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MTFC RESEARCH GROUP
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A NUMERICAL STUDY OF FIBER GLASS
DRAWING PROCESS
Quentin Chouffart, Vincent E. Terrapon
Multiphysics and Turbulent Flow Computation Research Group
University of Liรจge
19 October 2012
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Outline MTFC RESEARCH GROUP
โข General context
โข Physics of fiber drawing process
โข Numerical study โ Heat transfer
โข Numerical study โ Flow rate
โข Conclusion
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Fiberization process
โข Glass fibers are made by drawing thousands of fibers
from a bushing plate:
Glass melt flows through tip
Forming fibers are cooled by fins and water spray
Coating is applied to fibers
Fibers are drawn by a winder
โข Efficiency improvement of fiberglass drawing process is mostly driven
by fiber breakage reduction
โข Break implies :
1. Shut down of forming station and thus production loss
2. Large amount of unrecyclable glass waste
3. Barrier to optimization of manufacturing process
Quentin Chouffart - Numerical Study of Fiber Drawing Process 3
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Goal and impact of research
Goal
Understand the origins of fiber breaking during forming process
Identify strategy to reduce as much as possible the breaking rate
Impact
Fiber drawing process
โข Improved numerical modeling and simulations
โข Better understanding of breaking mechanisms
Manufacturing process
โข Energy and waste reduction
โข New design of tips, bushing plate, cooling fins โฆ
โข Lower costs to produce the same quantity of fiber glass
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Pathway to improved efficiency
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Improve knowledge of fiber drawing process
Understand underlying physics of filament
breaking
Devise strategy for reducing breaking rate
โข Physical models
โข Simulations
โข Experimental studies
โข Parameter studies
โข Characterize breaking:
When? Where? Why?
โข Probability of failure
โข Experimental studies
โข New design of
bushing unit
โข Modification of
operating windows
โข โฆ
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Physics of one fiber forming
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Glass melt
Viscous flow
Glass transition
Viscoelastic flow
Glassy state
Elastic solid
โข Convection
โข Conduction
โข Radiation
โข Convection
โข Conduction
โข Convection
โข Conduction
Heat transfer Fluid flow
๐ป > ๐ป๐
๐ป โ ๐ป๐
๐ป < ๐ป๐
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Governing glass flow equations
Gouverning viscous flow equations: Newtonian flow
Mass conservation: ๐ท๐
๐ท๐ก= 0
Momentum conservation: ๐ท ๐๐
๐ท๐ก= ๐ป. ๐ + ๐
Energy conservation: ๐ท ๐๐ถ๐๐
๐ท๐ก= ๐: ๐ป๐ โ ๐ป. ๐ + ๐
Assumptions:
โข Fulcher viscosity equation: ฮท = 10โ๐ด+
๐ต
๐โ๐0
โข Internal radiation, gravity and viscous heating neglected
โข External temperature remains constant around fiber
Quentin Chouffart - Numerical Study of Fiber Drawing Process 7
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Boundary conditions
Inlet
Volumetric flow rate: ๐๐ก๐๐ =๐
8ฮท โ
๐๐
๐๐ง ๐0
4
Constant temperature
Free surface
Heat flux: ๐ = โ ๐ โ ๐0 + ๐๐(๐4 โ ๐04)
Kase-Matsuo convective coefficient: โ = 0.42 ๐๐
๐ท
๐ข ๐ท
๐๐
0.334
Surface tension: ๐พ constant
Outlet
Drawing velocity: ๐ฃ = ๐ฃ๐
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๐ฃ = ๐ฃ๐
๐ฃ = 0 m/s
๐๐ก๐๐
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Numerical study - Plan
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Simulations
Validation
Heat
transfer
analysis
Flow rate
analysis
Governing equations are solved numerically with finite elements method
with computer simulations
Simulations performed with ANSYS Polyflow software
Three sets of simulation:
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Numerical study - Plan
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Simulations
Validation
Heat
transfer
analysis
Flow rate
analysis
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Initial validation of numerical approach
Validation from experimental data (L. R. Glicksman, PhD thesis, MIT, 1964)
Quentin Chouffart - Numerical Study of Fiber Drawing Process 11
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Fiber radius attenuation Case study
Material Glass M5
๐0 1227 ยฐ๐ถ
๐๐๐ 3.17 109 ๐3/๐
๐ฃ๐ 25.88 ๐3/๐
Good agreement between simulation
and experimental data.
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Numerical study - Plan
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Simulations
Validation
Heat
transfers
analysis
Flow rate
analysis
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Heat transfer study
Hypothesis : External temperature of environment ๐๐๐ฅ๐ก remains constant near tips exit
โข Heat fluxes acting on fiber surface come from convection and radiation:
๐ = โ ๐ โ ๐๐๐ฅ๐ก + ๐๐(๐4 โ ๐๐๐ฅ๐ก4 )
โข Kase-Matsuo convective coefficient: โ = 0.42 ๐๐
๐ท
๐ข ๐ท
๐๐
0.334
โข Convection coefficient is governed by:
Fiber radius
Fiber velocity
Air properties
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Convection Radiation
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Fiber temperature field
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Temperature profile along the fiber boundary
What is the impact of the external environment?
