Coupling of a micromixing model to computational fluid dynamics: Application to a stirred tank reactor

Kramers Laboratorium voor Fysische TechnologieApplied Science

Modelling and Simulation of Turbulent Bubbly Flow

Applied Science

An angular multigrid preconditioner for the radiation transport equation with Fokker–Planck scattering

In a previous paper (Hennink and Lathouwers, 2017) we developed a finite element discretization for the Boltzmann transport equation with forward peaked scatter modeled by the Fokker–Planck approximation. The discretization was based on the discontinuous Galerkin method in both space and angle. It was expected and found that the regular source iteration algorithm for the Boltzmann equation is not effective in solving the discretized system and becomes excessively expensive for problems with many angular degrees of freedom. The purpose of this paper is to develop a multigrid scheme as preconditioner for the above mentioned discretization. The method exploits the nested nature of the meshes and the natural prolongation/restriction between meshes by Galerkin projection. A set of test problems ranging from pure spherical diffusion to the complete Boltzmann transport problem in 3D are presented to illustrate that the method is very effective, resulting in iteration counts nearly independent of problem size even for highly non-isotropically refined angular meshes.Green Open Access added to TU Delft Institutional Repository ‘You share, we take care!’ – Taverne project https://www.openaccess.nl/en/you-share-we-take-care Otherwise as indicated in the copyright section: the publisher is the copyright holder of this work and the author uses the Dutch legislation to make this work public.RST/Reactor Physics and Nuclear Material

A discontinuous Galerkin method for the mono-energetic Fokker–Planck equation based on a spherical interior penalty formulation

We present a new discretization of the mono-energetic Fokker–Planck equation. We build on previous work (Kópházi and Lathouwers, 2015) where we devised an angular discretization for the Boltzmann equation, allowing for both heterogeneous and anisotropic angular refinement. The angular discretization is based on a discontinuous finite element method on the unit sphere. Here we extend the methodology to include the effect of the Fokker–Planck scatter operator describing small angle particle scatter. We describe the construction of an interior penalty method on the sphere surface. Results are provided for a variety of test cases, ranging from purely angular to fully three-dimensional. The results show that the scheme can resolve highly forward-peaked flux distributions with forward-peaked scatter.Green Open Access added to TU Delft Institutional Repository ‘You share, we take care!’ – Taverne project https://www.openaccess.nl/en/you-share-we-take-care Otherwise as indicated in the copyright section: the publisher is the copyright holder of this work and the author uses the Dutch legislation to make this work public.RST/Reactor Physics and Nuclear Material

A pressure-based solver for low-Mach number flow using a discontinuous Galerkin method

Over the past two decades, there has been much development in discontinuous Galerkin methods for incompressible flows and for compressible flows with a positive Mach number, but almost no attention has been paid to variable-density flows at low speeds. This paper presents a pressure-based discontinuous Galerkin method for flow in the low-Mach number limit. We use a variable-density pressure correction method, which is simplified by solving for the mass flux instead of the velocity. The fluid properties do not depend significantly on the pressure, but may vary strongly in space and time as a function of the temperature. We pay particular attention to the temporal discretization of the enthalpy equation, and show that the specific enthalpy needs to be ‘offset’ with a constant in order for the temporal finite difference method to be stable. We also show how one can solve for the specific enthalpy from the conservative enthalpy transport equation without needing a predictor step for the density. These findings do not depend on the spatial discretization. A series of manufactured solutions with variable fluid properties demonstrate full second-order temporal accuracy, without iterating the transport equations within a time step. We also simulate a Von Kármán vortex street in the wake of a heated circular cylinder, and show good agreement between our numerical results and experimental data.Green Open Access added to TU Delft Institutional Repository ‘You share, we take care!’ – Taverne project https://www.openaccess.nl/en/you-share-we-take-care Otherwise as indicated in the copyright section: the publisher is the copyright holder of this work and the author uses the Dutch legislation to make this work public.RST/Reactor Physics and Nuclear Material

A multi-physics solver for liquid-fueled fast systems based on the discontinuous Galerkin FEM discretization

Performing accurate numerical simulations of molten salt reactors is challenging, especially in case of fast-spectrum designs, due to the unique physics phenomena characterizing these systems. The limitations of codes traditionally used in the nuclear community often require the development of novel high-fidelity multi-physics tools to advance the design of these innovative reactors. In this work, we present the most recent code developed at Delft University of Technology for multi-physics simulations of liquid-fueled fast reactors. The coupling is realized between an incompressible RANS model and an SN neutron transport solver. The models are implemented in two in-house codes, based on the discontinuous Galerkin Finite Element discretization, which guarantees high-quality of the solution. We report and discuss the results of preliminary simulations of the Molten Salt Fast Reactor at steady-state and during a Total Loss of Power transient. Results prove our code has capabilities for steady-state and transient analysis of non-moderated liquid-fueled reactors.RST/Reactor Physics and Nuclear MaterialsRST/Radiation, Science and Technolog

A discontinuous Galerkin FEM multi-physics solver for the molten salt fast reactor

