Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “solution verification”

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.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 289 records · Page 16
All sourcesNASA NTRSDOE OSTI
DOE OSTI2021

Lattice Boltzmann simulation of the dissolution of slag in alkaline solution using real-shape particles

Highlights: • A dissolution numerical model was proposed to capture the real dissolution kinetics of slag in alkaline solution. • The log forward dissolution rate of Si was described as a function of NBO/T and solution pH. • A threshold solid volume fraction of 0.688 was found for a voxel in 3D, 63.8% larger than that for a pixel in 2D. • The proposed dissolution numerical model provides a reliable alternative to study the dissolution kinetics of slag. A dissolution numerical model was proposed in this study to capture the real dissolution kinetics of slag in alkaline solution. It consists of three modules, i.e. (i) simulation of the initial particle parking structure of slag in alkaline solution using real-shape particles of slag, (ii) simulation of the chemical reactions between slag and solution based on the transition state theory, and (iii) simulation of the physical transport of aqueous ions using the lattice Boltzmann method. This dissolution numerical model was verified using experimental results, showing reasonable accuracy. After verification, the dissolution numerical model was implemented to study the influences of temperature and particle shape using a proper recipe of slag in alkaline solution. This recipe was designed to avoid solid phase precipitation or gel formation via thermodynamic analysis. The simulation results showed faster dissolution kinetics of slag when using higher temperatures and more irregular particle shapes.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Lattice-Distortion-Enhanced Yield Strength in a Refractory High-Entropy Alloy

Severe distortion is one of the four core effects in single-phase high-entropy alloys (HEAs) and contributes significantly to the yield strength. However, the connection between the atomic-scale lattice distortion and macro-scale mechanical properties through experimental verification has yet to be fully achieved, owing to two critical challenges: 1) the difficulty in the development of homogeneous single-phase solid-solution HEAs and 2) the ambiguity in describing the lattice distortion and related measurements and calculations. Here, a single-phase body-centered-cubic (BCC) refractory HEA, NbTaTiVZr, using thermodynamic modeling coupled with experimental verifications, is developed. Compared to the previously developed single-phase NbTaTiV HEA, the NbTaTiVZr HEA shows a higher yield strength and comparable plasticity. The increase in yield strength is systematically and quantitatively studied in terms of lattice distortion using a theoretical model, first-principles calculations, synchrotron X-ray/neutron diffraction, atom-probe tomography, and scanning transmission electron microscopy techniques. These results demonstrate that severe lattice distortion is a core factor for developing high strengths in refractory HEAs.

36 MATERIALS SCIENCE↗
DOE OSTI2021

A process to verify numerical models for seismic fluid-structure interaction in advanced reactor vessels

Seismic design and qualification of a liquid-filled advanced nuclear reactor will have to account for fluid-structure interaction (FSI). Interaction between the tank, internal components, and contained liquid will rely on analysis of numerical models that must be verified and validated. Here this study demonstrates a verification process for models of a base-supported cylindrical tank by comparing numerical predictions and analytical solutions. The numerical models are consistent with the assumptions made to derive analytical solutions, namely, either a rigid or a linear elastic tank, ideal fluid, and small-amplitude, unidirectional, horizontal inputs. One software platform is used to illustrate the process. Seismic FSI analysis is performed using the Arbitrary Lagrangian-Eulerian (ALE) and Incompressible Computational Fluid Dynamics (ICFD) solvers in LS-DYNA. Reported responses are those used for design, including hydrodynamic pressures on the tank wall, shear forces and moments at the tank base, and wave heights of the contained liquid. The accuracy of the numerical results is discussed. The numerical models are verified for calculating the pressures on the tank wall and reactions at its base. Accurate simulation of wave action is challenging for both solvers. Recommendations for modeling, code development, and steps for verification are provided. Although focused on reactor vessels and one software platform, the verification process described herein is broadly applicable to liquid-filled vessels and other finite element codes.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2021

A new highly enriched 233 U reference material for improved simultaneous determination of uranium amount and isotope amount ratios in trace level samples

A highly-enriched 233 U reference material (>0.99987 n( 233 U)/n(U)) has been prepared and characterized for use as an isotope dilution mass spectrometry spike. An ion exchange separation was performed on 1 g of high purity 233 U to further reduce trace amounts of contaminant Pu in the material. The purified 233 U was then prepared as a master solution which was analyzed for molality of uranium by modified Davies and Gray titration. A portion of the master solution was quantitatively diluted and dispensed for reference material units. Selected units were analyzed for verification of uranium amount and to characterize uranium isotope amount ratios by multi-collector inductively couple plasma mass spectrometry. Furthermore, modelling of spike-corrected isotopic data show that the new spike will enable simultaneous measurements of uranium amount and isotope amount ratios with resulting uncertainties that are substantially less sensitive to over spiking than widely used 233 U certified reference materials.

