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Effect of blockage on fluid flow past a square cylinder at low Reynolds numbers

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Abstract

A channel confined flow around a bluff object is significantly different from its unconfined counterpart. A confined flow is presumably more stabilized due to the presence of the confinement. This causes a delay in the onset of flow separation and vortex shedding in comparison to the unconfined flow. While the above facts have been reported for the confined flow around a circular object in a channel, the same for a square object is infrequent. The present study focuses on the steady flow past a stationary square cylinder placed in a channel at low Reynolds numbers \(\left( {1 \le {\text{Re}} \le 30} \right)\). The behavior of the flow is observed through numerical simulation for various channel confinements (\(0.01 \le B \le 0.9\), blockage ratio). The steady state laminar two-dimensional incompressible flow equations are solved using a finite volume based technique. An effort is made to find the separation critical Reynolds number at all blockages. It is observed that the separation critical Reynolds number increases with an increase in the blockage ratio. Unsteady flow characteristics at various blockages are also studied at Re = 100. In the unsteady regime, the frequency of vortex shedding increases with an increase in the blockage.

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Abbreviations

B :

Blockage

B L :

Bubble length

C D :

Drag coefficient

C L :

Lift coefficient

C P :

Pressure coefficient

D :

Characteristic length

f :

Vortex shedding frequency

F D :

Drag force

F L :

Lift force

H :

Height of channel

p :

Dimensionless pressure

Re :

Reynolds number

St :

Strouhal number

t :

Dimensionless time

u, v :

Dimensionless velocities

x, y :

Dimensionless coordinates

\(\eta\) :

Kinematic viscosity of fluid

\(\rho\) :

Density of fluid

\(\omega\) :

Vorticity

cr :

Critical

s :

Separation

References

  1. Zdravkovich M M 1977 Review of flow interference between two circular cylinders in various arrangements. J. Fluids Eng. 99: 618–633

    Article  Google Scholar 

  2. Williamson C H K 1985 Evolution of a single wake behind a pair of bluff bodies. J. Fluid Mech. 159: 1–18

    Article  Google Scholar 

  3. Sumner D 2010 Two circular cylinders in cross-flow: a review. J. Fluids Struct. 26: 849–899

    Article  Google Scholar 

  4. Shair F H, Grove A S, Petersen E E and Acrivos A 1963 The effect of confining walls on the stability of the steady wake behind a circular cylinder. J. Fluid Mech. 17: 546–550

    Article  MATH  Google Scholar 

  5. Grove A S, Shair F H, Petersen E E and Acrivos A 1964 An experimental investigation of the steady separated flow past a circular cylinder. J. Fluid Mech. 19: 60–80

    Article  MATH  Google Scholar 

  6. Coutanceau M and Bouard R 1977 Experimental determination of the main features of the viscous flow in the wake of a circular cylinder in uniform translation. Part 1. Steady flow. J. Fluid Mech. 79: 231–256

    Article  Google Scholar 

  7. West G S and Apelt C J 1982 The effects of tunnel blockage and aspect ratio on the mean flow past a circular cylinder with Reynolds number between 104 and 105. J. Fluid Mech. 114: 361–377

    Article  Google Scholar 

  8. Behr M, Hastreiter D, Mittal S and Tezduyar T E 1995 Incompressible flow past a circular cylinder: dependence of the computed flow field on the location of the lateral boundaries. Comput. Methods Appl. Mech. Eng. 123: 309–316

    Article  Google Scholar 

  9. Mittal S, Singh S P, Kumar B and Kumar R 2006 Flow past bluff bodies: effect of blockage. Int. J. Comut. Fluid Dyn. 20: 163–173

    Article  MathSciNet  MATH  Google Scholar 

  10. Chen J H, Pritchard W G and Tavener S J 1995 Bifurcation for flow past a cylinder between parallel planes. J. Fluid Mech. 284: 23–41

    Article  MathSciNet  MATH  Google Scholar 

  11. Anagnostopoulos P, Iliadis G and Richardson S 1996 Numerical study of the blockage effects on viscous flow past a circular cylinder. Int. J. Numer. Methods Fluids 22: 1061–1074

