Citation:
Ansari SA, Żbikowski R, Knowles K. (2006) Non-linear unsteady aerodynamic model for insect-like flapping wings in the hover. Part 2: implementation and validation. Proceedings of the Institution of Mechanical Engineers, Part G: Journal of Aerospace Engineering. Volume 220, Issue 3, March 2006, pp. 169-86
Abstract:
The essence of this two-part paper is the analytical, aerodynamic modelling of
insect-like flapping wings in the hover for micro-air-vehicle applications. A
key feature of such flapping-wing flows is their unsteadiness and the formation
of a leading-edge vortex in addition to the conventional wake shed from the
trailing edge. What ensues is a complex interaction between the shed wakes,
which, in part, determines the forces and moments on the wing. In an attempt to
describe such a flow, two novel coupled, non-linear, wake integral equations
were developed in the first part of the paper. The governing equations derived
were exact, but did not have a closed analytical form. Solutions were,
therefore, to be found by numerical methods and implemented in Fortran. This is
the theme of the second part of the paper. The problem is implemented by means
of vortex methods, whereby discrete point vortices are used to represent the
wing and its wake. A number of numerical experiments are run to determine the
best values for numerical parameters. The calculation is performed using a time-
marching algorithm and the evolution of the wakes is tracked. In this way, both
flow field and force data are generated. The model is then validated against
existing experimental data and very good agreement is found both in terms of
flow field representation and force prediction. The temporal accuracy of the
simulations is also noteworthy, implying that the underlying flow features are
well captured, especially the unsteadiness. The model also shows the similarity
between two-dimensional and three-dimensional flows for insect-like flapping
wings at low Reynolds numbers of the order of Re similar to 200.