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Numerical simulation of flow of a shear-thinning Carreau fluid over a transversely oscillating cylinder

Published online by Cambridge University Press:  01 July 2021

Md. Irshad Alam ,
Apurva Raj ,
Piru Mohan Khan ,
Subrata Kumar  and
Somnath Roy Open the ORCID record for Somnath Roy [Opens in a new window]
Md. Irshad Alam
Affiliation:
Department of Mechanical Engineering, Indian Institute of Technology Patna, Bihta, Bihar801103, India
Apurva Raj
Affiliation:
Department of Aerospace Engineering, Indian Institute of Technology Kharagpur, Kharagpur, West Bengal721302, India
Piru Mohan Khan
Affiliation:
Department of Mechanical Engineering, Indian Institute of Technology Kharagpur, Kharagpur, West Bengal721302, India
Subrata Kumar
Affiliation:
Department of Mechanical Engineering, Indian Institute of Technology Patna, Bihta, Bihar801103, India
Somnath Roy*
Affiliation:
Department of Mechanical Engineering, Indian Institute of Technology Kharagpur, Kharagpur, West Bengal721302, India
*
†Email address for correspondence: somnath.roy@mech.iitkgp.ac.in
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Abstract

Flow of a shear-thinning fluid over curved and moving geometries demands special attention owing to its industrial and biological relevance. The present study reports a numerical simulation of the motion of a Carreau fluid over a transversely oscillating cylinder for a range of oscillation amplitudes and frequencies at Reynolds number $Re = 100$, and compares the flow behaviour with that of a Newtonian fluid. The numerical solver uses the sharp-interface immersed boundary method to reconstruct the flow variables at the intercepted cells in the vicinity of the moving cylinder geometry. Synchronized vortex shedding is observed during the locked-in oscillation mode, whereas paired counter-rotating vortices are shed during the non-locked-in mode. The generation of vorticity and enstrophy variations in the Carreau and Newtonian fluids are compared. The vortex patterns in the Carreau fluid show a strong difference from those of the Newtonian fluid at higher amplitude of oscillation ($A^{*} = 1.2$). This difference in the flow structures is explained through the behaviour of the diffusion terms in the vorticity transport equation. Further, the effect of the Carreau fluid properties on the flow structures and vorticity dynamics are also discussed.

JFM classification

Mathematical Foundations: Computational methods Non-Newtonian Flows: Rheology Vortex Flows: Vortex dynamics
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 921 , 25 August 2021 , A23
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Copyright
© The Author(s), 2021. Published by Cambridge University Press

