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All sourcesNASA NTRSDOE OSTI
DOE OSTI2017

Level set topology optimization of structural problems with interface cohesion

Summary This paper presents a finite element topology optimization framework for the design of two‐phase structural systems considering contact and cohesion phenomena along the interface. The geometry of the material interface is described by an explicit level set method, and the structural response is predicted by the extended finite element method. In this work, the interface condition is described by a bilinear cohesive zone model on the basis of the traction‐separation constitutive relation. The non‐penetration condition in the presence of compressive interface forces is enforced by a stabilized Lagrange multiplier method. The mechanical model assumes a linear elastic isotropic material, infinitesimal strain theory, and a quasi‐static response. The optimization problem is solved by a nonlinear programming method, and the design sensitivities are computed by the adjoint method. The performance of the presented method is evaluated by 2D and 3D numerical examples. The results obtained from topology optimization reveal distinct design characteristics for the various interface phenomena considered. In addition, 3D examples demonstrate optimal geometries that cannot be fully captured by reduced dimensionality. The optimization framework presented is limited to two‐phase structural systems where the material interface is coincident in the undeformed configuration, and to structural responses that remain valid considering small strain kinematics. Copyright © 2017 John Wiley & Sons, Ltd.

Behrou, Reza↗
DOE OSTI2017

Numerical comparison of bubbling in a waste glass melter

Radioactive tank waste is scheduled for vitrification at the Hanford Tank Waste Treatment and Immobilization Plant, also known as the Vit Plant, being constructed at the Hanford Site. Testing of the pilot-scale, joule-heated DuraMelter 1200 at the Vitreous State Laboratory has shown that bubbling increases the melt rate, and as a result, melter throughput. Computational fluid dynamics (CFD) models of this pilot-scale waste glass melter were developed to improve our understanding of the processes that occur within the melter to aid in process optimization and troubleshooting of the Vit Plant melters. Unfortunately, model validation is complicated by the difficulty of obtaining suitable experimental data for operational melters attributed to the large-scale, radioactivity and high temperatures at which these melters are operated. This study focuses on confirming the fidelity of the CFD models to accurately reproduce the bubbling behavior. Because of the paucity of experimental data at the resolution required for CFD validation, a code-to-code comparison was used to evaluate two common approaches for simulating flows of immiscible fluids on numerical grids and resolving multiphase interfaces. Here, the volume of fluid and level set methods are used to track the dynamically evolving interfaces between the molten glass and the air bubbles. To aid in the verification of the results of these codes, a comparison of the bubble behavior, growth, and frequency of bubble generation are presented and a grid convergence study is performed for the two approaches. In addition to comparing the numerical results to available experimental data and observations from pilot-scale testing, the results are evaluated in relation to laboratory experiments with bubbles injected into viscous fluids, empirical correlations obtained from the published literature, and the basic laws of fluid dynamics. Furthermore, the results of this work can assist in validating waste glass melter models and provide a better understanding of the flow patterns within the WTP melters.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗
DOE OSTI2017

A broadly-applicable unified closure relation for Taylor bubble rise velocity in pipes with stagnant liquid

Taylor bubble velocity in slug flow is a closure relation which significantly affects the prediction of liquid holdup (or void fraction) and pressure gradient in mechanistic models of slug flow for oil and gas pipe applications. In this work, we use a validated Computational Fluid Dynamics (CFD) approach to simulate the motion of Taylor bubbles in pipes; the interface is tracked with a Level-Set method implemented in a commercial code. A large numerical database is generated covering the most ample range of fluid properties and pipe inclination angles explored to date (Eo ∊ [10, 700],Mo ∊ [1 x 10 -6 , 5 x 10 3 , and θ ∊ [0°, 90°]). A unified Taylor bubble rise velocity correlation is extracted from that database. The new correlation predicts the numerical database with 8.6% absolute average relative error and a coefficient of determination R 2 = 0.97 and other available experimental data with 13.0% absolute average relative error and R 2 = 0.84 outperforming existing correlations and models.

