Unsteady vorticity force decomposition-evaluating gust distortion

The impulse theory used to calculate the force from a vorticity distribution in two-dimensional, incompressible flow, is re-cast with the aim of estimating the forces generated by a specific flow feature, such as a region of external vorticity passing an object. Specifically, the effect of gust shear layer distortion on the force during a flat plate sharp-edged gust encounter is studied. This is made possible because the force acting on any object is split up into several core contributions. The first component arises from the time variation of the bodies boundary layer. The second is generated by the advection of any free vorticity located in the flowfield by the objects 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 at incidence in close proximity. Force balance measurements and planar particle image velocimetry data are simultaneously obtained at Reynolds numbers of 10 000 and 20 000. The forces acting on the cylinder are successfully recovered from the vorticity data using the derived formulation, verifying its accuracy. Thereafter, the proposed force formulation is applied to the vorticity data of a flat plate gust encounter, to identify the force created by the gust shear layers. The gust is formed by a sharp-edged region of uniform cross flow, resembling a ‘top-hat’ vertical velocity profile. The gust ratios explored are 0.5, 1 and 1.5. It is found that with increasing gust ratio, gust distortion has an increasing influence on the magnitude of the non-circulatory gust force. At a gust ratio of 1.5, the real maximum noncirculatory force is approximately 50 % lower than the theoretical Küssner model equivalent, which assumes rigid gust shear layers. The deflection of the gust delays the growth of the gust vortex sheet contributing to the boundary layer and therefore reduces its force contribution. An additional force of opposite sign is created by the advection of the gust vorticity by the plate boundary layer. Together, these two force components lead to the observed reduction of the non-circulatory force