Numerical simulation of the three-dimensional flow field in four pneumatic compact spinning using the Finite Element Method

Abstract

Pneumatic compact spinning is one of the most widely used compact spinning systems, which is achieved by utilizing airflow condensing equipment to condense fibers in bundle and improve yarn properties. Therefore, research on flow field in the condensing zone is always the emphasis and difficulty for pneumatic compact spinning. In this paper, the three-dimensional flow field of four different kinds of pneumatic compact spinning systems, including two types of roller-type compact spinning, namely compact spinning with a perforated drum and compact spinning with a groovy drum, and two types of lattice apron-type compact spinning, namely three-line rollers compact spinning and four-line rollers compact spinning, are investigated using the Finite Element Method. Firstly, four three-dimensional physical models of the condensing zone are built by AutoCAD software respectively according to the measured geometric parameters of practical condensing zones. Then, using ANSYS software, the numerical simulations of the three-dimensional flow field in the condensing zone for four kinds of compact spinning systems are obtained. It is shown that the flow field distribution of the condensing zone of roller-type compact spinning is different from that of lattice apron-type compact spinning and the flow field distribution of the condensing zone is significantly related to yarn properties. Comparing with roller-type compact spinning, lattice apron-type compact spinning has lower negative value of the flow velocity in the X-axis direction, a higher value in the Y-axis direction and a higher value in the Z-axis direction. Combined with yarn experiments, it is shown that the flow velocity component in the X-axis direction has an assistant condensing effect and the negative value mainly increases yarn beneficial hairiness. Roller-type compact spinning has a higher negative value and more beneficial hairiness correspondingly than lattice apron-type compact spinning; the flow velocity component in the Y-axis direction has a direct condensing effect, which is of benefit mainly for improving strength and reducing hairiness. Lattice apron-type compact spinning has a higher value and higher strength and less hairiness than roller-type compact spinning; the flow velocity component in the Z-axis direction has an assistant condensing effect, which is mainly of benefit for improving yarn evenness. Lattice apron-type compact spinning has a higher value and better evenness than roller-type compact spinning.

Keywords

pneumatic compact spinning Finite Element Method flow field

Compact spinning is a new-type ring spinning technology, which utilizes airflow condensing equipment to achieve fibers in bundle condensing in order to improve yarn properties.^1–4 In compact spinning, the spinning triangle is eliminated and fibers are rolled into the yarn structure, which makes contribution to improving yarn evenness, improving strength and reducing yarn hairiness. According to the condensing principle, the compact spinning system is divided into a pneumatic compacting spinning system and a non-pneumatic compacting spinning system.⁵ Today, there are mainly four pneumatic compacting systems including compact spinning with a perforated drum, compact spinning with a groovy drum, three-line rollers compact spinning and four-line rollers compact spinning.⁶ The former two belong to roller-type compact spinning, while the other two belong to lattice apron-type compact spinning.

Currently, there are numerous scholars studying pneumatic compacting spinning.^7–13 Research on the flow field in the condensing zone is always the emphasis and difficulty for pneumatic compact spinning. The Finite Element Method (FEM) is one of significant numerical simulation methods in the engineering community. ANSYS software is one of the most widely used types of finite element analysis software and is widely used to analyze physical phenomena involving structural mechanics, heat transfer, the sound field, the flow field, the electromagnetic field and so on.¹⁴ Furthermore, FLOTRAN CFD is a significant module of ANSYS software, in which FLOTRAN 141and FLOTRAN 142 are respectively applied to research on the two-dimensional field and the three-dimensional field. Earlier researches in the textile field since 1980 emphasized structural mechanics and then expanded to the fiber, yarn, fabric and other flexible materials.¹⁵ In recent years, with the development of the new spinning technology, the application of ANSYS in the textile field continually expands. For example, the condensing principle of fibers in a bundle in compact spinning with a perforated drum^16,17 and the characterization of three-dimensional flow field in lattice apron type compact spinning⁵ were studied.

