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NASA NTRS1998

Integration of the Remote Agent for the NASA Deep Space One Autonomy Experiment

This paper describes the integration of the Remote Agent (RA), a spacecraft autonomy system which is scheduled to control the Deep Space 1 spacecraft during a flight experiment in 1999. The RA is a reusable, model-based autonomy system that is quite different from software typically used to control an aerospace system. We describe the integration challenges we faced, how we addressed them, and the lessons learned. We focus on those aspects of integrating the RA that were either easier or more difficult than integrating a more traditional large software application because the RA is a model-based autonomous system. A number of characteristics of the RA made integration process easier. One example is the model-based nature of RA. Since the RA is model-based, most of its behavior is not hard coded into procedural program code. Instead, engineers specify high level models of the spacecraft's components from which the Remote Agent automatically derives correct system-wide behavior on the fly. This high level, modular, and declarative software description allowed some interfaces between RA components and between RA and the flight software to be automatically generated and tested for completeness against the Remote Agent's models. In addition, the Remote Agent's model-based diagnosis system automatically diagnoses when the RA models are not consistent with the behavior of the spacecraft. In flight, this feature is used to diagnose failures in the spacecraft hardware. During integration, it proved valuable in finding problems in the spacecraft simulator or flight software. In addition, when modifications are made to the spacecraft hardware or flight software, the RA models are easily changed because they only capture a description of the spacecraft. one does not have to maintain procedural code that implements the correct behavior for every expected situation. On the other hand, several features of the RA made it more difficult to integrate than typical flight software. For example, the definition of correct behavior is more difficult to specify for a system that is expected to reason about and flexibly react to its environment than for a traditional flight software system. Consequently, whenever a change is made to the RA it is more time consuming to determine if the resulting behavior is correct. We conclude the paper with a discussion of future work on the Remote Agent as well as recommendations to ease integration of similar autonomy projects.

Dorais, Gregory A.↗

NASA NTRS2010

Quantitative Measures of Immersion in Cloud and the Biogeography of Cloud Forests

Sites described as tropical montane cloud forests differ greatly, in part because observers tend to differ in their opinion as to what constitutes frequent and prolonged immersion in cloud. This definitional difficulty interferes with hydrologic analyses, assessments of environmental impacts on ecosystems, and biogeographical analyses of cloud forest communities and species. Quantitative measurements of cloud immersion can be obtained on site, but the observations are necessarily spatially limited, although well-placed observers can examine 10 50 km of a mountain range under rainless conditions. Regional analyses, however, require observations at a broader scale. This chapter discusses remote sensing and modeling approaches that can provide quantitative measures of the spatiotemporal patterns of cloud cover and cloud immersion in tropical mountain ranges. These approaches integrate remote sensing tools of various spatial resolutions and frequencies of observation, digital elevation models, regional atmospheric models, and ground-based observations to provide measures of cloud cover, cloud base height, and the intersection of cloud and terrain. This combined approach was applied to the Monteverde region of northern Costa Rica to illustrate how the proportion of time the forest is immersed in cloud may vary spatially and temporally. The observed spatial variation was largely due to patterns of airflow over the mountains. The temporal variation reflected the diurnal rise and fall of the orographic cloud base, which was influenced in turn by synoptic weather conditions, the seasonal movement of the Intertropical Convergence Zone and the north-easterly trade winds. Knowledge of the proportion of the time that sites are immersed in clouds should facilitate ecological comparisons and biogeographical analyses, as well as land use planning and hydrologic assessments in areas where intensive on-site work is not feasible.

