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All sources NASA NTRS DOE OSTI

DOE OSTI2015

MEMS 3-DoF gyroscope design, modeling and simulation through equivalent circuit lumped parameter model

Pre-fabrication, behavioural and performance analysis with computer aided design (CAD) tools is a common and fabrication cost effective practice. In light of this we present a simulation methodology for a dual-mass oscillator based 3 Degree of Freedom (3-DoF) MEMS gyroscope. 3-DoF Gyroscope is modeled through lumped parameter models using equivalent circuit elements. These equivalent circuits consist of elementary components which are counterpart of their respective mechanical components, used to design and fabricate 3-DoF MEMS gyroscope. Complete designing of equivalent circuit model, mathematical modeling and simulation are being presented in this paper. Behaviors of the equivalent lumped models derived for the proposed device design are simulated in MEMSPRO T-SPICE software. Simulations are carried out with the design specifications following design rules of the MetalMUMPS fabrication process. Drive mass resonant frequencies simulated by this technique are 1.59 kHz and 2.05 kHz respectively, which are close to the resonant frequencies found by the analytical formulation of the gyroscope. The lumped equivalent circuit modeling technique proved to be a time efficient modeling technique for the analysis of complex MEMS devices like 3-DoF gyroscopes. The technique proves to be an alternative approach to the complex and time consuming couple field analysis Finite Element Analysis (FEA) previously used.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2017

Rapid methods for radionuclide contaminant transport in nuclear fuel cycle simulation

Here, nuclear fuel cycle and nuclear waste disposal decisions are technologically coupled. However, current nuclear fuel cycle simulators lack dynamic repository performance analysis due to the computational burden of high-fidelity hydrolgic contaminant transport models. The Cyder disposal environment and repository module was developed to fill this gap. It implements medium-fidelity hydrologic radionuclide transport models to support assessment appropriate for fuel cycle simulation in the Cyclus fuel cycle simulator. Rapid modeling of hundreds of discrete waste packages in a geologic environment is enabled within this module by a suite of four closed form models for advective, dispersive, coupled, and idealized con- taminant transport: a Degradation Rate model, a Mixed Cell model, a Lumped Parameter model, and a 1-D Permeable Porous Medium model. A summary of the Cyder module, its timestepping algorithm, and the mathematical models implemented within it are presented. Additionally, parametric demonstrations simulations performed with Cyder are presented and shown to demonstrate functional agreement with parametric simulations conducted in a standalone hydrologic transport model, the Clay Generic Disposal System Model developed by the Used Fuel Disposition Campaign Department of Energy Office of Nuclear Energy.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

DOE OSTI2022

Validation and Parametric Investigations of an Internal Permanent Magnet Motor Using a Lumped Parameter Thermal Model

One of the key challenges for the electric vehicle industry is to develop high-power-density electric motors. Achieving higher power density requires efficient heat removal from inside the motor. In order to improve thermal management, a multiphysics modeling framework that is able to accurately predict the behavior of the motor, while being computationally efficient, is essential. This paper first presents a detailed validation of a lumped parameter thermal network (LPTN) model of an Internal Permanent Magnet synchronous motor within the commercially available MOTOR-CAD modeling environment. The validation is based on temperature comparison with experimental data and with more detailed finite element analysis (FEA). All critical input parameters of the LPTN are considered in detail for each layer of the stator, especially the contact resistances between the impregnation, liner, laminations, and housing. Finally, a sensitivity analysis for each of the critical input parameters is provided. A maximum difference of 4% - for the highest temperature in the slot-winding and the end-winding - was found between the LPTN and the experimental data. Comparing the results from the LPTN and the FEA model, the maximum difference was 2% for the highest temperature in the slot-winding and end-winding. As for the LPTN sensitivity analysis, the thermal parameter with the highest sensitivity was found to be the liner-to-lamination contact resistance.

