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In the ring spinning process, the drafted strand leaves the front roller nip and is twisted into a yarn. This twist region between the front roller nip and the fiber convergence point is called the spinning triangle. This triangle zone influences the distribution of fiber tensions and the properties of spun yarns, especially the yarn strength, torque and hairiness.[1],[2] Consequently, increased attention is being paid to the subject of the spinning triangle in order to produce a high quality yarn. At present, most of the information available in the literature on the spinning triangle is based on spinning experiments and theoretical models.[1]-[5] Obviously, the formation of the triangle zone, that is, the fiber distribution, is closely related to the fiber dynamics in the airflow created by the rotating front roller-pairs and the air suction system. In this triangle, due to the interaction of the airflow-fiber and fiber-fiber, the flexible fibers are transferred and rotated around the neighboring fibers, resulting in the fibers twisting into the convergence point. This is an air/fiber two-phase problem. To the authors' knowledge, however, studies in this area are rather scarce. Therefore, in this paper, we will study the fiber dynamics in the airflow of a spinning triangle using a numerical method based on multiphase flow, and discuss the formation principle of the triangle zone.
Due to the inherent complexity of the textile industry, little work has been reported regarding the air-fiber flow in the textile area. Considering a fiber as a series of contiguous two-dimensional (2D) elastica, Smith and Roberts[6] computed the fiber motion in converging transport ducts. Kong and Platfoot[7] developed a 2D Lagrangian one-way coupling model to simulate fiber transportation in the transfer-channel of rotor spinning and evaluated the effect of circulation zones and the number of nodes of the fiber on fiber configurations. In their model, a fiber consisted of a discrete distribution of masses held together by weightless chains. Nevertheless, this model would not give a clear picture of elastic deformation of the fiber. To study the fiber motion in high-speed airflow of the air-jet spinning nozzle, Zeng and Yu[8] proposed a 2D bead-rod fiber model that was made up of beads connected by massless rods, by changing the distance...