CN110619141B - Calculation method for tube plate and tube bundle of floating head heat exchanger - Google Patents

Calculation method for tube plate and tube bundle of floating head heat exchanger Download PDF

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CN110619141B
CN110619141B CN201910673358.3A CN201910673358A CN110619141B CN 110619141 B CN110619141 B CN 110619141B CN 201910673358 A CN201910673358 A CN 201910673358A CN 110619141 B CN110619141 B CN 110619141B
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tube plate
sigma
end tube
floating
plate
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CN110619141A (en
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朱国栋
谢铁军
谢国山
徐峰
史进
钱才富
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China Special Equipment Inspection and Research Institute
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    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F17/00—Digital computing or data processing equipment or methods, specially adapted for specific functions
    • G06F17/10—Complex mathematical operations
    • G06F17/11—Complex mathematical operations for solving equations, e.g. nonlinear equations, general mathematical optimization problems
    • G06F17/12—Simultaneous equations, e.g. systems of linear equations
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F17/00—Digital computing or data processing equipment or methods, specially adapted for specific functions
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    • G06F17/15—Correlation function computation including computation of convolution operations
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F17/00—Digital computing or data processing equipment or methods, specially adapted for specific functions
    • G06F17/10—Complex mathematical operations
    • G06F17/16—Matrix or vector computation, e.g. matrix-matrix or matrix-vector multiplication, matrix factorization

Abstract

The invention provides a method for calculating tube plates and tube bundles of a floating head heat exchanger, which comprises the following steps: s1, respectively arranging materials of a fixed end tube plate and a floating end tube plate; s2, respectively setting the thickness and the diameter of the fixed end tube plate and the floating end tube plate; s3, calculating the corresponding bending stress value sigma of the fixed end tube platepBending stress value corresponding to floating end pipe plate
Figure DDA0003153251560000011
S4, comparing sigma respectivelypAnd [ sigma ]1]、
Figure DDA0003153251560000012
And [ sigma ]2]. S5, calculating axial stress sigma of heat exchange tubet. The method for calculating the tube plate and the tube bundle of the floating-head heat exchanger can select the materials of the fixed end tube plate and the floating end tube plate, calculate the stress on the upper surface and the lower surface of the fixed end tube plate and the floating end tube plate and further determine the thickness of the tube plates.

Description

Calculation method for tube plate and tube bundle of floating head heat exchanger
Technical Field
The invention relates to the technical field of shell-and-tube heat exchangers, in particular to a method for calculating tube plates and tube bundles of a floating head heat exchanger.
Background
The shell-and-tube heat exchanger is typically a pressure vessel, accounting for about 30% of petrochemical plant equipment. The shell-and-tube heat exchanger is divided into a U-shaped tube heat exchanger, a fixed tube plate heat exchanger and a floating head heat exchanger, wherein the floating head heat exchanger is mainly applied to the conditions of high temperature difference and easy scaling of internal media.
The floating head heat exchanger main elements comprise: the tube plate system is connected with the shell side cylinder body only through the fixed end tube plate, and the floating tube plate is in a free state in the axial direction of the heat exchanger, so that the temperature difference stress of the tube plate system and the shell side cylinder body can be released. The main heat exchange elements of the floating head heat exchanger comprise a fixed end tube plate, a floating end tube plate and a tube bundle, and are key elements for design and calculation.
However, in the prior art, the analytical solution formula is a main calculation means in formula calculation methods of various countries due to high calculation precision. The existing formula calculation requires that the materials and the thicknesses of the fixed end tube plate and the floating end tube plate are the same, so that the application range of the floating head heat exchanger is too small. The invention provides a calculation method for a floating head heat exchanger with an asymmetric tube plate structure based on an analytical method, which can calculate the stress of tube plates at two sides and a middle tube bundle and verifies that the asymmetric tube plate structure has good calculation accuracy by using a finite element case.
Disclosure of Invention
In order to solve the technical problems, a calculation method for checking and calculating the floating head heat exchanger tube plate and the tube bundle with different thicknesses, materials and diameters of the fixed end tube plate and the floating end tube plate is provided.
