Investigation on a New Annular Melt-Blowing Die Using Numerical

Mar 7, 2013 - In the local region, the centerline turbulence intensity for the new annular die is stronger than that for the corresponding annular die...
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Investigation on a New Annular Melt-Blowing Die Using Numerical Simulation Yudong Wang and Xinhou Wang* College of Textiles, Donghua University, 2999 North Renmin Road, Shanghai 201620, P. R. China ABSTRACT: In this study, a new annular melt-blowing die with an inner stabilizing piece was designed to obtain finer fibers and consume less energy than for the common annular die. The effects of the new annular die design on the velocity field, temperature field, and turbulence fluctuation field at the die centerline were investigated using numerical simulation. The simulation results reveal that, compared with the corresponding annular die, the new annular die decreases the negative velocity in the recirculation zone, enhances the mean velocity along the centerline, slows the temperature decay of the flow field, and reduces the velocity fluctuations of the air flow near the outlet of the polymer capillary. In the local region, the centerline turbulence intensity for the new annular die is stronger than that for the corresponding annular die, but the difference is not large.

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fields for dies with different convergence angles, obtaining agreement between the simulation results and the experimental data. Moore and Shambaugh10 used a compressible gas model in their simulations under isothermal conditions, thus excluding the temperature decay of the air. Krutka et al.11 utilized a CFD approach that was validated through experimental data to investigate the effects of nonisothermal conditions on the air flow for a slot die and considered the compressibility of the air in their simulations. To obtain the inherent physical principles of the airflow field of a slot die, Chen et al.12 simulated the subsonic velocity and temperature fields of the slot die and analyzed the effects of the slot angle, slot width, and nose piece width on the velocity and temperature fields. Sun and Wang13−15 combined numerical simulations and genetic algorithms or numerical simulations and orthogonal array design to optimize the air-flow field for a melt-blowing slot die. Krutka, Shambaugh, and Papavassiliou16,17 used CFD technology and experiments to analyze the air-flow fields from multiple jets in a Schwarz meltblowing die with arrays of annular jets. CFD simulations were used to investigate the influence of Laval nozzles on the air-flow field in a melt-blowing apparatus by Tan et al.18 For these computational fluid dynamics studies, the effects of the fibers on the air were assumed to be negligible. Krutka, Shambaugh, and Papavassiliou19,20 examined the effects of the polymer fibers on the air-flow field from an annular melt-blowing die and the air-flow field from a slot melt-blowing die by numerical simulations. The important finding was that the polymer fibers have a dampening effect on the turbulence. Annular dies are one of the most common types of meltblowing dies used in industry. A diagram of one hole of an annular melt blowing die, where a single annular air outlet surrounds each polymer outlet, is presented in Figure 1. The axis

INTRODUCTION Melt blowing is a single-step process to convert polymer pellets directly into a nonwoven mat of superfine fibers. In the meltblowing process, the polymer resin materials are fed into the hopper, melted, pressurized, and extruded from a heated die head. The high-velocity hot jet from the air nozzle rapidly attenuates the molten stream of polymer into fibers. Finally, the fibers deposit and form a nonwoven mat on a mesh screen placed some distance from the die. These resulting nonwoven fabrics are finding applications in an increasing number of fields such as filtration, absorbency, hygiene, and apparel. Different die heads, such as slot die heads, annular dies, and Schwarz melt-blowing dies, are used to produce polymer fibers in the melt-blowing process. The jets from these dies not only provide a substantial drag force but also play a function in preventing polymer solidification. The air-flow field created by the jets affects the size and strength of the polymer fibers. Therefore, some researchers have studied the air-flow fields below these dies by experimental methods or numerical simulations. In the laboratory, Shambaugh and co-workers1−6 measured velocity and temperature fields from a single-hole melt-blowing die with a pitot tube and a thermocouple. Xie and Zeng7 used a hot-wire anemometer to measure the turbulent airflow field below a single-orifice melt-blowing slot die. Bresee and Ko8 performed experimental measurements and obtained air velocity and temperature information for a 600-hole die. In recent years, computational fluid dynamics (CFD) technology has been used to study the air-flow fields of various melt-blowing dies. With experimental techniques, it is difficult to obtain velocity, pressure, and temperature data very close to the die, but numerical simulations do not have such restrictions. In addition, the use of CFD can avoid the cost of building dies and running experimental tests and save a great deal of time spent on the measurement in the laboratory. Using a CFD approach, Krutka and Shambaugh9 studied the isothermal air-jet flow fields of blunt and sharp dies, and the air velocities they used in their simulations were much smaller than those used in commercial melt-blowing processes. They adjusted the default values of the Reynolds stress turbulence model and then simulated the flow © 2013 American Chemical Society

