Skip to main content Accessibility help
×
Home
Hostname: page-component-78bd46657c-fstz4 Total loading time: 0.272 Render date: 2021-05-06T07:49:31.342Z Has data issue: true Feature Flags: { "shouldUseShareProductTool": true, "shouldUseHypothesis": true, "isUnsiloEnabled": true, "metricsAbstractViews": false, "figures": false, "newCiteModal": false, "newCitedByModal": true }

Simulations of three-dimensional viscoelastic flows past a circular cylinder at moderate Reynolds numbers

Published online by Cambridge University Press:  29 March 2010

DAVID RICHTER
Affiliation:
Department of Mechanical Engineering, Stanford University, Stanford, CA 94305, USA
GIANLUCA IACCARINO
Affiliation:
Department of Mechanical Engineering, Stanford University, Stanford, CA 94305, USA
ERIC S. G. SHAQFEH
Affiliation:
Department of Mechanical Engineering, Stanford University, Stanford, CA 94305, USA
Corresponding
E-mail address:

Abstract

The results from a numerical investigation of inertial viscoelastic flow past a circular cylinder are presented which illustrate the significant effect that dilute concentrations of polymer additives have on complex flows. In particular, effects of polymer extensibility are studied as well as the role of viscoelasticity during three-dimensional cylinder wake transition. Simulations at two distinct Reynolds numbers (Re = 100 and Re = 300) revealed dramatic differences based on the choice of the polymer extensibility (L2 in the FENE-P model), as well as a stabilizing tendency of viscoelasticity. For the Re = 100 case, attention was focused on the effects of increasing polymer extensibility, which included a lengthening of the recirculation region immediately behind the cylinder and a sharp increase in average drag when compared to both the low extensibility and Newtonian cases. For Re = 300, a suppression of the three-dimensional Newtonian mode B instability was observed. This effect is more pronounced for higher polymer extensibilities where all three-dimensional structure is eliminated, and mechanisms for this stabilization are described in the context of roll-up instability inhibition in a viscoelastic shear layer.

Type
Papers
Copyright
Copyright © Cambridge University Press 2010

Access options

Get access to the full version of this content by using one of the access options below.

