Ecoulements en rotation: Taylor-Couette, Couches limites,...
Méthodes numérique d'ordre élevé
Publications scientifiques au M2P2
2015
Seyed Amin Ghaffari, Stéphane Viazzo, Kai Schneider, Patrick Bontoux. Simulation of forced deformable bodies interacting with two-dimensional incompressible flows: Application to fish-like swimming. International Journal of Heat and Fluid Flow, Elsevier, 2015, Theme special issue celebrating the 75th birthdays of Brian Launder and Kemo Hanjalic, 51, pp.88-109. ⟨10.1016/j.ijheatfluidflow.2014.10.023⟩. ⟨hal-00967077v2⟩ Plus de détails...
We present an efficient algorithm for simulation of deformable bodies interacting with two-dimensional incompressible flows. The temporal and spatial discretizations of the Navier-Stokes equations in vorticity stream-function formulation are based on classical fourth-order Runge-Kutta and compact finite differences, respectively. Using a uniform Cartesian grid we benefit from the advantage of a new fourth-order direct solver for the Poisson equation to ensure the incompressibility constraint down to machine zero. For introducing a deformable body in fluid flow, the volume penalization method is used. A Lagrangian structured grid with prescribed motion covers the deformable body interacting with the surrounding fluid due to the hydrodynamic forces and moment calculated on the Eulerian reference grid. An efficient law for curvature control of an anguilliform fish, swimming to a prescribed goal, is proposed. Validation of the developed method shows the efficiency and expected accuracy of the algorithm for fish-like swimming and also for a variety of fluid/solid interaction problems.
Seyed Amin Ghaffari, Stéphane Viazzo, Kai Schneider, Patrick Bontoux. Simulation of forced deformable bodies interacting with two-dimensional incompressible flows: Application to fish-like swimming. International Journal of Heat and Fluid Flow, Elsevier, 2015, Theme special issue celebrating the 75th birthdays of Brian Launder and Kemo Hanjalic, 51, pp.88-109. ⟨10.1016/j.ijheatfluidflow.2014.10.023⟩. ⟨hal-00967077v2⟩
Journal: International Journal of Heat and Fluid Flow
Ouafa Bouloumou, Eric Serre, Patrick Bontoux, J. Fröhlich. A 3D pseudo-spectral low Mach-number solver for buoyancy driven flows with large temperature differences. Computers and Fluids, Elsevier, 2012, 66, pp.107-120. ⟨10.1016/j.compfluid.2012.05.014⟩. ⟨hal-00834130⟩ Plus de détails...
A three-dimensional spectral method based on a Chebyshev/Chebyshev/Fourier discretization is proposed to integrate the Navier-Stokes equations for natural convection flow with large temperature differences under the low Mach-number approximation. The generalized Stokes problem arising from the time discretization by a second-order semi-implicit scheme is solved by a preconditioned iterative Uzawa algorithm. The spectrally convergent algorithm is validated on well-documented Boussinesq and non-Boussinesq benchmarks. Finally, non-Boussineq convection is investigated in a tall differentially heated cavity of aspect ratio 8 with one homogeneous direction. The technique is shown to be efficient in terms of computing performances and accuracy. The study brings new stability results evidencing 3D effects compared to both Boussinesq convection and former two-dimensional non-Boussinesq solutions. In particular, for Ra ⩾ 105 two-dimensional solutions are shown to be unstable with respect to three-dimensional perturbations. A Görtler-type instability grows in the region of the curved streamlines at both ends of the cavity and gives rise to 3D steady and oscillatory solutions. At higher Rayleigh numbers, these vortices eventually interact with a boundary layer instability leading to complex dynamics with multiple steady and unsteady stable solutions.
Ouafa Bouloumou, Eric Serre, Patrick Bontoux, J. Fröhlich. A 3D pseudo-spectral low Mach-number solver for buoyancy driven flows with large temperature differences. Computers and Fluids, Elsevier, 2012, 66, pp.107-120. ⟨10.1016/j.compfluid.2012.05.014⟩. ⟨hal-00834130⟩
Stéphane Viazzo, Sébastien Poncet, Eric Serre, Anthony Randriamampianina, Patrick Bontoux. High-order Large Eddy Simulations of Confined Rotor-Stator Flows. Flow, Turbulence and Combustion, Springer Verlag (Germany), 2011, 88, pp.63-75. ⟨10.1007/s10494-011-9345-0⟩. ⟨hal-00678841⟩ Plus de détails...
In many engineering and industrial applications, the investigation of rotating turbulent flow is of great interest. In rotor-stator cavities, the centrifugal and Coriolis forces have a strong influence on the turbulence by producing a secondary flow in the meridian plane composed of two thin boundary layers along the disks separated by a non-viscous geostrophic core. Most numerical simulations have been performed using RANS and URANS modelling, and very few investigations have been performed using LES. This paper reports on quantitative comparisons of two high-order LES methods to predict a turbulent rotor-stator flow at the rotational Reynolds number Re=400000. The classical dynamic Smagorinsky model for the subgrid-scale stress (Germano et al., Phys Fluids A 3(7):1760-1765, 1991) is compared to a spectral vanishing viscosity technique (Séverac & Serre, J Comp Phys 226(2):1234-1255, 2007). Numerical results include both instantaneous data and postprocessed statistics. The results show that both LES methods are able to accurately describe the unsteady flow structures and to satisfactorily predict mean velocities as well as Reynolds stress tensor components. A slight advantage is given to the spectral SVV approach in terms of accuracy and CPU cost. The strong improvements obtained in the present results with respect to RANS results confirm that LES is the appropriate level of modelling for flows in which fully turbulent and transition regimes are involved.
Stéphane Viazzo, Sébastien Poncet, Eric Serre, Anthony Randriamampianina, Patrick Bontoux. High-order Large Eddy Simulations of Confined Rotor-Stator Flows. Flow, Turbulence and Combustion, Springer Verlag (Germany), 2011, 88, pp.63-75. ⟨10.1007/s10494-011-9345-0⟩. ⟨hal-00678841⟩
Stéphane Viazzo, Sébastien Poncet, Eric Serre, Anthony Randriamampianina, Patrick Bontoux. High-order Large Eddy Simulations of Confined Rotor-Stator Flows. Flow, Turbulence and Combustion, Springer Verlag (Germany), 2011, 88, pp.63-75. ⟨10.1007/s10494-011-9345-0⟩. ⟨hal-00822030⟩ Plus de détails...
In many engineering and industrial applications, the investigation of rotating turbulent flow is of great interest. In rotor-stator cavities, the centrifugal and Coriolis forces have a strong influence on the turbulence by producing a secondary flow in the meridian plane composed of two thin boundary layers along the disks separated by a non-viscous geostrophic core. Most numerical simulations have been performed using RANS and URANS modelling, and very few investigations have been performed using LES. This paper reports on quantitative comparisons of two high-order LES methods to predict a turbulent rotor-stator flow at the rotational Reynolds number Re=400000. The classical dynamic Smagorinsky model for the subgrid-scale stress (Germano et al., Phys Fluids A 3(7):1760-1765, 1991) is compared to a spectral vanishing viscosity technique (Séverac & Serre, J Comp Phys 226(2):1234-1255, 2007). Numerical results include both instantaneous data and postprocessed statistics. The results show that both LES methods are able to accurately describe the unsteady flow structures and to satisfactorily predict mean velocities as well as Reynolds stress tensor components. A slight advantage is given to the spectral SVV approach in terms of accuracy and CPU cost. The strong improvements obtained in the present results with respect to RANS results confirm that LES is the appropriate level of modelling for flows in which fully turbulent and transition regimes are involved.
Stéphane Viazzo, Sébastien Poncet, Eric Serre, Anthony Randriamampianina, Patrick Bontoux. High-order Large Eddy Simulations of Confined Rotor-Stator Flows. Flow, Turbulence and Combustion, Springer Verlag (Germany), 2011, 88, pp.63-75. ⟨10.1007/s10494-011-9345-0⟩. ⟨hal-00822030⟩
Christine Baur, Patrick Bontoux, Michael Kornhaas, Matthieu Minguez, Richard Pasquetti, et al.. High-order methods for large-eddy simulation in complex geometries. Christophe Brun & al. Numerical simulation of turbulent flows and noise generation, Springer Berlin Heidelberg, pp.309-334, 2009, Notes on Numerical Fluid Mechanics and Multidisciplinary Design, 978-3-540-89955-6. ⟨10.1007/978-3-540-89956-3_13⟩. ⟨hal-00834157⟩ Plus de détails...
