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Steady flow of a power-law non-Newtonian fluid across an unconfined square cylinder

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Abstract

A two-dimensional flow of a non-Newtonian power-law fluid directed normally to a horizontal cylinder with a square cross section is considered in the present paper. The problem is investigated numerically with a finite volume method by using the commercial code Ansys Fluent with a very large computational domain so that the flow could be considered unbounded. The investigation covers the power-law index from 0.1 to 2.0 and the Reynolds number range from 0.001 to 45.000. It is found that the drag coefficient for low Reynolds numbers and low power-law index (n ≤ 0.5) obeys the relationship C D = A/Re. An equation for the quantity A as a function of the power-law index is derived. The drag coefficient becomes almost independent of the power-law index at high Reynolds numbers and the wake length changes nonlinearly with the Reynolds number and power-law index.

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References

  1. M. M. Zdravkovich, Flow around Circular Cylinders (Oxford Univ. Press, Oxford, 1997), Vol.1.

  2. F. White, Viscous Fluid Flow (McGraw-Hill, New York, 2006).

    Google Scholar 

  3. R. L. Panton, Incompressible Flow (Wiley, 2005).

    MATH  Google Scholar 

  4. H. Glauert, “Wind Tunnel Interference on Wings, Bodies and Airscrews,” Aeronaut. Res. Counc. Repts Mem., No. 1566 (1933).

  5. E. C. Maskell, “A Theory of the Blockage Effects on Bluff Bodies and Stalled Wings in a Closed Wind Tunnel,” Aeronaut. Res. Counc. Repts Mem., No. 3400 (1963).

  6. F. M. Najjar and S. P. Vanka, “Simulations of the Unsteady Separated Flow Past a Normal Flat Plate,” Int. J. Numer. Methods Fluids 21, 525–547 (1995).

    Article  ADS  MATH  Google Scholar 

  7. K. I. Babenko, N. D. Vedenskaya, and M. G. Orlova, “Calculation of Stationary Viscous Liquid Flow Past a Circular Cylinder,” Comput. Math. Math. Phys. 15 (1) (1975).

    Google Scholar 

  8. B. Fornberg, “A Numerical Study of Steady Viscous Flow Past a Circular Cylinder,” J. Fluid Mech. 98, 819–855 (1980).

    Article  ADS  MATH  Google Scholar 

  9. C. F. Lange, F. Durst, and M. Breuer, “Momentum and Heat Transfer from Cylinders in Laminar Cross Flow at 10-4 ≤ Re ≤ 200,” Int. J. Heat Mass Transfer 41, 3409–3430 (1998).

    Article  MATH  Google Scholar 

  10. D. Stojkovich, M. Breuer, and F. Durst, “Effect of High Rotation Rates on the Laminar Flow around a Circular Cylinder,” Phys. Fluids 14, 3160–3178 (2002).

    Article  ADS  MathSciNet  MATH  Google Scholar 

  11. O. Posdziech and R. Grundmann, “A Systematic Approach to the Numerical Calculation of Fundamental Quantities of the Two-Dimensional Flow over a Circular Cylinder,” J. Fluids Structures 23, 479–499 (2007).

    Article  ADS  Google Scholar 

  12. P. Sivakumar, R. P. Bharti, and R. P. Chhabra, “Steady Flow of Power-Law Fluids across an Unconfined Elliptical Cylinder,” Chem. Eng. Sci. 62, 1682–1702 (2007).

    Article  Google Scholar 

  13. S. Sen, S. Mittal, and G. Biswas, “Steady Separated Flow Past a Circular Cylinder at Low Reynolds Numbers,” J. Fluid Mech. 620, 89–119 (2009).

    Article  ADS  MATH  Google Scholar 

  14. R. Franke, W. Rodi, and B. Schonung, “Numerical Calculation of Laminar Vortex-Shedding Flow Past Cylinders,” J. Wind Eng. Industr. Aerodyn. 35, 237–257 (1990).

    Article  Google Scholar 

  15. K. M. Kelkar and S. V. Patankar, “Numerical Prediction of Vortex Shedding behind a Square Cylinder,” Int. J. Numer. Methods Fluids 14, 327–341 (1992).

    Article  ADS  MATH  Google Scholar 

  16. A. Sohankar, C. Norberg, and L. Davidson, “Low-Reynolds Number Flow around a Square Cylinder at Incidence: Study of Blockage, Onset of Vortex Shedding and Outlet Boundary Condition,” Int. J. Numer. Methods Fluids 26, 39–56 (1998).

    Article  ADS  MATH  Google Scholar 

  17. A. Sharma and V. Eswaran, “Heat and Fluid Flow Across a Square Cylinder in the Two-Dimensional Laminar Regime,” Numer. Heat Transfer 45, 247–269 (2004).

    Article  ADS  Google Scholar 

  18. A. K. Dhiman, R. P. Chhabra, and V. Eswaran, “Steady Flow of Power-Law Fluids Across a Square Cylinder,” Chem. Eng. Res. Design. 84, 300–310 (2006).

