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DOE OSTI2021

Tensile and compressive plastic deformation behavior of medium-entropy Cr-Co-Ni single crystals from cryogenic to elevated temperatures

The equiatomic Cr-Co-Ni medium-entropy alloy has the face-centered cubic (FCC) structure. Bulk single crystals of this alloy were grown and tested in tension and compression between 14 K and 1373 K with the loading axis parallel to [23]. At room temperature, the critical resolved shear stress (CRSS) for {111}<10> slip is 65 ± 5 MPa and does not exhibit a tension-compression asymmetry. It does, however, increase significantly as the test temperature decreases. A dulling of this temperature dependence occurs below 50 K, which may be due to the inertia effect. When the measured values above 50 K are extrapolated to lower temperatures, a value of 225 MPa is estimated for the CRSS at 0 K. This is larger than that (168 MPa) previously determined for the equiatomic Cr-Mn-Fe-Co-Ni high-entropy alloy using a similar procedure. The stacking fault energy of the present Cr-Co-Ni is estimated to be about 14 mJm-2, which is sufficiently low to account for deformation twinning both at 77 K and room temperature. Twinning at 77 K occurs on conjugate (1) planes at an onset shear stress of 482 MPa after primary slip and propagates in the form of Lüders deformation. At room temperature, twinning occurs uniformly throughout the gauge section on primary (111) planes at an onset shear stress of 381 MPa after primary and subsequent conjugate slip. Thin layers with the hexagonal close-packed stacking are observed in association with twinning both at 77 K and room temperature.

36 MATERIALS SCIENCE↗

DOE OSTI2026

Asymptotic-preserving semi-implicit finite volume scheme for extended magnetohydrodynamics

A Finite Volume (FV) scheme is developed for solving the extended magnetohydrodynamic (XMHD) equations, yielding accurate results in the ideal, resistive, and Hall MHD limits. This is accomplished by first re-writing the XMHD equations such that it allows the algorithm to retain the use of ideal MHD Riemann solvers and the constrained transport method to preserve divergence-free magnetic fields. Incorporation of electron inertia and displacement current introduces additional numerical stiffness which motivates a semi-implicit FV scheme that re-formulates the XMHD model as a relaxation system. The equations are then advanced in time using an explicit 2nd-order Runge–Kutta scheme with operator splitting applied to the implicit source term updates at each sub-stage. For additional numerical stability, a density-dependent slope limiter is implemented to increase flux diffusivity at low density regions where non-ideal effects become significant. The algorithm is subsequently implemented in a scalable adaptive mesh refinement (AMR) framework. As the new algorithm retains many aspects of the ideal MHD formulations, it asymptotes naturally to the ideal MHD limit. Moreover, it shows promising results at the resistive and Hall MHD limits. This is verified against reference test problems for ideal, resistive and Hall MHD.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2022

High-resolution CH stretch spectroscopy of jet-cooled cyclopentyl radical: First insights into equilibrium structure, out-of-plane puckering, and IVR dynamics

First, high-resolution sub-Doppler infrared spectroscopic results for cyclopentyl radical (C 5 H 9 ) are reported on the α-CH stretch fundamental with suppression of spectral congestion achieved by adiabatic cooling to T rot ≈ 19(4) K in a slit jet expansion. Surprisingly, cyclopentyl radical exhibits a rotationally assignable infrared spectrum, despite 3N – 6 = 36 vibrational modes and an upper vibrational state density (ρ ≈ 40–90 #/cm –1 ) in the critical regime (ρ ≈ 100 #/cm –1 ) necessary for onset of intramolecular vibrational relaxation (IVR) dynamics. Such high-resolution data for cyclopentyl radical permit detailed fits to a rigid-rotor asymmetric top Hamiltonian, initial structural information for ground and vibrationally excited states, and opportunities for detailed comparison with theoretical predictions. Specifically, high level ab initio calculations at the coupled-cluster singles, doubles, and perturbative triples (CCSD(T))/ANO0, 1 level are used to calculate an out-of-plane bending potential, which reveals a C 2 symmetry double minimum 1D energy surface over a C 2v transition state. Here, the inversion barrier [V barrier ≈ 3.7(1) kcal/mol] is much larger than the effective moment of inertia for out-of-plane bending, resulting in localization of the cyclopentyl wavefunction near its C 2 symmetry equilibrium geometry and tunneling splittings for the ground state too small (<1 MHz) to be resolved under sub-Doppler slit jet conditions. The persistence of fully resolved high-resolution infrared spectroscopy for such large cyclic polyatomic radicals at high vibrational state densities suggests a “deceleration” of IVR for a cycloalkane ring topology, much as low frequency torsion/methyl rotation degrees of freedom have demonstrated a corresponding “acceleration” of IVR processes in linear hydrocarbons.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

