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DOE OSTI2021

Assessment of MOOSE-Based Tools for Calculating Radial Core Expansion

Radial core expansion in liquid-metal cooled fast reactor systems is a well-known phenomenon that produces strong reactivity feedback effects. An inherently safe reactor design takes advantage of negative reactivity feedback in accident scenarios by utilizing a core restraint system which produces a bowed shape that allows for radial expansion of the fuel regions. Detailed modeling and simulation of core radial expansion itself as well as subsequent reactivity feedback is a challenging task involving contact of many fuel assembly elements and physics feedback from neutronics, thermal hydraulics, and thermal mechanical response. A variety of physics codes have been developed to model aspects of radial core expansion but in general invoke geometrical or physics approximations. No code system currently exists which tightly and robustly couples these physics with enough detail to fully resolve the complex core radial expansion reactivity feedback effects. The future availability of such a code system is of vital importance to fully understanding the reactivity feedback effects that occur due to radial expansion, and consequently to optimizing the design of the core restraint system. A high-fidelity code will also be used to benchmark existing lower fidelity, faster running models to understand their benefits, limitations, and range of applications. A code development path using MOOSE-based tools is proposed in order to leverage the detailed geometry capabilities and natural tight coupling and robustness of MOOSE-based applications for modeling this complex phenomena. While simulation of the full phenomenon involves several physics, an assessment has been initiated on the capabilities and readiness of the currently available Tensor Mechanics module within MOOSE for calculation of the structural mechanical responses which occur within the reactor core. This report focuses on modeling the force-deformation response which mimics the physics of a duct contact deformation, as well as differential thermal expansion which produces a thermal bowed shaped for the fuel assemblies in a core. Simple examples were initially performed such as simple supported beam bending under load. The complexity of examples was progressively increased to better mimic the duct behavior by including a differential thermal example and inclusion of hexagonal cross-sections in the geometry. Further assessment of the structural mechanical response simulation capability is still required for modeling duct contact interactions and irradiation creep and swelling. Companion thermal hydraulic and neutronics assessments will also be required; these activities are planned for future years. Finally, integration of the multiple physics components through MOOSE is required to predict the core radial expansion and subsequent feedback effects.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

DOE OSTI2020

Review of Tools for Modeling Core Radial Expansion in Liquid Metal-Cooled Fast Reactors

Core radial expansion in liquid-metal cooled fast reactor systems is a well-known phenomenon that produces strong reactivity feedback effects. It is crucial from a safety standpoint to design a reactor with the proper core restraint system to guide expansion of the fuel assemblies into a formation that produces negative reactivity feedback in accident conditions. However, the modeling of core radial expansion and its associated reactivity feedback is extremely challenging. Liquid metal-cooled fast reactor designers (both industry and commercial) have pointed to improved modeling of core radial expansion as a key modeling challenge for these types of reactors. The Department of Energy Nuclear Energy Advanced Modeling and Simulation (DOE-NEAMS) program has an important role to play in helping to develop a robust, predictive tool for this phenomenon. A literature review has been performed to identify current simulation capabilities applicable to the prediction of core radial expansion in liquid metal-cooled fast reactors and the resultant reactivity feedback effects. An overview as well as a detailed description of the multi-physics phenomena underlying core radial expansion is given in the first two chapters. The objective of this report is to identify existing software that has been or could be applied to the core radial expansion problem, and then to identify possible paths to develop a robust, coupled Multiphysics tool for advanced analysis, in which all three physics (radiation transport, structural mechanics, thermal fluids) are taken into account considering feedback effects from each physics to the other. Several computer codes and workflows have been developed in the United States and abroad to perform individual aspects of radial expansion calculations or to perform loosely coupled analysis. No code system currently exists which tightly and robustly couples the neutronics, thermal hydraulics, and thermal mechanical physics with enough detail to fully resolve the complex core radial expansion reactivity feedback effects. The future availability of such a code system is of vital importance to fully understanding the reactivity feedback effects that occur due to radial expansion, and consequently to optimizing the design of the core restraint system. A potential code development path forward using MOOSE-based tools is suggested in order to leverage the natural tight coupling and robustness of MOOSE-based applications. Additionally, potential gaps for modeling and common assumptions are listed which require further investigation to ensure accuracy for prediction of deformations.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗

