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All sourcesNASA NTRSDOE OSTI
NASA NTRS1990

Real-time adaptive aircraft scheduling

One of the most important functions of any air traffic management system is the assignment of ground-holding times to flights, i.e., the determination of whether and by how much the take-off of a particular aircraft headed for a congested part of the air traffic control (ATC) system should be postponed in order to reduce the likelihood and extent of airborne delays. An analysis is presented for the fundamental case in which flights from many destinations must be scheduled for arrival at a single congested airport; the formulation is also useful in scheduling the landing of airborne flights within the extended terminal area. A set of approaches is described for addressing a deterministic and a probabilistic version of this problem. For the deterministic case, where airport capacities are known and fixed, several models were developed with associated low-order polynomial-time algorithms. For general delay cost functions, these algorithms find an optimal solution. Under a particular natural assumption regarding the delay cost function, an extremely fast (O(n ln n)) algorithm was developed. For the probabilistic case, using an estimated probability distribution of airport capacities, a model was developed with an associated low-order polynomial-time heuristic algorithm with useful properties.

Kolitz, Stephan E.↗
NASA NTRS1973

En route position and time control of aircraft using Kalman filtering of radio aid data

Fixed-time-of-arrival (FTA) guidance and navigation is investigated as a possible technique capable of operation within much more stringent en route separation standards and offering significant advantages in safety, higher traffic densities, and improved scheduling reliability, both en route and in the terminal areas. This study investigated the application of FTA guidance previously used in spacecraft guidance. These FTA guidance techniques have been modified and are employed to compute the velocity corrections necessary to return an aircraft to a specified great-circle reference path in order to exercise en route time and position control throughout the entire flight. The necessary position and velocity estimates to accomplish this task are provided by Kalman filtering of data from Loran-C, VORTAC/TACAN, Doppler radar, radio or barometric altitude,and altitude rate. The guidance and navigation system was evaluated using a digital simulation of the cruise phase of supersonic and subsonic flights between San Francisco and New York City, and between New York City and London.

Mcgee, L. A.↗
NASA NTRS1976

Behavior of queues at signalized intersections in heavy traffic

This paper derives the asymptotic behavior of traffic queues at signalized intersections when the excess of departure capacity over arrivals approaches zero from above. The most interesting result is that the distribution of queue length approaches a negative exponential, with fewer restrictive assumptions than hitherto known. The main improvement results from more precise use of a combinatorial lemma of Spitzer, giving the maximum of the partial sums of a sequence of independent identically distributed random variables, plus some specific constructive probability calculations, many of them involving the Fourier transform. New results are presented on the probability that the queue be below a fixed bound and/or on the probability that the queue be empty. Applications to on-line estimators for real-time traffic control are suggested.

Posner, E. C.↗
NASA NTRS2011

Dynamical Model for the Zodiacal Cloud and Sporadic Meteors

The solar system is dusty, and would become dustier over time as asteroids collide and comets disintegrate, except that small debris particles in interplanetary space do not last long. They can be ejected from the solar system by Jupiter, thermally destroyed near the Sun, or physically disrupted by collisions. Also, some are swept by the Earth (and other planets), producing meteors. Here we develop a dynamical model for the solar system meteoroids and use it to explain meteor radar observations. We find that the Jupiter Family Comets (JFCs) are the main source of the prominent concentrations of meteors arriving to the Earth from the helion and antihelion directions. To match the radiant and orbit distributions, as measured by the Canadian Meteor Orbit Radar (CMOR) and Advanced Meteor Orbit Radar (AMOR), our model implies that comets, and JFCs in particular, must frequently disintegrate when reaching orbits with low perihelion distance. Also, the collisional lifetimes of millimeter particles may be longer (approx. > 10(exp 5) yr at 1 AU) than postulated in the standard collisional models (approx 10(exp 4) yr at 1 AU), perhaps because these chondrule-sized meteoroids are stronger than thought before. Using observations of the Infrared Astronomical Satellite (IRAS) to calibrate the model, we find that the total cross section and mass of small meteoroids in the inner solar system are (1.7-3.5) 10(exp 11) sq km and approx. 4 10(exp 19) g, respectively, in a good agreement with previous studies. The mass input required to keep the Zodiacal Cloud (ZC) in a steady state is estimated to be approx. 10(exp 4)-10(exp 5) kg/s. The input is up to approx 10 times larger than found previously, mainly because particles released closer to the Sun have shorter collisional lifetimes, and need to be supplied at a faster rate. The total mass accreted by the Earth in particles between diameters D = 5 micron and 1 cm is found to be approx 15,000 tons/yr (factor of 2 uncertainty), which is a large share of the accretion flux measured by the Long Term Duration Facility (LDEF). Majority of JFC particles plunge into the upper atmosphere at <15 km/s speeds, should survive the atmospheric entry, and can produce micrometeorite falls. This could explain the compositional similarity of samples collected in the Antarctic ice and stratosphere, and those brought from comet Wild 2 by the Stardust spacecraft. Meteor radars such as CMOR and AMOR see only a fraction of the accretion flux (approx 1- 10% and approx 10-50%, respectively), because small particles impacting at low speeds produce ionization levels that are below these radars detection capabilities.

