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All sourcesNASA NTRSDOE OSTI
NASA NTRS2001

Coarse Grid Modeling of Turbine Film Cooling Flows Using Volumetric Source Terms

The recent trend in numerical modeling of turbine film cooling flows has been toward higher fidelity grids and more complex geometries. This trend has been enabled by the rapid increase in computing power available to researchers. However, the turbine design community requires fast turnaround time in its design computations, rendering these comprehensive simulations ineffective in the design cycle. The present study describes a methodology for implementing a volumetric source term distribution in a coarse grid calculation that can model the small-scale and three-dimensional effects present in turbine film cooling flows. This model could be implemented in turbine design codes or in multistage turbomachinery codes such as APNASA, where the computational grid size may be larger than the film hole size. Detailed computations of a single row of 35 deg round holes on a flat plate have been obtained for blowing ratios of 0.5, 0.8, and 1.0, and density ratios of 1.0 and 2.0 using a multiblock grid system to resolve the flows on both sides of the plate as well as inside the hole itself. These detailed flow fields were spatially averaged to generate a field of volumetric source terms for each conservative flow variable. Solutions were also obtained using three coarse grids having streamwise and spanwise grid spacings of 3d, 1d, and d/3. These coarse grid solutions used the integrated hole exit mass, momentum, energy, and turbulence quantities from the detailed solutions as volumetric source terms. It is shown that a uniform source term addition over a distance from the wall on the order of the hole diameter is able to predict adiabatic film effectiveness better than a near-wall source term model, while strictly enforcing correct values of integrated boundary layer quantities.

Heidmann, James D.↗
DOE OSTI2023

SAM Code Development for Source Term Modeling in Fluoride-salt-cooled High-temperature Reactors

The SAM code is under development and supported by DOE-NE’s Nuclear Energy Advanced Modeling and Simulation program as a modern system-level modeling and simulation tool for advanced non-light water reactor safety analyses. These advanced reactor concepts incorporate novel and improved approaches to achieve safety and economic feasibility. Many concepts leverage higher operating temperatures for improved efficiency with a variety of coolants and structural materials to support those needs. Such design choices may also pose unique radiological source term risks. There are continuous efforts to incorporate new physics and phenomena relevant to advanced reactor concepts, including capabilities to enable system-level source term modeling. The Pebble-Bed Fluoride-salt-cooled High-temperature Reactor (PB-FHR) is a promising candidate among advanced nuclear reactor concepts with its improved passive safety characteristics and high thermal efficiency. In addition to past efforts to support the development and utilization of SAM for PB-FHR safety analysis, the species transport modeling capabilities in SAM have been extended to simulate source term phenomena in concepts like the PB-FHR. The PB-FHR concept utilizes pebble-form TRISO fuel and FLiBe salt coolant to provide robust barriers to the release of almost all fission products and radiological source terms. However, tritium poses a unique radiological risk due to its significant production from neutron interactions with 6 Li and 9 Be in the FLiBe as well as its high mobility at elevated temperatures where it can permeate through structural metals. Secondly, the use of graphite at elevated temperatures poses the risk of oxidation damage to any structural components or fuel pebbles that are exposed to accidental air ingress. This report summarizes progress made in modeling these phenomena in SAM, which leverages the system-level multi-physics thermal hydraulic simulation to support an effective engineering-scale source term modeling capability. A tritium transport model is developed to simulate the various transport pathways in FHR and MSR concepts and is presented through verification and validation examples as well as demonstrations simulating experimental test loops and reference plant FHR models. A graphite oxidation model is also introduced to calculate local oxidation rates and is presented with initial validation results.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
NASA NTRS2013

Spurious Behavior of Shock-Capturing Methods: Problems Containing Stiff Source Terms and Discontinuities

