Stability of symmetric vortices in two dimensions and over three-dimensional slender conical bodies

Abstract

A general stability condition for vortices in a two-dimensional incompressible inviscid flow field is presented. This condition is first applied to analyse the stability of symmetric vortices behind elliptic cylinders and circular cylinders with a splitter plate at the rear stagnation point. The effect of the size of the splitter plate on the stability of the vortices is studied. It is also shown that no stable symmetric vortices exist behind two-dimensional bodies based on the stability condition. The two-dimensional stability condition is then extended to analyse the absolute (temporal) stability of a symmetric vortex pair over three-dimensional slender conical bodies. The threedimensional problem is reduced to a vortex stability problem for a pair of vortices in two dimensions by using the conical flow assumption, classical slender-body theory, and postulated separation positions. The bodies considered include circular cones and highly swept flat-plate wings with and without vertical fins, and elliptic cones of various eccentricities. There exists an intermediate cone with a finite thickness ratio between the circular cone and the flat-plate delta wing for which the symmetric vortices change from being unstable to being stable at a given angle of attack. The effects of the fin height and the separation position on the stability of the vortices are studied. Results agree well with known experimental observations.

Stability of symmetric and asymmetric vortex pairs over slender conical wings and bodies

“…The type of instability studied in Ref. 7 and in the present article refers to a temporal evolution of the conical symmetric or asymmetric vortices. The flow stays conical before or after the disturbance.…”

Mechanism of frequency lock-in in vortex-induced vibrations at low Reynolds numbers

“…Apart from the global LSA method (Cai, Liu & Luo 2003;Crouch, Garbaruk & Magidov 2007;Crouch et al 2009;Leontini, Thompson & Hourigan 2010), the system identification method Dahan, Morgans & Lardeau 2012;Illingworth, Morgans & Rowley 2012;Brunton, Rowley & Williams 2013) has also been utilized for the characteristic analysis of unsteady flows in recent years. The present study focuses on finding a more accurate aerodynamic model for the cylinder wake flow by using a system identification method.…”

Flow Control over a Conical Forebody Using Duty-Cycled Plasma Actuators

“…In addition, conventional aerodynamic control surfaces become ineffective in such situations because of vortex wakes generated by the forebody. Much theoretical, computational, and experimental work has been spent on the understanding, prediction, and control of the onset of vortex asymmetry [1][2][3][4][5][6][7][8][9]. It has been found both computationally and experimentally that the vortices are very sensitive to small perturbations near the apex of a forebody [3,5,9].…”