A Numerical Investigation of the Response of an Elastically Mounted Rigid Cylinder With Two Degrees of Freedom

2010 ◽  
Author(s):  
Bruno C. Ferreira ◽  
Marcelo A. Vitola ◽  
Juan B. V. Wanderley ◽  
Sergio H. Sphaier ◽  
Carlos A. Levi
Keyword(s):  
Experimental Data ◽  
Phase Angle ◽  
Degrees Of Freedom ◽  
Stokes Equations ◽  
Lift Coefficient ◽  
The Body ◽  
Curvilinear Coordinates ◽  
Two Degrees Of Freedom ◽  
Conservative Scheme ◽  
Rigid Cylinder

The vortex induced vibration (VIV) on a circular cylinder is investigated by the numerical solution of the Reynolds average Navier-Stokes equations. An upwind and Total Variation Diminishing (TVD) conservative scheme is used to solve the governing equations written in curvilinear coordinates and the k–ε turbulence model is used to simulate the turbulent flow in the wake of the body. The cylinder is supported by a spring and a damper and free to vibrate in the transverse and in-line directions. In previous work, numerical results for the amplitude of oscillation, vortex shedding frequency, and phase angle between lift and displacement were compared to experimental data obtained from Khalak and Williamson (1996) to validate the code for VIV simulations in the transverse direction. In the present work, results are obtained for phase angle, amplitude, frequency, and lift coefficient and compared to experimental data from Jauvtis and Williamson (2003) for an elastically mounted rigid cylinder with two degrees of freedom. Differences in the amplitude of oscillation between experimental and numerical data were observed for both direction. It seems that the fluid flow memory effect is an important aspect that should be taken in consideration on numerical simulation to reproduce the experimental results for VIV with 2DOF as pointed out by Moe and Wu [1].

A Numerical Investigation of the Hysteresis Effect on Vortex Induced Vibration on an Elastically Mounted Rigid Cylinder

2009 ◽  
Author(s):  
Juan B. V. Wanderley ◽  
Sergio H. Sphaier ◽  
Carlos Levi
Keyword(s):  
Vortex Shedding ◽  
Stokes Equations ◽  
Lift Coefficient ◽  
Practical Interest ◽  
Numerical Results ◽  
Hysteresis Effect ◽  
The Body ◽  
Curvilinear Coordinates ◽  
Vortex Induced Vibration ◽  
Conservative Scheme

The hysteresis effect on the vortex induced vibration (VIV) on a circular cylinder is investigated by the numerical solution of the Reynolds average Navier-Stokes equations. An upwind and Total Variation Diminishing (TVD) conservative scheme is used to solve the governing equations written in curvilinear coordinates and the k-ε turbulence model is used to simulate the turbulent flow in the wake of the body. The cylinder is supported by a spring and a damper and free to vibrate in the transverse direction. In previous work, numerical results for the amplitude of oscillation and vortex shedding frequency were compared to experimental data obtained from the literature to validate the code for VIV simulations. In the present work, results of practical interest are presented for the power absorbed by the system, phase angle, amplitude, frequency, and lift coefficient. The numerical results indicate that the hysteresis effect is observed only when the frequency of vortex shedding gets closer to the natural frequency of the structure in air.

The Response of an Elastically Mounted Rigid Cylinder Subjected to Vortex Shedding and Support Motion

2010 ◽  
Author(s):  
Luiz F. N. Soares ◽  
Juan B. V. Wanderley ◽  
Marcelo Vitola ◽  
Sergio H. Sphaier ◽  
Carlos Levi
Keyword(s):  
Vortex Shedding ◽  
Stokes Equations ◽  
The Body ◽  
Response Amplitude ◽  
Curvilinear Coordinates ◽  
Navier Stokes ◽  
Vortex Induced Vibration ◽  
Conservative Scheme ◽  
Rigid Cylinder ◽  
Support Motion

The vortex induced vibration (VIV) on a circular cylinder is investigated by the numerical solution of the two-dimensional Reynolds average Navier-Stokes equations. An upwind and Total Variation Diminishing (TVD) conservative scheme is used to solve the governing equations written in curvilinear coordinates and the k–ε turbulence model is used to simulate the turbulent flow in the wake of the body. The cylinder is supported by a spring and a damper and free to vibrate in the transverse direction. Results are obtained for the phase angle, amplitude, and frequency for an elastically mounted rigid cylinder subjected to vortex shedding and support motion. The numerical results showed the strong influence of the support motion on the response amplitude. This kind of scenario is found in the attachment between platform and riser. The motion of platforms on the ocean free surface can cause this kind of excitation and amplify the vortex induced vibration response amplitude of risers.

