Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “numerical integration”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 361 records · Page 20
All sourcesNASA NTRSDOE OSTI
NASA NTRS2018

Machine Learning Application to Atmospheric Chemistry Modeling

Atmospheric chemistry is a high-dimensionality, large-data problem and thus may be suited to machine-learning algorithms. We show here the potential of a random forest regression algorithm to replace the gas-phase chemistry solver in the GEOS-Chem chemistry model. In this proof-of-concept study, we used one month of model output to train random forest regression models to predict the concentrations of each long-lived chemical species after integration based upon the physical and chemical conditions before the chemical integration. The choice of prediction type has a strong impact on the skill of the regression model. We find best results from predicting the change in concentration for very long-lived species and the absolute concentration for shorter lived species. The skill of the machine learning algorithm is further improved by using a family approach for NO and NO2 rather than treating them independently.By replacing the numerical integrator with the random forest algorithm and running this model for one month, we find that the model is able to reproduce many of the features of the reference chemistry simulation. Replacing the integration methodology with a machine learning algorithm has the potential to be substantially faster. There are a wide range of applications for such an approach, e.g. to generate boundary conditions, for use in air quality forecasts or chemical data assimilation systems, etc.

Keller, Christoph A.↗
NASA NTRS2015

Efficient Trajectory Propagation for Orbit Determination Problems

Regularized formulations of orbital motion apply a series of techniques to improve the numerical integration of the orbit. Despite their advantages and potential applications little attention has been paid to the propagation of the partial derivatives of the corresponding set of elements or coordinates, required in many orbit-determination scenarios and optimization problems. This paper fills this gap by presenting the general procedure for integrating the state-transition matrix of the system together with the nominal trajectory using regularized formulations and different sets of elements. The main difficulty comes from introducing an independent variable different from time, because the solution needs to be synchronized. The correction of the time delay is treated from a generic perspective not focused on any particular formulation. The synchronization using time-elements is also discussed. Numerical examples include strongly-perturbed orbits in the Pluto system, motivated by the recent flyby of the New Horizons spacecraft, together with a geocentric flyby of the NEAR spacecraft.

numerical methods↗
NASA NTRS1978

On the attitude motion of an orbiting rigid body under the influence of gravity gradient torque

An investigation is made of the rotational motion of a rigid body orbiting the earth, under the influence of the geogravity-gradient torque. The attitude dynamics are formulated as perturbations from a nominal case. The perturbed equations are solved asymptotically, by the multiple scales technique. The independent variable, time, is extended into a space of higher dimension by means of new scales, fast, slow, etc. Integration of the equations is carried out separately in the new variables. The rapid and slow aspects of the attitude dynamics are systematically separated, resulting in a more efficient computer implementation and enhanced physical insight. The theory is applied to predict the attitude dynamics of an asymmetric rigid body satellite. A comparison is made of the maximum errors as the step size increases as predicted by the multiple scales solution and direct numerical integration. An improvement in computational speed of an order of magnitude is demonstrated.

Tao, Y. C.↗
NASA NTRS2011

G-DYN Multibody Dynamics Engine

G-DYN is a multi-body dynamic simulation software engine that automatically assembles and integrates equations of motion for arbitrarily connected multibody dynamic systems. The algorithm behind G-DYN is based on a primal-dual formulation of the dynamics that captures the position and velocity vectors (primal variables) of each body and the interaction forces (dual variables) between bodies, which are particularly useful for control and estimation analysis and synthesis. It also takes full advantage of the spare matrix structure resulting from the system dynamics to numerically integrate the equations of motion efficiently. Furthermore, the dynamic model for each body can easily be replaced without re-deriving the overall equations of motion, and the assembly of the equations of motion is done automatically. G-DYN proved an essential software tool in the simulation of spacecraft systems used for small celestial body surface sampling, specifically in simulating touch-and-go (TAG) maneuvers of a robotic sampling system from a comet and asteroid. It is used extensively in validating mission concepts for small body sample return, such as Comet Odyssey and Galahad New Frontiers proposals.