DOE OSTI2026

FY26 Progress on Demonstration of a Multiphysics Steady State Capability for Modeling Core Radial Expansion in SFRs

Under the U.S. Department of Energy Office of Nuclear Energy Advanced Modeling and Simulation (NEAMS) Program, an integrated multiphysics approach is being developed to model the core bowing phenomena important to liquid metal-cooled fast reactors. Core bowing is an important passive safety mechanism in liquid metal-cooled fast reactors and involves multiphysics effects including radiation transport, fluid flow, heat transfer, and mechanical response to temperature and flux gradients. This report summarizes recent progress on developing a multiphysics, MOOSE-based workflow to predict core bowing and associated reactivity feedback. Significant new capabilities in the reactor physics code Griffin - sodium backfill and pin power reconstruction for deformed geometries - were applied in this effort. This year’s work included verification, code comparisons, sensitivity studies, and coupled demonstrations that advance the state of MOOSE-based core bowing workflow. Griffin’s sodium backfill capability was verified by demonstrating that its automated treatment of geometry expansion and material-density updates reproduces manual calculations exactly, confirming solid mass conservation and proper coolant backfilling in expanded geometries. Reconstructed pin powers were compared for Griffin’s ductheterogeneous and ring-heterogeneous treatments in single-, seven-, and nineteen-assembly cases, with best agreement observed in lower-leakage configurations and the duct-heterogeneous approach offering substantially lower computational cost. Thermal-hydraulic sensitivity sensitivities showed that MOOSE SCM, SAM, and CFD are expected to produce similar deformation predictions despite variances in their temperature predictions, and that explicit treatment of inter-assembly flow becomes increasingly important as gap flow rate increases. Finally, coupled demonstrations on small multi-assembly configurations using Griffin, MOOSE Solid Mechanics, MOOSE SCM, and Heat Conduction produced physically consistent reactivity feedback from thermal expansion and bowing. The coupled demonstrations simulated grid plate expansion as well as resultant core bowing at full power conditions. Simplifications were made in current workflow, namely the assumption of instantaneous full power conditions following hot zero power, and pre-expanding the Griffin geometry axially due to lack of an axial fuel pin expansion model and temperature feedback to Griffin.

Wozniak, Nicholas↗

DOE OSTI2019

Reactivity Feedback Modeling in SAM

System Analysis Module (SAM) is being developed at Argonne National Laboratory as a modern system-level modeling and simulation tool for advanced non-light water reactor safety analyses. It utilizes the object-oriented application framework MOOSE to leverage the modern software environment and advanced numerical methods. The capabilities of SAM are being extended to enable the transient modeling, analysis, and design of various advanced nuclear reactor systems. This report presents the development of Point-Kinetics modeling and reactivity feedback mechanisms in SAM. It also presents a new capability for predicting the thermal expansion in various structural components by coupling SAM with an external thermomechanics module (Tensor Mechanics) from the MOOSE framework. The analysis of the transient behavior of a nuclear reactor requires the coupled simulation of reactor kinetics and thermal-hydraulics of the reactor core, especially for those unprotected transients where the reactor scram system may not function properly. The point kinetics model has been widely used for reactor safety analysis due to its simplicity to capture the transient behavior of the reactor. Various reactivity feedback models have been developed and integrated with the Point-Kinetics module, including fuel axial expansion, core radial expansion, fuel Doppler, and coolant density reactivity. The reactivity feedback models in SAM are similar to the respective models used in SAS4A/SASSYS-1. This report first presents the brief theory of the Point-Kinetics module and reactivity feedback models. A number of verification tests have been performed where the code simulations are compared to the analytical model results. The reactivity feedback due to the thermal deformation, such as the fuel axial expansion and core radial expansion, is important for SFR transient analysis. Simplified thermal expansion models for the fuel pin and reactor constrain system (e.g. grid plate) are developed and verified in SAM. Additionally, a coupling interface is developed to couple SAM with external thermomechanical analysis modules for more accurate predictions of the thermal expansion of different components during the transients. The current coupling interface has been tested with the Tensor Mechanics module from MOOSE. These point kinetics and reactivity feedback modeling capabilities have also been demonstrated by simulating the early stage of the unprotected loss-of-flow (ULOF) accident in the Advanced Burner Test Reactor (ABTR). Both the stand-alone SAM and coupled SAM and Tensor Mechanics simulations are performed. It is confirmed that the major physics phenomena in the heat transport system of the ABTR reactor are captured by SAM, and the point kinetics model, reactivity feedback models, and the coupling schemes are working well as expected.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

