Stéphane Viazzo

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

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(= Ωb2/ν) =4 × 105. 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 post-processed 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 simulations of Taylor-Couette-Poiseuille flows in a narrow-gap system

The present paper concerns Large-Eddy Simulations (LES) of turbulent Taylor-Couette-Poiseuille flows in a narrow-gap cavity for six different combinations of rotational and axial Reynolds numbers. The in-house numerical code has been first validated in a middle-gap cavity. Two sets of refined LES results, using the Wall-Adapting Local Eddy Viscosity (WALE) and the Dynamic Smagorinsky subgrid-scale models available within an in-house code based on high-order compact schemes, have been then compared with no noticeable difference on the mean flow field and the turbulent statistics. The WALE model enabling a saving of about 12% of computational effort has been finally used to investigate the influence on the hydrodynamics of the swirl parameter N within the range [1.49 − 6.71]. The swirl parameter N, which compares the effects of rotation of the inner cylinder and the axial flowrate, does not influence significantly the mean velocity profiles. Turbulence intensities are enhanced with increasing values of N with remarkably high peak values within the boundary layers. The inner rotating cylinder has a destabilizing effect inducing asymmetric profiles of the Reynolds stress tensor components. The rotor and stator boundary layers exhibit the main characteristics of two-dimensional boundary layers. Turbulence is also mainly at two-component there. Thin coherent structures appearing as negative (resp. positive) spiral rolls are observed along the rotor (resp. stator) side. Their inclination angle depends strongly on the value of the swirl parameter, which fixes the intensity of the crossflow. On the other hand, the intensity and the size of the coherent structures observed within the boundary layers are governed by the effective Reynolds number. For its highest value, they penetrate the whole gap. Finally, the results have been extended to the non-isothermal case in the forced convection regime. A correlation for the Nusselt number along the rotor has been provided showing a much larger dependence on the axial Reynolds number than expected from previous published works, while it depends classically on the Taylor number to the power 0.145 and on the Prandtl number to the power 0.3.

A parallelized multidomain compact solver for incompressible turbulent flows in cylindrical geometries

We present an efficient parallelized multidomain algorithm for solving the 3D Navier-Stokes equations in cylindrical geometries. The numerical method is based on fourth-order compact schemes in the two non-homogeneous directions and Fourier series expansion in the azimuthal direction. The temporal scheme is a second-order semi-implicit projection scheme leading to the solution of five Helmholtz/Poisson equations. To handle the singularity appearing at the axis in cylindrical coordinates, while being able to have a thinner or conversely a coarser mesh in this zone, parity conditions are imposed at r = 0 for each flow variable and azimuthal Fourier mode. To simulate flows in irregularly shaped cylindrical geometries and benefit from a hybrid OpenMP/MPI parallelization, an accurate perfectly free-divergence multidomain method based on the influence matrix technique is proposed. First, the accuracy of the present solver is checked by comparison with analytical solutions and the scalability is then evaluated. Simulations using the present code are then compared to reliable experimental and numerical results of the literature showing good quantitative agreements in the cases of the axisymmetric and 3D unsteady vortex breakdowns in a cylinder and turbulent pipe flow. Finally to show the capability of the algorithm to deal with more complex flows relevant of turbomachineries, the turbulent flow inside a simplified stage of High-Pressure compressor is considered.

Numerical Simulations of a Middle Gap Turbulent Taylor-Couette-Poiseuille Flow

Turbulent flows in an opened Taylor-Couette system with an axial throughflow is studied here by the means of large eddy simulations. The ultimate industrial application is the effective cooling of the rotor-stator gap of an electrical motor.

LES in a Concentric Annular Pipe: Analysis of Mesh Sensitivity and Wall Pressure Fluctuations

Annular pipe flows have varied application in the domains of nuclear reactors, heat exchangers, drilling operations in oil industry etc.

Total energy balance in a natural convection flow

Purpose The purpose of this paper is to show a thermodynamic analysis to determine the contribution of each term of the total energy balance. Design/methodology/approach The thermodynamic analysis comprises a number of numerical simulations where some terms, typically ignored by the commonly used approximations, are removed from the total energy equation to quantify the effects in the flow and heat transfer fields. The case study is the differentially heated square cavity flow, in which the effects of work done by the pressure forces contribute significantly to the energy balance. Because local magnitudes are computed here for discussion, the dimensional form of the governing equations is preferred and a numerical model without any restrictive approximation about the role of the pressure is used. Findings The results show that the work of gravity forces term is in perfect balance with the work of pressure forces term, and thus, ignoring the contribution of one of them yields an incorrect solution. In addition, it is shown that the assumption of zero divergence of the Boussinesq approximation can be erroneous, even for a natural convection flow case where the temperature difference is very small. Research limitations/implications As the flow and heat transfer governing equations are complex, simplifying assumptions are generally used; that is, the Boussinesq and low Mach number approximations. These assumptions are systematically adopted without any validation process and without considering that they modify the physical meaning of one or more of the thermodynamic quantities, particularly the pressure. This fact results in inconsistencies of the different forms of energy. Originality/value This is the first time that the terms of the total energy balance are quantified in such a way, in a differentially heated square cavity flow, which is a case study addressed by several authors.