Modelling and Experimentation in Two-Phase Flow pp 383-429 | Cite as

# Interaction between Turbulence Structures and Inertial Particles in Boundary Layer: Mechanisms for Particle Transfer and Preferential Distribution

## Abstract

Particle transfer in the wall region of turbulent boundary layers is dominated by the coherent structures which control the turbulence regeneration cycle. Coherent structures bring particles toward the wall and away from the wall and favour particle segregation in the viscous region. In this work we examine turbulent transfer of heavy particles to the wall and away from the wall in connection with the coherent structures of the boundary layer. First, a detailed analysis of wall turbulence phenomena in a boundary layer will be provided. We will focus on the evolutionary dynamics of the structures populating the boundary layer: according to Schoppa & Hussain (1996, 1997), we will identify the following turbulence regeneration cycle: (i) low-speed streaks generate quasi-streamwise vortices, (ii) quasi-streamwise vortices generate sweeps and ejections, (iii) sweeps and ejections contribute to maintain the low-speed streaks.

We will then examine the behaviour of a dilute dispersion of heavy particles — flyashes in air — in a vertical channel flow, using pseudo-spectral direct numerical simulation to calculate the turbulent flow field at a shear Reynolds number *Re* _{ τ } = 150, and Lagrangian tracking to describe the dynamics of particles. Drag force, gravity and Saffman lift are used in the equation of motion for the particles, which are assumed to have no influence on the flow field. Particles interaction with wall is fully elastic. As reported in several previous investigations, we found that particles are transferred by sweeps in the wall region, where they preferentially accumulate in the low-speed streak environments, whereas ejections transfer particles from the wall region to the outer flow. We quantify the efficiency of the instantaneous realizations of the Reynolds stresses — sweeps and ejections — in transferring different size particles to the wall and away from the wall, respectively. Our findings confirm that sweeps and ejections are efficient transfer mechanisms for particles. However, the efficiency of the transfer mechanisms is conditioned by the presence of particles to be transferred. In the case of ejections, particles are more rarely available since, when in the viscous wall layer, they are concentrated under the low-speed streaks. Even though the low-speed streaks are ejection-like environments, particles remain trapped for a long time. Following the parentoffspring regeneration cycle for near-wall quasi-streamwise vortices, suggested by Brooke & Hanratty (1993), we find some evidence that the coupling of mature vortices with associated newly-born vortices is responsible for particle trapping in a sediment layer confined under the low-speed streak, between the offspring vortex and the wall. This mechanism may help to explain the existence of net particle fluxes toward the wall (turbophoretic drift). Further analysis on particle distribution in the viscous sublayer confirmed that particles build-up under the low-speed streaks is due to the trapping action of the near-wall coherent structures. It is apparent that particles are not entrained in the coherent structures but rather accumulate in the proximity of a source point at the wall, located well below the low-speed streak.

## Keywords

Wall Shear Stress Turbulent Boundary Layer Coherent Structure Wall Layer Turbulence Structure## Preview

Unable to display preview. Download preview PDF.