DOE OSTI2024

Final Report on Predictive Analyses of PRD as Function of Anomalies

This report summarizes the work completed in FY-2024 to analyze the power reactivity decrement (PRD) concepts of the ARC-100 core. The PRD has been traditionally defined by the reactivity change from a hot zero power (HZP) to a particular power. Consequently, the PRD accounts for the core reactivity changes due to increase coolant temperature gradient axially and radially across the core, and increased fuel temperature. The coolant temperature gradient leads to sodium and structure density changes, to radial core expansion from assembly flowering and bowing (due to axial and radial temperature gradients within the assemblies), and to control rod driveline thermal expansion. The fuel temperature increase associated with coolant temperature and power increases leads to Doppler effect and axial thermal expansion. In this work, the normal operating Hot Full Power (HFP) state is the only power level of interest, so analyses focus on the PRD calculated from HZP to HFP. The PRD has been used to assess the reactor safety features asymptotically in unprotected accident scenarios, including the loss of heat sink (LOHS), loss of flow (LOF), and transient overpower (TOP) without scram. The PRD concept relies on the “global” reactivity coefficients A, B, and C that are estimated based on “individual” reactivity effects (Doppler, sodium density, etc.). The objectives of this work are: 1) to improve and verify the methodology used to calculate the ABC coefficients used in the PRD, 2) to assess if the PRD can be used to reliably identify abnormal events. This report fulfills the FY-2024 scope of WBS#1.15.8.3 activity, “ANL0120 – Predictive Analyses of PRD as function of deformation”. The PRD concept is described in Sections 2. Additional effort in refining the methodology for core bowing modeling is performed in Sections 3. Then, two verification exercises are proposed in Section 4 to benchmark these coefficients based on direct neutronic-only calculations and on dynamic core transient simulations. Finally, the PRD approach is assessed for the detection of several unexpected events, such as primary flow perturbation or improper fuel loading, in Section 5.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗

DOE OSTI2025

Transient Modeling and Simulation of a Generic Stable Salt Reactor

A SAM system-level model of a generic stable salt reactor has been developed to investigate thermal-hydraulic behavior and safety performance under steady and transient conditions. The model integrates information generated from a reactor physics analysis using PROTEUS and PERSENT, and a computation fluid dynamics (CFD) analysis using STAR-CCM+. A loose, iterative coupling scheme between PROTEUS and SAM is implemented to calculate the equilibrium power and temperature distributions in the steady-state critical core condition. The converged steady-state model is then used in PERSENT to calculate the four reactivity feedback temperature coefficients (Doppler, fuel density, coolant density, and core radial expansion) and kinetic parameters that are needed in SAM to model the temperature feedback effects in transient simulations. Within the fully enclosed liquid fuel pins, natural convection is the dominant heat transfer mechanism. The STAR-CCM+ model of the fuel pin considers conjugate heat transfer from the liquid fuel salt to the pin cladding and external reactor coolant. The CFD results of the axial and radial temperature profiles are used to empirically determine an effective fuel salt thermal conductivity in the SAM fuel pin model so that the temperatures predicted by the SAM model match as closely as possible the CFD results. In the central region of the fuel pin, the effective thermal conductivity is as high as similar to 60 times the physical fuel salt thermal conductivity. The whole-plant SAM model is then used to simulate an unprotected station blackout transient. The results of this simulation showed that the large negative fuel axial expansion reactivity feedback reduces fission power to similar to 2.4% nominal power. The core is cooled by natural circulation, which removes heat in the core to the emergency heat removal system, and ultimately, to the ambient. However, peak fuel salt and cladding temperatures can potentially reach as high as 1500 K, albeit briefly, if the shutdown mechanism fails to operate.

