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At least 271 records · Page 15

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NASA NTRS1986

Coupling between fluid dynamics and energy addition in arcjet and microwave thrusters

A new approach to numerically solving the problem of the constricted electric arcjet is presented. An Euler Implicit finite difference scheme is used to solve the full compressible Navier Stokes equations in two dimensions. The boundary and initial conditions represent the constrictor section of the arcjet, and hydrogen is used as a propellant. The arc is modeled as a Gaussian distribution across the centerline of the constrictor. Temperature, pressure and velocity profiles for steady state converged solutions show both axial and radial changes in distributions resulting from their interaction with the arc energy source for specific input conditions. The temperature rise is largest at the centerline where there is a the greatest concentration arc energy. The solution does not converge for all initial inputs and the limitations in the range of obtainable solutions are discussed.

Micci, M. M.↗

NASA NTRS1990

Numerical methods for systems of conservation laws of mixed type using flux splitting

The essentially non-oscillatory (ENO) finite difference scheme is applied to systems of conservation laws of mixed hyperbolic-elliptic type. A flux splitting, with the corresponding Jacobi matrices having real and positive/negative eigenvalues, is used. The hyperbolic ENO operator is applied separately. The scheme is numerically tested on the van der Waals equation in fluid dynamics. Convergence was observed with good resolution to weak solutions for various Riemann problems, which are then numerically checked to be admissible as the viscosity-capillarity limits. The interesting phenomena of the shrinking of elliptic regions if they are present in the initial conditions were also observed.

Shu, Chi-Wang↗

NASA NTRS1998

Insights Into the Fractional Order Initial Value Problem via Semi-Infinite Systems

This paper considers various aspects of the initial value problem for fractional order differential equations. The main contribution of this paper is to use the solutions to known spatially distributed systems to demonstrate that fractional differintegral operators require an initial condition term that is time-varying due to past distributed storage of information.

Hartley, Tom T.↗

NASA NTRS1976

Diffraction of a shock wave by a compression corner; regular and single Mach reflection

The two dimensional, time dependent Euler equations which govern the flow field resulting from the injection of a planar shock with a compression corner are solved with initial conditions that result in either regular reflection or single Mach reflection of the incident planar shock. The Euler equations which are hyperbolic are transformed to include the self similarity of the problem. A normalization procedure is employed to align the reflected shock and the Mach stem as computational boundaries to implement the shock fitting procedure. A special floating fitting scheme is developed in conjunction with the method of characteristics to fit the slip surface. The reflected shock, the Mach stem, and the slip surface are all treated as harp discontinuities, thus, resulting in a more accurate description of the inviscid flow field. The resulting numerical solutions are compared with available experimental data and existing first-order, shock-capturing numerical solutions.

Vijayashankar, V. S.↗

NASA NTRS1991

A trajectory planning scheme for spacecraft in the space station environment

Simulated annealing is used to solve a minimum fuel trajectory problem in the space station environment. The environment is special because the space station will define a multivehicle environment in space. The optimization surface is a complex nonlinear function of the initial conditions of the chase and target crafts. Small permutations in the input conditions can result in abrupt changes to the optimization surface. Since no prior knowledge about the number or location of local minima on the surface is available, the optimization must be capable of functioning on a multimodal surface. It was reported in the literature that the simulated annealing algorithm is more effective on such surfaces than descent techniques using random starting points. The simulated annealing optimization was found to be capable of identifying a minimum fuel, two-burn trajectory subject to four constraints which are integrated into the optimization using a barrier method. The computations required to solve the optimization are fast enough that missions could be planned on board the space station. Potential applications for on board planning of missions are numerous. Future research topics may include optimal planning of multi-waypoint maneuvers using a knowledge base to guide the optimization, and a study aimed at developing robust annealing schedules for potential on board missions.