This paper attempts to investigate the three-dimensional flow field in four types of pneumatic compacting spinning. According to three-dimensional physical models of the condensing zone built by AutoCAD, numerical studies on the three-dimensional flow field are analyzed by using ANSYS software and the principles of flow field distribution in the condensing zone are given. Combined with the yarn experiment, the relationship between the distribution of the three-dimensional flow field and yarn properties is studied.

Three-dimensional physical models for the condensing zone

Firstly, for building the accurate three-dimensional physical model of the condensing zone, the geometric parameters of four pneumatic compact spinning systems should be measured according to the actual equipment, and shown in Tables 1 and 2. Then, four three-dimensional physical models of the condensing zone are obtained by using AutoCAD Software (see Figure 1). Here, the X-axis, Y-axis and Z-axis describe the output, transverse condensing and thickness directions, respectively, of fibers in the bundle. In these models, the fibers in bundle are ignored since they are much smaller than the condensing zone.

Figure 1.

Three-dimensional physical model of the condensing zone of four pneumatic compact spinning systems: (a) compact spinning with perforated drum; (b) compact spinning with groovy drum; (c) three-line rollers compact spinning; (d) four-line compact spinning.

Table 1.

Geometrical parameters of the condensing zone of two types of roller-type compact spinning

Compact spinning	Outer diameter of front roller/mm	Inner diameter of front roller /mm	Round hole diameter (width of groove)/mm	Round hole (groove) distribution density/cm² (round)
Compact spinning with perforated drum	59	53	0.8	80
Compact spinning with groovy drum	50	49	0.9	100

Table 2.

Geometrical parameters of the condensing zone of two types of lattice apron-type compact spinning

Compact spinning	Front top roller diameter/mm	Output top diameter/mm	Length of air-suction chute/mm	Width of air-suction chute/mm	Inclination degree /angle
Three-line rollers compact spinning	40	28	20	1.5	7.39
Four-line rollers compact spinning	28	28	21	2	7.6

For convenience to comparative analysis, four straight lines, namely line1, line2, line3 and line4, are defined in each compact spinning system (see Figure 1), which are parallel to the X-axis, and cling to the outer surfaces of the perforated drum, groovy drum and rectangular pipe correspondingly. Furthermore, the vertical distance between the lines and the outer surface of the perforated drum groovy drum and rectangular pipe is 0.5 mm.

Numerical simulations

Boundary conditions

It is assumed that the flow in the condensing zone is perfect gas; perfect gas is incompressible and normal temperature, which means that the airflow density is constant. Since the flow velocity of the inlet boundary is much slower that of the outlet boundary, flow velocity in the X-axis, Y-axis and Z-axis directions of the inlet boundary are 0 m/s; inlet boundary pressure is 101,300 Pa; the outlet boundary negative pressure is –2500 Pa; other surfaces are non-slip walls.

Theoretical models

For convenience to obtain the simulations, the turbulence model adopts the $k - ɛ$ model. The continuity, momentum and k and ɛ equations are presented as follows.⁶

Continuity equation:

\frac{\partial u_{i}}{\partial x_{i}} = 0

(1)

Momentum equation:

\frac{{Du}_{i}}{Dt} = f_{i} - \frac{\partial p}{\partial x_{i}} + \frac{\partial}{\partial x_{j}} (γ \frac{\partial u_{i}}{\partial x_{j}} - \bar{u_{i}} \bar{u_{j}})

(2)

k equation:

\frac{Dk}{Dt} = \frac{\partial}{\partial x_{i}} [(ν + \frac{ν t}{σ x_{i}}) \frac{\partial k}{\partial x_{i}}] + G_{k} - ɛ

(3)

ɛ equation:

\frac{D ɛ}{Dt} = \frac{\partial}{\partial x_{i}} [(ν + \frac{ν t}{σ ɛ}) \frac{\partial ɛ}{\partial x}] + G_{1 ɛ} - C_{2 ɛ} \frac{ɛ^{2}}{k}

(4)

