Achievements and Challenges in Automated Parameter, Shape and - PowerPoint PPT Presentation

Achievements and Challenges in Automated Parameter, Shape and Topology Optimization ∞ for Divertor Design M. Baelmans a , M. Blommaert b,a , W. Dekeyser a,b , T. Van Oevelen a , D. Reiter b a Dept. Mechanical Engineering, KU Leuven, Belgium b Inst. of Energy & Climate Research (IEK-4), FZ Jülich, Germany

Divertor design challenges • Interpretation of experimental data To improve models for design o “Control” variables: modeling parameters to be o  ITER estimated: transport coefficients, boundary conditions at outermost flux surface, … • Divertor shape design “Control” variables: shape of targets, dome, o baffles,... • Design of divertor magnetic configuration “Control” variables: currents through coils, o location of coils,... • Design of cooling Valanju et al., Fusion Eng. “Control” variables: topology, size, mass flow Des. 85, 46-52 (2010). o rates, ... Ryutov et al., Phys. Plasmas 15, 092501 (2008) Note: “Control variable” refers to terminology used in optimization 2

Divertor design challenges A modeling perspective Large number of Complex physical model design variables Time consuming simulations (Parameterized) shape of divertor, currents Fluid plasma model (e.g. B2) through divertor coils,... kinetic neutrals (e.g. EIRENE) http://www.iter.org Physics, material and engineering constraints E.g. core stability, peak heat flux limits, neutron shielding,... 3

Design challenges in aerodynamics Drag reduction at Reduction of shock- Shocks constant lift blade interaction Unoptimized Optimized 32% drag reduction (Gauger, VKI LS on MDO, May 2010.) (Shahpar, VKI LS on MDO, May 2010.) Solved with adjoint based shape optimization 4

Design challenges in structural mechanics Design of light weight construction First fluid engineering application Lowest pressure drop for fluid volume max. 1/3 of domain O. Sigmund (2001), Struct. Multidisc. Optim. Borrvall & Peterson (2003), Int. J. Num. Meth.Fluids Solved with adjoint based topology optimization

Outline • Introduction • Edge plasma codes: from analysis to optimization tools? • Achievements and challenges 6

Edge codes as analysis tools Parameters, BCs,... Magnetic Vessel, Simulation Output equilibrium divertor (forward) 40 35 30 Q (MW m −2 ) 25 20 15 10 5 0 −0.02 0 0.020.04 r (m) Design variables (currents, shape) and constraints (stability, shielding,...) 7

Edge codes as analysis tools Parameters, Required for model BCs,... validation, simulation based design,...: Magnetic Vessel, Simulation Fluxes to equilibrium divertor (forward) PFCs Profiles of plasma parameters ... Relatively small > Relatively large number of number of outputs, inputs, constraints,... well defined objectives 8

Edge codes as optimization tools Magnetic Vessel, Simulation Analysis equilibrium divertor (forward) Experimental data Simulation result sensitivity information? Adapt transport Desired Adjoint coefficients, model change simulation parameters A way to compute sensitivities to all parameters at once 9

Outline • Introduction • Edge plasma codes: from analysis to optimization tools • Achievements and challenges Model parameter estimation from experimental data o Shape optimization in divertors o Magnetic optimization o Thermal-fluid optimization of heat sinks o 10

Proof of principle Model parameter estimation Status • Proof of principle • First results on real case 1 M. Baelmans et al. (2014), PPCF 56(11), 114009 Challenges • Introduce Bayesian/likelihood estimators to Incorporate a priori knowledge o Achieve most reliable models o corresponding to available data sets • Global vs. local optima might require hybrid approach (GA/adjoint)

Shape optimization Magnetic Vessel, Simulation Analysis equilibrium divertor (forward) 40 40 Q init Q d 35 35 30 30 Q (MW m −2 ) Q (MW m −2 ) 25 25 20 20 15 15 10 10 5 5 0 0 −0.02 0 0.020.04 −0.02 0 0.020.04 sensitivity r (m) r (m) information? Desired Change in Adjoint change design simulation 0 −5 −10 Q (MW m −2 ) −15 −20 −25 −30 −35 −40 −0.02 0 0.020.04 r (m) 12

Radiation and adjoint radiation models Vessel, Simulation Radiation Analysis divertor (forward) simulation 40 40 Q init Q d 35 35 30 30 Q (MW m −2 ) Q (MW m −2 ) 25 25 20 20 15 15 10 10 5 5 0 0 −0.02 0 0.020.04 −0.02 0 0.020.04 r (m) r (m) Desired Change in Adjoint Adjoint change design simulation radiation 0 −5 −10 Q (MW m −2 ) −15 −20 −25 −30 −35 −40 −0.02 0 0.020.04 r (m) 13