Soller, Jeffrey Alan↗

NASA NTRS1960

Problems Involved in an Emergency Method of Guiding a Gliding Vehicle from High Altitudes to a High Key Position

An investigation has been conducted to determine the problems involved in an emergency method of guiding a gliding vehicle from high altitudes to a high key position (initial position) above a landing field. A jet airplane in a simulated flameout condition, conventional ground-tracking radar, and a scaled wire for guidance programming on the radar plotting board were used in the tests. Starting test altitudes varied from 30,000 feet to 46,500 feet, and starting positions ranged 8.4 to 67 nautical miles from the high key. Specified altitudes of the high key were 12,000, 10,000 or 4,000 feet. Lift-drag ratios of the aircraft of either 17, 16, or 6 were held constant during any given flight; however, for a few flights the lift-drag ratio was varied from 11 to 6. Indicated airspeeds were held constant at either 160 or 250 knots. Results from these tests indicate that a gliding vehicle having a lift-drag ratio of 16 and an indicated approach speed of 160 knots can be guided to within 800 feet vertically and 2,400 feet laterally of a high key position. When the lift-drag ratio of the vehicle is reduced to 6 and the indicated approach speed is raised to 250 knots, the radar controller was able to guide the vehicle to within 2,400 feet vertically and au feet laterally of the high key. It was also found that radar stations which give only azimuth-distance information could control the glide path of a gliding vehicle as well as stations that receive azimuth-distance-altitude information, provided that altitude information is supplied by the pilot.

Jewel, Joseph W., Jr.↗

NASA NTRS2007

NASA Langley's Approach to the Sandia's Structural Dynamics Challenge Problem

The objective of this challenge is to develop a data-based probabilistic model of uncertainty to predict the behavior of subsystems (payloads) by themselves and while coupled to a primary (target) system. Although this type of analysis is routinely performed and representative of issues faced in real-world system design and integration, there are still several key technical challenges that must be addressed when analyzing uncertain interconnected systems. For example, one key technical challenge is related to the fact that there is limited data on target configurations. Moreover, it is typical to have multiple data sets from experiments conducted at the subsystem level, but often samples sizes are not sufficient to compute high confidence statistics. In this challenge problem additional constraints are placed as ground rules for the participants. One such rule is that mathematical models of the subsystem are limited to linear approximations of the nonlinear physics of the problem at hand. Also, participants are constrained to use these models and the multiple data sets to make predictions about the target system response under completely different input conditions. Our approach involved initially the screening of several different methods. Three of the ones considered are presented herein. The first one is based on the transformation of the modal data to an orthogonal space where the mean and covariance of the data are matched by the model. The other two approaches worked solutions in physical space where the uncertain parameter set is made of masses, stiffnesses and damping coefficients; one matches confidence intervals of low order moments of the statistics via optimization while the second one uses a Kernel density estimation approach. The paper will touch on all the approaches, lessons learned, validation 1 metrics and their comparison, data quantity restriction, and assumptions/limitations of each approach. Keywords: Probabilistic modeling, model validation, uncertainty quantification, kernel density

Horta, Lucas G.↗

NASA NTRS1973

Aircraft Range Optimization Using Singular Perturbations

An approximate analytic solution is developed for the problem of maximizing the range of an aircraft for a fixed end state. The problem is formulated as a singular perturbation and solved by matched inner and outer asymptotic expansions and the minimum principle of Pontryagin. Cruise in the stratosphere, and on transition to and from cruise at constant Mach number are discussed. The state vector includes altitude, flight path angle, and mass. Specific fuel consumption becomes a linear function of power approximating that of the cruise values. Cruise represents the outer solution; altitude and flight path angle are constants, and only mass changes. Transitions between cruise and the specified initial and final conditions correspond to the inner solutions. The mass is constant and altitude and velocity vary. A solution is developed which is valid for cruise but which is not for the initial and final conditions. Transforming of the independent variable near the initial and final conditions result in solutions which are valid for the two inner solutions but not for cruise. The inner solutions can not be obtained without simplifying the state equations. The singular perturbation approach overcomes this difficulty. A quadratic approximation of the state equations is made. The resulting problem is solved analytically, and the two inner solutions are matched to the outer solution.

