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NASA NTRS1980

Calculation of two-dimensional inlet flow fields in a supersonic free stream by an implicit marching code with nonorthogonal mesh generation: User's manual

An implicit, shock-capturing finite-difference code which is used to calculate two-dimensional inlet flow fields in a supersonic free stream is explained. The Euler equations are subjected to general nonorthogonal transformation and a body-fitted coordinate system is employed. The mathematical formulation of the problem is given along with the numerical algorithm. Initial and boundary conditions, numerical stability, program limitations, and accuracy is discussed. An overall program logic as well as instructions for program use and operation are also furnished.

Biringen, S. H.↗

NASA NTRS1960

Some Landing Studies Pertinent to Glider-Reentry Vehicles

Results are presented of some landing studies that may serve as guidelines in the consideration of landing problems of glider-reentry configurations. The effect of the initial conditions of sinking velocity, angle of attack, and pitch rate on impact severity and the effect of locating the rear gear in various positions are discussed. Some information is included regarding the influence of landing-gear location on effective masses. Preliminary experimental results on the slideout phase of landing include sliding and rolling friction coefficients that have been determined from tests of various skids and all-metal wheels.

Houbolt, John C.↗

NASA NTRS1995

Lyapunov exponents from CHUA's circuit time series using artificial neural networks

In this paper we present the general problem of identifying if a nonlinear dynamic system has a chaotic behavior. If the answer is positive the system will be sensitive to small perturbations in the initial conditions which will imply that there is a chaotic attractor in its state space. A particular problem would be that of identifying a chaotic oscillator. We present an example of three well known different chaotic oscillators where we have knowledge of the equations that govern the dynamical systems and from there we can obtain the corresponding time series. In a similar example we assume that we only know the time series and, finally, in another example we have to take measurements in the Chua's circuit to obtain sample points of the time series. With the knowledge about the time series the phase plane portraits are plotted and from them, by visual inspection, it is concluded whether or not the system is chaotic. This method has the problem of uncertainty and subjectivity and for that reason a different approach is needed. A quantitative approach is the computation of the Lyapunov exponents. We describe several methods for obtaining them and apply a little known method of artificial neural networks to the different examples mentioned above. We end the paper discussing the importance of the Lyapunov exponents in the interpretation of the dynamic behavior of biological neurons and biological neural networks.

Gonzalez, J. Jesus↗

NASA NTRS2021

Boundary and Initial Condition Issues for Computational Fluid Dynamics (CFD) and Modeling and Simulation (Mod-Sim)

For many important classes of Mod-Sim problems, even quantum computing will not enable accurate predictions/computation vis-à-vis the real world due to boundary/initial condition shortfalls in terms of both range of parameters and requisite amplitudes/coverage. The Mod-Sim community needs to consider going forward the knowability of initial and boundary conditions.

Dennis M. Bushnell↗

NASA NTRS1983

Closed-form solutions for feedback control with terminal constraints

The problem of closed-loop control of maneuvers between two states for linear dynamical systems, subject to an arbitrarily specified terminal state, is considered. The feedback controller design is based on finite-time quadratic regulator theory. Closed-form expressions for the optimal control law are developed. Solutions are presented for both conventional and smoothed control profiles with fixed and/or free end condition problems. In the maneuvers using control-rate penalties, smooth profiles are generated throughout the maneuvers, in the sense that the initial condition jump discontinuities have been eliminated. Several examples involving large-angle maneuvers of a spacecraft are demonstrated. Results include control maneuvers from one state to another such as rest to rest and spin to rest, which effectively justify the solutions developed in this paper.

Juang, J.-N.↗

NASA NTRS1995

Durability and life prediction modeling in polyimide composites

Sudden appearance of cracks on a macroscopically smooth surface of brittle materials due to cooling or drying shrinkage is a phenomenon related to many engineering problems. Although conventional strength theories can be used to predict the necessary condition for crack appearance, they are unable to predict crack spacing and depth. On the other hand, fracture mechanics theory can only study the behavior of existing cracks. The theory of crack initiation can be summarized into three conditions, which is a combination of a strength criterion and laws of energy conservation, the average crack spacing and depth can thus be determined. The problem of crack initiation from the surface of an elastic half plane is solved and compares quite well with available experimental evidence. The theory of crack initiation is also applied to concrete pavements. The influence of cracking is modeled by the additional compliance according to Okamura's method. The theoretical prediction by this structural mechanics type of model correlates very well with the field observation. The model may serve as a theoretical foundation for future pavement joint design. The initiation of interactive cracks of quasi-brittle material is studied based on a theory of cohesive crack model. These cracks may grow simultaneously, or some of them may close during certain stages. The concept of crack unloading of cohesive crack model is proposed. The critical behavior (crack bifurcation, maximum loads) of the cohesive crack model are characterized by rate equations. The post-critical behavior of crack initiation is also studied.

