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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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All sourcesNASA NTRSDOE OSTI
DOE OSTI2023

Preservation of kinetics parameters generated by Monte Carlo calculations in two-step deterministic calculations

The generation of accurate kinetic parameters such as mean generation time Λ and effective delayed neutron fraction β eff via Monte Carlo codes is established. Employing these in downstream deterministic codes warrants another step to ensure no additional error is introduced by the low-order transport operator when computing forward and adjoint fluxes for bilinear weighting of these parameters. Another complexity stems from applying superhomogenization (SPH) equivalence in non-fundamental mode approximations, where reference and low-order calculations rely on a 3D full core model. In these cases, SPH factors can optionally be computed for only part of the geometry while preserving reaction rates and K-effective, but the impact of such approximations on kinetics parameters has not been thoroughly studied. This paper aims at studying the preservation of bilinearly-weighted quantities in the Serpent–Griffin calculation procedure. Diffusion and transport evaluations of IPEN/MB-01, Godiva, and Flattop were carried out with the Griffin reactor physics code, testing available modeling options using Serpent-generated multigroup cross sections and equivalence data. Verifying Griffin against Serpent indicates sensitivities to multigroup energy grid selection and regional application of SPH equivalence, introducing significant errors; these were demonstrated to be reduced through the use of a transport method together with a finer energy grid.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2017

A practical globalization of one-shot optimization for optimal design of tokamak divertors

In past studies, nested optimization methods were successfully applied to design of the magnetic divertor configuration in nuclear fusion reactors. In this paper, so-called one-shot optimization methods are pursued. Due to convergence issues, a globalization strategy for the one-shot solver is sought. Whereas Griewank introduced a globalization strategy using a doubly augmented Lagrangian function that includes primal and adjoint residuals, its practical usability is limited by the necessity of second order derivatives and expensive line search iterations. In this paper, a practical alternative is offered that avoids these drawbacks by using a regular augmented Lagrangian merit function that penalizes only state residuals. Additionally, robust rank-two Hessian estimation is achieved by adaptation of Powell's damped BFGS update rule. The application of the novel one-shot approach to magnetic divertor design is considered in detail. For this purpose, the approach is adapted to be complementary with practical in parts adjoint sensitivities. Using the globalization strategy, stable convergence of the one-shot approach is achieved.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2014

Thermal Hydraulic Simulations, Error Estimation and Parameter Sensitivity Studies in Drekar::CFD

This report describes work directed towards completion of the Thermal Hydraulics Methods (THM) CFD Level 3 Milestone THM.CFD.P7.05 for the Consortium for Advanced Simulation of Light Water Reactors (CASL) Nuclear Hub effort. The focus of this milestone was to demonstrate the thermal hydraulics and adjoint based error estimation and parameter sensitivity capabilities in the CFD code called Drekar::CFD. This milestone builds upon the capabilities demonstrated in three earlier milestones; THM.CFD.P4.02, completed March, 31, 2012, THM.CFD.P5.01 completed June 30, 2012 and THM.CFD.P5.01 completed on October 31, 2012.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2024

Development of the tangent linear and adjoint models of the global online chemical transport model MPAS-CO 2 v7.3

