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DOE OSTI2025

Advancements in NEAMS Tool Capabilities for Multiphysics Simulation of Fast Reactor Core Bowing and Identification of Validation Test Data

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. Last year, thermal fluids and mechanics were coupled on a multi-assembly benchmark problem based on ABR-1000 design. This year, the reactor physics code Griffin was assessed for readiness of core bowing calculations. Preliminary integration of Griffin’s ring-heterogeneous model with thermal fluids and thermal mechanics solvers was performed. Specifically, thermal-mechanics and reactor physics were coupled for single- and multi-assembly problems, and reactor physics and subchannel methods were coupled for a single assembly model. Finally, the workflow of all three physics was preliminarily demonstrated on a single assembly model. Caveats and future development needed have been identified. To supplement the multiphysics demonstration, verification and assessment efforts of thermos-mechanical capabilities for modeling thermo-mechanical core bowing behavior were continued by analyzing IAEA Verification Problem 5 which includes radiation swelling and creep. Additionally, a small core reactor physics benchmark defined by Japan Atomic Energy Agency (JAEA) was performed to assess neutronics models for estimating reactivity feedback. Finally, Fast Flux Test Facility (FFTF) validation test data for core bowing phenomena has been identified and summarized, with a recommended path forward for validation once this capability is mature.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

DOE OSTI2022

Continued Verification of MOOSE Structural Mechanics Tools for Modeling Core Bowing Phenomena in Fast Reactors

Under the U.S. Department of Energy Office of Nuclear Energy’s 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 whereby increased power (which leads to temperature and flux gradients) influences the core to bow into less reactive configurations when the restraint system is properly designed. The phenomenon includes a complex interplay of radiation transport, duct temperature calculations involving fluid flow and heat transfer, and thermo-mechanical responses to the induced temperature and flux gradients. Structural material properties are also important to determining inelastic response to longer term flux gradients which cause irradiation creep and swelling. While core bowing provides a strong negative reactivity feedback when the restraint system is designed properly, it also results in additional forces between assemblies which increase the loads required to extricate them during refueling or control rod movement. Therefore, the restraint system must be designed with these tradeoffs in mind. The first stage of the work, which commenced in FY21 and continues through FY22, assesses thermo-mechanical modeling tools for producing core bowing predictions consistent with conventional tools. The Multiphysics Object Oriented Simulation Environment (MOOSE) Tensor Mechanics and Contact Modules are employed. This status report describes work on additional thermo-mechanical benchmark verification problems with increased complexity from the examples demonstrated in FY21. Several benchmark verification examples were selected from the IAEA verification and validation report. These examples involve clusters of ducts representative of a sector of a hexagonal reactor core which bow into each other and cause contact and load pad elevations, as well as single ducts subjected to irradiation fields undergoing swelling and subsequent bowing. The MOOSE-based results were compared to both IAEA benchmark participants’ results, analytic equations as available, and NUBOW-3D, a beam model code developed by Argonne National Laboratory. In every case, the MOOSE results agreed with other simulations results, providing additional verification basis of the tools for this particular physics application.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

DOE OSTI2023

FY23 Status Report on MOOSE-Based Approaches to Modeling Core Bowing in Fast Reactors

Under the U.S. Department of Energy Office of Nuclear Energy’s 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 whereby increased power (which leads to temperature and flux gradients) influences the core to bow into less reactive configurations when the restraint system is properly designed. The phenomenon includes a complex interplay of radiation transport, duct temperature calculations involving fluid flow and heat transfer, and thermo-mechanical responses to the induced temperature and flux gradients. Structural material properties are also important to determining inelastic response to longer term flux gradients which cause irradiation creep and swelling. While core bowing provides a strong negative reactivity feedback when the restraint system is designed properly, it also results in additional forces between assemblies which increase the loads required to extricate them during refueling or control rod movement. Therefore, the restraint system must be designed with these tradeoffs in mind. The first stage of the work, which commenced in FY21 and continues through FY23, assesses thermo-mechanical modeling tools for producing core bowing predictions consistent with conventional tools. The Multiphysics Object Oriented Simulation Environment (MOOSE) Tensor Mechanics and Contact Modules are employed. This status report describes work on additional thermo-mechanical benchmark verification problems with increased complexity from the examples demonstrated in FY21 and FY22. Several benchmark verification examples were selected from the IAEA verification and validation report with increased number of ducts and more complex contact interaction behavior. These examples involve a full symmetric sector with restraint rings at multiple load pad locations to simulate a limited free-bow restraint system concept, as well as irradiation induced swelling and creep effects in a sector. In addition, improvements to the contact module sideset assignment were assessed and compared with previous MOOSE results to verify the contact behavior. The MOOSE-based results were compared to IAEA benchmark participants’ results. In every case, the MOOSE results agreed with other simulations results for estimating bowing behavior, providing additional verification basis of the tools for this particular physics application. Estimation of contact forces were mostly in agreement, with a few outlier results. A plan was suggested for dealing with the discrepancies with estimating contact force values. In addition, a 1-way coupling demonstration was performed using subchannel analysis code Pronghorn-SC and MOOSE on an ABR-1000-design sodium-cooled fast reactor assembly to evaluate coolant and duct wall temperatures.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

