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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 451 records · Page 25
All sourcesNASA NTRSDOE OSTI
NASA NTRS1997

Large Scale Turbulent Structures in Supersonic Jets

Jet noise is a major concern in the design of commercial aircraft. Studies by various researchers suggest that aerodynamic noise is a major contributor to jet noise. Some of these studies indicate that most of the aerodynamic jet noise due to turbulent mixing occurs when there is a rapid variation in turbulent structure, i.e. rapidly growing or decaying vortices. The objective of this research was to simulate a compressible round jet to study the non-linear evolution of vortices and the resulting acoustic radiations. In particular, to understand the effect of turbulence structure on the noise. An ideal technique to study this problem is Direct Numerical Simulations(DNS), because it provides precise control on the initial and boundary conditions that lead to the turbulent structures studied. It also provides complete 3-dimensional time dependent data. Since the dynamics of a temporally evolving jet are not greatly different from those, of a spatially evolving jet, a temporal jet problem was solved, using periodicity ill the direction of the jet axis. This enables the application of Fourier spectral methods in the streamwise direction. Physically this means that turbulent structures in the jet are repeated in successive downstream cells instead of being gradually modified downstream into a jet plume. The DNS jet simulation helps us understand the various turbulent scales and mechanisms of turbulence generation in the evolution of a compressible round jet. These accurate flow solutions will be used in future research to estimate near-field acoustic radiation by computing the total outward flux across a surface and determine how it is related to the evolution of the turbulent solutions. Furthermore, these simulations allow us to investigate the sensitivity of acoustic radiations to inlet/boundary conditions, with possible application to active noise suppression. In addition, the data generated can be used to compute various turbulence quantities such as mean velocities, turbulent stresses, etc. which will aid in turbulence modeling. This report will be presented in two chapters. The first chapter describes some work on the linear stability of a supersonic round jet and the implications of this for the jet noise problem. The second chapter is an extensive discussion of numerical work using the spectral method which we use to solve the compressible Navier-Stokes equations to study turbulent jet flows. The method uses Fourier expansions in the azimuthal and streamwise direction and a 1-D B-spline basis representation in the radial direction. The B-spline basis is locally supported and this ensures block diagonal matrix equations which can be solved in O(N) steps. This is a modification of a boundary layer code developed by Robert Moser. A very accurate highly resolved Direct Numerical Simulation (DNS) of a turbulent jet flow is produced.

Rao, Ram Mohan↗
NASA NTRSDate not supplied

Achieving Equilibrium for Dense, Integrated, Vehicle Navigation

Drone usage has proliferated in recent years with many applications that have market-changing potential. Applications that include parcel delivery, wildlife protection, precision farming, law enforcement, and industrial inspection, just to name a few. In this paper, the term drone is used to mean both Unmanned Aerial Vehicle and small Unmanned Aircraft System vehicles. Flight infrastructure can currently only support a few thousand aircraft flying over the United States National Airspace System (NAS) at any given time. A delay atone airport sends ripple effects through the system, causing more delays and missed connections. Once regulations and safety policies are put in place to allow for the widespread use of unmanned drones, the number of aircraft in the NAS is expected to skyrocket to millions, potentially congesting the airspace resulting in possible separation violations. In air traffic control, separation is the concept of keeping an “ownship” aircraft outside a minimum distance from “intruder” aircraft to reduce the risk of the aircraft colliding, as well as preventing accidents due to secondary factors, such as wake turbulence. Maintaining proper separation is a safety critical property for drones in the airspace. This paper addresses separation in time and in distance for high volume corridors (en-route) and lanes(on ground). The requirements and necessary conditions for maintaining proper separation and reaching maximum throughput for a given corridor/lane are addressed assuming unidirectional corridors/lanes where an aircraft arrives from one side and departs from the opposite side. Simulation results are presented that show the presented solution guarantees a set of drones to reach the equilibrium state by adjusting their speed based on their distance to the aircraft in front of them. The equilibrium state is defined as a state when a set of n aircraft moving at a relatively constant speed and uniform spacing from each other in a congested system. A congested system is defined as a state when the aircraft cannot move at their maximum allowed speed. Unlike existing centralized and pre-planned approaches, the proposed solution is fully distributed and enables autonomous aircraft to decide to adjust their speed and distance with respect to the preceding aircraft, dynamically. Simulation results are presented that assess the feasibility of the approach using a large number of drones and evaluate the scalability of the proposed solution.

