Bellows Expansion Joint Analysis using FEA

FSE Drawing

This article explains the use of advanced FEA analysis for evaluating the structural behaviour of Economizer Heat Exchanger equipment and compares the designs obtained through different design codes.

This example is a heat exchanger with a bellow expansion joint and the reason of performing this study is because of a transition zone between two parts with different thickness, in order to assess the failure risk in that zone. On one hand, the heat exchanger design has been performed according to ASME VIII Div. 1 code using design by rules and shell thickness value obtained is 40 mm. On the other hand, the design of expansion joint has been performed according to Standards of the Expansion Joint Manufacturers Association (EJMA) and the minimum required thickness obtained is 30 mm. Is there a discrepancy? Keep reading if you are interested in finding what is going on. 

The SDEA advanced engineering team put their hands on the problem using design by analysis on the bellow design. 

Fixed Tubesheet Heat Exchanger

Flexible Shell Elements (FSE) are often used in fixed tubesheet heat exchanger in order to reduce shell and tube longitudinal stresses or tube-to-tubesheet joint loads. Ligth gauge bellows type expansion joints within the scope of the EJMA Standard are not included within the purview of this section.

The Tubular Exchanger Manufacturers Association (TEMA) Code, according to RCB-8 part, provided guidelines for determining stresses using a 2-dimensional Axisymmetric Finite Element Model (FEA) for the FSE or FSE combinations.

According to the problem described above, and considering the guidelines provided by TEMA for modelling FSE, the procedure used to obtain the answer to this problem is exposed in the following lines:

Boundary Conditions for FSE analysis RCB-8.42

At first, the CAD model (2D Axisymmetric geometry of FSE) is meshed considering eight node quadratic axisymmetric elements and the boundary conditions shown in figure RCB-8.42.  The axial translation of the FSE is restringed at the FSE axial plane, pressure of shell side is applied in the inner face of FSE and an axial displacement is applied for stress determination.

In order to evaluate the stress, it’s necessary to establish the minimum number of stress classification lines (SCL) and to compute linearized both membrane and membrane+bending stress intensities at each SCL in order to compare these stress values with the allowable stress limits defined in the design Code.

Stress Classification Lines for Evaluating Stresses RCB-8.62

The methodology for evaluating stresses is not specified in part RCB-8, so the code chosen for this purpose is ASME VIII Divisions 1 and 2.

In the context of bellows expansion joints design, Division 1 provides the allowable stress in bellows, according to part 6 of Mandatory Appendix 26 (Design of U-shaped unreinforced bellows):

  • S1 ≤ S
  • S2 ≤ S 
  • S3 + S4 ≤ KMS

where S1 is the circumferential membrane stress in bellows tangent; S2, circumferential membrane stress in bellows; S3 and S4 are meridional membrane and bending stresses, respectively, all of them obtained due to pressure. S is the allowable stress of bellows material at design temperature. Stresses in bellows due to deflection are only considered in fatigue analysis.

Stress in Bellows

Km is equal to 1.5·Ysm for as-formed bellows and 1.5 for annealed bellows, where Ysm is the yield strength multiplier which depends on the  material. The value of Km varies between 1.5 and 3.0Similarly, EJMA Standard collects the same stresses criteria in 4.13.1 (Design Equations for Unreinforced Bellows).
It is important to remark the fact that the combination of membrane plus bending stress on the convolution peak is compared against the allowable stress, scaled by a factor of 3 in this case. This is paramount and takes into account the hardening effect from the forming manufacture method, where the material goes well beyond yielding, resulting in hardening after the process.

Design Equations for Unreinforced Bellows [EJMA Standard]

On the other hand, according to Table 5.6 of ASME Section VIII Division 2, the next stresses classification should be used, depending on the location and the origin of the stresses:

  • Pm < S
  • PL < S 
  • PL + PB < 1.5S

where Pm is the maximum primary membrane stress; PL, local membrane stress and PB, primary bending stress.

So, in order to analyse the stresses in the different Stress Classification Lines of FSE, stresses classification provided by Division 2 and allowables stresses in bellows provided by Division 1 (and EJMA) are considered.

