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All sourcesNASA NTRSDOE OSTI
DOE OSTI2012

Development Status of PROTEUS-MOC

The PROTEUS-MOC solver is intended to resolve the outstanding computational challenges that the PROTEUS-SN is limited by and bridge the gap between PROTEUS-SN and existing homogenized structured grid solvers. The primary push behind all of this work is to carry out coupled thermal-mechanical, fluid dynamics, and neutronics physics problems. The PROTEUS-MOC development has taken advantage of the combined experience with PROTEUS-SN and DeCART with the goal of producing a tool which combines the best features of both tools. Taking the DeCART tool as the model, it merges a subgroup cross section interpolation technique with a 2D method of characteristics approach and a 1D SN formulation. DeCART has been specifically demonstrated to be accurate on PWR and VHTR problems, but it has displayed several issues with regard to accuracy on thin axial mesh sizes which are attributable to the 2D1D scheme it is built upon. There are also notable problems with performance and scalability all of which we hope to resolve in PROTEUS-MOC. PROTEUS-MOC is at its core, based upon the success achieved with MOCFE which demonstrated excellent parallelization with respect to angle and good parallelization with respect to space. More recent efforts have indicated parallelization with respect to energy is also feasible. The work completed yielded a novel methodology where the axial basis functions are treated separately from the radial ones, but the geometry is extruded. This eliminates the need to carry out and store 3D ray tracing data and simultaneously allows the coarse axial node sizes typical with DeCART. To rapidly build a prototype, a standard power iteration algorithm was constructed using an unpreconditioned GMRES solution algorithm for solving the flux vector in each fission source iteration. The new PROTEUS-MOC solver was deployed on two test problems: Takeda and a heterogeneous cylindrical heavy water system. The Takeda benchmark problem is a standard homogeneous test problem which was previously found to be too difficult for the 3D MOCFE code to solve. Using the PROTEUS-MOC we were able to show space-angle convergence although full convergence requires further improvements in performance. The second benchmark problem was constructed more for future work than this year, but the results generated are promising indicating that it will be very useful in highlighting the weaknesses and strengths of the PROTEUS-MOC tool. While we are far from a production tool, the results included in this report give us confidence that we are on the right path to constructing an interceding code between the plethora of structured grid homogenized assembly solvers and the supercomputer consuming PROTEUS-SN code. With time, the creation of a suitable preconditioner along with typical optimization should reduce the performance shortcomings that are observable today.

Marin-Lafleche, A.↗
DOE OSTI2017

Implicit mesh discontinuous Galerkin methods and interfacial gauge methods for high-order accurate interface dynamics, with applications to surface tension dynamics, rigid body fluid–structure interaction, and free surface flow: Part II