Which heat transfer mechanism is the most important?
Which assumptions are the most critical?
Temperature Field
1306 ยฐC
1150 ยฐC
๐๐๐ฅ๐ก = 600 ยฐ๐ถ
Advantexยฎ Glass
๐ฃ๐ = 21๐/๐
Fiberization at log 2.7
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Convection dominates very rapidly ( ~ 1 cm
from tip)
Attenuation of fiber radius occurs when
radiation dominates
Radiation vs. convection
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๐๐๐ฅ๐ก = 300ยฐ๐ถ
Convection
Radiation
50 ยต๐
Convection
Radiation
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Impact of external temperature : radiation part
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๐๐๐ฅ๐ก = 600 ยฐ๐ถ
๐๐๐ฅ๐ก = 400 ยฐ๐ถ
๐๐๐ฅ๐ก = 200 ยฐ๐ถ
๐๐๐ฅ๐ก has no impact when radiation
dominates
Fiber cooling at these temperature is
governed by emissivity of glass melt
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Impact of external temperature : convection part
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๐๐๐ฅ๐ก = 600 ยฐ๐ถ
๐๐๐ฅ๐ก = 400 ยฐ๐ถ
๐๐๐ฅ๐ก = 200 ยฐ๐ถ
๐๐๐ฅ๐ก has an important impact on cooling in case of convection
Fiber cooling at these temperature is governed by air environment
๐๐ does not occurs at the same distance
Hypothesis of ๐๐๐ฅ๐ก constant becomes not relevant at lower temperature
Convection
๐๐
more accurate if ๐ป๐๐๐ remains no constant
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Numerical study - Plan
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Simulations
Validation
Heat
transfer
analysis
Flow rate
analysis
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Flow rate impact
Flow rate inside the tip can be described by Hangen-Poiseuille law as:
๐๐ก๐๐~ ๐ฝ 1
8ฮท โ
๐๐
๐๐ง
Main parameters controlling flow rate:
- Tip temperature: ฮท = ฮท(๐)
- Tip shape: ๐ฝ
- Glass height (hydrostatic pressure): โ๐๐/๐๐ง
Tip shape and glass height remains (almost) constant on the bushing plate
Tip temperature has large impact on:
Fiber diameter quality
Fiber cooling
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Flow rate impact
Bushing plate may exhibit non-homogeneous temperature : T + ฮ๐
What is the impact of ฮ๐ on fiber diameter?
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โ๐ < 3 ยต๐
โ๐ < 2ยต๐
โ๐ < 1 ยต๐
Maximum โ๐ admissible for fiber diameter distribution given
Non-linear variation due to viscosity
law
unsymmetrical relative to โ๐ = 0 ยฐ๐ถ
More
robust
Goal : ๐๐๐๐๐๐ = 10 ยต๐ ยฑ 2 ยต๐
๐ = 1300 ยฐ๐ถ
โ๐ = +28ยฐ๐ถโ32 ยฐ๐ถ
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Flow rate impact
How does โ๐๐๐ข๐ โ๐๐๐ impacts on fiberization and fibers cooling ?
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Temperature between two fibers may varies
since tip plate exhibits ฮ๐๐๐ข๐ โ๐๐๐
ฮ๐๐๐๐๐๐ is amplified when fibers are cooling
ฮ๐๐๐๐๐๐ can reach 130 ยฐ๐ถ at ๐ง = 0.04 m
โ๐๐๐ข๐ โ๐๐๐ = 40 ยฐ๐ถ
โ๐๐๐ข๐ โ๐๐๐ = 30 ยฐ๐ถ
โ๐๐๐ข๐ โ๐๐๐ = 20 ยฐ๐ถ
โT between two fibers along axial component
Important to remove
inhomogeneous heat pattern on
bushing plate.
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Conclusion
โข Numerical simulations are very useful to understand physical mechanisms of fiber
forming:
Radiation seems to be more important very close to the tip
Convection becomes dominant very quickly due to the decrease in fiber radius
Heat pattern of bushing plate has to be as homogenous as possible to reduce
different cooling rates between fibers, and thus a broad diameter distribution
โข Mathematical model could be improved using a more complex model for the air
environment around the fiber
This tool provides a first step to reach the fundamental understanding of fiber
breaking
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Further work
Physical model of glass fiber drawing
โข Take in account viscoelasticity
โข Take in account internal radiation heat transfer
โข Study unsteady effects (drawing resonance)
โข Study impact of uncertainties on simulation results
Experimental devices
โข Study air environment around fiber
โข Link data to physical model
โข And โฆ characterize of fiber breaking by several experiments
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