Modeling Vortex Shedding Over a Stationary Circular Cylinder

2006 ◽  
Author(s):  
Osama Marzouk ◽  
Ali H. Nayfeh ◽  
Imran Akhtar ◽  
Haider N. Arafat
Keyword(s):  
Circular Cylinder ◽  
Stokes Equations ◽  
Reynolds Numbers ◽  
Offshore Structures ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Building Models ◽  
Vortex Induced Vibrations ◽  
The Time Domain ◽  
Lift And Drag

Numerical simulations of flow past a stationary circular cylinder at different Reynolds numbers have been performed using a computational fluid dynamics (CFD) solver that is based on the Reynolds-averaged Navier-Stokes equations (RANS). The results obtained are used to develop reduced-order models for the lift and drag coefficients. The models do not only match the numerical simulation results in the time domain, but also in the spectral domain. They capture the steady-state region with excellent accuracy. Further, the models are verified by comparing their results in the transient region with their counterparts from the CFD simulations and a very good agreement is found. The work performed here is a step towards building models for vortex-induced vibrations (VIV) encountered in offshore structures, such as risers and spars.

Unsteady flow past a rotating circular cylinder at Reynolds numbers 103 and 104

1990 ◽  
Vol 220 ◽  
pp. 459-484 ◽  
Author(s):  
H. M. Badr ◽  
M. Coutanceau ◽  
S. C. R. Dennis ◽  
C. Ménard
Keyword(s):  
Reynolds Number ◽  
Circular Cylinder ◽  
Unsteady Flow ◽  
Rotation Rate ◽  
Stokes Equations ◽  
Reynolds Numbers ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Number Range ◽  
Flow Past

The unsteady flow past a circular cylinder which starts translating and rotating impulsively from rest in a viscous fluid is investigated both theoretically and experimentally in the Reynolds number range 103 [les ] R [les ] 104 and for rotational to translational surface speed ratios between 0.5 and 3. The theoretical study is based on numerical solutions of the two-dimensional unsteady Navier–Stokes equations while the experimental investigation is based on visualization of the flow using very fine suspended particles. The object of the study is to examine the effect of increase of rotation on the flow structure. There is excellent agreement between the numerical and experimental results for all speed ratios considered, except in the case of the highest rotation rate. Here three-dimensional effects become more pronounced in the experiments and the laminar flow breaks down, while the calculated flow starts to approach a steady state. For lower rotation rates a periodic structure of vortex evolution and shedding develops in the calculations which is repeated exactly as time advances. Another feature of the calculations is the discrepancy in the lift and drag forces at high Reynolds numbers resulting from solving the boundary-layer limit of the equations of motion rather than the full Navier–Stokes equations. Typical results are given for selected values of the Reynolds number and rotation rate.

scholarly journals An asymptotic expansion for the vortex-induced vibrations of a circular cylinder

2011 ◽  
Vol 671 ◽  
pp. 137-167 ◽  
Author(s):  
PHILIPPE MELIGA ◽  
JEAN-MARC CHOMAZ
Keyword(s):  
Circular Cylinder ◽  
Stokes Equations ◽  
Structural Parameters ◽  
Coupled System ◽  
Reynolds Numbers ◽  
Navier Stokes ◽  
Fluid Equation ◽  
Wake Oscillator ◽  
Vortex Induced Vibrations ◽  
Lower Magnitude

This paper investigates the vortex-induced vibrations (VIV) of a spring-mounted circular cylinder. We compute analytically the leading-order equations describing the nonlinear interaction of the fluid and structure modes by carrying out an asymptotic analysis of the Navier–Stokes equations close to the threshold of instability of the fluid-only system. We show that vortex-shedding can occur at subcritical Reynolds numbers as a result of the coupled system being linearly unstable to the structure mode. We also show that resonance occurs when the frequency of the nonlinear limit cycle matches the natural frequency of the cylinder, the displacement being then in phase with the flow-induced lift fluctuations. Using an extension of this model meant to encompass the effect of the low-order added-mass and damping forces induced by the displaced fluid, we show that the amount of energy that can be extracted from the flow can be optimized by an appropriate choice of the structural parameters. Finally, we suggest a possible connection between the present ‘exact’ model and the empirical wake oscillator model used to study VIV at high Reynolds numbers. We show that for the low Reynolds numbers considered here, the effect of the structure on the fluid can be represented by a first coupling term proportional to the cylinder acceleration in the fluid equation, and by a second term of lower magnitude, which can stem either from an integral term or from a term proportional to the third derivative of the cylinder position.

scholarly journals Secondary frequencies in the wake of a circular cylinder with vortex shedding