stable salt reactor; transient simulations; system↗

DOE OSTI2019

Risk-Informed Mechanistic Source Term Calculation (Final CRADA Report)

As part of an FY18 U.S. Department of Energy (DOE) Gateway for Accelerated Innovation in Nuclear (GAIN) award, a CRADA agreement was established between Argonne National Laboratory (Argonne) and Oklo. The CRADA focused on the following three tasks to assist Oklo with the regulatory licensing of their innovative nuclear reactor design: • Task 1 – Coupling and Demonstration Analysis using The Nek5000, Diablo, and OpenMC Codes: Establishing a coupling between the neutronic, structural, and thermohydraulic analysis codes and utilizing the code package for a high-fidelity demonstration analysis of radial core expansion due to temperature changes and its impact on core reactivity. • Task 2 – Mechanistic Source Term Analysis: Performing a realistic evaluation of the potential release of radionuclides to the environment during postulated transient event sequences. • Task 3 – Data in Support of Metal Fuel Qualification: An assessment of past postirradiation examination data of metal fuel utilized in the Argonne EBR-II reactor to assist in the potential qualification of the fuel typer for regulatory licensing. The details regarding each analysis and the associated conclusions were provided to Oklo in three separate project reports. Due to the utilization of proprietary and export controlled information, the current summary report was created, which provides an uncontrolled overview of each of the three tasks.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

NASA NTRS1984

Ultraviolet and optical observations of metal deficient red giants and chromospheric models

Three metal deficient field stars were observed in the ultraviolet and optical spectral regions: HD 165195, HD 110281, and HD 232078. High dispersion spectra near H alpha, and low dispersion, long wavelength IUE spectra were obtained. The H alpha profiles have strong asymmetric emission with absorption cores that are frequently asymmetric. The surface flux of Mg II lines is similar to that of luminous Pop I stars in spite of the lower metal abundance. Semi-empirical atmospheric models suggest that the characteristic emission in the wings of the H alpha line can arise within static chromospheres. Radial expansion gives an asymmetric, blue-shifted H alpha core accompanied by greater emission in the red line wing than the blue wing. Wind models with extended atmospheres suggest mass loss rates - 2 billion M/yr. Thus H alpha provides no evidence that steady mass loss is substantial enough to significantly affect the evolution of stars on the red giant branch of globular clusters.

Duprele, A. K.↗

NASA NTRS1992

Characterization of gaseous helium jet dispersion to atmosphere

A major ground-based experiment to be performed for the Superfluid Helium On Orbit Transfer (SHOOT) program is the accidental loss of the vacuum guard of the super-insulated dewar. The design of the dewar vent-path requires adequate mass removal after a preset pressure is reached due to external heat transfer. The existing helium creates a turbulent buoyant jet, expanding in air with entrainment of the jet interface to the surrounding. Transient analysis is performed for axial and radial jet temperature prediction using the self-similarity assumption applied to mass, momentum, and the energy-balance equations of helium. The predicted jet temperature profiles with vertical and radial expansion up to 1.6 and 1.0 m, respectively, demonstrate the low temperature core established by gaseous helium. For all time steps, the axial and radial temperature predictions are observed to be within 8 and 20 percent, respectively.

Khan, H. J.↗

NASA NTRS1984

Chromospheres and mass loss in metal-deficient giant stars

Semiempirical atmospheric models indicate that the characteristic emission in the wings of the H-alpha line observed in Population II giant stars can arise naturally within static chromospheres. Radial expansion gives an asymmetric, blueshifted H-alpha core accompanied by greater emission in the red line wing than in the blue wing. Wind models with extended atmospheres suggest mass loss rates much smaller than 2 x 10 to the -9th solar mass per yr. Thus H-alpha provides no evidence that steady mass loss can significantly affect the evolution of stars on the red giant branch of globular clusters.

