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At least 1,279 records · Page 71
All sourcesNASA NTRSDOE OSTI
DOE OSTI2021

Computational Fluid Dynamics Simulations to Support Efficiency Improvements in Aluminum Smelting Process

Smelting is broadly described as the extraction of a metal from its ore. In the United States, aluminum is commonly produced by smelting alumina in bauxite using the Hall-Héroult process. Optimization of equipment and processes in conventional smelting is crucial to enhancing process efficiency and productivity, is necessary for improving the techno-economic feasibility, which directly manifests as the growth of the American economy. To achieve optima, insightful data on the multiphysics phenomena that are inherent to the process must be obtained through physical investigation or high-fidelity numerical simulations. The resolution of relevant scales in time and space for smelting operations requires intensive, high-performance computing (HPC) simulations. Hostile operating conditions limit physical data acquisition to specific techniques; therefore, these data do not describe the multiscale interaction of simultaneous effects. Fortunately, in recent decades, significant advancements in computing hardware and computational methods have made the numerical resolution of such a complex process possible. In this study, a high-fidelity simulation of aluminum smelting was performed using an open-source tool, OpenFOAM, which analyzed many parameters characteristic to underlying phenomena. A multiphysics model based on the Eulerian-Eulerian multifluid approach was adopted. This model can resolve critical issues in the electrolytic smelting of aluminum, such as bubbling of carbon dioxide from the anode(s), magnetohydrodynamics from electromagnetic effects, ionic dissolution of the alumina in the electrolyte, and the evolution of thermal profiles. This study provides valuable connectivity for characteristic data that can direct the future designs of efficient smelters. A basic framework to model and simulate the smelting process using OpenFOAM is presented for user modification in keeping with process development. Of relevance to the flow field, a detailed investigation of vortices produced by bubble motion and electromagnetics is discussed, along with their impact on the evolution of thermal profiles. The predictions show small-scale vortices in the clearance between the anode and cathode caused by magnetic forces. Predictions also indicate relatively large-scale vortices in the inter-anode space resulting from carbon dioxide rising through the electrolytic flow field. The formation of vortices at the edges of anodes was shown to direct alumina charged by the feeder to the bottom of the anodes, thus preventing the entrapment of gas bubbles in the periphery of the bottom of the anode. Symmetry was observed in the location of cold spots in the electrolytic mixture in the vicinity of the feeder. Cold spots were also observed in the clearance between the anode and cathode due to the flow’s transmission of unconverted alumina to this region.

36 MATERIALS SCIENCE↗
DOE OSTI2021

Calibration of the Diffusivity Predictions of Centipede Using Approximate Bayesian Computation and Applications in Nyx (Engineering Scale) and Xolotl-MARMOT (Meso-Scale) Simulations

Fission gas evolution and release in UO 2 nuclear fuel are important fuel performance metrics and occur in several distinct stages: 1) nucleation, growth and resolution of intra-granular bubbles, 2) diffusion to grain boundaries and 3) nucleation and growth of bubbles at grain boundaries, which eventually form a connected network (percolation) enabling release of gas from grain boundaries through connections to triple junctions, grain edges or free surfaces. The NE-SciDAC project is developing several computational tools to model this problem, which are connected in a hierarchical multi-scale framework. The information transfer in the multi-scale framework is a critical step that, in addition to best-estimates, should include uncertainty quantification. Despite taking a first-principles multi-scale approach, there is a need to perform parameter calibration to ensure consistency with available experimental data. In the present study, uncertainty quantification (UQ) and parameter calibration is demonstrated for one of the lower length scale codes in the multi-scale framework (Centipede) and then the results, including instances of the propagated uncertainties, are used in other codes within the framework, specifically Nyx and Xolotl-MARMOT. We calibrated the model parameters in Centipede, a computer code used to predict diffusivities of uranium (U) and xenon (Xe) in the context of the simulation of fission gas in uranium oxide (UO 2 ) nuclear fuel. The Centipede code depends on 183 parameters, all of which are subject to uncertainty. The three data sets used in our calibration effort are taken from the literature. This data is available as a set of measurements, including measurement errors. Our goal is to calibrate a statistical model that predicts both the value of the measurement and the uncertainty associated with the measurement. We perform a Bayesian calibration of the model parameters using a dedicated approximate Bayesian computation (ABC) likelihood function. To avoid excessive computational costs, we replace the expensive Centipede simulation code by a higher-order surrogate model, constructed using only the 9 most important parameters. These important parameters are identified by a preliminary global sensitivity analysis (GSA) study. Among the important parameters are T0 (the temperature at which UO 2 is perfectly stoichiometric) and Hf_pO2 (the temperature dependence of the oxygen (O) partial pressure) that should be considered as operating conditions to be estimated along with the other parameters. We consider two different cases: one where we define one set of these operating conditions for all data sets, and one where we define distinct operating condition parameters for each data set. The Xe diffusivities predicted by the latter case show distinct features that could not be observed in the former. Next, we use the diffusivity predictions by Centipede as input to Nyx, a reduced order fuel performance code focused on gas behavior alone, in order to estimate quantities associated with inter-granular bubble formation at conditions specified by the experiments. Finally, the diffusivities obtained from the calibrated Centipede runs were used in coupled Xolotl-MARMOT simulations of intra- and inter-granular gas evolution. The results are compared to simulations using the baseline diffusivities from Turnbull et al.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2023

