The three-dimensional unsteady boundary layer induced by a vortex filament moving outside a circular cylinder is considered. In the present paper, we focus attention on the situation where the inviscid flow is fully three-dimensional but is symmetric with respect to the top centreline of the cylinder. The motion of the vortex toward the cylinder leads to separation of the boundary layer; in the present work a large unsteady adverse pressure gradient develops as well. Results for the three-dimensional streamlines, the vorticity distribution, and the velocity component normal to the cylinder indicate the presence of a region of unsteady three-dimensional secondary flow structure of rather complex shape located deep within the boundary layer. Within this three-dimensional secondary flow the fluid is progressively squeezed into a narrow region under the main vortex and it is expected that a local three-dimensional jet will develop sending boundary-layer fluid out into the main stream. It is pointed out that such three-dimensional eruptive behaviour has been observed in experiments. The results indicate the development of a three-dimensional singularity in the boundary-layer equations.
The flowfield generated by a helicopter in flight is extremely complex, and it has been recognized that interactions among components can significantly affect helicopter performance. In the present work a simplified model for the interaction of a rotor tip vortex with the helicopter fuselage is developed. The tip vortex is idealized as a single three-dimensional vortex tube, and the fuselage is modeled as an infinite circular cylinder. The Biot-Savart law is employed to describe the flow induced by the vortex, and the flow is assumed to be inviscid and irrotational outside the core of the vortex. The numerical calculations indicate that a large adverse pressure gradient develops under the vortex on the fuselage causing a rapid drop in the pressure there; large variations in the curvature of the vortex are not observed. Numerical solutions for the vortex position and for the pressure on the airframe are calculated for the case where the vortex is embedded in a three-dimensional steady mean flow; the effect of vortex core size is also investigated. The nature of the initial stages of the breakdown of local axisymmetry of the core of the vortex filament is suggested based on both the numerical and experimental results.
The behavior of vortex systems in the vicinity of solid surfaces is a matter of intense interest in rotorcraft aerodynamics, as well as in many other areas of fluid dynamics. We consider the viscous flow on a simplified model of a helicopter airframe due to a helicopter rotor tip vortex both experimentally and computationally. As the tip vortex approaches the airframe, the computational results predict the genesis of a region just upstream of the main vortex, characterized by reversed flow and rapid growth in size. The experiments clearly show evidence of such a region under the tip vortex in the region predicted by the computations and at roughly the same time. The secondary vorticity field in the computations is of a sign opposite to the vorticity associated with the tip vortex. Results for the streamline patterns and vorticity field during the genesis of the secondary eddy are presented and compared with experimental flow visualization results.
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