Developing high-order methods for large-eddy simulation (LES) is of interest to avoid mixing between subgrid scale modeling contributions and approximation errors of the numerical method. Two different approaches are investigated. The first one focuses on the so-called Spectral Vanishing Viscosity LES (SVV-LES) approach, which allows to extend the well known capabilities of spectral methods from laminar to turbulent flows, while the second one rather investigates the possibility of extending a second order finite volume code to higher order approximations. For the SVV-LES approach, a volume penalization like technique is used to address complex geometries.
Christine Baur, Patrick Bontoux, Michael Kornhaas, Matthieu Minguez, Richard Pasquetti, et al.. High-order methods for large-eddy simulation in complex geometries. Christophe Brun & al. Numerical simulation of turbulent flows and noise generation, Springer Berlin Heidelberg, pp.309-334, 2009, Notes on Numerical Fluid Mechanics and Multidisciplinary Design, 978-3-540-89955-6. ⟨10.1007/978-3-540-89956-3_13⟩. ⟨hal-00834157⟩
Gilbert Accary, Patrick Bontoux, Bernard Zappoli. Turbulent Rayleigh-Bénard convection in a near-critical fluid by three-dimensional direct numerical simulation. Journal of Fluid Mechanics, Cambridge University Press (CUP), 2009, 619, pp.127-145. ⟨10.1017/S0022112008004175⟩. ⟨hal-00834173⟩ Plus de détails...
This paper presents state of the art three-dimensional numerical simulations of the Rayleigh-Bénard convection in a supercritical fluid. We consider a fluid slightly above its critical point in a cube-shaped cell heated from below with insulated sidewalls; the thermodynamic equilibrium of the fluid is described by the van der Waals equation of state. The acoustic filtering of the Navier-Stokes equations is revisited to account for the strong stratification of the fluid induced by its high compressibility under the effect of its own weight. The hydrodynamic stability of the fluid is briefly reviewed and we then focus on the convective regime and the transition to turbulence. Direct numerical simulations are carried out using a finite volume method for Rayleigh numbers varying from 106 up to 108. A spatiotemporal description of the flow is presented from the convection onset until the attainment of a statistically steady state of heat transfer. This description concerns mainly the identification of the vortical structures in the flow, the distribution of the Nusselt numbers on the horizontal isothermal walls, the structure of the temperature field and the global thermal balance of the cavity. We focus on the influence of the strong stratification of the fluid on the penetrability of the convective structures in the core of the cavity and on its global thermal balance. Finally, a comparison with the case of a perfect gas, at the same Rayleigh number, is presented.
Gilbert Accary, Patrick Bontoux, Bernard Zappoli. Turbulent Rayleigh-Bénard convection in a near-critical fluid by three-dimensional direct numerical simulation. Journal of Fluid Mechanics, Cambridge University Press (CUP), 2009, 619, pp.127-145. ⟨10.1017/S0022112008004175⟩. ⟨hal-00834173⟩
Richard Pasquetti, Eric Séverac, Eric Serre, Patrick Bontoux, Michael Schaefer. From stratified wake to rotor-stator flows by a SVV-LES method. Theoretical and Computational Fluid Dynamics, Springer Verlag, 2008, 22 (3-4), pp.261-273. ⟨hal-01023280⟩ Plus de détails...
Richard Pasquetti, Eric Séverac, Eric Serre, Patrick Bontoux, Michael Schaefer. From stratified wake to rotor-stator flows by a SVV-LES method. Theoretical and Computational Fluid Dynamics, Springer Verlag, 2008, 22 (3-4), pp.261-273. ⟨hal-01023280⟩
Journal: Theoretical and Computational Fluid Dynamics
R. Pasquetti, Eric Séverac, Eric Serre, Patrick Bontoux, M. Schäfer. From stratified wakes to rotor-stator flows by an SVV-LES method. Theoretical and Computational Fluid Dynamics, Springer Verlag, 2008, 22 (3-4), pp.261-273. ⟨10.1007/s00162-007-0070-1⟩. ⟨hal-00833881⟩ Plus de détails...
We extend a large-eddy simulation (LES) methodology, based on using the spectral vanishing viscosity (SVV) method to stabilize spectral collocation approximations, from the Cartesian to the cylindrical geometry. The capabilities of the SVV-LES approach are illustrated for two very different physical problems: (1) the influence of thermal stratification on the wake of a cylinder, and (2) the instabilities that develop in transitional and fully turbulent rotor-stator flows.
R. Pasquetti, Eric Séverac, Eric Serre, Patrick Bontoux, M. Schäfer. From stratified wakes to rotor-stator flows by an SVV-LES method. Theoretical and Computational Fluid Dynamics, Springer Verlag, 2008, 22 (3-4), pp.261-273. ⟨10.1007/s00162-007-0070-1⟩. ⟨hal-00833881⟩
Journal: Theoretical and Computational Fluid Dynamics
Gilbert Accary, Patrick Bontoux, Bernard Zappoli. Convection in a supercritical fluid: a reduced model for geophysical flows. Physics of Fluids, American Institute of Physics, 2007, 19 (1), pp.014104. ⟨10.1063/1.2432159⟩. ⟨hal-00833845⟩ Plus de détails...
Convection in a fluid, slightly above its gas-liquid critical point, is numerically investigated in two configurations where the strong stratification of the fluid--induced by its high compressibility--controls the development and/or the onset of convection: (i) the evolution of a thermal plume in a stable environment where the penetrative convection is found to be blocked by the fluid stratification, and (ii) the convection onset and outset in a supercritical fluid layer according to the Schwarzschild criterion, which usually occurs in the atmosphere when the local temperature gradient exceeds the adiabatic temperature one. Hence, two situations, commonly encountered in large-scale geophysical flows, are reproduced in a centimetric cell containing a supercritical fluid.
Gilbert Accary, Patrick Bontoux, Bernard Zappoli. Convection in a supercritical fluid: a reduced model for geophysical flows. Physics of Fluids, American Institute of Physics, 2007, 19 (1), pp.014104. ⟨10.1063/1.2432159⟩. ⟨hal-00833845⟩
Eric Serre, Patrick Bontoux. Vortex breakdown in a cylinder with a rotating bottom and a flat stress-free surface. International Journal of Heat and Fluid Flow, Elsevier, 2007, 28 (2), pp.229-248. ⟨10.1016/j.ijheatfluidflow.2006.04.004⟩. ⟨hal-00834166⟩ Plus de détails...
Vortex breakdown and transition to time-dependent regimes are investigated in a cylinder (H/R = 4) with a rotating disk and a free-surface. The aim of this study is to show how, by changing upstream conditions it is possible to alter on the flow, particularly the vortex breakdown process. The understanding of such effects on vortex breakdown is very useful in the development of a control strategy in order to intensify or remove the phenomenon. The flow dynamics are explored through numerical solution of the three-dimensional Navier-Stokes equations based on high-order spectral approximations. The use of a flat, stress-free model for the air/water interface is shown to be entirely satisfactory at least for moderate Reynolds numbers. A particular interest of these results is to show how the bubble related to the vortex breakdown becomes attached to the free-surface and grows in diameter as the Reynolds number is increased, Re ⩾ 2900. Such a phenomenon removes the cylindrical vortex core upstream of the breakdown which is usually included in classical theories based on idealized models of vortex flows. The flow is shown to be unstable to three-dimensional perturbations for sufficiently large rotation rates. The bifurcated state takes the form of a k = 3 rotating wave at Re = 3000. The existence of the free-surface promotes the onset of periodicity, with a critical Reynolds number about 15% lower than in the case with a rigid cover. Moreover, the successive bifurcations occur over a much shorter range of Reynolds numbers and lead rapidly to a multi-frequency regime with more than five different frequencies. In the unsteady regime, the vortex breakdown is characterized by an elongated, asymmetric recirculation zone, attached to the free-surface and precessing around the axis of the container. By increasing the rotation, the circular stagnation line on the free-surface takes a more irregular form and starts to move around the axis of the cylinder in the same sense as the rotating disk. Finally, our results show that the vertical boundary layer controls both the vortex breakdown process and the transition to unsteadiness.
Eric Serre, Patrick Bontoux. Vortex breakdown in a cylinder with a rotating bottom and a flat stress-free surface. International Journal of Heat and Fluid Flow, Elsevier, 2007, 28 (2), pp.229-248. ⟨10.1016/j.ijheatfluidflow.2006.04.004⟩. ⟨hal-00834166⟩
Journal: International Journal of Heat and Fluid Flow
Gilbert Accary, Isabelle Raspo, Patrick Bontoux, Bernard Zappoli. Rayleigh-Bénard and Schwarzschild instability in a supercritical fluid. Advances in Space Research, Elsevier, 2005, 36 (1), pp.11-16. ⟨10.1016/j.asr.2005.02.082⟩. ⟨hal-00836317⟩ Plus de détails...