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References

REFERENCES

Anagnostopoulos, P. 2000 Numerical study of the flow past a cylinder excited transversely to the incident stream. Part 1: Lock-in zone, hydrodynamic forces and wake geometry. J. Fluids Struct. 14, 819–851.CrossRefGoogle Scholar
Ashouri, A., Izadpanah, E., Hekmat, M.H. & Amini, Y. 2021 Numerical investigation on two-degree-of-freedom vortex-induced vibration of a circular cylinder in power-law fluids. J. Non-Newtonian Fluid Mech. 292, 104535.CrossRefGoogle Scholar
Bailoor, S., Seo, J.H. & Mittal, R. 2019 Vortex shedding from a circular cylinder in shear-thinning Carreau fluids. Phys. Fluids 31, 011703.CrossRefGoogle Scholar
Barbi, C., Favier, D.P., Maresca, C.A. & Telionis, D.P. 1986 Vortex shedding and lock-on of a circular cylinder in oscillatory flow. J. Fluid Mech. 170, 527–544.CrossRefGoogle Scholar
Bearman, P.W. 2009 Understanding and predicting vortex-induced vibrations. J. Fluid Mech. 634, 1–4.CrossRefGoogle Scholar
Bharti, R.P., Chhabra, R.P. & Eswaran, V. 2006 Steady flow of power law fluids across a circular cylinder. Can. J. Chem. Engng 84, 406–421.CrossRefGoogle Scholar
Bharti, R.P., Chhabra, R.P. & Eswaran, V. 2007 A numerical study of the steady forced convection heat transfer from an unconfined circular cylinder. Heat Mass Transfer 43, 639–648.CrossRefGoogle Scholar
Bharti, R.P., Sivakumar, P. & Chhabra, R.P. 2008 Forced convection heat transfer from an elliptical cylinder to power-law fluids. Intl J. Heat Mass Transfer 51, 1838–1853.CrossRefGoogle Scholar
Bishop, R.E.D. & Hassan, A.Y. 1964 The lift and drag forces on a circular cylinder in a flowing fluid. Proc. R. Soc. Lond. A 277, 32–50.Google Scholar
Blackburn, H.M. & Henderson, R.D. 1999 A study of two-dimensional flow past an oscillating cylinder. J. Fluid Mech. 385, 255–286.CrossRefGoogle Scholar
Carreau, P.J. 1972 Rheological equation from molecular network theories. J. Rheol. 16, 99–127.Google Scholar
Chhabra, R.P., Soares, A.A. & Ferreira, J.M. 2004 Steady non-Newtonian flow past a circular cylinder: a numerical study. Acta Mech. 172, 1–16.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-Newtonian Fluid Mech. 110, 143–176.CrossRefGoogle Scholar
Coelho, P. & Pinho, F. 2003 b Vortex shedding in cylinder flow of shear-thinning fluids: II. Flow characteristics. J. Non-Newtonian Fluid Mech. 110, 177–193.CrossRefGoogle Scholar
Coelho, P. & Pinho, F. 2004 Vortex shedding in cylinder flow of shear-thinning fluids: III. Pressure measurements. J. Non-Newtonian Fluid Mech. 121, 55–68.Google Scholar
Cressman, J.R., Bailey, Q. & Goldburg, W.I. 2001 Modification of a vortex street by a polymer additive. Phys. Fluids 13, 867–871.CrossRefGoogle Scholar
Dey, A.A., Modarres-Sadeghi, Y. & Rothstein, J.P. 2017 Experimental observation of viscoelastic fluid–structure interactions. J. Fluid Mech. 813, R5.CrossRefGoogle Scholar
Dhahir, S.A. & Walters, K. 1989 On non-Newtonian flow past a cylinder in a confined flow. J. Rheol. 33, 781–804.CrossRefGoogle Scholar
Gresho, P.M. 1990 On pressure boundary conditions for the incompressible Navier–Stokes equations. Intl J Numer. Meth. Fluids 7, 11–46.Google Scholar
Griffin, O.M. & Ramberg, S.E. 1976 Vortex shedding from a cylinder vibrating in line with an incident uniform flow. J. Fluid Mech. 75, 257–271.CrossRefGoogle Scholar
Harlow, F.H. & Welch, J.E. 1965 Numerical calculation of time-dependent viscous incompressible flow of fluid with free surface. Phys. Fluids 8, 2182–2189.CrossRefGoogle Scholar
Hopkins, C.C. & de Bruyn, J.R. 2019 Numerical simulations of the forced oscillation of a wire in Newtonian and shear-thinning fluids. Phys. Fluids 31, 013101.CrossRefGoogle Scholar
Hunt, J.C.R., Wray, A. & Moin, P. 1988 Eddies, stream, and convergence zones in turbulent flows. In Proceedings of the 1988 Summer Program, Report CTR-S88, Center for Turbulence Research. Stanford University.Google Scholar
Jiang, R. & Zheng, P. 2017 Resonance in flow past oscillating cylinder under subcritical conditions. Appl. Maths Mech. 38, 363–378.CrossRefGoogle Scholar
Jones, G.W. Jr. 1968 Unsteady lift forces generated by vortex shedding about a large, stationary, and oscillating cylinder at high Reynolds numbers. NASA Tech. Rep. NASA Langley Research Center.Google Scholar
Karnidakis, G. & Triantafyllou, G. 1989 Frequency selection and asymptotic states in laminar wakes. J. Fluid Mech. 199, 441.CrossRefGoogle Scholar
Koopmann, G.H. 1967 The vortex wakes of vibrating cylinders at low Reynolds numbers. J. Fluid Mech. 28, 501–512.CrossRefGoogle Scholar
Kravchenko, A.G., Moin, P. & Shariff, K. 1999 B-spline method and zonal grids for simulations of complex turbulent flows. J. Comput. Phys. 151, 757–789.CrossRefGoogle Scholar
Krishnan, H., Agrawal, A., Sharma, A., Thompson, M.C. & Sheridan, J. 2019 On the mechanism of symmetric vortex shedding. J. Fluids Struct. 91, 102706.Google Scholar
Krishnan, H., Agrawal, A., Sharma, A. & Sheridan, J. 2016 Near-body vorticity dynamics of a square cylinder subjected to an inline pulsatile free stream flow. Phys. Fluids 28, 093605.CrossRefGoogle Scholar
Kumar, M. & Roy, S. 2016 A sharp interface immersed boundary method for moving geometries with mass conservation and smooth pressure variation. Comput. Fluids 137, 15–35.CrossRefGoogle Scholar