A calculation method for tube plates and tube bundles of a floating head heat exchanger comprises the following steps:
s1, respectively selecting materials of a fixed end tube plate and a floating end tube plate of the floating head heat exchanger according to the medium condition, and determining allowable stress of the fixed end tube plateValue [ sigma ]1]Allowable stress value [ sigma ] of floating end tube plate2]Wherein, the materials of the fixed end tube plate and the floating end tube plate can be the same or different;
s2, setting the thickness of the fixed end tube plate of the floating head heat exchanger to be delta1And diameter, thickness δ of floating end tube sheet2And the diameter is used for calculating the radial or circumferential bending moment M (x) suffered by the fixed end tube plate and the radial or circumferential bending moment M suffered by the floating end tube platef1(x) Wherein the thickness and the diameter of the fixed end pipe plate and the thickness and the diameter of the floating end pipe plate can be the same or different;
s3, mixing M (x) and M obtained in S2f1(x) Respectively carry into stress equation
Figure GDA0002278199270000021
In the above method, the respective bending stress values σ on the upper and lower surfaces of the fixed-end tube sheet are calculated under the condition of setting the thickness of the tube sheetpCorresponding bending stress values on the upper and lower surfaces of the floating end tube plate
Figure GDA0002278199270000022
And axial stress of each heat exchange tube;
wherein μ is a bending reduction coefficient;
s4, comparing sigma respectivelypAnd [ sigma ]1]、
Figure GDA0002278199270000023
And [ sigma ]2]；
If σpGreater than 1.5[ sigma ]1]Or
Figure GDA0002278199270000024
Greater than 1.5[ sigma ]2]Then steps S2 and S3 are repeated, increasing δ1Or delta2Or replacing the material of the fixed end tube plate or the material of the floating end tube plate until sigmapLess than 1.5[ sigma ]1]And is
Figure GDA0002278199270000025
Less than 1.5[ sigma ]2]；
If σpLess than 1.5[ sigma ]]And is
Figure GDA0002278199270000026
Less than 1.5[ sigma ]2]And the tube plate meets the design requirements.
A plurality of heat exchange tubes are arranged between the fixed tube plate and the floating tube plate, and after the step S4, the method further comprises:
s5, determining the material of the heat exchange tube, and determining the allowable stress value [ sigma ] of the heat exchange tube according to the material and the supporting structure of the heat exchange tubet]And axial critical pressure stress sigma of heat exchange tubecr；
Calculating the axial stress sigma of each heat exchange tubetComparing σtAnd [ sigma ]t]And σcr；
At σt>When 0, when σt<[σt]The design requirements are met;
at σt<0, when σt|<σcrAnd the design requirements are met.
Step S2 further includes: respectively calculating the radial bending moment M borne by the fixed end tube plater(x) And circumferential bending moment Mθ(x) Radial bending moment born by floating end tube plate
Figure GDA0002278199270000031
And circumferential bending moment
Figure GDA0002278199270000032
Step S3 further includes: according to Mr(x)、Mθ(x)、
Figure GDA0002278199270000033
And
Figure GDA0002278199270000034
respectively calculating the radial bending stress sigma of the fixed end tube plateriCircumferential bending stress sigma of fixed end tube plateθiRadial bending stress of floating end tube sheet
Figure GDA0002278199270000035
And circumferential bending stress of floating end tube sheet
Figure GDA0002278199270000036
Step S4 also includes thatriAnd σθiAnd [ sigma ]1]And
Figure GDA0002278199270000037
and
Figure GDA0002278199270000038
and [ sigma ]2]Respectively, and determining the thickness delta of the fixed tube plate1And the thickness delta of the floating tube plate2Whether the requirements are met.
The step S2 further includes the steps of: calculating the axial displacement relation of the heat exchange tube by using the following formula:
displacement at the fixed end
Figure GDA0002278199270000039
Displacement at floating end
Figure GDA00022781992700000310
And determining the relationship between the bending moment and the displacement of the tube plate according to the following formula:
fixing a tube plate:
Figure GDA0002278199270000041
Figure GDA0002278199270000042
a floating end tube plate:
Figure GDA0002278199270000043
Figure GDA0002278199270000044
wherein, C1、C2、C4Constant, ber (x), bei (x) are Thomson functions, D is the bending stiffness of the fixed end tube sheet, Df1Bending rigidity of the floating end tube plate, eta is the weakening coefficient of the bending rigidity of the tube plate opening area, f1(x)、f2(x)、f3(x)、f4(x) Is an expression taking x as variable, v is the Poisson's ratio of the tube sheet material, MrRadial bending moment M of fixed end tube plateθIs the circumferential bending moment of the fixed end tube plate,
Figure GDA0002278199270000045
radial bending moment of the floating end tube plate,
Figure GDA0002278199270000046
The circumferential bending moment of the floating end tube plate is shown, and k is a dimensionless parameter.
