Optimal Plasma Edge Configurations for Next-Step Fusion Reactors (Optimale plasmarand-configuraties voor nieuwe generatie fusiereactoren)

The goal of the research is to significantly improve the working conditions of next-step fusion reactors (ITER, DEMO). More specifically, optimization techniques are developed for coupled plasma edge simulation codes. Primarily geometric optimization of fusion reactors subject to strong recycling conditions is aimed for. In a first stage, numerical optimization of the divertor targets with respect to optimal energy load spreading at fixed pumping capacity is envisaged. By using advanced adjoint-based optimization algorithms, the entire divertor design problem is solved at a computational cost only a small multiple of the cost of a single edge plasma simulation. The research opens further perspectives towards the optimization of transient operating conditions such as ELMs (edge-localizedmodes), optimal Carbon deposition and Helium removal.nrpages: 310status: publishe

IMPROVED MODELING APPROACH FOR HEAT SINK TOPOLOGY OPTIMIZATION

The ongoing pursuit for higher power densities in electronic devices poses severe demands on cooling solutions. To explore the full potential of liquid-cooled microchannel heat sinks, topology optimization has been proposed as a method to optimize the microchannel layout. This has led to novel tree-like microchannel layouts. However, deficiencies in the porous medium models used thus far often lead to designs with disconnected channels, that cannot be used in practice. In this contribution, a new modeling approach is proposed for microchannel based heat sink topology optimization. A virtual pressure is introduced in the solid phase of the topology. This pressure field together with a zero velocity field in the solid then can be used for the regularization of the binary design variable. As a result, continuous optimization techniques can be used. This leads to improved results compared to optimization based on porous medium models for the solid phase. Indeed, in the latter case small leakage flows through the solid need to be tolerated in the numerical implementation, leading to inaccurate thermal modeling or ill-conditioned matrix systems. The approach presented in this paper circumvents these problems. The absence of penetration in our new model is demonstrated by two benchmarks. Performance of this model for optimization is validated by a hydraulic inverse design problem.status: publishe

A new mean-field plasma edge transport model based on turbulent kinetic energy and enstrophy

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Divertor Design through Shape Optimization

Due to the conflicting requirements, complex physical processes and large number of design variables, divertor design for next step fusion reactors is a challenging problem, often relying on large numbers of computationally expensive numerical simulations. In this paper, we attempt to partially automate the design process by solving an appropriate shape optimization problem. Design requirements are incorporated in a cost functional which measures the performance of a certain design. By means of changes in the divertor shape, which in turn lead to changes in the plasma state, this cost functional can be minimized. Using advanced adjoint methods, optimal solutions are computed very efficiently. The approach is illustrated by designing divertor targets for optimal power load spreading, using a simplified edge plasma model.status: publishe

Optimal shape design for divertors

Owing to the complex physics of the plasma edge, numerical simulation tools are indispensable for the evaluation of novel divertor concepts. Simulation-based divertor design is computationally extremely expensive, however, not in the least due to the large number of design variables. In this work, we show how shape optimisation methods can prove very valuable in partially automating the design process. We apply the continuous adjoint method to design divertor targets for maximum power load spreading. Shape sensitivities are derived using the material derivative approach. The resulting sensitivities depend on boundary data only, and can be computed very efficiently. Through numerical tests, we also prove that their accuracy is good. Next, the performance of two gradient-based optimisation algorithms and a so-called one-shot method is compared. Using the latter method, optimal solutions are obtained in a computational effort less than five times the time needed for a single analysis simulatio

Automated divertor target design by adjoint shape sensitivity analysis and a one-shot method

As magnetic confinement fusion progresses towards the development of first reactor-scale devices, computational tokamak divertor design is a topic of high priority. Presently, edge plasma codes are used in a forward approach, where magnetic field and divertor geometry are manually adjusted to meet design requirements. Due to the complex edge plasma flows and large number of design variables, this method is computationally very demanding. On the other hand, efficient optimization-based design strategies have been developed in computational aerodynamics and fluid mechanics. Such an optimization approach to divertor target shape design is elaborated in the present paper. A general formulation of the design problems is given, and conditions characterizing the optimal designs are formulated. Using a continuous adjoint framework, design sensitivities can be computed at a cost of only two edge plasma simulations, independent of the number of design variables. Furthermore, by using a one-shot method the entire optimization problem can be solved at an equivalent cost of only a few forward simulations. The methodology is applied to target shape design for uniform power load, in simplified edge plasma geometry.publisher: Elsevier articletitle: Automated divertor target design by adjoint shape sensitivity analysis and a one-shot method journaltitle: Journal of Computational Physics articlelink: http://dx.doi.org/10.1016/j.jcp.2014.08.023 content_type: article copyright: Copyright © 2014 Elsevier Inc. All rights reserved.status: publishe