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December 4, 2012 March 4, 2013 March 7, 2013 March 7, 2013 dx.doi.org/10.1021/ie303338m | Ind. Eng. Chem. Res. 2013, 52, 4597−4605

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of each air nozzle is perpendicular to the die face. The inner (di) and outer (do) diameters for air can be varied.

Figure 2. Two-dimensional model of the new annular die head (crosssectional view).

the polymer capillary wall. The cross section of the inner stabilizing piece is a right triangle. We used four common annular dies (see Figure 1), which are referred to as die 1, die 2, die 3, and die 4, to compare with four corresponding new annular dies (i.e., new die 1, new die 2, new die 3, and new die 4). Table 1 lists the dimensions of all of the dies studied in this work.

Figure 1. Two-dimensional model of the common annular die head (cross-sectional view).

According to aerothermodynamic and turbulence characteristic analyses, the air-flow fields from common annular dies exhibit some adverse factors on the further attenuation of the fibers. First, the research results10 showed that a recirculation zone that is close to the die surface exists in the air-flow fields for the annular die. In this region, the polymer fibers might be subjected to reverse velocities that push them back toward the die. Second, a partial kinetic energy loss of the jets results from the interaction between the jets and the ambient air, that is, the lateral diffusion of the jets. In this interaction, exchanges of mass, momentum, and energy occur between the stream and the nearby gas. When the width of the gas jets increases, the speed of the core section of the jets becomes smaller, and then increasing numbers of gas parcels are entrained. Although the mass of the streams increases, the kinetic energy of the jets decreases. Finally, the angle between the jet inlet and the die face of the annular die is 90°, and there is a space between the axis of the air nozzle and the axis of the polymer capillary. Consequently, the annular die head does not focus the high-speed jet on the centerline of the air-flow field where the polymer fiber is located and cannot provide the maximum drawing force. Furthermore, because of the required use of a large quantity of hot air in the melt-blowing production process, energy consumption is particularly high, and the centerline temperature of the air flow decays rapidly.2 If the temperature decay and the velocity decay can be lowered, not only will the jet attenuate the molten polymer into finer fibers, but the gas consumption and heat energy consumption will also be greatly reduced. Based on this analysis, we made some improvements to the common annular die head, designed a new melt-blowing annular die, and then investigated the performance of the air-flow field from the new annular die using numerical simulations. Our goal was to find a more efficient design by changing the shape and structure of the annular die heads to reduce the fiber diameter and the energy consumption.

Table 1. Die Dimensions of the Two Different Kinds of Annular Dies die head

do (mm)

di (mm)

sh (mm)

sb (mm)

die 1 die 2 die 3 die 4 new die 1 new die 2 new die 3 new die 4

2.37 2.46 1.89 2.75 2.37 2.46 1.89 2.75

1.30 1.27 1.27 2.25 1.30 1.27 1.27 2.25

1.5 1.5 1.5 1.5

0.45 0.435 0.435 0.925

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NUMERICAL SIMULATION Because an annular die can be modeled as a two-dimensional jet,10 a two-dimensional approximation of the flow field is adequate to describe the flow field for practical distances below the die. Moreover, the use of a two-dimensional computational domain requires much less simulation time than use of its threedimensional equivalent. In this research, the air-flow field was obtained by solving the Navier−Stokes equations through the commercial software Fluent 6.3.26, and the presence of a polymer stream was ignored. Calculation Domain and Grid Generation. Taking the common annular die head as an example, Figure 3 shows the computational domain used in the simulations. The calculation domain of the air-flow field was developed on the basis of experiments performed by Uyttendaele and Shambaugh1 and was one-half of the total two-dimensional air-flow field, which was symmetric about the centerline. The point O is the coordinate system’s origin, located in the plane of the die face and at the center of the annulus. The positive y axis is aligned with the dominant flow and lies along the line OG, whereas the x axis is perpendicular to the y axis and lies along the line OI (see Figure 3). It was experimentally determined that, over the inlet length (nh in Figure 3) range used, the length had

