Numerical Simulation of Boiler Serpentine Tube Elbow Die Bending

Literature Overview

This paper by Sha Wanhua et al. from Shanghai Boiler Works Co., Ltd., published in Energy Research and Information (2017, Vol. 33, No. 3), presents a numerical simulation study of the die bending process for boiler serpentine tube elbows. Serpentine tubes are extensively used in large power plant boilers for economizers, superheaters, and reheaters operating under high-temperature and high-pressure conditions. The study models the structural deformation, dimensional changes, and residual stress evolution during die bending, and validates the numerical model against experimental data.

Core Technical Content

Serpentine Tube Service Conditions

Serpentine tubes in power plant boilers operate under demanding conditions:

The serpentine tube configuration, with its alternating up-and-down bends, subjects the elbow regions to complex thermal and mechanical loading, making the accuracy and quality of the elbow forming process critical to component integrity.

Numerical Simulation Methodology

The simulation employed a finite element model to capture the following aspects of the die bending process:

1. Structural deformation — tracking the evolution of tube geometry during bending, including changes in cross-sectional shape and bend angle.
2. Dimensional changes — predicting ovality development and wall thickness variation (thinning at outer arc, thickening at inner arc).
3. Residual stress distribution — mapping the residual stress state after unloading, which is critical for fatigue life prediction.

Key Simulation Results

Ovality Behavior:

• The ovality of the elbow cross-section increases with bend angle, reaching a peak near 45°, and then decreases at larger bend angles.
• This non-monotonic behavior is attributed to the progressive relaxation of deformation as the bend angle increases beyond 45°, where the material has sufficient plastic flow to partially recover the cross-sectional shape.

Wall Thickness Variation:

• The maximum wall thickness change exhibits a linear relationship with the elbow deformation rate (bend angle / bend radius).
• Higher deformation rates produce greater wall thinning at the outer arc and thickening at the inner arc.

Plastic Strain and Residual Stress:

• Both plastic strain and residual stress levels decrease as the deformation rate decreases (i.e., larger bend radius relative to tube diameter).
• The residual stress is more pronounced on the inner surface of the side subjected to roller compression, while the outer surface exhibits more significant plastic deformation.

Model Validation

The numerical model was validated against experimental data obtained from actual die bending trials. The agreement between predicted and measured values for ovality, wall thickness, and residual stress confirmed the reliability of the simulation approach.

Process Analysis and Optimization

Influence of Bend Radius

The bend radius (R/D ratio) is a primary design parameter:

Residual Stress and Fatigue Implications

The residual stress distribution has direct implications for the fatigue life of serpentine tube elbows:

1. Inner surface residual stress — the compressive residual stress on the inner surface can be beneficial for fatigue resistance, as compressive stresses retard crack initiation and propagation.
2. Outer surface plastic deformation — the significant plastic deformation on the outer surface may lead to work hardening, which can increase local strength but reduce ductility.
3. Stress superposition — in service, the residual stress superimposes with thermal and pressure-induced stresses, potentially creating regions of high tensile stress that are susceptible to creep-fatigue interaction.

Roller Configuration Effects

The roller (mandrel) configuration in die bending influences the deformation pattern:

• Mandrel support — the mandrel prevents excessive ovality by providing internal support during bending.
• Roller pressure — the contact pressure between the roller and the tube inner surface determines the degree of cross-sectional constraint.
• Roller geometry — the roller profile must match the desired bend geometry to ensure uniform contact and prevent localized deformation.

Engineering Practice Implications

Quality Control for Serpentine Tube Elbows

Based on the simulation findings, the following quality control measures are recommended:

• Ovality measurement — measure ovality at multiple bend angles during production to ensure compliance with specification limits (typically ≤ 5% for ASME B31.1).
• Wall thickness measurement — measure wall thickness at the outer arc at multiple locations around the bend to detect excessive thinning.
• Residual stress assessment — consider X-ray or neutron diffraction residual stress measurement on critical production lots to validate simulation predictions.
• Fatigue testing — conduct coupon fatigue testing on bent specimens to verify that the actual fatigue life meets design requirements.

Design Recommendations

1. Minimize deformation rate — use the largest practical bend radius to reduce wall thinning and residual stress.
2. Optimize roller design — tailor the roller profile and pressure to minimize ovality while ensuring adequate support.
3. Post-bend stress relief — consider stress relief heat treatment for high-cycle fatigue applications.
4. Material selection — select materials with good formability and fatigue resistance, such as TP304H for high-temperature service or 12Cr1MoV for moderate-temperature service.

Study Insights and Reflections

This paper demonstrates the value of numerical simulation as a tool for understanding and optimizing the die bending process for serpentine tube elbows. The finding that ovality peaks near 45° and then decreases is particularly interesting and has practical implications for production inspection — the 45° region of the bend should receive the most attention during dimensional inspection. The linear relationship between wall thickness change and deformation rate provides a useful design guideline: if the specification limits wall thinning to a certain percentage, the deformation rate can be calculated to ensure compliance. The residual stress findings reinforce the importance of considering forming-induced stresses in fatigue life assessment, which is often overlooked in practice. One reflection is that while numerical simulation provides valuable insights, it should complement rather than replace physical testing, particularly for qualification of new materials or novel forming processes. The validation against experimental data in this study is a model of good engineering practice.