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Influence of Laval nozzles on the air flow field in melt blowing apparatus
Chemical Engineering Science 80 (2012) 342–348
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Chemical Engineering Science journal homepage: www.elsevier.com/locate/ces
Influence of Laval nozzles on the air flow field in melt blowing apparatus Dawud H. Tan a, Peter K. Herman b, Arun Janakiraman b, Frank S. Bates a,n, Satish Kumar a, Christopher W. Macosko a,n a b
Department of Chemical Engineering and Materials Science, University of Minnesota, Minneapolis, MN 55455, United States Cummins Filtration, 1801 US Hwy 51/138, Stoughton, WI 53589, United States
H I G H L I G H T S c c c
Raising air pressure results in supersonic air flow and compression waves formation. Addition of Laval nozzles accelerates air flow and eliminates compression waves. Good agreement between computational fluid dynamics and Schlieren visualization.
a r t i c l e i n f o
a b s t r a c t
Article history: Received 4 January 2012 Received in revised form 29 May 2012 Accepted 13 June 2012 Available online 27 June 2012
Melt blowing combines extrusion of molten polymer through small orifices with stretching of the hot extrudate by hot air jets to create long, small diameter, fibers. Simulations and experiments were performed to examine: (1) the influence of increasing air pressure inside the melt blowing die (Pinlet) on the air jet in a typical melt blowing process and (2) the influence of a Laval nozzle (a converging– diverging nozzle) on the air jet. The baseline case without a nozzle was simulated and examined based on the y-component of the air velocity profile, vy(y), at the centerline as a function of Pinlet. As Pinlet increases: (1) the air flow goes from subsonic to supersonic and (2) the maximum value of vy(y) increases with increasing Pinlet, then starts to oscillate with the formation of compression waves in the supersonic region, Pinlet Z 15 psig. Simulation also showed that a Laval nozzle influences the air flow field by increasing the maximum value of vy(y) and eliminating the compression wave at a predictable value of Pinlet. Actual density oscillations in the supersonic flow field exiting a melt blowing die, with and without a Laval nozzle, were captured using a Schlieren visualization technique. In both limits the experimental results are in good agreement with the density oscillation in the supersonic flow field of the air jet anticipated by the simulations. & 2012 Elsevier Ltd. All rights reserved.
Keywords: Melt blowing Laval nozzle Supersonic Air flow CFD Schlieren
1. Introduction A nonwoven is a web of randomly oriented fibers bonded by physical entanglements or adhesion but not woven or knitted (Hutten, 2007). Nonwoven applications range from disposable wipes to medical apparel to filtration media (Russell, 2007). The future growth of the nonwoven industry relies on the capability of producing fibers with an average diameter less than 1 mm, commonly called nanofibers. Various techniques, such as electrospinning (Reneker and Chun, 1996; Frenot and Chronakis, 2003; Huang et al., 2003; Li and Xia, 2004), melt blowing (Wente, 1956), jet blowing (Borkar et al., 2006), centrifugal spinning (Sarkar et al., 2010), and laser-assisted supersonic drawing (Suzuki and
n
Corresponding authors. E-mail addresses: [email protected] (F.S. Bates), [email protected] (C.W. Macosko). 0009-2509/$ - see front matter & 2012 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.ces.2012.06.020
Aoki, 2008) can produce nanofibers, but melt blowing is of particular interest because it is solvent-free; this translates into a more economical process, higher production rate, and higher compatibility with many types of polymers. In short, the melt blowing process extrudes a molten polymer filament through a die and provided jets of hot air to rapidly extend the filament along its length and reduce its diameter. A significant amount of ambient air is entrained by the hot jet leading to rapid solidification of the fiber. Ellison et al. (2007) used a custom-built melt blowing equipment that mimics its industrial counterpart to generate nanofibers. They used higher air flow rates and lower polymer flow rates, which resulted in a greater attenuation force than what have been reported with industrial equipment. Ellison et al.’s method will allow nanofiber production with minimal modification on current industrial melt blowing equipment. However, reducing the polymer flow rate makes it industrially undesirable. Moreover, increasing the air flow rate (by increasing
D.H. Tan et al. / Chemical Engineering Science 80 (2012) 342–348
the air pressure in the melt blowing die, Pinlet) will cause the meltblown fibers to break and produce loose and uncollected fibers (commonly called ‘‘flies’’ in industry) (Breese and Qureshi, 2002; Buntin et al., 1972; Harding et al., 1972; Herman et al., 2008). These flies can aggregate and land on the fiber collector to form defects in the nonwoven. Herman et al. (2008) showed with numerical simulations that the air flow in the melt blowing process will become compressible and supersonic with increasing Pinlet ( Z15 psig). A compressible flow is one with large enough pressure gradient such that the change in density is no longer negligible. A supersonic flow is one in which the flow velocity is faster than the speed of sound (341 m/s at STP) (Anderson, 2003). Herman et al. (2008) suggest that the compression wave observed in supersonic flows will produce an unstable air flow field in the melt blowing process and thus will be responsible for the fly generation. They propose that the inclusion of a Laval nozzle in the melt blowing process will magnify the velocity and eliminate the instability in the air flow field, thus reducing the average fiber diameter and suppressing fly generation. A Laval nozzle is a convergent–divergent nozzle, invented by Gustav Patrik de Laval in 1888 for steam engine applications (de Laval, 1894), which can produce a supersonic flow in the divergent section, directly following the choked and sonic flow condition at the narrowest point in the nozzle. Both the scientific (Gerking, 2005) and patent (Gerking, 2004; Johnson et al., 2009; Nyssen et al., 1992; Reneker, 2002; Sodemann and Voges, 2008) literature have described the application of a Laval nozzle in melt blowing including various speculations regarding the production of nanofibers. Reneker (2002) and Johnson et al. (2009) claimed that polymer melt fibrillation within a Laval nozzle produces nanofibers, while Gerking (2004) and Sodemann and Voges (2008) suggested that the spontaneous burst of a molten polymer produces multiple nanofibers. Gerking’s (2005) photographic evidence of the spontaneous bursting process is inconclusive since the image could also be interpreted as fiber whipping. Moreover, spontaneous bursting, an unexpected event for viscoelastic materials, should lead to irregularly shaped fibers, which is not found; Gerking (2005) noted that all the produced fibers have a regular cylindrical shape. Laval nozzles have also been studied in the context of particle coating (Lee et al., 2011; Park et al., 2011). In this paper, we present numerical simulations of the air flow field associated with the melt blowing process (in the absence of meltblown fibers) with increasing Pinlet. The air flow field exiting a melt blowing die has been characterized experimentally with and without a Laval nozzle using a Schlieren visualization technique. To the best of our knowledge this represents the first experimental corroboration of simulated air flow in the melt blowing process.
