Étude des Scénarios de transition vers la turbulence dans la couche limite d’un disque d’une cavité en rotation (Post-Doc, 2016-2017)
Publications scientifiques au M2P2
2019
E. Yim, P. Meliga, F. Gallaire. Self-consistent triple decomposition of the turbulent flow over a backward-facing step under finite amplitude harmonic forcing. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, Royal Society, The, 2019, 475 (2225), pp.20190018. ⟨10.1098/rspa.2019.0018⟩. ⟨hal-02177032⟩ Plus de détails...
We investigate the saturation of harmonically forced disturbances in the turbulent flow over a backward-facing step subjected to a finite amplitude forcing. The analysis relies on a triple decomposition of the unsteady flow into mean, coherent and incoherent components. The coherent-incoherent interaction is lumped into a Reynolds averaged Navier-Stokes (RANS) eddy viscosity model, and the mean-coherent interaction is analysed via a semi-linear resolvent analysis building on the laminar approach by Mantic-Lugo & Gallaire (2016 J. Fluid Mech. 793, 777-797. (doi:10.1017/jfm.2016.109)). This provides a self-consistent modelling of the interaction between all three components, in the sense that the coherent perturbation structures selected by the resolvent analysis are those whose Reynolds stresses force the mean flow in such a way that the mean flow generates exactly the aforementioned perturbations, while also accounting for the effect of the incoherent scale. The model does not require any input from numerical or experimental data, and accurately predicts the saturation of the forced coherent disturbances, as established from comparison to time-averages of unsteady RANS simulation data.
E. Yim, P. Meliga, F. Gallaire. Self-consistent triple decomposition of the turbulent flow over a backward-facing step under finite amplitude harmonic forcing. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, Royal Society, The, 2019, 475 (2225), pp.20190018. ⟨10.1098/rspa.2019.0018⟩. ⟨hal-02177032⟩
Journal: Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
Eunok Yim, J.-M. Chomaz, Denis Martinand, Eric Serre. Transition to turbulence in the rotating disk boundary layer of a rotor–stator cavity. Journal of Fluid Mechanics, Cambridge University Press (CUP), 2018, 848, pp.631 - 647. ⟨10.1017/jfm.2018.239⟩. ⟨hal-02116221⟩ Plus de détails...
The transition to turbulence in the rotating disk boundary layer is investigated in a closed cylindrical rotor-stator cavity via direct numerical simulation (DNS) and linear stability analysis (LSA). The mean flow in the rotor boundary layer is qualitatively similar to the von Karman self-similarity solution. The mean velocity profiles, however, slightly depart from theory as the rotor edge is approached. Shear and centrifugal effects lead to a locally more unstable mean flow than the self-similarity solution, which acts as a strong source of perturbations. Fluctuations start rising there, as the Reynolds number is increased, eventually leading to an edge-driven global mode, characterized by spiral arms rotating counter-clockwise with respect to the rotor. At larger Reynolds numbers, fluctuations form a steep front, no longer driven by the edge, and followed downstream by a saturated spiral wave, eventually leading to incipient turbulence. Numerical results show that this front results from the superposition of several elephant front-forming global modes, corresponding to unstable azimuthal wavenumbers m, in the range m is an element of [32, 78 ]. The spatial growth along the radial direction of the energy of these fluctuations is quantitatively similar to that observed experimentally. This superposition of elephant modes could thus provide an explanation for the discrepancy observed in the single disk configuration, between the corresponding spatial growth rates values measured by experiments on the one hand, and predicted by LSA and DNS performed in an azimuthal sector, on the other hand.
Eunok Yim, J.-M. Chomaz, Denis Martinand, Eric Serre. Transition to turbulence in the rotating disk boundary layer of a rotor–stator cavity. Journal of Fluid Mechanics, Cambridge University Press (CUP), 2018, 848, pp.631 - 647. ⟨10.1017/jfm.2018.239⟩. ⟨hal-02116221⟩
Eunok Yim, J.-M Chomaz, Denis Martinand, Eric Serre. Transition to turbulence in the rotating disk boundary layer of a rotor-stator cavity. Journal of Fluid Mechanics, Cambridge University Press (CUP), 2018, 836, pp.43-71. ⟨10.1017/jfm.2017.771⟩. ⟨hal-02121890⟩ Plus de détails...