Here, $G_{k} = ν_{t} [\frac{\partial u_{i}}{\partial x_{j}} (\frac{\partial u_{i}}{\partial x_{j}} + \frac{\partial u_{j}}{\partial x_{i}})]$ represents the turbulent energy produced by the mean velocity gradient, $ν_{t} = \frac{CuK}{ɛ}$ is the turbulent viscosity coefficient, t represents the time (s), u_i and x_i denote the velocity and coordinate components (m/s), v is the moment viscosity coefficient (m²/s), p is the modified pressure (Pa) and f_i is the mass force (N). The constant items are set as follows:

C_{1 ɛ} = 1.44, C_{2 ɛ} = 1.92, C_{u} = 0.09, σ_{k} = 1.00, σ_{ɛ} 1.30

For numerical simulation, it is important that finite element mesh generation is one of critical techniques for FEM. The number of cells for compact spinning with a perforated drum, compact spinning with a groovy drum, lattice apron-type compact spinning and four-line rollers compact spinning are successively 792,334, 718,180, 566,770 and 570,089.

Simulation results of the streamline diagram of flow velocity

By using ANSYS software, the numerical simulation results of the streamline diagram of flow velocity are obtained and are shown in Figures 2 –5.

Figure 2.

Streamline diagram of flow velocity for compact spinning with a perforated drum: (a) X–Y section; (b) Y–Z section; (c) X–Z section.

Figure 3.

Streamline diagram of the flow velocity for compact spinning with a groovy drum: (a) X–Y section; (b) Y–Z section; (c) X–Z section.

Figure 4.

Streamline diagram of the flow velocity for three-line rollers compact spinning: (a) X–Y section; (b) X–Z section.

Figure 5.

Streamline diagram of the flow velocity for four-line rollers compact spinning: (a) X–Y section; (b) X–Z section.

The streamline diagrams of flow velocity for two types of roller-type compact spinning are shown in Figures 2 and 3.

The streamline diagrams of flow velocity in the X–Y section of two types of roller-type compact spinning are shown in Figures 2(a) and 3(a). It is shown that the result of the compact spinning system with a perforated drum is similar to that of compact spinning with a groovy drum and the flow field distribution is symmetric with respect to the central line of the air-suction flume. The fibers in the bundle, particularly border fibers, move toward the fiber bundle center, which enforces the transverse condensing effect. Compared to the compact spinning system with a perforated drum, the flow velocity distribution of compact spinning with a groovy drum is denser and achieves a better transverse condensing effect correspondingly.

The streamline diagrams of flow velocity in the Y–Z section of two types of roller-type compact spinning are shown in Figures 2(b) and 3(b). It is shown that with the guiding device, the airflow symmetrically inflows into the air-suction flume from two sides of the guiding device. Furthermore, the flow in the condensing zone is parallel to the outer surface of the perforated drum and the groovy drum and achieves the maximum at the central line of the air-suction flume.

The streamline diagrams of flow velocity in the X–Z section of two types of roller-type compact spinning are shown in Figures 2(c) and 3(c). It is shown that the flow inflows into the condensing zone from two sides of the guiding device respectively and the flow velocity reaches the maximum in the round hole and groove respectively, in which the fibers in the bundle move toward the bundle center and achieve the transverse condensing effect.

The streamline diagrams of flow velocity of two types of lattice apron-type compact spinning are shown in Figures 4 and 5.

The streamline diagrams of flow velocity in the X–Y section are shown in Figures 4(a) and 5(a). It shows that the streamline diagram of three-line rollers compact spinning is similar to that of four-line rollers compact spinning. Furthermore, the flow field distribution is symmetric with respect to the central line of the inclined air-suction flume and the flow velocity distribution in the middle of the inclined air-suction flume is denser than the two ends. Compared with four-line roller compact spinning, the flow velocity distribution of three-line rollers compact spinning is denser, and the fibers in the bundle achieve a better transverse condensing effect correspondingly.

