Skip to main content
SpringerLink
Log in

Mean and fluctuating components of drag and lift forces on an isolated finite-sized particle in turbulence

  • Original Paper
  • Published:
Theoretical and Computational Fluid Dynamics Aims and scope Submit manuscript

Abstract

We perform fully resolved direct numerical simulations of an isolated particle subjected to free-stream turbulence in order to investigate the effect of turbulence on the drag and lift forces at the level of a single particle, following Bagchi and Balachandar’s work (Bagchi and Balachandar in Phys Fluids 15:3496–3513, 2003). The particle Reynolds numbers based on the mean relative particle velocity and the particle diameter are Re = 100, 250 and 350, which covers three different regimes of wake evolution in a uniform flow: steady axisymmetric wake, steady planar symmetric wake, and unsteady planar symmetric vortex shedding. At each particle Reynolds number, the turbulent intensity is 5–10% of the mean relative particle velocity, and the corresponding diameter of the particle is comparable to or larger than the Kolmogorov scale. The simulation results show that standard drag values determined from uniform flow simulations can accurately predict the drag force if the turbulence intensity is sufficiently weak (5% or less compared to the mean relative velocity). However, it is shown that for finite-sized particles, flow non-uniformity, which is usually neglected in the case of the small particles, can play an important role in determining the forces as the relative turbulence intensity becomes large. The influence of flow non-uniformity on drag force could be qualitatively similar to the Faxen correction. In addition, finite-sized particles at sufficient Reynolds number are inherently subjected to stochastic forces arising from their self-induced vortex shedding in addition to lift force arising from the local ambient flow properties (vorticity and strain rate). The effect of rotational and strain rate of the ambient turbulence seen by the particle on the lift force is explored based on the conditional averaging using the generalized representation of the quasi-steady force proposed by Bagchi and Balachandar (J Fluid Mech 481:105–148, 2003). From the present study, it is shown that at Re = 100, the lift force is mainly influenced by the surrounding turbulence, but at Re = 250 and 350, the lift force is affected by the wake structure as well as the surrounding turbulence. Thus, for a finite-sized particle of sufficient Reynolds number supporting self-induced vortex shedding, the lift force will not be completely correlated with the ambient flow. Therefore, it appears that in order to reliably predict the motion of a finite-sized particle in turbulence, it is important to incorporate both a deterministic component and a stochastic component in the force model. The best deterministic contribution is given by the conditional average. The influence of ambient turbulence at the scale of the particle, which are not accounted for in the deterministic contribution, can be considered in stochastic manner. In the modeling of lift force, additional stochastic contribution arising from self-induced vortex shedding must also be included.

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. Bagchi P., Balachandar S.: Effect of turbulence on the drag and lift of a particle. Phys. Fluids 15, 3496–3513 (2003)

    Article  Google Scholar 

  2. Bagchi P., Balachandar S.: Inertial and viscous forces on a rigid sphere in straining flows at moderate Reynolds numbers. J. Fluid Mech. 481, 105–148 (2003)

    Article  MATH  Google Scholar 

  3. Balachandar S., Eaton J.: Turbulent dispersed multiphase flows. Annu. Rev. Fluid Mech. 42, 111–133 (2009)

    Article  Google Scholar 

  4. Pan Y., Banerjee S.: Numerical investigation of the effects of large particles on wall-turbulence. Phys. Fluids 9, 3786–3807 (1997)

    Article  Google Scholar 

  5. Kajishima T., Takiguchi S., Hamasaki H., Miyake Y.: Turbulence structure of particle-laden flow in a vertical plane channel due to vortex shedding. JSME Int. J. Series B: Fluids Thermal Eng. 44, 526–535 (2001)

    Article  Google Scholar 

  6. Ten Cate A., Derksen J.J., Portela L.M., Van den Akker H.E.A.: Fully resolved simulations of colliding monodisperse spheres in forced isotropic turbulence. J. Fluid Mech. 519, 233–271 (2004)

    Article  MATH  Google Scholar 

  7. Uhlmann M.: Interface-resolved direct numerical simulation of vertical particulate channel flow in the turbulent regime. Phys. Fluids 20, 053305 (2008)

