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DOE OSTI2023

A User’s Guide to the PLTEMP/ANL Code

PLTEMP/ANL V4.4 is a program that obtains a steady-state flow and temperature solution, in geometrical extent, for a nuclear reactor core, or a single fuel assembly, including the effect of manufacturing and modelling uncertainties by the means of hot channel factors. It is based on an evolutionary sequence of codes originally used for calculating plate temperatures, hence “PLTEMP”, developed at Argonne National Laboratory over the past 30 years. Fueled and non-fueled regions are modeled. Each fuel assembly consists of one or more plates or tubes separated by coolant channels. The fuel plates may have one to five layers of different materials, each with heat generation. The width of a fuel plate may be divided into multiple longitudinal stripes, each with its own axial power shape. Depending upon the heat transfer method selected, the temperature solution is effectively 2-dimensional or 3-dimensional. The geometry may be either slab or radial, corresponding to fuel assemblies made of a series of flat (or slightly curved) plates, or of nested tubes. A variety of thermal-hydraulic correlations are available to determine safety margins such as onset of nucleate boiling ratio (ONBR), departure from nucleate boiling ratio (DNBR), and onset of flow instability ratio (OFIR). Coolant properties for either light or heavy water are obtained from FORTRAN functions rather than from tables. The code is intended for thermal-hydraulic analysis of research reactor performance in the sub-cooled boiling regime. Both turbulent and laminar flow regimes can be modeled. Options to calculate both forced flow and natural circulation are available. A general search capability for select design and safety parameters is available to greatly reduce the reactor analyst’s time.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2023

A Conceptual Design of the Reactor Cavity Cooling System for the Horizontal Compact High Temperature Gas Reactor (HC-HTGR)

Horizontal Compact High Temperature Gas Reactor (HC-HTGR) is being designed by a multi-disciplinary team of nuclear, mechanical, and structural engineers under the support of a DOE-NE Advanced Reactor Demonstration Program’s Advanced Reactor Concepts-20 (ARC-20) award. The objective of this ARC-20 project is to deliver a conceptual design for the proposed HC-HTGR in 3 years and support its commercialization as a safe, low-cost HTGR. Argonne National Laboratory (Argonne) is responsible for the design and analysis of the reactor cavity cooling system (RCCS) as a safety system for passive decay heat removal of the reactor concept. This report documents the design study to derive a conceptual design study of the RCCS for the HC-HTGR. It includes the identification of the functions and requirements of the HC-HTGR RCCS, design analyses including high-level design consideration and the calculations for optimizing design space of the system with supporting component-level analysis to inform the material selection and performance of the water panel, the description of the conceptual design of the HC-HTGR RCCS derived based on the analyses results, and performance evaluation of the conceptual RCCS for the HC-HTGR. A detailed concept of the RCCS has been identified and high-level system requirements has been developed for the HC-HTGR. Design space focusing on the natural circulation loop portion of the RCCS has been investigated to optimize the system performance. The initial baseline dimensions were firstly derived based on the scoping calculations. A component level design analysis was conducted for the water panel to inform the material selection and to assess its conduction performance. A preliminary system-level performance analysis was performed for the 1/8th of the compartment of the initial baseline design of the RCCS using RELAP5-3D. To improve the system thermal performance, the RCCS design has been updated by exploring various design options by design parametric analyses. Based on the results, the conceptual design of the RCCS for the HC-HTGR has been derived, which satisfies the target performance of ~1 MWt at the elevated vessel wall temperature conditions. Transient simulations were conducted for the conceptual RCCS design for the HC-HTGR under various operation modes and heat load conditions using RELAP5-3D. The system dynamics in different operating states was investigated and the system performance under transients of interest was evaluated. The results demonstrated the overall system feasibility that the RCCS design maintains structures temperatures lower than maximum allowable temperature with sufficient system inventory without any active heat removal in the design process with certain transients addressed. The HC-HTGR RCCS will have additional design updates of subsystems or optimization of the system components during the preliminary and final design phases. Since the entire plant has not been integrated yet, this delivered conceptual design is subject to changes for integration, that require additional conceptual design activities and Quality and Assurance implementation (Q&A). The performance assessment of the RCCS for the HC-HTGR will be then revisited and optimized to finalize the system design, and the RCCS integrated primary system analysis will be utilized to simulate selective accident scenarios of interest where efforts are currently undergoing in the project.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗
DOE OSTI2024