## References

- Armenio, V. & Fiorotto, V. (2001). The importance of the forces acting on particles in turbulent flows.
*Phys. Fluids*,**13**, 2437–2440.Google Scholar - Armenio, V., Piomelli, U. & Fiorotto, V. (1999). Effect of the subgrid scales on particle motion.
*Phys. Fluids*,**11**, 3030–3042.MATHGoogle Scholar - Balachandar, S. & Maxey, M. R. (1989). Methods for evaluating fluid velocities in spectral simulations of turbulence.
*J. Comput. Phys.*,**83**, 96–125.MATHGoogle Scholar - Bernard, P. S., Thomas, J. M. & Handler, R. A. (1993). Vortex dynamics and the production of Reynolds stress.
*J. Fluid Mech.*,**253**, 385–419.MATHGoogle Scholar - Blackburn, H. M., Mansour, N.N. & Cantwell, B. J. (1996). Topology of fine-scale motions in turbulent channel flow.
*J. Fluid Mech.*,**310**, 269–292.MATHMathSciNetGoogle Scholar - Bonnet, J. P. & Delville, J. (1996). General concepts on structure identification. In Bonnet, J. R, ed.,
*Eddy Structure Identification*, Springer-Verlag, Wien, 1–59.Google Scholar - Brooke, J. W., Kontomaris, K., Hanratty, T. J.
*&*McLaughlin, J. B. (1992). Turbulent deposition and trapping of aerosols at a wall.*Phys. Fluids A*,**4**, 825–834.Google Scholar - Brooke, J. W. & Hanratty, T. J. (1993). Origin of turbulence-producing eddies in channel flow.
*Phys. Fluids A*,**5**, 1011–1022.MATHGoogle Scholar - Caporaloni, M., Tampieri, F., Trombetti, F & Vittori, O. (1975). Transfer of particles in nonisotropic air turbulence.
*J. Atmos. Sci*. (Boston),**32**, 565–568.Google Scholar - Cerbelli, S., Giusti, A. & Soldati, S. (2001). ADE approach to predicting dispersion of heavy particles in wall bounded turbulence.
*Int. J. Multiphase Flow*,**27**, 1861–1879.MATHGoogle Scholar - Choi, K. S. (2001). Turbulent drag reduction mechanisms: strategies for turbulence management. In
*Turbulence Modulation and Control*(ed. A. Soldati & R. Monti), CISM Courses and Lectures, vol.**415**, pp. 161–211, Springer.Google Scholar - Chong, M. S., Perry, A. & Cantwell, B. J. (1990). A general classification of three-dimensional flow fields.
*Phys. Fluids A*,**2**, 765–777.MathSciNetGoogle Scholar - Cleaver, J. W. & Yates, B. (1975). A sub layer model for the deposition of particles from a turbulent flow.
*Chemical Engineering Science*,**30**, 983–992.Google Scholar - Crowe, C. T., Chung, J. N. & Troutt, T. R. (1988). Particle mixing in free shear flows.
*Prog. Energy Combust. Sci.*,**14**, 171–194.CrossRefGoogle Scholar - De Angelis, V., Lombardi, P., Andreussi, R & Banerjee, S. (1997). Microphysics of scalar transfer at air-water interfaces. Invited Paper, IMA Conference on
*Wind over Wave Couplings*, Salford, UK, 8–10 April, 1997, Oxford University Press.Google Scholar - Dubief, Y. & Delcayre, E (2000). On coherent-vortex identification in turbulence.
*Journal of Turbulence*,**1**, 11–32. Retrieved at*http://jot.iop.org*.Google Scholar - Eaton, J. K. & Fessler, J. R. (1994). Preferential concentration of particles by turbulence.
*Int. J. Multiphase Flow*,**20**, 169–209.CrossRefMATHGoogle Scholar - Friedlander, S. K. & Johnstone, H. F. (1957). Deposition of suspended particles from turbulent gas streams.
*Ind. Eng. Chem.*,**49**, 1151–1156.Google Scholar - Guezennec, Y. G. & Choi, W. C. (1989). Stochastic estimation of coherent structures in turbulent boundary layers. In
*Proc. Zoran P Zaric Memorial International Seminar on Near Wall Turbulence*, May 1988 (ed. Guezennec, Y. G. & Choi, W. C ), pp. 420–436, Hemisphere.Google Scholar - Guezennec, Y. G., Piomelli, U. & Kim, J. (1989). On the shape and dynamics of wall structures in turbulent channel flow.
