2009 International Nuclear Atlantic Conference - INAC 2009 Rio de Janeiro,RJ, Brazil, September27 to October 2, 2009 ASSOCIAÇÃO BRASILEIRA DE ENERGIA NUCLEAR - ABEN ISBN: 978-85-99141-03-8

MEASUREMENT OF URANIUM DIOXIDE THERMOPHYSICAL PROPERTIES BY THE LASER FLASH METHOD

Pablo Andrade Grossi 1, Ricardo Alberto Neto Ferreira 2, Denise das Mercês Camarano 3, Roberto Márcio de Andrade 4

1,2,3 Centro de Desenvolvimento da Tecnologia Nuclear-CDTN Comissão Nacional de Energia Nuclear-CNEN Av. Presidente Antônio Carlos 6627 Cidade Universitária-Pampulha-Caixa Postal 941 CEP: 31.161-970 Belo Horizonte, MG 1 [email protected] 2 [email protected] 3 [email protected]

4 Departamento de Engenharia Mecânica Escola de Engenharia da Universidade Federal de Minas Gerais Av. Presidente Antônio Carlos 6627-Cidade Universitária-Pampulha CEP: 31.270-901 - Belo Horizonte – MG - Brasil 4 [email protected]

ABSTRACT

The evaluation of the thermophysical properties of uranium dioxide (UO 2), including a reliable uncertainty assessment, are required by the nuclear reactor design. These important informations are used by thermohydraulic codes to define operational aspects and to assure the safety, when analyzing various potential situations of accident. The Laser Flash Method had become the most popular method to measure the thermophysical properties of materials. Despite its several advantages, some experimental obstacles have been found due to the difficulty to obtain experimentally the ideals initial and boundary conditions required by the original method. An experimental apparatus and a methodology for estimating uncertainties of thermal diffusivity, thermal conductivity and specific heat measurements based on the Laser Flash Method are presented. A stochastic thermal diffusion modeling has been developed and validated by Standard Samples. Inverse Heat Conduction Problems (IHCPs) solved by Finite Volumes technique were applied to the measurement process with real initial and boundary conditions, and Monte Carlo Method (MCM) was used for propagating the uncertainties. The main sources of uncertainty were due to: pulse time, laser power, thermal exchanges, absorptivity, emissivity, sample thickness, specific mass and dynamic influence of temperature measurement system. As results, mean values and uncertainties of thermal diffusivity, thermal conductivity and specific heat of UO 2 are presented.

Key-words: uranium dioxide, thermal conductivity, thermal diffusivity, flash method, assessment of uncertainty, Monte Carlo Method.

1. INTRODUCTION

The sinterized ceramic pellets of uranium dioxide are widespread used in fuel elements of LWR Nuclear Power Plants, having several advantageous properties. The main important advantages of the uranium dioxide are, very high melting point, stability even in high temperatures, in case of an accidental contact with the cooling water of the nuclear reactor due to an eventual failure of the fuel cladding, and high capacity of fission products retention. The behavior of the nuclear fuel during irradiation is highly dependent on the themophysical and chemical properties of the fuel material, and their variation with temperature and burn- up. The fuel temperature is determined by the thermal conductivity, among others thermal and physical properties as specific heat, thermal diffusivity and specific mass. Such properties of the fuel are not constant during the irradiation period in the reactor, but change with the burn-up. A lower thermal conductivity leads to large temperature gradients across the fuel pellet and a high central temperature. Therefore the evaluation of the thermophysical properties of uranium dioxide (UO 2), including a reliable uncertainty assessment, are required by the nuclear reactor design. These important informations are used by thermohydraulic codes to define operational aspects and to assure the safety, when analyzing various potential situations of accident.

In this work, the thermophysical properties of pellets samples obtained from uranium dioxide kernels were studied, by means of the Flash Method, to support a project in development in the CDTN-Centro de Desenvolvimento da Tecnologia Nuclear – (Nuclear Technology Development Center). The kernels were produced using the sol-gel process developed by HOBEG/NUKEM group, that was absorbed, transferred and implanted in CDTN [1, 2, 3]. This sol-gel process was developed to fabricate fuel elements for high temperature gas cooled reactors. However it was adapted in order to manufacture fuel pellets for pressurized water reactors too [4, 5, 6, 7, 8, 9, 10, 11]. The pellets were pressed at 300 MPa and sinterized at 1600 oC for five hours. The percent of theoretical density of the samples was evaluated in 90%.

