scholarly journals Mathematical Modelling of the Elliptical Vortex Ring in a Viscous Fluid with the Vortex Filament Method

2021 ◽  
pp. 46-61
Author(s):  
O. S. Kotsur
Keyword(s):  
Viscous Fluid ◽  
Vortex Ring ◽  
Diffusion Rate ◽  
Grid Method ◽  
Vortex Method ◽  
Vortex Filament ◽  
Viscosity Model ◽  
Complete Agreement ◽  
Vortex Lines ◽  
Vortex Filament Method

The article deals with modelling an elliptical vortex ring in a viscous fluid using the Lagrangian vortex filament method. The novelty is that earlier only inviscid flows restricted vortex filament method application. The proposed viscosity model uses an analogue of the diffusion rate method, which is widely applied to simulate plane-parallel and axisymmetric flows of viscous fluid. A transfer of the formula of a diffusion rate from two-dimensional flows to the model of spatial vortex filament is due to assumption that swirling of vortex lines (helicity of vorticity) is unavailable. Despite the laxity of the diffusion rate model for general spatial flows, its application enables taking into account the effect of viscous diffusion of vorticity, which provides expansion of vortex tubes in space. The paper formulates the vortex filament method in which the filaments are broken into the vortex segments. Such discretization enables turning from the equation of vorticity evolution in partial derivatives to a system of ordinary differential equations with respect to the parameters of the segments. Formulas to calculate a filament system-induced flow rate as well as formulas to perform approximate calculation of an analogue of the diffusion rate are given.The objective is to propose the viscosity model as an application to the vortex filament method by the example of modelling the evolution of an elliptical vortex ring in viscous fluid. The calculation results obtained by the vortex method are compared with the existing experiment and with the calculation performed by the grid method in the OpenFOAM package. A feature of the problem is that there are zones of nonzero helicity of vorticity where the proposed model of viscosity, strictly speaking, is not correct. It is shown that the results of calculations are in good agreement with each other and are in complete agreement with experiment. This allows saying that the effects of swirling vortex lines do not significantly affect the results of modelling a specific example of the spatial flow of viscous fluid by the proposed modification of the vortex filament method.

scholarly journals Deformation of an elliptic vortex ring by three-dimensional discrete vortex filament method

1990 ◽  
Vol 10 (1Supplement) ◽  
pp. 79-82
Author(s):  
Tsutomu NOZAKI ◽  
Hiroshi MAEKAWA ◽  
Kazunobu FUTATUISHI ◽  
Tetsuo NURUKI
Keyword(s):  
Vortex Ring ◽  
Three Dimensional ◽  
Vortex Filament ◽  
Discrete Vortex ◽  
Vortex Filament Method

Vortex Filament Method

1990 ◽  
Vol 10 (1) ◽  
pp. 75-102 ◽  
Author(s):  
JUAN SOLER
Keyword(s):  
Vortex Filament ◽  
Vortex Filament Method

Lifting Line Free Wake Vortex Filament Method for the Evaluation of Floating Offshore Wind Turbines: First Step — Validation for Fixed Wind Turbines

2019 ◽  
Author(s):  
Raquel Martín-San-Román ◽  
José Azcona-Armendáriz ◽  
Alvaro Cuerva-Tejero
Keyword(s):  
Wind Turbines ◽  
Vortex Filament ◽  
Offshore Wind ◽  
Critical Parameters ◽  
Aerodynamic Model ◽  
Floating Offshore Wind Turbines ◽  
Free Wake ◽  
The Impact ◽  
Lifting Line ◽  
Vortex Filament Method

Abstract An in-house computational tool, called MIST, has been developed to improve the accuracy of the aerodynamic loads predictions of floating wind turbines. MIST has an aerodynamic module based on a Free Vortex filament Method (FVM) for the wake combined with a Lifting Line (LL) model for the blades. This aerodynamic model has been validated, in this first instance, for an onshore configuration against well known experimental data. Different options for the critical parameters of the code have been analyzed to get a deeper understanding of the impact of certain assumptions of this kind of models.

Vortices in Motionless Media

1990 ◽  
Vol 43 (12) ◽  
pp. 297-309 ◽  
Author(s):  
A. T. Winfree
Keyword(s):  
Mathematical Models ◽  
Chemical Reactions ◽  
Heart Muscle ◽  
Local Reaction ◽  
Three Dimensional ◽  
Vortex Filament ◽  
Local Geometry ◽  
Lateral Motion ◽  
Local Activation ◽  
Vortex Lines

Three-dimensional continua capable of recurrent local activation are observed—both in the laboratory and in mathematical models—to support persistent self-organizing patterns of activity most conveniently described in terms of vortex lines. These lines generally close in rings, which may be linked and knotted. In some cases they adopt stable configurations resembling tiny dynamos of millimeter dimensions. The dynamics of these “organizing centers” has been investigated in certain chemical reactions, in heart muscle, and numerically in digital computers. The pertinent mathematical principles appear to entail consequences of local reaction and neighborhood diffusion, in the form of a dependency of the vortex filament’s lateral motion upon its local geometry and, when too closely approached by another segment of vortex filament, upon the distance and orientation involved.