System Level Analysis Software Validation with Argonne's THETA Experimental Facility (Final CRADA Report)

Under this CRADA, the Contractor will be generating and collecting sodium-based experimental data with modern instrumentation. The Contractor will work symbiotically with the Participant to generate SAS4A/SASSYS-1 and SAM computational models of the THETA experimental facility for validation of the system-level analysis codes utilized by Oklo, Inc. This effort will be specifically focused on the design basis event space scoped by Chapter 15 of the NRC’s Standard Review Plan (NUREG-0800) with an emphasis on natural circulation and thermal stratification phenomena in a prototypic sodium-cooled fast reactor (SFR).

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2024

Experimental Validation of Thermal Hydraulic Behavior in Sodium Fast Reactors (SFR) with the Thermal Hydraulic Experimental Test Article (THETA)

Thermal stratification and transition to natural circulation pose two of the largest sources of uncertainty in systems-level modeling of liquid metal-cooled fast reactors. As these phenomena typically develop during transient event sequences, licensing-basis events analyzed using systemslevel models may have considerable uncertainties associated with thermal-hydraulic parameters of the system to account for these phenomena. As a result, the validation basis for these phenomena for systems-level codes is insufficient to fully support the wide range of liquid metal fast reactors being developed in the US. Currently, the most viable path for licensing a design is to take significant conservatisms and maintain sufficiently large safety margins to account for this uncertainty.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2022

Development of a MOOSE thermal model of the MPC-32 canister and HI-STORM overpack

Nuclear power is a significant source of electricity in the United States, but the average age of nuclear power plants is around 40 years old. Safe management of spent nuclear fuel (SNF) is a key aspect of the back end of the nuclear fuel cycle, and SNF dry storage systems are becoming a popular, effective solution in this area, given the absence of a final disposal system. The spent fuel cask system (dry cask method) provides a feasible solution for maintaining SNF (~60 years) prior to final disposal. This project aims to develop a thermal model of the MPC-32 canister and HI-STORM overpack, using the Multiphysics Object-Oriented Simulation Environment (MOOSE). MOOSE is an open-source framework developed by Idaho National Laboratory (INL) for multiscale, multiphysics simulations. This study will investigate and demonstrate the thermal-hydraulics capabilities of the MOOSE framework, including natural circulation, heat transfer, porous flows, etc. The ultimate goal of the project is to verify whether MOOSE tools (including Pronghorn) can be used to study the thermal performance of the SNF dry cask storage system. This study provides reliable and inclusive solving strategy for dry cask problems. The detailed information about the solving scheme and the governing equations related to the physics of the system is provided in the report. The results for thermal-hydraulic analysis of the HI-STORM system is produced with using open source modules of the MOOSE framework. This results highlights the flexibility and modularity of the MOOSE which makes it a unique candidate for the frameworks and code packages. Therefore, integration of the MOOSE to UNF ST&DARDS will improve the thermal-hydraulic capability of the system while providing distinctive features to users.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2025

Improvements to Passive Heat Removal Systems in SAS4A/SASSYS-1

Safe operation of a sodium cooled fast reactor (SFR) can be significantly aided by heat removal systems that do not rely on active power, but function using passive means. Passive heat removal from such reactors can employ systems that extract heat directly from sodium coolant by utilizing heat exchangers submerged in the coolant and natural circulation of a metal fluid sodium (or sodium potassium eutectic) to heat exchangers (generally air cooled) externally located. These types of systems are generally called Direct Reactor Auxiliary Cooling Systems (DRACS). Another type of passive heat removal system particularly suitable for pool-type SFRs relies on indirect extraction of heat by utilizing air flow in an annular region surrounding the reactor guard vessel which discharges the heat via the chimney effects to the atmosphere. These systems are generally called Reactor Vessel Auxiliary Cooling Systems (RVACS).