233U↗
DOE OSTI2025

The Method of Finite Averages

The Method of Finite Averages (MoFA) is a rigorous multiscale modeling methodology for efficiently modeling multi-physical phenomena in heterogeneous porous media. The code developed in this project aims to perform the numerical calculations required to formulate, implement, and verify MoFA models for Earth and Energy systems (i.e., model verification refers to performing fully-resolved simulations of the systems and comparing their results to those of the models). In general, MoFA transforms partial differential equations (PDEs) describing the fine-scale physics of a system into coupled ordinary differential equations (ODEs)---in time---that describe the coarse-scale---or "average"---physical behaviors of the system. This transformation significantly expedites system simulation, as the coarse-scale ODEs involve vastly fewer degrees of freedom than the fine-scale PDEs. The code developed under this project will allow users to 1.) generate system geometries and numerical meshes, 2.) solve the PDE and ODE systems required for MoFA model formulation and implementation, 3.) solve the PDE systems required to obtain fully-resolved simulation results for model verification, and 4.) compare and plot results (e.g., the model and fully-resolved simulation solutions, the error between the solutions, etc.).

Pietrzyk, KyleM [Lawrence Livermore National Labor↗
NASA NTRS1972

Laminar natural convection under nonuniform gravity.

Laminar natural convection is analyzed for cases in which gravity varies with the distance from the leading edge of an isothermal plate. The study includes situations in which gravity varies by virtue of the varying slope of a surface. A general integral solution method which includes certain known integral solutions as special cases is developed to account for arbitrary position-dependence of gravity. A series method of solution is also developed for the full equations. Although it is more cumbersome it provides verification of the integral method.

Lienhard, J.↗
NASA NTRS2013

Computational Fluid Dynamics Uncertainty Analysis for Payload Fairing Spacecraft Environmental Control Systems

Spacecraft thermal protection systems are at risk of being damaged due to airflow produced from Environmental Control Systems. There are inherent uncertainties and errors associated with using Computational Fluid Dynamics to predict the airflow field around a spacecraft from the Environmental Control System. This proposal describes an approach to validate the uncertainty in using Computational Fluid Dynamics to predict airflow speeds around an encapsulated spacecraft. The research described here is absolutely cutting edge. Quantifying the uncertainty in analytical predictions is imperative to the success of any simulation-based product. The method could provide an alternative to traditional"validation by test only'' mentality. This method could be extended to other disciplines and has potential to provide uncertainty for any numerical simulation, thus lowering the cost of performing these verifications while increasing the confidence in those predictions. Spacecraft requirements can include a maximum airflow speed to protect delicate instruments during ground processing. Computationaf Fluid Dynamics can be used to veritY these requirements; however, the model must be validated by test data. The proposed research project includes the following three objectives and methods. Objective one is develop, model, and perform a Computational Fluid Dynamics analysis of three (3) generic, non-proprietary, environmental control systems and spacecraft configurations. Several commercially available solvers have the capability to model the turbulent, highly three-dimensional, incompressible flow regime. The proposed method uses FLUENT and OPEN FOAM. Objective two is to perform an uncertainty analysis of the Computational Fluid . . . Dynamics model using the methodology found in "Comprehensive Approach to Verification and Validation of Computational Fluid Dynamics Simulations". This method requires three separate grids and solutions, which quantify the error bars around Computational Fluid Dynamics predictions. The method accounts for all uncertainty terms from both numerical and input variables. Objective three is to compile a table of uncertainty parameters that could be used to estimate the error in a Computational Fluid Dynamics model of the Environmental Control System /spacecraft system. Previous studies have looked at the uncertainty in a Computational Fluid Dynamics model for a single output variable at a single point, for example the re-attachment length of a backward facing step. To date, the author is the only person to look at the uncertainty in the entire computational domain. For the flow regime being analyzed (turbulent, threedimensional, incompressible), the error at a single point can propagate into the solution both via flow physics and numerical methods. Calculating the uncertainty in using Computational Fluid Dynamics to accurately predict airflow speeds around encapsulated spacecraft in is imperative to the success of future missions.