Here, in this two-part paper, a high-order accurate implicit mesh discontinuous Galerkin (dG) framework is developed for fluid interface dynamics, facilitating precise computation of interfacial fluid flow in evolving geometries. The framework uses implicitly defined meshes—wherein a reference quadtree or octree grid is combined with an implicit representation of evolving interfaces and moving domain boundaries—and allows physically prescribed interfacial jump conditions to be imposed or captured with high-order accuracy. Part one discusses the design of the framework, including: (i) high-order quadrature for implicitly defined elements and faces; (ii) high-order accurate discretisation of scalar and vector-valued elliptic partial differential equations with interfacial jumps in ellipticity coefficient, leading to optimal-order accuracy in the maximum norm and discrete linear systems that are symmetric positive (semi)definite; (iii) the design of incompressible fluid flow projection operators, which except for the influence of small penalty parameters, are discretely idempotent; and (iv) the design of geometric multigrid methods for elliptic interface problems on implicitly defined meshes and their use as preconditioners for the conjugate gradient method. Also discussed is a variety of aspects relating to moving interfaces, including: (v) dG discretisations of the level set method on implicitly defined meshes; (vi) transferring state between evolving implicit meshes; (vii) preserving mesh topology to accurately compute temporal derivatives; (viii) high-order accurate reinitialisation of level set functions; and (ix) the integration of adaptive mesh refinement. In part two, several applications of the implicit mesh dG framework in two and three dimensions are presented, including examples of single phase flow in nontrivial geometry, surface tension-driven two phase flow with phase-dependent fluid density and viscosity, rigid body fluid–structure interaction, and free surface flow. A class of techniques known as interfacial gauge methods is adopted to solve the corresponding incompressible Navier–Stokes equations, which, compared to archetypical projection methods, have a weaker coupling between fluid velocity, pressure, and interface position, and allow high-order accurate numerical methods to be developed more easily. Convergence analyses conducted throughout the work demonstrate high-order accuracy in the maximum norm for all of the applications considered; for example, fourth-order spatial accuracy in fluid velocity, pressure, and interface location is demonstrated for surface tension-driven two phase flow in 2D and 3D. Specific application examples include: vortex shedding in nontrivial geometry, capillary wave dynamics revealing fine-scale flow features, falling rigid bodies tumbling in unsteady flow, and free surface flow over a submersed obstacle, as well as high Reynolds number soap bubble oscillation dynamics and vortex shedding induced by a type of Plateau–Rayleigh instability in water ripple free surface flow. In these last two examples compare numerical results with experimental data and serve as an additional means of validation; they also reveal physical phenomena not visible in the experiments, highlight how small-scale interfacial features develop and affect macroscopic dynamics, and demonstrate the wide range of spatial scales often at play in interfacial fluid flow.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2017

Implicit mesh discontinuous Galerkin methods and interfacial gauge methods for high-order accurate interface dynamics, with applications to surface tension dynamics, rigid body fluid–structure interaction, and free surface flow: Part I

In this two-part paper, a high-order accurate implicit mesh discontinuous Galerkin (dG) framework is developed for fluid interface dynamics, facilitating precise computation of interfacial fluid flow in evolving geometries. The framework uses implicitly defined meshes—wherein a reference quadtree or octree grid is combined with an implicit representation of evolving interfaces and moving domain boundaries—and allows physically prescribed interfacial jump conditions to be imposed or captured with high-order accuracy. Part one discusses the design of the framework, including: (i) high-order quadrature for implicitly defined elements and faces; (ii) high-order accurate discretisation of scalar and vector-valued elliptic partial differential equations with interfacial jumps in ellipticity coefficient, leading to optimal-order accuracy in the maximum norm and discrete linear systems that are symmetric positive (semi)definite; (iii) the design of incompressible fluid flow projection operators, which except for the influence of small penalty parameters, are discretely idempotent; and (iv) the design of geometric multigrid methods for elliptic interface problems on implicitly defined meshes and their use as preconditioners for the conjugate gradient method. Also discussed is a variety of aspects relating to moving interfaces, including: (v) dG discretisations of the level set method on implicitly defined meshes; (vi) transferring state between evolving implicit meshes; (vii) preserving mesh topology to accurately compute temporal derivatives; (viii) high-order accurate reinitialisation of level set functions; and (ix) the integration of adaptive mesh refinement. In part two, several applications of the implicit mesh dG framework in two and three dimensions are presented, including examples of single phase flow in nontrivial geometry, surface tension-driven two phase flow with phase-dependent fluid density and viscosity, rigid body fluid–structure interaction, and free surface flow. A class of techniques known as interfacial gauge methods is adopted to solve the corresponding incompressible Navier–Stokes equations, which, compared to archetypical projection methods, have a weaker coupling between fluid velocity, pressure, and interface position, and allow high-order accurate numerical methods to be developed more easily. Convergence analyses conducted throughout the work demonstrate high-order accuracy in the maximum norm for all of the applications considered; for example, fourth-order spatial accuracy in fluid velocity, pressure, and interface location is demonstrated for surface tension-driven two phase flow in 2D and 3D. Specific application examples include: vortex shedding in nontrivial geometry, capillary wave dynamics revealing fine-scale flow features, falling rigid bodies tumbling in unsteady flow, and free surface flow over a submersed obstacle, as well as high Reynolds number soap bubble oscillation dynamics and vortex shedding induced by a type of Plateau–Rayleigh instability in water ripple free surface flow. In conclusion, these last two examples compare numerical results with experimental data and serve as an additional means of validation; they also reveal physical phenomena not visible in the experiments, highlight how small-scale interfacial features develop and affect macroscopic dynamics, and demonstrate the wide range of spatial scales often at play in interfacial fluid flow.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Modeling the Effects of Artificial Drainage on Agriculture-dominated Watersheds using a Fully Distributed Integrated Hydrology Model: Datasets, scripts, model files

