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At least 415 records · Page 23

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NASA NTRS1972

Locally nonsimilar solutions for radiating shock layer about smooth axisymmetric bodies

Locally nonsimilar solutions for nongray radiating shock layers about smooth axisymmetric bodies have been obtained based on a newly developed approximate method. Good agreement is found with numerical solutions for inviscid cases (both radiating and nonradiating) and with series solutions for the radiating viscous case. For the inviscid case, the effect of radiative cooling is to destroy the entropy layer; at a distance far from the stagnation point, the shock layer is nearly isothermal. For the viscous case, the radiative wall flux approaches that of the inviscid case at a distance far downstream of the stagnation point. The method can also treat surface mass injection.

Chou, Y. S.↗

NASA NTRS1971

Transpiration and film cooling boundary layer computer program. Volume 1: Numerical solutions of the turbulent boundary layer equations with equilibrium chemistry

A finite difference turbulent boundary layer computer program has been developed. The program is primarily oriented towards the calculation of boundary layer performance losses in rocket engines; however, the solution is general, and has much broader applicability. The effects of transpiration and film cooling as well as the effect of equilibrium chemical reactions (currently restricted to the H2-O2 system) can be calculated. The turbulent transport terms are evaluated using the phenomenological mixing length - eddy viscosity concept. The equations of motion are solved using the Crank-Nicolson implicit finite difference technique. The analysis and computer program have been checked out by solving a series of both laminar and turbulent test cases and comparing the results to data or other solutions. These comparisons have shown that the program is capable of producing very satisfactory results for a wide range of flows. Further refinements to the analysis and program, especially as applied to film cooling solutions, would be aided by the acquisition of a firm data base.

Levine, J. N.↗

NASA NTRS1972

Solar flare particle propagation: Comparision of a new analytic solution with spacecraft measurements

An analytic solution was obtained to the complete Fokker-Planck equation for solar flare particle propagation including the effects of convection, energy-change, corotation, and diffusion. It is assumed that the particles are injected impulsively at a single point in space, and that a boundary exists beyond which the particles are free to escape. Several solar flare particle events were observed with solar and galactic cosmic ray experiment aboard OGO 6. Detailed comparisons of the predictions of the solution with observations of 1 to 70 MeV protons show that the model adequately describes both the rise and decay times. The solution also yields a time evolution for the vector anisotropy which agrees well with reported observations.

Lupton, J. E.↗

NASA NTRS1972

A transient solution for domain wall motion

An analytic solution of transient wall motion in a bulk ferromagnetic material is obtained from the dynamic torque equations with a Gilbert damping term. The steady state solution reduces to previously obtained, well known solutions.

Bourne, H. C., Jr.↗

NASA NTRS1972

Numerical solutions of the Navier-Stokes equations for the supersonic laminar flow over a two-dimensional compression corner

Numerical solutions have been obtained for the supersonic, laminar flow over a two-dimensional compression corner. These solutions were obtained as steady-state solutions to the unsteady Navier-Stokes equations using the finite difference method of Brailovskaya, which has second-order accuracy in the spatial coordinates. Good agreement was obtained between the computed results and wall pressure distributions measured experimentally for Mach numbers of 4 and 6.06, and respective Reynolds numbers, based on free-stream conditions and the distance from the leading edge to the corner. In those calculations, as well as in others, sufficient resolution was obtained to show the streamline pattern in the separation bubble. Upstream boundary conditions to the compression corner flow were provided by numerically solving the unsteady Navier-Stokes equations for the flat plate flow field, beginning at the leading edge. The compression corner flow field was enclosed by a computational boundary with the unknown boundary conditions supplied by extrapolation from internally computed points.