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employed with CFD simulations performed at the UMN Supercomputing Institute is shown in Fig. 1; system boundaries are identified as air inlets (a and b), walls (c–h), and air outlets (i–k). Simulations were constrained by the following boundary conditions: (i) specified temperature and pressure for the air inlet (Tinlet and Pinlet); (ii) no slip and zero heat flux at the wall; and (iii) ambient temperature and pressure (25 1C and 1 atm) for the air outlet. Numerical simulations were run using the default iterative scheme until the following convergence (residual) criteria were satisfied: continuityo10 3, x-velocity (vx) and y-velocity (vy)o10 6, energyo10 6, turbulent model parameters ko10 4 and o o10 5. Fig. 2(a) shows schematically the location of the simulated 2D area with respect to the actual melt blowing die (illustrated in 3D). CFD simulation was used to investigate two different Laval nozzles that are illustrated in Fig. 3(a) and (b). The dimensions of the Laval nozzles were determined using software developed by NASA (Benson, 2011) that is based on the compressible flow principle (Anderson, 2003) and summarized in Table 1. Overexpanded nozzle dimensions were chosen to generate supersonic flow within the nozzle, with a normal-shock located roughly at the nozzle exit for a designated Pinlet. For supersonic flow through a Laval nozzle, a perfect expansion is achieved when the flow starts with a Pinlet value higher than the ambient pressure, steadily accelerates through the nozzle, and exits the nozzle at ambient pressure (Anderson, 2003). Eq. (1) shows that for any given Pinlet and Pexit value, an area ratio of the nozzle exit to its throat (Aex/Ath) that provides perfect expansion can be calculated simply based on the isentropic expansion factor of the gas (k¼Cp/Cv ¼1.4 for air) that flows through the nozzle (Sutton 1967): ( 1=ðk1Þ " ðk1Þ=k )#1=2 Ath k þ1 P exit 1=k k þ1 P 1 exit ¼ 2 k1 Aex Pinlet Pinlet
ð1Þ
2. Simulation
Fig. 1. An example of a 2D control area used in the simulation. The boundary types are: air inlets (a and b), walls (c–h), and air outlets (i–k). The arrows just below the die tip show the x–y coordinates used in the simulation.
Two dimensional (2D) numerical simulations of the air flow field in the melt blowing process were performed using computational fluid dynamics (CFD) software (Fluent ANSYS 12). The turbulent nature of the air flow was accounted for by applying the familiar SST k–o turbulence model (Menter, 1994; Wilcox, 1988), with default (Fluent 13) parameter settings. This is a popular two-equation eddyviscosity model that combines k–o model in the near-wall region and reverts to k–e in the free-stream, via a blending function. It is often recommended and used for simulating separating flow and adverse pressure gradients, as found in the Laval nozzles reported in this work. Different 2D meshes were created to mimic the dimension of the actual melt blowing die described in other publications (Ellison et al., 2007; Tan et al., 2010). An illustration of the 2D control area
Fig. 2. Schematics of the 2D plane in which the air density profile is: (a) Simulated with CFD. (b) Measured with Schlieren visualization. The dotted line in the 2D plane is the centerline location at which the comparison is made.
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Fig. 3. Schematics showing the cross sections of: (a)–(b) Laval nozzles 1 and 2 (See Table 1 for dimensions). (c) Top-view pictures showing the ease with which Laval nozzle 1 is attached onto the existing melt blowing die. In image (c), the tube above the air exit slot of the existing melt blowing die is an outlet for Pinlet measurement.
Table 1 Laval nozzle design. Nozzle
1 2
Fig. 4. A schematic of the Schlieren visualization setup.
which Laval nozzle 1 is attached onto the bottom of the melt blowing die where the air exit slot is located. 3.2. Optical visualization
Expansion
Shape
Length (mm)
Angle (1)
Aex/Ath
1.0 4.0 3.0
27 5 –
1.9 2.5 2.5
a
Two expansion zones Bell-shaped expansion
a Final expanded area, Aex, to initial throat area, Ath. These area ratios, 1.9 and 2.5, produce perfectly expanded flows when Pinlet is set to 130 and 215 psig, respectively.
For our industrial melt blowing application, Pinlet is practically limited to 45 psig due to the exponentially increasing cost of air compression (Nyssen et al., 1992). The corresponding area ratio for perfect expansion at Pinlet 50 psig calculated from Eq. (1) would be relatively small ( 1.3). Thus, the flow through the nozzle was substantially over-expanded by intentionally choosing area ratios in the 2 2.5 range, thereby creating high supersonic velocities in the nozzle followed by an abrupt shock positioned near the nozzle exit. In this study, the Pinlet values were set between 15 and 45 psig since the effect of compressible flow does not appear until Pinlet Z15 psig (i.e., exceeding critical pressure ratio for air with discharge to atmospheric pressure) and achieving Pinlet Z45 psig is not industrially feasible due to the exponential increase in the cost of air compression (Nyssen et al., 1992).
3. Experiment 3.1. Melt blowing equipment and Laval nozzle The melt blowing die and related equipment discussed in the previous publications (Ellison et al., 2007; Tan et al., 2010) were used in this work. The air flow field in the melt blowing process was examined as a function of Pinlet at Tinlet ¼25 1C in the absence of meltblown fibers. Based on the CFD simulations two Laval nozzles were fabricated out of 316-stainless steel, designed so they could be attached directly to the existing melt blowing die with minimal modification. Table 1 lists the different dimensions of the two nozzles, i.e., different expansion length, expansion angle, and area expansion ratio (ratio of the final expanded area to the initial throat area). Fig. 3(c) highlights the simplicity with
A Schlieren technique (Settles, 2001) was developed to visualize the air flow field in the melt blowing process. In short, the Schlieren technique uses the principle of light deflection associated with refractive index gradients to visualize density differences in fluids, including those found in compressible supersonic flows. Fig. 4 illustrates the Schlieren visualization equipment used in this work. A 15 cm diameter concave mirror with a 150 cm focal length (Edmund Optics) was used to direct light from a high intensity lamp (Volpi Intralux 6000-1) onto a digital camera (Canon PowerShot SD 1100 IS). The mirror was separated from the light source and camera (detector) by 300 cm, twice the focal length of the mirror. A razor blade, placed in front of the camera lens at the focal point acts as a Schlieren stop (Settles, 2001), partially blocking the incident light. The melt blowing die was positioned in the box labeled ‘‘Schlieren field of view’’ in Fig. 4 and the air jet images were acquired with the room completely darkened with the exception of the Schlieren optical source. Schlieren images were calibrated based on the known dimensions of the die assembly. Fig. 5(a) shows an image recorded under ambient light with no air flow. The diameter of the bottom piece of the melt blowing die (40 mm) was used to calibrate the camera. Fig. 5(b) was recorded with air flowing at a steady rate through the apparatus (and the room completely dark) revealing a periodic, oscillating pattern emanating from the exit of the melt blowing die. Image analysis software (NIH ImageJ) was employed to convert the variations in light intensity recorded by the camera along the centerline (identified by the white line) into relative brightness versus axial position y (see Fig. 1). The resulting normalized brightness is plotted in Fig. 5(c), along with a damped sinusoidal function (solid curve), which provides an accurate representation of the maxima and minima and the wavelength of the underlying compression waves.
