Year:    2008

International Journal of Numerical Analysis and Modeling, Vol. 5 (2008), Iss. 5 : pp. 17–35

Abstract

Very complex flow structures occur during separation that appear in a wide variety of applications involving flow over a bluff body. 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 $10^4$ based on cross stream characteristic length of the geometry. Accordingly, two configurations, a thin airfoil with flow at an angle of attack of $20^0$ and a square cylinder with normally incident flow are examined. A time-resolved, three-component PIV data set is collected in a symmetry plane for the airfoil, whereas direct numerical simulations are used to obtain flow over the square cylinder. The experimental data consists of the velocity field, whereas simulations provide both velocity and pressure-gradient fields. Two different approaches analyzing vector field and tensor field topologies are considered to identify vortical structures and local, swirl regions. The vector field topology uses (1) the $\Gamma$ function that maps the degree of rotation rate (or pressure-gradients) to identify local swirl regions, and (2) 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). The tensor field feature uses (1) the $\lambda_2$ method that examines the gradient fields of velocity or pressure-gradient to identify local regions of pressure minima, and (2) tensor field feature that decomposes the velocity-gradient or pressure Hessian tensor into isotropic scaling, rotation, and anisotropic stretching parts to identify regions of high swirl. The vector-field topology requires spatial integration of the velocity or pressure-gradient fields and represents a global descriptor of vortical structures. The tensor field feature, on the other hand, is based on gradients of the velocity of pressure-gradient vectors and represents a local descriptor. A detailed comparison of these techniques is performed by applying them to velocity or pressure-based data and using spatial filtered data sets to identify the multiscale features of the flow. It is shown that various techniques provide useful information about the flow field at different scales that can be used for further analysis of many fluid engineering problems of practical interest.