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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.

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All sourcesNASA NTRSDOE OSTI
NASA NTRS2013

Covariance Analysis Tool (G-CAT) for Computing Ascent, Descent, and Landing Errors

G-CAT is a covariance analysis tool that enables fast and accurate computation of error ellipses for descent, landing, ascent, and rendezvous scenarios, and quantifies knowledge error contributions needed for error budgeting purposes. Because GCAT supports hardware/system trade studies in spacecraft and mission design, it is useful in both early and late mission/ proposal phases where Monte Carlo simulation capability is not mature, Monte Carlo simulation takes too long to run, and/or there is a need to perform multiple parametric system design trades that would require an unwieldy number of Monte Carlo runs. G-CAT is formulated as a variable-order square-root linearized Kalman filter (LKF), typically using over 120 filter states. An important property of G-CAT is that it is based on a 6-DOF (degrees of freedom) formulation that completely captures the combined effects of both attitude and translation errors on the propagated trajectories. This ensures its accuracy for guidance, navigation, and control (GN&C) analysis. G-CAT provides the desired fast turnaround analysis needed for error budgeting in support of mission concept formulations, design trade studies, and proposal development efforts. The main usefulness of a covariance analysis tool such as G-CAT is its ability to calculate the performance envelope directly from a single run. This is in sharp contrast to running thousands of simulations to obtain similar information using Monte Carlo methods. It does this by propagating the "statistics" of the overall design, rather than simulating individual trajectories. G-CAT supports applications to lunar, planetary, and small body missions. It characterizes onboard knowledge propagation errors associated with inertial measurement unit (IMU) errors (gyro and accelerometer), gravity errors/dispersions (spherical harmonics, masscons), and radar errors (multiple altimeter beams, multiple Doppler velocimeter beams). G-CAT is a standalone MATLAB- based tool intended to run on any engineer's desktop computer.

Boussalis, Dhemetrios↗
NASA NTRS1990

Basic Mechanisms of Solar Variability

In order to simulate the behavior of a changing Sun in a realistic way, researchers have used a perturbation analysis (the results are summarized in Endal et al. 1985). In this approach, they use a standard solar model and then vary several of the model parameters to mimic the sudden or gradual change of some physical property within the Sun. The evolution following the perturbation is followed in a physically self-consistent way, that is, hydrostatic and thermal processes occur in their normal timescales. This treatment has allowed us to determine the sensitivity of the various global parameters to physical processes affecting the solar interior, and it has guided us in defining the least complex global solar model which can address the question of climatically significant variability. Not surprisingly, magnetic fields play the crucial role. The current status of the model, what researchers have already learned from it, and the future prospects are discussed.

Sofia, Sabatino↗
NASA NTRS1986

Mg II emission from shock waves in Mira variables

In order to investigate the atmospheric shock dynamics of Miras, a program to monitor the ultraviolet Mg II flux, the visual magnitude (using the IUE FES-magnitude) and whenever possible the hydrogen Balmer emission for several Miras was initiated. Results suggest that it should be possible to derive the density structure of the atmosphere and hence estimate quite accurately the kinetic energy input into the stellar atmosphere. The atmospheric shock models suggest that at phase equal 1.0 most of the energy which enters the region where the shock is located ends up in the wind. This is after the strongest Mg II emission is seen. From an observed velocity at infinity and an estimate of the energy input derived from the Mg II flux, it will be possible to determine the mass loss rate for these objects.

Brugel, Edward W.↗
NASA NTRS1985

Development and Testing of the Variable Vertical Resolution Fourth Order GCM

The vertical coordinate of the Fourth Order Model has been generalized so that the model can now run with an arbitrary number of vertical layers and so that the thicknesses of these layers can be arbitrarily specified (in the sigma coordinate). This Variable Vertical Resolution (VVR) version of the Fourth Order Model will soon replace the current production model. To assess the skill of the VVR model, it has been run with 9 equally spaced layers and compared with the current production model. In two Northern Hemispheric winter cases and one summer case, the two models were virtually identical in forecast skill for 6 to 7 days. After that the VVR model was slightly better in the winter cases and the production model was slightly better in the summer case. The only exception to this was that after 2 days the production model gave slightly more skillful 500 mb forecasts in the tropics for the summer case.

