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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 325 records · Page 18
All sourcesNASA NTRSDOE OSTI
DOE OSTI2026

Mechanisms of Metal Additive-Induced Ordering During SNIPS Membrane Formation

Isoporous membranes can be fabricated by combining self-assembly with nonsolvent induced phase separation (SNIPS) using an amphiphilic block copolymer like polystyrene-b-poly(4-vinylpyridine) (SV). Poly(4-vinylpyridine) (V) is known to complex with metal salts, which are hypothesized to stabilize solution ordering and preserve structure during casting. We explored how the molar ratio of metal additive to the poly(4-vinylpyridine) block affected the final membrane morphology via scanning electron microscopy (SEM). Dynamic light scattering (DLS), small-angle X-ray scattering (SAXS), and in situ grazing-incidence SAXS were used to track changes in solution ordering and chain conformation as a function of the molar ratio of the additive to the V block. Additives induced aggregation, promoted the formation of more compact conformations in solution, and facilitated micelle ordering onto lattices at optimal ratios. Furthermore, these experimental results were supported by random phase approximation calculations, which helped explain how the thermodynamic order–disorder transition shifts with additive binding strength. Stronger additive–polymer interactions reduced the block copolymer volume fraction required for ordering in solution, allowing ordered domains to form at lower polymer concentrations.

Additives↗
DOE OSTI2023

Improved Productivity with Multilaser Rotary Powder Bed Fusion Additive Manufacturing

Laser powder bed fusion (LPBF) enables the fabrication of intricate, geometrically complex structures with a sufficiently fine surface finish for many engineering applications with a diversity of available feedstock metals. However, the production rate of LPBF systems is not well suited for mass production in comparison to traditional manufacturing methods. LPBF systems measure their deposition rates in 100's of grams per hour, while other processes measure in kilograms per hour or even in the case of processes such as forming, stamping, and casting, 100's of kilograms per hour. To be widely adopted in industry for mass production, LPBF requires a new scalable architecture that enables many orders of magnitude improvement in deposition rate, while maintaining the geometry freedom of additive manufacturing. This article explores concepts that could achieve as much as four orders of magnitude increase in the production rate through the application of (1) rotary table kinematic arrangements; (2) a dramatic number of simultaneously operating lasers; (3) reductions of laser optic size; (4) improved scanning techniques; and (5) an optimization of toroidal build plate size. To theoretically demonstrate the possibilities of production improvements, a productivity analysis is proposed for synchronous reluctance motors with relevance to the electric vehicle industry, given the recent increase in the diversity of printable soft magnetic alloys. The analysis provides insights into the impact of the architecture and process parameters necessary to optimize rotary powder bed fusion for mass production.

36 MATERIALS SCIENCE↗
DOE OSTI2019

Bioinspired nacre-like alumina with a bulk-metallic glass-forming alloy as a compliant phase

Bioinspired ceramics with micron-scale ceramic "bricks" bonded by a metallic "mortar" are projected to result in higher strength and toughness ceramics, but their processing is challenging as metals do not typically wet ceramics. To resolve this issue, we made alumina structures using rapid pressureless infiltration of a zirconium-based bulk-metallic glass mortar that reactively wets the surface of freeze-cast alumina preforms. The mechanical properties of the resulting Al 2 O 3 with a glass-forming compliant-phase change with infiltration temperature and ceramic content, leading to a trade-off between flexural strength (varying from 89 to 800 MPa) and fracture toughness (varying from 4 to more than 9 MPa·m ½ ). The high toughness levels are attributed to brick pull-out and crack deflection along the ceramic/metal interfaces. Since these mechanisms are enabled by interfacial failure rather than failure within the metallic mortar, the potential for optimizing these bioinspired materials for damage tolerance has still not been fully realized.

36 MATERIALS SCIENCE↗
DOE OSTI2021

Structure and dynamics of small polyimide oligomers with silicon as a function of aging

The effect of UV curing and shearing on the structure and behavior of a polyimide (PI) binder as it disperses silicon particles in a battery electrode slurry was investigated. PI dispersant effectiveness increases with UV curing time, which controls the overall binder molecular weight. Here, the shear force during electrode casting causes higher molecular weight PI to agglomerate, resulting in battery anodes with poorly dispersed Si particles that do not cycle well. It is hypothesized that when PI binder is added above a critical amount, it conformally coats the silicon particles and greatly impedes Li ion transport. There is an “interzonal region” for binder loading where it disperses silicon well and provides a coverage that facilitates Li transport through the anode material and into the silicon particles. These results have implications in ensuring reproducible electrode manufacturing and increasing cell performance by optimizing the PI structure and coordination with the silicon precursor.