Dupree, A. K.↗

NASA NTRS1997

Fitting a 3-D analytic model of the coronal mass ejection to observations

The application of an analytic magnetohydrodynamic model is presented to observations of the time-dependent explusion of 3D coronal mass ejections (CMEs) out of the solar corona. This model relates the white-light appearance of the CME to its internal magnetic field, which takes the form of a closed bubble, filled with a partly anchored, twisted magnetic flux rope and embedded in an otherwise open background field. The density distribution frozen into the expanding CME expanding field is fully 3D, and can be integrated along the line of sight to reproduce observations of scattered white light. The model is able to reproduce the three conspicuous features often associated with CMEs as observed with white-light coronagraphs: a surrounding high-density region, an internal low-density cavity, and a high-density core. The model also describes the self-similar radial expansion of these structures. By varying the model parameters, the model can be fitted directly to observations of CMEs. It is shown how the model can quantitatively match the polarized brightness contrast of a dark cavity emerging through the lower corona as observed by the HAO Mauna Loa K-coronameter to within the noise level of the data.

Gibson, S. E.↗

DOE OSTI2020

ZPPR-15 Small Reactivity Worth Experiments

In addition to measuring the worth of sodium voiding and the worth of simulated control rods, the ZPPR staff measured the Doppler worth of four standard samples, the worth of axial expansion and the worth of radial bowing in ZPPR-15. Doppler sample worths were measured in ZPPR-15A, ZPPR-15B and ZPPR-15D. The Doppler samples were natural UO 2 , depleted uranium metal, depleted U-10Zr alloy and 33% enriched UO 2 . These samples were placed in a sample capsule in the inner core of ZPPR-15 and heated to various temperatures between 300 K and 1100 K. The resulting changes in reactivity relative to the reference configuration were measured to determine the Doppler worths of the samples. Special segmented drawers were constructed to measure the worth of axial expansion in ZPPR15. The segments were connected to each other, and the back segment was connected to a spring-loaded cable. Pulling the cable introduced small gaps between drawer segments to simulate axial expansion, and releasing the cable eliminated those gaps. The worth of this simulated axial expansion was measured in ZPPR-15A, ZPPR-15B and ZPPR-15D. The worth of radial bowing was measured in ZPPR-15, but the experimenters regarded the result as unsatisfactory. Radial bowing was measured by two methods in ZPPR-17A, so the ZPPR-17A bowing measurements were analyzed in place of the unpublished ZPPR-15 radial bowing measurement. The first ZPPR-17A measurement consisted of rearranging the plates in 96 core drawers at the core-radial blanket boundary to simulate outward motion of the fuel during bowing. The second ZPPR-17A measurement used a new bowing oscillator to move the core plates a small distance vertically in a special drawer. The published uncertainties for the Doppler worth, axial expansion worth and radial bowing worth measurements are the statistical uncertainties in the measurements. In reality, the published uncertainty for each of these measurements is just one component of the total uncertainty. There are additional uncertainties specific to each measurement and a common uncertainty related to conversion from the natural measurement units, cents, to pcm for calculations. A full uncertainty analysis was performed for each measurement. The significant uncertainties were quantified, and a total uncertainty was determined for each measurement. The ZPPR-15 and ZPPR-17A experimental records were used to create detailed as-built Monte Carlo models of the Doppler worth, axial expansion and radial bowing measurement configurations.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

DOE OSTI2025

Turbulence and transport in mirror geometries in the Large Plasma Device

Thanks to advances in plasma science and enabling technology, mirror machines are being reconsidered for fusion power plants and as possible fusion volumetric neutron sources. However, cross-field transport and turbulence in mirrors remains relatively understudied compared with toroidal devices. Turbulence and transport in mirror configurations were studied utilizing the flexible magnetic geometry of the Large Plasma Device (LAPD). Multiple mirror ratios from $M=1$ to $M=2.68$ and three mirror-cell lengths from $L=3.51$ to $L=10.86$ m were examined. Langmuir and magnetic probes were used to measure profiles of density, temperature, potential and magnetic field. The electric field-fluctuation-driven ${\tilde {\boldsymbol{E}}} \times {\boldsymbol{B}}$ particle flux, where $\boldsymbol{B}$ is the background field, was calculated from these quantities. Two probe correlation techniques were used to infer wavenumbers and two-dimensional structure. Cross-field particle flux and density fluctuation power decreased with increased mirror ratio. Core density and temperatures remain similar with mirror ratio, but radial line-integrated density increased. The physical expansion of the plasma in the mirror cell by using a higher field in the source region may have led to reduced density fluctuation power through the increased gradient scale length. This increased scale length reduced the growth rate and saturation level of rotational interchange and drift-like instabilities. Despite the introduction of magnetic curvature, no evidence of mirror-driven instabilities – interchange, velocity space or otherwise – were observed. For curvature-induced interchange, many possible stabilization mechanisms were present, suppressing the visibility of the instability.

