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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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At least 973 records · Page 54
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NASA NTRS1989

Error analysis of finite element solutions for postbuckled cylinders

A general method of error analysis and correction is investigated for the discrete finite-element results for cylindrical shell structures. The method for error analysis is an adaptation of the method of successive approximation. When applied to the equilibrium equations of shell theory, successive approximations derive an approximate continuous solution from the discrete finite-element results. The advantage of this continuous solution is that it contains continuous partial derivatives of an order higher than the basis functions of the finite-element solution. Preliminary numerical results are presented in this paper for the error analysis of finite-element results for a postbuckled stiffened cylindrical panel modeled by a general purpose shell code. Numerical results from the method have previously been reported for postbuckled stiffened plates. A procedure for correcting the continuous approximate solution by Newton's method is outlined.

Sistla, Rajaram↗
NASA NTRS1995

Ab Initio Studies of Fluorine and Chlorine Oxide and Nitrogen Oxide Species of Interest in Stratospheric Chemistry

The quality of fundamental vibrational frequencies determined using the CCSD(T) method (singles and doubles coupled-cluster theory plus a perturbational estimate of the effects of connected triple excitations) is shown to be very good, usually predicting band centers to within plus or minus 8 per centimeter. This approach is applied to several molecules of interest in atmospheric chemistry, such as HNO, cis-FONO, cis-ClONO, and ClOOH. The HNO molecule displays a large and unusual anharmonicity in the H-N stretch. For the calculation of ultraviolet (UV) spectra, the linear response CCSD (LRCCSD) approach (which is equivalent to EOM-CCSD) has been shown to yield vertical excitation energies that are accurate to approximately equal to 0.1 eV for singly excited electronic states. This method together with more approximate methods is used to examine the UV spectra of several molecules important in stratospheric chemistry, including HOCl, Cl2O, ClONO2, HONO2, ClOOCl, ClOOH, and HOOH.

Lee, Timothy J.↗
NASA NTRS1984

A multilevel method for structural synthesis

A multilevel method for structural synthesis based on finite element modeling at both the system and the substructure level is set forth. At the system level, the design is described using basis vectors generated via substructure design modification. Whenever possible, substructure constraints are satisfied via local material redistribution. At both the system level and the substructure level, design modification is carried out by solving a sequence of approximate problems. The method generates upper bound approximations for the optimum design and it has potential for substantial gains in computational efficiency, because the uncoupled substructure design modification problems can be processed in parallel.

Schmit, L. A.↗
NASA NTRS1993

A stable second order method for training back propagation networks

A simple method for improving the learning rate of the back-propagation algorithm is described. The basis of the method is that approximate second order corrections can be incorporated in the output units. The extended method leads to significant improvements in the convergence rate.

Nachtsheim, Philip R.↗
NASA NTRS2017

Time Dependence of Collision Probabilities During Satellite Conjunctions

The NASA Conjunction Assessment Risk Analysis (CARA) team has recently implemented updated software to calculate the probability of collision (P (sub c)) for Earth-orbiting satellites. The algorithm can employ complex dynamical models for orbital motion, and account for the effects of non-linear trajectories as well as both position and velocity uncertainties. This “3D P (sub c)” method entails computing a 3-dimensional numerical integral for each estimated probability. Our analysis indicates that the 3D method provides several new insights over the traditional “2D P (sub c)” method, even when approximating the orbital motion using the relatively simple Keplerian two-body dynamical model. First, the formulation provides the means to estimate variations in the time derivative of the collision probability, or the probability rate, R (sub c). For close-proximity satellites, such as those orbiting in formations or clusters, R (sub c) variations can show multiple peaks that repeat or blend with one another, providing insight into the ongoing temporal distribution of risk. For single, isolated conjunctions, R (sub c) analysis provides the means to identify and bound the times of peak collision risk. Additionally, analysis of multiple actual archived conjunctions demonstrates that the commonly used “2D P (sub c)” approximation can occasionally provide inaccurate estimates. These include cases in which the 2D method yields negligibly small probabilities (e.g., P (sub c)) is greater than 10 (sup -10)), but the 3D estimates are sufficiently large to prompt increased monitoring or collision mitigation (e.g., P (sub c) is greater than or equal to 10 (sup -5)). Finally, the archive analysis indicates that a relatively efficient calculation can be used to identify which conjunctions will have negligibly small probabilities. This small-P (sub c) screening test can significantly speed the overall risk analysis computation for large numbers of conjunctions.