NASA NTRS2018

Maps of Tethys' Thermophysical Properties

On 11th April 2015 Cassini's Composite Infrared Spectrometer (CIRS) made a series of observations of Tethys’ daytime anti-Saturn hemisphere over a nine-hour time period. During this time the sub-spacecraft position was remarkably stable (0.3° S to 3.9° S; 153.2° W to 221.8° W), and so these observations provide unprecedented coverage of diurnal temperature variations on Tethys’ anti-Saturn hemisphere. In 2012 a thermal anomaly was discovered at low latitudes on Tethys’ leading hemisphere; it appears cooler during the day and warmer at night than its surroundings (Howett et al., 2012) and is spatially correlated with a decrease in the IR3/UV3 visible color ratio (Schenk et al., 2011). The cause of this anomaly is believed to be surface alteration by high-energy electrons, which preferentially bombard low-latitudes of Tethys’ leading hemisphere (Schenk et al., 2011; Howett et al., 2012; Paranicas et al. 2014; Schaible et al., 2017). The thermal anomaly was quickly dubbed “Pac-Man” due to its resemblance to the 1980s video game icon. We use these daytime 2015 CIRS data, along with two sets of nighttime CIRS observations of Tethys (from 27 June 2007 and 17 August 2015) to make maps of bolometric Bond albedo and thermal inertia variations across the anti-Saturn hemisphere of Tethys (including the edge of its Pac-Man region). These maps confirm the presence of the Pac-Man thermal anomaly and show that while Tethys’ bolometric Bond albedo varies negligibly outside and inside the anomaly (0.69 plus or minus 0.02 inside, compared to 0.71 plus or minus 0.04 outside) the thermal inertia varies dramatically (29 plus or minus 10 J m−2 K−1 s−1/2 inside, compared to 9 plus or minus 4 J m−2 K−1 s−1/2 outside). These thermal inertias are in keeping with previously published values: 25 plus or minus 3 J m−2 K−1 s−1/2 inside, and 5 ± 1 J m−2 K−1 s−1/2 outside the anomaly (Howett et al., 2012). A detailed analysis shows that on smaller spatial-scales the bolometric Bond albedo does vary: increasing to a peak value at 180° W. For longitudes between approximately 100° W and approximately 160° W the thermal inertia increases from northern to southern latitudes, while the reverse is true for bolometric Bond albedo. The thermal inertia on Tethys generally increases towards the center of its leading hemisphere but also displays other notable small-scale variations. These thermal inertia and bolometric Bond albedo variations are perhaps due to differences in competing surface modification by E ring grains and high-energy electrons which both bombard Tethys’ leading hemisphere (but in different ways). A comparison between the observed temperatures and our best thermal model fits shows notable discrepancies in the morning warming curve, which may provide evidence of regional variations in surface roughness effects, perhaps again due to variations in surface alteration mechanisms.

Howett, C. J. A.↗

NASA NTRS2014

Incorporating Handling Qualities Analysis into Rotorcraft Conceptual Design

This paper describes the initial development of a framework to incorporate handling qualities analyses into a rotorcraft conceptual design process. In particular, the paper describes how rotorcraft conceptual design level data can be used to generate flight dynamics models for handling qualities analyses. Also, methods are described that couple a basic stability augmentation system to the rotorcraft flight dynamics model to extend analysis to beyond that of the bare airframe. A methodology for calculating the handling qualities characteristics of the flight dynamics models and for comparing the results to ADS-33E criteria is described. Preliminary results from the application of the handling qualities analysis for variations in key rotorcraft design parameters of main rotor radius, blade chord, hub stiffness and flap moment of inertia are shown. Varying relationships, with counteracting trends for different handling qualities criteria and different flight speeds are exhibited, with the action of the control system playing a complex part in the outcomes. Overall, the paper demonstrates how a broad array of technical issues across flight dynamics stability and control, simulation and modeling, control law design and handling qualities testing and evaluation had to be confronted to implement even a moderately comprehensive handling qualities analysis of relatively low fidelity models. A key outstanding issue is to how to 'close the loop' with an overall design process, and options for the exploration of how to feedback handling qualities results to a conceptual design process are proposed for future work.