Mechanics↗
DOE OSTI2015

Maximum probability domains for the analysis of the microscopic structure of liquids

We introduce the concept of maximum probability domains (MPDs), developed in the context of the analysis of electronic densities, in the study of the microscopic spatial structures of liquids. The idea of locating a particle in a three dimensional region, by determining the domain where the probability of finding that, and only that, particle is maximum, gives an interesting characterization of the local structure of the liquid. The optimization procedure, required for the search of the domain of maximum probability, is carried out by the implementation of the level set method. Results for a couple of case studies are presented, to illustrate the structure of liquid water at ambient conditions and upon increasing pressure from the point of view of MPDs and to compare the information encoded in the solvation shells of sodium in water with, once again, that extracted from the MPDs.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2014

TH-E-17A-11: Tracking Tumor’s Boundary in MV Image Sequences for Image-Guided Radiation Therapy

Purpose: To develop a level set method (LSM)-based algorithm to track the tumor’s boundary in MV image sequences for image-guided radiation therapy (IGRT). Method: Four MV image sequences, each of which consists of 100 frames at frame rate of 7.5 Hz, are acquired by using the electronic portal imaging device (EPID) (Varian Medical Systems, Pal Alto, USA) during the treatment of lung cancer. In the first frame of each sequence, we roughly delineate an initial contour of the target tumor by hand. Using a LSM-based algorithm, the initial contour can automatically shape itself to fit the tumor, and eventually detect the tumor’s boundary. We then employ the tumor’s boundary obtained from the previous frame as the initial contour in the subsequent frame, so that the LSM-based method can drive this initial contour to the tumor’s boundary quickly and fulfill a tracking task. Results: The proposed method has been evaluated on four MV image sequences. The mean tracking errors were 0.23, 0.29, 0.37, and 1.18 mm, and their corresponding standard deviations were 0.97, 0.75, 1.2 and 1.48 mm, respectively. Conclusion: Compared with conventional tumor tracking techniques, the proposed system is capable not only of tracking the tumor’s position, but also of detecting the tumor’s boundary varying with the respiration during the treatment. Considering current radiation therapy technique, for example, dynamical multi-leaf collimator (DMLC) has been widely applied in clinical treatment, this study indicates the potential for significant accuracy improvement in radiation therapy. This work was partially supported by a research grant from Varian Medical Systems (Palo Alto, California)

60 APPLIED LIFE SCIENCES↗
DOE OSTI2021

Computational Fluid Dynamics (CFD) Simulations of Taylor Bubbles in Vertical and Inclined Pipes with Upward and Downward Liquid Flow

Summary Two-phase flow is a common occurrence in pipes of oil and gas developments. Current predictive tools are based on the mechanistic two-fluid model, which requires the use of closure relations to predict integral flow parameters such as liquid holdup (or void fraction) and pressure gradient. However, these closure relations carry the highest uncertainties in the model. In particular, significant discrepancies have been found between experimental data and closure relations for the Taylor bubble velocity in slug flow, which has been determined to strongly affect the mechanistic model predictions (Lizarraga-García 2016). In this work, we study the behavior of Taylor bubbles in vertical and inclined pipes with upward and downward flow using a validated 3D computational fluid dynamics (CFD) approach with level set method implemented in a commercial code. A total of 56 cases are simulated, covering a wide range of fluid properties, pipe diameters, and inclination angles: Eo ∈ [10, 700]; Mo ∈ [1×10–6, 5×103]; ReSL ∈ [–40, 10]; θ ∈ [5°, 90°]. For bubbles in vertical upward flows, the simulated distribution parameter, C0, is successfully compared with an existing model. However, the C0 values of downward and inclined slug flows where the bubble becomes asymmetric are shown to be significantly different from their respective vertical upward flow values, and no current model exists for the fluids simulated here. The main contributions of this work are (1) the relatively large 3D numerical database generated for this type of flow, (2) the study of the asymmetric nature of inclined and some vertical downward slug flows, and (3) the analysis of its impact on the distribution parameter, C0.

