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NASA NTRSDate not supplied

Comparing Acoustic Prediction Methods for Additively Manufactured Porous Strutures

While macroscale methods for predicting the acoustic properties of porous structures have been popular in the past, they often require time-consuming manufacturing and testing workflows. Meanwhile, microscale approaches allow the prediction of transport parameters based exclusively on a periodic structure’s unit cell geometry. Here, we compare these methods to predict the characteristic impedance of additively manufactured porous structures. We use the microscale approach to estimate the geometry’s transport parameters, then predict the characteristic properties using the Johnson-Champoux-Allard (JCA) model. We measure the acoustic properties of the printed structures using a normal incidence impedance tube and estimate the transport parameters using an inverse characterization approach. We use the two-thickness method as a macroscale approach to predict the characteristic properties from the measured surface impedances of two sample thicknesses. Finally, we compare these characteristic prediction methods. Our results show that the inverse characterization and two-thickness methods offer the closest match to the measured values at low frequencies.

impedance↗

NASA NTRSDate not supplied

Assessment of Edge-Based Viscous Method for Corner-Flow Solutions on Graphics Processing Units

A highly efficient, edge-based viscous (EBV) discretization method has been recently implemented in a practical, unstructured-grid, node-centered, finite-volume flow solver and evaluated for Reynolds-averaged Navier-Stokes (RANS) formulations. In comparison to a well-established cell-based viscous (CBV) method, the EBV method has demonstrated multifold acceleration of all viscous-kernel computations on general unstructured mixed-element grids. The viscous kernels include evaluation of viscous fluxes, diffusion terms in turbulence models, and the corresponding Jacobian terms. In this paper, an EBV implementation of a nonlinear extension of the Spalart-Allmaras turbulence model, SA-neg-QCR2000, is presented and verified. The SA-neg-QCR2000 model is used for simulating turbulent corner flows. Previously reported EBV computations have been conducted on traditional computing architectures based on central processing units (CPU). This paper assesses benefits of the EBV method on modern high-performance computing architectures based on graphics processing units (GPU). The GPU implementations of the CBV and EBV methods are verified by comparing solutions and iterative convergence with those observed in CPU computations on the same grids. A comprehensive assessment of the EBV speedup on CPU and GPU architectures is presented for established benchmark corner flows, namely, a supersonic flow through a long square duct and a subsonic flow around a NASA juncture flow model.

CFD↗

NASA NTRSDate not supplied

Assessment of Edge-Based Viscous Method for Corner-Flow Solutions on Graphics Processing Units

CFD↗

DOE OSTI2023

Simulation of Reverse Osmosis Membrane Compaction Using Material Point Method (MPM)

Access to fresh drinking water in the future requires effective management of industrial wastewater and water purification from available resources. In this study, we present the simulation methodology and the analysis of a Reverse Osmosis (RO) membrane under various pressure conditions using the Material Point Method (MPM). In contrast to other numerical methods, MPM solves the continuum governing equations on material points in a Lagrangian framework. The method does not require a grid connecting the material points hence making it suitable to simulate large deformations during membrane compaction. The time integration is carried out using the explicit Euler method, while the spatial discretization is performed using linear or cubic-spline shape functions. A series of planar images containing detailed pore structures obtained from X-ray tomography experiments is converted to a three-dimensional collection of material points to simulate the membrane. Compressive loads are applied to the top layer of the membrane to simulate the experiments. The membrane deformation and pore size distribution before and after load application are reported and compared with the experimental measurements. The presentation discusses the numerical methods used, the performance of the solver on high-performance computing machines, and the results of membrane compaction in detail.

