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The problem of orthogonal penetration of a blade into the core of a vortex with non-zero axial flow was studied using a combination of scaling theory, a heuristic plug-flow model and full Navier–Stokes simulations. The particular focus of this paper was to understand the mechanics of the transient lift force that occurs during the initial penetration of the blade leading edge into the vortex core, and the relationship of this transient force to the steady-state lift force that develops due to the difference in vortex core radius over the blade surface. The three modelling approaches all lead to the conclusion that the maximum value of the lift coefficient for the transient blade penetration force is proportional to the impact parameter and inversely proportional to the axial flow parameter. This observation is used to develop a simple expression that collapses the predictions of the full Navier–Stokes simulations for lift coefficient over a wide range of parameter values.
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Vorticity reconnection during vortex cutting by a blade
A computational study of vorticity reconnection, associated with the breaking and reconnection of vortex lines, during vortex cutting by a blade is reported. A series of Navier–Stokes simulations of vortex cutting with different values of the vortex strength are described, and the different phases in the vortex cutting process are compared to those of the more traditional vortex tube reconnection process. Each of the three phases of vortex tube reconnection described by Melander & Hussain ( Phys. Fluids A, vol. 1(4), 1989, pp. 633–635) are found to have counterparts in the vortex cutting problem, although we also point out numerous differences in the detailed mechanics by which these phases are achieved. Of particular importance in the vortex cutting process is the presence of vorticity generation from the blade surface within the reconnection region and the presence of strong vortex stretching due to the ambient flow about the blade leading edge. A simple exact Navier–Stokes solution is presented that describes the process by which incident vorticity is stretched and carried towards the surface by the ambient flow, and then interacts with and is eventually annihilated by diffusive interaction with vorticity generated at the surface. The model combines a Hiemenz straining flow, a Burgers vortex sheet and a Stokes first problem boundary layer, resulting in a nonlinear ordinary differential equation and a partial differential equation in two scaled time and distance variables that must be solved numerically. The simple model predictions exhibit qualitative agreement with the full numerical simulation results for vorticity annihilation near the leading-edge stagnation point during vortex cutting.
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- Award ID(s):
- 1144388
- PAR ID:
- 10343133
- Date Published:
- Journal Name:
- Journal of Fluid Mechanics
- Volume:
- 782
- ISSN:
- 0022-1120
- Page Range / eLocation ID:
- 37 to 62
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1017/jfm.2015.531