Oconnor, Joseph Taffe↗

NASA NTRS1981

Evolution of magnetic field and atmospheric response. I - Three-dimensional formulation by the method of projected characteristics. II - Formulation of proper boundary equations

The method described as the method of nearcharacteristics by Nakagawa (1980) is renamed the method of projected characteristics. Making full use of properties of the projected characteristics, a new and simpler formulation is developed. As a result, the formulation for the examination of the general three-dimensional problems is presented. It is noted that since in practice numerical solutions must be obtained, the final formulation is given in the form of difference equations. The possibility of including effects of viscous and ohmic dissipations in the formulation is considered, and the physical interpretation is discussed. A systematic manner is then presented for deriving physically self-consistent, time-dependent boundary equations for MHD initial boundary problems. It is demonstrated that the full use of the compatibility equations (differential equations relating variations at two spatial locations and times) is required in determining the time-dependent boundary conditions. In order to provide a clear physical picture as an example, the evolution of axisymmetric global magnetic field by photospheric differential rotation is considered.

Nakagawa, Y.↗

NASA NTRS1990

The route to chaos for the Kuramoto-Sivashinsky equation

The results of extensive numerical experiments of the spatially periodic initial value problem for the Kuramoto-Sivashinsky equation. This paper is concerned with the asymptotic nonlinear dynamics at the dissipation parameter decreases and spatio-temporal chaos sets in. To this end the initial condition is taken to be the same for all numerical experiments (a single sine wave is used) and the large time evolution of the system is followed numerically. Numerous computations were performed to establish the existence of windows, in parameter space, in which the solution has the following characteristics as the viscosity is decreased: a steady fully modal attractor to a steady bimodal attractor to another steady fully modal attractor to a steady trimodal attractor to a periodic attractor, to another steady fully modal attractor, to another periodic attractor, to a steady tetramodal attractor, to another periodic attractor having a full sequence of period-doublings (in parameter space) to chaos. Numerous solutions are presented which provide conclusive evidence of the period-doubling cascades which precede chaos for this infinite-dimensional dynamical system. These results permit a computation of the length of subwindows which in turn provide an estimate for their successive ratios as the cascade develops. A calculation based on the numerical results is also presented to show that the period doubling sequences found here for the Kuramoto-Sivashinsky equation, are in complete agreement with Feigenbaum's universal constant of 4,669201609... . Some preliminary work shows several other windows following the first chaotic one including periodic, chaotic, and a steady octamodal window; however, the windows shrink significantly in size to enable concrete quantitative conclusions to be made.

Papageorgiou, Demetrios T.↗

NASA NTRS1991

The route to chaos for the Kuramoto-Sivashinsky equation

The results of extensive numerical experiments of the spatially periodic initial value problem for the Kuramoto-Sivashinsky equation. This paper is concerned with the asymptotic nonlinear dynamics at the dissipation parameter decreases and spatio-temporal chaos sets in. To this end the initial condition is taken to be the same for all numerical experiments (a single sine wave is used) and the large time evolution of the system is followed numerically. Numerous computations were performed to establish the existence of windows, in parameter space, in which the solution has the following characteristics as the viscosity is decreased: a steady fully modal attractor to a steady bimodal attractor to another steady fully modal attractor to a steady trimodal attractor to a periodic attractor, to another steady fully modal attractor, to another periodic attractor, to a steady tetramodal attractor, to another periodic attractor having a full sequence of period-doublings (in parameter space) to chaos. Numerous solutions are presented which provide conclusive evidence of the period-doubling cascades which precede chaos for this infinite-dimensional dynamical system. These results permit a computation of the length of subwindows which in turn provide an estimate for their successive ratios as the cascade develops. A calculation based on the numerical results is also presented to show that the period doubling sequences found here for the Kuramoto-Sivashinsky equation, are in complete agreement with Feigenbaum's universal constant of 4,669201609 .... Some preliminary work shows several other windows following the first chaotic one including periodic, chaotic, and a steady octamodal window; however, the windows shrink significantly in size to enable concrete quantitative conclusions to be made.