42 ENGINEERING↗

DOE OSTI2020

Validation and Parametric Investigations Using a Lumped Thermal Parameter Model of an Internal Permanent Magnet Motor

One of the key challenges for the electric vehicle industry is to develop high-power-density electric motors. Achieving higher power density requires efficient heat removal from inside the motor. In order to improve thermal management, a multi-physics modeling framework that is able to accurately predict the behavior of the motor, while being computationally efficient, is essential. This paper first presents a detailed validation of a Lumped Parameter Thermal Network (LPTN) model of an Internal Permanent Magnet (IPM) synchronous motor within the commercially available Motor-CAD® modeling environment. The IPM motor’s stator is studied at steady state, and winding losses are generated by a constant DC current. The validation is based on temperature comparison with experimental data and with more detailed Finite Element Analysis (FEA). All critical input parameters of the LPTN are considered in detail for each layer of the stator, especially the contact resistances between the impregnation, liner, laminations and housing. Finally, a sensitivity analysis for each of the critical input parameters is provided. A maximum difference of 4% — for the highest temperature in the slot windings and the end windings — was found between the LPTN and the experimental data. Comparing the results from the LPTN and the FEA model, the maximum difference was 2% for the highest temperature in the slot windings and end windings. As for the LTPN sensitivity analysis, the thermal parameter with the highest sensitivity was found to be the liner-to-lamination contact resistance. The latter is often ignored in the literature, whereas its impact on temperature rise was found to be more significant than any other contact resistance within the stator.

47 OTHER INSTRUMENTATION↗

DOE OSTI2020

Validation and Parametric Investigations Using a Lumped Thermal Parameter Model of an Internal Permanent Magnet Motor: Preprint

One of the key challenges for the electric vehicle industry is to develop high-power-density electric motors. Achieving higher power density requires efficient heat removal from inside the motor. In order to improve thermal management, a multi-physics modeling framework that is able to accurately predict the behavior of the motor, while being computationally efficient, is essential. This paper first presents a detailed validation of a Lumped Parameter Thermal Network (LPTN) model of an Internal Permanent Magnet (IPM) synchronous motor within the commercially available Motor-CAD® modeling environment. The IPM motor’s stator is studied at steady state, and winding losses are generated by a constant DC current. The validation is based on temperature comparison with experimental data and with more detailed Finite Element Analysis (FEA). All critical input parameters of the LPTN are considered in detail for each layer of the stator, especially the contact resistances between the impregnation, liner, laminations and housing. Finally, a sensitivity analysis for each of the critical input parameters is provided. A maximum difference of 4% - for the highest temperature in the slot windings and the end windings - was found between the LPTN and the experimental data. Comparing the results from the LPTN and the FEA model, the maximum difference was 2% for the highest temperature in the slot windings and end windings. As for the LTPN sensitivity analysis, the thermal parameter with the highest sensitivity was found to be the liner-to-lamination contact resistance. The latter is often ignored in the literature, whereas its impact on temperature rise was found to be more significant than any other contact resistance within the stator.

ADVANCED PROPULSION SYSTEMS↗

DOE OSTI2021

DEVELOPMENT OF A LUMPED-PARAMETER THERMAL MODEL FOR ELECTRO-HYDRAULIC ACTUATORS

This paper describes a thermal-hydraulic modeling method of a closed-circuit electro-hydraulic actuator (EHA). Despite the high energy efficiency of EHAs, it is always important to assess their cooling requirements, to guarantee that the operating temperature remains within an acceptable range. The method proposed in this paper is based on a lumped parameter approach and simplifies some of the complex heat transfer processes by introducing empirical correction factors. The model is validated by means of temperature measurements on an EHA architecture developed by the author. The good match between the simulation results and experiments confirms the capability of the proposed methodology to predict the temperature performance of the reference EHA under different drive cycles. The paper presents a detailed analysis of the power losses and passive heat dissipation for the reference system. Based on this analysis, the cooling requirements of the EHA are studied.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

DOE OSTI2019

Multi-Scale Modeling of Thermal-Fluid Phenomena Related to Loss of Forced Circulation Transient in HTGRs

