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At least 829 records · Page 46

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NASA NTRS1981

Radiative transfer theory for passive microwave remote sensing of random media

The radiative transfer theory is applied to a random medium for the case of passive remote sensing. A general numerical solution with Gaussian quadrature method is studied. For a medium with laminar structure or a medium with cylindrical structure, closed form solutions are obtained by solving the radiative transfer equations of a two-layer random medium. Numerical results for the general case and the two limiting cases are compared.

Chuang, S. L.↗

NASA NTRS1984

Direct numerical simulation of reacting flows

The objectives of this work are: (1) to extend the technique of direct numerical simulations to turbulent, chemically reacting flows, (2) to test the validity of the method by comparing computational results with laboratory data, and (3) to use the simulations to gain a better understanding of the effects of turbulence on chemical reactions. The effects of both the large scale structure and the smaller scale turbulence on the overall reaction rates are addressed. The relationship between infinite reaction rate and finite reaction rate chemistry is compared with some of the results of calculations with existing theories and laboratory data. The direct numerical simulation method involves the numerical solution of the detailed evolution of the complex turbulent velocity and concentration fields. Using very efficient numerical methods (e.g., pseudospectral methods), the fully nonlinear (possibly low pass filtered) equations of motion are solved and no closure assumptions or turbulence models are used. Statistical data are obtained by performing spatial, temporal, and/or ensemble averages over the computed flow fields.

Riley, J. J.↗

NASA NTRS1986

A two-dimensional numerical study of the flow inside the combustion chambers of a motored rotary engine

A numerical study was performed to investigate the unsteady, multidimensional flow inside the combustion chambers of an idealized, two-dimensional, rotary engine under motored conditions. The numerical study was based on the time-dependent, two-dimensional, density-weighted, ensemble-averaged conservation equations of mass, species, momentum, and total energy valid for two-component ideal gas mixtures. The ensemble-averaged conservation equations were closed by a K-epsilon model of turbulence. This K-epsilon model of turbulence was modified to account for some of the effects of compressibility, streamline curvature, low-Reynolds number, and preferential stress dissipation. Numerical solutions to the conservation equations were obtained by the highly efficient implicit-factored method of Beam and Warming. The grid system needed to obtain solutions were generated by an algebraic grid generation technique based on transfinite interpolation. Results of the numerical study are presented in graphical form illustrating the flow patterns during intake, compression, gaseous fuel injection, expansion, and exhaust.

Shih, T. I. P.↗

NASA NTRS1986

A two-dimensional numerical study of the flow inside the combustion chamber of a motored rotary engine

Shih, T. I-P.↗

NASA NTRS1988

Accurate boundary conditions for exterior problems in gas dynamics

The numerical solution of exterior problems is typically accomplished by introducing an artificial, far field boundary and solving the equations on a truncated domain. For hyperbolic systems, boundary conditions at this boundary are often derived by imposing a principle of no reflection. However, waves with spherical symmetry in gas dynamics satisfy equations where incoming and outgoing Riemann variables are coupled. This suggests that natural reflections may be important. A reflecting boundary condition is proposed based on an asymptotic solution of the far field equations. Nonlinear energy estimates are obtained for the truncated problem and numerical experiments presented to validate the theory.

Hagstrom, Thomas↗

NASA NTRS1992

Pressure wave propagation studies for oscillating cascades

The unsteady flow field around an oscillating cascade of flat plates is studied using a time marching Euler code. Exact solutions based on linear theory serve as model problems to study pressure wave propagation in the numerical solution. The importance of using proper unsteady boundary conditions, grid resolution, and time step is demonstrated. Results show that an approximate non-reflecting boundary condition based on linear theory does a good job of minimizing reflections from the inflow and outflow boundaries and allows the placement of the boundaries to be closer than cases using reflective boundary conditions. Stretching the boundary to dampen the unsteady waves is another way to minimize reflections. Grid clustering near the plates does a better job of capturing the unsteady flow field than cases using uniform grids as long as the CFL number is less than one for a sufficient portion of the grid. Results for various stagger angles and oscillation frequencies show good agreement with linear theory as long as the grid is properly resolved.

