code_saturne is a general computational fluid dynamics open source software developed by EDF. Based on the finite volume method, supports many types of meshes and solves the Navier-Stokes equations to handle a variety of computational problems such as two-dimensional, two-dimensional symmetry, three-dimensional, steady or unstable, laminar or turbulent, non-compressible or micropressible fluids, isothermal or non-isothermal. The software covers a variety of physics modules for industrial applications, such as atmospheric simulation, combustion of pulverized coal, heavy fuels and biomass, arc and Joule effect, particle tracking, fluid mechanical rotor-stator interaction, etc., and has been widely used and recognized in the industrial field.
Research background
Around 20% of the electricity in the UK is provided by improved gas-cooled reactors, but as of 2014 most reactors were running for nearly 30 years of their design life. In order to improve its efficiency, it is necessary to evaluate the condition of the reactor and overhaul it, and extend its life to 2024 while ensuring its safety.
During the inspection, structural defects were found in the spine of the Heysham steam generator used by the reactor. However, due to design reasons, the steam generator could not be replaced. In addition, if the reactor is shut down, the operating company will suffer a significant loss of profits.
In order to investigate the possibility of repair and reinforcement directly without stopping the reactor, numerical modeling and simulation of spinal maintenance of steam generators in the operating state (600°C) were required.
Steam generator spine
In this case, a model of the spine after welding was constructed to evaluate its energy release rate G, elastic and elastoplastic material properties, and the effect of residual stress on energy release rate in the case of four-point bending. The results of the simulation will be benchmarked by different calculation software and J integrals.
The modeling of the steam generator spine was simplified and meshed, the mesh was made of hexahedral elements with a total number of about 500 000 elements, the density of the mesh in the welded area and the crack area increased, and the cracks were divided into pointed cracks and notched cracks.
This is shown in the following figure.
Assuming that the material is a homogeneous medium (including the welded part), different material properties are used for pure elasticity and elastoplasticity. The residual stress field of the original ring weld and the repair weld is measured by the experiment, and the input residual stress field is iterated continuously as the initial value until the post-equilibrium stress field is consistent with the experimental data, and the experimental data is shown in the following figure.
Simulation results
The results of the parametric study use a sufficiently fine mesh and smoothing function.
The simulation used two FEA software, code_aster and ABAQUS, to compare the results more reliably. Take the calculation of the notched crack model as an example:
- The size of the crack tip unit is 0.15mm
- The energy release rate of the crack tip (G(θ) and J) is calculated at a fixed distance at the front of the crack
(1) Comparison of the calculation results of the energy release rate under elastic/plastic conditions
Figure 1
Figure 2
Through the post-processing of the calculation results, it can be observed that:
1) Under elastic conditions, the calculations of code_aster and ABAKURS match well, with a difference of less than 2% (black curve in Figure 1). Residual stress increases G and uncertainty, but the calculations still match well, with a difference of less than 5% (blue curve in Figure 1). The total calculation time using code_aster and ABAKURS is 2.5h and 3h, respectively.
2) Under plastic conditions, it was found that the model had significant crack propagation. The calculation results of code_aster and ABAQUS are quite different (less than 12%, the red curve in Figure 2), and the residual stress will increase G but the difference in the calculation results of the two software is not significantly changed (< 15%, green curve in Figure 2). The calculation time code_aster one hour shorter than THATBAQUS.
(2) Path dependence research
The calculated path gradually moves away from the tip of the rift
Figure 3
Figure 4
1) Under elastic conditions, the solution using the G(θ) method is stable and equivalent to J integral (difference <2%, Figure 3 black curve). Residual stress does not affect the stability of the energy release rate in the relevant region at the front of the crack (Figure 3 blue curve).
2) The G(θ) method is unstable under plastic conditions and differs greatly from the J integral (difference <40%, Figure 4 red curve). The addition of residual stresses further expands the uncertainty of the solution results (Figure 4 green curve). The two softwares also differ greatly in the results of crack propagation.
conclusion
The calculated energy release rate G is derived from the assumed strain energy density, and the stress condition can also be calculated from the strain energy. Due to the hypothetical limitations of the model, the calculation results have certain limitations:
- The calculation results do not actually describe irreversible plastic deformations, but only apply to hyperelastic and nonlinear elastic behavior. The results do not include any local unloading process, nor do they include any reconstruction of local stresses.
- Suppose that the loading path of the stress remains radial to ensure that the proportion of the principal stress does not change over time. The global monotonic loading is obviously not enough to ensure the performance of the model under non-uniform stress fields.
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