We describe the development of the tangent linear (TL) and adjoint models of the Model for Prediction Across Scales (MPAS)-CO 2 transport model, which is a global online chemical transport model developed upon the non-hydrostatic Model for Prediction Across Scales – Atmosphere (MPAS-A). The primary goal is to make the model system a valuable research tool for investigating atmospheric carbon transport and inverse modeling. First, we develop the TL code, encompassing all CO 2 transport processes within the MPAS-CO 2 forward model. Then, we construct the adjoint model using a combined strategy involving re-calculation and storage of the essential meteorological variables needed for CO 2 transport. This strategy allows the adjoint model to undertake a long-period integration with moderate memory demands. To ensure accuracy, the TL and adjoint models undergo vigorous verifications through a series of standard tests. The adjoint model, through backward-in-time integration, calculates the sensitivity of atmospheric CO 2 observations to surface CO 2 fluxes and the initial atmospheric CO 2 mixing ratio. To demonstrate the utility of the newly developed adjoint model, we conduct simulations for two types of atmospheric CO 2 observations, namely the tower-based in situ CO 2 mixing ratio and satellite-derived column-averaged CO 2 mixing ratio (X CO 2 ). A comparison between the sensitivity to surface flux calculated by the MPAS-CO 2 adjoint model with its counterpart from CarbonTracker–Lagrange (CT-L) reveals a spatial agreement but notable magnitude differences. These differences, particularly evident for X CO 2 , might be attributed to the two model systems' differences in the simulation configuration, spatial resolution, and treatment of vertical mixing processes. Moreover, this comparison highlights the substantial loss of information in the atmospheric CO 2 observations due to CT-L's spatial domain limitation. Furthermore, the adjoint sensitivity analysis demonstrates that the sensitivities to both surface flux and initial CO 2 conditions spread out throughout the entire Northern Hemisphere within a month. MPAS-CO 2 forward, TL, and adjoint models stand out for their calculation efficiency and variable-resolution capability, making them competitive in computational cost. In conclusion, the successful development of the MPAS-CO 2 TL and adjoint models, and their integration into the MPAS-CO 2 system, establish the possibility of using MPAS's unique features in atmospheric CO 2 transport sensitivity studies and in inverse modeling with advanced methods such as variational data assimilation.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2012

Sensitivity analysis of coupled criticality calculations

Perturbation theory based sensitivity analysis is a vital part of todays' nuclear reactor design. This paper presents an extension of standard techniques to examine coupled criticality problems with mutual feedback between neutronics and an augmenting system (for example thermal-hydraulics). The proposed procedure uses a neutronic and an augmenting adjoint function to efficiently calculate the first order change in responses of interest due to variations of the parameters describing the coupled problem. The effect of the perturbations is considered in two different ways in our study: either a change is allowed in the power level while maintaining criticality (power perturbation) or a change is allowed in the eigenvalue while the power is constrained (eigenvalue perturbation). The calculated response can be the change in the power level, the reactivity worth of the perturbation, or the change in any functional of the flux, the augmenting dependent variables and the input parameters. To obtain power- and criticality-constrained sensitivities power- and k-reset procedures can be applied yielding identical results. Both the theoretical background and an application to a one dimensional slab problem are presented, along with an iterative procedure to compute the necessary adjoint functions using the neutronics and the augmenting codes separately, thus eliminating the need of developing new programs to solve the coupled adjoint problem. (authors)

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2020

Predicting mesoscale spectral thermal conductivity using advanced deterministic phonon transport techniques

We present a review, demonstration and simulation of phonon transport for the purposes of predicting materials performance at the mesoscale. We focus primarily on the development and implementation of a unified methodology to enable predictive heat transport. We report on the current state of the art as it pertains to deterministic phonon transport methodologies, discussing various topics concerning phonons. In application, we focus on the Self-Adjoint Angular Flux (SAAF) formulation of the Boltzmann transport equation for phonons, and develop the spatial, angular, and material property discretization required to accurately simulate the predictive physics of heat transport in dielectrics. We discuss thermal interfacial resistance and present our formulation of the diffuse mismatch model for simulating phonon interactions at internal boundaries. We have recently developed a deterministic, spectral phonon transport method for predicting effective thermal conductivity ($\kappa_{\textrm{eff}}$), using Bose-Einstein source terms coupled through an average material temperature. In this method, we introduce a closure term to the phonon transport system which acts as a redistribution function for the total energy of the system, and serves as a guide for the amount of non-equilibrium behavior occurring in the system. This method predicts thermal conductivity and equilibrium temperature distributions in homogeneous and heterogeneous materials using data generated by ab initio density functional theory methods. We employ polarization, density of states and full dispersion spectra to resolve thermal conductivity with numerous angular and spatial discretizations. Our implementation utilizes a Richardson iteration on a modified version of the phonon scattering source. The equations associated with this method are solved via a modification of traditional source iteration. We compare the performance of source iteration applied to an existing uncoupled, traditional SAAF method to our new method and comment on the iterative performance of each. We observe ballistic and diffusive phonon scattering as acoustic thickness of the domain changes, and are able to make comparisons between the accuracy and efficiency of both methods.