Analysis into Rotorcraft↗

NASA NTRSDate not supplied

Hybrid-Electric Aero-Propulsion Controls Laboratory: Overview and Capability

A hardware-in-the-loop (HIL) laboratory is developed to investigate control technologies for electrified aircraft propulsion (EAP). The laboratory emulates a propulsion system by reproducing the mechanical shaft interface to the electrical power system in hardware. The experimental electric power system includes supercapacitor energy storage and a dynamically variable electrical load. A novel method of scaling power and inertia is provided in software to accurately reproduce the transient, off-design turbomachinery performance dynamics without including actual turbomachinery. An overview of how the HIL system can accommodate a broad range of EAP architectures, including power extraction and insertion, with capability for transient energy management is described. The real-time system operates in the 100kW power class and is instrumented to emulate turbomachinery – power system interactions. The platform is an agile, flexible laboratory for low-cost, risk-reduction development and testing of propulsion control, operability, and energy management technologies.

Controls↗

NASA NTRSDate not supplied

Hybrid-Electric Aero-Propulsion Controls Laboratory: Overview and Capability

controls↗

NASA NTRSDate not supplied

Sliding Mode Transient Scaling Controller for Gas Turbine Engine Emulation on an Electric Machine

The testing of hybrid-electric aircraft propulsion system components and control strategies has dictated the need for a low-cost gas turbine engine (GTE) emulation testbed. Within that testbed, electric machines (EMs) are used to emulate the dynamics of a GTE. GTE mathematical models are used to provide control torque commands to EMs. Most GTEs operate at much higher power levels than commercially available EMs. Therefore, the transient shaft dynamics of the GTE must be scaled appropriately. The sliding mode controller being presented here aims to deliver a control torque to an electric machine with a fixed inertia that will allow it to mimic the response of a GTE with a different inertia. This solution provides an easily scalable and tunable transient emulation method without having to scale the GTE mathematical model and/or add inertia to the physical EM shaft. This controller has been proven in simulation to produce nearly identical transient rotational speed response to a reference GTE shaft model which has a large difference in rotational inertia compared to the motor. Also, the inherent robustness of the sliding mode control scheme results in negligible changes in performance for large amounts of parameter uncertainty while minimizing high frequency fluctuations in the control signal.

sliding mode↗

NASA NTRS1993

Torque equilibrium attitudes for the Space Station

All spacecraft orbiting in a low earth orbit (LEO) experience external torques due to environmental effects. Examples of these torques include those induced by aerodynamic, gravity-gradient, and solar forces. It is the gravity-gradient and aerodynamic torques that produce the greatest disturbances to the attitude of a spacecraft in LEO, and large asymmetric spacecraft, such as the space station, are affected to a greater degree because the magnitude of the torques will, in general, be larger in proportion to the moments of inertia. If left unchecked, these torques would cause the attitude of the space station to oscillate in a complex manner and the resulting motion would destroy the micro-gravity environment as well as prohibit the orbiter from docking. The application of control torques will maintain the proper attitude, but the controllers have limited momentum capacity. When any controller reaches its limit, propellant must then be used while the device is reset to a zero or negatively-biased momentum state. Consequently, the rate at which momentum is accumulated is a significant factor in the amount of propellant used and the frequency of resupply necessary to operate the station. A torque profile in which the area curve for a positive torque is not equal to the area under the curve for a negative torque is 'biased,' and the consequent momentum build-up about that axis is defined as secular momentum because it continues to grow with time. Conversely, when the areas are equal, the momentum is cyclic and bounded. A Torque Equilibrium Attitude (TEA) is thus defined as an attitude at which the external torques 'balance' each other as much as possible, and which will result in lower momentum growth in the controllers. Ideally, the positive and negative external moments experienced by a spacecraft at the TEA would exactly cancel each other out and small cyclic control torques would be required only for precise attitude control. Over time, the only momentum build-up in the controllers would be due to electro-mechanical losses within the device. However, the atmospheric torques are proportional to the density of the atmosphere and the density varies with the orbital position, time of day, time of year, and the solar cycle. In addition, there are unmodeled disturbances and uncertainties in the mass and inertias. Therefore, there is no constant attitude that will completely balance the environmental torques and the dynamic TEA cannot be solved in closed form. The objective of this research was to determine a method to calculate a dynamic TEA such that the rate of momentum build-up in the controllers would be minimized and to implement this method in the MATRIX(x) simulation software by Integrated Systems, Inc.

