction region) or cannot be predicted at all (ie. unsteady pressure loads), observations which cannot be satisfactory explained, and physical processes which are not well understood. This paper is concerned with the understanding of phenomena associated with waves in non-uniform transonic flows and how they affect the unsteady surface pressure distribution and the far field radiated sound. More precisely, the unsteady interaction of upstream propagating acoustic waves with a shock in two dimensional transonic convergent-divergent nozzle is presented.
HAL (Le Centre pour la Communication Scientifique Directe), Aug 26, 2019
HAL is a multidisciplinary open access archive for the deposit and dissemination of scientific re... more HAL is a multidisciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L'archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés. Copyright
HAL (Le Centre pour la Communication Scientifique Directe), Sep 1, 2010
The design of new geometries for one aerodynamic conception leads to difficulties of CPU costs wh... more The design of new geometries for one aerodynamic conception leads to difficulties of CPU costs when discrete methods are used (one run per configuration). Strategies of simplification must be chosen either to restrict the number of calculations, or to limit the CPU time associated with each run. The approach proposed here consists in associating two strategies: using a meta-model and adjusting the limits of the parameters domain. A continuous database is so built of which size varies according to the number of parameters. The meta-model is based on high-order derivatives of flow variables (Turb'Opty TM solver). These are obtained by automatic differentiation of the discretized averaged Navier-Stokes 3D equations around a reference solution. The equations are therefore like those of conventional solvers (like SC/Tetra, Fluent, Star CD), but the unknown factors are here the derivatives of order 1, 2, ..., N of the field with respect to the parameters of operation or shape. These successive derivatives are stored in a database and their exploitation makes it possible to instantaneously obtain the new solution fields corresponding to the configurations sought by the user. The limits of the exploration domain depend on the derivatives order, the possible evaluation of the coupled terms, imposed constraints and physical high non-linearities. A continuous database can then be explored directly or coupled with other physics solvers, as well as with optimization tools. Some simplified applications show the validity of this approach. As an illustration, the database is coupled with a multi-objective Genetic Algorithm (GA) in order to solve large scale global optimization problems.
HAL (Le Centre pour la Communication Scientifique Directe), Sep 24, 2018
HAL is a multidisciplinary open access archive for the deposit and dissemination of scientific re... more HAL is a multidisciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L'archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.
ABSTRACT The upwind schemes are well suited to inviscid transonic flow but not to viscous flow. I... more ABSTRACT The upwind schemes are well suited to inviscid transonic flow but not to viscous flow. It is the opposite for central schemes. This paper presents a new approach which combines the central scheme and the upwind scheme. Liou's flux splitting is selected to define this new mixed AUSM+ Liou scheme. The results, obtained on supersonic viscous configuration, are compared to other schemes' results and to semi-empirical results. These calculations show the benefit of the present approach.
ABSTRACT Within the framework of aerospace turbines, an isolated integral bladed disk is examined... more ABSTRACT Within the framework of aerospace turbines, an isolated integral bladed disk is examined. The blisk presents very high eigenfrequencies with complex deformations of the blades. A 3D steady RANS computation is at first performed with the aim of characterizing the subsonic flow. Then a simplified 2D approach is considered in order to study fluid-structure interaction and to evaluate the stability: the blades have been found stable. In addition, an original method to better understand the level of stability is presented: the blade vibration is decomposed into elementary geometric movements in order to dissociate the different mechanisms that participate to reach stability. With the assumption of first-order behaviors, the linearized RANS unsteady fields corresponding to both the full deformation and the elementary movements are calculated. Some elementary relative blade movements appear to be either stabilizing or destabilizing when looking at the aerodynamic damping coefficient. The coupling between these elementary movements has also been investigated. Either constructive or destructive interference have been observed. The conclusions that emerge from this study are in line with the results of the classical bending-torsion flutter theory and lead to the improvement of the structure in terms of stability by modifying its mode shape.
International audienceIn this paper, an Ultra High Bypass Ratio fan is analyzed using a time-line... more International audienceIn this paper, an Ultra High Bypass Ratio fan is analyzed using a time-linearized Reynolds-Averaged Navier-Stokes equation solver to investigate the choke flutter. Simulations have been performed on a 2D blade to blade extraction. The steady flow exhibits a strong shock-wave which chokes the blade to blade channel. A flow separation zone can be noticed near the shock-wave on the suction side. The inter blade phase angle (IBPA) and the reduced frequency have been set to obtain a case with a choke flutter instability. The blade is decomposed in 424 subsections to track the contribution of local vibration to the global damping. Results analysis point to a restricted number of excitation sources at the trailing edge which induce a large part of the work exchange on a limited region of the airfoil. Main phenomena suspected are the shock-wave motion and the shock-wave / boundary layer interaction
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