Document Type : Full Length Research Article

**Authors**

Mechanical Engineering Department., Amirkabir University of Technology, Tehran, Iran

**Abstract**

This study is concerned with the prediction of particles’ velocity in a dilute turbulent gas-solid

boundary layer flow using a fully Eulerian two-fluid model. The closures required for equations

describing the particulate phase are derived from the kinetic theory of granular flows. Gas phase

turbulence is modeled by one-equation model and solid phase turbulence by MLH theory. Results

of one-way and two-way coupled approaches are compared with the available experimental and

numerical results. Results show that one-way coupled approach is more efficient for particulate

velocity prediction in dilute flows. But, if the gas-phase flow characteristics are desired, the twoway

coupled approach should be used. Effects of free stream velocity on the coupling are

discussed.

boundary layer flow using a fully Eulerian two-fluid model. The closures required for equations

describing the particulate phase are derived from the kinetic theory of granular flows. Gas phase

turbulence is modeled by one-equation model and solid phase turbulence by MLH theory. Results

of one-way and two-way coupled approaches are compared with the available experimental and

numerical results. Results show that one-way coupled approach is more efficient for particulate

velocity prediction in dilute flows. But, if the gas-phase flow characteristics are desired, the twoway

coupled approach should be used. Effects of free stream velocity on the coupling are

discussed.

**Keywords**

[1]. Li J., H. Wang, Z. Liu, S. Chen, C. Zheng, An experimental study on turbulence modification in the near-wall boundary layer of a dilute gas-particle channel flow, Exp Fluids, 53, 1385–1403 (2012).

[2]. Y. Tsuji, Y. Morikawa, LDV measurements of an air-solid twophase flow in a horizontal pipe, J Fluid Mech., 120, 385–409 (1982).

[3]. A. Taniere, B. Oesterle, J.C. Monnier, On the behavior of solid particles in a horizontal boundary layer with turbulence and saltation effects. Experiments in Fluids, 23, 463-471 (1997).

[4]. Y. Sato, U. Fukuichi, K. Hishida, Effect of inter-particle spacing on turbulence modulation by Lagrangian PIV, Int J Heat Fluid Flow, 21, 554–561 (2000).

[5]. S.E. Elghobashi, On predicting particle-laden turbulent flows. App. Sci. Res., 52, 309-329 (1994).

[6]. F. Li, H. Qi, C. You, Phase Doppler anemometry measurements and analysis of turbulence modulation in dilute gas–solid two phase shear flows, J Fluid Mech., 663, 434–455 (2010).

[7]. M. Mirzaei, M. Dehghan, Investigation of flow and heat transfer of nanofluid in microchannel with variable property approach, Heat Mass Transfer, 49, 1803-1811 (2013).

[8]. M. Di Giacinto, R. Piva, F. Sabetta., Two-way coupling effects in dilute gas-particle flows, ASME Transactions Journal of Fluids Engineering, 104, 304-311 (1982).

[9]. H. Nasr, G. Ahmadi, the effect of two-way coupling and inter particle collisions on turbulence modulation in a vertical channel flow, Int. J. Heat Fluid Flow, 28, 1507-1517 (2007).

[10]. H. Nasr, G. Ahmadi, J.B. McLaughin, A DNS study of effects of particle-particle collisions and two-way coupling on particle deposition and phase fluctuations, J. Fluid Mech., 640, p. 507-536 (2009).

[11]. S.A. Slater, A.D. Leeming, J.B. Young, Particle deposition from two-dimentional turbulent gas flows. Int. J. Multiphase Flow, 29, 721-750 (2003).

[12]. D. Gidaspow, Multiphase flow and fluidization: continuum and kinetic theory descriptions, Boston: Academic press, (1994).

[13]. L. Huilin, D. Gidaspow, J. Bouillard, L. Wenti, Hydrodynamics simulation of gas-solid flow in a riser using kinetic theory of granular flow. chemical Engineering Journal, 95, 1-13 (2003).

