Plane mixing layer simulation using FEniCS libraries

Resumo

The plane mixing layer is a common phenomena encountered in many engineering applications [3], for example, combustion, and transport and mixing process of chemical substances [5]. The mixing layer is produced by the interaction of two parallel fluid streams, away from the wall, with different velocities U2 > U1 ≥ 0 [6]. Due to the velocity differences in the interface, the shear stress is generated producing the Kelvin-Helmholtz instability [3], which is characterized for the enrolled vortex structures enhancing the momentum, heat and mass transfer.  The plane mixing layer is considered a bi-dimensional flow, but the turbulences present in the flow have tri-dimensional characteristics [7]. The aim of this work is to evaluate the bi-dimensional numerical simulation of plane mixing layer on a refined mesh. A reduced computational domain is used in order to obtain an initial result. The averaged velocity profile is compared to the results from the experiments [1]. The FEniCS Project [4] is used for the numerical simulation, specially the CBC.PDESys package which is an application of FEniCS written in Python for the resolution of partial differential equations for fluid dynamics using finite element method. The flow is considered incompressible, and time dependent perturbations [2] are applied in order to model the instability inherent to the real phenomena. The dominant direction of flow is x, the variations of flow are predominately in the y direction, and it is homogeneous and symmetric in z direction. The flow is modelled by the continuity and Navier-Stokes equations. These equations in two dimensional flow are reduced to  […].