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NASA NTRS1984

Dilution Jets in Accelerated Cross Flows

Results of flow visualization experiments and measurements of the temperature field produced by a single jet and a row of dilution jets issued into a reverse flow combustor are presented. The flow in such combustors is typified by transverse and longitudinal acceleration during the passage through its bending section. The flow visualization experiments were designed to examine the separate effects of longitudinal and transverse acceleration on the jet trajectory and spreading rate. A model describing a dense single jet in a lighter accelerating cross flow is developed. The model is based on integral conservation equations, including the pressure terms appropriate to accelerating flows. It uses a modified entrainment correlation obtained from previous experiments of a jet in a cross stream. The flow visualization results are compared with the model calculations in terms of trajectories and spreading rates. Each experiment is typified by a set of three parameters: momentum ratio, density ratio, and the densimetric Froude number. When injection velocities are large or densities are small, the Froude number becomes very large and hence, unimportant. Therefore, the Froude number is generally significant in describing liquid experiments but is unimportant for the gas experiments in the combustor. Agreement between test and calculated results is encouraging but tends to become poorer with increasing momentum ratio. The temperature measurements are presented primarily in the form of consecutive normalized temperature profiles. Some interpolated isothermal contours are also shown. The single jet trajectories are consistently found to be swept towards the inner wall of the bend, whether injection is from the outer or the inner wall. This behavior is explained by a drifting effect which consists of a transverse velocity component across the combustor due to the developing nature of the flow along it. Plots of lateral temperature distributions of the jet indicate that under longitudinal acceleration conditions the thermal spreading of the jet may be completely suppressed. Comparison between combustor experimental results and model calculations shows poor agreement due to the drifting effect which is not taken into consideration in the model calculations. The row of jets experiments are characterized by two additional parameters: spacing ratio and confinement parameter. The results are shown in the form of consecutive normalized temperature profiles. The confinement parameter appears to become increasingly important with decreasing spacing ratio, in particular when its effect is enhanced by the drifting phenomenon and associated pressure field. A tightly spaced row of jets injected from the inner wall, prior to the bend, is surprisingly kept attached to the inner wall in spite of the strong turning. A similar attachment for a jet injected from the outer wall is not observed.

Lipshitz, Abraham↗

NASA NTRS1984

Dilution jets in accelerated cross flows

Lipshitz, A.↗

DOE OSTI2024

An implicit solution for Asay foil trajectories generated by separable, sustained-production ejecta source models

We present a simple implicit solution for the time-dependent trajectory of a thin Asay foil ejecta diagnostic for the general case where the impinging ejecta cloud is generated by a source function characterized by an arbitrary (sustained) time dependence and a time-independent (stationary) particle velocity distribution. In the limit that the source function time dependence becomes a delta function, this solution—which is amenable to rapid numerical calculations of arbitrary accuracy—exactly recovers a previously published solution for the special case of instantaneous ejecta production. We also derive simple expressions for the free-surface arrival (catch-up) time as well as the true ejecta areal mass accumulation on the accelerating foil and place bounds on the level of error incurred when applying instant-production mass solutions to a sustained-production trajectory. We demonstrate these solutions with example calculations for hypothetical source functions spanning a wide range of ejecta production durations, velocity distributions, and temporal behaviors. These calculations demonstrate how the foil trajectory is often insensitive to the temporal dependence of the source function, instead being dominated by the velocity distribution. We quantify this insensitivity using a “compatibility score” metric. Under certain conditions, one may capitalize upon this insensitivity to obtain a good approximation of the second integral of the velocity distribution from the observed foil trajectory.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

NASA NTRS1979

Air breathing engine/rocket trajectory optimization

This research has focused on improving the mathematical models of the air-breathing propulsion systems, which can be mated with the rocket engine model and incorporated in trajectory optimization codes. Improved engine simulations provided accurate representation of the complex cycles proposed for advanced launch vehicles, thereby increasing the confidence in propellant use and payload calculations. The versatile QNEP (Quick Navy Engine Program) was modified to allow treatment of advanced turboaccelerator cycles using hydrogen or hydrocarbon fuels and operating in the vehicle flow field.