Binienda, Wieslaw K.↗

NASA NTRS1993

The theoretical accuracy of Runge-Kutta time discretizations for the initial boundary value problem: A careful study of the boundary error

The conventional method of imposing time dependent boundary conditions for Runge-Kutta (RK) time advancement reduces the formal accuracy of the space-time method to first order locally, and second order globally, independently of the spatial operator. This counter intuitive result is analyzed in this paper. Two methods of eliminating this problem are proposed for the linear constant coefficient case: (1) impose the exact boundary condition only at the end of the complete RK cycle, (2) impose consistent intermediate boundary conditions derived from the physical boundary condition and its derivatives. The first method, while retaining the RK accuracy in all cases, results in a scheme with much reduced CFL condition, rendering the RK scheme less attractive. The second method retains the same allowable time step as the periodic problem. However it is a general remedy only for the linear case. For non-linear hyperbolic equations the second method is effective only for for RK schemes of third order accuracy or less. Numerical studies are presented to verify the efficacy of each approach.

Carpenter, Mark H.↗

NASA NTRS1997

Large Scale Turbulent Structures in Supersonic Jets

Jet noise is a major concern in the design of commercial aircraft. Studies by various researchers suggest that aerodynamic noise is a major contributor to jet noise. Some of these studies indicate that most of the aerodynamic jet noise due to turbulent mixing occurs when there is a rapid variation in turbulent structure, i.e. rapidly growing or decaying vortices. The objective of this research was to simulate a compressible round jet to study the non-linear evolution of vortices and the resulting acoustic radiations. In particular, to understand the effect of turbulence structure on the noise. An ideal technique to study this problem is Direct Numerical Simulations (DNS), because it provides precise control on the initial and boundary conditions that lead to the turbulent structures studied. It also provides complete 3-dimensional time dependent data. Since the dynamics of a temporally evolving jet are not greatly different from those of a spatially evolving jet, a temporal jet problem was solved, using periodicity in the direction of the jet axis. This enables the application of Fourier spectral methods in the streamwise direction. Physically this means that turbulent structures in the jet are repeated in successive downstream cells instead of being gradually modified downstream into a jet plume. The DNS jet simulation helps us understand the various turbulent scales and mechanisms of turbulence generation in the evolution of a compressible round jet. These accurate flow solutions will be used in future research to estimate near-field acoustic radiation by computing the total outward flux across a surface and determine how it is related to the evolution of the turbulent solutions. Furthermore, these simulations allow us to investigate the sensitivity of acoustic radiations to inlet/boundary conditions, with possible appli(,a- tion to active noise suppression. In addition, the data generated can be used to compute, various turbulence quantities such as mean velocities, turbulent stresses, etc. which will aid in turbulence modeling. This report will be presented in two chapters. The first chapter describes some work on the linear stability of a supersonic round jet and the implications of this for the jet noise problem. The second chapter is an extensive discussion of numerical work using the spectral method which we use to solve the compressible Navier-Stokes equations to study turbulent jet flows. The method uses Fourier expansions in the azimuthal and streamwise direction and a 1-D B-spline basis representation in the radial direction. The B-spline basis is locally supported and this ensures block diagonal matrix equations which can be solved in O(N) steps. This is a modification of a boundary layer code developed by Robert Moser. A very accurate highly resolved DNS of a turbulent jet flow is produced.

Rao, Ram Mohan↗

NASA NTRS1997

Large Scale Turbulent Structures in Supersonic Jets

Jet noise is a major concern in the design of commercial aircraft. Studies by various researchers suggest that aerodynamic noise is a major contributor to jet noise. Some of these studies indicate that most of the aerodynamic jet noise due to turbulent mixing occurs when there is a rapid variation in turbulent structure, i.e. rapidly growing or decaying vortices. The objective of this research was to simulate a compressible round jet to study the non-linear evolution of vortices and the resulting acoustic radiations. In particular, to understand the effect of turbulence structure on the noise. An ideal technique to study this problem is Direct Numerical Simulations(DNS), because it provides precise control on the initial and boundary conditions that lead to the turbulent structures studied. It also provides complete 3-dimensional time dependent data. Since the dynamics of a temporally evolving jet are not greatly different from those, of a spatially evolving jet, a temporal jet problem was solved, using periodicity ill the direction of the jet axis. This enables the application of Fourier spectral methods in the streamwise direction. Physically this means that turbulent structures in the jet are repeated in successive downstream cells instead of being gradually modified downstream into a jet plume. The DNS jet simulation helps us understand the various turbulent scales and mechanisms of turbulence generation in the evolution of a compressible round jet. These accurate flow solutions will be used in future research to estimate near-field acoustic radiation by computing the total outward flux across a surface and determine how it is related to the evolution of the turbulent solutions. Furthermore, these simulations allow us to investigate the sensitivity of acoustic radiations to inlet/boundary conditions, with possible application to active noise suppression. In addition, the data generated can be used to compute various turbulence quantities such as mean velocities, turbulent stresses, etc. which will aid in turbulence modeling. This report will be presented in two chapters. The first chapter describes some work on the linear stability of a supersonic round jet and the implications of this for the jet noise problem. The second chapter is an extensive discussion of numerical work using the spectral method which we use to solve the compressible Navier-Stokes equations to study turbulent jet flows. The method uses Fourier expansions in the azimuthal and streamwise direction and a 1-D B-spline basis representation in the radial direction. The B-spline basis is locally supported and this ensures block diagonal matrix equations which can be solved in O(N) steps. This is a modification of a boundary layer code developed by Robert Moser. A very accurate highly resolved Direct Numerical Simulation (DNS) of a turbulent jet flow is produced.