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NEW ANNULAR DIE Figure 2 shows a two-dimensional model of a new annular die that has an inner stabilizing piece around the outlet of the polymer capillary. The inner stabilizing piece is next to the air discharge orifice and is the extended parts of the external end of 4598

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to the width of the air nozzle. At the pressure outlets, the turbulence intensity was 10%, and the length scale was 20 mm. Grid-Resolution Effects. To test for grid-resolution effects, three additional cases were run on grids that had different levels of refinement. The cases depicted here are for die 2 with an inlet pressure of 1.1 atm, and the mean velocities along the centerline for these meshes were compared as presented in Figure 4. These

Figure 3. Computational domain.

little effect on the jet development. In our simulations, nh was 0.005 m, the same value as used by Moore and Shambaugh,10 and the computational domain below the die face was 0.07 m for the jet region. The line segment OI (i.e., the radius of the upper surface containing the air orifice) was 0.005 m, and the line segment GH (the radius of the lower surface) was set at 0.02 mm. The basic grid was created in Gambit, and the grid resolution was increased in the area of greatest interest using Fluent 6.3.26. Because of the rectangular shape of the computational domain, it was convenient to use a structured grid with quadrilateral cells. The area where the convergence of the two air jets occurs had a finer gridding. Consequently, throughout the gas inlet and in the region up to 15 mm from the die face for the entire width of the domain, all of the quadrilateral cells were refined, and in this way, the mesh for die 2 had 62300 cells. Turbulence Modeling. The Reynolds stress model (RSM)21 is more sophisticated for turbulent flow simulations than the popular k−ε model, and it is based on the solution of equations for the individual Reynolds stresses that are used to obtain closure of the Reynolds-averaged momentum equations. Because the transport equations for the Reynolds stresses result from the Reynolds averaging of the momentum equation multiplied by a velocity fluctuation, the RSM should be more exact than the popular k−ε model. Thus, research10 showed that the RSM was more accurate than the k−ε model for capturing the behavior of the jets from a slot die. For die 1, die 2, and die 3, experimental data and numerical simulations are available under some conditions, and the RSM parameters were calibrated.1,2,10 Moore and Shambaugh10 found that, when the turbulence parameters Cε1 and Cε2 were set as 1.24 and 1.82, respectively, and seven of the nine parameters were set to the values used by Krutka and Shambaugh,9 the computational results agreed well with the experimental data (specifically, for the velocity magnitude, velocity decay rate, and velocity spreading rate). Therefore, in this work, the RSM was chosen as the turbulence model. Simulation Parameters. The inlet of the calculation domain (EF) was defined as a “pressure inlet” with three different absolute pressures (i.e., 1.1, 1.2, and 1.3 atm) and a static temperature of 400 K. Under the pressure-inlet boundary conditions, the air jet was considered to be compressible. The outlets of the computational domain (IH and GH) were defined as pressure outlets with atmospheric conditions. The boundary condition of “symmetry” was used at the centerline (OG) of the air-flow field. All other boundaries were assigned the default setting of being a nonslip wall whose static temperature was 480 K. As a result, the turbulence specifications of the inlet boundary were set with an intensity of 10% and a hydraulic diameter equal

Figure 4. Centerline velocity profiles of the air-flow field for different grid resolutions.

additional grids had 35300, 144800, and 234800 cells. The mesh for the lowest-resolution run was created in Gambit, and the other two with more cells utilized a region of refined resolution. The case with 62300 cells gave the same result as the two cases with more cells and exhibited substantial differences from the case with 35300 cells. Therefore, the 62300-cell grid was deemed large enough to be grid-independent, and in this work, this grid partition approach was used for the other dies.

