Coarse-Grid-CFD for a Wire Wrapped Fuel Assembly

Computational fluid dynamics (CFD) simulations of complete nuclear reactor core geometries requires exceedingly large computational resources. However, in most cases there are repetitive geometry- and flow patterns allowing the general approach of creating a parameterized model for one segment and composing many of these reduced models to obtain the entire reactor simulation. Traditionally, this approach lead to so-called subchannel analysis codes that are relying heavily on transport models based on experimental and empirical correlations. With our method, the Coarse-Grid-CFD (CGCFD), we intend to replace the experimental or empirical input with CFD data. Our method is based on detailed and well-resolved CFD simulations of representative segments. From these simulations we extract and tabulate volumetric source terms. Parameterized data is used to close an otherwise strongly under resolved, coarsely meshed model of a complete reactor setup. In the previous formulation only forces created internally in the fluid are accounted for. The Anisotropic Porosity (AP) formulation wich is subject of the present investigation adresses other influences, like obstruction and flow guidance through spacers and in particular geometric details which are under resolved or ignored by the coarse mesh. (© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Two Way Coupled Micro/Meso Scale Method for Wind Farms

Wind turbines extract energy from the approaching flow field resulting in reduced wind speeds, increased turbulence and a wake downstream of the wind turbine. The wake has a multitude of negative effects on downstream wind turbines. This includes reduced efficiency and increased unsteadiness resulting in vibrations and potentially in material fatigue. Moreover, the maintenance can increase compared to non-interfering wind turbines. The simulation of these effects is challenging. Computational fluid dynamics (CFD) simulations of these large and complex geometries requires exceedingly large computational resources. With present Reynolds Averaged Navier-Stokes (RANS) or Large Eddy Simulation (LES) based CFD methods it is virtually impossible to perform such simulations of the interaction between individual wind turbines in a complete wind turbine farm. Coupling to the mesoscale accounting for local weather situations becomes yet more challenging. This is due to the wide range of length and time scales that have to be considered for these simulations and therefore the tremendous computational power needed to perform such simulations. To investigate these effects we propose to combine ideas from existing methods, the Coarse-Grid-CFD (CGCFD) ( [1]) developed at the KIT and the meso-/ micro scale method developed at the University of Thessaloniki ( [2]). Goal of the proposed methodology is to provide a numerical method that allows to implement a wind farm in a meso-scale weather simulation which includes two-way coupling. Thus both the micro and the meso scale wind and energy production of wind farms can be addressed. This proposed multi scale coupling strategy can also be applied in two hierarchies reducing the numerical effort of the global approach yet more. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Downscaling data assimilation algorithm with applications to statistical solutions of the Navier–Stokes equations

Based on a previously introduced downscaling data assimilation algorithm, which employs a nudging term to synchronize the coarse mesh spatial scales, we construct a determining map for recovering the full trajectories from their corresponding coarse mesh spatial trajectories, and investigate its properties. This map is then used to develop a downscaling data assimilation scheme for statistical solutions of the two-dimensional Navier–Stokes equations, where the coarse mesh spatial statistics of the system is obtained from discrete spatial measurements. As a corollary, we deduce that statistical solutions for the Navier–Stokes equations are determined by their coarse mesh spatial distributions. Notably, we present our results in the context of the Navier–Stokes equations; however, the tools are general enough to be implemented for other dissipative evolution equations.     

