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Optics Express

  • Editor: Michael Duncan
  • Vol. 11, Iss. 15 — Jul. 28, 2003
  • pp: 1770–1779
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Effect of unsteady natural convection on the diameter of drawn polymer optical fiber

Hayden M. Reeve and Ann M. Mescher  »View Author Affiliations


Optics Express, Vol. 11, Issue 15, pp. 1770-1779 (2003)
http://dx.doi.org/10.1364/OE.11.001770


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Abstract

This paper presents experimental results showing the effect various natural convection heating regimes have on the diameter of drawn polymer optical fiber. The airflow, adjacent to the polymer, can be either laminar, oscillatory, or chaotic, depending on the imposed thermal boundary conditions at the furnace and iris walls. When subject to oscillatory and chaotic natural convection, the drawn fiber varies in diameter 2.5 to 10 times more than that measured under laminar heating conditions. Particle image velocimetry shows that unsteady natural convection occurs with the interplay between two asymmetric counter-rotating convective cells. This represents a significant instability mechanism, one that has not been previously identified.

© 2003 Optical Society of America

1. Introduction

This paper presents experimental results showing the effect various natural convection heating regimes have on the diameter of drawn polymer optical fiber (POF). Although the contribution of natural convection in glass optical fiber drawing has generally been neglected, natural convection accounts for approximately 30% of the heating during POF drawing in the absence of forced convection [1

1. H.M. Reeve, A.M. Mescher, and A.F. Emery, “Investigation of polymer optical fiber drawing force and heat transfer.” in Proceedings of 2003 ASME Summer Heat Transfer Conference, HT2003-47445 (to be published).

]. Furthermore, unsteady natural convection during POF drawing can cause large (±15µm) variations in the fiber diameter. The evidence presented in this paper suggests that unsteady natural convection during POF drawing, which has not been investigated to date, may indeed be a primary cause of the fiber diameter variations currently plaguing POF development.

POF is manufactured by heating a preform, with a prescribed radial refractive index profile, in a cylindrical furnace as shown in Fig. 1. The furnace wall typically has a parabolic axial temperature profile in order to control the location of the neck-down region, which occurs in close proximity to the maximum furnace wall temperature. The preform is fed at a specified velocity (Vp) into the heated furnace, whereupon the polymer’s viscosity drops by several orders of magnitude. The preform then necks-down under tension to the final fiber diameter (df) before leaving the furnace at a specified draw speed (Vf). Downstream of the furnace a laser diameter gauge measures the diameter of the fiber.

Fig. 1. The polymer optical fiber draw furnace. Thermocouple locations are marked with ‘x’.

In order to reduce fiber diameter variations, the manufacturing process can be actively controlled by varying the draw speed in response to real-time diameter measurements recorded downstream of the furnace. Smithgall [3

3. D.H. Smithgall, “Application of optimization theory to the control of the optical fiber drawing process,” AT&T Tech. J. 58, 1425–1435 (1979).

] found that active control of a glass fiber drawing process removed slowly varying bias and reduced the standard deviation of the fiber diameter from 0.8 µm to 0.3 µm.

Nevertheless, Smithgall also showed that active control is limited by a measurement time delay between when diameter variations originate in the neck-down region and when they are measured down-stream; therefore, active control does not eliminate the need for a robust and stable drawing environment. This has motivated analysis of the steady-state glass drawing environment (see for example Ref. [4

4. U.C. Paek and R.B. Runk, “Physical behavior of the neck-down region during furnace drawing of silica fibers,” J. Appl. Phys. 49, 4417–4422 (1978). [CrossRef]

,5

5. S. Roy Choudhury, Y. Jaluria, and S.H.-K. Lee, “A computational method for generating the free surface neck-down profile for glass flow in optical fiber drawing,” Numer. Heat Tr. A-Appl. 35, 1–24 (1999). [CrossRef]

]). Investigators have also studied the hydrodynamic stability of glass and polymer extensional flows and draw resonance, a phenomenon in which sustained cyclic variations occur in the fiber diameter under certain drawing conditions [6

6. F.T. Geyling, “Basic fluid-dynamic considerations in the drawing of optical fibers,” AT&T Tech. J. 55, 1011–1056 (1976).

