Computation of Unsteady Separated Flow Fields Using Anisotropic Vorticity Elements

Abstract

A novel computational methodology to compute two-dimensional unsteady separated flow fields using a vorticity based formulation is presented. Unlike traditional vortex methods, the elements used in this method are designed to take advantage of the natural anisotropy of most external flows. These vortex elements are disjoint and of compact support. The vorticity is uniform over rectangular elements whose initial thickness is set by a diffusion length scale. The elements are a mathematical construction which enables the vorticity of the flow to be created and followed numerically, and the Biot-Savart integral to be performed. This integral specifies the associated velocity field. Since the vorticity of a single element is of finite extent, the velocity associated with an element is given by a nonsingular expression. Viscous diffusion effects are modeled using random walk and the advection term is computed by transporting the vorticity elements with the local velocity field. Consequently, this Lagrangian mesh continually evolves through time. Since pressure does not explicitly appear in the formulation, surface pressures are computed using a stagnation enthalpy formulation. These elements are used to compute vorticity production, accumulation, transport and viscous diffusion mechanisms for unsteady separated flow fields past a pitching airfoil. Dynamic stall vortex initiation and development were examined and compared with existing experimental data. Surface pressure data and integrated force coefficient data were found to be in excellent agreement with experimental data. Effects of geometry were provided with baseline calculations of the unsteady flow past an impulsively started cylinder. Both qualitative and quantitative comparisons with experimental data for equivalent test conditions establish the applicability of this approach to depict unsteady separated flow fields.