Experimental and numerical analysis of an improved melt-blowing slot-die

2.1 The improved slot die and the common slot die

In this work, an improved slot die in Figure 3 was conceived and manufactured. The improved slot die was designed based on the common slot die (see Figure 1). The improved slot die and the corresponding common slot die had the same the slot width b, the angle a that the gas slot was with respect to the die surface, the distance h between the two outer ends of the gas slots, and the slot length l₁. The angle α and the length l₁ were 60° and 12 mm respectively. In order to facilitate the processing of the die and the convenience of experimental measurement, the sizes of the width b and the distance h have been enlarged and were twice that of Shambaugh’s works (3,4,9). The width b was 1.3 mm and the length h was 6.64 mm.

Figure 3

The detailed schematic of the modified slot die: (a) cross-sectional view, (b) the horizontal view of the die face.

In Figure 3, on the inner sides of the two gas slots, there were two same internal stabilizers, which was different from the common slot die. The internal stabilizer was designed to reduce the inward diffusion of the jet and suppress the generation of separation vortices. The internal stabilizer had a cross section of a right-angled triangular. The inclined surface of the internal stabilizer and the inner wall of the gas slot are on the same plane. Therefore, the angle β between the slope of the internal stabilizer and the horizontal plane was equal to the inclination angle α. The internal stabilizer height I_h was 3.0 mm and the internal stabilizer length l₂ was 12 mm which was the same as the extent of the gas slot.

2.2 Experimental equipment and procedures

The devices used in this flow-field measurement experiment mainly consisted of a common slot die or an improved slot die with internal stabilizers, a hot wire anemometer, a stepper motor and a 3-D traverse unit (Figure 4). During the experiment, the high-speed jets of the two slot-dies were supplied by an air compressor. When the high-pressure stream from the air compressor was filtered, it was stably conveyed into the air chamber of the slot die through the control of the air pressure gauge and was at a pressure value of 0.05 MPa. Since there was no heating equipment, the temperature of the airflow in this experiment is equal to the atmospheric temperature and was set at 310 K. The air-flow field was measured online by means of a hot wire anemometer. The hot wire anemometer used in this experiment installed a one-dimensional probe (Dantec Dynamic 55P11) and appeared in Sun’s research (16). The 3-D traverse unit was driven by stepper motor, which could make the one-dimensional probe have a movement accuracy of 0.01 mm along the z-axis and guarantee the accuracy of the experimental results. The deviation of the measurements data obtained by the hot-wire anemometry could be corrected (20). In addition, the influence of melt-blown fibers on the flow field was not considered. The reason is that the fibers move substantially near the centerline of the flow field, and the proportion of space occupied by the fibers is small.

Figure 4

The experimental equipment and experimental setup.

It can be seen in Figures 1, 3 and 4, the origin of the coordinates was at the surface center of the slot dies. The y-direction was vertical to the two slots and the z-direction was straight down. It is known from previous studies (3,4,9) that the air-flow fields of the two slot dies were symmetric about the yz plane and the xz plane (see Figures 1, 3 and 4). Therefore, as shown in Figure 5, only one quarter of the flow field needed to be measured, which could save a lot of experiment time.

Figure 5

The overall distribution of measurement points.

The measurement area had a range of 5 mm ≤ z ≤ 103 mm, 0 mm ≤ x ≤ 4.5 cm, and 0 mm ≤ y ≤ 3 cm. There are two reasons here that the z value cannot be taken to 0 mm. During the measurements, it is found that when the 1-D probe of the hot wire anemometer approaches the slot dies, it easily touches the internal stabilizers or the die surface and is destroyed. Moreover, because the velocity of the two jets in the flow field close to the common slot die and the improved slot die is very large and the probe diameter of the hot wire anemometer is very small, it often causes a high breakage rate of the one-dimensional probe and a interrupting of the experiment.

In this experiment, the distance between every two test points in the direction parallel to the z-axis was 2 mm, which was that the stepper motor controller transmits 80 pulses, and the displacement of the one-dimensional probe was 2 mm, and a total of 50 data points was get. In the direction parallel to the y-axis, the measuring point interval was not equal, there were 19 data points on a line segment; the interval in the range of [0, 1.0] was 0.1 cm, and the interval in the remaining area was 2.5 mm. In the direction parallel to the x direction, the measurement points were four, which were {0, 1.5, 3, 4.5}.

3.1 Three-dimensional velocity field distribution

Figure 6 shows the distributions of airflow velocity over different xy planes in the flow field of the improved slot die. It can be seen from Figure 6 that there is a raised half-peak in each xy plane in the flow field of the improved slot die. These half-peaks are the maximum values of the air-flow velocity in different xy planes. As the value increases, the half-peak on the xy plane gradually flattens, meaning that the maximum velocity of the airflow gradually decreases.

Figure 6

Three-dimensional velocity field distributions.

