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Figure 5: Comparison with experimental data for the “36 mesh” woven forming surface

Figure 5 Comparison with experimental data for the “36 mesh” woven forming surface

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Figure la: Schematic diagram of the problem and the computational domain In the hydroentanglement process, the impinging jets induce vortices within the fluid region, the fiberweb, and the interstices between the forming wires. The water vortices in the fiberweb cause the interaction between the impinging water and fibers in the fiberweb, involve fibers in vortices, align them along the water flow streamlines, and swirl them with the vortices. The rotational effect of fluid flow on a solid particle or a fiber is determined by flow vorticity. Shahcheraghi and Dwyer [7], for example, evaluated the rotation rate of a sphere in a flow field by one-half of the local flow vorticity at the sphere-center position. It is the rotational force on a fiber imposed by the water flow that causes the fiber to swirl and entangle with nearby fibers. It is therefore assumed that the degree of fiber entanglement is proportional to the average vorticity in the fiberweb region.
Figure la: Schematic diagram of the problem and the computational domain In the hydroentanglement process, the impinging jets induce vortices within the fluid region, the fiberweb, and the interstices between the forming wires. The water vortices in the fiberweb cause the interaction between the impinging water and fibers in the fiberweb, involve fibers in vortices, align them along the water flow streamlines, and swirl them with the vortices. The rotational effect of fluid flow on a solid particle or a fiber is determined by flow vorticity. Shahcheraghi and Dwyer [7], for example, evaluated the rotation rate of a sphere in a flow field by one-half of the local flow vorticity at the sphere-center position. It is the rotational force on a fiber imposed by the water flow that causes the fiber to swirl and entangle with nearby fibers. It is therefore assumed that the degree of fiber entanglement is proportional to the average vorticity in the fiberweb region.
Figure 1b: Projection of forming wires on the MD-CD plane
Figure 1b: Projection of forming wires on the MD-CD plane
Figure 2: Computational domain for 3D simulations Since the impinging jet velocity is very high, the flow in the fluid layer, porous fiberweb layer, and in the interstices between the forming wires (see Figure Ja) is turbulent. A turbulent flow model is used to simulate 3D flow in all three layers. The geometry of the computational domain for 3D simulations is shown in Figure 2, in which only two water jets are included. This is because all water jets in one manifold are identical and a manifold can be separated into many unit cells shown in Figure 2, in which the water flow field is similar and fiber entanglement simply accumulates when moving from one unit cell to the next.
Figure 2: Computational domain for 3D simulations Since the impinging jet velocity is very high, the flow in the fluid layer, porous fiberweb layer, and in the interstices between the forming wires (see Figure Ja) is turbulent. A turbulent flow model is used to simulate 3D flow in all three layers. The geometry of the computational domain for 3D simulations is shown in Figure 2, in which only two water jets are included. This is because all water jets in one manifold are identical and a manifold can be separated into many unit cells shown in Figure 2, in which the water flow field is similar and fiber entanglement simply accumulates when moving from one unit cell to the next.
To compare with experimental results, simulations are performed to model experimental conditions as closely as possible. Since the Perfojet® sleeve is micro-perforated with a small open area (8%), in simulations it could be shown that 95% of the impinging water is reflected back by the sleeve. This is because it is assumed that the micro-perforated holes in the sleeve have cylindrical geometry with discharge coefficient of Cz = 0.62. It is also assumed that the water velocity does not change from the inlet to the exit of the holes in the sleeve. Table 1: Parameters of the fiberweb processed using the Perfojet ® sleeve
To compare with experimental results, simulations are performed to model experimental conditions as closely as possible. Since the Perfojet® sleeve is micro-perforated with a small open area (8%), in simulations it could be shown that 95% of the impinging water is reflected back by the sleeve. This is because it is assumed that the micro-perforated holes in the sleeve have cylindrical geometry with discharge coefficient of Cz = 0.62. It is also assumed that the water velocity does not change from the inlet to the exit of the holes in the sleeve. Table 1: Parameters of the fiberweb processed using the Perfojet ® sleeve
Woven forming wires: The straight lines in Figure 3 are the linear fit lines between the simulated and experimental results. The correlation coefficient, R, of the linear fit line for the results in the MD is 0.99407, while that for the results in the CD is 0.97641, which means that the correlation coefficients in both the machine and cross-machine directions are very close to unity. This indicated that there is a linear correlation between the fabric tensile strength and the average vorticity in the fiberweb. Since the fabric tensile strength is proportional to the degree of fiber entanglement, it is evident that the degree of fiber entanglement is linearly correlated to the average vorticity in the fiberweb, which validates the major assumption of this research.
