Search NASA⌕ Search

SEARCH · Search NASA

Results for “APPROXIMATION METHOD”

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

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

At least 181 records · Page 10
All sourcesNASA NTRSDOE OSTI
NASA NTRS1984

The uniform asymptotic swallowtail approximation - Practical methods for oscillating integrals with four coalescing saddle points

Methods that can be used in the numerical implementation of the uniform swallowtail approximation are described. An explicit expression for that approximation is presented to the lowest order, showing that there are three problems which must be overcome in practice before the approximation can be applied to any given problem. It is shown that a recently developed quadrature method can be used for the accurate numerical evaluation of the swallowtail canonical integral and its partial derivatives. Isometric plots of these are presented to illustrate some of their properties. The problem of obtaining the arguments of the swallowtail integral from an analytical function of its argument is considered, describing two methods of solving this problem. The asymptotic evaluation of the butterfly canonical integral is addressed.

Connor, J. N. L.↗
NASA NTRS1998

Variable-Complexity Multidisciplinary Optimization on Parallel Computers

This report covers work conducted under grant NAG1-1562 for the NASA High Performance Computing and Communications Program (HPCCP) from December 7, 1993, to December 31, 1997. The objective of the research was to develop new multidisciplinary design optimization (MDO) techniques which exploit parallel computing to reduce the computational burden of aircraft MDO. The design of the High-Speed Civil Transport (HSCT) air-craft was selected as a test case to demonstrate the utility of our MDO methods. The three major tasks of this research grant included: development of parallel multipoint approximation methods for the aerodynamic design of the HSCT, use of parallel multipoint approximation methods for structural optimization of the HSCT, mathematical and algorithmic development including support in the integration of parallel computation for items (1) and (2). These tasks have been accomplished with the development of a response surface methodology that incorporates multi-fidelity models. For the aerodynamic design we were able to optimize with up to 20 design variables using hundreds of expensive Euler analyses together with thousands of inexpensive linear theory simulations. We have thereby demonstrated the application of CFD to a large aerodynamic design problem. For the predicting structural weight we were able to combine hundreds of structural optimizations of refined finite element models with thousands of optimizations based on coarse models. Computations have been carried out on the Intel Paragon with up to 128 nodes. The parallel computation allowed us to perform combined aerodynamic-structural optimization using state of the art models of a complex aircraft configurations.

Grossman, Bernard↗
NASA NTRS1984

Monte Carlo calculations of elementary particle properties

The object of this project is to calculate the masses of the elementary particles. This ambitious goal apparently is not possible using analytic methods or known approximation methods. However, it is probable that the power of a modern super computer will make at least part of the low lying mass spectrum accessible through direct numerical computation. Initial attempts by several groups at calculating this spectrum on small lattices of space time points have been very promising. Using new methods and super computers considerable progress has been made towards evaluating the mass spectrum on comparatively large lattices. Only more time and faster machines with increased storage will allow calculations of systems with guaranteed minimal boundary effects. The ideas that currently go into this calculation are outlined.

Guralnik, G. S.↗
NASA NTRS1985

Three-dimensional viscous-shock-layer applications for the Space Shuttle orbiter

A nonorthogonal three-dimensional viscous-shock-layer code was modified and used to compute the windward surface flowfield over a Shuttle-like configuration. Code modifications were made in the methods used to evaluate shock boundary conditions and in the implementation of the equilibrium air models. Additional viscous terms were also retained in the governing equations. Effects of these modifications are demonstrated. Three-dimensional flowfield solutions obtained with the modified code showed good comparison of surface heating and pressure with actual flight data. An apparently three-dimensional effect, characterized by a drop in surface heating on the Shuttle windward centerline in the wing root area, was predicted by the present method. A preliminary review of Shuttle ground-based experimental and flight data confirmed this trend. The present three-dimensional solutions were also compared with the predictions of several approximate methods. Those comparisons showed the approximate methods to be valid for predicting heating along the Shuttle windward centerline uner both perfect gas and equilibrium air conditions.

Thompson, R. A.↗
NASA NTRS1991

An efficient method for estimating neighboring steady-state numerical solutions to the Euler equations

The paper concentrates on a linear approximation method for predicting the changes occurring in steady-state numerical solutions of the Euler equations as a consequence of small changes in the independent variables which control the problem. The importance of proper boundary-condition treatment and other issues concerning the problem are covered along with the importance of proper algorithm selection for a fully supersonic inviscid flow. The method is applied to a subsonic nozzle involving variation of the pressure on the outflow boundary and to a supersonic inlet involving variation of the inflow Mach number. In the subsonic test case, the comparisons between the predicted and conventional numerical solutions are shown to be good, while in the supersonic test case, the agreement between the approximation method and conventional numerical solution starts out well but rapidly degenerates at some point in the flowfield as the perturbation of the boundary conditions is increased.

