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The issue of fiber suspension flow has received great substantial attention in the last decades. In contrast with the abundant researches of normal size fiber suspensions flow, this paper is devoted to the small size fiber suspension composed of water and polyarmide fiber where Brownian motion plays an important role and thus cannot be neglected. The spatial distribution and orientation of fiber, streamwise mean velocity profile, turbulent kinetic energy, Reynolds stress and rheological property of fiber suspension in a turbulent channel flow are obtained and analyzed both numerically and experimentally. To simulate the small fiber suspension flow well, the well-known Reynolds averaged Navier-Stokes (N-S) equation governing the suspension flow is modified in consideration of the effect of fibers on base flow. The equation describing the probability density functions for fiber orientation is derived in view of the rotary Brownian diffusion. The general dynamic equation for fibers is reshaped in the effect of spatial Brownian diffusion. For the sake of the closure of the N-S equation, the turbulence kinetic energy and turbulence dissipation rate equations with fiber term are employed. The conditional finite difference method is adopted to discrete these partial differential equations. And the diffusion term and convective term are discretized by the central finite differences and the second-order upwind finite difference schemes, respectively. The second and fourth-order orientation tensors are integrated by the Simpson formula. Experiment is also performed to validate some numerical results. The results show that most fibers tend to align parallelly to the flow direction in the flow, especially in regions near the wall. Such a phenomenon is more obvious with the decreases of Reynolds number and fiber concentration, and with the increase of fiber aspect ratio. Fiber volume fraction distribution is non-uniform across the channel, and becomes more uniform with increasing Reynolds number, and with reducing fiber aspect ratio. The changes of fiber orientation distribution and spatial distribution are not sensitive to fiber aspect ratio for 5. Streamwise mean velocity profile in fiber suspension has a steeper slope than that in single phase flow, and the steepness increases as the fiber concentration and fiber aspect ratio increase, and as the Reynolds number decreases. The presence of fiber will reduce the turbulence kinetic energy and Reynolds stress. The effect of fiber on the turbulence suppression becomes more obvious with the increases of fiber concentration and aspect ratio, and with the decrease of Reynolds number. The first normal stress difference is less than 0.05 and much less than the shear stress. From the wall to the center of the channel, the shear stress increases while the first normal stress difference decreases. Both the shear stress and the first normal stress difference increase with increasing fiber concentration and aspect ratio. Shear stress increases while the first normal stress difference decreases with increasing Reynolds number. The effects of fiber concentration on the shear stress and the first normal stress difference are larger than the fiber aspect ratio.
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Keywords:
- fiber suspension /
- Brownian diffusion /
- turbulent diffusion /
- rheological property
[1] Zhang H F, Ahmadi G, Fan F G, McLaughlin J B 2001 Int. J. Multiphas. Flow 27 971
[2] Lin J Z, Shi X, You Z J 2003 J. Aerosol Sci. 34 909
[3] Lin J Z, Shi X, Yu Z S 2003 Int. J. Multiphas. Flow 29 1355