Rao, Ram Mohan↗

NASA NTRS1981

Improved liquid phase epitaxial GaAs for low series resistance Schottky barrier mixer diodes

Millimeter wave Schottky barrier mixer diodes are extremely important devices for radio astronomy. The performance of the Schottky diodes depends largely on the characteristics and quality of the GaAs epitaxial materials used. Systematic manipulation of the liquid phase epitaxial growth conditions and substrate surface treatments has yielded significantly improved surface morphology. Initial problems of high resistivity interfacial layers have been reduced without the use of an in situ etchback. Two-micron diameter Schottky diodes fabricated from epitaxial layers grown at 725 C exhibit a 9-ohm series resistance very near the theoretical minimum.

Binari, S. C.↗

NASA NTRS1987

Numerical comparison of strong Langmuir turbulence models

Two models of Langmuir turbulence, the nonlinear Schroedinger equation and the Zakharov equations, are solved numerically for an initial value problem in which the electric field evolves from an almost flat initial condition via the modulational instability and finally saturates into a set of solitons. The two models agree well with each other only when the initial dimensionless electric field has an amplitude less than unity. An analytic soliton gas model consisting of equal-amplitude, randomly spaced, zero-speed solitons is remarkably good at reproducing the time-averaged Fourier spectra in both cases.

Shen, Mei-Mei↗

NASA NTRS1998

Application of Rapid Prototyping Methods to High-Speed Wind Tunnel Testing

This study was undertaken in MSFC's 14-Inch Trisonic Wind Tunnel to determine if rapid prototyping methods could be used in the design and manufacturing of high speed wind tunnel models in direct testing applications, and if these methods would reduce model design/fabrication time and cost while providing models of high enough fidelity to provide adequate aerodynamic data, and of sufficient strength to survive the test environment. Rapid prototyping methods utilized to construct wind tunnel models in a wing-body-tail configuration were: fused deposition method using both ABS plastic and PEEK as building materials, stereolithography using the photopolymer SL-5170, selective laser sintering using glass reinforced nylon, and laminated object manufacturing using plastic reinforced with glass and 'paper'. This study revealed good agreement between the SLA model, the metal model with an FDM-ABS nose, an SLA nose, and the metal model for most operating conditions, while the FDM-ABS data diverged at higher loading conditions. Data from the initial SLS model showed poor agreement due to problems in post-processing, resulting in a different configuration. A second SLS model was tested and showed relatively good agreement. It can be concluded that rapid prototyping models show promise in preliminary aerodynamic development studies at subsonic, transonic, and supersonic speeds.

Springer, A. M.↗

NASA NTRS1998

Eclipses by the Earth and by the Moon as Constraints on the AXAF Mission

The Advanced X-ray Astrophysics Facility (AXAF) is scheduled for launch on September 1, 1998, on a mission lasting ten years. During this time AXAF will be subject to eclipses by the Earth and the Moon. Eclipses by the Earth will occur during regular 'seasons' six months apart. AXAF requires that none last longer than 120 minutes, and this constrains the orbit orientation. Eclipses by the Moon occur infrequently, but may pose serious operational problems. The AXAF perigee altitude can be chosen, once the other initial conditions are known, so that objectionable Moon-eclipses can be avoided by targeting the final burn.

Evans, Steven W.↗

NASA NTRS1980

Central configurations and hyperbolic-elliptic motion in the three-body problem

A refined classification of motion for the planar three-body problem with zero-sum total energy is presented. The structure and dimensions of the sets of initial conditions leading to parabolic expansion or hyperbolic-elliptic motion are found. Attention is given to the use of the Hamiltonian of the system and to the two- and three-dimensional problem. It is verified that the new coordinates of position and linear momentum approaches limits as t (time) approaches infinity, and that these limits constitute equilibrium solutions to the three-body problem representing control configurations.