This model-data archive supports the research paper that demonstrates the integration of agricultural drainage features—specifically, narrow engineered ditches and tile drains—into a fully distributed, basin-scale integrated surface-subsurface hydrology model (ISSHM), Amanzi-ATS. The model employs innovative computational meshes aligned with agricultural ditches and incorporates the physically based Hooghoudt's drainage equation to simulate tile drainage, offering a novel strategy that enhances the accuracy of hydrological simulations.The archived dataset includes input parameters, model configurations, and select simulation outputs for the Amanzi-ATS model that successfully captured the streamflow patterns in the Portage River Watershed as validated by USGS gauge readings. Jupyter notebook for the preparation of model inputs and post-processing of outputs are also included. The model's predictive performance achieved a normalized Kling-Gupta Efficiency (KGE) of 0.81, surpassing SWAT without the necessity for site-specific calibration.The Amanzi-ATS model presented in this modeL-data archive allows for numerical experiments to explore the shifts in the flow structure under different drainage scenarios. As a tool for advancing the understanding of distributed hydrological responses and nutrient cycling, this archived model provides valuable insights for researchers, modelers, and decision-makers involved in watershed management and environmental modeling.The Watershed Workflow package is implemented in Python3. The Jupyter notebooks can be executed through multiple open-source tools, for example, Anaconda Jupyter Lab, VS Studio Code, etc. Other data files include CSV and HDF5 files, which can be read through Python scripts. The input files for the ATS model, open-source integrated hydrology, and transport model, are in XML format and can be edited in any commonly used text editors.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2022

Reducing Memory Consumption in Calico with Shared Memory

This document details the work to reduce memory consumption in Calico. Calico is SimTools’ Constructive Solid Geometry (CSG) and geometry painting library. It is primarily used to paint material volume fractions in the Eulerian meshes of the physics codes. Calico provides point-in-body checks for the geometry supplied by an Oso model, which are then aggregated by the host codes. In addition, Calico can be used to build Oso models and is used by Ingen for that purpose. Oso models, and thus Calico, provide support for various CSG primitives such as spheres, cylinders, surfaces generated by rotating tabular curve data, and STL files as well as binary combinations of those primitives. Prior to refactoring Calico will run out of memory on CTS-1 machines when 36 MPI ranks are used per node when reading STL models on the order of 1.5 GB. This limitation is a bottleneck in designer workflow. This problem has been alleviated through the use of data structures to both reduce memory consumption and to leverage MPI-3 shared memory. This report details the data structures targeted for refactoring in Calico, the methods and implementation details for reducing memory consumption and leveraging shared memory, and results for one test problem. Results show a memory reduction when loading a 1 GB STL file by a factor of 27.5, from 93.4 to 3.4 GB.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2016

Uniaxial Compression of Cellular Materials at a 10 -1 s -1 Strain Rate Simultaneously with Synchrotron X-ray Computed Tomographic Imaging

