Transcript 2 - Dominique VREL

High temperature thermal
diffusivity of combustion
synthesized samples
Dominique Vrel
CNRS-LIMHP, UPR 1311,
99 avenue Jean-Baptiste Clément, 93430 Villetaneuse, France
Nikhil Karnatak, Ellen M. Heian, Sylvain Dubois,
Marie-France Beaufort, Benoît Cochepin
CNRS-LMP, UMR 6630, Bât. SP2MI, Bd M. & P. Curie, BP 30179
86962 Futuroscope-Chasseneuil du Poitou Cedex, France
Modeling studies
Equation in 1D with the following approximation :
Importance
 in modeling before scaling-up;
 in determination of kinetic parameters such as use
of Boddington model (thermal profile analysis, TPA)
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Measuring thermal diffusivity
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Easy at low temperature on reactants and
products
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Impossible at high temperature on reactants
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… Not practically possible on products at high
temperature: re-crystallization, sintering, stress
relaxation, homogenization of structure and
composition (long time at high temperature)
 Not possible during reaction
(coupled equations with kinetics)
We need to find a way to determine thermal
diffusivity as fast as possible, just after reaction
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A weird sample
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IR streak image - principle
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IR streak image - result
Reaction re-starts – Hot spot
Reaction pauses
Reaction propagates
Igniter is on
Reference frame
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TRXRD – no second reaction
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XRD, 25 pps
Left shift = temperature
increase
2d sin q = l; if q, d
1 reaction only
1 re-heating
can be used to estimate
thermal diffusivity
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Hot spot diffusion
i for the space step; n for the time step
 77 space steps (77 pixels on the IR image)
 25 time steps per second
 2 unknowns: a and x
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Golden section search
To determine the unknowns, starting from an
experimental temperature profile, we model the
evolution of temperature with arbitrary values of a
and x, and then minimize the sum of differences
between the final calculated profile and the final
experimental profile
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Flow chart
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Modeling results
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Thermal diffusivity – results
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Weaker hot spots
with nickel
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with finer C
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Finer C particles
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Calculated thermal diffusivity
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And before reaction ?
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Noisy data
Calculated value of thermal diffusivity sets the
lower limit for the real value : method measures
only the part of the heat flowing through the
sample that contributes to the temperature
increase and neglects the part that contributes to
the heat losses.
System might reach equilibrium, where the heat
flowing through the sample only compensate the
heat losses
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Results before reaction
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Summary
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Conclusions
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Method is easy and seems trustworthy
Should be applied with care
Cannot be used on any sample; needs instability
Could be improved by a « controlled hot spot ».
References
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Dominique Vrel, Nikhil Karnatak, Marie-France Beaufort, Sylvain Dubois, In-situ
measurement of high-temperature thermal diffusivity in a combustion-synthesized
ceramic, European Physical Journal B 33 (2003), 31-39.
Dominique Vrel, Nikhil Karnatak, Ellen M. Heian, Sylvain Dubois and Marie-France
Beaufort, Measurement of thermal diffusivities during self-propagating high
temperature synthesis, submitted, International Journal of Self-Propagating HighTemperature Synthesis.
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