Nesvorny, David↗
NASA NTRS1994

Differential GPS and system integration of the Low Visibility Landing and Surface Operations (LVLASO) demonstration

The LVLASO Flight Demonstration of ASTA concepts (FDAC) integrates NASA-Langley's electronic moving map display and Transport Systems Research Vehicle (TSRV) (a modified Boeing 737 aircraft); ARINC's VHF data link, GPS ground station, and automated controller workstation; and Norden's surface radar/airport movement safety system. Aircraft location is shown on the electronic map display in the cockpit. An approved taxi route as well as other aircraft and surface traffic are also displayed. An Ashtech Z12 Global Positioning System (GPS) receiver on the TSRV estimates the aircraft's position. In Differential mode (DSPS), the Ashtech receiver accepts differential C/A code pseudorange corrections from a GPS ground station. The GPS ground station provides corrections up to ten satellites. The corrections are transmitted on a VHF data link at a 1 Hz. rate using the RTCM-104 format. DGPS position estimates will be within 5 meters of actual aircraft position. DGPS position estimates are blended with position, velocity, acceleration, and heading data from the TSRV Air Data/Inertial Reference System (ADIRS). The ADIRS data is accurate in the short-term, but drifts over time. The DGPS data is used to keep the ADIRS position accurate. Ownship position, velocity, heading, and turn rate are sent at a 20 Hz. rate to the electronic map display. Airport traffic is detected by the airport surface radar system. Aircraft and vehicles such as fuel trucks and baggage carts are detected. The traffic's location, velocity, and heading are sent to the TSRV. To prevent traffic symbology from jumping each second when a location update arrives, velocity and heading are used to predict a new traffic location for each display update. Possible runway incursions and collisions can be shown on the electronic map. Integrating the different systems used in the FDAC requires attention to the underlying coordinate systems. The airport diagram displayed on the electronic map is obtained from published navigational charts. The charts reference the North American Datum of 1927 (NAD27) or a local state-plane coordinate system. GPS uses the World Geodetic Standard of 1984 (WGS84). Both NAD27 and WGS84 model the Earth as an ellipsoid, however, they use a different origin and different size ellipsoids. Latitudes and longitudes given in these systems can be converted to a Cartesian system with the origin at the Earth's center. The surface radar detects traffic in a locally-level, rho-theta coordiante system. The electronic airport diagram is stored using a flat XY coordinate system. The map origin is at the tower and is referenced as True North up. All ownship and other traffic positions must be converted to the electronic map's frame of reference for display.

Rankin, James M.↗
NASA NTRSDate not supplied

Predicting Airport Runway Configurations for Decision-Support Using Supervised Learning

One of the most challenging tasks for air traffic controllers is runway configuration management (RCM). It deals with the optimal selection of runways to operate on (for arrivals and departures) based on traffic, surface wind speed, wind direction, other environmental variables, noise constraints, and several other airport-specific factors. It affects the efficiency of the National Airspace System (NAS) and both surface and airspace operations can benefit from better understanding future runway configurations. In this paper, we present a comprehensive implementation of predictive models for runway configuration estimation from large volumes of historical data. Specifically, operational data from two full years (2018 and 2019) is collected, analyzed, and fused together to build the data product used in this work. The data set differs from prior work in the field in terms of its scope, resolution, and variety of factors collected and considered. Meteorological data is collected from two different sources – current weather conditions from METAR (Meteorological Terminal Aviation Routine Weather Report) and forecast weather conditions from Localized Aviation MOS Program (LAMP). Operational data from the Federal Aviation Administration (FAA) Aviation System Performance Metrics (ASPM) related to scheduled and actual number of arrivals and departures, average taxi times, etc. are collected. NASA’s Sherlock Data Warehouse is used to identify critical information such as go-arounds, and other events that might impact RCM decision-making. All data is collected and aggregated over 15-minute intervals throughout the two years. This provides a resolution like the timescales that might be necessary for runway configuration management decision-making. A variety of supervised learning algorithms are tested including Support Vector Machine, Random Forest, Gradient Boosting, etc. including tuning of the model hyperparameters. The modeling process is applied and presented on two representative U.S. airports – Charlotte Douglas International Airport (KCLT) and Denver International Airport (KDEN). The two airports present different levels of complexity in terms of the total number of configurations used and provide a balanced perspective on the generalizability of the developed approach to other airports in the NAS. Initial results are promising (F1 score of 0.91 at KCLT and 0.83 at KDEN) for data in the test set. The final paper will contain a comprehensive comparison between different models and model building strategies as well as further refined results. Most important predictors for each airport will be identified along with a discussion and recommendations on adapting the framework to other scenarios.