Smith, V. K., III↗

NASA NTRS2019

Management by Trajectory: Improving Predictability for Airspace Operations

In the present-day National Airspace System, the air traffic management system attempts to predict the trajectory for each flight based on the flight plan and scheduled or controlled departure time. However, gaps in trajectory data and models, coupled with tactical control actions that are not communicated to automation systems or other stakeholders, lead to trajectory predictions that are less accurate than they could be. This affects traffic flow management performance. Management by Trajectory (MBT) is a NASA concept for air traffic management in which every flight operates in accordance with a 4D trajectory that is negotiated between the airspace user and the FAA to account for the airspace user’s goals while complying with NAS constraints. The primary benefit of MBT is an improvement in system performance due to increased trajectory predictability and stability, which result from managing traffic in all four dimensions (2D route, vertical, and time), ensuring that changes to the flight’s trajectory are incorporated into the assigned trajectory, and utilizing improved time or arrival control standards. Importantly, the performance improvements support increasing efficiency without increasing collision risk. This paper provides an overview of MBT and describes fast-time simulation results evaluating the safety, performance, and efficiency effects of MBT.

Fernandes, Alicia B.↗

DOE OSTI2025

Langevin Dynamics modeling of gas-phase ion-ion recombination (Final Technical Report)

A self-consistent trajectory simulation approach to model MN reactions (Fig. 1) which incorporates the probability of electron transfer as a Monte Carlo operator (Fig. 2) was developed and published as Liu et al. J. Chem. Phys. 159, 114111 (2023). The electron transfer probability p ET estimated using the two-state Landau-Zener (LZ) theory was incorporated into classical trajectory simulations to elicit predictions of MN reaction cross-section σ (vacuum) or rate constant β (finite pressure). Electronic structure calculations with multireference configuration interaction (MRCI) and large correlation consistent basis sets were used to derive inputs to the LZ theory. The key advance of our trajectory simulation approach is the incorporation of electron transfer probability and the inclusion of the effect of ion-neutral interactions on MN using a Langevin representation of the effect of neutral gas on ions. For H + – H - and Li + – H(D) - pairs, our approach quantitatively agrees with measured speed-dependent cross-sections for up to ~10 5 m/s. For the ion pair Ne + – Cl - , our predictions of the MN rate constant at ~1 torr are a factor of ~2 – 3 higher than the experimentally measured value. Similarly, for Xe + – F - in the pressure range of ~20000 – 80000 Pa, our predictions of the MN rate constant are ~20% lower but are in excellent qualitative agreement with experimental data. The paradigm of using trajectory simulations to self-consistently model MN reactions is the basis for inclusion of additional non-classical, and static magnetic and electric field effects. Subsequent work, published as Roy et al. focused on modeling recombination rate constant for three ion pairs (rare gas Ar + cation and halide anions): Ar + – Cl - , Ar + – Br - , Ar + – I - , 2) considering spin-orbit couplings in the electronic structure calculations to obtain high-fidelity estimates of the electron transfer probability and incorporated within the classical trajectory simulations to elicit predictions. In addition to calculations of ion-ion recombination rate constants, a classical trajectory simulation technique (published as Roy et al. J. Chem. Phys. 162(9), 094104 (2023)) that uses quaternions to represent orientation of non-spherical particles (ions or aerosol particles) was developed to simulate the recombination of diatomic or more generally, polyatomic molecules. Finally, several other ion pairs such as Ne + – Cl - , Kr + – Cl - , were explored using the developed semi-classical trajectory simulations to understand various challenges in tackling electronic structure calculations. Using empirical approaches to parameterize the electron transfer radius, trajectory simulations were also used to probe the effect of ion number density on MN rate constant.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

NASA NTRS2007

Evaluation of Bulk Charging in Geostationary Transfer Orbit and Earth Escape Trajectories Using the Numit 1-D Charging Model

