tube sheet paper

20th International Conference on Structural Mechanics in Reactor Technology (SMiRT 20)

Espoo, Finland, August 9-14, 2009

SMiRT 20-Division III, Paper 1699

1 Copyright © 2009 by SMIRT 20

FE Analysis of Heat Exchanger NTIW Tubesheets According to New ASME

VIII 2007 Div 2 Code. Methodology and Automated Analysis Tool Development

Julio A. Guirao Guijarro

a, Silvia Iglesias Benéitez

b, Angel Bayón Villajos

c, and Joaquín Polo

Ruizd

aNumerical Analysis TEChnologies (NATEC), C/ Marqués de San Esteban 9, 4

th floor D, 33206 Gijón,

SPAIN, e-mail: [email protected] bNumerical Analysis TEChnologies (NATEC), C/ Marqués de San Esteban 9, 4

th floor D, 33206 Gijón,

SPAIN, e-mail: [email protected] cIberdrola Ingeniería y Construcción, División de Generación Nuclear, Avda. Manoteras 20, Ed. C, 28050,

Madrid, SPAIN, e-mail: [email protected] dIberdrola Ingeniería y Construcción, División de Generación Nuclear, Avda. Manoteras 20, Ed. C, 28050,

Madrid, SPAIN, e-mail: [email protected]

Keywords: Tubesheet, No Tubes In Window, ASME, Heat Exchanger, Finite Element Analysis.

1 ABSTRACT

The use of No Tubes In Window (NTIW) bundle configuration in Heat Exchangers (HEX) design is

justified by the reduction on shellside pressure drop. However, these configurations have a main

consequence on the mechanical analysis: The perforated region becomes non-axisymmetric.

A widely deployed analytical method in the design of tubesheets is the one proposed in ASME Section

VIII Div.1 in the UHX subsection. This method, consisting in analytical formulas, is based on the

consideration of equivalent characteristics in the perforated zone, depending on the effective ligament

efficiency, a geometric parameter based on the tubesheet configuration and which characterizes the bending

stiffness of the plate in the perforated zone. The application of this method isn’t intuitive due to the high

number of complex formulas whose physical sense and interpretation is not clear.

On the other hand, the method given in UHX is based on certain hypotheses (consideration of a uniform

circular perforated zone) which are not respected in NTIW configuration. Other codes (EN13445, AD

Merkblatt, BS, CODAP …) don’t reference alternative methods to solve these situations. The alternative in

these cases consists in an analysis of the component through the Finite Element (FE) Method (DBA “Design

By Analysis”).

2 INTRODUCTION

Heat Exchangers’ Tubesheets calculation methods prescribed by most design codes are based on a uniform

circular perforated area as well as a uniform thickness of the tubesheet. However, some bundle

configurations do not respect this prescription as an important portion of the tubesheet is untubed in order to

reduce the pressure loss shellside (NTIW configurations). These configurations do not fall within the scope

of these habitual methods.

In this context, thanks to the high computation capacity increase in computers as well as the progressive

upgrade on Finite Element (FE) based software, latest editions of design codes start incorporating specific

design by analysis methodologies orientated to solve non standard problems as this with the non habitual

tubesheets.

Nevertheless, for complex equipment or with a high number of tubes, the detailed FE model of the

tubesheet requires high computational capacity and complex geometry which highly increases the difficulty

of these analyses. The usual alternative to this complex modeling was to use a plate with equivalent

mechanical properties based on UHX method. This option, not enough justified, presents also some


problems like the pressures acting in these perforated zones and the consideration of the additional stiffness

given by the tube bundle.

