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http://hdl.handle.net/10985/8638
Multi-Size-Mesh, Multi-Time-Step Algorithm for Noise Computation on Curvilinear Meshes
LE GARREC, Thomas; CORRE, Christophe; GLOERFELT, Xavier
Aeroacoustic problems are often multi-scale and a zonal refinement technique is thus desirable to reduce computational effort while preserving low dissipation and low dispersion errors from the numerical scheme. For that purpose, the multi-size-mesh multi-time-step algorithm of Tam and Kurbatskii [AIAA Journal, 2000, 38(8), p. 1331–1339] allows changes by a factor of two between adjacent blocks, accompanied by a doubling in the time step. This local time stepping avoids wasting calculation time, which would result from imposing a unique time step dictated by the smallest grid size for explicit time marching. In the present study, the multi-size-mesh multi-time-step method is extended to general curvilinear grids by using a suitable coordinate transformation and by performing the necessary interpolations directly in the physical space due to multidimensional interpolations combining order constraints and optimization in the wave number space. A particular attention is paid to the properties of the Adams–Bashforth schemes used for time marching. The optimization of the coefficients by minimizing an error in the wave number space rather than satisfying a formal order is shown to be inefficient for Adams–Bashforth schemes. The accuracy of the extended multi-size-mesh multi-time-step algorithm is first demonstrated for acoustic propagation on a sinusoidal grid and for a computation of laminar trailing edge noise. In the latter test-case, the mesh doubling is close to the airfoil and the vortical structures are crossing the doubling interface without affecting the quality of the radiated field. The applicability of the algorithm in three dimensions is eventually demonstrated by computing tonal noise from a moderate Reynolds number flow over an airfoil.
Tue, 01 Jan 2013 00:00:00 GMThttp://hdl.handle.net/10985/86382013-01-01T00:00:00ZLE GARREC, ThomasCORRE, ChristopheGLOERFELT, XavierAeroacoustic problems are often multi-scale and a zonal refinement technique is thus desirable to reduce computational effort while preserving low dissipation and low dispersion errors from the numerical scheme. For that purpose, the multi-size-mesh multi-time-step algorithm of Tam and Kurbatskii [AIAA Journal, 2000, 38(8), p. 1331–1339] allows changes by a factor of two between adjacent blocks, accompanied by a doubling in the time step. This local time stepping avoids wasting calculation time, which would result from imposing a unique time step dictated by the smallest grid size for explicit time marching. In the present study, the multi-size-mesh multi-time-step method is extended to general curvilinear grids by using a suitable coordinate transformation and by performing the necessary interpolations directly in the physical space due to multidimensional interpolations combining order constraints and optimization in the wave number space. A particular attention is paid to the properties of the Adams–Bashforth schemes used for time marching. The optimization of the coefficients by minimizing an error in the wave number space rather than satisfying a formal order is shown to be inefficient for Adams–Bashforth schemes. The accuracy of the extended multi-size-mesh multi-time-step algorithm is first demonstrated for acoustic propagation on a sinusoidal grid and for a computation of laminar trailing edge noise. In the latter test-case, the mesh doubling is close to the airfoil and the vortical structures are crossing the doubling interface without affecting the quality of the radiated field. The applicability of the algorithm in three dimensions is eventually demonstrated by computing tonal noise from a moderate Reynolds number flow over an airfoil.Comparison of Subgrid-scale Viscosity Models and Selective Filtering Strategy for Large-eddy Simulations
http://hdl.handle.net/10985/8637
Comparison of Subgrid-scale Viscosity Models and Selective Filtering Strategy for Large-eddy Simulations
AUBARD, Guillaume; STEFANIN VOLPIANI, Pedro; ROBINET, Jean-Christophe; GLOERFELT, Xavier
Explicitly filtered large-eddy simulations (LES), combining high-accuracy schemes with the use of a selective filtering without adding an explicit subgrid-scales (SGS) model, are carried out for the Taylor-Green-vortex and the supersonic-boundary-layer cases. First, the present approach is validated against direct numerical simulation (DNS) results. Subsequently, several SGS models are implemented in order to investigate if they can improve the initial filter-based methodology. It is shown that the most accurate results are obtained when the filtering is used alone as an implicit model, and for a minimal cost. Moreover, the tests for the Taylor-Green vortex indicate that the discretization error from the numerical methods, notably the dissipation error from the high-order filtering, can have a greater influence than the SGS models.
