Achievements and challenges in automated parameter, shape and topology optimization for divertor design

Plasma edge transport codes play a key role in the design of future divertor concepts. Their long simulation times in combination with a large number of control parameters turn the design into a challenging task. In aerodynamics and structural mechanics, adjoint-based optimization techniques have proven successful to tackle similar design challenges. This paper provides an overview of achievements and remaining challenges with these techniques for complex divertor design. It is shown how these developments pave the way for fast sensitivity analysis and improved design from different perspectives.

[1]  Martine Baelmans,et al.  Designing divertor targets for uniform power load , 2015 .

[2]  A. S. Kukushkin,et al.  Finalizing the ITER divertor design: The key role of SOLPS modeling , 2011 .

[3]  Matthew MacDonald,et al.  Shapes and Geometries , 1987 .

[4]  P. Valanju,et al.  On heat loading, novel divertors, and fusion reactors , 2006 .

[5]  Ole Sigmund,et al.  On the usefulness of non-gradient approaches in topology optimization , 2011 .

[6]  F. Blom Considerations on the spring analogy , 2000 .

[7]  D. P. Coster,et al.  DIVIMP-B2-EIRENE modelling of 13C migration and deposition in ASDEX Upgrade L-mode plasmas , 2010 .

[8]  Martine Baelmans,et al.  A one shot method for divertor target shape optimization , 2014 .

[9]  A. Jameson Optimum aerodynamic design using CFD and control theory , 1995 .

[10]  Wouter Dekeyser Optimal Plasma Edge Configurations for Next-Step Fusion Reactors (Optimale plasmarand-configuraties voor nieuwe generatie fusiereactoren) , 2014 .

[11]  D. Reiter,et al.  The EIRENE and B2-EIRENE Codes , 2005 .

[12]  Tijs Van Oevelen Optimal Heat Sink Design for Liquid Cooling of Electronics , 2014 .

[13]  Martine Baelmans,et al.  Numerical Topology Optimization of Heat Sinks , 2014 .

[14]  Martine Baelmans,et al.  Accuracy and Convergence of Coupled Finite-Volume / Monte-Carlo Codes for Plasma Edge Simulations , 2016 .

[15]  M. Baelmans,et al.  Accuracy and convergence of coupled finite-volume/Monte Carlo codes for plasma edge simulations of nuclear fusion reactors , 2016, J. Comput. Phys..

[16]  Martine Baelmans,et al.  Automated divertor target design by adjoint shape sensitivity analysis and a one-shot method , 2014, J. Comput. Phys..

[17]  A. S. Kukushkin,et al.  Radiative power loading in the ITER divertor , 2011 .

[18]  Martine Baelmans,et al.  A novel approach to magnetic divertor configuration design , 2014 .

[19]  Martine Baelmans,et al.  Divertor target shape optimization in realistic edge plasma geometry , 2014 .

[20]  Martine Baelmans,et al.  Application of topology optimization in a conjugate heat transfer problem , 2014 .

[21]  Kyriakos C. Giannakoglou,et al.  A multilevel approach to single- and multiobjective aerodynamic optimization , 2008 .

[22]  Martine Baelmans,et al.  Optimal shape design for divertors , 2014, Int. J. Comput. Sci. Eng..

[23]  O. Pironneau,et al.  SHAPE OPTIMIZATION IN FLUID MECHANICS , 2004 .

[24]  A. Jameson,et al.  Optimum Aerodynamic Design Using the Navier–Stokes Equations , 1997 .

[25]  M. C. Delfour,et al.  Shapes and Geometries - Metrics, Analysis, Differential Calculus, and Optimization, Second Edition , 2011, Advances in design and control.

[26]  K. Svanberg The method of moving asymptotes—a new method for structural optimization , 1987 .

[27]  J. Petersson,et al.  Topology optimization of fluids in Stokes flow , 2003 .

[28]  J. Zolésio,et al.  Introduction to shape optimization : shape sensitivity analysis , 1992 .

[29]  Martine Baelmans,et al.  Divertor Design through Shape Optimization , 2012 .

[30]  Martine Baelmans,et al.  Towards Automated Magnetic Divertor Design for Optimal Heat Exhaust , 2016 .

[31]  Martine Baelmans,et al.  A practical globalization of one-shot optimization for optimal design of tokamak divertors , 2017, J. Comput. Phys..

[32]  M. Bendsøe,et al.  Generating optimal topologies in structural design using a homogenization method , 1988 .

[33]  D. P. Coster,et al.  ASDEX-Upgrade edge transport scalings from the two-dimensional interpretative code B2.5-I , 2001 .

[34]  Joel Brezillon,et al.  Aerodynamic shape optimization using simultaneous pseudo-timestepping , 2005 .

[35]  M. D. Salas,et al.  Aerodynamic design and optimization in one shot , 1992 .

[36]  C. Gil,et al.  The WEST project: Testing ITER divertor high heat flux component technology in a steady state tokamak environment , 2014 .

[37]  Martine Baelmans,et al.  An automated approach to magnetic divertor configuration design, using an efficient optimization methodology (presentation) , 2015 .

[38]  Kyriakos C. Giannakoglou,et al.  Adjoint Methods for Shape Optimization , 2008 .

[39]  Olivier Pironneau,et al.  Applied optimal shape design , 2002 .

[40]  Martine Baelmans,et al.  Fluid Neutral Model for Use in Hybrid Neutral Simulations of a Detached Case , 2016 .

[41]  Martine Baelmans,et al.  Magnetic Field Models and their Application in Optimal Magnetic Divertor Design , 2016 .

[42]  Martine Baelmans,et al.  Efficient parameter estimation in 2D transport models based on an adjoint formalism , 2014 .

[43]  A. Loarte,et al.  Analysis of performance of the optimized divertor in ITER , 2009 .

[44]  M. D. Salas,et al.  Airfoil Design and Optimization by the One-Shot Method , 1995 .