Numerical Simulation of Vortex Induced Vibration Using the K-ε Model

2006 ◽  
Author(s):  
Juan B. V. Wanderley ◽  
Gisele H. B. Souza ◽  
Carlos Levi
Keyword(s):  
Numerical Simulation ◽  
Stokes Equations ◽  
Body Motion ◽  
Navier Stokes ◽  
Experimental Investigations ◽  
Real Problem ◽  
Navier Stokes Equations ◽  
Vortex Induced Vibration ◽  
Selection Of

Numerical simulations of Vortex Induced Vibration have been failing to duplicate accurately experimental data mostly due to the complexity of the physics involved in the real problem. Therefore, a careful and comprehensive investigation on CFD algorithms is still required to indicate the most suitable numerical scheme to handle such a complicate problem. Grid generation, boundary condition implementation, and coupling between the fluid flow governing equations and body motion equation are known to have strong influence on the qualities of the numerical results. This work presents results obtained from a long-term investigation featuring different CFD methods. The investigations enabled the selection of a very effective algorithm that showed an outstanding agreement between experiment and numerical simulation of the VIV phenomenon. Good agreement is obtained in the entire range of reduced velocity covered by the experimental investigations. The successful algorithm discussed here applies the Beam and Warming implicit scheme to solve the two-dimensional slightly compressible Navier–Stokes equations with the K-ε turbulence model to simulate the turbulent flow at the wake of the cylinder.

On Direct Numerical Simulation of Turbulent Flows

2011 ◽  
Vol 64 (2) ◽  
Author(s):  
Giancarlo Alfonsi
Keyword(s):  
Numerical Simulation ◽  
Direct Numerical Simulation ◽  
High Performance Computing ◽  
Turbulent Flows ◽  
High Performance ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Turbulent Shear ◽  
Navier Stokes Equations ◽  
Performance Computing

The direct numerical simulation of turbulence (DNS) has become a method of outmost importance for the investigation of turbulence physics, and its relevance is constantly growing due to the increasing popularity of high-performance-computing techniques. In the present work, the DNS approach is discussed mainly with regard to turbulent shear flows of incompressible fluids with constant properties. A body of literature is reviewed, dealing with the numerical integration of the Navier-Stokes equations, results obtained from the simulations, and appropriate use of the numerical databases for a better understanding of turbulence physics. Overall, it appears that high-performance computing is the only way to advance in turbulence research through the front of the direct numerical simulation.

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.

scholarly journals Effects of Hydrostatic Pocket Shape on the Flow Pattern and Pressure Distribution

1995 ◽  
Vol 1 (3-4) ◽  
pp. 225-235 ◽  
Author(s):  
M. J. Braun ◽  
M. Dzodzo
Keyword(s):  
Numerical Simulation ◽  
Pressure Distribution ◽  
Flow Pattern ◽  
Stokes Equations ◽  
The Other ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Hydrostatic Bearing ◽  
Collocated Grid ◽  
Dimensionless Formulation

The flow in a hydrostatic pocket is numerically simulated using a dimensionless formulation of the 2-D Navier-Stokes equations written in primitive variables, for a body fitted coordinates system, and applied through a collocated grid. In essence, we continue the work of Braun et al. 1993a, 1993b] and extend it to the study of the effects of the pocket geometric format on the flow pattern and pressure distribution. The model includes the coupling between the pocket flow and a finite length feedline flow, on one hand, and the pocket and its adjacent lands on the other hand. In this context we shall present, on a comparative basis, the flow and the pressure patterns at the runner surface for square, ramped-Rayleigh step, and arc of circle pockets. Geometrically all pockets have the same footprint, same lands length, and same capillary feedline. The numerical simulation uses the Reynolds number based on the lid(runner) velocity and the inlet jet strengthFas the dynamic similarity parameters. The study aims at establishing criteria for the optimization of the pocket geometry in the larger context of the performance of a hydrostatic bearing.

Viscosity Effects on the Radiation Hydrodynamics of Horizontal Cylinders

1991 ◽  
Vol 113 (4) ◽  
pp. 334-343 ◽  
Author(s):  
R. W. Yeung ◽  
C.-F. Wu
Keyword(s):  
Numerical Solutions ◽  
Stokes Equations ◽  
Small Body ◽  
Low Frequency ◽  
Body Motion ◽  
Navier Stokes ◽  
Inviscid Fluid ◽  
Viscous Effects ◽  
Navier Stokes Equations ◽  
Horizontal Cylinders

The problem of a body oscillating in a viscous fluid with a free surface is examined. The Navier-Stokes equations and boundary conditions are linearized using the assumption of small body-motion to wavelength ratio. Generation and diffusion of vorticity, but not its convection, are accounted for. Rotational and irrotational Green functions for a divergent and a vorticity source are presented, with the effects of viscosity represented by a frequency Reynolds number Rσ = g2/νσ3. Numerical solutions for a pair of coupled integral equations are obtained for flows about a submerged cylinder, circular or square. Viscosity-modified added-mass and damping coefficients are developed as functions of frequency. It is found that as Rσ approaches infinity, inviscid-fluid results can be recovered. However, viscous effects are important in the low-frequency range, particularly when Rσ is smaller than O(104).

Numerical Calculation on Vortex-Induced Vibration of the Circular Cylinder Using Low Reynolds Model in Hybrid Method

2009 ◽  
Author(s):  
Xingwei Zhang ◽  
Chaoying Zhou
Keyword(s):  
Numerical Calculation ◽  
Finite Volume Method ◽  
Finite Volume ◽  
Turbulence Model ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Vortex Induced Vibration ◽  
Mesh Method ◽  
Volume Method

Fundamental research on interaction between flow and structure is presented for computation the fluid dynamics of different two-dimensional oscillating models. The Navier-Stokes equations are solved using finite volume method. A multigrid mesh method which was applied to the situation of flow past the stagnating or vibrating cylinder is developed to simulate this type of flow. The interactive results between flow and structure rigid cylinders have been present. The computation fluid dynamic codes mainly with low Reynolds RANS solver are used to solve the impressible viscous Navier-Stokes equations. Finite volume method which is coupled with conformal hybrid mesh method is developed to simulate this type of flow. Numerical investigation focused on the response and the fluid forces on the cylinders and also observed the different shedding model in the wake. The numerical results are compared in detail with recent experimental and computational work. Present numerical comparison also showed that solution using different turbulence model will make the result have a little discrepancy and each turbulence model has respective characteristics in numerical solution on the vortex-induced vibration of the cylinder. In addition, the formation of the 2P vortex shedding model through the lock-in region and the beginning of the shedding model transformation in numerical calculation from 2S model to 2P model has been analyzed.

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