*Phys. Fluids A*,**1**, 764–766.CrossRefGoogle Scholar - Hunt, J. C. R., Wray, A. A. & Moin, E (1998). Eddies, stream and covergence zones in turbulent flows.
*Center of Turbulence Research Rep*., CTR-S88, 193.Google Scholar - Jimenez, J. & Moin, P. (1991). The minimal flow unit in near-wall turbulence.
*Journal of Fluid Mechanics*,**225**, 213–233.CrossRefMATHGoogle Scholar - Jimenez, J. & Pinelli, A. (1999). The autonomous cycle of near-wall turbulence.
*J. Fluid Mech.*,**389**, 335–359.MATHMathSciNetGoogle Scholar - Jeong, J.
*&*Hussain, E (1995). On the identification of a vortex.*J. Fluid Mech.*,**285**, 69–83.Google Scholar - Jeong, J., Hussain, F., Schoppa, W. & Kim, J. (1997). Coherent structures near the wall in a turbulent channel flow.
*J. Fluid Mech.*,**332**, 185–214.MATHGoogle Scholar - Kaftori, D., Hetsroni, G. & Banerjee, S. (1995a). Particle behavior in the turbulent boundary layer. I. Motion, deposition, and entrainment.
*Phys. Fluids*,**7**, 1095–1106.Google Scholar - Kaftori, D., Hetsroni, G. & Banerjee, S. (1995b). Particle behavior in the turbulent boundary layer. II. Velocity and distribution profiles.
*Phys. Fluids*,**7**, 1107–1121.Google Scholar - Kallio, G. A. & Reeks, M. W. (1989). A numerical simulation of particle deposition in turbulent boundary layers.
*Int..1. Multiphase Flow*, 15, 433–446.Google Scholar - Kasagi, N.
*&*Iida, O. (1999). Progress in direct numerical simulation of turbulent heat transfer. Keynote Paper,*5th ASME/JSME Joint Thermal Engineering Conference*, San Diego, CD-ROM Publication, ASME, March, 1999.Google Scholar - Kim, J. & Hussain, F. (1993). Propagation velocity of perturbations in turbulent channel flow.
*Physics of Fluids A*,**5**, 695–706.Google Scholar - Kim, J., Moin, P.
*&*Moser, R. (1987). Turbulence statistics in fully developed channel flow at low Reynolds number.*J. Fluid Mech.*,**177**, 133–166.Google Scholar - Kline, S. J., Reynolds, W. C., Schraub, F. A. & Runstadler, P. W. (1967). The structure of turbulent boundary layer.
*Journal of Fluid Mechanics*,**70**, 741–773.CrossRefGoogle Scholar - Kline, S. J.
*&*Robinson, S. K. (1990). Quasi-coherent structures in the turbulent boundary Iayer:Part 1. Status report on community-wide survey of the data. In Kline, S. J., Afgan, N. H., eds.,*Near-Wall Turbulence.*Hemisphere, New York.Google Scholar - Kontomaris, K., Hanratty, T. J. & McLaughlin, J. B. (1992). An algorithm for tracking fluid particles in a spectral simulation of turbulent channel flow.
*J. Comput. Phys.*,**103**, 231–242.CrossRefMATHGoogle Scholar - Kulick, J. D., Fessler, J. R. & Eaton, J. K. (1994). Particle response and turbulence modification in fully developed channel flow. J.
*Fluid Mech.*,**277**, 109–134.CrossRefGoogle Scholar - Lam, K. & Banerjee, S. (1992). On the condition of streak formation in bounded flows.
*Phys. Fluids A*,**4**, 306–320.MATHGoogle Scholar - Lombardi, P., De Angelis, V. & Banerjee, S. (1996). Direct numerical simulation of near-interface turbulence in coupled gas-liquid flow.
*Phys. Fluids*,**8**, 1643–1665.Google Scholar - Lu, D. M.
*&*Hetsroni, G. (1995). Direct numerical simulation of a turbulent channel flow with heat transfer.*Int. J. Heat Mass Transfer*,**38**, 3241–3251.Google Scholar - Lyons, S. L., Hanratty, T. J. & McLaughlin, J. B. (1991). Large-scale computer simulation of fully developed turbulent channel flow with heat transfer.
