Skip to main content
SpringerLink
Log in

Characteristics of drag and lift forces on a hemisphere under linear shear

  • Published:
Journal of Mechanical Science and Technology Aims and scope Submit manuscript

Abstract

In this study, the flow characteristics over a hemisphere under a linear shear are numerically investigated. The Reynolds number (Re) based on the velocity ( u c ) at the center of the inlet flow and the base diameter of the hemisphere ( d ) is in the range of 100 ≤ Re ≤ 300, and dimensionless inlet shear rate defined as s =|∇ u |d / u c is up to 0.1 where |∇u| the shear rate at inlet. In terms of the Reynolds number and the inlet shear rate, the vortical structures behind the hemisphere show various flow regimes such as steady axisymmetric, steady planar-symmetric, unsteady planar-symmetric and unsteady asymmetric. Associated with the change in the vortical structures, the drag force slightly increases with the inlet shear rate. However, the drag fluctuations show more complicated behavior in terms of the inlet shear rate, showing that they are more influenced by the change in vortical structures than the drag force itself. On the other hand, the magnitude and direction of the lift force change drastically depending on both the Reynolds number and the inlet shear rate. Inside the Reynolds number range (100 ≤ Re ≤ 300), the mean lift and lift fluctuations show maximum value at around Re = 190 and 210, respectively, which is different from the fact that for the sphere, they increase with increasing the Reynolds number in the range of 100 ≤ Re ≤ 300. This might be attributed to the fact that for the hemisphere, the change in the flow regime from steady to unsteady or from planarsymmetric to asymmetric occurs at lower Reynolds numbers than for the sphere. Also, the orientation characteristics of the lift force were investigated with the phase diagram (C y , C z ), together with the vortical structures existing behind the hemisphere. In the absence of the shear, the lift force is generated along any arbitrary direction because the location where vortex shedding happens is not determined a priori. However, when the inlet shear is applied to the hemisphere, the location of the vortex-loop detachment is restricted to the high-velocity side. Thus the lift force acts from the high-velocity side to the low-velocity side. However at very small Reynolds numbers such as Re = 1 the direction of the lift force becomes opposite. For the hemisphere considered in this study, the Reynolds number corresponding to the lift reversal is much smaller than that for the sphere studied by Kurose and Komori (1999).

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. V. Armenio and V. Fiorotto, The importance of the forces acting on particles in turbulent flows, Phys. Fluids, 13 (2001) 2437–2440.

    Article  Google Scholar 

  2. S. Balachandar and J. K. Eaton, Turbulent dispersed multiphase flow, Annu. Rev. Fluid Mech., 42 (2010) 111–133.

    Article  Google Scholar 

  3. J. Kim and S. Balachandar, Mean and fluctuating components of drag and lift forces on an isolated finite-sized particle in turbulence, Theoret. Comput. Fluid Dyn., 26 (2012) 185–204.

    Article  MATH  Google Scholar 

  4. E. E. Michaelides, Hydrodynamic force and heat/mass transfer from particles, bubbles and drops, J. Fluids Eng., 125 (2003) 209–238.

    Article  Google Scholar 

  5. A. Giusti, F. Lucci and A. Soldati, Influence of the lift force in direct numerical simulation of upward/downward turbulent channel flow laden with surfactant contaminated microbubbles, Chem. Eng. Sci., 60 (2005) 6176–6187.

    Article  Google Scholar 

  6. M. Jenny, J. Dusek and G. Bouchet, Instabilities and transition of a sphere falling or ascending freely in a Newtonian fluid, J. Fluid Mech., 508 (2004) 201–239.

    Article  MATH  MathSciNet  Google Scholar 

  7. C. Marchioli, M. Picciotto and A. Soldati, Influence of gravity and lift on particle velocity statistics and transfer rates in turbulent vertical channel flow, Int. J. Multiphase Flow, 33 (2007) 227–251.

    Article  Google Scholar 

  8. J. Lu, S. Biswas and G. Tryggvason, A DNS study of laminar bubbly flows in a vertical channel, Int. J. Multiphase Flow, 32 (2006) 643–660.

    Article  MATH  Google Scholar 

  9. Q. Wang, K. D. Squires, M. Chen and J. B. McLaughlin, On the role of the lift force in turbulence simulations of particle deposition, Int. J. Multiphase Flow, 23 (1997) 749–763.

    Article  MATH  Google Scholar 

  10. P. G. Saffman, The lift on a simple sphere in slow linear flow, J. Fluid Mech., 22 (1965) 385–400.

    Article  MATH  Google Scholar 

  11. P. Bagchi and S. Balachandar, Shear versus vortex-induced lift force on a rigid sphere at moderate Re, J. Fluid Mech., 473 (2002) 379–388.

    Article  MATH  MathSciNet  Google Scholar 

  12. P. Bagchi and S. Balachandar, Effect of free rotation on the motion of a solid sphere in linear shear flow at moderate Reynolds number, Phys. Fluids, 14 (2003) 2719–2737.

    Article  Google Scholar 

  13. R. Kurose and S. Komori, Drag and lift forces on a rotating sphere in a linear shear flow, J. Fluid Mech., 384 (1999) 183–206.

    Article  MATH  MathSciNet  Google Scholar 

  14. A. Tomiyama, H. Tamai, I. Zun and S. Hosokawa, Transverse migration of single bubbles in simple shear flows, Chem. Eng. Sci., 57 (2002) 1849–1858.