9

9. J. Cao, “Studies on the mechanism of draw resonance in melt spinning,” J. App. Polym. Sci. 42, 143–151 (1991). [CrossRef]

].

Less work has been carried out modeling and observing the sensitivity of the fiber drawing environment to thermal perturbations. Kase and Matsuo [10

10. S. Kase and T. Matsuo, “studies on melt spinning. II: Steady-state and transient solutions of fundamental equations compared with experimental results,” J. App. Polym. Sci. 11, 251–287 (1967). [CrossRef]

] and Young and Denn [11

11. D.G. Young and M.M. Denn, “Disturbance propagation in melt spinning,” Chem. Eng. Sci. 44, 1807–1818 (1989). [CrossRef]

] investigated the sensitivity of a spin-line to changes in the quench airflow rate. Vasil’ev et al. [12

12. V.N. Vasil’ev, G.N. Dul’nev, and V.D. Naumchik, “Investigation of nonstationary conditions of optical fiber formation. III. Drawing process reaction under thermal actions and perturbations of the blank radius,” J. Eng. Phys. 58, 370–375 (1990). [CrossRef]

] numerically investigated the effect that fluctuations in the furnace wall temperature had on the final fiber radius. More recently, Forest and Zhou [13

13. M.G. Forest and H. Zhou, “Unsteady analyses of thermal glass fiber drawing processes,” Eur. J. Appl. Math. 12, 479–496 (2001). [CrossRef]

] used a non-isothermal quasi-one-dimensional model to investigate the sensitivity of a stable fiber drawing environment to unsteady disturbances in the boundary conditions. Their simulation results indicate that the fiber diameter shows “relative insensitivity to mechanical effects (such as take up rates, feed-in rates), but a strong sensitivity to thermal fluctuations.” Papamichael et al. [14

14. H. Papamichael, C. Pellon, and I.N. Miaoulis, “Air flow patterns in the optical fibre drawing furnace,” Glass Technol. 38, 22–29 (1997).

] investigated the effect of natural convection on glass fiber drawing and appreciated that “convection induced perturbations in the furnace can affect diameter uniformity.” Yet despite their citation of Choi and Korpela’s natural convection stability investigation [15

15. I.G. Choi and S.A. Korpela, “Stability of the conduction regime of natural convection in a tall vertical annulus,” J. Fluid Mech. 99, 725–738 (1980). [CrossRef]

], they reported no time-varying flow behavior, nor commented on the significance of possible natural convection instabilities. All of these studies [10

10. S. Kase and T. Matsuo, “studies on melt spinning. II: Steady-state and transient solutions of fundamental equations compared with experimental results,” J. App. Polym. Sci. 11, 251–287 (1967). [CrossRef]

14

14. H. Papamichael, C. Pellon, and I.N. Miaoulis, “Air flow patterns in the optical fibre drawing furnace,” Glass Technol. 38, 22–29 (1997).

] addressed the sensitivity of the fiber drawing process to thermal perturbations, but not the underlying stability of the heat transfer in the fiber manufacturing process.

Prior investigators have shown that unsteady natural convection can occur in tall, air filled, differentially heated annuli [15

15. I.G. Choi and S.A. Korpela, “Stability of the conduction regime of natural convection in a tall vertical annulus,” J. Fluid Mech. 99, 725–738 (1980). [CrossRef]

18

18. G.B. McFadden, S.R. Croiell, R.F. Boisvert, and M.E. Glicksman, “Asymmetric instabilities in buoyancy-driven flow in a tall vertical annulus,” Phys. Fluids 27, 1359–1361 (1984). [CrossRef]