This pellet manufacturing technology is under development at CDTN to be used on production of a new type of fuel manufactured from such uranium dioxide kernels with beryllium oxide filling the voids between the kernels [12]. The addition of beryllium oxide is expected to improve the fuel thermal conductivity, in order to avoid premature degradation of the fuel pellet, allowing a longer permanence in the reactor meaning significant economic gains. Thus, an assessment of improvements can be performed by comparison of thermal properties of pure uranium dioxide samples with samples with addition of beryllium oxide. The Flash Method [13] has been considered by INMETRO-Instituto Nacional de Metrologia, Normalização e Qualidade Industial (National Institute for Metrology, Standardization and Industrial Quality) and other organizations as the standard method in Brazil for thermal diffusivity measurements. Despite its several advantages, inherent experimental features become obstacles to a coherent expression of the measurement results. Several corrections to deal with such effects has been presented in the literature and summarized on ASTM-E-1461-07 [14]. Due its experimental obstacles the original flash method has been reviewed and some alternative and effective approaches are proposed [15, 16, 17, 18].

The measurements on uranium dioxide samples were carried out in the LMPT – Laboratório de Medição de Propriedades Termofísicas (Thermophysical Properties Measurement Laboratory). The thermal diffusivity, specific heat and thermal conductivity of uranium dioxide were evaluated applying a central model of thermal diffusion on the experimental measurements. This numerical approach applied to the original Flash Method [13] consider all real initial and boundary conditions identified for the physical model of the LMPT experimental bench [15]. Consequently, additional corrections are not needed. The validation of this stochastic thermal diffusion modeling was accomplished by standard samples of BSC Pure Iron, Inconel 600 and Pyroceram 9606.

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An effective methodology for uncertainty evaluation, based on Monte Carlo Method (MCM), was applied to the experimental measurements, to determine the corresponding uncertainties.

2. EXPERIMENTAL APPARATUS

The Figure 1 shows schematically the thermophysical properties measurement laboratory experimental apparatus based on Flash Method. The bench basically consists of a CO 2 laser, a sample holder placed inside a tubular furnace and an infrared temperature measurement and data acquisition system.

Laser beam Infrared detector signal

Furnace and Temperature CO 2 Laser sample holder Measurement System

Figure 1. Experimental apparatus of the Thermophysical Properties Measurement Laboratory.

The CO 2 laser (wavelength of 10.6 µm, power up to 25 W, continuous emission and beam diameter of 8 mm) is responsible for the application of the energy pulse on the front face of the sample. To ensure the one-dimensional heat flow, the sample must have the same diameter of the laser beam (8 mm). A power meter device evaluates the effective emitted power.

The furnace can drive the measurements from room temperature up to 1700 oC under controlled atmosphere or vacuum. The sample is placed in an inner sample-holding system. The oven temperature control is set by a PID controller that feeds a Platinum (70%) / Rhodium (30%) heating resistance.

The temperature of the sample opposite face is obtained by an infrared temperature measurement system. The detector is an optical infrared thermometer with a response time of 150 ms. Ferreira et al. [19] and Grossi [15] have presented additional information about this experimental bench and a detailed characterization and evaluation of the measurement parameters and sources of uncertainty.

3. STOCHASTIC MODEL OF THERMAL DIFFUSION PROCESS

The experimental apparatus of the Thermophysical Properties Measurement Laboratory was based on the Flash Method. Due to technological restrictions, the real experimental conditions do not satisfy all initial and boundary conditions required on the original Flash

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Method. To consider this real initial and boundary conditions, direct numerical solutions to the thermal diffusion process by the Finite Volume Method [20] were proposed [15]. This deterministic modeling is implemented by the CONDUCT.for subroutine (Figure 2). The ADAPT.for subroutine implements all real initial and boundary conditions.

From the experimental data of a measured sample an Inverse Heat Conduction Problem must be solved to obtain representative numerical solutions for the real thermal diffusion process. Such task is implemented on FLASH.for subroutine. The reevaluation of the search ranges for each quantity is performed by ARRANGE.for subroutine.