36 MATERIALS SCIENCE↗
DOE OSTI2024

Custom-form iron trifluoride Li-batteries using material extrusion and electrolyte exchanged ionogels

Custom-form factor batteries fabricated in non-conventional shapes can maximize the overall energy density of the systems they power, particularly when used in conjunction with energy dense materials (e.g., Li metal anodes and conversion cathodes). Additive manufacturing (AM), and specifically material extrusion (ME), have been shown as effective methods for producing custom-form cell components, particularly electrodes. However, the AM of several promising energy dense materials (conversion electrodes such as iron trifluoride) have yet to be demonstrated or optimized. Furthermore, the integration of multiple AM produced cell components, such as electrodes and separators, along with a custom package remains largely unexplored. In this work, iron trifluoride (FeF 3 ) and ionogel (IG) separators are conformally printed using ME onto non-planar surfaces to enable the fabrication of custom-form Li-FeF 3 batteries. Further, to demonstrate printing on non-planar surfaces, cathodes and separators were deposited onto cylindrical rods using a 5-axis ME printer. ME printed FeF 3 was shown to have performance commensurate with FeF 3 cast using conventional means, both in coin cell and cylindrical rod formats, with capacities exceeding 700 mAh/g on the first cycle and ranging between 600 and 400 mAh/g over the next 50 cycles. Additionally, a ME process for printing polyvinylidene fluoride-co-hexafluoropropylene (PVDF-HFP) based IGs directly onto FeF 3 is developed and enabled using an electrolyte exchange process. In coin cells, this process is shown to produce cells with similar capacity to cells built with Celgard separators out to 50 cycles, with the exception that cycling instabilities are observed during cycles 8–20. When using printed and exchanged IGs in a custom cylindrical cell package, 6 stable high-capacity cycles are achieved. Overall, this work demonstrates approaches for producing high-energy-density Li-FeF 3 cells in coin and cylindrical rod formats, which are translatable to customized, arbitrary geometries compatible with ME printing and electrolyte exchange.

25 ENERGY STORAGE↗
DOE OSTI2018

Enhancement of Structural Health Monitoring Framework by Optimizing Vibro-Acoustic Modulation Technique to Localize Alkali-Silica Reaction Degradation in Medium-Sized Concrete Samples

Assessment and management of aging concrete structures in nuclear power plants require a more systematic approach than simple reliance on existing code margins of safety. Health monitoring of concrete structures is performed to understand the current condition of a structure based on heterogeneous measurements and then produce high confidence actionable information regarding structural integrity. This information can then be used to support operational and maintenance decisions. The objectives of this ongoing research project focus on health monitoring and data analytics of concrete slabs containing reactive aggregates and thus subjected to degradation due to alkali-silica reaction (ASR). A controlled concrete slab with four pockets of reactive aggregates (pure silica, wells, placitas, and spratt) was cast at Vanderbilt University and cured in representative conditions to accelerate degradation due to ASR. A set of four concrete samples were also cast and cured at the University of Alabama for ASR testing. Of these four samples, two slabs contained reactive aggregates while the other two had the non-reactive aggregate counterparts mixed throughout the samples. Vibro-acoustic methods were used on these slabs to locate large pockets of ASR within the reactive samples and determine the effects of rebar using the non-reactive slabs. Vibro-acoustic modulation (VAM) is a vibration-based NDE method that utilizes signatures of nonlinear dynamic interactions on contact surfaces of crack or delamination damage to detect and localize the damage. VAM analysis was conducted on both Vanderbilt and Alabama’s samples using multiple variables for damage detection and localization. The results from the data analysis of the NDE vibro-acoustic techniques on concrete slabs cured at Vanderbilt University and the University of Alabama are discussed in detail in this report. The major outcome of the analysis suggests that the VAM method can be used to detect damage within the concrete samples by comparing the results found in different sections of the samples. Results for damage localization are dependent on multiple variables used in the vibro-acoustic modulation experiments. Digital image correlation (DIC) is a three-dimensional, full-field, optical NDE technique to measure contour, deformation, vibration, and strain. The application of the digital image correlation technique to study ASR-related degradation on a large concrete sample at the University of Tennessee Knoxville is discussed and observations are presented in this report.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2021

