scholarly journals Numerical Simulation of Air Vortex Ring discharged by Air Cannon

2008 ◽  
Vol 28-1 (1) ◽  
pp. 223-223
Author(s):  
Toru KOMORIYA
Keyword(s):  
Numerical Simulation ◽  
Vortex Ring

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.

Passive scalar mixing in vortex rings

2007 ◽  
Vol 582 ◽  
pp. 449-461 ◽  
Author(s):  
RAJES SAU ◽  
KRISHNAN MAHESH
Keyword(s):  
Numerical Simulation ◽  
Direct Numerical Simulation ◽  
Vortex Ring ◽  
Nozzle Exit ◽  
Passive Scalar ◽  
Rate Of Change ◽  
Vortex Rings ◽  
Ambient Fluid ◽  
Stroke Length ◽  
Formation Number

Direct numerical simulation is used to study the mixing of a passive scalar by a vortex ring issuing from a nozzle into stationary fluid. The ‘formation number’ (Gharibet al. J. Fluid Mech.vol. 360, 1998, p. 121), is found to be 3.6. Simulations are performed for a range of stroke ratios (ratio of stroke length to nozzle exit diameter) encompassing the formation number, and the effect of stroke ratio on entrainment and mixing is examined. When the stroke ratio is greater than the formation number, the resulting vortex ring with trailing column of fluid is shown to be less effective at mixing and entrainment. As the ring forms, ambient fluid is entrained radially into the ring from the region outside the nozzle exit. This entrainment stops once the ring forms, and is absent in the trailing column. The rate of change of scalar-containing fluid is found to depend linearly on stroke ratio until the formation number is reached, and falls below the linear curve for stroke ratios greater than the formation number. This behaviour is explained by considering the entrainment to be a combination of that due to the leading vortex ring and that due to the trailing column. For stroke ratios less than the formation number, the trailing column is absent, and the size of the vortex ring increases with stroke ratio, resulting in increased mixing. For stroke ratios above the formation number, the leading vortex ring remains the same, and the length of the trailing column increases with stroke ratio. The overall entrainment decreases as a result.

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
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