Further contributions on the flow past a stationary and confined cylinder: Creeping and slowly moving flow of Power law fluids

Abstract The steady flow of generalized Newtonian fluid around a stationary cylinder placed between two parallel plates was studied numerically. Finite volume method was applied to solve the momentum equations along with the continuity equation and the Power law rheological model within the laminar flow regime for a range of the Reynolds number Re and the Power law index n values. The values of the Reynolds number, based on physical and rheological properties, cylinder radius and bulk velocity, were varied between 0.0001 ≤ Re ≤ 10 , while the Power law index values mapped the 0.50 ≤ n ≤ 1.50 range, allowing for the investigation of both shear-thinning and shear-thickening effects at the creeping as well as slowly moving fluid flow conditions. We report accurate results of a systematic study with a focus on the most important characteristics of fluid flow past circular cylinder. It is shown that for the creeping flow regime there exist finite sized redevelopment length, drag and loss coefficient. Last but not least, the present numerical results indicate that the shear-thinning viscous behaviour decreases the onset of flow separation.

[1]  F. Pinho,et al.  A convergent and universally bounded interpolation scheme for the treatment of advection , 2003 .

[2]  E. Mitsoulis.  On creeping drag flow of a viscoplastic fluid past a circular cylinder: wall effects , 2004 .

[3]  Weeratunge Malalasekera,et al.  An introduction to computational fluid dynamics - the finite volume method , 2007 .

[4]  R. P. Chhabra,et al.  Steady non–Newtonian flow past a circular cylinder: a numerical study , 2004 .

[5]  N. Phan-Thien,et al.  Viscoelastic flow past a confined cylinder : Instability and velocity inflection , 2007 .

[6]  W. Shyy,et al.  Second-order upwind and central difference schemes for recirculating flow computation , 1992 .

[7]  G. Biswas,et al.  Three-dimensional study of flow past a square cylinder at low Reynolds numbers , 2003 .

[8]  J. P. Pascal,et al.  Steady flow of a power-law fluid past a cylinder , 1996 .

[9]  P. Roache.  Perspective: A Method for Uniform Reporting of Grid Refinement Studies , 1994 .

[10]  S. Yen,et al.  Time-averaged topological flow patterns and their influence on vortex shedding of a square cylinder in crossflow at incidence , 2010 .

[11]  Roger I. Tanner.  Stokes paradox for power-law flow around a cylinder , 1993 .

[12]  T. Papanastasiou.  Flows of Materials with Yield , 1987 .

[13]  P. Ternik,et al.  New contributions on laminar flow of inelastic non-Newtonian fluid in the two-dimensional symmetric expansion: Creeping and slowly moving flow conditions , 2010 .

[14]  Yukio Tamura,et al.  Numerical simulation of Reynolds number effects on velocity shear flow around a circular cylinder , 2010 .

[15]  Kit Ming Lam,et al.  Vortex shedding flow behind a slowly rotating circular cylinder , 2009 .

[16]  Robert C. Armstrong,et al.  Finite element method for viscoelastic flows based on the discrete adaptive viscoelastic stress splitting and the discontinuous Galerkin method : DAVSS-G/DG , 1999 .

[17]  R. Chhabra,et al.  Power law fluid flow over a bundle of cylinders at intermediate Reynolds numbers , 2001 .

[18]  Evan Mitsoulis,et al.  Creeping motion of a sphere in tubes filled with Herschel–Bulkley fluids , 1997 .

[19]  J.J. Shea,et al.  Rheology of Polymeric Systems , 1998, IEEE Electrical Insulation Magazine.

[20]  S. Balachandar,et al.  A numerical study on the flow patterns of two oscillating cylinders , 2009 .

[21]  S. Patankar.  Numerical Heat Transfer and Fluid Flow , 2018, Lecture Notes in Mechanical Engineering.

[22]  R. Chhabra,et al.  Wall effects in flow past a circular cylinder in a plane channel: a numerical study , 2004 .

[23]  P. M. Coelho,et al.  Vortex shedding in cylinder flow of shear-thinning fluids II. Flow characteristics , 2003 .

[24]  N. Phan-Thien,et al.  Galerkin/least-square finite-element methods for steady viscoelastic flows , 1999 .

[25]  Paulo J. Oliveira,et al.  A numerical study of steady and unsteady viscoelastic flow past bounded cylinders , 2005 .

[26]  D. Spalding,et al.  A calculation procedure for heat, mass and momentum transfer in three-dimensional parabolic flows , 1972 .

[27]  S. Mittal,et al.  Prediction of the critical Reynolds number for flow past a circular cylinder , 2006 .

[28]  S. Bhattacharyya,et al.  Vortex shedding in shear flow past tandem square cylinders in the vicinity of a plane wall , 2008 .

[29]  G. Biswas,et al.  Numerical simulation of flow past row of square cylinders for various separation ratios , 2010 .

[30]  P. C. Sousa,et al.  Three-dimensional flow of Newtonian and Boger fluids in square-square contractions , 2009 .

[31]  R. Chhabra,et al.  Laminar flow of power-law fluids past a rotating cylinder , 2010 .

[32]  Robert C. Armstrong,et al.  Viscoelastic flow of polymer solutions around a periodic, linear array of cylinders: comparisons of predictions for microstructure and flow fields , 1998 .

[33]  Robert J. Poole,et al.  Plane sudden expansion flows of viscoelastic liquids , 2007 .

[34]  M. Mackay,et al.  An explanation of the rheological properties of Boger fluids , 1987 .

[35]  P. Sivakumar,et al.  Steady flow of power-law fluids across an unconfined elliptical cylinder , 2007 .

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

[37]  Hrvoje Jasak,et al.  A tensorial approach to computational continuum mechanics using object-oriented techniques , 1998 .

[38]  Albert Magnin,et al.  Interaction between two circular cylinders in slow flow of Bingham viscoplastic fluid , 2009 .

[39]  Fernando T. Pinho,et al.  The flow of viscoelastic fluids past a cylinder : finite-volume high-resolution methods , 2001 .

[40]  Evan Mitsoulis,et al.  Creeping motion of a sphere in tubes filled with a Bingham plastic material , 1997 .

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

[42]  D. V. Boger.  Viscoelastic fluid mechanics: Interaction between prediction and experiment , 1996 .

[43]  F. Pinho,et al.  Vortex shedding in cylinder flow of shear-thinning fluids I. Identification and demarcation of flow regimes , 2003 .

[44]  N. Phan-Thien,et al.  The flow of an Oldroyd-B fluid past a cylinder in a channel: adaptive viscosity vorticity (DAVSS-ω) formulation , 1999 .