Numerical simulations of fast MSRs constitute a challenging task. In fact, classical codes employed in reactor physics cannot be used, and new dedicated multi-physics tools must be developed, to capture the unique features of these systems: the strong coupling between neutronics and thermal-hydraulics due to the use of a liquid fuel, the effects on reactor kinetics induced by the precursors drift, the internal heat generation, and the shape of the core having no fuel pins as a repeated structure. In this work, we present a novel multi-physics tool being developed at TU Delft. The coupling is realized between an SN radiation transport code (PHANTOM-SN) and a RANS solver (DGFlows). Both in-house tools are based on a Discontinuous Galerkin Finite Element space discretization, characterized by local conservation, high-order accuracy, and allowing for high geometric flexibility. Implicit discretization in time is performed adopting Backward Differentiation Formulae. Cross sections are computed on an element base, starting from the local average temperature and a set of libraries generated at reference temperatures with Monte Carlo or deterministic codes. Comparison of the results obtained performing a suitable numerical benchmark created at LPSC/CNRS/Grenoble with those available in literature shows that the multi-physics tool is able to capture the unique phenomena characterizing fast liquid-fueled systems.RST/Reactor Physics and Nuclear MaterialsRST/Radiation, Science and Technolog

A Deterministic Adjoint-Based Semi-Analytical Algorithm for Fast Response Change Computations in Proton Therapy

In this paper we propose a solution to the need for a fast particle transport algorithm in Online Adaptive Proton Therapy capable of cheaply, but accurately computing the changes in patient dose metrics as a result of changes in the system parameters. We obtain the proton phase-space density through the product of the numerical solution to the one-dimensional Fokker-Planck equation and the analytical solution to the Fermi-Eyges equation. Moreover, a corresponding adjoint system was derived and solved for the adjoint flux. The proton phase-space density together with the adjoint flux and the metric (chosen as the energy deposited by the beam in a variable region of interest) allowed assessing the accuracy of our algorithm to different perturbation ranges in the system parameters and regions of interest. The algorithm achieved negligible errors ((Formula presented.)) for small Hounsfield unit (HU) perturbation ranges (–40 HU to 40 HU) and small to moderate errors (3% to 17%)–in line with the well-known limitation of adjoint approaches–for large perturbation ranges (–400 HU to 400 HU) in the case of most clinical interest where the region of interest surrounds the Bragg peak. Given these results coupled with the capability of further improving the timing performance it can be concluded that our algorithm presents a viable solution for the specific purpose of Online Adaptive Proton Therapy.RST/Medical Physics & TechnologyRST/Reactor Physics and Nuclear Material

A semi-supervised autoencoder framework for joint generation and classification of breathing

Background and objective: One of the main problems with biomedical signals is the limited amount of patient-specific data and the significant amount of time needed to record the sufficient number of samples needed for diagnostic and treatment purposes. In this study, we present a framework to simultaneously generate and classify biomedical time series based on a modified Adversarial Autoencoder (AAE) algorithm and one-dimensional convolutions. Our work is based on breathing time series, with specific motivation to capture breathing motion during radiotherapy lung cancer treatments. Methods: First, we explore the potential in using the Variational Autoencoder (VAE) and AAE algorithms to model breathing signals from individual patients. We then extend the AAE algorithm to allow joint semi-supervised classification and generation of different types of signals within a single framework. To simplify the modeling task, we introduce a pre-processing and post-processing compressing algorithm that transforms the multi-dimensional time series into vectors containing time and position values, which are transformed back into time series through an additional neural network. Results: The resulting models are able to generate realistic and varied samples of breathing. By incorporating 4% and 12% of the labeled samples during training, our model outperforms other purely discriminative networks in classifying breathing baseline shift irregularities from a dataset completely different from the training set, achieving an average macro F1-score of 94.91% and 96.54%, respectively. Conclusion: To our knowledge, the presented framework is the first approach that unifies generation and classification within a single model for this type of biomedical data, enabling both computer aided diagnosis and augmentation of labeled samples within a single framework.RST/Medical Physics & TechnologyRST/Reactor Physics and Nuclear Material

A high-order discontinuous Galerkin solver for the incompressible RANS equations coupled to the k−ϵ turbulence model

Accurate methods to solve the Reynolds-Averaged Navier-Stokes (RANS) equations coupled to turbulence models are still of great interest, as this is often the only computationally feasible approach to simulate complex turbulent flows in large engineering applications. In this work, we present a novel discontinuous Galerkin (DG) solver for the RANS equations coupled to the k−ϵ model (in logarithmic form, to ensure positivity of the turbulence quantities). We investigate the possibility of modeling walls with a wall function approach in combination with DG. The solver features an algebraic pressure correction scheme to solve the coupled RANS system, implicit backward differentiation formulae for time discretization, and adopts the Symmetric Interior Penalty method and the Lax-Friedrichs flux to discretize diffusive and convective terms respectively. We pay special attention to the choice of polynomial order for any transported scalar quantity and show it has to be the same as the pressure order to avoid numerical instability. A manufactured solution is used to verify that the solution converges with the expected order of accuracy in space and time. We then simulate a stationary flow over a backward-facing step and a Von Kármán vortex street in the wake of a square cylinder to validate our approach.RST/Reactor Physics and Nuclear MaterialsRST/Radiation, Science and Technolog