Papageorgiou, Demetrios T.↗

NASA NTRS2004

Simulation of Multiple Shocks in the Solar Atmosphere using a High-Order Shock-Capturing Scheme

We present a simulation of shock phenomena in the solar atmosphere using high-order shock capturing central-upwind schemes, based on the Euler equation in gravity. These simulations use observation-based initial conditions, with results matching observation. Various difficulties are highlighted, including very high gradients in the initial data, multiple scales, and initialization in hydrostatic equilibrium. We focus on the design of algorithms to address these problems, as well as the interaction with observational data.

Bryson, Steve↗

NASA NTRS2015

Check-Cases for Verification of 6-Degree-of-Freedom Flight Vehicle Simulations

The rise of innovative unmanned aeronautical systems and the emergence of commercial space activities have resulted in a number of relatively new aerospace organizations that are designing innovative systems and solutions. These organizations use a variety of commercial off-the-shelf and in-house-developed simulation and analysis tools including 6-degree-of-freedom (6-DOF) flight simulation tools. The increased affordability of computing capability has made highfidelity flight simulation practical for all participants. Verification of the tools' equations-of-motion and environment models (e.g., atmosphere, gravitation, and geodesy) is desirable to assure accuracy of results. However, aside from simple textbook examples, minimal verification data exists in open literature for 6-DOF flight simulation problems. This assessment compared multiple solution trajectories to a set of verification check-cases that covered atmospheric and exo-atmospheric (i.e., orbital) flight. Each scenario consisted of predefined flight vehicles, initial conditions, and maneuvers. These scenarios were implemented and executed in a variety of analytical and real-time simulation tools. This tool-set included simulation tools in a variety of programming languages based on modified flat-Earth, round- Earth, and rotating oblate spheroidal Earth geodesy and gravitation models, and independently derived equations-of-motion and propagation techniques. The resulting simulated parameter trajectories were compared by over-plotting and difference-plotting to yield a family of solutions. In total, seven simulation tools were exercised.

Murri, Daniel G.↗

NASA NTRS2014

Analysis of Airport Ground Delay Program Decisions Using Data Mining Techniques

Air traffic service providers have to make decisions regarding changes to air traffic flow in the event of major weather disturbances and traffic congestions to maintain safety of the system. The behavior of the air traffic management system will be more predictable if consistent decisions are made under similar traffic and weather conditions. Consistency of deciding on control action depends on the weather and traffic conditions as well as accuracy in predicting these conditions. Weather parameters (defined in terms of forecast and actual weather and traffic conditions) on different days can be used to categorize days into days with little decision consistency, days with moderate decision consistency and days with high decision consistency. Four years of traffic, weather and ground delay program decisions data at major airports in the United States are used in the analysis. This paper examines performance of different data mining methods in the three regions of decision consistency. Not surprisingly, data mining methods have the best performance in the region of most decision consistency and have the poorest performance in the region of little decision consistency. In applications where data mining methods have differing performance in differing regions, it would be more useful to characterize the region specific performance instead of characterizing performance by a single parameter. Finally, the results show no significant variation in the performance of different data mining methods for this particular problem. The fact that different mining methods show no significant variation also provides further confidence in the results of data mining methods. Work in this abstract discusses initial results. This paper describes the results in terms of both forecast and actual environmental conditions and discusses how prediction errors impact decision consistency.