Huff, Dennis L.↗

NASA NTRS1992

Physics of heat pipe rewetting

Although several studies have been made to determine the rewetting characteristics of liquid films on heated rods, tubes, and flat plates, no solutions are yet available to describe the rewetting process of a hot plate subjected to a uniform heating. A model is presented to analyze the rewetting process of such plates with and without grooves. Approximate analytical solutions are presented for the prediction of the rewetting velocity and the transient temperature profiles of the plates. It is shown that the present rewetting velocity solution reduces correctly to the existing solution for the rewetting of an initially hot isothermal plate without heating from beneath the plate. Numerical solutions have also been obtained to validate the analytical solutions.

Chan, S. H.↗

NASA NTRS1991

Analysis of metal-matrix composite structures. I - Micromechanics constitutive theory. II - Laminate analyses

The micromechanical constitutive theory is used to examine the nonlinear behavior of continuous-fiber-reinforced metal-matrix composite structures. Effective lamina constitutive relations based on the Abouli micromechanics theory are presented. The inelastic matrix behavior is modeled by the unified viscoplasticity theory of Bodner and Partom. The laminate constitutive relations are incorporated into a first-order deformation plate theory. The resulting boundary value problem is solved by utilizing the finite element method. Attention is also given to computational aspects of the numerical solution, including the temporal integration of the inelastic strains and the spatial integration of bending moments. Numerical results the nonlinear response of metal matrix composites subjected to extensional and bending loads are presented.

Arenburg, R. T.↗

NASA NTRS1992

Pressure wave propagation studies for oscillating cascades

The unsteady flowfield around an oscillating cascade of flat plates is studied using a time marching Euler code. Exact solutions based on linear theory serve as model problems to study pressure wave propagation in the numerical solution. The importance of using proper unsteady boundary conditions, grid resolution, and time step is demonstrated. Results show that an approximate non-reflecting boundary condition based on linear theory does a good job of minimizing reflections from the inflow and outflow boundaries and allows the placement of the boundaries to be closer than cases using reflective boundary conditions. Stretching the boundary to dampen the unsteady waves is another way to minimize reflections. Grid clustering near the plates does a better job of capturing the unsteady flowfield than cases using uniform grids as long as the CFL number is less than one for a sufficient portion of the grid. Results for various stagger angles and oscillation frequencies show good agreement with linear theory as long as the grid is properly resolved.

Huff, Dennis L.↗

NASA NTRS1992

Calculation of stress intensity factors in an isotropic multicracked plate. Part 1: Theoretical development

An essential part of describing the damage state and predicting the damage growth in a multicracked plate is the accurate calculation of stress intensity factors (SIF's). Here, a methodology and rigorous solution formulation for SIF's of a multicracked plate, with fully interacting cracks, subjected to a far-field arbitrary stress state is presented. The fundamental perturbation problem is derived, and the steps needed to formulate the system of singular integral equations whose solution gives rise to the evaluation of the SIF's are identified. This analytical derivation and numerical solution are obtained by using intelligent application of symbolic computations and automatic FORTRAN generation capabilities (described in the second part of this paper). As a result, a symbolic/FORTRAN package, named SYMFRAC, that is capable of providing accurate SIF's at each crack tip was developed and validated.

Binienda, W. K.↗

NASA NTRS1992

Parabolized Navier-Stokes methods for hypersonic flows

The development and numerical solution of the Parabolized Navier-Stokes (PNS) equations is discussed. Special emphasis is placed on numerical integration algorithms for PNS solvers, most notably recent applications of upwind schemes. Application of this technology to high speed, high Reynolds number flows was the focus, and modeling techniques for real gas effects and turbulence were discussed. Experiences in validating the UPS upwind PNS flow solver for relatively simple body shapes are presented. The test cases range in complexity from two dimensional perfect gas cases to three dimensional finite rate chemistry cases.

Lawrence, S. L.↗

NASA NTRS1993

Equilibrium models of mass distribution and collisional lifetimes of asteroids

An understanding of the steady state distribution expected in the present day asteroid belt is important to our understanding of the collisional evolution of the asteroids and their physical properties. We have extended earlier work to show that, in the absence of gravity, a simple power law distribution as a function of mass with constant exponent will give an equilibrium distribution of asteroids for all bodies much smaller than the largest asteroids. This result holds for realistic fragmentation mechanisms and is independent of the physical properties of the asteroids. Inclusion of the effects of gravity on disruption and fragmentation of asteroids precludes an analytic solution to this problem, and rules out a simple power law distribution. We are currently calculating numerical solutions in order to determine the expected steady state mass distribution in the asteroid belt.