4. Results and discussion 4.1. CFD simulation Computational fluid dynamics simulations were employed to model the air flow field at the exit of a conventional melt blowing die (i.e., no Laval nozzle) in the absence of fibers. The influence of Pinlet on the y-component of the air velocity (vy), air density (r), and air temperature (T) was investigated at constant Tinlet ¼25 1C.
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Fig. 5. (a) An image that provides a reference length (white arrow). (b) An image of the compression wave at Tinlet ¼ 25 1C and Pinlet ¼56 psig. Fig. 2(b) shows the 2D plane at which images (a) and (b) were recorded in relation to the 3D location of the die. (c) A normalized brightness profile of the white line in (b) measured with ImageJ and fitted with a damped sinusoidal function.
The air velocity maybe represented in terms of Mach number, which is calculated ‘‘locally’’ by Fluent as a function of local temperature condition based on the equation for the speed of sound, c (c¼ (Cp/Cv R T) ^ (1/2); Cp/Cv ¼1.4 for air). Ideal gas properties were used for compressibility characteristics, which are adequate to simulate the dry air conditions that were typically used in test conditions and practice for MB nozzles. Fig. 6(a) shows a representative simulation result for vy in the form of a 2D contour plot, from which the centerline vy(y) profile (x¼0) was extracted. Fig. 6(b) illustrates how vy(y) reaches a nearly constant level beyond the die exit for 1oyo10 mm and how the centerline air velocity increases with increasing Pinlet. Significantly, vy(y) begins to oscillate when Pinlet Z17 psig, indicating compression waves that can be characterized by an amplitude and wavelength of oscillation. Comparing the vy(y) profiles at Pinlet ¼ 17 and 20 psig in Fig. 6(b) reveals that both the amplitude and wavelength of the compression waves increase with increasing Pinlet. One of the authors has shown elsewhere that these oscillations in centerline air velocity are accompanied by oscillations in density, r(y), and temperature, T(y), all characterized by a common wavelength (Tan, 2011). Also, simulations at Tinlet ¼265 1C, representative of actual melt blowing conditions, demonstrate that the absolute values of vy(y), r(y), and T(y) change but do not alter the amplitude and wavelength of the compression wave (Tan, 2011). Laval nozzles 1 and 2 were simulated in the absence of fibers at fixed Pinlet ¼20 psig and Tinlet ¼265 1C. The resulting centerline vy (y) profiles were compared with the baseline case, i.e., no Laval nozzle. The goal was to determine the ability of the nozzle to produce a higher maximum vy and reduce wave compression in the air flow field after the exit of the melt blowing die. Fig. 7 demonstrates that both Laval nozzles (see Table 1) increase the maximum vy above the baseline value (reaching E2.52.9 Mach) and appear to suppress oscillation to some extent, although these benefits are accompanied by a near discontinuity in flow velocity between 2 and 4 mm from the die exit. The effect of the nozzle geometry on flow stability has been addressed elsewhere (Tan, 2011). For example, two expansion zones (nozzle 1) induce chaotic flow separation from the nozzle wall for Pinlet r40 psig, but this effect is suppressed with a single bell-shaped expansion zone (nozzle 2) (Tan, 2011). 4.2. Schlieren visualization Air flowing from the melt blowing die was visualized in the absence of fibers at various inlet pressures, with and without the
Fig. 6. CFD simulation results of the air flow field without a Laval nozzle, i.e., baseline. (a) An example of a contour plot of the y-component of the air velocity (vy, in unit of Mach) at Pinlet ¼ 20 psig and Tinlet ¼ 25 1C. (b) The effect of Pinlet on vy(y) at the centerline, x¼ 0, when Tinlet ¼ 25 1C.
Laval nozzle, using the Schlieren technique. Fig. 8 shows results obtained without the Laval nozzle at Tinlet ¼25 1C when Pinlet was increased from 25 psig, where compression waves first appear, to 56 psig. Dark and light bands in the Schlieren images, corresponding to regions of higher and lower gas densities, respectively, are in qualitative agreement with the simulated results shown in Fig. 6(a). Clearly, increasing the inlet pressure increases the spacing between the compression waves as anticipated by the numerical calculations (Fig. 6(b)). Similar results were obtained
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formation of compression waves with similar wavelength to that of the unmodified (baseline) die (this is sometimes referred to as nozzle stall; cf. Fig. 12). Fig. 10 (d) shows that at Pinlet E40 psig the normal shock is generated right at the exit of nozzle 2 and the compression wave formation appears to be suppressed completely. Fig. 10 (e)–(g) shows that increasing the pressure further leads to the re-appearance of compression waves but with different characteristics than the compression waves produced without a Laval nozzle because the normal shock is now generated outside of nozzle 2. 4.3. Comparison of simulation and Schlieren visualization Fig. 7. Simulations of the influence of Laval nozzles 1 and 2 on vy(y) at the centerline (x ¼0) in comparison to the case without nozzle, i.e., baseline. The simulations were done for Pinlet ¼ 20 psig and Tinlet ¼ 265 1C.
Fig. 8. Schlieren images of air flow recorded at Tinlet ¼ 25 1C and various Pinlet.
Fig. 9. (a)–(g) Schlieren images of air flow with Laval nozzle 1 at Tinlet ¼25 1C and various Pinlet.
