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At least 253 records · Page 14

Computer modeling of large asteroid impacts into continental and oceanic sites: Atmospheric, cratering, and ejecta dynamics

Numerous impact cratering events have occurred on the Earth during the last several billion years that have seriously affected our planet and its atmosphere. The largest cratering events, which were caused by asteroids and comets with kinetic energies equivalent to tens of millions of megatons of TNT, have distributed substantial quantities of terrestrial and extraterrestrial material over much or all of the Earth. In order to study a large-scale impact event in detail, computer simulations were completed that model the passage of a 10 km-diameter asteroid through the Earth's atmosphere and the subsequent cratering and ejecta dynamics associated with impact of the asteroid into two different targets, i.e., an oceanic site and a continental site. The calcuations were designed to broadly represent giant impact events that have occurred on the Earth since its formation and specifically represent an impact cratering event proposed to have occurred at the end of Cretaceous time. Calculation of the passage of the asteroid through a U.S. Standard Atmosphere showed development of a strong bow shock that expanded radially outward. Behind the shock front was a region of highly shock compressed and intensely heated air. Behind the asteroid, rapid expansion of this shocked air created a large region of very low density that also expanded away from the impact area. Calculations of the cratering events in both the continental and oceanic targets were carried to 120 s. Despite geologic differences, impacts in both targets developed comparable dynamic flow fields, and by approx. 29 s similar-sized transient craters approx. 39 km deep and approx. 62 km across had formed. For all practical purposes, the atmosphere was nearly completely removed from the impact area for tens of seconds, i.e., air pressures were less than fractions of a bar out to ranges of over 50 km. Consequently, much of the asteroid and target materials were ejected upward into a near vacuum. Effects of secondary volcanism and return of the ocean over hot oceanic crater floor could also be expected to add substantial solid and vaporized material to the atmosphere, but these conditions were not studied.

Roddy, D. J.↗

Development of Multiresolution Capabilities for the Holistic Energy Resource Optimization Network (HERON) tool A progress update

INL researchers work on technoeconomic analyses for integrated energy systems (IES) using the Framework for Optimization of ResourCes and Economics (FORCE). Within FORCE, researchers use the Holistic Energy Resource Optimization Network (HERON) tool to conduct optimization of grid portfolios under uncertain market conditions. These optimizations determine optimal capacities for all IES components and strategies for resource dispatch which maximize some economic metric (e.g., net present value). Resource dispatch occurs on finer timescales (typically hours) and thus are asked to respond to a given time series (e.g. hourly load demand profiles for a grid, or pre-determined electricity prices). Volatile and complex bidding dynamics as well as poorly forecasted weather events within deregulated markets add uncertainty to the time series; FORCE can address this uncertainty by training a reduced order model on historical time series and generate unique synthetic time series which represent individual scenarios or realizations of the market. The IES configuration can be simulated under these different sampled realizations and a stochastic optimization is conducted which optimizes the expected value of the desired economic metric. The training of a synthetic time series generator is limited by the chosen time resolution; dynamics can occur on different time scales. Seasonal demand trends can dominate faster dynamical events (such as power outages from certain sectors or severe weather events) which might not get captured correctly by the trained model. In this report, we investigate different ways of addressing the training and generation of time series on multiple time scales using three main algorithms: wavelet decomposition, dynamic mode decomposition, and generative adversarial networks for time series. We demonstrate a time series analysis that yields information on not just the frequency space but also temporal space: where a fast Fourier transform can provide what frequencies dominate, the new algorithms can provide when the frequencies dominate as well. These analyses can help improve IES optimization by allowing researchers to couple simulations at different timescales when it is most needed - seasonal, day-ahead, and real time optimization - with greater computational efficiency. Future work will include implementation of a subset of the proposed algorithms into the FORCE toolset and application of these analyses into multiple timescale optimization.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

Full-Scale Crash Test and Finite Element Simulation of a Composite Prototype Helicopter

