Hostname: page-component-cd9895bd7-mkpzs Total loading time: 0 Render date: 2024-12-22T01:23:05.208Z Has data issue: false hasContentIssue false
  • English
  • Français

Particle dynamics in the channel flow of a turbulent particle–gas suspension at high Stokes number. Part 2. Comparison of fluctuating force simulations and experiments

Published online by Cambridge University Press:  06 October 2011

Partha S. Goswami  and
V. Kumaran
Partha S. Goswami
Affiliation:
Department of Chemical Engineering, Indian Institute of Science, Bangalore 560 012, India
V. Kumaran*
Affiliation:
Department of Chemical Engineering, Indian Institute of Science, Bangalore 560 012, India
*
†Email address for correspondence: kumaran@chemeng.iisc.ernet.in
Get access Rights & Permissions [Opens in a new window]

Abstract

The particle and fluid velocity fluctuations in a turbulent gas–particle suspension are studied experimentally using two-dimensional particle image velocimetry with the objective of comparing the experiments with the predictions of fluctuating force simulations. Since the fluctuating force simulations employ force distributions which do not incorporate the modification of fluid turbulence due to the particles, it is of importance to quantify the turbulence modification in the experiments. For experiments carried out at a low volume fraction of (mass loading is 0.19), where the viscous relaxation time is small compared with the time between collisions, it is found that the gas-phase turbulence is not significantly modified by the presence of particles. Owing to this, quantitative agreement is obtained between the results of experiments and fluctuating force simulations for the mean velocity and the root mean square of the fluctuating velocity, provided that the polydispersity in the particle size is incorporated in the simulations. This is because the polydispersity results in a variation in the terminal velocity of the particles which could induce collisions and generate fluctuations; this mechanism is absent if all of the particles are of equal size. It is found that there is some variation in the particle mean velocity very close to the wall depending on the wall-collision model used in the simulations, and agreement with experiments is obtained only when the tangential wall–particle coefficient of restitution is 0.7. The mean particle velocity is in quantitative agreement for locations more than 10 wall units from the wall of the channel. However, there are systematic differences between the simulations and theory for the particle concentrations, possibly due to inadequate control over the particle feeding at the entrance. The particle velocity distributions are compared both at the centre of the channel and near the wall, and the shape of the distribution function near the wall obtained in experiments is accurately predicted by the simulations. At the centre, there is some discrepancy between simulations and experiment for the distribution of the fluctuating velocity in the flow direction, where the simulations predict a bi-modal distribution whereas only a single maximum is observed in the experiments, although both distributions are skewed towards negative fluctuating velocities. At a much higher particle mass loading of 1.7, where the time between collisions is smaller than the viscous relaxation time, there is a significant increase in the turbulent velocity fluctuations by –2 orders of magnitude. Therefore, it becomes necessary to incorporate the modified fluid-phase intensity in the fluctuating force simulation; with this modification, the mean and mean-square fluctuating velocities are within 20–30 % of the experimental values.

JFM classification

Multiphase and Particle-laden Flows: Particle/fluid flow Turbulent Flows: Turbulent Flows
Type
Papers
Information
Journal of Fluid Mechanics , Volume 687 , 25 November 2011 , pp. 41 - 71
Copyright
Copyright © Cambridge University Press 2011

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Footnotes

‡

Present address: CSIR Centre for Mathematical Modelling and Computer Simulation, Bangalore, India.