The topic is presented as a series of slides. Motivation for the work included the following: X-ray tomography is a fantastic technique for characterizing a material’s starting structure as well as for non-destructive, in situ experiments to investigate material response; 3D X-ray tomography is needed to fully characterize the morphology of cellular materials; and synchrotron micro-CT can capture 3D images without pausing experiment. Among the conclusions reached are these: High-rate radiographic and tomographic imaging (0.25 s 3D frame rate) using synchrotron CT can capture full 3D images of hyper-elastic materials at a 10 -2 strain rate; dynamic true in situ uniaxial loading can be accurately captured; the three stages of compression can be imaged: bending, buckling, and breaking; implementation of linear modeling is completed; meshes have been imported into LANL modeling codes--testing and validation is underway and direct comparison and validation between in situ data and modeled mechanical response is possible.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
NASA NTRS1992

The Keck keyword layer

Each Keck instrument presents a consistent software view to the user interface programmer. The view consists of a small library of functions, which are identical for all instruments, and a large set of keywords, that vary from instrument to instrument. All knowledge of the underlying task structure is hidden from the application programmer by the keyword layer. Image capture software uses the same function library to collect data for the image header. Because the image capture software and the instrument control software are built on top of the same keyword layer, a given observation can be 'replayed' by extracting keyword-value pairs from the image header and passing them back to the control system. The keyword layer features non-blocking as well as blocking I/O. A non-blocking keyword write operation (such as setting a filter position) specifies a callback to be invoked when the operation is complete. A non-blocking keyword read operation specifies a callback to be invoked whenever the keyword changes state. The keyword-callback style meshes well with the widget-callback style commonly used in X window programs. The first keyword library was built for the two Keck optical instruments. More recently, keyword libraries have been developed for the infrared instruments and for telescope control. Although the underlying mechanisms used for inter-process communication by each of these systems vary widely (Lick MUSIC, Sun RPC, and direct socket I/O, respectively), a basic user interface has been written that can be used with any of these systems. Since the keyword libraries are bound to user interface programs dynamically at run time, only a single set of user interface executables is needed. For example, the same program, 'xshow', can be used to display continuously the telescope's position, the time left in an instrument's exposure, or both values simultaneously. Less generic tools that operate on specific keywords, for example an X display that controls optical instrument exposures, have also been written using the keyword layer.

Conrad, A. R.↗
DOE OSTI2017

A scalable design of experiments framework for optimal sensor placement

Here, we present a scalable design of an experiments framework for sensor placement in systems described by partial differential equations (PDEs). In particular, we aim to compute optimal sensor locations by minimizing the uncertainty of parameters estimated from Bayesian inverse problems and where the system. The resulting problem is a computationally intractable mixed-integer nonlinear program constrained by PDEs. We approach this problem with two heuristics used in compressed sensing and optimal control literature: a sparsity-inducing approach and a sum-up rounding approach. We also investigate metrics to guide the design of experiments (the total flow variance and the A-optimal design criterion) and analyze the effect of different noise structures (white and colored). Using an application in natural gas pipelines, we conclude that the sum-up rounding approach approach gives the best results and produces shrinking gaps with increasing mesh resolution. We also observe that convergence for the white noise measurement error case is slower than for the colored noise case. For A-optimal design, the solution is close to a uniform distribution of sensors along the pipeline while for the flow variance design the distribution is unstructured.

42 ENGINEERING↗
DOE OSTI2021

A linked-scale coupled model of mass erosion and redistribution in plasma-exposed micro-foam surfaces

Surface evolution due to exposure to harsh environments is of importance in many scientific and technological applications. In plasma-exposed materials, the surface receives charged particles from the plasma, leading to a series of processes that drive the system far from equilibrium and may lead to the severe deterioration of the surface properties. Although surface morphological changes are driven by atomic collisions taking place over picoseconds and nanometers, these processes result in mass loss and redistribution of matter over much larger length and time scales. This necessitates a multi-scale approach capable of capturing the range of processes linking primary atomic collision events with engineering-level surface geometry changes. In this paper, we develop a computational model to simulate the morphological evolution and effective erosion rate of micro-architected tungsten foams during low-energy plasma ion bombardment. Furthermore, the model acts on several length scales, with the energy and angular dependence of the sputtering yield of flat tungsten surfaces determined using the SRIM code based on the binary collision approximation. This information is introduced into a low-fluence, short-term Monte Carlo raytracing model, and further into a high-fluence, long-term particle transport model. In the latter, material particles representing billions of atoms are described in a digitized 3-D representation of the foam structure from X-ray tomography data, and are sputtered off and redeposited using the atomistic information. We show that the redeposition of sputtered atoms leads to partial self-healing in the bottom layers with a sharp reduction in the sputtering coefficient of low density foams, roughly 25% of the solid W value. This is in qualitative agreement with recent experiments on low porosity W structures. At high fluence, the foam structure degrades considerably as there are fewer ligaments available to recapture sputtered atoms and, consequently, the sputtering rate increases again.