1991 ◽  
Vol 225 ◽  
pp. 557-574 ◽  
Author(s):  
Saul S. Abarbanel ◽  
Wai Sun Don ◽  
David Gottlieb ◽  
David H. Rudy ◽  
James C. Townsend
Keyword(s):  
Circular Cylinder ◽  
Boundary Conditions ◽  
Stokes Equations ◽  
Numerical Study ◽  
Numerical Algorithms ◽  
Reynolds Numbers ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Low Reynolds Numbers ◽  
Two Dimensional Flow

A detailed numerical study of two-dimensional flow past a circular cylinder at moderately low Reynolds numbers has been conducted using three different numerical algorithms for solving the time-dependent compressible Navier–Stokes equations. It was found that if the algorithm and associated boundary conditions were consistent and stable, then the major features of the unsteady wake were well predicted. However, it was also found that even stable and consistent boundary conditions could introduce additional periodic phenomena reminiscent of the type seen in previous wind-tunnel experiments. However, these additional frequencies were eliminated by formulating the boundary conditions in terms of the characteristic variables. An analysis based on a simplified model provides an explanation for this behaviour.

scholarly journals The flow induced by a rotationally oscillating and translating circular cylinder

2000 ◽  
Vol 407 ◽  
pp. 123-144 ◽  
Author(s):  
S. C. R. DENNIS ◽  
P. NGUYEN ◽  
SERPIL KOCABIYIK
Keyword(s):  
Reynolds Number ◽  
Circular Cylinder ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Interesting Phenomenon ◽  
Navier Stokes Equations ◽  
Drag Coefficients ◽  
Small Times ◽  
High Reynolds ◽  
Lift And Drag

The temporal development of two-dimensional viscous incompressible flow induced by an impulsively started circular cylinder which performs time-dependent rotational oscillations about its axis and translates at right angles to this axis is investigated. The investigation is based on the solutions of the unsteady Navier–Stokes equations. A series expansion for small times is developed. The Navier–Stokes equations are also integrated by a spectral–finite difference method for moderate values of time for both moderate and high Reynolds numbers. The numerical method is checked with the results of the analytical solution. The effects of the Reynolds number and of the forcing Strouhal number S on the laminar asymmetric flow structure in the near-wake region are studied. The lift and drag coefficients are also extracted from numerical results. An interesting phenomenon has been observed both in the flow patterns and in the behaviour of drag coefficients for S = π/2 at Reynolds number R = 500 and is discussed. For comparison purposes the start-up flow is determined numerically at a low Reynolds number and is found to be in good agreement with previous experimental predictions.

3D Simulation of Vortex Shedding Past Tapered Circular Cylinders in Subcritical Reynolds Numbers

2012 ◽  
Author(s):  
V. Tamimi ◽  
M. Zeinoddini ◽  
A. Bakhtiari ◽  
M. Golestani
Keyword(s):  
Circular Cylinder ◽  
Vortex Shedding ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Flow Characteristics ◽  
Reynolds Numbers ◽  
Circular Cylinders ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
High Reynolds

In this paper results from simulating the vortex shedding phenomena behind a fixed tapered circular cylinder, at relatively high Reynolds numbers, are reported. Ansys-CFX computational fluid dynamics model, based on solving three-dimensional (3D) incompressible transient Navier Stokes equations, is employed for this purpose. The geometries applied in the models resemble those used in wind tunnel experiments by other researchers. The taper slope along the cylinder span is uniform with a tangent of 24:1. The diameter at mid-span of the cylinder equals to 0.0389 m. The Reynolds number (based on the mid-span diameter) is around 29,000. The computational model has first been calibrated against experiments for uniform 3D cylinders as well as results from a Direct Numerical Simulation of turbulent wake with vortex shedding past a uniform circular cylinder, as obtained by other researchers. The main flow characteristics for tapered cylinders such as vortex dislocations and splitting, cellular vortex shedding, oblique vortex shedding and the variation of the vorticity patterns along the tapered cylinder could be obtained from the simulations.

A Numerical Study of Unsteady Laminar Forced Convection From a Circular Cylinder

1976 ◽  
Vol 98 (2) ◽  
pp. 303-307 ◽  
Author(s):  
P. C. Jain ◽  
B. S. Goel
Keyword(s):  
Nusselt Number ◽  
Circular Cylinder ◽  
Forced Convection ◽  
Stokes Equations ◽  
Numerical Study ◽  
Reynolds Numbers ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Laminar Forced Convection ◽  
Good Agreement

A numerical investigation of an unsteady laminar forced convection from a circular cylinder is presented. The Navier-Stokes equations and the energy equation for an unsteady incompressible fluid flow are solved by the finite difference method. The results are obtained at Reynolds numbers 100 and 200. The temperature field around the cylinder is obtained throughout the region of computation and is shown by isotherms at different times. The variations of the local Nusselt number around the cylinder at different times are computed and shown by graphs. The mean Nusselt number and the Strouhal number are also calculated. The computed results are compared with the other available experimental and theoretical results and are found to be in good agreement with them.

