Ind. Eng. Chem. Res. 2004, 43, 5405-5410
5405
Temperature Fields below Melt-Blowing Dies of Various Geometries Brian D. Tate and Robert L. Shambaugh* Department of Chemical Engineering and Materials Science, University of Oklahoma, Norman, Oklahoma 73019
Temperature fields were measured below two parallel, rectangular air nozzles. These are the types of nozzles that are commonly used in the melt-blowing process to produce fine polymer fibers. Each rectangular nozzle had a large length-to-width ratio, and the nozzles were closely spaced. Three types of nozzles were compared: (1) a die where the jets meet at a 60° angle and the die tip was blunt, (2) a die with a 60° angle and a sharp tip, and (3) a die with a 70° angle and a sharp tip. Correlations were developed to predict the temperature fields below these die types. Introduction Both air velocity and air temperature are important parameters in the use of air to attenuate and orient polymer fibers in the melt-blowing process (see Figure 1). As the polymer exits the melt-blowing die, the velocity of the air causes momentum transfer to the fiber, which results in rapid attenuation of the polymer strand. Concurrently, the high temperature of the air keeps the polymer strand at a high temperature, which aids attenuation by keeping the polymer viscosity low. The rectangular slot die (“Exxon” die) shown in Figure 1 is typical of the dies used in industry to produce meltblown fibers. Tate and Shambaugh1 examined the isothermal flow of air below slot dies of this type. They examined various geometries including 60° blunt dies (Figure 1), 60° sharp dies (Figure 2), and 70° sharp dies (Figure 3). However, they did not examine the nonisothermal behavior of these various dies. Harpham and Shambaugh2 did some initial work on nonisothermal slot dies when they studied the temperature fields below a 60° blunt die. However, they did not analyze any other die geometry. Our current research is an expansion of the work of Harpham and Shambaugh to rectangular slot dies of the various geometries shown in Figures 2 and 3. An objective of the present work is to compare the temperature fields below the various slot die geometries in order to predict an optimum die design. An additional objective is to provide correlations for the air temperature fields below the melt-blowing dies. These correlations can be used as boundary conditions for the solution of equations that model the melt-blowing process (see work by Marla and Shambaugh3). A third objective is to provide experimental data that can be used to calibrate the parameters in computational fluid dynamics (CFD) models of the air field below a melt-blowing die. As shown by Krutka et al.,4,5 the parameters in a CFD model need to be calibrated with experimental results in order to produce quantitative simulations of melt-blowing dies. The slot jets in Figures 1-3 are a type of dual rectangular nozzles. Single rectangular nozzles have been studied by a number of investigators such as Miller and Comings,6 Heskestad,7 Van der Hegge Zijnen,8 * To whom correspondence should be addressed. Tel.: (405) 325-6070. Fax: (405) 325-5813. E-mail:
[email protected].
Figure 1. Cross-sectional view of the 60° blunt air die. This is the same die used by Harpham and Shambaugh.15 The y axis (not shown) is perpendicular to the plane of this drawing.
Figure 2. Cross-sectional view of the 60° sharp die.
Sforza et al.,9 Trentacoste and Sforza,10 Kotsovinos,11 Jenkins and Goldschmidt,12 and Sfier.13 Mohammed and Shambaugh14 reference past work on linear arrays of rectangular nozzles. Only the work of Harpham and Shambaugh2,15 and Tate and Shambaugh1 involved experiments with dual jets that have sharp-edged air plates. Experimental Equipment The experimental setup used is shown in Figure 4. The air gap width d (see Figures 1-3) was first set with a feeler gauge, and then the slot width b was checked
10.1021/ie040066t CCC: $27.50 © 2004 American Chemical Society Published on Web 07/22/2004
5406 Ind. Eng. Chem. Res., Vol. 43, No. 17, 2004 Table 1. Experimental Conditions for the Temperature Measurements
Figure 3. 70° sharp die.
nose piece
b (mm)
d (mm)
Q (L/min)
Θ0 (° C)
vj0 (m/s)
60° blunt
0.44 0.65
0.38 0.56
100 100
60° sharp
1.35 0.44 0.65
1.17 0.38 0.56
200 200 100 100
70° sharp
1.35 0.44 0.65
1.17 0.41 0.61
200 200 100 100
1.35
1.27
200 200
200 100 200 300 300 200 200 100 200 300 200 200 200 100 200 300 200 200
42.7 23.2 29.1 35.0 70.0 27.8 40.6 21.7 27.5 33.3 55.0 26.5 40.6 21.7 27.5 33.3 55.5 26.5
Figure 4. Experimental setup.