]. Work on tall annular geometries (with a hot isothermal inner cylinder and cold outer cylinder) has identified four characteristic features of this unsteady natural convection. First, as the buoyant potential (i.e., Rayleigh number) of the flow within the cavity is increased, the flow transitions through a Hopf bifurcation from steady-state to a time-varying periodic state. The steady unicellular flow pattern gives way to a multi-cellular flow pattern in which the natural convection cells migrate upward in the annulus, causing periodic heating [15

15. I.G. Choi and S.A. Korpela, “Stability of the conduction regime of natural convection in a tall vertical annulus,” J. Fluid Mech. 99, 725–738 (1980). [CrossRef]

,16

16. P. Le Quéré and J. Pécheux, 1989, “Numerical simulations of multiple flow transitions in axisymmetric annulus convection,” J. Fluid Mech. 206, 517–544 (1989). [CrossRef]

]. The second characteristic is that the period of these oscillations is a function of the Rayleigh number [16

16. P. Le Quéré and J. Pécheux, 1989, “Numerical simulations of multiple flow transitions in axisymmetric annulus convection,” J. Fluid Mech. 206, 517–544 (1989). [CrossRef]

]. As the Rayleigh number increases the period of the oscillations increases. Third, phenomena such as period doubling, quasi-periodic flow, and chaotic flow were observed at higher Rayleigh numbers for select geometries [17

17. J. Pécheux, P. Le Quéré, and F. Abcha, “Curvature effects on axisymmetric instability of conduction regime in a tall air-filled annulus,” Phys. Fluids 6, 3247–3255 (1994). [CrossRef]

]. The fourth and final characteristic worth noting is that for small radius ratios η (the ratio of inner to outer radii), the primary instability mode is asymmetric. McFadden et al. [18

18. G.B. McFadden, S.R. Croiell, R.F. Boisvert, and M.E. Glicksman, “Asymmetric instabilities in buoyancy-driven flow in a tall vertical annulus,” Phys. Fluids 27, 1359–1361 (1984). [CrossRef]

] predicted, through the use of linear stability theory, that the primary instability mode for air is three-dimensional (helical) in nature for η<0.44.

2. Experimental system and procedure

2.1 Fiber drawing furnace

The experimental system is shown in Fig. 1. The furnace has a height (H) of 0.39 m (15.5″), an inner diameter (dw) of 0.064 m (2.5″), and was capped at both ends by irises that allowed polymer to enter and exit but effectively prohibited bulk air flow into or out of the furnace. A 25.4 mm (1″) diameter extruded Poly(methyl methacrylate) perform was fed through the top iris with a velocity of 25 µm/s. Fiber with an average diameter of 400 µm exited the furnace though a 1.6 mm hole in the bottom iris. The fiber diameter was not actively controlled and the draw speed (Vf) was held constant at 0.10 m/s. The measured profile of the quenched neck-down region is shown in Fig. 2(a) in terms of the radius ratio, η(z)=Rp/Rw.

Fourteen K-type thermocouples located in the furnace wall and top and bottom irises were used to maintain near constant thermal conditions from one experiment to the next. The peak furnace wall temperature was maintained at 170°C using a proportional controller (with a 15 second cycle time). The axial temperature profile of the furnace wall is shown in Fig. 2(b). The top iris was independently heated allowing a range of top iris temperatures to be achieved (Tt=90 to 130°C). Prior work with this apparatus [19

19. H.M. Reeve, A.M. Mescher, and A.F. Emery, “Experimental and numerical investigation of polymer preform heating,” J. Mater. Process. Manu. 9, 285–301 (2001). [CrossRef]

] indicates that the furnace wall temperature profile is axi-symmetric (to within 0.3°C).

Fig. 2. Axial variation of: (a) the polymer neck-down profile, η(z)=Rp/Rw, (including the radial and axial location of the thermocouples in air) and (b) the wall temperature profile, Tw(z).

