A rotating three-dimensional body in coupled fluid motion near a wall: Stabilization and blow up

The three-dimensional interaction and evolution of a thin rotating body's motion within a surrounding fluid is presented here. The motion of each is shown to affect the other significantly through a dynamic fluid–body interaction. The consideration of three-dimensional spatial effects and the time-dependent rotating motion of the body are new features for this near-wall unsteady problem. The non-linear fluid motion is formulated for an inviscid incompressible fluid and several scenarios are explored in which the body shape, body rotation, and body motion are studied. The problem reduces to solving Poisson's equation within the underbody planform, subject to mixed boundary conditions and to coupling with integral equations. To incorporate rotation and elliptical body shapes, the boundary conditions are rotated about the fixed mesh over each time step, producing a computationally efficient method. Through numerical and analytical investigations, stabilization of the body motion is shown with increased rotational frequency. Additionally, varying the body's ellipticity and center of mass further affects the body's stability and position in the fluid flow.