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Title: A Jacobian-free Newton Krylov method for mortar-discretized thermomechanical contact problems

Abstract

Multibody contact problems are common within the field of multiphysics simulation. Applications involving thermomechanical contact scenarios are also quite prevalent. Such problems can be challenging to solve due to the likelihood of thermal expansion affecting contact geometry which, in turn, can change the thermal behavior of the components being analyzed. This paper explores a simple model of a light water reactor nuclear fuel rod, which consists of cylindrical pellets of uranium dioxide (UO{sub 2}) fuel sealed within a Zircalloy cladding tube. The tube is initially filled with helium gas, which fills the gap between the pellets and cladding tube. The accurate modeling of heat transfer across the gap between fuel pellets and the protective cladding is essential to understanding fuel performance, including cladding stress and behavior under irradiated conditions, which are factors that affect the lifetime of the fuel. The thermomechanical contact approach developed here is based on the mortar finite element method, where Lagrange multipliers are used to enforce weak continuity constraints at participating interfaces. In this formulation, the heat equation couples to linear mechanics through a thermal expansion term. Lagrange multipliers are used to formulate the continuity constraints for both heat flux and interface traction at contact interfaces.more » The resulting system of nonlinear algebraic equations are cast in residual form for solution of the transient problem. A Jacobian-free Newton Krylov method is used to provide for fully-coupled solution of the coupled thermal contact and heat equations.« less

Authors:
 [1]
  1. Idaho National Laboratory, P.O. Box 1625, Idaho Falls, ID 83415-3840 (United States)
Publication Date:
OSTI Identifier:
21592601
Resource Type:
Journal Article
Journal Name:
Journal of Computational Physics
Additional Journal Information:
Journal Volume: 230; Journal Issue: 17; Other Information: DOI: 10.1016/j.jcp.2011.04.038; PII: S0021-9991(11)00286-5; Copyright (c) 2011 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved.; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 0021-9991
Country of Publication:
United States
Language:
English
Subject:
22 GENERAL STUDIES OF NUCLEAR REACTORS; 11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS; 97 MATHEMATICAL METHODS AND COMPUTING; CLADDING; COMPUTERIZED SIMULATION; CYLINDRICAL CONFIGURATION; EQUATIONS; FINITE ELEMENT METHOD; FUEL PELLETS; GEOMETRY; HEAT; HEAT FLUX; HEAT TRANSFER; HELIUM; MORTARS; NONLINEAR PROBLEMS; NUCLEAR FUELS; PERFORMANCE; REACTOR FUELING; THERMAL EXPANSION; URANIUM DIOXIDE; WATER COOLED REACTORS; WATER MODERATED REACTORS; ACTINIDE COMPOUNDS; CALCULATION METHODS; CHALCOGENIDES; CONFIGURATION; DEPOSITION; ELEMENTS; ENERGY; ENERGY SOURCES; ENERGY TRANSFER; EXPANSION; FLUIDS; FUELS; GASES; MATERIALS; MATHEMATICAL SOLUTIONS; MATHEMATICS; NONMETALS; NUMERICAL SOLUTION; OXIDES; OXYGEN COMPOUNDS; PELLETS; RARE GASES; REACTOR MATERIALS; REACTORS; SIMULATION; SURFACE COATING; URANIUM COMPOUNDS; URANIUM OXIDES

Citation Formats

Hansen, Glen, E-mail: Glen.Hansen@inl.gov. A Jacobian-free Newton Krylov method for mortar-discretized thermomechanical contact problems. United States: N. p., 2011. Web. doi:10.1016/j.jcp.2011.04.038.
Hansen, Glen, E-mail: Glen.Hansen@inl.gov. A Jacobian-free Newton Krylov method for mortar-discretized thermomechanical contact problems. United States. doi:10.1016/j.jcp.2011.04.038.
Hansen, Glen, E-mail: Glen.Hansen@inl.gov. Wed . "A Jacobian-free Newton Krylov method for mortar-discretized thermomechanical contact problems". United States. doi:10.1016/j.jcp.2011.04.038.
@article{osti_21592601,
title = {A Jacobian-free Newton Krylov method for mortar-discretized thermomechanical contact problems},
author = {Hansen, Glen, E-mail: Glen.Hansen@inl.gov},
abstractNote = {Multibody contact problems are common within the field of multiphysics simulation. Applications involving thermomechanical contact scenarios are also quite prevalent. Such problems can be challenging to solve due to the likelihood of thermal expansion affecting contact geometry which, in turn, can change the thermal behavior of the components being analyzed. This paper explores a simple model of a light water reactor nuclear fuel rod, which consists of cylindrical pellets of uranium dioxide (UO{sub 2}) fuel sealed within a Zircalloy cladding tube. The tube is initially filled with helium gas, which fills the gap between the pellets and cladding tube. The accurate modeling of heat transfer across the gap between fuel pellets and the protective cladding is essential to understanding fuel performance, including cladding stress and behavior under irradiated conditions, which are factors that affect the lifetime of the fuel. The thermomechanical contact approach developed here is based on the mortar finite element method, where Lagrange multipliers are used to enforce weak continuity constraints at participating interfaces. In this formulation, the heat equation couples to linear mechanics through a thermal expansion term. Lagrange multipliers are used to formulate the continuity constraints for both heat flux and interface traction at contact interfaces. The resulting system of nonlinear algebraic equations are cast in residual form for solution of the transient problem. A Jacobian-free Newton Krylov method is used to provide for fully-coupled solution of the coupled thermal contact and heat equations.},
doi = {10.1016/j.jcp.2011.04.038},
journal = {Journal of Computational Physics},
issn = {0021-9991},
number = 17,
volume = 230,
place = {United States},
year = {2011},
month = {7}
}