Philippe Villedieu - Academia.edu (original) (raw)

Papers by Philippe Villedieu

Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, 2012

ABSTRACT The fragmentation process is a main concern in many engineering applications such as pre... more ABSTRACT The fragmentation process is a main concern in many engineering applications such as preventing flameouts of aircraft engines. The authors of this article are interested in measuring the critical impact velocity for ice fragmentation. Precisely, a dropweight technique was applied to study the ice ball impacts on glass plates. The influence of ice ball temperature, diameter and impact angle is also investigated. The after-impact ice ball state was found to be classified into two cases: an altered state and a non-altered state. The critical impact velocity is defined as the minimum impact velocity for which the ice ball is altered after impact or the maximum impact velocity for which the ice ball is not altered after impact. The experimental results are analysed by a model, assuming that the alteration regime is observed as soon as the ice ball normal kinetic energy is higher than a critical value of its deformation energy. This model depends on one parameter which is determined in this study. This last result is the major achievement of this article as there is almost no measurement of this parameter in the literature.

The numerical simulation of gas-particle flows is divided into two families of methods. In Euler-... more The numerical simulation of gas-particle flows is divided into two families of methods. In Euler-Lagrange methods individual particle trajectories are computed, whereas in Euler-Euler methods particles are characterized by statistical descriptors. Lagrangian methods are very precise but their computational cost increases with instationarity and particle volume fraction. In Eulerian methods (also called moment methods) the particlephase computational cost is comparable to that of the fluid phase but requires strong simplifications. Existing Eulerian models consider unimodal or close-to-equilibrium particle velocity distributions and then fail when the actual distribution is far from equilibrium. Quadrature-based Eulerian methods introduce a new reconstruction of the velocity distribution, written as a sum of delta functions in phase space constrained to give the right values for selected low-order moments. Two of these quadrature-based Eulerian methods, differing by their reconstruction algorithm, are the focus of this work. Computational results for two academic cases (crossing jets, Taylor-Green flow) are compared to those of a Lagrangian method (considered as the reference solution) and of an existing second-order moment method. With the quadrature-based Eulerian methods, significant qualitative improvement is noticed compared to the second-order moment method in the two test cases.

Large Eddy Simulation (LES) coupled with discrete particle simulation (DPS) has emerged as a powe... more Large Eddy Simulation (LES) coupled with discrete particle simulation (DPS) has emerged as a powerful tool for the numerical prediction of particle dynamics in turbulent flows. To further advance the technique, several issues require investigation. These include, for the fluid phase, the effect of the particles on subgrid-scale fluid turbulence, and for the particulate phase, the effect of the subgrid fluid turbulence on particle dispersion and inter-particle collision rates. The present study focuses on the modeling of the subgrid fluid velocity fluctuations along inertial particle trajectories. The focus of this work is particles with relaxation times close to the subgrid turbulent time scale of the fluid. A Langevin model has been derived that ensures that the resulting equation for the variance of the subgrid velocity along particle paths is consistent with the mean subgrid kinetic energy equation derived from the filtered Navier-Stokes system. To assess the model, one-and two-point statistics measured from discrete particle simulations using fluid velocity fields computed using DNS of homogeneous isotropic turbulence are compared with results obtained using filtered velocity fields (obtained from the DNS ones) and the stochastic Langevin equation for the subgrid velocity reconstruction. The results show that the stochastic subgrid model enables accurate prediction of the particle kinetic energy, with a reasonable match to the DNS database. In contrast, the PDF of the particle concentration undergoes relatively stronger modifications due to the incorporation of the model, with the simulations showing that the random contribution added by the stochastic model is over-predicted. † ONERA-CERT,

ESAIM Mathematical Modelling and Numerical Analysis

Comptes Rendus Mathematique

En utilisant la technique développée dans [7], nous donnons une estimation d'erreur, d'ordre 1/2 ... more En utilisant la technique développée dans [7], nous donnons une estimation d'erreur, d'ordre 1/2 par rapport à la taille du maillage, pour une approximation volumes finis explicite en temps, pour la résolution des systèmes hyperboliques linéaires symétriques. Le résultat s'applique à des maillages non structurés quelconques. Une attention particulière est portée sur la discrétisation des conditions aux limites, afin d'assurer la stabilité du schéma.