A full-scale crash test of a prototype composite helicopter was performed at the Impact Dynamics Research Facility at NASA Langley Research Center in 1999 to obtain data for validation of a finite element crash simulation. The helicopter was the flight test article built by Sikorsky Aircraft during the Advanced Composite Airframe Program (ACAP). The composite helicopter was designed to meet the stringent Military Standard (MIL-STD-1290A) crashworthiness criteria and was outfitted with two crew and two troop seats and four anthropomorphic dummies. The test was performed at 38-ft/s vertical and 32.5-ft/s horizontal velocity onto a rigid surface. An existing modal-vibration model of the Sikorsky ACAP helicopter was converted into a model suitable for crash simulation. A two-stage modeling approach was implemented and an external user-defined subroutine was developed to represent the complex landing gear response. The crash simulation was executed with a nonlinear, explicit transient dynamic finite element code. Predictions of structural deformation and failure, the sequence of events, and the dynamic response of the airframe structure were generated and the numerical results were correlated with the experimental data to validate the simulation. The test results, the model development, and the test-analysis correlation are described.

Jackson, Karen E.↗

Solar wind dynamic pressure variations and possible ground signatures of flux transfer events

The effects of a series of solar wind dynamic pressure pulses are followed through the solar wind, across the bow shock and magnetosheath, into the magnetosphere, and down to the dayside ionosphere. Each pressure pulse had an intrinsic solar wind origin, i.e., was not generated by processes occurring at the earth's bow shock. Both upstream and downstream of the earth's bow shock, the pulses were identified by depressed magnetic field strengths and enhanced plasma densities. The pulses compressed the magnetosheath and magnetosphere, causing satellites in the magnetosphere to briefly observe enhanced magnetic field strengths, and/or enter the low-latitude boundary layer or magnetosheath. Satellites already in the magnetosheath observed a brief burst of enhanced magnetosheath flow caused by the relative inward motion of magnetosheath flow patterns. Alfven and fast mode compressional waves propagated rapidly down to the polar ionosphere, where they produced transient ionospheric flows at latitudes equatorward of the convection reversal boundary. The flow patterns moved westward around the auroral oval.

Sibeck, D. G.↗

Sensitivity of puff dynamics and airborne droplet nuclei distribution to variations in violent expiration events

Here, we use large eddy simulations to investigate the puff and droplet dynamics from violent expiratory events such as coughs and sneezes in the first few seconds following an ejection. For each of the eleven simulations considered, over 60,000 droplets are ejected and individually tracked using the point-particle Euler–Lagrange approach. We test the sensitivity of the puff and droplet dynamics to various parameters including the ejection volume, momentum, and orientation. We also explore the effect of the mouth shape on the aforementioned dynamics by considering elliptical and circular inlet cross-sections. The results from the simulations compare favorably with a recent theoretical framework put forth by Balachandar et al. in terms of the puff size and propagation velocity. More importantly however, the theory is able to accurately predict the number and size spectra of the potentially virus-laden droplet nuclei that remain airborne within the puff. We observe that the ejection angle and mouth shape do not significantly affect the puff and droplet dynamics. Additionally, we quantify the carrying capacity of the detached puff portions in terms of the number and size spectra of droplets/droplet nuclei suspended within.

59 BASIC BIOLOGICAL SCIENCES↗

Simulation of Compound Flooding Using River‐Ocean Two‐Way Coupled E3SM Ensemble on Variable‐Resolution Meshes

Abstract Coastal zone compound flooding (CF) can be caused by the interactive fluvial and oceanic processes, particularly when coastal backwater propagates upstream and interacts with high river discharge. The modeling of CF is limited in existing Earth System Models (ESMs) due to coarse mesh resolutions and one‐way coupled river‐ocean components. In this study, we present a novel multi‐scale coupling framework within the Energy Exascale Earth System Model (E3SM), integrating global atmosphere and land with interactively coupled river and ocean models using different meshes with refined resolutions near the coastline. To evaluate this framework, we conducted ensemble simulations of a CF event (Hurricane Irene in 2011) in a Mid‐Atlantic estuary. The results demonstrate that the novel E3SM configuration can reasonably reproduce river discharge and sea surface height variations. The two‐way river‐ocean coupling improves the representation of coastal backwater effects at the terrestrial‐aquatic interface that are caused by the combined actions of tide and storm surge during the CF event, thus providing a valuable modeling tool for better understanding the river‐estuary‐ocean dynamics in extreme events under climate change. Notably, our results show that the most significant CF impacts occur when the highest storm surge generated by a tropical cyclone meets with a moderate river discharge. This study highlights the state‐of‐the‐art advancements developed within E3SM for simulating multi‐scale coastal processes.

