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At least 487 records · Page 27

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NASA NTRS1990

Improved boundary layer heat transfer calculations near a stagnation point

A thermal design of a solar receiver has been developed for the solutions of problems involving phase-change thermal energy storage and natural convection loss. Two dimensional axisymmetrical solidification and melting of materials contained between two concentric cylinders of finite length has been studied for thermal energy storage analysis. For calculation of free convection loss inside receiver cavity, two dimensional axisymmetrical, laminar, transient free convection including radiation effects has been studied using integral/finite difference method. Finite difference equations are derived for the above analysis subject to constant or variable material properties, initial conditions, and boundary conditions. The validity of the analyses has been substantiated by comparing results of the present general method with available analytic solutions or numerical results reported in the literature. Both explicit and implicit schemes are tested in phase change analysis with different number of nodes ranging from 4 to 18. The above numerical methods have been applied to the existing solar receiver analyzing computer code as additional subroutines. The results were computed for one of the proposed Brayton cycle solar receiver models running under the actual environmental conditions. Effect of thermal energy storage on the thermal behavior of the receiver has been estimated. Due to the thermal energy storage, about 65% reduction on working gas outlet temperature fluctuation has been obtained; however, maximum temperature of thermal energy storage containment has been increased about 18%. Also, effect of natural convection inside a receiver cavity on the receiver heat transfer has been analyzed. The finding indicated that thermal stratification occurs during the sun time resulting in higher receiver temperatures at the outlet section of the gas tube, and lower temperatures at the inlet section of the gas tube when compared with the results with no natural convection. Due to heat supply from the air during the shade time, minimum temperature has been increased, while maximum temperature has been reduced due to convection loss to air. Consequently, cyclic temperature fluctuation has been reduced 29% for working gas and 16% for thermal energy storage containment. On the other hand, despite the presence of the natural convection the time-averaged temperatures for receiver components were found to be similar for two cases with/without natural convection (maximum difference was 1.8%).

Ahn, Kyung Hwan↗

NASA NTRSDate not supplied

Intent Modeling and Intent Conflict Probability Calculation for Operations in Upper Class E Airspace

This work presents probabilistic intent models for two typical vehicles in ETM operational environment. Several methods, including analytical methods for approximated solutions and a numerical method for exact solution, are presented and applied to compute the intent conflict probability for ETM operations. A comparison of these methods will be conducted in the final paper. Furthermore, simulations will be performed to verify the probabilistic intent model and verify the results of intent conflict probability from different methods.

Operational intent↗

NASA NTRS1982

Error propagation in the numerical solutions of the differential equations of orbital mechanics

The relationship between the eigenvalues of the linearized differential equations of orbital mechanics and the stability characteristics of numerical methods is presented. It is shown that the Cowell, Encke, and Encke formulation with an independent variable related to the eccentric anomaly all have a real positive eigenvalue when linearized about the initial conditions. The real positive eigenvalue causes an amplification of the error of the solution when used in conjunction with a numerical integration method. In contrast an element formulation has zero eigenvalues and is numerically stable.

Bond, V. R.↗

NASA NTRS1993

Numerical investigation of complex, transitional, and chemically reacting flows

This document is divided into two parts. Part A, on turbulent transport of chemical species in compressible reacting flows, includes the following topics: mixing of chemical species in reacting flows; chemically reacting turbulent flows; turbulent mixing of chemical species in reacting flows, which includes large eddy mixing, turbulent mixing, and molecular mixing; multiple time scale turbulence equations; species conservation equations for reacting flows; and a finite volume numerical method. Part B, on unsteady transitional flows over forced oscillatory surfaces, discusses unsteady transitional flow equations with moving boundaries and the application of the finite volume numerical solution method.

Kim, S.-W.↗

NASA NTRS1990

Scientific study of data analysis

We present a comparison between two numerical methods for the extrapolation of nonlinear force-free magnetic fields, the Iterative Method (IM) and the Progressive Extension Method (PEM). The advantages and disadvantages of these two methods are summarized and the accuracy and numerical instability are discussed. On the basis of this investigation, we claim that the two methods do resemble each other qualitatively.

Wu, S. T.↗

NASA NTRS2000

Solving ODE Initial Value Problems With Implicit Taylor Series Methods

In this paper we introduce a new class of numerical methods for integrating ODE initial value problems. Specifically, we propose an extension of the Taylor series method which significantly improves its accuracy and stability while also increasing its range of applicability. To advance the solution from t (sub n) to t (sub n+1), we expand a series about the intermediate point t (sub n+mu):=t (sub n) + mu h, where h is the stepsize and mu is an arbitrary parameter called an expansion coefficient. We show that, in general, a Taylor series of degree k has exactly k expansion coefficients which raise its order of accuracy. The accuracy is raised by one order if k is odd, and by two orders if k is even. In addition, if k is three or greater, local extrapolation can be used to raise the accuracy two additional orders. We also examine stability for the problem y'= lambda y, Re (lambda) less than 0, and identify several A-stable schemes. Numerical results are presented for both fixed and variable stepsizes. It is shown that implicit Taylor series methods provide an effective integration tool for most problems, including stiff systems and ODE's with a singular point.