    Article  MATH  Google Scholar 

  19. A. K. Dhiman, N. Anjaiah, R. P. Chhabra, and V. Eswaran, “Mixed Convection from a Heated Square Cylinder to Newtonian and Power Law Fluids,” Trans. ASME, J. Fluids Eng. 129, 506–513 (2007).

    Article  Google Scholar 

  20. A. K. Sahu, R. P. Chhabra, and V. Eswaran, “Two-Dimensional Unsteady Laminar Flow of a Power Law Fluid Across a Square Cylinder,” J. Non-Newtonian Fluid Mech. 160, 157–167 (2009).

    Article  MATH  Google Scholar 

  21. P. K. Rao, A. K. Sahu, and R. P. Chhabra, “Momentum and Heat Transfer from a Square Cylinder in Power-Law Fluids,” Int. J. Heat Mass Transfer 54, 390–403 (2011).

    Article  MATH  Google Scholar 

  22. P. K. Rao, C. Sasmal, A. K. Sahu, et al., “Effect of Power-Law Fluid Behavior on Momentum and Heat Transfer Characteristics of an Inclined Square Cylinder in Steady Flow Regime,” Int. J. Heat Mass Transfer 54, 2854–2867 (2011).

    Article  MATH  Google Scholar 

  23. S. U. Islam, C. Y. Zhou, A. Shah, and P. Xie, “Numerical Simulation of Flow Past Rectangular Cylinders with Different Aspect Ratios using the Incompressible Lattice Boltzmann Method,” J. Mech. Sci. Technol. 26, 1027–1041 (2012).

    Article  Google Scholar 

  24. S. Krishnan and A. Kannan, “Effect of Blockage Ratio on Drag and Heat Transfer from a Centrally Located Sphere in Pipe Flow,” Eng. Appl. Comput. Fluid Mech. 4, 396–414 (2010).

    Google Scholar 

  25. A. K. Dhiman, R. P. Chhabra, and V. Eswaran, “Flow and Heat Transfer across a Confined Square Cylinder in the Steady Flow Regime: Effect of Peclet Number,” Int. J. Heat Mass Transfer 48, 4598–4614 (2005).

    Article  MATH  Google Scholar 

  26. D-H. Yoon, K-S. Yang, and C-B. Choi, “Flow Past a Square Cylinder with an Angle of Incidence,” Phys. Fluids 22, 043603 (2010).

    Article  ADS  MATH  Google Scholar 

  27. F. White, Fluid Mechanics (McGraw-Hill, New York, 1998).

    Google Scholar 

  28. J. P. Denier and P. P. Dabrowski, “On the Boundary-Layer Equations for Power-Law Fluids,” Proc. Roy. Soc. London, Ser. A 460, 3143–3158 (2004).

    Article  ADS  MathSciNet  MATH  Google Scholar 

  29. P. Sivakumar, R. P. Bharti, and R. P. Chhabra, “Effect of Power-Law Index on Critical Parameters for Power-Law Flow across an Unconfined Circular Cylinder,” Chem. Eng. Sci. 61, 6035–6046 (2006).

    Article  Google Scholar 

  30. B. Wu and S. Chen, “Simulation of Non-Newtonian Fluid Flow in Anaerobic Digesters,” Biotechnol. Bioeng. 99, 700–711 (2008).

    Article  Google Scholar 

  31. A. Pantokratoras, “Further Results on Non-Newtonian Power-Law Flows Past a Two-Dimensional Flat Plate with Finite Length,” J. Mech. Sci. Technol. 27, 1995–2003 (2013).

    Article  Google Scholar 

  32. A. Pantokratoras, “Steady Laminar Assisted Mixed Convection Normally to a Heated Horizontal Plate with Finite Length,” Int._J. Thermal Sci. 65, 158–169 (2013).

    Article  Google Scholar 

  33. S. Sen, S. Mittal, and G. Biswas, “Flow Past a Square Cylinder at Low Reynolds Numbers,” Int. J. Numer. Methods Fluids 67, 1160–1174 (2011).

    Article  ADS  MATH  Google Scholar 

  34. A. Beaudoin, S. Huberson, and E. Rivoalen, “From Navier–Stokes to Stokes by Means of Particle Methods,” J. Comput. Phys. 214, 264–283 (2006).

    Article  ADS  MathSciNet  MATH  Google Scholar 

  35. S. C. R. Dennis, W. Qiang, M. Coutanceau, and J. L. Launay, “Viscous Flow Normal to a Flat Plate at Moderate Reynolds Numbers,” J. Fluid Mech. 248, 605–635 (1993).

    Article  ADS  Google Scholar 

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Authors and Affiliations

  1. School of Engineering, Democritus University of Thrace, Xanthi, 67100, Greece

    A. Pantokratoras

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Correspondence to A. Pantokratoras.

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Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 57, No. 2, pp. 83–95, March–April, 2016.

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Pantokratoras, A. Steady flow of a power-law non-Newtonian fluid across an unconfined square cylinder. J Appl Mech Tech Phy 57, 264–274 (2016). https://doi.org/10.1134/S0021894416020097

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  • DOI: https://doi.org/10.1134/S0021894416020097

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