The NUMIT 1-dimensional bulk charging model is used as a screening to ol for evaluating time-dependent bulk internal or deep dielectric) ch arging of dielectrics exposed to penetrating electron environments. T he code is modified to accept time dependent electron flux time serie s along satellite orbits for the electron environment inputs instead of using the static electron flux environment input originally used b y the code and widely adopted in bulk charging models. Application of the screening technique ts demonstrated for three cases of spacecraf t exposure within the Earth's radiation belts including a geostationa ry transfer orbit and an Earth-Moon transit trajectory for a range of orbit inclinations. Electric fields and charge densities are compute d for dielectric materials with varying electrical properties exposed to relativistic electron environments along the orbits. Our objectiv e is to demonstrate a preliminary application of the time-dependent e nvironments input to the NUMIT code for evaluating charging risks to exposed dielectrics used on spacecraft when exposed to the Earth's ra diation belts. The results demonstrate that the NUMIT electric field values in GTO orbits with multiple encounters with the Earth's radiat ion belts are consistent with previous studies of charging in GTO orb its and that potential threat conditions for electrostatic discharge exist on lunar transit trajectories depending on the electrical proper ties of the materials exposed to the radiation environment.

Minow, Joseph I.↗

NASA NTRS1975

Cloud motion in relation to the ambient wind field

Trajectories of convective clouds were computed from a mathematical model and compared with trajectories observed by radar. The ambient wind field was determined from the AVE IIP data. The model includes gradient, coriolis, drag, lift, and lateral forces. The results show that rotational effects may account for large differences between the computed and observed trajectories and that convective clouds may move 10 to 20 degrees to the right or left of the average wind vector and at speeds 5 to 10 m/sec faster or slower than the average ambient wind speed.

Fuelberg, H. E.↗

NASA NTRS2006

Titan Explorer Entry, Descent and Landing Trajectory Design

The Titan Explorer mission concept includes an orbiter, entry probe and inflatable airship designed to take remote and in-situ measurements of Titan's atmosphere. A modified entry, descent and landing trajectory at Titan that incorporates mid-air airship inflation (under a parachute) and separation is developed and examined for Titan Explorer. The feasibility of mid-air inflation and deployment of an airship under a parachute is determined by implementing and validating an airship buoyancy and inflation model in the trajectory simulation program, Program to Optimize Simulated Trajectories II (POST2). A nominal POST2 trajectory simulation case study is generated which examines different descent scenarios by varying airship inflation duration, orientation, and separation. The buoyancy model incorporation into POST2 is new to the software and may be used in future trajectory simulations. Each case from the nominal POST2 trajectory case study simulates a successful separation between the parachute and airship systems with sufficient velocity change as to alter their paths to avoid collision throughout their descent. The airship and heatshield also separate acceptably with a minimum distance of separation from the parachute system of 1.5 km. This analysis shows the feasibility of airship inflation on a parachute for different orientations, airship separation at various inflation times, and preparation for level-flight at Titan.

Fisher, Jody L.↗

NASA NTRSDate not supplied

Probabalistic Risk Analysis and Thermal Margin Process for an Inflatable Aeroshell