DOE OSTI2024

MOOSE-Based Fast Reactor Core Bowing Capabilities: Coupled Structural Mechanics – Thermal Fluids Demonstration and Related Verification Efforts

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

DOE OSTI2024

Demonstration and Verification of Thermo-Mechanical Bowing in a Limited Free-Bow SFR Concept Using MOOSE

Core bowing due to thermal gradients and irradiation induced swelling and creep introduces significant reactivity feedback effects in liquid metal-cooled fast spectrum reactors. During startup, normal operations, and transient events, differential thermal and flux gradients cause expansion, creep, and swelling, which results in bowing in preferential directions depending on local material properties and load-pad and restraint-ring design. The bowing phenomenon produces negative reactivity during accident conditions provided the restraint system has been properly designed to optimally guide the deformation outwards in the active core region. Under the Department of Energy Nuclear Energy Advanced Modeling and Simulation program, a Multiphysics Object Oriented Simulation Environment (MOOSE)-based multiphysics approach to model core bowing is being developed. The present work expands on previous modeling of simpler International Atomic Energy Agency (IAEA) verification problems with these tools by modeling IAEA Verification Problem 4, which involves a symmetric sector of a reactor core with ducted assemblies undergoing differential thermal expansion due to thermal gradients bowing outward with duct-to-duct contact. This model is available on the National Reactor Innovation Center Virtual Test Bed repository. This example was verified against benchmark participant results, which includes bowing deformation evaluation and duct-to-duct interactions at load pads with mechanical contact.

22 - GENERAL STUDIES OF NUCLEAR REACTORS↗

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 OSTI2024

Multiphysics Demonstration of Temperature-Driven Assembly Bowing in SFRs using MOOSE-Based Codes

Core bowing is an important passive safety mechanism in liquid metal cooled fast reactors. When the core restraint system is properly designed, temperature and flux gradients influence assemblies in the core to bow into less reactive configurations during accident scenarios, resulting in negative reactivity feedback. Prediction of core bowing involves complex interplay of radiation transport, impacts of fluid flow and heat transfer on duct temperature, and mechanical responses to the induced temperature and flux gradients. Under the U.S. Department of Energy Office of Nuclear Energy’s Advanced Modeling and Simulation (NEAMS) Program [1], an integrated multiphysics approach is being developed to model the core bowing phenomena in liquid metal-cooled fast reactors with the Multiphysics Object Oriented Simulation Environment (MOOSE) [2]. In this methodology, the MOOSE-based reactor physics code Griffin [3] will solve the neutron transport equation and determine the power distribution. With the detailed power distribution from Griffin, the subchannel analysis codes MOOSE-Subchannel [4] and Pronghorn [5] are utilized to calculate the assembly temperature distribution. MOOSE’s Solid Mechanics [6] and Contact [7] Modules are leveraged to calculate the thermal expansion and duct bowing displacement with the duct wall temperature from thermal hydraulics calculation. In this work, an initial one-way coupling demonstration of the integrated multiphysics approach has been performed on a seven-assembly problem based on the sodium-cooled fast reactor ABR-1000 design [8]. The neutronics calculation with Griffin is not yet involved in the current simulation. MOOSE-Subchannel and Pronghorn evaluate fluid and solid temperature based on a fixed power distribution. In addition, one-way coupling is utilized in this coupled calculation, via Pronghorn passing the duct temperature data to the MOOSE Solid Mechanics calculation. An assessment of the Solid Mechanics module was performed in parallel to verify duct bowing behavior with duct-to-duct contact phenomenon [9]. The displacement from MOOSE Solid Mechanics is not yet transferred back and utilized in the Pronghorn and MOOSE-Subchannel calculation. This model will be available on the National Reactor Innovation Center (NRIC) Virtual Test Bed (VTB) repository [10]. Future stages of this work will involve solving problems of increasing complexity as well as adding more physics (e.g. reactor physics) to the integrated workflow to reach the end goal of modeling the core bowing phenomenon with an integrated multiphysics workflow.

