Numerical Simulation and Analysis of Airflow in the Condensing Zone of Compact Spinning with Lattice Apron

Abstract The airflow field pattern in the condensing zone plays a vital role in the pneumatic compact spinning, which significantly affects the yarn's qualities. This study aimed to analyze the effects of the different negative air pressures on fiber condensing in compact spinning with lattice apron using ANSYS. The results of airflow simulations reveal that by increasing the negative pressure, the flow velocity increases, leading to a more tremendous increase in the transverse condensing effects. Additionally, a better convergence led to reduced fiber width and eliminated the spinning triangle. Experimental results showed that the three yarns spun with the highest negative pressure had better strength, hairiness, and evenness than those spun with lower negative pressure.


Introduction
The air negative pressure plays a very important role in compact spinning as it is utilized to condense the fi ber bundle in a pneumatic compact spinning mechanism [1,2]. To eliminate the spinning triangle, which leads to improving the quality of spun yarn in terms of hairiness and strength, a few studies have been reported [3][4][5]. Numerical simulation technique is one among the signifi cant approaches that are used to solve numerous problems in traditional ring spinning [6]. The compact spinning system was built on the foundation of the traditional ring-spinning system [7]. However, numerous researchers consider it to be a modern spinning technique [8][9][10]. The fi rst compact spinning system was introduced to industrial application at ITMA in 1995 [11,12]. Compact spinning is classifi ed into pneumatic and mechanical compacting based on the condensing principle [13]. Recently, the dominant type is the pneumatic compact spinning systems [14,15] and it is mainly classifi ed into perforated drum and lattice apron compact spinning systems [16,17].
Compact spinning with lattice apron is the most widely used pneumatic compact spinning system, and it has three-line compact spinning (TLCS) and four-line compact spinning (FLCS) [4,16]. The condensing zone's fl ow fi eld pattern plays an essential role in the pneumatic compact spinning, which directly affects the qualities of yarn [18]. Therefore, the fl ow fi eld investigations in the condensing zone of pneumatic compact spinning have received more attention recently [19]. Recent research on the condensing zone in pneumatic compact spinning use computational fl uid dynamics (CFD) [20]. CFD is one of the powerful methods to investigate fl ow fi eld-based problems [1,21,22] because of its ability to investigate theoretical phenomena of fl uid fl ow based on the physical model [23][24][25]. Employing the self-designed MATLAB procedure, Dou et al. [26] obtained the motion trajectory of cotton fi ber in the fl ow zone and the compact effect of fi ber strands due to the airfl ow. Zhang et al. [27] have used CFD to build a model for compact spinning with an inspiratory groove for cotton using numerical investigation calculations and characterized the fl ow state in the compact zone.
In this article, we investigate the condensing zone of compact spinning systems with lattice apron and the effects of different negative air pressure on fi ber condensing as well as the mechanical properties of yarn. In the next sections, numerical simulation steps, model setup, simulation data, and analysis are presented. A comprehensive conclusion is then drawn based on the results.

Numerical simulations
2.1. Three-dimensional physical models for the condensing zone Figure 1 represents the side view of the condensing zone of the compact spinning system with a lattice apron. The 3D fl ow fi eld's numerical simulations in the condensing zones of three different negative air pressure will be studied. The physical parameters of the model are shown in Figure 2.
In these models, the fi ber strand's output direction is defi ned as the negative direction of the x-axis. In contrast, the transverse condensing direction of the fi ber strand is defi ned as y-axis, whereas the width of the fi ber strand is defi ned as z-axis. The midpoint of the lower end of the suction groove is taken as the origin. The fi ber strand was ignored because, theoretically, the fi ber strand volume is smaller than the condensing zone.