In ASME Sec. VIII Div, 2 Ed. 2007, in its 5th appendix, for the first time it is presented a systemized

methodology for a design by analysis approach and, in particular, appendix 5E references the case of

perforated plates without any limitation on the perforated zone pattern or axially symmetric pattern contrary

to the restrictions imposed by UHX. In the quoted reference the calculation conditions and applications are

established for an orthotropic equivalent material in the perforated zone, as well as the acting pressures in

each side of the plate to take into account the reduces area due to perforations. It also establishes an

exhaustive methodology to validate the stresses for cyclic loads (fatigue assessment). However, its

application is quite complex and still lets some undefined points such as the way in which tube bundle

additional stiffness should be considered, the inclusion the thermal dilatation effects of the tube bundle or

the general treatment of thermal loads.

A similar approach to the problem described is included in appendix A17 of RCC-MR, Design and

Construction Rules for Mechanical Components of Nuclear Installations Ed. 2007, where an equivalent

orthotropic material is used to characterize the perforated zone of the tubesheet.

In the present paper a complete methodology for the general treatment of problems linked to tubesheets

analyses through appendix 5 of ASME Sec. VIII Div. 2 Ed. 2007 and taking into account all the aspects

previously mentioned is presented. In the same way its application through a parametric tool (programmed

with APDL and Tcl Tk inside the ANSYS Finite Element Code) which, once given all the geometric

characteristics of the component as well as the mechanical properties of the materials and the working

conditions (pressures and temperatures), builds automatically the FE model, solves the coupled thermo

mechanical load case and checks the stresses generated in the tubesheet according to the design code.

3 DIFFERENT APPROACHES DESCRIBED IN THE CALCULATION CODES

TEMA code (Tubular Exchangers Manufacturers Association) includes one of the simplest methods for

tubesheet dimensioning that can be found in literature. This method, applicable for different constructive

configurations, calculates minimum thicknesses for bending and shear. For this last case, the most shear

loaded perimeter concept in both sides is applied, and it takes into account both shellside and tubeside

pressures. In the same way, depending on the constructive configuration, the method takes also into account

differential thermal expansion effects between shell and tubes. At last, in includes additional provisions to

check tube stresses. BS PD-5500 code (3.9 Flat heat exchanger tubesheets) includes a simplified method

analogous to the one given by TEMA code. However, one of the calculation hypotheses in both codes

(paragraph RCB-7.11 (3) in TEMA and paragraph 3.9 in BS PD-5500) is the uniform circular perforated

area without large untubed areas so these two codes are not applicable for NTIW configurations.

Pressure vessels code ASME VIII Div. 1 in its UHX subsection states the design rules for HEX

tubesheets. The method proposed is based on the consideration of an equivalent plate with modified elastic

properties depending on the effective ligament efficiency on the perforated zone. The solution to the stress

problem is obtained by analysis using the equivalent plate. On the other hand, it also takes into account

thermal effects caused by differential thermal expansion between shell and tubes and the differential radial

thermal expansion between the integral shell and the tubesheet. The proposed rules cover different

constructive configurations (U-tube tubesheets in UHX-12, fixed tubesheets in UHX-13 and floating

tubesheets in UHX-14) but in all cases the nominal uniform circular perforated area is assumed (UHX-

10(a)) although some untubed lanes are permitted for pass partition plates’ installation. Therefore, NTIW

configurations do not fall within the scope of UHX rules as it is established in VIII-1-04-61 interpretation.

European Code EN-13445 proposes two similar methods (Chapter 13 and appendix J) that cover most

constructive possibilities. The approach on this code is very similar as the one described in UHX subsection

of ASME VIII Div. 1, presenting an analytical iterative solution based on equivalent plate consideration

whose elastic properties are modified depending on the effective ligament efficiency. EN method

complexity is very similar to ASME, both taking into account all thermal effects to define equivalent acting

pressures and even offers additional rules to calculate shell thicknesses. As in the other codes, NTIW

designs do not respect the prescriptions given (Paragraphs 13.4.2.1(e) and J.4.1).