36 MATERIALS SCIENCE↗
DOE OSTI2011

COMBINE7.1 - A Portable ENDF/B-VII.0 Based Neutron Spectrum and Cross-Section Generation Program

COMBINE7.1 is a FORTRAN 90 computer code that generates multigroup neutron constants for use in the deterministic diffusion and transport theory neutronics analysis. The cross-section database used by COMBINE7.1 is derived from the Evaluated Nuclear Data Files (ENDF/B-VII.0). The neutron energy range covered is from 20 MeV to 1.0E-5 eV. The Los Alamos National Laboratory NJOY code is used as the processing code to generate a 167 fine-group cross-section library in MATXS format for Bondarenko self-shielding treatment. Resolved resonance parameters are extracted from ENDF/B-VII.0 File 2 for a separate library to be used in an alternate Nordheim self-shielding treatment in the resolved resonance energy range. The equations solved for energy dependent neutron spectrum in the 167 fine-group structure are the B3 or B1 zero-dimensional approximations to the transport equation. The fine group cross sections needed for the spectrum calculation are first prepared by Bondarenko self-shielding interpolation in terms of background cross section and temperature. The geometric lump effect, when present, is accounted for by augmenting the background cross section. Nordheim self-shielded fine group cross sections for a material having resolved resonance parameters overwrite correspondingly the existing self-shielded fine group cross sections when this option is used. COMBINE7.1 coalesces fine group cross sections into broad group macroscopic and microscopic constants. The coalescing is performed by utilizing fine-group fluxes and/or currents obtained by spectrum calculation as the weighting functions. The multigroup constants may be output in any of several standard formats including INL format, ANISN 14** free format, CCCC ISOTXS format, and AMPX working library format. ANISN-PC, a one-dimensional (1-D) discrete-ordinate transport code, is incorporated into COMBINE7.1. As an option, the 167 fine-group constants generated by zero-dimensional COMBINE portion in the program can be used to calculate regionwise spectra in the 1-D ANISN portion, all internally to reflect the 1-D transport correction. The regionwise spectra are then used to generate mutigroup regionwise neutron constants. The 1-D neutron transport can be performed up to three stages, e.g., from a TRISO fuel to PEBBLE to 1-D full core wedge. In addition, COMBINE7.1 has now the capability of adjoint flux calculation through the 1-D ANISN transport. Photon transport capability is also added. For this, a photon production and photo-atomic cross section library, MATNG.LIB, was generated in MATXS format through NJOY code. The photon production cross section matrix is of 167 neutron - 18 photon groups. Photo-atomic cross sections, including heating, are in 18 energy groups.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
NASA NTRS2019

A New Recycling Method to Generate Turbulent Inflow Profiles

The accuracy of the scale-resolving simulations for practical geometries strongly depends on the inflow boundary conditions. Imposing experimentally observed turbulent inflow profiles for the numerical simulations is a major challenge. Existing methods available in the literature assume self-similar behavior, which is not true for most of the experiments. In the present work, we formulate the turbulent inflow profile generation technique as an optimization problem. An adjoint technique is exploited to evaluate the sensitivities of multiple input parameters for the present problem. The present formulation is then tested to generate a laminar boundary layer profile, turbulent boundary layer profile, and turbulent jet profile.