Groves, Curtis E.↗
NASA NTRS2014

Dissertation Defense Computational Fluid Dynamics Uncertainty Analysis for Payload Fairing Spacecraft Environmental Control Systems

Spacecraft thermal protection systems are at risk of being damaged due to airflow produced from Environmental Control Systems. There are inherent uncertainties and errors associated with using Computational Fluid Dynamics to predict the airflow field around a spacecraft from the Environmental Control System. This paper describes an approach to quantify the uncertainty in using Computational Fluid Dynamics to predict airflow speeds around an encapsulated spacecraft without the use of test data. Quantifying the uncertainty in analytical predictions is imperative to the success of any simulation-based product. The method could provide an alternative to traditional "validation by test only" mentality. This method could be extended to other disciplines and has potential to provide uncertainty for any numerical simulation, thus lowering the cost of performing these verifications while increasing the confidence in those predictions. Spacecraft requirements can include a maximum airflow speed to protect delicate instruments during ground processing. Computational Fluid Dynamics can be used to verify these requirements; however, the model must be validated by test data. This research includes the following three objectives and methods. Objective one is develop, model, and perform a Computational Fluid Dynamics analysis of three (3) generic, non-proprietary, environmental control systems and spacecraft configurations. Several commercially available and open source solvers have the capability to model the turbulent, highly three-dimensional, incompressible flow regime. The proposed method uses FLUENT, STARCCM+, and OPENFOAM. Objective two is to perform an uncertainty analysis of the Computational Fluid Dynamics model using the methodology found in "Comprehensive Approach to Verification and Validation of Computational Fluid Dynamics Simulations". This method requires three separate grids and solutions, which quantify the error bars around Computational Fluid Dynamics predictions. The method accounts for all uncertainty terms from both numerical and input variables. Objective three is to compile a table of uncertainty parameters that could be used to estimate the error in a Computational Fluid Dynamics model of the Environmental Control System /spacecraft system. Previous studies have looked at the uncertainty in a Computational Fluid Dynamics model for a single output variable at a single point, for example the re-attachment length of a backward facing step. For the flow regime being analyzed (turbulent, three-dimensional, incompressible), the error at a single point can propagate into the solution both via flow physics and numerical methods. Calculating the uncertainty in using Computational Fluid Dynamics to accurately predict airflow speeds around encapsulated spacecraft in is imperative to the success of future missions.

CFD↗
NASA NTRS2014

Dissertation Defense: Computational Fluid Dynamics Uncertainty Analysis for Payload Fairing Spacecraft Environmental Control Systems

Spacecraft thermal protection systems are at risk of being damaged due to airflow produced from Environmental Control Systems. There are inherent uncertainties and errors associated with using Computational Fluid Dynamics to predict the airflow field around a spacecraft from the Environmental Control System. This paper describes an approach to quantify the uncertainty in using Computational Fluid Dynamics to predict airflow speeds around an encapsulated spacecraft without the use of test data. Quantifying the uncertainty in analytical predictions is imperative to the success of any simulation-based product. The method could provide an alternative to traditional validation by test only mentality. This method could be extended to other disciplines and has potential to provide uncertainty for any numerical simulation, thus lowering the cost of performing these verifications while increasing the confidence in those predictions.Spacecraft requirements can include a maximum airflow speed to protect delicate instruments during ground processing. Computational Fluid Dynamics can be used to verify these requirements; however, the model must be validated by test data. This research includes the following three objectives and methods. Objective one is develop, model, and perform a Computational Fluid Dynamics analysis of three (3) generic, non-proprietary, environmental control systems and spacecraft configurations. Several commercially available and open source solvers have the capability to model the turbulent, highly three-dimensional, incompressible flow regime. The proposed method uses FLUENT, STARCCM+, and OPENFOAM. Objective two is to perform an uncertainty analysis of the Computational Fluid Dynamics model using the methodology found in Comprehensive Approach to Verification and Validation of Computational Fluid Dynamics Simulations. This method requires three separate grids and solutions, which quantify the error bars around Computational Fluid Dynamics predictions. The method accounts for all uncertainty terms from both numerical and input variables. Objective three is to compile a table of uncertainty parameters that could be used to estimate the error in a Computational Fluid Dynamics model of the Environmental Control System spacecraft system.Previous studies have looked at the uncertainty in a Computational Fluid Dynamics model for a single output variable at a single point, for example the re-attachment length of a backward facing step. For the flow regime being analyzed (turbulent, three-dimensional, incompressible), the error at a single point can propagate into the solution both via flow physics and numerical methods. Calculating the uncertainty in using Computational Fluid Dynamics to accurately predict airflow speeds around encapsulated spacecraft in is imperative to the success of future missions.