54 ENVIRONMENTAL SCIENCES↗

Compound Mesoscale Convective Systems and Low‐Pressure Systems in Tropical Monsoon Regions: Assessing Their Meteorology and Precipitation

Mesoscale convective systems (MCS) and low-pressure systems (LPS) are both strongly associated with precipitation across the regions where they occur, particularly within global monsoon systems; however, their co-occurrence and its relationship to precipitation have not been systematically examined. Here, we use LPS and MCS trackers to detect compound MCS and LPS events in five monsoon regions and assess the association of this co-occurrence with anomalies of winds, precipitation, and other atmospheric variables. Additionally, we investigate the spatial distribution of precipitating MCS and LPS events. Our results show that most (∼60%) MCS and LPS co-occurrences are located in the lower latitudes, where they contribute up to 40% of annual precipitation. We find that compound events generally produce more extreme precipitation than MCS-only or LPS-only events. Furthermore, our assessment of the synoptic and mesoscale composites reveals that the underlying dynamics of compound events exhibit anomalously positive convective available potential energy and an anomalously low-pressure within the location of the event. In terms of the synoptic environment of the features, the compound MCS and LPS events are associated with inverted troughs in three out of five monsoon locations assessed.

Environmental sciences↗

Smart Charging for Electric Ride-Hailing Vehicles using Renewables: A San Francisco Case Study

Charging large fleets of electric ride-hailing vehicles (ERVs) is a complex matter that could serve different objectives: lower carbon dioxide emissions, lower monetary expenditures, or maximize solar photovoltaics (PV) energy consumption. Currently, it is unclear how each of those objectives could impact the business and performance of a ride-hailing fleet. In order to fill this gap, this article employs a dynamic transportation model: a smart charging simulation that combines agent-based, discrete-event, and system dynamic modelling by comparing the above-mentioned objectives in separate scenarios. The results show that each scenario successfully manages to shift between 34% and 87% of all load to hours of the day when the objectives of those scenarios are met. Therefore, in comparison to the baseline, smart charging can save between 5% and 26% of monthly emissions and between 4% and 57% of monthly expenditures. The solar PV scenario, however, results in the highest savings, while ensuring profitable economics via net metering in the short- as well as long term. Finally, the sensitivity analysis points to important trade-offs between several fleet performance metrics. The article concludes by giving business and policy recommendations for maximising the economic, energy and environmental efficiency of large ERV fleets.

ADVANCED PROPULSION SYSTEMS,SOLAR ENERGY↗

Computer Science Research Needs for Parallel Discrete Event Simulation (PDES)

Historically, scientific computing efforts have demonstrated the clear need for, and effective use of, supercomputing with traditional time-stepped simulations. Nevertheless, there are several areas in the mission spaces of the U.S. Department of Energy and other agencies waiting to tap advanced computing research using a different, discrete event style of modeling, simulation, and analysis. These span a wide spectrum of applications including energy grid resilience, urban planning and policy, transportation science, building technologies, emergency response and planning, environmental impact analysis, computational epidemiology, Internet communications, cyber security, and cyber-physical systems, to name only a few. Even within traditional scientific applications, the role of discrete event modes of execution is increasing in the form of new event-based mathematical solvers such as quantized state integration methods and discrete-continuous hybrid system solvers. Co-design of advanced supercomputing hardware systems is another area that exploits discrete event simulation at its core for effective analyses. Complex systems, entity behaviors and interconnections play a significant role in all these applications, which are mapped to large-scale models with discrete event formulations. To make advancements in all the aforementioned scientific areas, many technical aspects need to be more thoroughly studied and deeply understood in parallel discrete event simulation (PDES). The unique dynamics inherent in a discrete event modeling approach, by their very nature, intersect and influence the entire stack of the computing system, including (a) the unique nature of the instruction sets exercised in PDES workloads without a predominance of high-precision floating point operations, (b) virtual time-constrained multi-threaded execution of many logical processes per processor, (c) extremely variable and difficult to predict network traffic characteristics, (d) interfaces and inter-dependencies with machine learning and artificial intelligence codes at higher software layers, and (e) highly challenging load balancing needs, especially in effectively accounting for accelerated/extremely heterogeneous computing in current and future high-performance computing systems. Efficient and accurate parallel execution of PDES workloads is also dominated by challenges in dealing with their asynchronous concurrency fundamentally present at the model level. Conservative synchronization, optimistic/speculative synchronization, and their hybrid schemes open new questions in fundamental computer science with respect to reversibility of computation and prediction (lookahead) of behaviors inherent within model codes. On the implementation front, there are relatively few scalable, general-purpose parallel discrete event simulators in the world, and even fewer have been studied on emerging hardware platforms. To enable scientific advances using PDES, the research needs in computer science must also be pursued and met in the intersection of the algorithmic and hardware-aware aspects of scalable PDES engines. This report is aimed at capturing a computer science-oriented view of this important area of research in PDES, presenting a sample of important applications with their inherent discrete event technology elements. Needs are outlined in core areas of parallel discrete event research as well as cross-cutting directions in computer science research that positively impact scientific advancements across several important application areas. A selection of priority research opportunities in advanced computing for PDES is identified to serve as reference for key research topics and their order of importance for scientific advancements.