Due to the density stratification, the convection onset criterion in a supercritical fluid layer heated from below includes a stabilizing effect known as the Schwarzschild criterion, which requires an adaptation of the classical low Mach number approximation. We numerically solve the mathematical model describing the motion of a supercritical fluid in the classical Rayleigh-Bénard configuration and we bring to the fore two main events: (i) the reverse transition of an unstable layer to stability without any external intervention; (ii) the convection onset according to the Schwarzschild criterion. In addition, the 3D extension of the study is briefly described.
Gilbert Accary, Isabelle Raspo, Patrick Bontoux, Bernard Zappoli. Rayleigh-Bénard and Schwarzschild instability in a supercritical fluid. Advances in Space Research, Elsevier, 2005, 36 (1), pp.11-16. ⟨10.1016/j.asr.2005.02.082⟩. ⟨hal-00836317⟩
E. Crespo del Arco, Eric Serre, Patrick Bontoux, Brian Launder. Stability, transition and turbulence in rotating cavities. M. Rahman. Instability of flows, WIT Press, pp.141-195, 2005, Advances in Fluid Mechanics, 1-85312-785-X. ⟨10.2495/1-85312-785-X/05⟩. ⟨hal-00833957⟩ Plus de détails...
This chapter reviews striking features of boundary-layer instabilities induced by different mechanisms and related to transition to turbulence in rotating flows with walls. Besides its fundamental importance as a three-dimensional prototype flow, confined flow between rotating discs has been extensively examined because of its relevance to many industrial applications such as turbomachinery and engineering processes. Many studies using stability analyses and experiments have been devoted to the onset of unstable waves and to the mechanisms associated with them. Here, we focus on how numerical investigations may provide insights and complement experimental data and analytical results by providing the full velocity field in well-controlled flows within idealized configurations. Rotor-stator and rotating cavity with radial throughflow are investigated. At a critical rotation rate, axisymmetric and/or three-dimensional structures appear in the Bödewadt and Ekman layers. All features of the transitions in these rotating cavities are documented. A comparison of the wave numbers, frequencies, and phase velocities of the instabilities with available theoretical and experimental results shows that both Type II (or A) and Type I (or B) instabilities appear, depending on flow and geometric control parameters. Interesting patterns exhibiting the coexistence of circular and spiral waves are found under certain conditions.
E. Crespo del Arco, Eric Serre, Patrick Bontoux, Brian Launder. Stability, transition and turbulence in rotating cavities. M. Rahman. Instability of flows, WIT Press, pp.141-195, 2005, Advances in Fluid Mechanics, 1-85312-785-X. ⟨10.2495/1-85312-785-X/05⟩. ⟨hal-00833957⟩
Gilbert Accary, Isabelle Raspo, Patrick Bontoux, Bernard Zappoli. An adaptation of the low Mach number approximation for supercritical fluid buoyant flows. Comptes Rendus Mécanique, Elsevier Masson, 2005, 333 (5), pp.397-404. ⟨10.1016/j.crme.2005.03.004⟩. ⟨hal-00836294⟩ Plus de détails...
This Note describes an acoustic filtering of the equations governing the supercritical fluid buoyant flow driven by a weak heating. The resulting low Mach number approximation takes into account the compressibility of the fluid with respect to the hydrostatic pressure. Using the direct numerical simulation of a supercritical fluid flow in the Rayleigh-Bénard configuration, we show that the density stratification may be taken into account without further numerical effort and is fundamental for the prediction of the convective instability threshold induced by a weak heating.
Gilbert Accary, Isabelle Raspo, Patrick Bontoux, Bernard Zappoli. An adaptation of the low Mach number approximation for supercritical fluid buoyant flows. Comptes Rendus Mécanique, Elsevier Masson, 2005, 333 (5), pp.397-404. ⟨10.1016/j.crme.2005.03.004⟩. ⟨hal-00836294⟩
Gilbert Accary, Isabelle Raspo, Patrick Bontoux, Bernard Zappoli. Stability of a supercritical fluid diffusing layer with mixed boundary conditions. Physics of Fluids, American Institute of Physics, 2005, 17 (10), pp.104105. ⟨10.1063/1.2011469⟩. ⟨hal-00833819⟩ Plus de détails...
We consider a fluid close to its gas-liquid critical point in the Rayleigh-Bénard configuration. Owing to thermoacoustic effects, the bottom heating induces thermal boundary layers along both the lower and the upper horizontal plates. The hydrodynamic stability of these diffusing layers, whose bounding conditions are interchanged, is studied numerically in a two-dimensional (2D) approximation. As far as the convection onset criterion and the critical wave number are concerned, some discrepancies are found between the simulations and the predictions obtained by means of linear analysis. The extension of the study to three-dimensional configurations confirms the validity of the 2D approximation for the analysis of the hydrodynamic stability and shows its inadequacy when the layers become convection dominated.
Gilbert Accary, Isabelle Raspo, Patrick Bontoux, Bernard Zappoli. Stability of a supercritical fluid diffusing layer with mixed boundary conditions. Physics of Fluids, American Institute of Physics, 2005, 17 (10), pp.104105. ⟨10.1063/1.2011469⟩. ⟨hal-00833819⟩
Patrick Bontoux, Michael Schäfer, Eric Serre. High-order methods for the numerical simulation of vortical and turbulent flows: Foreword. Comptes Rendus Mécanique, Elsevier Masson, 2005, 333 (1), pp.1-2. ⟨10.1016/j.crme.2004.11.007⟩. ⟨hal-00836620⟩ Plus de détails...
Patrick Bontoux, Michael Schäfer, Eric Serre. High-order methods for the numerical simulation of vortical and turbulent flows: Foreword. Comptes Rendus Mécanique, Elsevier Masson, 2005, 333 (1), pp.1-2. ⟨10.1016/j.crme.2004.11.007⟩. ⟨hal-00836620⟩
Gilbert Accary, Isabelle Raspo, Patrick Bontoux, Bernard Zappoli. Reverse transition to hydrodynamic stability through the Schwarzschild line in a supercritical fluid layer. Physical Review E : Statistical, Nonlinear, and Soft Matter Physics, American Physical Society, 2005, 72 (3), pp.035301. ⟨10.1103/PhysRevE.72.035301⟩. ⟨hal-00833850⟩ Plus de détails...
We consider a fluid close to its gas-liquid critical point in a bottom-heated cavity. Due to strong density stratification, both the Schwarzschild and the Rayleigh stability criteria are relevant at the same space scale. Taking advantage of the competition between these two limits of the convection-onset criterion, we numerically exhibit striking non-Boussinesq effects: the reverse transition to stability through the Schwarzschild line of a heat diffusing layer subjected to convection, and the convection onset inside a few-millimeters-thick layer according to the Schwarzschild criterion.
Gilbert Accary, Isabelle Raspo, Patrick Bontoux, Bernard Zappoli. Reverse transition to hydrodynamic stability through the Schwarzschild line in a supercritical fluid layer. Physical Review E : Statistical, Nonlinear, and Soft Matter Physics, American Physical Society, 2005, 72 (3), pp.035301. ⟨10.1103/PhysRevE.72.035301⟩. ⟨hal-00833850⟩
Journal: Physical Review E : Statistical, Nonlinear, and Soft Matter Physics
Eric Serre, Patrick Bontoux, Brian Launder. Transitional-turbulent flow with heat transfer in a closed rotor-stator cavity. Journal of Turbulence, Taylor & Francis, 2004, 5, pp.008. ⟨10.1088/1468-5248/5/1/008⟩. ⟨hal-00838385⟩ Plus de détails...
In this paper, a non-isothermal flow confined between a rotating and a stationary disc is investigated using direct numerical simulation. Besides its fundamental importance as a three-dimensional prototype flow, such flows arise in many industrial devices, especially in turbomachinery applications. Our aim is to include the effects of density variation as this introduces a quasi-buoyant effect on the near-wall layers due to the radial acceleration, Ω2 r. None of the detailed experimental studies of disc-cavity flows has examined this effect due to the extreme flow conditions arising in an actual gas turbine. As a preliminary exploration we show here the effects on the mean flow of Rayleigh numbers up to 2 × 106. The direct numerical simulation is performed by integrating the time-dependent Navier-Stokes equations with a three-dimensional spectral method. The Boussinesq approximation is used to take into account the centrifugal-buoyancy effects. The effects of thermal convection have been examined for a transitional-turbulent flow at Re (=ΩR 1 2/ν) = 110 000 in an annular cavity of aspect ratio L (=ΔR/H) = 2.35. These DNS results provide accurate, instantaneous quantities which are of interest in understanding the physics of turbulent flow and heat transfer in a rotating disc cavity. Moreover, the averaged results show small effects of density variation and provide target data for researchers employing RANS schemes.