The streamline diagrams of flow velocity in the X–Z section are shown in Figures 4(b) and 5(b). It shows that the flow inflows into the air-suction flume from two sides and the upper under the negative pressure. The flow velocity of lattice apron-type compact spinning reaches the maximum at the center line of the inclined air-suction flume. The flow velocity distribution of three-line rollers compact spinning is denser than four-line rollers compact spinning and achieves a better transverse condensing effect.

Results of flow velocity

In order to reveal the principles and the difference distributions of flow velocity between roller-type compact spinning and lattice apron-type compact spinning, the simulation results of the flow velocity component on three axis directions of four pneumatic compact spinning are given in Figure 6.

Figure 6.

Diagrams of flow velocity component in three directions: (a) X-axis direction; (b) Y-axis direction; (c) Z-axis direction.

In Figure 6, plots of the flow velocity component in the X-axis, Y-axis and Z-axis directions of four pneumatic compact spinning are shown in Figures 6(a), 6(b) and 6(c), respectively.

The diagram of the flow velocity component in the X-axis direction (output direction of fibers in the bundle) is given in Figure 6(a). Here, the positive and negative values represent that the velocity direction follows the positive and negative directions of the X-axis, respectively. In addition, the flow velocity component possibly keeps beneficial hairiness. It is shown that the negative value of roller-type compact spinning is higher than that of lattice apron-type compact spinning. Specifically, the absolute value of roller-type compact spinning reaches minimum at the center point; the range is from 1.5 to 4.5 m/s. In addition, the absolute value of lattice apron-type compact spinning is less than or equal to zero and reaches minimum at the center line; the effect of transportation force can be negligible.

The diagram of the flow velocity component in the Y-axis direction (transverse condensing direction of fibers in the bundle) is given in Figure 6(b). Here, the positive and negative values represent that the velocity direction follows the positive and negative directions of the Y-axis. It is shown that the flow velocity component reaches maximum and it is symmetric about the center point, which implies that border fibers on two sides keep condensing toward the bundle center under the transverse forces. In addition, the flow velocity component possibly is beneficial for increasing strength and eliminating hairiness. The flow velocity of lattice apron-type compact spinning is much higher than roller-type compact spinning. Specifically, the maximum value of roller-type compact spinning is from 6 to 10 m/s. In addition, the value of lattice apron-type compact spinning is from 2 to 4 m/s. This can infer that lattice apron-type compact spinning has higher strength and less hairiness than roller-type compact spinning.

The diagram of the flow velocity component in the Z-axis direction (thickness direction of fibers in the bundle) is given in Figure 6(c). The flow velocity component makes fibers in the bundle stick to the outer surface of the perforated drum, groovy drum and rectangular pipe and may improve the transverse condensing effect. The flow velocity component possibly is beneficial for improving evenness. It is shown that the flow velocity distribution in this direction of roller-type compact spinning is different from that of lattice apron-type compact spinning. Specifically, the value of the flow velocity component of roller-type compact spinning reaches maximum at the center line and the value is from 10 to 20 m/s; the value of the flow velocity component of lattice apron-type compact spinning reaches minimum at the center line. In addition, the value is less than or equal to zero; the effect of transportation force can be negligible.

Experiments

In this part, in order to verify the results obtained above, four kinds of 9.7 tex yarns were spun in the four pneumatic compact spinning systems. The hairiness, breaking strength and evenness of the spun yarns were measured. For each kind of yarn, 10 samples were spun. Detailed spinning parameters are shown in Table 3.

Table 3.