Kumar, M., Roy, S. & Ali, M.S. 2016 a An efficient immersed boundary algorithm for simulation of flows in curved and moving geometries. Comput. Fluids 129, 159–178.CrossRefGoogle Scholar
Kumar, S., Navrose, , & Mittal, S. 2016 b Lock-in in forced vibration of a circular cylinder. Phys. Fluids 28, 113605.CrossRefGoogle Scholar
Lashgari, I., Pralits, J.O., Giannetti, F. & Brandt, L. 2012 First instability of the flow of shear-thinning and shear-thickening fluids past a circular cylinder. J. Fluid Mech. 701, 201–227.CrossRefGoogle Scholar
Leontini, J.S., Stewart, B.E., Thompson, M.C. & Hourigan, K. 2006 Wake state and energy transitions of an oscillating cylinder at low Reynolds number. Phys. Fluids 18, 067101.CrossRefGoogle Scholar
Meneghini, J.R. & Bearman, P.W. 1995 Numerical simulation of high amplitude oscillatory flow about a circular cylinder. J. Fluids Struct. 9, 435–455.CrossRefGoogle Scholar
Mittal, S. 2005 Excitation of shear layer instability in flow past a cylinder at low Reynolds number. Intl J. Numer. Meth. Fluids 49, 1147–1167.CrossRefGoogle Scholar
Mittal, S. & Singh, S. 2005 Vortex-induced vibrations at subcritical Re. J. Fluid Mech. 534, 185.CrossRefGoogle Scholar
Morse, T.L. & Williamson, C.H.K. 2009 Prediction of vortex-induced vibration response by employing controlled motion. J. Fluid Mech. 634, 5–39.CrossRefGoogle Scholar
Nobari, M.R.H. & Naderan, H. 2006 A numerical study of flow past a cylinder with cross flow and inline oscillation. Comput. Fluids 35, 393–415.CrossRefGoogle Scholar
Olsthoorn, J., Stastna, M. & Steinmoeller, D. 2014 On the dynamics of vortex-wall interaction in low viscosity shear thinning fluids. Phys. Fluids 26, 013101.CrossRefGoogle Scholar
Orlanski, I. 1976 A simple boundary condition for unbounded hyperbolic flows. J. Comput. Phys. 21, 251–269.CrossRefGoogle Scholar
Pantokratoras, A. 2016 Steady flow of a non-Newtonian Carreau fluid across an unconfined circular cylinder. Meccanica 51, 1007–1016.CrossRefGoogle Scholar
Panton, R.L. 2013 Incompressible Flow. John Wiley & Sons.CrossRefGoogle Scholar
Patnana, V.K., Bharti, R.P. & Chhabra, R.P. 2009 Two-dimensional unsteady flow of power-law fluids over a cylinder. Chem. Engng Sci. 64, 2978–2999.CrossRefGoogle Scholar
Roshko, A. 1953 On the development of turbulent wakes from vortex streets. NACA Tech. Rep. TN-2913. California Institute of Technology.Google Scholar
Sahin, C. & Atalık, K. 2019 Comparison of inelastic and elastic non-Newtonian effects on the flow around a circular cylinder in periodic vortex shedding. J. Non-Newtonian Fluid Mech. 263, 1–14.CrossRefGoogle Scholar
Seo, J.H. & Mittal, R. 2011 A sharp-interface immersed boundary method with improved mass conservation and reduced spurious pressure oscillations. J. Comput. Phys. 230 (19), 7347–7363.CrossRefGoogle ScholarPubMed
Seshadri, P.K. & De, A. 2019 A robust sharp interface based immersed boundary framework for moving body problems with applications to laminar incompressible flows. Comput. Maths Appl. 263, 1–14.Google Scholar
Shimizu, K., Minekawa, K., Hirose, T. & Kawase, Y. 1999 Drop breakage in stirred tanks with Newtonian and non-newtonian fluid systems. Chem. Engng J. 72, 117–124.CrossRefGoogle Scholar
Sood, T., Roy, S. & Pathak, M. 2018 Effect of pulse rate variation on blood flow through axisymmetric and asymmetric stenotic artery models. Math. Biosci. 298, 1–18.CrossRefGoogle ScholarPubMed
Stansby, P.K. 1976 The locking-on of vortex shedding due to the cross-stream vibration of circular cylinders in uniform and shear flows. J. Fluid Mech. 74, 641–665.CrossRefGoogle Scholar
Story, A., Jaworski, Z., Simmons, M.J. & Nowak, E. 2018 Comparative PIV and LDA studies of newtonian and non-newtonian flows in an agitated tank. Chem. Papers 72, 593–602.CrossRefGoogle Scholar
Tang, G., Lu, L., Zhao, M., Liu, M. & Zong, Z. 2017 Phase jump and energy transfer of forced oscillating circular cylinder in uniform flow. Proc. Inst. Mech. Engrs M 231, 496–510.Google Scholar
Tanida, Y., Okajima, A. & Watanabe, Y. 1973 Stability of a circular cylinder oscillating in uniform flow or in a wake. J. Fluid Mech. 61, 769–784.CrossRefGoogle Scholar
Williamson, C.H.K. 1996 Vortex dynamics in the cylinder wake. Annu. Rev. Fluid Mech. 28, 477–539.CrossRefGoogle Scholar
Williamson, C.H.K. & Govardhan, R. 2004 Vortex-induced vibrations. Annu. Rev. Fluid Mech. 36, 413–455.CrossRefGoogle Scholar
Williamson, C.H.K. & Roshko, A. 1988 Vortex formation in the wake of an oscillating cylinder. J. Fluids Struct. 2, 355–381.CrossRefGoogle Scholar
Xiong, Y., Peng, S., Zhang, M. & Yang, D. 2019 Numerical study on the vortex-induced vibration of a circular cylinder in viscoelastic fluids. J. Non-Newtonian Fluid Mech. 272, 104170.CrossRefGoogle Scholar
Yokoi, Y. & Kamemoto, K. 1994 Vortex shedding from an oscillating circular cylinder in a uniform flow. Expl Therm. Fluid Sci. 8, 121–127.CrossRefGoogle Scholar
Yu, B. & Kawaguchi, Y. 2005 DNS of drag-reducing turbulent channel flow with coexisting newtonian and non-newtonian fluid. Trans. ASME: J. Fluids Engng 127, 929–935.Google Scholar
Yun, Y., Jee, S. & Lee, J. 2020 Unsteady flow of Carreau fluids around an impulsively moving cylinder. Phys. Fluids 32 (12), 123105.CrossRefGoogle Scholar
Zdravkovich, M. 1997 Flow around circular cylinders; vol. I. Fundamentals. J. Fluid Mech. 350, 377–378.Google Scholar

