Functionally graded materials (FGMs) have the potential to reduce high stress concentrations near material interfaces.In the ITER divertor monoblock, this may be achieved by replacing the distinct W-Cu interface by an FGM, which gradually changes the coefficient of thermal expansion (CTE) from copper to tungsten. To assess the full potential of FGMs in improving the thermal and mechanical behavior, a first proof-of-principle study is performed in this paper to numerically optimize the tungsten volume fraction distribution of a W-Cu FGM based ITER monoblock for minimal thermal stresses using a simple thermal conduction model. We show that the optimizer can ensure that the temperature remains below the recrystallization temperature of tungsten and that it minimizes the chosen cost function, based on the fractional margin between the local temperature and melting temperature, in a computationally efficient way. Furthermore, the resulting design has a lower Von Mises stress measure at the original position of the W-Cu interface. However, a new material interface is introduced, which results in an additional undesired stress concentration. Future work should therefore aim at integrating a complete stress evaluation in the optimization method.
Functionally Graded Materials (FGMs) are a means to remove discrete material interfaces which lead to high local stress concentrations, such as the Tungsten-Copper (W-Cu) interface of the current ITER monoblock design. This paper employs adjoint-based optimization methods to identify the highest potential reduction of stresses that could be reached with these materials, while ensuring that the local temperature does not exceed the material temperature operational window. The cheap sensitivity evaluation inherent to the adjoint approach enables the optimization of the detailed 3D material distribution. Furthermore, a novel optimization method based on an augmented Lagrangian formulation is proposed that allows accurate treatment of the material temperature window constraints. The temperature and stresses are modeled by the steady heat conduction and Navier's equation, respectively.We compare the results of different optimization formulations, with cost functions based on the von Mises stress and corresponding yield criterion, and considering different values of the stress free temperature. To assess the performance under off-design conditions, two optimized designs were chosen and compared to the ITER and flat tile (FT) design, which consists of a copper block protected by a tungsten layer on top. The optimized designs lead to a factor 2 − 4 decrease in maximal stress near the original W-Cu interface of the FT design and a factor 10 decrease in yield criterion measure near the cooling duct. Under off-design conditions, they realized a factor 2 − 10 decrease in yield criterion in the upper part of the monoblock. This confirms numerically that FGMs can lead to significant design improvements. Finally, the inclusion of the material temperature operation window constraints leads to a decrease of 30 − 55 vol% W compared to the unconstrained cases, thus profoundly influencing the final design. The stress free temperature was found to have a comparably weaker influence on the final design with differences of 5 − 30 vol% W.
In this paper, the framework for gradient‐based optimization of snowflake magnetic divertor topologies is discussed. A continuous in‐parts adjoint approach is adopted to calculate the gradient. A robust grid generator developed within the in‐house DivOpt code enables different topologies in an automated way. However, a large flux expansion exists near second‐order and closely spaced first‐order X‐points. This might induce significant discretization errors. As accurate gradients are needed for the correct functioning of the numerical optimization algorithm, the importance of the discretization error is assessed by calculating the gradient with both finite differences and the continuous adjoint approach on three systematically refined grids. It is shown that sufficiently fine grids are needed to achieve accurate gradient calculation and a corresponding good functioning of the optimization algorithm.
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