    Article  Google Scholar 

  8. Auton T.R.: The lift force on a spherical body in a rotational flow. J. Fluid Mech. 183, 199–218 (1987)

    Article  MATH  Google Scholar 

  9. Auton T.R., Hunt J.C.R., Prud’Homme M.: The force exerted on a body in inviscid unsteady non-uniform rotational flow. J. Fluid Mech. 197, 241–257 (1988)

    Article  MATH  MathSciNet  Google Scholar 

  10. Maxey M.R., Riley J.J.: Equation of motion for a small rigid sphere in nonuniform flow. Phys. Fluids 26, 883–889 (1983)

    Article  MATH  Google Scholar 

  11. Saffman P.G.: The lift on a small sphere in a slow shear flow. J. Fluid Mech. 22, 385–400 (1965)

    Article  MATH  Google Scholar 

  12. Schiller L., Neumann A.: Uber die grundlegenden Berechungen bei der Schwer kraftaufbereitung. Verein Deutscher Ingenieure 77, 318–320 (1933)

    Google Scholar 

  13. Magnaudet J., Eames I.: The motion of high-Reynolds-mumber bubbles in inhomogeneous flows. Annu. Rev. Fluid Mech. 32, 659–708 (2000)

    Article  MathSciNet  Google Scholar 

  14. Lumley J.L.: Two-phase and non-newtonian flows. Topic Phys. 12, 290–324 (1978)

    Google Scholar 

  15. Elghobashi S.E., Truesdell G.C.: Direct simulation of particle dispersion in decaying isotropic turbulence. J. Fluid Mech. 242, 655–700 (1992)

    Article  Google Scholar 

  16. Natarajan R., Acrivos A.: The instability of the steady flow past spheres and disks. J. Fluid Mech. 254, 323–344 (1993)

    Article  MATH  Google Scholar 

  17. Mittal R.: Response of the sphere wake to freestream fluctuations. Theor. Comput. Fluid Dyn. 13, 397–419 (2000)

    Article  MATH  Google Scholar 

  18. Bagchi P., Balachandar S.: Response of the wake of an isolated particle to an isotropic turbulent flow. J. Fluid Mech. 518, 95–123 (2004)

    Article  MATH  Google Scholar 

  19. Burton T.M., Eaton J.K.: Fully resolved simulations of particle-turbulence interaction. J. Fluid Mech. 545, 67–111 (2005)

    Article  MATH  Google Scholar 

  20. Merle A., Legendre D., Magnaudet J.: Forces on a high-Reynolds-number spherical bubble in a turbulent flow. J. Fluid Mech. 532, 53–62 (2005)

    Article  MATH  Google Scholar 

  21. Langford J., Moser R.D.: Optimal LES formulations for isotropic turbulence. J. Fluid Mech. 398, 321–346 (1999)

    Article  MATH  MathSciNet  Google Scholar 

  22. Wakaba, L.: On the response of a spherical particle to unsteady flows at finite Reynolds numbers, Ph.D. thesis, University of Illinois at Urbana-Champaign (2006)

  23. Bagchi P., Ha M.Y., Balachandar S.: Direct numerical simulation of flow and heat transfer from a sphere in a uniform cross-flow. Trans. ASME: J. Fluids Eng. 123, 347–358 (2001)

    Article  Google Scholar 

  24. Johnson T.A., Patel V.C.: Flow past a sphere up to a Reynolds number of 300. J. Fluid Mech. 378, 19–70 (1999)

    Article  Google Scholar 

  25. Kim D., Choi H.: Laminar flow past a sphere rotating in the streamwise direction. J. Fluid Mech. 461, 365–386 (2002)

    Article  MATH  MathSciNet  Google Scholar 

  26. Brucato A., Grisafi F., Montante G.: Particle drag coefficients in turbulent fluids. Chem. Eng. Sci. 53, 3295–3314 (1998)

    Article  Google Scholar 

  27. Kulick J.D., Fessler J.R., Eaton J.K.: Particle response and turbulence modulation in fully developed channel flow. J. Fluid Mech. 277, 109–134 (1994)

    Article  Google Scholar 

  28. Longmire E.K., Eaton J.K.: Structure of a particle-laden round jet. J. Fluid Mech. 236, 217–257 (1992)

    Article  Google Scholar 

  29. Parthasarathy R.N., Faeth G.M.: Turbulence modulation in homogeneous dilute-particle laden flows. J. Fluid Mech. 220, 485–514 (1990)