ENGINEERING,MATHEMATICS AND COMPUTING↗

DOE OSTI2016

Investigation on numerical method of one-dimensional drift flux model for boiling two-phase flow

A numerical method for the solution of one-dimension drift-flux model has been developed. Correlations for heat and mass transfer and kinematic constitutive equation were used to close the set of the partial differential equations. The finite volume method based on the staggered grid and fully implicit backward Euler method were applied to discretize the spatial and time differential items, respectively. The discretization equations were solved iteratively in a same manner as in SIMPLE method for a single-phase flow. The verification and validation of the numerical method and closure model for one-dimension drift-flux model have been performed by comparing the code solution with the experimental data. Furthermore, the axial distribution of void fraction and pressure also have been investigated under different heated case. (authors)

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

DOE OSTI2016

Validation of KENO Thermal Moderator Doppler Broadening Method in SCALE 6.2 Beta5 Using Continuous-Energy B-VII.1 Library

KENO, the Monte Carlo criticality safety program within the SCALE code package, has until recently used continuous-energy (CE) cross sections corresponding to the set of evaluated nuclear data closest to the temperature of interest. This method, which is used for both 1-D cross sections and thermal scattering probability data, does not fully represent the phenomenon of Doppler broadening (DB) and can result in significant differences in eigenvalues when the material temperature lies between the evaluated data sets. A method for creating temperature-dependent nuclear data has been implemented in KENO for CE calculations. This work summarizes the results of incorporating this method into two critical experiments using low-enriched uranium (LEU) in light water moderated pin lattices. The LEUCOMP-THERM-046 (LCT-046) experiment is a benchmark documented in the International Handbook of Evaluated Criticality Safety Benchmark Experiments (ICSBEP Handbook); it consists of 22 critical configurations or cases. The KRITZ-2:1 experiment, a part of the International Reactor Physics Experiment Evaluation Project (IRPhEP), consists of two cases which span a significant range of moderator temperatures. The results of this work give a good indication of the value of the newly incorporated cross section processing. However, more diverse evaluations should be performed to provide a broader validation of this method. The results suggest that when dealing with systems similar to LCT-046, there is a significant improvement made when the moderator scattering data are properly broadened and sampled. The DB of the hydrogen (in water) 2-D cross sections resulted in a consistent C/E value across the temperature range, whereas the DB of the 1-D only cross sections did not exhibit this improvement. With respect to criticality safety, this consistency adds precision to the calculational method, which could potentially impact subcriticality limits. After comparing the KRITZ and LCT-046 results, the most plausible conclusion to make as to why the added thermal moderator treatment improved the results for LCT-046 and not for the KRITZ experiment is that the two systems were dissimilar with respect to their temperatures. That is, the relative temperature differences among the cases in each experiment are more significant for LCT-046 than for KRITZ. The cross section changes as a function of temperature are also smaller at higher temperatures. This difference resulted in a lesser impact of broadening in general for the KRITZ hot case.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

DOE OSTI2016

The Iterated Fission Matrix Method

The fission matrix (FM) method has been successfully demonstrated for different applications. One of the interesting features of this method, which is not possible via standard criticality source Monte Carlo calculations, is the capability to calculate higher forward and adjoint Eigenmodes; however, the accuracy of the estimates for higher eigenvalues strongly depends on the spatial discretization adopted for the fission matrix. A fine mesh ensures accurate results but requires matrices of large size. This is considered a limitation to the applicability of the FM method due to the memory requirements for storage of large full matrices. The adoption of sparse matrix storage (e.g., in MCNP) partially overcomes this problem; nonetheless, the sparse matrix indexing increases the complexity of the implementation of the FM algorithm and introduces the additional task of sparsifying the fission matrix. This summary presents a new method, named the iterated fission matrix (IFM), that allows to estimate higher eigenvalues of multiplying systems on much smaller meshes, but with the same level of accuracy in terms of spatial discretization errors, as compared to the FM method. The following Sections describe this new approach and provide a demonstration using two case studies: a PWR fuel assembly, and a 2D PWR core. (authors)