Lawton, R. O.↗

NASA NTRS2014

ldentifying Episodes of Earth Science Phenomena Using a Big-Data Technology

A significant portion of Earth Science investigations is phenomenon- (or event-) based, such as the studies of Rossby waves, volcano eruptions, tsunamis, mesoscale convective systems, and tropical cyclones. However, except for a few high-impact phenomena, e.g. tropical cyclones, comprehensive records are absent for the occurrences or events of these phenomena. Phenomenon-based studies therefore often focus on a few prominent cases while the lesser ones are overlooked. Without an automated means to gather the events, comprehensive investigation of a phenomenon is at least time-consuming if not impossible. We have constructed a prototype Automated Event Service (AES) system that is used to methodically mine custom-defined events in the reanalysis data sets of atmospheric general circulation models. Our AES will enable researchers to specify their custom, numeric event criteria using a user-friendly web interface to search the reanalysis data sets. Moreover, we have included a social component to enable dynamic formation of collaboration groups for researchers to cooperate on event definitions of common interest and for the analysis of these events. An Earth Science event (ES event) is defined here as an episode of an Earth Science phenomenon (ES phenomenon). A cumulus cloud, a thunderstorm shower, a rogue wave, a tornado, an earthquake, a tsunami, a hurricane, or an El Nino, is each an episode of a named ES phenomenon, and, from the small and insignificant to the large and potent, all are examples of ES events. An ES event has a duration (often finite) and an associated geo-location as a function of time; it's therefore an entity embedded in four-dimensional (4D) spatiotemporal space. Earth Science phenomena with the potential to cause massive economic disruption or loss of life often rivet the attention of researchers. But, broader scientific curiosity also drives the study of phenomena that pose no immediate danger, such as land/sea breezes. Due to Earth System's intricate dynamics, we are continuously discovering novel ES phenomena. We generally gain understanding of a given phenomenon by observing and studying individual events. This process usually begins by identifying the occurrences of these events. Once representative events are identified or found, we must locate associated observed or simulated data prior to commencing analysis and concerted studies of the phenomenon. Knowledge concerning the phenomenon can accumulate only after analysis has started. However, as mentioned previously, comprehensive records only exist for a very limited set of high-impact phenomena; aside from these, finding events and locating associated data currently may take a prohibitive amount of time and effort on the part of an individual investigator. The reason for the lack of comprehensive records for most of the ES phenomena is mainly due to the perception that they do not pose immediate and/or severe threat to life and property. Thus they are not consistently tracked, monitored, and catalogued. Many phenomena even lack precise and/or commonly accepted criteria for definitions. Moreover, various Earth Science observations and data have accumulated to a previously unfathomable volume; NASA Earth Observing System Data Information System (EOSDIS) alone archives several petabytes (PB) of satellite remote sensing data, which are steadily increasing. All of these factors contribute to the difficulty of methodically identifying events corresponding to a given phenomenon and significantly impede systematic investigations. We have not only envisioned AES as an environment for identifying customdefined events but also aspired for it to be an interactive environment with quick turnaround time for revisions of query criteria and results, as well as a collaborative environment where geographically distributed experts may work together on the same phenomena. A Big Data technology is thus required for the realization of such a system. In the following, we first introduce the technology selected for AES in the next section. We then demonstrate the utility of AES using a use case, Blizzard, before we conclude.

Kuo, Kwo-Sen↗

DOE OSTI2021

ARM Aerosol Measurement Science Group 2019 Strategic Planning Workshop Report

This report summarizes the results of a U.S. Department of Energy Atmospheric Radiation Measurement (ARM) user facility workshop held in November 2019 to advance a science-based strategy for ARM’s aerosol measurement program. This was the second such workshop since the Aerosol Measurement Science Group (AMSG) was chartered in 2015 to enhance coordination of ARM observations of aerosols and atmospheric trace gases with the needs of ARM users. The results presented here reflect the AMSG’s focus in recent years on science-based strategies that will contribute to the increased use of ARM data to fulfill its mission of improving process representations and predictability in climate models. Sessions held during the workshop range from interfacing with models through aerosol sampling strategies to calibration protocols and data products. The strategies set forth here were also developed to be directly relevant to ARM’s updated Decadal Vision. The AMSG workshops have been designed to recommend actions that will enable ARM to evolve and continue to meet its mission. To that end, the AMSG will develop an actionable plan from the recommendations outlined here. Some are well defined and can reasonably be accomplished in the short term. Others are less definite or of a larger scope that calls for a longer-term implementation. Further discussion will be required to develop and prioritize actionable items related to such areas. Task teams comprising the appropriate expertise and perspective from the AMSG and other members of the community will be formed to achieve this outcome. Some particular topics are recognized as high priority, so plans are underway to develop task teams and to hold follow-on discussions to address them. Four areas currently being considered for short, focused discussion are 1) aerosol measurements on the North Slope of Alaska, 2) improving data usability for modeling, 3) strategies for advancing remote sensing, vertical profiling, and distributed measurements of aerosols, and 4) aerosol sampling strategies at existing ARM sites to provide intensive modes of operation to promote data usage for process and modeling studies.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2023

