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At least 181 records · Page 10
All sourcesNASA NTRSDOE OSTI
NASA NTRS1981

New approach to the solution of large, full matrix equations

A new approach to the solution of matrix equations resulting from integral equations is presented and applied to the solution of two-dimensional Neumann problems describing the inviscid, incompressible flow past an airfoil. The problem is reformulated in terms of a preselected set of mode functions giving an equivalent matrix equation to be solved for the mode-function expansion coefficients. Because of the inherent smoothness of the original problem, the coefficient problem can be solved approximately without significantly affecting the accuracy of the final solution. Very promising two-dimensional results are obtained and the extension of the method to three-dimensional problems is investigated. On the basis of these results it is shown that the computing time for the matrix solution for a large three-dimensional panel method calculation could be reduced by an order of magnitude compared with that required for a direct solution.

Clark, R. W.↗
NASA NTRS1981

Finite-analytic numerical solution of heat transfer in two-dimensional cavity flow

Heat transfer in cavity flow is numerically analyzed by a new numerical method called the finite-analytic method. The basic idea of the finite-analytic method is the incorporation of local analytic solutions in the numerical solutions of linear or nonlinear partial differential equations. In the present investigation, the local analytic solutions for temperature, stream function, and vorticity distributions are derived. When the local analytic solution is evaluated at a given nodal point, it gives an algebraic relationship between a nodal value in a subregion and its neighboring nodal points. A system of algebraic equations is solved to provide the numerical solution of the problem. The finite-analytic method is used to solve heat transfer in the cavity flow at high Reynolds number (1000) for Prandtl numbers of 0.1, 1, and 10.

Chen, C.-J.↗
NASA NTRS1982

Boundary-layer effects in composite laminates. I - Free-edge stress singularities. II - Free-edge stress solutions and basic characteristics

The fundamental nature of the boundary-layer effect in fiber-reinforced composite laminates is formulated in terms of the theory of anisotropic elasticity. The basic structure of the boundary-layer field solution is obtained by using Lekhnitskii's stress potentials (1963). The boundary-layer stress field is found to be singular at composite laminate edges, and the exact order or strength of the boundary layer stress singularity is determined using an eigenfunction expansion method. A complete solution to the boundary-layer problem is then derived, and the convergence and accuracy of the solution are analyzed, comparing results with existing approximate numerical solutions. The solution method is demonstrated for a symmetric graphite-epoxy composite.

Wang, S. S.↗
NASA NTRS1982

Investigation of compositional segregation during unidirectional solidification of solid solution semiconducting alloys

Compositional segregation of solid solution semiconducting alloys in the radial direction during unidirectional solidification was investigated by calculating the effect of a curved solid liquid interface on solute concentration at the interface on the solid. The formulation is similar to that given by Coriell, Boisvert, Rehm, and Sekerka except that a more realistic cylindrical coordinate system which is moving with the interface is used. Analytical results were obtained for very small and very large values of beta with beta = VR/D, where V is the velocity of solidification, R the radius of the specimen, and D the diffusivity of solute in the liquid. For both very small and very large beta, the solute concentration at the interface in the solid C(si) approaches C(o) (original solute concentration) i.e., the deviation is minimal. The maximum deviation of C(si) from C(o) occurs for some intermediate value of beta.

Wang, J. C.↗
NASA NTRS1983

A class of nonideal solutions. 2: Application to experimental data

Functions for the representation of the thermodynamic properties of nonideal solutions were applied to the experimental data for several highly nonideal solutions. The test solutions were selected to cover both electrolyte behavior. The results imply that the functions are fully capable of representing the experimental data within their accuracy over the whole composition range and demonstrate that many nonideal solutions can be regarded as members of the defined class of nonideal solutions.

Zeleznik, F. J.↗
NASA NTRS1983

A class of nonideal solutions. 1: Definition and properties

A class of nonideal solutions is defined by constructing a function to represent the composition dependence of thermodynamic properties for members of the class, and some properties of these solutions are studied. The constructed function has several useful features: (1) its parameters occur linearly; (2) it contains a logarithmic singularity in the dilute solution region and contains ideal solutions and regular solutions as special cases; and (3) it is applicable to N-ary systems and reduces to M-ary systems (M or = N) in a form-invariant manner.

Zeleznik, F. J.↗
NASA NTRS1983

An investigation of the accuracy of finite difference methods in the solution of linear elasticity problems

The accuracy of the finite difference method in the solution of linear elasticity problems that involve either a stress discontinuity or a stress singularity is considered. Solutions to three elasticity problems are discussed in detail: a semi-infinite plane subjected to a uniform load over a portion of its boundary; a bimetallic plate under uniform tensile stress; and a long, midplane symmetric, fiber reinforced laminate subjected to uniform axial strain. Finite difference solutions to the three problems are compared with finite element solutions to corresponding problems. For the first problem a comparison with the exact solution is also made. The finite difference formulations for the three problems are based on second order finite difference formulas that provide for variable spacings in two perpendicular directions. Forward and backward difference formulas are used near boundaries where their use eliminates the need for fictitious grid points.

