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A Verification and Validation Approach for COMSOL Multiphysics to Support High Flux Isotope Reactor (HFIR)

Over the last several decades, many reactors have successfully been converted from high enriched uranium (HEU) to low enriched uranium (LEU) fuels in United States in support of its global non-proliferation objectives. Of the reactors slated for conversion, five high-performance research reactors (HPRRs) remain. The high-flux isotope reactor (HFIR) at Oak Ridge National Laboratory (ORNL) is one of the five. Conversion of HFIR requires the qualification of a new fuel. To aid in the conversion process as well as improve safety margins, COMSOL Multiphysics was chosen to support and eventually supplement the steady-state heat-transfer code (SSHTC). In order to use COMSOL as a supplementary tool, i.e. one used for safety basis calculations, the code needs to undergo a verification and validation process. Verification and validation are important processes for the use of any software; however, physics-based solvers have a unique challenge, in that the validation is much more rigorous and its domain is only applicable to the general scope of the problem. This document details the verification and validation of COMOSL for analysis of HFIR. This report is intended for two different users: (1) current and future users of COMSOL for HFIR and (2) for individuals interested in assessing the scope of the validation of COMSOL for HFIR. This report is divided into six sections. The first of which details the process of verification and validation. Section one provides an overview of key concepts from ASME V&V 10, 20, and 40 and how these concepts are used to provide a validation of any multiphysics software. Section two covers the approach needed in order to validate multiphysics software for a given HFIR analysis. Parts three through five split up the key concepts highlighted in section two. The final section provides concluding remarks which demonstrate the scope and limitations of the validation study and how these may be expanded and improved.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗

A guide on modeling electrostatics of semiconductor detectors in COMSOL Multiphysics ® for DRiFT

Adding a new semiconductor detector into the detector response function toolkit (DRiFT) requires a model of the electric potential and the electric field. To get an accurate electrostatics model, the geometry of the detector should be modeled as closely to the real geometry as feasible, including the semiconductor materials, doping layers and concentrations, and contacts. Since the electric field and potential are used to calculate the induced signal, the results of the detector response functions are largely influenced by the electrostatics models. Initial electrostatics models were completed using Silvaco, however, this document provides guidance on using COMSOL Mulitphysics ® (COMSOL) to model the detectors to give users additional flexibility. Guidance on using COMSOL and its user interface are mostly left out of this document, but best practices for geometry, modeling methods, and data format/exporting are included to help users generate models that are compatible with DRiFT, prevents bugs, issues, and inaccuracies during charge collection calculations. The following summary provides an overview of the document.

42 ENGINEERING↗

Transformer Analysis with ANSYS Maxwell and COMSOL

This is an extension of work described by Rodriguez et al . (2021). It continues analyses of a generic transformer design by Wes Greenwood. In this report, we summarize that work and add comparable results using the ANSYS Maxwell software (henceforward, “ANSYS”), and with COMSOL . We found the ANSYS and COMSOL calculations of inductance agreed well with previous results for simplified coils in air, and with a ferromagnetic core. We then describe the ANSYS and COMSOL approach and show results for a full transformer model based on magnetic field analyses. Finally, we present electrostatic analyses of E field enhancement, once again resolving individual wires. The purpose is to assess the electrostatic fields in order to locate where electric breakdown is likely to originate. We found the maximum enhancement between the secondary and either the primary or the tertiary at the end of the windings with a large potential difference.

42 ENGINEERING↗

A COUPLED DETERMINISTIC TRANSPORT CALCULATION IN COMSOL USING PROPER ORTHOGONAL DECOMPOSITION

A coupled physics problem consisting of radiation transport and heat transfer was modeled using COMSOL Multiphysics to simulate a criticality accident. Reduced order models (ROM) were created to accelerate the radiation transport calculation through Proper Orthogonal Decomposition (POD). Additionally, on-the-fly neutron cross sections were generated from a non-linear function through a feed forward neural network. The Livelink for MATLAB module allowed for data transfer between an otherwise independent solver and in-house modules. A data driven approach to POD was developed to act as a surrogate model to couple with heat transfer, with the POD module written in MATLAB coupled to an isolated heat transfer solve in COMSOL. A coupled transient solution resulted in a good approximation of the flux and temperature, with the maximum error being 3E-2 and 2.5E-3 respectively.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