In this paper, the modelling of particle-particle collisions by Stochastic Lagrangian approach in... more In this paper, the modelling of particle-particle collisions by Stochastic Lagrangian approach in gas-particle homogeneous shear turbulent flows is investigated. This study is limited to the case of monodispersed particle flows without two-way coupling. The only external force acting on particles is the drag force. Particle statistics (particle velocities, fluid velocities ''viewed by the particles'') are given in terms of the joint fluid-particle probability density function (pdf). The evolution of this pdf obeys a Boltzmann type equation. The collision part of this equation is closed by assuming the correlated colliding particle closure. The fluid velocities ''viewed by the particles'' need also to be closed. The equation of evolution of the fluid-particle pdf is solved using a Lagrangian stochastic approach. Monte Carlo collision algorithm which takes into account the correlation between the colliding particles are tested in homogeneous isotropic t...

International Journal of Multiphase Flow, 2010

The Continuous Thermodynamics Model (CTM) is a suitable method to reduce computational cost of mu... more The Continuous Thermodynamics Model (CTM) is a suitable method to reduce computational cost of multi-component vaporization models. The droplet composition is described by a probability density function (PDF) rather than tens of components in the classical Discrete Component Model (DCM). In the first CTM method developed for this application, the PDF was assumed to be a Γ -function , but some problems had appeared in the case of vapor condensation at the droplet surface . The method put forward in this article, the Quadrature Method of Moments (QMoM), enables one to avoid any assumption on the PDF mathematical form. Following Lage who has developed this method for phase equilibria , this article widens the scope of QMoM to the modelling of multi-component droplet vaporization. The different CTM approaches are presented in the first part and the results obtained for a vapor condensation test case are then compared and analysed to illustrate improvements made by QMoM. To cite this article: C. Laurent et al., C. R. Mecanique 337 (2009).

Our study deals with numerical modelling of gaz-particles turbulent flows. The particles are move... more Our study deals with numerical modelling of gaz-particles turbulent flows. The particles are moved only by the drag force. The collisions are treated by a Monte-Carlo method. The results are compared with theoritical predictions of moments method.

In the present paper we analyze the effect of the crossing trajectory on the sugrid fluid turbule... more In the present paper we analyze the effect of the crossing trajectory on the sugrid fluid turbulence measured along solid particle trajectories. Numerical simulation have been carried out using Direct Numerical Simulation (DNS) coupled with Discrete Particle Simulation (DPS). To ensure an accurate spatial resolution of the sugrid fluid velocity field the DNS have been carried out with N = 1283 grid point and a Reynolds number of the order of ReL = 50. Relevant subgrid turbulence statistics have been extracted such as subgrid kinetic energy, spatial correlation function, Lagrangian and Eulerian time-correlation function. The results show that the crossing trajectory leads to decrease the interaction time between solid particles and the subgrid turbulence. An extension of Yudine (1959), and later Csanady (1963), theory allows to derive a model of the crossing trajectory effect on the subgrid turbulence. The model is based on the assumption that the subgrid fluid fluctuations are trans...

5th AIAA Atmospheric and Space Environments Conference, 2013

In this communication we shall focus on the main governing equations and building blocks of the M... more In this communication we shall focus on the main governing equations and building blocks of the M.A.D (Anti-icing Deicing Modelling) numerical tool, which is now renamed as INUIT (Integrated NUmerical model of Ice protection sysTems) and part of the new generation of ONERA icing codes. The code simulates the functionning of an electrothermal de-icing system. We shall also discuss the various improvements and new features we have added, especially a mechanical model of the ice block in order to improve the ice-shedding criterion. * Phd Student, EGAMT2 † Senior scientist, DMAE-MH, AIAA Member ‡ Professor, DMSM

International Journal of Multiphase Flow, 2007

ABSTRACT

Lecture Notes in Physics, 1998

Nous presentons dans cette Note une equation cinetique prenant en compte les collisions dam un sp... more Nous presentons dans cette Note une equation cinetique prenant en compte les collisions dam un spray dense de gouttelettes liquides transportees par un Ccoulement gazeux. Notre modele repose sur l'hypothbse que toute collision donne lieu soit 9 un rebond tlastique soit Ft une coalescence. Nous montrons que l'operateur de collision obtenu possede des proprietes analogues B celui de Boltzmann et nous exploitons cette analogie pour construire, en suivant les idees de Babovski (v&r [l]), une m&ode particulaire aleatoire permettant de le discretiser.

Notes on Numerical Fluid Mechanics and Multidisciplinary Design, 2010

A comparative parameter study is performed in order to analyze the influence of turbulence on the... more A comparative parameter study is performed in order to analyze the influence of turbulence on the rate of droplet coalescence. Therefore, Direct Numerical Simulations (DNS) of the fluid turbulence are coupled with a Lagrangian tracking of the particle phase (DPS) accounting for collisions leading to coalescence and to a broad droplet size distribution. In addition the accuracy of stochastic collision models is evaluated by comparison of Monte-Carlo predictions with the obtained results from the DNS/DPS simulations and statistical collision models are evaluated.