The stochastic structure of the model is implemented by using the Monte Carlo Method for uncertainty propagation [21, 22]. The random draws for input quantities of the model are performed by NORMAL.for subroutine based on Uniform, Gaussian or Triangular distributions assign to each input quantity.

Expected mean values and uncertainties for the multiple output parameters ( k, c p and α) are obtained as final results.

(CONDUCT.for) Numerical solution for the thermal diffusion process

(ADAPT.for) (NORMAL.for) (FLASH.for) Estimation and insertion of the Generation of random MCM and implementation of input quantities, initial and draws inverse heat -conduction problem boundary conditions

(ARRANGE.for) Reassessment of quantity search values

Figure 2. Schematic diagram of the model structure: main software and subroutines.

The detailed structure of the model is divided into the following steps: 1. Initialization of the simulation process. a. Acquirement of a set of standard sample opposite face transients (measurements by LMPT apparatus under repetitive conditions) and generation of a mean transient; b. Evaluation of mean values, uncertainties and PDF types of the N input quantities of the model (see Table 1); c. Definition of the M number of Monte Carlo trials to be made; d. Definition of the search range of the R output quantities, ensuring the physical meaning of the Inverse Heat Conduction Solutions; 2. Beginning of Loop 1: Implementation of Monte Carlo Method. e. Generation of one random value for each N input quantities. (Note: this step will be performed M times by sampling from the PDFs of the N input quantities; 3. Beginning of Loop 2: Inverse Heat Conduction Problem.

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f. Definition of 4 values within the search range of output quantities (lower limit, two intermediate points, 38.2 % and 61.8 % and upper limit, according to the Golden Section Method); g. For each value of step f, evaluation of the model considering the N input values from step e. (Note: this deterministic modeling gives direct solutions for heat diffusion in the sample and consider the dynamic effects of temperature measurement system, that should not be neglected in this case); h. For each discrete time, the mean value of the experimental transients (acquired in step a) is compared to each numerical transient of step g. A quadratic mean deviation among the curves is performed and the convergence criterion is verified. If the solution gets convergence, go to step i, else, it is necessary to redefine the output search values (by elimination of the limit value nearer from the worst quadratic mean deviation) and go back to step f; 4. End of Loop 2. i. The optimal values (numerical solutions and output quantities) are stored. If the number of optimal solutions is equal to the M required Monte Carlo trials, go to the next step, else, a new iteration of the Monte Carlo Loop is performed (go to step e); 5. End of Loop 1. j. A set of M values for the R output quantities are estimated as a model response when excited by each of the M random values for the N input quantities; k. The Optimal Parameters Matrix ( OPM ) is created by grouping the M input vectors and their respective optimal output quantities (model responses for each Monte Carlo trial) according to the Eq. (1);

 y L y   x L x   1,1 ,1 M   1,1 ,1 M  OPM =  M O M  = f  M O M  (3)  L   L  yR 1, yR,M  xN 1, xN ,M 

l. The mean values of the input and output quantities are estimated; m. The Optimal Parameter Matrix Corrected, OPM *, is created, where the individual M values of each quantity in the OPM are subtracted from its respective mean (calculated in the previous step). Thus, the OPM * represents the deviation values between each optimal solution and the mean values of each parameter of the model (input and output quantities); n. The Variance and Covariance Matrix, V, or Uncertainty (dispersion) Matrix associated to the quantities is obtained as shown below:

1 V = OPM * (OPM * )T (4) M −1

o. The expected (mean) value of the output quantities and standard uncertainties associated are calculated from:

1 M y = y (m) (5) R M ∑ R m=1 and M 1 2 u (y ) = s (y ) = []y (m) − y . (6) R R M (M − )1 ∑ R R m=1

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p. The output values are sorted into non-decreasing order to provide a discrete representation of its PDFs [21, 22]; q. The mean value and uncertainty associated to the output quantities are estimated for a 95% coverage interval from the discrete PDFs obtained in the step p.

The Figure 3 shows the computer algorithm flowchart developed and implemented using the Compaq Visual FORTRAN platform [15].