Stress Classification Lines for Stress Evaluation

Bellows SCLs Contours

Von Mises Stress Contours of FSE

2D-Axisymmetric FEA is performed for the FSE applying the boundary contidions described above and the stress values are evaluated in one of each SCL chosen for this model. According to the criteria exposed previously, table with SCL values is presented and the stress values obtained are below of the allowable ones:

SCL Results

Stress Classification Lines Results

This work was addressed in order to give an answer to the question if there is some discrepancy between design codes used for the design of the heat exchanger (ASME VII Div 1 Code used for calculating the minimum required thickness of the shell and EJMA Code used for mechanical design of bellow expansion joint) and to predict the structural behaviour in the transition zone between both. In this scope, a FEA method was used in order to analyse this problem. In view of the FEA analysis results , it can be reasuring to see the good behaviour of the system and the transition zone between the parts with different thickness: it is safe under the design conditions for different pressure and temperature parameters considered. It’s a good practice to combine Design by Rules with Design by Analysis, using FEA methods in order to validate the design by rules performed beforehand.

Pressure Vessels Design

Stationary Tubesheet Configurations

Pressure Vessels are used in the industry to store process fluids under certain temperature and pressure conditions. Commonly, pressure vessels have cylindrical or spherical shape, can be disposed in a horizontal or vertical way and are provided of heads with different shapes (Ellipsoidal, Hemispherical, Toroidal, etc.). These equipments are fitted with different elements such as nozzles (used to control the entry and/or exit of the fluids), cooling or heating jackets to maintain the temperature of the stored fluid, or other non-pressurized elements capable of supporting and transporting the equipment such as saddles, skirts, legs and lugs. In the SDEA_Engineering solutions team we accumulate ample experience in pressure vessels among other process engineering equipment design.

Design by Rules approach is a widely used method in several industrial sectors. This approach is based on a set of rules that specifies the design method, loads, allowable stress and materials requirements. The objective of design by rules is to determine the minimum thickness of the part considering design pressure, allowable materials and the specific formulas for the component geometry.

The most used and recognized code was proposed by the American Society of Mechanical Engineers (ASME), and is known as ASME Boiler and Pressure Vessel Code (BPVC). Other commonly used codes are EN-13445 (Europe), BS 5500 (UK), CODAP (France) and AD Merkblatt (Germany).

In particular, ASME Section VIII, Division 1 provides formulas for determining thickness and maximum allowable stress of basic components for Pressure Vessels. Equipment design according to this code does not require a detailed assessment of stresses.

The design method uses design pressure, allowable stress and specific formulas according to geometry of the component subject to design. ASME requires that pressure vessels are designed considering the most severe conditions subjected to the vessel, including the normal operation and other conditions such as start-up and shut-down. It’s necessary to have in mind several considerations for the adequate design. One of them is the design pressure, in order to determine it is necessary to know the Maximum Allowable Working Pressure (MAWP) of the component. That is, the maximum pressure permissible at the top of the vessel in its normal operating position at a specific temperature. Other consideration is the Design Temperature: the maximum and minimum design temperatures will determine the maximum (and minimum) allowable stress for the material to be used in the vessel. The minimum design temperature would be MDMT (Minimum Design Metal Temperature). Other important factor is the maximum allowable stress of the material which, as mentioned, depends on the temperature design and these values of stresses include certain safety margins. Also, it’s necessary to take into account an extra thickness in order to avoid the negative effects that may appear due to corrosion. All design considerations for the complete design of a pressure vessel are collected in paragraphs UG-16 to UG-35 of ASME VIII Division 1.

The designer must be familiar with the different failures that may occur and to take them into account in the design stage. These different failure modes are grouped in four categories:

  • Material: Can be due to improper material selection and / or material corrosion, among others.
  • Design: An incorrect input data or design procedure can lead to design failure
  • Fabrication: Due to gross fabrication errors or poor welding qualities
  • Service: Change in service condition or unexpected operations

The four previous categories describe “why” the vessel failure may occur. The failure types are: Elastic deformation, excessive plastic deformation, brittle fracture, stress rupture, plastic instability, high strain, stress corrosion and corrosion fatigue. More details about fatigue failure can be found here

In order to avoid equipment failure, the designer must take into account which loads will be involved in the process: steady loads applied continuously such as internal or external pressure, thermal loads and wind loads among others, are sometimes combined with Non-Steady loads, variable and short duration, like earthquakes, erection, transportation or start up – shut down. In particular, part UG-22 of the mentioned code collects all loadings to be considered in the design of a vessel.

On the other hand, several processes involve cyclic loads and thermal stresses, and other approaches more adequate for these cases are needed. Usually, instead of design by rules, design by analysis is used. This approach is collected by ASME in Section VIII Division 2. The combination of both approaches (Design by rules and Design by Analysis) results in a safer, more accurate and economically efficient design.