Acikmese, Behcet↗
NASA NTRSDate not supplied

Numerical Modeling of No Vent Filling of a Cryogenic Tank

This paper presents a multi-node finite volume model of the chilling and filling of a cryogenic tank using the Generalized Fluid System Simulation Program (GFSSP), a general purpose flow network code. Vented Chill and No Vent Fill (VCNVF) tests were conducted at Marshall Space Flight Center where a flight-like tank was filled with liquid nitrogen from a supply tank. In the VCNVF tests, the tank was partially chilled while the vent valve was open. After the partial chilling, the vent valve was closed and the tank was filled without any venting. An integrated numerical model of the test set up was developed. The model included the transfer line from the supply tank, the target tank with the spray nozzle and solid walls, and the discharge line with the vent valve. The tank was discretized into multiple fluid nodes and branches to represent the ullage and liquid nitrogen and multiple solid nodes to represent the tank wall and structure. The heat transfer between solid to fluid was calculated from pool boiling correlations which include film, transition, and nucleate boiling, as well as natural convection during pre- and post-boiling. The model also accounts for the condensation of vapor in the tank when it comes in contact with the liquid spray. The predicted pressure, resident mass, wall and ullage temperature in the tank were compared with the test data.

Alok Majumdar↗
NASA NTRSDate not supplied

Numerical Modeling of No Vent Filling of a Cryogenic Tank

This paper presents a multi-node finite volume model of the chilling and filling of a cryogenic tank using the Generalized Fluid System Simulation Program (GFSSP), a general purpose flow network code. Vented Chill and No Vent Fill (VCNVF) tests were conducted at Marshall Space Flight Center where a flight-like tank was filled with liquid nitrogen from a supply tank. In the VCNVF tests, the tank was partially chilled while the vent valve was open. After the partial chilling, the vent valve was closed and the tank was filled without any venting. An integrated numerical model of the test set up was developed. The model included the transfer line from the supply tank, the target tank with the spray nozzle and solid walls, and the discharge line with the vent valve. The tank was discretized into multiple fluid nodes and branches to represent the ullage and liquid nitrogen and multiple solid nodes to represent the tank wall and structure. The heat transfer between solid to fluid was calculated from pool boiling correlations which include film, transition, and nucleate boiling, as well as natural convection during pre- and post-boiling. The model also accounts for the condensation of vapor in the tank when it comes in contact with the liquid spray. The predicted pressure, resident mass, wall and ullage temperature in the tank were compared with the test data.

Alok Majumdar↗
NASA NTRS1996

Kuiper Belt Dust Grains as a Source of Interplanetary Dust Particles

The recent discovery of the so-called Kuiper belt objects has prompted the idea that these objects produce dust grains that may contribute significantly to the interplanetary dust population. In this paper, the orbital evolution of dust grains, of diameters 1 to 9 microns, that originate in the region of the Kuiper belt is studied by means of direct numerical integration. Gravitational forces of the Sun and planets, solar radiation pressure, as well as Poynting-Robertson drag and solar wind drag are included. The interactions between charged dust grains and solar magnetic field are not considered in the model. Because of the effects of drag forces, small dust grains will spiral toward the Sun once they are released from their large parent bodies. This motion leads dust grains to pass by planets as well as encounter numerous mean motion resonances associated with planets. Our results show that about 80% of the Kuiper belt grains are ejected from the Solar System by the giant planets, while the remaining 20% of the grains evolve all the way to the Sun. Surprisingly, the latter dust grains have small orbital eccentricities and inclinations when they cross the orbit of the Earth. This makes them behave more like asteroidal than cometary-type dust particles. This also enhances their chances of being captured by the Earth and makes them a possible source of the collected interplanetary dust particles; in particular, they represent a possible source that brings primitive/organic materials from the outer Solar System to the Earth. When collisions with interstellar dust grains are considered, however, Kuiper belt dust grains around 9 microns appear likely to be collisionally shattered before they can evolve toward the inner part of the Solar System. The collision destruction can be applied to Kuiper belt grains up to about 50 microns. Therefore, Kuiper belt dust grains within this range may not be a significant part of the interplanetary dust complex in the inner Solar System.

Liou, Jer-Chyi↗
NASA NTRS1971

Techniques of orbital decay and long-term ephemeris prediction for satellites in earth orbit

In the special perturbation method, Cowell and variation-of-parameters formulations of the motion equations are implemented and numerically integrated. Variations in the orbital elements due to drag are computed using the 1970 Jacchia atmospheric density model, which includes the effects of semiannual variations, diurnal bulge, solar activity, and geomagnetic activity. In the general perturbation method, two-variable asymptotic series and automated manipulation capabilities are used to obtain analytical solutions to the variation-of-parameters equations. Solutions are obtained considering the effect of oblateness only and the combined effects of oblateness and drag. These solutions are then numerically evaluated by means of a FORTRAN program in which an updating scheme is used to maintain accurate epoch values of the elements. The atmospheric density function is approximated by a Fourier series in true anomaly, and the 1970 Jacchia model is used to periodically update the Fourier coefficients. The accuracy of both methods is demonstrated by comparing computed orbital elements to actual elements over time spans of up to 8 days for the special perturbation method and up to 356 days for the general perturbation method.