The goal of this paper is to relate numerical dissipations that are inherited in high order shock-capturing schemes with the onset of wrong propagation speed of discontinuities. For pointwise evaluation of the source term, previous studies indicated that the phenomenon of wrong propagation speed of discontinuities is connected with the smearing of the discontinuity caused by the discretization of the advection term. The smearing introduces a nonequilibrium state into the calculation. Thus as soon as a nonequilibrium value is introduced in this manner, the source term turns on and immediately restores equilibrium, while at the same time shifting the discontinuity to a cell boundary. The present study is to show that the degree of wrong propagation speed of discontinuities is highly dependent on the accuracy of the numerical method. The manner in which the smearing of discontinuities is contained by the numerical method and the overall amount of numerical dissipation being employed play major roles. Moreover, employing finite time steps and grid spacings that are below the standard Courant-Friedrich-Levy (CFL) limit on shockcapturing methods for compressible Euler and Navier-Stokes equations containing stiff reacting source terms and discontinuities reveals surprising counter-intuitive results. Unlike non-reacting flows, for stiff reactions with discontinuities, employing a time step and grid spacing that are below the CFL limit (based on the homogeneous part or non-reacting part of the governing equations) does not guarantee a correct solution of the chosen governing equations. Instead, depending on the numerical method, time step and grid spacing, the numerical simulation may lead to (a) the correct solution (within the truncation error of the scheme), (b) a divergent solution, (c) a wrong propagation speed of discontinuities solution or (d) other spurious solutions that are solutions of the discretized counterparts but are not solutions of the governing equations. The present investigation for three very different stiff system cases confirms some of the findings of Lafon & Yee (1996) and LeVeque & Yee (1990) for a model scalar PDE. The findings might shed some light on the reported difficulties in numerical combustion and problems with stiff nonlinear (homogeneous) source terms and discontinuities in general.

Yee, Helen M. C.↗
DOE OSTI2021

Mechanistic Source Term Considerations for Advanced Non-LWRs (Revision 1)

This report is a functional review of the radionuclide containment strategies of fluoride-salt-cooled high temperature reactor (FHR), molten salt reactor (MSR) and high temperature gas reactor (HTGR) systems. This analysis serves as a starting point for further, more in-depth analyses geared towards identifying phenomenological gaps that still exist, hindering the creation of a mechanistic source term for these reactor types. As background information to this review, an overview of how a mechanistic source term is created and used for consequence assessment necessary for licensing is provided. How a mechanistic source term is used within the Licensing Modernization Project (LMP) is also provided. Lastly, the characteristics of non-LWR mechanistic source terms are examined. This report does not assess the viability of any software system for use with advanced reactor designs, but instead covers system function requirements. Future work within the Nuclear Energy Advanced Modeling and Simulations (NEAMS) program will address such gaps. This document is an update of SAND 2020-6730. An additional chapter is included as well as edits to original content.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗
DOE OSTI2024

"Source Term Modeling for Advanced Gas Micro-Reactors"

Maintaining the safety of the public, environment, and operating personnel is the most important factor in designing, operating, maintaining, and decommissioning nuclear reactors. In recent years, there has been a growing interest in the development of micro-reactors employing TRi-structural ISOtropic (TRISO)-coated particle fuel. In gas reactors, TRISO fuel plays an important role in the safety case for high temperature reactors because of the fission product retention properties of the fuel. This ability enables the use of a functional containment strategy for the reactor where multiple barriers are used to prevent fission product release to the environment. Part of the safety analysis of these advanced reactors is the assessment of radionuclide releases under normal and accident conditions through the multiple credited safety barriers. Using conservative assumptions, a mechanistic analysis can be performed to quantify these releases that combines the probabilistic assessment of failure with analytic solutions to radionuclide transport equations. Source term modeling for TRISO fuel has been performed for previous reactor designs; however, these models are outdated, in many cases proprietary, and need updates to be applied to the current state of TRISO fuel technology and alternative gas reactor core configurations [1]. Currently, the only publicly available source term assessment for gas reactors is an expert-based Monte Carlo simulation based on the effectiveness of the fuel kernel, coating layers, and graphite block in a modular high temperature gas reactor [2]. Thus, there is a need to develop a simple, versatile, and mechanistic model of fission product release and transport in gas reactor cores that could be applied to a variety of reactors through user inputs and reactor-specific radionuclide inventories. The release is calculated by the diffusion of the key safety important fission products through the kernel, silicon carbide (SiC), graphite for both intact and defective TRISO particles based on fuel and graphite temperatures in the reactor under normal operation. These releases from the fuel enter the coolant where they can plate-out on cooler surfaces. A clean-up model is included for designs with a coolant purification system to remove fission gases. This initial distribution of fission products in the reactor serves as an initial condition for potential releases under postulated accident conditions. The model then can calculate the fission product release for any transient temperature profile and fission product releases can then be used to assess radiological dose to the workers and the public using conventional dose tools. Data on the diffusion of fission products is based on historic German TRISO experiments and the more current Department of Energy (DOE) Advanced Gas Reactor (AGR) TRISO fuel development program. The model is coded in python with inputs and outputs in excel spreadsheets, as well as python plotting utilities to aid in the interpretation of the results. References: [1] INL, NGNP Mechanistic Source Term White Paper, INL-10-17997, July 2010. [2] David A. Petti, Richard R. Hobbins, Peter Lowry, Hans Gougar, “Representative Source Terms and The Influence of Reactor Attributes on Functional Containment in Modular High Temperature Gas-cooled Reactors,” Nuclear Technology, Vol. 184, p. 181-197, Nov. 2013.

