Specimen Size Effects in the Determination of Nuclear Grade Graphite Thermal Diffusivity ASTM D02F000 Symposium on Graphite Testing for Nuclear Applications: the Significance of Test Specimen Volume and Geometry and the Statistical Significance of Test Specimen Population September 19-20, 2013 Seattle Hilton; Seattle, WA Dave Swank Will Windes

Outline: Description of measurement technique Sources of Uncertainty – Limitations of heat loss correction models – Limitations of finite laser pulse corrections Example of estimating measurement uncertainty Summarize and conclude

Why do we need to measure thermal diffusivity? Thermal conductivity Conduction through the graphite is how we get the energy out of the fuel Diffusivity of graphite is significantly reduced by irradiation Engineers need to understand this relationship for design Passive safety of system – get the heat out Measurement is performed to ASTM E 1461 Generic standard covering the measurement of diffusivity by the laser flash technique for all materials. Graphite and irradiation experiments of graphite have some special considerations - specimen geometry and homogeneity

Laser Flash Apparatus (LFA) Operation Radiation to detector Laser Specimen Small, thin, disk-shaped specimen held in a controlled atmosphere furnace. Nd-YAG pulsed laser is used to subject one surface of the specimen to a high- intensity, short-duration energy pulse. Energy is absorbed on the front surface of the specimen’ Resulting rise in rear-face temperature is recorded with a sensitive IR detector.

Thermal Diffusivity One-dimensional heat flow No heat loss Homogenous specimen Uniform absorption of the laser energy Short pulse length of the laser compared to the heat transport times Thermal Diffusivity for a Laser Flash Apparatus (LFA) solved analytically for adiabatic conditions by Parker et. al., 1961 Radiation to detector Laser Specimen L Detector Signal Laser Pulse t 1/2

Heat transport time - t 1/2 Non uniform heating Multi directional conduction Heat Loss: Radiation, Conduction, Convection Finite laser pulse width Heterogeneity - # of grains, cracks/pores size and density Where are the Sources of Uncertainty Length measurement - L ASTM E : L ± 0.2% —Realistically we can machine and measure specimens down to ± ~20 µm

L= 1.6 mm L = 3.2 mm L= 6.4 mm Effects of Heat Loss: Adiabatic Conditions? (AXF-5Q graphite, 12.7mm diameter at 800°C) Detector signal Adiabatic model

Sources of Specimen Heat Loss Convection – negligible if purge gas flow rates are kept low Conduction – negligible if specimen holder is properly designed Radiation – —Top and bottom surface – early in the develop of LFA it was determined this can have a significant effect (1963 Cowan). —Circumferential – specimen holder can be designed to minimize exposure to other surfaces Radiation to detector Radiation heat loss Laser Specimen L

Radiation Heat Loss Correction Models Cowan, 1963 Assumes a finite square wave impulse of energy Linearizes the radiation heat loss based on data at 5t 1/2 and 10t 1/2 Assumes one dimensional conduction heat transfer in the specimen Therefore radiation loss from the circumference is not considered Only radiation from the top and bottom surfaces is considered.

Cape-Lehman, 1963 Assumes Two dimensional conduction Therefore considers radiation exchange at the circumference of the specimen Maintains higher order terms and therefore is a nonlinear solution which is more accurate at higher temperatures Radiation to detector Radiatio n heat loss Laser Specimen L Radiation Heat Loss Correction Models (cont.)

Model Comparison for AXF-5Q 12.7 mm diameter x 12.7 mm thick Cowan method chosen here because: Adequate for current specimen fixturing designs Relative simplicity Universal availability Proven results

Application of the Cowan Heat Loss model (AXF-5Q graphite) Cowan 0.25” (6.4 mm) 800°C Adiabatic 0.25” (6.4 mm) 800°C Cowen 9.6 mm 900°C Adiabatic 9.6 mm 900°C Detector signal Adiabatic model

Empirically evaluate the Cowan heat loss correction (AXF-5Q graphite) 12.7 mm diameter Apparent lower diffusivity for thicker samples. Deviation >300°V

Stefan-Boltzmann Law E b = σT 4 AXF-5Q 12.7 mm diameter specimens With Cowan radiation heat loss Radiation heat transfer becomes significant at 400°C and above Empirical test (cont.) 9.6 (mm) Temp (°C)

9.6 (mm) Temp (°C) PCEA Graphite (12.7mm dia.)