Precise magnetic field mapping of the EMPHATIC Phase 1 magnet with COMSOL

A compact Halbach array magnet is used to measure the momentum of the secondary particles in EMPHATIC(Experiment to Measure the Production ofHadrons At a Test beam InChicagoland). Hall probe data was taken for the central cylindrical bore of the magnet and a field map was constructed. COMSOL Multiphysics® Software is used for modeling the magnet and constructing the corresponding magnetic field map. Here, we present a fitting approach where the hall probe data is used to determine a 1mm-spacing map of the entire volume of the magnet using COMSOL. The new map will allow for linear interpolation within the volume, and expand the map to outside the measurement volume, thus increasing the acceptance and precision of EMPHATIC's tracking system.

47 OTHER INSTRUMENTATION↗

COMSOL Models and Simulation Results for Closed-Loop Geothermal Systems with Thermal Enhancements

The Closed-Loop Geothermal Working Group and the National Renewable Energy Laboratory (NREL) have studied the performance of disc-shaped and linear thermal enhancements (conductive material introduced around a wellbore) in closed-loop geothermal systems. COMSOL models were developed to investigate the increase in heat production in systems with thermal enhancements compared to those without, across a range of scenarios. This dataset includes two example COMSOL models, a summary of the simulation results, and a link to an accompanying paper. Studied are idealized versions of two thermal enhancement designs: (1) existing or newly created fractures surrounding the wellbore, filled with highly conductive material, and (2) a 'fishbone structure,' where short wellbores are drilled radially outward from the main wellbore and filled with highly conductive material.

15 GEOTHERMAL ENERGY↗

COMSOL Results for the Nominal Steady-State Operation of the Proposed 95-MW LEU Silicide Core for HFIR Conversion

Engineering design studies are being performed to determine the feasibility of converting the High Flux Isotope Reactor (HFIR) from highly enriched uranium (HEU) to low-enriched uranium (LEU) fuel at Oak Ridge National Laboratory. This activity is sponsored by the Office of Reactor Conversion and Uranium Supply (ORCUS) under the auspices of the US Department of Energy National Nuclear Security Administration’s Office of Material Management and Minimization. HFIR is a very high flux, pressurized, light water–cooled and moderated, flux trap–type research reactor with a core made of involute shaped U 3 O 8 /Al cermet fuel plates and coolant channels. HFIR currently operates at a thermal power of 85 MW and supports key national and international missions in neutron scattering, isotope production, materials/fuels irradiation, neutron activation analysis, gamma irradiation, and neutrino research. Advanced multiphysics computational fluid dynamics models have been developed in the COMSOL Multiphysics software to simulate the steady-state operating conditions for the proposed low-and high-density LEU U 3 Si 2 -Al (uranium silicide dispersion) fuel designs. The COMSOL models for HFIR inner and outer fuel element models incorporate various essential inputs and physics such as spatially dependent nuclear heat deposition, multilayer heat conduction, conjugate heat transfer, turbulent flows (using Reynolds-averaged Navier Stokes turbulence models), structural mechanics (thermal–structural interactions and fuel swelling), and oxide layer build-up. This report presents the best-estimate thermal hydraulics results for the low- and high-density optimized silicide LEU core designs at 95 MW steady-state nominal operation.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗

Solid Rocket Motor Combustion Instability Modeling in COMSOL Multiphysics

Combustion instability modeling of Solid Rocket Motors (SRM) remains a topic of active research. Many rockets display violent fluctuations in pressure, velocity, and temperature originating from the complex interactions between the combustion process, acoustics, and steady-state gas dynamics. Recent advances in defining the energy transport of disturbances within steady flow-fields have been applied by combustion stability modelers to improve the analysis framework. Employing this more accurate global energy balance requires a higher fidelity model of the SRM flow-field and acoustic mode shapes. The current industry standard analysis tool utilizes a one dimensional analysis of the time dependent fluid dynamics along with a quasi-three dimensional propellant grain regression model to determine the SRM ballistics. The code then couples with another application that calculates the eigenvalues of the one dimensional homogenous wave equation. The mean flow parameters and acoustic normal modes are coupled to evaluate the stability theory developed and popularized by Culick. The assumption of a linear, non-dissipative wave in a quiescent fluid remains valid while acoustic amplitudes are small and local gas velocities stay below Mach 0.2. The current study employs the COMSOL Multiphysics finite element framework to model the steady flow-field parameters and acoustic normal modes of a generic SRM. This work builds upon previous efforts to verify the use of the acoustic velocity potential equation (AVPE) laid out by Campos. The acoustic velocity potential (psi) describing the acoustic wave motion in the presence of an inhomogeneous steady high-speed flow is defined by, del squared psi - (lambda/c) squared psi - M x [M x del((del)(psi))] - 2((lambda)(M)/c + M x del(M) x (del)(psi) - 2(lambda)(psi)[M x del(1/c)] = 0. with M as the Mach vector, c as the speed of sound, and λ as the complex eigenvalue. The study requires one way coupling of the CFD High Mach Number Flow (HMNF) and mathematics module. The HMNF module evaluates the gas flow inside of a SRM using St. Robert's law to model the solid propellant burn rate, slip boundary conditions, and the supersonic outflow condition. Results from the HMNF model are verified by comparing the pertinent ballistics parameters with the industry standard code outputs (i.e. pressure drop, axial velocity, exit velocity). These results are then used by the coefficient form of the mathematics module to determine the complex eigenvalues of the AVPE. The mathematics model is truncated at the nozzle sonic line, where a zero flux boundary condition is self-satisfying. The remaining boundaries are modeled with a zero flux boundary condition, assuming zero acoustic absorption on all surfaces. The one way coupled analysis is perform four times utilizing geometries determined through traditional SRM modeling procedures. The results of the steady-state CFD and AVPE analyses are used to calculate the linear acoustic growth rate as is defined by Flandro and Jacob. In order to verify the process implemented within COMSOL we first employ the Culick theory and compare the results with the industry standard. After the process is verified, the Flandro/Jacob energy balance theory is employed and results displayed.

Fischbach, S. R.↗

Solid Rocket Motor Combustion Instability Modeling in COMSOL Multiphysics

Combustion instability modeling of Solid Rocket Motors (SRM) remains a topic of active research. Many rockets display violent fluctuations in pressure, velocity, and temperature originating from the complex interactions between the combustion process, acoustics, and steady-state gas dynamics. Recent advances in defining the energy transport of disturbances within steady flow-fields have been applied by combustion stability modelers to improve the analysis framework [1, 2, 3]. Employing this more accurate global energy balance requires a higher fidelity model of the SRM flow-field and acoustic mode shapes. The current industry standard analysis tool utilizes a one dimensional analysis of the time dependent fluid dynamics along with a quasi-three dimensional propellant grain regression model to determine the SRM ballistics. The code then couples with another application that calculates the eigenvalues of the one dimensional homogenous wave equation. The mean flow parameters and acoustic normal modes are coupled to evaluate the stability theory developed and popularized by Culick [4, 5]. The assumption of a linear, non-dissipative wave in a quiescent fluid remains valid while acoustic amplitudes are small and local gas velocities stay below Mach 0.2. The current study employs the COMSOL multiphysics finite element framework to model the steady flow-field parameters and acoustic normal modes of a generic SRM. The study requires one way coupling of the CFD High Mach Number Flow (HMNF) and mathematics module. The HMNF module evaluates the gas flow inside of a SRM using St. Robert's law to model the solid propellant burn rate, no slip boundary conditions, and the hybrid outflow condition. Results from the HMNF model are verified by comparing the pertinent ballistics parameters with the industry standard code outputs (i.e. pressure drop, thrust, ect.). These results are then used by the coefficient form of the mathematics module to determine the complex eigenvalues of the Acoustic Velocity Potential Equation (AVPE). The mathematics model is truncated at the nozzle sonic line, where a zero flux boundary condition is self-satisfying. The remaining boundaries are modeled with a zero flux boundary condition, assuming zero acoustic absorption on all surfaces. The results of the steady-state CFD and AVPE analyses are used to calculate the linear acoustic growth rate as is defined by Flandro and Jacob [2, 3]. In order to verify the process implemented within COMSOL we first employ the Culick theory and compare the results with the industry standard. After the process is verified, the Flandro/Jacob energy balance theory is employed and results displayed.