A Two-Dimensional Numerical Investigation of the Hysteresis Effect on Vortex Induced Vibration on an Elastically Mounted Rigid Cylinder

2011 ◽  
Vol 134 (2) ◽  
Author(s):  
Juan B. V. Wanderley ◽  
Sergio H. Sphaier ◽  
Carlos Levi
Keyword(s):  
Vortex Shedding ◽  
Stokes Equations ◽  
Lift Coefficient ◽  
Practical Interest ◽  
Numerical Results ◽  
Hysteresis Effect ◽  
The Body ◽  
Curvilinear Coordinates ◽  
Two Dimensional ◽  
Vortex Induced Vibration

The hysteresis effect on the vortex induced vibration (VIV) on a circular cylinder is investigated by the numerical solution of the two-dimensional Reynolds averaged Navier-Stokes equations. An upwind and total variation diminishing (TVD) conservative scheme is used to solve the governing equations written in curvilinear coordinates and the k-ɛ turbulence model is used to simulate the turbulent flow in the wake of the body. The cylinder is supported by a spring and a damper and free to vibrate in the transverse direction. In previous work, numerical results for the amplitude of oscillation and vortex shedding frequency were compared to experimental data obtained from the literature to validate the code for VIV simulations. In the present work, results of practical interest are presented for the power absorbed by the system, phase angle, amplitude, frequency, and lift coefficient. The numerical results indicate that the hysteresis effect is observed only when the frequency of vortex shedding gets closer to the natural frequency of the structure in air.

Validation of Vortex Induced Vibration With One Degree of Freedom

2010 ◽  
Author(s):  
Sicilia Pacheco ◽  
Marcelo A. Vitola ◽  
Juan B. V. Wanderley ◽  
Sergio H. Sphaier ◽  
Carlos A. Levi
Keyword(s):  
Stokes Equations ◽  
Lift Coefficient ◽  
Numerical Data ◽  
Curvilinear Coordinates ◽  
Navier Stokes ◽  
Vortex Induced Vibration ◽  
Conservative Scheme ◽  
End Plate ◽  
The Difference ◽  
Offshore Industry

The vortex induced vibration is an important problem for the offshore industry, due to the frequent use of structures, such as risers and umbilicals. In the last decade, the use of numerical methods to study the vortex induced vibration has increased. Some disagreement between numerical and experimental results has been verified in the literature. In the present work, the numerical model solves the Reynolds average Navier-Stokes equations using an upwind and a Total Variation Diminishing (TVD) conservative scheme, written in curvilinear coordinates. The turbulent flow in the wake of the cylinder has been modelled using the k–ε model. The cylinder is supported by a spring and a damper and free to vibrate in the transverse direction. Results obtained for phase angle, amplitude, frequency, and lift coefficient are compared to experimental data from Morse et al. [1]. The results indicate that the two dimensional simulation represents better the behaviour of cylinder displacement obtained experimentally using the unattached or attached end plate setup used by Morse et al. [1]. These results suggest that some difference between experimental and numerical data could be associated with the end condition used in the experiments. For the case using the unattached or attached end plate the difference in the peak amplitude between experimental and present results seems to be related with the initial condition adopted.

scholarly journals Euler Solutions for Transonic Oscillating Cascade Flows Using Dynamic Triangular Meshes

1993 ◽  
Author(s):  
C. J. Hwang ◽  
S. Y. Yang
Keyword(s):  
Experimental Data ◽  
Phase Angle ◽  
Transonic Flow ◽  
Lift Coefficient ◽  
Pressure Coefficient ◽  
Oscillation Amplitude ◽  
Time History ◽  
Present Approach ◽  
Instantaneous Pressure ◽  
Interblade Phase Angle