Fig. 10. (a)–(g) Schlieren images of air flow with Laval nozzle 2 at Tinlet ¼ 25 1C and various Pinlet.
while visualizing: (1) the air flow in the absence of fibers at Tinlet ¼265 1C as anticipated by the CFD simulations and (2) the air flow at Tinlet ¼ 25 1C in the presence of fibers; these results are presented elsewhere (Tan, 2011). Attaching a Laval nozzle to the melt blowing die produces dramatic changes in the Schlieren images as shown in Figs. 9 and 10 (recorded with Tinlet ¼25 1C). Fig. 9 shows that nozzle 1 (Table 1) appears to damp the formation of compression waves up to inlet pressure of 40 psig due to flow separation (see above). Compression waves first appear at 45 psig and grow in magnitude and wavelength as Pinlet is raised. Careful inspection of these pictures reveals certain qualitative differences in the form of the flow field relative to the baseline case (Fig. 8). Visual images obtained while operating nozzle 2, which contains a more idealized expansion zone (see Fig. 3), are presented in Fig. 10. Based on the area ratio (Aex/Ath) of nozzle 2, Eq. (1) establishes that the air flow is always over expanded at all the Pinlet values investigated in this study (Sutton, 1967; Anderson, 2003). Fig. 10(a)–(c) shows that between 25 and 35 psig, the normal shock is generated inside nozzle 2 and it is displaying the
As illustrated in Fig. 2, the CFD simulations and Schlieren experiments access orthogonal planes in the 3D air flow field beyond the melt blowing die. Nevertheless, these projections share a common centerline, coincident with the y direction in Fig. 6, which is used in comparing the theory and visualization experiments. A single damped sinusoidal function characterized by wavelength lcw can be extracted from the Schlieren experiments (Fig. 5) and from the simulated centerline air flow profiles (Fig. 6) both at Tinlet ¼25 1C and various Pinlet. The numerical and experimental results for lcw are remarkably similar as shown in Fig. 11. Although the simulated lcw values are all slightly larger than the experimental data, within the uncertainties in the calculations and measurements, the experimental trend in lcw versus Pinlet is exactly accounted for by the CFD calculations. Fig. 12 provides a direct comparison of Schlieren images and simulated flow fields obtained with nozzle 2 for various values of Pinlet. Here we note that a point of reference is provided by the dashed white line in the first panel, which identifies the edge of the die. When Pinlet o40 psig, the normal shock is generated inside nozzle 2 and the experiment and simulation both show compression waves with characteristics similar to those seen without a Laval nozzle, i.e., the compression waves grow with increasing Pinlet and the simulation overestimates the experiment. At Pinlet E40 psig, the normal shock is generated right at the nozzle exit and suppression of the compression waves is evident in both the simulation and experiment. When Pinlet 440 psig, the normal shock is generated outside nozzle 2 and the experiment and simulation both show re-appearance of compression waves with characteristics that differ from the compression waves
Fig. 11. The wavelength of compression wave (lcw) as a function of Pinlet from simulation in comparison to that measured from Schlieren visualization. In all cases, Tinlet ¼ 25 1C and no Laval nozzle is used.
D.H. Tan et al. / Chemical Engineering Science 80 (2012) 342–348
seen without the Laval nozzle. Quantitative comparison of lcw at these elevated pressures is complicated by the fact that the maximum simulated air flow profiles no longer occur along the
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centerline, obviating direct comparison with the centerline brightness data.
5. Conclusion Computational fluid dynamics simulations were used to model the air flow field in the melt blowing process in the absence of meltblown fibers. The baseline case (without a nozzle) was investigated based on the y-component of the air velocity profile, vy(y), at the centerline as a function of inlet air pressure (Pinlet), ranging from subsonic to supersonic flows. The maximum value of vy(y) increases with increasing Pinlet, then begins to oscillate accompanied by the formation of compression waves in the supersonic region, Pinlet Z15 psig. Simulation demonstrates that a Laval nozzle influences the air flow field by increasing the maximum value of vy(y) and eliminating the compression waves at a specific predictable value of Pinlet. Performance of an actual melt blowing die was characterized using Schlieren visualization experiments, which revealed density oscillation in the air flow field as a function of Pinlet. The results of the simulations and experiments are in excellent agreement.
Acknowledgments This work is funded by Cummins Filtration. Parts of this work were also carried out using computing resources at the University of Minnesota Supercomputing Institute.
Appendix A. Supplementary information
Fig. 12. Wavelength of compression wave (lcw) predicted by simulation and measured with Schlieren visualization as a function of Pinlet at Tinlet ¼25 1C when Laval nozzle 2 is used. Black and white arrows in CFD result (top left) indicate the area that is invisible and visible, respectively in Schlieren visualization.
We compared the results from different turbulence models (k–e, realizable k–e, RSM, etc.) and found a non-negligible variation in the nature/onset of lower pressure ‘‘stall’’ where the flow detaches from the nozzle wall. Upon consultation with experts at Fluent, it was suggested that the SST k–o model was widely used in this specific field/application (rocket nozzle type flows), and is
Fig. A1. Observation of non-negligible variation in the CFD simulation results when two different turbulent models, k–e versus SST k–o, were used.
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Fig. A2. Simulation results obtained with two different ambient air temperatures, 25 and 1001 C, highlighting the negligible effect of ambient air temperature on the centerline velocity.
more conservative in predicting stall onset (which we observed/ confirmed in several nozzle configurations, once we switched to SST k–o from realizable k–e or RSM). The stall condition appeared to be qualitatively confirmed in physical testing/imaging. The comparison in Fig. A1 shows an example (same conditions) for realizable k–e versus SST k–o (all results in this paper were from the SST k–o model). The effect of ambient air temperature in our study can be safely ignored because it does not substantively affect the parameters of interest in the near-die fiber attenuation zone (velocity and temperature). To illustrate this, we simulated two cases where the local ambient air temperature was set to 251 and 1001 C and it is clear in Fig. A2 that there is no effect of ambient air temperature on the parameters of interest (centerline air velocity is shown here). References Anderson, J.D., 2003. Modern Compressible Flow, with Historical Perspective, third ed. McGraw-Hill, New York, NY. Benson, T., June 4th 2011. Interactive nozzle. o http://www.grc.nasa.gov/WWW/ K-12/airplane/ienzl.html 4. Borkar, S., Gu, B., Dirmyer, M., Delicado, R., Sen, A., Jackson, B.R., Badding, J.V., 2006. Polytetrafluoroethylene nano/microfibers by jet blowing. Polym. 47, 8337–8343. Breese, R.R., Qureshi, U.A., 2002. Fiber motion near the collector during melt blowing part 2: fly formation. Int. Nonwoven J. 11, 21–27. Buntin, R.R., Keller, J.P., Harding, J.W., February 22nd 1972. Non-woven mats by melt blowing. U.S. Patent 3,849,241. de Laval, G.P., June 26th 1894. Steam turbine. U.S. Patent 522,066.
