A 3D pseudospectral method for cylindrical coordinates. Application to the simulations of rotating cavity flows

International audienceThe present work proposes a collocation spectral method for solving the three-dimensional Navier-Stokes equations using cylindrical coordinates. The whole diameter -R < r < R is discretized with an even number of radial Gauss-Lobatto collocation points and an angular shift is introduced in the Fourier transform that avoid pole and parity conditions usually required. The method keeps the spectral convergence that reduces the number of grid points with respect to lower-order numerical methods. The grid-points distribution densifies the mesh only near the boundaries that makes the algorithm well-suited to simulate rotating cavity flows where thin layers develop along the walls. Comparisons with reliable experimental and numerical results of the literature show good quantitative agreements for flows driven by rotating discs in tall cylinders and thin inter-disc cavities. Associated to a spectral vanishing viscosity [E. Séverac, E. Serre, A spectral vanishing viscosity for the LES of turbulent flows within rotating cavities, J. Comp. Phys. 226 (2007) 1234-1255], the method provides very promising LES results of turbulent cavity flows

Large Eddy Simulation of Non-Isothermal Turbulent Rotor-Stator Flows

Non-isothermal turbulent flows in an enclosed rotorstator cavity are here investigated using large eddy simulation (LES). Besides their fundamental importance as three-dimensional prototype flows, such flows arise in many industrial applications and especially in turbomachineries. The LES is performed using a Spectral Vanishing Viscosity technique, which is shown leading to stable discretizations without sacrificing the formal accuracy of the spectral approximation. The LES results have been favorably compared to velocity measurements in the isothermal case. The Boussinesq approximation is then used to take into account the centrifugal-buoyancy effects. The thermal effects have been examined for Re equal to 1 million in a rotor-stator cavity of aspect ratio G=(b-a)/h=5 and curvature parameter Rm=(b-a)/(b+a)=1.8 (a, b the inner and outer radii of the rotor and h the interdisk spacing) and for Rayleigh numbers up to Ra=108. These LES results provide accurate, instantaneous quantities which are of interest in understanding the physics of turbulent flows and heat transfers in an interdisk cavity. The averaged results show small effects of density variation on the mean and turbulent fields

High-order Large Eddy Simulations of Confined Rotor-Stator Flows

International audienceIn 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

Large eddy simulation and measurements of turbulent enclosed rotor-stator flows

International audienceTurbulent flows are studied in an actual enclosed rotor-stator configuration with a rotating hub and a stationary shroud. Besides its fundamental importance - the disk boundary layer is one of the simplest platforms for investigating the underlying structure of three-dimensional boundary layers - this cavity models more complex configurations relevant to rotating machinery. Large Eddy Simulation (LES) is performed using a Spectral Vanishing Viscosity (SVV) technique which is shown leading to stable discretizations without sacrificing the formal accuracy of the spectral approximation. Numerical results and velocity measurements have been favorably compared for a large range of rotational Reynolds numbers up to one million in an annular cavity of curvature parameter Rm=(b+a)/(b-a)=1.8 and of aspect ratio G=(b-a)/h=5, where a and b are respectively the inner and outer radii of the rotating disk and h is the interdisk spacing. In the detailed picture of the flow structure that emerges, the turbulence is mainly confined in the boundary layers including in the Stewartson layer along the external cylinder. For Reynolds numbers larger than 0.1 million, the stator boundary layer is turbulent over most of the cavity. On the other hand, the rotor layer becomes progressively turbulent from the outer radial locations although the rotating hub is shown to destabilize the inner part of the boundary layers. The isosurface maps of the Q-criterion reveal that the three-dimensional spiral arms observed in the unstable laminar regime evolve to more axisymmetric structures when turbulence occurs. At Re equal to one million, the flow is fully turbulent and the anisotropy invariant map highlights turbulence structuring, which can be either a ``cigar-shaped'' structuring aligned on the tangential direction or a ``pancake-shaped'' structuring depending on the axial location. The reduction of the structural parameter a1 (the ratio of the magnitude of the shear stress vector to twice the turbulence kinetic energy) under the typical limit 0.15, as well as the misalignment between the shear stress vector and the mean velocity gradient vector, highlight the three-dimensional nature of both rotor and stator boundary layers with a degree of three-dimensionality much higher than in the idealized system studied by Lygren and Andersson (2001-2006)