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗

DOE OSTI2016

Improved Quasi-Static Method with Step Doubling Time Adaptation

The imminent restart of the Transient Reactor Testing Facility (TREAT) at Idaho National Laboratory (INL) has brought significant attention to the development of transient reactor modeling. TREAT was designed to subject fuels and other reactor components to various degrees of neutron pulses, from minor transients to accident scenario. Inherently, this task requires predicting pulse responses due to various control rod movements; which is a complicated endeavor. Originally, this was done using an iterative process of rod movements and measuring the resulting response. With the advances in computer modeling, the current goal, preceding the restart, is to use simulation to characterize responses before experiments take place. However, neutron transient modeling is extremely computationally expensive due to the required implicit time-stepping. Therefore, methods that mitigate computation time, with minimal detriment to accuracy, are highly desired. This paper will describe the improved quasi-static method (IQS), which hopes to decrease computation time significantly from traditional 'brute force' transient methods. IQS is a spatial kinetics method that involves factorizing the flux solution into time-dependent amplitude and space- and time-dependent shape. The impetus of the method is the assumption that shape is weakly time-dependent, so expensive space-dependent evaluations are only required on large time steps. While inexpensive amplitude evaluations are performed on much smaller time steps to retain accuracy. IQS has been tested extensively on kinetics benchmarks with constant time steps. However, to test it's viability for TREAT simulations, evaluating IQS's performance with time adaptation is required. The rest of this paper will briefly describe the derivation of IQS, the time adaptation technique used, and results from a kinetic benchmarks. (authors)

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗

DOE OSTI2016

Assessment of a Smoothed Particle Hydrodynamics Method for Thin Film on Textured Surfaces

A large number of previous studies suggest that the behavior of the near-wall liquid micro-layer plays a key role in boiling heat transfer and boiling crisis; see examples. The thin liquid layer interacts with heater surface and 'external' two-phase flow. The net effects of these interactions define the micro-hydrodynamics that leads to dryout. As a result, a good understanding of the thin-layer hydrodynamics is significant for the accurate prediction of CHF. Recently, with the advent of nanotechnology including micro-scale manufacturing, it becomes possible to perform high heat-flux boiling experiments with controlled surface conditions. Although many reports show rich observations about the effects of surface characteristics on CHF, physical mechanisms remain not fully understood. In order to have better understanding of the above phenomena, several computational models are developed, ranging from the lubrication theory to CFD methods. The former models are limited to one-dimensional formulation and unable to deal with the dry-out phenomena. It turns out that CFD methods have a greater potential for the mechanistic study of boiling. Towards the study objective, a particle-based CFD method called Smoothed Particle Hydrodynamics (SPH) is adopted. SPH is a Lagrangian particle method for solving systems of partial differential equations. Originally SPH is proposed for fluid dynamics in the context of astrophysical problems. Because mass and density are introduced during the particle approximation, SPH is also applied in fluid dynamic problems, where mass and density are important parameters to determine, without mass loss (a limitation of interface capturing schemes in mesh-based methods). Besides, geometrically complex and/or dynamic boundaries and interfaces can be handled without undue difficulty in SPH. Currently, most SPH simulations focus on large-scale scenarios (meter scale), like flooding and solitary wave. Also some works have been done with SPH in pore-scale. As for micro- or nano-scale simulation, people usually apply Dissipative Particle Dynamics (DPD) and Molecular Dynamics (MD) for particle-based simulation. Almost no work has been done on micro-scale with SPH, so assessments are needed to investigate the capability of SPH in application of micro-hydrodynamics. The Phenomena Identification and Ranking Table (PIRT) is applied to align application's technical requirements with associated physics and materials, models, simulation code capabilities and verification, validation and uncertainty quantification activities. The figures of merit are determined as: (1) Timing of micro-layer rewetting dry surface; (2) Effects of surface features. The corresponding key phenomena are determined as: (1) Hydrodynamics; (2) Interface Dynamics; (3) Energy; (4) Surface Effect. This study deals with isothermal scenario and no energy term is considered. Based on the current needs, a new SPH package, Micro-SPH, is compiled based on SPHysics with surface tension and wettability built in. Test cases are performed with Micro-SPH to assess the capability of SPH to each phenomenon identified. NEUTRINO with incompressible SPH solver is employed to investigate micro-fluid dynamics on a surface with uniformly distributed cylindrical pillars for application purposes. (authors)