Woven forming wires: The straight lines in Figure 3 are the linear fit lines between the simulated and experimental results. The correlation coefficient, R, of the linear fit line for the results in the MD is 0.99407, while that for the results in the CD is 0.97641, which means that the correlation coefficients in both the machine and cross-machine directions are very close to unity. This indicated that there is a linear correlation between the fabric tensile strength and the average vorticity in the fiberweb. Since the fabric tensile strength is proportional to the degree of fiber entanglement, it is evident that the degree of fiber entanglement is linearly correlated to the average vorticity in the fiberweb, which validates the major assumption of this research.
Simulations are performed exactly for the same conditions as experiments. The measured thicknesses of the four woven forming surfaces are given in Table 2. For the woven forming surface, since it has a structure of interconnected wires and empty spaces between the wires, some of the inlet water is reflected back by the wires and the rest of water is evacuated through he interstices between the wires. Based on industry observations [10], it is assumed that 16% of he water that impinges on the wires is reflected back by the forming wires. Thus, the reflected portion of the water brought into the fiberweb by the jets is calculated as Ri =0.16x(1-9), where @ is the open area of the forming wires, which depends on geometry of the forming wires see Table 2). In the present study, the migration of fibers into the interstices between the forming wires is neglected. Table 2: Geometrical parameters of woven forming wires
Simulations are performed exactly for the same conditions as experiments. The measured thicknesses of the four woven forming surfaces are given in Table 2. For the woven forming surface, since it has a structure of interconnected wires and empty spaces between the wires, some of the inlet water is reflected back by the wires and the rest of water is evacuated through he interstices between the wires. Based on industry observations [10], it is assumed that 16% of he water that impinges on the wires is reflected back by the forming wires. Thus, the reflected portion of the water brought into the fiberweb by the jets is calculated as Ri =0.16x(1-9), where @ is the open area of the forming wires, which depends on geometry of the forming wires see Table 2). In the present study, the migration of fibers into the interstices between the forming wires is neglected. Table 2: Geometrical parameters of woven forming wires
Comparing the correlation results in Figures 5-7 with those in Figure 4, it is evident that the correlation coefficients for the “36 mesh,” “14 mesh,” and “10 mesh” forming surfaces are smaller than that for the “100 mesh” surface. This indicates that this model is more accurate for a fine mesh woven forming surface than a coarse one.
Comparing the correlation results in Figures 5-7 with those in Figure 4, it is evident that the correlation coefficients for the “36 mesh,” “14 mesh,” and “10 mesh” forming surfaces are smaller than that for the “100 mesh” surface. This indicates that this model is more accurate for a fine mesh woven forming surface than a coarse one.
dissipates as water filters through the fiberweb. For the fiberweb of a large thickness, the kinetic energy completely dissipates in the upper portion of the fiberweb causing almost no entanglement in its lower portion. This means the process is only efficient for fiberwebs with a critical thickness (about 1.5 mm) in a single manifold. Figure 8: Effect of fiberweb thickness on the average vorticity in the fiberweb for the “100 mesh” woven forming surface Figure 9: Effect of fiberweb thickness on the average vorticity in the fiberweb for the “36 mesh” woven forming surface
dissipates as water filters through the fiberweb. For the fiberweb of a large thickness, the kinetic energy completely dissipates in the upper portion of the fiberweb causing almost no entanglement in its lower portion. This means the process is only efficient for fiberwebs with a critical thickness (about 1.5 mm) in a single manifold. Figure 8: Effect of fiberweb thickness on the average vorticity in the fiberweb for the “100 mesh” woven forming surface Figure 9: Effect of fiberweb thickness on the average vorticity in the fiberweb for the “36 mesh” woven forming surface
Figure 11: Effect of fiberweb thickness on the average vorticity in the fiberweb for the “10 mesh” woven forming surface
Figure 11: Effect of fiberweb thickness on the average vorticity in the fiberweb for the “10 mesh” woven forming surface
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