An impulse-based approach to estimating forces in unsteady flow

Abstract

The ready availability of full-field velocity measurements in present-day experiments has kindled interest in using such data for force estimation, especially in situations where direct measurements are difficult. Among the methods proposed, a formulation based on impulse is attractive, for both practical and physical reasons. However, evaluation of the impulse requires a complete description of the vorticity field, and this is particularly hard to achieve in the important region close to a body surface. This paper presents a solution to the problem. The incomplete experimental-vorticity field is augmented by a vortex sheet on the body, with strength determined by the no-slip boundary condition. The impulse is then found from the sum of vortex-sheet and experimental contributions. Components of physical interest can straightforwardly be recognised; for example, the classical ‘added mass’ associated with fluid inertia is represented by an explicit term in the formulation for the vortex sheet. The method is implemented in the context of two-dimensional flat-plate flow, and tested on velocity-field data from a translating wing experiment. The results show that the vortex-sheet contribution is significant for the test data set. Furthermore, when it is included, good agreement with force-balance measurements is found. It is thus recommended that any impulse-based force calculation should correct for (likely) data incompleteness in this way.

On the development and early observations from a towing tank-based transverse wing–gust encounter test rig

“…In a viscous flow, the forces acting on a body can be deconstructed into two components. The first is attributed to body motion in an irrotational fluid and the second is due to vorticity in the flow field about the body (Eldredge 2010;Graham et al 2017). Acceleration of the wing in the direction perpendicular to its chord causes an added mass force, which is realised by a pressure difference across the plate surface.…”

Force Production Mechanisms for a Flat Plate Wing at Low Reynolds Numbers

“…The net force attained is equivalent to the 'non-circulatory' added mass force given previously in section A. A variation of equation (10) has additionally been used by Graham et al, 13 who showed that with knowledge of the plate kinematics and PIV measurements of the starting vortex, the impulse due to the bound vortex sheet can be determined. The authors successfully matched the force as calculated from flow field measurements with that directly measured with a force balance.…”

Vortex force maps for three-dimensional unsteady flows with application to a delta wing

“…provided by particle image velocimetry (PIV), it is very helpful if only free vortices near the body are required in the vortex force approaches. Some approaches requiring incomplete knowledge of the vorticity distribution have been derived, see for instance Noca, Shiels & Jeon (1997), Graham, Pitt Ford & Babinsky (2017) and Kang et al (2018).…”