Tejas G Puranik↗
NASA NTRS2011

A Concept for Flexible Operations and Optimized Traffic into Metroplex Regions

A "Flexible Flight Operations" concept for airport metroplexes was studied. A flexible flight is one whose destination airport is not assigned until a threshold is reached near the arrival area at which time the runway which reduces overall delay is assigned. The concept seeks to increase throughput by exploiting flexibility. The quantification of best-case benefits from the concept was pursued to establish whether concept research is warranted. Findings indicate that indeed the concept has potential for significant reductions in delay (and cost due to delay) in the N90 (NY/NJ) and SCT (Southern California) metroplexes. Delay reductions of nearly 26% are possible in N90 when 30% of the commercial airline flights are flexible (smartly selected by their low probability of connecting passengers); nearly 40% delay reduction is found when 50% of the flights are flexible. In the SCT metroplex, delay reductions estimates are greater. Greater reductions result at SCT since it is less constrained currently than N90, providing "more room" to take advantage of flexibility. Using the flexible operations concept for on-demand/air taxi and General Aviation flights were found to be beneficial at NY/NJ, indicating the flexible operations concepts may be useful to wide variety of users..

DeLaurentis, Daniel↗
NASA NTRS1985

Thickness of the particle swarm in cosmic ray air showers

The average dispersion in arrival time of air shower particles detected with a scintillator at an impact parameter r is described with accuracy 5-10% by the empirical formula sigma = Sigma sub to (1+r/r sub t) sup b, where Sigma sub to = 2.6 ns, r sub t = 30m and b = (1.94 + or - .08) (0.39 + or - .06) sec Theta, for r 2 km, 10 to the 8th power E 10 to the 11th power GeV, and Theta 60 deg. (E is the primary energy and theta is the zenith angle). The amount of fluctuation in sigma sub t due to fluctuations in the level of origin and shower development is less than 20%. These results provide a basis for estimating the impact parameters of very larger showers with data from very small detector arrays (mini-arrays). The energy of such showers can then be estimated from the local particle density. The formula also provides a basis for estimating the angular resolution of air shower array-telescopes.

Linsley, J.↗
NASA NTRS2013

A Major Solar Eruptive Event in July 2012: Defining Extreme Space Weather Scenarios

A key goal for space weather studies is to define severe and extreme conditions that might plausibly afflict human technology. On 23 July 2012, solar active region 1520 (approx. 141 deg W heliographic longitude) gave rise to a powerful coronal mass ejection (CME) with an initial speed that was determined to be 2500+/-500 km/s. The eruption was directed away from Earth toward 125 deg W longitude. STEREO-A sensors detected the CME arrival only about 19 h later and made in situ measurements of the solar wind and interplanetary magnetic field. In this paper, we address the question of what would have happened if this powerful interplanetary event had been Earthward directed. Using a well-proven geomagnetic storm forecast model, we find that the 23-24 July event would certainly have produced a geomagnetic storm that was comparable to the largest events of the twentieth century (Dst approx. - 500 nT). Using plausible assumptions about seasonal and time-of-day orientation of the Earth's magnetic dipole, the most extreme modeled value of storm-time disturbance would have been Dst= - 1182 nT. This is considerably larger than estimates for the famous Carrington storm of 1859. This finding has far reaching implications because it demonstrates that extreme space weather conditions such as those during March of 1989 or September of 1859 can happen even during a modest solar activity cycle such as the one presently underway. We argue that this extreme event should immediately be employed by the space weather community to model severe space weather effects on technological systems such as the electric power grid.