[4] Lin J Z, Zhang W F, Yu Z S 2004 J. Aerosol Sci. 35 63
[5] Lin J Z, Zhang L X, Zhang W F 2006 J. Colloid Interf. Sci. 296 721
[6] Lin J Z, Gao Z Y, Zhou K, Chan T L 2006 Appl. Math. Model. 30 1010
[7] Manhart M, Friedrich R 2004 Direct and Large-eddy Simulation V (Dordrecht: Springer Netherlands) p287
[8] Manhart M 2003 J. Non-Newton. Fluid. 112 269
[9] Manhart M 2004 Eur. J. Mech. B: Fluid. 23 461
[10] Gillissen J J J, Boersma B J, Nieuwstadt F T M, Lamballais E, Friedrich R, Geurts B J, Metais O 2006 Direct and Large-eddy Simulation VI (Dordrecht: Springer Netherlands) p303
[11] Moosaie A, Manhart M 2013 Acta Mech. 224 2385
[12] Moosaie A 2013 J. Disper. Sci. Technol. 34 870
[13] Batchelor G K 1971 J. Fluid Mech. 46 813
[14] Mackaplow M B, Shaqfeh E S G 1996 J. Fluid Mech. 329 155
[15] Advani S G, Tucker C L 1987 J. Rheol. 31 751
[16] Cintra J S, Tucker C L 1995 J. Rheol. 39 1095
[17] Koch D L 1995 Phys. Fluids 7 2086
[18] Folgar F, Tucker C L Ⅲ 1984 J. Reinf. Plast. Comp. 3 98
[19] Olson J A 2001 Int. J. Multiphas. Flow 27 2083
[20] Li G, Tang J X 2004 Phys. Rev. E 69 061921
[21] De La Torre J G, Bloomfield V A 1981 Q. Rev. Biophys. 14 81
[22] Lin J Z, Shen S H 2010 Sci. China: Phys. Mech. Astron. 53 1659
[23] Friedlander S K 2000 Smoke, Dust and Haze: Fundamentals of Aerosol Behavior (New York, Oxford: Oxford University Press) p59
[24] Chen H S, Ding Y L, Lapkin A, Fan X L 2009 J. Nanopart. Res. 11 1513
[25] Chen H S, Ding Y L, Lapkin A 2009 Powder Technol. 194 132
[26] Yu L, Liu D, Botz F 2012 Exp. Therm. Fluid Sci. 37 72
[27] Bernstein O, Shapiro M 1994 J. Aerosol Sci. 25 113
[28] Cox R G 1971 J. Fluid Mech. 45 625
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[1] Zhang H F, Ahmadi G, Fan F G, McLaughlin J B 2001 Int. J. Multiphas. Flow 27 971
[2] Lin J Z, Shi X, You Z J 2003 J. Aerosol Sci. 34 909
[3] Lin J Z, Shi X, Yu Z S 2003 Int. J. Multiphas. Flow 29 1355
[4] Lin J Z, Zhang W F, Yu Z S 2004 J. Aerosol Sci. 35 63
[5] Lin J Z, Zhang L X, Zhang W F 2006 J. Colloid Interf. Sci. 296 721
[6] Lin J Z, Gao Z Y, Zhou K, Chan T L 2006 Appl. Math. Model. 30 1010
[7] Manhart M, Friedrich R 2004 Direct and Large-eddy Simulation V (Dordrecht: Springer Netherlands) p287
[8] Manhart M 2003 J. Non-Newton. Fluid. 112 269
[9] Manhart M 2004 Eur. J. Mech. B: Fluid. 23 461
[10] Gillissen J J J, Boersma B J, Nieuwstadt F T M, Lamballais E, Friedrich R, Geurts B J, Metais O 2006 Direct and Large-eddy Simulation VI (Dordrecht: Springer Netherlands) p303
[11] Moosaie A, Manhart M 2013 Acta Mech. 224 2385
[12] Moosaie A 2013 J. Disper. Sci. Technol. 34 870
[13] Batchelor G K 1971 J. Fluid Mech. 46 813
[14] Mackaplow M B, Shaqfeh E S G 1996 J. Fluid Mech. 329 155
[15] Advani S G, Tucker C L 1987 J. Rheol. 31 751
[16] Cintra J S, Tucker C L 1995 J. Rheol. 39 1095
[17] Koch D L 1995 Phys. Fluids 7 2086
[18] Folgar F, Tucker C L Ⅲ 1984 J. Reinf. Plast. Comp. 3 98
[19] Olson J A 2001 Int. J. Multiphas. Flow 27 2083
[20] Li G, Tang J X 2004 Phys. Rev. E 69 061921
[21] De La Torre J G, Bloomfield V A 1981 Q. Rev. Biophys. 14 81
[22] Lin J Z, Shen S H 2010 Sci. China: Phys. Mech. Astron. 53 1659
[23] Friedlander S K 2000 Smoke, Dust and Haze: Fundamentals of Aerosol Behavior (New York, Oxford: Oxford University Press) p59
[24] Chen H S, Ding Y L, Lapkin A, Fan X L 2009 J. Nanopart. Res. 11 1513
[25] Chen H S, Ding Y L, Lapkin A 2009 Powder Technol. 194 132
[26] Yu L, Liu D, Botz F 2012 Exp. Therm. Fluid Sci. 37 72
[27] Bernstein O, Shapiro M 1994 J. Aerosol Sci. 25 113
[28] Cox R G 1971 J. Fluid Mech. 45 625
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