Travis, Phil (ORCID:0000000343170432)↗

DOE OSTI2026

Extension of Clad Damage Propagation Model for Fission Gas Dispersal and Two-Phase Flow Effects in MOOSE SubChannel Module

This report presents an extension of the Clad Damage Propagation (CDAP) model implemented in the MOOSE SubChannel Module (SCM) to capture post-failure fission-gas dispersal and two-phase flow effects in sodium-cooled fast reactor assemblies. The extended model tracks discharged gas axially and radially, computes channel-averaged flow quality and void fraction using a Lockhart–Martinelli framework, evaluates two-phase frictional pressure-drop multipliers, determines inlet mass-flow degradation under fixed core pressures, and applies an intensified-void-based heat-transfer degradation to affected fuel pins. Radial plume expansion is parameterized using mineral-oil jet experiments mapped to sodium conditions via Reynolds–Weber similarity. Implementation details are documented, along with the new methods and user inputs needed to control plume mapping and two-phase behavior. Demonstration simulations for 19- and 37-pin bundles show that breach size and inlet velocity strongly influence propagation potential: small breaches (≤0.5 mm) produce limited degradation while larger breaches (~1 mm) can drive oscillatory temperature spikes and enhanced failure propagation, especially at higher velocities. These results demonstrate that the extended CDAP model provides a more complete framework for quantifying cladding damage propagation and evaluating propagation potential in transient scenarios. The approach remains computationally efficient, consistent with subchannel-level analysis, yet incorporates sufficient physics to bridge localized post-failure effects with bundle- and assembly-scale degradation.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

DOE OSTI2017

Flexible Spatial Partitions in MPACT Through Module-Based Data Passing

As part of the Consortium for Advanced Simulation of Light Water Reactors (CASL), the Virtual Environment for Reactor Applications (VERA) is being developed to provide high-fidelity multiphysics simulations of nuclear reactor cores. The MPACT code being developed collaboratively by Oak Ridge National Laboratory and the University of Michigan is the primary deterministic neutron transport solver available within VERA. MPACT employs the 2D/1D method to solve 3D problems using 2D method of characteristics (MOC) radial transport solvers with 1D nodal expansion method-based P3 (NEM-P3) axial transport solvers, which are coupled using axial and radial transverse leakages. A 3D coarse mesh finite difference (CMFD) solver is used to provide accelerated convergence and stability. Quarter-core problems in MPACT are typically run on moderately sized clusters ({approx}500-10,000 cores). As such, it relies heavily on spatial decomposition, both radially and axially, using MPI data communication along spatial domain boundaries to pass angular flux boundary condition and neighboring data. The initial spatial decomposition strategy implemented into MPACT overlaid a Cartesian grid over the core to form the domain boundaries. With this approach, a single buffer spanning across the entire boundary between two spatial domains is passed to a domain's neighbor. Additionally, only one neighboring domain index was allowed in each direction. For example, the entire eastern boundary of a domain must be the entire western boundary of the corresponding neighbour's domain. This implementation helped to execute cases on several thousand cores, where substantial radial decomposition was used. The default for several years was to use assembly decomposition, which yielded 73 radial partitions in the Watts Bar Unit 1 (WBN1) models being analyzed. However, as CASL formed stronger connections with industry partners, there was a strong push to allow MPACT to run on fewer cores, preferably in the 500-1,000 core range. Such cases require much less radial decomposition, typically with 8-16 radial domains on each plane. Unfortunately, the previous decomposition strategy is very limited in its ability to yield well-balanced domains, and it does not permit partitions with an arbitrary number of domains, particularly with small numbers of radial domains (3, 5, 7, 11, 13, etc.). With these limitations, a more flexible approach that provided more even-load balancing was needed. The details of this new strategy are outlined here, along with insights to its advantages. The examples provided are for the WBN1 core, which has been the focus of several initial CASL analyses. It is worth noting that spatial decomposition strategies have been employed in many codes with focus on a number of different transport methodologies. The references cited are not exhaustive as this has been very important research topic across many areas.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