Thompson, Roger C.↗

DOE OSTI2026

Quantum Choreography of the Nucleus: Rotations, Vibrations, and Emergent Structure

Abstract Nuclei are complex many-body quantum systems where interactions of the neutrons and protons via the strong, the weak, and the electromagnetic forces lead to the emergence of simple patterns of energy states that have been described by various theoretical approaches. One of the goals of all the theoretical models is the development of a universal theory that can be applied across the entire chart of nuclides. Significant progress has been made by experiments as well as the increasing sophistication of models, but a universal theory has yet to be established. A recent review of nuclei in the Z = 50–82 region of the chart of nuclides has analyzed all the available compiled data from several decades of studies towards a clarification of the low-lying structure of nuclei. Other reviews have reported and explained the emergence of multiple different shapes in nuclei at somewhat higher excitation energies than the ground state. Some have challenged the interpretation of the first excited K π = 0 + band as a vibration of ground state. This work attempts to provide a guide to determining the nature of the first excited K π = 0 + band in nuclei by the combined use of nuclear lifetimes, energy level evolutions, dynamic moments of inertia, and intrinsic quadrupole moments extracted from transition probabilities. The result is that for a subset of the nuclei in this region, the K π = 0 + band is consistent with the traditional 𝛽-vibration description of an oscillation built on the ground state.

CHFB+5DCH↗

DOE OSTI2025

Explosive Soot Challenge (Final Report)

This project assembled a broad ensemble of modeling and experimentation tools to study the morphological and optical properties of detonation soots in explosive fireballs. A gram-scale hemispherical high explosive was studied in a low-pressure controlled environment using in-situ experimentation with diffusely illuminated visible absorption spectroscopy, particle sizing through light scattering techniques, and post-test collections with subsequent morphological analysis. Hydrocode modeling was performed to replicate the detonation flow observations, and subsequent aerosol kinetics models provided particle size distributions and extinction coefficients from the hydrocode results. Experimentally observed soot morphologies agreed with expectation from the literature - a bimodal distribution was found, brought upon by the particles growing to a size where their inertia and fluid wakes are non-negligible. The aerosol kinetics model did not replicate the observed bimodal size distribution for lack of a coagulation kernel to represent the behavior. To recover particulate optical properties, a spectrally resolved absorption spectroscopy method termed Spectral diffuse back-illuminated extinction imaging (SBI-EI) was developed and implemented on two explosive types. Inverting the absorption spectra using a Kramers-Kronig consistent method yielded the complex index of refraction for the soots produced by the explosives. This method resulted in an unrealistic index of refraction for one of the two explosives, and this is suspected to be due to the model neglecting scattering brought upon by the large particle sizes observed. In addition to the core work, three additional studies were performed in parallel. These investigated the impact of scattering on diffuse absorption spectroscopy, studied how soots oxidate and sublimate in a well-controlled shock tube, and laid the theoretical groundwork for a new collision kernel to replicate the bimodal size distribution from the observations. Summaries of these efforts are included at the end of this report.

45 MILITARY TECHNOLOGY, WEAPONRY, AND NATIONAL DEF↗

DOE OSTI2021

Distributed Wind Controls: A Research Roadmap for Microgrids, Infrastructure Resilience, and Controls Launchpad (MIRACL)