    Article  MATH  Google Scholar 

  12. Chen J H 2000 Laminar separation of flow past a circular cylinder between two parallel plates. Proc. National Sci. Council Republic China Part A: Phys. Sci. Eng. 24: 341–351

    Google Scholar 

  13. Sahin M and Owens R G A numerical investigation of wall effects up to high blockage ratios on two-dimensional flow past a confined circular cylinder. Phys. Fluids 16: 1305–1320

  14. Chakraborty J, Verma N and Chhabra R P 2004 Wall effects in flow past a circular cylinder in a plane channel: a numerical study. Chem. Eng. Process. 43: 1529–1537

    Article  Google Scholar 

  15. Kumar B and Mittal S 2006 Effect of blockage on critical parameters for flow past a circular cylinder. Int. J. Numer. Methods Fluids 50: 987–1001

    Article  MATH  Google Scholar 

  16. Posdziech O and Grundmann R 2007 A systematic approach to the numerical calculation of fundamental quantities of the two-dimensional flow over a circular cylinder. J. Fluids Struct. 23: 479–499

    Article  Google Scholar 

  17. Sen S, Mittal S and Biswas G 2009 Steady separated flow past a circular cylinder at low Reynolds numbers. J. Fluid Mech. 620: 89–119

    Article  MATH  Google Scholar 

  18. Singha S and Sinhamahapatra K P 2010 Flow past a circular cylinder between parallel walls at low Reynolds number. Ocean Eng. 37: 757–769

    Article  Google Scholar 

  19. Rao M K, Sahu A K and Chhabra R P 2011 Effect of confinement on power-law fluid flow past a circular cylinder. Polym. Eng. Sci. 51: 2044–2065

    Article  Google Scholar 

  20. Mishra S K, Sen S and Verma A 2021 Steady flow past a circular cylinder under large blockage. Eur. J. Mech. B Fluids 87: 135–150

    Article  MathSciNet  MATH  Google Scholar 

  21. Okajima A, Yi D, Sakuda A and Nakano T 1997 Numerical study of blockage effects on aerodynamic characteristics of an oscillating rectangular cylinder. J. Wind Eng. Ind. Aerodyn. 67–68: 91–102

    Article  Google Scholar 

  22. Sohankar A, Norberg C and Davidson L 1998 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

    Article  MATH  Google Scholar 

  23. Patil P P and Tiwari S 2008 Effect of blockage ratio on wake transition for flow past square cylinder. Fluid Dyn. Res. 40: 753–778

    Article  MATH  Google Scholar 

  24. Breuer M, Bernsdorf J, Zeiser T and Durst F 2000 Accurate computations of the laminar flow past a square cylinder based on two different methods: Lattice-Boltzmann and finite-volume. Int. J. Heat Fluid Flow 21: 186–196

    Article  Google Scholar 

  25. Gupta A K, Sharma A, Chhabra R P and Eswaran V 2003 Two-dimensional steady flow of a power-law fluid past a square cylinder in a plane channel: momentum and heat-transfer characteristics. Ind. Eng. Chem. Res. 42: 5674–5686

    Article  Google Scholar 

  26. Paliwal B, Sharma A, Chhabra R P and Eswaran V 2003 Power law fluid flow past a square cylinder: momentum and heat transfer characteristics. Chem. Eng. Sci. 58: 5315–5329

    Article  Google Scholar 

  27. Sen S, Mittal S and Biswas G 2010 Flow past a square cylinder at low Reynolds numbers. Int. J. Numer. Methods Fluids 67: 1160–1174

    Article  MATH  Google Scholar 

  28. Sharma A and Eswaran V 2004 Heat and fluid flow across a square cylinder in the two-dimensional laminar flow regime. Numer. Heat Transf. A Appl. 45: 247–269

    Article  Google Scholar 

  29. Dhiman A K, Chhabra R P, Sharma A and Eswaran V 2006 Effects of Reynolds and Prandtl numbers on heat transfer across a square cylinder in the steady flow regime. Numer. Heat Transf. A Appl. 49: 717–731