The modified total-variation-diminishing scheme and an improved dynamic triangular mesh algorithm are presented to investigate the transonic oscillating cascade flows. In a Cartesian coordinate system, the unsteady Euler equations are solved. To validate the accuracy of the present approach, transonic flow around single NACA 0012 airfoil pitching harmonically about the quarter chord is computed first. The calculated instantaneous pressure coefficient distributions during a cycle of motion compare well with the related numerical and experimental data. To further evaluate the present approach involving nonzero interblade phase angle, the calculations of transonic flow around oscillating cascade of two unstaggered NACA 0006 blades with interblade phase angle equal to 180 deg are performed. From the instantaneous pressure coefficient distributions and time history of lift coefficient, the present approach, where a simple spatial treatment is utilized on the periodic boundaries, gives satisfactory results. By using the above solution procedure, transonic flows around oscillating cascade of four biconvex blades with different oscillation amplitudes, reduced frequencies and interblade phase angles are investigated. From the distributions of magnitude and phase angle of the dynamic pressure difference coefficient, the present numerical results show better agreement with the experimental data than those from the linearized theory in most of the cases. For every quarter of one cycle, the pressure contours repeat and proceed one pitch distance in the upward or downward direction for interblade phase angle equal to −90 deg or 90 deg, respectively. The unsteady pressure wave and shock behaviors are observed. From the lift coefficient distributions, it is further confirmed that the oscillation amplitude, interblade phase angle and reduced frequency all have significant effects on the transonic oscillating cascade flows.

Euler Solutions for Transonic Oscillating Cascade Flows Using Dynamic Triangular Meshes

1995 ◽  
Vol 117 (3) ◽  
pp. 393-400 ◽  
Author(s):  
C. J. Hwang ◽  
S. Y. Yang
Keyword(s):  
Experimental Data ◽  
Phase Angle ◽  
Transonic Flow ◽  
Lift Coefficient ◽  
Pressure Coefficient ◽  
Oscillation Amplitude ◽  
Time History ◽  
Present Approach ◽  
Instantaneous Pressure ◽  
Interblade Phase Angle

The modified total-variation-diminishing scheme and an improved dynamic triangular mesh algorithm are presented to investigate the transonic oscillating cascade flows. In a Cartesian coordinate system, the unsteady Euler equations are solved. To validate the accuracy of the present approach, transonic flow around a single NACA 0012 airfoil pitching harmonically about the quarter chord is computed first. The calculated instantaneous pressure coefficient distribution during a cycle of motion compare well with the related numerical and experimental data. To evaluate further the present approach involving nonzero interblade phase angle, the calculations of transonic flow around an oscillating cascade of two unstaggered NACA 0006 blades with interblade phase angle equal to 180 deg are performed. From the instantaneous pressure coefficient distributions and time history of lift coefficient, the present approach, where a simple spatial treatment is utilized on the periodic boundaries, gives satisfactory results. By using this solution procedure, transonic flows around an oscillating cascade of four biconvex blades with different oscillation amplitudes, reduced frequencies, and interblade phase angles are investigated. From the distributions of magnitude and phase angle of the dynamic pressure difference coefficient, the present numerical results show better agreement with the experimental data than those from the linearized theory in most of the cases. For every quarter of one cycle, the pressure contours repeat and proceed one pitch distance in the upward or downward direction for interblade phase angle equal to −90 deg or 90 deg, respectively. The unsteady pressure wave and shock behaviors are observed. From the lift coefficient distributions, it is further confirmed that the oscillation amplitude, interblade phase angle, and reduced frequency all have significant effects on the transonic oscillating cascade flows.

Reynolds Number Effect on Vortex-Induced Vibration on a Two-Dimensional Circular Cylinder With Low Mass-Damping Parameter

2011 ◽  
Author(s):  
Juan B. V. Wanderley ◽  
Luiz F. Soares ◽  
Marcelo Vitola ◽  
Sergio H. Sphaier ◽  
Carlos Levi
Keyword(s):  
Reynolds Number ◽  
Circular Cylinder ◽  
Lift Coefficient ◽  
The Body ◽  
Response Amplitude ◽  
Curvilinear Coordinates ◽  
Number Range ◽  
Vortex Induced Vibration ◽  
Damping Parameter ◽  
Low Mass

The vortex induced vibration (VIV) on a circular cylinder with low mass-damping parameter and low Reynolds number is investigated numerically as basis for applications on dynamics of risers used in the offshore oil and gas industry and as a first step before tackling the harder high Reynolds number problem. The cylinder is supported by a spring and a damper and free to vibrate in the transverse direction. The numerical solution of the Reynolds average Navier-Stokes equations written in curvilinear coordinates is obtained using an upwind and Total Variation Diminishing conservative scheme and the k-ε turbulence model is used to simulate the turbulent flow in the wake of the body. Results were obtained for the phase angle, response amplitude, frequency, and lift coefficient for a variation of reduced velocity from 2 to 12 and three different proportional variations of Reynolds number, 2000–6000, 2000–12000, and 2000–24000. The numerical results indicate the strong effect of the Reynolds number range on the response amplitude, lift coefficient, and frequency of oscillation for a low mass-damping parameter.