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

DOE OSTI2017

Determining Physical Parameters of Shielded Uranium using Gamma Spectroscopy and the Differential Evolution Adaptive Metropolis (DREAM) Method

Inverse radiation transport is a well-established method for determining unknown parameters within a system that exhibits particle leakage. Two significant challenges of solving inverse transport problems are (1) to determine multiple unknowns without false convergence on local minima and (2) to be able to quantify uncertainty. It was recently demonstrated that the Differential Evolution Adaptive Metropolis (DREAM) method effectively meets both of these challenges. In Bledsoe's 2014 article, the DREAM method was only applied to numerical test cases in which measured data were simulated using MCNP. This paper provides results of research conducted at Oak Ridge National Laboratory (ORNL) in which DREAM was applied to two-dimensional inverse transport problems using real-world measurements. The DREAM method uses a Markov chain Monte Carlo (MCMC) method to obtain a posterior distribution of unknown parameters. In this application, the posterior distribution is determined by using a uniform prior distribution and a likelihood function. The goal of the inverse problem is to find the regions in which the likelihood function is at or near its maximum. In the traditional MCMC approach, a single Markov chain is employed. In practice, MCMC approaches have a high acceptance rate to solutions that are near the current point of sampling, but they exhibit slow convergence to solutions far from the sampling point. The DREAM algorithm was designed to alleviate this issue by initiating multiple Markov chains and using the differential evolution algorithm to generate trial points for each chain. Solving for the mass of radioactive material within a voluminous source is a challenging problem for gamma-ray spectroscopy. Inverse gamma-ray transport can supply a range of possible material compositions, but reducing the differences between predicted and actual measurements can lead to false results. DREAM is a rapid technique for determining the most likely solution for several unknown parameters in an inverse transport problem. This work applies DREAM to a series of gamma spectroscopy experiments performed at ORNL.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

DOE OSTI2017

The Half Monte Carlo Method: Combining Total Monte Carlo with Nuclear Data Sensitivity Profiles

Both Total Monte Carlo (TMC) and Generalized Linear Least Squares (GLLS) algorithms have been used extensively to perform nuclear uncertainty propagation. Both methods have strengths and weaknesses, for example, the time required to perform TMC limits its attractiveness, while GLLS cannot generate higher order moments of output distributions and also has trouble dealing with nonlinear distributions. This work uses a new method that overcomes many of the aforementioned limitations of TMC and GLLS, while at the same time reasonably reproduces the TMC result. The concept is a simple combination of the two methods i.e., generate the random nuclear data files using the TMC approach, and then propagate the effect on the integral parameters like k{sub eff} using sensitivity coefficients, as opposed to cumbersome neutron transport calculations. Agreement is demonstrated for the Jezebel sphere ICSBEP benchmark. Since the method is part TMC part GLLS, the term Half Monte Method (HMM) will be used.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2018

Global variance reduction method applied to HBR-2 benchmark - 25144

It is a great challenge to obtain reliable results in reasonable time by the Monte Carlo (MC) method in solving deep-penetration shielding problems. Global variance reduction (GVR) method uses biased source and weight window to decrease MC calculation tally error for deep-penetration problems. However, excessive splitting of large weight particles out of the source region is time-consuming for problems with significant fluence rate variation. A new GVR method, which performs space and energy splitting/roulette based on the importance of the phase space, is proposed in this paper to avoid excessive splitting of large weight particles. The improved GVR method is applied to HBR-2 benchmark. Numerical results show that the new GVR method achieves good corresponding results to those of references. (authors)

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗

DOE OSTI2018

Performance study of atomic tally methods for GPU-accelerated Monte Carlo dose calculation - 25352