Fischbach, Sean R.↗

Experimental Evaluation of Acoustic Engine Liner Models Developed with COMSOL Multiphysics

Accurate modeling tools are needed to design new engine liners capable of reducing aircraft noise. The purpose of this study is to determine if a commercially-available finite element package, COMSOL Multiphysics, can be used to accurately model a range of different acoustic engine liner designs, and in the process, collect and document a benchmark dataset that can be used in both current and future code evaluation activities. To achieve these goals, a variety of liner samples, ranging from conventional perforate-over-honeycomb to extended-reaction designs, were installed in one wall of the grazing flow impedance tube at the NASA Langley Research Center. The liners were exposed to high sound pressure levels and grazing flow, and the effect of the liner on the sound field in the flow duct was measured. These measurements were then compared with predictions. While this report only includes comparisons for a subset of the configurations, the full database of all measurements and predictions is available in electronic format upon request. The results demonstrate that both conventional perforate-over-honeycomb and extended-reaction liners can be accurately modeled using COMSOL. Therefore, this modeling tool can be used with confidence to supplement the current suite of acoustic propagation codes, and ultimately develop new acoustic engine liners designed to reduce aircraft noise.

Schiller, Noah H.↗

COMSOL Simulation of Optical Whispering Gallery Mode (WGM) Resonator

We simulate whispering-gallery mode coupling in a Si$_3$N$_4$--LiNbO$_3$ waveguide--resonator system using 2D and 3D COMSOL models. Results show that the TM$_{00}$ mode couples far more efficiently than TE$_{00}$ due to weaker confinement and stronger evanescent overlap, with critical coupling reached near a 0.20~µm gap. The study highlights polarization dependence, geometric sensitivity, and birefringence as key factors shaping resonant behavior.

42 ENGINEERING↗

COMSOL Simulation of Optical Whispering Gallery Mode (WGM) Resonator

We simulate whispering-gallery mode coupling in a Si$_3$N$_4$--LiNbO$_3$ waveguide--resonator system using 2D and 3D COMSOL models. Results show that the TM$_{00}$ mode couples far more efficiently than TE$_{00}$ due to weaker confinement and stronger evanescent overlap, with critical coupling reached near a 0.20~µm gap. The study highlights polarization dependence, geometric sensitivity, and birefringence as key factors shaping resonant behavior.

Xiaoyu, Chen [Fermilab]↗

Improving the W Coating Uniformity by a COMSOL Model-Based CVD Parameter Study for Denser W f /W Composites

Tungsten (W) has the unique combination of excellent thermal properties, low sputter yield, low hydrogen retention, and acceptable activation. Therefore, W is presently the main candidate for the first wall and armor material for future fusion devices. However, its intrinsic brittleness and its embrittlement during operation bears the risk of a sudden and catastrophic component failure. As a countermeasure, tungsten fiber-reinforced tungsten (W f /W) composites exhibiting extrinsic toughening are being developed. A possible W f /W production route is chemical vapor deposition (CVD) by reducing WF 6 with H 2 on heated W fabrics. The challenge here is that the growing CVD-W can seal gaseous domains leading to strength reducing pores. In previous work, CVD models for W f /W synthesis were developed with COMSOL Multiphysics and validated experimentally. In the present article, these models were applied to conduct a parameter study to optimize the coating uniformity, the relative density, the WF 6 demand, and the process time. A low temperature and a low total pressure increase the process time, but in return lead to very uniform W layers at the micro and macro scales and thus to an optimized relative density of the W f /W composite. High H 2 and low WF 6 gas flow rates lead to a slightly shorter process time and an improved coating uniformity as long as WF 6 is not depleted, which can be avoided by applying the presented reactor model.

36 MATERIALS SCIENCE↗

Acoustic Modeling of Novel Over-The-Rotor Acoustic Liner Concepts Using COMSOL Multiphysics Simulation Software

This paper presents simulation predictions of novel over-the-rotor acoustic liner configurations compared with experimental data. This is a follow on to the investigation on the effect of grazing flow on grooved over-the-rotor casing treatments. The purpose of this modeling investigation stems from the determination that traditional liner modeling techniques are inadequate for nontraditional internal liner cavity geometries. A series of these expansion chamber type liner design concepts were previously developed by Glenn Research Center and tested using the Langley Research Center Normal Incidence Tube. The measured normalized impedance and absorption coefficient is compared with that obtained from the COMSOL Multiphysics® simulation. Additionally, using a parametric case study, another series of simulations were conducted to determine what additional benefits, if any, this genre of liner has to offer the acoustics community. A total of 53 permutations of this concept was investigated. The results indicate that with longer internal fins, the resonance is sifted to lower frequencies.

Acoustics↗