Evaluating unsteady fluid dynamic forces in viscous flows from the vorticity field

The vortex force map (VFM) method is a promising low-cost technique for predicting unsteady aerodynamic load from the vorticity field. Developed under potential flow assumption and applied to high-resolution computational fluid dynamics (CFD) data, the original VFM method needs to be further explored for viscous flows, especially at low Reynolds numbers and with incomplete knowledge of the flow data. In this paper, the VFM method is extended to general viscous flows, with both forces contributed from vorticity in the flowfield and on the body surface considered. We find that viscosity contributes to not only the skin-friction force but also a pressure force term. We also show that the extended vortex pressure force maps for general flow problems without the potential flow assumption lead to vanishing contributions from the far-field. The extended VFM method is applied to CFD flowfields for the starting flow of a cylinder and a NACA0012 airfoil, and it is used to analyze the force contribution effect of a given vortex. Moreover, acceptable accuracy of the method on truncated domains and under coarse sampling of typical particle image velocimetry measurement size is demonstrated