Helfand, H. M.↗
NASA NTRS1978

Applied Routh approximation

The Routh approximation technique for reducing the complexity of system models was applied in the frequency domain to a 16th order, state variable model of the F100 engine and to a 43d order, transfer function model of a launch vehicle boost pump pressure regulator. The results motivate extending the frequency domain formulation of the Routh method to the time domain in order to handle the state variable formulation directly. The time domain formulation was derived and a characterization that specifies all possible Routh similarity transformations was given. The characterization was computed by solving two eigenvalue-eigenvector problems. The application of the time domain Routh technique to the state variable engine model is described, and some results are given. Additional computational problems are discussed, including an optimization procedure that can improve the approximation accuracy by taking advantage of the transformation characterization.

Merrill, W. C.↗
NASA NTRS2015

Simscape Modeling of a Custom Closed-Volume Tank

The library for Mathworks Simscape does not currently contain a model for a closed volume fluid tank where the ullage pressure is variable. In order to model a closed-volume variable ullage pressure tank, it was necessary to consider at least two separate cases: a vertical cylinder, and a sphere. Using library components, it was possible to construct a rough model for the cylindrical tank. It was not possible to construct a model for a spherical tank, using library components, due to the variable area. It was decided that, for these cases, it would be preferable to create a custom library component to represent each case, using the Simscape language. Once completed, the components were added to models, where filling and draining the tanks could be simulated. When the models were performing as expected, it was necessary to generate code from the models and run them in Trick (a real-time simulation program). The data output from Trick was then compared to the output from Simscape and found to be within acceptable limits.

Simscape↗
NASA NTRS2000

First-Order Model Management With Variable-Fidelity Physics Applied to Multi-Element Airfoil Optimization

First-order approximation and model management is a methodology for a systematic use of variable-fidelity models or approximations in optimization. The intent of model management is to attain convergence to high-fidelity solutions with minimal expense in high-fidelity computations. The savings in terms of computationally intensive evaluations depends on the ability of the available lower-fidelity model or a suite of models to predict the improvement trends for the high-fidelity problem, Variable-fidelity models can be represented by data-fitting approximations, variable-resolution models. variable-convergence models. or variable physical fidelity models. The present work considers the use of variable-fidelity physics models. We demonstrate the performance of model management on an aerodynamic optimization of a multi-element airfoil designed to operate in the transonic regime. Reynolds-averaged Navier-Stokes equations represent the high-fidelity model, while the Euler equations represent the low-fidelity model. An unstructured mesh-based analysis code FUN2D evaluates functions and sensitivity derivatives for both models. Model management for the present demonstration problem yields fivefold savings in terms of high-fidelity evaluations compared to optimization done with high-fidelity computations alone.

Alexandrov, N. M.↗
NASA NTRS1987

Analysis of eccentric annular incompressible seals. II - Effects of eccentricity on rotordynamic coefficients

A new analysis procedure has been presented which solves for the flow variables of an annular pressure seal in which the rotor has a large static displacement (eccentricity) from the centered position. The present paper incorporates the solutions to investigate the effect of eccentricity on the rotordynamic coefficients. The analysis begins with a set of governing equations based on a turbulent bulk-flow model and Moody's friction factor equation. Perturbations of the flow variables yields a set of zeroth- and first-order equations. After integration of the zeroth-order equations, the resulting zeroth-order flow variables are used as input in the solution of the first-order equations. Further integration of the first order pressures yields the eccentric rotordynamic coefficients. The results from this procedure compare well with available experimental and theoretical data, with accuracy just as good or slightly better than the predictions based on a finite-element model.

Nelson, C. C.↗
NASA NTRS1986

Reconstruction and robust reduced-order observation of flexible variables

This paper discusses reconstruction and estimation of flexible variables from multiple strain measurements for use in state feedback control of flexible manipulators. Reconstruction is proposed for obtaining flexible mode amplitudes from the measurements, and estimation for the modal velocities. Design of the observer for estimation of the velocities is discussed with regard to robust implementation. The performance of the observer is examined experimentally for several specifications of the error dynamics.