NASA NTRS1978

Contribution of tidal dissipation to lunar thermal history

Possible contributions of tidal heating to the thermal history of the moon are investigated, and conditions under which such heating would have been an important factor in the evolution of the moon are defined as precisely as possible within the bounds of the uncertainties. The tidal dissipation is defined as a function of position in the moon and of the earth-moon separation for a homogeneous incompressible moon. Results for the dissipation are given for eccentricities of zero and 0.055 as well as for the lunar obliquity as determined by the equilibrium Cassini states. Possible orbital resonances which interrupt the assumed simplified expansion of the lunar orbit are considered, along with radial variations in rigidity. The dissipation in a two-layer model moon with a molten inner core and an outer mantle with the moon's present rigidity is determined, and implications of the results for the role of tidal heating in the history of the moon are discussed.

Peale, S. J.↗

NASA NTRS1984

Swirl, confinement and nozzle effects on confined turbulent flow

Predictions of swirl, confinement and nozzle effects on confined turbulent flow are exhibited and compared with five-hole pitot-probe time-mean velocity measurements. Two sets of computations are given, one using the standard k-epsilon turbulence model and the other using a C sub mu formulation model deduced from recent six-orientation single-wire hot-wire measurements. Results confirm that the accuracy of the latter model is superior. To highlight the effects of confinement and exit nozzle area on this flow, three expansion ratios and two contraction ratios are used. Predictions are given for a full range of swirl strengths using measured inlet conditions for axial, radial and swirl velocity profiles. The predicted velocity profiles illustrate the large-scale effects of inlet swirl on flowfields. It appears that a strong contraction nozzle has a pronounced effect, on swirl flow cases, with discouragement of central recirculation zones, and forward flow in highly swirled vortex core regions. The expansion ratio value has large-scale effects on the size and location of the recirculation zones.

Abujelala, M. T.↗

NASA NTRS2005

High-Temperature, High-Load-Capacity Radial Magnetic Bearing

A radial heteropolar magnetic bearing capable of operating at a temperature as high as 1,000 F (=540 C) has been developed. This is a prototype of bearings for use in gas turbine engines operating at temperatures and speeds much higher than can be withstood by lubricated rolling-element bearings. It is possible to increase the maximum allowable operating temperatures and speeds of rolling-element bearings by use of cooling-air systems, sophisticated lubrication systems, and rotor-vibration- damping systems that are subsystems of the lubrication systems, but such systems and subsystems are troublesome. In contrast, a properly designed radial magnetic bearing can suspend a rotor without contact, and, hence, without need for lubrication or for cooling. Moreover, a magnetic bearing eliminates the need for a separate damping system, inasmuch as a damping function is typically an integral part of the design of the control system of a magnetic bearing. The present high-temperature radial heteropolar magnetic bearing has a unique combination of four features that contribute to its suitability for the intended application: 1. The wires in its electromagnet coils are covered with an insulating material that does not undergo dielectric breakdown at high temperature and is pliable enough to enable the winding of the wires to small radii. 2. The processes used in winding and potting of the coils yields a packing factor close to 0.7 . a relatively high value that helps in maximizing the magnetic fields generated by the coils for a given supplied current. These processes also make the coils structurally robust. 3. The electromagnets are of a modular C-core design that enables replacement of components and semiautomated winding of coils. 4. The stator is mounted in such a manner as to provide stable support under radial and axial thermal expansion and under a load as large as 1,000 lb (.4.4 kN).

Provenza, Andrew↗