*Int. J. Numez Methods Fluids*,**13**, 999–1028.CrossRefMATHGoogle Scholar - Marchioli, C. & Soldati, A. (2002). Mechanisms for particle transfer and segregation in turbulent boundary layer.
*J. Fluid Mech.*,**468**, 283–315.MATHGoogle Scholar - Marchioli, C., Giusti, A., Salvetti, M. V.
*&*Soldati, A. (2003). Direct numerical simulation of particle wall transfer and deposition in upward turbulent pipe flow.*Int. J. Multiphase Flow*,**29**, 1017–1038.Google Scholar - McLaughlin, J. B. (1989). Aerosol particle deposition in numerically simulated channel flow.
*Phys. Fluids*,**1**, 1211–1224.CrossRefGoogle Scholar - McLaughlin, J. B. (1991). Inertial migration of a small sphere in linear shear flows.
*J. Fluid Mech.*,**224**, 261–274.CrossRefMATHGoogle Scholar - Narayanan, C., Lakehal, D., Botto, L., Soldati, A. (2003). Mechanisms of particle deposition in a fully-developed turbulent open channel flow.
*Phys. Fluids*,**15**, 763–775.CrossRefGoogle Scholar - Nino, Y.
*&*Garcia, M. H. (1996). Experiments on particle-turbulence interactions in the near-wall region of an open channel flow: implications for sediment transport.*J. Fluid Mech.*,**326**, 285–319.Google Scholar - Orlandi, R. & Jimenez, J. (1994). On the generation of turbulent wall friction.
*Phys. Fluids*,**6**, 634–641.Google Scholar - Ounis, H., Ahmadi, G. & McLaughlin, J. B. (1993). Brownian particle deposition in a directly simulated channel flow.
*Phys. Fluids*,**5**, 1427–1432.CrossRefGoogle Scholar - Pan, Y. & Banerjee, S. (1996). Numerical simulation of particle interactions with wall turbulence.
*Phys. Fluids*,**8**, 2733–2755.Google Scholar - Papavassiliou, D. V. & Hanratty, T. J. (1995). The use of Lagrangian methods to describe turbulent transport of heat from a wall.
*Industrial and Engineering Chemistry Research*,**34**, 3359–3367.Google Scholar - Pedinotti, S., Mariotti, G.
*&*Banerjee, S. (1992). Direct numerical simulation of particle behavior in the wall region of turbulent flow in horizontal channels.*Int. J. Multiphase Flow*,**18**, 927–941.Google Scholar - Perry, A. & Chong, M. S. (1987). A description of eddying motions and flow patterns using critical point concepts.
*Annu. Rev. Fluid Mech.*,**9**, 125–148.Google Scholar - Reeks, M. W. (1983). The transport of discrete particles in inhomogeneous turbulence.
*J. Aerosol Sci.*,**14**, 729–739.CrossRefGoogle Scholar - Rizk, M. A. & Elghobashi, S. E. (1985). The motion of a spherical particle suspended in a turbulent flow near a plane wall.
*Phys. Fluids*,**28**, 806–817.MATHGoogle Scholar - Robinson, S. K. (1991). Coherent motions in the turbulent boundary layer.
*Ann. Rev Fluid Mech.*,**23**, 601–639.CrossRefGoogle Scholar - Rouson, D. W. I.
*&*Eaton, J. K. (2001). On the preferential concentration of solid particles in turbulent channel flow.*J. Fluid Mech.*,**428**, 149–169.Google Scholar - Saffman, P. G. (1965). The lift on a small sphere in a slow shear flow.
*J. Fluid Mech.*$122, 385–400. [Corrigendum**31**, 624 (1968)].Google Scholar - Schoppa, W. & Hussain, F. (1996). New aspects of vortex dynamics relevant to coherent structures in turbulent flows. In
*Eddy Structure Identification*(ed. J. R. Bonnet), CISM Courses and Lectures, vol.**353**, pp. 61–143, Springer.Google Scholar - Schoppa, W.
*&*Hussain, R (1997). Genesis and dynamics of coherent structures in near-wall turbulence. In*Self-sustaining Mechanisms of Wall Turbulence*(ed. R. Panton), Advances in Fluid Mechanicsi, vol.**15**, pp. 385–422, Computational Mechanics Publications.Google Scholar - Schoppa, W. & Hussain, F. (2000). Coherent structure dynamics in near-wall turbulence.