Alam et al Supplementary Movie 1

The variations in viscosity during the cylinder oscillation cycles at A*=0.4, f*=0.6, Cu = 1.0 and n = 0.25.

Download Alam et al Supplementary Movie 1(Video)
Video 2.3 MB

Alam et al Supplementary Movie 2

The variations in viscosity during the cylinder oscillation cycles at A*=0.4, f*=1.0, Cu = 1.0 and n = 0.25.

Download Alam et al Supplementary Movie 2(Video)
Video 1.4 MB

Alam et al Supplementary Movie 3

The variations in viscosity during the cylinder oscillation cycles at A*=1.0, f*=1.0, Cu = 1.0 and n = 0.25.

Download Alam et al Supplementary Movie 3(Video)
Video 1.5 MB

Alam et al Supplementary Movie 4

The variations in viscosity during the cylinder oscillation cycles at A*=1.2, f*=1.0, Cu = 1.0 and n = 0.25.

Download Alam et al Supplementary Movie 4(Video)
Video 1.5 MB

Alam et al Supplementary Movie 5

The variations in viscosity during the cylinder oscillation cycles at A*=0.4, f*=1.0, Cu = 10.0 and n = 0.25.

Download Alam et al Supplementary Movie 5(Video)
Video 2.6 MB

Alam et al Supplementary Movie 6

The variations in vorticity during the cylinder oscillation cycles at A*=0.4, f*=0.6, Cu = 1.0 and n = 0.25.

Download Alam et al Supplementary Movie 6(Video)
Video 2.3 MB

Alam et al Supplementary Movie 7

The variations in vorticity during the cylinder oscillation cycles at A*=0.4, f*=1.0, Cu = 1.0 and n = 0.25.

Download Alam et al Supplementary Movie 7(Video)
Video 1.5 MB

Alam et al Supplementary Movie 8

The variations in vorticity during the cylinder oscillation cycles at A*=1.0, f*=1.0, Cu = 1.0 and n = 0.25.

Download Alam et al Supplementary Movie 8(Video)
Video 1.6 MB

Alam et al Supplementary Movie 9

The variations in vorticity during the cylinder oscillation cycles at A*=1.2, f*=1.0, Cu = 1.0 and n = 0.25.

Download Alam et al Supplementary Movie 9(Video)
Video 1.6 MB

Alam et al Supplementary Movie 10

The variations in vorticity during the cylinder oscillation cycles at A*=0.4, f*=1.0, Cu = 10.0 and n = 0.25.

Download Alam et al Supplementary Movie 10(Video)
Video 2.2 MB