Vortex force map method to estimate unsteady forces from snapshot flowfield measurements

Abstract An accurate non-intrusive force measurement is challenging in many situations, especially those involving animals and vehicles. This paper reports a non-intrusive technique based on the vortex force map (VFM) method, which computes forces from snapshot velocity and vorticity fields obtained from the particle image velocimetry (PIV) flow measurement. This study is the first application of the VFM method to PIV velocity data. The VFM method is applied to three different kinematic families for surging flat plates and pitching NACA 0018 aerofoils at Reynolds numbers of $${ \mathcal {O}\left( {10^{4}}\right) }$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>O</mml:mi> <mml:mfenced> <mml:msup> <mml:mn>10</mml:mn> <mml:mn>4</mml:mn> </mml:msup> </mml:mfenced> </mml:mrow> </mml:math> , where flowfields are characterised by massive flow separation with the shedding of the coherent leading-edge and trailing-edge vortices. In all three cases, we observe an agreement between the direct force measurements and the VFM method even if a relatively small region around aerofoils is captured for PIV. Moreover, physical explanations of the linkage between the forces and vortical structures are provided based on the visualised force contribution of each vortex. The VFM method is highly robust to noise (a significant feature in experimental fluid mechanics) and can be applied to snapshot data.