22 - GENERAL STUDIES OF NUCLEAR REACTORS↗

NASA NTRS1999

CYGNUS A: Hot Spots, Bow Shocks, Core Emission, and Exclusion of Cluster Gas by Radio Lobes

This report covers work preformed on three ROSAT projects: (1) Monitoring the X-ray Intensity of the Core and Jet of M87; (2) The radio-optical jet in 3C-120 and (3) A search for cluster emission at high redshift.

Harris, Daniel E.↗

DOE OSTI2022

Benchmark Specification for FFTF LOFWOS Test #13

The Fast Flux Test Facility (FFTF) at the Hanford site in Washington was designed by the Westinghouse Electric Corporation for the U.S. Department of Energy. FFTF was a 400 MW thermal, oxide-fueled, liquid sodium cooled test reactor, built to assist development and testing of advanced fuels and materials for fast breeder reactors. After reaching criticality in 1980, FFTF operated until 1992, providing the U.S. Department of Energy (DOE) with the means to test fuels, materials, and other components in a fast neutron flux environment. In July 1986, a series of unprotected transients (with the plant protection system intentionally disabled) were performed in FFTF as part of the passive safety demonstration program. Among these were thirteen loss of flow without scram (LOFWOS) tests. The goals of this program included confirming the liquid metal reactor safety margins, providing data for computer code validation, and demonstrating the inherent and passive safety benefits of specific design features. The test defined in this benchmark is LOFWOS Test #13, which was initiated at 50% power and 100% flow with the pump pony motors turned off. This benchmark specification is intended to support collaborative efforts within international partnerships on the validation of simulation tools and models in the area of Sodium-cooled Fast Reactor (SFR) safety. Validated tools and models are needed to evaluate SFR inherent safety characteristics and assess the impact of passive design features in response to accident initiators. Comparisons with experimental data and the results of safety analyses from other groups create unique opportunities to improve predictive capabilities of computational codes and methods for SFR modeling and simulation. The conditions of the LOFWOS test along with the feedback from FFTF’s limited free bow core restraint system and the novel passive reactivity control Gas-Expansion Modules (GEMs) pose a very challenging and uniquely valuable benchmark exercise.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗

DOE OSTI2026

Assembly Bowing Reactivity Calculation Methodology Applied to Lead Fast Reactor

Ducted assemblies bow during operation due to power and temperature gradients which can be influenced by operating flow rates. For fast spectrum cores using ducted assemblies, the bowing behavior follows that of the duct and because there are gaps between the ducts, the bowing can result in compaction or expansion of the active core. This local displacement can have a positive or negative impact and knowing the net effect during transients is important for system reactivity control. Keeping the net bowing reactivity worth low is possible with attentive placement of load pads above the active core and selecting load pad gap thicknesses that result in a desired behavior at standard operating conditions. This paper considers a Lead Fast Reactor (LFR) concept fueled by HALEU UO2 developed by Westinghouse Electric Company (WEC) and applies a workflow of Argonne-developed codes to estimate the core bowing reactivity worth. Using orifice flow rates grouped by assembly type, the net reactivity impact due to core assembly bowing for the LFR was found to be small and in line with other liquid metal fast reactors: +29/+32/+35 pcm, or about +$0.049/+$0.055/+$0.059, for BOEC/MOEC/EOEC, respectively.

bowing reactivity↗

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 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↗

NASA NTRS1988

The origin and energetics of CTB 80

Deep narrow-band images of the core of the unusual supernova remnant CTB 80 are presented, and the origin and energetics of the remnant are discussed. Based on a description of the core as a wind-blown bubble or bow shock around a pulsar, a scenario is presented relating the core and extended components to a single supernova explosion about 100,000 yr ago. The physical nature of the interface between the pulsar wind and the ambient thermal plasma is considered, and it is concluded that the pulsar is probably moving through shock-compressed material associated with the evolved remnant. It is argued that the core geometry is probably a bow shock viewed partially face-on.