Uncertainties always exist in atmospheric entry aeroheating environments and the thermal response of thermal protection system (TPS) material. These uncertainties are mitigated in the design by ap-plying margin and factors of safety to the TPS. Entry vehicle TPS is often conservatively over-sized for the heat loads that are experienced along the entry trajectory by stacking worst-case scenarios together. Additionally, the current TPS design and margin process used by NASA offers very little insight into the risk of over-temperature during flight and the reliability of the heat shield performance [1,3]. A probabilistic margin process can be used to calculate the amount of TPS margin necessary to survive a given entry heat load at a specified level of risk [2,3,4]. The vehicle’s initial entry state (entry velocity, flight path angle, and entry mass) determines the expected atmospheric entry environmental conditions and resulting heat load that the entry vehicle will experience. If there is flexibility in the entry state, then this process can be used to select an appropriate combination of entry state parameters and TPS size to target a desired reentry reliability. This probabilistic margin process allows engineers to make informed aeroshell design, entry-trajectory design, and TPS performance risk trades while preventing excessive TPS margin from being applied. The probabilistic TPS margin process has been performed to determine TPS thickness and entry heating constraints given an acceptable risk level for the Low Earth Orbit Flight Experiment of an Inflatable Decelerator (LOFTID) flight project. The process is used in a manner to size the entry heat load for a given flexible TPS (FTPS) thickness so that it meets project reliability standards while allowing the FTPS and the underlying inflatable structure (IS) to be pushed to adequately high temperatures. Since the LOFTID project is an experimental flight demonstration, it is de-sired to drive the FTPS and IS to temperatures that cover a large range of their thermal response models’ applicability. This will allow the thermal response models to be better improved and validated post-flight using LOFTID’s extensive instrumentation embedded within the aeroshell. The presentation demonstrates how uncertainty analysis is carried out using an end-to-end Monte Carlo process where three separate Monte Carlo simulations are run in sequence. The first Monte Carlo simulation operates on the entry trajectory model to generate trajectory parameter dispersions that are fed into the second Monte Carlo simulation. The second Monte Carlo simulation operates on the aerothermodynamics model to generate aeroheating parameter dispersions that are fed into the third Monte Carlo simulation. The third Monte Carlo simulation operates on the FTPS material thermal response model to generate the final FTPS/IS thermal response dispersions. The end-to-end Monte Carlo simulation propagates the uncertainties of each model into the next to quantify the resulting uncertainty of the FTPS/IS thermal response. The fractional contributions of the uncertain parameters in the trajectory, aerothermal, and thermal response models to the variance in the FTPS/IS thermal response is determined as a byproduct of the Monte Carlo analysis. The structural uncertainty of the FTPS thermal response model is evaluated by flight relevant ground testing and model error analysis using test measurements. This probabilistic TPS margin process had never been applied to an entry vehicle and it is one of the LOFTID project’s goals to demonstrate its merits.

Steven A. Tobin↗

NASA NTRS2017

Multilayer Insulation Ascent Venting Model

The thermal and venting transient experienced by tank-applied multilayer insulation (MLI) in the Earth-to-orbit environment is very dynamic and not well characterized. This new predictive code is a first principles-based engineering model which tracks the time history of the mass and temperature (internal energy) of the gas in each MLI layer. A continuum-based model is used for early portions of the trajectory while a kinetic theory-based model is used for the later portions of the trajectory, and the models are blended based on a reference mean free path. This new capability should improve understanding of the Earth-to-orbit transient and enable better insulation system designs for in-space cryogenic propellant systems.

Tramel, R. W.↗

NASA NTRS2022

A Generalized Approach to Aircraft Trajectory Prediction via Supervised Deep Learning

As research advances diverse forms and missions of aircraft, the National Airspace System (NAS) will become increasingly crowded, limiting current communications resources to accommodate aviation operations. Ongoing research proposes a paradigm of airspace communications, such that resources are autonomously and dynamically allocated via intelligent agents; this allocation requires accurate representations of the NAS, including the predicted positions of aircraft. State-of-the-art research emphasizes the importance of a hybrid-recurrent framework for trajectory prediction and compares the impact of commonly considered weather data on prediction accuracy. However, current research has been limited in its scope of efforts, frequently utilizing a unique flight route, architecture, set of weather data, and date range. This article considers the challenges of generalizing hybrid-recurrent predictive models for flight trajectories. Results illustrate an increase in error variance when identical models are trained over a generalized set of flights; this may be mitigated with careful tuning of hyperparameters, both in the network structure and optimization algorithms. Even so, an irreducible vertical error was identified, resulting from the complex takeoff and landing procedures which can not be correlated to functions of weather or additional assumptions of aircraft behavior. Finally, the use of a test route indicates that generalized models still do not possess sufficient knowledge for general aircraft predictions, with mean error increases ranging from 70-500%. These results illustrate the need for continued efforts on improving model versatility, as well as potential limitations for spectrum allocation near airports and other centers.

