JP2021014993A - Local thermal stress calculation method of pipeline - Google Patents

Abstract

To provide a local thermal stress calculation method for calculating a local thermal stress on a pipeline with welded lugs in consideration of the pipeline shape, lug shapes, and lug intervals.SOLUTION: A local thermal stress calculation method, which is for calculating a local thermal stress σ on a pipeline 1 with welded lugs 2 at a thermal transient time, calculates the local thermal stress σ using the following formula including a correction coefficient C. σ=C×E×α×ΔT (E: Young's modulus of the pipeline 1; α: the coefficient of thermal expansion of the pipeline 1; ΔT: temperature difference between the pipeline 1 and the lug 2).SELECTED DRAWING: Figure 2

Description

The present invention relates to a local thermal stress calculation method for calculating a local thermal stress generated in a pipe during a thermal transient due to the influence of a lug welded to the pipe.

As illustrated in FIGS. 3 to 6 of Patent Document 1, a plurality of lugs are welded to the pipes laid in the power plant or the like at the contact points with the pipe support structure. Therefore, at the time of thermal transient when the fluid temperature in the pipe changes, the thermal deformation of the pipe is restrained by the lug due to the difference in thermal expansion between the pipe and the lug, and local thermal stress is generated in the pipe.

It is desirable to use the finite element method analysis to calculate this local thermal stress with high accuracy, but if the calculation by the finite element method analysis is always executed, the amount of calculation becomes enormous, so the calculation cost is reduced and the design period is shortened. Therefore, in some places, the local thermal stress σ ₀ is simply calculated using Equation 1.

σ ₀ = E × α × ΔT ・ ・ ・ (Equation 1)
In Equation 1, E is the Young's modulus of the pipe, α is the coefficient of thermal expansion of the pipe, and ΔT is the temperature difference between the pipe and the lag.

Japanese Unexamined Patent Publication No. 2011-64288

It is specified that the shape of the lug to be welded to the pipe is rectangular or cylindrical and the number of lugs to be welded to the pipe is single, so that the local thermal stress of the pipe can be appropriately calculated by using the above formula 1. Limited to conditions.

However, since the shapes of lugs used in actual piping systems are diverse and multiple lugs are often welded to one location, simple local heat that can be used even under such conditions. A stress calculation method is required.

Therefore, an object of the present invention is to provide a method for calculating the local thermal stress of a pipe, which can easily calculate the local thermal stress generated in the pipe based on the lug shape and the number of lugs, which are not covered by the equation 1. ..

In order to solve the above problems, the local thermal stress calculation method of the present invention is a local thermal stress calculation method for calculating the local thermal stress σ generated at the time of thermal transient in a pipe welded with a lug, and includes a correction coefficient C. The local thermal stress σ was calculated by the following formula. σ = C × E × α × ΔT (E: Young's modulus of piping, α: Thermal expansion coefficient of piping, ΔT: Temperature difference between piping and lug)

According to the local thermal stress calculation method of the present invention, even when the lug shape and the number of lugs that are not covered by the equation 1 are adopted, the local thermal stress of the pipe can be simply calculated.

Flowchart of local thermal stress calculation method of one embodiment Sectional view of piping and lug to which the local thermal stress calculation method of one embodiment is applied. Perspective view of the lug of FIG. Schematic diagram of the piping of FIG. Schematic diagram showing the effect of the interval L on stress Schematic diagram showing the effect of lug height H on stress Schematic diagram showing the comparison results of each local thermal stress calculation method Schematic diagram showing the effect of the correction coefficient C

Hereinafter, a method for calculating the local thermal stress according to an embodiment of the present invention will be described with reference to FIGS. 1 to 8. The local thermal stress calculation method of this embodiment is used in a computer such as a personal computer equipped with an arithmetic unit such as a CPU, a main storage device such as a semiconductor memory, an auxiliary storage device such as a hard disk, and hardware such as a communication device. , It is realized by the arithmetic unit executing the program loaded in the main memory while referring to the database recorded in the auxiliary storage device. In the following, such well-known techniques in the computer field. Will be described while omitting as appropriate.

