Detection and Analysis of Separated Flow Induced Vortical Structures

This study examines the ability to detect the dynamic interactions of vortical structures generated from a Helmholtz instability caused by separation over bluff bodies at large Reynolds number of approximately 104 based on a cross stream characteristic length of the geometry. Accordingly, two configurations, a square cylinder with normally incident flow and a thin airfoil with flow at an angle of attack of 200 are examined. Direct numerical simulation is used to obtain flow over the square cylinder. A time-resolved, three-component PIV data set is collected in a symmetry plane for the airfoil. Different approaches analyzing vector field and tensor field topologies are considered to identify vortical structures and local, swirl regions: (i) the Γ function that maps the degree of rotation rate (or pressure-gradients) to identify local swirl regions, (ii) Entity Connection Graph (ECG) that combines the Conley theory and Morse decomposition to identify vector field topology consisting of fixed points (sources, sinks, saddles, and periodic orbits), together with separatrices (links connecting them), and (iii) the λ2 method that examines the gradient fields of velocity to identify local regions of pressure minima. Both velocity and pressure-gradient fields are analyzed for the DNS data, whereas only velocity field is used for the experimental data set. The vector-field topology requires spatial integration of the velocity or pressure-gradient fields. The tensor field topology, on the other hand, is based on gradients of the velocity of pressure-gradient vectors. A detailed comparison of these techniques is performed by applying them to velocity or pressure-based data and using spatial filtering of the data sets to identify the multiscale features of the flow. It is shown that various techniques provide useful information about the flowfield at different scales that can be used for further analysis of many fluid engineering problems of practical interest.