Other conventional codes such as CODAP Div. 1 and Div. 2 give similar methods as those in ASME

VIII Div. 1 and EN-13445 based on the same hypotheses (Section C7 Règles de calcul des échangeurs de

chaleur à plaques tubulaires) but with the same restrictions for its application in NTIW configurations

(paragraph C7.A2.2.1).

A very different approach is presented in German code AD 2000 Merkblatt, posing a simplified

analysis (Part B5 Unstayed and stayed flat ends and plates) in which there are no peforated area restrictions.

However the method seems too simplified as it does not consider differential thermal expansion effects

between shell and tubes. For this reason, its application for NTIW designs with important temperature

gradients does not seem suitable.

In nuclear design codes, alternative methods with a similar approach based on stress analysis where the

commonly neglected effects on previous codes are considered. In ASME III Div. 1, the use of a stress

analysis method based on an equivalent perforated plate whose constants depend on ligament efficiency is

recommended. This method, presented on paragraph A-8000 of appendix A, does not mention explicitly the

requirement of a uniform circular pattern. However, the stress obtaining procedure is based on axisymmetric

approach, so the previously mentioned condition is implicitly considered. Besides, the method includes the

consideration of larger solid circular zones between the perforated zone and the shell (rim) and takes into

account in a more detailed way the coupled thermo-mechanical effects (it gives additional rules for the

thermal gradients through the tubesheet thickness). Additional secondary effects such as the tube

contribution to ligament efficiency, the stiffness increase due to tube bundle or the internal pressure effect

over the tubes in the tube portion located inside the plate are also treated.

Most general analysis procedures found in literature are those described in codes ASME VIII Div.2

Ed.2007 (Part 5, Annex 5.E) and RCC-MR 2007 (Appendix A-17). Both procedures approach is very similar

based on equivalent solid plate consideration. This equivalent solid plate region is characterized by an

elastic orthotropic material behavior law whose elastic constants depend on effective ligament efficiency.

Even though these treatments have several similarities with ASME III Div.1 (especially on the consideration

of all secondary effects), it represents an important upgrade compared to the others as it guides in the

modeling and characterization of the materials involved. It also provides additional acceptance criteria

depending on the kind of damage analyzed. These methods are highly orientated to DBA and are especially

suitable for its use with FE analysis based tools.

Therefore, as these methods exclude from their hypotheses the requirement of a circular uniform

pattern (hypothesis linked to the axisymmetric approach for stress calculation) can be applied satisfactorily

to NTIW designs.

In the following paragraphs the way the rules exposed in ASME VIII Div.2 Ed.2007 have been

implemented and automated using ANSYS FE software environment will be explained as well as its

application to a practical case.

4 BRIEF DESCRIPTION OF THE APROACH PROPOSED IN ASME VIII DIV. 2 ED.

2007

A brief description of the method exposed in appendix 5.E of ASME VIII Div.2 Ed.2007 is given below.

The method is based on the following hypotheses (Par. 5.E.1.1):

a) The holes are in an equilateral triangular or square penetration pattern.

b) The holes are circular and the axis of the hole is perpendicular to the surface of the plate.

c) There are 19 or more holes.

d) The effective efficiency satisfies the conditions established in par 5.E.4

The perforated zone is analyzed from the equivalent solid plate point of view. For that reason, in the

mechanical analysis, mechanical properties for the perforated zone are substituted by a material model

which simulates stiffness properties of the perforated zone. The material model proposed (par. 5.E.4)

considers the directional dependence on the elastic constants, proposing an elastic linear isotropic material

model where the parameters that define the new elastic constants depend on tubesheet material as well as


tube bundle arrangement and effective ligament efficiency on the perforated zone. In paragraph 5.E.9 are

detailed the constants to determine matrix behavior for triangular and square perforation patterns.