Volume 1: Symposia, Parts A and B, 2006

Lecture Notes in Physics, 1995

ABSTRACT We present a new second order kinetic flux-splitting schemes for the compressible Euler ... more ABSTRACT We present a new second order kinetic flux-splitting schemes for the compressible Euler equations and we prove that this scheme is positivity preserving (i.e and T remain 0). Our first order kinetic scheme is based on the Maxwellian equilibrium function and was initially proposed by Pullin. Our higher order extension can be seen as a variant of the so called corrected anti-diffusive flux approach. The necessity of a limitation on the antidiffusive correction appears naturally in order to satisfy the constraint of positivity.

5th AIAA Atmospheric and Space Environments Conference, 2013

5th AIAA Atmospheric and Space Environments Conference, 2013

Volume 1: Symposia, Parts A, B and C, 2009

ABSTRACT We present here a new method of moments for the numerical simulation of particle-laden f... more ABSTRACT We present here a new method of moments for the numerical simulation of particle-laden flows. The closure needed in Eulerian methods relies on writing the kinetic descriptor, the velocity destribution function, as a sum of delta-functions instead of the one-delta-function or close-to-Maxwellian assumption in existing methods. The closure velocity distribution function parameters are computed from the transported moments using a quadrature method. Simulation results are compared to those of a close-to-Maxwellian-based Eulerian method and those of a reference Lagrangian simulation, considering only transport and drag of particles in a Taylor-Green fluid flow. For a particular Stokes number of 1 the velocity distribution function is far from equilibrium and particle trajectory crossing is an important feature. We find that the quadrature-based method performs better than the close-to-equilibrium-based method, giving moment profiles closer to those of the Lagrangian reference simulation. However significant differences still remain between quadrature-based and Lagrangian methods results.

International Journal of Multiphase Flow, 2010

Please cite this article as: Schneider, L., Lostec, N.L., Villedieu, P., Sadiki, A., A moment met... more Please cite this article as: Schneider, L., Lostec, N.L., Villedieu, P., Sadiki, A., A moment method for splashing and evaporation processes of polydisperse sprays.

Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, 2012

ABSTRACT The fragmentation process is a main concern in many engineering applications such as pre... more ABSTRACT The fragmentation process is a main concern in many engineering applications such as preventing flameouts of aircraft engines. The authors of this article are interested in measuring the critical impact velocity for ice fragmentation. Precisely, a dropweight technique was applied to study the ice ball impacts on glass plates. The influence of ice ball temperature, diameter and impact angle is also investigated. The after-impact ice ball state was found to be classified into two cases: an altered state and a non-altered state. The critical impact velocity is defined as the minimum impact velocity for which the ice ball is altered after impact or the maximum impact velocity for which the ice ball is not altered after impact. The experimental results are analysed by a model, assuming that the alteration regime is observed as soon as the ice ball normal kinetic energy is higher than a critical value of its deformation energy. This model depends on one parameter which is determined in this study. This last result is the major achievement of this article as there is almost no measurement of this parameter in the literature.

The numerical simulation of gas-particle flows is divided into two families of methods. In Euler-... more The numerical simulation of gas-particle flows is divided into two families of methods. In Euler-Lagrange methods individual particle trajectories are computed, whereas in Euler-Euler methods particles are characterized by statistical descriptors. Lagrangian methods are very precise but their computational cost increases with instationarity and particle volume fraction. In Eulerian methods (also called moment methods) the particlephase computational cost is comparable to that of the fluid phase but requires strong simplifications. Existing Eulerian models consider unimodal or close-to-equilibrium particle velocity distributions and then fail when the actual distribution is far from equilibrium. Quadrature-based Eulerian methods introduce a new reconstruction of the velocity distribution, written as a sum of delta functions in phase space constrained to give the right values for selected low-order moments. Two of these quadrature-based Eulerian methods, differing by their reconstruction algorithm, are the focus of this work. Computational results for two academic cases (crossing jets, Taylor-Green flow) are compared to those of a Lagrangian method (considered as the reference solution) and of an existing second-order moment method. With the quadrature-based Eulerian methods, significant qualitative improvement is noticed compared to the second-order moment method in the two test cases.