A coupled numerical/experimental investigation of a turbulent rotor-stator flow

International audienceTurbulent incompressible flows are studied both numerically and experimentally within an annular rotor-stator cavity of aspect ratio G=(b-a)/h=5 and radius ratio a/b=0.286 (where a and b are the inner and outer radii of the rotating disk and h the interdisk spacing). Besides its fundamental importance as a three-dimensional prototype flow, such flows are crude models of flows arising in many industrial devices, especially in turbomachinary ap-plications. Our aim is to investigate turbulent regimes at three Reynolds numbers up to one million (Ω the rotation speed of the rotor and ν the kinematic viscosity of the fluid) corresponding to different flow prop-erties as the rotation of the rotor is increased. Experimental measurements have been obtained using a laser Dop-pler anemometer (LDA) technique. Numerical modelling is based on a Large Eddy Simulation (LES) using a spectral vanishing viscosity (SVV) technique implemented in a Chebyshev-collocation Fourier-Galerkin pseudo-spectral code. As far as the authors are aware, LES of fully turbulent flow in an actual shrouded ro-tor-stator cavity have not been performed before. Turbulent quantities are shown to compare very favourably with experimental measurements and are shown of interest in understanding the physics of turbulent rotor-stator flows from transitional to turbulent regimes. Moreover, averaged results may provide target data for workers employing RANS schemes

High-order LES of turbulent heat transfer in a rotor–stator cavity

International audienceThe present work examines the turbulent flow in an enclosed rotor–stator system subjected to heat transfer effects. Besides their fundamental importance as three-dimensional prototype flows, such flows arise in many industrial applications but also in many geophysical and astrophysical settings. Large eddy simulations(LES) are here performed using a spectral vanishing viscosity technique. The LES results have already been favorably compared to velocity measurements in the isothermal case (Séverac et al. 2007) for a large range of Reynolds numbers in an annular cavity of large aspect ratio and weak curvature parameter. The purpose of this paper is to extend these previous results in the non-isothermal case using the Boussinesq approximation to take into account the buoyancy effects. Thus, the effects of thermal convection have been examined for a turbulent flow of air in the same rotor–stator system for Rayleigh numbers up to 100 millions. These LES results provide accurate, instantaneous quantities which are of interest in understanding the physics of turbulent flows and heat transfers in an interdisk cavity. Even at high Rayleigh numbers, the structure of the iso-values of the instantaneous normal temperature gradient at the disk surfaces resembles the one of the iso-values of the tangential velocity with large spiral arms along the rotor and more thin structures along the stator. The averaged results show small effects of density variation on the mean and turbulent fields. The turbulent Prandtl number is a decreasing function of the distance to the wall with 1.4 close to the disks and about 0.3 in the outer layers. The local Nusselt number is found to be proportional to the local Reynolds number to the power 0.7. The evolution of the averaged Bolgiano length scale with the Rayleigh number indicates that temperature fluctuations may have a large influence on the dynamics only at the largest scales of the system for Ra larger than 10 millions, since the averaged Bolgiano length scale remains lower than the thermal boundary layer thicknesses

France South Pilot Centre - Main activities of the MSNM-GP laboratory

ERCOFTAC Bulletin 77Presentation of the main activities of the MSNM-GP laborator

Large eddy simulation and measurements in a turbulent rotor-stator flow

International audienceThere have been numerous numerical simulations and experimental studies of flow between rotating and stationary discs with a stationary shroud and no throughflow (a “rotor-stator cavity”) (see references in Serre et al. 2001; Poncet et al. 2005; Randriamampianina & Poncet 2006). The flow has significant industrial applications, such as internal gas-turbine flows and computer hard disks, and the geometry is relatively simple. A characteristic feature of such flows is the coexistence of adjacent coupled flow regions that are radically different in terms of the flow properties (Serre et al. 2004). Moreover, the confinement, the flow curvature and the rotation effects create a strongly inhomogeneous and anisotropic turbulence. Consequently, these flows are very challenging for numerical modelling particularly in turbulent regimes (see a review in Crespo del Arco et al. 2005). Turbulent regimes are investigated here in an annular rotor-stator cavity, using experimental measurements as well as Large-Eddy Simulation (LES). At our knowledge, there has been no efficient investigation of turbulent rotor-stator flows within a closed interdisk cavity using LES. The mean flow is mainly governed by three control parameters: the aspect ratio of the cavity G(=(b-a)/h)=5, the rotational Reynolds number Re based on the outer radius b of the rotating disk and the radius ratio s(=a/b)=0.286. In this work, LES and experimental measurements have been used to characterize statistical properties of turbulent rotor-stator flows for Reynolds numbers up to one million. Till now, LES predictions have compared very favourably with experimental measurements for Reynolds number up to 0.7 million. In the oral presentation of this work it will be possible to show computations still in progress at the moment at Re equal to one million