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Chemical Engineering Science journal homepage: www.elsevier.com/locate/ces
Influence of Laval nozzles on the air flow field in melt blowing apparatus Dawud H. Tan a, Peter K. Herman b, Arun Janakiraman b, Frank S. Bates a,n, Satish Kumar a, Christopher W. Macosko a,n a b
Department of Chemical Engineering and Materials Science, University of Minnesota, Minneapolis, MN 55455, United States Cummins Filtration, 1801 US Hwy 51/138, Stoughton, WI 53589, United States
H I G H L I G H T S c c c
Raising air pressure results in supersonic air flow and compression waves formation. Addition of Laval nozzles accelerates air flow and eliminates compression waves. Good agreement between computational fluid dynamics and Schlieren visualization.
a r t i c l e i n f o
a b s t r a c t
Article history: Received 4 January 2012 Received in revised form 29 May 2012 Accepted 13 June 2012 Available online 27 June 2012
Melt blowing combines extrusion of molten polymer through small orifices with stretching of the hot extrudate by hot air jets to create long, small diameter, fibers. Simulations and experiments were performed to examine: (1) the influence of increasing air pressure inside the melt blowing die (Pinlet) on the air jet in a typical melt blowing process and (2) the influence of a Laval nozzle (a converging– diverging nozzle) on the air jet. The baseline case without a nozzle was simulated and examined based on the y-component of the air velocity profile, vy(y), at the centerline as a function of Pinlet. As Pinlet increases: (1) the air flow goes from subsonic to supersonic and (2) the maximum value of vy(y) increases with increasing Pinlet, then starts to oscillate with the formation of compression waves in the supersonic region, Pinlet Z 15 psig. Simulation also showed that a Laval nozzle influences the air flow field by increasing the maximum value of vy(y) and eliminating the compression wave at a predictable value of Pinlet. Actual density oscillations in the supersonic flow field exiting a melt blowing die, with and without a Laval nozzle, were captured using a Schlieren visualization technique. In both limits the experimental results are in good agreement with the density oscillation in the supersonic flow field of the air jet anticipated by the simulations. & 2012 Elsevier Ltd. All rights reserved.
Keywords: Melt blowing Laval nozzle Supersonic Air flow CFD Schlieren
1. Introduction A nonwoven is a web of randomly oriented fibers bonded by physical entanglements or adhesion but not woven or knitted (Hutten, 2007). Nonwoven applications range from disposable wipes to medical apparel to filtration media (Russell, 2007). The future growth of the nonwoven industry relies on the capability of producing fibers with an average diameter less than 1 mm, commonly called nanofibers. Various techniques, such as electrospinning (Reneker and Chun, 1996; Frenot and Chronakis, 2003; Huang et al., 2003; Li and Xia, 2004), melt blowing (Wente, 1956), jet blowing (Borkar et al., 2006), centrifugal spinning (Sarkar et al., 2010), and laser-assisted supersonic drawing (Suzuki and
n
Corresponding authors. E-mail addresses: [email protected] (F.S. Bates), [email protected] (C.W. Macosko). 0009-2509/$ - see front matter & 2012 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.ces.2012.06.020
Aoki, 2008) can produce nanofibers, but melt blowing is of particular interest because it is solvent-free; this translates into a more economical process, higher production rate, and higher compatibility with many types of polymers. In short, the melt blowing process extrudes a molten polymer filament through a die and provided jets of hot air to rapidly extend the filament along its length and reduce its diameter. A significant amount of ambient air is entrained by the hot jet leading to rapid solidification of the fiber. Ellison et al. (2007) used a custom-built melt blowing equipment that mimics its industrial counterpart to generate nanofibers. They used higher air flow rates and lower polymer flow rates, which resulted in a greater attenuation force than what have been reported with industrial equipment. Ellison et al.’s method will allow nanofiber production with minimal modification on current industrial melt blowing equipment. However, reducing the polymer flow rate makes it industrially undesirable. Moreover, increasing the air flow rate (by increasing
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the air pressure in the melt blowing die, Pinlet) will cause the meltblown fibers to break and produce loose and uncollected fibers (commonly called ‘‘flies’’ in industry) (Breese and Qureshi, 2002; Buntin et al., 1972; Harding et al., 1972; Herman et al., 2008). These flies can aggregate and land on the fiber collector to form defects in the nonwoven. Herman et al. (2008) showed with numerical simulations that the air flow in the melt blowing process will become compressible and supersonic with increasing Pinlet ( Z15 psig). A compressible flow is one with large enough pressure gradient such that the change in density is no longer negligible. A supersonic flow is one in which the flow velocity is faster than the speed of sound (341 m/s at STP) (Anderson, 2003). Herman et al. (2008) suggest that the compression wave observed in supersonic flows will produce an unstable air flow field in the melt blowing process and thus will be responsible for the fly generation. They propose that the inclusion of a Laval nozzle in the melt blowing process will magnify the velocity and eliminate the instability in the air flow field, thus reducing the average fiber diameter and suppressing fly generation. A Laval nozzle is a convergent–divergent nozzle, invented by Gustav Patrik de Laval in 1888 for steam engine applications (de Laval, 1894), which can produce a supersonic flow in the divergent section, directly following the choked and sonic flow condition at the narrowest point in the nozzle. Both the scientific (Gerking, 2005) and patent (Gerking, 2004; Johnson et al., 2009; Nyssen et al., 1992; Reneker, 2002; Sodemann and Voges, 2008) literature have described the application of a Laval nozzle in melt blowing including various speculations regarding the production of nanofibers. Reneker (2002) and Johnson et al. (2009) claimed that polymer melt fibrillation within a Laval nozzle produces nanofibers, while Gerking (2004) and Sodemann and Voges (2008) suggested that the spontaneous burst of a molten polymer produces multiple nanofibers. Gerking’s (2005) photographic evidence of the spontaneous bursting process is inconclusive since the image could also be interpreted as fiber whipping. Moreover, spontaneous bursting, an unexpected event for viscoelastic materials, should lead to irregularly shaped fibers, which is not found; Gerking (2005) noted that all the produced fibers have a regular cylindrical shape. Laval nozzles have also been studied in the context of particle coating (Lee et al., 2011; Park et al., 2011). In this paper, we present numerical simulations of the air flow field associated with the melt blowing process (in the absence of meltblown fibers) with increasing Pinlet. The air flow field exiting a melt blowing die has been characterized experimentally with and without a Laval nozzle using a Schlieren visualization technique. To the best of our knowledge this represents the first experimental corroboration of simulated air flow in the melt blowing process.