Concerning the additional stiffness provided by the tube bundle, the code considers two separate

effects. Stiffness increase in the plate plane and orthogonal to the plate plane. For the first consideration,

code proposes to consider tube wall in the effective ligament efficiency calculation according to paragraph

4.18.6.4. Stiffness increase effect may be very important especially for fixed tubesheet designs. Code

establishes that in those cases axial rigidity of tubes must be taken into account. It also establishes that

differential strain between shell-tubesheets and tube bundle due to pressure (Poisson’s effects) as well as

differential thermal strain must be considered. In the following paragraphs the way these effects have been

taken into account will be detailed.

For load application over the tubesheet elastic model, once shellside and tubeside pressures are given,

the code proposes a simple load superposition scheme in order to consider pressure effects over the

perforations. Figure shows the different zones for pressure loads application. The values on each zone

(P1..P5) depend not only on shellside and tubeside pressures, but also on the tube to tubesheet joint foreseen

(Table 5.E.19). Therefore, once design pressures are defined for both tubeside (Pt) and shellside (Pc),

equations provided in Table 5.E.19 define the pressure to apply in the 5 zones considered.

At last, for design validation, the code proposes two different checks. The first one establishes criteria

against plastic collapse failure based on primary and secondary stresses in the perforated and non perforated

zones. The second one establishes criteria against cyclic (fatigue) failure, also proposing different limits

depending on the localization (perforated vs. non-perforated). The following paragraphs will detail just the

plastic collapse failure check as cyclic failure check is not yet implemented.

5 ANALYSIS METHODOLOGY

As it has already been said, one of the main characteristics of RCC-MR 2007 and ASME VIII Div.2

Ed.2007 approaches compared to other design codes is their suitability to be implemented with numerical

analysis software to obtain the stress solution. This way, stress solution can be obtained for models without

axisymmetric arrangements (NTIW) and code criteria can be applied for each failure mode.

The method given by the code describes accurately the material model behavior to apply in order to get

an adequate stiffness on the perforated zone and establishes rules for pressure load cases construction.

However, the way thermal effects must be considered and tubes influence over tubesheet strain is not

covered (independently of the mechanical or thermal origin of the loads). In order to include such effects,

several rules are given that affect both modeling and analysis.

Figure . Tube bundle modelling strategy

As for modeling, starting from the FE model of the tubesheet and its junction with the Shell (or

channel), the more realistic way to include the described effects avoiding a detail model of the tubes to

tubesheet junctions is to include an equivalent tube bundle linked to the orthotropic part of the plate. The

equivalent tube bundle can be modeled by an assembly of pin-jointed elements (LINK8) joined to the mid-

plane of the tubesheet orthotropic part through solid elements (SOLID185) with 3 DOF per node (Figure ).

Nevertheless, this procedure conditions the number of elements and mesh shape for the perforated part,

which should be structured (hexahedral mesh). Furthermore, the number of elements will usually be


different from the number of tubes in the actual bundle. For pin-jointed elements characterized by their

cross-sectional area and material properties, the modeling problems described may have a big impact in

equivalent bundle stiffness leading thus to values different from real.

A way to characterize this part of the model, independently of mesh and tube number is, in a first step,

to modify cross-sectional properties (A: cross-sectional area) of each pin-jointed element, making the

product EA (E: modulus of elasticity) be close to the real axial rigidity contribution of the element. To do

this, starting from the uniform contribution to axial stress of the bundle (uniform perforation pattern), it is

possible to define the elementary stiffness of a tube as:

Kt=Et At (1)

Subscript “t” makes reference to the elementary unit, tube.

Thus, if n is the number of tubes in the bundle, the overall bundle stiffness contribution will be:

K=nKt (2)

As every pin-jointed element is associated with a node in the orthotropic mid-surface, the overall area

of the orthotropic plate can be distributed between the pin-jointed elements connection points assembly

(internal nodes), proportionally to the element influence surface. In fact each element contribution has to be

proportional to the influence surface associated to i element (Ai) but the following condition must be

respected: the stiffness sum of all tubes in the equivalent bundle must be equal to the overall stiffness of the

actual bundle (K). The stiffness associated to each element can be formulated as follows:

Ki= K(Ai /A)=(nKt Ai )/A=)=(n Et At Ai )/A (3)

The previous equation guarantees the equivalence between actual and equivalent bundle. In the other

hand, the more uniform mesh in the orthotropic part, the more accurate stiffness distribution will be

obtained. The local calculation of individual stiffness to assign to each tube element is performed through a

programmed loop which builds up the tube elements and evaluates the influence area associated to each.

