scholarly journals Numerical Simulation of a Vortex Ring Interaction with a Density Interface

1991 ◽  
Vol 3 (9) ◽  
pp. 2028-2028 ◽  
Author(s):  
Daniel L. Marcus ◽  
John B. Bell ◽  
Michael Welcome ◽  
Michael Allison
Keyword(s):  
Numerical Simulation ◽  
Vortex Ring ◽  
Density Interface ◽  
Ring Interaction

scholarly journals Numerical stability analysis of a vortex ring with swirl

2019 ◽  
Vol 878 ◽  
pp. 5-36 ◽  
Author(s):  
Yuji Hattori ◽  
Francisco J. Blanco-Rodríguez ◽  
Stéphane Le Dizès
Keyword(s):  
Numerical Simulation ◽  
Growth Rate ◽  
Direct Numerical Simulation ◽  
Vortex Ring ◽  
Stokes Equations ◽  
Base Flow ◽  
Critical Layer ◽  
Navier Stokes ◽  
Instability Mode ◽  
Navier Stokes Equations

The linear instability of a vortex ring with swirl with Gaussian distributions of azimuthal vorticity and velocity in its core is studied by direct numerical simulation. The numerical study is carried out in two steps: first, an axisymmetric simulation of the Navier–Stokes equations is performed to obtain the quasi-steady state that forms a base flow; then, the equations are linearized around this base flow and integrated for a sufficiently long time to obtain the characteristics of the most unstable mode. It is shown that the vortex rings are subjected to curvature instability as predicted analytically by Blanco-Rodríguez & Le Dizès (J. Fluid Mech., vol. 814, 2017, pp. 397–415). Both the structure and the growth rate of the unstable modes obtained numerically are in good agreement with the analytical results. However, a small overestimation (e.g. 22 % for a curvature instability mode) by the theory of the numerical growth rate is found for some instability modes. This is most likely due to evaluation of the critical layer damping which is performed for the waves on axisymmetric line vortices in the analysis. The actual position of the critical layer is affected by deformation of the core due to the curvature effect; as a result, the damping rate changes since it is sensitive to the position of the critical layer. Competition between the curvature and elliptic instabilities is also investigated. Without swirl, only the elliptic instability is observed in agreement with previous numerical and experimental results. In the presence of swirl, sharp bands of both curvature and elliptic instabilities are obtained for $\unicode[STIX]{x1D700}=a/R=0.1$, where $a$ is the vortex core radius and $R$ the ring radius, while the elliptic instability dominates for $\unicode[STIX]{x1D700}=0.18$. New types of instability mode are also obtained: a special curvature mode composed of three waves is observed and spiral modes that do not seem to be related to any wave resonance. The curvature instability is also confirmed by direct numerical simulation of the full Navier–Stokes equations. Weakly nonlinear saturation and subsequent decay of the curvature instability are also observed.

Spectrum study on unsteadiness of shock wave–vortex ring interaction

2018 ◽  
Vol 30 (5) ◽  
pp. 056101 ◽  
Author(s):  
Xiangrui Dong ◽  
Yonghua Yan ◽  
Yong Yang ◽  
Gang Dong ◽  
Chaoqun Liu
Keyword(s):  
Shock Wave ◽  
Vortex Ring ◽  
Ring Interaction

Frequency Investigation on Unsteadiness of Shock-Vortex Ring Interaction

2018 ◽  
Author(s):  
Xiangrui Dong ◽  
Yonghua Yan ◽  
Yong Yang ◽  
Chaoqun Liu
Keyword(s):  
Vortex Ring ◽  
Ring Interaction
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