Bauld, N. R., Jr.↗
NASA NTRS1983

A study of non-unique solutions of the two-dimensional boundary layer equations at laminar separation and reattachment points

Nonunique laminar boundary layer equation solutions in direct problem calculations are identified for the case of accelerating flow. As a separation or reattachment point is approached, the multiple solutions approach each other and become identical. The computer code used to generate these results was developed for the solution of compressible, laminar or turbulent boundary layer, and free wake problems, in either direct or inverse mode. Similarity solutions in either a primitive variable or a stream function form are possible, and the resulting equations are solved by means of a modified Keller's Box scheme in which the energy equation and turbulence modeling equations are solved simultaneously with the continuity and momentum equations. Examples illustrating the nature of the solutions at the separation and reattachment points are presented.

Drela, M.↗
NASA NTRS1983

Elasticity solutions for a class of composite laminate problems with stress singularities

A study on the fundamental mechanics of fiber-reinforced composite laminates with stress singularities is presented. Based on the theory of anisotropic elasticity and Lekhnitskii's complex-variable stress potentials, a system of coupled governing partial differential equations are established. An eigenfunction expansion method is introduced to determine the orders of stress singularities in composite laminates with various geometric configurations and material systems. Complete elasticity solutions are obtained for this class of singular composite laminate mechanics problems. Homogeneous solutions in eigenfunction series and particular solutions in polynomials are presented for several cases of interest. Three examples are given to illustrate the method of approach and the basic nature of the singular laminate elasticity solutions. The first problem is the well-known laminate free-edge stress problem, which has a rather weak stress singularity. The second problem is the important composite delamination problem, which has a strong crack-tip stress singularity. The third problem is the commonly encountered bonded composite joints, which has a complex solution structure with moderate orders of stress singularities.

Wang, S. S.↗
NASA NTRS1985

On the Solution of the Three-Dimensional Flowfield About a Flow-Through Nacelle

The solution of the three dimensional flow field for a flow through nacelle was studied. Both inviscid and viscous inviscid interacting solutions were examined. Inviscid solutions were obtained with two different computational procedures for solving the three dimensional Euler equations. The first procedure employs an alternating direction implicit numerical algorithm, and required the development of a complete computational model for the nacelle problem. The second computational technique employs a fourth order Runge-Kutta numerical algorithm which was modified to fit the nacelle problem. Viscous effects on the flow field were evaluated with a viscous inviscid interacting computational model. This model was constructed by coupling the explicit Euler solution procedure with a flag entrainment boundary layer solution procedure in a global iteration scheme. The computational techniques were used to compute the flow field for a long duct turbofan engine nacelle at free stream Mach numbers of 0.80 and 0.94 and angles of attack of 0 and 4 deg.

Compton, William Bernard↗
NASA NTRS1985

Solution Growth of Crystals in Zero-Gravity

In a low-g environment, buoyancy driven convection effects in solution crystal growth are greatly reduced and, thus, one can study diffusion mass transport which in 1-g is masked by convective phenomena. Crystals of triglycine sulfate (TGS) will be grown aboard the Spacelab 3 mission, using a specially developed Fluids Experiments System (FES). The objectives of the experiment are: (1) to develop a technique for solution crystal growth in a low-g environment, (2) to characterize the growth environment provided by an orbiting spacecraft and to determine the influence of the environment on the growth behavior, and (3) to determine how gravity in a low-gravity environment influences the properties of a resulting TGS crystal. Single crystals of TGS have been grown using conventional low-temperature solution crystal growth method and the growth process has been extensively characterized. Various physical properties of TGS solution have been measured. Also, a unique technique of growing solution growth crystals by extracting heat at a programmed rate from the crystal through a semi-insulating sting has been developed and tested in 1-g environment.

Lal, R. B.↗
NASA NTRS1986

Steady supersonic Navier-Stokes solutions of a 75 deg delta wing

Steady solutions about a slender sharp edged delta wing in a supersonic freestream for moderate and high angles of attack are obtained numerically by time integration of the unsteady compressible three dimensional laminar Navier-Stokes equations. The main features of the flow, including primary and secondary separation, and vortex position and strength, are adequately simulated in the numerical solutions. Improved resolution of the computational grid in the leading edge region from a previous solution had considerable effect on the accuracy of the solutions. Good agreement between numerical solutions and experimental data was obtained for two cases. A local timestepping procedure is used to speed convergence by approximately a factor of two.