Engineering↗
DOE OSTI2013

HERMES Model Modifications and Applications 2012

HERMES was developed to meet requirements for a model to describe explosive response to impacts that do not produce prompt detonation, but can include delayed detonations such as DDT and XDT. Such response is termed High Explosive Violent Response (HEVR). The HERMES model includes a constitutive description of strength as a function of pressure, strain-rate, strain, and ambient temperature; the development of damage including fragmentation and porosity; the conditions leading to ignition; the propagation of a burning reaction through the volume of damaged explosive; the burn-up of the damaged and undamaged explosive; and the development of detonation using the Computational Reaction Evolution dependent on Entropy (S) and Time (CREST) detonation model. CREST can distinguish gradual pressure increases from shock waves, and also predict the increase in shock sensitivity to detonation that results from increased porosity. This year HERMES has been implemented as a User Defined Function in ALE 3D. As a result, modifications to the model can be implemented in a timely fashion asynchronously from the ALE 3D distribution process. There are differences between the implementation of HERMES in ALE 3D and the implementation in LS DYNA. The major difference is the propagation of an ignition front from an element that has started to burn. In LS DYNA, the time at which an element begins to burn is based on the minimum line-of-sight distance between the element and any previously ignited element. In ALE 3D the time to burn is based on a level-set method that propagates the ignition front from all elements that were previously ignited. The ALE 3D implementation modifies the time of ignition when element deformation changes the distance from the element to the source. The LS DYNA implementation does not. There are also differences in the implementation of artificial viscosity, which is important for CREST since the artificial viscosity increases the element entropy in a shock. In general, however, the differences have proven minor. In collaboration with the Atomic Weapons Establishment, UK (AWE), we have characterized two additional explosives – PETN and Composition B, a mixture of 60% RDX and 40% TNT by weight. Applications of HERMES to these explosives are described below.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2024

MOSCATO Development and Integration in Fiscal Year 2024

MOSCATO (Molten Salt Chemistry and Transport) is a multiphysics code that provides high-fidelity, coupled simulations of fluid flow, heat transfer, mass transfer, chemistry, electrochemical phenomena, and alloy evolution for molten salt equipment. In FY24, significant developments were made to the code package, enhancing its capabilities in many aspects. The improvements and advancements can be summarized as follows: 1. Implementation of tritium transport capabilities and validation with experimental data: To enable modeling of tritium and other fission gases within MSRs, we implemented gas transport within MOSCATO via inclusion of couple mass transport equations within the salt and structural alloys. Comparisons to experimental data from literature showed good agreement with respect to tritium release rates. 2. Preliminary implementation of two-phase flow models in MOSCATO: To model tritium and other gases above their solubility limits, we implemented preliminary two-phase flow models within MOSCATO to account for bubble transport. The first model adopted was the Level-Set approach, which can handle the high void fraction regime, but with a requirement for high mesh resolution thus high computational expense. In this report, we present a verification of the Level-Set method using a simple benchmark case. We also performed a demonstration of the code as applied to an experimental case involving cover gas flow through salt in an experimental vessel. The second model adopted was the Eulerian-Eulerian dispersed flow model, which is computationally cheaper but limited to low void fraction regimes, such as bubbly flow. Validation and verification have not yet been performed for the Eulerian-Eulerian approach, but a preliminary implementation was completed. 3. Validation with static corrosion experiments: Static corrosion experimental data for stainless steel coupons within molten salts was used to further validate the corrosion model in MOSCATO. To do so, we leveraged the existing models in MOSCATO and simulated the sample mass loss and mass gain phenomena. Several ion species, including Cr 2+ , Fe 2+ and H + , were simulated in salt using the PNP solver, while Cr 0 and Fe 0 were simulated with a diffusion solver in stainless steel. The mass loss of the samples was compared with experimental data, and good agreement was achieved. These combined activities served to further expand the capabilities of MOSCATO and make it more generally applicable to the full range of phenomena that can control chemistry and corrosion in molten salt reactors.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2012