    Article  Google Scholar 

  30. Davis R W, Moore E F and Purtell L P 1984 A numerical-experimental study of confined flow around rectangular cylinders. Phys. Fluids 27: 46–59

    Article  Google Scholar 

  31. Davis R W and Moore E F 1982 A numerical study of vortex shedding from rectangles. J. Fluid Mech. 116: 475–506

    Article  MATH  Google Scholar 

  32. Franke R, Rodi W and Schönung B 1990 Numerical calculation of laminar vortex-shedding flow past cylinders. J. Wind Eng. Ind. Aerodyn. 35: 237–257

    Article  Google Scholar 

  33. Mukhopadhaya A, Biswas G and Sundararajan T 1984 Numerical investigation of confined wakes behind a square cylinder in a channel. Int. J. Numer. Methods Fluids 14: 1473–1484

    Article  MATH  Google Scholar 

  34. Robichaux J, Balachandar S and Vanka S P 1999 Three-dimensional floquet instability of the wake of square cylinder. Phys. Fluids 11: 560–578

    Article  MathSciNet  MATH  Google Scholar 

  35. Saha A K, Biswas G and Muralidhar K 2003 Three-dimensional study of flow past a square cylinder at low Reynolds numbers. Int. J. Heat Fluid Flow 24: 54–66

    Article  Google Scholar 

  36. Kumar D, Sourav K, Sen S and Yadav P K 2018 Steady separation of flow from an inclined square cylinder with sharp and rounded base. Comput. Fluids 171: 29–40

    Article  MathSciNet  MATH  Google Scholar 

  37. Jiang H and Cheng L 2020 Flow separation around a square cylinder at low to moderate Reynolds numbers. Phys. Fluids 32: 044103

  38. Kumar D and Dhiman A 2016 Opposing buoyancy characteristics of Newtonian fluid flow around a confined square cylinder at low and moderate Reynolds numbers. Numer. Heat Transf. A Appl. 69: 874–897

    Article  Google Scholar 

  39. Dhiman A K, Sharma A and Kumar S 2012 Wall effects on the cross-buoyancy around a square cylinder in the steady regime. Braz. J. Chem. Eng. 29: 253–264

    Article  Google Scholar 

  40. Kumar D and Dhiman A K 2018 Effects of aiding buoyancy and channel confinement on the flow and heat transfer of dilatant fluids from a square obstacle. Comput. Therm. Sci. 10: 121–149

    Article  Google Scholar 

  41. Kumar D and Dhiman A K 2017 Effects of shear-thinning nature and opposing buoyancy from a square geometry in a confined framework. Numer. Heat Transf. A Appl. 72: 433–457

    Article  Google Scholar 

  42. Dhiman A, Sharma N and Kumar S 2014 Buoyancy-aided momentum and heat transfer in a vertical channel with a built-in square cylinder. Int. J. Sustain. Energy 33: 963–984

    Article  Google Scholar 

  43. Ansys Fluent, ver. 13: Theory Guide, Ansys Inc., USA, 2011

  44. Singh A P, De A K, Carpenter V K, Eswaran V and Muralidhar K 2009 Flow past a transversely oscillating square cylinder in free stream at low Reynolds numbers. Int. J. Numer. Methods Fluids 61: 658–682

    Article  MATH  Google Scholar 

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Authors and Affiliations

  1. CSIR - Central Mechanical Engineering Research Institute, Durgapur, 713209, India

    KRISHNA CHAITANYA N V V & DIPANKAR CHATTERJEE

  2. Academy of Scientific and Innovative Research, Ghaziabad, 201002, India

    KRISHNA CHAITANYA N V V & DIPANKAR CHATTERJEE

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  1. KRISHNA CHAITANYA N V V
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Correspondence to DIPANKAR CHATTERJEE.

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N V V, K.C., CHATTERJEE, D. Effect of blockage on fluid flow past a square cylinder at low Reynolds numbers. Sādhanā 47, 4 (2022). https://doi.org/10.1007/s12046-021-01777-z

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  • DOI: https://doi.org/10.1007/s12046-021-01777-z

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