In any of the xy planes in Figure 6, the velocity of the gas stream decreases along the y-axis. In each xy plane, the airflow velocity in the y-axis direction varies drastically in the range of 0 cm ≤ y ≤ 1 cm; while in the range of 2 cm ≤ y ≤ 3 cm, the gas velocity does not substantially change in the y-axis direction. Therefore, in the range of 0 cm to 1 cm, the measurement points are denser than the rest. It can effectively reduce measurement data and experimental test time and can ensure that the one-dimensional probe of the hot wire anemometer completely captures the flow below the improved slot die. As the z value increases, the gas velocity in the xy plane changes within a range of 1 cm ≤ y ≤ 2 cm, and the velocity value increases. This is because the high-speed air flow in the core zone diffuses and drives the surrounding low-speed air-flow and the still air movement.

It can also be seen from the figure that the velocity of the air flow is higher near the center of the flow field; in the region far from the center of the flow field, the draft of the meltblown fiber is basically ineffective because there is almost no gradient change in the velocity of the flow field.

In addition, it is revealed from Figure 6 that the velocity on the yz plane at x = 4.5 mm is lower than that of the other yz planes. This indicates that the end face of the slot hole has a certain influence on the flow field distribution in the vicinity. Therefore, it can be inferred that the gas velocity on the yz plane decreases as the x value increases further. The effect of the end face of the gas slot on the flow field causes the tensile strength of the polymer melt to be different, which affects the fineness and internal structure of the final meltblown fiber.

3.2 Velocity distribution of the central plane

The velocity distributions on different yz planes are basically the same in the area away from the end face of the gas slot (see Figure 6). Because the length of the slot used by the factory is generally large, the flow field below the improved slot die can be regarded as a two-dimensional flow field distribution and the velocity distribution of the central plane (the yz plane at x = 0 mm) is representative (16). Figures 7 and 8 show the velocity distribution on the yz plane at x = 0 mm.

Figure 7

The average velocity distributions of the yz pane for the improved slot die in the y-direction at positions of different z-values.

Figure 8

The average velocity distributions of the yz pane for the new modified slot-die along the z-direction at different y-positions (x = 0).

It can be clearly seen from Figure 7 that as the z-value increases from 5 mm to 85 mm, the half peak of the average velocity has gradually become gentle. It can be seen from Figure 7 that as the z value increases, the velocity of the high-speed flow in the region far from the die changes and increases within a range of 1 cm ≤ y ≤ 2 cm. This is the same trend as the reaction in Figure 6.

Figure 8 gives the mean-velocity profiles for the improved slot die along the z-direction at different y-positions, which is similar to that of the common slot die (7). Shown in Figure 6, the mean velocities on the center line of the air-flow field from the modified slot die is the maximal, and in the regions far from the z-axis, the mean-velocity values along the z-direction at different y-position from 0 cm to 1 cm decreases in turn and approach gradually in the end point. The air mean velocities of y = 3 cm have nearly the same values and it is the smallest relative to other profiles. It means that when the distance to the center-line (i.e., the z-axis) of the air field increases, the average velocity values along the z-direction at different y-positions significantly reduce and further illustrate the spreading effect of the high-speed airflow formed by the confluence of two jets. The mean-velocity profiles shows that the range of the high speeds along the z-direction for the improved slot die is near to the centerline of the air flow field, which means that the polymer melt should be drawn along the spinning line and it is advantageous to the drawing of melt-blowing fibers. In the area far away from the center line of the air-flow field, the mean velocities are very small and it is impossible to contribute to the drawing of the polymer stream.

3.3 Centerline velocities comparison of the two kinds of slot dies

In order to verify the effectiveness of the improved die, the velocities on the flow field are compared with that of the common slot die (Figures 9 and 10). Comparing Figures 9a-d it can be clearly seen that the average velocities of the two slot-dies in the y-direction vary at different z-positions. The mean velocity of the new improved slot die has greater advantage than that of the common slot die, in particular, in the area close to the center line of the air flow field. In the area far from the die, the speeds of the two slot dies are almost equal. As shown in Figure 9a at z = 5 mm, the average velocity profile of the common slot die has a complete peak close to the z-axis, indicating that the two jets have not yet merged and maintain its own characteristics. However, when z = 5 mm, the velocity in the flow field of the improved die has only one half-peak. This is because the internal stabilizers helps the two jets merge earlier, and it has a great influence on the flow field.

Figure 9

Velocity distributions of two types of slot-dies in the y-direction on the yz plane at x = 0 mm. (a) z = 5 mm; (b) z = 9 mm; (c) z = 19 mm; (d) z = 39 mm.

Figure 10

The centerline velocities of the common die and the modified die on the yz plane at x = 0 mm.

A comparison of the airflow velocity on the centerline of the flow field for the common slot die and the improved slot die is shown in Figure 10. It can be seen that the average velocity in center line of the improved slot die is higher than that of the corresponding common die. Firstly, a large percentage of the recirculation region is occupied by the two inner stabilizers and the creation of the vortex, for the most part, is suppressed, which effectively decay the velocity magnitude of the recirculation region. Secondly, the inner stabilizers can prevent the jets spreading inward and reduce the loss in the kinetic energy of the jets. Therefore, the velocity on the centerline of the flow field from the improved die increases, in contrast to the common one.