Phase segregation mechanisms of small molecule-polymer blends unraveled by varying polymer chain architecture

As phase separation between the small-molecule semiconductor and the polymer binder is the key enabler of blend-based organic field-effect transistors (OFETs) fabricated by low-cost solution processing, it is crucial to understand the underlying phase separation mechanisms that determine the phase morphology, which significantly impacts device performance. Beyond the parameter space investigated in previous work, here we investigate the formation of blends by varying the branch architecture of the polymer binder and by shortening the solvent dry time using ultrasonic spray casting. The phase morphologies of the resulting blend films have been thoroughly characterized with a variety of techniques in three dimensions over multiple length scales, including AFM, energy-filtered transmission electron microscope, and neutron reflectivity, and have been correlated with electrical transport performance. From the results, we have inferred that the phase morphology is kinetically determined, limited by the inherent slow movement of polymer macromolecules. The kinetic picture, supported by molecular dynamics modeling, not only consistently explains our observations but also resolves inconsistencies in previous works. The achieved mechanistic understanding will guide further optimization of blend-based organic electronics, such as OFETs and organic photovoltaics.

36 MATERIALS SCIENCE↗
NASA NTRS1993

Mathmatical modeling for diffractive optics

We consider a 'diffractive optic' to be a biperiodic surface separating two half-spaces, each having constant constitutive parameters; within a unit cell of the periodic surface and across the transition zone between the two half-spaces, the constitutive parameters can be a continuous, complex-valued function. Mathematical models for diffractive optics have been developed, and implemented as numerical codes, both for the 'direct' problem and for the 'inverse' problem. In problems of the 'direct' class, the diffractive optic is specified, and the full set of Maxwell's equations is cast in a variational form and solved numerically by a finite element approach. This approach is well-posed in the sense that existence and uniqueness of the solution can be proved and specific convergence conditions can be derived. An example of a metallic grating at a Wood anomaly is presented as a case where other approaches are known to have convergence problems. In problems of the 'inverse' class, some information about the diffracted field (e.g., the far-field intensity) is given, and the problem is to find the periodic structure in some optimal sense. Two approaches are described: phase reconstruction in the far-field approximation; and relaxed optimal design based on the Helmholtz equation. Practical examples are discussed for each approach to the inverse problem, including array generators in the far-field case and antireflective structures for the relaxed optimal design.

Dobson, David↗
DOE OSTI2023

Design, Fabrication, and Screening of Environmental‐Thermal Barrier Coatings Prepared by Ultrafast High‐Temperature Sintering

Abstract The demand for more efficient gas turbines relies heavily on the development of new environmental‐thermal barrier coatings (ETBCs). However, there is still uncertainty about which alloys and composites will be used for the next generation of turbine blades, as well as the most promising coating materials. Herein, an ETBCs development strategy is presented by integrating the coating design, synthesis, and screening using an ultrafast high temperature sintering (UHS) technique to accelerate coating improvements. The initial basis for composition selection is their thermal expansion mismatch with the substrate alloys; for which a temperature‐dependent coefficient of thermal expansion database is created. By combining tape casting method with the UHS technique a high‐throughput synthesis of single and multi‐layer coatings are realized with different compositions, layer stacking sequences, and layer thicknesses. To evaluate the coatings, thermal cycling tests from room temperature to 1300 °C are conducted. The approach enabled coatings on objects with complex geometries, multi‐layer ETBCs, and porosity tailoring by using staged UHS that runs with different temperatures and durations. The fast iteration strategy is more cost‐effective for the screening of ETBCs compared to conventional methods and greater throughput which can be further extended for rapid optimization of other materials systems.