Fluid Dynamics↗
NASA NTRSDate not supplied

Toward Verification of the γ-Reθt Transition Model in OVERFLOW and FUN3D

The results of an ongoing assessment of the transition modeling capability in NASA's OVERFLOW and FUN3D programs are presented, with a focus on the Langtry-Menter γ-Reθt transition model in combination with the shear-stress transport (SST) turbulence model. While the effect of numerics and boundary conditions on the accuracy and iterative convergence of RANS solutions for fully turbulent flows has been well documented, especially in the context of canonical flow configurations, the same cannot be said for transport-equation-based transition models coupled with RANS-based turbulence models. Given the criticality of transition modeling for new aircraft design and optimization, there has been a renewed focus on the accuracy of such transition models and their inconsistent implementation across different flow solvers as seen from the AIAA and NATO-AVT workshops. In this work, we aim to establish the verification of such models via these two well established CFD codes with different numerics. The goal is to produce high-quality data, such as grids, solutions, and other auxiliary data, that may be utilized for code verification by others in the CFD community. As a first step, the work reported here is focused on the Langtry-Menter transition model as applied to two simple 2D configurations, namely the flat plate, and the NLF-0416, respectively. The paper also highlights how the boundary conditions and baseline turbulence model can affect the solutions from the SST-based Langtry-Menter transition model. A preliminary evaluation of the automatic mesh adaption capabilities of these solvers and potential benefits for flow configurations involving a mix of laminar, transitional, and fully turbulent flows is also reported.

CFD Modeling↗
NASA NTRSDate not supplied

USM3D-ME Contributions to the 5th AIAA High Lift Prediction Workshop

This paper presents the results of Reynolds-averaged Navier-Stokes (RANS) simulations conducted by NASA’s flow solver, mixed-element USM3D (USM3D-ME), for the 5th AIAA High-Lift Prediction Workshop. As part of the Fixed-Grid RANS Technology Focus Group (TFG), these simulations were performed to assess the accuracy and efficiency of the USM3D-ME solutions in predicting high-lift flows. The High-Lift Common Research Model (CRM-HL) served as the primary geometry. Several CRM-HL configurations were used for three case studies: a verification study (Case 1), a configuration buildup study (Case 2), and a Reynolds-number variation study (Case 3). Overall, USM3D-ME RANS results aligned with the solutions selected by the Fixed-Grid RANS TFG and available wind tunnel data Simulations for Cases 1 and Configuration 2.1 achieved machine-zero residual convergence, with aerodynamic coefficients converging to steady-state values. However, Configurations 2.2-2.4 and Case 3 encountered iterative- and grid-convergence challenges, particularly at high angles of attack. Compared with the experimental data available for Configurations 2.2-2.4, close agreement was demonstrated at low angles of attack. However, for angles of attack approaching the maximum lift conditions, the predicted lift coefficient and pitching moment deviated from experimental values. The drag-coefficient predictions were in a relatively good agreement, however, slight overpredictions were observed at the highest angle of attack corresponding to the maximum-lift condition. Although iterative convergence for Configurations 2.2-2.4 at high angles of attack remains a persistent challenge, averaging aerodynamic coefficients over the last 5000 iterations yielded satisfactory agreement with the available wind tunnel experimental data. During the workshop, the lack of iterative convergence was attributed to the vortex structures emanating from the slat brackets. To investigate this issue further, post-workshop simulations were conducted on Configuration 2.2. In one study, RANS simulations were performed on a simplified geometry with the slat brackets removed. The second study focused on performing URANS simulations on the original Configuration 2.2 geometry. Preliminary results from both studies are presented and compared with wind tunnel data for Configuration 2.2. Consistent with the findings of other participants in the Fixed-Grid RANS TFG, this study emphasizes the necessity for further exploration and advancement in RANS technology for predicting high-lift flows.