Tue, 01 Jan 2013 00:00:00 GMThttp://hdl.handle.net/10985/86372013-01-01T00:00:00ZAUBARD, GuillaumeSTEFANIN VOLPIANI, PedroROBINET, Jean-ChristopheGLOERFELT, XavierExplicitly filtered large-eddy simulations (LES), combining high-accuracy schemes with the use of a selective filtering without adding an explicit subgrid-scales (SGS) model, are carried out for the Taylor-Green-vortex and the supersonic-boundary-layer cases. First, the present approach is validated against direct numerical simulation (DNS) results. Subsequently, several SGS models are implemented in order to investigate if they can improve the initial filter-based methodology. It is shown that the most accurate results are obtained when the filtering is used alone as an implicit model, and for a minimal cost. Moreover, the tests for the Taylor-Green vortex indicate that the discretization error from the numerical methods, notably the dissipation error from the high-order filtering, can have a greater influence than the SGS models.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.Global and Koopman modes analysis of sound generation in mixing layers
http://hdl.handle.net/10985/8642
Global and Koopman modes analysis of sound generation in mixing layers
SONG, Ge; ALIZARD, Frédéric; ROBINET, Jean-Christophe; GLOERFELT, Xavier
It is now well established that linear and nonlinear instability waves play a significant role in the noise generation process for a wide variety of shear flows such as jets or mixing layers. In that context, the problem of acoustic radiation generated by spatially growing instability waves of two-dimensional subsonic and supersonic mixing layers are revisited in a global point of view, i.e., without any assumption about the base flow, in both a linear and a nonlinear framework by using global and Koopman mode decompositions. In that respect, a timestepping technique based on disturbance equations is employed to extract the most dynamically relevant coherent structures for both linear and nonlinear regimes. The present analysis proposes thus a general strategy for analysing the near-field coherent structures which are responsible for the acoustic noise in these configurations. In particular, we illustrate the failure of linear global modes to describe the noise generation mechanism associated with the vortex pairing for the subsonic regime whereas they appropriately explain the Mach wave radiation of instability waves in the supersonic regime. By contrast, the Dynamic Mode Decomposition (DMD) analysis captures both the near-field dynamics and the far-field acoustics with a few number of modes for both configurations. In addition, the combination of DMD and linear global modes analyses provides new insight about the influence on the radiated noise of nonlinear interactions and saturation of instability waves as well as their interaction with the mean flow.
Tue, 01 Jan 2013 00:00:00 GMThttp://hdl.handle.net/10985/86422013-01-01T00:00:00ZSONG, GeALIZARD, FrédéricROBINET, Jean-ChristopheGLOERFELT, XavierIt is now well established that linear and nonlinear instability waves play a significant role in the noise generation process for a wide variety of shear flows such as jets or mixing layers. In that context, the problem of acoustic radiation generated by spatially growing instability waves of two-dimensional subsonic and supersonic mixing layers are revisited in a global point of view, i.e., without any assumption about the base flow, in both a linear and a nonlinear framework by using global and Koopman mode decompositions. In that respect, a timestepping technique based on disturbance equations is employed to extract the most dynamically relevant coherent structures for both linear and nonlinear regimes. The present analysis proposes thus a general strategy for analysing the near-field coherent structures which are responsible for the acoustic noise in these configurations. In particular, we illustrate the failure of linear global modes to describe the noise generation mechanism associated with the vortex pairing for the subsonic regime whereas they appropriately explain the Mach wave radiation of instability waves in the supersonic regime. By contrast, the Dynamic Mode Decomposition (DMD) analysis captures both the near-field dynamics and the far-field acoustics with a few number of modes for both configurations. In addition, the combination of DMD and linear global modes analyses provides new insight about the influence on the radiated noise of nonlinear interactions and saturation of instability waves as well as their interaction with the mean flow.Investigation of flow structures involved in sound generation by two- and three-dimensional cavity flows
http://hdl.handle.net/10985/8645
Investigation of flow structures involved in sound generation by two- and three-dimensional cavity flows
DRUAULT, Philippe; MERVANT, Thomas; GLOERFELT, Xavier
Proper Orthogonal Decomposition and Stochastic Estimation are combined to shed some light on the link between organized flow structures and noise generation by turbulent flows. Proper Orthogonal Decomposition (POD) is firstly used to extract selected flow events. Based on the knowledge of these structures, the Quadratic Stochastic Estimation of the acoustic pressure field is secondly performed. Both procedures are successively applied to two- and three-dimensional numerical databases of a flow over a cavity. It is demonstrated that POD can extract selected aerodynamic events which can be associated with selected frequencies in the acoustic spectra. Reconstructed acoustic fields also indicate the aerodynamic events which are responsible of the main energy of the noise emission. Such mathematical tools offer new perspectives in analysing flow structures involved in sound generation by turbulent flows and in the experimental design of a flow control strategy.