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RESULTS AND DISCUSSION The centerline velocity, centerline temperature, and centerline turbulence intensity were used to evaluate the performance of the new annular die with the inner stabilizing piece, because the three parameters are vitally important for producing melt-blown fibers. Mean Velocities along the Centerline for Two Different Kinds of Dies. Figure 5 provides the mean velocity along the centerline for two different kinds of dies. The centerline velocity of the flow field is important, because the path of the polymer fibers during attenuation generally follows the line of symmetry in the air-flow field. A higher air velocity on the centerline results in a faster attenuation and a lower final fiber diameter.22 The curves from Figure 5 show that the negative velocities close to the outlet of the polymer capillary for the four new annular die heads become much smaller than those for the four corresponding annular die heads. Meanwhile, after the local minimum zone, the mean velocities in the rest of the region for the four new annular die heads are higher than those for the four corresponding annular die heads. In particular, the peak−peak difference between new die 4 and die 4 was the maximum of all. In Figure 6, the area of flow recirculation is seen between the converging jets, and the cases depicted here are for die 2 and new die 2 with an inlet pressure of 1.2 atm. Note the recirculation areas that occur in a subtriangular space that is located within a 4599

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Figure 5. Centerline velocity profiles of the two different kinds of annular dies under the same inlet pressure: (a) die 1 and new die 1, (b) die 2 and new die 2, (c) die 3 and new die 3, (d) die 4 and new die 4.

could reduce the fiber whipping and its associated defects.23 Moreover, the inner stabilizing piece prevents the partial interaction of the jets and the air inside the inner stabilizing piece and reduces the kinetic energy loss of the jets. Therefore, in the air-flow field of the new annular die, the centerline velocity increases significantly. The simulation results reveal that the inner stabilizing piece contributes to the enhancement of the centerline velocity in the air-flow field and the reduction of the negative velocity in the recirculation zone. If it is desirable to increase the mean velocity along the centerline without increasing the gas consumption of the die or to achieve the same mean velocity along the centerline by lowering the gas emissions, an annular die head with an inner stabilizing piece is a better option than the corresponding annular die head. Static Temperatures along the Centerline for Two Different Kinds of Dies. Figure 7 presents the static temperatures along the line of symmetry in the air-flow field for two different kinds of die heads. For the two different kinds of dies, the decay profiles of the centerline static temperature indicate similar change trends. In the range from the origin O to the point at about 0.01 m, the centerline static temperatures for

few millimeters of the center of the die and immediately close to the polymer outlet. This area is full of eddies that result from the sudden enlargement of the air nozzle. The jet from the air nozzle of the new annular die changes its path and flows along the inner stabilizing wall, which is because of the Coanda effect. The inner stabilizing piece occupies a large proportion of the position of the recirculation area; prevents the stream spreading into the area close to the polymer outlet; and thus, to a surprising extent, suppresses the generation of the eddy. For this reason, the negative velocity for the new annular die head is much smaller than that for the corresponding annular die head. For common annular dies, the jet from the air nozzle expands outward and entrains the air around the centerline to flow downward. The air velocity around the centerline is higher than that from the annular jet. According to the Bernoulli principle, the centerline air pressure should be lower than that from the annular jet. Therefore, the jet is pushed toward the center of the air field. Based on the Coanda effect, the inner stabilizing piece has a significant effect on the movement path of the air stream and the merging of the jet. Consequently, the new annular die makes more high-speed streams centralize along the centerline of the air-flow field compared with the common annular die, which 4600

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Figure 6. Velocity vector fields close to the die head for the two different kinds of annular dies under the same inlet pressure: (a) die 2, (b) new die 2.

near the die head falls sharply. Whereas the recirculation area severely decreases and the negative velocity becomes smaller and smoother for the new annular die heads, the effects of air convection weaken, and then the static temperature along the centerline in the corresponding area is much hotter than that for the common annular die head. A higher air temperature will result in a higher fiber temperature along the centerline. It is expected that, at a higher air temperature, there should be a reduced driving force for heat transfer from fibers to air. Higher air temperature will delay the solidification of the polymer and lower the polymer viscosity, which was found to control the diameter distribution of meltblown fibers,24 and therefore, the period of fiber attenuation will increase. Thus, the research25 showed that an increase in air temperature causes an increase in the attenuation rate of the fiber and produces a finer filament. For the sake of finer melt-blowing fibers, the use of the new annular die head with an inner stabilizing piece is a better choice. Because a lot of hot air is used in the melt-blowing process, this phenomenon that the inner stabilizing piece has good effect on