36 MATERIALS SCIENCE↗
NASA NTRS2001

Parallel Processing of Adaptive Meshes with Load Balancing

Many scientific applications involve grids that lack a uniform underlying structure. These applications are often also dynamic in nature in that the grid structure significantly changes between successive phases of execution. In parallel computing environments, mesh adaptation of unstructured grids through selective refinement/coarsening has proven to be an effective approach. However, achieving load balance while minimizing interprocessor communication and redistribution costs is a difficult problem. Traditional dynamic load balancers are mostly inadequate because they lack a global view of system loads across processors. In this paper, we propose a novel and general-purpose load balancer that utilizes symmetric broadcast networks (SBN) as the underlying communication topology, and compare its performance with a successful global load balancing environment, called PLUM, specifically created to handle adaptive unstructured applications. Our experimental results on an IBM SP2 demonstrate that the SBN-based load balancer achieves lower redistribution costs than that under PLUM by overlapping processing and data migration.

Das, Sajal K.↗
NASA NTRS2017

Parametric Structural Model for a Mars Entry Concept

This paper outlines the process of developing a parametric model for a vehicle that can withstand Earth launch and Mars entry conditions. This model allows the user to change a variety of parameters ranging from dimensions and meshing to materials and atmospheric entry angles to perform finite element analysis on the model for the specified load cases. While this work focuses on an aeroshell for Earth launch aboard the Space Launch System (SLS) and Mars entry, the model can be applied to different vehicles and destinations. This specific project derived from the need to deliver large payloads to Mars efficiently, safely, and cheaply. Doing so requires minimizing the structural mass of the body as much as possible. The code developed for this project allows for dozens of cases to be run with the single click of a button. The end result of the parametric model gives the user a sense of how the body reacts under different loading cases so that it can be optimized for its purpose. The data are reported in this paper and can provide engineers with a good understanding of the model and valuable information for improving the design of the vehicle. In addition, conclusions show that the frequency analysis drives the design and suggestions are made to reduce the significance of normal modes in the design.

Lane, Brittney M.↗
DOE OSTI2022

Development of a high fidelity model of the CROCUS experimental reactor

Measurements of scalar flux distributions with fine spatial and energy resolutions are needed to remedy one of the validation shortcomings of the novel neutronics full core solvers, such as MPACT and nTRACER. While a very detailed resolution of the flux can be calculated with such codes, only a limited experimental data set is available to check their accuracy. Such type of measurements are on-going at the zero power reactor CROCUS, operated at the Laboratory for Reactor Physics and System Behaviours of the EPFL, thanks to the development of advanced miniature neutron detection systems. This kind of experimental data would provide the community with a suitable benchmark for the validation of high fidelity neutronics solvers. In parallel, a multi-physics solver for steady-state and transient analysis of nuclear reactors, named GeN-Foam, has been developed. Based on the finite-volume OpenFOAM library, GeN-Foam provides us with enough flexibility to analyze non-conventional reactor geometries such as that of CROCUS. While CROCUS heterogeneities cannot be modeled by MPACT and nTRACER for the moment, GeN-Foam offers a unique opportunity to build a high fidelity model which mimics these codes' method to reach sub-pin simulation resolution. This document aims at describing the work achieved to get from the existing GeN-Foam model of the CROCUS reactor based on a structured mesh and using the neutron diffusion, the first high-fidelity model using discrete ordinates method as an approximation to neutron transport and an unstructured mesh for inter lattice water gap description and sub-pin heterogeneous modeling. (authors)