Mahyar R. Malekpour↗
DOE OSTI2025

Modular Processing of Flare Gas for Carbon Nanoproducts

This project demonstrated the technical viability and economic promise of a modular system for converting flared natural gas into valuable carbon nanoproducts (CNPs) through catalytic chemical vapor deposition (CVD). All major project milestones were successfully completed, including reactor design and commissioning, catalyst development, process optimization, technoeconomic analysis, and application testing in concrete systems. The overarching goal was to create a scalable, field-deployable process that valorizes stranded methane by producing high-value carbon materials for use in cementitious composites. At the lab scale, the team designed and built a fluidized bed reactor optimized for use with silica fume-supported nickel catalysts synthesized via atomic layer deposition (ALD). A statistically designed sintering study enabled precise tuning of nickel nanoparticle size, identifying the influence of oxygen partial pressure, time, and temperature on catalyst morphology and performance. These insights allowed the team to target catalyst conditions that maximize carbon nanofilament growth. Subsequent CVD experiments achieved up to 31.8 wt% carbon deposition under optimized conditions, with TEM confirming the presence of nanofilament structures and sustained hydrogen evolution during reaction. Reactor upgrades and empirical fluidization studies supported the development of reliable, repeatable experimental protocols. The modular pilot-scale skid reactor was fully constructed, instrumented, and commissioned. Capable of operating at 675–800°C and pressures up to 290 psig, the system was designed for continuous operation at a carbon production rate of 1 kg/hr. Initial demonstration runs confirmed solids handling, thermal control, and system leak-tightness, although a critical reactor component (the downfeed tube) was inadvertently omitted during final assembly. This omission limited gas–solid contact and prevented meaningful carbon deposition during pilot-scale CVD runs. Nonetheless, the system operated safely under design conditions, and the root cause of performance limitations was clearly identified. Complementary work on UHPC formulations demonstrated that small additions of carbon nanoproducts, including those derived from flare gas, can significantly enhance mechanical performance while preserving workability. A comprehensive study of CNF dispersion techniques and mix design optimization led to a clear protocol for integrating these nanomaterials into concrete. Incorporation of CNPs improved flexural toughness and reduced porosity, supporting their use in high-performance infrastructure applications. A technoeconomic analysis (TEA) confirmed that this process can produce CNP-loaded catalyst material at a levelized cost below $\$$7/kg across a range of catalyst loadings and reaction yields. With estimated market values for the carbon composite product ranging from $\$$14 to over $\$$60/kg, and the ability to blend CNPs into concrete at sub-percent levels with less than 10% added cost, the system presents a compelling economic case. While additional engineering work is needed to optimize fluidization and heat transfer at scale, this project establishes a strong foundation for commercial development. The process is not only technically sound but also economically promising, representing a viable pathway for flare gas mitigation through modular carbon nanomaterial production.

03 NATURAL GAS↗
DOE OSTI2024

Molecular Dynamics Simulation of Complex Reactivity with the Rapid Approach for Proton Transport and Other Reactions (RAPTOR) Software Package

Simulating chemically reactive phenomena such as proton transport on nanosecond to microsecond and beyond time scales is a challenging task. Ab initio methods are unable to currently access these time scales routinely, and traditional molecular dynamics methods feature fixed bonding arrangements that cannot account for changes in the system’s bonding topology. The Multiscale Reactive Molecular Dynamics (MS-RMD) method, as implemented in the Rapid Approach for Proton Transport and Other Reactions (RAPTOR) software package for the LAMMPS molecular dynamics code, offers a method to routinely sample longer time scale reactive simulation data with statistical precision. RAPTOR may also be interfaced with enhanced sampling methods to drive simulations toward the analysis of reactive rare events, and a number of collective variables (CVs) have been developed to facilitate this. Key advances to this methodology, including GPU acceleration efforts and novel CVs to model water wire formation are reviewed, along with recent applications of the method which demonstrate its versatility and robustness.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
NASA NTRS1973

High performance S-band horn antennas for radiometer use

Horn antennas of four types: pyramidal corrugated, conical corrugated, pyramidal dual mode and conical dual mode, have been constructed and evaluated for use as S-band radiometer antennas. Each of the structures is described and radiation patterns and impedance and resistive loss measurements including a layer of foreign material on a thin radome, are presented. A precision method for determining reflection losses is described using a multiprobe reflectometer technique. The same technique is also applied to the measurement of resistive losses by closing the ends of the antennas with short circuit plates and determining the losses from an accurate measurement of the reflection coefficient. The radiation patterns were recorded with the aid of a real-time digital computer. The stored patterns were then processed to yield gain and beam efficiency. It was concluded that it is possible to design a highly efficient antenna for radiometer use and to measure its parameters precisely. However, it was found that it is necessary to modify the conventional definition of beamwidth somewhat if this term is to be meaningful for radiometer applications.