Gulf of Mexico Offshore Wind Energy Hurricane Risk Assessment

NREL's feasibility assessment of offshore wind in the Gulf of Mexico concluded that hurricane risk was one of the major challenges that would need to be overcome for a mature offshore wind industry to develop in the Gulf of Mexico. To ensure the robust design of wind turbines in the Gulf of Mexico, it is critical to understand the added risk posed by the threat of major hurricanes, as those affecting the Gulf of Mexico region have a significant potential to exceed design limits prescribed by the International Electrotechnical Commission (IEC) wind design standards. To satisfy this charge, this project defines the wind hazard for the Gulf of Mexico Offshore Wind Energy area using the hurricane hazard model develop by Applied Research Associates and published extensively in the open literature. In doing so, the return periods associated with the IEC Class 1A and Typhoon Class limit-state hurricanes are estimated on a grid with nominal resolution of 10 km to determine where hurricane risk results in the exceedance of the IEC design criteria. On the same grid, wind speeds hazard contours associated with return periods varying from 50 to 1,000 years are also estimated. An additional challenge in assessing hurricane wind speed risk in the Gulf of Mexico arises from inconsistent terminology across the Saffir-Simpson hurricane scale and the IEC design criteria. Saffir-Simpson definitions are based on 1-minute sustained wind speeds estimated at 10-m height over marine terrain, while the IEC uses a different averaging period (3-second versus 1-minute) and reference height (assumed herein a hub height of 150 m versus 10 m). Employing the latest research on turbulence characteristics of the hurricane boundary layer, conversions between various durations (e.g., 3-seconds, 1-minute, 10-minutes, 1-hour) and between elevations near the surface (10 m) to near hub height (assumed herein 150 m) are developed. IEC Class 1A and Typhoon Class limit states are also provided in terms of an equivalent Saffir-Simpson hurricane wind speed category.

17 WIND ENERGY↗

NASA NTRS1961

Aerodynamic Loads at Mach Numbers from 0.70 to 2.22 on an Airplane Model Having a Wing and Canard of Triangular Plan Form and Either Single or Twin Vertical Tails Supplement I-Tabulated Data for the Model with Single Vertical Tails: Tabulated Data for the Model with Single Vertical Tail - Supplement 1

Tabulated results of a wind-tunnel investigation of the aerodynamic loads on a canard airplane model with a single vertical tail are presented for Mach numbers from 0.70 to 2.22. The Reynolds number for the measurements was 2.9 x 10(exp 6) based on the wing mean aerodynamic chord. The results include local static pressure coefficients measured on the wing, body, and vertical tail for angles of attack from -4 deg to + 16 deg, angles of sideslip of 0 deg and 5.3 deg, vertical-tail settings of 0 deg and 5 deg, and nominal canard deflections of 0 deg and 10 deg. Also included are section force and moment coefficients obtained from integrations of the local pressures and model-component force and moment coefficients obtained from integrations of the section coefficients. Geometric details of the model and the locations of the pressure orifices are shown. An index to the data contained herein is presented and definitions of nomenclature are given.

Peterson, Victor L.↗

NASA NTRS2010

Interference Analysis for an Aeronautical Mobile Airport Communications System

The next generation of aeronautical communications for airport surface applications has been identified through a NASA research program and an international collaborative future communications study. The result, endorsed by both the United States and European regulatory agencies is called AeroMACS (Aeronautical Mobile Airport Communications System) and is based upon the IEEE 802.16e mobile wireless standard. Coordinated efforts to develop appropriate aviation standards for the AeroMACS system are now underway within RTCA (United States) and Eurocae (Europe). AeroMACS will be implemented in a recently allocated frequency band, 5091- 5150 MHz. As this band is also occupied by fixed satellite service uplinks, AeroMACS must be designed to avoid interference with this incumbent service. The aspects of AeroMACS operation that present potential interference to the fixed satellite service are under analysis in order to enable the definition of standards that assure that such interference will be avoided. The NASA Glenn Research Center has been involved in this analysis, and the first results of modeling and simulation efforts directed at this analysis are the subject of this paper.12

Wilson, Jeffrey D.↗

NASA NTRS2011

Interference Analysis for an Aeronautical Mobile Airport Communications System

The next generation of aeronautical communications for airport surface applications has been identified through a NASA research program and an international collaborative future communications study. The result, endorsed by both the United States and European regulatory agencies is called AeroMACS (Aeronautical Mobile Airport Communications System) and is based upon the IEEE 802.16e mobile wireless standard. Coordinated efforts to develop appropriate aviation standards for the AeroMACS system are now underway within RTCA (United States) and Eurocae (Europe). AeroMACS will be implemented in a recently allocated frequency band, 5091-5150 MHz. As this band is also occupied by fixed satellite service uplinks, AeroMACS must be designed to avoid interference with this incumbent service. The aspects of AeroMACS operation that present potential interference to the fixed satellite service are under analysis in order to enable the definition of standards that assure that such interference will be avoided. The NASA Glenn Research Center has been involved in this analysis, and the first results of modeling and simulation efforts directed at this analysis are the subject of this presentation.