Taylor, Arthur C., III↗
NASA NTRS1976

Methods for comparative evaluation of propulsion system designs for supersonic aircraft

The propulsion system comparative evaluation study was conducted to define a rapid, approximate method for evaluating the effects of propulsion system changes for an advanced supersonic cruise airplane, and to verify the approximate method by comparing its mission performance results with those from a more detailed analysis. A table look up computer program was developed to determine nacelle drag increments for a range of parametric nacelle shapes and sizes. Aircraft sensitivities to propulsion parameters were defined. Nacelle shapes, installed weights, and installed performance was determined for four study engines selected from the NASA supersonic cruise aircraft research (SCAR) engine studies program. Both rapid evaluation method (using sensitivities) and traditional preliminary design methods were then used to assess the four engines. The method was found to compare well with the more detailed analyses.

Tyson, R. M.↗
DOE OSTI2024

An extension of Thwaites’ method for turbulent boundary layers

Thwaites developed an approximate method for determining the evolution of laminar boundary layers. The approximation follows from an assumption that the growth of a laminar boundary layer in the presence of pressure gradients could be parameterized solely as a function of the Holstein–Bohlen flow parameter, thus reducing the von Kármán momentum integral to a first-order ordinary differential equation. This method is useful for the analysis of laminar flows, and in computational potential flow solvers to account for the viscous effects. In this work, an approximate method for determining the momentum thickness of a two-dimensional, turbulent boundary layer is proposed following Thwaites’ work. It is shown that the method provides good estimates of the momentum thickness for multiple boundary layers, including both favourable and adverse pressure gradient effects, up to the point of separation. In the limit of high Reynolds numbers, it is possible to derive a criterion for the onset of separation from the proposed model, which is shown to be in agreement with prior empirical observations. The sensitivity of the separation location with respect to upstream perturbations is also analysed through this model for the NASA/Boeing speed bump and the transonic Bachalo–Johnson bump.

17 WIND ENERGY↗
NASA NTRS1982

Kinematic precision of gear trains

Kinematic precision is affected by errors which are the result of either intentional adjustments or accidental defects in manufacturing and assembly of gear trains. A method for the determination of kinematic precision of gear trains is described. The method is based on the exact kinematic relations for the contact point motions of the gear tooth surfaces under the influence of errors. An approximate method is also explained. Example applications of the general approximate methods are demonstrated for gear trains consisting of involute (spur and helical) gears, circular arc (Wildhaber-Novikov) gears, and spiral bevel gears. Gear noise measurements from a helicopter transmission are presented and discussed with relation to the kinematic precision theory.

Litvin, F. L.↗
NASA NTRS1983

Kinematic precision of gear trains

Kinematic precision is affected by errors which are the result of either intentional adjustments or accidental defects in manufacturing and assembly of gear trains. A method for the determination of kinematic precision of gear trains is described. The method is based on the exact kinematic relations for the contact point motions of the gear tooth surfaces under the influence of errors. An approximate method is also explained. Example applications of the general approximate methods are demonstrated for gear trains consisting of involute (spur and helical) gears, circular arc (Wildhaber-Novikov) gears, and spiral bevel gears. Gear noise measurements from a helicopter transmission are presented and discussed with relation to the kinematic precision theory. Previously announced in STAR as N82-32733

Litvin, F. L.↗
NASA NTRS1985

Evaluation of fault-tolerant system performance by approximate techniques

An approximate method for calculating the statistics of the performance of a fault-tolerant system is developed. An approximate method is necessary because the statistical model of the system behavior is large-scale and the time horizon of interest encompasses many cycles of the Redundancy Management logic. In the development, a compact representation of the necessary information called the v-transform is introduced and discussed. Based upon this representation, an approximation that leads to a very efficient computational procedure is suggested and numerically analyzed. A very brief discussion of other related work is also presented.

Walker, B. K.↗
NASA NTRS1972

Inviscid surface streamline program for use in predicting shuttle heating rates

A number of methods are currently under development for computing the exact three-dimensional flow field about real configurations. However, even when these methods are available, they will require large computational times on present generation computers. Thus, there is still a need to develop approximate methods to solve three-dimensional flow problems. An inviscid-surface-streamline program (for predicting shuttle heating rates) which uses approximate methods to obtain a solution is described.

