PSI - Issue 5

S. Sahnoun et al. / Procedia Structural Integrity 5 (2017) 1267–1274 A. aifi et al / Structural Integrity Procedia 00 (2017) 0 0 – 000

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Fig.5: the variation of temperature along the AB axis for three pipes that have different diameters.

We note the curves of the variation in absolute contrast along the axis AB are also superimposed; so the dimensions of the pipe have practically no influence on the variation in absolute contrast.

3. Regression polynomial to estimate the thickness of the scale from the maximum absolute contrast measured on the heated surface. After a preliminary study the effects of the geometric parameters (thickness of scale, thickness and diameter of the pipe), we searched a mathematical model which allows us to estimate the thickness of the scale from the maximum absolute contrast measured on the heated surface of the inspected steel pipe. We worked under the same conditions with a pipe of diameter 10 cm and a thickness equal to 2 cm. The heating flux density is 100 W / m 2 and we have shown in the figure below the variation of maximum absolute contrast (1) as a function of the scale thickness. .

Fig 6: Variation of maximum absolute contrast as a function of tartar thickness

The polynomial regression allows us to adjust a polynomial on the series of points obtained, in order to describe them by an empirical law that is easy to exploit. We have used a program on MATLAB which allowed us to propose the model (1) to estimate the thickness of limestone in a steel pipe: To test the model, we have superimposed the results obtained by the simulation (figure 7) and the results obtained by the model proposed in the relation (1): 2 . 0.0002 - 0.0049. 0.0085 m m C C y   (2)