Once the tube bundle modeled, the differential thermal expansion effects inclusion is achieved

considering a thermal load case characterizing the temperatures in each point of the model and equivalent

tube bundle. This load case can be derived from a previous thermal analysis whose boundary conditions are

obtained from the thermo-hydraulic design (Figure )

6 FINITE ELEMENT MODEL DESCRIPTION

An application programmed in APDL has been built to carry out the analysis automatically. Starting from

the geometric parameters of the equipment and the chosen tubesheet configuration, a FE model is built using

solid elements (SOLID185) which represents the actual geometry of the HEX. The axial stiffness increase

effect of the tube bundle is included automatically following the procedure described in the previous

paragraph, giving each pin-jointed element (LINK8) the axial stiffness (EiAi) corresponding to the influence

area associated to it.

Figure shows two programmed arrangements consisting in an integral tubesheet configuration and an

extended as a flange one. In both cases, bundle orientation (horizontal or vertical) and length can be

controlled parametrically while building the model.

In flanged arrangements, assembly conditions are also implemented in the model. Contact between two

different parts (channel and shell-tubesheet) is modeled through node-to-node contacts (CONTAC52).

Likewise flange bolts and their effect are included through pin-jointed elements only resisting tension forces

(LINK10). These elements are characterized by an initial strain imposed to simulate bolting torque

pretension on bolts (Figure ).

For the thermal analysis, a FE model with solid elements (SOLID70) is built substituting the solid

elements for the mechanical analysis (SOLID185). As the only purpose of the thermal analysis is to provide

an approximate temperature map on all the points of the HEX starting from the temperatures obtained in the


thermo-hydraulic design, tube bundle is not included in this analysis. In the other hand, for flanged

configurations, node-to-node contact elements are substituted by thermal DOF coupling. At last, elements

modeling bolts are eliminated.

Figure . FE model for integral tubesheet configuration and extended as a flange tubesheet configuration

Figure . FE model: Flange detail

During the construction process of the FE models for the thermal and mechanical analyses, several

node groups are created where boundary conditions will be applied afterwards for both analyses. Zone

definition for the thermal analysis depends on tubeside and shellside number of passes of the HEX. The

application built can consider one or two passes tubeside and shellside, having therefore 4 different flow

configuration possibilities.

7 MATERIAL MODELLING

As the method to carry out the analysis is based on static analyses and stress categorization, behavior models

for the materials considered are all linear, elastic and characterized by two elastic constants, Poisson

modulus (n) and elastic modulus (E). In order to simulate the perforated plate, the modeled equivalent solid

plate considers a linear, elastic and orthotropic behavior characterized by equation 4 whose elastic constants

depend on the effective ligament efficiency calculated and the perforations pattern (square of triangular).

Elastic constants are obtained as prescribed in paragraph 5.E.9 of ASME VIII Div.2 Ed.2007.

(4)

For the thermal analysis, materials are characterized just by their thermal conductivity.


The application automatically includes the orthotropic behavior from the geometric input (effective

ligament efficiency), perforations pattern and mechanical properties of the tubesheet material. All these data

have to be included as input prior to start the analysis.

8 BOUNDARY CONDITIONS, LOADS AND LOAD COMBINATIONS CONSIDERED

As it has been explained, the only purpose of the thermal analysis is to obtain an approximate temperature

map from the mean temperatures calculated for the most important zones (inlet and outlet in each side) in

thermo-hydraulic analysis. To carry out the thermal analysis, these temperatures are imposed in the

corresponding zones, obtaining a stationary temperature map taking into account just conductivity effects.