Eric Serre, Patrick Bontoux, Brian Launder. Transitional-turbulent flow with heat transfer in a closed rotor-stator cavity. Journal of Turbulence, Taylor & Francis, 2004, 5, pp.008. ⟨10.1088/1468-5248/5/1/008⟩. ⟨hal-00838385⟩
Eric Serre, Ewa Tuliszka-Sznitko, Patrick Bontoux. Coupled numerical and theoretical study of the flow transition between a rotating and stationary disk. Physics of Fluids, American Institute of Physics, 2004, 16 (3), pp.688-706. ⟨10.1063/1.1644144⟩. ⟨hal-00838390⟩ Plus de détails...
Both direct numerical simulation and theoretical stability analysis are performed together in order to study the transition process to turbulence in a flow between a rotating and a stationary disk. This linear stability analysis considers the complete rotor-stator flow and then extends the results of Lingwood [J. Fluid Mech. 299, 17 (1995); 314, 373 (1996)] obtained in a single disk case. The present linear analysis also extends the former two-disk computations of Itoh [ASME FED 114, 83 (1991)], only limited to a hydrodynamic spatial instability analysis. Moreover, in the present work, this approach is completed by discussing the effects of buoyancy-driven convection on the flow stability and by absolute/convective analysis of the flow. Coupled with accurate numerical computations based on an efficient pseudo-spectral Chebyshev-Fourier method, this study brings new insight on the spatio-temporal characteristics of this flow during the first stages of transition. For instance, an exchange of stability from a steady to a periodic flow with spiral structures is observed for the first time numerically in such cavity of large aspect ratio. The nature of the first bifurcation is discussed as well as the influence on it of disturbances coming from the end-wall boundary layer. Annular and spiral patterns are observed in the unstable stationary disk layer with characteristic parameters agreeing very well with the present theoretical results. Then, these structures are interpreted in terms of type I and type II generic instabilities. Moreover, the absolute instability regions which are supposed to be strongly connected with the turbulent breakdown process are also identified and the critical Reynolds numbers of the convective/absolute transition in both Ekman and Bödewadt layers are given.
Eric Serre, Ewa Tuliszka-Sznitko, Patrick Bontoux. Coupled numerical and theoretical study of the flow transition between a rotating and stationary disk. Physics of Fluids, American Institute of Physics, 2004, 16 (3), pp.688-706. ⟨10.1063/1.1644144⟩. ⟨hal-00838390⟩
Olivier Czarny, Eric Serre, Patrick Bontoux, Richard M. Lueptow. Interaction of wavy cylindrical couette flow with endwalls. Physics of Fluids, American Institute of Physics, 2004, 16 (4), pp.1140-1148. ⟨10.1063/1.1652671⟩. ⟨hal-00836628⟩ Plus de détails...
The finite length of a Taylor-Couette cell introduces endwall effects that interact with the centrifugal instability and the subsequent wavy vortex flow. We investigate the interaction between the endwall Ekman boundary layers and the wavy vortices in a finite-length cavity via direct numerical simulation using a three-dimensional spectral method. To analyze the nature of the interaction between the vortices and the endwall layers, we consider three endwall boundary conditions: fixed endwalls, endwalls rotating with the inner cylinder, and stress-free endwalls. Near the endwalls, the waviness is diminished, primarily due to the effect of the flatness of the endwall rather than as a result of the no-slip boundary condition at the endwall. However, the waviness is present just one or two vortices away from the endwalls, indicating that the effect of the endwall on waviness does not penetrate far from the endwall. The interaction of the waviness with the endwall Ekman layer does not appear to result in disorder in the flow, either in the endwall vortex or farther from the endwall. Likewise, the waviness does not significantly alter Ekman layer thickness from that predicted based on theory
Olivier Czarny, Eric Serre, Patrick Bontoux, Richard M. Lueptow. Interaction of wavy cylindrical couette flow with endwalls. Physics of Fluids, American Institute of Physics, 2004, 16 (4), pp.1140-1148. ⟨10.1063/1.1652671⟩. ⟨hal-00836628⟩
Gilbert Accary, Isabelle Raspo, Patrick Bontoux, Bernard Zappoli. Three-dimensional Rayleigh-Bénard instability in a supercritical fluid. Comptes Rendus Mécanique, Elsevier Masson, 2004, 332 (3), pp.209-216. ⟨10.1016/j.crme.2004.01.009⟩. ⟨hal-00833947⟩ Plus de détails...
This paper describes the unsteady convective flow of a supercritical fluid in the Rayleigh-Bénard configuration. Two-dimensional earlier studies reported fast temperature equilibrium due to the piston effect and the development of a convective instability when the local Rayleigh number exceeds a critical value. In the present work, a high order 3D finite volume method has been developed and optimized, and to our knowledge, we show for the first time a three-dimensional convective instability in a supercritical fluid. Inspecting the time-evolution of temperature field patterns, we exhibit corner effects and a three-dimensional behavior of the flow.
Gilbert Accary, Isabelle Raspo, Patrick Bontoux, Bernard Zappoli. Three-dimensional Rayleigh-Bénard instability in a supercritical fluid. Comptes Rendus Mécanique, Elsevier Masson, 2004, 332 (3), pp.209-216. ⟨10.1016/j.crme.2004.01.009⟩. ⟨hal-00833947⟩
Olivier Czarny, Eric Serre, Patrick Bontoux, Richard M. Lueptow. Ekman vorticities and the centrifugal instability in counter-rotating cylindrical Couette flow. Theoretical and Computational Fluid Dynamics, Springer Verlag, 2004, 18 (2-4), pp.151-168. ⟨10.1007/s00162-004-0140-6⟩. ⟨hal-00838377⟩ Plus de détails...
The finite length of a Taylor-Couette cell introduces endwall effects that interact with the centrifugal instability. We investigate the interaction between the endwall Ekman boundary layers and the vortical structures in a finite-length cavity with counter-rotating cylinders via direct numerical simulation using a three-dimensional spectral method. To analyze the nature of the interaction between the vortices and the endwall layers we consider four endwall boundary conditions: fixed endwalls, endwalls rotating with the outer cylinder, endwalls rotating with the inner cylinder, and stress-free endwalls. The vortical structure of the flow depends on the endwall conditions. The waviness of the vortices is suppressed only very near the endwall, primarily due to zero axial velocity at the endwall rather than viscous effects. In spite of their waviness and random behavior, the vortices generally stay inside of the vθ=0 isosurface by adjusting quickly to the radial transport of azimuthal momentum. The thickness and strength of the Ekman layer at the endwall match with that predicted from a simple theoretical approach.
Olivier Czarny, Eric Serre, Patrick Bontoux, Richard M. Lueptow. Ekman vorticities and the centrifugal instability in counter-rotating cylindrical Couette flow. Theoretical and Computational Fluid Dynamics, Springer Verlag, 2004, 18 (2-4), pp.151-168. ⟨10.1007/s00162-004-0140-6⟩. ⟨hal-00838377⟩
Journal: Theoretical and Computational Fluid Dynamics
Olivier Czarny, Eric Serre, Patrick Bontoux, Richard M. Lueptow. Ekman vortices and the centrifugal instability in the counter-rotating cylindrical Couette flow. Theoretical and Computational Fluid Dynamics, Springer Verlag, 2004, 18 (2-4), pp.151-168. ⟨hal-01023276⟩ Plus de détails...
Olivier Czarny, Eric Serre, Patrick Bontoux, Richard M. Lueptow. Ekman vortices and the centrifugal instability in the counter-rotating cylindrical Couette flow. Theoretical and Computational Fluid Dynamics, Springer Verlag, 2004, 18 (2-4), pp.151-168. ⟨hal-01023276⟩
Journal: Theoretical and Computational Fluid Dynamics
Eric Serre, Ewa Tuliszka-Sznitko, Patrick Bontoux. Coupled theoretical and numerical study of the flow transition between a rotating and a stationary disk. Physics of Fluids, American Institute of Physics, 2004, 16 (3), pp.688-706. ⟨hal-01023275⟩ Plus de détails...
Eric Serre, Ewa Tuliszka-Sznitko, Patrick Bontoux. Coupled theoretical and numerical study of the flow transition between a rotating and a stationary disk. Physics of Fluids, American Institute of Physics, 2004, 16 (3), pp.688-706. ⟨hal-01023275⟩
Isabelle Raspo, Bernard Zappoli, Patrick Bontoux. Unsteady two-dimensional convection in a bottom heated supercritical fluid. Comptes Rendus Mécanique, Elsevier Masson, 2004, 332 (5-6), pp.353-360. ⟨10.1016/j.crme.2004.02.003⟩. ⟨hal-00838378⟩ Plus de détails...