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2025

The SAS4A/SASSYS-1 Version 5.8 Safety Analysis Code System

SAS4A/SASSYS-1 is a software simulation tool used to perform deterministic analysis of anticipated events as well as design basis and beyond design basis accidents for advanced nuclear reactors. Detailed, mechanistic models of steady-state and transient thermal, hydraulic, kinetic, and mechanical phenomena are employed to describe the response of the reactor core, the reactor primary and secondary coolant loops, the reactor control and protection systems, and the balance-of-plant to accidents caused by changes in coolant flow, loss of heat rejection, or reactivity insertion. The consequences of single and double-fault accidents can be modeled, including fuel and coolant heating, fuel and cladding mechanical behavior, core reactivity feedbacks, coolant loop performance including natural circulation, and decay heat removal. Analyses are typically terminated upon demonstration of reactor and plant shutdown to permanently coolable conditions, or upon violation of design basis margins. The objective of the analysis is to quantify accident consequences as measured by the transient behavior of system performance parameters, such as fuel and cladding temperatures, reactivity, and cladding strain. Originally developed for analysis of sodium cooled reactors with oxide fuel clad by stainless steel, the models were subsequently extended and specialized to metallic fuel clad with advanced alloys and to several other coolant options, including lead, LBE, and water.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2026

HTGR Multiphysics Application Drivers FY26 Updates

This report summarizes FY26 progress under the Nuclear Energy Advanced Modeling and Simulation (NEAMS) program's high-temperature gas-cooled reactor (HTGR) application driver work, covering a wide range of activities such as code validation and multi-physics code assessment. 1) A detailed SAM model of the High-Temperature Engineering Test Reactor (HTTR) was developed using a unique-block grouping approach, with an extended parallel thermal network method to capture block-to-block conduction and radiation heat transfer, and applied to steady-state simulations of the HTTR 30~MW and 9~MW cases. 2) In another activity, SAM's newly implemented multi-component gas flow model was validated against the Natural convection Shutdown heat removal Test Facility (NSTF) argon ingress experiment, correctly capturing the density-driven suppression and thermal recovery of natural circulation observed when argon is introduced into the air-cooled Reactor Cavity Cooling System (RCCS) loop. 3) For the OECD/NEA High Temperature Test Facility (HTTF) benchmark, we co-led the international benchmark activities as well as the OECD/NEA final benchmark report to be released at the end of this year. 4) Finally, the coupled Griffin-SAM modeling capability for pebble-bed HTGRs was advanced by verifying the Griffin neutronics solution against Serpent Monte Carlo for a realistic non-uniform temperature distribution, resolving several deficiencies in the SAM-to-Griffin temperature transfer scheme, and enabling distinct fuel kernel, moderator, and coolant temperatures for cross section feedback. These new features were demonstrated in a PBR load-following transient.

Lee, Alvin↗
DOE OSTI2025

Comparison of spatial dynamics and point kinetics approaches in multiphysics modeling of the molten salt reactor experiment

In this work, we present validation test results of fully coupled neutronics and thermal-hydraulics models of the Molten Salt Reactor Experiment (MSRE) against experimental data of the zero power pump transients and the natural circulation tests at low power. To capture the strong coupling between neutronics and thermal-hydraulics due to fuel circulation, and to account for the delayed neutron precursor (DNP) distribution, the porous media thermal-hydraulics solver Pronghorn was fully coupled to the spatial neutron dynamics code Griffin, which solves the neutron diffusion equation, and to the 0-D point kinetics solver Squirrel, using a 2-D homogenized representation of the MSRE. The validation test results show very good agreement with experimental data for both point kinetics and spatial dynamics simulations, capturing the strong feedback effect and DNP losses in the MSRE. The 0-D code Squirrel accurately predicted the time-dependent behavior in the MSRE given the steady-state spatial dynamics solution of Griffin.