solar longitude↗
NASA NTRS1976

Structure of the lunar mantle

The structure of the lunar mantle is examined by using data on the decay of shear wave amplitude with distance and the relative arrival times of P and S waves. The new analysis confirms a previous lunar model based primarily upon travel times and more closely defines certain properties of the lunar mantle. A negative shear wave velocity gradient of 0.0013 (km/s)/km, shear wave Q of 4000, and Poisson's ratio of 0.250 plus or minus 0.025 are found for the upper mantle, which lies between the depths of 60 and 300 km. A rapid decrease of shear wave velocity with increasing depth is observed starting at around a 300-km depth, associated with a lower Q for shear waves. Poisson's ratio in the lower part of the middle mantle, which extends to a depth of about 1000 km, is estimated to be 0.36 plus or minus 0.02.

Nakamura, Y.↗
NASA NTRS1998

Vertical and Horizontal Wind Structure Prior to and During the 1997/1998 ENSO Event

Analyses of ECMWF and satellite wind products are used to investigate low frequency fluctuations in the wind fields immediately preceding and during the 1997/1998 ENSO event. An extended EOF analysis of the horizontal and vertical wind structure that allows for the study of propagating features indicates that the dominant mode of variability established in the lower levels of the atmosphere is a convergence in the central tropical Pacific. At mid-levels, the westerlies increase with time over most of the equatorial Pacific, and there are closed cyclonic features on either side of the equator. At upper levels, the flow tends to become divergent across the equatorial Pacific, and there is a strong flow from the northwest Pacific across Indonesia that then turns to the west along the equator in the Indian Ocean. The addition of satellite data for improved surface wind estimates reveal that the Indian Ocean winds were anomalously strong during the winter preceding the initiation of the ENSO event. An analysis of the momentum convergence flux at the surface indicates a very strong anomaly 9 months prior to the ENSO event that begins in the western Indian Ocean and propagates to the east, arriving over the Pacific warm pool area coincident with the beginning of the El Nino. Changes in the near surface thermal and water vapor structure over the Indian Ocean during this period will also be discussed.

Adamec, David↗
NASA NTRS1996

An Atmospheric Tape Recorder: The Imprint of Tropical Tropopause Temperatures on Stratospheric Water Vapor

We describe observations of tropical stratospheric water vapor q that show clear evidence of large-scale upward advection of the signal from annual fluctuations in the effective 'entry mixing ratio' q(sub E) of air entering the tropical stratosphere. In other words, air is 'marked,' on emergence above the highest cloud tops, like a signal recorded on an upward moving magnetic tape. We define q(sub E) as the mean water vapor mixing ratio, at the tropical tropopause, of air that will subsequently rise and enter the stratospheric 'overworld' at about 400 K. The observations show a systematic phase lag, increasing with altitude, between the annual cycle in q(sub E) and the annual cycle in q at higher altitudes. The observed phase lag agrees with the phase lag calculated assuming advection by the transformed Eulerian-mean vertical velocity of a q(sub E) crudely estimated from 100-hPa temperatures, which we use as a convenient proxy for tropopause temperatures. The phase agreement confirms the overall robustness of the calculation and strongly supports the tape recorder hypothesis. Establishing a quantitative link between q(sub E) and observed tropopause temperatures, however, proves difficult because the process of marking the tape depends subtly on both small- and large-scale processes. The tape speed, or large-scale upward advection speed, has a substantial annual variation and a smaller variation due to the quasi-biennial oscillation, which delays or accelerates the arrival of the signal by a month or two in the middle stratosphere. As the tape moves upward, the signal is attenuated with an e-folding time of about 7 to 9 months between 100 and 50 hPa and about 15 to 18 months between 50 and 20 hPa, constraining possible orders of magnitude both of vertical diffusion K(sub z) and of rates of mixing in from the extratropics. For instance, if there were no mixing in, then K(sub z) would be in the range 0.03-0.09 m(exp 2)/s; this is an upper bound on K(sub z).