Parallel Smoothed Aggregation Multilevel Schwarz Preconditioned Newton-Krylov Algorithms for Poisson-Boltzmann Problems

We study a multilevel Schwarz preconditioned Newton-Krylov algorithm to solve the Poisson-Boltzmann equation with applications in multi-particle colloidal simulation. The smoothed aggregation-type coarse mesh space is introduced in collaboration with the one-level Schwarz method as a composite preconditioner for accelerating the convergence of a Krylov subspace method for solving the Jacobian system at each Newton step. The important feature of the proposed solution algorithm is that the geometric mesh information needed for constructing the multilevel preconditioner is the same as the one-level Schwarz method on the fine mesh. Other components, such as the definition of the coarse mesh, all the mesh transfer operators, and the coarse mesh problem, are taken care of by the Trillinos/ML packages of the Sandia National Laboratories in the United States. After algorithmic parameter tuning, we show that the proposed smoothed aggregation multilevel Newton-Krylov-Schwarz (NKS) algorithm numerically outperforms than smoothed aggregation multigrid method and one-level version of the NKS algorithm with satisfactory parallel performances up to a few thousand cores. Besides, we investigate how the electrostatic forces between particles for the separation distance depend on the radius of spherical colloidal particles and valence ratios of cation and anion in a cubic system.     

Robust iterative methods for elliptic problems with highly varying coefficients in thin substructures

Summary. In this paper we introduce a class of robust multilevel interface solvers for two-dimensional finite element discrete elliptic problems with highly varying coefficients corresponding to geometric decompositions by a tensor product of strongly non-uniform meshes. The global iterations convergence rate is shown to be of the order with respect to the number of degrees of freedom on the single subdomain boundaries, uniformly upon the coarse and fine mesh sizes, jumps in the coefficients and aspect ratios of substructures. As the first approach, we adapt the frequency filtering techniques [28] to construct robust smoothers on the highly non-uniform coarse grid. As an alternative, a multilevel averaging procedure for successive coarse grid correction is proposed and analyzed. The resultant multilevel coarse grid preconditioner is shown to have (in a two level case) the condition number independent of the coarse mesh grading and jumps in the coefficients related to the coarsest refinement level. The proposed technique exhibited high serial and parallel performance in the skin diffusion processes modelling [20] where the high dimensional coarse mesh problem inherits a strong geometrical and coefficients anisotropy. The approach may be also applied to magnetostatics problems as well as in some composite materials simulation. Received December 27, 1994     

Energy analysis and improved regularity estimates for multiscale deconvolution models of incompressible flows

This paper presents new analytical results and the first numerical results for a recently proposed multiscale deconvolution model (MDM) recently proposed. The model involves a large‐eddy simulation closure that uses a novel deconvolution approach based on the introduction of two distinct filtering length scales. We establish connections between the MDM and two other models, and, on the basis of one of these connections, we establish an improved regularity estimate for MDM solutions. We also prove that the MDM preserves Taylor‐eddy solutions of the Navier–Stokes equations and therefore does not distort this particular vortex structure. Simulations of the MDM are performed to examine the accuracy of the MDM and the effect of the filtering length scales on energy spectra for three‐dimensional homogeneous and isotropic flows. Numerical evidence for all tests clearly indicates that the MDM gives very accurate coarse‐mesh solutions and that this multiscale approach to deconvolution is effective. Copyright © 2015 John Wiley & Sons, Ltd.     

A new approach for the optimal distribution of assemblies in a nuclear reactor

Summary. The aim of this paper is to propose a new approach for optimizing the position of fuel assemblies in a nuclear reactor core. This is a control problem for the neutronic diffusion equation where the control acts on the coefficients of the equation. The goal is to minimize the power peak (i.e. the neutron flux must be as spatially uniform as possible) and maximize the reactivity (i.e. the efficiency of the reactor measured by the inverse of the first eigenvalue). Although this is truly a discrete optimization problem, our strategy is to embed it in a continuous one which is solved by the homogenization method. Then, the homogenized continuous solution is numerically projected on a discrete admissible distribution of assemblies. Received January 13, 2000 / Published online February 5, 2001     

Absorbing Interface Conditions for the Simulation of Wave Propagation on Non-Uniform Meshes

We proposed absorbing interface conditions for the simulation of linear wave propagation on non-uniform meshes. Based on the superposition principle of second-order linear wave equations, we decompose the interface condition problem into two subproblems around the interface: for the first one the conventional artificial absorbing boundary conditions is applied, while for the second one, the local analytic solutions can be derived. The proposed interface conditions permit a two-way transmission of low-frequency waves across mesh interfaces which can be supported by both coarse and fine meshes, and perform a one-way absorption of high-frequency waves which can only be supported by fine meshes when they travel from fine mesh regions to coarse ones. Numerical examples are presented to illustrate the efficiency of the proposed absorbing interface conditions.     