07 ISOTOPE AND RADIATION SOURCES↗
NASA NTRS1988

A study of numerical methods for hyperbolic conservation laws with stiff source terms

The proper modeling of nonequilibrium gas dynamics is required in certain regimes of hypersonic flow. For inviscid flow this gives a system of conservation laws coupled with source terms representing the chemistry. Often a wide range of time scales is present in the problem, leading to numerical difficulties as in stiff systems of ordinary differential equations. Stability can be achieved by using implicit methods, but other numerical difficulties are observed. The behavior of typical numerical methods on a simple advection equation with a parameter-dependent source term was studied. Two approaches to incorporate the source term were utilized: MacCormack type predictor-corrector methods with flux limiters, and splitting methods in which the fluid dynamics and chemistry are handled in separate steps. Various comparisons over a wide range of parameter values were made. In the stiff case where the solution contains discontinuities, incorrect numerical propagation speeds are observed with all of the methods considered. This phenomenon is studied and explained.

Leveque, R. J.↗
DOE OSTI2024

Current State of Neutron Source Term Calculations

SOURCES-4C has some significant deficiencies that are mostly due to problems with the default data libraries that it uses. Some research groups have modified these libraries to fix most of the problems, but not all of them. Adding modern data libraries to SOURCES-4C is one of the most promising approaches to resolving these issues. Other promising options include using either NEDIS or a GEANT4 tool. Both of these codes approximately match the accuracy of the modified SOURCES-4C code. The NEDIS code is Russian. The GEANT4 tool might be computationally slow and it might also no longer be actively maintained. There are a handful of other (α,n) codes, but they are not accurate.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2023

ECAR-6076 Rev 0 MARVEL Reactor End of Life Enveloping Radiological Source Term

As part of the Microreactor Applications Research Validation and Evaluation Project (MARVEL) design effort, an enveloping end of life radiological source term for the reactor fuel and sodiumpotassium (NaK) eutectic coolant is calculated in support of the MARVEL preliminary hazard evaluation. The source term calculation assumes slightly more than two-years of uninterrupted operations at a power of about 120 kW for a total energy of 7,600,000 MJ which exceeds the planned two-year operation at 100 kW. The Reactor modeling was performed with MCNP6 Version 1.0 and the depletion was performed using the COUPLE and ORIGEN modules from the SCALE Version 6.2 code package.

21 - SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLAN↗
DOE OSTI2026

ALPHANSO: Open-source modeling of (α, n) neutron source terms

Applications ranging from nuclear safeguards to dark matter detection require accurate predictions of neutron yields and energy spectra produced by (α, n) reactions. Legacy tools like SOURCES-4C remain widely used despite significant limitations, including outdated nuclear data, missing target nuclides, and restricted accessibility. Here, we present ALPHANSO, an open-source Python package for calculating (α, n) neutron source terms. ALPHANSO incorporates modern nuclear data libraries and formats covering all naturally occurring target nuclides and provides a transparent, modular framework for updating or extending the data as new evaluations are released. Comparison with an updated version of SOURCES-4A, NeuCBOT, and experimental measurements across a range of elements and materials shows that ALPHANSO reproduces neutron yields and spectra in good agreement with experimental data and state-of-the-art (α, n) calculations. These results demonstrate that ALPHANSO is a reliable, accessible, and modern alternative to legacy (α, n) source term codes such as SOURCES-4C. Its open-source design and modular data handling make it readily extensible to future evaluated nuclear data and low-background applications.