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗
NASA NTRS1995

The National Grid Project: A system overview

The National Grid Project (NGP) is a comprehensive numerical grid generation software system that is being developed at the National Science Foundation (NSF) Engineering Research Center (ERC) for Computational Field Simulation (CFS) at Mississippi State University (MSU). NGP is supported by a coalition of U.S. industries and federal laboratories. The objective of the NGP is to significantly decrease the amount of time it takes to generate a numerical grid for complex geometries and to increase the quality of these grids to enable computational field simulations for applications in industry. A geometric configuration can be discretized into grids (or meshes) that have two fundamental forms: structured and unstructured. Structured grids are formed by intersecting curvilinear coordinate lines and are composed of quadrilateral (2D) and hexahedral (3D) logically rectangular cells. The connectivity of a structured grid provides for trivial identification of neighboring points by incrementing coordinate indices. Unstructured grids are composed of cells of any shape (commonly triangles, quadrilaterals, tetrahedra and hexahedra), but do not have trivial identification of neighbors by incrementing an index. For unstructured grids, a set of points and an associated connectivity table is generated to define unstructured cell shapes and neighboring points. Hybrid grids are a combination of structured grids and unstructured grids. Chimera (overset) grids are intersecting or overlapping structured grids. The NGP system currently provides a user interface that integrates both 2D and 3D structured and unstructured grid generation, a solid modeling topology data management system, an internal Computer Aided Design (CAD) system based on Non-Uniform Rational B-Splines (NURBS), a journaling language, and a grid/solution visualization system.

Gaither, Adam↗
DOE OSTI2021

Air Blast Mesh Sensitivity and Pressure Mapping Study

Nose cone structural and aerodynamic characteristics are essential for intelligent design of aircraft, spacecraft, and ballistic systems. Finite element analysis can be used to help understand the structural integrity and flight characteristics of different nose cones. A mesh sensitivity study was undertaken for a particular nose cone geometry that was used in tests at LANL facilities in order to confirm the integrity of the meshed geometry. A simple cone that best matched closed-form theoretical solutions was modeled, and received good correlation to the theory. Complexity was then added back to the nose cone. Parameters applied to the simple cone were then implemented in the nose cone geometry giving assurance of accuracy after the geometry was changed. Nose cone results averaged 6.3% error for radial displacement when compared with the theoretical. Hoop stress averaged 6.0% error and meridional stress averaged 5.7% error at the finest mesh level. Meshes showed signs of convergence when compared to all three theoretical solutions. Finally, pressure time-history data from LANL computational fluid dynamics simulations was applied to the surface of the final nose cone geometry. The pressure data was interpolated from pressure gauge locations onto nearby meshed elements, which allowed for FEA software to run simulations on the cone with the pressure data as a loading condition. The pressure mapping resulted in the ability to understand the nose cone’s rigid body motion that in turn can inform design of future nose cones.

42 ENGINEERING↗
DOE OSTI2012

Adding a MOAB Geometry Interface to SHARP Structural Mechanics

The authors briefly summarize the development of, and test experience with, an initial data interface between the structural mechanics code Diablo and the SHARP reactor simulation system data hub MOAB. That interface has been exercised both to write MOAB databases from Diablo, and then also to use such a database to read in part of a simulation definition for a subsequent Diablo execution. All enhancements are integrated into the central Diablo source repository. The SHARP software system for advanced simulation of nuclear reactors and power plant systems is sponsored by DOE's Nuclear Energy Advanced Modeling and Simulation (NEAMS) program. SHARP has been architected as a federation of single-physics simulation tools to permit flexibility in programming languages and leveraging of past and on-going investments. Solution of multi-physics problems will be coordinated by, and data passed through, a central 'hub'. SHARP's hub implementation is utilizing MOAB: a Mesh-Oriented datABase. This same data hub approach is also intended to enable multi-resolution simulations, e.g, lower-dimension plant-scale simulations can be informed by high-fidelity 3D models of particular critical components.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗
NASA NTRS1992