Numerical approximation of the Smagorinsky model by a two-level method

A two-level method for discretizing the Smagorinsky model for the numerical simulation of turbulent flows is proposed. In the two-level algorithm, the solution to the fully nonlinear coarse mesh problem is utilized in a single-step linear fine mesh problem. When modeling parameters are chosen appropriately, the error in the two-level algorithm is comparable to the error in solving the fully nonlinear problem on the fine mesh. We provide an a priori error estimate for the two-level method, which yields appropriate scalings between the coarse and fine mesh-sizes (H and h, respectively), and the radius of the spatial filter used in the Smagorinsky model (δ). In addition, we provide an algorithm in which a coarse mesh correction is performed to further enhance the accuracy. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Hybrid Surface Mesh Adaptation for Climate Modeling

Solution-driven mesh adaptation is becoming quite popular for spatial error control in the numerical simulation of complex computational physics applications, such as climate modeling. Typically, spatial adaptation is achieved by element subdivision （h adaptation） with a primary goal of resolving the local length scales of interest. A sec- ond, less-popular method of spatial adaptivity is called ＂mesh motion＂ （r adaptation）; the smooth repositioning of mesh node points aimed at resizing existing elements to capture the local length scales. This paper proposes an adaptation method based on a combination of both element subdivision and node point repositioning （rh adaptation）. By combining these two methods using the notion of a mobility function, the proposed approach seeks to increase the flexibility and extensibility of mesh motion algorithms while providing a somewhat smoother transition between refined regions than is pro- duced by element subdivision alone. Further, in an attempt to support the requirements of a very general class of climate simulation applications, the proposed method is designed to accommodate unstructured, polygonal mesh topologies in addition to the most popular mesh types.     

Two‐level discretization of the Navier‐Stokes equations with r‐Laplacian subgridscale viscosity

The r‐Laplacian has played an important role in the development of computationally efficient models for applications, such as numerical simulation of turbulent flows. In this article, we examine two‐level finite element approximation schemes applied to the Navier‐Stokes equations with r‐Laplacian subgridscale viscosity, where r is the order of the power‐law artificial viscosity term. In the two‐level algorithm, the solution to the fully nonlinear coarse mesh problem is utilized in a single‐step linear fine mesh problem. When modeling parameters are chosen appropriately, the error in the two‐level algorithm is comparable to the error in solving the fully nonlinear problem on the fine mesh. We provide rigorous numerical analysis of the two‐level approximation scheme and derive scalings which vary based on the coefficient r, coarse mesh size H, fine mesh size h, and filter radius δ. We also investigate the two‐level algorithm in several computational settings, including the 3D numerical simulation of flow past a backward‐facing step at Reynolds number Re = 5100. In all numerical tests, the two‐level algorithm was proven to achieve the same order of accuracy as the standard one‐level algorithm, at a fraction of the computational cost. © 2011 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2011     

Anisotropic mesh adaptation for numerical solution of boundary value problems

We present an efficient mesh adaptation algorithm that can be successfully applied to numerical solutions of a wide range of 2D problems of physics and engineering described by partial differential equations. We are interested in the numerical solution of a general boundary value problem discretized on triangular grids. We formulate a necessary condition for properties of the triangulation on which the discretization error is below the prescribed tolerance and control this necessary condition by the interpolation error. For a sufficiently smooth function, we recall the strategy how to construct the mesh on which the interpolation error is below the prescribed tolerance. Solving the boundary value problem we apply this strategy to the smoothed approximate solution. The novelty of the method lies in the smoothing procedure that, followed by the anisotropic mesh adaptation (AMA) algorithm, leads to the significant improvement of numerical results. We apply AMA to the numerical solution of an elliptic equation where the exact solution is known and demonstrate practical aspects of the adaptation procedure: how to control the ratio between the longest and the shortest edge of the triangulation and how to control the transition of the coarsest part of the mesh to the finest one if the two length scales of all the triangles are clearly different. An example of the use of AMA for the physically relevant numerical simulation of a geometrically challenging industrial problem (inviscid transonic flow around NACA0012 profile) is presented. © 2004 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2004.     