Wilson, Jeffrey D.↗

NASA NTRS2014

Comparison of GEOS-5 AGCM Planetary Boundary Layer Depths Computed with Various Definitions

Accurate models of planetary boundary layer (PBL) processes are important for forecasting weather and climate. The present study compares seven methods of calculating PBL depth in the GEOS-5 atmospheric general circulation model (AGCM) over land. These methods depend on the eddy diffusion coefficients, bulk and local Richardson numbers, and the turbulent kinetic energy. The computed PBL depths are aggregated to the Koppen climate classes, and some limited comparisons are made using radiosonde profiles. Most methods produce similar midday PBL depths, although in the warm, moist climate classes, the bulk Richardson number method gives midday results that are lower than those given by the eddy diffusion coefficient methods. Additional analysis revealed that methods sensitive to turbulence driven by radiative cooling produce greater PBL depths, this effect being most significant during the evening transition. Nocturnal PBLs based on Richardson number are generally shallower than eddy diffusion coefficient based estimates. The bulk Richardson number estimate is recommended as the PBL height to inform the choice of the turbulent length scale, based on the similarity to other methods during the day, and the improved nighttime behavior.

AGCM↗

NASA NTRS2006

Microgravity Geyser and Flow Field Prediction

Modeling and prediction of flow fields and geyser formation in microgravity cryogenic propellant tanks was investigated. A computational simulation was used to reproduce the test matrix of experimental results performed by other investigators, as well as to model the flows in a larger tank. An underprediction of geyser height by the model led to a sensitivity study to determine if variations in surface tension coefficient, contact angle, or jet pipe turbulence significantly influence the simulations. It was determined that computational geyser height is not sensitive to slight variations in any of these items. An existing empirical correlation based on dimensionless parameters was re-examined in an effort to improve the accuracy of geyser prediction. This resulted in the proposal for a re-formulation of two dimensionless parameters used in the correlation; the non-dimensional geyser height and the Bond number. It was concluded that the new non-dimensional geyser height shows little promise. Although further data will be required to make a definite judgement, the reformulation of the Bond number provided correlations that are more accurate and appear to be more general than the previously established correlation.

Hochstein, J. I.↗

NASA NTRS1990

Circumnutations of sunflower hypocotyls in satellite orbit

The principal objective of the research reported here was to determine whether a plant's periodic growth oscillations, called circumnutations, would persist in the absence of a significant gravitational or inertial force. The definitive experiment was made possible by access to the condition of protracted near weightlessness in an earth satellite. The experiment, performed during the first flight of Spacelab on the National Aeronautics and Space Administration shuttle, Columbia, in November and December, 1983, tested a biophysical model, proposed in 1967, that might account for circumnutation as a gravity-dependent growth response. However, circumnutations were observed in microgravity. They continued for many hours without stimulation by a significant g-force. Therefore, neither a gravitational nor an inertial g-force was an absolute requirement for initiation [correction of initation] or continuation of circumnutation. On average, circumnutation was significantly more vigorous in satellite orbit than on earth-based clinostats. Therefore, at least for sunflower (Helianthus annuus L.) circumnutation, clinostatting is not the functional equivalent of weightlessness.

NASA Discipline Plant Biology↗

DOE OSTI2020

Validation of emission-line galaxies target selection algorithms for the Dark Energy Spectroscopic Instrument using the MMT Binospec

ABSTRACT The forthcoming Dark Energy Spectroscopic Instrument (DESI) experiment plans to measure the effects of dark energy on the expansion of the Universe and create a 3D map of the Universe using galaxies up to z ∼ 1.6 and QSOs up to z ∼ 3.5. In order to create this map, DESI will obtain spectroscopic redshifts of over 30 million objects; among them, a majority are [O ii] emitting star-forming galaxies known as emission-line galaxies (ELGs). These ELG targets will be pre-selected by drawing a selection region on the g − r versus r − z colour–colour plot, where high-redshift ELGs form a separate locus from the lower redshift ELGs and interlopers. In this paper, we study the efficiency of three ELG target selection algorithms – the Final Design Report (FDR) cut based on the DEEP2 photometry, Number Density Modelling (NDM) and Random Forest – to determine how the combination of these three algorithms can be best used to yield a simple selection boundary that will be best suited to meet DESI’s science goals. To do this, we selected 17 small patches in the DESI footprint where we run the three target selection algorithms to pre-select ELGs based on their photometry. We observed the pre-selected ELGs using the MMT Binospec, which is similar in functionality to the DESI instrument, to obtain their spectroscopic redshifts and fluxes of 1054 ELGs. By analysing the redshift and fluxing distribution of these galaxies, we find that although NDM performed the best, simple changes in the FDR definition would also yield sufficient performance.

