Multiscale development of a fission gas thermal conductivity model: Coupling atomic, meso and continuum level simulations Michael R. Tonks a,⇑ , Paul C. Millett a , Pankaj Nerikar b , Shiyu Du b , David Andersson b , Christopher R. Stanek b , Derek Gaston a , David Andrs a , Richard Williamson a a Fuel Modeling and Simulation, Idaho National Laboratory, P.O. Box 1625, Idaho Falls, ID 83415, United States b Materials Science and Technology Division, Los Alamos National Laboratory, P.O. Box 1663, Los Alamos, NM 87545, United States article info Article history: Received 20 June 2012 Accepted 3 May 2013 Available online 16 May 2013 abstract Fission gas production and evolution significantly impact the fuel performance, causing swelling, a reduc- tion in the thermal conductivity and fission gas release. However, typical empirical models of fuel prop- erties treat each of these effects separately and uncoupled. Here, we couple a fission gas release model to a model of the impact of fission gas on the fuel thermal conductivity. To quantify the specific impact of grain boundary (GB) bubbles on the thermal conductivity, we use atomistic and mesoscale simulations. Atomistic molecular dynamic simulations were employed to determine the GB thermal resistance. These values were then used in mesoscale heat conduction simulations to develop a mechanistic expression for the effective GB thermal resistance of a GB containing gas bubbles, as a function of the percentage of the GB covered by fission gas. The coupled fission gas release and thermal conductivity model was imple- mented in Idaho National Laboratory’s BISON fuel performance code to model the behavior of a 10-pellet LWR fuel rodlet, showing how the fission gas impacts the UO 2 thermal conductivity. Furthermore, addi- tional BISON simulations were conducted to demonstrate the impact of average grain size on both the fuel thermal conductivity and the fission gas release. Published by Elsevier B.V. 1. Introduction Fission gas produced within the fuel during light water reactor (LWR) operation significantly impacts the fuel performance. Fis- sion gas atoms cluster to form both intra- and intergranular bub- bles that result in fuel swelling and reduce the fuel thermal conductivity. In addition, the intergranular gas bubbles eventually interconnect and release the fission gas into the gap between the fuel and cladding, increasing cladding pressure and reducing the gap gas thermal conductivity. Current fuel performance codes account for the impact of fis- sion gas using empirical or semiemperical materials models to pre- dict the impact of the fission gas on swelling, thermal conductivity and fission gas release (e.g. [1,2]). However, each of these models is independent, even though they are caused by the same physical phenomena. Recently, efforts have been made to couple a fission gas release model to the swelling [3], but work is still needed to couple the fission gas evolution to the fuel thermal conductivity. To develop a physics-based model of the impact of fission gas on thermal conductivity would require an understanding of how basic microstructural features impact the thermal conductivity, such as GBs and bubbles. In recent years, atomistic simulation, primarily molecular dynamics, has been applied to understand the effect of microstructure on the fuel thermal conductivity, focusing on unirradiated UO 2 [4–6]. Mesoscale models of thermal conductivity in UO 2 have also been developed, focusing on the ef- fect of bubble distribution [7–13]. However, these models have not considered information from atomistic simulation, nor have they been coupled to macroscale fuel performance models. In their review article, Rashid et al. [14] state ‘‘it has now be- come possible to consider the potential for atomistic methodolo- gies to inform the engineering-scale models and provide better science-based modeling of nuclear fuel behavior.’’ They go onto state that a likely approach is to use lower length-scale modeling to ‘‘inform and improve empirical or reduced-order physics’’ mate- rials models that are used in current fuel performance codes. A common approach used to inform engineering scale models from lower length-scale simulation is internal state variable (ISV) theory [15]. In this approach, dependent state variables are em- ployed to describe the current state of the material microstructure. Expressions used to define the value for each material property are functions of operating conditions (temperature, displacement) and state variables. This approach has the potential to enable more sci- ence-based modeling of fission gas behavior. However, such an ISV model would require expressions defining the evolution of the fis- sion gas, as well as how the fission gas influences material proper- ties. These expressions can be developed from experimental data 0022-3115/$ - see front matter Published by Elsevier B.V. http://dx.doi.org/10.1016/j.jnucmat.2013.05.008 ⇑ Corresponding author. Tel.: +1 208 526 6319. E-mail address: Michael.Tonks@inl.gov (M.R. Tonks). Journal of Nuclear Materials 440 (2013) 193–200 Contents lists available at SciVerse ScienceDirect Journal of Nuclear Materials journal homepage: www.elsevier.com/locate/jnucmat