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On the starting vortex generated by a translating and rotating flat plate

Published online by Cambridge University Press:  10 November 2020

D. I. Pullin  and
John E. Sader Open the ORCID record for John E. Sader [Opens in a new window]
D. I. Pullin*
Affiliation:
Graduate Aerospace Laboratories, California Institute of Technology, Pasadena, CA91125, USA
John E. Sader
Affiliation:
ARC Centre of Excellence in Exciton Science, School of Mathematics and Statistics, University of Melbourne, Victoria3010, Australia Department of Physics, California Institute of Technology, Pasadena, CA91125, USA
*
†Email address for correspondence: [email protected]
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Abstract

We consider the trailing-edge vortex produced in an inviscid fluid by the start-up motion of a two-dimensional flat plate. A general starting motion is studied that includes the initial angle-of-attack of the plate (which may be zero), individual time power laws for plate translational and rotational speeds and the pivot position for plate rotation. A vortex-sheet representation for a start-up separated flow at the trailing edge is developed whose time-wise evolution is described by a Birkhoff–Rott equation coupled to an appropriate Kutta condition. This description includes convection by the outer flow, rotation and vortex-image self-induction. It admits a power-law similarity solution for the (small-time) primitive vortex, leading to an equation set where each term carries its own time-wise power-law factor. A set of four general plate motions is defined. Dominant-balance analysis of this set leads to discovery of three distinct start-up vortex-structure types that form the basis for all vortex motion. The properties of each type are developed in detail for some special cases. Numerical and analytical solutions are described and transition between solution types is discussed. Singular and degenerate vortex behaviour is discovered which may be due to the absence of fluid viscosity. An interesting case is start-up motion with zero initial angle of attack coupled to power-law plate rotation for which time-series examples are given that can be compared to high Reynolds number viscous flows.

JFM classification

Vortex Flows: Vortex dynamics Vortex Flows: Vortex shedding
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 906 , 10 January 2021 , A9
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Copyright
© The Author(s), 2020. Published by Cambridge University Press

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References

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