When calculating the local thermal stress of a pipe generated during a thermal transient, if the shape of the lug to be welded to the pipe is rectangular or cylindrical and the number of lugs to be welded is singular, the above equation 1 is used. The local thermal stress of the pipe can be calculated appropriately. However, when the shape of the lug to be welded to the pipe is not rectangular or cylindrical, or when the number of lugs to be welded is multiple, the local thermal stress of the pipe cannot be appropriately calculated even by using Equation 1. Therefore, in this embodiment, by using the following formula 2 instead of the formula 1, the local thermal stress σ of the pipe can be appropriately calculated even when the shape and the number of lugs to be welded to the pipe are various. I made it.

σ = C × σ ₀ ... (Equation 2)
In Equation 2, C is a correction coefficient determined based on Equations 3 to 6 described later, and σ ₀ is a local thermal stress calculated using Equation 1.

First, using the flowchart of FIG. 1, the calculation method of the local thermal stress σ generated in the pipe during the thermal transient according to the present embodiment will be outlined.

First, in step S1, the Young's modulus E of the pipe 1, the coefficient of thermal expansion α of the pipe 1, and the temperature difference ΔT between the pipe 1 and the lug 2 are acquired. Since these are also used in the conventional formula 1 and the acquisition method thereof is well known, detailed description of the acquisition method of Young's modulus E, thermal expansion coefficient α, and temperature difference ΔT will be omitted below. Next, in step S2, the correction coefficient C is determined. Finally, in step S3, the Young's modulus E, the coefficient of thermal expansion α, the temperature difference ΔT acquired in step S1, the correction coefficient C determined in step S2, and the above equation 2 are used to obtain the local thermal stress of the pipe 1. Calculate σ. Hereinafter, the method of determining the correction coefficient C in step S2 and the method of calculating the local thermal stress σ in step S3 will be described in detail in order.
<Method of determining the correction coefficient C in step S2>
FIG. 2 is a cross-sectional view showing an example of the laid state of the pipe 1. The pipe 1 illustrated here is welded with a lug 2a on the right side, a lug 2b on the lower side, a lug 2c on the left side, and a lug 2d on the upper side. Then, by contacting the pipe support structure 3 via these four lugs 2, movement of the pipe 1 in two directions perpendicular to the axis is prevented. In the pipe 1 of FIG. 2, four lugs 2 are attached, but if the movement of the pipe 1 can be prevented, for example, two lugs 2 may be attached.

FIG. 3 is a perspective view illustrating the shape of each lug 2. As shown here, the lug 2 is a U-shaped lug having a height H formed by bending a metal plate having a plate thickness of t _L. The lugs 2a to 2d may all have the same shape, or the plate thickness t _L and height H may be different from each other.

FIG. 4 is a schematic view for explaining various dimensions in the vicinity of the lug 2a, and is a simulated plane representation of the range from the lug 2a in FIG. 2 to the right side of the adjacent lug 2b. In the figure, L _a is the spacing between the ends of the U-shaped lug 2a, the L _ab is the spacing innermost lugs 2a and lugs 2b. In the following, the minimum interval (interval _{Lab in} the example of FIG. 4) is defined as the interval L with respect to the lag 2a.

Further, t _P is the plate thickness of the pipe 1, and t _L is the plate thickness of the lug 2a. In the following, the value calculated by the following equation 3 is defined as the plate thickness ratio τ with respect to the lug 2a.

τ = t _P / t _L ... (Equation 3)
When the height H, the interval L, and the plate thickness ratio τ of the lug 2a are obtained, the correction coefficient C used when calculating the local thermal stress σ in the vicinity of the lug 2a is determined by using these.

As shown in Equation 4 below, the correction coefficient C can be considered to be obtained by multiplying the correction coefficient C _H according to the height _H and the correction coefficient C _L according to the interval L.

C = C _H × C _L ... (Equation 4)
In order to obtain the correction coefficients C _H and C _L , the effects of the height H, the interval L, and the plate thickness ratio τ on the local thermal stress σ were investigated. FIG. 5A is a diagram schematically showing the effect of a change in the interval L on the local thermal stress σ when the height H is constant, and FIG. 5B is a diagram showing the height when the interval L is constant. It is a figure which represented typically the influence which the change of H H has on the local thermal stress σ.

From both figures, it can be seen that the stress ratio tends to decrease as the plate thickness ratio τ increases, and the stress ratio tends to decrease as the interval L increases or the height H increases. The stress ratio here is the ratio of stress when there is an influence of length or height and when there is no influence thereof, and represents the influence of each variable on stress.