    Article  Google Scholar 

  30. Tsuji Y., Morikawa Y., Shiomi H.: LDV measurement of an air-solid two-phase flow in a vertical pipe. J. Fluid Mech. 139, 417–434 (1984)

    Article  Google Scholar 

  31. Tsuji Y., Morikawa Y., Tanaka T., Karimine K., Nishida S.: Measurement of an axisymmetric jet laden with coarse particles. Int. J. Multiphase Flow 14, 565–574 (1988)

    Article  Google Scholar 

  32. Wu J.-S., Faeth G.M.: Sphere wakes at moderate Reynolds numbers in a turbulent environment. AIAA J. 32, 535–541 (1994)

    Article  Google Scholar 

  33. Wu J.-S., Faeth G.M.: Effect of ambient turbulence intensity on sphere wakes at intermediate Reynolds numbers. AIAA J. 33, 171–173 (1994)

    Article  Google Scholar 

  34. Yusof, J.: Interaction of massive particles with turbulence, Ph.D. thesis, Department of Mechanical Engineering, Cornell University (1996)

  35. Zeng L., Balachandar S., Fischer P., Najjar F.: Interactions of a stationary finite-sized particle with wall turbulence. J. Fluid Mech. 594, 271–305 (2008)

    Article  MATH  Google Scholar 

  36. Papoulis A.: Probability, random variables and stochastic theory, vol. 2nd Edn. McGraw-Hill, Newyork (1984)

    Google Scholar 

  37. Moreau A., Teytaud O., Bertoglio J.P.: Optimal estimation for large-eddy simulation of turbulence and application to the analysis of subgrid models. Phys. Fluids 18, 105101 (2006)

    Article  MathSciNet  Google Scholar 

  38. Sawford B.: Turbulent relative dispersion. Annu. Rev. Fluid Mech. 33, 265–287 (2001)

    Article  Google Scholar 

  39. Faxen H.: Der Widerstand gegen die Bewegung einer starren Kugel in einer zum den Flussigkeit, die zwischen zwei parallelen, ebener Wanden eingeschlossen ist. Ann. Phys. (Leipzig) 68, 89–119 (1922)

    Google Scholar 

  40. Bouchet G., Mebarek M., Dusek J.: Hydrodynamic forces acting on a rigid fixed sphere in early transitional regimes. Eur. J. Mech. B/Fluids 25, 321–336 (2006)

    Article  MATH  Google Scholar 

  41. Tomboulides A.G., Orszag S.A.: Numerical investigation of transitional and weak turbulent flow past a sphere. J. Fluid Mech. 416, 45–73 (2000)

    Article  MATH  MathSciNet  Google Scholar 

  42. Jimenez J., Wray A.A., Saffman P.G., Rogallo R.S.: The structure of intense vorticity in isotropic turbulence. J. Fluid Mech. 255, 65–90 (1993)

    Article  MATH  MathSciNet  Google Scholar 

  43. Wang C.C.: A new representative theorem for isotropic functions. Arch. Rat. Mech. Anal. 36, 166–197 (1970)

    Article  MATH  Google Scholar 

  44. Smith G.F.: On isotropic functions of symmetric tensors, skew-symmetric tensors and vectors. Int. J. Eng. Sci. 9, 899–916 (1971)

    Article  MATH  Google Scholar 

  45. Snyder W.H., Lumley J.L.: Some measurements of particle velocity autocorrelation functions in a turbulent flow. J. Fluid Mech. 48, 41–71 (1971)

    Article  Google Scholar 

Download references

Author information

Author notes

  1. Jungwoo Kim

    Present address: Korea Atomic Energy Research Institute, Deokjin 150, Yuseong, Daejeon, 305-353, Korea

Authors and Affiliations

  1. Department of Mechanical and Aerospace Engineering, University of Florida, Gainesville, FL, 32611, USA

    Jungwoo Kim & S. Balachandar

Authors
  1. Jungwoo Kim
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. S. Balachandar
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to S. Balachandar.

Additional information

Communicated by Eldredge.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Kim, J., Balachandar, S. Mean and fluctuating components of drag and lift forces on an isolated finite-sized particle in turbulence. Theor. Comput. Fluid Dyn. 26, 185–204 (2012). https://doi.org/10.1007/s00162-010-0219-1

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00162-010-0219-1

Keywords

Search

Navigation