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Optimization of thermal processes using an Eulerian formulation and application in laser surface hardening
Author(s) -
Rajadhyaksha S. M.,
Michaleris P.
Publication year - 2000
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/(sici)1097-0207(20000420)47:11<1807::aid-nme819>3.0.co;2-d
Subject(s) - mechanics , heat transfer , eulerian path , heat flux , petrov–galerkin method , galerkin method , finite element method , materials science , thermal , thermodynamics , mathematics , physics , lagrangian
A systematic design approach has been developed for thermal processes combining the finite element method, design sensitivity analysis and optimization. Conductive heat transfer is solved in an Eulerian formulation, where the heat flux is fixed in space and the material flows through a control volume. For constant velocity and heat flux distribution, the Eulerian formulation reduces to a steady‐state problem, whereas the Lagrangian formulation remains transient. The reduction to a steady‐state problem drastically improves the computational efficiency. Streamline Upwinding Petrov–Galerkin stabilization is employed to suppress the spurious oscillations. Design sensitivities of the temperature field are computed using both the direct differentiation and the adjoint methods. The systematic approach is applied in optimizing the laser surfacing process, where a moving laser beam heats the surface of a plate, and hardening is achieved by rapid cooling due to the heat transfer below the surface. The optimization objective is to maximize the rate of surface hardening. Constraints are introduced on the computed temperature and temperature rate fields to ensure that phase transformations are activated and that melting does not occur. Copyright © 2000 John Wiley & Sons, Ltd.