The fiber diameter was measured 0.10 m downstream of the bottom iris by a Beta LI800SF laser diameter gauge. When reading a stationary constant diameter sample, the gauge demonstrated a root mean square (RMS) excursion of approximately 0.5 microns with a constant bias of ±5 microns. The air temperature was recorded at four locations (z=150±0.5 mm, r=20.6±0.5 mm, θ=0°; 90°; 180°; 270°) by 0.1 mm diameter bare K-type thermocouples strung vertically though the furnace. The axial and radial location of the thermocouples in the air region is shown in relation to the neck-down profile in Fig. 2(a). The axial location corresponds to the lower neck-down region, which is the region most vulnerable to heating variations.

The experimental procedure was as follows. Steady-state drawing conditions were achieved with a top iris temperature in excess of 120°C. The top iris temperature was then decreased in 2°C increments, although 1°C increments were used around transition regions, which were found though trial and error. At each iris temperature the system was allowed to equilibrate for 10 minutes before readings were taken. The air temperature responded fairly quickly to changes in the thermal boundary conditions, typically reaching its asymptotic state within 5 minutes. The iris temperature was lowered in the above stepwise manner until chaotic flow was observed.

Fig. 3. The model furnace. The inset of frame ‘A’ shows a sample raw PIV image in which the ‘necking’ polymer preform and olive oil particles can be seen.

2.2 Particle image velocimetry model

A full-scale transparent model of the POF drawing furnace, shown in Fig. 3, was constructed in order to allow particle image velocimetry (PIV) visualization of the unsteady natural convection flow phenomenon. In order to recreate the inner surface geometry of the necking polymer, a quenched preform was held stationary in the model furnace. Fiber drawing experiments show that the motion of the polymer does not affect the nature of the unsteady natural convection and numerical work has confirmed that buoyant forces dominate shear effects from the moving polymer [1

1. H.M. Reeve, A.M. Mescher, and A.F. Emery, “Investigation of polymer optical fiber drawing force and heat transfer.” in Proceedings of 2003 ASME Summer Heat Transfer Conference, HT2003-47445 (to be published).

]. A wall temperature profile characteristic of that measured in the experimental furnace was recreated by two heating bands attached to the external glass tube. The maximum model wall temperature was lower than that used in the actual fiber drawing experiment and was held well below the glass transition temperature of PMMA (~90°C) in order to prevent any subsequent deformation of the quenched preform. Thermocouple measurements within the air region of the model furnace confirmed that as the heating to the model wall was increased, all three characteristic flow regimes (laminar, oscillatory, and chaotic) were successfully recreated.

The air within the model furnace was seeded with olive oil atomized by a Laskin nozzle [20

20. A. Melling, “Tracer particles and seeding for particle image velocimetry,” Meas. Sci. Tech. 8, 1406–1416 (1997). [CrossRef]

]. These tracer particles were introduced into the model furnace through entry ports in the top and bottom irises in order to achieve near homogeneous seeding of the air region. Laser Induced Fluorescence (LIF) of the oil droplets was achieved with a vertical Ar-ion laser light-sheet that passed through the transparent bottom iris and along the axis of the furnace. A digital camera then recorded the progression of the flow tracers in the upper region of the furnace (frame ‘A’ in Fig. 3). Sequential image pairs taken by the camera were then interrogated and the resulting velocity field of the fluid flow was calculated.

3. Results and discussion

3.1 Effect of unsteady heating on the fiber diameter

Air temperature measurements indicate that as the temperature of the top iris is decreased (thus increasing the buoyant potential within the furnace), the natural convection flow transitions from laminar to oscillatory, and then finally, to chaotic flow. Figure 4(a) shows the air temperature history recorded within the fiber draw furnace when the top iris was held at approximately 115.5°C. The air temperature was essentially constant with a standard deviation of 0.03°C. When the top iris temperature was lowered by only 1°C to 114.5°C, the recorded air temperatures started to oscillate at a frequency of 0.23 Hz as shown in Fig. 4(c). These oscillations persisted for a range of decreasing top iris temperatures until the flow became chaotic at Tt=104.8°C. As can be seen in Fig. 4(e) the excursion of the chaotic air temperature from the sample mean is considerable (±3°C). As the top iris was further cooled, no reverse transition back to steady-state or oscillatory conditions was observed.