the new die heads are higher than those for the corresponding annular die heads. In particular, near the polymer capillary outlet, the temperature difference is maximal. In the rest of the air-flow field, the new annular die heads no longer have obvious advantages. As is well-known, three modes of heat transfer are heat conduction, heat convection, and thermal radiation. In our study, there was no essential difference in the heat conduction and thermal radiation for the annular die heads and new annular die heads. For the gas, heat convection was the main mode of heat transfer, and the order of magnitude for the heat convection was much greater than the orders of magnitude for heat conduction and thermal radiation. In the transfer process of heat convection transfer, not only does the heat exchange happen because of the existence of temperature gradient, but also the gas flows take much more thermal energy than the former. There is a large recirculation zone, and the reverse speed is very high (see Figure 5) and intense (see Figure 8) close to the polymer capillary for annular die heads, so there is a very strong process of heat transfer by convection and the static temperature along the centerline 4601

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Figure 7. Centerline temperature profiles of the two different kinds of annular dies under the same inlet pressure: (a) die 1 and new die 1, (b) die 2 and new die 2, (c) die 3 and new die 3, (d) die 4 and new die 4.

heat preservation is very important for not only rapid fiber attenuation but also energy conservation. Turbulence Intensities along the Centerline for Two Different Kinds of Dies. Figure 8 shows several plots of the turbulence intensity in the centerline of the air-flow field for several different die heads. For the new annular die, the turbulence intensity starts at 0, whereas for the annular die, the turbulence intensity is not like that. According to a comparison of Figure 8 with Figure 5, for the annular dies and the new annular dies, the positions of maximum turbulence occur earlier than the positions of maximum velocity. In the area near the die face, the turbulence intensity along the central line for the new annular die head is much weaker than that for the corresponding annular die head. This is because the inner stabilizing piece prevents the partial interaction and diminishes the recirculation zone, which makes the flow for the new annular die head smoother than that for the annular die head. The turbulence intensity is a measure of the relative strength of the velocity fluctuations. In a general way, it is expected to have a smooth air flow around the location of a polymer fiber. Especially near the outlet of the polymer capillary, the strong velocity fluctuations might make the fiber bend, twist, and move relative to the centerline, which will lead to breakage of the fiber. The

peak value of the turbulence intensity occurs close to the common annular die head, and the results might be the sticking of the bent fiber to the die or to adjacent fibers, which is a highly undesirable event. In the remainder of the flow field, the centerline turbulence intensity for the new annular die head is higher than that for the common annular die head. However, the difference is not large. In this region, the centerline temperature and the centerline velocity are falling, and eventually, they all reach a plateau (see Figures 5 and 7). Because the experimental study25 revealed that most of the fiber attenuation, more than 96% in some cases, occurred within 0.015 m from the die face and that, after this distance, there was a decrease of the rate at which the diameter reduces. In the area where the turbulence intensity is higher for the new annular dies, it does not much affect the fiber drawing during the melt-blowing process. Because the inner stabilizing piece reduces the velocity fluctuations of the air flow near the outlet of the polymer capillary, the configuration of the new annular die head is desirable and will help prevent fiber breakage and polymer accumulation on the die. Effect of the New Annular Die on the Air-Flow Field for Different Inlet Pressures. As shown in Figure 9, for the two 4602

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Figure 8. Centerline turbulence intensity profiles of the two different kinds of annular dies under the same inlet pressure: (a) die 1 and new die 1, (b) die 2 and new die 2, (c) die 3 and new die 3, (d) die 4 and new die 4.

the inlet pressure. For the new annular dies, under different inlet pressures, it still inhibits the backflow in the recirculation zone and enhances the centerline velocity. Figure 10 shows that, for the common annular die and the new die, the centerline temperatures of the air-flow field decrease with the enhancement of the inlet pressure. As expected, for different inlet pressures, the inner stabilizing piece can weaken the effect of heat convection in the recirculation area and delay the reduction of the centerline temperature. Figure 11 indicates that, for the two different kinds of dies, the turbulence intensities along the centerline gradually rise with the inlet pressure. It is desirable that, under different inlet pressures, the die with the inner stabilizing piece all the same can reduce the fluctuations close to the outlet of the polymer capillary. When the inlet pressure increases, the centerline velocities for the two different kinds of dies increase, which is helpful for the drawing of the melt-blowing fiber. However, the negative velocities and the turbulence intensities become higher, and the static temperatures fall, which is adverse to the production of finer fibers.