Nathan Schimpf↗

DOE OSTI2025

An Advanced Microscopic Energy Consumption Model for Automated Vehicle:Development, Calibration, Verification

The automated vehicle (AV) equipped with the Adaptive Cruise Control (ACC) system is expected to reduce the fuel consumption for the intelligent transportation system. This paper presents the Advanced ACC-Micro (AA-Micro) model, a new energy consumption model based on micro trajectory data, calibrated and verified by empirical data. Utilizing a commercial AV equipped with the ACC system as the test platform, experiments were conducted at the Columbus 151 Speedway, capturing data from multiple ACC and Human-Driven (HV) test runs. The calibrated AA-Micro model integrates features from traditional energy consumption models and demonstrates superior goodness of fit, achieving an impressive 90% accuracy in predicting ACC system energy consumption without overfitting. A comprehensive statistical evaluation of the AA-Micro model's applicability and adaptability in predicting energy consumption and vehicle trajectories indicated strong model consistency and reliability for ACC vehicles, evidenced by minimal variance in RMSE values and uniform RSS distributions. Conversely, significant discrepancies were observed when applying the model to HV data, underscoring the necessity for specialized models to accurately predict energy consumption for HV and ACC systems, potentially due to their distinct energy consumption characteristics.

Ma, Ke↗

NASA NTRS1992

Trajectory fitting in function space with application to analytic modeling of surfaces

A theory for representing a parameter-dependent function as a function trajectory is described. Additionally, a theory for determining a piecewise analytic fit to the trajectory is described. An example is given that illustrates the application of the theory to generating a smooth surface through a discrete set of input cross-section shapes. A simple procedure for smoothing in the parameter direction is discussed, and a computed example is given. Application of the theory to aerodynamic surface modeling is demonstrated by applying it to a blended wing-fuselage surface.

Barger, Raymond L.↗

NASA NTRS2000

The Sensitivity of Model Ozone to Advective and Photochemical Processes in the High Latitude Winter Lower Stratosphere

Three dimensional chemistry and transport models (CTMs) contain a set of coupled continuity equations which describe the evolution of constituents such as ozone and other minor species which affect ozone. Both advection and photochemical processes contribute to constituent evolution, and a CTM provides a means to evaluate these contributions separately. Such evaluation is particularly useful when both terms are important to the modeled tendency. An example is the ozone tendency in the high latitude winter lower stratosphere, where advection tends to increase ozone, and catalytic processes involving chlorine radicals tend to decrease ozone. The Goddard three dimensional chemistry and transport model uses meteorological fields from the Goddard Earth Observing System Data Assimilation System, thus the modeled ozone evolution may reproduce the observed evolution and provide a test of the model representation of photochemical processes if the transport is shown to be modeled appropriately. We have investigated the model advection further using diabatic trajectory calculations. For long lived constituents such as N2O, the model field for a particular time on a potential temperature surface is compared with a field produced by calculating 15 day back trajectories for a fixed latitude longitude grid, and mapping model N2O at the terminus of the back trajectories onto the initial grid. This provides a quantitative means to evaluate two aspects of the CTM transport: one, the model horizontal gradient between middle latitudes and the polar vortex is compared with the gradient produced using the non-diffusive trajectory calculation; two, the model vertical advection, which is produced by the divergence of the horizontal winds, is compared with the vertical transport expected from diabatic cooling.