Caldecott, R.↗
DOE OSTI2024

Device response principles and the impact on energy resolution of epitaxial quantum dot scintillators with monolithic photodetector integration

Abstract Epitaxial quantum dot (QD) scintillator crystals with picosecond-scale timing and high light yield have been created for medical imaging, high energy physics and national security applications. Monolithic photodetector (PD) integration enables the sensing of photons generated within the waveguiding crystal and allows a wide range of scintillator-photodetector coupling geometries. Until recently, these doubly novel devices have suffered from complex, high variance responses to monoenergetic sources which significantly reduces their precision and accuracy. The principles governing the overall device response have now been discerned and embodied by an expression derived within a geometrical optics framework which considers optical properties, surface roughness and photodetector coupling geometry. Response variation due to these factors was sufficiently reduced to obtain material-related energy resolution values of 2.4% with alpha particles. These findings place energy resolution alongside luminescence timescale, photon yield, and radiation hardness as outstanding properties of these engineered materials.

36 MATERIALS SCIENCE↗
DOE OSTI2022

The scientific potential and technological challenges of the High-Luminosity Large Hadron Collider program

Here, we present an overview of the High-Luminosity (HL-LHC) program at the Large Hadron Collider (LHC), its scientific potential and technological challenges for both the accelerator and detectors. The HL-LHC program is expected to start circa 2027 and aims to increase the integrated luminosity delivered by the LHC by an order of magnitude at the collision energy of 14 TeV. This requires upgrades to the injector system, accelerator complex and luminosity levelling. The two experiments, ATLAS and CMS, require substantial upgrades to most of their systems in order to cope with the increased interaction rate, and much higher radiation levels than at the current LHC. We present selected examples based on novel ideas and technologies for applications at a hadron collider. Both experiments will replace their tracking systems. We describe the ATLAS pixel detector upgrade featuring novel tilted modules, and the CMS Outer Tracker upgrade with a new module design enabling use of tracks in the level-1 trigger system. CMS will also install state-of-the-art highly segmented calorimeter endcaps. Finally, we describe new picosecond precision timing detectors of both experiments. In addition, we discuss how the upgrades will enhance the physics performance of the experiments, and solve the computing challenges posed by the expected large data sets. The physics program of the HL-LHC is focused on precision measurements probing the limits of the Standard Model (SM) of particle physics and discovering new physics. We present a selection of studies that have been carried out to motivate the HL-LHC program. A central topic of exploration will be the characterization of the Higgs boson. The large HL-LHC data samples will extend the sensitivity of searches for new particles or new interactions whose existence has been hypothesized in order to explain shortcomings of the SM. Finally, we comment on the nature of large scientific collaborations.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
NASA NTRS2006

UWB Tracking System Design for Lunar/Mars Exploration

This paper describes a design effort for a prototype ultra-wideband (UWB) tracking system that is currently under development at NASA Johnson Space Center (JSC). The system is being studied for use in tracking of lunar/Mars rovers during early exploration missions when satellite navigation systems are not available. The UWB technology is exploited to implement the tracking system due to its properties such as high data rate, fine time resolution, low power spectral density, and multipath immunity. A two-cluster prototype design using commercially available UWB products is proposed to implement the Angle Of Arrival (AOA) tracking methodology in this research effort. An AOA technique using the Time Difference Of Arrival (TDOA) information is utilized for location estimation in the prototype system, not only to exploit the precise time resolution possible with UWB signals, but also to eliminate the need for synchronization between the transmitter and the receiver. After the UWB radio at each cluster is used to obtain the TDOA estimates from the UWB signal sent from the target, the TDOA data is converted to AOA data to find the angle of arrival, assuming this is a far field application. Since the distance between two clusters is known, the target position is computed by a simple triangulation. Simulations show that the average tracking error at a range of 610 meters is 2.7595 meters, less than 0.5% of the tracking range. Outdoor tests to track the SCOUT vehicle (The Science Crew Operations and Utility Testbed) near the Meteor Crater, Flagstaff, Arizona were performed on September 12-13, 2005. The tracking performance was obtained with less than 1% tracking error at ranges up to 2000 feet. No RF interference with on-board GPS, video, voice and telemetry systems was detected. Outdoor tests demonstrated the UWB tracking capability.