References

1. Bagchi, P. & Balachandar, S. 2003 Effect of turbulence on the drag and lift of a particle. Phys. Fluids 15, 3496–3513.CrossRefGoogle Scholar
2. Balachandar, S. & Eaton, J. K. 2010 Turbulent dispersed multiphase flow. Annu. Rev. Fluid Mech. 42, 111–133.CrossRefGoogle Scholar
3. Bose, M. & Kumaran, V. 2004 Velocity distribution for a two-dimensional sheared granular flow. Phys. Rev. E 69, 061301.CrossRefGoogle ScholarPubMed
4. Burton, T. M. & Eaton, J. K. 2005 Fully resolved simulation of particle-turbulence interaction. J. Fluid Mech. 545, 67–111.CrossRefGoogle Scholar
5. Coulson, J. M., Richardson, J. F., Backhurst, J. R. & Harker, J. H. 1998 Chemical Engineering. Asian Books Private Limited.Google Scholar
6. Elghobashi, S. & Truesdell, G. C. 1993 On the two-way interaction between homogeneous turbulence and the dispersed solid particles 1: turbulence modification. Phys. Fluids A 5, 1790.CrossRefGoogle Scholar
7. Fessler, J. R., Kulick, J. D. & Eaton, J. K. 1994 Preferential concentration of heavy particles in a turbulent channel flow. Phys. Fluids 6, 3742–3749.Google Scholar
8. Gore, R. A. & Crowe, C. T. 1989 Effect of particle size on modulating turbulent intensity. Intl J. Multiphase Flow 15, 279.CrossRefGoogle Scholar
9. Goswami, P. S. 2009 Particle dynamics in a turbulent particle–gas suspension at high Stokes number. PhD thesis, Indian Institute of Science, India.Google Scholar
10. Goswami, P. S. & Kumaran, V. 2010a Particle dynamics in a turbulent particle–gas suspension at high Stokes number. Part 1. Velocity and acceleration distributions. J. Fluid Mech. 646, 59–90.Google Scholar
11. Goswami, P. S. & Kumaran, V. 2010b Particle dynamics in a turbulent particle–gas suspension at high Stokes number. Part 2. The fluctuating force model. J. Fluid Mech. 646, 91–125.CrossRefGoogle Scholar
12. Goswami, P. S. & Kumaran, V. 2011 Particle dynamics in the channel flow of a turbulent particle–gas suspension at high Stokes number. Part 1. DNS and fluctuating force model. J. Fluid Mech. 687, 1–40.CrossRefGoogle Scholar
13. Hetsroni, G. 1989 Particle–turbulence interaction. Intl J. Multiphase Flow 15, 735.CrossRefGoogle Scholar
14. Hwang, W. & Eaton, J. K. 2006 Homogeneous and isotropic turbulence modulation by small heavy (St 50) particles. J. Fluid Mech. 564, 361–393.CrossRefGoogle Scholar
15. Kallio, G. A. & Reeks, M. W. 1989 A numerical simulation of particle deposition in turbulent boundary layers. Intl J. Multiphase Flow 15, 433.CrossRefGoogle Scholar
16. Khalitov, D. A. & Longmire, E. K. 2002 Simultaneous two-phase piv by two-parameter phase discrimination. Exp. Fluids 32, 252–268.Google Scholar
17. Khalitov, D. A. & Longmire, E. K. 2003 Effect of particle size on the velocity correlations in turbulent channel flow. FEDSM45730, 445, ASME/JSME Joint Fluid Engineering Conference, Honolulu.Google Scholar
18. Khalitov, D. A. & Longmire, E. K. 2004 Gas–particle interaction in turbulent channel flow. Tech Rep. 2004-1. University of Minnesota.Google Scholar
19. Kiger, K. T. & Pan, C. 2002 Suspension and turbulence modification effects of solid particulates on a horizontal turbulent channel flow. J. Turbul. 3, 1–21.CrossRefGoogle Scholar
20. Krothapalli, A., Venkatakrishnan, L., Lourenco, L., Greska, B. & Elavarasan, R. 2003 Turbulence and noise suppression of a high-speed jet by water injection. J. Fluid Mech. 491, 131–159.CrossRefGoogle Scholar
21. Kulick, J. D., Fessler, J. R. & Eaton, J. K. 1994 Prticle response and turbulence modification in a fully developed channel flow. J. Fluid Mech. 277, 109–134.Google Scholar
22. Kumaran, V. 1997 Velocity distribution function for a dilute granular material in shear flow. J. Fluid Mech. 340, 319–341.Google Scholar
23. Kumaran, V. 2003 Stability of a sheared particle suspension. Phys. Fluids 15, 3625–3637.CrossRefGoogle Scholar
24. Kumaran, V. 2005 Kinetic model for sheared granular flows in the high Knudsen number limit. Phys. Rev. Lett. 95, 108001.CrossRefGoogle ScholarPubMed
25. Kumaran, V. 2006 The constitutive relations for the granular flow of rough particles, and its application to the flow down an inclined plane. J. Fluid Mech. 561, 1–42.CrossRefGoogle Scholar