Under the support of DOE-NE’s Nuclear Energy Advanced Modeling and Simulation (NEAMS), an effort had been pursued to support High Temperature Gas-cooled Reactors (HTGR) technology development and its modeling and simulation needs. There was a particular need for advanced modeling & simulation tools to predict thermal-fluid behavior in the nuclear reactor primary system, especially the core and lower and upper plena, during safety-related transients. In this report, two main such activities were presented: 1) system level HTGR simulations using system analysis code SAM for both normal operating and accident conditions; and 2) three-dimensional (3D) computational fluid dynamics (CFD) simulations on Deteriorated Turbulent Heat Transfer (DTHT) of interest to HTGR transients, including code benchmark and closure correlation development. In this work, Modular High Temperature Gas-cooled Reactor (MHTGR) full loop simulations were performed using System Analysis Module (SAM) code. Two approaches were used to model the reactor core; (i) unit-cell or lumped parameter model, and (ii) detailed ring model, to address the different needs under different reactor conditions. Aside from the core model changes other reactor components in the primary system, such as upper/lower plenum, heat exchanger and blower etc, were kept the same. In the unit-cell core model, the lumped parameter approach was used to model the coolant channels and the heat structures using 1-D and 2-D components, respectively. The fuel assembly heat structure was modeled based on unit-cell thickness approximation. In normal and controlled operating conditions, the calculated maximum temperatures for both coolant and heat structures were within the designed limits. The unit-cell model is, however, not able to capture the radial heat conduction through fuel assemblies, which is the dominant heat transfer mechanism during accident transients, such as pressurized conduction cooldown (PCC) event. To address this modeling challenge, ring models were developed. A simplified ring model was developed first. In this simplified model, the active core was simulated with 9 circular rings consists of 6 rings for homogenized fuel heat structure and 3 rings for gas coolant. It was quickly found that this model gives rather large simulation error as it was not able to correctly capture the solid structure representative geometries. A detailed ring model was developed to address this issue. The active core was simulated with 99 circular rings consists of 66 rings for homogenized fuel heat structure and 33 rings for gas coolant. In both ring models, six additional rings were included to represent inner reflector, outer reflector, core barrel, Reactor Pressure Vessel (RPV), RPV coolant channel, and Reactive Cavity Cooling System (RCCS). The detailed ring model was applied in two different SAM simulations; (i) normal operating conditions, and (ii) accident scenarios (more specifically, PCC event), for MHTGR design. In both simulations, the SAM calculated results for coolant and heat structure temperatures were within the reactor designed limits. The newly proposed detailed ring model approach in this work has proved to be a promising method to address the challenging modeling and simulation needs in the MHTGR design. As demonstrated in this work, this model was suitable for MHTGR simulations under both normal and accident conditions. Apart from the SAM model development for gas-cooled reactors, 3D Computational Fluid Dynamics (CFD) models were developed and validated with relaminarized Deteriorated Turbulent Heat Transfer (DTHT) MIT benchmark test. Two different CFD codes, Nek5000 and STAR-CCM+, were used for this benchmark activity. Compared with MIT data, Nek5000 shows very good agreement between its simulated and experimentally measured wall temperatures. In contrast, STAR-CCM+ under-predicted wall temperature due to over predicted turbulence in the wall region. The Nek5000 code was also used to develop wall-heat transfer correlations for laminar flow in cylindrical tube. Several simulations were performed for various Reynolds flow and wall heat fluxes. Significant deviations were found when compared the predicted heat transfer coefficient and the Sieder-Tate correlation. A new set of heat transfer correlation was proposed for laminar flow which is valid for 400<Re<2000.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

DOE OSTI2012

Crosstalk Compensation for a Rapid, Higher Resolution Impedance Spectrum Measurement

