Three-dimensional evolution of body and fluid motion near a wall

Abstract

Evolution of three-dimensional body motion within surrounding three-dimensional fluid motion is addressed, each motion affecting the other significantly in a dynamic fluid–body interaction. This unsteady problem is set near a wall. The spatial three-dimensionality present is a new feature. For inviscid incompressible fluid, a basic nonlinear formulation is described, followed by a linearised form as a first exploration of parameter space and solution responses. The problem reduces to solving Poisson’s equation within the underbody planform, subject to mixed boundary conditions and to coupling with integral equations. Numerical and analytical properties show dependence mainly on the normal and pitch motions, as well as instability or bounded oscillations depending on the position of the centre of mass of the body, and a variety of three-dimensional shapes is examined.

On modelling fluid/body interactions, impacts and lift-offs

“…There is also a call for increased allowance for flow separation, whether inviscid or viscous, during fluidbody evolutions. Dynamic interactions involving time and three spatial dimensions [23] are still in their infancy as regards physical understanding and modelling. This list of challenges is not an exhaustive one but is meant to indicate potential areas of interest.…”

“…If the contact point is not at x = C then the body is initially rocking, a case that is considered in Refs. [11,22] whereas we will address the initially stationary case (23). Lift-off is induced when the surrounding fluid is set into motion impulsively at time t = 0 + by means of a free oncoming uniform stream u = 1 parallel to the wall at atmospheric pressure p of zero.…”

“…These are mostly on interactions arising in two spatial dimensions (say x, y) and time t. A very recent development is in Ref. [23] which is concerned with three spatial dimensions (thus x, y, z, t). The above studies examine twodimensional (2D) dynamic fluid-body interactions in boundary layers of nonzero shear flow, e.g., Refs.…”