Hall, Doyle T.↗
NASA NTRS1985

A new theory for multistep discretizations of stiff ordinary differential equations: Stability with large step sizes

A large set of variable coefficient linear systems of ordinary differential equations which possess two different time scales, a slow one and a fast one is considered. A small parameter epsilon characterizes the stiffness of these systems. A system of o.d.e.s. in this set is approximated by a general class of multistep discretizations which includes both one-leg and linear multistep methods. Sufficient conditions are determined under which each solution of a multistep method is uniformly bounded, with a bound which is independent of the stiffness of the system of o.d.e.s., when the step size resolves the slow time scale, but not the fast one. This property is called stability with large step sizes. The theory presented lets one compare properties of one-leg methods and linear multistep methods when they approximate variable coefficient systems of stiff o.d.e.s. In particular, it is shown that one-leg methods have better stability properties with large step sizes than their linear multistep counter parts. The theory also allows one to relate the concept of D-stability to the usual notions of stability and stability domains and to the propagation of errors for multistep methods which use large step sizes.

Majda, G.↗
NASA NTRS1991

Nonequilibrium radiative heating prediction method for aeroassist flowfields with coupling to flowfield solvers

A method for predicting radiation adsorption and emission coefficients in thermochemical nonequilibrium flows is developed. The method is called the Langley optimized radiative nonequilibrium code (LORAN). It applies the smeared band approximation for molecular radiation to produce moderately detailed results and is intended to fill the gap between detailed but costly prediction methods and very fast but highly approximate methods. The optimization of the method to provide efficient solutions allowing coupling to flowfield solvers is discussed. Representative results are obtained and compared to previous nonequilibrium radiation methods, as well as to ground- and flight-measured data. Reasonable agreement is found in all cases. A multidimensional radiative transport method is also developed for axisymmetric flows. Its predictions for wall radiative flux are 20 to 25 percent lower than those of the tangent slab transport method, as expected, though additional investigation of the symmetry and outflow boundary conditions is indicated. The method was applied to the peak heating condition of the aeroassist flight experiment (AFE) trajectory, with results comparable to predictions from other methods. The LORAN method was also applied in conjunction with the computational fluid dynamics (CFD) code LAURA to study the sensitivity of the radiative heating prediction to various models used in nonequilibrium CFD. This study suggests that radiation measurements can provide diagnostic information about the detailed processes occurring in a nonequilibrium flowfield because radiation phenomena are very sensitive to these processes.

Hartung, Lin C.↗
NASA NTRS1991

Approximate factorization with source terms

A comparative evaluation is made of three methodologies with a view to that which offers the best approximate factorization error. While two of these methods are found to lead to more efficient algorithms in cases where factors which do not contain source terms can be diagonalized, the third method used generates the lowest approximate factorization error. This method may be preferred when the norms of source terms are large, and transient solutions are of interest.

Shih, T. I.-P.↗
NASA NTRS1975

An investigation of several numerical procedures for time-asymptotic compressible Navier-Stokes solutions

The status of an investigation of four numerical techniques for the time-dependent compressible Navier-Stokes equations is presented. Results for free shear layer calculations in the Reynolds number range from 1000 to 81000 indicate that a sequential alternating-direction implicit (ADI) finite-difference procedure requires longer computing times to reach steady state than a low-storage hopscotch finite-difference procedure. A finite-element method with cubic approximating functions was found to require excessive computer storage and computation times. A fourth method, an alternating-direction cubic spline technique which is still being tested, is also described.

Rudy, D. H.↗
NASA NTRS1991

On the integration of reinforcement learning and approximate reasoning for control

The author discusses the importance of strengthening the knowledge representation characteristic of reinforcement learning techniques using methods such as approximate reasoning. The ARIC (approximate reasoning-based intelligent control) architecture is an example of such a hybrid approach in which the fuzzy control rules are modified (fine-tuned) using reinforcement learning. ARIC also demonstrates that it is possible to start with an approximately correct control knowledge base and learn to refine this knowledge through further experience. On the other hand, techniques such as the TD (temporal difference) algorithm and Q-learning establish stronger theoretical foundations for their use in adaptive control and also in stability analysis of hybrid reinforcement learning and approximate reasoning-based controllers.

