Generalized thick strip modelling for vortex-induced vibration of long flexible cylinders

We propose a generalized strip modelling method that is computationally efficient for the VIV prediction of long flexible cylinders in three-dimensional incompressible flow. In order to overcome the shortcomings of conventional strip-theory-based 2D models, the fluid domain is divided into "thick" strips, which are sufficiently thick to locally resolve the small scale turbulence effects and three dimensionality of the flow around the cylinder. An attractive feature of the model is that we independently construct a three-dimensional scale resolving model for individual strips, which have local spanwise scale along the cylinder's axial direction and are only coupled through the structural model of the cylinder. Therefore, this approach is able to cover the full spectrum for fully resolved 3D modelling to 2D strip theory. The connection between these strips is achieved through the calculation of a tensioned beam equation, which is used to represent the dynamics of the flexible body. In the limit, however, a single "thick" strip would fill the full 3D domain. A parallel Fourier spectral/hp element method is employed to solve the 3D flow dynamics in the strip-domain, and then the VIV response prediction is achieved through the strip-structure interactions. Numerical tests on both laminar and turbulent flows as well as the comparison against the fully resolved DNS are presented to demonstrate the applicability of this approach.

[1]  J. M. R. Graham,et al.  NUMERICAL PREDICTION OF VIV ON LONG FLEXIBLE CIRCULAR CYLINDERS , 2001 .

[2]  Julio Romano Meneghini,et al.  Numerical simulations of VIV on long flexible cylinders immersed in complex flow fields , 2004 .

[3]  Yue Yu,et al.  Generalized fictitious methods for fluid-structure interactions: Analysis and simulations , 2013, J. Comput. Phys..

[4]  Cassio T. Yamamoto,et al.  Numerical simulations of vortex-induced vibration on flexible cylinders , 2004 .

[5]  Spencer J. Sherwin,et al.  A moving frame of reference algorithm for fluid/structure interaction of rotating and translating bodies , 2002 .

[6]  George Em Karniadakis,et al.  Vortex dislocations and force distribution of long flexible cylinders subjected to sheared flows , 2001 .

[7]  Samuel Holmes,et al.  Simulation of Riser VIV Using Fully Three Dimensional CFD Simulations , 2006 .

[8]  R. Henderson,et al.  Three-dimensional Floquet stability analysis of the wake of a circular cylinder , 1996, Journal of Fluid Mechanics.

[9]  G. Karniadakis,et al.  Spectral/hp Element Methods for Computational Fluid Dynamics , 2005 .

[10]  Leslie Greengard,et al.  Accelerating the Nonuniform Fast Fourier Transform , 2004, SIAM Rev..

[11]  Jeffrey A. Fessler,et al.  Nonuniform fast Fourier transforms using min-max interpolation , 2003, IEEE Trans. Signal Process..

[12]  P. Moin,et al.  Numerical studies of flow over a circular cylinder at ReD=3900 , 2000 .

[13]  E. Tadmor,et al.  Convergence of spectral methods for nonlinear conservation laws. Final report , 1989 .

[14]  Suchuan Dong,et al.  A robust and accurate outflow boundary condition for incompressible flow simulations on severely-truncated unbounded domains , 2014, J. Comput. Phys..

[15]  C. Williamson.  Three-dimensional wake transition , 1996, Journal of Fluid Mechanics.

[16]  J. Michael R. Graham,et al.  Multi-modal Vortex-Induced Vibrations of a vertical riser pipe subject to a uniform current profile , 2004 .

[17]  S. Sherwin,et al.  STABILISATION OF SPECTRAL/HP ELEMENT METHODS THROUGH SPECTRAL VANISHING VISCOSITY: APPLICATION TO FLUID MECHANICS MODELLING , 2006 .

[18]  S. Orszag,et al.  High-order splitting methods for the incompressible Navier-Stokes equations , 1991 .

[19]  Charles H. K. Williamson,et al.  A brief review of recent results in vortex-induced vibrations , 2008 .

[20]  E. Ramm,et al.  Artificial added mass instabilities in sequential staggered coupling of nonlinear structures and incompressible viscous flows , 2007 .

[21]  E. de Langre,et al.  Coupling of Structure and Wake Oscillators in Vortex-Induced Vibrations , 2004 .

[22]  Licheng Sun,et al.  Stripwise discrete vortex method for VIV analysis of flexible risers , 2012 .

[23]  George Em Karniadakis,et al.  Dynamics and flow structures in the turbulent wake of rigid and flexible cylinders subject to vortex-induced vibrations , 1999, Journal of Fluid Mechanics.

[24]  George Em Karniadakis,et al.  DNS-DERIVED FORCE DISTRIBUTION ON FLEXIBLE CYLINDERS SUBJECT TO VORTEX-INDUCED VIBRATION , 2000 .

[25]  Bifurcation theory for three-dimensional flow in the wake of a circular cylinder , 2000, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[26]  George Em Karniadakis,et al.  A Spectral Vanishing Viscosity Method for Large-Eddy Simulations , 2000 .

[27]  Alessandro Bolis,et al.  Fourier spectral/hp element method: investigation of time-stepping and parallelisation strategies , 2013 .

[28]  Xiaodong Wu,et al.  A review of recent studies on vortex-induced vibrations of long slender cylinders , 2012 .

[29]  G. Karniadakis,et al.  Vortex-induced vibrations of a long flexible cylinder in shear flow , 2011, Journal of Fluid Mechanics.

[30]  G. Karniadakis,et al.  A direct numerical simulation study of flow past a freely vibrating cable , 1997, Journal of Fluid Mechanics.

[31]  Kostas F. Lambrakos,et al.  Blind predictions of laboratory measurements of vortex-induced vibrations of a tension riser , 2005 .

[32]  Yiannis Constantinides,et al.  Numerical Simulations of Cylinder VIV Focusing on High Harmonics , 2009 .

[33]  G. Karniadakis,et al.  Distributed lock-in drives broadband vortex-induced vibrations of a long flexible cylinder in shear flow , 2013, Journal of Fluid Mechanics.

[34]  Jie Shen,et al.  Velocity-Correction Projection Methods for Incompressible Flows , 2003, SIAM J. Numer. Anal..

[35]  Chia-Rong Chen,et al.  Numerical scheme for riser motion calculation during 3-D VIV simulation , 2011 .

[36]  Haym Benaroya,et al.  An overview of modeling and experiments of vortex-induced vibration of circular cylinders , 2005 .

[37]  George Em Karniadakis,et al.  SIMULATIONS OF FLOW OVER A FLEXIBLE CABLE: A COMPARISON OF FORCED AND FLOW-INDUCED VIBRATION , 1996 .

[38]  E. Lamballais,et al.  Experimental and numerical studies of the flow over a circular cylinder at Reynolds number 3900 , 2008 .

[39]  Robert Michael Kirby,et al.  Nektar++: An open-source spectral/hp element framework , 2015, Comput. Phys. Commun..

[40]  George E. Karniadakis,et al.  A convergence study of a new partitioned fluid-structure interaction algorithm based on fictitious mass and damping , 2012, J. Comput. Phys..