under a microscope with a calibrated eyepiece. Each slot had a length (perpendicular to the planes of Figures 1-3) of 73.7 mm; this is large enough so that the jets may be approximated as two-dimensional. A 3-kW gas heater was used to heat air prior to entering the die head, heating tape and fiberglass insulation were wrapped around the piping to limit temperature loss, and four 250-W cartridge heaters were placed in the die head to ensure a constant discharge temperature. Air temperatures below the die were measured using a fine iron-constantan thermocouple of the exposed-junction type with a junction diameter of 0.7 mm. To minimize disturbance to the air flow, the junction end of the thermocouple was oriented parallel to the flow direction. The thermocouple was mounted on a Velmex threedimensional traverse system; this system allowed x, y, and z motions in 0.025-mm increments. For ease in recording temperature data, the thermocouple was connected to an Omega OMD-5508TC eight-channel thermocouple measurement board installed in a personal computer. Temperature measurements were taken for excess temperatures (Θ∞) of 100, 200, and 300 °C above room temperature as outlined in Table 1. Results and Discussion In melt blowing, it is generally desirable to have the air stream temperature equal to or greater than the polymer temperature. Furthermore, it is usually desirable to maintain a high air temperature along a long section of the threadline. This high temperature allows the proper attenuation of the fiber. However, because heating the air is one of the largest costs in the meltblowing process, maintaining high-temperature air at
Figure 5. Development of the temperature profile for positions near the die face of the 60° blunt die. These data are from Harpham and Shambaugh.2
great (horizontal) distances from the polymer fiber is unnecessary. High temperatures in these regions merely increase the cost of air heating without increasing the quality of polymer fibers produced. So, the best air temperature profile is a fairly narrow column of hot air and not a wide column of air. One goal in this work is to determine those die geometries that give this narrow column. Temperature Profiles near the Die Face. For positions near the die face, Figure 5 shows temperature profiles for the 60° blunt die studied by Harpham and Shambaugh.2 Distinguishing features of these profiles include the plateau in temperature at positions close to the die and the relatively large width of the profiles. In comparison, Figures 6 and 7 are temperature profiles for the 60° and 70° sharp dies, respectively. These graphs illustrate that sharp dies produce considerably narrower temperature profiles than the blunt die. As suggested above, narrow profiles are more efficient for melt blowing. Furthermore, the 60° sharp die produces a slightly narrower profile than the 70° sharp die. This observation parallels the conclusion reached by Harpham and Shambaugh:2 they observed that 60° sharp dies give higher (and thus superior) velocity profiles compared with 70° degree sharp dies. Nondimensional Temperature Profiles. For the die geometries studied herein, previous isothermal work (see work by Tate and Shambaugh1) showed that the velocity profiles were fairly well developed by z ) 5 mm. Our nonisothermal studies show that temperature
Ind. Eng. Chem. Res., Vol. 43, No. 17, 2004 5407
Figure 6. Development of the temperature profile for the 60° sharp die. The operating conditions were the same as those for Figure 5, and the same b value (0.65 mm) was used.
Figure 9. Nondimensional temperature profiles for positions near the 60° sharp die. Data are given for die settings (b values) of 0.44, 0.65, and 1.35 mm and flow rates of 100 and 200 L/min.
Figure 7. Development of the temperature profile for the 70° sharp die. The operating conditions were the same as those for Figure 5, and the same b value (0.65 mm) was used.
Figure 10. Nondimensional temperature profiles for positions near the 70° sharp die. Data are given for die settings (b values) of 0.44, 0.65, and 1.35 mm and flow rates of 100 and 200 L/min.