For example, the relationship between the distance L and the stress ratio shown in FIG. 5A, the correction coefficient C _L corresponding to the distance L is found can be represented by the following formula 5.

C _L = A × τ ^B ... (Equation 5)
Note that A and B in Equation 5 are variables according to the interval L, and are determined based on, for example, Table 1 below.

Further, from Equations 4 and 5, it can be seen that the correction coefficient C used in Equation 2 can be expressed by the following Equation 6.

C = _CH × A × τ ^B ... (Equation 6)
Here, the correction coefficient C _H is a coefficient corresponding to the height H, and is determined based on, for example, Table 2 below.

Summarizing the above description, the correction coefficient C is determined, for example, based on the following Table 3 according to the combination of the height H and the interval L.

It should be noted that Tables 1 to 3 are merely examples, and the correction coefficient C according to the combination of the height H and the interval L may be determined by another method.
<Calculation method of local thermal stress σ of pipe 1 in step S3>
After calculating the correction coefficient C in step S2, in step S3, the local thermal stress σ according to the local thermal stress evaluation method of this embodiment is calculated based on the following equation 7 in which the above equations 1 to 6 are aggregated. ..

σ = C × E × α × ΔT
= _CH x A x (t _P / t _L ) ^B x E x α x ΔT ... (Equation 7)
In the example of FIG. 6, the local thermal stress σ ₀ obtained by Equation 1 is always smaller than σ _FEM , and the local thermal stress σ obtained by Equation 2 (Equation 7) is always larger than σ _FEM . In this case, the local thermal stress σ ₀ is likely to be smaller than the actually generated local thermal stress. Therefore, if the design is performed on the premise of this local thermal stress σ ₀ , the pipe 1, the lug 2, and the pipe support structure are designed. There is a possibility that problems such as insufficient strength may occur in 3. On the other hand, the local thermal stress σ is considered to be larger than the actually generated local thermal stress. Therefore, if the design is performed on the premise of this local thermal stress σ, the pipe 1, the lug 2, the pipe support structure 3, etc. Sufficient strength can be ensured.

FIG. 7 is a diagram schematically showing the difference in local thermal stress calculated from Equation 1 and Equation 2. Although not shown, the result of the finite element method analysis is located between Equation 1 and Equation 2.

According to the present embodiment described above, it is possible to appropriately calculate the local thermal stress even for a pipe welded with a shape and a number of lugs that are not covered by the equation 1. This eliminates the need for local thermal stress evaluation using the finite element method analysis, and makes it possible to easily calculate the local thermal stress, so that it is possible to reduce the design process and the like.

1 Piping 2, 2a to 2c lugs 3 Piping support structure H Lag height L Lag spacing t _P Piping plate thickness t _L Lag plate thickness

Claims (6)

This is a local thermal stress calculation method that calculates the local thermal stress σ generated during thermal transients in a pipe with welded lugs.
A method for calculating a local thermal stress, which comprises calculating the local thermal stress σ by the following formula including a correction coefficient C.
σ = C × E × α × ΔT
E: Young's modulus of piping, α: Thermal expansion coefficient of piping, ΔT: Temperature difference between piping and lug In the local thermal stress calculation method according to claim 1,
The local thermal stress calculation method, wherein the correction coefficient C is determined according to the ratio of the plate thickness t _{P of the} pipe and the plate thickness t _L of the lug. In the local thermal stress calculation method according to claim 1,
The local thermal stress calculation method, wherein the correction coefficient C is determined according to the height of the lag. In the local thermal stress calculation method according to claim 1,
The local thermal stress calculation method, wherein the correction coefficient C is determined according to the distance between the lag and the adjacent lag. In the local thermal stress calculation method according to claim 1,
A method for calculating a local thermal stress, wherein the correction coefficient C is determined according to the distance between one end and the other end of the lag. In the local thermal stress calculation method according to claim 1,
The local thermal stress calculation method, characterized in that the correction coefficient C is determined by the following formula.
C = _CH × A × (t _P / t _L ) ^B
_CH : Correction coefficient according to lag height, A, B: Variable according to lag interval,
t _P : Piping plate thickness, t _L : Lag plate thickness

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