Hester, J. Jeff↗

NASA NTRS2017

THEMIS Satellite Observations of Hot Flow Anomalies at Earth's Bow Shock

Hot flow anomalies (HFAs) at Earth's bow shock were identified in Time History of Events and Macroscale Interactions During Substorms (THEMIS) satellite data from 2007 to 2009. The events were classified as young or mature and also as regular or spontaneous hot flow anomalies (SHFAs). The dataset has 17 young SHFAs, 49 mature SHFAs, 15 young HFAs, and 55 mature HFAs. They span a wide range of magnetic local times (MLTs) from approximately 7 to 16.5MLT. The largest ratio of solar wind to HFA core density occurred near dusk and at larger distances from the bow shock. In this study, HFAs and SHFAs were observed up to 6.3 RE and 6.1 RE (Earth radii), respectively, upstream from the model bow shock. HFA-SHFA occurrence decreases with distance upstream from the bow shock. HFAs of the highest event core ion temperatures were not seen at the flanks. The ratio of HFA ion temperature increase to HFA electron temperature increase is highest around 12MLT and slightly duskward. For SHFAs, (Tihfa=Tisw)/(Tehfa=Tesw) generally increased with distance from the bow shock. Both mature and young HFAs are more prevalent when there is an approximately radial interplanetary magnetic field. HFAs occur most preferentially for solar wind speeds from 550 to 600 km s-1. The correlation coefficient between the HFA increase in thermal energy density from solar wind values and the decrease in kinetic energy density from solar wind values is 0.62. SHFAs and HFAs do not show major differences in this study.

Interplanetary physics (planetary bow shocks; sola↗

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↗

NASA NTRS2013

Spontaneous Hot Flow Anomalies at Quasi-Parallel Shocks: 2. Hybrid Simulations

Motivated by recent THEMIS observations, this paper uses 2.5-D electromagnetic hybrid simulations to investigate the formation of Spontaneous Hot Flow Anomalies (SHFA) upstream of quasi-parallel bow shocks during steady solar wind conditions and in the absence of discontinuities. The results show the formation of a large number of structures along and upstream of the quasi-parallel bow shock. Their outer edges exhibit density and magnetic field enhancements, while their cores exhibit drops in density, magnetic field, solar wind velocity and enhancements in ion temperature. Using virtual spacecraft in the simulation, we show that the signatures of these structures in the time series data are very similar to those of SHFAs seen in THEMIS data and conclude that they correspond to SHFAs. Examination of the simulation data shows that SHFAs form as the result of foreshock cavitons interacting with the bow shock. Foreshock cavitons in turn form due to the nonlinear evolution of ULF waves generated by the interaction of the solar wind with the backstreaming ions. Because foreshock cavitons are an inherent part of the shock dissipation process, the formation of SHFAs is also an inherent part of the dissipation process leading to a highly non-uniform plasma in the quasi-parallel magnetosheath including large scale density and magnetic field cavities.

Quasi-Parallel↗

NASA NTRS2001

Determining the Mass Density Along Magnetic Field Lines from Toroida Eigenfrequencies

Toroidal eigenfrequencies can be used to remotely sense the equatorial mass density rho(sub eq) and the density dependence along a magnetic field line. Here we present improvements to the method of Schulz [1996], which allows rho(sub eq) and the power law index alpha (for mass density along a field line proportional to R(sup -alpha), where R is the radial distance from the center of the Earth) to be determined from the y intercept and slope of a plot of toroidal frequency versus toroidal harmonic number n. Our modifications include a model form for eigenfrequencies with a fractional precision of 0.0005 for -6 less than or = alpha less than or = 6 and 2 less than or = L less than or = 8 (accuracy is doubtful beyond L = 5) and an iterative procedure for getting more accurate results than those found using Schulz's method. In addition, we do an analysis of the effect of random measurement errors. Observed frequencies need to be accurate to approx. 6% (3%) of the fundamental frequency in order to determine rho(sub eq) (alpha) to a precision of 30% (unity). We then apply our method to data generated using the Global Core Plasma Model for plasmaspheric mass density; our analysis demonstrates clearly bow the alpha index represents the mass density dependence on the outer part of the field line (R/(LR(sub E)) greater than or approx. 2/3).

Denton, R.↗

NASA NTRS1982

Three-dimensional flow calculations including boundary layer effects for supersonic inlets at angle of attack

An analysis is presented for calculating the steady three-dimensional flow field in supersonic mixed-compression inlets at incidence. A zonal modeling approach is employed to obtain the solution. The supersonic core flow is computed using a second-order pentahedral bicharacteristic algorithm. The bow shock wave and the reflected internal shock train are determined using a three-dimensional discrete shock fitting procedure. The boundary layer flow adjacent to both the centerbody and the cowl is computed using a second-order implicit finite difference method. The flow in a shock wave-boundary layer interaction region is computed using an integral formulation. The culmination of the present research effort is the development of a production-type computer program capable of analyzing flow in a variety of mixed-compression aircraft inlets. Numerical results and experimental correlations are presented to illustrate application of the analysis.

Vadyak, J.↗