Garai, Anirban↗
DOE OSTI2015

Efficient Algorithms for Estimating the Absorption Spectrum within Linear Response TDDFT

We present a special symmetric Lanczos algorithm and a kernel polynomial method (KPM) for approximating the absorption spectrum of molecules within the linear response time-dependent density functional theory (TDDFT) framework in the product form. In contrast to existing algorithms, the new algorithms are based on reformulating the original non-Hermitian eigenvalue problem as a product eigenvalue problem and the observation that the product eigenvalue problem is self-adjoint with respect to an appropriately chosen inner product. This allows a simple symmetric Lanczos algorithm to be used to compute the desired absorption spectrum. The use of a symmetric Lanczos algorithm only requires half of the memory compared with the nonsymmetric variant of the Lanczos algorithm. The symmetric Lanczos algorithm is also numerically more stable than the nonsymmetric version. The KPM algorithm is also presented as a low-memory alternative to the Lanczos approach, but the algorithm may require more matrix-vector multiplications in practice. We discuss the pros and cons of these methods in terms of their accuracy as well as their computational and storage cost. Applications to a set of small and medium-sized molecules are also presented.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2025

An Analytic Benchmark for Neutron Boltzmann Transport with Downscattering—Part IV: PFNS and $\bar{ν}$ Uncertainty Propagation

An analytic benchmark with continuous-energy cross sections was previously derived to validate criticality calculations. Here, to extend the utility of the analytic benchmark to verify the implementation of $\bar{ν}$ and prompt fission neutron spectrum (PFNS) uncertainty propagation methods, new simplified forms that are dependent on the incident (fission-causing) neutron energy, as well as the outgoing neutron energy for the PFNS, are introduced in this work. The analytical forms for the flux and adjoint flux are derived for the extended benchmark and used to determine the 𝑘-eigenvalue sensitivity to $\bar{ν}$ and PFNS. The 𝑘-eigenvalue uncertainty due to $\bar{ν}$ and PFNS is calculated for the analytic benchmark using simplified$\bar{ν}$ and PFNS representations based on the ENDF-B/VIII.0 239 Pu evaluation. Because of the low sensitivity of the analytic benchmark to the physical PFNS, a nonphysical high-sensitivity PFNS is also presented.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2013

Fission matrix capability for MCNP, Part I - Theory

The theory underlying the fission matrix method is derived using a rigorous Green's function approach. The method is then used to investigate fundamental properties of the transport equation for a continuous-energy physics treatment. We provide evidence that an infinite set of discrete, real eigenvalues and eigenfunctions exist for the continuous-energy problem, and that the eigenvalue spectrum converges smoothly as the spatial mesh for the fission matrix is refined. We also derive equations for the adjoint solution. We show that if the mesh is sufficiently refined so that both forward and adjoint solutions are valid, then the adjoint fission matrix is identical to the transpose of the forward matrix. While the energy-dependent transport equation is strictly bi-orthogonal, we provide surprising results that the forward modes are very nearly self-adjoint for a variety of continuous-energy problems. A companion paper (Part II - Applications) describes the initial experience and results from implementing this fission matrix capability into the MCNP Monte Carlo code. (authors)

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2014

The coupling of the neutron transport application RATTLESNAKE to the nuclear fuels performance application BISON under the MOOSE framework

The MOOSE neutron transport application RATTLESNAKE was coupled to the fuels performance application BISON to provide a higher fidelity tool for fuel performance simulation. This project is motivated by the desire to couple a high fidelity core analysis program (based on the self-adjoint angular flux equations) to a high fidelity fuel performance program, both of which can simulate on unstructured meshes. RATTLESNAKE solves self-adjoint angular flux transport equation and provides a sub-pin level resolution of the multigroup neutron flux with resonance treatment during burnup or a fast transient. BISON solves the coupled thermomechanical equations for the fuel on a sub-millimeter scale. Both applications are able to solve their respective systems on aligned and unaligned unstructured finite element meshes. The power density and local burnup was transferred from RATTLESNAKE to BISON with the MOOSE Multiapp transfer system. Multiple depletion cases were run with one-way data transfer from RATTLESNAKE to BISON. The eigenvalues are shown to agree well with values obtained from the lattice physics code DRAGON. The one-way data transfer of power density is shown to agree with the power density obtained from an internal Lassman-style model in BISON.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2011

