Eric Serre

High-order large-eddy simulation of flow over the “Ahmed body” car model

The structure of the turbulent flow over a simplified automotive model, the Ahmed body (S. R. Ahmed and G. Ramm, SAE Paper No. 8403001, 1984) with a 25° slanted back face, is investigated using high-order large-eddy simulations (LESs) at Reynolds number Re=768000. The numerical approach is carried out with a multidomain spectral Chebyshev–Fourier solver and the bluff body is modeled with a pseudopenalization method. The LES capability is implemented thanks to a spectral vanishing viscosity (SVV) technique, with particular attention to the near wall region. Such a SVV-LES approach is extended for the first time to an industrial three-dimensional turbulent flow over a complex geometry. In order to better understand the interactions between flow separations and the dynamic behavior of the released vortex wake, a detailed analysis of the flow structures is provided. The topology of the flow is well captured showing a partial separation of the boundary layer over the slanted face and the occurrence of two stro...

Annular and spiral patterns in flows between rotating and stationary discs

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 Bodewadt 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.

A spectral projection method for the simulation of complex three-dimensional rotating flows

Abstract 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 Godas 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.

Vortex breakdown in a three-dimensional swirling flow

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.

A three-dimensional pseudospectral method for rotating flows in a cylinder

Abstract A pseudospectral method is proposed for the computation of the three-dimensional (3D) Navier–Stokes equations inside a rotating cavity. The method uses a second-order semi-implicit scheme for the time integration and a projection scheme to maintain the incompressibility constraint. The spatial discretization uses a Fourier–Galerkin approximation leading to a set of two-dimensional (2D) elliptic equations depending on the radial and axial directions. Each equation is solved with a Chebyshev-collocation method coupled with a full diagonalization technique. The dependent variables are transformed to avoid the singularity due to cylindrical coordinates. This transformation leads to new operators with complex eigenvalues requiring complex fast fourier transformation. The method was first tested on analytical solutions and compared with other reliable 2D numerical results. It was applied to the complex flow induced by a rotating disk. Good agreement with earlier experimental and numerical studies is obtained. A transition from an axisymmetric flow to a 3D flow is shown via an instability mechanism near the stationary walls. For smaller aspect ratios (radius smaller than height), the vortex breakdown phenomenon is exhibited in the form of between one and three bubbles along the axis.

Sensitivity of 2-D turbulent flow past a D-shaped cylinder using global stability

We use adjoint-based gradients to analyze the sensitivity of turbulent wake past a D-shaped cylinder at Re = 13000. We assess the ability of a much smaller control cylinder in altering the shedding frequency, as predicted by the eigenfrequency of the most unstable global mode to the mean flow. This allows performing beforehand identification of the sensitive regions, i.e., without computing the actually controlled states. Our results obtained in the frame of 2-D, unsteady Reynolds-averaged Navier–Stokes compare favorably with experimental data reported by Parezanovic and Cadot [J. Fluid Mech. 693, 115 (2012)] and suggest that the control cylinder acts primarily through a local modification of the mean flow profiles.

Coupled numerical and theoretical study of the flow transition between a rotating and a stationary disk

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 Bodewadt layers are given.

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

Turbulent 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 is performed using a spectral vanishing viscosity technique that 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 (105⩽Re=Ωb2∕ν⩽106) 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 confined mainly in ...

Interaction between Ekman pumping and the centrifugal instability in Taylor–Couette flow

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 t...

A spectral vanishing viscosity for the LES of turbulent flows within rotating cavities

A spectral vanishing viscosity technique (SVV) is presented for the simulation of 3D turbulent incompressible flows within a rotor-stator cavity. One characteristic of this technique is that the SVV is active only for the short length scales, a feature which is reminiscent of Large Eddy Simulation models. The Spectral Vanishing Viscosity, first introduced by E. Tadmor for the inviscid Burgers equation E. Tadmor, Convergence of spectral methods for nonlinear conservation laws, SIAM J. Numer. Anal. 26 (1) (1989) 30], is incorporated into the cylindrical Navier-Stokes equations written in velocity pressure formulation. The second-order operator involved in the SVV-method is implemented in a Chebyshev-collocation Fourier-Galerkin pseudo-spectral code. The SVV is shown to lead to stable discretizations without sacrificing the formal accuracy, i.e., exponential convergence, in the proposed discretization. LES results are presented here for rotational Reynolds numbers ranging from Re = 7 i? 10 4 to Re = 7 i? 10 5 . Turbulent quantities are shown to compare very favorably with results of direct numerical simulation (DNS) and experimental measurements.