We consider a closed Rayleigh-Bénard cell containing a fluid near its gas-liquid critical point (CP). Due to the divergence of several physical properties near the CP, large Rayleigh numbers can be obtained even for small temperature differences. In the convective regime, the heat flow which is obtained on long time scales exhibits some characteristics of that observed in turbulent convection in normally compressible fluids: it is composed of plumes in thermal boundary layers, jets on lateral walls and a large-scale flow. Our results show that, as it is the case in turbulent convection, this large-scale flow can suddenly change its orientation.
Isabelle Raspo, Bernard Zappoli, Patrick Bontoux. Unsteady two-dimensional convection in a bottom heated supercritical fluid. Comptes Rendus Mécanique, Elsevier Masson, 2004, 332 (5-6), pp.353-360. ⟨10.1016/j.crme.2004.02.003⟩. ⟨hal-00838378⟩
Elalami Semma, Mohammed El Ganaoui, Abdelkhalek Cheddadi, Patrick Bontoux. Instability of melt flow and solidification front during horizontal growth. Comptes Rendus Mécanique, Elsevier Masson, 2003, 331 (9), pp.631-639. ⟨10.1016/S1631-0721(03)00150-5⟩. ⟨hal-00838417⟩ Plus de détails...
Convective instabilities of low Prandtl number fluids are subject to various studies. The purpose here is an extension to hydrodynamic transitions in the fluid phase with a free or rigid surface under phase change and to construct the corresponding bifurcation diagram. Investigations interesting the process control by using the latent heat and the solid/liquid thermal conductivity difference are considered. The solution methodology is based on a front localisation approach showing a very good ability to describe convection regimes coupled to the phase change transition in the case of vertical solidification with confinement.
Elalami Semma, Mohammed El Ganaoui, Abdelkhalek Cheddadi, Patrick Bontoux. Instability of melt flow and solidification front during horizontal growth. Comptes Rendus Mécanique, Elsevier Masson, 2003, 331 (9), pp.631-639. ⟨10.1016/S1631-0721(03)00150-5⟩. ⟨hal-00838417⟩
Olivier Czarny, Eric Serre, Patrick Bontoux, Richard M. Lueptow. Interaction between the Ekman pumping and the centrifugal instability in Taylor-Couette flow. Physics of Fluids, American Institute of Physics, 2003, 15 (2), pp.467-477. ⟨10.1063/1.1534108⟩. ⟨hal-00838408⟩ Plus de détails...
The endwalls in a Taylor-Couette cell introduce adjacent boundary layers that interact with the centrifugal instability. We investigate the interaction between the endwall Ekman layers and the Taylor vortices near transition from nonvortical to vortical flow via direct numerical simulation using a spectral method. We consider a radius ratio of η = 0.75 in a short annulus having a length-to-gap ratio of Γ = 6. To analyze the nature of the interaction between the vortices and the endwall layers, three endwall boundary conditions were considered: fixed endwalls, endwalls rotating with the inner cylinder, and stress-free endwalls. Below the critical Taylor number, endwall vortices for rotating endwalls are more than twice the strength of the vortices for fixed endwalls. This trend continues well above the transition to vortical flow, consistent with a simple force balance analysis near the endwalls. Stress-free endwalls result in endwall vortices that are similar in strength to those for rotating endwalls above the critical Taylor number. The endwall conditions significantly change the bifurcation diagram based on the radial velocity near the center of the annulus. For stress-free endwall conditions, the bifurcation is quite sharp, although only one fork of the bifurcation results unless the initial conditions are specifically set to favor the other fork. For rotating and fixed endwalls, there is a continuous transition from a featureless flow to a vortical flow due to the endwall vortices.
Olivier Czarny, Eric Serre, Patrick Bontoux, Richard M. Lueptow. Interaction between the Ekman pumping and the centrifugal instability in Taylor-Couette flow. Physics of Fluids, American Institute of Physics, 2003, 15 (2), pp.467-477. ⟨10.1063/1.1534108⟩. ⟨hal-00838408⟩
P. Droll, M. Schafer, Eric Serre, Patrick Bontoux. An implicit pseudospectral multi-domain method for the simulation of incompressible flows. International Journal for Numerical Methods in Fluids, Wiley, 2003, 41 (5), pp.447-470. ⟨10.1002/fld.441⟩. ⟨hal-00838397⟩ Plus de détails...
A pseudo-spectral method for the solution of incompressible flow problems based on an iterative solver involving an implicit treatment of linearized convective terms is presented. The method allows the treatment of moderately complex geometries by means of a multi-domain approach and it is able to cope with non-constant fluid properties and non-orthogonal problem domains. In addition, the fully implicit scheme yields improved stability properties as opposed to semi-implicit schemes commonly employed. Key components of the method are a Chebyshev collocation discretization, a special pressure-correction scheme, and a restarted GMRES method with a preconditioner derived from a fast direct solver. The performance of the proposed method is investigated by considering several numerical examples of different complexity, and also includes comparisons to alternative solution approaches based on finite-volume discretizations.
P. Droll, M. Schafer, Eric Serre, Patrick Bontoux. An implicit pseudospectral multi-domain method for the simulation of incompressible flows. International Journal for Numerical Methods in Fluids, Wiley, 2003, 41 (5), pp.447-470. ⟨10.1002/fld.441⟩. ⟨hal-00838397⟩
Journal: International Journal for Numerical Methods in Fluids
Eric Serre, Patrick Bontoux. Vortex breakdown in a three-dimensional swirling flow. Journal of Fluid Mechanics, Cambridge University Press (CUP), 2002, 459, pp.347-370. ⟨10.1017/S0022112002007875⟩. ⟨hal-00838446⟩ Plus de détails...
Time-dependent swirling flows inside an enclosed cylindrical rotor-stator cavity with aspect ratio H/R = 4, larger than the ones usually considered in the literature, are studied. Within a certain range of governing parameters, vortex breakdown phenomena can arise along the axis. Very recent papers exhibiting some particular three-dimensional effects have stimulated new interest in this topic. The study is carried out by a numerical resolution of the three-dimensional Navier-Stokes equations, based on high-order spectral approximations in order to ensure very high accuracy of the solutions. The first transition to an oscillatory regime occurs through an axisymmetric bifurcation (a supercritical Hopf bifurcation) at Re = 3500. The oscillatory regime is caused by an axisymmetric mode of centrifugal instability of the vertical boundary layer and the vortex breakdown is axisymmetric, being composed of two stationary bubbles. For Reynolds numbers up to Re = 3500, different three-dimensional solutions are identified. At Re = 4000, the flow supports the k = 5 mode of centrifugal instability. By increasing the rotation speed to Re = 4500, the vortex breakdown evolves to an S-shaped type after a long computational time. The structure is asymmetric and gyrates around the axis inducing a new time-dependent regime. At Re = 5500, the structure of the vortex breakdown is more complex: the upper part of the structure takes a spiral form. The maximum rotation speed is reached at Re = 10000 and the flow behaviour is now chaotic. The upper structure of the breakdown can be related to the spiral-type. Asymmetric flow separation on the container wall in the form of spiral arms of different angles is also prominent.
Eric Serre, Patrick Bontoux. Vortex breakdown in a three-dimensional swirling flow. Journal of Fluid Mechanics, Cambridge University Press (CUP), 2002, 459, pp.347-370. ⟨10.1017/S0022112002007875⟩. ⟨hal-00838446⟩
Isabelle Raspo, Sandrine Hugues, Eric Serre, Anthony Randriamampianina, Patrick Bontoux. Spectral projection methods for the simulation of complex three-dimensional rotating flows. Computers and Fluids, Elsevier, 2002, 31 (4-7), pp.745-767. ⟨hal-01023173⟩ Plus de détails...
Isabelle Raspo, Sandrine Hugues, Eric Serre, Anthony Randriamampianina, Patrick Bontoux. Spectral projection methods for the simulation of complex three-dimensional rotating flows. Computers and Fluids, Elsevier, 2002, 31 (4-7), pp.745-767. ⟨hal-01023173⟩
Mohammed El Ganaoui, Patrick Bontoux, A. Lamazouade, Emilio Leonardi, G. de Vahl Davis. Computational model for solutal convection during directional solidification. Numerical Heat Transfer, Part B Fundamentals, Taylor & Francis, 2002, 41 (3-4), pp.325-338. ⟨10.1080/104077902753541041⟩. ⟨hal-00838441⟩ Plus de détails...
