Adaptation anisotrope sur des structures Lagrangiennes coherentes en mecanique des fluides.
详细信息
文摘
Several methods can help us to analyse the behavior of flows that govern the operation of fluid flow systems encountered in the industry aerospace,marine and terrestrial transportation,power generation,etc..). For transient or turbulent flows,experimental methods are used in conjunction with numerical simulations direct simulation or based on models) to extract as much information as possible. In both cases,these methods generate massive amounts of data which must then be processed and analyzed. This research project aims to improve the post-processing algorithms to facilitate the study of numerically simulated flows and those obtained using measurement techniques e.g. particle image velocimetry PIV). The absence,even until today,of an objective definition of a vortex has led to the use of several Eulerian methods vorticity,the Q and the Lambda-2 criteria,etc..),often unsuitable to extract the flow characteristics. The Lyapunov exponent,calculated on a finite time the so-called FTLE ),is an effective Lagrangian alternative to these standard methods. However,the computation methodology currently used to obtain the FTLE requires numerical evaluation of a large number of fluid particle trajectories on a Cartesian grid that is superimposed on the simulated or measured velocity fields. The number of nodes required to visualize a FTLE field of an unsteady 3D flow can easily reach several millions,which requires significant computing resources for an adequate analysis. In this project,we aim to improve the computational efficiency of the FTLE field by providing an alternative to the conventional calculation of the components of the Cauchy-Green deformation tensor. A set of ordinary differential equations ODEs) is used to calculate the particle trajectories and simultaneously the first and the second derivatives of the displacement field,resulting in a highly improved accuracy of nodal tensor components. The first derivatives are used to calculate the Lyapunov exponent and the second derivatives to estimate the interpolation error. Hessian matrices of the displacement field two matrices in 2D and three matrices in 3D) allow us to build a multi-scale optimal metric and generate an unstructured anisotropic mesh to efficiently distribute nodes and to minimize the interpolation error. The flexibility of anisotropic meshes allows to add and align nodes near the structures of the flow and to remove those in areas of low interest. The mesh adaptation is based on the intersection of the Hessian matrices of the displacement field and not on the FTLE field. Empirically,we show that this method can effectively reveal the ridges of the FTLE field and avoid the introduction of noise generated by the derivation of the resulting field. The method is also effective in presence of noise on velocity signals,so that no pre-processing of velocity fields is required,which is particularly adapted to measured flows.