Berenji, Hamid R.↗
NASA NTRS1983

A lifting surface computer code with jet-in-crossflow interference effects. Volume 1: Theoretical description

A method is proposed to combine a numerical description of a jet in a crossflow with a lifting surface panel code to calculate the jet/aerodynamic-surface interference effects on a V/STOL aircraft. An iterative technique is suggested that starts with a model for the properties of a jet/flat plate configuration and modifies these properties based on the flow field calculated for the configuration of interest. The method would estimate the pressures, forces, and moments on an aircraft out of ground effect. A first-order approximation to the method suggested is developed and applied to two simple configurations. The first-order approximation is a noniterative precedure which does not allow for interactions between multiple jets in a crossflow and also does not account for the influence of lifting surfaces on the jet properties. The jet/flat plate model utilized in the examples presented is restricted to a uniform round jet injected perpendicularly into a uniform crossflow for a range of jet-to-crossflow velocity ratios from three to ten.

Furlong, K. L.↗
NASA NTRS1991

Computation of three-dimensional flows using two stream functions

An approach to compute 3-D flows using two stream functions is presented. The method generates a boundary fitted grid as part of its solution. Commonly used two steps for computing the flow fields are combined into a single step in the present approach: (1) boundary fitted grid generation; and (2) solution of Navier-Stokes equations on the generated grid. The presented method can be used to directly compute 3-D viscous flows, or the potential flow approximation of this method can be used to generate grids for other algorithms to compute 3-D viscous flows. The independent variables used are chi, a spatial coordinate, and xi and eta, values of stream functions along two sets of suitably chosen intersecting stream surfaces. The dependent variables used are the streamwise velocity, and two functions that describe the stream surfaces. Since for a 3-D flow there is no unique way to define two sets of intersecting stream surfaces to cover the given flow, different types of two sets of intersecting stream surfaces are considered. First, the metric of the (chi, xi, eta) curvilinear coordinate system associated with each type is presented. Next, equations for the steady state transport of mass, momentum, and energy are presented in terms of the metric of the (chi, xi, eta) coordinate system. Also included are the inviscid and the parabolized approximations to the general transport equations.

Greywall, Mahesh S.↗
NASA NTRS1971

Shock wave structure using nonlinear model Boltzmann equations

The structure of a strong plane shock wave in a monatomic rarefied perfect gas is one of the simplest problems able to be posed in kinetic theory, and one of the hardest to solve. Its simplicity lies in the absence of solid boundaries, geometrical complications, or internal molecular energy. Its difficulty arises from the great departure of the gas from equilibrium within the shock, which invalidates many of the techniques used successfully elsewhere in kinetic theory. In addition to this theoretical challenge, the modern development of ballistics and hypersonic flight has helped to stimulate extensive theoretical and experimental interest in the shock problem. The experimenters in turn have encountered great difficulties on account of the very small physical dimensions of shocks. In fact, until very recently indeed, any close comparisons of theoretical and experimental shock structure results have been rather unprofitable due to the inadequacies of both theory and experiment. During the last few years this situation has been appreciably improved by development of the Monte Carlo method. This allows idealized 'experiments' to be performed on large computers instead of in wind tunnels, using a known intermolecular force law. The most developed of these methods has been shown to be equivalent theoretically to the Boltzmann equation and to give results which agree extremely closely with measurements of high accuracy. Thus Monte Carlo results not only form the soundest basis for our present theoretical knowledge of shock wave structure, but, for purposes of developing other theories, can also be considered a very valuable experimental resource. However, such results remain very expensive to obtain. In this thesis we develop more economical kinetic theory methods for the approximate prediction of shock structure, and compare our results with those of the Monte Carlo method.

Segal, Ben Maurice↗
NASA NTRSDate not supplied

Copula-based Method to Generate Consistent Surface Pressures Under Uncertainty

This paper establishes a method to create surface pressure databases that allow for uncertainty quantification. Aerodynamic databases are critical products for launch vehicles and other aeronautical systems, and surface pressure databases are one such database that constains large quantities of data. The focus of this work is the relationship between the integrated force and moment data base and the surface pressure database. In particular, the work attempts to provide a method that maintains consistency between these two databases when accounting for uncertainty. The integrated force and moment database and surface pressure databases are constructed from CFD data which is high-density but low-trust. However, the force and moment database will often also include data from high-trust but low-density sources such as from wind tunnel experiments. This means that the quantified uncertainty of the force and moment database is higher quality as it includes this high fidelity wind tunnel data. This motivates the idea to use the force and moment database uncertainty when constructing the surface pressure database uncertainty. The method utilizes the statistical idea of a copula in order to generate surface pressures that match with uncertain integrated force and moment distributions as well as being consistent with known CFD data. This statistical consistency is quantified by using the Maximum Mean Discrepancy two-sample test. The predictive error of the method is also approximated using leave-one-out error estimation and the good overall performance of the method is presented using probability boxes in a simulated uncertainty scenario.