Large Eddy Simulation (LES) coupled with discrete particle simulation (DPS) has emerged as a powe... more Large Eddy Simulation (LES) coupled with discrete particle simulation (DPS) has emerged as a powerful tool for the numerical prediction of particle dynamics in turbulent flows. To further advance the technique, several issues require investigation. These include, for the fluid phase, the effect of the particles on subgrid-scale fluid turbulence, and for the particulate phase, the effect of the subgrid fluid turbulence on particle dispersion and inter-particle collision rates. The present study focuses on the modeling of the subgrid fluid velocity fluctuations along inertial particle trajectories. The focus of this work is particles with relaxation times close to the subgrid turbulent time scale of the fluid. A Langevin model has been derived that ensures that the resulting equation for the variance of the subgrid velocity along particle paths is consistent with the mean subgrid kinetic energy equation derived from the filtered Navier-Stokes system. To assess the model, one-and two-point statistics measured from discrete particle simulations using fluid velocity fields computed using DNS of homogeneous isotropic turbulence are compared with results obtained using filtered velocity fields (obtained from the DNS ones) and the stochastic Langevin equation for the subgrid velocity reconstruction. The results show that the stochastic subgrid model enables accurate prediction of the particle kinetic energy, with a reasonable match to the DNS database. In contrast, the PDF of the particle concentration undergoes relatively stronger modifications due to the incorporation of the model, with the simulations showing that the random contribution added by the stochastic model is over-predicted. † ONERA-CERT,

ESAIM Mathematical Modelling and Numerical Analysis

Comptes Rendus Mathematique

En utilisant la technique développée dans [7], nous donnons une estimation d'erreur, d'ordre 1/2 ... more En utilisant la technique développée dans [7], nous donnons une estimation d'erreur, d'ordre 1/2 par rapport à la taille du maillage, pour une approximation volumes finis explicite en temps, pour la résolution des systèmes hyperboliques linéaires symétriques. Le résultat s'applique à des maillages non structurés quelconques. Une attention particulière est portée sur la discrétisation des conditions aux limites, afin d'assurer la stabilité du schéma.

In this paper, the modelling of particle-particle collisions by Stochastic Lagrangian approach in... more In this paper, the modelling of particle-particle collisions by Stochastic Lagrangian approach in gas-particle homogeneous shear turbulent flows is investigated. This study is limited to the case of monodispersed particle flows without two-way coupling. The only external force acting on particles is the drag force. Particle statistics (particle velocities, fluid velocities ''viewed by the particles'') are given in terms of the joint fluid-particle probability density function (pdf). The evolution of this pdf obeys a Boltzmann type equation. The collision part of this equation is closed by assuming the correlated colliding particle closure. The fluid velocities ''viewed by the particles'' need also to be closed. The equation of evolution of the fluid-particle pdf is solved using a Lagrangian stochastic approach. Monte Carlo collision algorithm which takes into account the correlation between the colliding particles are tested in homogeneous isotropic t...

International Journal of Multiphase Flow, 2010

The Continuous Thermodynamics Model (CTM) is a suitable method to reduce computational cost of mu... more The Continuous Thermodynamics Model (CTM) is a suitable method to reduce computational cost of multi-component vaporization models. The droplet composition is described by a probability density function (PDF) rather than tens of components in the classical Discrete Component Model (DCM). In the first CTM method developed for this application, the PDF was assumed to be a Γ -function , but some problems had appeared in the case of vapor condensation at the droplet surface . The method put forward in this article, the Quadrature Method of Moments (QMoM), enables one to avoid any assumption on the PDF mathematical form. Following Lage who has developed this method for phase equilibria , this article widens the scope of QMoM to the modelling of multi-component droplet vaporization. The different CTM approaches are presented in the first part and the results obtained for a vapor condensation test case are then compared and analysed to illustrate improvements made by QMoM. To cite this article: C. Laurent et al., C. R. Mecanique 337 (2009).

Our study deals with numerical modelling of gaz-particles turbulent flows. The particles are move... more Our study deals with numerical modelling of gaz-particles turbulent flows. The particles are moved only by the drag force. The collisions are treated by a Monte-Carlo method. The results are compared with theoritical predictions of moments method.

In the present paper we analyze the effect of the crossing trajectory on the sugrid fluid turbule... more In the present paper we analyze the effect of the crossing trajectory on the sugrid fluid turbulence measured along solid particle trajectories. Numerical simulation have been carried out using Direct Numerical Simulation (DNS) coupled with Discrete Particle Simulation (DPS). To ensure an accurate spatial resolution of the sugrid fluid velocity field the DNS have been carried out with N = 1283 grid point and a Reynolds number of the order of ReL = 50. Relevant subgrid turbulence statistics have been extracted such as subgrid kinetic energy, spatial correlation function, Lagrangian and Eulerian time-correlation function. The results show that the crossing trajectory leads to decrease the interaction time between solid particles and the subgrid turbulence. An extension of Yudine (1959), and later Csanady (1963), theory allows to derive a model of the crossing trajectory effect on the subgrid turbulence. The model is based on the assumption that the subgrid fluid fluctuations are trans...

