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Achievements and Challenges in Automated Parameter, Shape and Topology Optimization for Divertor Design

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Particle and power exhaust is a key performance issue for next step fusion reactors. Divertors need to be designed to handle power exhaust and to provide sufficient Helium pumping capacity. Plasma edge transport codes such as B2-Eirene [1,2] are indispensable for the design of future divertor concepts, as they allow for the extrapolation of the current understanding of the edge plasma physics to fusion reactor relevant operating regimes. Due to the long simulation times, it is impossible to consider many different geometries and operating points during the design process. Thus, different design requirements and constraints, combined with the large number of control variables turn divertor design into a challenging problem.Over the past decades similar design challenges are faced both in aerodynamics and in structural mechanics. In aerodynamics, shape optimization was introduced to design airfoils for drag reduction or lift maximization [3]. In structural mechanics topology optimization was used to design sufficiently strong constructions at minimal weight and material costs [4]. The method was further developed in fluid mechanics applications to achieve optimal flow configurations [5]. All problems have been treated very effectively by using optimization approaches including adjoint PDE formalisms for computing design sensitivities. Recently, adjoint based automated design methods were explored for fusion reactor and heat sink design. These methods start from a cost functional, which is a measure for the performance of a certain design, and identify optimal solutions by minimizing this cost functional. The minimum is hereby achieved through gradient-based optimization algorithms, where adjoint sensitivity analysis is used to keep gradient evaluation costs sufficiently low.With a detailed parameterization of the divertor shape, and the use of several divertor coils, the number of design variables can easily exceed hundreds or even thousands. For topology optimization of heat sinks every grid cell contains the porosity as a control parameter to assess whether a cooling channel or a fin structure is desired. In previous work [6,7], it is demonstrated that shape optimization methods applied to divertor shape design can efficiently propose divertors which optimize target power load spreading. Typically, V-shaped targets are found. Using adjoint methods for sensitivity analysis, simulation times needed for the optimization cycle are of the order of only a few simulations of the corresponding analysis problem. Also radiation heat loads, computed by a Monte Carlo method, could be incorporated within this methodology [8]. A similar methodology is developed for magnetic configuration design. However, adjoint sensitivities of the plasma edge grid generator are difficult to obtain. Therefore in parts adjoint techniques were developed [9,10]. Again, the optimization methodology successfully alters the magnetic configuration to reduced heat peaks. Further, the perspectives of topology optimization for cooling designs was investigated and led to branch-like cooling channel patterns for micro-channel heat sinks [11].In the present paper, the status, perspectives and challenges for optimization tools both in divertor configurations and cooling designs will be reviewed.[1] Reiter, D. et al. (2005). Fus.Sci.Techn. 47, 172–186.[2] Kukushkin, A.S., Pacher, H.D., Kotov, V., Pacher, G.W., Reiter, D. (2011). Finalizing the ITER divertor design: The key role of SOLPS modelling. Fusion Engineering and Design, 86, 2865-2873.[3] Jameson, A., Martinelli, L., Pierce, N. A. (1998). Optimum aerodynamic design using the Navier-Stokes equations. Theoretical and Computational Fluid Dynamics, 10, 213-237.[4] Bendsøe, M.P. and Kikuchi, N, (1988). Generating optimal topologies in structural design using a homogenization method. Computer Methods in Applied Mechanics and Engineering, 71:197–224.[5] Borrvall, T. and Petersson, J. (2003). Topology optimization of fluids in Stokes flow. International journal for numerical methods in fluids, 41:77–107, 2003.[6] Dekeyser, W., Reiter, D., Baelmans, M. (2014). Automated divertor target design by adjoint shape sensitivity analysis and a one-shot method. Journal of Computational Physics, 278, 117-132.[7] Dekeyser, W., Reiter, D., Baelmans, M. (2014). Divertor target shape optimization in realistic edge plasma geometry. Nuclear Fusion, 54, art.nr. 073022.[8] Dekeyser, W., Reiter, D., Baelmans, T. (2015). Designing divertor targets for uniform power load. Journal of Nuclear Materials, 463, 1243-1247.[9] M. Blommaert, M. Baelmans, W. Dekeyser, N. Gauger, and D. Reiter, “A novel approach to magnetic divertor configuration design”, Journal of Nuclear Materials, vol. 463, pp. 1220-1224, Aug. 2015.[10] Blommaert, M., Dekeyser, W., Baelmans, M., Gauger, N., Reiter, D. (2015). An automated approach to magnetic divertor configuration design. Nuclear Fusion, 55, art.nr. 013001.[11] Van Oevelen, T. and Baelmans, M. (2014). Numerical topology optimization of heat sinks”, Proc. of the 15th International Heat Transfer Conference, August 2014, Kyoto (Japan).
Tijdschrift: Nuclear Fusion
ISSN: 0029-5515
Volume: 57
Jaar van publicatie:2017