    Article  Google Scholar 

  15. F. Gentile, C. Chiappini, D. Fine, R. C. Bhavane, M. S. Peluccio, M. M.-C. Cheng, X. Liu, M. Ferrari and P. Decuzzi, The effect of shape on the margination dynamics of non-neutrally buoyant particles in two-dimensional shear flows, J. Biomech., 41 (2008) 2312–2138.

    Article  Google Scholar 

  16. S.-Y. Lee, M. Ferrari and P. Decuzzi, Shaping nano-/microparticles for enhanced vascular interaction in laminar flows, Nanotechnology, 29 (2009) 495101.

    Article  Google Scholar 

  17. M. Zastawny, G. Mallouppas, F. Zhao and B. van Wachem, Derivation of drag and lift force and torque coefficients for non-spherical particles in flows, Int. J. Multiphase Flow, 39 (2011) 227–239.

    Article  Google Scholar 

  18. G. Bellani, M. L. Byron, A. G. Collignon, C. R. Meyer and E. A. Variano, Shape effects on turbulent modulation by large nearly neutrally buoyant particles, J. Fluid Mech., 712 (2012) 41–60.

    Article  MATH  MathSciNet  Google Scholar 

  19. M. Rastello, J.-L. Marie and M. Lance, Drag and lift forces on clean spherical and ellipsoidal bubbles in a solid-body rotating flow, J. Fluid Mech., 682 (2011) 434–459.

    Article  MATH  Google Scholar 

  20. A. Richter and P. A. Nikrityuk, Drag forces and heat transfer coefficients for spherical, cuboidal and ellipsoidal particles in cross flow at sub-critical Reynolds numbers, Int. J. Heat Mass Transfer, 55 (2012) 1343–1354.

    Article  MATH  Google Scholar 

  21. C. Sasmal, R. Shyam and R. P. Chhabra, Laminar flow of power-law fluids past a hemisphere: momentum and force convection heat transfer characteristics, Int. J. Heat Mass Transfer, 63 (2013) 51–64.

    Article  Google Scholar 

  22. J. Kim, D. Kim and H. Choi, An immersed-boundary finite-volume method for simulations of flow in complex geometries, J. Comput. Phys., 171 (2001) 132–150.

    Article  MATH  MathSciNet  Google Scholar 

  23. D. Kim and H. Choi, Laminar flow past a hemisphere, Phys. Fluids, 15 (2003) 2457–2460.

    Article  Google Scholar 

  24. K. Akselvoll and P. Moin, An efficient method for temporal integration of the Navier-Stokes equations in confined axisymmetric geometries, J. Comput. Phys., 125 (1996) 454–463.

    Article  MATH  MathSciNet  Google Scholar 

  25. D. Kim, H. Choi and H. Choi, Characteristics of laminar flow past a sphere in uniform shear, Phys. Fluids, 17 (2005) 103602.

    Article  Google Scholar 

  26. S. Kang, Uniform-shear flow over a circular cylinder at low Reynolds numbers, J. Fluids Struct., 22 (2006) 541–555.

    Article  Google Scholar 

  27. D. Fabre, F. Auguste and J. Magnaudet, Bifurcations and symmetry breaking in the wake of axisymmetric bodies, Phys. Fluids, 20 (2008) 051702.

    Article  Google Scholar 

  28. J. Magnaudet and G. Mougin, Wake instability of a fixed spheroidal bubble, J. Fluid Mech., 572 (2007) 311–337.

    Article  MATH  MathSciNet  Google Scholar 

  29. B. Yang and A. Prosperetti, Linear stability of the flow past a spheroidal bubble, J. Fluid Mech., 582 (2007) 53–78.

    Article  MATH  MathSciNet  Google Scholar 

  30. J. Jeong and F. Hussain, On the identification of a vortex, J. Fluid Mech., 285 (1995) 69–94.

    Article  MATH  MathSciNet  Google Scholar 

  31. S. Sen, S. Mittal and G. Biswas, Flow past a square cylinder at low Reynolds numbers, Int. J. Numer. Meth. Fluids, 67 (2011) 1160–1174.

    Article  MATH  Google Scholar 

  32. J. H. C. Coppus, K. Rietema and S. P. P. Ottengraf, Wake phenomena behind spherical-cap bubbles and solid spherical-cap bodies, Trans. Instn. Chem. Engrs., 55 (1977) 122–129.

    Google Scholar 

  33. Y. Suh and C. Lee, A numerical method for the calculation of drag and lift of a deformable droplet in shear flow, J. Comput. Phys., 241 (2013) 35–57.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mechanical System Design Engineering, Seoul National University of Science and Technology, Seoul, 139-743, Korea

    Jungwoo Kim

Authors
  1. Jungwoo Kim
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Jungwoo Kim.

Additional information

Recommended by Associate Editor Hyoung-gwon Choi

Jungwoo Kim obtained his B.S., M.S. and Ph.D. degrees at the Department of Mechanical Engineering, Seoul National University, Korea, in 1999, 2001 and 2005, respectively. Dr. Kim is currently an assistant professor at the Department of Mechanical System Design Engineering, Seoul National University of Science and Technology.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Kim, J. Characteristics of drag and lift forces on a hemisphere under linear shear. J Mech Sci Technol 29, 4223–4230 (2015). https://doi.org/10.1007/s12206-015-0917-0

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s12206-015-0917-0

Keywords

Search

Navigation