Advanced Multiscale Microscopy Characterization of High Burnup LWR UO 2 Before and After LOCA Testing

Previous microscopy work within the campaign has observed increased porosity coupled with subgrain formation in the mid-radial region of the fuel. However, examinations of high burnup fuel taken from multiple reactors with different operating conditions have shown that this structure can move radially inward depending on the fuel operating conditions. It is currently theorized that inter- and intragranular fission gas bubble nucleation is precursory to the grain subdivision observed in the mid-radial and central regions of the fuel. Characterization of samples after loss-of-coolant accident (LOCA) testing has revealed that these restructured regions with a high density of bubbles and subgrains pulverize during the transient test. It appears that the increase in fission gas bubbles coupled with grain subdivision renders the fuel mechanically weaker during a LOCA transient and thus susceptible to fuel fragmentation relocation and dispersal (FFRD). Work this past fiscal year has prioritized understanding this behavior by using advanced microscopy to investigate fission gas behavior in the as-irradiated and post-LOCA state. Additional work has been performed to verify the theory described above by analyzing multiple post-LOCA optical micrographs and comparing that to as-irradiated microstructural data. This document reports progress in the post-irradiation characterization of high burnup nuclear fuel with emphasis on the restructured fuel regions, particularly how microstructural features influence FFRD and fission gas release behavior in LOCA conditions.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2020

Mesoscale simulations of High Burnup Fuel Fragmentation: Applying phase-field modeling to understand high burnup fuel fragmentation during loss of coolant accident conditions

During a loss-of-coolant accident (LOCA) in a nuclear power plant, a rapid increase in temperature is experienced in the fuel. In commercial light water reactors (LWRs), the high burnup structure (HBS) forms in regions of the UO 2 fuel where local burnup is high, characterized by smaller grain sizes and large, overpressurized bubbles. During a LOCA transient, fuel in the HBS region is susceptible to fine fragmentation, where the fuel breaks up into micron-size fragments (sometimes referred to as pulverization). To better understand the mechanisms behind this phenomenon, mesoscale computational modeling using the Idaho National Laboratory code Marmot has been employed to simulate the process of HBS formation and response to a LOCA transient. The process of complete and partial HBS formation was demonstrated in prototypical LWR conditions. The simulated HBS microstructures from these simulations were passed to a phase-field model of fracture. To provide a more direct comparison with experiments, a set of experiments conducted by Studsvik on fine fragmentation/pulverization during LOCA conditions was simulated using the BISON fuel performance code. The temperature profiles from the BISON simulations were passed to a phase-field model to determine the gas bubble pressure as a function of time. These pressure histories were used in a phase-field model of fracture to determine under what conditions and in which types of bubbles fine fragmentation was likely to occur.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2024