Axisymmetric boundary integral formulation for a two fluid system

A 3D axisymmetric Galerkin boundary integral formulation for modeling the motion of one inviscid fluid enclosed inside another is described. The interface variables are the velocity potential and the normal velocity, and they can be solved for separately, the second linear system being symmetric. The algorithm is validated by comparing with the analytic solutions for a static interior spherical drop, over a range of values for the relative densities D=rho_E/rho_I of exterior and interior fluids, and various boundary conditions. For time dependent simulations utilizing a Level Set method for the interface tracking, the accuracy has been checked by comparing against the known oscillation frequency of the sphere. Pinch-off profiles corresponding to an initial two lobe geometry drop and D=6 are also presented.

42 ENGINEERING↗
DOE OSTI2012

Multi-scale approach to the modeling of fission gas discharge during hypothetical loss-of-flow accident in gen-IV sodium fast reactor

The required technological and safety standards for future Gen IV Reactors can only be achieved if advanced simulation capabilities become available, which combine high performance computing with the necessary level of modeling detail and high accuracy of predictions. The purpose of this paper is to present new results of multi-scale three-dimensional (3D) simulations of the inter-related phenomena, which occur as a result of fuel element heat-up and cladding failure, including the injection of a jet of gaseous fission products into a partially blocked Sodium Fast Reactor (SFR) coolant channel, and gas/molten sodium transport along the coolant channels. The computational approach to the analysis of the overall accident scenario is based on using two different inter-communicating computational multiphase fluid dynamics (CMFD) codes: a CFD code, PHASTA, and a RANS code, NPHASE-CMFD. Using the geometry and time history of cladding failure and the gas injection rate, direct numerical simulations (DNS), combined with the Level Set method, of two-phase turbulent flow have been performed by the PHASTA code. The model allows one to track the evolution of gas/liquid interfaces at a centimeter scale. The simulated phenomena include the formation and breakup of the jet of fission products injected into the liquid sodium coolant. The PHASTA outflow has been averaged over time to obtain mean phasic velocities and volumetric concentrations, as well as the liquid turbulent kinetic energy and turbulence dissipation rate, all of which have served as the input to the core-scale simulations using the NPHASE-CMFD code. A sliding window time averaging has been used to capture mean flow parameters for transient cases. The results presented in the paper include testing and validation of the proposed models, as well the predictions of fission-gas/liquid-sodium transport along a multi-rod fuel assembly of SFR during a partial loss-of-flow accident. (authors)

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗
DOE OSTI2017

An arbitrary-order Runge–Kutta discontinuous Galerkin approach to reinitialization for banded conservative level sets

Here, we present a Runge-Kutta discontinuous Galerkin method for solving conservative reinitialization in the context of the conservative level set method. This represents an extension of the method recently proposed by Owkes and Desjardins [21], by solving the level set equations on the refined level set grid and projecting all spatially-dependent variables into the full basis used by the discontinuous Galerkin discretization. By doing so, we achieve the full k+1 order convergence rate in the L1 norm of the level set field predicted for RKDG methods given kth degree basis functions when the level set profile thickness is held constant with grid refinement. Shape and volume errors for the 0.5-contour of the level set, on the other hand, are found to converge between first and second order. We show a variety of test results, including the method of manufactured solutions, reinitialization of a circle and sphere, Zalesak's disk, and deforming columns and spheres, all showing substantial improvements over the high-order finite difference traditional level set method studied for example by Herrmann. We also demonstrate the need for kth order accurate normal vectors, as lower order normals are found to degrade the convergence rate of the method.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2016

TH-CD-206-08: An Anthropopathic Deformable Phantom for Geometric and Dose Accumulation Accuracy Validation of Deformable Image Registration