Buter, T. A.↗
NASA NTRS1986

Hierarchial implicit dynamic least-square solution algorithm

This paper develops an implicit type transient solution strategy which possesses hierarchial levels of application. In particular, due to the manner of formulation, stiffness updating, assembly inversion, solution constraint, as well as iteration are all performed at a localized level. The level of iterative calculations depends on the type of hierarchial partitioning employed, namely degree of freedom, nodal, elemental, material/nonlinear group, substructural, and so on. Since the iterative solution process and application of constraints are applied at a local level, the resulting so-called hierarchial implicit solution algorithm possesses very stable and efficient numerical properties and is highly storage efficient. To demonstrate the scheme, the results of several benchmark examples are presented. These enable comparisons with the Newton-Raphson solved implicit transient solution method. Overall the comparisons illustrate the superior stability and efficiency of the hierarchial scheme.

Padovan, J.↗
NASA NTRS1985

Numerical solution of the unsteady Navier-Stokes equation

The construction and the analysis of nonoscillatory shock capturing methods for the approximation of hyperbolic conservation laws are discussed. These schemes share many desirable properties with total variation diminishing schemes, but TVD schemes have at most first-order accuracy, in the sense of truncation error, at extrema of the solution. In this paper a uniformly second-order approximation is constructed, which is nonoscillatory in the sense that the number of extrema of the discrete solution is not increasing in time. This is achieved via a nonoscillatory piecewise linear reconstruction of the solution from its cell averages, time evolution through an approximate solution of the resulting initial value problem, and averaging of this approximate solution over each cell.

Osher, Stanley J.↗
NASA NTRS1987

A method for overcoming the velocity space filamentation problem in collisionless plasma model solutions

The solution of filtered Vlasov-Maxwell equations, rather than the Vlasov-Maxwell equations themselves, is shown to ameliorate the velocity space filamentation problem in collisionless plasma models. Exact field solutions and filtered velocity distribution functions are obtained without introducing errors. Proper selection of the filter width is demonstrated to inhibit development of velocity space filamentation and, it is conjectured, position space filamentation. The results of sample calculations of both filtered and nonfiltered field solutions illustrate a high degree of agreement between both solutions, with significant savings in computational time and memory requirements with the filtered solutions.

Klimas, Alexander J.↗
NASA NTRS1988

Solutal convection during directional solidification

During directional solidification of a binary alloy at constant velocity, buoyancy-driven fluid flow may occur due to the solute gradients generated by the solidification process. Numerical calculations of the solute and fluid flow fields in the melt have been carried out using finite differences in a two-dimensional, time-dependent model that assumes a planar crystal-melt interface and allows time-dependent gravitational accelerations. The container walls are rigid and perfectly insulating for solute. For constant vertical gravitational accelerations, as the solutal Rayleigh number is varied, multiple steady states and time-dependent states may occur. The bifurcation from the quiescent state may be subcritical or transcritical, depending on the aspect ratio of the container. Calculations have also been performed for a gravitational acceleration that is assumed to be uniform in magnitude with its direction rotating uniformly. Numerical results have been obtained for a Schmidt number of 10 and a gravitational acceleration of 0.0001 G. The maximum variation in the solute concentration at the crystal-melt interface is calculated for various values of the rotation rate of the gravitational acceleration.

Mcfadden, G. B.↗
NASA NTRS1989

Apparatus Makes Precisely Saturated Solutions

Simple laboratory apparatus establishes equilibrium conditions of temperature and concentration in solutions for use in precise measurements of saturation conditions. With equipment typical measurement of saturation concentration of protein in solution established and measured within about 24 hours. Precisely saturated solution made by passing solvent or solution slowly along column packed with solute at precisely controlled temperature. If necessary, flow stopped for experimentally determined interval to allow equilibrium to be established in column.

Pusey, Marc L.↗
NASA NTRS1988

Comparison of shock structure solutions using independent continuum and kinetic theory approaches

A vehicle traversing the atmosphere will experience flight regimes at high altitudes in which the thickness of a hypersonic shock wave is not small compared to the shock standoff distance from the hard body. When this occurs, it is essential to compute accurate flow field solutions within the shock structure. In this paper, one-dimensional shock structure is investigated for various monatomic gases from Mach 1.4 to Mach 35. Kinetic theory solutions are computed using the Direct Simulation Monte Carlo method. Steady-state solutions of the Navier-Stokes equations and of a slightly truncated form of the Burnett equations are determined by relaxation to a steady state of the time-dependent continuum equations. Monte Carlo results are in excellent agreement with published experimental data and are used as bases of comparison for continuum solutions. For a Maxwellian gas, the truncated Burnett equations are shown to produce far more accurate solutions of shock structure than the Navier-Stokes equations.

Fiscko, Kurt A.↗