Xie, Hua↗
NASA NTRS1996

Methodology for Sensitivity Analysis, Approximate Analysis, and Design Optimization in CFD for Multidisciplinary Applications

An incremental iterative formulation together with the well-known spatially split approximate-factorization algorithm, is presented for solving the large, sparse systems of linear equations that are associated with aerodynamic sensitivity analysis. This formulation is also known as the 'delta' or 'correction' form. For the smaller two dimensional problems, a direct method can be applied to solve these linear equations in either the standard or the incremental form, in which case the two are equivalent. However, iterative methods are needed for larger two-dimensional and three dimensional applications because direct methods require more computer memory than is currently available. Iterative methods for solving these equations in the standard form are generally unsatisfactory due to an ill-conditioned coefficient matrix; this problem is overcome when these equations are cast in the incremental form. The methodology is successfully implemented and tested using an upwind cell-centered finite-volume formulation applied in two dimensions to the thin-layer Navier-Stokes equations for external flow over an airfoil. In three dimensions this methodology is demonstrated with a marching-solution algorithm for the Euler equations to calculate supersonic flow over the High-Speed Civil Transport configuration (HSCT 24E). The sensitivity derivatives obtained with the incremental iterative method from a marching Euler code are used in a design-improvement study of the HSCT configuration that involves thickness. camber, and planform design variables.

Taylor, Arthur C., III↗
DOE OSTI2024

Solid-State Mixed-Potential Electrochemical Sensors for Natural Gas Leak Detection and Quality Control (Final Technical Report)

Mitigation of methane emissions are a critical factor to limiting the impact of the natural gas industry on global climate change. Throughout the period of 2020-2024, the University of New Mexico and its commercialization partner and subcontractor, SensorComm Technologies, Inc. (SCT), have worked together to develop a low-cost Artificial Intelligence (AI)-driven Internet of Things (IoT)-based multi-gas sensor platform for methane emissions detection. In the final year of the project, we extended this work to include hydrogen detection in support of a transition to a hydrogen economy where hydrogen could be transported through existing natural gas infrastructure. Mixed potential electrochemical sensors were first prototyped by ceramic additive manufacturing and then transitioned to conventional ceramic manufacturing tape casting and screen-printing technologies in preparation for mass production. Demonstrated limits of detection of 5 ppm of methane in natural gas and 1 ppm of hydrogen were measured. These limits of detection are among the lowest of solid-state electrochemical sensors that have been reported in the literature or available in the industry. Machine learning algorithms were developed to identify natural gas mixtures with > 98% accuracy level and quantify methane concentrations at 97% accuracy. The presence of hydrogen could also be identified, and its concentration quantified at these accuracy levels. These algorithms were optimized for running on portable computing hardware which enabled > 1 Hz processing rates. A portable packaged IoT system was integrated with the electrochemical sensor in collaboration with SCT. The package consists of readout electronics with < 1 mV resolution, sensor temperature control, and data transmission over cellular wireless and/or Wi-Fi networks. Field testing was performed in two rounds at Colorado State University’s Methane Emissions Technology Evaluation Center (CSU METEC). The first round of testing demonstrated successful measurements of methane from an underground natural gas leak of 20 standard liters per minute (SLPM), which agreed with previously published literature using more sophisticated and expensive analytical equipment. The second round of testing showed that an above ground leak of 2 SLPM of hydrogen could be detected at 32 ft. This project has resulted in six published peer reviewed journal articles, over ten presentations at professional conferences, and one full patent application filed in 2023. Future work on this project includes increased sensitivity, higher production yields, and applications in the hydrogen safety and flare emissions monitoring spaces.