Over the past several years, the graphics processing unit (GPU) technology has rapidly gained ground in scientific computing due to its outstanding performance and programmability. GPU implementation of Monte Carlo radiation transport for dose calculations has been reported by many investigators. The majority of these studies adopted single-precision floating point format because of the higher peak floating point operations per second (FLOPS) the GPUs can deliver than double-precision. It has been known that calculation using single-precision is more prone to numerical round-off errors, especially when a single tally data is accumulated 'atomically' and repeatedly by thousands of GPU threads. To mitigate this problem, the least intrusive solution in theory is to replace the single-precision atomic-add tally function with a double-precision version. However, the complexity lies in the fact that some GPUs (Nvidia GPUs prior to the Pascal generation; all current AMD GPUs) do not readily offer such double-precision function at hardware level, and that software emulation is too slow to use if not optimized properly. This paper discusses several atomic-add tally methods with reduced numerical errors used throughout ARCHER development. The original software-based compare-and-swap method (CAS) was shown to be inefficient due to high intra-warp thread contention, whereas the improved software-based warp-aggregated method (WAG) and Kahan summation method (KAS) eliminated the thread contention and performed very well on Kepler and Maxwell GPUs, being more than 13 times faster than CAS in our tests. The hardware-based (HB) double-precision atomic-add feature available on Pascal and Volta GPUs exceeded software emulation and offered the best performance universally, so did WIB, a combination of WAG and HB methods. It was also shown that in a single-precision dose engine, KAS managed to maintain high reliability when the single-precision atomic-add tally underestimated the dose by 25%. (authors)

61 RADIATION PROTECTION AND DOSIMETRY↗

DOE OSTI2022

High-order accurate solutions of the point kinetics equations with the spectral deferred correction method

Solving initial value problems with higher-order methods can improve the accuracy of the simulation results or the efficiency of the calculation. In this paper, we apply the spectral deferred correction (SDC) method to solve the initial value problem of the point kinetics equations (PKE). SDC is a stable, robust, and efficient high-order time-integration method capable of an arbitrary order of accuracy. For our implementation we show that it is A-stable for orders up to 8 and the order of accuracy is verified for PKE problems with a range of different reactivities. A 5.-order SDC method was then implemented to solve the exact PKE (EPKE) in the Transient Multilevel (TML) method of MPACT. The error from solutions of the EPKE is shown to be negligible. (authors)

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

DOE OSTI2016

Intercomparison of 3D pore-scale flow and solute transport simulation methods

Multiple numerical approaches have been developed to simulate porous media fluid flow and solute transport at the pore scale. These include methods that 1) explicitly model the three-dimensional geometry of pore spaces and 2) those that conceptualize the pore space as a topologically consistent set of stylized pore bodies and pore throats. In previous work we validated a model of class 1, based on direct numerical simulation using computational fluid dynamics (CFD) codes, against magnetic resonance velocimetry (MRV) measurements of pore-scale velocities. Here we expand that validation to include additional models of class 1 based on the immersed-boundary method (IMB), lattice Boltzmann method (LBM), smoothed particle hydrodynamics (SPH), as well as a model of class 2 (a pore-network model or PNM). The PNM approach used in the current study was recently improved and demonstrated to accurately simulate solute transport in a two-dimensional experiment. While the PNM approach is computationally much less demanding than direct numerical simulation methods, the effect of conceptualizing complex three-dimensional pore geometries on solute transport in the manner of PNMs has not been fully determined. We apply all four approaches (CFD, LBM, SPH and PNM) to simulate pore-scale velocity distributions and nonreactive solute transport, and intercompare the model results with previously reported experimental observations. Experimental observations are limited to measured pore-scale velocities, so solute transport comparisons are made only among the various models. Comparisons are drawn both in terms of macroscopic variables (e.g., permeability, solute breakthrough curves) and microscopic variables (e.g., local velocities and concentrations).

