Vortex force decomposition—forces associated with individual elements of a vorticity field

Abstract

The impulse theory used to calculate the force from a vorticity distribution in two-dimensional, incompressible flow, is re-cast with the aim of approximating, to a first order, the forces generated by a specific flow feature, such as a free vortex passing by an object. To achieve this, the force acting on the body is split up into several core contributions. The first component arises from the time variation of the body’s boundary layer. The second is generated by the advection of any free vorticity located in the flowfield by the object’s boundary layer vorticity. The final force contribution is due to new vorticity being shed. To test the theory, it is applied to two multi-body flowfields consisting of a circular cylinder and a flat plate wing at incidence in close proximity. Force balance measurements and planar particle image velocimetry data are simultaneously obtained at Reynolds numbers of $$10\,000$$ 10 000 and $$20\,000$$ 20 000 . The forces acting on the cylinder are successfully recovered from the vorticity data using the derived formulation, verifying its accuracy. Subsequently, the proposed force formulation is used to create force heat maps that demonstrate how the location of a leading edge vortex affects its force contribution around a pitching NACA-0021 wing translating at a Reynolds number of $$10\, 000$$ 10 000 .

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

“…Limacher et al (2018) derived the added mass force term through impulse theory and later in Limacher et al (2019), they validated it against PIV data on a two-dimensional flow around a cylinder accelerated from rest. Meanwhile, Gehlert and Babinsky (2019) and Gehlert et al (2023) successfully recovered and validated the lift and drag from PIV data on accelerating and rotating cylinder flows using the impulse method. Here the added mass forces are linked to a vortex sheet by applying the rotational and translational boundary conditions to the cylinder surface.…”