CFD simulation of deflagration–detonation processes using vector- and parallel computing systems

In this paper, we describe the state of computational fluid dynamics simulations (CFD) of deflagration and detonation processes in hydrogen–air mixtures, using vector- and parallel computing systems, which have been provided in the Institute for Safety Research and Reactor Technology (ISR) at the Forschungszentrum Jülich (FZJ). The R&D work is performed within the scope of an EC project on hydrogen safety that is addressed to the verification of models and criteria for the prediction of Deflagration-to-Detonation Transition (DDT) in hydrogen–air–steam systems under severe accident conditions. Particularly, we report on the present state and recent progress made in the establishment of the CRAY hardware cluster (T90, T3E, J90) with vector and parallel processing capabilities, as well as on the current achievement of the CFD software cluster (CFX, ERCO, DET, IFSAS), including test cases for verification and validation, with some illustrating examples. Emphasis is put on the multi-dimensional simulation of fast turbulent hydrogen flames, for instance, using the general purpose field code CFX from AEA. The numerical results are compared with experimental results, which have been obtained for various conditions in the Russian large scale RUT test facility. Specifically, we outline deflagration–detonation processes concerning the numerical resolution of reacting flows in complex geometries, applying mesh refinement or massively parallel processing. First test cases indicate that our modern field code cluster (MFCC) with high-performance supercomputer networking (HPCN) will be a suitable constellation to resolve DDT processes in safety enclosures of innovative nuclear reactor containments or other industrial plants, e.g. solar hydrogen demonstration facilities.     

Adaptation of the law of the wall boundary treatment to include volumetric heating effects

Computational Fluid Dynamics (CFD) simulations of liquid–metal spallation targets, such as MEGAPIE and ESS, which utilize the High Reynolds number k–ε turbulence model, invariably incorporate an implicit law of the wall treatment in which a linear or logarithmic fit to the velocity and temperature profiles is made next to heated, non-slip surfaces. The law is well-established, but has been derived from the assumptions that the wall shear stress and the normal heat flux are constant through the viscous sub-layer and buffer zone, which lie beneath the turbulent boundary layer. However, in the case of the heat flux, this condition will be violated for applications in which there is intense volumetric heating in the near-wall layers. This is just the case for the spallation reactions taking place in liquid–metal targets as a result of proton bombardment. In this article, a modified law of the wall is derived to be used under such conditions. Use of the law is illustrated by means of flow in a flat channel and one application to a spallation target. From the applications considered, it is found that the effect of the modification is small, provided the local mesh resolution is chosen appropriately. Specific recommendations regarding optimum mesh size for liquid–metal heat transfer problems are given, which will be of general interest, with or without volumetric heating.     

Energy-momentum conserving discretization of mixed shell elements for large deformation problems

In the present paper we consider structure-preserving integration methods in the context of mixed finite elements. The used low-order mixed finite elements typically exhibit improved coarse mesh accuracy. On the other hand energy-momentum (EM) consistent time-stepping schemes have been developed in the realm of nonlinear structural dynamics to enhance the numerical stability properties. EM schemes typically exhibit superior robustness and thus offer the possibility to use large time steps while still producing physically meaningful results. Accordingly, combining mixed finite element discretizations in space with EM consistent discretizations in time shows great promise for the design of numerical methods with superior coarse mesh accuracy in space and time. Starting with a general Hu-Washizu-type variational formulation we develop a second-order accurate structure-preserving integration scheme. The present approach is applicable to a large number of mixed finite element formulations. As sample application we deal with a specific mixed shell element. Numerical examples dealing with large deformations will show the improved coarse mesh accuracy in space and time of the advocated approach. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

