URANS calculations for smooth circular cylinder flow in a wide range of Reynolds Numbers: solution verification and validation

The flow around circular smooth fixed cylinder in a large range of Reynolds numbers is considered in this paper. In order to investigate this canonical case, we perform CFD calculations and apply verification & validation (V&V) procedures to draw conclusions regarding numerical error and, afterwards, assess the modeling errors and capabilities of this (U)RANS method to solve the problem. Eight Reynolds numbers between Re = 10 and Re=5×105 will be presented with, at least, four geometrically similar grids and five discretization in time for each case (when unsteady), together with strict control of iterative and round-off errors, allowing a consistent verification analysis with uncertainty estimation. Two-dimensional RANS, steady or unsteady, laminar or turbulent calculations are performed. The original 1994 k-ω SST turbulence model by Menter is used to model turbulence. The validation procedure is performed by comparing the numerical results with an extensive set of experimental results compiled from the literature.

[1]  S. Mittal,et al.  Flow past a cylinder: shear layer instability and drag crisis , 2005 .

[2]  Dag Myrhaug,et al.  Numerical simulation of flow around a smooth circular cylinder at very high Reynolds numbers , 2009 .

[3]  G. Karniadakis,et al.  Three-dimensional dynamics and transition to turbulence in the wake of bluff objects , 1992, Journal of Fluid Mechanics.

[4]  Florian R. Menter,et al.  Sensitization of the SST Turbulence Model to Rotation and Curvature by Applying the Spalart–Shur Correction Term , 2009 .

[5]  S. Dennis,et al.  Numerical solutions for steady flow past a circular cylinder at Reynolds numbers up to 100 , 1970, Journal of Fluid Mechanics.

[6]  Philippe R. Spalart,et al.  Detached-Eddy Simulations Past a Circular Cylinder , 2000 .

[7]  Samuel Holmes,et al.  Calculation of Manoeuvring Forces on Submarines Using Two Viscous-Flow Solvers , 2010 .

[8]  M. D. Olson,et al.  Numerical studies of the flow around a circular cylinder by a finite element method , 1978 .

[9]  Hideo Takami,et al.  Steady Two‐Dimensional Viscous Flow of an Incompressible Fluid past a Circular Cylinder , 1969 .

[10]  D. K. Walters,et al.  A New Model for Boundary Layer Transition Using a Single-Point RANS Approach , 2004 .

[11]  C. Shu,et al.  Simulation of incompressible viscous flows past a circular cylinder by hybrid FD scheme and meshless least square-based finite difference method , 2004 .

[12]  Xiaoyi He,et al.  Lattice Boltzmann method on a curvilinear coordinate system: Vortex shedding behind a circular cylinder , 1997 .

[13]  Guilherme Vaz,et al.  Free-Surface Viscous Flow Computations: Validation of URANS Code FreSCo , 2009 .

[14]  Sanjay Mittal,et al.  Effect of a slip splitter plate on vortex shedding from a cylinder , 2003 .

[15]  C. Williamson.  Vortex Dynamics in the Cylinder Wake , 1996 .

[16]  M. Braza,et al.  Numerical study and physical analysis of the pressure and velocity fields in the near wake of a circular cylinder , 1986, Journal of Fluid Mechanics.

[17]  C. Norberg.  Fluctuating lift on a circular cylinder: review and new measurements , 2003 .

[18]  Simulating vortex shedding at high Reynolds numbers , 2000 .

[19]  L. Eça,et al.  Evaluation of numerical error estimation based on grid refinement studies with the method of the manufactured solutions , 2009 .

[20]  S. Balachandar,et al.  Effect of three‐dimensionality on the lift and drag of nominally two‐dimensional cylinders , 1995 .

[21]  S. C. R. Dennis.  The numerical solution of the vorticity transport equation , 1973 .

[22]  F. Menter.  Two-equation eddy-viscosity turbulence models for engineering applications , 1994 .

[23]  Arjen Koop,et al.  Predicting Wind Loads for FPSO Tandem Offloading Using CFD , 2010 .

[24]  Sanjay Mittal,et al.  Unsteady incompressible flows past two cylinders in tandem and staggered arrangements , 1997 .

[25]  Chih-Yung Wen,et al.  Experimental and numerical study of the separation angle for flow around a circular cylinder at low Reynolds number , 2004, Journal of Fluid Mechanics.

[26]  V. Gushchin,et al.  A numerical method of solving the navier-stokes equations☆ , 1974 .

[27]  Arjen Koop,et al.  Viscous-Flow Calculations for Model and Full-Scale Current Loads on Typical Offshore Structures , 2013 .

[28]  Christophe Mabilat,et al.  Viscous Flow Computations on a Smooth Cylinders: A Detailed Numerical Study With Validation , 2007 .

[29]  Arjen Koop,et al.  Predicting Loads on a LNG Carrier With CFD , 2010 .

[30]  H. Schlichting.  Boundary Layer Theory , 1955 .

[31]  André L. C. Fujarra,et al.  Experimental Forces Measurements on the Flow Around a Fixed and Yawed Cylinder in the Presence of Free-Surface , 2012 .

[32]  Chaoqun Liu,et al.  Preconditioned Multigrid Methods for Unsteady Incompressible Flows , 1997 .

[33]  R. Henderson.  Details of the drag curve near the onset of vortex shedding , 1995 .

[34]  D. K. Walters,et al.  A Three-Equation Eddy-Viscosity Model for Reynolds-Averaged Navier-Stokes Simulations of Transitional Flow , 2008 .

[35]  H. B. Keller,et al.  Viscous flow past circular cylinders , 1973 .

[36]  B. Fornberg.  A numerical study of steady viscous flow past a circular cylinder , 1980, Journal of Fluid Mechanics.

[37]  A. E. Holdø.  The Use of Solution Adaptive Grid for Modeling Small Scale Turbulent Structures , 2005 .

[38]  Joel H. Ferziger,et al.  Computational methods for fluid dynamics , 1996 .

[39]  S. Mittal,et al.  FLOW-INDUCED VIBRATIONS OF A LIGHT CIRCULAR CYLINDER AT REYNOLDS NUMBERS 103TO 104 , 2001 .