Figure shows the temperature map obtained this way for a two pass shellside and two pass tubeside HEX.

At in can be observed, the temperature map allows the inclusion of thermal gradients in an approximate

way.

To obtain the temperature map, the following temperature data from thermo-hydraulic design have been

employed:

TMS1=79.6, mean shellside fluid temperature in 1st pass.

TMS2=44.93, mean shellside fluid temperature in 2nd pass.

TMT1=33.9, mean tubeside fluid temperature in 1st pass.

TMT2=61.15, mean tubeside fluid temperature in 2nd

KTSH=47. 91 W/m2K Shell material thermal conductivity (Carbon Steel)

KTTB=16.42 W/m2K Tube material thermal conductivity (Stainless Austenitic Steel)

As boundary conditions for the mechanical analysis, symmetry conditions in the longitudinal mid-plane

of the model are employed, constraining displacements perpendicular to the symmetry plane on all nodes

belonging to it. To avoid solid rigid displacement of the model, displacements on two points of the

symmetry plane are constrained avoiding translations and rotations of the assembly.

Figure . Zones defined for surface load application

For fixed tubesheets configurations in which tube bundle is included in the analysis, the model is cut by

the mid-plane between tubesheets, imposing symmetry conditions in the free end of the pin-jointed elements

which simulate the tubes.

As loads to consider there are pressure loads and thermal effects derived from the temperature map

obtained previously. The effect of internal pressure in the perforated plate can be considered through simple

load superposition as it is proposed in paragraph 5.E.10 of ASME VIII Div.2 Ed.2007. This way, from the

acting pressures shellside and tubeside, it is possible to define an equivalent load case characterized by the

different surface loads distributed on the 5 zones represented in Figure .

As the method followed does not guide on the combined load cases to analyze, the combination

definition is similar to the one proposed in UHX Subsection of ASME VIII Div.1, considering 4 design

situations and two test situations.

Combined case 1: Shellside design pressure + no pressure tubeside. (Ps= Pdes

s ; Pt=Patm).


Combined case 2: Tubeside design pressure + no pressure shellside. (Ps=Patm ; Pt=Pdes

t)

Combined case 3: Shellside design pressure + tubeside design pressure. (Ps= Pdes

s ; Pt=Pdes

t)

Combined case 4: Shellside design pressure + vacuum tubeside. (Ps= Pdes

s ; Pt=0)

Combined case 5: Shellside test pressure + no pressure tubeside. (Ps= Ptest

s ; Pt=Patm)

Combined case 6: Tubeside test pressure + no pressure shellside. (Ps=Patm ; Pt=Ptest)

Thermal effects are included in the first four combinations (spatial thermal gradients). All loads must

be considered acting simultaneously, at least for the flanged configurations, due to the fact of non linearity

introduced by contact elements (Figure ) which make superposition principle not applicable.

Figure . Temperature map on the model and non-linear effects induced by contacts

On the other hand, at channel rim, an external equivalent pressure is applied to simulate the force

induced by channel cover and the longitudinal stress induced as a result of internal pressure. For U-tube

configurations, where symmetry conditions on the mid-plane between tubesheets are not applied, this effect

is also taken into account on shellside. Built up of load cases and solution is done automatically.

9 ANALYSIS RESULTS AND DISCUSSION

As the method contained in ASME VIII Div.2 Ed.2007 is based on elastic analysis, a stress breakdown has

to be done for stress check, having therefore membrane, bending and peak stresses and considering them as

primary or secondary stresses. Stress categorization is a non intuitive process which requires experience

from the designer and interpretation of the results obtained. For this reason, stress categorization should not

be automated. Each analysis situation may require different interpretations depending on the zone analyzed

but also on the acting loads and the strain magnitude obtained. For post-processing purposes, an ad-hoc tool

has been developed, permitting code stress check for protection against plastic collapse interactively.