Figure 8. Nondimensional temperature profiles for intermediate positions below the 60° blunt die. Data for die settings (b values) of 0.44, 0.65, and 1.35 mm and flow rates of 100 and 200 L/min are given. These data are from Harpham and Shambaugh.2
and for positions less than 1.2 times the temperature half-width, the overall R2 is 0.984. The data tend to lie above the Bradbury curve for distances far from the center of the die. This behavior may be caused by the close proximity of the die face: heat radiating off of the die head causes high thermocouple readings. In support of this hypothesis, Harpham and Shambaugh2 showed that, as the distance below the die increases, the Bradbury curve fits the data increasingly well. Figure 8 also shows that, regardless of the air velocity (i.e., air flow fed to the die), the Bradbury equation describes the temperature profiles of air exiting a blunt die. To test if the Bradbury equation can be applied to dies of varying geometries, nondimensional temperature profiles were developed for the 60° and 70° sharp dies. Both the data and the Bradbury predictions are shown in Figures 9-12. Figure 9 shows results for positions near the face of a 60° sharp die, while Figure 10 shows results for positions close to the 70° sharp die. As with the 60° degree blunt die (see Figure 8), there is a discrepancy between the Bradbury equation and the data for positions relatively far from the center of the nose piece. Figure 9 (R2 from 0.985 to 0.993, with an overall R2 of 0.990) shows that, at positions close to the die face, the Bradbury equation accurately describes the temperature field below 60° sharp melt-blowing dies for x positions less than 1.2 times the temperature halfwidth. Figure 10 shows that the same is true for 70° sharp dies. For intermediate positions below the dies, Figures 11 and 12 reveal that the Bradbury equation accurately describes the behavior of air below the 60°
profiles also become well-developed by z ) 5 mm. For the nondimensionalization of the temperature profiles, the abscissa values are determined by dividing the x position by the temperature half-width (i.e., the x position at which the temperature decreases to half of the centerline temperature). The ordinate values are produced by plotting excess temperature at a specific x location divided by excess temperature at the centerline (in the same z plane). Figure 8 is the nondimensional temperature profile for the 60° blunt die. Also shown on this graph is a plot of the Bradbury16 equation. From this graph, it is seen that the data fit the Bradbury equation very well: R2 values range from 0.960 to 0.933,
5408 Ind. Eng. Chem. Res., Vol. 43, No. 17, 2004
Figure 11. Nondimensional temperature profiles for intermediate positions below the 60° sharp die. Data are given for die settings (b values) of 0.44, 0.65, and 1.35 mm and flow rates of 100 and 200 L/min.
Figure 13. Centerline temperature decay for the 60° blunt die. Die settings were b ) 0.44, 0.65, and 1.35 mm, and flow rates were 100 and 200 L/min. These data are from Harpham and Shambaugh.2
Figure 12. Nondimensional temperature profiles for intermediate positions below the 70° sharp die. Data are given for die settings (b values) of 0.44, 0.65, and 1.35 mm and flow rates of 100 and 200 L/min.
Figure 14. Centerline temperature decay for the 60° sharp die. Die settings were b ) 0.44, 0.65, and 1.35 mm, and flow rates were 100 and 200 L/min.
Table 2. R2 Values for the Nondimensional Temperature Profiles nose piece
z positions
figure
overall R2
R2 range
60° blunt 60° sharp 70° sharp 60° sharp 70° sharp
near near near intermediate intermediate
10 11 12 13 14
0.984 0.990 0.991 0.999 0.997
0.960-0.993 0.985-0.993 0.985-0.994 0.996-0.999 0.994-0.999
and 70° sharp dies. Table 2 summarizes the quality of the fit of the Bradbury equation to the experimental data. Centerline Temperature Decay. Harpham and Shambaugh2 showed that, by modifying velocity decay correlations to account for temperature rather than velocity, it is possible to develop a correlation to calculate the centerline temperature at any position below the die. This modification accounts for the change in the density of air at different temperatures. In a manner similar to that suggested by Majumdar and Shambaugh,17 this modification can be accomplished by replacing the distance z below the die head with the equation
Z(h) ) (z/h)(F∞/F0)1/2
(1)
where c1 and c2 are empirical constants, Z(h) is calculated from eq 1, and h and Θj0 are inputs. Equation 2 allows a straightforward calculation of Θ0. Note that h, not 2b, is used as a characteristic dimension in eq 1. h is used because, for a 60° blunt die, Harpham and Shambaugh2 found that nondimensionalizing the data by dividing z by h produced a single curve, but when they nondimensionalized the data by dividing z by twice the slot width, 2b, the correlation produced a separate curve for each slot width. Data for centerline temperature decay are shown in Figures 13-15 for the 60° blunt, 60° sharp, and 70° sharp dies. The R2 values for these plots are shown in Table 3. In Figure 13, the data are fit with eq 2 for the case where both c1 and c2 are variables and where c2 is fixed as 0.5. In Figure 14 for the 60° sharp die, correlations are given for each of the three experimental h values. In Figure 15 for the 70° sharp die, one correlation is given for the large h value of 2.70 mm, while a second correlation covers both h ) 0.88 and 1.30 mm. Temperature Half-Width Growth. Harpham and Shambaugh2 suggested that the temperature spreading rate of a 60° blunt die can be correlated with a linear equation. Specifically, they fit their data with an equation of the form
When this substitution is made, the correlation for determining the centerline temperature becomes
t1/2/h ) m1(z/h + m2)
Θ0/Θj0 ) c1[Z(h)]c2
where m1 and m2 are correlation constants. This type of equation was originally developed by Kotsovinos11 to
(2)
(3)
Ind. Eng. Chem. Res., Vol. 43, No. 17, 2004 5409
Figure 15. Centerline temperature decay for the 70° sharp die. Die settings were b ) 0.44, 0.65, and 1.35 mm, and flow rates were 100 and 200 L/min.