Fig. 4. Excursion of the air temperature and fiber diameter histories from the sample mean, illustrating: (a,b) laminar, (c,d) oscillatory, and (e,f) chaotic natural convection conditions. Note different scales on the y-axes.

The air temperature variations characteristic of the oscillatory and chaotic heating regimes have a direct and detrimental impact on the drawn fiber diameter. Figures 4(b), (d), and (f) show the corresponding fiber diameter histories recorded for the laminar, oscillatory, and chaotic regimes respectively. The standard deviation of the fiber diameter history recorded under laminar conditions (σ=0.6 µm) was only slightly more than the measurement precision of the laser diameter gauge (σ=0.5 µm). The fiber drawn under oscillatory heating conditions displays clear cyclic diameter variations (Fig. 4(d)). The diameter variation caused by chaotic air temperatures is even more dramatic with excursions of ±15 µm (Fig. 4(f)). The diameter’s standard deviation for the oscillatory and chaotic drawing regimes was typically 2.5 and 10 times greater, respectively, than that observed in the laminar case, mirroring the rise in the local air temperature variation.

The frequency of the oscillations was found to be a function of the top iris temperature, a trend similar to that reported by Le Quéré and Pécheux [16

16. P. Le Quéré and J. Pécheux, 1989, “Numerical simulations of multiple flow transitions in axisymmetric annulus convection,” J. Fluid Mech. 206, 517–544 (1989). [CrossRef]

] for unsteady natural convection in a tall annulus. Unlike their work, however, the results from this study indicate that the period of the oscillations decreases as the driving buoyant potential increases. Oscillations initiated (with a frequency of 0.23 Hz) when the top iris temperature was lowered to 114.5°C. As the top iris temperature was further decreased (analogous to increasing the Rayleigh number), the frequency of the oscillations increased, reaching 0.33 Hz at Tt=106.9°C, before further cooling caused the onset of chaotic flow.

The air temperature oscillations recorded at the four azimuth positions were not identically in-phase. The thermocouple signals at locations θ=90°, 180°, and 270° lagged the reading at location θ=0° by phase angles of approximately 48°, 160°, and 323°, respectively. This indicates the oscillatory flow is asymmetric. The possibility of a three-dimensional flow structure is consistent with the work of McFadden et al. [18

18. G.B. McFadden, S.R. Croiell, R.F. Boisvert, and M.E. Glicksman, “Asymmetric instabilities in buoyancy-driven flow in a tall vertical annulus,” Phys. Fluids 27, 1359–1361 (1984). [CrossRef]

] as the radius ratio within the furnace is always less than 0.44 (see Fig. 2(a)).

Fig. 5. Frequency spectrums of: (a) the air temperature and (b) the fiber diameter observations for the oscillatory (Tt=114.5°C) and chaotic (Tt=104.8°C) flow regimes.

Figure 5 shows the frequency spectrums of both the air temperature and fiber diameter histories for the oscillatory and chaotic regimes. Both the temperature and diameter signals recorded in the oscillatory regime exhibit a characteristic frequency of 0.23 Hz (for Tt=114.5°C) with negligible low frequency noise. For the chaotic regime the air temperature’s frequency spectrum exhibits a wide band of low frequency components. The chaotic air temperature signal did, however, have distinct contributions at 0.1025 and 0.334 Hz. These frequencies correspond to psuedo-periodic structures that were observed intermittently within the air temperature signal, as can be seen in Fig. 4(e).