Purpose: To design and construct a three-dimensional (3D) anthropopathic abdominal phantom for evaluating deformable image registration (DIR) accuracy on images and dose deformation in adaptive radiation therapy (ART). Method: Organ moulds, including liver, kidney, spleen, stomach, vertebra and two metastasis tumors, are 3D printed using the contours from an ovarian cancer patient. The organ moulds are molded with deformable gels that made of different mixtures of polyvinyl chloride (PVC) and the softener dioctyl terephthalate. Gels with different densities are obtained by a polynomial fitting curve which describes the relation between the CT number and PVC-softener blending ratio. The rigid vertebras are constructed by moulding with white cement. The final abdominal phantom is assembled by arranging all the fabricated organs inside a hollow dummy according to their anatomies and sealed with deformable gel with averaged CT number of muscle and fat. Geometric and dosimetric landmarks are embedded inside the phantom for spatial accuracy and dose accumulation accuracy studies. Three DIR algorithms available in the open source DIR toolkit-DIRART, including the Demons, the Horn-Schunck and Lucas-Kanade method and the Level-Set Motion method, are tested using the constructed phantom. Results: Viscoelastic behavior is observed in the constructed deformable gel, which serves as an ideal material for the deformable phantom. The constructed abdominal phantom consists of highly realistic anatomy and the fabricated organs inside have close CT number to its reference patient. DIR accuracy studies conducted on the constructed phantom using three DIR approaches indicate that geometric accuracy of a DIR algorithm has achieved does not guarantee accuracy in dose accumulation. Conclusions: We have designed and constructed an anthropopathic abdominal deformable phantom with satisfactory elastic property, realistic organ density and anatomy. This physical phantom is recyclable and can be used for routine validations of DIR geometric accuracy and dose accumulation accuracy in ART. This work is supported in part by grant from VARIAN MEDICAL SYSTEMS INC, the National Natural Science Foundation of China (no 81428019 and no 81301940), the Guangdong Natural Science Foundation (2015A030313302) and the 2015 Pearl River S&T Nova Program of Guangzhou (201506010096).

60 APPLIED LIFE SCIENCES↗
DOE OSTI2013

A discontinuous Galerkin conservative level set scheme for interface capturing in multiphase flows

The accurate conservative level set (ACLS) method of Desjardins et al. [O. Desjardins, V. Moureau, H. Pitsch, An accurate conservative level set/ghost fluid method for simulating turbulent atomization, J. Comput. Phys. 227 (18) (2008) 8395–8416] is extended by using a discontinuous Galerkin (DG) discretization. DG allows for the scheme to have an arbitrarily high order of accuracy with the smallest possible computational stencil resulting in an accurate method with good parallel scaling. This work includes a DG implementation of the level set transport equation, which moves the level set with the flow field velocity, and a DG implementation of the reinitialization equation, which is used to maintain the shape of the level set profile to promote good mass conservation. A near second order converging interface curvature is obtained by following a height function methodology (common amongst volume of fluid schemes) in the context of the conservative level set. Various numerical experiments are conducted to test the properties of the method and show excellent results, even on coarse meshes. The tests include Zalesak’s disk, two-dimensional deformation of a circle, time evolution of a standing wave, and a study of the Kelvin–Helmholtz instability. Finally, this novel methodology is employed to simulate the break-up of a turbulent liquid jet.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2024

Level-set topology optimization with PDE generated conformal meshes

This paper presents a level-set topology optimization approach that uses conformal meshes for the analysis of the displacement field. The structure’s boundary is represented by the iso-contour of a level-set field discretized on a fixed background design mesh. The conformal mesh is updated for each design iteration via a PDE based mesh morphing process that identifies the set of facets in the background mesh that are homeomorphic to the boundary and relaxes the homeomorphic mesh to conform to the structure’s boundary and ensure high element quality. The conformal mesh allows for a more accurate computation of the response versus density and some level-set based methods which interpolate material properties using the volume fraction. Numerical examples illustrate the proposed approach by optimizing linear-elastic two- and three-dimensional structures, wherein insight into the performance of the mesh morphing process is provided. The examples also highlight the scalability of the approach.

42 ENGINEERING↗