Ni, Jianjun↗
DOE OSTI2021

Outlier classification using autoencoders: application for fluctuation driven flows in fusion plasmas

Understanding the statistics of fluctuation driven flows in the boundary layer of magnetically confined plasmas is desired to accurately model the lifetime of the vacuum vessel components. Mirror Langmuir probes (MLPs) are a novel diagnostic that uniquely allow us to sample the plasma parameters on a time scale shorter than the characteristic time scale of their fluctuations. Sudden large-amplitude fluctuations in the plasma degrade the precision and accuracy of the plasma parameters reported by MLPs for cases in which the probe bias range is of insufficient amplitude. While some data samples can readily be classified as valid and invalid, we find that such a classification may be ambiguous for up to 40% of data sampled for the plasma parameters and bias voltages considered in this study. In this contribution, we employ an autoencoder (AE) to learn a low-dimensional representation of valid data samples. By definition, the coordinates in this space are the features that mostly characterize valid data. Ambiguous data samples are classified in this space using standard classifiers for vectorial data. In this way, we avoid defining complicated threshold rules to identify outliers, which require strong assumptions and introduce biases in the analysis. By removing the outliers that are identified in the latent low-dimensional space of the AE, we find that the average conductive and convective radial heat fluxes are between approximately 5% and 15% lower as when removing outliers identified by threshold values. For contributions to the radial heat flux due to triple correlations, the difference is up to 40%.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
NASA NTRSDate not supplied

The Additive Manufacturing Moment Measure - A Parallel Computation Technique for Determining Build Variance in the Laser Powder Bed Fusion Process

Additive manufacturing (AM) has unique process attributes that facilitate the creation of optimized, complex, and unique parts for aerospace applications. However, the multi-scale and complicated building process for AM parts can cause unexpected build conditions that result in microstructural variability within the deposited material. The need for richer datasets and computational modeling capabilities to improve AM process reliability is a consequence of this microstructural variability. A computational approach, referred to as the Additive Manufacturing Moment Measure (AM3), addresses this need by leveraging the way AM processes fuse material in precise, incremental steps. During the layering sequence, each previous step contributes to the condition of the current step at the center of the heat source. The precise steps can be selected to systematically create a time-space point field with co-located machine input and in-situ sensor data. The sequential nature of the AM process, coupled with nearest neighbor calculations, allows for a fully parallel computation for part-scale build profile analysis. The AM3 concept introduced here enables part-scale assessment directly from build files and in-situ process monitoring sensors alike. The AM moment measures were calculated for build point fields and compared with co-located in-situ and ex-situ nondestructive evaluation and optical microscopy observations. These comparisons permit a better understanding of how the sequential process actions can affect the quality of a laser powder bed fusion (LPBF) build. Details of the AM3technique will be discussed and compared to measured LPBF part characteristics. The AM3 results indicate a strong potential to advance the qualification process for aerospace applications.

Additive Manufacturing↗
DOE OSTI2024

Performance Test of Mini LVDT - ELVIS

The Institute for Energy (IFE) Technology has been a pioneer in the development of Linear Variable Differential Transformers (LVDTs) for in-pile testing, deploying over 2,200 units in various reactor environments with less than a 10% failure rate after five years of operation. This report focuses on the performance testing of IFE’s Mini LVDT, a compact sensor ideal for material test reactor experiments. The Mini LVDT, with a limited range of +/- 1.5 mm, offers excellent performance comparable to larger LVDTs, making it valuable in space-constrained applications. The development of an Enhanced Linear Variable Intrinsic Sensor (ELVIS) with internal temperature monitoring capabilities represents a significant advancement, addressing the critical need for real-time, accurate measurements in high-radiation and high-temperature environments. Two ELVIS prototypes were evaluated in terms of both temperature and displacement, showcasing promising results, though challenges with noise during temperature measurements were identified. This report summarizes the rigorous testing performed at Idaho National Laboratory (INL) and highlights the potential applications of Mini LVDTs and ELVIS in nuclear and other high-precision industries.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
NASA NTRS1994