The frequency response of the fiber diameter to thermal perturbations is determined in part by the mass of the necking polymer. This limits the fiber diameter’s response to high frequency perturbations. For example, unlike the oscillatory air temperature spectrum, the fiber diameter does not exhibit a first harmonic contribution at 0.46 Hz. Also, in the chaotic regime there is almost no contribution to the fiber diameter variations from frequencies above 0.3 Hz. None of the air temperature or diameter histories showed appreciable frequency components above 0.6 Hz.

The onset of period doubling more dramatically demonstrates the frequency response of the fiber diameter to variations in the convective heat transfer. Subharmonics were often (but not always) observed within the oscillatory regime as the flow neared the transition to chaos, a trend again consistent with the work of Le Quéré and Pécheux [16

16. P. Le Quéré and J. Pécheux, 1989, “Numerical simulations of multiple flow transitions in axisymmetric annulus convection,” J. Fluid Mech. 206, 517–544 (1989). [CrossRef]

]. Figure 6(a) shows an oscillatory air temperature history observed when the top iris was held constant at 108°C. The recorded air temperatures exhibited a frequency of 0.368 Hz with a standard deviation of 0.35°C. When the top iris temperature was decreased to 106°C, the fundamental frequency increased to 0.38 Hz (due to the increased buoyant potential), and a clearly visible subharmonic formed with a frequency of 0.19 Hz as shown in Fig. 6(c). The standard deviation of the air temperature shown in Fig. 6(c) is 0.67°C. As can be seen in Fig. 6(b), when Tt=108°C, the fiber diameter shows little response to the high frequency perturbation (ω=0.368 Hz), exhibiting a standard deviation of 0.73 µm (only slightly more than that observed under laminar drawing conditions). However, the period doubling seen in Fig. 6(c) results in a significant increase in the magnitude of the observed diameter variations (σ=3.1 µm) as illustrated in Fig. 6(d).

Fig. 6. Air temperature and fiber diameter histories recorded at: (a, b) Tt=108°C and (c, d) Tt=106°C, illustrating the occurrence of period doubling and its effect on the fiber diameter.

3.2 PIV visualization of the natural convection flow

Fig. 7. PIV vector plot of time-invariant, axi-symmetric, laminar flow in the furnace model.
Fig. 8. Time history of the axial velocity measured at x=-0.018 m and z=0.096 m showing unsteady natural convection. A movie of one complete oscillation is shown in Fig. 9.
Fig. 9. (1.21 MB) Movie showing the asymmetric oscillating flow field within the model furnace (4.50 MB version). (Location x=-0.018 m, z=0.096 m is marked with a white cross.)

Figure 7 shows the time-invariant laminar flow from PIV observed in frame ‘A’ of the model furnace. The vector plots are color-coded using the local value of the axial velocity. The bi-cellular pattern is observed within the model furnace, consistent with numerical predictions of the fiber-drawing environment [1

1. H.M. Reeve, A.M. Mescher, and A.F. Emery, “Investigation of polymer optical fiber drawing force and heat transfer.” in Proceedings of 2003 ASME Summer Heat Transfer Conference, HT2003-47445 (to be published).

]. Figure 7 also shows that the flow is axisymmetric and the interface between the upper and lower cells lies at approximately z=0.09 m.

When the heating to the model furnace was increased, the air temperature oscillated at 0.265 Hz, a frequency consistent with the oscillations observed during fiber drawing. The PIV results confirm that these recorded temperature oscillations stem from oscillations in the natural convection flow. The time history of the axial velocity observed at location x=-0.018 m, z=0.096 m is shown in Fig. 8. The flow at that location has a strong vertical component at t=2.48 s which then decreases in magnitude to a minimum at t=5.16 s, when the flow is almost entirely radial. A movie of the oscillating flow field is shown in Fig. 9. The unsteady flow has several key features. First, the natural convection circulation is still bi-cellular. Second, the flow is asymmetric, with both the location of the cell interface and the intensity of the flow being substantially different on either side of the polymer. This three-dimensional flow is consistent with asymmetric temperature measurements taken in the air region of the furnace during fiber production. Third, the intensity of the flow and location of the cell interface oscillates considerably. This oscillation in the interface between the upper and lower natural convection cells is a phenomenon that we have not seen discussed in the literature. We have carried out initial numerical simulations which confirm that the interface between two counter-rotating cells can become unstable in tall annular geometries [21

21. H.M. Reeve, A.M. Mescher, and A.F. Emery, “Unsteady natural convection of air in a tall axi-symmetric non-isothermal annulus,” Numer. Heat Tr. A-Appl. (submitted for publication).