Hastings, Gordon G.↗
NASA NTRS1990

Singular perturbation analysis of AOTV-related trajectory optimization problems

The problem of real time guidance and optimal control of Aeroassisted Orbit Transfer Vehicles (AOTV's) was addressed using singular perturbation theory as an underlying method of analysis. Trajectories were optimized with the objective of minimum energy expenditure in the atmospheric phase of the maneuver. Two major problem areas were addressed: optimal reentry, and synergetic plane change with aeroglide. For the reentry problem, several reduced order models were analyzed with the objective of optimal changes in heading with minimum energy loss. It was demonstrated that a further model order reduction to a single state model is possible through the application of singular perturbation theory. The optimal solution for the reduced problem defines an optimal altitude profile dependent on the current energy level of the vehicle. A separate boundary layer analysis is used to account for altitude and flight path angle dynamics, and to obtain lift and bank angle control solutions. By considering alternative approximations to solve the boundary layer problem, three guidance laws were derived, each having an analytic feedback form. The guidance laws were evaluated using a Maneuvering Reentry Research Vehicle model and all three laws were found to be near optimal. For the problem of synergetic plane change with aeroglide, a difficult terminal boundary layer control problem arises which to date is found to be analytically intractable. Thus a predictive/corrective solution was developed to satisfy the terminal constraints on altitude and flight path angle. A composite guidance solution was obtained by combining the optimal reentry solution with the predictive/corrective guidance method. Numerical comparisons with the corresponding optimal trajectory solutions show that the resulting performance is very close to optimal. An attempt was made to obtain numerically optimized trajectories for the case where heating rate is constrained. A first order state variable inequality constraint was imposed on the full order AOTV point mass equations of motion, using a simple aerodynamic heating rate model.

Calise, Anthony J.↗
NASA NTRS1985

Parameterization of Surface Fluxes in the VVR Fourth Order GCM

The Variable Vertical Resolution (VVR) option of the GLAS Fourth Order General Circulation Model (GCM) allows one to enhance the vertical resolution of the region of the atmosphere adjacent to the Earth's surface. This, in turn, makes it possible to compute turbulent surface fluxes of heat, momentum and moisture directly from the prognosticated properties of the lowest model layer by use of the Monin-Obukhov surface layer similarity theory. The similarity theory applies formally only to the constant flux surface layer which is but a few tens of meters deep. It is not practically feasible to work with a lowest GCM layer thin enough to satisfy these formal constraints. It is shown that at least under conditions of neutral stratification, the similarity theory can be extended beyond its formal limits. The theory still gives reasonable looking results, when the distance from the ground becomes as large as 150 m. It is not infeasible to run the VVR model with a lowest layer thickness on the order of 300 m (the center of the layer would then be 150 m above the Earth's surface), and so if one can prescribe similarity functions phi sub m (zeta) and phi sub h (zeta) to adequately describe the entire extended surface layer, the problem of surface flux parameterization is solved.

Helfand, H. M.↗
NASA NTRS1993

Order-sorting filter transmittance measured with an array detector

The simultaneous measurement of the spectrally and spatially variant transmittance of a linear variable order-sorting filter in a manner that closely resembles its conditions of actual use is described. The transmittance of a prototype order-sorting filter was measured in the 400- to 880-nm wavelength region by illuminating it with the output beam of a spectrophotometer while the filter was attached to the front of a 30 x 32 pixel silicon array detector. The filter was designed to be used in the output beam of a grating spectrometer to prevent the dispersal of higher diffracted orders onto an array detector. Areas of the filter that were spatially matched to the corresponding detector pixel column had measured peak transmittances of about 90 percent that were uniform to within +/- 1.5 percent along a given column. Transmittances for incident wavelengths shorter than the desired bandpass, corresponding to the order overlap region, were measured in the 0.003 range. Line spread function measurements made with the array detector indicated no significant beam spreading caused by inserting the filter into the beam.