9.6 (mm) Temp (°C) Gilso Graphite (12.7mm dia.)

6.4 (mm) Temp (°C) 12.7 (mm) Temp (°C) NBG-18 Graphite 12.7 mm diameter 25.4 mm diameter

Summary of Thickness Limitations (Due to radiation heat loss up to 1000°C) Graphite Type Average grain size Maximum thickness (mm) Diameter (mm) Minimum diameter to thickness ratio AXF-5Q5 µm Gilso Carbon134 µm PCEA750 µm NBG µm 1.7 mm max NBG µm 1.7 mm max

Specimen Minimum Thickness? NBG-18 (12.7 mm dia.) Specimen Thickness

Material Effects on Measurement Uncertainty (cont.) 20% Samples above ~400°C but 1 mm thick do not exhibit the error Similar results seen for PCEA, AXF-5Q, and Gilso graphite NBG-18 (12.7 mm dia.) (1.7 mm max, 0.6 mm avg. grain size) Sources of error come from breakdowns in assumptions? —Heat loss —Heterogeneity # of grains Cracks/pores —Non uniform heating —Multi directional cond. —Finite laser pulse width

Laser Pulse Width Effects on Half Rise Time Laser pulse, fit and smoothed detector data for 1mm specimen at 200°C Graphite thermal conductivity at RT is similar to Cu. “Fast Material” Over prediction of t 1/2 would result in erroneously low calculation of the diffusivity. τ is 15-20% of t 1/2

6% Material Effects on Measurement Uncertainty (cont.) Solid = Azumi laser pulse corrected, Hollow = uncorrected Finite Laser pulse corrections: —Cape-Lehman 1963 Square pulse —Azumi-Takahashi 1981 Delta function NBG mm dia. With Cowan heat loss correction applied Finite pulse corrections have a limit Establish a more generic limit for τ /t 1/2

Limit of Laser Pulse Correction to Half Rise Time For T > 400°C and L>4 mm defines a limit of : τ / t 1/2 < For τ = 0.5 mSec t 1/2 = 20 mSec

Propagation of Error/Uncertainty Estimate (after Kline and McClintock 1953) Where: α = Thermal diffusivity ω = Uncertainty L = Specimen thickness t 1/2 = Half rise time *Based on the standard deviation of t 1/2 (length normalized). **Based on ½ of the manufactures specified laser pulse width of 0.5 msec. Rules: D/L > 2 τ /t 1/2 < 0.025

Summary and Conclusions ASTM E guide lines: L = 1 to 6 mm L ± 0.2% t 1/2 = 10 to 1000 ms Heat Loss Correction Limit: (upper limit on thickness) The extent to which any of the heat loss models tested can correct for radiation heat loss is limited. Specimen dimensions with a D/L > 2 will result in acceptable heat loss corrections when using the Cowan model. Finite Laser Pulse Correction: (lower limit on heat diffusion time) As with the heat loss models, the accuracy of the laser pulse width correction is limited. The Azumi pulse width correction to the t 1/2 timing start position is acceptable for τ / t 1/2 > (t 1/2 > 40 τ )

Summary and Conclusions (cont.) Comment on representing the bulk material: The thermal diffusivity remained unchanged for specimens of PCEA and NBG-18 down to 1 mm thick when the condition of τ/t 1/2 > was met (T>400°C). This indicates that the homogeneity of these relatively large grained graphite's is sufficient down to 1mm thick for LFA determination of diffusivity.

Thank you For you Attention… Dave Swank (208)