5th AIAA Atmospheric and Space Environments Conference, 2013

In this communication we shall focus on the main governing equations and building blocks of the M... more In this communication we shall focus on the main governing equations and building blocks of the M.A.D (Anti-icing Deicing Modelling) numerical tool, which is now renamed as INUIT (Integrated NUmerical model of Ice protection sysTems) and part of the new generation of ONERA icing codes. The code simulates the functionning of an electrothermal de-icing system. We shall also discuss the various improvements and new features we have added, especially a mechanical model of the ice block in order to improve the ice-shedding criterion. * Phd Student, EGAMT2 † Senior scientist, DMAE-MH, AIAA Member ‡ Professor, DMSM

International Journal of Multiphase Flow, 2007

ABSTRACT

Lecture Notes in Physics, 1998

Nous presentons dans cette Note une equation cinetique prenant en compte les collisions dam un sp... more Nous presentons dans cette Note une equation cinetique prenant en compte les collisions dam un spray dense de gouttelettes liquides transportees par un Ccoulement gazeux. Notre modele repose sur l'hypothbse que toute collision donne lieu soit 9 un rebond tlastique soit Ft une coalescence. Nous montrons que l'operateur de collision obtenu possede des proprietes analogues B celui de Boltzmann et nous exploitons cette analogie pour construire, en suivant les idees de Babovski (v&r [l]), une m&ode particulaire aleatoire permettant de le discretiser.

Notes on Numerical Fluid Mechanics and Multidisciplinary Design, 2010

A comparative parameter study is performed in order to analyze the influence of turbulence on the... more A comparative parameter study is performed in order to analyze the influence of turbulence on the rate of droplet coalescence. Therefore, Direct Numerical Simulations (DNS) of the fluid turbulence are coupled with a Lagrangian tracking of the particle phase (DPS) accounting for collisions leading to coalescence and to a broad droplet size distribution. In addition the accuracy of stochastic collision models is evaluated by comparison of Monte-Carlo predictions with the obtained results from the DNS/DPS simulations and statistical collision models are evaluated.

Volume 1: Symposia, Parts A and B, 2006

Lecture Notes in Physics, 1995

ABSTRACT We present a new second order kinetic flux-splitting schemes for the compressible Euler ... more ABSTRACT We present a new second order kinetic flux-splitting schemes for the compressible Euler equations and we prove that this scheme is positivity preserving (i.e and T remain 0). Our first order kinetic scheme is based on the Maxwellian equilibrium function and was initially proposed by Pullin. Our higher order extension can be seen as a variant of the so called corrected anti-diffusive flux approach. The necessity of a limitation on the antidiffusive correction appears naturally in order to satisfy the constraint of positivity.

5th AIAA Atmospheric and Space Environments Conference, 2013

5th AIAA Atmospheric and Space Environments Conference, 2013

Volume 1: Symposia, Parts A, B and C, 2009

ABSTRACT We present here a new method of moments for the numerical simulation of particle-laden f... more ABSTRACT We present here a new method of moments for the numerical simulation of particle-laden flows. The closure needed in Eulerian methods relies on writing the kinetic descriptor, the velocity destribution function, as a sum of delta-functions instead of the one-delta-function or close-to-Maxwellian assumption in existing methods. The closure velocity distribution function parameters are computed from the transported moments using a quadrature method. Simulation results are compared to those of a close-to-Maxwellian-based Eulerian method and those of a reference Lagrangian simulation, considering only transport and drag of particles in a Taylor-Green fluid flow. For a particular Stokes number of 1 the velocity distribution function is far from equilibrium and particle trajectory crossing is an important feature. We find that the quadrature-based method performs better than the close-to-equilibrium-based method, giving moment profiles closer to those of the Lagrangian reference simulation. However significant differences still remain between quadrature-based and Lagrangian methods results.

International Journal of Multiphase Flow, 2010

Please cite this article as: Schneider, L., Lostec, N.L., Villedieu, P., Sadiki, A., A moment met... more Please cite this article as: Schneider, L., Lostec, N.L., Villedieu, P., Sadiki, A., A moment method for splashing and evaporation processes of polydisperse sprays.