Proper Orthogonal Decomposition Analysis and Modelling of the wake deviation behind a squareback Ahmed body

We investigate numerically the 3-D flow around a squareback Ahmed body at Reynolds number Re = 104. Proper Orthogonal Decomposition (POD) is applied to a symmetry-augmented database in order to describe and model the flow dynamics. Comparison with experiments at a higher Reynolds number in a plane section of the near-wake at mid-height shows that the simulation captures several features of the experimental flow, in particular the antisymmetric quasi-steady deviation mode. 3-D POD analysis allows us to classify the different physical processes in terms of mode contribution to the kinetic energy over the entire domain. It is found that the dominant fluctuating mode on the entire domain corresponds to the 3-D quasi-steady wake deviation, and that its amplitude is well estimated from 2-D near-wake data. The next most energetic flow fluctuations consist of vortex shedding and bubble pumping mechanisms. It is found that the amplitude of the deviation is negatively correlated with the intensity of the vortex shedding in the spanwise direction and the suction drag coefficient. Finally, we find that despite the slow convergence of the decomposition, a POD-based low-dimensional model reproduces the dynamics of the wake deviation observed experimentally, as well as the main characteristics of the global modes identified in the simulation

Period-doubling scenario and crisis-induced intermittency in natural convection between two vertical differentially heated plates

Nous étudions la transition vers le chaos de l’écoulement entre deux plaques verticales différentiellement chauffées. Nous nous appuyons sur la simulation numérique directe (DNS) pour étudier le comportement spatio-temporel de l’écoulement en faisant augmenter le nombre de Rayleigh. A partir du régime de conduction pure, l’écoulement devient temporellement mono-périodique, après avoir traversé trois bifurcations supercritiques dont deux du type de fourche et une du type de Hopf. Si on restreint le domaine de simulation afin d’admettre une seule longueur critique dans la direction verticale, une cascade de doublement de période est observée. Le comportement temporel de l’écoulement peut être décrit à l’aide d’une itération unidimensionnelle, et correspond physiquement à la déformation périodique d’une structure tourbillonnaire dite en œil de chat. Le régime du chaos temporel est atteint à Ra_infini estimé à 12330. La constante de Feigenbaum est calculée à partir des premiers doublements de période et un accord relatif est obtenu avec la valeur théorique. Au-delà de Ra_infini, des fenêtres correspondant à des régimes périodiques apparaissent à nouveau. Quand Ra est augmenté au delà de Ra = 15500, une intermittence est observée entre deux structures en œil de chat, séparées d’une demi-période. Les observations de l’écoulement sont cohérentes avec un scénario de crise par fusion, et réminiscentes de cycles hétéroclines structurellement stables dus à la présence d’une symétrie O(2). Le temps caractéristique séparant deux passages d’une structure à une autre obéit à une loi exponentielle

Proper Orthogonal Decomposition Analysis and Modelling of the wake deviation behind a squareback Ahmed body

We investigate numerically the 3-D flow around a squareback Ahmed body at Reynolds number Re = 104. Proper Orthogonal Decomposition (POD) is applied to a symmetry-augmented database in order to describe and model the flow dynamics. Comparison with experiments at a higher Reynolds number in a plane section of the near-wake at mid-height shows that the simulation captures several features of the experimental flow, in particular the antisymmetric quasi-steady deviation mode. 3-D POD analysis allows us to classify the different physical processes in terms of mode contribution to the kinetic energy over the entire domain. It is found that the dominant fluctuating mode on the entire domain corresponds to the 3-D quasi-steady wake deviation, and that its amplitude is well estimated from 2-D near-wake data. The next most energetic flow fluctuations consist of vortex shedding and bubble pumping mechanisms. It is found that the amplitude of the deviation is negatively correlated with the intensity of the vortex shedding in the spanwise direction and the suction drag coefficient. Finally, we find that despite the slow convergence of the decomposition, a POD-based low-dimensional model reproduces the dynamics of the wake deviation observed experimentally, as well as the main characteristics of the global modes identified in the simulation