A Sequential Inverse Heat Conduction Problem in OpenFOAM

Abstract

The solution of the inverse heat conduction problem (IHCP) is commonly found with thesequential algorithm known as the function specification method with explicit updating formulas andsensitivity coefficients of heat flux. This paper presents a different approach namely a direct mathemat-ical optimization of minimizing the least squares norm between experimental data and simulation. ACFD open-source code OpenFOAM is used together with NLOPT and DLIB optimization libraries. Toguarantee credibility of the simulation tool developed herein, real experimental data is used from spraycooling of a fast-moving hot steel plate. As the IHCP is inherently an ill-posed problem, the proposedsequential algorithm is stabilized using future time stepping and thereof the optimal number is explained.An assumption about the profile of thermal boundary condition during future steps must be made. Itis shown that assuming a linear change of the heat transfer coefficient during each sequence of futuretime steps yields more accurate results than setting a constant value. For the problem size consideredwith less than 10k cells, the preconditioned conjugate gradient (FDIC) linear solver converges fasterthan the multigrid solver (GAMG). However, the latter performs better as the accuracy is concerned.Concerning the best choice of minimizer, the BOBYQA algorithm (quadratic approximation) is foundsuperior to other methods. The proposed IHCP solver is compared with the well-established one.The solution of the inverse heat conduction problem (IHCP) is commonly found with thesequential algorithm known as the function specification method with explicit updating formulas andsensitivity coefficients of heat flux. This paper presents a different approach namely a direct mathemat-ical optimization of minimizing the least squares norm between experimental data and simulation. ACFD open-source code OpenFOAM is used together with NLOPT and DLIB optimization libraries. Toguarantee credibility of the simulation tool developed herein, real experimental data is used from spraycooling of a fast-moving hot steel plate. As the IHCP is inherently an ill-posed problem, the proposedsequential algorithm is stabilized using future time stepping and thereof the optimal number is explained.An assumption about the profile of thermal boundary condition during future steps must be made. Itis shown that assuming a linear change of the heat transfer coefficient during each sequence of futuretime steps yields more accurate results than setting a constant value. For the problem size consideredwith less than 10k cells, the preconditioned conjugate gradient (FDIC) linear solver converges fasterthan the multigrid solver (GAMG). However, the latter performs better as the accuracy is concerned.Concerning the best choice of minimizer, the BOBYQA algorithm (quadratic approximation) is foundsuperior to other methods. The proposed IHCP solver is compared with the well-established one.