Batteries and other energy storage devices are playing larger roles in various industries (e.g., military, automotive, electric utilities, etc.) as the U.S. seeks to reduce its dependence on foreign energy resources. As such, there exists a significant need for accurate, robust state-of-health assessment techniques. Present techniques tend to focus on simple, passive monitoring of voltage and current at a given ambient temperature. However, this approach has the disadvantage of ignoring key elements of health, that is, changes in resistance growth and power fade. Impedance spectroscopy is considered a useful laboratory tool in gauging changes in the resistance and power performance, but it has not been widely considered as an onboard diagnostic tool due to the length of time required to complete the measurement. Cross-Talk Compensation (CTC) is a novel approach that enables rapid, high resolution impedance spectra measurements using a hardware platform that could be designed as an embedded system. This input signal consists of a sum-of-sines excitation current that has a known frequency spread and a duration of one period of the lowest frequency. The voltage response is then captured at a sufficiently fast sample rate. Previously developed rapid impedance spectrum measurement techniques either required a longer excitation signal or a sum-of-sines signal that was separated by harmonic frequencies to reduce or eliminate, respectively, the cross-talk interference in the calculated results. The distinct advantage of CTC, however, is that non-harmonic frequencies can now be included within the excitation signal while still keeping the signal duration at one period of the lowest frequency. Since the frequency spread of the input signal is known, the crosstalk interference between sinusoidal signals within the sum-of-sines at a given frequency of interest can be pre-determined and assigned to an error matrix. Consequently, the real and imaginary components of the impedance at each frequency of interest can be calculated using simple linear algebra based on the error matrix and measured response from the energy storage device given the excitation signal. Analytical validation of CTC over a frequency range between 2000 and 0.1 Hz (i.e., a ten-second input signal duration) was performed using a standardized battery lumped parameter model. The results indicated that the CTC was able to successfully resolve more than 45 frequencies within a sum-of-sines excitation signal, whereas previous techniques could only resolve up to 15 frequencies. A simplified derivation of the CTC technique and its corresponding analytical validation studies using the lumped-parameter model will be presented.

25 ENERGY STORAGE↗

DOE OSTI2016

Torsional Vibration in the National Wind Technology Center’s 2.5-Megawatt Dynamometer

This report documents the torsional drivetrain dynamics of the NWTC's 2.5-megawatt dynamometer as identified experimentally and as calculated using lumped parameter models using known inertia and stiffness parameters. The report is presented in two parts beginning with the identification of the primary torsional modes followed by the investigation of approaches to damp the torsional vibrations. The key mechanical parameters for the lumped parameter models and justification for the element grouping used in the derivation of the torsional modes are presented. The sensitivities of the torsional modes to different test article properties are discussed. The oscillations observed from the low-speed and generator torque measurements were used to identify the extent of damping inherently achieved through active and passive compensation techniques. A simplified Simulink model of the dynamometer test article integrating the electro-mechanical power conversion and control features was established to emulate the torque behavior that was observed during testing. The torque response in the high-speed, low-speed, and generator shafts were tested and validated against experimental measurements involving step changes in load with the dynamometer operating under speed-regulation mode. The Simulink model serves as a ready reference to identify the torque sensitivities to various system parameters and to explore opportunities to improve torsional damping under different conditions.

17 WIND ENERGY↗

DOE OSTI2013

A momentum source model for wire-wrapped rod bundles—Concept, validation, and application

Large uncertainties still exist in the treatment of wire-spacers and drag models for momentum transfer in current lumped parameter models. Here, to improve the hydraulic modeling of wire-wrap spacers in a rod bundle, a three-dimensional momentum source model (MSM) has been developed to model the anisotropic flow without the need to resolve the geometric details of the wire-wraps. The MSM is examined for 7-pin and 37-pin bundles steady-state simulations using the commercial CFD code STAR-CCM+. The calculated steady-state inter-subchannel cross flow velocities match very well in comparisons between bare bundles with the MSM applied and the wire-wrapped bundles with explicit geometry. The validity of the model is further verified by mesh and parameter sensitivity studies. Furthermore, the MSM is applied to a 61-pin EBR-II experimental subassembly for both steady state and PLOF transient simulations. Reasonably accurate predictions of temperature, pressure, and fluid flow velocities have been achieved using the MSM for both steady-state and transient conditions. Significant computing resources are saved with the MSM since it can be used on a much coarser computational mesh.

42 ENGINEERING↗

DOE OSTI2014

Energy Signal Tool for Decision Support in Building Energy Systems

A prototype energy signal tool is demonstrated for operational whole-building and system-level energy use evaluation. The purpose of the tool is to give a summary of building energy use which allows a building operator to quickly distinguish normal and abnormal energy use. Toward that end, energy use status is displayed as a traffic light, which is a visual metaphor for energy use that is either substantially different from expected (red and yellow lights) or approximately the same as expected (green light). Which light to display for a given energy end use is determined by comparing expected to actual energy use. As expected, energy use is necessarily uncertain; we cannot choose the appropriate light with certainty. Instead, the energy signal tool chooses the light by minimizing the expected cost of displaying the wrong light. The expected energy use is represented by a probability distribution. Energy use is modeled by a low-order lumped parameter model. Uncertainty in energy use is quantified by a Monte Carlo exploration of the influence of model parameters on energy use. Distributions over model parameters are updated over time via Bayes' theorem. The simulation study was devised to assess whole-building energy signal accuracy in the presence of uncertainty and faults at the submetered level, which may lead to tradeoffs at the whole-building level that are not detectable without submetering.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