Sat, 01 Jan 2011 00:00:00 GMThttp://hdl.handle.net/10985/86452011-01-01T00:00:00ZDRUAULT, PhilippeMERVANT, ThomasGLOERFELT, XavierProper Orthogonal Decomposition and Stochastic Estimation are combined to shed some light on the link between organized flow structures and noise generation by turbulent flows. Proper Orthogonal Decomposition (POD) is firstly used to extract selected flow events. Based on the knowledge of these structures, the Quadratic Stochastic Estimation of the acoustic pressure field is secondly performed. Both procedures are successively applied to two- and three-dimensional numerical databases of a flow over a cavity. It is demonstrated that POD can extract selected aerodynamic events which can be associated with selected frequencies in the acoustic spectra. Reconstructed acoustic fields also indicate the aerodynamic events which are responsible of the main energy of the noise emission. Such mathematical tools offer new perspectives in analysing flow structures involved in sound generation by turbulent flows and in the experimental design of a flow control strategy.Turbulent boundary layer noise : direct radiation at Mach number 0.5
http://hdl.handle.net/10985/8636
Turbulent boundary layer noise : direct radiation at Mach number 0.5
BERLAND, Julien; GLOERFELT, Xavier
Boundary layers constitute a fundamental source of aerodynamic noise. A turbulent boundary layer over a plane wall can provide an indirect contribution to the noise by exciting the structure, and a direct noise contribution. The latter part can play a significant role even if its intensity is very low, explaining why it is hardly measured unambiguously. In the present study, the aerodynamic noise generated by a spatially developing turbulent boundary layer is computed directly by solving the compressible Navier-Stokes equations. This numerical experiment aims at giving some insight into the noise radiation characteristics. The acoustic wavefronts have a large wavelength and are oriented in the direction opposite to the flow. Their amplitude is only 0.7 % of the aerodynamic pressure for a flat-plate flow at Mach 0.5. The particular directivity is mainly explained by convection effects by the mean flow, giving an indication about the compactness of the sources. These vortical events correspond to low-frequencies, and have thus a large life time. They cannot be directly associated with the main structures populating the boundary layer such as hairpin or horseshoe vortices. The analysis of the wall pressure can provide a picture of the flow in the frequency-wavenumber space. The main features of wall pressure beneath a turbulent boundary layer as described in the literature are well reproduced. The acoustic domain, corresponding to supersonic wavenumbers, is detectable but can hardly be separated from the convective ridge at this relatively high speed. This is also due to the low frequencies of sound emission as noted previously.
Tue, 01 Jan 2013 00:00:00 GMThttp://hdl.handle.net/10985/86362013-01-01T00:00:00ZBERLAND, JulienGLOERFELT, XavierBoundary layers constitute a fundamental source of aerodynamic noise. A turbulent boundary layer over a plane wall can provide an indirect contribution to the noise by exciting the structure, and a direct noise contribution. The latter part can play a significant role even if its intensity is very low, explaining why it is hardly measured unambiguously. In the present study, the aerodynamic noise generated by a spatially developing turbulent boundary layer is computed directly by solving the compressible Navier-Stokes equations. This numerical experiment aims at giving some insight into the noise radiation characteristics. The acoustic wavefronts have a large wavelength and are oriented in the direction opposite to the flow. Their amplitude is only 0.7 % of the aerodynamic pressure for a flat-plate flow at Mach 0.5. The particular directivity is mainly explained by convection effects by the mean flow, giving an indication about the compactness of the sources. These vortical events correspond to low-frequencies, and have thus a large life time. They cannot be directly associated with the main structures populating the boundary layer such as hairpin or horseshoe vortices. The analysis of the wall pressure can provide a picture of the flow in the frequency-wavenumber space. The main features of wall pressure beneath a turbulent boundary layer as described in the literature are well reproduced. The acoustic domain, corresponding to supersonic wavenumbers, is detectable but can hardly be separated from the convective ridge at this relatively high speed. This is also due to the low frequencies of sound emission as noted previously.Study of interpolation methods for high-accuracy computations on overlapping grids
http://hdl.handle.net/10985/8639
Study of interpolation methods for high-accuracy computations on overlapping grids
CHICHEPORTICHE, Jérémie; GLOERFELT, Xavier