CFD↗
NASA NTRSDate not supplied

USM3D-ME Contributions to the 5th AIAA High Lift Prediction Workshop

This paper presents the results of Reynolds-averaged Navier-Stokes (RANS) simulations conducted by the NASA flow solver, mixed-element USM3D (USM3D-ME), for the 5th AIAA High-Lift Prediction Workshop. As part of the Fixed-Grid RANS Technology Focus Group (TFG), these simulations were performed to assess the accuracy and efficiency of the USM3D-ME solutions in predicting high-lift flows. The High-Lift Common Research Model (CRM-HL) served as the primary geometry. Several CRM-HL configurations were used for three case studies: a verification study (Case 1), a configuration buildup study (Case 2), and a Reynolds-number variation study (Case 3). Overall, USM3D-ME RANS results aligned with the solutions selected by the Fixed-Grid RANS TFG and available wind tunnel data. Simulations for Case 1 and Configuration 2.1 achieved machine-zero residual convergence, with aerodynamic coefficients converging to steady-state values. However, Configurations 2.2-2.4 and Case 3 encountered iterative- and grid-convergence challenges, particularly at high angles of attack. Compared with the experimental data available for Configurations 2.2-2.4, close agreement was demonstrated at low angles of attack. However, for angles of attack approaching the maximum lift conditions, the predicted lift coefficient and pitching moment deviated from experimental values. The drag-coefficient predictions were in relatively good agreement, however, slight overpredictions were observed at the highest angle of attack corresponding to the maximum-lift condition. Although iterative convergence for Configurations 2.2-2.4 at high angles of attack remains a persistent challenge, averaging aerodynamic coefficients over the last 5000 iterations yielded satisfactory agreement with the available wind tunnel experimental data. During the workshop, the lack of iterative convergence was attributed to the vortex structures emanating from the slat brackets. To investigate this issue further, post-workshop simulations were conducted on Configuration 2.2. In one study, RANS simulations were performed on a simplified geometry with the slat brackets removed. The second study focused on performing unsteady RANS (URANS) simulations on the original Configuration 2.2 geometry. Preliminary results from both studies are presented and compared with wind tunnel data for Configuration 2.2. Consistent with the findings of other participants in the Fixed-Grid RANS TFG, this study emphasizes the necessity for further exploration and advancement in RANS technology for predicting high-lift flows.

Aerodynamics↗
NASA NTRS1991

Structural behavior of scientific balloons - Finite element simulation and verification

An off-the-shelf nonlinear finite element code was used to analyze fully inflated scientific balloons. The thin balloon film was modeled by shell bending elements. Numerical difficulties caused by insignificant bending stiffness terms were overcome by introducing some artificial bending stiffness. This approximation is justified by the fact that in thin shells with nonzero Gaussian curvature the membrane solution component is essentially independent of the bending solution component. Perturbation of the coveraged solution by increasing the bending stiffness by a full decade verified this assertion. This analytical approach was experimentally verified. As a result of this verification process it was discovered that the generally accepted linearly visco-elastic model for polyethylene film is inappropriate for a significant planar (as opposed to uniaxial) stress state. A linear elastic model presents a good approximation for planar stress states.

Schur, Willi W.↗
NASA NTRSDate not supplied

Exploration Helmet Permanent Anti-fog Study

For the current Extravehicular Mobility Unit (EMU) spacesuit, an astronaut applies an anti-fog solution to the interior of the helmet bubble before each EVA. However, the anti-fog solution has been reported to cause eye discomfort during at least seven EMU EVAs when the anti-fog solution contacted the crew member’s eyes. During STS-100, astronaut Chris Hadfield reported the eye irritation temporarily blinded him during his spacewalk. In addition, the wipe on anti-fog solution is a consumable that needs to be accounted for and a supply launched for missions. To solve this, the Exploration EMU (xEMU) pressure bubble investigated using a permanent anti-fog coating during Design Verification and Test (DVT) human in the loop (HITL) events. Chosen for previous use in Constellation Space Suit develop, HTAF-601, a water based permanent anti-fog solution, was tested. However, major issues have arisen with further HITL testing with the coating. Cleaning the helmet has been a challenge to avoid damaging the permanent anti-fog coating. NASA has completed a set of different methods for cleaning the anti-fog to try to document a preferred method. It was found isopropyl alcohol (IPA) cannot be used to clean the interior of the helmet because it will strip and delaminate the permanent anti-fog coating. Even with using a very gentle cleaning method of flushing with distilled or DI water and dabbing at facial oils, the permanent anti-fog starts to delaminate consistently after 50 hours manned pressurized time (MPT). Finally, the HTAF-601 coating is being discontinued by the vendor. Due to these issues, further investigation is being completed evaluating two solvent based anti-fog solutions: Exxene’s HCF-100 and FSI’s Visgard 106-94. Each coating will be evaluated on polycarbonate samples for application consistency, steam cycles (mimicking breath cycles), cleaning durability, haze, and light transmission. This study will determine if either coating is a viable option to pursue as a permanent anti-fog for spacesuit helmet applications.