Boundary conditions
The fl ow fi eld in the condensing zone is assumed as incompressible and the turbulence model adopted is the standard k-epsilon two-equation model. As shown in Figure  2, there are three pressure inlet points that are assigned the static pressure values equal to the atmospheric pressure (101,325 Pa). The collecting pipe is connected to the centrifugal fan, and the air inside the collecting pipe is sucked from one side of the pipe; therefore, the side is set as a pressure outlet boundary, that is, −1,000 pa, −2,000 pa, and −3,000 pa (see Figure 2) concurrently.

Porous jump boundary condition
To simulate the effect of the lattice apron on the airfl ow characteristics, the plane covered by the grid circle is set to a porous jump boundary (see Figure 2). The pressure changes (Δp) above and below the plane can be defi ned by Darcy's law and an inertia loss term: In the above formula, μ is the laminar viscosity, α is the permeability, C 2 is the pressure jump coeffi cient, v is the normal velocity, and ∆m is the plane thickness. The effect of grid circles of different thicknesses and porosity on the airfl ow can be simulated by setting the permeability and the thickness of the porous plane. According to the grid circle's actual state, the permeability and the thickness of the porous plane are set at 1e −07 and 0.09 mm, respectively.

Solid wall boundary condition
The other faces of the calculation area are solid walls. The condition of the nonslip boundary is observed on the solid wall, which means that the velocity on the wall is zero. The solvers were implemented with a single-precision implicit split operator, and thereby the coupling problem between pressure and velocity was resolved. SIMPLEC algorithm is used, and grid spacing 0.5 mm and convergence precision 1e -4 are set to reduce the error to acceptable levels.

Numerical simulation results with different negative air pressure
In this section, the effects of three different negative pressures on fl ow velocity were simulated. Figures 3 and 4 indicate that by varying the negative pressure from -1,000 pa to -2,000 pa and -3,000 pa, the airfl ow velocity will increase from 37.32 m/s to 53.97 m/s and 67.54 m/s, respectively. Figure 3 shows the streamline diagram of fl ow velocity in the X-Z section when Y is equal to zero (along the x-axis) with the velocity vector colored according to velocity magnitude in m/s. The results from Figure 3 reveal that the whole area of air suction slot is covered by the fl ow fi eld and this is attributable to the signifi cant rise of negative pressure effective

The effect of different negative air pressure on fl ow velocity
In this section, numerical simulation of the fl ow velocity along the motion trajectory of the fi ber strand in the condensing zone was studied. In the condensing zone, there are three kinds of forces acting on the fi bers generally. First, the transverse condensing force on y-axis direction: under this force the width of the fi ber strand is reduced and the spinning triangle is decreased. Second, the output force on x-axis direction: under this force the fi bers strands can be straightened and the condensing effect is improved. Third, the assisted condensing force on z-axis direction: under this force the fi ber strands are made to cling to the outer surface of lattice apron, the strand structure is kept stable, and there is an improvement in fi ber-condensing effect. The effects of output force on the x-axis direction produced by the airfl ow can be ignored towing to the fact that the fi ber strand was mainly affected by the drafting force on the x-axis direction. For the convenience of the subsequent comparative analysis, a straight line located in the middle condensing zone is defi ned, which is parallel to y-axis[X = 10 mm, Z = 1.2 mm].
range. Additionally, above the area of air suction slot, the fl ow velocity compared to other areas is very large. Further, the fl ow velocity streamlines' distribution is denser and the active area of the negative pressure was observed to increase when the negative pressure is increased. This is envisaged to improve the condensing of fi bers. Figure 4 indicates that with respect to the central line of the air-suction slot, the fl ow fi eld distribution is symmetric and the fl ow velocity reaches the maximum. This means that the fi bers in the area of air suction slot are undergoing the largest air transverse condensing force, and the fi bers have more ability to move toward the center strand and the effects of transverse condensing are obtained. Additionally, with increasing negative pressure, the fl ow velocity increases, and this increase leads to a greater increase in the transverse condensing effects and a better convergence. This phenomenon reduces fi ber width and eliminates the spinning triangle.