The Microgrids, Infrastructure Resilience, and Advanced Controls Launchpad (MIRACL) project’s controls research area aims to expand the benefits from distributed wind (DW) generation assets beyond solely providing low cost power directly to consumers. To make distributed wind turbines operate more effectively there is a need for more advanced ways to control them, allowing power companies, businesses, and energy consumers to take advantage of the unique characteristics of wind energy. DW can contribute to the safe and secure operation of grid by providing services such as voltage regulation, frequency regulation, spinning reserves, and even black start capabilities. In the larger DER context where much of the research has focused around solar technologies, the inertia available in wind technologies has generally not been considered. For wind turbines to provide these services in an optimal and expanded way, development and demonstration of control methods and communication interfaces within a grid and microgrid framework are required. In this document, NREL led the literature review in collaboration with SNL, of DER controls-focused integration research to establish a baseline for the controls research under the MIRACL project to identify specific control functions to be focused on throughout this project. This literature review focused primarily on the control functions of variable distributed generation, largely pulling from past solar PV and battery controls works, with a specific focus on applicability for distributed wind energy systems. The goal of this document is to identify a research roadmap based on the open literature and past national laboratory works to inform advanced wind turbine and power electronics control functions for four use cases: 1) distributed wind in isolated systems, 2) grid-connected microgrids (wind-hybrid systems and islanded operation), 3) behind-the-meter distributed wind applications in the power distribution systems, and 4) front-of-the-meter distributed wind applications in the power distribution systems.

17 WIND ENERGY↗

DOE OSTI2023

Modular, Multifunction, Multiport and Medium Voltage Utility Scale SiC PV Inverter (Final Report)

This project is to develop and demonstrate a Modular, Multi-function, Multiport and Medium Voltage utility scale SiC solar inverter (M4 Inverter). The M4 Inverter is a next generation utility scale PV + storage inverter that can substantially reduce the levelized cost of energy (LCOE) while providing grid friendly ancillary services. Conventional utility scale solar inverters includes three parts, a megawatt rated solar inverter, a low frequency transformer (LFT) and a medium voltage switch gear. The proposed M4 Inverter directly converts the DC output of solar panels to medium voltage AC, eliminating the bulky and costly LFT. The M4 Inverter also has a DC port to interface with an additional energy storage device. This plus its bidirectional power flow capability, allows multiple functions in addition to PV maximum power tracking be achieved. These additional functionalities include but not limited to reactive power support, peak shaving, fast frequency regulation and synthetic inertia. Predicted LCOE reductions with these added functionalities, improved efficiency and longer lifetime time are more than 30% compared with the 2017 utility scale solar LCOE. A 1MVA SiC M4 Inverter was developed and tested at high power level. The project has also advanced the state of the art in controller hardware in the loop simulation capability. Power electronic innovations introduced in the M4 Inverter includes 1700V SiC MOSFET application in 1500V PV system, soft switching three-port power converters and modular converter architecture.

24 POWER TRANSMISSION AND DISTRIBUTION↗

NASA NTRS1985

Advanced seals for Liquid Oxygen (LOX) turbopumps

Reliability, life and vehicle pay load can be enhanced by improved seals on space vehicle propulsion systems. Development of two types of fluid-film seals for application to advanced LOX turbomachines are summarized. The first is a floating ring, helium buffered seal whose function is to exclude intrusion of liquid oxygen (LOX) into the turbine drive. The other is a spiral groove, LOX, face-type configuration designed to break down pressure and minimize leakage of LOX. The Rayleigh-step, floating ring gas seals require low clearances to minimize leakage and stiff films to assure tracking excursions of the rotor and to overcome Coulomb friction between the rings and housings. The design and test results of these buffer seals are described. Results indicate significant performance improvement over seals used on contemporary engines. The possibilities of reducing helium storage requirements and thus increasing payload appear promising. A unique configuration of spiral groove LOX seal was required to avoid detrimental vaporization in the flow path. It was found that fluid turbulence and inertia influence groove geometry and in particular groove depth must be much greater than spiral groove seals using conventional fluids.

Shapiro, W.↗

NASA NTRS1949

Investigation of Stability and Control Characteristics of a 1/10-scale Model of a Canadian Tailless Glider in the Langley Free-flight Tunnel