spacesuit↗
DOE OSTI2022

Code verification for practically singular equations

We report the method-of-moments implementation of the electric-field integral equation (EFIE) yields many code-verification challenges due to the various sources of numerical error and their possible interactions. Matters are further complicated by singular integrals, which arise from the presence of a Green's function. To address these singular integrals, an approach is presented in wherein both the solution and Green's function are manufactured. Because the arising equations are poorly conditioned, they are reformulated as a set of constraints for an optimization problem that selects the solution closest to the manufactured solution. In this paper, we demonstrate how, for such practically singular systems of equations, computing the truncation error by inserting the exact solution into the discretized equations cannot detect certain orders of coding errors. On the other hand, the discretization error from the optimal solution is a more sensitive metric that can detect orders less than those of the expected convergence rate.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

A new HALEU isotopic certified reference material

Candidate certified reference material (CRM) U196 was prepared by gravimetrically mixing and dissolving NNSA NRMP CRM 112-A (natural uranium metal) and CRM 116-A (highly enriched 93.2% 235 U metal) to achieve a high-assay low-enriched uranium (HALEU) isotopic abundance reference material. CRM U196 will be certified for the 233 U/ 238 U, 234 U/ 238 U, 235 U/ 238 U, and 236 U/ 238 U ratios. Gravimetrically determined uranium isotope amount ratios and values derived from the isotope data were calculated from the buoyancy corrected mass data and from certified values for the metal CRMs used to create the solution. The 235 U isotope amount fraction (·100) and expanded uncertainty is 19.5846 ± 0.0028. For attribute verification, total evaporation and modified total evaporation isotope ratio measurements were performed. In conclusion, the reference material is to be distributed as a unit containing 5 mg uranium as dry uranyl nitrate.

High-assay low-enriched uranium↗
DOE OSTI2025

TInCup

SAND2025-11464O TInCuP (Tag Invoked Customization Points) is a modern, header-only C++20 library that addresses the boilerplate problem in tag invoke based customization points. It provides comprehensive code generation and verification tools. Sandia National Laboratories is a multimission laboratory managed and operated by National Technology & Engineering Solutions of Sandia, LLC, a wholly owned subsidiary of Honeywell International Inc., for the U.S. Department of Energy’s National Nuclear Security Administration under contract DE-NA0003525.

von Winckel, Gregory [Sandia National Lab. (SNL-CA↗
DOE OSTI2022

CTF Theory Manual: Version 4.3

Coolant-Boiling in Rod Arrays—Two Fluids (COBRA-TF) is a thermal/hydraulic (T/H) simulation code designed for light water reactor (LWR) vessel analysis. It uses a two-fluid, three-field (i.e., fluid film, fluid drops, and vapor) modeling approach. Both subchannel and three-dimensional Cartesian forms of its governing equations are available for the solution. The code was originally developed by Pacific Northwest Laboratory in 1980, and had been used and modified by several institutions over the last few decades. COBRA-TF also found use at the Pennsylvania State University (PSU) by the Reactor Dynamics and Fuel Modeling Group (RDFMG) and has been improved, updated, and subsequently rebranded as CTF. CTF was later adopted in the early 2010s by Oak Ridge National Laboratory (ORNL) for use in the Consortium for Advanced Simulation of Light Water Reactors (CASL) program, which led to a significant advancement of the code software quality, modeling accuracy, testing systems, and capabilities for improved support of modeling of common LWR nominal and transient behavior. As part of the improvement process, it was necessary to generate sufficient documentation for the public domain code which had lacked such material upon being adopted by RDFMG. This document serves as a theory manual for CTF, detailing the many two-phase heat transfer, drag, and important accident scenario models contained in the code, as well as the numerical solution process utilized. Additional documents available in the CTF documentation suite include the user manual and verification and validation manual.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