97 MATHEMATICS AND COMPUTING↗

Assessment of Model Outcomes Between the Integrated Medical Model (IMM) and the Medical Extensible Dynamic Probabilistic Risk Assessment Tool (MEDPRAT)

The Medical Extensible Dynamic Probabilistic Risk Assessment Tool (MEDPRAT) is a computational model that provides human health and medical risk predictions for crewed spaceflight missions. MEDPRAT utilizes discrete event modeling and dynamic probabilistic simulation to predict critical mission outcomes (total medical events, crew health index, quality time lost, loss of crew life, removal to definitive care), condition occurrences, and resource consumption. Input parameters for MEDPRAT include crew attributes (e.g., sex), types of mission activities (e.g., whether and where crew members perform an extravehicular activity (EVA)), available resources, treatment information, and probability distributions for medical conditions. As an evolution of the Integrated Medical Model (IMM), MEDPRAT provides enhanced capabilities and higher fidelity, and incorporates more appropriate assumptions for long-duration spaceflight. IMM is the currently accepted standard for quantifying spaceflight mission medical risk in NASA operations that uses a probabilistic risk assessment (PRA) approach. MEDPRAT builds on the same logical foundation as IMM but implements the model architecture through highly optimized Monte Carlo sampling methods. An analysis is performed comparing the outputs from IMM with those from MEDPRAT V1.0 and V2.0 for the same reference missions in order to quantify similarities and differences in the model outcomes. The juxtaposition between IMM and MEDPRAT V1.0 and 2.0 shown in this report demonstrates that these two models generate very similar results; where differences in outcomes are shown, these are in accordance with the underlying assumptions and differences in the model architectures. This validation effort further establishes the credibility and reliability of the MEDPRAT software.

Matthew T Prelich↗

Merging Analytic Collaborative Frameworks with New Observing Strategies Toward a Digital Twin: Earth – Episodic Pulse Event Impacts on Ocean Carbon Cycle as an Example

Virtual representations of the Earth will allow us to address some of the most critical environmental issues of our time. Here, we show the first steps toward representation of riverine, estuarine, and coastal carbon processes to enable scenario driven “what-if” analyses of the carbon system and human footprint. Excess sediment and nutrient runoff from land-based human activities impact water quality and can pose serious threats to coastal and marine ecosystems. Episodic pulse events, such as extreme precipitation events, can increase the amount of nutrients entering estuaries and coastal regions, potentially leading to large phytoplankton blooms followed by anoxic conditions. Consequences of coastal runoff are predicted to increase with the higher intensity and frequency of extreme events. Beyond the threat to coastal ecosystems, recent findings suggest these episodic pulses might play a significant role for biological production influencing regional and global carbon fluxes and budgets. An improved understanding of these events through optimal, dynamic observing strategies will increase our knowledge of the land-ocean continuum and how regional events and nutrient fluxes affect the carbon cycle and ocean ecosystem. This conceptual framework enables focused science investigations by pairing data analytics and artificial intelligence tools (otherwise termed an Analytic Center Framework, ACF) with targeted measurement acquisition through distributed sensing and intelligent asset tasking (or New Observing Strategies, NOS). This NOS and ACF iterative approach acquires and integrates complementary and coincident satellite, in-situ and model data to build a more complete and in-depth picture of science phenomena. Specifically, Apache Science Data Analytic Platform (SDAP) is extended to incorporate relevant datasets for data access, harmonized analysis, and anomaly detection. When conditions are met for a likely pulse event, NASA’s D-SHIELD (Distributed Spacecraft with Heuristic Intelligence to Enable Logistical Decisions) tool is triggered to optimize asset overpass frequency and schedule observations for persistent monitoring. Targeted data is ingested by SDAP for enhanced investigation via iterative analysis until the trigger criteria is no longer met - steps toward a digital twin.

