4.1. Effects of the Cross-Sectional Shape of the Yarn Channel
The design of the yarn nozzle in air-jet spinning technology is crucial for producing high-quality yarns, characterized by well-separated and minimally damaged fibers [
7]. In this study, two typical cross-sections of the yarn channel were simulated and compared: a square with rounded corners and a circular cross-section. Both the width of the square and the diameter of the circle are 2 mm, resulting in nearly identical cross-sectional area. For both cross-sections, the air orifice diameter was consistently set at 0.6 mm. Additionally, all simulations were performed under identical boundary conditions to ensure a fair comparison.
Figure 5 illustrates the velocity distribution across the cross-sections at three axial locations along the yarn channel: at the center, 0.002 mm to the left, and 0.002 mm to the right. At each location, well-developed vortex flows are observed, regardless of the cross-section shape. Notably, the primary vortex flow at the center of the yarn channel forms beneath the airflow from the air orifice, causing a significant portion of the supplied air to exit through the slit above. Consequently, the size and intensity of the vortex are greatly influenced by the airflow through the air orifice. The remaining airflow impacts the opposite wall of the yarn channel, developing into rotational flow along both sides of the yarn channel. This vortex airflow generally aids in migrating fibers in a helical form and reduces the hairiness of the spun yarn.
The vortices on the left and right sides are considerably larger, occupying almost the entire cross-section. This suggests that the vortex originates at the center and develops along both sides of the yarn channel. Although the overall flow patterns for the two different cross-section shapes appear similar, there are notable differences. In the square cross-section, a smaller counter-rotating vortex appears around the left upper corner, leading to unnecessary energy loss. Conversely, in the circular cross-section, a single strong vortex is formed.
Figure 6 compares the axial vorticity averaged across the cross-section along the yarn channel’s direction. It shows that the vorticity is significantly influenced by the shape of the yarn channel, the vorticity with the circular shape being 7~26% higher than that with the square cross-section. This is an advantage of the circular cross-section over the square cross-section. Another thing to note is that the vorticity reaches its maximum near the edge of air orifice, regardless of the shape of the yarn cross-section.
4.2. Effects of the Diameter of the Air Orifice
The diameter of the air orifice is a crucial design parameter in the development of the yarn channel for air-jet spinning technology. This study explored the effects of varying the air orifice diameter on the air vortex flow within the yarn channel. Diameters ranging from 0.6 mm to 2.0 mm were investigated, considering the size of migration nozzles manufactured by CeraTrak [
23]. Specifically, simulations were conducted for diameters of 0.6 mm, 1.0 mm, 1.3 mm, 1.5 mm, and 2.0 mm. All simulations were performed under identical boundary conditions, with the exception of the air orifice diameter size, to isolate its impact on the vortex flow dynamics.
Figure 7 illustrates the streamline patterns for air orifice diameters of 0.6 mm, 1.3 mm, and 2.0 mm. The maximum velocities reached are 387.6 m/s, 466.8 m/s, and 479.8 m/s for these respective diameters. A higher velocity magnitude indicates an increased airflow rate into the yarn channel, attributed to reduced flow blockage resulting from a larger air orifice diameter. This change in velocity magnitude significantly alters the vortex structure within the yarn channel.
One of the most notable effects of varying the air orifice diameter is on the swirling flow along the yarn channel. As shown in
Figure 7, the swirling flow becomes noticeably weaker as the air orifice diameter increases. Another significant change in the flow pattern is the increase in airflow rate through the slit outlet with larger air orifice diameters. This means that more airflow exits through the slit rather than the ends of the yarn channel as the orifice diameter grows.
These findings align with the research conducted by Chau et al. [
6], who noted that both insufficient and excessive inlet opening sizes result in fewer knots per unit length. Thus, the air orifice diameter has two opposing effects on the flow structure within the yarn channel: it reduces flow blockage, enhancing airflow into the channel, but also increases airflow leakage through the slit, weakening the swirling flow.
These observations suggest that there is an optimal air orifice size that maximizes the swirl motion within the yarn channel, balancing the benefits of increased airflow with the drawbacks of excessive leakage.