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employed with CFD simulations performed at the UMN Supercomputing Institute is shown in Fig. 1; system boundaries are identified as air inlets (a and b), walls (c–h), and air outlets (i–k). Simulations were constrained by the following boundary conditions: (i) specified temperature and pressure for the air inlet (Tinlet and Pinlet); (ii) no slip and zero heat flux at the wall; and (iii) ambient temperature and pressure (25 1C and 1 atm) for the air outlet. Numerical simulations were run using the default iterative scheme until the following convergence (residual) criteria were satisfied: continuityo10 3, x-velocity (vx) and y-velocity (vy)o10 6, energyo10 6, turbulent model parameters ko10 4 and o o10 5. Fig. 2(a) shows schematically the location of the simulated 2D area with respect to the actual melt blowing die (illustrated in 3D). CFD simulation was used to investigate two different Laval nozzles that are illustrated in Fig. 3(a) and (b). The dimensions of the Laval nozzles were determined using software developed by NASA (Benson, 2011) that is based on the compressible flow principle (Anderson, 2003) and summarized in Table 1. Overexpanded nozzle dimensions were chosen to generate supersonic flow within the nozzle, with a normal-shock located roughly at the nozzle exit for a designated Pinlet. For supersonic flow through a Laval nozzle, a perfect expansion is achieved when the flow starts with a Pinlet value higher than the ambient pressure, steadily accelerates through the nozzle, and exits the nozzle at ambient pressure (Anderson, 2003). Eq. (1) shows that for any given Pinlet and Pexit value, an area ratio of the nozzle exit to its throat (Aex/Ath) that provides perfect expansion can be calculated simply based on the isentropic expansion factor of the gas (k¼Cp/Cv ¼1.4 for air) that flows through the nozzle (Sutton 1967): ( 1=ðk1Þ " ðk1Þ=k )#1=2 Ath k þ1 P exit 1=k k þ1 P 1 exit ¼ 2 k1 Aex Pinlet Pinlet
ð1Þ
2. Simulation
Fig. 1. An example of a 2D control area used in the simulation. The boundary types are: air inlets (a and b), walls (c–h), and air outlets (i–k). The arrows just below the die tip show the x–y coordinates used in the simulation.
Two dimensional (2D) numerical simulations of the air flow field in the melt blowing process were performed using computational fluid dynamics (CFD) software (Fluent ANSYS 12). The turbulent nature of the air flow was accounted for by applying the familiar SST k–o turbulence model (Menter, 1994; Wilcox, 1988), with default (Fluent 13) parameter settings. This is a popular two-equation eddyviscosity model that combines k–o model in the near-wall region and reverts to k–e in the free-stream, via a blending function. It is often recommended and used for simulating separating flow and adverse pressure gradients, as found in the Laval nozzles reported in this work. Different 2D meshes were created to mimic the dimension of the actual melt blowing die described in other publications (Ellison et al., 2007; Tan et al., 2010). An illustration of the 2D control area
Fig. 2. Schematics of the 2D plane in which the air density profile is: (a) Simulated with CFD. (b) Measured with Schlieren visualization. The dotted line in the 2D plane is the centerline location at which the comparison is made.
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Fig. 3. Schematics showing the cross sections of: (a)–(b) Laval nozzles 1 and 2 (See Table 1 for dimensions). (c) Top-view pictures showing the ease with which Laval nozzle 1 is attached onto the existing melt blowing die. In image (c), the tube above the air exit slot of the existing melt blowing die is an outlet for Pinlet measurement.
Table 1 Laval nozzle design. Nozzle
1 2
Fig. 4. A schematic of the Schlieren visualization setup.
which Laval nozzle 1 is attached onto the bottom of the melt blowing die where the air exit slot is located. 3.2. Optical visualization
Expansion
Shape
Length (mm)
Angle (1)
Aex/Ath
1.0 4.0 3.0
27 5 –
1.9 2.5 2.5
a
Two expansion zones Bell-shaped expansion
a Final expanded area, Aex, to initial throat area, Ath. These area ratios, 1.9 and 2.5, produce perfectly expanded flows when Pinlet is set to 130 and 215 psig, respectively.
For our industrial melt blowing application, Pinlet is practically limited to 45 psig due to the exponentially increasing cost of air compression (Nyssen et al., 1992). The corresponding area ratio for perfect expansion at Pinlet 50 psig calculated from Eq. (1) would be relatively small ( 1.3). Thus, the flow through the nozzle was substantially over-expanded by intentionally choosing area ratios in the 2 2.5 range, thereby creating high supersonic velocities in the nozzle followed by an abrupt shock positioned near the nozzle exit. In this study, the Pinlet values were set between 15 and 45 psig since the effect of compressible flow does not appear until Pinlet Z15 psig (i.e., exceeding critical pressure ratio for air with discharge to atmospheric pressure) and achieving Pinlet Z45 psig is not industrially feasible due to the exponential increase in the cost of air compression (Nyssen et al., 1992).
3. Experiment 3.1. Melt blowing equipment and Laval nozzle The melt blowing die and related equipment discussed in the previous publications (Ellison et al., 2007; Tan et al., 2010) were used in this work. The air flow field in the melt blowing process was examined as a function of Pinlet at Tinlet ¼25 1C in the absence of meltblown fibers. Based on the CFD simulations two Laval nozzles were fabricated out of 316-stainless steel, designed so they could be attached directly to the existing melt blowing die with minimal modification. Table 1 lists the different dimensions of the two nozzles, i.e., different expansion length, expansion angle, and area expansion ratio (ratio of the final expanded area to the initial throat area). Fig. 3(c) highlights the simplicity with
A Schlieren technique (Settles, 2001) was developed to visualize the air flow field in the melt blowing process. In short, the Schlieren technique uses the principle of light deflection associated with refractive index gradients to visualize density differences in fluids, including those found in compressible supersonic flows. Fig. 4 illustrates the Schlieren visualization equipment used in this work. A 15 cm diameter concave mirror with a 150 cm focal length (Edmund Optics) was used to direct light from a high intensity lamp (Volpi Intralux 6000-1) onto a digital camera (Canon PowerShot SD 1100 IS). The mirror was separated from the light source and camera (detector) by 300 cm, twice the focal length of the mirror. A razor blade, placed in front of the camera lens at the focal point acts as a Schlieren stop (Settles, 2001), partially blocking the incident light. The melt blowing die was positioned in the box labeled ‘‘Schlieren field of view’’ in Fig. 4 and the air jet images were acquired with the room completely darkened with the exception of the Schlieren optical source. Schlieren images were calibrated based on the known dimensions of the die assembly. Fig. 5(a) shows an image recorded under ambient light with no air flow. The diameter of the bottom piece of the melt blowing die (40 mm) was used to calibrate the camera. Fig. 5(b) was recorded with air flowing at a steady rate through the apparatus (and the room completely dark) revealing a periodic, oscillating pattern emanating from the exit of the melt blowing die. Image analysis software (NIH ImageJ) was employed to convert the variations in light intensity recorded by the camera along the centerline (identified by the white line) into relative brightness versus axial position y (see Fig. 1). The resulting normalized brightness is plotted in Fig. 5(c), along with a damped sinusoidal function (solid curve), which provides an accurate representation of the maxima and minima and the wavelength of the underlying compression waves.