References

Azaiez, J. & Homsy, G. 1994 a Linear stability of free shear flow of viscoelastic liquids. J. Fluid Mech. 268, 3769.CrossRefGoogle Scholar
Azaiez, J. & Homsy, G. 1994 b Numerical simulation of non-newtonian free shear flows at high Reynolds numbers. J. Non-Newton. Fluid Mech. 52, 333374.CrossRefGoogle Scholar
Bird, R. B., Armstrong, R. C. & Hassager, O. 1987 Dynamics of Polymeric Liquids, Volume 1, 2nd edn.Wiley.Google Scholar
Bird, R. & Wiest, J. 1995 Constitutive equations for polymeric liquids. Annu. Rev. Fluid Mech. 27, 167193.CrossRefGoogle Scholar
Broadbent, M. & Mena, B. 1974 Slow flow of an elastico-viscous fluid past cylinders and spheres. Chem. Engng J. 8, 1119.CrossRefGoogle Scholar
Cadot, O. & Kumar, S. 2000 Experimental characterization of viscoelastic effects on two- and three-dimensional shear instabilities. J. Fluid Mech. 416, 151172.CrossRefGoogle Scholar
Cadot, O. & Lebey, M. 1998 Shear instability inhibition in a cylinder wake by local injection of a viscoelastic fluid. Phys. Fluids 11 (2), 494496.CrossRefGoogle Scholar
Chilcott, M. & Rallison, J. 1998 Creeping flow of dilute polymer solutions past cylinders and spheres. J. Non-Newton. Fluid Mech. 1988, 381432.Google Scholar
Coates, P., Armstrong, R. & Brown, R. 1992 Calculation of steady-state viscoelastic flow through axisymmetric contractions with the eeme formulation. J. Non-Newton. Fluid Mech. 42, 141188.CrossRefGoogle Scholar
Coelho, P. & Pinho, F. 2003 a Vortex shedding in cylinder flow of shear-thinning fluids. I. Identification and demarcation of flow regimes. J. Non-Newton. Fluid Mech. 110, 143176.CrossRefGoogle Scholar
Coelho, P. & Pinho, F. 2003 b Vortex shedding in cylinder flow of shear-thinning fluids. II. Flow characteristics. J. Non-Newton. Fluid Mech. 110, 177193.CrossRefGoogle Scholar
Coelho, P. M. & Pinho, F. T. 2004 Vortex shedding in cylinder flow of shear-thinning fluids. III. pressure measurements. J. Non-Newton. Fluid Mech. 121, 5568.Google Scholar
Cressman, J. R., Bailey, Q. & Goldburg, W. I. 2001 Modification of a vortex street by a polymer additive. Phy. Fluids 13 (4), 867871.CrossRefGoogle Scholar
Cruz, D. O. A., Pinho, F. T. & Oliveira, P. J. 2005 Analytical solutions for fully developed laminar flow of some viscoelastic liquids with a newtonian solvent contribution. J. Non-Newton. Fluid Mech. 132, 2835.CrossRefGoogle Scholar
Dimitropoulos, C. D., Dubief, Y., Shaqfeh, E. S. G. & Moin, P. 2006 Direct numerical simulation of polymer-induced drag reduction in turbulent boundary layer flow of inhomogeneous polymer solutions. J. Fluid Mech. 566, 153162.CrossRefGoogle Scholar
Dimitropoulos, C. D., Dubief, Y., Shaqfeh, E. S. G., Moin, P. & Lele, S. K. 2005 Direct numerical simulation of polymer-induced drag reduction in turbulent boundary layer flow. Phys. Fluids 17 (1), 011705.CrossRefGoogle Scholar
Dimitropoulos, C., Sureshkumar, R. & Beris, A. 1998 Direct numerical simulation of viscoelastic turbulent channel flow exhibiting drag reduction: effect of the variation of rheological parameters. J. Non-Newton. Fluid Mech. 79, 433468.CrossRefGoogle Scholar
Dubief, Y., Terrapon, V. E., White, C. M., Shaqfeh, E. S. G., Moin, P. & Lele, S. K. 2005 New answers on the interaction between polymers and vortices in turbulent flows. Flow Turbul. Combust. 74 (4), 311329.CrossRefGoogle Scholar
Dubief, Y., White, C. M., Terrapon, V. E., Shaqfeh, E. S. G., Moin, P. & Lele, S. K. 2004 On the coherent drag-reducing and turbulence-enhancing behaviour of polymers in wall flows. J. Fluid Mech. 514, 271280.CrossRefGoogle Scholar
Fan, Y., Tanner, R. & Phan-Thien, N. 1999 Galerkin/least-square finite-element methods for steady viscoelastic flows. J. Non-Newton. Fluid Mech. 84, 233256.CrossRefGoogle Scholar
Gadd, G. 1966 Effects of long-chain molecule additives in water on vortex streets. Nature 211, 169170.CrossRefGoogle Scholar
Gupta, V., Sureshkumar, R. & Khomami, B. 2005 Passive scalar transport in polymer drag-reduced turbulent channel flow. AIChE J. 51 (7), 19381950.CrossRefGoogle Scholar
Ham, F. & Iaccarino, G. 2004 Energy conservation in collocated discretization schemes on unstructured meshes. In CTR Annual Research Briefs, pp. 3–14.Google Scholar
Ham, F., Mattsson, K. & Iaccarino, G. 2006 Accurate and stable finite volume operators for unstructured flow solvers. In CTR Annual Research Briefs, pp. 243–261.Google Scholar
James, D. & Gupta, O. 1971 Drag on circular cylinders in dilute polymer solutions. Chem. Engng Prog. Symp. Ser. 67 (111), 6273.Google Scholar
Kalashnikov, V. & Kudin, A. 1970 Kármán vortices in the flow of drag-reducing polymer solutions. Nature 225, 445446.CrossRefGoogle Scholar
Kato, H. & Mizuno, Y. 1983 An experimental investigation of viscoelastic flow past a circular cylinder. Bull. Japan Soc. Mech. Eng. 26 (214), 529536.CrossRefGoogle Scholar
Kim, K., Li, C., Sureshkumar, R., Balachandar, S. & Adrian, R. 2007 Effects of polymer stresses on eddy structures in drag-reduced turbulent channel flow. J. Fluid Mech. 584, 281299.CrossRefGoogle Scholar
Kumar, S. & Homsy, G. 1999 Direct numerical simulation of hydrodynamic instabilities in two- and three-dimensional viscoelastic free shear layers. J. Non-Newton. Fluid Mech. 83, 249276.CrossRefGoogle Scholar
Li, C., Sureshkumar, R. & Khomami, B. 2006 Influence of rheological parameters on polymer induced turbulent drag reduction. J. Non-Newton. Fluid Mech. 140, 2340.CrossRefGoogle Scholar
