# zbMATH — the first resource for mathematics

Numerical simulation of fiber conveyance in a confined channel by the immersed boundary-lattice Boltzmann method. (English) Zbl 07073389
Summary: Fluid-structure interaction (FSI) phenomenon is very common in pneumatic-type textile field. However, the motion of flexible bodies, for instance, fibers or yarns, are usually difficult to simulate due to their large fineness ratio and high flexibility. Conventional FSI solvers based on the body-fitted grid method are difficult to handle the large deformation due to severe grid distortion. In this paper, we studied the fluid-fiber interaction for fiber conveyance in a fiber transport channel (FTC) using the immersed boundary-lattice Boltzmann method (IB-LBM). The effect of three parameters on fiber conveyance, i.e., the conical degree of the FTC ($$\tan\alpha$$), the bending rigidity of fiber ($$\hat K_b$$) and the flow Reynolds number (Re), are particularly investigated. The calculated results indicate that the converging shape of FTC helps to straighten fiber and adjust its orientation to a more horizontal degree during the conveyance, however, it may not improve fiber delivery efficiency. A larger conical degree would bring a better straighten effect and a smaller leading angle if fiber-wall contact does not occur. Under the conditions that $$\tan\alpha>0$$, $$\mathrm{Re}<400$$ and $$\hat K_b<1e-3$$, the straightness undergoes a “leap-slump-grow-drop” evolution process and the leading angle follows an “increase-decline” tendency. Moreover, the simulation results show that the bending rigidity have a significant effect on fiber configuration and orientation during its conveyance. A fiber with a larger bending rigidity is more likely to maintain a straighter configuration and a more horizontal orientation during its conveyance. As Re increases in simulations, the fiber gets less straight in configuration and more vertical in orientation, and deviates more from the horizontal path.
##### MSC:
 76-XX Fluid mechanics
Full Text:
##### References:
 [1] Kong, L. X.; Platfoot, R. A., Fibre transportation in confined channel with recirculations, Comput. Struct., 78, 1-3, 237-245, (2000), Article; Proceedings Paper [2] Lawrence, C. A.; Chen, K. Z., A study of the fiber-transfer-channel design in rotor-spinning.1. The fiber trajectory, J. Text. Inst., 79, 3, 367-392, (1988), Article [3] Lawrence, C. A.; Chen, K. Z., A study of the fiber-transfer-channel design in rotor-spinning.2. Optimization of the transfer-channel design, J. Text. Inst., 79, 3, 393-408, (1988), Article [4] Jin, Y. Z.; Cui, J. Y.; Li, X. D.; Chen, H. L., An investigation on the distribution of massive fiber granules in rotor spinning units, Text. Res. J., 87, 7, 865-877, (2017), Article [5] Kong, L. X.; Platfoot, R. A., Computational two-phase air/fiber flow within transfer channels of rotor spinning machines, Text. Res. J., 67, 4, 269-278, (1997), Article [6] Pei, Z. G.; Yu, C. W., Numerical study on the effect of nozzle pressure and yarn delivery speed on the fiber motion in the nozzle of murata vortex spinning, J. Fluids Struct., 27, 1, 121-133, (2011), Article [7] Peskin, C. S., Numerical analysis of blood flow in the heart, J. Comput. Phys., 25, 3, 220-252, (1977) · Zbl 0403.76100 [8] Peskin, C. S., The fluid-dynamics of heart-valves - experimental, theoretical, and computational methods, Annu. Rev. Fluid Mech. Rev., 14, 235-259, (1982) [9] Peskin, C. S., The immersed boundary method, Acta Numer., 11, 479-517, (2003) · Zbl 1123.74309 [10] Eggleton, C. D.; Popel, A. S., Large deformation of red blood cell ghosts in a simple shear flow, Phys. Fluids, 10, 8, 1834-1845, (1998), Article [11] Fauci, L. J.; McDonald, A., Sperm motility in the presence of boundaries, Bull. Math. Biol., 57, 5, 679-699, (1995), Article · Zbl 0826.92017 [12] Fauci, L. J.; Peskin, C. S., A computational model of aquatic animal locomotion, J. Comput. Phys., 77, 1, 85-108, (1988), Article · Zbl 0641.76140 [13] Miller, L. A.; Peskin, C. S., When vortices stick: an aerodynamic transition in tiny insect flight, J. Exp. Biol., 207, 17, 3073-3088, (2004), Article [14] Chen, S.; Doolen, G. D., Lattice boltzmann method for fluid flows, Annu. Rev. Fluid Mech., 30, 1, 329-364, (1998) · Zbl 1398.76180 [15] Vahidkhah, K.; Abdollahi, V., Numerical simulation of a flexible fiber deformation in a viscous flow by the immersed boundary-lattice Boltzmann method, Commun. Nonlinear Sci. Numer. Simul., 17, 3, 1475-1484, (2012), Article · Zbl 1364.76191 [16] Tian, F. B.; Luo, H. X.; Zhu, L. D.; Liao, J. C.; Lu, X. Y., An efficient immersed boundary-lattice Boltzmann method for the hydrodynamic interaction of elastic filaments, J. Comput. Phys., 230, 19, 7266-7283, (2011), Article · Zbl 1327.76106 [17] Yuan, H. Z.; Niu, X. D.; Shu, S.; Li, M. J.; Yamaguchi, H., A momentum exchange-based immersed boundary-lattice Boltzmann method for simulating a flexible filament in an incompressible flow, Comput. Math. Appl., 67, 5, 1039-1056, (2014), Article · Zbl 1381.74085 [18] Zhang, J.; Childress, S.; Libchaber, A.; Shelley, M., Flexible filaments in a flowing soap film as a model for one-dimensional flags in a two-dimensional wind, Nature, 408, 6814, 835-839, (2000), Article [19] Connell, B. S.H.; Yue, D. K.P., Flapping dynamics of a flag in a uniform stream, J. Fluid Mech., 581, 33-68, (2007), Article · Zbl 1124.76011 [20] Zhu, L. D.; Peskin, C. S., Interaction of two flapping filaments in a flowing soap film, Phys. Fluids, 15, 7, 1954-1960, (2003), Article · Zbl 1186.76611 [21] Niu, X. D.; Shu, C.; Chew, Y. T.; Peng, Y., A momentum exchange-based immersed boundary-lattice Boltzmann method for simulating incompressible viscous flows, Phys. Lett. A, 354, 3, 173-182, (2006), Article · Zbl 1181.76111 [22] Ladd, A. J.C., Numerical simulations of particulate suspensions via a discretized boltzmann-equation.1. Theoretical foundation, J. Fluid Mech., 271, 285-309, (1994), Article · Zbl 0815.76085 [23] Ladd, A. J.C., Numerical simulations of particulate suspensions via a discretized boltzmann-equation.2. Numerical results, J. Fluid Mech., 271, 311-339, (1994), Article · Zbl 0815.76085
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. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.