42 - ENGINEERING↗
DOE OSTI2024

Investigation of Point-Contact Strategies for CFD Simulations of Pebble-Bed Reactor Cores

This study numerically investigated the effects of various contact strategies on the thermal hydraulic behavior within a structured bed of 100 explicitly modeled pebbles. Four contact strategies and two thermal hydraulic conditions were considered. The strategies to avoid contact singularities include decreasing the pebble diameter, increasing the pebble diameter, bridging the pebble surfaces near the contact region, and capping the pebble surfaces near the contact region. One strategy, Strategy 3a, which involves bridging with a cylinder equal to 10% of the pebble diameter, was selected as the baseline strategy because it addressed the contact singularity while minimizing the geometric changes that affect the bed porosity. The two thermal hydraulic conditions were full-power operation (Case 1) and pressurized loss of forced cooling or PLOFC (Case 2). Simulations of the conjugate heat transfer within the structured bed were performed using the Reynolds-averaged Navier–Stokes approach with the realizable k-ϵ turbulence model and two-layer all y + wall treatment. The thermal-fluid quantities of interest were compared between the contact strategies for each case. In Case 1, the hydraulic behavior was sensitive to the contact strategy, with large differences in the pressure drop (30%) and volume-average velocity (4%). The thermal behavior was not sensitive, with less than a 0.5% difference across the strategies. To better understand the separate effects of each heat transfer mode, Case 2 was divided into the following subcases: conduction (Case 2a); conduction/radiation (Case 2b); and conduction/radiation/convection (Case 2c). Case 2a represents an early phase of the PLOFC transient. Case 2b represents an intermediate phase of the PLOFC transient, with the pebble temperatures sufficiently high for the radiative heat transfer to be non-negligible. Case 2c represents a late phase of the PLOFC transient after the establishment of the natural circulation of the heat transfer fluid. For Case 2, large differences in the contact strategy were observed only in Case 2a with only conduction. The difference in the maximum pebble temperature was 23% in Case 2a, 2% in Case 2b, and 0.3% in Case 2c.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2024

Experimental Operation of a Prototype 750C Advanced Chloride Molten Salt Bellows Valve

To achieve DOE 2030 SunShot targets that reduce the cost of liquid-based solar by an additional 40% to 70% beyond 2018 costs, a more reliable, highly manufacturable flow valve, capable of achieving operational temperatures of >700°C is required [1]. This paper investigates the development of an innovative high-temperature chloride molten salt valve, with operation up to 750°C. This valve is intended to be employed within Gen 3 CSP liquid-based thermal energy storage (TES) systems as well as Gen 4 modular salt reactor (MSR) technologies. This work details the general design and flow testing of a bellows-seal flow control valve (FCV). This design includes an integrated closed-loop thermal control system to ensure robust design for freeze-thaw cycles. The self-contained thermal management STM system, is unique in the salt valve industry since it is an integrated solution to provide a consistent, repeatable alternative to typical heat tracing. Additionally, the design includes the employment of a novel heat pipe valve stem to facilitate enhanced passive thermal management into the valve assembly. This valve stem heat pipe is designed to facilitate natural circulation within the bonnet to ensure robust operation, during both nominal and transient thermal operation. The valve body and trim will be designed using SS316H, consistent with Flowserve Corporation’s existing product base and is code qualified but will utilize clad material for materials corrosion, manufacturing cost reduction and compatibility to ensure design flexibility. A test campaign was performed in this investigation utilizing a novel 750°C ternary chloride (20%NaCl/40%MgCl2/40%KCl by mol. wt. %) molten salt flow loop. A discussion about the design and installation of the valves within this test bed is provided for this investigation. Valve test results from this study assessed Cv curves as well as multiple actuator cycles, under varying thermodynamic and operational mode conditions, which would be characteristic within a commercial molten salt facility. The results indicate nominal operation for the baseline design, though improved performance and reliability is expected with the full designed FCV.

Armijo, Kenneth (ORCID:0000000346832147)↗
NASA NTRS1980

Combined solar collector and energy storage system

A combined solar energy collector, fluid chiller and energy storage system is disclosed. A movable interior insulated panel in a storage tank is positionable flush against the storage tank wall to insulate the tank for energy storage. The movable interior insulated panel is alternately positionable to form a solar collector or fluid chiller through which the fluid flows by natural circulation.

Jensen, R. N.↗
NASA NTRS1992

Cooling options for Astromag

A comparison of the various cooling options for the Astromag particle physics experiment is presented. The baseline design for the cryogenic system involves using a natural circulation fountain-effect driven flow loop (Hofmann type). The present paper considers two alternative options for cooling. The first design involves a thermal strap made of a high-conductivity metal, e.g., high-purity aluminum or copper, which connects the coil to the helium reservoir. Venting helium vapor can also be used to minimize the temperature of the magnet and recover from a quench. The second design is based on an He II heat pipe concept where steady state heat transport is by counterflow. Cavitation is prevented by use of a porous plug. Forced flow He II is also available but only during extraordinary operating conditions.