Figure 17. Growth of the temperature half-width with increasing distance from the die. The data were taken with the 60° sharp die. Die settings were b ) 0.44, 0.65, and 1.35 mm, and flow rates were 100 and 200 L/min.
Figure 16. Growth of the temperature half-width with increasing distance from the die. The data were taken with the 60° blunt die. Die settings were b ) 0.44, 0.65, and 1.35, and flow rates were 100 and 200 L/min. These data are from Harpham and Shambaugh.2
Figure 18. Growth of the temperature half-width with increasing distance from the die. The data were taken with the 70° sharp die. Die settings were b ) 0.44, 0.65, and 1.35 mm, and flow rates were 100 and 200 L/min. Table 4. Temperature Half-Width Correlation Constants for Equation 3
Table 3. Centerline Temperature Decay Correlation Constants for Equation 2 nose piece
b (mm)
d (mm)
60° blunt 60° sharp
all 0.44 0.65 1.35 0.44 0.65 1.35
all 0.38 0.56 1.17 0.41 0.61 1.27
70° sharp
c1
c2
R2
1.20 1.82 1.82 1.29 1.73 1.54 1.38
-0.615 -0.527 -0.511 -0.527 -0.526 -0.515 -0.548
0.989 0.991 0.981 0.993 0.992 0.984 0.993
describe the velocity half-width growth; the equation form was modified by Majumdar and Shambaugh17 to describe the temperature half-width growth. Figures 16-18 show experimental spreading rate data for the 60° blunt, 60° sharp, and 70° sharp dies, respectively. Also shown on these figures are fits to eq 3. As can be observed, a linear equation does a good job of correlating the spreading rate. Table 4 lists the die dimensions, correlation parameters, and r2 values for Figures 1618. As can be seen, the r2 values are very high. The temperature fields below dies of geometries other than those tested can be predicted by interpolating and extrapolating with the correlations that have been developed herein. For example, the correlation for the temperature spread below a 60° blunt die could be averaged with the correlation for temperature spread below the 60° sharp die to produce a correlation for a die of “in-between” dimensions, e.g., a die with a blunt distance (see Figure 1) between 0 and 2.032 mm. The
nose piece
b (mm)
d (mm)
0.44 0.65 1.35 0.44 0.65 1.35
0.38 0.56 1.17 0.41 0.61 1.27
60° blunt 60° sharp 70° sharp
c1
c2
r2
0.198 0.231
0.970 1.49
0.990 0.978
0.286 0.160 0.248
0.86 5.22 1.64
0.997 0.968 0.992
average would be weighted based on the ratio of the blunt distance (for the die in question) to 2.032 mm. An even more sophisticated use of the correlations is as calibration standards for a CFD software package. The CFD simulations would then provide a seamless prediction of temperature profiles for geometries that were not actually tested in the laboratory. Furthermore, CFD simulations can give predictions of parameters that are difficult to experimentally measure. For example, CFD simulations can predict velocities at positions that are very close to the die tip. Also, CFD simulations give turbulence predictions. See work by Krutka et al.4,5 for examples of how experimental correlations can be used with a CFD package. Conclusions The temperature fields for slot dies of various geometries (60° blunt, 60° sharp, and 70° sharp) were compared. These fields were correlated with (a) the
5410 Ind. Eng. Chem. Res., Vol. 43, No. 17, 2004