Figure 9. Centerline velocity profiles of the two different kinds of annular dies under different inlet pressures.

different kinds of dies, the negative velocity and maximum velocity along the centerline gradually increase when to change 4603

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With the enhancement of the inlet pressure, for the two different kinds of dies, the centerline velocity increased, but the negative velocity and the turbulence intensity become higher and the static temperature falls slightly. On one hand, if the new annular die head with the inner stabilizing piece is implemented in the melt-blowing production process, it will contribute to the manufacturing of much finer fibers or even nanofibers. On the other hand, to ensure the quality of products, the new annular die head can reduce the gas consumption and the heat energy consumption, thus significantly decreasing the costs.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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Figure 10. Centerline static temperature profiles of the two different kinds of annular dies under different inlet pressures.

ACKNOWLEDGMENTS This work was financially supported by the National Natural Science Foundation of China (50976091) and the Chinese Universities Scientific Fund (Grant CUSF-DH-D-2013036).

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Figure 11. Centerline turbulence intensity profiles of the two different kinds of annular dies under different inlet pressures.

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NOMENCLATURE Cε1 = parameter for the dissipation equation of the RSM model Cε2 = parameter for the dissipation equation of the RSM model di = inner diameter of the annular orifice, mm do = outer diameter of the annular orifice, mm E, F, G, H, I = points of the coordinate system of the computation domain k = turbulent kinetic energy = 1/2(uiui ), m2/s2 nh = inlet length, m O = origin of the coordinate system of the computation domain sh = height of the cross section of the inner stabilizing piece, mm sb = base of the cross section of the inner stabilizing piece, mm x = horizontal coordinate, m y = vertical coordinate, m

Greek Letters

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CONCLUSIONS In this work, a new annular die with an inner stabilizing piece was designed and compared with the common annular die. The flow fields resulting from common annular dies and the new annular dies were predicted using a CFD approach. The contribution of the present work is the investigation of the effects of the design of the new annular die on the velocity field, temperature field, and turbulence fluctuation field at the die centerline. The inner stabilizing piece can diminish the recirculation area, inhibit the interaction of the jet and the nearby gas, and change the path of the air stream. Thus, the simulation results reveal that, under the same inlet pressure, the new annular die with the inner stabilizing piece decreases the negative velocity in the recirculation zone, enhances the centerline velocity, slows the decay of the centerline temperature, and diminishes the velocity fluctuations of the air flow near the die head compared with the corresponding annular die. In the local area of the centerline, the turbulence intensity for the new annular die head is higher than that for the annular die head, but the difference is not large.

ε = dissipation rate of turbulent kinetic energy, m2/s3

REFERENCES

(1) Uyttendaele, M. A. J.; Shambaugh, R. L. The Flow Field of Annular Jets at Moderate Reynolds Numbers. Ind. Eng. Chem. 1989, 28, 1735. (2) Majumdar, B.; Shambaugh, R. L. Velocity and Temperature Fields of Annular Jets. Ind. Eng. Chem. Res. 1991, 30, 1300. (3) Harpham, A. S.; Shambaugh, R. L. Flow Field of Practical Dual Rectangular Jets. Ind. Eng. Chem. Res. 1996, 35, 3776. (4) Harpham, A. S.; Shambaugh, R. L. Velocity and Temperature Fields of Dual Rectangular Jets. Ind. Eng. Chem. Res. 1997, 36, 3937. (5) Tate, B. D.; Shambaugh, R. L. Modified Dual Rectangular Jets for Fiber Production. Ind. Eng. Chem. Res. 1998, 37, 3772. (6) Tate, B. D.; Shambaugh, R. L. Temperature Fields below MeltBlowing Dies of Various Geometries. Ind. Eng. Chem. Res. 2004, 43, 5405. (7) Xie, S.; Zeng, Y. Turbulent Air Flow Field and Fiber Whipping Motion in the Melt Blowing Process: Experimental Study. Ind. Eng. Chem. Res. 2012, 51, 5346. (8) Bresee, R. R.; Ko, W. C. Fiber formation during melt blowing. Int. Nonwovens J. 2003, 12, 21.