Hamilton, H. Harris↗
NASA NTRS1960

An Approximate Analytical Method for Studying Atmosphere Entry of Vehicles with Modulated Aerodynamic Forces

The dimensionless, transformed, nonlinear differential equation developed in NASA TR R-11 for describing the approximate motion and heating during entry into planetary atmospheres for constant aerodynamic coefficients and vehicle shape has been modified to include entries during which the aerodynamic coefficients and the vehicle shape are varied. The generality of the application of the original equation to vehicles of arbitrary weight, size, and shape and to arbitrary atmospheres is retained. A closed-form solution for the motion, heating, and the variation of drag loading parameter m/C(D)A has been obtained for the case of constant maximum resultant deceleration during nonlifting entries. This solution requires certain simplifying assumptions which do not compromise the accuracy of the results. The closed-form solution has been used to determine the variation of m/C(D)A required to reduce peak decelerations and to broaden the corridor for nonlifting entry into the earth's atmosphere at escape velocity. The attendant heating penalty is also studied.

Levy, Lionel L., Jr.↗
NASA NTRS2017

3DHZETRN: Inhomogeneous Geometry Issues

Historical methods for assessing radiation exposure inside complicated geometries for space applications were limited by computational constraints and lack of knowledge associated with nuclear processes occurring over a broad range of particles and energies. Various methods were developed and utilized to simplify geometric representations and enable coupling with simplified but efficient particle transport codes. Recent transport code development efforts, leading to 3DHZETRN, now enable such approximate methods to be carefully assessed to determine if past exposure analyses and validation efforts based on those approximate methods need to be revisited. In this work, historical methods of representing inhomogeneous spacecraft geometry for radiation protection analysis are first reviewed. Two inhomogeneous geometry cases, previously studied with 3DHZETRN and Monte Carlo codes, are considered with various levels of geometric approximation. Fluence, dose, and dose equivalent values are computed in all cases and compared. It is found that although these historical geometry approximations can induce large errors in neutron fluences up to 100 MeV, errors on dose and dose equivalent are modest (<10%) for the cases studied here.

Wilson, John W.↗
NASA NTRS1984

Methods for analysis of cracks in three-dimensional solids

Various analytical and numerical methods used to evaluate the stress intensity factors for cracks in three-dimensional (3-D) solids are reviewed. Classical exact solutions and many of the approximate methods used in 3-D analyses of cracks are reviewed. The exact solutions for embedded elliptic cracks in infinite solids are discussed. The approximate methods reviewed are the finite element methods, the boundary integral equation (BIE) method, the mixed methods (superposition of analytical and finite element method, stress difference method, discretization-error method, alternating method, finite element-alternating method), and the line-spring model. The finite element method with singularity elements is the most widely used method. The BIE method only needs modeling of the surfaces of the solid and so is gaining popularity. The line-spring model appears to be the quickest way to obtain good estimates of the stress intensity factors. The finite element-alternating method appears to yield the most accurate solution at the minimum cost.

Raju, I. S.↗
DOE OSTI2026

Solar and Storage Integration in the U.S. Southeast: Implications for Resource Adequacy [Slides]

In this study, we evaluate how an iterative portfolio approach compares to a more traditional capacity credit method, using the U.S. Southeast as a case study region. Using open-source planning and resource adequacy tools, we compare results using a capacity credit approximation method with those from iterating behind the two. We also explore how the iterative approach performs under a range of sensitivities, including higher load growth, regional coordination, and alternative weather years. We find that traditional capacity credit approximation methods can function well in today's system, but may face challenges for systems with higher levels of solar and storage. As such, integrating planning and resource adequacy models can address some of these gaps, helping planners deliver more reliable systems.

14 SOLAR ENERGY↗
NASA NTRS1990

Differential equation based method for accurate approximations in optimization

This paper describes a method to efficiently and accurately approximate the effect of design changes on structural response. The key to this new method is to interpret sensitivity equations as differential equations that may be solved explicitly for closed form approximations, hence, the method is denoted the Differential Equation Based (DEB) method. Approximations were developed for vibration frequencies, mode shapes and static displacements. The DEB approximation method was applied to a cantilever beam and results compared with the commonly-used linear Taylor series approximations and exact solutions. The test calculations involved perturbing the height, width, cross-sectional area, tip mass, and bending inertia of the beam. The DEB method proved to be very accurate, and in msot cases, was more accurate than the linear Taylor series approximation. The method is applicable to simultaneous perturbation of several design variables. Also, the approximations may be used to calculate other system response quantities. For example, the approximations for displacement are used to approximate bending stresses.

Pritchard, Jocelyn I.↗