*J. Fluid Dynamics Research*,**26**, 119–139.Google Scholar - Slater, S. A. & Young, J. B. (2001). The calculation of inertial particle transport in dilute gas-particle flows.
*Int. J. Multiphase Flow*,**27**, 61–87.CrossRefMATHGoogle Scholar - Squires, K. D. & Eaton, J. K. (1991). Preferential concentration of particles by turbulence.
*Phys. Fluids A*,**3**, 1169–1178.CrossRefGoogle Scholar - Soldati, A., Casal, M., Andreussi, P. & Banerjee, S. (1997). Lagrangian simulation of turbulent particle dispersion in Electrostatic Precipitators.
*AIChE J*.,**43**, 1403–1413.CrossRefGoogle Scholar - Soldati, A.
*&*Banerjee, S. (1998). Turbulence modification by large scale organized electrohydrodynamic flows.*Phys. Fluids*,**10**, 1742–1756.Google Scholar - Soldati, A. (2000). Modulation of turbulent boundary layer by EHD flows.
*ERCOFTAC Bulletin*,**44**, 50–56.Google Scholar - Soldati, A. & Marchioli, C. (2001). Prospects for modulation of turbulent boundary layer by EHD flows. In
*Turbulence Structure and Modulation*(ed. A. Soldati & R. Monti), CISM Courses and Lectures, vol.**415**, pp. 119–160, Springer.Google Scholar - Sun, Y. F. & Lin, S. R (1986). Aerosol concentration in a turbulent flow.
*J. Colloid Interface Sci.*,**113**, 315–320.Google Scholar - Tchen, C. M. (1947). Mean value and correlation problems connected with the motion of small particles suspended in a turbulent fluid. Ph.D. Thesis, Delft.Google Scholar
- Uijttewaal, W. S. J.
*&*Oliemans, R. V. A. (1996). Particle dispersion and deposition in direct numerical and large eddy simulations of vertical pipe flows.*Phys. Fluids*,**8**, 2590–2604.Google Scholar - van Haarlem, B., Boersma, B. J.
*&*Nieuwstadt, F. T. M. (1998). Direct numerical simulation of particle deposition onto a free-slip and no-slip surface.*Phys. Fluids*,**10**, 2608–2620.Google Scholar - Wallace, J. M., Eckelmann, H., Brodkey, R. S. (1972). The wall region in turbulent shear flow.
*J. Fluid Mech.*,**54**, 39–48.CrossRefGoogle Scholar - Wang, Q.
*&*Squires, K. D. (1996). Large eddy simulation of particle deposition in a vertical turbulent channel flow.*Int. J. Multiphase Flow*,**22**, 667–683.Google Scholar - Wei Ling, Chung, J. N., Troutt, T. R.
*&*Crowe, C. T. (1998). Direct numerical simulation of a threedimensional temporal mixing layer with particle dispersion.*J. Fluid Mech.*,**358**, 61–85.Google Scholar - Wells, M. R. & Stock, D. E. (1983). The effect of crossing trajectories on the dispersion of particles in turbulent flow.
*J. Fluid Mech.*,**136**, 31–62.Google Scholar - Willmarth, W. W. & Lu, S. S. (1972). Structure of the Reynolds stress near the wall.
*J. Fluid Mech.*,**55**, 65–92.Google Scholar - Yeung, P. K.
*&*Pope, S. B. (1988). An algorithm for tracking fluid particles in numerical simulations of homogeneous turbulence.*J. Comput. Phys.*,**79**, 373–416.Google Scholar - Young, J.
*&*Leeming, A. (1997). A theory of particle deposition in a turbulent pipe flow.*J. Fluid Mech.*,**340**, 129–159.Google Scholar - Zhang, H.
*&*Ahmadi, G. (2000). Aerosol particle transport and deposition in vertical and horizontal turbulent duct flows.*J. Fluid Mech.*,**406**, 55–80.Google Scholar - Zhou, J., Adrian, R. J., Balachandar, S. & Kendall, T. M. (1999). Mechanisms for generating coherent packets of hairpin vortices in channel flow.
*J. Fluid Mech.*,**387**, 353–396.MATHMathSciNetGoogle Scholar