Barry, B. F.↗
NASA NTRS2011

Designing the Space Shuttle Propulsion System

The major elements of the Space Shuttle Main Propulsion System include two reusable solid rocket motors integrated into recoverable solid rocket boosters, an expendable external fuel and oxidizer tank, and three reusable Space Shuttle Main Engines. Both the solid rocket motors and space shuttle main engines ignite prior to liftoff, with the solid rocket boosters separating about two minutes into flight. The external tank separates after main engine shutdown and is safely expended in the ocean. The SSME's, integrated into the Space Shuttle Orbiter aft structure, are reused after post landing inspections. Both the solid rocket motors and the space shuttle main engine throttle during early ascent flight to limit aerodynamic loads on the structure. The configuration is called a stage and a half as all the propulsion elements are active during the boost phase, and the SSME's continue operation to achieve orbital velocity approximately eight and a half minutes after liftoff. Design and performance challenges were numerous, beginning with development work in the 1970 s. The solid rocket motors were large, and this technology had never been used for human space flight. The SSME s were both reusable and very high performance staged combustion cycle engines, also unique to the Space Shuttle. The multi body side mount configuration was unique and posed numerous integration and interface challenges across the elements. Operation of the system was complex and time consuming. This paper discusses a number of the system level technical challenges including development and operations.

Owen, James↗
NASA NTRS1995

Nonstandard finite difference schemes

The major research activities of this proposal center on the construction and analysis of nonstandard finite-difference schemes for ordinary and partial differential equations. In particular, we investigate schemes that either have zero truncation errors (exact schemes) or possess other significant features of importance for numerical integration. Our eventual goal is to bring these methods to bear on problems that arise in the modeling of various physical, engineering, and technological systems. At present, these efforts are extended in the direction of understanding the exact nature of these nonstandard procedures and extending their use to more complicated model equations. Our presentation will give a listing (obtained to date) of the nonstandard rules, their application to a number of linear and nonlinear, ordinary and partial differential equations. In certain cases, numerical results will be presented.

Mickens, Ronald E.↗
NASA NTRS1986

Electron-positron pair production by ultrarelativistic electrons in a soft photon field

The fully differential cross section for photon-electron pair production is integrated numerically over phase space. Results are obtained for the astrophysically interesting case in which the interaction between an ultrarelativistic electron and a soft photon results in electron-positron pair production. The positron spectrum is a function of the energies of both the photon and the electron, as well as the angle of interaction. It is found that the energy at which the positron distribution peaks is inversely proportional to the photon energy and independent of the electron energy. The positron spectrum is integrated once more over initial electron energies for a power-law energy distribution of primary electrons. The same procedure is repeated for the recoil particle; it is shown that the peak of the recoil energy distribution depends linearly on the energy of the primary electron. Finally, semianalytical expressions are obtained for the energy losses of the primary electrons.

Mastichiadis, A.↗
NASA NTRS1981

Blade loss transient dynamics analysis, volume 2. Task 2: Theoretical and analytical development. Task 3: Experimental verification

The component element method was used to develop a transient dynamic analysis computer program which is essentially based on modal synthesis combined with a central, finite difference, numerical integration scheme. The methodology leads to a modular or building-block technique that is amenable to computer programming. To verify the analytical method, turbine engine transient response analysis (TETRA), was applied to two blade-out test vehicles that had been previously instrumented and tested. Comparison of the time dependent test data with those predicted by TETRA led to recommendations for refinement or extension of the analytical method to improve its accuracy and overcome its shortcomings. The development of working equations, their discretization, numerical solution scheme, the modular concept of engine modelling, the program logical structure and some illustrated results are discussed. The blade-loss test vehicles (rig full engine), the type of measured data, and the engine structural model are described.