Real (experimental) Search ranges of PDFs of the N Thermal Transients output quantities input quantities Térmicos Reais Monte Carlo Method Random sampling from the PDFs of the N input quantities

Inverse Heat Estimation of 4 output quantities values Conduction Problem (Optimal solutions) within the search ranges (Golden Section)

Redefinition of the Thermal Diffusion Model output quantities YR = f (XN) search ranges Thermal Analogue Model of the Temperature Measurement System No

Do experimental and Discrete solutions for the numerical transients rear-face transients converge? (deterministic evaluations of the model)

Yes

Storage the Optimum: numerical solutions and output quantity values

No Number of Monte M optimal Carlo trials , M solutions? Yes

Estimate the Variance Matrix, V, the mean values, yR , and standard

uncertainties, u (yR ) , from the M optimal values for the R output quantities

Expression of the measurement results (including coverage intervals) based on the means and standard uncertainties associated to the R output quantities

Figure 3. Flowchart of the Stochastic Model of Thermal Diffusion Process: solution of the Inverse Heat Conduction Problem and assessment of uncertainties using the Monte Carlo Method.

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The entire stochastic model was validated using Inconel 600, BSC Pure Iron and Pyroceram 9606 standard samples supplied by Netzsch.

4. RESULTS AND DISCUSSIONS

The developed model was applied to the average of seven measured transients on a sample of uranium dioxide produced at CDTN from UO 2 kernels (Figure 4). The mean values and uncertainties of thermal diffusivity, thermal conductivity and specific heat are presented in Table 1 (based on a sample of 7 transients and considering for that 2,36 as the coverage factor). The Figure 5 shows graphically the convergence of the mathematical model to the average of the measured transients, demonstrating the reliability of the results presented in Table 1.

25

24

C 23 o

22

21

Temperature / Temperature RAA 920 RAA 921 20 RAA 870 RAA 923 RAA 924 19 RAA 925 RAA 926 1: Mean (Experimental Transients) 18 0 5 10 15 20 25 30 35 40 time / s

Figure 4. Experimental transients of measurements on uranium dioxide sample.

Table 1 Thermophysical properties of uranium dioxide at 25 ºC.

α ⋅ 10 6 / k / c / Sample p (m 2 ⋅ s-1) (W ⋅ m-1 ⋅ K-1) (J ⋅ kg -1 ⋅ K-1)

Uranium Dioxide mean value 2.77 7.08 258.5 standard uncertainty 3.37% 2.32% 2.90% 95% coverage interval [2.55, 2.99] [6.69, 7.47] [241, 276]

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25

24 C

o 1 23

22 2

3 Temperature / Temperature 21 4

20 1: Mean (Experimental Transients) 2 2: Upper and Lower Limits (Experimental Transients)

19 3: Mean plus Noise (Deterministic Model - IHCP )

4: Mean (Deterministic Model - IHCP ) 18 0 5 10 15 20 25 30 35 40 time / s

Figure 5. Convergence of the deterministic model to the average of the measured transients of a uranium dioxide pellet sample including upper and lower limits for 95 % coverage interval.

The results of uranium dioxide thermophysical properties measurements, showed on Table 1, are in accordance with material properties database for LWRs [23] and recent and extensive revisions of solid UO 2 properties [24, 25, 26] including analysis of data to obtain new recommendations, assessment of uncertainties, regression, fitting equations to thermophysical properties experimental data and comparisons of new recommendations with data and previous recommendations.

7 CONCLUSIONS

The results of uranium dioxide thermophysical properties measurements are in accordance with material properties database for LWRs and recent and extensive revisions of solid UO 2 properties. The observed divergences of the obtained values with the values reported in the literature can be attributed to differences between the percents of theoretical densities of the measured samples (estimated on 90%) and those presented on the literature (varying from 93 to 99.5 %).

The developed models perform an efficient and simultaneous implementation of corrections for all experimental problems associated to the Flash Method, encompassing evaluation of thermal diffusivity, thermal conductivity, specific heat and the corresponding uncertainties. The standard uncertainty associated to the thermophysical properties varied between 2.09 % and 3.37 %, as function of the model validation process and the number of measured transients.

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ACKNOWLEDGMENTS

Work supported by the Nuclear Technology Development Center – CDTN-CNEN ( Centro de Desenvolvimento da Tecnologia Nuclear ) and Minas Gerais State FAPEMIG ( Fundação de Amparo a Pesquisa do Estado de Minas Gerais )

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