Phase-field modeling for restructuring in the dark zone of high burnup UO 2

This report summarizes the mesoscale modeling work performed in fiscal year 2024 under the Nuclear Energy Advanced Modeling and Simulation (NEAMS) program to capture the microstructural evolution and restructuring observed in the dark regions of high burnup UO 2 nuclear fuel. This is the first attempt to realistically simulate the restructuring behavior observed in different region of a high burnup fuel. We employ a grand-potential based phase-field model to concurrently evaluate the formation of subgrains and growth of fission bubbles within the fuel. A energy-based subgrain formation criteria is introduced to simulate the restructuring process. Effect of different initial conditions and different modeling parameters are studies systematically to capture how each of these parameters influence the characteristics of the restructured fuel. It is observed that the subgrain formation begins around existing fission gas bubbles and then proceeds towards triple junctions, grain boundaries and grain interiors. It is demonstrated that restructuring is influenced by a combination of initial dislocation densities, subgrain formation rate, and temperature. Rate of restructuring increases with increase in fuel temperature. A restructuring bias is observed within the microstructure due to variation in defect accumulation among different grains. Furthermore, bubble sizes and distribution does not have a significant effect on rate of restructuring. The predicted microstructures resembles the characteristics of the restructured regions as observed in experiments. Finally, a correlation is presented that demonstrates the evolution of the restructuring volume fraction as a function of local effective burnup. This work provides a first of its kind restructuring model for darkzone that can be used by BISON for performance prediction of high burnup UO 2 fuel.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2024

Coupled Experimental/Computational Investigation of the Dynamics of Interacting Magnetized Plasmas

The interaction, or interpenetration, of magnetized plasmas of different density and/or pressure occurs in a wide variety of natural and man-made systems. Such systems include extragalactic jets propagating into the intergalactic medium, solar coronal mass ejections into background solar wind, compact toroid (CT) fueling of magnetic fusion plasmas, and jets of capsule shell impurities into DT fusion fuel, which can lead to enhanced impurity mix in inertial fusion implosions. These plasmas may take the form of jets, with open, helical magnetic structure, or plasma “bubbles” with closed magnetic fields (B-fields), such as spheromaks or CT’s. Such structures, both open and closed B-field cases, can transport heat, particles and magnetic flux or magnetic helicity into background plasma regions. For example, the origin of extragalactic magnetic fields may be due, at least in part, to transport by astrophysical jets. The goal of this proposed work was to elucidate the detailed plasma and magnetic field dynamics of high-density plasma jets (open B-field) and bubbles (closed B-field) propagating into lower density background magnetized plasma through controlled laboratory experiments and closely coupled nonlinear MHD modeling. These experiments were conducted in the HelCat (Helicon-Cathode) linear plasma device at the University of New Mexico (UNM). Plasma jets and bubbles were launched via an existing compact coaxial plasma gun, mounted on the HelCat device. This gun produced plasmas tens of cm in scale and lasting tens of microseconds, thereby allowing detailed multipoint, space- and time-resolved measurements to be made routinely. The experiments were directly modeled using the extended magnetohydrodynamic (XMHD) PERSEUS code, developed at Cornell University [23,24]. Both experimental and numerical modeling work are ongoing. The main results to date are reported here. Additional supplemental funding for one year (8/1/2019 – 7/31/2020) supported numerical investigation of photoionization processes important in many low temperature plasmas, including the HelCat device. Initial results of this modeling work is also reported.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2025

Corrosion Testing of Refractory inContact with Molten Glasses Designed for Waste Vitrification - VSL Touchpoint Matrix Glasses