(α, n) reactions↗
DOE OSTI2022

Advanced Finite-Volume Numerics and Source Term Assumptions for Kernel and G-Equation Modelling of Propane/Air Flames

Here G-Equation models represent propagating flame fronts with an implicit two-dimensional surface representation (level-set). Level-set methods are fast, as transport source terms for the implicit surface can be solved with finite-volume operators on the finite-volume domain, without having to build the actual surface. However, they include approximations whose practical effects are not properly understood. In this study, we improved the numerics of the FRESCO CFD code’s G-Equation solver and developed a new method to simulate kernel growth using signed distance functions and the analytical sphere-mesh overlap. We analyzed their role for simulating propane/air flames, using three well-established constant-volume configurations: a one-dimensional, freely propagating laminar flame; a disc-shaped, constant-volume swirl combustor; and torch-jet flame development through an orifice from a two-chamber device. We tested the explicit (sub-cycled) vs. implicit formulation for the standard transport operators (advection, diffusion, compressibility). In addition to the accurate flame swept-volume method for chemistry and species source term, we developed a more accurate estimator for the burnt/unburnt split cell composition. Then, we developed a signed-distance-function (SDF) based method which provides a more stable reinitialization of the level-set field at every time-step. We found that simplifying assumptions common to several G-Equation implementations, for straightforward terms such as compressibility and advection, lead to large errors in predicting the propagation of even laminar flames, with deviations up to ~300% in simulated vs. formulated flame speed. Conversely, the enhanced numerics enabled through the SDF field reinitialization and improved chemistry source term improve simulation stability and smooth flame propagation even with significantly larger solver time-steps.

42 ENGINEERING↗
NASA NTRS1989

On the application of subcell resolution to conservation laws with stiff source terms

LeVeque and Yee recently investigated a one-dimensional scalar conservation law with stiff source terms modeling the reacting flow problems and discovered that for the very stiff case most of the current finite difference methods developed for non-reacting flows would produce wrong solutions when there is a propagating discontinuity. A numerical scheme, essentially nonoscillatory/subcell resolution - characteristic direction (ENO/SRCD), is proposed for solving conservation laws with stiff source terms. This scheme is a modification of Harten's ENO scheme with subcell resolution, ENO/SR. The locations of the discontinuities and the characteristic directions are essential in the design. Strang's time-splitting method is used and time evolutions are done by advancing along the characteristics. Numerical experiment using this scheme shows excellent results on the model problem of LeVeque and Yee. Comparisons of the results of ENO, ENO/SR, and ENO/SRCD are also presented.

Chang, Shih-Hung↗
NASA NTRS2020

Implementation of Acceleration Source Term in FUN3D

Implementation of the acceleration source term in FUN3D is described. The method is evaluated using analytical and idealized test cases in two and three dimensions. It is also compared with results obtained from the moving mesh and six-degree-of-freedom simulations. The method shows promise in simulating the flight of accelerating vehicles as they make their ascent through varying reference conditions.

Nash’at N Ahmad↗
DOE OSTI2024

Documentation of Air Emissions Source Term for Radionuclide NESHAP Compliance: TA-53 Building 0984 Isotope Production Facility

This paper will document the air emissions source term for the TA-53 Building 0984 Isotope Production Facility (IPF). The facility has historically been managed as a minor source under Radionuclide NESHAP regulations, but began using a wider variety of irradiation targets and a higher beam current. To support expanded generation of actinium-225 for medical diagnostic and therapeutic uses, IPF is now irradiating thorium targets and the beam current is planned to increase from 250 microamperes up to 600 microamperes. These changes merit a review of the anticipated source term under the new proposed operational conditions. The end result of the review indicates the main stack (Exhaust Stack ES-1) needs to be managed as a major source with continuous emissions monitoring. No additional advance notifications or permitting is required as a result of these operational changes.