First of all, the target zone to be checked has to be selected. Criteria are different if the selected area is

the equivalent solid plate. To make the check process easier, 4 different regions are defined as shown in

Figure . Likewise, in the same figure the applicable criteria are presented for each stress categorization. For

the equivalent solid plate, criteria include a KPS factor which takes into account the radial and hoop stress

ratio present in the zone analyzed.

Once the target check region is chosen, the application presents Von Misses equivalent stress

distribution so that the user may select the points to analyze and define the Stress Classification Lines

(SCL’s). These SCLs will be the stress linearization paths (Figure ). Stress linearization is done

automatically and global stress is broken onto membrane, bending and peak. The user is later on asked to

classify stresses as primary or secondary through interactive windows, and also to classify membrane stress

as general or local.

Finally, stress check is done automatically according to the stress categorization given by the user.

Results are written in a text file which records the analysis performed. Figure shows an example of primary

stress check on the two SCL’s showed on Figure .


Figure . Stress analysis zones and applicable criteria according to 5.E.6 of ASME VIII Div. 2 Ed.2007

Figure . Selection of Stress Classification Lines

PRIMARY STRESSES ASSESSMENT FOR TUBESHEET (PERFORATED

AREA)

ACCORDING TO ASME Secc.VIII Div.2 Ed.2007 Appendix 5

NUMBER OF SCL's 2 (STRESS CLASSIFICATION LINE) ANALIZED

STRESS ASSESSMENT SUMMARY

SCL 1 STRESS SUMMARY

MEMBRANE STRESS, Pm/Pl=12.99 MPa

BENDING STRESS START/END OF PATH, Pb=20.55 MPa

PEAK STRESS START OF PATH, F=3.27 MPa

PEAK STRESS CENTER OF PATH, F=2.23 MPa

PEAK STRESS END OF PATH, F=3.13 MPa

MEMBRANE PLUS BENDING STRESS START OF PATH, Pb=30.71 MPa

MEMBRANE PLUS BENDING STRESS CENTER OF PATH, Pb=12.99 MPa

MEMBRANE PLUS BENDING STRESS END OF PATH, Pb=15.46 MPa

BETA COEFFICIENT FOR THE PATH, b=-0.243494593

Kps COEFFICIENT FOR THE PATH , Kps=1.15406425

EFFECTIVE LIGAMENT EFFICIENCY, m*=0.300389454

ALLOWABLE STRESS (ASME Secc.II Part D Ed.2007, TABLE

3.A)=137.9 MPa

CHECK FOR MEMBRANE STRESS

Pm/m*=43.23 MPa

ALLOWABLE (S)=137.9 MPa

CHECK:OK!

SAFETY MARGIN:68.65 %

CHECK FOR MEMBRANE PLUS BENDING STRESS

(Pm/Pl+Pb)Kps/m*=117.99 MPa

ALLOWABLE (1.5xS)=206.85 MPa

CHECK:OK!


SCL 2 STRESS SUMMARY

MEMBRANE STRESS, Pm/Pl=13.46 MPa

BENDING STRESS START/END OF PATH, Pb=17.7807171 MPa

PEAK STRESS START OF PATH, F=4.63 MPa

PEAK STRESS CENTER OF PATH, F=2.49 MPa

PEAK STRESS END OF PATH, F=3.26 MPa

MEMBRANE PLUS BENDING STRESS START OF PATH, Pb=26.75 MPa

MEMBRANE PLUS BENDING STRESS CENTER OF PATH, Pb=13.46

MPa

MEMBRANE PLUS BENDING STRESS END OF PATH, Pb=16.71 MPa

BETA COEFFICIENT FOR THE PATH, b=-0.141117934

Kps COEFFICIENT FOR THE PATH , Kps=1.1028354

EFFECTIVE LIGAMENT EFFICIENCY, m*=0.300389454

ALLOWABLE STRESS (ASME Secc.II Part D Ed.2007, TABLE

3.A)=137.9 MPa

CHECK FOR MEMBRANE STRESS

Pm/M*=44.82 MPa

ALLOWABLE (S)=137.9 MPa

CHECK:OK!