Spinning parameters

Compact spinning system	Compact spinning with perforated drum	Compact spinning with groovy drum	Three-line rollers compact spinning	Four-line rollers compact spinning
Cradle spacer thickness (mm)	2.5	2.75	2.75	2.75
Negative pressure (Pa)	2359	2430	2477	2460
Ring diameter(mm)	42	42	42	42
Traveler	10.0	10.0	10.0	10.0

All tests were performed after the yarns were kept in standard atmospheric conditions for at least 24 hours under standard conditions (65 ± 5% relative humidity, 20 ± 2℃). Each sample was measured 10 times to obtained yarn evenness, strength and hairiness. Results of yarn qualities are the average of 10 samples. The evenness was tested using an USTER TESTER.5-S800 evenness tester under a speed of 400 m/min. The hairiness was tested using a YG172A hairiness tester under a speed of 100 m/min and 5 g pretension. The breaking force of yarns was tested on a YG068C fully automatic single yarn strength tester at a speed of 500 mm/min with pre-tension of 0.5 CN/tex. The measurement results are given in Table 4.

Table 4.

Testing results of yarn qualities

Compact spinning system	Compact spinning with perforated drum	Compact spinning with groovy drum	Three-line rollers compact spinning	Four-line rollers compact spinning
Evenness/CV%	13.17	13.01	12.89	12.95
Thin–50%	0.0	0.0	0.0	0.0
Thick+50%	35.5	34.2	25.7	26.5
Neps+200%	85	95	60.0	57.5
Breaking force/CN	201.51	211.33	233.99	220.55
Breaking force (CV)/%	9.22	8.09	7.10	10.37
Hairiness (≥2 mm)/(10 m)	130.20	134.26	51.50	61.00
Hairiness (≥3 mm)/(10 m)	25.0	24.8	9.20	11.80

From Table 4, it is obviously shown that compared with roller-type compact spinning, lattice apron-type compact spinning has better evenness, higher strength and less hairiness. The possible reason is that lattice apron-type compact spinning has a lower negative value of flow velocity component in the X-axis direction and a higher value in the Y-axis direction and Z-axis direction than roller-type compact spinning.

In the roller-type compact spinning system, compact spinning with a groovy drum has higher strength and more beneficial hairiness than compact spinning with a perforated drum. The possible reason is that compact spinning with a groovy drum has the higher negative value of flow velocity component in the X-axis direction and the higher value of the flow velocity component in the Y-axis direction than that of compact spinning with a perforated drum.

In lattice apron-type compact spinning, three-line rollers compact spinning has higher strength and less hairiness than four-line rollers compact spinning. The possible reason is that three-line rollers compact spinning has a higher value of flow velocity component in the Y-axis direction than four-line rollers compact spinning.

Conclusions

In this paper, numerical studies on three-dimensional flow fields in the condensing zone of four pneumatic compact spinning systems have been investigated using ANSYS software. Corresponding three-dimensional physical models of the condensing zone have been given according to the measured parameters of a practical compact spinning system using AutoCAD software. Four kinds of 9.7 tex yarns have been spun in four pneumatic compact spinning systems and the hairiness, breaking strength and evenness of the spun yarns were measured. Combined with the yarn experiment, the relationship between the distribution of the flow field in the condensing zone and yarn properties has been discussed.

The flow velocity component in the X-axis direction has an assistant effect on fiber condensing and affects beneficial hairiness. Furthermore, with an increase of the negative value, yarn beneficial hairiness is increased. Specifically, roller-type compact spinning has a higher negative value and the yarn has more beneficial hairiness than lattice apron-type compact spinning.

The flow velocity component in the Y-axis direction mainly affects fiber condensing. Furthermore, with an increase of the value, yarn strength is increased and hairiness is decreased. Lattice apron-type compact spinning has a higher value than roller-type compact spinning and the yarn has higher strength and less hairiness.

The flow velocity component in the Z-axis direction also has an assistant effect on fiber condensing. With an increase of the value, yarn evenness is mainly improved. Compared with roller-type compact spinning, lattice apron-type compact spinning has a higher value and the yarn has better evenness.

Footnotes

Funding

This work was supported by the National Natural Science Foundation of P. R. China under Grant 11102072, the Natural Science Foundation of Jiangsu Province under Grant BK2012254, Prospective industry-university-research project of Jiangsu Province BY2014023-13, Henan collaborative innovation of textile and clothing industry (hnfz14002), the Fundamental Research Funds for the Central Universities (No. JUSRP51301A).

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