scholarly journals STOCHASTIC VORTEX BLOBS METHOD TO STUDY AXISYMMETRIC FLOWS OF INCOMPRESSIBLE VISCOUS FLUID

2016 ◽  
Vol 12 (10) ◽  
pp. 6739-6750
Author(s):  
M. R Hedar ◽  
R. S Kamel
Keyword(s):  
Viscous Fluid ◽  
Legendre Polynomials ◽  
Vortex Method ◽  
Stochastic Equations ◽  
Velocity Fields ◽  
Boundary Integral ◽  
Incompressible Viscous Fluid ◽  
Two Dimensional ◽  
Complete Elliptic Integrals ◽  
Total Velocity

This paper presents the mathematical and computational formulations of the stochastic Vortex Blobs Method (VBM). It isshow that how the method can be used to cover axisymmetric flows of incompressible viscous fluid. Also, the initialboundary problem is solved by using the Lagrangian vortex method. This method seems to be an extension of the well known two dimensional vortex blob method. When applying and extending this method two steps are required. First, wehave to design an axisymmetric vorticity carrier by using the standard functions as complete elliptic integrals and Legendre polynomials. Second, it is necessary to formulate the appropriate Neumann problem and boundary integral equation to find the potential velocity fields. Both steps are used to describe and compute the total velocity field and formulate the Ito stochastic equations which describing the motion of vorticity carriers.

scholarly journals Real-Time Smoke Simulation based on Vortex Method

2021 ◽  
Author(s):  
Fei Wan ◽  
Jingpu Zhang ◽  
Lizheng Guo ◽  
Yunchang Liu
Keyword(s):  
Fluid Dynamics ◽  
Real Time ◽  
Hybrid Method ◽  
Grid Method ◽  
Particle Method ◽  
Vortex Method ◽  
Experimental Methods ◽  
Numerical Dissipation ◽  
Simulation Based ◽  
Smoke Simulation

In this paper, we use three different experimental methods (particle method, grid method and hybrid method) to model and simulate the smoke from the perspective of fluid dynamics. Through the comparison of different methods, we conclude: The particle method can avoid the numerical dissipation problem caused by grid calculation, but it also brings problems such as the distortion of the trajectory of the example. The grid method is accurate in calculation, but it is prone to numerical dissipation and loss of details. Finally, we choose the hybrid method to store the vorticity in the form of particles in vortex particles, avoiding the numerical dissipation problem caused by the use of grids, and including rich turbulence, which perfectly shows the simulation effect of smoke.

scholarly journals Quantized Vortex Rings and Loop Solitons

2020 ◽  
Vol 201 (1-2) ◽  
pp. 11-17
Author(s):  
P. J. Green ◽  
M. J. Grant ◽  
J. W. Nevin ◽  
P. M. Walmsley ◽  
A. I. Golov
Keyword(s):  
Vortex Ring ◽  
Vortex Line ◽  
Quantum Turbulence ◽  
Temperature Limit ◽  
Quantized Vortex ◽  
Vortex Rings ◽  
Zero Temperature ◽  
Vortex Lines ◽  
Small Vortex ◽  
Vortex Filament Model

Abstract The vortex filament model is used to investigate the interaction of a quantized vortex ring with a straight vortex line and also the interaction of two solitons traveling in opposite directions along a vortex. When a ring reconnects with a line, we find that a likely outcome is the formation of a loop soliton. When they collide, loop solitons reconnect as they overlap each other producing either one or two vortex rings. These simulations are relevant for experiments on quantum turbulence in the zero temperature limit where small vortex rings are expected to be numerous. It seems that loop solitons might also commonly occur on vortex lines as they act as transient states between the absorption of a vortex ring before another ring is emitted when the soliton is involved in a reconnection.

Dynamics of thin vortex rings

2008 ◽  
Vol 609 ◽  
pp. 319-347 ◽  
Author(s):  
IAN S. SULLIVAN ◽  
JOSEPH J. NIEMELA ◽  
ROBERT E. HERSHBERGER ◽  
DIOGO BOLSTER ◽  
RUSSELL J. DONNELLY
Keyword(s):  
Viscous Fluid ◽  
Vortex Ring ◽  
Long Range ◽  
Direct Measurement ◽  
Vortex Rings ◽  
Inviscid Fluid ◽  
Core Size ◽  
Physical Pendulum ◽  
Range Study

As part of a long-range study of vortex rings, their dynamics, interactions with boundaries and with each other, we present the results of experiments on thin core rings generated by a piston gun in water. We characterize the dynamics of these rings by means of the traditional equations for such rings in an inviscid fluid suitably modifying them to be applicable to a viscous fluid. We develop expressions for the radius, core size, circulation and bubble dimensions of these rings. We report the direct measurement of the impulse of a vortex ring by means of a physical pendulum.

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