Overset strategy can be an efficient way to keep high-accuracy discretization by decomposing a complex geometry in topologically simple subdomains. Apart from the grid assembly algorithm, the key point of overset technique lies in the interpolation processes which ensure the communications between the overlapping grids. The family of explicit Lagrange and optimized interpolation schemes is studied. The a priori interpolation error is analyzed in the Fourier space, and combined with the error of the chosen discretization to highlight the modification of the numerical error. When high-accuracy algorithms are used an optimization of the interpolation coefficients can enhance the resolvality, which can be useful when high-frequency waves or small turbulent scales need to be supported by a grid. For general curvilinear grids in more than one space dimension, a mapping in a computational space followed by a tensorization of 1-D interpolations is preferred to a direct evaluation of the coefficient in the physical domain. A high-order extension of the isoparametric mapping is accurate and robust since it avoids the inversion of a matrix which may be ill-conditioned. A posteriori error analyses indicate that the interpolation stencil size must be tailored to the accuracy of the discretization scheme. For well discretized wavelengthes, the results show that the choice of a stencil smaller than the stencil of the corresponding finite-difference scheme can be acceptable. Besides the gain of optimization to capture high-frequency phenomena is also underlined. Adding order constraints to the optimization allows an interesting trade-off when a large range of scales is considered. Finally, the ability of the present overset strategy to preserve accuracy is illustrated by the diffraction of an acoustic source by two cylinders, and the generation of acoustic tones in a rotor–stator interaction. Some recommandations are formulated in the closing section.
Sun, 01 Jan 2012 00:00:00 GMThttp://hdl.handle.net/10985/86392012-01-01T00:00:00ZCHICHEPORTICHE, JérémieGLOERFELT, XavierOverset strategy can be an efficient way to keep high-accuracy discretization by decomposing a complex geometry in topologically simple subdomains. Apart from the grid assembly algorithm, the key point of overset technique lies in the interpolation processes which ensure the communications between the overlapping grids. The family of explicit Lagrange and optimized interpolation schemes is studied. The a priori interpolation error is analyzed in the Fourier space, and combined with the error of the chosen discretization to highlight the modification of the numerical error. When high-accuracy algorithms are used an optimization of the interpolation coefficients can enhance the resolvality, which can be useful when high-frequency waves or small turbulent scales need to be supported by a grid. For general curvilinear grids in more than one space dimension, a mapping in a computational space followed by a tensorization of 1-D interpolations is preferred to a direct evaluation of the coefficient in the physical domain. A high-order extension of the isoparametric mapping is accurate and robust since it avoids the inversion of a matrix which may be ill-conditioned. A posteriori error analyses indicate that the interpolation stencil size must be tailored to the accuracy of the discretization scheme. For well discretized wavelengthes, the results show that the choice of a stencil smaller than the stencil of the corresponding finite-difference scheme can be acceptable. Besides the gain of optimization to capture high-frequency phenomena is also underlined. Adding order constraints to the optimization allows an interesting trade-off when a large range of scales is considered. Finally, the ability of the present overset strategy to preserve accuracy is illustrated by the diffraction of an acoustic source by two cylinders, and the generation of acoustic tones in a rotor–stator interaction. Some recommandations are formulated in the closing section.On compressibility assumptions in aeroacoustic integrals: a numerical study with subsonic mixing layers
http://hdl.handle.net/10985/8641
On compressibility assumptions in aeroacoustic integrals: a numerical study with subsonic mixing layers
MARGNAT, Florent; GLOERFELT, Xavier
Two assumptions commonly made in predictions based on Lighthill’s formalism are investigated: a constant density in the quadrupole expression, and the evaluation of the source quantity from incompressible simulations. Numerical predictions of the acoustic field are conducted in the case of a subsonic spatially evolving two-dimensional mixing layer at Re = 400. Published results of the direct noise computation (DNC) of the flow are use as reference and input for hybrid approaches before the assumptions on density are progressively introduced. Divergence free velocity fields are obtained from an incompressible simulation of the same flow case, exhibiting the same hydrodynamic field as the DNC. Fair comparisons of the hybrid predictions with the reference acoustic field valid both assumptions in the source region for the tested values of the Mach number. However, in the observer region, the inclusion of flow effects in the Lighthill source term is not preserved, which is illustrated through a comparison with the Kirchhoff wave-extrapolation formalism, and with the use of a convected Green function in the integration process.
