FSI with Prescribed Solid Motion: Flapping Wing

In Simcenter STAR-CCM+, you can analyse the two-way coupled fluid-structure interaction of systems whose motion paths are described by multiple superposed motions.

In this tutorial, you model the periodic motion of a flapping wing in air. As the main focus is the definition of superposed motions, you can reduce the solution time by applying simplified physics. In this simulation, you model the wing as a linear solid surrounded by a fluid in laminar regime. The FE solid stress solver accounts for wing displacement due to the deformation caused by wing acceleration and the forces exerted by the surrounding fluid.

Wing kinematics are based on the high-frequency flapping motion of a hummingbird wing at hover [996]. The flapping wing motion observed for hummingbirds and insects results in lift-enhancing mechanisms, which inspire the design of indoor aerial vehicles on small scales—for example, micro-aerial vehicles (MAVs) and nano-aerial vehicles (NAVs).

For visualization purposes, the flapping wing that you model in this tutorial is attached to a hummingbird-shaped body, which is not part of the analysis.

Flapping Wing kinematics

In this simplified description, the prescribed wing motion is a harmonic motion with a flapping frequency of 40 Hz. In Simcenter STAR-CCM+ the motion is defined by the superposition of two rigid motions:

• Sweeping—wing rotation in the stroke plane.

  During the forward and backward strokes, the wing motion is confined in a plane (the stroke plane). The stroke angle $\varphi$ , which defines the wing position on the stroke plane, varies harmonically with time with an amplitude of 70°.

• Pitching—wing rotation about its axis.

  During stroke reversals, the wing rotates around its longitudinal axis to maintain a positive angle of attack. The pitch rotation before a forward stroke is called supination; the pitch rotation before a backward stroke is called pronation. In the model used for this tutorial, the pitch angle $\alpha$ , which defines the angle of attack, varies linearly with time during pronation and supination, then remains constant until the next reversal.

The prescribed stroke and pitch angles that are used in this tutorial are based on experimental work [996]. The motion profiles are provided in a predefined table that you import in Simcenter STAR-CCM+.