To quantitatively evaluate the impact of the orifice diameter, the vorticity across the cross-section in the direction of the yarn channel was calculated.
Figure 8 presents a comparison of the axial vorticity averaged across the cross-section for three different air orifice diameters. These results confirm that the averaged vorticity is significantly influenced by the orifice diameter. The maximum averaged vorticity is observed with an orifice diameter of 1.3 mm, suggesting that this diameter is optimal for achieving the best yarn quality given the current geometric and operational conditions of the yarn channel. This optimal diameter balances the advantages of enhanced airflow with minimized adverse effects, such as excessive leakage, thereby maximizing the swirl motion essential for high-quality yarn production.
Figure 6 also confirms that the vorticity reaches its maximum near the edge of air orifice, regardless of the magnitude of the orifice diameter.
Figure 9 shows the velocity vectors on cross-sections at three axial locations along the yarn channel with an air orifice diameter of 1.3 mm: at the center, 0.002 mm apart to the left, and 0.002 mm apart to the right. Compared to the 0.6 mm diameter case depicted in
Figure 5, the 1.3 mm diameter results in a significantly larger airflow rate exiting the yarn channel through the slit at all three cross-sections.
While a larger orifice diameter allows for a greater airflow rate into the yarn channel, it negatively impacts fiber twisting and increases the hairiness of the spun yarn. This comparison indicates that there might be other designs to improve the performance of the yarn channel by optimizing the vortex structure within the channel. While the 1.3 mm diameter with single air orifice offers some benefits, further refinement of the design could enhance yarn quality by balancing airflow and vortex dynamics more effectively.
4.3. Effects of the Number of the Air Orifice
To improve the performance of the yarn channel regarding the vortex structure within the channel, we investigated the effects of varying the number of air orifices. Generally, the number of air orifices is a critical parameter in designing yarn channels for air-jet spinning technology, although its impact on the vortex structure within the yarn channel is not yet fully understood. In this study, we conducted a comparative analysis of single and double air orifice designs. Aside from the number and diameter of the air orifices, all other geometric and boundary conditions remained consistent with those used in the previous simulations. This approach aimed to isolate the influence of the number of orifices on the vortex dynamics, providing insights into potential design optimizations for enhanced yarn quality.
Figure 10 illustrates the variation in average axial vorticity along the yarn channel for three different air orifice diameters in a double orifice configuration. Compared to
Figure 6, which represents the single orifice configuration, the vorticity distribution with double orifices is notably different. Specifically, with double orifices, a diameter of 0.9 mm achieves the highest vorticity in the air orifice area, while a diameter of 1.3 mm yields the highest vorticity outside the air orifice area. In the single orifice configuration, the maximum average vorticity was achieved with a 1.3 mm diameter.
This finding suggests that optimizing the diameter of the air orifice should consider the number of orifices used.
Figure 11 further compares the variation in axial vorticity along the centerline of the yarn channel, highlighting a strong dependency on the air orifice diameter, particularly in the area of air orifice. The diameter of 0.9 mm shows the best performance in terms of the centerline vorticity. Additionally, it is important to note that the centerline vorticity decreases rapidly along the yarn channel. In the case of 0.9 mm diameter, it drops by more than 60% within 2 mm from the center. Another thing to note is that there is a slight difference between the vorticities on the left and right. It helps the yarn movement inside the yarn channel.
The rapid decline in vorticity suggests that the vorticity in the air orifice area is crucial for enhancing yarn channel performance. By focusing on this region, the design can be fine-tuned to maximize the desirable vortex effects throughout the channel.
Figure 12 illustrates the velocity vectors on cross-sections at three axial locations along the yarn channel with double air orifices of 1.3 mm diameter: at the center, 0.002 mm to the left, and 0.002 mm to the right. Compared to the single orifice configuration shown in
Figure 7, a notable difference is that the center of vortex moved to the centerline of the yarn channel. In addition, it is energized by the two streams from the double orifices. Comparing
Figure 6 and
Figure 8, this flow pattern explains how the averaged vorticity for double air orifice is higher than that for single air orifice. The enhanced rotational airflow created by the double air orifice setup is beneficial for achieving improved yarn performance.