In step S2, the radial bending moment M experienced by the fixed tube sheet is calculated as followsr(x) And circumferential bending moment Mθ(x) Radial bending moment borne by the floating tube plate
Figure GDA0002278199270000047
And circumferential bending moment
Figure GDA0002278199270000048
S301, according to an equation set:
Figure GDA0002278199270000049
Figure GDA00022781992700000410
Figure GDA00022781992700000411
Figure GDA0002278199270000051
Figure GDA0002278199270000052
Figure GDA0002278199270000053
Figure GDA0002278199270000054
a seven-element linear matrix equation set is established according to the following formula:
Figure GDA0002278199270000055
calculating an unknown quantity matrix according to the equation set:
Figure GDA0002278199270000056
wherein j is 1,2.. 7;
wherein P is the pressure of the current calculation working condition, RtIs one half of Dt, f1(K)、f2(K) For expression with K as variable, MRFor fixing the radial bending moment M at the periphery of the tube laying region at the periphery of the tube platetIn order to fix the radial bending moment at the periphery of the pipe distribution area at the center of the pipe plate,
Figure GDA0002278199270000057
for the periphery of the floating tube plateRadial bending moment at the periphery of the pipe distribution area,
Figure GDA0002278199270000058
Radial bending moment for the central tube laying area of the floating tube plate, KtR、Ktt、Ktp、KtV、KRR、KRp、Kf、KRt、KRVIn order to fix the flexibility coefficient of the tube-not-laid region at the periphery of the tube plate,
Figure GDA0002278199270000059
the flexibility coefficient of the non-tube distribution area at the periphery of the floating tube plate is rhot＝RtR is the ratio of the equivalent circle radius of the tube area of the fixed end tube plate to the support radius of the tube plate, R is the support radius of the fixed end tube platef1To support the radius for the floating end tube sheet,
Figure GDA0002278199270000061
the ratio of the equivalent circle radius of the floating end tube plate distribution area to the tube plate support radius;
s302, substituting the result obtained in the S301 into the following equation to respectively calculate the bending moment of each position in the fixed end pipe plate distribution area and the bending moment of each position in the floating end pipe plate distribution area:
fixing end:
Figure GDA0002278199270000062
Figure GDA0002278199270000063
calculating Mr(x) And Mθ(x)；
Floating end:
Figure GDA0002278199270000064
Figure GDA0002278199270000065
computing
Figure GDA0002278199270000066
And
Figure GDA0002278199270000067
step S5 further includes: the unknown quantity C is obtained in step S3011,C2Substituting into the calculation formula of the stress of the heat exchange tube
Figure GDA0002278199270000068
In obtaining the stress sigma of each heat exchange tubet。
The method for calculating the tube plate and the tube bundle of the floating head heat exchanger can respectively select the materials, the thicknesses and the diameters of the fixed end tube plate and the floating end tube plate, and determine the tube plate thickness according to the stress level of the fixed end tube plate and the floating end tube plate and the stress level of the heat exchange tube, so that the materials of the fixed end tube plate and the floating end tube plate can be different, the thicknesses and the diameters can be different, and the application range of the floating head heat exchanger is enlarged.
Drawings
FIG. 1 is a schematic structural diagram of a floating head heat exchanger in the prior art;
FIG. 2 is a floating head heat exchanger mechanical model symbol;
FIG. 3 is a graph comparing tube sheet stress at various locations at shell side pressure;
FIG. 4 is a graph comparing stress at various locations of tube sheet stress at tube side pressure;
FIG. 5 is a graph comparing axial stress of heat exchange tubes at tube side and shell side pressures;
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention will be described in further detail with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention.
When the floating head heat exchanger is designed, the calculation of the tube plate strength and the tube bundle stress is a calculation project which is required to be carried out by the heat exchanger, and the formula calculation in the prior art is a main design means. In the existing formula calculation, the thickness of the fixed end tube plate and the floating end tube plate is determined on the premise that the materials and the thicknesses of the fixed end tube plate and the floating end tube plate are the same, so that the problem that the application range of the floating-head heat exchanger is too small is caused. For the asymmetric construction of the fixed and floating end tube plates, no simple and precise solution has been found.
