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=0r=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.
Romain Oguic, Stéphane Viazzo, Sébastien Poncet. A parallelized multidomain compact solver for incompressible turbulent flows in cylindrical geometries. Journal of Computational Physics, Elsevier, 2015, 300, pp.710-731. ⟨10.1016/j.jcp.2015.08.003⟩. ⟨hal-01299082⟩
Sébastien Poncet, Stéphane Viazzo, Oguic Romain. Large eddy simulations of Taylor-Couette-Poiseuille flows in a narrow-gap system. Physics of Fluids, American Institute of Physics, 2014, 26 (10), pp.105108. ⟨10.1063/1.4899196⟩. ⟨hal-01083052⟩ Plus de détails...
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 EddyViscosity(WALE) and theDynamic Smagorinsky subgrid-scale models availablewithin an in-house code based on high-order compact schemes, have been then compared with no noticeable difference on the mean flow field and theturbulent 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 thanexpected 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.
Sébastien Poncet, Stéphane Viazzo, Oguic Romain. Large eddy simulations of Taylor-Couette-Poiseuille flows in a narrow-gap system. Physics of Fluids, American Institute of Physics, 2014, 26 (10), pp.105108. ⟨10.1063/1.4899196⟩. ⟨hal-01083052⟩