high temperature thermal diffusivity of combustion synthesized samples dominique vrel cnrs-limhp,...

High temperature thermal High temperature thermal diffusivity of combustion diffusivity of combustion

synthesized samplessynthesized samples

Dominique VrelDominique VrelCNRS-LIMHP, UPR 1311, CNRS-LIMHP, UPR 1311,

99 avenue Jean-Baptiste Clément, 93430 Villetaneuse, France99 avenue Jean-Baptiste Clément, 93430 Villetaneuse, France

Nikhil Karnatak, Ellen M. Heian, Sylvain Dubois, Nikhil Karnatak, Ellen M. Heian, Sylvain Dubois, Marie-France Beaufort, Benoît CochepinMarie-France Beaufort, Benoît Cochepin

CNRS-LMP, UMR 6630, Bât. SP2MI, Bd M. & P. Curie, BP 30179CNRS-LMP, UMR 6630, Bât. SP2MI, Bd M. & P. Curie, BP 3017986962 Futuroscope-Chasseneuil du Poitou Cedex, France86962 Futuroscope-Chasseneuil du Poitou Cedex, France

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Modeling studies 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 diffusivityMeasuring thermal diffusivity

Impossible at high temperature on reactantsImpossible at high temperature on reactants

Easy at low temperature on reactants and Easy at low temperature on reactants and productsproducts

Not possible during reaction Not possible during reaction (coupled equations with kinetics)(coupled equations with kinetics)

… … Not practically possible on products at high Not practically possible on products at high temperature: retemperature: re--crystallization, sintering, stress crystallization, sintering, stress relaxation, homogenization of structure and relaxation, homogenization of structure and composition (long time at high temperature)composition (long time at high temperature)

We need to find a way to determine thermalWe need to find a way to determine thermal diffusivity as fast as possible, just after reactiondiffusivity as fast as possible, just after reaction

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A weird sampleA weird sample

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IR streak image - principleIR streak image - principle

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IR streak image - resultIR streak image - result

Reference frameReference frame

Igniter is onIgniter is on

Reaction propagatesReaction propagates

Reaction pausesReaction pauses

Reaction re-starts – Hot spotReaction re-starts – Hot spot

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TRXRD – no second reactionTRXRD – no second reaction

XRD, 25 ppsXRD, 25 pps Left shift = temperature Left shift = temperature

increaseincrease2d sin 2d sin = = ififdd

1 reaction only1 reaction only 1 re-heating1 re-heating

can be used to estimate can be used to estimate thermal diffusivitythermal diffusivity

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Hot spot diffusionHot spot diffusion

ii for the space step; for the space step; nn for the time step for the time step 77 space steps (77 pixels on the IR image)77 space steps (77 pixels on the IR image) 25 time steps per second25 time steps per second 2 unknowns: 2 unknowns: and and

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Golden section searchGolden section search

To determine the unknowns, starting from an To determine the unknowns, starting from an experimental temperature profile, we model the experimental temperature profile, we model the evolution of temperature with arbitrary values of evolution of temperature with arbitrary values of and and , and then minimize the sum of differences , and then minimize the sum of differences between the final calculated profile and the final between the final calculated profile and the final experimental profileexperimental profile

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Flow chartFlow chart

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Modeling resultsModeling results

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Thermal diffusivity – resultsThermal diffusivity – results

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Weaker hot spotsWeaker hot spots

with nickelwith nickel with finer Cwith finer C

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Finer C particlesFiner C particles

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Calculated thermal diffusivityCalculated thermal diffusivity

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And before reaction ?And before reaction ?

Noisy dataNoisy data Calculated value of thermal diffusivity sets the Calculated value of thermal diffusivity sets the

lower limit for the real value : method measures lower limit for the real value : method measures only the part of the heat flowing through the only the part of the heat flowing through the sample that contributes to the temperature sample that contributes to the temperature increase and neglects the part that contributes to increase and neglects the part that contributes to the heat losses.the heat losses.

System might reach equilibrium, where the heat System might reach equilibrium, where the heat flowing through the sample only compensate the flowing through the sample only compensate the heat lossesheat losses

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Results before reactionResults before reaction

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SummarySummary

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Conclusions Conclusions Method is easy and seems trustworthyMethod is easy and seems trustworthy

ReferencesReferences Dominique Vrel, Nikhil Karnatak, Marie-France Beaufort, Sylvain Dubois, In-situ Dominique Vrel, Nikhil Karnatak, Marie-France Beaufort, Sylvain Dubois, In-situ

measurement of high-temperature thermal diffusivity in a combustion-synthesized measurement of high-temperature thermal diffusivity in a combustion-synthesized ceramic, ceramic, European Physical Journal BEuropean Physical Journal B 3333 (2003), 31-39. (2003), 31-39.

Dominique Vrel, Nikhil Karnatak, Ellen M. Heian, Sylvain Dubois and Marie-France Dominique Vrel, Nikhil Karnatak, Ellen M. Heian, Sylvain Dubois and Marie-France Beaufort, Measurement of thermal diffusivities during self-propagating high Beaufort, Measurement of thermal diffusivities during self-propagating high temperature synthesis, submitted, temperature synthesis, submitted, International Journal of Self-Propagating High-International Journal of Self-Propagating High-Temperature Synthesis. Temperature Synthesis.

Should be applied with careShould be applied with care Cannot be used on any sample; needs instabilityCannot be used on any sample; needs instability Could be improved by a « controlled hot spot ».Could be improved by a « controlled hot spot ».