It is known that the predictive life of the refractory ceramic liner of nuclear waste glass melters is conservative, as demonstrated by performance of these materials such as in the Defense Waste Processing Facility (DWPF). The motivation for this task is to maximize the useful life of the melters that will be operated at the Waste Treatment and Immobilization Plant (WTP), which will in turn minimize procurement and disposal costs and melter outage times, as well as to identify maximum loadings in the waste glass of those species that corrode melter components. This task was initiated jointly with Pacific Northwest National Laboratory (PNNL) with the objective to develop a methodology and model to enable more accurate prediction of refractory service life under prototypic conditions from laboratory-scale material corrosion tests. Refractory corrosion is generally reported as physical material loss, measured in units of distance (e.g., inch) or as physical material loss rate, measured in units of distance per time (e.g., inch/day). In post-operational melters, the refractory corrosion is measured directly, sometimes reported as corrosion depth. Crucible tests are used in the laboratory to accelerate the refractory corrosion to facilitate a meaningful measurement in a commensurate amount of time. Crucible tests are particularly useful in understanding refractory corrosion across a large glass composition space, where operational testing would be prohibitive. Some of the critical parameters that are known to influence refractory corrosion by molten glass in a crucible test are temperature, system redox, molten salt phases, glass chemistry, and test duration. The majority of data collected for Monofrax® K-3 (hereafter referred to as K-3) corrosion is from crucible tests, but a small amount comes directly from scaled and production melters. Crucible test data has been collected under varying conditions, whereas data collected from operational melters is relatively fewer and represents conditions specific to the melter campaign. The result is that the published data can be grouped and analyzed in multiple ways, not all of which are readily comparable. The Standard Test Method for Isothermal Corrosion Resistance of Refractories to Molten Glass (ASTM C621) outlines the general guidelines used across industry. That method describes a sealed, static test in which the surface area of the refractory coupon and the volume of glass are fixed. A significant portion of the crucible data pertaining to nuclear waste glasses has been collected in a modified configuration; the most notable differences being the surface area of the refractory coupon to volume of the glass and use of a method for bubbling the melt. To our knowledge, the influence of those parameters on the refractory corrosion has not been quantified. In this work, it was determined that static tests and bubbled tests would be performed. Savannah River National Laboratory (SRNL) was tasked with setting up and performing static testing while PNNL was tasked with setting up and performing bubbled testing. Initial activities were performed to establish laboratory methods that reproduce data comparable to existing data sets of K-3 refractory corrosion by low activity waste (LAW) and high-level waste (HLW) glass compositions. Later activities were focused on refining the test parameters to establish a standard test practice to be used between Laboratories and collecting additional data to be used in the enhanced waste glass model development. This document serves primarily to convey the refractory loss measurement results from corrosion testing of K-3 refractory with waste glass compositions developed for use in the WTP melters. The data will be used in the enhanced property/composition models being developed for waste glass vitrification and melter operations.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗
DOE OSTI2021

Microstructural Changes and Chemical Analysis of Fission Products in Irradiated Uranium-7 wt.% Molybdenum Metallic Fuel Using Atom Probe Tomography

Understanding the microstructural and phase changes occurring during irradiation and their impact on metallic fuel behavior is integral to research and development of nuclear fuel programs. This paper reports systematic analysis of as-fabricated and irradiated low-enriched U-Mo (uranium-molybdenum metal alloy) fuel using atom probe tomography (APT). This study is carried out on U-7 wt.% Mo fuel particles coated with a ZrN layer contained within an Al matrix during irradiation. The dispersion fuel plates from which the fuel samples were extracted are irradiated at Belgian Nuclear Research Centre (SCK CEN) with burn-up of 52% and 66% in the framework of the SELENIUM (Surface Engineering of Low ENrIched Uranium-Molybdenum) project. The APT studies on U-Mo particles from as-fabricated fuel plates enriched to 19.8% revealed predominantly γ-phase U-Mo, along with a network of the cell boundary decorated with α-U, γ’-U2Mo, and UC precipitates along the grain boundaries. The corresponding APT characterization of irradiated fuel samples showed formation of fission gas bubbles enriched with solid fission products. The intermediate burnup sample showed a uniform distribution of the typical bubble superlattice with a radius of 2 nm arranged in a regular lattice, while the high burnup sample showed a non-uniform distribution of bubbles in grain-refined regions. There was no evidence of remnant α-U, γ’-U2Mo, and UC phases in the irradiated U-7 wt.% Mo samples.

Bachhav, Mukesh↗
DOE OSTI2024

Mathematical Modeling of Multi-Phenomena Anisotropic Systems: Ejection of Primary Aerosols during the Fast Pyrolysis of Biomass

This study introduces a novel particle model for biomass fast pyrolysis, incorporating an anisotropic cylindrical particle to address mass and energy transport coupled with aerosol ejection, which previous models have overlooked. The main contribution lies in developing a model that considers aerosol generation in anisotropic cylindrical particles for the first time, addressing bubbling dynamics and bursting within the liquid phase. The population balance equation describes bubble dynamics and aerosol formation, capturing phenomena like nucleation, growth, coalescence, and bursting. The model employs the method of moments with bubble volume as an internal variable, substantially reducing computational costs by eliminating dependence on this variable. Results highlight the significant impact of anisotropy and particle size on aerosol ejection: smaller, less elongated particles experience faster heating, quicker conversion, and the increased accumulation of the liquid intermediate phase. Specifically, 1 mm diameter particles yield higher concentrations of metaplast and bio-oil aerosols, exceeding 15%, compared to concentrations below 11% for 3 mm particles. This model provides insights into aerosol structure (volume, surface area), aiding in understanding aerosol reactivity at the reactor scale.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2022