Computational investigation is conducted during time-dependent behaviors induced by solutal convection in the melt for directional solidification of a binary alloy. Effects of solutal Rayleigh number on flow, heat, and mass transfer are studied for upward Bridgman configuration restricted to fluid phase. The results compare well with spectral ones exhibiting various hydrodynamic solutal transitions (symmetric, asymmetric, time-dependent). The finite-volumes method is tested for various uniform and refined meshes near the walls to obtain spectral accuracy. Calculations are extended to configurations including melt/solid interactions by the use of a homogeneous formulation and a linearized equilibrium phase diagram.
Mohammed El Ganaoui, Patrick Bontoux, A. Lamazouade, Emilio Leonardi, G. de Vahl Davis. Computational model for solutal convection during directional solidification. Numerical Heat Transfer, Part B Fundamentals, Taylor & Francis, 2002, 41 (3-4), pp.325-338. ⟨10.1080/104077902753541041⟩. ⟨hal-00838441⟩
Journal: Numerical Heat Transfer, Part B Fundamentals
Olivier Czarny, Eric Serre, Patrick Bontoux, Richard M. Lueptow. Spiral and wavy vortex flows in short counter-rotating Taylor-Couette cells. International Journal of Theoretical and Computational Fluid dynamics, 2002, 16, pp.5-15. ⟨hal-01023184⟩ Plus de détails...
Olivier Czarny, Eric Serre, Patrick Bontoux, Richard M. Lueptow. Spiral and wavy vortex flows in short counter-rotating Taylor-Couette cells. International Journal of Theoretical and Computational Fluid dynamics, 2002, 16, pp.5-15. ⟨hal-01023184⟩
Journal: International Journal of Theoretical and Computational Fluid dynamics
Ewa Tuliszka-Sznitko, Eric Serre, Patrick Bontoux. On the nature of the boundary layer instability in a closed rotor-stator cavity. Comptes rendus de l’Académie des sciences. Série IIb, Mécanique, Elsevier, 2002, 329, pp.91-99. ⟨hal-01023180⟩ Plus de détails...
Ewa Tuliszka-Sznitko, Eric Serre, Patrick Bontoux. On the nature of the boundary layer instability in a closed rotor-stator cavity. Comptes rendus de l’Académie des sciences. Série IIb, Mécanique, Elsevier, 2002, 329, pp.91-99. ⟨hal-01023180⟩
Journal: Comptes rendus de l’Académie des sciences. Série IIb, Mécanique
Isabelle Raspo, Sandrine Hugues, Eric Serre, Anthony Randriamampianina, Patrick Bontoux. A spectral projection method for the simulation of complex three-dimensional rotating flows. Computers and Fluids, Elsevier, 2002, 31 (4-7), pp.745-767. ⟨10.1016/S0045-7930(01)00070-6⟩. ⟨hal-00833836⟩ Plus de détails...
In this paper, we present an efficient projection method to solve the three-dimensional time-dependent incompressible Navier-Stokes equations in primitive variables formulation using spectral approximations. This method is based on a modification of the algorithm proposed by Goda [J. Comp. Phys. 30 (1979) 76]. It brings an improvement by introducing a preliminary step for the pressure in order to allow a temporal evolution of the normal pressure gradient at the boundaries. Its efficiency is brought to the fore by comparison with the Goda's algorithm. The modified projection method is then applied to the simulation of complex three-dimensional flows in rotating cavities, involving either a throughflow or a differential rotation.
Isabelle Raspo, Sandrine Hugues, Eric Serre, Anthony Randriamampianina, Patrick Bontoux. A spectral projection method for the simulation of complex three-dimensional rotating flows. Computers and Fluids, Elsevier, 2002, 31 (4-7), pp.745-767. ⟨10.1016/S0045-7930(01)00070-6⟩. ⟨hal-00833836⟩
Mohammed El Ganaoui, A. Lamazouade, Patrick Bontoux, Dominique Morvan. Computational solution for fluid flow under solid/liquid phase change conditions. Computers and Fluids, Elsevier, 2002, 31 (4-7), pp.539-556. ⟨10.1016/S0045-7930(01)00067-6⟩. ⟨hal-00838453⟩ Plus de détails...
A fixed grid method based on an enthalpy-porosity formulation for liquid/solid phase transition is extended to compute the time-dependent solutal convection in the melt during directional solidification of alloys. A finite volumes approximation is used for uniform and refined grids with a second order Euler scheme. The ability of the method to describe accurately the flow transitions and regimes is considered with respect to the results of the linear theory of stability and of available spectral accurate calculations.
Mohammed El Ganaoui, A. Lamazouade, Patrick Bontoux, Dominique Morvan. Computational solution for fluid flow under solid/liquid phase change conditions. Computers and Fluids, Elsevier, 2002, 31 (4-7), pp.539-556. ⟨10.1016/S0045-7930(01)00067-6⟩. ⟨hal-00838453⟩
Eric Serre, Patrick Bontoux. Vortex breakdown in a three-dimensional swirling flow. Journal of Fluid Mechanics, Cambridge University Press (CUP), 2002, 459, pp.347-370. ⟨hal-01023166⟩ Plus de détails...
Eric Serre, Patrick Bontoux. Vortex breakdown in a three-dimensional swirling flow. Journal of Fluid Mechanics, Cambridge University Press (CUP), 2002, 459, pp.347-370. ⟨hal-01023166⟩
Eric Serre, Patrick Bontoux, Brian Launder. Direct numerical simulation of transitional turbulent flow in an enclosed rotor-stator cavity. Flow, Turbulence and Combustion, Springer Verlag (Germany), 2002, 69 (1), pp.35-50. ⟨10.1023/A:1022467232348⟩. ⟨hal-00838458⟩ Plus de détails...
The transitional turbulent regime in confined flow between a rotating and a stationary disc is studied using direct numerical simulation. Besides its fundamental importance as a three-dimensional prototype flow, such flows frequently arise in many industrial devices, especially in turbomachinary applications. The present contribution extends the DNS simulation into the turbulent flow regime, to a rotational Reynolds number Re =3 × 105. An annular rotor-stator cavity of radial extension ΔR and height H, is considered with L = 4.72(L = ΔR/H) and Rm = 2.33 (Rm = (R 1+ R 0)/ΔR). The direct numerical simulation is performed by integrating the time-dependent Navier-Stokes equations until a statistically steady state is reached. A three-dimensional spectral method is used with the aim of providing both very accurate instantaneous fields and reliable statistical data. The instantaneous quantities are analysed in order to enhance our knowledge of the physics of turbulent rotating flows. Also, the results have been averaged so as to provide target turbulence data for any subsequent modelling attempts at reproducing the flow.
Eric Serre, Patrick Bontoux, Brian Launder. Direct numerical simulation of transitional turbulent flow in an enclosed rotor-stator cavity. Flow, Turbulence and Combustion, Springer Verlag (Germany), 2002, 69 (1), pp.35-50. ⟨10.1023/A:1022467232348⟩. ⟨hal-00838458⟩
Olivier Czarny, Eric Serre, Patrick Bontoux, Richard M. Lueptow. Spiral and wavy vortex flows in short counter-rotating Taylor-Couette cells. Theoretical and Computational Fluid Dynamics, Springer Verlag, 2002, 16 (1), pp.5-15. ⟨10.1007/s00162-002-0070-0⟩. ⟨hal-00833861⟩ Plus de détails...
Differentially rotating cylinders result in a rich variety of vortical flows for cylindrical Couette flow. In this study we investigate the case of a short, finite-length cavity with counter-rotating cylinders via direct numerical simulation using a three-dimensional spectral method. We consider aspect ratios ranging from 5 to 6. Two complex flow regimes, wavy vortices and interpenetrating spirals, occur with similar appearance to those found experimentally for much larger aspect ratios. For wavy vortices the wave speed is similar to that found for counter-rotating systems and systems in which the outer cylinder is stationary. For the interpenetrating spiral structure, the vortices are largely confined to the unstable region near the inner cylinder. The endwalls appear to damp and stabilize the flow as the aspect ratio is reduced to the point that in some cases the vortical flow is suppressed. At higher inner cylinder speeds, the interpenetrating spirals acquire a waviness and the vortices, while generally near the inner cylinder, can extend all of the way to the outer cylinder.
Olivier Czarny, Eric Serre, Patrick Bontoux, Richard M. Lueptow. Spiral and wavy vortex flows in short counter-rotating Taylor-Couette cells. Theoretical and Computational Fluid Dynamics, Springer Verlag, 2002, 16 (1), pp.5-15. ⟨10.1007/s00162-002-0070-0⟩. ⟨hal-00833861⟩
Journal: Theoretical and Computational Fluid Dynamics
Eric Serre, E. Crespo del Arco, Patrick Bontoux. Annular and spiral patterns in flows between rotating and stationary discs. Journal of Fluid Mechanics, Cambridge University Press (CUP), 2001, 434, pp.65-100. ⟨10.1017/S0022112001003494⟩. ⟨hal-00834951⟩ Plus de détails...
