Polymer Optical Fiber Manufacturing - Preform Heating
- Overview
- Preform Heating
- Fiber Drawing
- Heating Instabilities
Experimental and numerical investigation of the
initial preform heating
was conducted in order to understand the heat transfer phenomena involved
in fiber production. A better understanding of the system will help
minimize preform waste and minimize the time required to reach
steady-state drawing.
The experimental setup is shown above. A cold one-inch diameter preform was inserted into the furnace and allowed to heat until it reached thermal equilibrium. Thermocouples at locations 1-4 monitored the temperature within the preform as a function of time. Irises at the top and bottom of the furnace prevented the flow of air into or out of the furnace. Thermocouples were located in the irises and flush with the inner surface of the furnace wall.
Numerical Model
The heat transfer from the furnace wall to the air and
preform was calculated using the numerical domain shown in red in the figure above.
In order to accurately capture the natural convection heat transfer the conjugate
problem was solved. Therefore, the full axi-symmetric continuity,
momentum, and energy equations were solved for the entire numerical
domain. The initial preform temperature was uniform at 20 C and the
furnace was preheated. The experimentally measured
temperature profile of the furnace wall was used as the thermal boundary
condition in the numerical model. The no-slip condition was applied to
all bounding surfaces.
The governing equations were solved using the SIMPLER finite volume
algorithm. The air was considered incompressible and buoyancy forces were
modeled using the Boussinesq approximation. The exchange of radiative
heat transfer was solved using the net enclosure method. All surfaces
were modeled as gray and diffuse. The air did not participate in the
radiative exchange.
The numerical domain was discretized into 434 axial nodes and 32 radial
nodes. The fully implicit SIMPLER method used a time-step of 0.5 seconds.
The numerical model displayed satisfactory self-consistency when subject
to both spatial and temporal refinement. Results obtained with a mesh of
twice the nodal density (866x462) gave results within 0.6%. Using a time
step of 0.01s gave temperature fields within 1% of those found using a time step of 0.5s.
The plots below show the numerically predicted velocity and temperature
fields within the preform and furnace at three different times during the
transient heating of a preform. The furnace wall was approximately
isothermal with a temperature of 85 C.
After 100 seconds there is strong
natural convection due to the large temperature difference between the hot
wall and the cold preform. After 2000 seconds natural convection continues
strongly with a unicellular flow pattern. As the furnace environment
reaches steady state (t=14 hours) the majority of the lower preform is
isothermal. Unlike before, the convection is multicellular and weak as the
natural convection is now driven by the vertical variation in both the
wall and the preform surface temperatures, not the radial temperature
difference as before.
Effect of Preform Emissivity
To test the numerical model, experimentally measured
preform temperature histories were compared with predicted values for a
range of well-defined preform emissivities.
Preforms coated with both black paint and aluminum foil were used. The
discrepancies between the predicted preform temperatures and the
experimental observations never exceeded 1.3 C (see below). These
results show that not only does the numerical model accurately predict the
total transient heating, but it also successfully predicts the individual
contribution of radiative heat transfer over almost the entire range of
surface emissivities. This allows us to make an accurate estimation of
the relative contributions of thermal radiation and natural convection
heat transfer.
Contribution of Thermal Radiation
The above figure shows the predicted rate of radiative
and total heat transfer
experienced by a half-inch diameter poly(methyl) methacrylate (PMMA)
preform exposed to a parabolic axial wall temperature profile.
Natural convection and thermal radiation contribute
approximately equal heating to
the cold preform when it is initially introduced into the preheated
furnace. As the preform temperature rises, the fraction of convective
heating decreases due to the weakening of the air circulation cells
between the furnace wall and preform. By the end of the initial preform
heating radiation typically accounts for 90% of the total heat
transfer.
Hence natural convection, in comparison to radiation, contributes
a smaller fraction of the total energy required during the transient
heating of the preform and also during the fiber drawing.
Preform Temperature Profile
Due to the importance of radiative heat transfer the resulting vertical
temperature profile within the preform is coupled to that of the furnace
wall. This is because radiative heat transfer is greatest between
surfaces in close proximity to each other. That is why the preform
temperature profile seen below closely resembles the parabolic
temperature profile of the furnace wall.
This has important implications because the initial reduction in the
polymer's viscosity and the onset of necking typically occurs at the
hottest point in the preform provided there is sufficient weight of
polymer below. Therefore the location of initial necking can be
controlled by modifying the furnace wall temperature. This can aid in the
reduction of preform waste. Finally, the furnace wall temperature profile can be used
to generate a preform temperature distribution that most resembles that of
steady-state drawing, thereby minimizing initial setup time.