Scott, James R.↗

NASA NTRS1983

Finite area method for nonlinear supersonic conical flows

A fully conservative numerical method for the computation of steady inviscid supersonic flow about general conical bodies at incidence is described. The procedure utilizes the potential approximation and implements a body conforming mesh generator. The conical potential is assumed to have its best linear variation inside each mesh cell; a secondary interlocking cell system is used to establish the flux balance required to conserve mass. In the supersonic regions the scheme is symmetrized by adding artificial viscosity in conservation form. The algorithm is nearly an order of a magnitude faster than present Euler methods and predicts known results accurately and qualitative features such as nodal point lift off correctly. Results are compared with those of other investigators.

Sritharan, S. S.↗

NASA NTRS1987

A method for nonlinear optimization with discrete design variables

A numerical method is presented for the solution of nonlinear discrete optimization problems. The applicability of discrete optimization to engineering design is discussed, and several standard structural optimization problems are solved using discrete design variables. The method uses approximation techniques to create subproblems suitable for linear mixed-integer programming methods. The method employs existing software for continuous optimization and integer programming.

Olsen, Gregory R.↗

NASA NTRSDate not supplied

Parallelized Quadrupole Simulations of Thermographic Responses of Composites

Thermography has been shown to be a viable technique for inspection of composites. Model inversion of the thermography data requires a fast method for performing the forward problem. Viable numerical methods for the thermal response forward problem are finite element, finite difference and the quadrupole method. Normally both the finite element and finite difference methods solve for the thermal response in the time domain which limits one’s ability to increase the speed of the simulation by parallelization. In contrast, the quadrupole method solves for the Laplace transform of the thermal response. One of the features of the Laplace transform methodology is the solution at any discrete time is independent of the solution at all other times. Therefore, it is easy to separate into a set of independent calculations with each of the times of interest being performed in parallel. Additionally, the numeric inversion of the Laplace transform typically involves numerically solving for the Laplace transform at multiple Laplace frequencies. Each of those solutions are also independent of solutions at other frequencies and can be calculated in parallel. By parallelization of this method, it is possible to perform the simulations of three-dimensional configurations in seconds. When the input stimulus for thermal response is a delta function heat flux (a reasonable approximation for flash heating), the thermal response is smooth. For this case, it is possible to accurately estimate the thermal response at any time within a given time interval from a set of simulations separated by exponentially increasing time steps. From these simulations, it is possible to accurately interpolate to find the response at intermediate times by a spline interpolation of the logarithm of time versus logarithm of temperature. The thermal response with exponential time stepping is shown to produce values for the thermal response which are within 1% of values within the time interval. The simulations are compared to finite element simulations of the same inspection configurations. The simulations are also compared to the thermographic measurements on composites where shape and depth of the delaminations are obtained from other inspection methods.

Thermography↗

NASA NTRSDate not supplied

Parallelized Quadrupole Simulations of Thermographic Responses of Composites

Thermography↗

NASA NTRS1992

Calculation of fully three-dimensional separated flow with an unsteady viscous-inviscid interaction method

Three previous papers have shown that the viscous inviscid numerical methods were capable of calculating separated turbulent flows. The 'Semi-inverse method' and the models of the first author allow the computation of massive separations, stalled flows, and shock wave-boundary layer interactions, in two-dimensional or quasi-three-dimensional conditions, from low speeds to supersonic speeds. The 'Semi-implicit' method for time-consistent coupling allows for the computation of time-accurate transonic separated flow and buffer computations in two-dimensions. The present paper shows that the viscous-inviscid interaction approach is also able to compute the fully three-dimensional flow separation phenomena. The method is based on a thin-layer approximation of the theory of 'Defect-Formulation' that provides the viscous-inviscid splitting of the Navier-Stokes equations. A parametric analytical modelling of the 3D-turbulent velocity profiles is involved. Numerically, the 3D-velocity profiles are discretized in the normal z-direction and driven by parametric integral 3D-equations in direct or inverse modes in the x-direction. The viscous-inviscid coupling is fully 3D and solved the time-consistency problem with an extension of the 'Semi-implicit' method previously suggested in two-dimensions. A 3D inviscid subroutine with TSP approximation is used. Results are obtained for transonic steady flows over wings with shock-induced transonic separation. The method provides results for highly three-dimensional flow separations, such as induced by a three-dimensional through at the wall of a flat plate. The 3D viscous-inviscid coupling and the 3D model of the velocity field provide three-dimensional instantaneous skin-friction lines whose patterns exhibit the same complex topology as Navier-Stokes solvers, with foci, nodes, and saddle-points.