4.4. Experimental Validation
Air jet vortex spinning technology is widely recognized as a key flow feature that enhances the quality of spun yarn in the textile industry. Yarn produced using this technology undergoes significant structural changes, resulting in well-separated, straightened, and minimally damaged fibers [
2,
24,
25,
26,
27]. In fluid dynamics, this vortex flow is quantified as vorticity. Thus, the effects of vorticity, as a critical parameter in the design assessment of migration nozzles, can be evaluated by examining the properties of the spun yarn. All design parameters should ultimately be evaluated from the perspective of the spun yarn. Consequently, the effects of increased axial vorticity are experimentally assessed based on yarn properties. To achieve this, yarn produced with two different nozzles was analyzed, focusing on two mechanical properties and three quality-related properties.
In this study, a migration nozzle developed by CeraTrak [
23] was chosen as the basis design. This nozzle features a yarn channel with a diameter of 2.0 mm and a length of 10 mm. The test nozzles were manufactured from aluminum AES-11 by Sumitomo, Japan [
28]. This material has a purity of 99.7% and a bulk density of 1.3 g/cm
3. After manufacturing, hot isostatic pressing was applied as a surface treatment to eliminate any surface voids larger than 2 μm, at 1550 °C and 1000 bar.
The present CFD analysis confirms that a 1.3 mm diameter produces the highest vorticity along the centerline of the yarn channel, making it an optimal choice for single orifice configuration. However, for the double air orifice configuration, the diameter should be 0.9 mm based on the vorticity along the centerline in the air orifice area.
Figure 13 compares the variations in axial vorticity along the centerline. The double air orifice with a 0.9 mm diameter exhibits a significantly higher vorticity at the centerline compared with the single orifice with a 1.3 mm diameter. The difference between the double 0.9 mm and single 1.3 mm configurations is most pronounced in the air orifice area. Higher vorticity is expected to result in improved yarn performance.
For these two cases, polyester fiber PET 75D/36F was used, and the two migration nozzles were operated with the same interlacing nozzle [
7]. Compressed air was supplied at a pressure of 3 bar, and the spun yarn was produced at a speed of 600 m/min. These experiment conditions represent a typical set of operation parameters for migration nozzles manufactured by CeraTrak [
23].
Figure 14 shows a schematic diagram of the yarn experiment system, and
Table 3 summarizes the experimental conditions. The manufactured synthetic fibers were evaluated based on two mechanical properties: tensile strength and elongation rate at break. For these measurements, a yarn string of 250 mm in length was stretched using a universal testing machine (UTM) equipped with suitable clamps.
Figure 15 shows the UTM used in this study. This UTM is an electromechanical device that applies tensile force until the fabric breaks, measuring the corresponding strength and elongation rate at break. Tensile stress measurement was performed in accordance with ASTM D2256 (Standard Test for Tensile Properties of Yarns by the Single-Strand Method) [
29]. For each test, a yarn specimen of 250 mm was mounted on pneumatic clamps and was stretched at a constant rate of extension until rupture. Specimens were tested in a standard textile atmospheric condition of 20 °C and 65% relative humidity (RH). The crosshead speed was set to achieve an average time-to-break
s as specified in D2256, equivalently 300 mm/min at 250 mm gauge. Pre-tension of 0.5 cN/tex was applied to remove slack before the run. Break was detected when the real-time force dropped by 40% within 50 ms. The UTM (MTS Insight 1 [
30]) records both the maximum tensile force and the corresponding elongation rate at break. Generally, higher values of elongation rate and tensile strength indicate improved flexibility and/or filament twisting of the yarn. In addition to these mechanical properties, yarn quality is also assessed in terms of knot number, hairiness and migration index. The number of knots was manually counted for each yarn sample. There is not one single international standard protocol used exclusively for counting knots in spun yarn, it is typically addressed as part of a larger quality control process.