Williams, David R.↗

NASA NTRS1980

A solution of one dimensional Fredholm integral equations of the second kind

Fredholm integral equations of the second kind of the one dimension are numerically solved. It is proven that the numerical solution converges to the exact solution of the integral equation. This is shown for periodic kernels and then extended to nonperiodic kernels. This development helps delineate a basic theory which has the potential of solving very complex problems.

Gabrielsen, R. E.↗

NASA NTRS1982

Numerical methods and computers used in elastohydrodynamic lubrication

Some of the methods of obtaining approximate numerical solutions to boundary value problems that arise in elastohydrodynamic lubrication are reviewed. The highlights of four general approaches (direct, inverse, quasi-inverse, and Newton-Raphson) are sketched. Advantages and disadvantages of these approaches are presented along with a flow chart showing some of the details of each. The basic question of numerical stability of the elastohydrodynamic lubrication solutions, especially in the pressure spike region, is considered. Computers used to solve this important class of lubrication problems are briefly described, with emphasis on supercomputers.

Hamrock, B. J.↗

NASA NTRS1986

Efficient inverse solution of Kepler's equation

A bicubic polynomial approximation to Kepler's equation for elliptic orbits is shown to provide accurate starting values for efficient numerical solution of this equation for eccentric anomaly. In the approximate equation, a cubic in mean anomaly is set equal to a cubic in eccentric anomaly. The coefficients in the two cubics are obtained as functions of eccentricity by specifying values of function and slope at the midpoint and the endpoint of the complete interval (0 to pi). The initial estimate of eccentric anomaly to use in an iteration formula is obtained by evaluating the cubic in mean anomaly and finding the single real root of the cubic in eccentric anomaly. Numerical results are presented which indicate that the estimate accuracy of this method is roughly an order of magnitude better than that of other recently-reported formulas.

Boltz, Frederick W.↗

DOE OSTI2020

Columnar-to-equiaxed transition in a laser scan for metal additive manufacturing

In laser powder bed fusion additive manufacturing (LPBFAM), different solidification conditions, e.g., thermal gradient and cooling rate, can be achieved by controlling the process parameters, such as laser power and laser speed. Tailoring the behaviour of the columnar to equiaxed transition (CET) of the printed alloy during fabrication can facilitate the production of highly customized microstructures. In this study, effective analytical solutions for both thermal conduction and solidification are employed to model solidifying melt pools. Microstructure textures and solidification conditions are evaluated for numerous combinations of laser power and laser speed under bead-on-plate conditions. This analytical-based high-throughput tool was demonstrated to select specific process parameters that lead to desired microstructures. Two selected process conditions were examined in detail by a highly parallelized microstructural solidification model to reveal both nucleation and grain growth. Both numerical solutions agree well with experiments that are performed based on bead-on-plate conditions, indicating that these numerical models aid evaluation of the nucleation parameters, providing insights for controlling CET during the LPBFAM processing.

Lang, Yuan↗

NASA NTRS1991

Krylov Subspace Methods for Complex Non-Hermitian Linear Systems

We consider Krylov subspace methods for the solution of large sparse linear systems Ax = b with complex non-Hermitian coefficient matrices. Such linear systems arise in important applications, such as inverse scattering, numerical solution of time-dependent Schrodinger equations, underwater acoustics, eddy current computations, numerical computations in quantum chromodynamics, and numerical conformal mapping. Typically, the resulting coefficient matrices A exhibit special structures, such as complex symmetry, or they are shifted Hermitian matrices. In this paper, we first describe a Krylov subspace approach with iterates defined by a quasi-minimal residual property, the QMR method, for solving general complex non-Hermitian linear systems. Then, we study special Krylov subspace methods designed for the two families of complex symmetric respectively shifted Hermitian linear systems. We also include some results concerning the obvious approach to general complex linear systems by solving equivalent real linear systems for the real and imaginary parts of x. Finally, numerical experiments for linear systems arising from the complex Helmholtz equation are reported.

Freund, Roland W.↗

NASA NTRS1988

Navier-Stokes solutions of flowfield characteristics produced by ice accretion

The flowfield and resultant heat transfer rates over a series of ice accretion shapes have been obtained through numerical solutions of the Navier-Stokes equations. The influence of roughness is modeled by including blockage, form drag and stagnation heating effects as source terms in the governing equations. Using the flowfield information obtained from the Navier-Stokes equations the droplet impingement efficiencies are computed using a PNS-type solving scheme. Good agreement is achieved between the numerical results and experimental data.

Scott, J. N.↗