A two-grid method with backtracking for the mixed Navier–Stokes/Darcy model

In this paper, we consider the effect of adding a coarse mesh correction to the two-grid algorithm for the mixed Navier–Stokes/Darcy model. The method yields both L² and H¹ optimal velocity and piezometric head approximations and an L² optimal pressure approximation. The method involves solving one small, coupled, nonlinear coarse mesh problem, two independent subproblems (linear Navier–Stokes equation and Darcy equation) on the fine mesh, and a correction problem on the coarse mesh. Theoretical analysis and numerical tests are done to indicate the significance of this method.     

Static contact analysis of spiral bevel gear based on modified VFIFE (vector form intrinsic finite element) method

Since the intrinsic limitations of FEM (Finite element method) and lumped-mass method, we derive the formula of 8-node hexahedral element based on VFIFE (vector form intrinsic finite element method) method and applied it in contact analysis of gears. This paper proposed a new method to determine pure nodal deformation, which could simplify the computation compared to the traditional VFIFE method. Combining the VFIFE method and matching contact algorithm, we analyzed spiral bevel gear meshing problems. Spiral bevel models with two different mesh densities are calculated analyzed by the VFIFE method and FEM. Performance indicators of gears are extracted and compared, including contact forces, contact and bending stresses, contact stress patterns and loaded transmission errors. The results show that the VFIFE method has a stable performance and reliable accuracy under coarse or refined mesh conditions, while the FEM inaccurately calculates the contact stress of the coarse mesh model. The examples demonstrate that the proposed method could precisely analyze gear meshing problems with a coarse mesh model, which provides a new solution for gear mechanics.     

基于修正积分模型的油量表重新标定与储油罐变位识别的研究

针对储油罐在使用一定时间后会发生变位即纵向倾斜和横向偏转导致罐容表度量不准确的问题，利用修正的积分方法分别建立椭圆油罐变位后储油量与油位高度模型和两头为球冠体储油罐变位后储油量与油位高度模型及变位参数确定模型，针对上述模型通过Matlab软件求解，得到了重新标定的椭圆储油罐和两头为球冠体储油罐的油量表，确定了储油罐的纵...     

A Multiscale Approach for the Modelling of Failure

In the present contribution a multi–scale – or rather two–scale – framework for the modelling of propagating discontinuities is introduced. The method is based on the Variational Multiscale Method. The displacement field is additively decomposed into a coarse– and a fine–scale part. This kinematic assumption implies a separation of the weak form in two equations, corresponding to the coarse–scale and the fine–scale problem. Both scales are discretized by means of finite elements. On the fine–scale, due to a much finer discretization, a heteregeneous mesostructure and propagating mesocracks can be considered. The propagation of the mesocracks is simulated independently of the underlying finite element mesh by discontinuous elements. The performance of the multi–scale approach is shown by a numerical example. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

GasTurbnLab: a multidisciplinary problem solving environment for gas turbine engine design on a network of nonhomogeneous machines

Gas turbine engines are very complex (with 20–40,000 parts) and have extreme operating conditions. The important physical phenomena take place on scales from 10–100 microns to meters. A complete and accurate dynamic simulation of an entire engine is enormously demanding. Designing a complex system, like a gas turbine engine, will require fast, accurate simulations of computational models from multiple engineering disciplines along with sophisticated optimization techniques to help guide the design process. In this paper, we describe the architecture of an agent-based software framework for the simulation of various aspects of a gas turbine engine, utilizing a “network” of collaborating numerical objects through a set of interfaces among the engine parts. Moreover, we present its implementation using the Grasshopper agent middleware and provide simulation results that show the feasibility of the computational paradigm implemented.