Time transfer using geostationary satellites: Implementation of a Kalman filter

Since 1988, various experiments have shown that the TV signals transmitted by direct TV satellites may easily be used to perform time transfers at the level of a few tens of nanoseconds, the main source of error being the uncertainty on the satellite position. We first present the two methods used in our experiment to reduce the effects of the satellite residual motion: the first one consists in estimating the longitude variations of the satellite and then using this information to improve other measurements. This allows reducing the uncertainty to values between 9 and 50 nanoseconds according to the position of the involved stations. In the second method we determine the satellite position by using the data collected by three calibrated stations. Time transfer between each of these stations and a fourth one has been shown to be achievable at the precision level of ten nanoseconds. A new approach based on the use of a Kalman filter is proposed in order to take into account the dynamics of the geostationary satellite. The precisions on orbital elements and clock differences and rates determination given by the first simulated applications of the Kalman filter are presented and compared to those obtained by the other methods.

Meyer, F.↗
DOE OSTI2024

Validation of the stochastic inversion algorithm for acoustic travel-time tomography: a large eddy simulation study

Acoustic tomography (AT) is explored as a remote sensing technique to obtain instantaneous snapshots of temperature and velocity fluctuations for wind energy applications. This study integrates Large Eddy Simulation (LES) with the Stochastic Inversion (SI) method to validate the algorithm’s capacity for accurate reconstruction of atmospheric fluctuations. The initial findings demonstrate the efficacy of the method in accurately capturing the predominant flow structures. Normalized L2 error evaluations further inform the algorithm’s precision, with errors accentuated in less sampled peripheral regions. The results underscore the method’s promise as a non-intrusive observational tool, with ongoing development poised to improve its precision and reliability.

17 WIND ENERGY↗
NASA NTRS2015

Enhancements of Bayesian Blocks; Application to Large Light Curve Databases

Bayesian Blocks are optimal piecewise linear representations (step function fits) of light-curves. The simple algorithm implementing this idea, using dynamic programming, has been extended to include more data modes and fitness metrics, multivariate analysis, and data on the circle (Studies in Astronomical Time Series Analysis. VI. Bayesian Block Representations, Scargle, Norris, Jackson and Chiang 2013, ApJ, 764, 167), as well as new results on background subtraction and refinement of the procedure for precise timing of transient events in sparse data. Example demonstrations will include exploratory analysis of the Kepler light curve archive in a search for "star-tickling" signals from extraterrestrial civilizations. (The Cepheid Galactic Internet, Learned, Kudritzki, Pakvasa1, and Zee, 2008, arXiv: 0809.0339; Walkowicz et al., in progress).

Kepler light curve archive↗
NASA NTRS2011

Reconfigurable Microwave Phase Delay Element for Frequency Reference and Phase-Shifter Applications

A technique was developed to provide a reconfigurable high-precision micro - wave electrical phase delay for resonators and phase shifters. The invention employs multiple branches of transmission lines with open-ended or ground-ended terminations as configurable bits or digits. This technique minimizes the errors due to limited precision of switching devices. In addition, the proposed linear analytical approach significantly produces a much simpler design than that of other prior inventions at the time of this reporting. Microwave components such as filters, phase delay elements, or resonators require a method that can accurately adjust their frequency responses. Most tuning techniques offer very wide frequency tuning range; however, it is often difficult and expensive to tune their response in a very narrow operating frequency, especially when the tuning element reaches its minimum discrete step due to fabrication tolerances. The problem becomes worse as the operating frequency is in mm-wave frequency range (>26 GHz). The electrical tuning sensitivity of a microwave line is dependent on the position of the tuning element with respect to the reference termination. By placing this tuning element away from this reference with the main transmission line connecting the two elements together the sensitivity of the tuning element can change significantly. This concept can be used in the system that requires multiple tuning sensitivities. In this case, multiple tuning branches are superimposed in the main transmission line. The proposed invention allows the transmission-line electrical length to be accurately programmed using switching elements that have limited accuracy. The invention consists of multiple branches of transmission lines connected to discrete switching devices with open-ended terminations. They are used as discrete tuning elements. These elements are connected to the main microwave transmission line and are separated by a well-defined electrical degree spacing. Each branch is programmed to have different electrical degree sensitivity, such as a combination of discrete steps in each branch, which results in a reflective line with a unique effective phase response. To reduce the number of switching devices, it is desirable to program the devices in binary configuration where each branch represents one bit in the base-2 number system. This invention allows the transmission line electrical length to be tuned precisely with customizable sensitivity based on the known sensitivity of the base tuning circuit. The tuning resolution is dependent on the distance among tuning branches.