Hulkower, N. D.↗

NASA NTRS2003

Estimation of Model Error Variances During Data Assimilation

Data assimilation is all about understanding the error characteristics of the data and models that are used in the assimilation process. Reliable error estimates are needed to implement observational quality control, bias correction of observations and model fields, and intelligent data selection. Meaningful covariance specifications are obviously required for the analysis as well, since the impact of any single observation strongly depends on the assumed structure of the background errors. Operational atmospheric data assimilation systems still rely primarily on climatological background error covariances. To obtain error estimates that reflect both the character of the flow and the current state of the observing system, it is necessary to solve three problems: (1) how to account for the short-term evolution of errors in the initial conditions; (2) how to estimate the additional component of error caused by model defects; and (3) how to compute the error reduction in the analysis due to observational information. Various approaches are now available that provide approximate solutions to the first and third of these problems. However, the useful accuracy of these solutions very much depends on the size and character of the model errors and the ability to account for them. Model errors represent the real-world forcing of the error evolution in a data assimilation system. Clearly, meaningful model error estimates and/or statistics must be based on information external to the model itself. The most obvious information source is observational, and since the volume of available geophysical data is growing rapidly, there is some hope that a purely statistical approach to model error estimation can be viable. This requires that the observation errors themselves are well understood and quantifiable. We will discuss some of these challenges and present a new sequential scheme for estimating model error variances from observations in the context of an atmospheric data assimilation system.

Dee, Dick↗

NASA NTRS1990

Unsteady flow computation of oscillating flexible wings

The problem of unsteady flow around flexible wings is solved using the unsteady, compressible, thin-layer Navier-Stokes equations in conjunction with the unsteady, linearized, Navier-displacement equations. Starting with the initial shape of the wing, the Navier-Stokes equations are solved on an initial structured grid to obtain the steady-flow solution which is used for the initial conditions. The forced deformation motion of the wing boundaries is then applied, and the problem is solved accurately in time. During the time-accurate stepping, the Navier-displacement equations are used to solve for the grid deformation and sequently, the Navier-Stokes equations are used to solve for the flowfield. Two applications are presented; the first is for a pulsating oscillation of a bending-mode airfoil in transonic flow, and the second is for a bending-mode oscillation of a sharp-edged delta wing in supersonic flow.

Kandil, Osama A.↗

NASA NTRS1981

Influence of exit impedance on finite difference solutions of transient acoustic mode propagation in ducts

The cutoff mode instability problem associated with a transient finite difference solution to the wave equation is explained. The steady-state impedance boundary condition is found to produce acoustic reflections during the initial transient, which cause finite instabilities in the cutoff modes. The stability problem is resolved by extending the duct length to prevent transient reflections. Numerical calculations are presented at forcing frequencies above, below, and nearly at the cutoff frequency, and exit impedance models are presented for use in the practical design of turbofan inlets.

Baumeister, K. J.↗

NASA NTRS2010

Regional Model Nesting Within GFS Daily Forecasts Over West Africa

The study uses the RM3, the regional climate model at the Center for Climate Systems Research of Columbia University and the NASA/Goddard Institute for Space Studies (CCSR/GISS). The paper evaluates 30 48-hour RM3 weather forecasts over West Africa during September 2006 made on a 0.5 grid nested within 1 Global Forecast System (GFS) global forecasts. September 2006 was the Special Observing Period #3 of the African Monsoon Multidisciplinary Analysis (AMMA). Archived GFS initial conditions and lateral boundary conditions for the simulations from the US National Weather Service, National Oceanographic and Atmospheric Administration were interpolated four times daily. Results for precipitation forecasts are validated against Tropical Rainfall Measurement Mission (TRMM) satellite estimates and data from the Famine Early Warning System (FEWS), which includes rain gauge measurements, and forecasts of circulation are compared to reanalysis 2. Performance statistics for the precipitation forecasts include bias, root-mean-square errors and spatial correlation coefficients. The nested regional model forecasts are compared to GFS forecasts to gauge whether nesting provides additional realistic information. They are also compared to RM3 simulations driven by reanalysis 2, representing high potential skill forecasts, to gauge the sensitivity of results to lateral boundary conditions. Nested RM3/GFS forecasts generate excessive moisture advection toward West Africa, which in turn causes prodigious amounts of model precipitation. This problem is corrected by empirical adjustments in the preparation of lateral boundary conditions and initial conditions. The resulting modified simulations improve on the GFS precipitation forecasts, achieving time-space correlations with TRMM of 0.77 on the first day and 0.63 on the second day. One realtime RM3/GFS precipitation forecast made at and posted by the African Centre of Meteorological Application for Development (ACMAD) in Niamey, Niger is shown.

Druyan, Leonard M.↗