Laboratory Heat Flux Estimates of Seawater Foam for Low Wind Speeds

Laboratory experiments were conducted to measure the heat flux from seafoam continuously generated in natural seawater. Using a control volume technique, heat flux was calculated from foam and foam-free surfaces as a function of ambient humidity (ranged from 40% to 78%), air–water temperature difference (ranged from -9 °C to 0 °C), and wind speed (variable up to 3 m s-1). Water-surface skin temperature was imaged with a calibrated thermal infrared camera, and near-surface temperature profiles in the air, water, and foam were recorded. Net heat flux from foam surfaces increased with increasing wind speed and was shown to be up to four times greater than a foam-free surface. The fraction of the total heat flux due to the latent heat flux was observed for foam to be 0.75, with this value being relatively constant with wind speed. In contrast, for a foam-free surface the fraction of the total heat flux due to the latent heat flux decreased at higher wind speeds. Temperature profiles through foam are linear and have larger gradients, which increased with wind speed, while foam free surfaces show the expected logarithmic profile and show no variation with temperature. The radiometric surface temperatures show that foam is cooler and more variable than a foam-free surface, and bubble-resolving thermal images show that radiometrically transparent bubble caps and burst bubbles reveal warm foam below the cool surface layer, contributing to the enhanced variability.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2021

The impact of entrained air on ocean waves

We make a physical–mathematical analysis of the implications that the presence of a large number of tiny bubbles may have, when present, on the thin upper layer of the sea. In our oceanographic example, the bubbles are due to intense rain. It was found that the bubbles increase momentum dissipation in the near surface and affect the surface tension force. For short waves, the implications of increased vorticity are momentum exchanges between wave and mean flow and modifications to the wave dispersion relation. For the direct effect we have analyzed, the implications are estimated to be non-significant when compared to other processes of the ocean. However, we hint at the possibility that our analysis may be useful in other areas of research or practical application.

58 GEOSCIENCES↗
NASA NTRS1971

Sound propagation and absorption in foam - A distributed parameter model.

Liquid-base foams are highly effective sound absorbers. A better understanding of the mechanisms of sound absorption in foams was sought by exploration of a mathematical model of bubble pulsation and coupling and the development of a distributed-parameter mechanical analog. A solution by electric-circuit analogy was thus obtained and transmission-line theory was used to relate the physical properties of the foams to the characteristic impedance and propagation constants of the analog transmission line. Comparison of measured physical properties of the foam with values obtained from measured acoustic impedance and propagation constants and the transmission-line theory showed good agreement. We may therefore conclude that the sound propagation and absorption mechanisms in foam are accurately described by the resonant response of individual bubbles coupled to neighboring bubbles.

Manson, L.↗
NASA NTRS1972

Weldability, strength, and high temperature stability of chemically vapor deposited tungsten

Three types of CVD tungsten (fluoride-produced, chloride-produced and the combination of the two which is termed duplex) were evaluated to determine their weldability, high temperature strength and structural stability during 5000 hour exposure to temperatures of 1540 C and 1700 C. Each type of CVD tungsten could be successfully electron beam welded but the results for the chloride product were not as satisfactory as those of the other two materials. The high temperature strength behavior of the three materials did not differ greatly. However a large difference was noted for the grain growth behavior of the two basic CVD tungsten materials. Fluoride tungsten was found to be relatively stable while for the most part the grain size of chloride tungsten increased appreciably. The examination of freshly fractured surfaces with a scanning electron microscope revealed numerous bubbles in the fluoride material following its exposure to 1700 C for 5000 hours. Less severe thermal treatments produced relatively few bubbles in this material. Only at certain locations within the chloride material associated with the interruption of tungsten were bubbles noted.

Bryant, W. A.↗
NASA NTRS1972

On the mechanism of dynamic stall.