Kulkarni, Deepak↗

NASA NTRS1976

Interplanetary disturbances in the solar wind produced by density, temperature, or velocity pulses at 0.08 AU

Time-dependent solutions of a one-fluid model of the interplanetary medium are investigated. This set of unsteady hydrodynamic equations has been written in conserved form in order to apply the Lax-Wendroff (1960) method for the solution of this problem. The initial disturbance is specified by a pulse at 0.08 AU. Physically, this pulse can be interpreted as having been caused by a solar flare, surge, or any other solar disturbance. The equilibrium condition is determined to be the steady solution of the governing equations and represents the quiet solar wind. Results are presented in terms of density, temperature, and velocity profiles of the interplanetary gas flow at heliocentric distances up to 6 AU at several times. Also, the trajectories of disturbances for various initial pulses are shown. Some June 1972 interplanetary observational data are compared with these theoretical calculations. On the basis of these results, the effects of solar disturbances on the interplanetary environment (such as the generation of large nonlinear wave trains in the shock wakes) can be inferred.

Wu, S. T.↗

NASA NTRS1988

Solving time-dependent two-dimensional eddy current problems

Results of transient eddy current calculations are reported. For simplicity, a two-dimensional transverse magnetic field which is incident on an infinitely long conductor is considered. The conductor is assumed to be a good but not perfect conductor. The resulting problem is an interface initial boundary value problem with the boundary of the conductor being the interface. A finite difference method is used to march the solution explicitly in time. The method is shown. Treatment of appropriate radiation conditions is given special consideration. Results are validated with approximate analytic solutions. Two stringent test cases of high and low frequency incident waves are considered to validate the results.

Lee, Min Eig↗

NASA NTRS1989

Performance of the active sidewall boundary-layer removal system for the Langley 0.3-meter Transonic Cryogenic Tunnel

A performance evaluation of an active sidewall boundary-layer removal system for the Langley 0.3-m Transonic Cryogenic Tunnel (TCT) was evaluated in 1988. This system uses a compressor and two throttling digital valves to control the boundary-layer mass flow removal from the tunnel. The compressor operates near the maximum pressure ratio for all conditions. The system uses a surge prevention and flow recirculation scheme. A microprocessor based controller is used to provide the necessary mass flow and compressor pressure ratio control. Initial tests on the system indicated problems in realizing smooth mass flow control while running the compressor at high speed and high pressure ratios. An alternate method has been conceived to realize boundary-layer mass flow control which avoids the recirculation of the compressor mass flow and operation near the compressor surge point. This scheme is based on varying the speed of the compressor for a sufficient pressure ratio to provide needed mass flow removal. The system has a mass flow removal capability of about 10 percent of test section flow at M = 0.3 and 4 percent at M = 0.8. The system performance has been evaluated in the form of the compressor map, and compressor tunnel interface characteristics covering most of the 0.3-m TCT operational envelope.

Balakrishna, S.↗

NASA NTRS1990

Finite-volume application of high order ENO schemes to multi-dimensional boundary-value problems

The finite volume approach in developing multi-dimensional, high-order accurate essentially non-oscillatory (ENO) schemes is considered. In particular, a two dimensional extension is proposed for the Euler equation of gas dynamics. This requires a spatial reconstruction operator that attains formal high order of accuracy in two dimensions by taking account of cross gradients. Given a set of cell averages in two spatial variables, polynomial interpolation of a two dimensional primitive function is employed in order to extract high-order pointwise values on cell interfaces. These points are appropriately chosen so that correspondingly high-order flux integrals are obtained through each interface by quadrature, at each point having calculated a flux contribution in an upwind fashion. The solution-in-the-small of Riemann's initial value problem (IVP) that is required for this pointwise flux computation is achieved using Roe's approximate Riemann solver. Issues to be considered in this two dimensional extension include the implementation of boundary conditions and application to general curvilinear coordinates. Results of numerical experiments are presented for qualitative and quantitative examination. These results contain the first successful application of ENO schemes to boundary value problems with solid walls.

Casper, Jay↗