Inverse Determination of Smelter Wall Erosion Shapes Using a Fourier Series Method

An algorithm has been developed for the non-destructive determination of local thickness of the refractory material walls in smelter furnaces. This method uses measurements of temperature and heat flux at a number of points on the outer (fixed) 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 furnace wall subject to the measured temperature values on the external surface and the isothermal solidus temperature on the inner surface of the wall. The shape determination method then uses the difference between the measured and the computed heat fluxes on the outer surface of the furnace as a forcing function in an elastic membrane concept for the determination of the inner (melt refractory) surface shape. The initial guess of the wall inner shape can be significantly different from the final (unknown) wall shape. The entire wall shape determination procedure requires typically 5-15 temperature field analysis in the furnace wall material.