[14]. C.K.K. Lun, S.B. Savage, D.J. Jefferey, N. Chepurniy, Kinetic theories for granular flow: inelastic particles in Couette flow and slightly inelastic particles in a general flow field. J. Fluid Mechanics, 140, 223-256 (1984).

[15]. J.L Sinclair, R. Jackson, Gas-particle flow in a vertical pipe with particle-particle interactions. AIChE J., 35, 1473-1486 (1989).

[16]. J. Ding, D. Gidaspow, A bubbling fluidization model using kinetic theory of granular flow. AIChE J., 36, 523-538 (1990).

[17]. F. Vejahati, N. Mahinpey, N. Ellis, M.B. Nikoo, CFD simulation of gas–solid bubbling fluidized bed: A new method for adjusting drag law, Canadian J. Chem. Eng., 87 (1), 19-30 (2009).

[18]. M. Dehghan, H. Basirat Tabrizi, On near-wall behavior of particles in a dilute turbulent gas–solid flow using kinetic theory of granular flows, Powder Technology, 224, 273–280 (2012).

[19]. R. Yusuf, B. Halvorsen, M.C. Melaaen, Computational fluid dynamic simulation of ethylene hydrogenation in a fluidised bed of porous catalyst particles, Canadian J. Chem. Eng., 90 (3), 544-557 (2012).

[20]. J. Wang, E.K. Levy, Particle motions and distributions in turbulent boundary layer of air-particle flow past a vertical flat plate. Experimental Thermal and Fluid science, 27, 845-853 (2003).

[21]. J. Wang, E.K. Levy, Particle behavior in the turbulent boundary layer of a dilute gas-partilce flow past a flat plate. Experimental Thermal and Fluid science, 30, 473-483 (2006).

[22]. M. Dehghan, H. Basirat Tabrizi, Turbulence effects on the granular model of particle motion in a boundary layer flow, Canadian J. Chem. Eng., 92, 189–195 (2014).

[23]. V.S. Arpaci, P.S. Larsen, Convective heat transfer, Prentice-Hall Inc, (1984).

[24]. S. Dartevelle, Numerical and granulometric approaches to geophysical granular flows, PhD thesis, Department of Geological and Mining Engineering, Michigan Technological University: Houghton, (2003).

[25]. V.S. Syamlal, W. Rogers, T.J. O'Brien, MFIX documentation: volume I, theory guide: National Technical information service, Springfield, (1993).

[26]. D. Gidaspow, J. Jung, R.K. Singh, Hydrodynamics of fluidization using kinetic theory: an emerging paradigm 2002 Flour-Daniel lecture. Powder Technology, 148, 123-141 (2004).

[27]. Y. Cheng, F. Wei , Y. Guo, Y. Jin, CFD simulation of hydrodynamics in the entrance region of a downer. Chemical Engineering Science, 56(4), 1687-1696 (2001).

[28]. A.H. Govan, G.F. Hewitt, C.F. Ngan, Particle motion in the turbulent pipe flow. Int. J. Multiphase Flow, 15, 471-481 (1989).

[29]. M. Dehghan, M. Mirzaei, A. Mohammadzadeh, Numerical formulation and simulation of a non-Newtonian magnetic fluid flow in the boundary layer of a stretching sheet, Journal of Modeling in Engineering 11 (34), 73-82 (2013).

[30]. M. Dehghan, M. Mirzaei, M.S. Valipour, S. Saedodin, Flow of a non-Newtonian fluid over a linearly moving sheet at a transient state; new similarity variable and numerical solution scheme, Journal of Modeling in Engineering, (2014) (accepted manuscript).

[31]. P.R. Spalart, Direct numerical simulation of turbulent boundary layer up to Reθ=1410. J. Fluid Mechanics, 187, 61-98 (1988).

**Receive Date:**11 July 2013**Revise Date:**16 September 2013**Accept Date:**27 October 2013