The air drafting force on the melt-blowing fiber is proportional to the square of the difference between the airflow velocity and the fiber velocity. Therefore, a higher air velocity in the centerline will favor the production of the polymer fiber, resulting in faster drafting form and lower the polymer fiber diameter (21, 22, 23, 24). The experimental results of Figures 9 and 10 reveal that the improved slot die with internal stabilizers could produce finer fibers than the common die.

4.1 Calculation domain and grid generation

The common slot die (i.e. die 1, see Figure 1) used in the numerical simulation part is the standard die in the factory (3,4). It was taken to compare to with improved slot one, namely new die 1 (Figure 3). The slot-angles making with the die faces for die 1 and new die 1 were 60°. The slot width b and the length h for the two kinds of die-heads were 0.65 mm and 3.32 mm, respectively. The height I_h of the inner stabilizer for the improved slot die was set 1.403 mm.

In the numerical simulation, the two-dimensional numerical simulation of the flow field was performed, which could reduce calculation time (9,18). Take the calculation domain (Figure 11) of the common die as an example (3,9), the origin point O was at the middle of the two slot nozzles, OD was on the z axis and OF was on the y axis. The area of the computational domain under the die was 100 mm × 30 mm and the height of the slot was 5 mm. For the improved slot die, the computational domain and the coordinate systems used in the simulations were basically the same to that for the common slot die.

Figure 11

Computational domain used in the simulation.

The structured grids with large size for the slot dies were obtained in Gambit and the adaptive mesh refinement was employed in FLUENT 6.3.26. For the two kinds of slot-dies, the grid generations were all the same to those in previous work (9,18). In the region from OD to 6 mm in the y direction and from AB to 30 mm in the z direction, the size of cells was 5 ×10^-2 mm and in the other zone the size of cells was 1 ×10^-1 mm.

4.2 Turbulence modeling and simulation parameters

Reynolds Stress Model (RSM) was applied to get an approximate solution for the slot dies (9). Therefore, RSM was used in simulation for the common slot die and the modified slot die in this study. In this work, AB was designated as a pressure-inlet boundary and under an absolutely pressure of 1.1 atm. The static temperature of the hot air at the entrance was 390 K. DE and EF were designated as pressure-outlets under atmospheric condition. Moreover, the slot walls and the die surface were designated as nonslip walls and their static temperature was 470 K. The hydraulic diameters and turbulence specifications of the inlet boundary and the outlets boundary referred to the previous studies (9,18).

4.3 Experimental verification

Figure 12 provides the numerical computation data and the measurement results along the center line of the flow field. Compared with the experimental data in this paper, the numerical simulation data of RSM is accurate.

Figure 12

Comparison of CFD data with experiment data.

4.4 Simulation results and discussion

Figure 13 shows that the reverse velocities are in the recirculation zone (Figure 2), which are difficult to measure by experimental methods. The reverse velocities are opposite to the direction in which the fiber is stretched, and it is possible to push the polymer melt back into the orifice. In Figure 13, the curve shows that the reverse velocity near the die face for the modified slot die is much lower than that of the corresponding common die.

Figure 13

Velocity values of two kinds of slot-dies at the centerline.

In most of the rest region, the centerline velocity of the modified slot die is basically greater and it is in agreement with the experimental result in Figure 10. Therefore, the simulation results also reveal that the modified slot die has speed advantage on the fiber drawing and should contribute to produce the thinner fibers, compared with the common slot die.

Figure 14 reveals the temperature curves on the centerlines of the flow fields from two types of slot dies. Within the range of 0 mm and 10 mm on the z-axis, the centerline temperature of the new slot die is much higher than that of the common slot die. Especially in the area near the nose of the slot die, the new die has a greater temperature advantage. The temperature on the centerline plays a key role in fiber drawing (21). The reason is that higher air temperature can reduce the viscosity of the polymer stream and is helpful to refine the diameter of the meltblowing fibers. According to the statistics of Bansal and Shambaugh (21), approximately 96% of the fiber diameter attenuation occurs within 15 mm from the spinneret orifice. After the distance of 15 mm, the diameter decrease rate of the fiber is sharply slowed down. Because the new slot die has a higher airflow temperature in the area close to the die, it is expected to obtain thinner fibers, compared to the common die.

Figure 14

Temperature values of two kinds of slot-dies at the centerline.

Figure 15 gives the turbulent kinetic energies on the centerlines of the airflow fields for the two different kinds of slot dies. For the new slot die and the common slot die, the position for the peak value of turbulent kinetic energy comes earlier than that of the air velocity (Figures 13 and 15). The turbulent kinetic energy of the new slot die start at the position z = 0 mm and significantly different from that of the common slot die. In the area close to the die face, the maximum value of the turbulent kinetic energy of the modified slot die is much smaller than that of the common slot die. The turbulent kinetic energy can be used to evaluate the fluctuation of the airflow velocity on the centerline and it should be small in the melt-blowing process, which is good for the fiber drafting. If the turbulent kinetic energy on the centerline is very great, it can intensify the fiber whipping and can cause the associated defects (25).

Figure 15

Turbulent kinetic energy values of two kinds of slot-dies at the centerline.