Adaptive finite element analysis of transient thermal problems
Abstract
An adaptive finite element methodology for general heat transfer problems is proposed. The proposed error estimator takes into account the coupling effects of the dependent variables (e.g. velocity, pressure, temperature) on the discretization error and, consequently, on the adaptive meshes. The error estimator is also capable of accounting for the effect of convective boundary conditions on the discretization error. An adaptive strategy that incorporates the effect of error behavior for transient problems is also presented. This strategy avoids unnecessary remeshing, i.e., remeshing when the error is decreasing with time at a reasonable rate. The methodology was applied to both diffusion-type and convection-type problems. Such problems are very common in the processing of food and agricultural materials. Applications include heat conduction in solids, air flow inside grain dryers, and thermal processing operations such as sterilization, pasteurization and microwave heating. The desired accuracy level was attained in all the cases studied. Refined meshes reflected the physical characteristics of the problems, i.e., refinements were concentrated in the same regions where high gradients were located. There was very good agreement between simulation and experimental results, and this substantiates the reliability of the proposed methodology. Also, comparison between results from the proposed adaptive methodology and results from a conventional finite element approach demonstrated the efficiency of the method. Higher accuracy was obtained with quadratic triangular elements compared to linear triangular elements. An averaging procedure was also proposed as a substitute for the smoothing procedure used to evaluate gradients. Very similar results were obtained with both procedures. However, the averaging procedure was shown to be much less computationally expensive than smoothing, leading to a substantial reduction in CPU time and thus resulting in a more efficient approach.
Degree
Ph.D.
Advisors
Haghighi, Purdue University.
Subject Area
Agricultural engineering|Mechanical engineering|Food science
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