26. Kumaran, V. & Koch, D. L. 1993a Properties of a bidisperse particle – gas suspension. Part 1. Collision time small compared to viscous relaxation time. J. Fluid Mech. 247, 623–642.CrossRefGoogle Scholar
27. Kumaran, V. & Koch, D. L. 1993b Properties of a bidisperse particle – gas suspension. Part 2. Viscous relaxation time small compared to collision relaxation time. J. Fluid Mech. 247, 643–660.CrossRefGoogle Scholar
28. Li, Y. & McLaughlin, J. B. 2001 Numerical simulation of particle–laden turbulent channel flow. Phys. Fluids 13, 2957.Google Scholar
29. Lourenco, L. & Krothapalli, A. 2000 True resolution piv: a mesh-free second order accurate algorithm. In Proceedings of the 10th International Symposium on Applications of Laser Techniques in Fluid Mechanics Lisbon, Portugal.Google Scholar
30. McLaughlin, J. B. 1989 Aerosol particle deposition in numerically simulated channel flow. Phys. Fluids A 1, 1211.Google Scholar
31. Niederschulte, M. A., Adrian, R. J. & Hanratty, T. J. 1990 Measurements of turbulent flow in a channel at low Reynolds numbers. Exp. Fluids 9, 222–230.CrossRefGoogle Scholar
32. Pan, Y. & Banerjee, S. 1997 Numerical investigation of the effects of large particles on wall-turbulence. Phys. Fluids 12, 3786–3807.Google Scholar
33. Paris, A. D. 2001 Turbulence attenuation in a particle–laden channel flow. PhD thesis, Stanford University.Google Scholar
34. Paris, A. D. & Eaton, J. K. 1999 Piv measurements in a particle–laden channel flow. In Proceedings of the third ASME/JSME Joint Fluid Engineering Conference, San Francisco, CA (ed. P. A. Pfund).Google Scholar
35. Rasband, W. S. 2006 ImageJ Version 1.34 U.S. National Institute of Health Available at http://rsb.info.nih.gov/ij/.Google Scholar
36. Sato, Y. & Hishida, K. 1996 Transport process of turbulence energy in particle–laden turbulent flow. Intl J. Heat Fluid Flow 17, 202–210.CrossRefGoogle Scholar
37. Squires, K. D. & Eaton, J. K. 1990 Particle responce and turbulence modification in isotropic turbulence. Phys. Fluids A 2, 1191.CrossRefGoogle Scholar
38. Squires, K. D. & Eaton, J. K. 1991 Preferential concentration of particles by turbulence. Phys. Fluids A 3, 1169.Google Scholar
39. Suzuki, Y., Ikenya, M. & Kasagi, N. 2000 Simultaneous measurement of fluid and dispersed phases in a particle–laden turbulent channel flow with the aid of 3-D PTV. Exp. Fluids 29, S185–S193.CrossRefGoogle Scholar
40. Tanaka, T. & Eaton, J. K. 2008 Classification of turbulence modification by dispersed spheres using a novel dimensionless number. Phys. Rev. Lett. 101, 114502.Google Scholar
41. Tanaka, T. & Eaton, J. K. 2010 Sub-Kolmogorov resolution partical image velocimetry measurements of particle–laden forced turbulence. J. Fluid Mech. 643, 117–206.Google Scholar
42. Tsuji, Y. & Morikawa, Y. 1982 LDV measurements of an air–solid two-phase flow in a horizontal pipe. J. Fluid Mech. 120, 385–409.CrossRefGoogle Scholar
43. Tsuji, Y., Morikawa, Y. & Shiomi, H. H. 1984 LDV measurements of an air–solid two-phase flow in a vertical pipe. J. Fluid Mech. 139, 417–434.Google Scholar
44. Uhlmann, M. 2008 Interface-resolved direct numerical simulation of vertical particulate channel flow in the turbulent regime. Phys. Fluids 20, 053305.CrossRefGoogle Scholar
45. Vreman, A. W. 2007 Turbulence characteristics of particle–laden pipe flow. J. Fluid Mech. 584, 235–279.Google Scholar
46. Wang, Q. & Squires, K. D. 1996 Large eddy simulation of particle–laden channel flow. Phys. Fluids 8, 1207–1223.CrossRefGoogle Scholar
47. Yamamoto, Y., Potthoff, M., Tanaka, T., Kajishima, T. & Tsuji, Y. 2001 Large-eddy simulation of turbulent gas–particle flow in a vericle channel: effect of considering interparticle collisions. J. Fluid Mech. 442, 303–334.Google Scholar
48. Yang, T. S. & Shy, S. S. 2005 Two-way interaction between solid particles and homogeneous air turbulence: particle settling rate and turbulence modification measurements. J. Fluid Mech. 526, 171–216.Google Scholar
49. Zeng, L., Balachandar, S., Fischer, P. & Najjar, F. M. 2008 Interactions of a stationary finite-sized particle with wall turbulence. J. Fluid Mech. 594, 271–305.Google Scholar