Douglass, A.↗

NASA NTRS2017

Fusion-Enabled Pluto Orbiter and Lander

The Pluto orbiter mission proposed here is credible and exciting. The benefits to this and all outer-planet and interstellar-probe missions are difficult to overstate. The enabling technology, Direct Fusion Drive, is a unique fusion engine concept based on the Princeton Field-Reversed Configuration (PFRC) fusion reactor under development at the Princeton Plasma Physics Laboratory. The truly game-changing levels of thrust and power in a modestly sized package could integrate with our current launch infrastructure while radically expanding the science capability of these missions. During this Phase I effort, we made great strides in modeling the engine efficiency, thrust, and specific impulse and analyzing feasible trajectories. Based on 2D fluid modeling of the fusion reactors outer stratum, its scrape-off-layer (SOL), we estimate achieving 2.5 to 5 N of thrust for each megawatt of fusion power, reaching a specific impulse, Isp, of about 10,000 s. Supporting this model are particle-in-cell calculations of energy transfer from the fusion products to the SOL electrons. Subsequently, this energy is transferred to the ions as they expand through the magnetic nozzle and beyond. Our point solution for the Pluto mission now delivers 1000 kg of payload to Pluto orbit in 3.75 years using 7.5 N constant thrust. This could potentially be achieved with a single 1 MW engine. The departure spiral from Earth orbit and insertion spiral to Pluto orbit require only a small portion of the total delta-V. Departing from low Earth orbit reduces mission cost while increasing available mission mass. The payload includes a lander, which utilizes a standard green propellant engine for the landing sequence. The lander has about 4 square meters of solar panels mounted on a gimbal that allows it to track the orbiter, which beams 30 to 50 kW of power using a 1080 nm laser. Optical communication provides dramatically high data rates back to Earth. Our mass modeling investigations revealed that if current high-temperature superconductors are utilized at liquid nitrogen temperatures, they drive the mass of the engine, partly because of the shielding required to maintain their critical temperature. Second generation materials are thinner but the superconductor is a very thin layer deposited on a substrate with additional layers of metallic classing. Tremendous research is being performed on a variety of these superconducting materials, and new irradiation data is now available. This raises the possibility of operating nearfuture high-temperature superconductors at a moderately low temperature to dramatically reduce the amount of shielding required. At the same time, a first generation space engine may require low-temperature superconductors, which are higher TRL and have been designed for space coils before (AMS-02 experiment for the ISS). We performed detailed analysis of the startup system and thermal conversion system components. The ideal working fluid was determined to be a blend of Helium and Xenon. No significant problems were identified with these subsystems. For the RF system, we conceived of a new, more efficient design using state-of-the-art switch amplifiers, which have the potential for 100% efficiency. This report presents details of our engine and trajectory analyses, mass modeling efforts, and updated vehicle designs.

temperature↗

NASA NTRS1990

Ionospheric refraction effects on orbit determination using the orbit determination error analysis system

The influence of ionospheric refraction on orbit determination was studied through the use of the Orbit Determination Error Analysis System (ODEAS). The results of a study of the orbital state estimate errors due to the ionospheric refraction corrections, particularly for measurements involving spacecraft-to-spacecraft tracking links, are presented. In current operational practice at the Goddard Space Flight Center (GSFC) Flight Dynamics Facility (FDF), the ionospheric refraction effects on the tracking measurements are modeled in the Goddard Trajectory Determination System (GTDS) using the Bent ionospheric model. While GTDS has the capability of incorporating the ionospheric refraction effects for measurements involving ground-to-spacecraft tracking links, such as those generated by the Ground Spaceflight Tracking and Data Network (GSTDN), it does not have the capability to incorporate the refraction effects for spacecraft-to-spacecraft tracking links for measurements generated by the Tracking and Data Relay Satellite System (TDRSS). The lack of this particular capability in GTDS raised some concern about the achievable accuracy of the estimated orbit for certain classes of spacecraft missions that require high-precision orbits. Using an enhanced research version of GTDS, some efforts have already been made to assess the importance of the spacecraft-to-spacecraft ionospheric refraction corrections in an orbit determination process. While these studies were performed using simulated data or real tracking data in definitive orbit determination modes, the study results presented here were obtained by means of covariance analysis simulating the weighted least-squares method used in orbit determination.

Yee, C. P.↗

NASA NTRS1975

Mission Analysis Program for Solar Electric Propulsion (MAPSEP). Volume 1: Analytical manual for earth orbital MAPSEP

An introduction to the MAPSEP organization and a detailed analytical description of all models and algorithms are given. These include trajectory and error covariance propagation methods, orbit determination processes, thrust modeling, and trajectory correction (guidance) schemes. Earth orbital MAPSEP contains the capability of analyzing almost any currently projected low thrust mission from low earth orbit to super synchronous altitudes. Furthermore, MAPSEP is sufficiently flexible to incorporate extended dynamic models, alternate mission strategies, and almost any other system requirement imposed by the user. As in the interplanetary version, earth orbital MAPSEP represents a trade-off between precision modeling and computational speed consistent with defining necessary system requirements. It can be used in feasibility studies as well as in flight operational support. Pertinent operational constraints are available both implicitly and explicitly. However, the reader should be warned that because of program complexity, MAPSEP is only as good as the user and will quickly succumb to faulty user inputs.

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