Maytal, B. Z.↗
NASA NTRS2008

A Review of Radiolysis Concerns for Water Shielding in Fission Surface Power Applications

This paper presents an overview of radiolysis concerns with regard to water shields for fission surface power. A review of the radiolysis process is presented and key parameters and trends are identified. From this understanding of the radiolytic decomposition of water, shield pressurization and corrosion are identified as the primary concerns. Existing experimental and modeling data addressing concerns are summarized. It was found that radiolysis of pure water in a closed volume results in minimal, if any net decomposition, and therefore reduces the potential for shield pressurization and corrosion. With the space program focus m emphasize more on permanent return to the Moon and eventually manned exploration of Mars, there has been a renewed look at fission power to meet the difficult technical & design challenges associated with this effort. This is due to the ability of fission power to provide a power rich environment that is insensitive to solar intensity and related aspects such as duration of night, dusty environments, and distance from the sun, etc. One critical aspect in the utilization of fission power for these applications of manned exploration is shielding. Although not typically considered for space applications, water shields have been identified as one potential option due to benefits in mass savings and reduced development cost and technical risk (Poston, 2006). However, the water shield option requires demonstration of its ability to meet key technical challenges including such things as adequate natural circulation for thermal management and capability for operational periods up to 8 years. Thermal management concerns have begun to be addressed and are not expected to be a problem (Pearson, 2007). One significant concern remaining is the ability to maintain the shield integrity through its operational lifetime. Shield integrity could be compromised through shield pressurization and corrosion resulting from the radiolytic decomposition of water.

Schoenfeld, Michael P.↗
NASA NTRS2017

Non-Intrusive Velocity Measurements with MTV During DCC Event in the HTTF

Velocity profiles are measured using molecular tagging velocimetry (MTV) in the high temperature test facility (HTTF) at Oregon State University during a depressurized conduction cooldown (DCC) event. The HTTF is a quarter scale electrically heated nuclear reactor simulator designed to replicate various accident scenarios. During a DCC, a double ended guillotine break results in the reactor pressure vessel (RPV) depressurizing into the reactor cavity and ultimately leading to air ingress in the reactor core (lock-exchange and gas diffusion). It is critical to understand the resulting buoyancy-driven flow to characterize the reactor self-cooling capacity through natural circulation. During tests conducted at ambient pressure and temperature, the RPV containing helium is opened (via the hot and cold legs) to a large vessel filled with nitrogen to simulate the atmosphere. The velocity profile on the hot leg pipe centerline is recorded at 10 Hz with MTV based on NO tracers. The precision of the velocimetry was measured to be 0.02 m/s in quiescent flow prior to the tests. A helium flow from the RPV is initially observed in the top quarter of the pipe. During the first 20 seconds of the event, helium flows out of the RPV with a maximum velocity below 2 m/s. The velocity profile transitions from parabolic to linear in character and decays slowly over the rest of the recording; peak velocities of 0.2 m/s are observed after 30 min. A counter-flow of nitrogen is also observed intermittently, which occurs at lower velocities (>0.1 m/s).

Andre, M. A.↗
NASA NTRS2016

Modernization of NASA's Johnson Space Center Chamber: A Liquid Nitrogen System to Support Cryogenic Vacuum Optical Testing of the James Webb Space Telescope (JWST)

NASA is the mission lead for the James Webb Space Telescope (JWST), the next of the “Great Observatories”, scheduled for launch in 2018. It is directly responsible for the integration and test (I&T) program that will culminate in an end-to-end cryo vacuum optical test of the flight telescope and instrument module in Chamber A at NASA Johnson Space Center. Historic Chamber A is the largest thermal vacuum chamber at Johnson Space Center and one of the largest space simulation chambers in the world. Chamber A has undergone a major modernization effort to support the deep cryogenic, vacuum and cleanliness requirements for testing the JWST. This paper describes the steps performed in efforts to convert the existing the 60’s era Liquid Nitrogen System from a forced flow (pumped) process to a natural circulation (thermo-siphon) process. In addition, the paper will describe the dramatic conservation of liquid nitrogen to support the long duration thermal vacuum testing. Lastly, describe the simplistic and effective control system which results in zero to minimal human inputs during steady state conditions.