DOE OSTI2011

U32: Vehicle Stability and Dynamics: Longer Combination Vehicles

This study investigated the safety and stability of longer combination vehicles (LCVs), in particular a triple trailer combination behind a commercial tractor, which has more complicated dynamics than the more common tractor in combination with a single semitrailer. The goal was to measure and model the behavior of LCVs in simple maneuvers. Example maneuvers tested and modeled were single and double lane changes, a gradual lane change, and a constant radius curve. In addition to test track data collection and a brief highway test, two computer models of LCVs were developed. One model is based on TruckSim , a lumped parameter model widely used for single semitrailer combinations. The other model was built in Adams software, which more explicitly models the geometry of the components of the vehicle, in terms of compliant structural members. Among other results, the models were able to duplicate the experimentally measured rearward amplification behavior that is characteristic of multi-unit combination vehicles.

99 GENERAL AND MISCELLANEOUS↗

DOE OSTI2012

Modelling of the internal dynamics and density in a tens of joules plasma focus device

Using MHD theory, coupled differential equations were generated using a lumped parameter model to describe the internal behaviour of the pinch compression phase in plasma focus discharges. In order to provide these equations with appropriate initial conditions, the modelling of previous phases was included by describing the plasma sheath as planar shockwaves. The equations were solved numerically, and the results were contrasted against experimental measurements performed on the device PF-50J. The model is able to predict satisfactorily the timing and the radial electron density profile at the maximum compression.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2020

MoorDyn V2: New Capabilities in Mooring System Components and Load Cases

MoorDyn, an open-source mooring dynamics model, is being expanded with capabilities for additional mooring system features and load cases. As floating wind turbine technology matures, mooring systems are becoming more sophisticated and more complex scenarios need to be considered in the design process. Mooring systems may have synthetic line materials, ballast/buoyancy bodies along the lines, or interconnections between platforms. Failure modes may involve multiple cascading line failures that depend on mooring system dynamics. Features recently added to MoorDyn aim to address these emerging needs. MoorDyn’s linear elasticity model has been supplemented to support user-defined stress-strain curves, which can be adjusted to represent synthetic mooring materials. Rigid six-degree-of-freedom bodies in the mooring system can now be modeled using two new model objects. “Rod” objects provide an option for rigid cylindrical bodies. They use the existing Morison equation-based hydrodynamics model and can be connected to mooring lines at either end. “Body” objects provide a generic six-degree-of-freedom rigid-body representation based on a lumped-parameter model of translational and rotational properties. Rod objects can be added to Body objects and mooring lines can be attached at any location, allowing a wide variety of submerged structures to be integrated into the mooring system. Lastly, a means of dynamically simulating mooring line failures has been implemented. These new features, currently in the C++ version of MoorDyn, are described and then demonstrated on a two-turbine shared-mooring array. A qualitative view of the results suggests the new features are functioning as expected.

49 EE - Wind and Water Power Program - Wind (EE-4W↗

DOE OSTI2020

MoorDyn V2: New Capabilities in Mooring System Components and Load Cases: Preprint