Gallardo, V. C.↗
NASA NTRS1992

The response of the SSM/I to the marine environment. I - An analytic model for the atmospheric component of observed brightness temperatures

A detailed parameterization is developed for the contribution of the nonprecipitating atmosphere to the microwave brightness temperatures observed by the Special Sensor Microwave/Imager (SSM/I). The atmospheric variables considered include the viewing angle, the integrated water vapor amount and scale height, the effective tropospheric lapse rate and near-surface temperature, the total cloud liquid water, the effective cloud height, and the surface pressure. The dependence of the radiative variables on meteorological variables is determined for each of the SSM/I frequencies 19.35, 22.235, 37.0, and 85.5 GHz, based on the values computed from 16,893 maritime temperature and humidity profiles representing all latitude belts and all seasons. A comparison of the predicted brightness temperatures with brightness temperatures obtained by direct numerical integration of the radiative transfer equation for the radiosonde-profile dataset yielded rms differences well below 1 K for all four SSM/I frequencies.

Petty, Grant W.↗
NASA NTRS1993

Efficient and accurate computation of the incomplete Airy functions

The incomplete Airy integrals serve as canonical functions for the uniform ray optical solutions to several high-frequency scattering and diffraction problems that involve a class of integrals characterized by two stationary points that are arbitrarily close to one another or to an integration endpoint. Integrals with such analytical properties describe transition region phenomena associated with composite shadow boundaries. An efficient and accurate method for computing the incomplete Airy functions would make the solutions to such problems useful for engineering purposes. In this paper a convergent series solution for the incomplete Airy functions is derived. Asymptotic expansions involving several terms are also developed and serve as large argument approximations. The combination of the series solution with the asymptotic formulae provides for an efficient and accurate computation of the incomplete Airy functions. Validation of accuracy is accomplished using direct numerical integration data.

Constantinides, E. D.↗
NASA NTRS1986

Computation of three-dimensional, rotational flow through turbomachinery blade rows for improved aerodynamic design studies

The performance of a three dimensional computer code developed for predicting the flowfield in stationary and rotating turbomachinery blade rows is described in this study. The four stage Runge-Kutta numerical integration scheme is used for solving the governing flow equations and yields solution to the full, three dimensional, unsteady Euler equations in cylindrical coordinates. This method is fully explicit and uses the finite volume, time marching procedure. In order to demonstrate the accuracy and efficiency of the code, steady solutions were obtained for several cascade geometries under widely varying flow conditions. Computed flowfield results are presented for a fully subsonic turbine stator and a low aspect ratio, transonic compressor rotor blade under maximum flow and peak efficiency design conditions. Comparisons with Laser Anemometer measurements and other numerical predictions are also provided to illustrate that the present method predicts important flow features with good accuracy and can be used for cost effective aerodynamic design studies.

Subramanian, S. V.↗
NASA NTRS1980

Analysis and testing of numerical formulas for the initial value problem

Three computer programs for evaluating and testing numerical integration formulas used with fixed stepsize programs to solve initial value systems of ordinary differential equations are described. A program written in PASCAL SERIES, takes as input the differential equations and produces a FORTRAN subroutine for the derivatives of the system and for computing the actual solution through recursive power series techniques. Both of these are used by STAN, a FORTRAN program that interactively displays a discrete analog of the Liapunov stability region of any two dimensional subspace of the system. The derivatives may be used by CLMP, a FORTRAN program, to test the fixed stepsize formula against a good numerical result and interactively display the solutions.

Brown, R. L.↗
NASA NTRS2018

Planetary Probe Entry Models for Concurrent and Integrated Interplanetary Mission Design

There are many prospective mission opportunities involving atmospheric entry probes. The Planetary Science Deep Space SmallSat Studies (PSDS3) re-cently selected probe missions to Venus, Mars, and the outer planets as part of the 10 selected studies. Two of the six themes in the most recent New Fron-tiers call were a Saturn probe and a Venus in situ explorer. The 2013-2022 Planetary Science Decadal Survey includes probe missions at Venus, Mars, Saturn, Titan, Uranus, and Neptune. Across mission destinations and mission classes there is growing interest in planetary probes. While interplanetary trajectory specialists may like to use a broad sweep of low-fidelity solutions to find a wide array of trajectory options, probe specialists typically start off with mid- to high-fidelity point designs for the entry probe since the equations of motion for atmospheric probes require numerical integration and are so directly linked with some of the probe's subsystem design. Cur-rently, there are no alternatives to this design ap-proach as there are no tools capable of automatical-ly and concurrently designing interplanetary and atmospheric trajectories. Unfortunately, this makes us reliant on point designs in the early stages of the mission design process. The reliance on point de-signs for atmospheric probes hinders the flexibility of the design, making the design process cumber-some and restricting decision-making down the road. The research presented here addresses this problem by providing low-fidelity models for the automated, rapid design of atmospheric trajectories and probe's models which may be solved concur-rently with the interplanetary trajectory.

atmospheric probes↗