4. Results and discussion 4.1. CFD simulation Computational fluid dynamics simulations were employed to model the air flow field at the exit of a conventional melt blowing die (i.e., no Laval nozzle) in the absence of fibers. The influence of Pinlet on the y-component of the air velocity (vy), air density (r), and air temperature (T) was investigated at constant Tinlet ¼25 1C.
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Fig. 5. (a) An image that provides a reference length (white arrow). (b) An image of the compression wave at Tinlet ¼ 25 1C and Pinlet ¼56 psig. Fig. 2(b) shows the 2D plane at which images (a) and (b) were recorded in relation to the 3D location of the die. (c) A normalized brightness profile of the white line in (b) measured with ImageJ and fitted with a damped sinusoidal function.
The air velocity maybe represented in terms of Mach number, which is calculated ‘‘locally’’ by Fluent as a function of local temperature condition based on the equation for the speed of sound, c (c¼ (Cp/Cv R T) ^ (1/2); Cp/Cv ¼1.4 for air). Ideal gas properties were used for compressibility characteristics, which are adequate to simulate the dry air conditions that were typically used in test conditions and practice for MB nozzles. Fig. 6(a) shows a representative simulation result for vy in the form of a 2D contour plot, from which the centerline vy(y) profile (x¼0) was extracted. Fig. 6(b) illustrates how vy(y) reaches a nearly constant level beyond the die exit for 1oyo10 mm and how the centerline air velocity increases with increasing Pinlet. Significantly, vy(y) begins to oscillate when Pinlet Z17 psig, indicating compression waves that can be characterized by an amplitude and wavelength of oscillation. Comparing the vy(y) profiles at Pinlet ¼ 17 and 20 psig in Fig. 6(b) reveals that both the amplitude and wavelength of the compression waves increase with increasing Pinlet. One of the authors has shown elsewhere that these oscillations in centerline air velocity are accompanied by oscillations in density, r(y), and temperature, T(y), all characterized by a common wavelength (Tan, 2011). Also, simulations at Tinlet ¼265 1C, representative of actual melt blowing conditions, demonstrate that the absolute values of vy(y), r(y), and T(y) change but do not alter the amplitude and wavelength of the compression wave (Tan, 2011). Laval nozzles 1 and 2 were simulated in the absence of fibers at fixed Pinlet ¼20 psig and Tinlet ¼265 1C. The resulting centerline vy (y) profiles were compared with the baseline case, i.e., no Laval nozzle. The goal was to determine the ability of the nozzle to produce a higher maximum vy and reduce wave compression in the air flow field after the exit of the melt blowing die. Fig. 7 demonstrates that both Laval nozzles (see Table 1) increase the maximum vy above the baseline value (reaching E2.52.9 Mach) and appear to suppress oscillation to some extent, although these benefits are accompanied by a near discontinuity in flow velocity between 2 and 4 mm from the die exit. The effect of the nozzle geometry on flow stability has been addressed elsewhere (Tan, 2011). For example, two expansion zones (nozzle 1) induce chaotic flow separation from the nozzle wall for Pinlet r40 psig, but this effect is suppressed with a single bell-shaped expansion zone (nozzle 2) (Tan, 2011). 4.2. Schlieren visualization Air flowing from the melt blowing die was visualized in the absence of fibers at various inlet pressures, with and without the
Fig. 6. CFD simulation results of the air flow field without a Laval nozzle, i.e., baseline. (a) An example of a contour plot of the y-component of the air velocity (vy, in unit of Mach) at Pinlet ¼ 20 psig and Tinlet ¼ 25 1C. (b) The effect of Pinlet on vy(y) at the centerline, x¼ 0, when Tinlet ¼ 25 1C.
Laval nozzle, using the Schlieren technique. Fig. 8 shows results obtained without the Laval nozzle at Tinlet ¼25 1C when Pinlet was increased from 25 psig, where compression waves first appear, to 56 psig. Dark and light bands in the Schlieren images, corresponding to regions of higher and lower gas densities, respectively, are in qualitative agreement with the simulated results shown in Fig. 6(a). Clearly, increasing the inlet pressure increases the spacing between the compression waves as anticipated by the numerical calculations (Fig. 6(b)). Similar results were obtained
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formation of compression waves with similar wavelength to that of the unmodified (baseline) die (this is sometimes referred to as nozzle stall; cf. Fig. 12). Fig. 10 (d) shows that at Pinlet E40 psig the normal shock is generated right at the exit of nozzle 2 and the compression wave formation appears to be suppressed completely. Fig. 10 (e)–(g) shows that increasing the pressure further leads to the re-appearance of compression waves but with different characteristics than the compression waves produced without a Laval nozzle because the normal shock is now generated outside of nozzle 2. 4.3. Comparison of simulation and Schlieren visualization Fig. 7. Simulations of the influence of Laval nozzles 1 and 2 on vy(y) at the centerline (x ¼0) in comparison to the case without nozzle, i.e., baseline. The simulations were done for Pinlet ¼ 20 psig and Tinlet ¼ 265 1C.
Fig. 8. Schlieren images of air flow recorded at Tinlet ¼ 25 1C and various Pinlet.
Fig. 9. (a)–(g) Schlieren images of air flow with Laval nozzle 1 at Tinlet ¼25 1C and various Pinlet.
