Particle movement in a boundary layer

Abstract

The study here is concerned with a thin solid body passing through a boundary layer or channel flow and interacting with the flow. Relevant new features from modelling, analysis and computation are presented along with comparisons. Three scenarios of such fluid-body interactive evolution in two-dimensional settings are considered in turn, namely a long body translating upstream or downstream, a long body with little or no translation and a short body with or without translation. The main progress and findings concern predictions of the time taken by the body to traverse the flow and impact upon the underlying wall, the delicate behaviour at the onset of impact, the dependence on parameters such as the initial conditions and the mass and shape of the body, and the influence of streamwise translation of the body in the surrounding fluid flow.

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

“…Third, the centre of mass positions x c , y c might vary, travelling at constant nonzero speed, and there may be a rotation of the body planform, as for a thrown discus or Frisbee, implying that the underbody shape can rotate. Finally here, other cases of dynamic fluid-body interaction such as in boundary layers and channel flows (Smith and Ellis [20], Smith and Wilson [21], Palmer and Smith [16], Jolley et al [9]) would seem to call for spatially three-dimensional investigations. Although rather little progress has been seen previously, we believe there are many intriguing facets to explore in the future within this area of three-dimensional freely moving objects.…”

“…The works mentioned above are, to repeat, predominantly computational or experimental studies and much of the interest in those works as well as in the background motivations is centred on properties at fairly high Reynolds numbers. In that parameter range relatively little exploration of fluid-body interaction has been undertaken even for two spatial dimensions in terms of applied mathematical studies apart perhaps from quite recent papers by Smith and Ellis [20], Smith and Wilson [21], Palmer and Smith [16], Jolley et al [9] for inviscid fluids concerning bodies in boundary layers and channel flows. This sets the scene for the present study which is focussed on an applied mathematical investigation of a dynamic fluid-body interaction in three spatial dimensions.…”