computational fluid dynamics↗

DOE OSTI2020

The second-generation Shifted Boundary Method and its numerical analysis

Recently, the Shifted Boundary Method (SBM) was proposed within the class of unfitted (or immersed, or embedded) finite element methods. By reformulating the original boundary value problem over a surrogate (approximate) computational domain, the SBM avoids integration over cut cells and the associated problematic issues regarding numerical stability and matrix conditioning. Accuracy is maintained by modifying the original boundary conditions using Taylor expansions. Hence the name of the method, that shifts the location and values of the boundary conditions. In this article, we present enhanced variational SBM formulations for the Poisson and Stokes problems with improved flexibility and robustness. These simplified variational forms allow to relax some of the assumptions required by the mathematical proofs of stability and convergence of earlier implementations. First, we show that these new SBM implementations can be proved asymptotically stable and convergent even without the rather restrictive assumption that the inner product between the normals to the true and surrogate boundaries is positive. Second, we show that it is not necessary to introduce a stabilization term involving the tangential derivatives of the solution at Dirichlet boundaries, therefore avoiding the calibration of an additional stabilization parameter. Finally, we prove enhanced L 2 -estimates without the cumbersome assumption – of earlier proofs – that the surrogate domain is convex. Instead we rely on a conventional assumption that the boundary of the true domain is smooth, which can also be replaced by requiring convexity of the true domain. The aforementioned improvements open the way to a more general and efficient implementation of the Shifted Boundary Method, particularly in complex three-dimensional geometries. We complement these theoretical developments with numerical experiments in two and three dimensions.

42 ENGINEERING↗

DOE OSTI2016

A new weak Galerkin finite element method for elliptic interface problems

We introduce and analyze a new weak Galerkin (WG) finite element method in this paper for solving second order elliptic equations with discontinuous coefficients and interfaces. Comparing with the existing WG algorithm for solving the same type problems, the present WG method has a simpler variational formulation and fewer unknowns. Moreover, the new WG algorithm allows the use of finite element partitions consisting of general polytopal meshes and can be easily generalized to high orders. Optimal order error estimates in both H1 and L2 norms are established for the present WG finite element solutions. We conducted extensive numerical experiments in order to examine the accuracy, flexibility, and robustness of the proposed WG interface approach. In solving regular elliptic interface problems, high order convergences are numerically confirmed by using piecewise polynomial basis functions of high degrees. Moreover, the WG method is shown to be able to accommodate very complicated interfaces, due to its flexibility in choosing finite element partitions. Finally, in dealing with challenging problems with low regularities, the piecewise linear WG method is capable of delivering a second order of accuracy in L∞ norm for both C1 and H2 continuous solutions.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2024

A weighted shifted boundary method for immersed moving boundary simulations of Stokes' flow

The Shifted Boundary Method (SBM) belongs to the class of unfitted (or immersed, or embedded) finite element methods, and relies on reformulating the original boundary value problem over a surrogate (approximate) computational domain. The surrogate domain is constructed so as to avoid cut cells and the associated problematic implementation and numerical integration issues. Accuracy is maintained by modifying the original boundary conditions using Taylor expansions: hence the name of the method, that shifts the location and values of the boundary conditions. Here, in this article, we extend the SBM to the simulation of incompressible Stokes flow, by appropriately weighting its variational form with the elemental volume fraction of active fluid. This approach allows to drastically reduce spurious pressure oscillations in time, which are produced if the total volume of active fluid were to change abruptly over a time step. The proposed Weighted SBM (W-SBM) exactly preserves states of hydrostatic equilibrium, and induces small mass and momentum conservation errors, which converge as the grid is refined. This is in analogy to cutFEMs and related unfitted approaches, which rely on an affine representation of cut boundaries. We demonstrate the robustness and accuracy of the proposed method with an extensive suite of two-dimensional tests.

97 MATHEMATICS AND COMPUTING↗