79 ASTRONOMY AND ASTROPHYSICS↗

NASA NTRS1971

On a programming language for graph algorithms

An algorithmic language, GRAAL, is presented for describing and implementing graph algorithms of the type primarily arising in applications. The language is based on a set algebraic model of graph theory which defines the graph structure in terms of morphisms between certain set algebraic structures over the node set and arc set. GRAAL is modular in the sense that the user specifies which of these mappings are available with any graph. This allows flexibility in the selection of the storage representation for different graph structures. In line with its set theoretic foundation, the language introduces sets as a basic data type and provides for the efficient execution of all set and graph operators. At present, GRAAL is defined as an extension of ALGOL 60 (revised) and its formal description is given as a supplement to the syntactic and semantic definition of ALGOL. Several typical graph algorithms are written in GRAAL to illustrate various features of the language and to show its applicability.

Rheinboldt, W. C.↗

NASA NTRS2004

Meeting the Deadline: Why, When and How

A normative system is defined as any set of interacting agents whose behavior can usefully be regarded as norm-directed. Most organizations, and more specifically institutions, fall under this definition. Interactions in these normative systems are regulated by normative templates that describe desired behavior in terms of deontic concepts (obligations, prohibitions and permissions), deadlines, violations and sanctions. Agreements between agents, and between an agent and the society, can then be specified by means of contracts. Contracts provide flexible but verifiable means to integrate society requirements and agent autonomy. and are an adequate means for the explicit specification of interactions. From the society perspective, it is important that these contracts adhere to the specifications described in the model of the organization. If we want to automate such verifications, we have to formalize the languages used for contracts and for the specification of organizations. The logic LCR is based on deontic temporal logic. LCR is an expressive language for describing interaction in multi-agent systems, including obligations with deadlines. Deadlines are important norms in most interactions between agents. Intuitively, a deadline states that an agent should perform an action before a certain point in time. The obligation to perform the action starts at the moment the deadline becomes active. E.g. when a contract is signed or approved. If the action is not performed in time a violation of the deadline occurs. It can be specified independently what measure has to be taken in this case. In this paper we investigate the deadline concept in more detail. The paper is organized as follows. Section 2 defines the variant of CTL we use. In section 3, we discuss the basic intuitions of deadlines. Section 4 presents a first intuitive formalization for deadlines. In section 5, we look at a more complex model for deadlines trying to catch some more practical aspects. Finally, in section 6 we present issues for future work and our conciusions.

Dignum, Frank↗

NASA NTRS2017

A Quantitative Risk-Benefit Analysis of Prophylactic Surgery Prior to Extended-Duration Spaceflight

INTRODUCTION: Among otherwise healthy astronauts undertaking deep space missions, the risks for acute appendicitis (AA) and cholecystitis (AC) are not zero. If these conditions were to occur during spaceflight they may require surgery for definitive care. The proposed study quantifies and compares the risks of developing de novo AA and AC in-flight to the surgical risks of prophylactic laparoscopic appendectomy (LA) and cholecystectomy (LC) using NASA's Integrated Medical Model (IMM). METHODS: The IMM is a Monte Carlo simulation that forecasts medical events during spaceflight missions and estimates the impact of these medical events on crew health. In this study, four Design Reference Missions (DRMs) were created to assess the probability of an astronaut developing in-flight small-bowel obstruction (SBO) following prophylactic 1) LA, 2) LC, 3) LA and LC, or 4) neither surgery (SR# S-20160407-351). Model inputs were drawn from a large, population-based 2011 Swedish study that examined the incidence and risks of post-operative SBO over a 5-year follow-up period. The study group included 1,152 patients who underwent LA, and 16,371 who underwent LC. RESULTS: Preliminary results indicate that prophylactic LA may yield higher mission risks than the control DRM. Complete analyses are pending and will be subsequently available. DISCUSSION: The risk versus benefits of prophylactic surgery in astronauts to decrease the probability of acute surgical events during spaceflight has only been qualitatively examined in prior studies. Within the assumptions and limitations of the IMM, this work provides the first quantitative guidance that has previously been lacking to this important question for future deep space exploration missions.