Fig. 10. (a)–(g) Schlieren images of air flow with Laval nozzle 2 at Tinlet ¼ 25 1C and various Pinlet.
while visualizing: (1) the air flow in the absence of fibers at Tinlet ¼265 1C as anticipated by the CFD simulations and (2) the air flow at Tinlet ¼ 25 1C in the presence of fibers; these results are presented elsewhere (Tan, 2011). Attaching a Laval nozzle to the melt blowing die produces dramatic changes in the Schlieren images as shown in Figs. 9 and 10 (recorded with Tinlet ¼25 1C). Fig. 9 shows that nozzle 1 (Table 1) appears to damp the formation of compression waves up to inlet pressure of 40 psig due to flow separation (see above). Compression waves first appear at 45 psig and grow in magnitude and wavelength as Pinlet is raised. Careful inspection of these pictures reveals certain qualitative differences in the form of the flow field relative to the baseline case (Fig. 8). Visual images obtained while operating nozzle 2, which contains a more idealized expansion zone (see Fig. 3), are presented in Fig. 10. Based on the area ratio (Aex/Ath) of nozzle 2, Eq. (1) establishes that the air flow is always over expanded at all the Pinlet values investigated in this study (Sutton, 1967; Anderson, 2003). Fig. 10(a)–(c) shows that between 25 and 35 psig, the normal shock is generated inside nozzle 2 and it is displaying the
As illustrated in Fig. 2, the CFD simulations and Schlieren experiments access orthogonal planes in the 3D air flow field beyond the melt blowing die. Nevertheless, these projections share a common centerline, coincident with the y direction in Fig. 6, which is used in comparing the theory and visualization experiments. A single damped sinusoidal function characterized by wavelength lcw can be extracted from the Schlieren experiments (Fig. 5) and from the simulated centerline air flow profiles (Fig. 6) both at Tinlet ¼25 1C and various Pinlet. The numerical and experimental results for lcw are remarkably similar as shown in Fig. 11. Although the simulated lcw values are all slightly larger than the experimental data, within the uncertainties in the calculations and measurements, the experimental trend in lcw versus Pinlet is exactly accounted for by the CFD calculations. Fig. 12 provides a direct comparison of Schlieren images and simulated flow fields obtained with nozzle 2 for various values of Pinlet. Here we note that a point of reference is provided by the dashed white line in the first panel, which identifies the edge of the die. When Pinlet o40 psig, the normal shock is generated inside nozzle 2 and the experiment and simulation both show compression waves with characteristics similar to those seen without a Laval nozzle, i.e., the compression waves grow with increasing Pinlet and the simulation overestimates the experiment. At Pinlet E40 psig, the normal shock is generated right at the nozzle exit and suppression of the compression waves is evident in both the simulation and experiment. When Pinlet 440 psig, the normal shock is generated outside nozzle 2 and the experiment and simulation both show re-appearance of compression waves with characteristics that differ from the compression waves
Fig. 11. The wavelength of compression wave (lcw) as a function of Pinlet from simulation in comparison to that measured from Schlieren visualization. In all cases, Tinlet ¼ 25 1C and no Laval nozzle is used.
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seen without the Laval nozzle. Quantitative comparison of lcw at these elevated pressures is complicated by the fact that the maximum simulated air flow profiles no longer occur along the
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centerline, obviating direct comparison with the centerline brightness data.
5. Conclusion Computational fluid dynamics simulations were used to model the air flow field in the melt blowing process in the absence of meltblown fibers. The baseline case (without a nozzle) was investigated based on the y-component of the air velocity profile, vy(y), at the centerline as a function of inlet air pressure (Pinlet), ranging from subsonic to supersonic flows. The maximum value of vy(y) increases with increasing Pinlet, then begins to oscillate accompanied by the formation of compression waves in the supersonic region, Pinlet Z15 psig. Simulation demonstrates that a Laval nozzle influences the air flow field by increasing the maximum value of vy(y) and eliminating the compression waves at a specific predictable value of Pinlet. Performance of an actual melt blowing die was characterized using Schlieren visualization experiments, which revealed density oscillation in the air flow field as a function of Pinlet. The results of the simulations and experiments are in excellent agreement.
Acknowledgments This work is funded by Cummins Filtration. Parts of this work were also carried out using computing resources at the University of Minnesota Supercomputing Institute.
Appendix A. Supplementary information
Fig. 12. Wavelength of compression wave (lcw) predicted by simulation and measured with Schlieren visualization as a function of Pinlet at Tinlet ¼25 1C when Laval nozzle 2 is used. Black and white arrows in CFD result (top left) indicate the area that is invisible and visible, respectively in Schlieren visualization.
We compared the results from different turbulence models (k–e, realizable k–e, RSM, etc.) and found a non-negligible variation in the nature/onset of lower pressure ‘‘stall’’ where the flow detaches from the nozzle wall. Upon consultation with experts at Fluent, it was suggested that the SST k–o model was widely used in this specific field/application (rocket nozzle type flows), and is
Fig. A1. Observation of non-negligible variation in the CFD simulation results when two different turbulent models, k–e versus SST k–o, were used.
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Fig. A2. Simulation results obtained with two different ambient air temperatures, 25 and 1001 C, highlighting the negligible effect of ambient air temperature on the centerline velocity.
more conservative in predicting stall onset (which we observed/ confirmed in several nozzle configurations, once we switched to SST k–o from realizable k–e or RSM). The stall condition appeared to be qualitatively confirmed in physical testing/imaging. The comparison in Fig. A1 shows an example (same conditions) for realizable k–e versus SST k–o (all results in this paper were from the SST k–o model). The effect of ambient air temperature in our study can be safely ignored because it does not substantively affect the parameters of interest in the near-die fiber attenuation zone (velocity and temperature). To illustrate this, we simulated two cases where the local ambient air temperature was set to 251 and 1001 C and it is clear in Fig. A2 that there is no effect of ambient air temperature on the parameters of interest (centerline air velocity is shown here). References Anderson, J.D., 2003. Modern Compressible Flow, with Historical Perspective, third ed. McGraw-Hill, New York, NY. Benson, T., June 4th 2011. Interactive nozzle. o http://www.grc.nasa.gov/WWW/ K-12/airplane/ienzl.html 4. Borkar, S., Gu, B., Dirmyer, M., Delicado, R., Sen, A., Jackson, B.R., Badding, J.V., 2006. Polytetrafluoroethylene nano/microfibers by jet blowing. Polym. 47, 8337–8343. Breese, R.R., Qureshi, U.A., 2002. Fiber motion near the collector during melt blowing part 2: fly formation. Int. Nonwoven J. 11, 21–27. Buntin, R.R., Keller, J.P., Harding, J.W., February 22nd 1972. Non-woven mats by melt blowing. U.S. Patent 3,849,241. de Laval, G.P., June 26th 1894. Steam turbine. U.S. Patent 522,066.
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