Cartesian based grid generation/adaptive mesh refinement

Grid adaptation has recently received attention in the computational fluid dynamics (CFD) community as a means to capture the salient features of a flowfield by either moving grid points of a structured or by adding cells in an unstructured manner. An approach based on a background cartesian mesh is investigated from which the geometry is 'cut' out of the mesh. Once the mesh is obtained, a solution on this coarse grid is found, that indicates which cells need to be refined. This process of refining/solving continues until the flow is grid refined in terms of a user specified global parameter (such as drag coefficient etc.). The advantages of this approach are twofold: the generation of the base grid is independent of the topology of the bodies or surfaces around/through which the flow is to be computed, and the resulting grid (in uncut regions) is highly isotropic, so that the truncation error is low. The flow solver (which, along with the grid generation is still under development) uses a completely unstructured data base, and is a finite volume, upwinding scheme. Current and future work will address generating Navier-Stokes suitable grids by using locally aligned and normal face/cell refining. The attached plot shows a simple grid about two turbine blades.

Coirier, William J.↗
DOE OSTI2018

3-D Unsteady Model for Be-Steam Reaction in Water-Cooled Ceramic Breeder Blanket

Here, the design of the water-cooled ceramic breeder (WCCB) blanket includes beryllium multiplier layers. At elevated temperature, beryllium reacts with steam in an exothermic reaction producing beryllium oxide and hydrogen. Such situation may occur in WCCB in the case of the rupture of one of the cooling pipes in the blanket module. This process occurs locally in a complex 3-D geometry of the blanket containing several different granular levels and a network of cooling pipes and structural supports. The process is also inherently unsteady since reaction rate depends on concentration of steam and pure beryllium which changes in time. In order to perform the detailed analysis of the process, the model of the reacting flowthrough porous media was developed and introduced into 3-D computational fluid dynamics code. In this model, granular beds are introduced as porous solids simplifying the model geometry and reducing typical mesh size to manageable amount of tens of millions of elements. A reaction rate between solid beryllium and steam is obtained from experimental results, and depends on temperature and concentration of the reactants. The differential equation for beryllium oxide fraction is introduced, allowing obtaining distributions of beryllium oxide in space and time. Multicomponent flow consisting of a homogenous mixture of steam and hydrogen is considered flowing through the porous solid with variable properties. Sink and source terms for steam and hydrogen fractions are determined by local beryllium oxide mass fraction source according to the molar ratios of beryllium steam reaction. The conjugated heat transfer approach is applied to calculate heat transfer in support structures as well as coolant flow, simultaneously with the porous medium steam flow in a blanket's granular beds. The model is validated using experimental data on beryllium steam reaction for granular bed samples.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
NASA NTRS2007

Simulating Space Capsule Water Landing with Explicit Finite Element Method

A study of using an explicit nonlinear dynamic finite element code for simulating the water landing of a space capsule was performed. The finite element model contains Lagrangian shell elements for the space capsule and Eulerian solid elements for the water and air. An Arbitrary Lagrangian Eulerian (ALE) solver and a penalty coupling method were used for predicting the fluid and structure interaction forces. The space capsule was first assumed to be rigid, so the numerical results could be correlated with closed form solutions. The water and air meshes were continuously refined until the solution was converged. The converged maximum deceleration predicted is bounded by the classical von Karman and Wagner solutions and is considered to be an adequate solution. The refined water and air meshes were then used in the models for simulating the water landing of a capsule model that has a flexible bottom. For small pitch angle cases, the maximum deceleration from the flexible capsule model was found to be significantly greater than the maximum deceleration obtained from the corresponding rigid model. For large pitch angle cases, the difference between the maximum deceleration of the flexible model and that of its corresponding rigid model is smaller. Test data of Apollo space capsules with a flexible heat shield qualitatively support the findings presented in this paper.

Wang, John T.↗