Heaney, James B.↗
NASA NTRS1994

Methodology for sensitivity analysis, approximate analysis, and design optimization in CFD for multidisciplinary applications

The straightforward automatic-differentiation and the hand-differentiated incremental iterative methods are interwoven to produce a hybrid scheme that captures some of the strengths of each strategy. With this compromise, discrete aerodynamic sensitivity derivatives are calculated with the efficient incremental iterative solution algorithm of the original flow code. Moreover, the principal advantage of automatic differentiation is retained (i.e., all complicated source code for the derivative calculations is constructed quickly with accuracy). The basic equations for second-order sensitivity derivatives are presented; four methods are compared. Each scheme requires that large systems are solved first for the first-order derivatives and, in all but one method, for the first-order adjoint variables. Of these latter three schemes, two require no solutions of large systems thereafter. For the other two for which additional systems are solved, the equations and solution procedures are analogous to those for the first order derivatives. From a practical viewpoint, implementation of the second-order methods is feasible only with software tools such as automatic differentiation, because of the extreme complexity and large number of terms. First- and second-order sensitivities are calculated accurately for two airfoil problems, including a turbulent flow example; both geometric-shape and flow-condition design variables are considered. Several methods are tested; results are compared on the basis of accuracy, computational time, and computer memory. For first-order derivatives, the hybrid incremental iterative scheme obtained with automatic differentiation is competitive with the best hand-differentiated method; for six independent variables, it is at least two to four times faster than central finite differences and requires only 60 percent more memory than the original code; the performance is expected to improve further in the future.

Taylor, Arthur C., III↗
NASA NTRS1972

Reflecting Solutions of High Order Elliptic Differential Equations in Two Independent Variables Across Analytic Arcs

Consideration is given specifically to sixth order elliptic partial differential equations in two independent real variables x, y such that the coefficients of the highest order terms are real constants. It is assumed that the differential operator has distinct characteristics and that it can be factored as a product of second order operators. By analytically continuing into the complex domain and using the complex characteristic coordinates of the differential equation, it is shown that its solutions, u, may be reflected across analytic arcs on which u satisfies certain analytic boundary conditions. Moreover, a method is given whereby one can determine a region into which the solution is extensible. It is seen that this region of reflection is dependent on the original domain of difinition of the solution, the arc and the coefficients of the highest order terms of the equation and not on any sufficiently small quantities; i.e., the reflection is global in nature. The method employed may be applied to similar differential equations of order 2n.

Carleton, O.↗
NASA NTRS2018

A Simple, Velocity Dependent, Collision Probability Algorithm for Small Combined Hard Body Radii Close Approach Events

Over the last few years progress has been made in the velocity dependent collision probability problem. Recent progress in this problem has been approached via integration of the probability flux into the surface of the combined hard body object. The algorithm presented uses the surface flux approach and is designed to compute the collision probability rate between two objects given their time dependent states and state error covariance matrices. With regards to the computation of the collision probability (Pc) rate, two major differences exist between the development of this algorithm and the usual Pc algorithm. First, the shape of the at-risk volume is assumed to be a cube rather than a sphere. The size of the cube is chosen so that it circumscribes the usual hard body sphere chosen for the spherical Pc problem. This will result in half the length of a side of the cube being equal to the hard body radius (HBR) of the sphere. Second, it is assumed that the HBR of the cube is much smaller than the smallest combined position uncertainty (σ(sub min) > 5*HBR) at each time point of evaluation. This is necessary as the actual collision probability calculation is based on a first order, small variable expansion in the position components of the Gaussian probability density function. This leads to the collision probability rate being to second order in the combined HBR. The collision probability rate is in a concise, closed form containing exponential and error functions.

Frisbee, Joe↗
NASA NTRS1988

Modes of variability in a low-order two-level model

A low-order two-level mode in a beta-plane channel is integrated over long periods of time to investigate low-frequency midlatitude variability. The model takes into account nonlinear wave-wave and wave-mean flow interactions as well as zonally asymmetric forcing by topography. The following properties of the model are examined: model scaling and response to variation of parameters, extra damping at the shortest scale, time-mean model flow, and variance.

O'Brien, Enda↗