Symmetrical flow past a uniformly accelerated circular cylinder

1974 ◽  
Vol 65 (3) ◽  
pp. 461-480 ◽  
Author(s):  
W. M. Collins ◽  
S. C. R. Dennis
Keyword(s):  
Circular Cylinder ◽  
Stokes Equations ◽  
Reynolds Numbers ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Method Of Solution ◽  
Small Times ◽  
Accurate Procedure ◽  
Logical Extension ◽  
Good Agreement

The flow normal to an infinite circular cylinder which is uniformly accelerated from rest in a viscous fluid is considered. The flow is assumed to remain symmetrical about the direction of motion of the cylinder. Two types of solution are presented. In the first an expansion in powers of the time from the start of the motion is given which extends the results of boundary-layer theory by taking into account corrections for finite Reynolds numbers. Physical properties of the flow for small times and finite but large Reynolds numbers are calculated from this expansion. In the second method of solution the Navier-Stokes equations are integrated by an accurate procedure which is a logical extension of the solution in powers of the time. Results are obtained forR2= 97·5, 5850, 122 × 103and ∞, whereRis the Reynolds number. This is defined asR= 2a(ab)½/v, whereais the radius of the cylinder,bthe uniform acceleration andvthe kinematic viscosity of the fluid. The methods are in good agreement for small times.The numerical method of integration has been carried to moderate times and various flow properties have been calculated. The growth of the length of the separated wake behind the cylinder forR2= 97·5, 5850 and 122 × 103is compared with the results of recent experimental measurements. The agreement is only moderate forR2= 97·5 but it improves greatly asRincreases. The numerical integrations were continued in each case until the implicit method of integration failed to converge, which terminated the procedure. A secondary vortex appeared on the surface of the cylinder for the caseR2= 122 × 103.

Simulation of Unsteady Flow Around a Cylinder

2015 ◽  
Vol 3 (2) ◽  
pp. 28-49
Author(s):  
Ridha Alwan Ahmed
Keyword(s):  
Stokes Equations ◽  
Lift Coefficient ◽  
Reynolds Numbers ◽  
Mean Value ◽  
Navier Stokes ◽  
Cylinder Surface ◽  
Navier Stokes Equations ◽  
Flow Around A Cylinder ◽  
Numerical Grid ◽  
Good Agreement

       In this paper, the phenomena of vortex shedding from the circular cylinder surface has been studied at several Reynolds Numbers (40≤Re≤ 300).The 2D, unsteady, incompressible, Laminar flow, continuity and Navier Stokes equations have been solved numerically by using CFD Package FLUENT. In this package PISO algorithm is used in the pressure-velocity coupling.        The numerical grid is generated by using Gambit program. The velocity and pressure fields are obtained upstream and downstream of the cylinder at each time and it is also calculated the mean value of drag coefficient and value of lift coefficient .The results showed that the flow is strongly unsteady and unsymmetrical at Re>60. The results have been compared with the available experiments and a good agreement has been found between them

Burgers turbulence model for a channel flow

1971 ◽  
Vol 47 (2) ◽  
pp. 321-335 ◽  
Author(s):  
Jon Lee
Keyword(s):  
Channel Flow ◽  
Stokes Equations ◽  
Turbulent Channel Flow ◽  
Reynolds Numbers ◽  
Navier Stokes ◽  
Amplitude Equations ◽  
Fourier Amplitude ◽  
Navier Stokes Equations ◽  
Burgers Model ◽  
Model Dynamics

The truncated Burgers models have a unique equilibrium state which is defined continuously for all the Reynolds numbers and attainable from a realizable class of initial disturbances. Hence, they represent a sequence of convergent approximations to the original (untruncated) Burgers problem. We have pointed out that consideration of certain degenerate equilibrium states can lead to the successive turbulence-turbulence transitions and finite-jump transitions that were suggested by Case & Chiu. As a prototype of the Navier–Stokes equations, Burgers model can simulate the initial-value type of numerical integration of the Fourier amplitude equations for a turbulent channel flow. Thus, the Burgers model dynamics display certain idiosyncrasies of the actual channel flow problem described by a truncated set of Fourier amplitude equations, which includes only a modest number of modes due to the limited capability of the computer at hand.

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