Mathematical modeling of turbulent fiber suspension and successive iteration solution in the channel flow. (English) Zbl 1197.76074
Summary: The modified Reynolds mean motion equation of turbulent fiber suspension and the equation of probability distribution function for mean fiber orientation are firstly derived. A new successive iteration method is developed to calculate the mean orientation distribution of fiber, and the mean and fluctuation-correlated quantities of suspension in a turbulent channel flow. The derived equations and successive iteration method are verified by comparing the computational results with the experimental ones. The obtained results show that the flow rate of the fiber suspension is large under the same pressure drop in comparison with the rate of Newtonian fluid in the absence of fiber suspension. Fibers play a significant role in the drag reduction. The amount of drag reduction augments with increasing of the fiber mass concentration. The relative turbulent intensity and the Reynolds stress in the fiber suspension are smaller than those in the Newtonian flow, which illustrates that the fibers have an effect on suppressing the turbulence. The amount of suppression is also directly proportional to the fiber mass concentration.
MSC:
| 76F99 | Turbulence |
References:
| [1] | Asgharian, B.; Yu, C., Deposition of fibers in the rat lung, J. Aerosol Sci., 30, 355-366 (1989) |
| [2] | Kagermann, H.; Kohler, W., On the motion of non-spherical particles in a turbulent flow, Physica, 116A, 178-198 (1984) |
| [3] | Krushkal, E.; Gallily, I., On the orientation distribution function of non-spherical aerosol particles in a general shear flow-ii. The turbulent case, J. Aerosol Sci., 19, 197-211 (1988) |
| [4] | Olson, J. A., The motion of fibres in turbulent flow, stochastic simulation of isotropic homogeneous turbulence, Int. J. Multiphase Flow, 27, 2083-2103 (2001) · Zbl 1137.76702 |
| [5] | Olson, J. A.; Richerd, J. K., The motion of fibres in turbulent flow, J. Fluid Mech., 377, 47-64 (1998) · Zbl 0933.76093 |
| [6] | G. Lo Iacono, P.G. Tucker, A.M. Reynolds, Predictions for particle deposition from LES of a ribbed channel flow, Int. J. Heat Fluid Flow, in press.; G. Lo Iacono, P.G. Tucker, A.M. Reynolds, Predictions for particle deposition from LES of a ribbed channel flow, Int. J. Heat Fluid Flow, in press. |
| [7] | Lin, J. Z.; Shi, X.; Yu, Z. S., The motion of cylindrical particles in an evolving mixing layer, Int. J. Multiphase Flow, 29, 8, 1355-1372 (2003) · Zbl 1388.76421 |
| [8] | Lin, J. Z.; Zhang, W. F.; Yu, Z. S., Numerical research on the orientation distribution of fibers immersed in laminar and turbulent pipe flows, J. Aerosol Sci., 35, 1, 63-82 (2004) |
| [9] | Gao, Z. Y.; Lin, J. Z., Research on the dispersion of cylindrical particles in turbulent flows, J. Hydrodyn., 16, 1, 1-6 (2004) · Zbl 1158.76443 |
| [10] | Lin, J. Z.; Lin, J.; Shi, X., Research on the effect of cylindrical particles on the turbulent properties in particulate flows, Appl. Math. Mech., 23, 5, 542-548 (2002) · Zbl 1009.76510 |
| [11] | Zeng, Y. C.; Yang, J. P.; Yu, C. W., Mixed Euler-Lagrange approach to modeling fiber motion in high speed air flow, Appl. Math. Model., 29, 253-261 (2005) · Zbl 1129.76328 |
| [12] | McComb, W. D.; Chan, K. T.J., Drag reduction in fibre suspensions: transitional behavior due to fibre degradation, Nature (Lond.), 280, 45-46 (1979) |
| [13] | McComb, W. D.; Chan, K. T.J., Laser-Doppler anemometer measurements of turbulent structure in drag-reducing fibre suspensions, J. Fluid Mech., 152, 455-478 (1985) |
| [14] | Mih, W.; Parker, J., Velocity profile measurements and a phenomenological description of turbulent fiber suspension pipe flow, Tappi., 50, 273-279 (1967) |
| [15] | Pirih, R. J.; Swanson, W. M., Drag reduction and turbulence modification in rigid particles suspensions, Can. J. Chem. Eng., 50, 2, 221-228 (1972) |
| [16] | Sharma, R. S.; Seshadri, V.; Malhotra, R. C., Drag reduction in dilute fibre suspensions: Some mechanistic aspects, Chem. Eng. Sci., 34, 703-713 (1979) |
| [17] | Simacek, P.; Advani, S. G., Approximate numerical method for prediction of temperature distribution in flow through narrow gaps containing porous media, Comput. Mech., 32, 1-2, 1-9 (2003) · Zbl 1045.76539 |
| [18] | Kamiński, M. M., On probabilistic viscous incompressible flow of some composite fluids, Comput. Mech., 28, 6, 505-517 (2002) · Zbl 1076.76578 |
| [19] | Batchelor, G. K., The stress generated in a non-dilute suspension of elongated particles by pure straining motion, J. Fluid Mech., 46, 813-829 (1971) · Zbl 0225.76003 |
| [20] | Shaqfeh, E. S.G.; Fredrickson, G. H., The hydrodynamic stress in a suspension of rods. Phys. Fluids A, 2, 1, 7-24 (1990) · Zbl 0705.76033 |
| [21] | Advani, S. G.; Tucke, C. L., The use of tensors to describe and predict fiber orientation in short fiber composites, J. Rheol., 31, 8, 751-784 (1987) |
| [22] | Hinch, E. J.; Leal, L. G., Constitutive equations in suspension mechanics. Part 2. Approximate forms for a suspension of rigid particles affected by Brownian rotations, J. Fluid Mech., 76, 187-208 (1976) · Zbl 0352.76005 |
| [23] | Cintra, J. S.; Tucker, C. L., Orthotropic closure approximations for flow-induced fiber orientation, J. Rheol., 39, 1095-1122 (1995) |
| [24] | Olson, J. A.; Frigaard, I.; Chan, C.; Hamalainen, J. P., Modeling a turbulent fiber suspension flowing in a planar contraction: The one-dimensional headbox, Int. J. Multiphase Flow, 30, 51-66 (2004) · Zbl 1136.76598 |
| [25] | Launder, B. E.; Spalding, D. B., The numerical computation of turbulent flows, Comput. Meth. Appl. Mech. Eng., 3, 269-289 (1974) · Zbl 0277.76049 |
| [26] | Bernstein, O.; Shapiro, M., Direct determination of the orientation distribution function of cylindrical particles immersed in laminar and turbulent flow, Journal of Aerosol Science, 25, 1, 113-136 (1994) |
| [27] | Nikuradse, J., Stromungsgesetze in rauhen rohren, Forschg. Arb. Ing. Wes, 361 (1933) · JFM 59.1462.02 |
| [28] | Clark, J. A., A study of incompressible turbulent boundary layers in channel flows, Trans. ASME, J. Basic Eng., 90, 455-462 (1968) |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