SAFETY MARGIN:67.5%

CHECK FOR MEMBRANE PLUS BENDING STRESS

(Pm/Pl+Pb)Kps/m*=98.21 MPa

ALLOWABLE (1.5xS)=206.85 MPa

CHECK:OK!


Figure . Primary stress check


10 CONCLUSIONS

The tool developed covers the analysis of most common tubesheet designs allowing a great time saving.

The preprocessing and solution tasks are fully automatic. Though the stress check requires designer

intervention (stress categorization), the process is easy and intuitive, generating also a complete stress report

with the main aspects of the calculation performed.

This methodology provides accurate results through a detailed model permitting even the check of any part

near the tubesheet (rim).

11 REFERENCES

AD 2000-Merkblatt Design of Pressure Vessels Ed. January 2003. Part B5: Unstayed and Stayed Flat Ends

and Plates.

ASME Boiler and Pressure Vessel Code Section III Division 1 Appendices Ed. 2007: Rules for Construction

of Nuclear Facility Components. Nonmandatory Appendix A, Article A-8000 Stresses in Perforated Flat

Plates.

ASME Boiler and Pressure Vessel Code Section VIII Division 1 Ed. 2004: Rules for Construction of

Pressure Vessels. Part UHX Rules for Shell-and-Tube Heat Exchangers.


Pressure Vessels. Part UHX Rules for Shell-and-Tube Heat Exchangers.


Pressure Vessels. Alternative Rules. Part 4: Design by rule requirements. Paragraph 4.18, Design Rules for

Shell-and-Tube Heat Exchangers.


Pressure Vessels. Alternative Rules. Part 5: Design by analysis requirements. Annex 5.e: Design Method for

Perforated Plates Based on Elastic Stress Analysis.

ASME Boiler and Pressure Vessel Code Section VIII-1 Interpretations Vol 56 2005. Interpretation VIII-1-

04-61.

BS PD-5500:2006, Specification for unfired fusion welded pressure vessels. Part 3.9: Flat heat exchanger

tubesheets.

CODAP, Code de construccion des Appareils à Pression non soumis à l’action de la flame 2005, Division1.

Section C7, Regles de Calcul de Echangeurs de Chaleur a Plaques Tubulaires.

CODAP, Code de construccion des Appareils à Pression non soumis à l’action de la flame 2005, Division2.

Section C7, Regles de Calcul de Echangeurs de Chaleur a Plaques Tubulaires.

RCC-MR, Design and Construction Rules for Mechanical Components of Nuclear Installations Ed. 2007,

Section 1 – Subsection B: Class 1 Components. Part RB-3900, Design Rules for Heat Exchanger Elements.

RCC-MR, Design and Construction Rules for Mechanical Components of Nuclear Installations Ed. 2007,

Section 1 – Subsection Z: Technical Appendices. Appendix A-17: Design of Flat Tubeplates.

TEMA, Standards of the Tubular Exchanger Manufactures Association, eighth edition - 1999. Par. RCB-7

Tubesheets.

UNE-EN-13445 Ed. Mayo 2006. Recipientes a Presión no Sometidos a la Acción de la Llama. Parte 3:

Design. Aptdo 13, Placas de Tubos de Intercambiadores de Calor.

UNE-EN-13445 Ed. Mayo 2006. Recipientes a Presión no Sometidos a la Acción de la Llama. Parte 3:

Design. Annexo J: Método Alternativo para el Diseño de Placas de Tubos de Intercambiadores de Calor.

tube sheet paper

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