Reactor shape optimization • Thermal flow (PDE) and Radiation (MC) Initial Optimal w. radiation Inner target Outer target 14

Shape optimization Status • Proof of principle • Results on real geometry 1 • Results on FV with MC radiation simulations 2 Need for additional filtering for smooth gradient o • Improved optimization procedures 3 Improvement achieved in approximately 15 equivalent forward o simulations Challenges • Introduce more accurate neutral models (MC or hybrid MC/FV  ER) • Improve speed and convergence issues in plasma edge models 1 W. Dekeyser et al. (2014), Nucl.Fus. 54 2 W. Dekeyser et al. (2015), J.Nucl.Mat. 463 3 W. Dekeyser et al. (2014), JCP 278

Magnetic field optimization Magnetic Grid Simulation equilibrium (forward) Analysis Sensivity Adjoint Design Adjoint calculation simulation update simulation Finite Make step in differences coil currents + Adjoint sensitivity information? 16

Magnetic field optimization • Heat load optimization for WEST Optimized Initial Peak heat load decreases with more than 50% 17

Magnetic field optimization Status • Proof of principle • Results on real geometry (JET 1, WEST 2 ) • Results including free boundary equilibrium FEM code 3 In parts adjoint procedure o • Improved grid generation procedure 50% reduction in cost function after 10 equivalents forward o simulations Challenges • Increase flexibility in magnetic configurations • Further acceleration by one-shot procedure • Integrated magnetic field and plasma simulations (incl. core model) 1 M. Blommaert et al. (2015), Nucl.Fus. 55 1 M. Blommaert et al. (2015), J.Nucl.Mat. 463 2 M. Blommaert et al. (2015), PET-2015 3 M. Blommaert et al. (2015), ESAIM, accepted for publ.

Topology optimization for cooling Electronics cooling Silicon micro heat sink: 1cm x 1cm x 500µm Fixed pressure drop: 10 kPa Heat source 40 K above coolant inlet T Heat sink for constant heat flux Heat sink for constant source: temperature heat source Objective : Objective: Minimal deviation from desired Maximal heat removal from the temperature heat source Easily extended to given heat flux profile and desired temperature

Topology optimization for cooling Compute Compute Build a grid Outcome pressure and temperature fulfilling velocity field constraints field Thermal Solve resistance Pressure drop energy or over heat sink equation hotspot temperature Design variables Compute Desired Compute adj. grey-values sensitivities change temperature Lower Thermal Solve Solve resistance adjoint flow adjoint or hotspot field thermal field temperature

Heat sink topology optimization Constant T • Start with grey; evolve to b/w • Total heat removed: 794 W ( ≈ 8MW/m 2 ) • 30x better than empty cooler

Topology optimization Status • Only recently developed for heat transfer applications • Limited to low Re-flows • First use in micro-electronics cooling applications • Account for production limits is possible Challenges • Improve modeling assumptions • Expand to other applications • Flexible introduction of production limits T. Van Oevelen and Baelmans, M. (2014), Proc. 15th International Heat Transfer Conference (IHTC), Kyoto (Japan).

Conclusions Adjoint methods provide sensitivities Optimization methodology from aerodynamics is extended for use in fusion research: • Model parameter estimation from experimental data • Shape optimization in divertors • Magnetic optimization Optimization methodology from structural mechanics is interesting for innovative cooling concepts • Thermal-fluid optimization of heat sinks • First results in micro-electronics cooling applications reaching 8 MW/m 2 with water cooling

Questions & comments Thank you for your attention

Extra slides

What can the adjoint approach do? • Efficient computation of sensitivities w.r.t. all input parameters (cost of 1 flow simulation per output variable) Design variables: divertor shape, magnetic field, … o (Uncertain) model parameters: anomalous transport coefficients, boundary o conditions,… Operational window o • Automated simulation procedure Automated design o • Divertor shape (W. Dekeyser) • Magnetic field (M. Blommaert) • Topology of coolers (T. Van Oevelen) Automated Uncertainty Quantification (several MSc students) o • ‘Forward’: determine uncertainty on output due to uncertain inputs • ‘Backward’: parameter estimation Robust design (i.e. a combination of these two...) o • Natural framework to include various (design) constraints • Optimal numerical procedures (grids, iterative procedures) 26