SLS↗
NASA NTRS1992

Receiver characteristics of laser altimeters with avalanche photodiodes

The receiver characteristics of a laser altimeter system containing an avalanche photodiode photodetector are analyzed using the Gaussian approximation, the saddle-point approximation, and a nearly exact analysis. The last two methods are shown to yield very similar results except when the background noise is extremely low and the probability of false alarm is high. However, the Gaussian approximation method is shown to cause significant errors even under relatively high levels of background noise and received signal energy.

Sun, Xiaoli↗
NASA NTRS1996

On the Generation of Turbulent Inflow Conditions for Boundary Layer Simulations

Turbulent flows that exhibit inhomogeneities in the streamwise direction pose a particular challenge to numerical simulation approaches due to the need to prescribe time-dependent turbulent inflow conditions. In most cases the flow downstream is more or less 'driven' by the conditions at the inlet, making it necessary to specify realistic turbulent fluctuations that are in equilibrium with the assumed mean flow. This requirement often dictates that the inflow data should satisfy the Navier-Stokes equations, which in turn implies that an independent simulation be used to generate them. Detailed simulations for the purpose of creating inflow conditions can be costly and thus certain levels of approximation are desirable. In this paper we shall focus on an approximate yet accurate method for generating inflow conditions for spatially-developing boundary layer simulations. The proposed method is essentially a simplification of the method of Spalart and Leonard (1985), who devised an ingenious transformation that allows for the calculation of spatially evolving boundary layers in conjunction with periodic boundary conditions applied in the streamwise direction. While this method is elegant and highly accurate, it is more complicated than is necessary for the purpose of generating inflow data. A few key approximations are used in this work to arrive at a 'modified Spalart method' that is very easy to implement and efficient to use. The new method is shown to yield results that compare well with the computations of Spalart (1988). When used as a means of generating inflow data, the modified Spalart method is shown to be superior to existing approaches.

Lund, T. S.↗
NASA NTRS1980

Two-stream approximations to radiative transfer in planetary atmospheres - A unified description of existing methods and a new improvement

Existing two-stream approximations to radiative transfer theory for particulate media are shown to be represented by identical forms of coupled differential equations if the intensity is replaced by integrals of the intensity over hemispheres. One set of solutions thus suffices for all methods and provides convenient analytical comparisons. The equations also suggest modifications of the standard techniques so as to duplicate exact solutions for thin atmospheres and thus permit accurate determinations of the effects of typical aerosol layers. Numerical results for the plane albedos of plane-parallel atmospheres are given for conventional and modified Eddington approximations, conventional and modified two-point quadrature schemes, the hemispheric-constant method and the delta-function method, all for comparison with accurate discrete-ordinate solutions. A new two-stream approximation is introduced that reduces to the modified Eddington approximation in the limit of isotropic phase functions and to the exact solution in the limit of extreme anisotropic scattering. Comparisons of plane albedos and transmittances show the new method to be generally superior over a wide range of atmospheric conditions (including cloud and aerosol layers), especially in the case of nonconservative scattering.

Meador, W. E.↗
NASA NTRS1984

Flutter of swept fan blades

The effect of sweep on fan blade flutter is studied by applying the analytical methods developed for aeroelastic analysis of advance turboprops. Two methods are used. The first method utilizes an approximate structural model in which the blade is represented by a swept, nonuniform beam. The second method utilizes a finite element technique to conduct modal flutter analysis. For both methods the unsteady aerodynamic loads are calculated using two dimensional cascade theories which are modified to account for sweep. An advanced fan stage is analyzed with 0, 15 and 30 degrees of sweep. It is shown that sweep has a beneficial effect on predominantly torsional flutter and a detrimental effect on predominantly bending flutter. This detrimental effect is shown to be significantly destabilizing for 30 degrees of sweep.

Kielb, R. E.↗