Bradbury equation, (b) a power law equation for the centerline temperature decay, and (c) a linear equation for the growth of the jet half-width. These correlations can be used to predict the temperature field below a broad range of slot die geometries that are run under a broad range of operating conditions (e.g., air flow rate, air temperature, etc.). The correlations can also prove invaluable in the calibration of a CFD simulation. Acknowledgment This work was supported by NSF GOALI Grant DMII-0245324. The support of 3M, Procter & Gamble, and Du Pont is also gratefully acknowledged. Nomenclature b ) slot width (see Figures 1-3), mm c1 ) constant in eq 2, mm1/2 c2 ) exponent in the power law fit of the centerline velocity decay (eq 2) d ) air gap width (see Figures 1-3), mm m1 ) correlation constant in eq 3 m2 ) correlation constant in eq 3 h ) characteristic die dimension as defined in Figures 1-3, mm t1/2 ) temperature half-width, mm v ) velocity, m/s v0 ) maximum velocity of the jet at a specified z level, m/s vj0 ) discharge velocity, m/s x ) Cartesian coordinate defined in Figure 2, mm x1/2 ) jet velocity half-width, mm y ) Cartesian coordinate in a direction perpendicular to the plane of Figure 2, mm z ) distance below the die, mm Z(h) ) (z/h)(F∞/F0)1/2 Greek Symbols θ ) angle that either air gap slot makes with the face of the die, deg Θ0 ) excess temperature above ambient along the centerline, °C Θj0) excess temperature above ambient at the nozzle exit, °C F∞ ) air density at ambient conditions, kg/m3 F0 ) air density along the centerline downstream from the die, kg/m3
Literature Cited (1) Tate, B. D.; Shambaugh, R. L. Modified Dual Rectangular Jets for Fiber Production. Ind. Eng. Chem. Res. 1998, 37 (9), 37723779. (2) Harpham, A. S.; Shambaugh, R. L. Velocity and Temperature Fields of Dual Rectangular Jets. Ind. Eng. Chem. Res. 1997, 36 (9), 3937-3943. (3) Marla, V. T.; Shambaugh, R. L. Three-dimensional Model of the Melt Blowing Process. Ind. Eng. Chem. Res. 2003, 42 (26), 6993-7005. (4) Krutka, H. M.; Shambaugh, R. L.; Papavassiliou, D. V. Analysis of a Melt Blowing Die: Comparison of CFD and Experiments. Ind. Eng. Chem. Res. 2002, 41, 5125-5138. (5) Krutka, H. M.; Shambaugh, R. L.; Papavassiliou, D. V. Effects of Die Geometry on the Flow Field of the Melt Blowing Process. Ind. Eng. Chem. Res. 2003, 42 (22), 5541-5553. (6) Miller, D. R.; Comings, E. W. Static Pressure Distribution in the Free Turbulent Jet. J. Fluid Mech. 1957, 3, 1-16. (7) Heskestad, G. Hot Wire Measurements in a Plane Turbulent Jet. J. Appl. Mech. 1965, Dec, 721-734. (8) Van der Hegge Zijnen, B. G. Measurements of the Velocity Distributions in a Plane Turbulent Jet of Air. Appl. Sci. Res., Sect. A 1958, 7 (4), 292-313. (9) Sforza, P. M.; Steiger, M. H.; Trentacoste, N. Studies on Three-Dimensional Viscous Jets. AIAA J. 1966, 4 (5), 800-806. (10) Trentacoste, N.; Sforza, P. M. Further Experimental Results for Three-Dimensional Free Jets. AIAA J. 1967, 5, 885891. (11) Kotsovinos, N. E. A Note on the Spreading Rate and Virtual Origin of a Plane Turbulent Jet. J. Fluid Mech. 1976, 77 (2), 305-311. (12) Jenkins, P. E.; Goldschmidt, V. W. Mean Temperature and Velocity in a Plane Turbulent Jet. J. Fluid Eng. 1973, Dec, 581584. (13) Sfier, A. Investigation of Three-Dimensional Turbulent Rectangular Jets. AIAA 11th Fluid and Plasma Dynamics Conference, Seattle, WA, July 10-12, 1978; Paper 78-1185. (14) Mohammed, A.; Shambaugh, R. L. Three-Dimensional Flow Field of a Rectangular Array of Practical Air Jets. Ind. Eng. Chem. Res. 1993, 32 (5), 976-980. (15) Harpham, A. S.; Shambaugh, R. L. The Flow Field of Practical Dual Rectangular Jets. Ind. Eng. Chem. Res. 1996, 35 (10), 3776-3781. (16) Bradbury, L. J. S. The Structure of a Self-Preserving Turbulent Plane Jet. J. Fluid Mech. 1965, 23 (1), 31-64. (17) Majumdar, B.; Shambaugh, R. L. Velocity and Temperature Fields of Annular Jets. Ind. Eng. Chem. Res. 1991, 30 (6), 1300-1306.
Received for review February 27, 2004 Revised manuscript received June 4, 2004 Accepted June 9, 2004 IE040066T