Laura Rogers↗

Analysis of Impact Induced Damage and its Effect on Structural Integrity of Space Flight Composite Overwrapped Pressure Vessels

The objective of this research work has been to provide analytical background and support to the ongoing experimental program at NASA, White Sands Test Facility, involving testing composite overwrapped pressure vessels (COPV) for impact damage and cyclic pressurization. Preliminary theoretical basis, including the governing equations for a shallow shell subjected to internal pressure, has been established. Effects of the Griffith type cracks on the structural integrity of the cylindrical vessel were evaluated by methods of Fracture Mechanics. The results indicate that the effective mass of the pressure vessel is an important factor influencing the response to impact events. We also have found that the material properties of the target, contained in the constitutive equations of the composite attached to the Aluminum liner, dominate the impact event in the low velocity range, the material properties become less important, while the target mass distribution and the impactor mass become more significant as the velocity of the impactor increases. Therefore, at high-velocity impact it is not only the kinetic energy of the impactor but also its mass which has a significant effect on the dynamics of the event, and consequently on the induced damage. This work also suggests a methodology for an assessment of the rate of loading effects on the degradation of the material toughness associated with a high-velocity impact where the rate effects become significant. To model the rate dependence of the material response a viscoelastic-plastic constitutive equations were assumed, and on this basis predictions are made regarding the rate dependent material resistance curve. Other dynamic phenomena associated with the impact event have been treated in the framework of the Computational Mechanics using the courtesy of Prof. P. Guebelle and his graduate student at University of Illinois at Urbana-Champaign who have an access to a super-fast computer located on their campus. Finally, the guidelines for a follow-up research program are provided in the body of this report. They address three major areas: theoretical research, numerical studies, and further experimental work.

Wnuk, Michael P.↗

Predicting rare events using neural networks and short-trajectory data

Estimating the likelihood, timing, and nature of events is a major goal of modeling stochastic dynamical systems. When the event is rare in comparison with the timescales of simulation and/or measurement needed to resolve the elemental dynamics, accurate prediction from direct observations becomes challenging. In such cases a more effective approach is to cast statistics of interest as solutions to Feynman-Kac equations (partial differential equations). Here, we develop an approach to solve Feynman-Kac equations by training neural networks on short-trajectory data. Our approach is based on a Markov approximation but otherwise avoids assumptions about the underlying model and dynamics. This makes it applicable to treating complex computational models and observational data. Additionally, we illustrate the advantages of our method using a low-dimensional model that facilitates visualization, and this analysis motivates an adaptive sampling strategy that allows on-the-fly identification of and addition of data to regions important for predicting the statistics of interest. Finally, we demonstrate that we can compute accurate statistics for a 75-dimensional model of sudden stratospheric warming. This system provides a stringent test bed for our method.

97 MATHEMATICS AND COMPUTING↗

Mesospheric Dynamical Changes Induced by the Solar Proton Events in October-November 2003

The very large solar storms in October-November 2003 caused solar proton events (SPEs) at the Earth that impacted the upper atmospheric polar cap regions. The Thermosphere Ionosphere Mesosphere Electrodynamic General Circulation Model (TIME-GCM) was used to study the atmospheric dynamical influence of the solar protons that occurred in Oct-Nov 2003, the fourth largest period of SPEs measured in the past 40 years. The highly energetic solar protons caused ionization, as well as dissociation processes, and ultimately produced odd hydrogen (HOx) and odd nitrogen (NOy). Significant short-lived ozone decreases (10-70%) followed these enhancements of HOx and NOy and led to a cooling of most of the lower mesosphere. This cooling caused an atmospheric circulation change that led to adiabatic heating of the upper mesosphere. Temperature changes up to plus or minus 2.6 K were computed as well as wind (zonal, meridional, vertical) perturbations up to 20-25% of the background winds as a result of 22 the solar protons. The solar proton-induced mesospheric temperature and wind perturbations diminished over a period of 4-6 weeks after the SPEs. The Joule heating in the mesosphere, induced by the solar protons, was computed to be relatively insignificant for these solar storms with most of the temperature and circulation perturbations caused by ozone depletion in the sunlit hemisphere.