Therefore, the invention provides a calculation method for tube plates and tube bundles of a floating head heat exchanger, which guarantees calculation accuracy based on plate shell theory analysis, solves unknowns by using a seven-element linear equation set, and is convenient and quick. The method comprises the following steps:
s1, respectively selecting materials of a fixed end tube plate and a floating end tube plate of the floating head heat exchanger according to the medium condition, and determining allowable stress value [ sigma ] of the fixed end tube plate1]And allowable stress value [ sigma ] of floating tube plate2]；
S2, setting the thickness of the fixed end tube plate of the floating head heat exchanger to be delta1And diameter, thickness δ of floating end tube sheet2And the diameter is used for calculating the radial or circumferential bending moment M (x) suffered by the fixed end tube plate and the radial or circumferential bending moment M suffered by the floating end tube platef1(x)；
S3, mixing M (x) and M obtained in S2f1(x) Respectively carry into stress equation
Figure GDA0002278199270000081
In the above method, the respective bending stress values σ on the upper and lower surfaces of the fixed-end tube sheet are calculated under the condition of setting the thickness of the tube sheetpCorresponding bending stress values on the upper and lower surfaces of the floating end tube plate
Figure GDA0002278199270000082
Wherein μ is a bending reduction coefficient;
s4, comparing sigma respectivelypAnd [ sigma ]1]、
Figure GDA0002278199270000083
And [ sigma ]2]Judging the strength of the tube plate;
if σpGreater than 1.5[ sigma ]1]Or
Figure GDA0002278199270000084
Greater than 1.5[ sigma ]2]Then steps S2 and S3 are repeated, increasing δ1Or delta2Or replacing the material of the fixed end tube plate or the material of the floating end tube plate until sigmapLess than 1.5[ sigma ]1]And is
Figure GDA0002278199270000085
Less than 1.5[ sigma ]2]；
If σpLess than 1.5[ sigma ]1]And is
Figure GDA0002278199270000086
Less than 1.5[ sigma ]2]And the tube plate meets the design requirements.
A plurality of heat exchange tubes are arranged between the fixed tube plate and the floating tube plate, and after the step S4, the method further comprises:
s5, determining the material of the heat exchange tube, and determining the allowable stress value [ sigma ] of the heat exchange tube according to the material of the heat exchange tubet]And axial critical pressure stress sigma of heat exchange tubecr；
Calculating the axial stress sigma of each heat exchange tubetTaking the maximum positive value and the minimum negative value to respectively compare sigmatAnd [ sigma ]t]And σcrJudging the strength and stability;
at σt>When 0, when σt<[σt]The design requirements are met, and if the design requirements are not met, structural parameters or materials are adjusted, wherein the structural parameters or materials comprise the adjustment of the thickness of the fixed end pipe plate or the adjustment of the thickness of the floating end pipe plate;
if σt<0, needs to satisfy | σt|<σcrIf not, adjusting structural parameters or materials, including adjusting the thickness of the fixed end tube plate or the floating end tube plate or adjusting the distance between the baffle plates, and the like;
when the above condition σ is satisfiedt<[σt]Or satisfy | σ |t|<σcrAnd satisfaction of tubesheet design in S4And determining the thickness of the fixed end tube plate and the thickness of the floating end tube plate as the final tube plate thickness and determining the distance between the heat exchange tube and the baffle plate as the final specification and the support structure of the heat exchange tube.
More specifically:
step S2 further includes: respectively calculating the radial bending moment M borne by the fixed end tube plater(x) And circumferential bending moment Mθ(x) Radial bending moment born by floating end tube plate
Figure GDA0002278199270000091
And circumferential bending moment
Figure GDA0002278199270000092
Step S3 further includes: according to Mr(x)、Mθ(x)、
Figure GDA0002278199270000093
And
Figure GDA0002278199270000094
respectively calculating the radial bending stress sigma of the fixed end tube plateriCircumferential bending stress sigma of fixed end tube plateθiRadial bending stress of floating end tube sheet
Figure GDA0002278199270000095
And circumferential bending stress of floating end tube sheet
Figure GDA0002278199270000096
Step S4 also includes thatriAnd σ θiAnd [ sigma ]1]And
Figure GDA0002278199270000097
and
Figure GDA0002278199270000098
and [ sigma ]2]Respectively, and determining the thickness delta of the fixed tube plate1And the thickness delta of the floating tube plate2Whether the requirements are met.
