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Research Papers: Heat Transfer in Manufacturing

Inverse Determination of Eroded Smelter Wall Thickness Variation Using an Elastic Membrane Concept

[+] Author and Article Information
Daniel Baker

P. O. Box 124, Lemont, PA 16851

George S. Dulikravich1

Department of Mechanical and Materials Engineering, Multidisciplinary Analysis, Inverse Design, Robust Optimization and Control (MAIDROC), Florida International University, 10555 West Flagler Street, EC 3474, Miami, FL 33174dulikrav@fiu.edu

Brian H. Dennis

Department of Mechanical and Aerospace Engineering, University of Texas at Arlington, UTA Box 19018, Arlington, TX 76019

Thomas J. Martin

 Pratt & Whitney Engine Company, Turbine Discipline Engineering and Optimization Group, M/S 169-20, 400 Main Street, East Hartford, CT 06108

1

Corresponding author.

J. Heat Transfer 132(5), 052101 (Mar 04, 2010) (8 pages) doi:10.1115/1.4000436 History: Received September 21, 2008; Revised September 17, 2009; Published March 04, 2010; Online March 04, 2010

A novel algorithm has been developed for the nondestructive determination of the shape of the interface between a melt and a refractory material wall in smelter furnaces. This method uses measurements of temperature and heat flux at a number of points on the outer surface of the furnace, and assumes that the inner (guessed) surface of the furnace wall is isothermal. The temperature field is then predicted in the entire furnace wall material by numerically solving a steady state heat conduction equation subject to the measured temperature values on the external surface and the isothermal melt material solidus temperature on the inner surface of the wall. The byproduct of this analysis is the computed heat flux on the external surface. The difference between the measured and the computed heat fluxes on the outer surface of the furnace is then used as a forcing function in an elastic membrane motion concept to determine perturbations to the inner (melt-refractory) surface motion. The inverse determination of the melt-refractory interface shape can be achieved by utilizing this algorithm and any available analysis software for the temperature field in the refractory wall. The initial guess of the inner shape of the wall can be significantly different from the final (unknown) wall shape. The entire wall shape determination procedure requires typically 5–15 temperature field analyses in the furnace wall material.

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Copyright © 2010 by American Society of Mechanical Engineers
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Figures

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Figure 1

Symmetric test geometry: target shape of the inner surface (vertical oval) and the outer surface (circle of radius 2.0 m) of the furnace wall with indication of the locations of eight temperature and heat flux probes

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Figure 2

Asymmetric test geometry: target shape of the inner surface and the outer surface (circle of radius 2.0 m) of the furnace wall with indication of the locations of eight temperature and heat flux probes

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Figure 3

Symmetric case: convergence history of the outer surface heat flux

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Figure 4

Symmetric case: convergence history of the inner surface geometry

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Figure 5

Symmetric case: convergence history of the RMS error of the outer surface heat flux and of the inner surface geometry

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Figure 6

Asymmetric case: convergence history of the outer surface heat flux

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Figure 7

Asymmetric case: convergence history of the inner surface geometry

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Figure 8

Asymmetric case: convergence history of the RMS error of the outer surface heat flux and of the inner surface geometry

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Figure 9

An example of actual (solid line), measured (actual with stochastically added noise at only eight locations on the outer surface of the furnace wall), and interpolated measured heat fluxes (dashed line) for the geometrically symmetric test case

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Figure 10

Initial, target, intermediate, and final shapes of the inner surface of the smelter wall in meridian plane

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Figure 11

Initial configuration, temperature field computed using least-squares finite element method (28) and nonstructured computational grid (29)

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Figure 12

Final configuration, temperature field computed using least-squares finite element method (28), and computational grid (29)

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Figure 13

Convergence history of the inner surface shape error

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Figure 14

Convergence history of the inner surface temperature error

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