03 NATURAL GAS↗
NASA NTRS2003

NASA Tech Briefs, February 2003

opics covered include: Integrated Electrode Arrays for Neuro-Prosthetic Implants; Eroding Potentiometers; Common/Dependent-Pressure-Vessel Nickel-Hydrogen Batteries; 120-GHz HEMT Oscillator With Surface-Wave-Assisted Antenna; 80-GHz MMIC HEMT Voltage-Controlled Oscillator; High-Energy-Density Capacitors; Microscale Thermal-Transpiration Gas Pump; Instrument for Measuring Temperature of Water; Improved Measurement of Coherence in Presence of Instrument Noise; Compact Instruments Measure Helium-Leak Rates; Irreversible Entropy Production in Two-Phase Mixing Layers; Subsonic and Supersonic Effects in Bose-Einstein Condensate; Nanolaminate Mirrors With "Piston" Figure-Control Actuators; Mixed Conducting Electrodes for Better AMTEC Cells; Process for Encapsulating Protein Crystals; Lightweight, Self-Deployable Wheels; Grease-Resistant O Rings for Joints in Solid Rocket Motors; LabVIEW Serial Driver Software for an Electronic Load; Software Computes Tape-Casting Parameters; Software for Tracking Costs of Mars Projects; Software for Replicating Data Between X.500 and LDAP Directories; The Technical Work Plan Tracking Tool; Improved Multiple-DOF SAW Piezoelectric Motors; Propulsion Flight-Test Fixture; Mechanical Amplifier for a Piezoelectric Transducer; Swell Sleeves for Testing Explosive Devices; Linear Back-Drive Differentials; Miniature Inchworm Actuators Fabricated by Use of LIGA; Using ERF Devices to Control Deployments of Space Structures; High-Temperature Switched-Reluctance Electric Motor; System for Centering a Turbofan in a Nacelle During Tests; Fabricating Composite-Material Structures Containing SMA Ribbons; Optimal Feedback Control of Thermal Networks; Artifacts for Calibration of Submicron Width Measurements; Navigating a Mobile Robot Across Terrain Using Fuzzy Logic; Designing Facilities for Collaborative Operations; and Quantitating Iron in Serum Ferritin by Use of ICP-MS.

Source record↗
DOE OSTI2019

Microstructures and Impact Wear Behavior of Al-Alloyed High-Mn Austenitic Cast Steel After Aging Treatment

The microstructural evolution and impact wear behavior of Al-alloyed ultra-high-Mn austenitic cast steel were investigated after different heat treatments, including quenching (Q) and quenching + aging (Q + A). Another ultra-high-Mn austenitic cast steel without Al was compared under the same experimental condition. After Q + A, Al addition contributed to the precipitation of κ-carbides which improves the yield strength and wear resistance of the austenite matrix. However, the mechanical properties and wear resistance of the Al-free steel were strongly deteriorated due to the precipitation of plate-like M{sub 3}C-type carbides, as well as the worn surface of the Al-free steel had the feature of micro-scratches. After Q + A (2 h), the Al-alloyed steel obtained optimal wear resistance and the main wear feature was strain fatigue. But, excessive aging time (4 h) would lead to a large fragile peeling from the worn surface and the wear resistance was decreased. Also, the worn subsurface microstructures with different heat treatments were observed by transmission electron microscopy (TEM). These results show that the deformation microstructures of the Al-free steel contained stacking faults, dislocation tangle and deformation twins. The deformation character of Al-alloyed steel is dominated by planar glide, and with increase in the aging time, planar dislocation substructures gradually evolved, relating to dislocation pileups, Taylor lattices and micro-bands.

36 MATERIALS SCIENCE↗
NASA NTRS2003

A Tabletop Tool for Modeling Life Support Systems

This paper describes the development plan for a comprehensive research and diagnostic tool for aspects of advanced life support systems in space-based laboratories. Specifically it aims to build a high fidelity tabletop model that can be used for the purpose of risk mitigation, failure mode analysis, contamination tracking, and testing reliability. We envision a comprehensive approach involving experimental work coupled with numerical simulation to develop this diagnostic tool. It envisions a 10% scale transparent model of a space platform such as the International Space Station that operates with water or a specific matched index of refraction liquid as the working fluid. This allows the scaling of a 10 ft x 10 ft x 10 ft room with air flow to 1 ft x 1 ft x 1 ft tabletop model with water/liquid flow. Dynamic similitude for this length scale dictates model velocities to be 67% of full-scale and thereby the time scale of the model to represent 15% of the full- scale system; meaning identical processes in the model are completed in 15% of the full- scale time. The use of an index matching fluid (fluid that matches the refractive index of cast acrylic, the model material) allows making the entire model (with complex internal geometry) transparent and hence conducive to non-intrusive optical diagnostics. So using such a system one can test environment control parameters such as core flows (axial flows), cross flows (from registers and diffusers), potential problem areas such as flow short circuits, inadequate oxygen content, build up of other gases beyond desirable levels, test mixing processes within the system at local nodes or compartments and assess the overall system performance. The system allows quantitative measurements of contaminants introduced in the system and allows testing and optimizing the tracking process and removal of contaminants. The envisaged system will be modular and hence flexible for quick configuration change and subsequent testing. The data and inferences from the tests will allow for improvements in the development and design of next generation life support systems and configurations.