Different instabilities of the boundary layer flows that appear in the cavity between stationary and rotating discs are investigated using three-dimensional direct numerical simulations. The influence of curvature and confinement is studied using two geometrical configurations: (i) a cylindrical cavity including the rotation axis and (ii) an annular cavity radially confined by a shaft and a shroud. The numerical computations are based on a pseudo-spectral Chebyshev-Fourier method for solving the incompressible Navier-Stokes equations written in primitive variables. The high level accuracy of the spectral methods is imperative for the investigation of such instability structures. The basic flow is steady and of the Batchelor type. At a critical rotation rate, stationary axisymmetric and/or three-dimensional structures appear in the Bödewadt and Ekman layers while at higher rotation rates a second transition to unsteady flow is observed. All features of the transitions are documented. A comparison of the wavenumbers, frequencies, and phase velocities of the instabilities with available theoretical and experimental results shows that both type II (or A) and type I (or B) instabilities appear, depending on flow and geometric control parameters. Interesting patterns exhibiting the coexistence of circular and spiral waves are found under certain conditions.
Eric Serre, E. Crespo del Arco, Patrick Bontoux. Annular and spiral patterns in flows between rotating and stationary discs. Journal of Fluid Mechanics, Cambridge University Press (CUP), 2001, 434, pp.65-100. ⟨10.1017/S0022112001003494⟩. ⟨hal-00834951⟩
Eric Serre, Patrick Bontoux. Three-dimensional swirling flow with a precessing vortex breakdown in a rotor-stator cylinder. Physics of Fluids, American Institute of Physics, 2001, 13 (11), pp.3500-3503. ⟨hal-01023121⟩ Plus de détails...
Eric Serre, Patrick Bontoux. Three-dimensional swirling flow with a precessing vortex breakdown in a rotor-stator cylinder. Physics of Fluids, American Institute of Physics, 2001, 13 (11), pp.3500-3503. ⟨hal-01023121⟩
Eric Serre, Isabelle Raspo, Patrick Bontoux, Roger Peyret. Spectral solutions of the Navier-Stokes equations for rotating flow,. Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik, Wiley-VCH Verlag, 2001, 81 (1), pp.533-536. ⟨hal-01023113⟩ Plus de détails...
Eric Serre, Isabelle Raspo, Patrick Bontoux, Roger Peyret. Spectral solutions of the Navier-Stokes equations for rotating flow,. Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik, Wiley-VCH Verlag, 2001, 81 (1), pp.533-536. ⟨hal-01023113⟩
Journal: Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik
Rafael Delgado-Buscalioni, E. Crespo del Arco, Patrick Bontoux. Flow transition of a low Prandtl number fluid in an inclined three-dimensional cavity. European Journal of Mechanics - B/Fluids, Elsevier, 2001, 20 (5), pp.657-672. ⟨hal-00835759⟩ Plus de détails...
We present a numerical and theoretical investigation on the natural convection of a low Prandtl number fluid (Pr = 0.025) in 2D and 3D side-heated enclosures tilted a = 80° with respect to the vertical position. The choice of this inclination angle comes from a previous linear stability analysis of the basic (plane-parallel) flow that predicts the same critical Ra for longitudinal oscillatory and stationary transversal modes. In both the 2D and 3D enclosures the first transition gradually leads to a transversal stationary centered shear roll. In the 2D geometry the flow becomes time-dependent and multicellular (3 rolls) at the onset of a Hopf bifurcation, followed by subsequent period-doubling. On the other hand, in the 3D enclosure, the onset of oscillations is due to a fully three-dimensional standing wave composed of three counter-rotating longitudinal rolls
Rafael Delgado-Buscalioni, E. Crespo del Arco, Patrick Bontoux. Flow transition of a low Prandtl number fluid in an inclined three-dimensional cavity. European Journal of Mechanics - B/Fluids, Elsevier, 2001, 20 (5), pp.657-672. ⟨hal-00835759⟩
Eric Serre, Emilia Crespo del Arco, Patrick Bontoux. Annular and spiral patterns in flows between rotating and stationary discs. Journal of Fluid Mechanics, Cambridge University Press (CUP), 2001, 434, pp.65-100. ⟨hal-01023110⟩ Plus de détails...
Different instabilities of the boundary layer flows that appear in the cavity between stationary and rotating discs are investigated using three-dimensional direct numerical simulations. The influence of curvature and confinement is studied using two geometrical configurations: (i) a cylindrical cavity including the rotation axis and (ii) an annular cavity radially confined by a shaft and a shroud. The numerical computations are based on a pseudo-spectral Chebyshev{Fourier method for solving the incompressible Navier{Stokes equations written in primitive variables. The high level accuracy of the spectral methods is imperative for the investigation of such instability structures. The basic flow is steady and of the Batchelor type. At a critical rotation rate, stationary axisymmetric and/or three-dimensional structures appear in the B¨odewadt and Ekman layers while at higher rotation rates a second transition to unsteady flow is observed. All features of the transitions are documented. A comparison of the wavenumbers, frequencies, and phase velocities of the instabilities with available theoretical and experimental results shows that both type II (or A) and type I (or B) instabilities appear, depending on flow and geometric control parameters. Interesting patterns exhibiting the coexistence of circular and spiral waves are found under certain conditions.
Eric Serre, Emilia Crespo del Arco, Patrick Bontoux. Annular and spiral patterns in flows between rotating and stationary discs. Journal of Fluid Mechanics, Cambridge University Press (CUP), 2001, 434, pp.65-100. ⟨hal-01023110⟩
Eric Serre, Patrick Bontoux. Eclatement tourbillonnaire dans une cavité rotor-stator cylindrique. Comptes rendus de l’Académie des sciences. Série IIb, Mécanique, Elsevier, 2001, 329, pp.727-733. ⟨hal-01023151⟩ Plus de détails...
Eric Serre, Patrick Bontoux. Eclatement tourbillonnaire dans une cavité rotor-stator cylindrique. Comptes rendus de l’Académie des sciences. Série IIb, Mécanique, Elsevier, 2001, 329, pp.727-733. ⟨hal-01023151⟩
Journal: Comptes rendus de l’Académie des sciences. Série IIb, Mécanique
Olivier Czarny, Eric Serre, Patrick Bontoux, Richard M. Lueptow. Direct numerical simulation and identification of complex flows in Taylor-Couette counter-rotating cavities. Comptes rendus de l’Académie des sciences. Série IIb, Mécanique, Elsevier, 2001, 329, pp.727-733. ⟨hal-01023161⟩ Plus de détails...
Olivier Czarny, Eric Serre, Patrick Bontoux, Richard M. Lueptow. Direct numerical simulation and identification of complex flows in Taylor-Couette counter-rotating cavities. Comptes rendus de l’Académie des sciences. Série IIb, Mécanique, Elsevier, 2001, 329, pp.727-733. ⟨hal-01023161⟩
Journal: Comptes rendus de l’Académie des sciences. Série IIb, Mécanique
Eric Serre, Sandrine Hugues, Emilia Crespo del Arco, Anthony Randriamampianina, Patrick Bontoux. Axisymmetric and three-dimensional instabilities in an Ekman boundary layer flow. International Journal of Heat and Fluid Flow, Elsevier, 2001, 22 (1), pp.82-93. ⟨hal-01023080⟩ Plus de détails...
Eric Serre, Sandrine Hugues, Emilia Crespo del Arco, Anthony Randriamampianina, Patrick Bontoux. Axisymmetric and three-dimensional instabilities in an Ekman boundary layer flow. International Journal of Heat and Fluid Flow, Elsevier, 2001, 22 (1), pp.82-93. ⟨hal-01023080⟩
Journal: International Journal of Heat and Fluid Flow
Eric Serre, Patrick Bontoux, Richard Kotarba. Numerical simulation of the transition in three-dimensional rotating flows with walls : boundary layers instabilities. International Journal of Computational Fluid Dynamics, Taylor & Francis, 2001, 5, pp.2. ⟨hal-00835770⟩ Plus de détails...
The purpose of this article is the direct numerical simulation (DNS) of the complex phenomena that precede the transition to turbulence inside a cavity subjected to rotation. The configurations of cylindrical cavities subjected to a radial throughflow or to a differential rotation of the walls are relevant to rotating machinery devices. At a high rotation rate, the DNS exhibits instability patterns arising inside the thin layers close to the disks. The efficient spectral solver is based on a Chebyshev-Fourier approximation. For large aspect ratio and at high Reynolds number, an instability occurs inside the Ekman and Bödewadt layers in the form of annular and spiral vortices that are characteristic of type I and type II instabilities.