Liu, A., Bornside, D., Armstrong, R. & Brown, R. 1998 Viscoelastic flow of polymer solutions around a periodic, linear array of cylinders: comparisons of predictions for microstructure and flow fields. J. Non-Newton. Fluid Mech. 77, 153190.CrossRefGoogle Scholar
Ma, X., Symeonidis, V. & Karniadakis, G. 2003 A spectral vanishing viscosity method for stabilizing viscoelastic flows. J. Non-Newton. Fluid Mech. 115, 125155.CrossRefGoogle Scholar
Mahesh, K., Constantinescu, G. & Moin, P. 2004 A numerical method for large-eddy simulation in complex geometries. J. Comput. Phys. 197, 215240.CrossRefGoogle Scholar
Manero, O. & Mena, B. 1981 On the slow flow of viscoelastic fluids past a circular cylinder. J. Non-Newton. Fluid Mech. 9, 379387.CrossRefGoogle Scholar
McKinley, G., Armstrong, R. & Brown, R. 1993 The wake instability in viscoelastic flow past confined circular cylinders. Phil. Trans. R. Soc. Lond. 344 (1671), 265304.CrossRefGoogle Scholar
McKinley, G. & Sridhar, T. 2002 Filament-stretching rheometry of complex fluids. Annu. Rev. Fluid Mech. 34, 375415.CrossRefGoogle Scholar
Mena, B. & Caswell, B. 1974 Slow flow of an elastic-viscous fluid past an immersed body. Chem. Engng J. 8, 125134.CrossRefGoogle Scholar
Metzner, A. & Astarita, G. 1967 External flows of viscoelastic materials: fluid property restrictions on the use of velocity-sensitive probes. AIChE J. 13 (3), 550555.CrossRefGoogle Scholar
Oliveira, P. J. 2001 Method for time-dependent simulations of viscoelastic flows: vortex shedding behind cylinder. J. Non-Newton. Fluid Mech. 101, 113137.CrossRefGoogle Scholar
Oliveira, P., Pinho, F. & Pinto, G. 1998 Numerical simulation of nonlinear elastic flows with a general collocated finite-volume method. J. Non-Newton. Fluid Mech. 79, 143.CrossRefGoogle Scholar
Phan-Thien, N. & Dou, H. 1999 Viscoelastic flow past a cylinder: drag coefficient. Comput. Methods Appl. Mech. Engng 180, 243266.CrossRefGoogle Scholar
Pipe, C. J. & Monkewitz, P. A. 2006 Vortex shedding in flows of dilute polymer solutions. J. Non-Newton. Fluid Mech. 139, 5467.CrossRefGoogle Scholar
Purnode, B. & Legat, V. 1996 Hyperbolicity and change of type in flows of fene-p fluids. J. Non-Newton. Fluid Mech. 65, 111129.CrossRefGoogle Scholar
Sahin, M. & Owens, R. G. 2004 On the effects of viscoelasticity on two-dimensional vortex dynamics in the cylinder wake. J. Non-Newton. Fluid Mech. 123, 121139.CrossRefGoogle Scholar
Sibilla, S. & Baron, A. 2002 Polymer stress statistics in the near-wall turbulent flow of a drag-reducing solution. Phys. Fluids 14, 11231136.CrossRefGoogle Scholar
Stone, P., Roy, A., Larson, R., Waleffe, F. & Graham, M. 2004 Polymer drag reduction in exact coherent structures of plane shear flow. Phys. Fluids 16 (9), 34703482.CrossRefGoogle Scholar
Sureshkumar, R. & Beris, A. 1995 Effect of artificial stress diffusivity on the stability of numerical calculations and the flow dynamics of time-dependent viscoelastic flows. J. Non-Newton. Fluid Mech. 60, 5380.CrossRefGoogle Scholar
Sureshkumar, R., Beris, A. N. & Handler, R. A. 1997 Direct numerical simulation of the turbulent channel flow of a polymer solution. Phys. Fluids 9 (3), 743755.CrossRefGoogle Scholar
Townsend, P. 1980 A numerical simulation of newtonian and visco-elastic flow past stationary and rotating cylinders. J. Non-Newton. Fluid Mech. 6, 219243.CrossRefGoogle Scholar
Ultman, J. & Denn, M. 1971 Slow viscoelastic flow past submerged objects. Chem. Engng J. 2, 8189.CrossRefGoogle Scholar
Usui, H., Shibata, T. & Sano, Y. 1980 Kármán vortex behind a circular cylinder in dilute polymer solutions. J. Chem. Engng Japan 13 (1), 7779.CrossRefGoogle Scholar
Wapperom, P. & Webster, W. 1999 Simulation for viscoelastic flow by a finite volume/element method. Comput. Methods Appl. Mech. Engng 180, 281304.CrossRefGoogle Scholar
Williamson, C. H. K. 1996 a Three-dimensional wake transition. J. Fluid Mech. 328, 345407.CrossRefGoogle Scholar
Williamson, C. H. K. 1996 b Vortex dynamics in the cylinder wake. Annu. Rev. Fluid Mech. 28, 477539.CrossRefGoogle Scholar
Zdravkovich, M. M. 1997 Flow Around Circular Cylinders Volume 1: Fundamentals. Oxford University Press.Google Scholar

Send article to Kindle

To send this article to your Kindle, first ensure no-reply@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about sending to your Kindle. Find out more about sending to your Kindle.

Note you can select to send to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be sent to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

Find out more about the Kindle Personal Document Service.

Simulations of three-dimensional viscoelastic flows past a circular cylinder at moderate Reynolds numbers
Available formats
×

Send article to Dropbox

To send this article to your Dropbox account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your <service> account. Find out more about sending content to Dropbox.

Simulations of three-dimensional viscoelastic flows past a circular cylinder at moderate Reynolds numbers
Available formats
×

Send article to Google Drive

To send this article to your Google Drive account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your <service> account. Find out more about sending content to Google Drive.

Simulations of three-dimensional viscoelastic flows past a circular cylinder at moderate Reynolds numbers
Available formats
×
×

Reply to: Submit a response


Your details


Conflicting interests

Do you have any conflicting interests? *