54 ENVIRONMENTAL SCIENCES↗
NASA NTRS1990

A study of numerical methods for hyperbolic conservation laws with stiff source terms

In the present study of the behavior of typical numerical methods in the case of a model advection equation having a parameter-dependent source term, two approaches to the incorporation of the source terms are used: MacCormack-type predictor-corrector methods with flux limiters, and splitting methods in which the fluid dynamics and chemistry are handled in separate steps. The latter are found to perform slightly better. The model scalar equation is used to show that the incorrectness of the propagation speeds of discontinuities observed in the stiff case is due to the introduction of nonequilibrium values through numerical dissipation in the advection step.

Leveque, R. J.↗
DOE OSTI2021

Identification and Resolution of Gaps in Mechanistic Source Term and Consequence Analysis Modeling for Molten Salt Reactors Salt Spill Scenarios

This report represents an assessment of the gaps in Mechanistic Source Term (MST) and consequence assessment modeling for Molten Salt Reactors (MSRs). The current capabilities for MELCOR and the MELCOR Accident Code System (MACCS) are discussed, along with updates needed in order to address specific needs for MSRs. A test plan developed by Argonne National Laboratories is discussed as addressing some of these gaps, while some will require additional attention. Further recommendations are made on addressing these gaps. This report satisfies the DOE NE Milestone M2RD-21SN0601061 to leverage MELCOR and MACCS to identify parameters of importance for source term assessments for salt spill experiments.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗
DOE OSTI2026

Pressurized Water Reactor Containment Aerosol Settling Rate for Accident Source Terms

This report documents results from MELCOR calculations performed to determine the aerosol settling rate in pressurized water reactor containments in support of the Nuclear Regulatory Commission (NRC) Regulatory Guide (RG) 1.183, “Alternative Radiological Source Terms for Evaluating Design Basis Accidents at Nuclear Power Reactors,” which is the methodology for determining alternate source terms in design basis accidents at nuclear power reactors.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2025

Investigating the Role of Accident Tolerant Cladding on Source Term Reduction for High-Burnup PWRs Using MELCOR

The use of accident tolerant fuel (ATF) cladding can increase coping times during and beyond design basis accidents. While such gains may be incremental, they provide a margin that can potentially be recovered to enable high-burnup (HBU) operation. Realizing such a margin requires demonstrating that the combination of HBU and ATF has not led to an overall increase in source term. This study investigates the influence of cladding technology (Zr-based, Cr-coated Zr, and FeCrAl) and fuel cycle length (18 and 24 months) on radiological dose at the boundary of the exclusion zone for a four-loop pressurized water reactor to investigate whether ATF claddings can provide such benefits. We analyze a recovered large break loss-of-coolant accident scenario to investigate the impact of transient timescale on the benefits of such coping time increases. The simulations have been performed using the MELCOR and MELCOR Accident Consequence Code System codes. For the cases analyzed, increased fuel cycle length did not necessarily increase radionuclide release and hydrogen generation, as these were found to be sensitive to the core power distribution. Similarly, off-site dose consequence is dominated by short-lived radionuclides that tend to saturate earlier in the burnup, so higher burnup operation did not necessarily increase the source term for the phenomena and transients analyzed here. Delays in recovery of the lowpressure safety injection system increase hydrogen production and radionuclide release, especially between 780 s and 1620 s, due to the nonlinear oxidation and core degradation behavior. Results show that Cr-coated Zr enhances safety by delaying heatup and gap release. Here, when uncertainty propagation on oxidation properties is considered, FeCrAl exhibits the lowest overall radionuclide release and off-site dose throughout the spectrum. However, while the considered “base model” performance is superior under delayed injection scenarios, upper-bound cases display hydrogen generation risk comparable to the Zr-based cladding.

Accident Tolerant Fuel↗
NASA NTRS1991

Approximate factorization with source terms

A comparative evaluation is made of three methodologies with a view to that which offers the best approximate factorization error. While two of these methods are found to lead to more efficient algorithms in cases where factors which do not contain source terms can be diagonalized, the third method used generates the lowest approximate factorization error. This method may be preferred when the norms of source terms are large, and transient solutions are of interest.

Shih, T. I.-P.↗