Three-dimensional instability of a ow past a sphere: Mach evolution of the regular and Hopf bifurcations
TypeArticles dans des revues avec comité de lecture
A fully three-dimensional linear stability analysis is carried out to investigate the unstable bifurcations of a compressible viscous fluid past a sphere. A time-stepper technique is used to compute both equilibrium states and leading eigenmodes. In agreement with previous studies, the numerical results reveal a regular bifurcation under the action of a steady mode and a supercritical Hopf bifurcation that causes the onset of unsteadiness but also illustrate the limitations of previous linear approaches, based on parallel and axisymmetric base flow assumptions, or weakly nonlinear theories. The evolution of the unstable bifurcations is investigated up to low-supersonic speeds. For increasing Mach numbers, the thresholds move towards higher Reynolds numbers. The unsteady fluctuations are weakened and an axisymmetrization of the base flow occurs. For a sufficiently high Reynolds number, the regular bifurcation disappears and the flow directly passes from an unsteady planar-symmetric solution to a stationary axisymmetric stable one when the Mach number is increased. A stability map is drawn by tracking the bifurcation boundaries for different Reynolds and Mach numbers. When supersonic conditions are reached, the flow becomes globally stable and switches to a noise-amplifier system. A continuous Gaussian white noise forcing is applied in front of the shock to examine the convective nature of the flow. A Fourier analysis and a dynamic mode decomposition show a modal response that recalls that of the incompressible unsteady cases. Although transition in the wake does not occur for the chosen Reynolds number and forcing amplitude, this suggests a link between subsonic and supersonic dynamics.
Files in this item
Showing items related by title, author, creator and subject.
ALIZARD, Frédéric; ROBINET, Jean-Christophe; GLOERFELT, Xavier (Elsevier, 2012)This work is dedicated to the presentation of a matrix-free method for global linear stability analysis in geometries composed of multi-connected rectangular subdomains. An Arnoldi technique using snapshots in subdomains ...
The onset of three-dimensional centrifugal global modes and their nonlinear development in a recirculating flow over a flat surface CHERUBINI, Stefania; ROBINET, Jean-Christophe; DE PALMA, Pietro; ALIZARD, Frédéric (American Institute of Physics, 2010)The three-dimensional stability dynamics of a separation bubble over a flat plate has been studied in both linear and nonlinear conditions. Using a global eigenvalue analysis, two centrifugal global modes are identified: ...
SONG, Ge; ALIZARD, Frédéric; ROBINET, Jean-Christophe; GLOERFELT, Xavier (AIP Publishing, 2013)It is now well established that linear and nonlinear instability waves play a significant role in the noise generation process for a wide variety of shear flows such as jets or mixing layers. In that context, the problem ...
ALIZARD, Frédéric; CHERUBINI, Stefania; ROBINET, Jean-Christophe (AIP, 2009)The optimal asymptotic response to time harmonic forcing of a convectively unstable two-dimensional separated boundary layer on a flat plate is numerically revisited from a global point of view. By expanding the flow ...
Multiple-correction hybrid k -exact schemes for high-order compressible RANS-LES simulations on fully unstructured grids PONT, Grégoire; PONT, Grégoire; BRENNER, Pierre; BRENNER, Pierre; CINNELLA, Paola; CINNELLA, Paola; MAUGARS, Bruno; MAUGARS, Bruno; ROBINET, Jean-Christophe; ROBINET, Jean-Christophe (Elsevier BVElsevier BV, 2017)A Godunov's type unstructured finite volume method suitable for highly compressible turbulent scale-resolving simulations around complex geometries is constructed by using a successive correction technique. First, a family ...