Yarn spinning and testing
After spinning, all the yarn samples were kept in the lab for at least 48 h under standard conditions, namely, 20 ± 2°C and 65 ± 2% relative humidity (RH). To study the effect of different negative pressure, yarn properties such as the yarn evenness (CV), hairiness index, and breaking strength were measured. The yarn hairiness was measured 10 times for each yarn bobbin using a YG172A hairiness tester under 30 m/min speed, and the average value of the 10 tested results was taken as the hairiness of any particular single bobbin yarn. The average

Flow velocity component on the y-axis direction
The diagram of fl ow velocity component on y-axis direction is shown in Figure 5. It shows the fl ow velocity is positive in the left side of the fi ber strand, whereas the same is negative in the right side in the whole condensing zone. The fl ow velocity on the y-axis direction denotes the transverse condensing direction of the fi ber strand, which indicates the need for reducing the fi ber strand width and decreasing the spinning triangle. Further, with increasing negative pressure, the transverse condensing force is benefi cial for reducing fi ber width. Consequently, the fl ow velocity component possibly is benefi cial for increasing strength and eliminating hairiness.

Flow velocity component on the z-axis direction
The fl ow velocity component on the z-axis and the positive value of fl ow velocity describe the movement of the fi ber strand away from the outer surface of lattice apron and the negative value describes the fi ber strand that is clung to the outer surface of lattice apron.
The diagram of fl ow velocity component on z-axis direction is shown in Figure 6. The value of fl ow velocity component on the z-axis is negative. However, with increasing negative pressure, the negative value of fl ow velocity is highly increased.

Experimental
The spinning experiments were carried out using DHU X01 multifunction digital spinning machine whose condensing device had three-rollers lattice negative-pressure type. To verify the results obtained from the simulation discussed above, the three different yarn counts used were spun 29.2 tex, 19.6 tex, and 14.6 tex at different negative air pressures. The yarn count range was selected to cover the common of the yarn produced. The cotton fi ber properties and the details of the spinning parameters are shown in Tables 2 and 3, respectively. A cotton roving of 600 tex was used.   When the negative pressure was increased, the total velocity of airfl ow is increased as well. Accordingly, decreasing the transfer of border fi bers and the fi bers' distribution in the yarn body became more uniform and advantageous for enhancing CV.

Conclusions
To summarize, we have established the 3D physical model of the condensing zone by implementing numerical simulations based on a standard k-epsilon model. The numerical simulations of the 3D fl ow fi eld in the condensing zone for compact spinning systems with lattice apron and the effects of different negative pressures on fi ber condensing were extensively evaluated. The results reveal that the airfl ow fi eld helps to achieve convergence of the fi ber bundle in compact spinning systems with lattice apron. The optimization of the airfl ow fi eld resulted in signifi cant increase in yarn mechanical properties.
values of ten yarn bobbins were taken as the corresponding hairiness of spun yarn; the measured results are shown in Figure 7. The results show that by increasing the negative pressure, the hairiness is reduced, because the total velocity of airfl ow is increased, which is resulting in the elimination of the spinning triangle as shown in the simulation result.
The breaking force of yarn was also tested 10 times on XL-1A fully automatic single yarn strength tester at a speed of 500 mm/min with a pre-tension of 0.5 cN based on ASTM D2256 international standards (ASTMD2256, 1997) [28]. The average value of the breaking force of each yarn was recorded and the results are shown in Figure 8. Results show that as a result of increasing the negative pressure, the breaking force of yarn is increased, because the total velocity of airfl ow is increased, which in turn is due to the elimination of the spinning triangle. This further results in additional twist to free fi bers, as shown in the simulation result.
The CV was done by CT3000 evenness tester at a speed of 200 m/min based on D1425/D1425 M-14 (ASTMD3822/ D3822M-14, 2014) standards [29]. The average values of 10 bobbin yarns were taken as the corresponding evenness of spun yarn; the measured results are shown in Figure 9.