The step S2 further includes the steps of: calculating the axial displacement relation of the heat exchange tube by using the following formula:
displacement of fixed end
Figure GDA0002278199270000099
Displacement of floating end
Figure GDA00022781992700000910
And determining the relationship between the bending moment and the displacement of the tube plate according to the following formula:
fixing a tube plate:
Figure GDA00022781992700000911
Figure GDA00022781992700000912
a floating end tube plate:
Figure GDA00022781992700000913
Figure GDA0002278199270000101
description of the symbols:
C1、C2、C4is an unknown constant;
ber (x), bei (x) are thomson functions;
d is the bending rigidity of the fixed end tube plate;
Df1bending rigidity of the floating end tube plate;
eta is the weakening coefficient of bending rigidity of the opening area of the tube plate;
f1(x)、f2(x)、f3(x)、f4(x) Is an expression with x as a variable;
ν is the poisson ratio of the tube sheet material;
Mrradial bending moment of the fixed end tube plate;
Mθthe circumferential bending moment is the circumferential bending moment of the fixed end tube plate;
Figure GDA0002278199270000102
the radial bending moment of the floating end tube plate is adopted;
Figure GDA0002278199270000103
the circumferential bending moment of the floating end tube plate is adopted;
k is a dimensionless parameter.
In step S2, the radial bending moment M experienced by the fixed tube sheet is calculated as followsr(x) And circumferential bending moment Mθ(x) Radial bending moment borne by the floating tube plate
Figure GDA0002278199270000104
And circumferential bending moment
Figure GDA0002278199270000105
S301, according to an equation set:
Figure GDA0002278199270000106
Figure GDA0002278199270000107
Figure GDA0002278199270000108
Figure GDA0002278199270000111
Figure GDA0002278199270000112
Figure GDA0002278199270000113
Figure GDA0002278199270000114
a seven-element linear matrix equation set is established according to the following formula:
Figure GDA0002278199270000115
calculating an unknown quantity matrix according to the equation set:
Figure GDA0002278199270000116
wherein j is 1,2.. 7;
description of the symbols:
p is the pressure of the current calculation working condition;
Rtis one half of Dt;
f1(K)、f2(K) is an expression with K as a variable;
MRradial bending moment at the periphery of a pipe laying-free area at the periphery of the fixed pipe plate;
Mtradial bending moment at the periphery of the tube distribution area at the center of the fixed tube plate;
Figure GDA0002278199270000117
radial bending moment at the periphery of the pipe laying-free area at the periphery of the floating pipe plate;
Figure GDA0002278199270000118
radial bending moment at the periphery of the tube distribution area at the center of the floating tube plate;
KtR、Ktt、Ktp、KtV、KRR、KRp、Kf、KRt、KRVthe flexibility coefficient of the non-tube distribution area at the periphery of the fixed tube plate;
Figure GDA0002278199270000121
the flexibility coefficient of the peripheral non-pipe distribution area of the floating pipe plate;
r is the support radius of the fixed end tube plate, rhot＝Rtthe/R is the ratio of the equivalent circle radius of the tube plate area of the fixed end tube plate to the support radius of the tube plate;
Rf1to support the radius for the floating end tube sheet,
Figure GDA0002278199270000122
the ratio of the equivalent circle radius of the floating end tube plate distribution area to the tube plate support radius;
s302, substituting the result obtained in the step S301 into the following equation to respectively calculate the bending moment of each position in the fixed end pipe plate distribution area and the bending moment of each position in the floating end pipe plate distribution area:
fixing end:
Figure GDA0002278199270000123
Figure GDA0002278199270000124
calculating Mr(x) And Mθ(x)；
Floating end:
Figure GDA0002278199270000125
Figure GDA0002278199270000126
computing
Figure GDA0002278199270000127
And
Figure GDA0002278199270000128
step S5 further includes: substituting the unknowns C1 and C C2. obtained in the step S301 into a heat exchange tube stress calculation formula
Figure GDA0002278199270000129
In obtaining the stress sigma of each heat exchange tubet。
FIGS. 3 to 5 are graphs comparing the tube sheet thickness obtained by the determination method of the present invention with the results of finite element calculation, in which DBF represents the calculation method of the present invention, DBA represents the results of finite element calculation, and other symbols are shown in the symbols. 3-5 show that the calculation results of the present invention have better conformity with finite element calculation. By using the method, the thickness of the tube plate needs to be thinner, so that the cost can be saved.