Jackman, Charles H.↗

REACTER: A Versatile Tool for Large-Scale Reactive Molecular Dynamics

Accurately describing reactive events over long length and time scales remains a grand challenge of computational materials science. REACTER is a general protocol for modeling chemical reactions using classical force fields, and is implemented in the popular molecular dynamics software LAMMPS. REACTER has a growing user base and has been used as a model-building tool for a variety of materials, including thermoplastics, thermosets, glassy materials and composites. The method has also been applied to accelerated modeling of reversible chemical reactions, such as the formation of electrochemical components for batteries. Recently, the REACTER protocol has received some major upgrades to enhance its ability to predict when reactions occur and to make it easier to use. Force field parameters can now be automatically assigned to newly created bonds, angles and other interactions. Advanced reaction constraints have also been added, including an Arrhenius constraint to enforce an effective activation energy, a root-mean-square-deviation option for complex geometrical constraints, and a constraint based on the total potential energy of the atoms involved in a reactive site. This potential energy constraint allows for the accurate reproduction of DFT-based tight-binding (DFTB3) predicted bond dissociation curves for mechanically induced bond breaking.

polymer simulations, molecular dynamics↗

Enhanced dynamic equivalent identification method of large-scale power systems using multiple events

The increasing complexity of the interconnected power system makes high-fidelity dynamic simulation models computationally more intensive. To improve computation efficiency, model reduction techniques have been investigated to only preserve the dynamics in a limited area of interest (study area), while deriving equivalent representation for the external area. For this purpose, a measurement-based reduction approach using system identification techniques has been previously proposed. Accordingly, external areas are represented by dynamic equivalent loads using transfer function estimation. In this paper, in order to enhance the accuracy of the reduced model in preserving dynamics of the study area, multiple “grid” events of different types and at different locations are considered for identifying the parameters of the equivalent loads. Additionally, case studies are carried out in the NPCC 140-bus system. Comparisons are made between multiple events training and single event training, highlighting the advantages of the proposed method in providing a better representation of the grid dynamics under different operating conditions.

24 POWER TRANSMISSION AND DISTRIBUTION↗

Enhanced Dynamic Equivalent Identification Method of Large-Scale Power Systems Using Multiple Event

The increasing complexity of the interconnected power system makes high-fidelity dynamic simulation models computationally more intensive. To improve computation efficiency, model reduction techniques have been investigated to only preserve the dynamics in a limited area of interest (study area), while deriving equivalent representation for the external area. For this purpose, a measurement-based reduction approach using system identification techniques has been previously proposed. In that case, external areas are represented by dynamic equivalent loads using transfer function estimation. In this paper, in order to enhance the accuracy of the reduced model in preserving dynamics of the study area, multiple “grid” events of different types and at different locations are considered for identifying the parameters of the equivalent loads. Case studies are carried out in the NPCC 140-bus system. Comparison are made between multiple events training and single event training, highlighting the advantages of the proposed method in providing a better representation of the grid dynamics under different operating conditions.

Xue, Yaosuo↗

Analysis of the development of dynamic stall based on oscillating airfoil experiments

The effects of dynamic stall on airfoils oscillating in pitch were investigated by experimentally determining the viscous and inviscid characteristics of the airflow on the NACA 0012 airfoil and on several leading-edge modifications. The test parameters included a wide range of frequencies, Reynolds numbers, and amplitudes-of-oscillation. Three distinct types of separation development were observed within the boundary layer, each leading to classical dynamic stall. The NACA 0012 airfoil is shown to stall by the mechanism of abrupt turbulent leading-edge separation. A detailed step-by-step analysis of the events leading to dynamic stall, and of the results of the stall process, is presented for each of these three types of stall. Techniques for flow analysis in the dynamic stall environment are discussed. A method is presented that reduces most of the oscillating airfoil normal force and pitching-moment data to a single curve, independent of frequency or Reynolds number.

Carr, L. W.↗