改进了壳管式换热器管板强度计算方法

I. Andreiev
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It is proposed to approximate these dependencies with simple mathematical equations.\nAs 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. 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引用次数: 0

摘要

本文的目的是对乌克兰现行州际标准规定的管壳式换热器管板强度计算进行改进。在标准表的基础上,考虑管-板系统无量纲参数ω对管道的支撑作用Ф1, Ф2, Ф3,以及穿孔板刚度系数对管板侧压力效应系数ηТ的依赖关系,构建了系数变化点阵图并进行了分析。建议用简单的数学方程来近似这些依赖关系。因此,提出用三次回归Ф1 = 0,0422ω3 + 0,2305ω2 - 0,2367ω + 2,0179来描述Ф1 = f1(ω)在ω 0 ~ 3范围内的依赖关系,当ω从3 ~ 11变化时,采用二次回归Ф1 = - 0,0286ω2 + 1,8012ω - 0,6171。在ω从0到0,5变化范围内,由于函数的微小变化,Ф2 = f2(ω)的依赖关系可以用线性方程Ф2 = 0.04ω来描述,当ω从0,5变化到2 -通过三次回归Ф2 = 0,0133ω3 + 0,48ω2 - 0,4033ω + 0,1,当ω从2变化到11 -通过三次回归Ф2 = 0,0046ω3 - 0,1129ω2 + 1,8692ω - 1,8821。在ω从0到0,5的变化范围内,相关性Ф3 = f3(ω)由线性方程Ф3 = 0,38ω描述,当ω从0,5到3变化时,通过三次回归Ф3 = - 0,2296ω3 + 1,3541ω2 - 0,4884ω + 0,1233,当ω从3到11变化时,三次回归Ф3 = - 0,0054ω3 + 0,1060ω2 + 0,7576ω + 1,6129。用三次回归可以近似地表示出ψ0对ηТ的离散表依赖关系,即:ψ0 = - 0,3419ηТ3 + 1,8834ηТ2 - 0,6915ηТ + 0,1153。所得到的公式使得在进行计算时可以不使用标准表,不需要额外插补系数Ф1、Ф2、Ф3和ψ0的中间值,从而简化了计算本身和相应计算机程序的开发。所进行的近似误差的平均值在0% ~ 2.05%之间,表明回归方程与实际值有较高的符合性。利用所提出的Ф1 = f1(ω)、Ф2 = f2(ω)、Ф3 = f3(ω)和ψ0 = f(ηТ)等系数的关系公式,可以简化管壳式换热器管板强度的计算。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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.
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