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(9) Krutka, H. M.; Shambaugh, R. L. Analysis of a Melt-Blowing Die: Comparison of CFD and Experiments. Ind. Eng. Chem. Res. 2002, 41, 5125. (10) Moore, E. M.; Shambaugh, R. L. Analysis of Isothermal Annular Jets: Comparison of Computational Fluid Dynamics and Experimental Data. J. Appl. Polym. Sci. 2004, 94, 909. (11) Krutka, H. M.; Shambaugh, R. L.; Papavassiliou, D. V. Effects of temperature and geometry on the flow field of the melt blowing process. Ind. Eng. Chem. Res. 2004, 43, 4199. (12) Chen, T.; Wang, X.; Huang, X. Modeling the air-jet flow field of a dual slot die in the melt-blowing nonwoven process. Text. Res. J. 2004, 74, 1018. (13) Sun, Y.; Wang, X. Optimal geometry design of the melt-blowing slot die with high stagnation temperature via the orthogonal array method and numerical simulation. J. Text. Inst. 2011, 102, 65. (14) Sun, Y.; Wang, X. Optimization of Air Flow Field of the Melt Blowing Slot Die via Numerical Simulation and Genetic Algorithm. J. Appl. Polym. Sci. 2010, 115, 1540. (15) Sun, Y.; Liu, B.; Wang, X.; Zeng, Y. Air-Flow Field of the MeltBlowing Slot Die via Numerical Simulation and Multiobjective Genetic Algorithms. J. Appl. Polym. Sci. 2011, 112, 3520. (16) Krutka, H. M.; Shambaugh, R. L.; Papavassiliou, D. V. Analysis of Multiple Jets in the Schwarz Melt-Blowing Die Using Computational Fluid Dynamics. Ind. Eng. Chem. Res. 2005, 44, 8922. (17) Krutka, H. M.; Shambaugh, R. L.; Papavassiliou, D. V. Analysis of the Temperature Field from Multiple Jets in the Schwarz Melt Blowing Die Using Computational Fluid Dynamics. Ind. Eng. Chem. Res. 2006, 45, 5098. (18) Tan, D. H.; Herman, P. K.; Janakiraman, A.; Bates, F. S.; Kumar, S.; Macosko, C. M. Influence of Laval nozzles on the air flow field in melt blowing apparatus. Chem. Eng. Sci. 2012, 80, 342. (19) Krutka, H. M.; Shambaugh, R. L.; Papavassiliou, D. V. Effects of the Polymer Fiber on the Flow Field from an Annular Melt-Blowing Die. Ind. Eng. Chem. Res. 2007, 46, 655. (20) Krutka, H. M.; Shambaugh, R. L.; Papavassiliou, D. V. Effects of the Polymer Fiber on the Flow Field from a Slot Melt Blowing Die. Ind. Eng. Chem. Res. 2008, 47, 935. (21) Launder, B. E.; Reece, G. J.; Rodi, W. Progress in the development of a Reynolds-stress turbulence closure. J. Fluid Mech. 1975, 68, 537. (22) Zhou, C.; Tan, D. H; Janakiraman, A. P.; Kumar, S. Modeling the melt blowing of viscoelastic materials. Chem. Eng. Sci. 2011, 66, 4172. (23) Chung, C.; Kumar, S. Onset of whipping in the melt blowing process. J. Non-Newtonian Fluid Mech. 2013, 192, 37. (24) Tan, D. H.; Zhou, C.; Ellison, C. J.; Kumar, S. Meltblown fibers: Influence of viscosity and elasticity on diameter distribution. J. NonNewtonian Fluid Mech. 2010, 165, 892. (25) Bansal, V.; Shambaugh, R. L. On-line Determination of Diameter and Temperature during Melt Blowing of Polypropylene. Ind. Eng. Chem. Res. 1998, 37, 1799.

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