This paper proposes a resolution to the conundrum of the roles of convective and absolute instability in transition of the rotating-disk boundary layer. It also draws some comparison with swept-wing flows. Direct numerical simulations based on the incompressible Navier–Stokes equations of the flow over the surface of a rotating disk with modelled roughness elements are presented. The rotating-disk flow has been of particular interest for stability and transition research since the work by Lingwood (J. Fluid Mech., vol. 299, 1995, pp. 17–33) where an absolute instability was found. Here stationary disturbances develop from roughness elements on the disk and are followed from the linear stage, growing to saturation and finally transitioning to turbulence. Several simulations are presented with varying disturbance amplitudes. The lowest amplitude corresponds approximately to the experiment by Imayama et al. (J. Fluid Mech., vol. 745, 2014a, pp. 132–163). For all cases, the primary instability was found to be convectively unstable, and secondary modes were found to be triggered spontaneously while the flow was developing. The secondary modes further stayed within the domain, and an explanation for this is a proposed globally unstable secondary instability. For the low-amplitude roughness cases, the disturbances propagate beyond the threshold for secondary global instability before becoming turbulent, and for the high-amplitude roughness cases the transition scenario gives a turbulent flow directly at the critical Reynolds number for the secondary global instability. These results correspond to the theory of Pier (J. Engng Maths, vol. 57, 2007, pp. 237–251) predicting a secondary absolute instability. In our simulations, high temporal frequencies were found to grow with a large amplification rate where the secondary global instability occurred. For smaller radial positions, low-frequency secondary instabilities were observed, tripped by the global instability. The transition to turbulence in the rotating disk boundary layer is investigated in a closed cylindrical rotor-stator cavity via direct numerical simulation (DNS) and linear stability analysis (LSA). The mean flow in the rotor boundary layer is qualitatively similar to the von Kármán self-similarity solution. The mean velocity profiles, however, slightly depart from theory as the rotor edge is approached. Shear and centrifugal effects lead to a locally more unstable mean flow than the self-similarity solution, which acts as a strong source of perturbations. Fluctuations start rising there, as the Reynolds number is increased, eventually leading to an edge-driven global mode, characterized by spiral arms rotating counterclockwise with respect to the rotor. At larger Reynolds numbers, fluctuations form a steep front, no longer driven by the edge, and followed downstream by a saturated spiral wave, eventually leading to incipient turbulence. Numerical results show that this front results from the superposition of several elephant front-forming global modes, corresponding to unstable azimuthal wavenumbers m, in the range m ∈ [32, 78]. The spatial growth along the radial direction of the energy of these fluctuations is quantitatively similar to that observed experimentally. This superposition of elephant modes could thus provide an explanation for the discrepancy observed in the single disk configuration, between the corresponding spatial growth rates values measured by experiments on the one hand, and predicted by LSA and DNS performed in an azimuthal sector, on the other hand.
Eunok Yim, J.-M Chomaz, Denis Martinand, Eric Serre. Transition to turbulence in the rotating disk boundary layer of a rotor-stator cavity. Journal of Fluid Mechanics, Cambridge University Press (CUP), 2018, 836, pp.43-71. ⟨10.1017/jfm.2017.771⟩. ⟨hal-02121890⟩
Eunok Yim, J.-M Chomaz, D Martinand, E Serre. Transition to turbulence in the rotating disk boundary layer of a rotor-stator cavity. Journal of Fluid Mechanics, Cambridge University Press (CUP), 2018. ⟨hal-02927579⟩ Plus de détails...
The transition to turbulence in the rotating disk boundary layer is investigated in a closed cylindrical rotor-stator cavity via direct numerical simulation (DNS) and linear stability analysis (LSA). The mean flow in the rotor boundary layer is qualitatively similar to the von Kármán self-similarity solution. The mean velocity profiles, however, slightly depart from theory as the rotor edge is approached. Shear and centrifugal effects lead to a locally more unstable mean flow than the self-similarity solution, which acts as a strong source of perturbations. Fluctuations start rising there, as the Reynolds number is increased, eventually leading to an edge-driven global mode, characterized by spiral arms rotating counterclockwise with respect to the rotor. At larger Reynolds numbers, fluctuations form a steep front, no longer driven by the edge, and followed downstream by a saturated spiral wave, eventually leading to incipient turbulence. Numerical results show that this front results from the superposition of several elephant front-forming global modes, corresponding to unstable azimuthal wavenumbers m, in the range m ∈ [32, 78]. The spatial growth along the radial direction of the energy of these fluctuations is quantitatively similar to that observed experimentally. This superposition of elephant-modes could thus provide an explanation for the discrepancy observed in the single disk configuration, between the corresponding spatial growth rates values measured by experiments on the one hand, and predicted by LSA and DNS performed in an azimuthal sector, on the other hand.
Eunok Yim, J.-M Chomaz, D Martinand, E Serre. Transition to turbulence in the rotating disk boundary layer of a rotor-stator cavity. Journal of Fluid Mechanics, Cambridge University Press (CUP), 2018. ⟨hal-02927579⟩