Mote, Philip W.↗
NASA NTRS1999

Implications of the Improved Understanding of the Gravitational and Topography Fields

The Mars Orbiter Laser Altimeter (MOLA) has been successfully mapping the shape and topography of Mars on an intermittent basis since the Mars Global Surveyor (MGS) spacecraft arrived at Mars in Sept. 1997. In early April, MGS reached it's mapping orbit and began the mapping phase of the mission. Since that time MOLA has been operating continuously. MOLA is a laser altimeter with a pulse rate of 10 Hz and a precision of about 30 to 40 cm over flat surfaces. The laser pulses are approximately 330 meters apart on the surface of Mars and each pulse illuminates an area approximately 150 meters in diameter. The orbital accuracy of MGS is a few meters in the radial direction enabling the topography to be interpreted at the few meter accuracy level. The initial data have provided a new geodetic description of the size and shape of Mars, including accurate estimates for the equatorial and polar radii, and the planetary flattening. The data have revealed the northern hemisphere to be very low in elevation, very flat, and almost devoid of craters. The north polar icecap lies in a basin about 5 km below the average altitude and reaches to a height of 3 km. The heavily cratered southern hemisphere is high and the terrain is rough. The south polar icecap is about 5 km above the average planetary altitude and 2 km above the surrounding terrain. The MOLA profile data show the gradual but steady increase in altitude of the surface of Mars from the north pole to the south pole. This is a consistent feature for all north-south profiles and reflects the 3 km separation of the center of figure for Mars from the center of mass along the rotation axis.

Smith, David E.↗
NASA NTRS2018

Simulated Encounters of the Parker Solar Probe with a Coronal-Hole Jet

Solar coronal jets are small, transient, collimated ejections most easily observed in coronal holes (CHs). The upcoming Parker Solar Probe (PSP) mission provides the first opportunity to encounter CH jets in situ near the Sun and examine their internal structure and dynamics. Using projected mission orbital parameters, we have simulated PSP encounters with a fully three-dimensional magnetohydrodynamic (MHD) model of a CH jet. We find that three internal jet regions, featuring different wave modes and levels of compressibility, have distinct identifying signatures detectable by PSP. The leading Alfvén wave front and its immediate wake are characterized by transAlfvénic plasma flows with mild density enhancements. This front exhibits characteristics of a fast switch-on MHD shock, whose arrival is signaled by the sudden onset of large-amplitude transverse velocity and magnetic-field oscillations highly correlated in space and time. The trailing portion is characterized by supersonic but subAlfvénicout flows of dense plasma with uncorrelated velocity and magnetic-field oscillations. This compressible region contains most of the jet's mass. The volume between the immediate wake and dense jet, the remote wake,mixes and transitions the characteristics of the two other regions. In addition to probing each region separately, we also simulate a corotational PSP-jet encounter. In this scenario, the simulated spacecraft hovers over the jet producing CH, as may occur during the mission's corotational phases, sampling each jet region in turn. We estimate that PSP will encounter numerous CH jets over the lifetime of the mission.

Roberts, Merrill A.↗
NASA NTRS2016

Analysis of One-Way Laser Ranging Data to LRO, Time Transfer and Clock Characterization

We processed and analyzed one-way laser ranging data from International Laser Ranging Service ground stations to NASA's Lunar Reconnaissance Orbiter (LRO), obtained from June 13, 2009 until September 30, 2014. We pair and analyze the one-way range observables from station laser fire and spacecraft laser arrival times by using nominal LRO orbit models based on the GRAIL gravity field. We apply corrections for instrument range walk, as well as for atmospheric and relativistic effects. In total we derived a tracking data volume of approximately 3000 hours featuring 64 million Full Rate and 1.5 million Normal Point observations. From a statistical analysis of the dataset we evaluate the experiment and the ground station performance. We observe a laser ranging measurement precision of 12.3 centimeters in case of the Full Rate data which surpasses the LOLA (Lunar Orbiting Laser Altimeter) timestamp precision of 15 centimeters. The averaging to Normal Point data further reduces the measurement precision to 5.6 centimeters. We characterized the LRO clock with fits throughout the mission time and estimated the rate to 6.9 times10 (sup -8), the aging to 1.6 times 10 (sup -12) per day and the change of aging to 2.3 times 10 (sup -14) per day squared over all mission phases. The fits also provide referencing of onboard time to the TDB (Barycentric Dynamical Time) time scale at a precision of 166 nanoseconds over two and 256 nanoseconds over all mission phases, representing ground to space time transfer. Furthermore we measure ground station clock differences from the fits as well as from simultaneous passes which we use for ground to ground time transfer from common view observations. We observed relative offsets ranging from 33 to 560 nanoseconds and relative rates ranging from 2 times 10 (sup -13) to 6 times 10 (sup -12) between the ground station clocks during selected mission phases. We study the results from the different methods and discuss their applicability for time transfer.