When counting knots, the number of knots in a given length of yarn, such as a meter or an inch, is a traditional measure [
31]. In this study, the number of knots in a 1 m length of the spun yarn was counted repeatedly three times per sample by two different engineers. The average value was then recorded.
Figure 16 illustrates an example of the spun yarn with several knots.
Hairiness was measured using a Uster hairiness tester [
32,
33] under the standard textile atmospheric condition of 20 °C and 65% relative humidity (RH). The tester uses a series of optical sensors (OH module) to scan the yarn and calculates the hairiness value (H value) by analyzing the yarn, providing a basis for comparison with global benchmarks and yarn trading standards. The measurement was repeated twenty times, with data collected three times for each measurement after a short break, ensuring randomization of data. Detailed information on these testers is provided in
Table 4.
The fiber migration index (MI) was determined as the average number of exchanges between sheath and core fibers per 100 mm of yarn using the dye tracer method. In this method, the sheath and core filaments are dyed different colors, and their movement is counted using a microscope by different engineers, recording the mean value. Specifically, the sheath fibers were dyed black while the core fibers were white. Using a microscope, the points where the color changes were observed, and the number of exchanges between sheath and core fibers was counted.
Due to experimental uncertainties from factors like manufacturing tolerances and measurement errors, we conducted a statistical analysis of all data. To determine a reasonable number of specimens, we carried out a power analysis using G*Power 3.1 [
34]. With α (significance level) = 0.05, power = 0.8, and d (effect size) = 0.85, at least eighteen specimens were needed. To do this, a sufficient number of specimens were collected from the spun yarn produced with the two migration nozzle settings. From this collection, we randomly selected twenty yarn specimens (n = 20) and tested. One engineer produced more than twenty specimens without specifying their intended use. Each specimen was marked with a different number of dots. Another engineer conducted testing without being informed of the markings. The results, summarized with mean and standard deviation in
Table 5, were analyzed using a one-way ANOVA with Tukey’s post hoc test. The
p values indicate a significant improvement in the four properties including mechanical properties. As the centerline vorticity increased by 62% from 5.03 × 10
5 (1/s) to 8.16 × 10
5 (1/s), the tensile strength rose from 3.2 N to 3.7 N, marking a 15.6% improvement. Similarly, the elongation rate at break improved from 19% to 22%, a 15.8% increase. Both improvements are statistically significant (
p-value < 0.05). The number of knots per meter increased from 23.21 to 24.01, a 3.4% increase that is also statistically significant (
p-value < 0.05). The migration index also increased from 0.57 to 0.63, a 10.5% increase that is also statistically significant (
p-value < 0.05). Therefore, the two mechanical properties exhibit a positive correlation with the centerline axial vorticity, with a slope of 1/4 while the migration index shows a slope of 1/6. A slight improvement was obtained in the number of knots per meter. We also analyzed the effect size by calculating Cohen’s d value using
. Here, M
1 and M
2 are the means of the single air orifice data and double air orifice data, respectively. The pooled standard deviation, s, was calculated as
. n
1 and n
2 are the numbers of specimens for the single air orifice and double air orifice, respectively. sd
1 and sd
2 are the standard deviations of two specimens 1 and 2. The values for tensile strength, elongation at break, knots per meter and migration index are 1.41, 2.46, 1.15, and 1.29, respectively. These indicate that the four properties are not only statistically significant but also practically meaningful. However, the improvements in these properties are 15.6%, 15.8%, and 10.5%, respectively. This suggests that both the single and double air orifice designs are effective, as they are already optimized for the diameter of the air orifice. The design change based on the centerline axial vorticity led to further enhancement of the spun yarn properties. In contrast, the hairiness showed only slight improvements that are not statistically significant (
p-value > 0.05). The hairiness index also shows the smallest effect size.
These distinctive improvements in both mechanical properties, number of knots per meter and yarn migration index, coupled with the significant difference in the centerline vorticity between the double 0.9 mm and single 1.3 mm configurations, suggest that the axial vorticity along the centerline is a crucial and practical parameter for the design assessment of migration nozzles.