].

5. Conclusion

Although fiber drawing has been subject to considerable investigation, it appears no prior work has focused on the effect that convective instabilities have on the resulting fiber quality. This study illustrates that time-varying natural convection flows can develop within a fiber drawing furnace. Furthermore, the resulting convective heating variations have a finite and detrimental impact on the diameter of drawn POF. Observations show that oscillatory and chaotic natural convection heating regimes can promote fiber diameter variations 2.5 to 10 times greater than those observed under laminar conditions.

Experimental observations show that the frequency of this oscillatory flow is a function of the buoyant potential within the furnace. Visualization of the flow indicates that the unsteady behavior is due to the oscillatory motion between two counter-rotating convective cells within the furnace. This instability mode has not been previously reported.

Unsteady natural convection may in fact be a leading cause of fiber diameter variations currently seen in the manufacture of POF. Our results indicate that care needs to be taken in choosing the thermal boundary conditions of the fiber draw furnace to ensure that the buoyant potential of the air remains low enough for steady natural convection to occur. Given the desire for sub-micron diameter tolerances, further investigation of the effect that convective instabilities have on POF drawing is warranted. This is especially important for POF manufacture where active diameter control may be less effective in controlling the impact of relatively high frequency gas-phase oscillations.

Acknowledgements

We would like to thank Professor Dana Dabiri and Jeremy Wimer for their assistance with the PIV apparatus. We are also pleased to acknowledge support for this work from the National Science Foundation, Grant # ECS 9734438.

References and links

1.

H.M. Reeve, A.M. Mescher, and A.F. Emery, “Investigation of polymer optical fiber drawing force and heat transfer.” in Proceedings of 2003 ASME Summer Heat Transfer Conference, HT2003-47445 (to be published).

2.

H.F. Wolf, Handbook of fiber optics, (Garland STPM Press, 1979) Chap. 2.

3.

D.H. Smithgall, “Application of optimization theory to the control of the optical fiber drawing process,” AT&T Tech. J. 58, 1425–1435 (1979).

4.

U.C. Paek and R.B. Runk, “Physical behavior of the neck-down region during furnace drawing of silica fibers,” J. Appl. Phys. 49, 4417–4422 (1978). [CrossRef]

5.

S. Roy Choudhury, Y. Jaluria, and S.H.-K. Lee, “A computational method for generating the free surface neck-down profile for glass flow in optical fiber drawing,” Numer. Heat Tr. A-Appl. 35, 1–24 (1999). [CrossRef]

6.

F.T. Geyling, “Basic fluid-dynamic considerations in the drawing of optical fibers,” AT&T Tech. J. 55, 1011–1056 (1976).

7.

F.T. Geyling and G.M. Homsey, “Extensional instabilities of the glass fiber drawing process,” Glass Technol. 21, 95–102 (1980).

8.

V.N. Vasiljev and V.D. Naumchic, “Analysis of the hydrodynamic stability of the glass fibre drawing process,” Glass Technol. 31, 240–244 (1990).

9.

J. Cao, “Studies on the mechanism of draw resonance in melt spinning,” J. App. Polym. Sci. 42, 143–151 (1991). [CrossRef]

10.

S. Kase and T. Matsuo, “studies on melt spinning. II: Steady-state and transient solutions of fundamental equations compared with experimental results,” J. App. Polym. Sci. 11, 251–287 (1967). [CrossRef]

11.