49 EE - Wind and Water Power Program - Wind (EE-4W↗

DOE OSTI2025

Openpronghorn

OpenPronghorn is a simulation tool specifically tailored for modeling thermal-hydraulic phenomena in advanced nuclear reactors. It is built on the Multiphysics Object-Oriented Simulation Environment (MOOSE), an open-source platform that facilitates the development of high-performance scientific computing applications. OpenPronghorn solves the Navier-Stokes equations, which describe the conservation of mass, momentum, and energy in fluid flows, using the finite volume numerical method. The code supports a wide range of fluid flow conditions that are applicable to nuclear reactors, including incompressible and weakly compressible flows, as well as single-phase and multiphase flows. It is capable of modeling diverse flow regimes, including laminar and turbulent flows, using various turbulence models such as the standard k-epsilon models, the v2f model, and the mixing length model. For multiphase flows, OpenPronghorn employs a mixture a Eulerian modeling approach with mixture, drift-flux, and full Eulerian models, and includes open-sourced interfacial transfer correlations for drag, exchange, and heat transfer coming from the scientific literature. OpenPronghorn's modular design allows it to handle multiscale simulations, ranging from detailed Reynolds-Averaged Navier Stokes (RANS) simulations to coarse-mesh and lumped parameter models. This flexibility enables users to perform high-fidelity simulations of specific reactor components as well as system-level analyses of entire reactor circuits. The code can be coupled with other MOOSE-based tools using the MultiApp system, allowing for the transfer of coupling quantities such as mass flow rates, heat fluxes, and boundary conditions between different simulation scales. One of the main features of OpenPronghorn is the it includes built-in validation cases from the open-source scientific literature and supports the implementation of user-defined models and correlations through MOOSE's FunctorMaterial system. OpenPronghorn is designed to be computationally efficient, leveraging the SIMPLE projection method for large-scale problems, and can be run on high-performance computing systems to handle the extensive computational demands of detailed reactor simulations. Overall, OpenPronghorn is a versatile and robust tool that provides critical insights into the thermal-hydraulic behavior of advanced nuclear reactors, supporting the design, safety, and optimization of next-generation nuclear energy systems.

Retamales, Mauricio Eduardo Tano [Idaho National L↗

DOE OSTI2024

Leveraging Optimal Sparse Sensor Placement to Aggregate a Network of Digital Twins for Nuclear Subsystems

Nuclear power plants (NPPs) require continuous monitoring of various systems, structures, and components to ensure safe and efficient operations. The critical safety testing of new fuel compositions and the analysis of the effects of power transients on core temperatures can be achieved through modeling and simulations. They capture the dynamics of the physical phenomenon associated with failure modes and facilitate the creation of digital twins (DTs). Accurate reconstruction of fields of interest (e.g., temperature, pressure, velocity) from sensor measurements is crucial to establish a two-way communication between physical experiments and models. Sensor placement is highly constrained in most nuclear subsystems due to challenging operating conditions and inherent spatial limitations. This study develops optimized data-driven sensor placements for full-field reconstruction within reactor and steam generator subsystems of NPPs. Optimized constrained sensors reconstruct field of interest within a tri-structural isotropic (TRISO) fuel irradiation experiment, a lumped parameter model of a nuclear fuel test rod and a steam generator. The optimization procedure leverages reduced-order models of flow physics to provide a highly accurate full-field reconstruction of responses of interest, noise-induced uncertainty quantification and physically feasible sensor locations. Accurate sensor-based reconstructions establish a foundation for the digital twinning of subsystems, culminating in a comprehensive DT aggregate of an NPP.

42 ENGINEERING↗

DOE OSTI2022

Closed-form existence conditions for bandgap resonances in a finite periodic chain under general boundary conditions

Bragg scattering in periodic media generates bandgaps, frequency bands where waves attenuate rather than propagate. Yet, a finite periodic structure may exhibit resonance frequencies within these bandgaps. This is caused by boundary effects introduced by the truncation of the nominal infinite medium. Previous studies of discrete systems determined existence conditions for bandgap resonances, although the focus has been limited to mainly periodic chains with free–free boundaries. In this paper, we present closed-form existence conditions for bandgap resonances in discrete diatomic chains with general boundary conditions (free–free, free–fixed, fixed–free, or fixed–fixed), odd or even chain parity (contrasting or identical masses at the ends), and the possibility of attaching a unique component (mass and/or spring) at one or both ends. The derived conditions are consistent with those theoretically presented or experimentally observed in prior studies of structures that can be modeled as linear discrete diatomic chains with free–free boundary conditions. An intriguing case is a free–free chain with even parity and an arbitrary additional mass at one end of the chain. Introducing such an arbitrary mass underscores a transition among a set of distinct existence conditions, depending on the type of chain boundaries and parity. The proposed analysis is applicable to linear periodic chains in the form of lumped-parameter models, examined across the frequency spectrum, as well as continuous granular media models, or similar configurations, examined in the low-frequency regime.

Bastawrous, Mary V.↗