Carroll, Danielle↗

NASA NTRS1994

Precision orbit determination for TOPEX/POSEIDON

The TOPEX/POSEIDON mission objective requires that the radial position of the spacecraft be determined with an accuracy better than 13 cm RMS (root mean square). This stringent requirement is an order of magnitude below the accuracy achieved for any altimeter mission prior to the definition of the TOPEX/POSEIDON mission. To satislfy this objective, the TOPEX Precision Orbit determination (POD) Team was established as a joint effort between the NASA Goddard Space Flight Center and the University of Texas at Austin, with collaboration from the University of Colorado and the Jet Propulsion Laboratory. During the prelaunch development and the post launch verification phases, the POD team improved, calibrated, and validated the precision orbit determination computer software systems. The accomplishments include (1) increased accuracy of the gravity and surface force models and (2) improved peformance of both laser ranging and Doppler tracking systems. The result of these efforts led to orbit accuracies for TOPEX/POSEIDON which are significantly better than the original mission requirement. Tests based on data fits, covariance analysis, and orbit comparisons indicate that the radial component of the TOPEX/POSEIDON spacecraft is determined, relative to the Earth's mass center, with an root mean square (RMS) error in the range of 3 to 4 cm RMS. This orbit accuracy, together with the near continuous dual-frequency altimetry from this mission, provides the means to determine the ocean's dynamic topography with an unprecedented accuracy.

Tapley, B. D.↗

NASA NTRS2017

Medical Systems Engineering to Support Mars Mission Crew Autonomy

Human spaceflight missions to Mars face exceptionally challenging resource limitations that far exceed those faced before. Increasing transit times, decreasing opportunity for resupply, communications challenges, and extended time to evacuate a crew to definitive medical care dictate a level of crew autonomy in medical care that is beyond the current medical model. To approach this challenge, a medical systems engineering approach is proposed that relies on a clearly articulated Concept of Operations and risk analysis tools that are in development at NASA. This paper proposes an operational clinical model with key terminology and concepts translated to a controls theory paradigm to frame a common language between clinical and engineering teams. This common language will be used for design and validation of an exploration medical system that is fully integrated into a Mars transit vehicle. This approach merges medical simulation, human factors evaluation techniques, and human-in-the-loop testing in ground based analogs to tie medical hardware and software subsystem performance and overall medical system functionality to metrics of operational medical autonomy. Merging increases in operational clinical autonomy with a more restricted vehicle system resource scenario in interplanetary spaceflight will require an unprecedented level of medical and engineering integration. Full integration of medical capabilities into a Mars vehicle system may require a new approach to integrating medical system design and operations into the vehicle Program structure. Prior to the standing-up of a Mars Mission Program, proof of concept is proposed through the Human Research Program.

Antonsen, Erik↗

NASA NTRS2019

Nonmodal Growth of TravelingWaves on Blunt Cones at Hypersonic Speeds

The existing database of transition measurements in hypersonic ground facilities has established that, as the nosetip bluntness is increased, the onset of boundary layer transition over a circular cone at zero angle of attack shifts downstream. However, this trend is reversed at sufficiently large values of the nose Reynolds number, so that the transition onset location eventually moves upstream with a further increase in nose-tip bluntness. Because modal amplification is too weak to initiate transition at moderate-to-large bluntness values, nonmodal growth has been investigated as the potential basis for a physics-based model for the frustum transition. The present analysis investigates the nonmodal growth of traveling disturbances initiated within the nose-tip vicinity that peak within the entropy layer. Results show that, with increasing nose bluntness, both planar and oblique traveling disturbances experience appreciable energy amplification up to successively higher frequencies. For moderately blunt cones, the initial nonmmodal growth is followed by a partial decay that is more than overcome by an eventual, modal growth as Mack-mode waves. For larger bluntness values, the Mack-mode waves are not amplified anywhere upstream of the experimentally measured transition location, but the traveling modes still undergo a significant amount of nonmodal growth. This finding does not provide a definitive link between optimal growth and the onset of transition, but it is qualitatively consistent with the experimental observations that frustum transition in the absence of sufficient Mack-mode amplification implies a double peak in disturbance amplification and the appearance of transitional events above the boundary-layer edge.

Hypersonic speed↗