D.G. Young and M.M. Denn, “Disturbance propagation in melt spinning,” Chem. Eng. Sci. 44, 1807–1818 (1989). [CrossRef]

12.

V.N. Vasil’ev, G.N. Dul’nev, and V.D. Naumchik, “Investigation of nonstationary conditions of optical fiber formation. III. Drawing process reaction under thermal actions and perturbations of the blank radius,” J. Eng. Phys. 58, 370–375 (1990). [CrossRef]

13.

M.G. Forest and H. Zhou, “Unsteady analyses of thermal glass fiber drawing processes,” Eur. J. Appl. Math. 12, 479–496 (2001). [CrossRef]

14.

H. Papamichael, C. Pellon, and I.N. Miaoulis, “Air flow patterns in the optical fibre drawing furnace,” Glass Technol. 38, 22–29 (1997).

15.

I.G. Choi and S.A. Korpela, “Stability of the conduction regime of natural convection in a tall vertical annulus,” J. Fluid Mech. 99, 725–738 (1980). [CrossRef]

16.

P. Le Quéré and J. Pécheux, 1989, “Numerical simulations of multiple flow transitions in axisymmetric annulus convection,” J. Fluid Mech. 206, 517–544 (1989). [CrossRef]

17.

J. Pécheux, P. Le Quéré, and F. Abcha, “Curvature effects on axisymmetric instability of conduction regime in a tall air-filled annulus,” Phys. Fluids 6, 3247–3255 (1994). [CrossRef]

18.

G.B. McFadden, S.R. Croiell, R.F. Boisvert, and M.E. Glicksman, “Asymmetric instabilities in buoyancy-driven flow in a tall vertical annulus,” Phys. Fluids 27, 1359–1361 (1984). [CrossRef]

19.

H.M. Reeve, A.M. Mescher, and A.F. Emery, “Experimental and numerical investigation of polymer preform heating,” J. Mater. Process. Manu. 9, 285–301 (2001). [CrossRef]

20.

A. Melling, “Tracer particles and seeding for particle image velocimetry,” Meas. Sci. Tech. 8, 1406–1416 (1997). [CrossRef]

21.

H.M. Reeve, A.M. Mescher, and A.F. Emery, “Unsteady natural convection of air in a tall axi-symmetric non-isothermal annulus,” Numer. Heat Tr. A-Appl. (submitted for publication).

OCIS Codes
(060.2280) Fiber optics and optical communications : Fiber design and fabrication
(060.2400) Fiber optics and optical communications : Fiber properties

ToC Category:
Research Papers

History
Original Manuscript: June 27, 2003
Revised Manuscript: July 18, 2003
Published: July 28, 2003

Citation
Hayden Reeve and Ann Mescher, "Effect of unsteady natural convection on the diameter of drawn polymer optical fiber," Opt. Express 11, 1770-1779 (2003)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-11-15-1770


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References

  1. H.M. Reeve, A.M. Mescher, and A.F. Emery, "Investigation of polymer optical fiber drawing force and heat transfer." in Proceedings of 2003 ASME Summer Heat Transfer Conference, HT2003-47445 (to be published).
  2. H.F. Wolf, Handbook of fiber optics, (Garland STPM Press, 1979) Chap. 2.
  3. D.H. Smithgall, �??Application of optimization theory to the control of the optical fiber drawing process,�?? AT&T Tech. J. 58, 1425-1435 (1979).
  4. U.C. Paek and R.B. Runk, �??Physical behavior of the neck-down region during furnace drawing of silica fibers,�?? J. Appl. Phys. 49, 4417-4422 (1978). [CrossRef]
  5. S. Roy Choudhury, Y. Jaluria, and S.H.-K. Lee, �?? A computational method for generating the free surface neckdown profile for glass flow in optical fiber drawing,�?? Numer. Heat Tr. A-Appl. 35, 1-24 (1999). [CrossRef]
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