Hsieh, Wen-Ting↗
DOE OSTI2022

Lightweight jet reconstruction and identification as an object detection task

We apply object detection techniques based on deep convolutional blocks to end-to-end jet identification and reconstruction tasks encountered at the CERN large hadron collider (LHC). Collision events produced at the LHC and represented as an image composed of calorimeter and tracker cells are given as an input to a Single Shot Detection network. The algorithm, named PFJet-SSD performs simultaneous localization, classification and regression tasks to cluster jets and reconstruct their features. This all-in-one single feed-forward pass gives advantages in terms of execution time and an improved accuracy w.r.t. traditional rule-based methods. A further gain is obtained from network slimming, homogeneous quantization, and optimized runtime for meeting memory and latency constraints of a typical real-time processing environment. We experiment with 8-bit and ternary quantization, benchmarking their accuracy and inference latency against a single-precision floating-point. We show that the ternary network closely matches the performance of its full-precision equivalent and outperforms the state-of-the-art rule-based algorithm. Finally, we report the inference latency on different hardware platforms and discuss future applications.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2022

Region-adaptive, Error-controlled Scientific Data Compression using Multilevel Decomposition

The increase of computer processing speed is significantly outpacing improvements in network and storage bandwidth, leading to the big data challenge in modern science, where scientific applications can quickly generate much more data than that can be transferred and stored. As a result, big scientific data must be reduced by a few orders of magnitude while the accuracy of the reduced data needs to be guaranteed for further scientific explorations. Moreover, scientists are often interested in some specific spatial/temporal regions in their data, where higher accuracy is required. The locations of the regions requiring high accuracy can sometimes be prescribed based on application knowledge, while other times they must be estimated based on general spatial/temporal variation. In this paper, we develop a novel multilevel approach which allows users to impose region-wise compression error bounds. Our method utilizes the byproduct of a multilevel compressor to detect regions where details are rich and we provide the theoretical underpinning for region-wise error control. With spatially varying precision preservation, our approach can achieve significantly higher compression ratios than single-error bounded compression approaches and control errors in the regions of interest.We conduct the evaluations on two climate use cases – one targeting small-scale, node features and the other focusing on long, areal features. For both use cases, the locations of the features were unknown ahead of the compression. By selecting approximately 16% of the data based on multi-scale spatial variations and compressing those regions with smaller error tolerances than the rest, our approach improves the accuracy of post-analysis by approximately 2 × compared to single-error-bounded compression at the same compression ratio. Using the same error bound for the region of interest, our approach can achieve an increase of more than 50% in overall compression ratio.

Gong, Qian↗
NASA NTRSDate not supplied

Fast Aircraft Separation Calculations for Gradient Based Optimization of Airspace Simulations

Simulations of airspace operational concepts can play a significant role in determining future paradigms that would allow for a safe increase in airspace density. In particular, airspace simulations which are capable of handling large numbers of aircraft act as an enabling capability for the testing of proposed airspace operational concepts. Simulations allowing for gradient based optimization methods are particularly attractive, since they would potentially allow for an efficient and empirical means to derive best operational practices. These could also allow for vehicle multidisciplinary design and optimization studies to include air traffic management considerations as a discipline. But any large scale simulation of airspace operations must include some methodology for addressing airspace separation requirements, which in the most direct sense would be tracked in a manner that computationally grows as a quadratic function of the number of simulated aircraft. Efficient indirect methods have been developed in certain contexts to address this limitation. However, any means of addressing separation requirements in a gradient based optimization context should be implemented by functions which provide analytic derivative information to maximize numerical precision and computational efficiency. In this paper, a fast and differentiable separation metric is described in application to gradient based optimization of airspace operations. Rather than computing the separation distance between every pair of aircraft in a simulation, this method effectively reduces the problem to a smaller relevant set using a geometric decomposition. This method guarantees that the smallest distance at all points in simulated time is determined exactly. When used in an optimization constraint context, this guarantees that a minimum separation is maintained between all pairs of aircraft. The presented metric has logarithmic computational growth with respect to the number of simulated aircraft, and is shown to perform well in a series of notional 2D airspace optimization problems when used to enforce specified airborne separation constraints. Results show that this is notably faster than a direct pairwise distance computing metric for optimizations involving both small and large numbers of aircraft, yet enforce separation requirements to the same tolerance. It is shown that this favorable scalability is an enabling capability for more sophisticated air traffic management conceptual studies.

Optimization↗