Bauer, S.↗
NASA NTRS2009

Observations and Interpretations of Energetic Neutral Hydrogen Atoms from the December 5, 2006 Solar Event

We discuss recently reported observations of energetic neutral hydrogen atoms (ENAs) from an X9 solar flare/coronal mass ejection event on 5 December 2006, located at E79. The observations were made by the Low Energy Telescopes (LETs) on STEREO A and B. Prior to the arrival of the main solar energetic particle (SEP) event at Earth, both LETs observed a sudden burst of 1.6 to 15 MeV energetic neutral hydrogen atoms produced by either flare or shock-accelerated protons. RHESSI measurements of the 2.2-MeV gamma-ray line provide an estimate of the number of interacting flare-accelerated protons in this event, which leads to an improved estimate of ENA production by flare-accelerated protons. Taking into account ENA losses, we find that the observed ENAs must have been produced in the high corona at heliocentric distances > or equal to 2 solar radii. Although there are no CME images from this event, it is shown that CME-shock-accelerated protons can, in principle, produce a time-history consistent with the observations.

Mewaldt, R. A.↗
NASA NTRS2011

Imaging the Moon's Core with Seismology

Constraining the structure of the lunar core is necessary to improve our understanding of the present-day thermal structure of the interior and the history of a lunar dynamo, as well as the origin and thermal and compositional evolution of the Moon. We analyze Apollo deep moonquake seismograms using terrestrial array processing methods to search for the presence of reflected and converted energy from the lunar core. Although moonquake fault parameters are not constrained, we first explore a suite of theoretical focal spheres to verify that fault planes exist that can produce favorable core reflection amplitudes relative to direct up-going energy at the Apollo stations. Beginning with stacks of event seismograms from the known distribution of deep moonquake clusters, we apply a polarization filter to account for the effects of seismic scattering that (a) partitions energy away from expected components of ground motion, and (b) obscures all but the main P- and S-wave arrivals. The filtered traces are then shifted to the predicted arrival time of a core phase (e.g. PcP) and stacked to enhance subtle arrivals associated with the Moon s core. This combination of filtering and array processing is well suited for detecting deep lunar seismic reflections, since we do not expect scattered wave energy from near surface (or deeper) structure recorded at varying epicentral distances and stations from varying moonquakes at varying depths to stack coherently. Our results indicate the presence of a solid inner and fluid outer core, overlain by a partial-melt-containing boundary layer (Table 1). These layers are consistently observed among stacks from four classes of reflections: P-to-P, S-to-P, P-to-S, and S-to-S, and are consistent with current indirect geophysical estimates of core and deep mantle properties, including mass, moment of inertia, lunar laser ranging, and electromagnetic induction. Future refinements are expected following the successful launch of the GRAIL lunar orbiter and SELENE 2 lunar lander missions.

Weber, Renee C.↗
NASA NTRS2002

On the Exit Boundary Condition for One-Dimensional Calculations of Pulsed Detonation Engine Performance

In one-dimensional calculations of pulsed detonation engine (PDE) performance, the exit boundary condition is frequently taken to be a constant static pressure. In reality, for an isolated detonation tube, after the detonation wave arrives at the exit plane, there will be a region of high pressure, which will gradually return to ambient pressure as an almost spherical shock wave expands away from the exit, and weakens. Initially, the flow is supersonic, unaffected by external pressure, but later becomes subsonic. Previous authors have accounted for this situation either by assuming the subsonic pressure decay to be a relaxation phenomenon, or by running a two-dimensional calculation first, including a domain external to the detonation tube, and using the resulting exit pressure temporal distribution as the boundary condition for one-dimensional calculations. These calculations show that the increased pressure does affect the PDE performance. In the present work, a simple model of the exit process is used to estimate the pressure decay time. The planar shock wave emerging from the tube is assumed to transform into a spherical shock wave. The initial strength of the spherical shock wave is determined from comparison with experimental results. Its subsequent propagation, and resulting pressure at the tube exit, is given by a numerical blast wave calculation. The model agrees reasonably well with other, limited, results. Finally, the model was used as the exit boundary condition for a one-dimensional calculation of PDE performance to obtain the thrust wall pressure for a hydrogen-air detonation in tubes of length to diameter ratio (L/D) of 4, and 10, as well as for the original, constant pressure boundary condition. The modified boundary condition had no performance impact for values of L/D > 10, and moderate impact for L/D = 4.

Wilson, Jack↗