Ramachandran, N.↗
NASA NTRS2005

Space Laboratory on a Table Top: A Next Generative ECLSS design and diagnostic tool

This paper describes the development plan for a comprehensive research and diagnostic tool for aspects of advanced life support systems in space-based laboratories. Specifically it aims to build a high fidelity tabletop model that can be used for the purpose of risk mitigation, failure mode analysis, contamination tracking, and testing reliability. We envision a comprehensive approach involving experimental work coupled with numerical simulation to develop this diagnostic tool. It envisions a 10% scale transparent model of a space platform such as the International Space Station that operates with water or a specific matched index of refraction liquid as the working fluid. This allows the scaling of a 10 ft x 10 ft x 10 ft room with air flow to 1 ft x 1 ft x 1 ft tabletop model with water/liquid flow. Dynamic similitude for this length scale dictates model velocities to be 67% of full-scale and thereby the time scale of the model to represent 15% of the full- scale system; meaning identical processes in the model are completed in 15% of the full- scale-time. The use of an index matching fluid (fluid that matches the refractive index of cast acrylic, the model material) allows making the entire model (with complex internal geometry) transparent and hence conducive to non-intrusive optical diagnostics. So using such a system one can test environment control parameters such as core flows (axial flows), cross flows (from registers and diffusers), potential problem areas such as flow short circuits, inadequate oxygen content, build up of other gases beyond desirable levels, test mixing processes within the system at local nodes or compartments and assess the overall system performance. The system allows quantitative measurements of contaminants introduced in the system and allows testing and optimizing the tracking process and removal of contaminants. The envisaged system will be modular and hence flexible for quick configuration change and subsequent testing. The data and inferences from the tests will allow for improvements in the development and design of next generation life support systems and configurations. Preliminary experimental and modeling work in this area will be presented. This involves testing of a single inlet-exit model with detailed 3-D flow visualization and quantitative diagnostics and computational modeling of the system.

Ramachandran, N.↗
DOE OSTI2018

Importance of Nucleation during Morphology Evolution of the Blade-Cast PffBT4T-2OD-Based Organic Solar Cells

Different temperatures, solvents, and additives are used as influencing parameters to drive molecular packing and phase separation for the development of the controlled evolution of nanostructures for organic solar cells (OSCs). The temperature-dependent aggregation (TDA) features of polymers are explored by investigating aggregation in solution and solid thin-film states using solution small-angle neutron scattering (SANS), soft/hard X-ray scattering, and transmission electron microscopy (TEM) characterizations. In situ grazing incidence wide angle X-ray scattering (GIWAXS) reveals that the nucleation process is highly significant and responsible for the ultimate film morphology. Processing conditions such as temperatures, solvents, and additives were used to influence the nucleation and evolution of film morphology. The nucleation process may improve the polymer packing and phase separation. It may also translate into optimized multilength scale domains and efficient charge percolation pathways, a strong implication to control the nucleation process for the efficient separation and transportation of charges in bulk heterojunction (BHJ) devices.

14 SOLAR ENERGY↗
NASA NTRS1993

Methodology for sensitivity analysis, approximate analysis, and design optimization in CFD for multidisciplinary applications

In this study involving advanced fluid flow codes, an incremental iterative formulation (also known as the delta or correction form) together with the well-known spatially-split approximate factorization algorithm, is presented for solving the very large sparse systems of linear equations which are associated with aerodynamic sensitivity analysis. For smaller 2D problems, a direct method can be applied to solve these linear equations in either the standard or the incremental form, in which case the two are equivalent. Iterative methods are needed for larger 2D and future 3D applications, however, because direct methods require much more computer memory than is currently available. Iterative methods for solving these equations in the standard form are generally unsatisfactory due to an ill-conditioning of the coefficient matrix; this problem can be overcome when these equations are cast in the incremental form. These and other benefits are discussed. The methodology is successfully implemented and tested in 2D using an upwind, cell-centered, finite volume formulation applied to the thin-layer Navier-Stokes equations. Results are presented for two sample airfoil problems: (1) subsonic low Reynolds number laminar flow; and (2) transonic high Reynolds number turbulent flow.

Taylor, Arthur C., III↗