Wed, 01 Jan 2014 00:00:00 GMThttp://hdl.handle.net/10985/86412014-01-01T00:00:00ZMARGNAT, FlorentGLOERFELT, XavierTwo assumptions commonly made in predictions based on Lighthill’s formalism are investigated: a constant density in the quadrupole expression, and the evaluation of the source quantity from incompressible simulations. Numerical predictions of the acoustic field are conducted in the case of a subsonic spatially evolving two-dimensional mixing layer at Re = 400. Published results of the direct noise computation (DNC) of the flow are use as reference and input for hybrid approaches before the assumptions on density are progressively introduced. Divergence free velocity fields are obtained from an incompressible simulation of the same flow case, exhibiting the same hydrodynamic field as the DNC. Fair comparisons of the hybrid predictions with the reference acoustic field valid both assumptions in the source region for the tested values of the Mach number. However, in the observer region, the inclusion of flow effects in the Lighthill source term is not preserved, which is illustrated through a comparison with the Kirchhoff wave-extrapolation formalism, and with the use of a convected Green function in the integration process.Dynamical selective ltering for the Lattice Boltzmann Method
http://hdl.handle.net/10985/10416
Dynamical selective ltering for the Lattice Boltzmann Method
MARIÉ, Simon; GLOERFELT, Xavier
In this study, a new selective ltering technique is proposed for the Lattice Boltzmann Method. This technique is based on dynamical implementation of the selective filter coefficient . The proposed model makes the latter coe cient dependent on the shear stress in order to restrict the use of the spatial ltering technique in the sheared stress region where numerical instabilities may occur. Di erent parameters are tested on a 3D decaying Taylor Green Vortex and compared to the classical static ltering technique and to the use of a standard subgrid-scale model.
Thu, 01 Jan 2015 00:00:00 GMThttp://hdl.handle.net/10985/104162015-01-01T00:00:00ZMARIÉ, SimonGLOERFELT, XavierIn this study, a new selective ltering technique is proposed for the Lattice Boltzmann Method. This technique is based on dynamical implementation of the selective filter coefficient . The proposed model makes the latter coe cient dependent on the shear stress in order to restrict the use of the spatial ltering technique in the sheared stress region where numerical instabilities may occur. Di erent parameters are tested on a 3D decaying Taylor Green Vortex and compared to the classical static ltering technique and to the use of a standard subgrid-scale model.Investigation of the flow dynamics in a channel constricted by periodic hills
http://hdl.handle.net/10985/15319
Investigation of the flow dynamics in a channel constricted by periodic hills
CINNELLA, Paola; GLOERFELT, Xavier
The present study aims at getting better insight of the complex flow dynamics in a channel constricted by periodic hills. This is a popular test case ofer used to assess LES and RANS/LES models, which appears as a compendium of flow separation and reattachment from a curved boundary, generation of an unsteady shear layer surrounding the recirculation bubble, strong acceleration on the convex windward wall of the next hill, attached boundary layer on the ceiling subject to intense instantaneous pressure gradients, recycling of the turbulence due to the periodicity assumption. One unresolved issue which is addressed in the present work concerns the early birth of the shear layer and the rapid eruption of large scales, with a characteristic length-scale many times greater than the thickness of the initial shear. The mechanism leading to large vortices in the shear layer indeed bears similarities with the collective interaction phenomenon, which has been encountered for mixing layer excited by a low-frequency component. The present results are a first attempt to characterize this complex process highly disrupted by the turbulent fluctuations turning into the periodic box.
Thu, 01 Jan 2015 00:00:00 GMThttp://hdl.handle.net/10985/153192015-01-01T00:00:00ZCINNELLA, PaolaGLOERFELT, XavierThe present study aims at getting better insight of the complex flow dynamics in a channel constricted by periodic hills. This is a popular test case ofer used to assess LES and RANS/LES models, which appears as a compendium of flow separation and reattachment from a curved boundary, generation of an unsteady shear layer surrounding the recirculation bubble, strong acceleration on the convex windward wall of the next hill, attached boundary layer on the ceiling subject to intense instantaneous pressure gradients, recycling of the turbulence due to the periodicity assumption. One unresolved issue which is addressed in the present work concerns the early birth of the shear layer and the rapid eruption of large scales, with a characteristic length-scale many times greater than the thickness of the initial shear. The mechanism leading to large vortices in the shear layer indeed bears similarities with the collective interaction phenomenon, which has been encountered for mixing layer excited by a low-frequency component. The present results are a first attempt to characterize this complex process highly disrupted by the turbulent fluctuations turning into the periodic box.