Garcia, Sammy↗
DOE OSTI2021

Modeling of HTTF test PG-26 using RELAP5-3D and SAM

The High Temperature Test Facility (HTTF) at Oregon State University (OSU) is a scaled integral effects experiment designed to investigate transient behavior in high-temperature gas-cooled nuclear reactors (HTGR) with prismatic fuel and reflector blocks [1]. Several tests have been completed at the HTTF including depressurized conduction cooldown (DCC) and pressurized conduction cooldown (PCC) transients. This summary reports on the analysis of test PG-26 using the INL system code REALP5-3D [2] as well as the ANL system code SAM [3]. Test PG-26 is a progression of the Double Ended Inlet-Outlet Crossover Duct Break transient that is referred to as a DCC [4]. Core initial conditions (i.e., before the DCC started) have been met using low power (<100 kW) and two of ten available electric heater banks. The DCC transient was initiated during the 50th hour of the test. The break valves were opened, and hot helium from the core and cold helium from the reactor cavity simulation tank (RCST) started mixing. The gases flowed in a countercurrent fashion, where the top half of the hot duct contained hot helium that flowed in one direction and cold helium that flowed in the other direction in the bottom half of the duct. After the pressure and density reached equilibrium, the event entered a diffusion mode. The onset of a reverse natural circulation was not observed during the DCC period of the test.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Radiative Heat Transport and Optical Characterization of High Temperature Molten Salts

The goal of this project was to advance the field of molten fluoride radiative heat transfer (RHT), through optical property measurements, heat transfer loop construction and operation, and computational fluid dynamics simulations. The following outcomes have been accomplished. A comprehensive review has been conducted to compile all available RHT-relevant optical absorption data for molten fluorides. The various measurement methods have also been compiled and critiqued. Thermal emission measurement methods have been refined and documented. A unique thermal emissivity measurement facility has been constructed and used to measure the emissivity of flowing FLiBe-exposed SS316 samples. A slight increase has been observed in the emissivity compared to unexposed SS316. A dual reflectance-emission setup was partially demonstrated for the purpose of molten fluoride absorption measurement. Preliminary infrared edge data for FLiNaK was obtained. A visible near-infrared (NIR) measurement setup has been constructed and will be used to measure absorption of corrosion products in FLiBe. A new multi-band thermal radiation method using blackbody-weighted spectral bands for the absorption-coefficient was deployed to investigate the thermal performance of the UW Natural Circulation FLiBe Loop under various power levels and operating conditions. The results showed an increasing and decreasing trend in the overall heat transfer with optical thickness with a maximum at optical thickness τ D ≈Ο(1). A forced convection FLiBe loop was constructed for the purpose of studying corrosion and thermal hydraulic phenomena. A vertical cantilever pump is used to achieve up to 5 gpm and 5 m/s flow velocity in hot and cold test sections. A methodology has been established for modeling radiative heat transfer (RHT) in molten salt coolants for the purpose of quantifying the contribution of thermal radiation in conditions relevant to FHR or MSR systems. The comparison between the results obtained for forced and mixed convection showed that in the studied ranges of optical thickness, the maximum effect of RHT on overall heat transfer was 60% improvement observed at z/D = 250 for forced convection; whereas for mixed convection, that value was higher at 170% observed at z/D = 30. The highest effect of RHT on the overall energy distribution was observed at τ D ≈3.4. Negligible effect (<20%) was observed above τ D =18 and below τ D ≈0.002. A CFD code-to-code comparison was conducted using COMSOL Multiphysics at UW-Madison and STAR-CCM at MIT, for a forced and mixed convection laminar flow for a grey medium in a vertical heated using both COMSOL Multiphysics at UW-Madison and STAR-CCM at MIT. The relative error was the largest at τ D =40 for the radiative heat flux, bulk temperature, and Nusselt number. On the other hand, the relative error was the least at τ D =0.002 for the conductive heat flux, bulk temperature, and Nusselt number.

Anderson, Mark↗