The sequence of events comprising dynamic stall of an airfoil is discussed, with emphasis on the role of the leading edge laminar separation bubble and shed vortex. A simple bubble model, based on a combination of theoretical and experimental investigations, is used to discuss the events prior to the shedding of the vortex, and provides the basis for a heuristic estimate of the delay in the occurrence of dynamic stall on a pitching airfoil. The evidence for the existence and dominant effect of the leading edge vortex on the dynamic stall required (but in most cases not presently available) for the prediction of the effects of stall on helicopter rotor blades are discussed. It is the intention of this paper to focus attention on the laminar separation bubble and the shed leading edge vortex as the dominant features of the dynamic stall mechanism in the hope of stimulating greater emphasis on these features in future dynamic stall research.

Johnson, W.↗
NASA NTRS1973

The effects of leading-edge serrations on reducing flow unsteadiness about airfoils.

High frequency surface pressure measurements were obtained from wind-tunnel tests over the Reynolds number range 1.2 x 1,000,000 to 6.2 x 1,000,000 on a rectangular wing of NACA 63-009 airfoil section. A wide selection of leading-edge serrations were also added to the basic airfoil. Under a two-dimensional laminar bubble very close to the leading edge of the basic airfoil there is a large peak in rms pressure, which is interpreted as an oscillation in size and position of the bubble. The serrations divide the bubble into segments and reduce the peak rms pressures. A low Reynolds number flow visualization test on a hydrofoil in water was also conducted. A von Karman vortex street was found trailing from the rear of the foil. Its frequency is at a much lower Strouhal number than in the high Reynolds number experiment, and is related mathematically to the airfoil trailing-edge and boundary-layer thicknesses.

Schwind, R. G.↗
NASA NTRS1973

The effects of leading-edge serrations on reducing flow unsteadiness about airfoils, an experimental and analytical investigation

High frequency surface pressure measurements were obtained from wind-tunnel tests over the Reynolds number range 1.2 times one million to 6.2 times one million on a rectangular wing of NACA 63-009 airfoil section. Measurements were also obtained with a wide selection of leading-edge serrations added to the basic airfoil. Under a two-dimensional laminar bubble very close to the leading edge of the basic airfoil there is a large apatial peak in rms pressure. Frequency analysis of the pressure signals in this region show a large, high-frequency energy peak which is interpreted as an oscillation in size and position of the bubble. The serrations divide the bubble into segments and reduce the peak rms pressures. A low Reynolds number flow visualization test on a hydrofoil in water was also conducted. A von Karman vortex street was found trailing from the rear of the foil. Its frequency is at a much lower Strouhal number than in the high Reynolds number experiment, and is related to the trailing-edge and boundary-layer thicknesses.

Schwind, R. G.↗
NASA NTRS1978

Visualization of the separation and subsequent transition near the leading edge of airfoils

A visual study was performed using the low speed smoke wind tunnels with the objective of obtaining a better understanding of the structure of leading edge separation bubbles on airfoils. The location of separation, transition and reattachment for a cylindrical nose constant-thickness airfoil model were obtained from smoke photographs and surface oil flow techniques. These data, together with static pressure distributions along the leading edge and upper surface of the model, produced the influence of Reynolds number, angle of attack, and trailing edge flap angle on the size and characteristics of the bubble. Additional visual insight into the unsteady nature of the separation bubble was provided by high speed 16 mm movies. The 8 mm color movies taken of the surface oil flow supported the findings of the high speed movies and clearly showed the formation of a scalloped spanwise separation line at the higher Reynolds number.

Arena, A. V.↗
NASA NTRS1979

Improved prediction of laminar leading edge separation

Research was conducted to provide a definite criterion for the prediction of the bubble burst on airfoils typical of those used for fighter wings. The approach taken was to correlate existing airfoil bubble burst data using various parameters at the laminar separation point. The method due to Weber was modified to provide a continuous analytic solution for the velocity distribution around the airfoil leading edge. Coupling the modified Weber method with the Stratford laminar separation prediction method leads to a universal chart giving the conditions at separation as a function of stagnation location and leading edge radius. Application of the combined method to available two-dimensional airfoil data resulted in an empirical criterion presenting the limiting local velocity gradient at separation as a function of the boundary layer momentum thickness at separation for bubble burst. The correlation leads as well to the qualitative explanation of two types of laminar stall: thin airfoil and leading edge. The validity of the correlation is demonstrated by predicting the lift coefficient and angle of attack for stall on airfoils with leading edge or trailing edge flaps.

Herring, R. N.↗