The method for calculating the tube plate and the tube bundle of the floating head heat exchanger can respectively select the materials, the thicknesses and the diameters of the fixed end tube plate and the floating end tube plate, and determine the tube plate thickness according to the stress level of the fixed end tube plate and the floating end tube plate and the stress level of the heat exchange tube, so that the materials of the fixed end tube plate and the floating end tube plate can be different, the thicknesses and the diameters can be different, the application range of the floating head heat exchanger is enlarged, and the method has better conformity with the numerical calculation result and has better calculation precision through numerical calculation comparison.
The above-mentioned embodiments only express several embodiments of the present invention, and the description thereof is more specific and detailed, but not construed as limiting the scope of the present invention. It should be noted that, for a person skilled in the art, several variations and modifications can be made without departing from the inventive concept, which falls within the scope of the present invention. Therefore, the protection scope of the present patent shall be subject to the appended claims.

Claims (5)

1. A method for calculating tube plates and tube bundles of a floating head heat exchanger is characterized by comprising the following steps: the method comprises the following steps:
s1, respectively selecting materials of a fixed end tube plate and a floating end tube plate of the floating head heat exchanger according to the medium condition, and determining allowable stress value [ sigma ] of the fixed end tube plate1]Allowable stress value [ sigma ] of floating end tube plate2]；
S2, setting the thickness of the fixed end tube plate of the floating head heat exchanger to be delta1And diameter, thickness δ of floating end tube sheet2And the diameter is used for respectively calculating the radial bending moment M born by the fixed end tube plater(x) And circumferential bending moment Mθ(x) Radial bending moment born by floating end tube plate
Figure FDA0003183919160000011
And circumferential bending moment
Figure FDA0003183919160000012
S3, mixing M (x) and M obtained in S2f1(x) Respectively carry into stress equation
Figure FDA0003183919160000013
In the above method, the respective bending stress values σ on the upper and lower surfaces of the fixed-end tube sheet are calculated under the condition of setting the thickness of the tube sheetpCorresponding bending stress values on the upper and lower surfaces of the floating end tube plate
Figure FDA0003183919160000014
Wherein μ is a bending reduction coefficient;
s4, comparing sigma respectivelypAnd [ sigma ]1]、
Figure FDA0003183919160000015
And [ sigma ]2]；
If σpGreater than 1.5[ sigma ]1]Or
Figure FDA0003183919160000016
Greater than 1.5[ sigma ]2]Then steps S2 and S3 are repeated, increasing δ1Or delta2Or replacing the material of the fixed end tube plate or the material of the floating end tube plate until sigmapLess than or equal to 1.5[ sigma ]1]And is
Figure FDA0003183919160000017
Less than or equal to 1.5[ sigma ]2]；
If σpLess than or equal to 1.5[ sigma ]1]And is
Figure FDA0003183919160000018
Less than or equal to 1.5[ sigma ]2]The tube plate meets the design requirements;
a plurality of heat exchange tubes are arranged between the fixed end tube plate and the floating end tube plate, and the method further comprises the following steps after the step S4:
s5, determining the material of the heat exchange tube, and determining the allowable stress value [ sigma ] of the heat exchange tube according to the material of the heat exchange tubet]And axial critical pressure stress sigma of heat exchange tubecr；
Calculating the axial stress sigma of each heat exchange tubetAnd comparing σtAnd [ sigma ]t]And σcr；
At σtWhen > 0, when σt＜[σt]The design requirements are met;
at σt< 0, when | σt|＜σcrThe design requirements are met;
the step S2 further includes the steps of: calculating the axial displacement relation of the heat exchange tube by using the following formula:
displacement at the fixed end:
Figure FDA0003183919160000021
displacement at the floating end:
Figure FDA0003183919160000022
and determining the relationship between the bending moment and the displacement of the tube plate according to the following formula:
fixing a tube plate:
Figure FDA0003183919160000023
Figure FDA0003183919160000024
a floating end tube plate:
Figure FDA0003183919160000025
Figure FDA0003183919160000026
wherein C1, C2, C3 and C4 are constants, ber (x), bei (x) are Thomson functions, D is bending rigidity of a fixed end tube plate, and D isf1Bending rigidity of the floating end tube plate, eta is the weakening coefficient of the bending rigidity of the tube plate opening area, f1(x)、f2(x)、f3(x)、f4(x) Is an expression taking x as variable, v is the Poisson's ratio of the tube sheet material, MrRadial bending moment M of fixed end tube plateθIs the circumferential bending moment of the fixed end tube plate,
Figure FDA0003183919160000031
radial bending moment of the floating end tube plate,
Figure FDA0003183919160000032
The circumferential bending moment of the floating end tube plate is shown, and k is a dimensionless parameter.