Eric Serre, Patrick Bontoux, Richard Kotarba. Numerical simulation of the transition in three-dimensional rotating flows with walls : boundary layers instabilities. International Journal of Computational Fluid Dynamics, Taylor & Francis, 2001, 5, pp.2. ⟨hal-00835770⟩
Journal: International Journal of Computational Fluid Dynamics
Eric Serre, Isabelle Raspo, Patrick Bontoux. High order accurate spectral approximation for Navier-Stokes problems. Nonlinear Analysis: Theory, Methods and Applications, Elsevier, 2001, 47 (6), pp.4257-4268. ⟨hal-01023116⟩ Plus de détails...
Eric Serre, Isabelle Raspo, Patrick Bontoux. High order accurate spectral approximation for Navier-Stokes problems. Nonlinear Analysis: Theory, Methods and Applications, Elsevier, 2001, 47 (6), pp.4257-4268. ⟨hal-01023116⟩
Journal: Nonlinear Analysis: Theory, Methods and Applications
Eric Serre, Isabelle Raspo, Patrick Bontoux. High-order accurate spectral approximations for Navier-Stokes problems. Nonlinear Analysis: Theory, Methods and Applications, Elsevier, 2001, 47 (6), pp.4257-4268. ⟨10.1016/S0362-546X(01)00541-7⟩. ⟨hal-00835795⟩ Plus de détails...
Olivier Czarny, Eric Serre, Patrick Bontoux, Richard M. Lueptow. Identification of complex flows in Taylor-Couette counter-rotating cavities. Comptes rendus de l’Académie des sciences. Série IIb, Mécanique, Elsevier, 2001, 329 (10), pp.727-733. ⟨10.1016/S1620-7742(01)01392-7⟩. ⟨hal-00835783⟩ Plus de détails...
The transition in confined rotating flows is a topical problem with many industrial and fundamental applications. The purpose of this study is to investigate the Taylor-Couette flow in a finite-length cavity with counter-rotating walls, for two aspect ratios L=5 or L=6. Two complex regimes of wavy vortex and spirals are emphasized for the first time via direct numerical simulation, by using a three-dimensional spectral method. The spatio-temporal behavior of the solutions is analyzed and compared to the few data actually available.
Olivier Czarny, Eric Serre, Patrick Bontoux, Richard M. Lueptow. Identification of complex flows in Taylor-Couette counter-rotating cavities. Comptes rendus de l’Académie des sciences. Série IIb, Mécanique, Elsevier, 2001, 329 (10), pp.727-733. ⟨10.1016/S1620-7742(01)01392-7⟩. ⟨hal-00835783⟩
Journal: Comptes rendus de l’Académie des sciences. Série IIb, Mécanique
Eric Serre, Patrick Bontoux, Richard Kotarba. Numerical Simulation of the transition in three-dimensional rotating flows with walls. Boundary layer instabilities. International Journal of Computational Fluid Dynamics, Taylor & Francis, 2001, 5 (2), pp.873-879. ⟨hal-01023068⟩ Plus de détails...
Eric Serre, Patrick Bontoux, Richard Kotarba. Numerical Simulation of the transition in three-dimensional rotating flows with walls. Boundary layer instabilities. International Journal of Computational Fluid Dynamics, Taylor & Francis, 2001, 5 (2), pp.873-879. ⟨hal-01023068⟩
Journal: International Journal of Computational Fluid Dynamics
Eric Serre, Emilia Crespo del Arco, Patrick Bontoux. Instabilité tridimensionnelle dans une cavité inter-disque de type rotor-stator. Comptes rendus de l’Académie des sciences. Série IIb, Mécanique, Elsevier, 1999, 326, pp.1139-1146. ⟨hal-01024305⟩ Plus de détails...
Eric Serre, Emilia Crespo del Arco, Patrick Bontoux. Instabilité tridimensionnelle dans une cavité inter-disque de type rotor-stator. Comptes rendus de l’Académie des sciences. Série IIb, Mécanique, Elsevier, 1999, 326, pp.1139-1146. ⟨hal-01024305⟩
Journal: Comptes rendus de l’Académie des sciences. Série IIb, Mécanique
Sandrine Hugues, Eric Serre, Emilia Crespo del Arco, Anthony Randriamampianina, Patrick Bontoux. Instabilité tridimensionnelle de la couche d'Ekman dans une configuration annulaire avec flux forcé. Comptes rendus de l’Académie des sciences. Série IIb, Mécanique, Elsevier, 1998, 326, pp.873-879. ⟨hal-01024308⟩ Plus de détails...
Sandrine Hugues, Eric Serre, Emilia Crespo del Arco, Anthony Randriamampianina, Patrick Bontoux. Instabilité tridimensionnelle de la couche d'Ekman dans une configuration annulaire avec flux forcé. Comptes rendus de l’Académie des sciences. Série IIb, Mécanique, Elsevier, 1998, 326, pp.873-879. ⟨hal-01024308⟩
Journal: Comptes rendus de l’Académie des sciences. Série IIb, Mécanique
Patrick Bontoux, F. Elie, Claude Smutek, E. Crespo, Bernard Roux, et al.. Numerical simulations of buoyancy driven flows in cylinders and cavities for vapour crystal growth. Kluwer Academic Publisher. Physico-Chemical hydrodynamics, Kluwer Academic Publisher, pp.963-995, 1988, NATO ASI Series, Vol 174. ⟨hal-00229875⟩ Plus de détails...
Patrick Bontoux, F. Elie, Claude Smutek, E. Crespo, Bernard Roux, et al.. Numerical simulations of buoyancy driven flows in cylinders and cavities for vapour crystal growth. Kluwer Academic Publisher. Physico-Chemical hydrodynamics, Kluwer Academic Publisher, pp.963-995, 1988, NATO ASI Series, Vol 174. ⟨hal-00229875⟩
E. Crespo del Arco, Patrick Bontoux, R. L. Sani, G.P. Extrémet. Steady and oscillatory convection in vertical cylinders heated from below. Numerical simulation of asymmetric flow regimes. Advances in Space Research, Elsevier, 1988, 8 (12), pp.281-292. ⟨10.1016/0273-1177(88)90030-0⟩. ⟨hal-00833917⟩ Plus de détails...
Three-dimensional buoyancy driven flows in vertical cylinders are simulated with a finite difference technique. Asymmetric convective flows are studied for three values of the (length-to-radius) aspect ratio A. One result concerns the occurrence of asymmetric convection in a flat A=0.485 cylinder for Pr=6.7, near the threshold and up to 3Rac (where Rac is the critical Rayleigh number and Pr is the Prandtl number). Complex (steady and time-dependent) supercritical regimes have been simulated in cylinders of aspect ratios A=2 and A=4 for Pr=0.02 and in ranges of Ra up to 8Rac and 6Rac, respectively. The flow patterns are analysed graphically and discussed with respect to a weakly nonlinear analysis and to experiments. In a particular case, A=4 and Pr=0.02, an oscillatory motion has been obtained and some features of the flow pattern are shown during a period.
E. Crespo del Arco, Patrick Bontoux, R. L. Sani, G.P. Extrémet. Steady and oscillatory convection in vertical cylinders heated from below. Numerical simulation of asymmetric flow regimes. Advances in Space Research, Elsevier, 1988, 8 (12), pp.281-292. ⟨10.1016/0273-1177(88)90030-0⟩. ⟨hal-00833917⟩
Jean Marc Vanel, Roger Peyret, Patrick Bontoux. A pseudo-spectral solution of vorticity-stream function equations using the influence matrix technique. Morton K W and Baines M J. Numerical Methods for Fluid Dynamics II, Clarendon Press Oxford, pp.463-475, 1986. ⟨hal-00974966⟩ Plus de détails...
A method for computing unsteady two dimensional incompressible flows, using the vorticity and the stream function as dependent variables approximated by Chebyshev polynomial expansions is presented. Boundary conditions for the vorticity are derived by the influence matrix technique. The theoretical and numerical difficulties associated with the two-dimensional formulation of the method are discussed. Numerical results illustrate the properties of the method.
Jean Marc Vanel, Roger Peyret, Patrick Bontoux. A pseudo-spectral solution of vorticity-stream function equations using the influence matrix technique. Morton K W and Baines M J. Numerical Methods for Fluid Dynamics II, Clarendon Press Oxford, pp.463-475, 1986. ⟨hal-00974966⟩