Leballeur, J. C.↗

NASA NTRS2004

Sensitivity of Simulated Warm Rain Formation to Collision and Coalescence Efficiencies, Breakup, and Turbulence: Comparison of Two Bin-Resolved Numerical Models

Numerical models that resolve cloud particles into discrete mass size distributions on an Eulerian grid provide a uniquely powerful means of studying the closely coupled interaction of aerosols, cloud microphysics, and transport that determine cloud properties and evolution. However, such models require many experimentally derived paramaterizations in order to properly represent the complex interactions of droplets within turbulent flow. Many of these parameterizations remain poorly quantified, and the numerical methods of solving the equations for temporal evolution of the mass size distribution can also vary considerably in terms of efficiency and accuracy. In this work, we compare results from two size-resolved microphysics models that employ various widely-used parameterizations and numerical solution methods for several aspects of stochastic collection.

Fridlind, Ann↗

NASA NTRS1974

Analysis of twisting stiffness for a multifiber composite layer

The twisting stiffness of a rectangular cross section consisting of a single row of solid circular cross-section fibers embedded in a matrix is analyzed. The problem is formulated as a Dirichlet torsion problem of a multielement region and solved by the boundary-point least-squares method. Numerical results for a single-fiber square cross section compare favorably with previous relaxation-method results. New numerical results for three and five-fiber composites suggest that the torsional rigidity of a multifiber composite can be approximated from the torsional rigidities of single and three-fiber models.

Bert, C. W.↗

NASA NTRS1989

LU-SGS implicit algorithm for three-dimensional incompressible Navier-Stokes equations with source term

A numerical method is developed for solving the incompressible Navier-Stokes equations using the concept of pseudocompressibility. A lower-upper symmetric-Gauss-Seidel implicit scheme is developed for three-dimensional incompressible viscous flow computations. The present algorithm offers additional advantages when solving the flow equations with source terms. Complete vectorizability of the algorithm on oblique planes of sweep in three-dimensions is accomplished in a new flow solver, INS3D-LU code. Spatial differencing is a second-order accurate semi-discrete finite-volume method augmented by a third-order accurate numerical dissipation model which is based on spectral-radii. Comparison of numerical solutions for a curved duct with experimental data shows good agreement. The method is applied to calculate the inducer flow of the Space Shuttle Main Engine turbopump.

Yoon, Seokkwan↗

NASA NTRS1974

Viscous shock-layer flows for the space shuttle windward plane of symmetry

Predictions are presented for hypersonic, nonequilibrium viscous flows over nonanalytic blunt bodies at reentry conditions. Emphasis is placed on predictions of the viscous flowfield for the windward plane of symmetry of the space shuttle and other axisymmetric bodies which approximate the space shuttle geometry. The equations which govern the viscous shock-layer flow are presented, and the method by which the equations are solved is discussed. The predictions of the present finite-difference method are compared with predictions of other numerical methods as well as with experimental data.

Miner, E. W.↗

NASA NTRS1977

Initial development of a method of significant waveheight estimation for GEOS-III

The numerical method by which ocean surface significant waveheight estimates are produced from the GEOS-3 radar altimeter data is described. Four parameters characterizing the expected radar mean return waveform are determined from the altimeter's sixteen sample-and-hold waveform samplers through use of an iterative, least squares approach. One of the four parameters is a risetime term which has contributions from both the transmitted radar pulse width and the rms ocean surface height; the estimated significant waveheight is extracted from this risetime. The noise character of the estimation process leads to occasional negative significant waveheight estimates, and the origin of these nonphysical negative results is discussed. Possible modifications and areas for additional investigation are indicated.

Hayne, G. S.↗

NASA NTRS1978

A comparative study of Conroy and Monte Carlo methods applied to multiple quadratures and multiple scattering

An efficient numerical method of multiple quadratures, the Conroy method, is applied to the problem of computing multiple scattering contributions in the radiative transfer through realistic planetary atmospheres. A brief error analysis of the method is given and comparisons are drawn with the more familiar Monte Carlo method. Both methods are stochastic problem-solving models of a physical or mathematical process and utilize the sampling scheme for points distributed over a definite region. In the Monte Carlo scheme the sample points are distributed randomly over the integration region. In the Conroy method, the sample points are distributed systematically, such that the point distribution forms a unique, closed, symmetrical pattern which effectively fills the region of the multidimensional integration. The methods are illustrated by two simple examples: one, of multidimensional integration involving two independent variables, and the other, of computing the second order scattering contribution to the sky radiance.

Deepak, A.↗

NASA NTRS1989

An explicit Runge-Kutta method for turbulent reacting flow calculations

The paper presents a numerical method for the solution of the conservation equations governing steady, reacting, turbulent viscous flow in two-dimensional geometries, in both Cartesian and axisymmetric coordinates. These equations are written in Favre-averaged form and closed with a first order model. A two-equation K-epsilon model, where low Reynolds number and compressibility effects are included, and a modified eddy-break up model are used to simulate fluid mechanics turbulence, chemistry and turbulence-combustion interaction. The solution is obtained by using a pseudo-unsteady method with improved perturbation propagation properties. The equations are discretized in space by using a finite volume formulation. An explicit multi-stage dissipative Runge-Kutta algorithm is then used to advance the flow equations in the pseudo-time. The method is applied to the computation of both diffusion and premixed turbulent reacting flows. The computed temperature distributions compare favorably with experimental data.

Boretti, A. A.↗