Numerical Analysis of Super-Cavitating Flow Around a Two-Dimensional Cavitator Geometry

2011 ◽  
Author(s):  
Sunho Park ◽  
Shin Hyung Rhee
Keyword(s):  
Experimental Data ◽  
High Speed ◽  
Cavity Length ◽  
Stokes Equations ◽  
Cavitating Flow ◽  
The Body ◽  
Computational Method ◽  
Computational Results ◽  
Two Dimensional ◽  
Cell Counts

Mostly for military purposes, which require high speed and low drag, super-cavitating flows around under-water bodies have been an interesting, yet difficult research subject for many years. In the present study, high speed super-cavitating flow around a two-dimensional symmetric wedge-shaped cavitator was studied using an unsteady Reynolds-averaged Navier-Stokes equations solver based on a cell-centered finite volume method. To verify the computational method, flow over a hemispherical head-form body was simulated and validated against existing experimental data. Through the verification tests, the appropriate selection of domain extents, cell counts, numerical schemes, turbulence models, and cavitation models was studied carefully. A cavitation model based on the two-phase mixture flow modeling was selected with the standard k-epsilon model for turbulence closure. The cavity length, surface pressure distribution, and the flow velocity at the interface were compared with experimental data and analytic solutions. Various computational conditions, such as different wedge angles and caviation numbers, were considered for super-cavitating flow around the wedge-shaped cavitator. Super-cavitation begins to form in the low pressure region and propagates downstream. The computed cavity length and drag on the body were compared with analytic solution and computational results using a potential flow solver. Fairly good agreement was observed in the three-way comparison. The computed velocity on the cavity interface was also predicted quite closely to that derived from the Bernoulli equation. Finally, comparison was made between the computational results and cavitation tunnel test data, along with suggestions for cavitator designs.

Power Extraction from Water Waves

1976 ◽  
Vol 20 (02) ◽  
pp. 63-66 ◽  
Author(s):  
Chiang C. Mei
Keyword(s):  
Water Waves ◽  
Degrees Of Freedom ◽  
Vertical Axis ◽  
Horizontal Cylinder ◽  
The Body ◽  
Floating Body ◽  
Maximum Efficiency ◽  
Viscous Effects ◽  
Two Degrees Of Freedom ◽  
Power Extraction

Salter has demonstrated experimentally that a horizontal cylinder in the free surface of water can be a device to extract energy from the incident waves. This paper proposes a design which is based on the idea of a tethered-float breakwater, and gives the theoretical design criteria for maximum power extraction from a general floating cylinder with one or two degrees of freedom. It is shown that the rate of energy extraction must be equal to the rate of radiation damping and that the floating body must be made to resonate then for a body with one degree of freedom, the maximum efficiency at a given frequency can be at leastone half if the body is symmetrical about a vertical axis, and greater for an asymmetrical body. For a body with two degrees of freedom, all the wave power can be extracted. Hydrodynamical aspects of the controlled motion are examined. Viscous effects are ignored.

A Numerical Investigation of Vortex Induced Vibration on an Elastically Mounted Rigid Cylinder

2008 ◽  
Author(s):  
Juan B. V. Wanderley ◽  
Sergio H. Sphaier ◽  
Carlos Levi
Keyword(s):  
Experimental Data ◽  
Stokes Equations ◽  
Lift Coefficient ◽  
Navier Stokes ◽  
Tvd Scheme ◽  
Navier Stokes Equations ◽  
Vortex Induced Vibration ◽  
Moving Cylinder ◽  
Frequency Phase

The Vortex-Induced Vibration on an elastically mounted circular cylinder is investigated by the numerical solution of the two-dimensional Reynolds Averaged Navier-Stokes equations and results are compared with experimental data. The upwind TVD scheme of Roe – Sweby is used to solve the governing equations and the k-ε turbulence model is used to simulate the turbulent flow in the wake of the cylinder. The cylinder is laterally supported by a spring and a damper and is free to oscillate in the transverse direction. Results for the lift coefficient amplitude, displacement amplitude, frequency, phase angle, and power absorbed by the system are presented and compared to experimental data. The code was tested for the fixed cylinder case, and for the moving cylinder. The comparison with experimental data obtained from the literature showed the good quality of the numerical results and validated the code for simulations of vortex-induced vibration.

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