2. The computing method according to claim 1, characterized in that: step S3 further includes: according to Mr(x)、Mθ(x)、
Figure FDA0003183919160000033
And
Figure FDA0003183919160000034
respectively calculating the radial bending stress sigma at each position of the fixed end tube plateriCircumferential bending stress σ at each location of the fixed end tube sheetθiRadial bending stress everywhere in floating end tube sheet
Figure FDA0003183919160000035
And circumferential bending stress everywhere in the floating end tube sheet
Figure FDA0003183919160000036
3. The computing method according to claim 2, characterized in that: step S4 also includes thatriAnd σθiAnd [ sigma ]1]And
Figure FDA0003183919160000037
and
Figure FDA0003183919160000038
and [ sigma ]2]Respectively comparing the two and determining the thickness delta of the fixed end tube plate1And the thickness delta of the floating end tube plate2Whether the requirements are met.
4. The computing method according to claim 1, characterized in that: in step S2, the radial bending moment M experienced by the fixed end tube plate is calculated as followsr(x) And circumferential bending moment Mθ(x) The floatingRadial bending moment borne by end tube plate
Figure FDA0003183919160000039
And circumferential bending moment
Figure FDA00031839191600000310
S301, according to an equation set:
Figure FDA00031839191600000311
Figure FDA00031839191600000312
Figure FDA00031839191600000313
Figure FDA00031839191600000314
Figure FDA00031839191600000315
Figure FDA0003183919160000041
Figure FDA0003183919160000042
a seven-element linear matrix equation set is established according to the following formula:
Figure FDA0003183919160000043
calculating an unknown quantity matrix according to the equation set:
Figure FDA0003183919160000044
wherein j is 1,2.. 7;
wherein P is the pressure of the current calculation working condition, RtIs DtOne half of (f)1(K)、f2(K) For expression with K as variable, MRRadial bending moment M at the periphery of the tube laying-out region at the periphery of the fixed end tube platetIs radial bending moment at the periphery of the pipe distribution area at the center of the fixed end pipe plate,
Figure FDA0003183919160000045
radial bending moment at the periphery of the pipe distribution-free area at the periphery of the floating end pipe plate,
Figure FDA0003183919160000046
Is the radial bending moment of the central pipe laying area of the floating end pipe plate, KtR、Ktt、Ktp、KtV、KRR、KRp、Kf、KRt、KRVThe flexibility coefficient of the pipe distribution-free area at the periphery of the fixed end pipe plate,
Figure FDA0003183919160000047
Figure FDA0003183919160000048
the flexibility coefficient of the pipe distribution-free area at the periphery of the floating end pipe plate is rhot＝RtR is the ratio of the equivalent circle radius of the tube area of the fixed end tube plate to the support radius of the tube plate, R is the support radius of the fixed end tube platef1To support the radius for the floating end tube sheet,
Figure FDA0003183919160000049
equivalent circle radius for floating end pipe plate distribution areaThe ratio of the tube sheet support radius;
s302, substituting the result obtained in the step S301 into the following equation to respectively calculate the bending moment of each position in the fixed end pipe plate distribution area and the bending moment of each position in the floating end pipe plate distribution area:
fixing end pipe plate distribution area:
Figure FDA0003183919160000051
Figure FDA0003183919160000052
calculating Mr (x) and M theta (x);
the floating end tube plate distribution area:
Figure FDA0003183919160000053
Figure FDA0003183919160000054
computing
Figure FDA0003183919160000055
And
Figure FDA0003183919160000056
5. the computing method according to claim 4, wherein: step S5 further includes: the unknown constant C is obtained in step S3011，C2Substituting into the calculation formula of the stress of the heat exchange tube
Figure FDA0003183919160000057
In obtaining the stress sigma of each heat exchange tubet。
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