An investigation of the stability and control characteristics of a 1/10-scale model of a Canadian tailless glider has been conducted in the 10 Langley free-flight tunnel. The glider designated the N.R.L. tailless glider has a straight center section and outboard panels sweptback 43 deg. along the leading edge of the wing. The aspect ratio is 5.83 and the taper ratio is 0.323. From the results of the investigation and on the basis of comparison with higher-scale static tests of the National Research Council of Canada, it is expected that the longitudinal stability of the airplane will be satisfactory with flap up but unsatisfactory near the stall with flap down. The airplane is expected to have unsatisfactory lateral stability and control characteristics in the design configuration with either flap up or flap down. The model flights showed very low damping of the lateral oscillation. Increasing the vertical-tail area improved the lateral stability, and it appeared that a value of the directional-stability parameter C(sub n beta) of at least 0.002 per degree would probably be necessary for satisfactory lateral flying characteristics. A comparison of the calculated dynamic lateral stability characteristics of the N.R.L. tailless glider with those of a conventional-type sweptback airplane having a similar wing plan form and about the same inclination of the principal longitudinal axis of inertia showed that the tailless glider had poorer lateral stability because of the relatively larger radius of gyration in roll and the smaller damping-in-yaw factor C(sub nr).

Johnson, Joseph L.↗

DOE OSTI2025

Initial assessment of alternative carbon fiber geometries for design of cost-effective compressive performance: Size effect studies

Carbon fiber provides opportunity to reduce weight in structural composites, including wind turbine blades, due to the material's superior specific stiffness and specific strength compared to alternatives. Despite these advantages, cost and compressive performance are considered weaknesses for carbon fiber products available today. Studies to produce low-cost carbon fiber alternatives, including the use of textile-derived precursor systems, have shown progress and merit through the DOE/ORNL low-cost carbon fiber initiatives. Here, this work focuses on enabling increases in compressive strength through design of the carbon fiber geometry, applicable to both textile and conventional precursor systems, while also providing opportunities to reduce carbon fiber processing costs. Fiber-resin interface and fiber alignment are among the most frequently cited factors controlling composite compressive performance. However, it is believed that there is opportunity in traditionally unexplored routes to increasing compressive strength through alteration of the carbon fiber geometry by increasing the fiber area moment of inertia and/or the fiber perimeter and interfacial area. This paper presents initial results from manufacturing carbon fiber materials to assess the impacts of carbon fiber size on tested composite compressive performance with projected neutral or even beneficial impact on fiber and composite manufacturing economics. Carbon fiber systems with increasing size illustrate a favorable correlation for compressive performance greater than predicted from a micromechanical failure model. The manufacturing and mechanical test results support the hypothesis of this work that alterations to fiber geometry can be used to produce improvements of the compressive strength of carbon fiber reinforced polymers and provide incentive for related work in designing alternative shapes to further enhance compressive performance.

42 ENGINEERING↗

NASA NTRS1992

A 23.2:1 ratio, 300-watt, 26 N-m output torque, planetary roller-gear robotic transmission: Design and evaluation

The design philosophy and measurements performed on a new roller-gear transmission prototype for a robotic manipulator are described. The design incorporates smooth rollers in a planetary configuration integrated with conventional toothed gears. The rollers were designed to handle low torque with low backlash and friction while the complementary gears support higher torques and prevent accumulated creep or slip of the rollers. The introduction of gears with finite numbers of teeth to function in parallel with the rollers imposes severe limits on available designs. Solutions for two-planet row designs are discussed. A two-planet row, four-planet design was conceived, fabricated, and tested. Detailed calculations of cluster geometry, gear stresses, and gear geometry are given. Measurement data reported here include transmission linearity, static and dynamic friction, inertia, backlash, stiffness, and forward and reverse efficiency. Initial test results are reported describing performance of the transmission in a servomechanism with torque feedback.

Newman, Wyatt S.↗

NASA NTRS1972

Gas-core reactor power transient analysis

The gas core reactor is a proposed device which features high temperatures. It has applications in high specific impulse space missions, and possibly in low thermal pollution MHD power plants. The nuclear fuel is a ball of uranium plasma radiating thermal photons as opposed to gamma rays. This thermal energy is picked up before it reaches the solid cavity liner by an inflowing seeded propellant stream and convected out through a rocket nozzle. A wall-burnout condition will exist if there is not enough flow of propellant to convect the energy back into the cavity. A reactor must therefore operate with a certain amount of excess propellant flow. Due to the thermal inertia of the flowing propellant, the reactor can undergo power transients in excess of the steady-state wall burnout power for short periods of time. The objective of this study was to determine how long the wall burnout power could be exceeded without burning out the cavity liner. The model used in the heat-transfer calculation was one-dimensional, and thermal radiation was assumed to be a diffusion process.

Kascak, A. F.↗