Development of INSPCT-S for inspection of spent fuel pool

In this paper, we discuss an accurate and fast software tool (INSPCT-S, Inspection of Nuclear Spent fuel-Pool Calculation Tool, version Spreadsheet) developed for calculation of the response of fission chambers placed in a spent fuel pool, such as Atucha-I. INSPCT-S is developed for identification of suspicious regions of the pool that may have missing or substitute assemblies. INSPCT-S uses a hybrid algorithm based on the adjoint function methodology. The neutron source is comprised of spontaneous fission, ({alpha}, n) interactions, and subcritical multiplication. The former is evaluated using the ORIGEN-ARP code, and the latter is obtained with the fission matrix (FM) formulation. The FM coefficients are determined using the MCNP Monte Carlo code, and the importance function is determined using the PENTRAN 3-D parallel Sn code. Three databases for the neutron source, FM elements, and adjoint flux are prepared as functions of different parameters including burnup, cooling time, enrichment, and pool lattice size. INSPCT-S uses the aforementioned databases and systems of equations to calculate detector responses, which are subsequently compared with normalized experimental data. If this comparison is not satisfied, INSPCT-S utilizes color coding to identify the suspicious regions of a spent fuel pool. (authors)

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2020

Blood flow imaging by optimal matching of computational fluid dynamics to 4D-flow data

Three-dimensional, time-resolved blood flow measurement (4D-flow) is a powerful research and clinical tool, but improved resolution and scan times are needed. Therefore, this study aims to (1) present a postprocessing framework for optimization-driven simulation-based flow imaging, called 4D-flow High-resolution Imaging with a priori Knowledge Incorporating the Navier-Stokes equations and the discontinuous Galerkin method (4D-flow HIKING), (2) investigate the framework in synthetic tests, (3) perform phantom validation using laser particle imaging velocimetry, and (4) demonstrate the use of the framework in vivo. An optimizing computational fluid dynamics solver including adjoint-based optimization was developed to fit computational fluid dynamics solutions to 4D-flow data. Synthetic tests were performed in 2D, and phantom validation was performed with pulsatile flow. Reference velocity data were acquired using particle imaging velocimetry, and 4D-flow data were acquired at 1.5 T. In vivo testing was performed on intracranial arteries in a healthy volunteer at 7 T, with 2D flow as the reference. Results Synthetic tests showed low error (0.4%-0.7%). Phantom validation showed improved agreement with laser particle imaging velocimetry compared with input 4D-flow in the horizontal (mean -0.05 vs -1.11 cm/s, P < .001; SD 1.86 vs 4.26 cm/s, P < .001) and vertical directions (mean 0.05 vs -0.04 cm/s, P = .29; SD 1.36 vs 3.95 cm/s, P < .001). In vivo data show a reduction in flow rate error from 14% to 3.5%. Phantom and in vivo results from 4D-flow HIKING show promise for future applications with higher resolution, shorter scan times, and accurate quantification of physiological parameters.

4D-flow MRI↗
DOE OSTI2016

Actuator selection and placement for localized feedback flow control

The selection and placement of actuators and sensors to control compressible viscous flows is addressed by developing a novel methodology based upon the eigensystem structural sensitivity of the linearized evolution operator appropriate for linear feedback control. Forward and adjoint global modes are used to construct a space of possible perturbations to the linearized operator, which yields a small optimization problem for selecting the parameters that best achieve the control objective, including where they should be placed. The method is demonstrated by informing actuation to suppress amplification of the instabilities in boundary layer separation in a high-subsonic diffuser. Complete stabilization is observed in the separated shear layer for short downstream distances at modest Reynolds number. Higher Reynolds numbers and longer distances are expected to be more challenging to stabilize; here the control informed by the procedure still substantively suppresses amplification of instabilities. It is also demonstrated that more complex actuator–sensor selections may not yield superior controllers.

