Improvement of the strength calculation of the tube plate of the shell-tube heat exchanger

The purpose of the article is to improve the strength calculation of the tube plate of the shell-and-tube heat exchanger, which is regulated by the interstate standard in force in Ukraine. On the basis of standard tables, dot plots of the change in coefficients were constructed and analyzed, which take into account the supporting effect of pipes Ф1, Ф2, Ф3 depending on the dimensionless parameter of the board-pipe system ω and the dependence of the stiffness coefficient of the perforated board  on the coefficient of pressure effect on the tube plate from the side of the tube space ηТ. It is proposed to approximate these dependencies with simple mathematical equations. As a result, it was proposed to use the cubic regression Ф1 = 0,0422ω3 + 0,2305ω2 – 0,2367ω + 2,0179 to describe the dependence of Ф1 = f1(ω) in the range of ω from 0 to 3 and when changing ω from 3 to 11, apply quadratic regression Ф1 = – 0,0286ω2 + 1,8012ω – 0,6171. The dependence of Ф2 = f2(ω) in the range of changing ω from 0 to 0,5 due to a slight change in the function can be described by the linear equation Ф2 = 0.04ω, when changing ω from 0,5 to 2 - by the cubic regression Ф2 = 0,0133ω3 + 0,48ω2 – 0,4033ω + 0,1, and when changing ω from 2 to 11 – by cubic regression Ф2 = 0,0046ω3 – 0,1129ω2 + 1,8692ω – 1,8821. The dependence Ф3 = f3(ω) in the range of ω change from 0 to 0,5 is described by the linear equation Ф3 = 0,38ω, when ω changes from 0,5 to 3 – by cubic regression Ф3 = – 0,2296ω3 + 1,3541ω2 – 0,4884ω + 0,1233, and when ω changes from 3 to 11 – cubic regression Ф3 = – 0,0054ω3 + 0,1060ω2 + 0,7576ω + 1,6129. The discrete tabular dependence of ψ0 on ηТ can be approximated by cubic regression ψ0  =  – 0,3419ηТ3 + 1,8834ηТ2 – 0,6915ηТ + 0,1153.    The obtained formulas make it possible to abandon the use of standard tables and additional interpolation of intermediate values of the coefficients Ф1, Ф2, Ф3 and ψ0 when performing calculations, which in turn simplifies both the calculation itself and the development of appropriate computer programs. The average value of the errors of the performed approximations is in the range from 0% to 2.05%, which indicates a high level of coincidence of the regression equations with the actual values. The use of the proposed formulas for the dependences of the coefficients Ф1 = f1(ω), Ф2 = f2(ω), Ф3 = f3(ω) and ψ0 = f(ηТ) makes it possible to simplify the calculation of the tube plate of shell-and-tube heat exchangers for strength.