Designing divertor targets for uniform power load

Divertor design for next step fusion reactors heavily relies on 2D edge plasma modeling with codes as e.g. B2-EIRENE. While these codes are typically used in a design-by-analysis approach, in previous work we have shown that divertor design can alternatively be posed as a mathematical optimization problem, and solved very efficiently using adjoint methods adapted from computational aerodynamics. This approach has been applied successfully to divertor target shape design for more uniform power load. In this paper, the concept is further extended to include all contributions to the target power load, with particular focus on radiation. In a simplified test problem, we show the potential benefits of fully including the radiation load in the design cycle as compared to only assessing this load in a post-processing step.publisher: Elsevier articletitle: Designing divertor targets for uniform power load journaltitle: Journal of Nuclear Materials articlelink: http://dx.doi.org/10.1016/j.jnucmat.2014.10.064 content_type: article copyright: Copyright © 2014 Elsevier B.V. All rights reserved.status: publishe

Assessment of fluid neutral models for a detached ITER case

© 2016 EURATOM We compare the plasma sources (particle, parallel momentum and ion energy) due to plasma-neutral interactions computed with different fluid neutral models with the sources from a Monte Carlo simulation of the kinetic neutral equation. This is done for a fixed background plasma, which is representative for an ITER detached case. We illustrate that the reaction data from the AMJUEL-HYDHEL databases can be incorporated in the fluid models. A pure pressure-diffusion equation gives already accurate results for the particle source, but it is inaccurate for the momentum and energy source. A parallel momentum equation has to be added to achieve predictions of the momentum and energy source within 30% of accuracy. Newly developed boundary conditions, based on the diffusion approximation for incident neutrals, show to be crucial for accurate results of the fluid models close to the divertor target. The slight overestimation of the momentum and energy sources can be further reduced by adding a separate neutral energy equation.status: publishe

Accuracy and convergence of coupled finite-volume / Monte-Carlo codes for plasma edge simulations of nuclear fusion reactors

© 2016 Elsevier Inc. The plasma and neutral transport in the plasma edge of a nuclear fusion reactor is usually simulated using coupled finite volume (FV)/Monte Carlo (MC) codes. However, under conditions of future reactors like ITER and DEMO, convergence issues become apparent. This paper examines the convergence behaviour and the numerical error contributions with a simplified FV/MC model for three coupling techniques: Correlated Sampling, Random Noise and Robbins Monro. Also, practical procedures to estimate the errors in complex codes are proposed. Moreover, first results with more complex models show that an order of magnitude speedup can be achieved without any loss in accuracy by making use of averaging in the Random Noise coupling technique.publisher: Elsevier articletitle: Accuracy and convergence of coupled finite-volume/Monte Carlo codes for plasma edge simulations of nuclear fusion reactors journaltitle: Journal of Computational Physics articlelink: http://dx.doi.org/10.1016/j.jcp.2016.06.049 content_type: article copyright: © 2016 Elsevier Inc. All rights reserved.status: publishe

Filtering in Microchannel Heat Sink Topology Optimization

In recent years, the design of microchannel heat sinks has shifted from an empirical approach to more optimization based mathematical approaches. This tactic of numerically simulating the design problem using topology optimization allows for further improvement of existing designs and development of novel lay-outs with enhanced performance. From a physical point of view, the smaller the channel size in these optimized designs, the larger the heat transfer from the source to the cooling fluid, hence the better the performance, though inferring higher pressure drops. This forces microchannel topologies to incorporate ever smaller and shorter channels. Consequently, a disadvantage of using numerical simulation is the dependency of the optimized design on the coarseness of the grid used to perform the simulations. On the other hand, for very fine grids, designs are obtained that lack manufacturability due to optimized channel sizes that are too small. In structural topology optimization, regularization methods are used to overcome these problems. A number of approaches exist, and among them mesh-independent filtering methods are one of the most popular. Two subcategories of filtering methods can be identified, namely density and sensitivity filtering. In this research, both density and sensitivity filtering are tested within topology optimization of liquid cooling microchannel heat sinks. To this end, the conjugate heat transfer equations are numerically simulated using the finite volume method. The optimized designs are evaluated based on the level of grid independence and manufacturability achieved by using the filters. Results indicate that a lack of grid independence remains even after application of filtering. Reasons for this behavior include the non-convexity of the optimization problem, which has a tendency to get stuck in different local minima, and insufficient resolution of the flow in the smallest channels for coarse grids. Additionally, it is difficult to ensure manufacturability by using filtering since the production constraints cannot directly be translated into equivalent parameter values for the filter in the optimization process. Both filtering methods also have their own distinct effect on the optimized designs stemming from how the design constraints are handled in the optimization algorithm. Finally, the two filter methods are also mutually compared in order to determine if the exact same optimized design can be attained, irrespective of which filter method is used. It can be proven that for unconstrained optimization problems with certain conditions relating the filters, this is in fact the case.status: accepte