Mechanics↗
DOE OSTI2024

A Stochastic Calculus Approach to Boltzmann Transport

Traditional Monte Carlo methods for particle transport utilize source iteration to express the solution, the flux density, of the transport equation as a Neumann series. Our contribution is to show that the particle paths simulated within source iteration are associated with the adjoint flux density and the adjoint particle paths are associated with the flux density. Here, we make our assertion rigorous through the use of stochastic calculus by representing the particle path used in source iteration as a solution to a stochastic differential equation (SDE). The solution to the adjoint Boltzmann equation is then expressed in terms of the same SDE, and the solution to the Boltzmann equation is expressed in terms of the SDE associated with the adjoint particle process. An important consequence is that the particle paths used within source iteration simultaneously provide Monte Carlo samples of the flux density and adjoint flux density in the detector and source regions, respectively. The significant practical implication is that particle trajectories can be reused to obtain both forward and adjoint quantities of interest. To the best our knowledge, the reuse of entire particles paths has not appeared in the literature. Monte Carlo simulations are presented to support the reuse of the particle paths.

Boltzmann transport↗
DOE OSTI2015

A method for including external feed in depletion calculations with CRAM and implementation into ORIGEN

A method for including external feed with polynomial time dependence in depletion calculations with the Chebyshev Rational Approximation Method (CRAM) is presented and the implementation of CRAM to the ORIGEN module of the SCALE suite is described. In addition to being able to handle time-dependent feed rates, the new solver also adds the capability to perform adjoint calculations. Results obtained with the new CRAM solver and the original depletion solver of ORIGEN are compared to high precision reference calculations, which shows the new solver to be orders of magnitude more accurate. Lastly, in most cases, the new solver is up to several times faster due to not requiring similar substepping as the original one.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2015

Issues in measure-preserving three dimensional flow integrators: Self-adjointness, reversibility, and non-uniform time stepping

Properties of integration schemes for solenoidal fields in three dimensions are studied, with a focus on integrating magnetic field lines in a plasma using adaptive time stepping. It is shown that implicit midpoint (IM) and a scheme we call three-dimensional leapfrog (LF) can do a good job (in the sense of preserving KAM tori) of integrating fields that are reversible, or (for LF) have a “special divergence-free” (SDF) property. We review the notion of a self-adjoint scheme, showing that such schemes are at least second order accurate and can always be formed by composing an arbitrary scheme with its adjoint. We also review the concept of reversibility, showing that a reversible but not exactly volume-preserving scheme can lead to a fractal invariant measure in a chaotic region, although this property may not often be observable. We also show numerical results indicating that the IM and LF schemes can fail to preserve KAM tori when the reversibility property (and the SDF property for LF) of the field is broken. We discuss extensions to measure preserving flows, the integration of magnetic field lines in a plasma and the integration of rays for several plasma waves. The main new result of this paper relates to non-uniform time stepping for volume-preserving flows. We investigate two potential schemes, both based on the general method of Feng and Shang [Numer. Math. 71, 451 (1995)], in which the flow is integrated in split time steps, each Hamiltonian in two dimensions. The first scheme is an extension of the method of extended phase space, a well-proven method of symplectic integration with non-uniform time steps. This method is found not to work, and an explanation is given. The second method investigated is a method based on transformation to canonical variables for the two split-step Hamiltonian systems. This method, which is related to the method of non-canonical generating functions of Richardson and Finn [Plasma Phys. Controlled Fusion 54, 014004 (2012)], appears to work very well.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