PSI - Issue 50

S.V. Maslov et al. / Procedia Structural Integrity 50 (2023) 178–183 Author name / Structural Integrity Procedia 00 (2019) 000 – 000

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In the first stage, the problem of constructing the internal temperature of the horizontal section of the 2nd circuit pipeline (at the IHE outlet) is solved. This can be carried out by solving the inverse problem of thermoelasticity, which uses the results of stress measurements on the outer surface of the pipeline to construct the desired temperature function. The stresses measured on the outer surface at the time interval [0,  N ] under consideration are represented as:

k

0     i i

T

1    n

n i 

(1)

where n  is the stresses on the outer surface of the cylinder at the end of the division of the time interval with the number " n ", 1 i   is the matrix of the transformation operator, n i T   is the unknown linear temperature rise in the division of the time interval with the number ( n – i ). The elements of the matrix operator 1 i   are the values of stresses at the end of the time interval 1 i   and caused by a single linear increase in the temperature of the inner surface in the time interval ( n-i-1, n-i ). The physical meaning of the matrix operator implies its invariance regarding the start time n  , each element of the matrix is determined only by the difference between the numbers " i ". Calculation of matrix elements is performed by numerical calculation; the initial data are the known physical and mechanical characteristics of materials and geometric parameters of the structure. In formula (1), it is meant that the influence of the linear temperature step on the stresses extends only to a certain number of steps, denoted by the index " k ". This approach to the problem uses the principle of summing up the temperature fields caused by various temperature influences from the inner surface. The method of constructing the inner surface temperature change function and the discretization order of the stress change function on the outer surface are shown in Fig. 3. When the initial and final temperatures of the coolant are known, the function is selected, using which the calculated temperature values at the intermediate points of the time interval division are closest to the measured values; for this purpose, the method of least squares is used.

(a)

(b)

Fig. 3. Modeling the process of loading a structure: а) constructing the inner surface temperature change function; б) – discretization order of the stress change function on the outer surface

5. Results and summary As a result of bench tests, it was found that the developed means of experimental control of the internal surfaces of nuclear reactors with liquid metal coolant were operable in the medium of liquid sodium at temperatures up to