Carter, J. E.↗

NASA NTRS1972

Numerical method for the solution of large systems of differential equations of the boundary layer type

A numerical method for the solution of large systems of nonlinear differential equations of the boundary-layer type is described. The method is a modification of the technique for satisfying asymptotic boundary conditions. The present method employs inverse interpolation instead of the Newton method to adjust the initial conditions of the related initial-value problem. This eliminates the so-called perturbation equations. The elimination of the perturbation equations not only reduces the user's preliminary work in the application of the method, but also reduces the number of time-consuming initial-value problems to be numerically solved at each iteration. For further ease of application, the solution of the overdetermined system for the unknown initial conditions is obtained automatically by applying Golub's linear least-squares algorithm. The relative ease of application of the proposed numerical method increases directly as the order of the differential-equation system increases. Hence, the method is especially attractive for the solution of large-order systems. After the method is described, it is applied to a fifth-order problem from boundary-layer theory.

Green, M. J.↗

NASA NTRS1971

Specular reflectance of aqueous solutions.

Description of two laboratory instruments for measuring the specular reflectance of aqueous solutions. The instruments are an organic-dye-laser spectrophotometer for the 360- to 650-nm wavelength region and a reflectometer accessory for a Perkin-Elmer E-system spectrophotometer which will operate in the 0.2- to 20-micron wavelength region. The reflectometer accessory has been used to measure the relative infrared specular reflectance in limited spectral regions for aqueous solutions of NaCl, K2SO4, ZnSO4, (NH4)2SO4, and NH4H2PO4 with radiant flux incident at about 70 deg and polarized perpendicular to the plane of incidence. The laser spectrometer has been used to measure the absolute reflectance of aqueous solutions of NaCl in the wavelength region from 575 to 610 nm for light incident at angles of about 60, 65, and 70 deg and polarized parallel to the plane of incidence.

Querry, M. R.↗

NASA NTRS1972

Variational solutions by the use of stepwise constant functions. I - Linear case.

Demonstration that accurate solutions to the integral equation or to the extremal function can be easily obtained by the variational method in many cases when a stepwise constant function is used for the trial function. The evaluation procedure is simple and straightforward; integrals of the kernel function can be evaluated analytically; the method provides, when the solution involves singularities, the best mean value across the singularity; the results are accurate in both the detailed physical quantities and their averages; the resultant solution can be further integrated analytically over the parameters associated with the problem; and the method can be readily applied to nonlinear integral equations.

Yoshikawa, K. K.↗

NASA NTRS1972

The entropy rate admissibility criterion for solution of hyperbolic conservation laws

The entropy rate admissibility criterion for solutions of hyperbolic conservation laws is numerically analyzed. The following admissibility criterion for solutions of hyperbolic conservation laws is proposed: a weak solution is admissible if the total entropy decays with the highest possible rate. The equivalence of this criterion and viscosity criterion is established for the single equation and the system of equations of one dimensional nonlinear elasticity.

Dafermos, C. M.↗

NASA NTRS1972

The accuracy of geopotential solutions from resonant satellite data

Tracking data from a significant number of strongly resonant satellites have not yet been incorporated into recent comprehensive geopotential solutions. This data furnishes excellent comparative and absolute tests of these solutions for resonant coefficients of order (m) 2, 3, 4, 9 and 14. Tracking arcs of from 1 month to 6 years are examined on seven satellites of 1 rev/day, three of 2 revs/day, and one each of 9 and 14 revs/day. Current values for these fully normalized resonant coefficients as judged by this independent and sensitive data, range in accuracy from 2 x 10 to the minus 8th power to 5 x 10 to the minus 8th power. This represents an increase in accuracy by a factor from 3 to 5 over solutions current in the mid 1960's.

Wagner, C. A.↗

NASA NTRS1973

A two-dimensional, iterative solution for the jet flap

A solution is presented for the jet-flapped wing in two dimensions. The main flow is assumed to be inviscid and incompressible. The flow inside the jet is considered irrotational and the upper and lower boundaries between the jet and free stream are assumed to behave as vortex sheets which allow no mixing. The solution is found to be in satisfactory agreement with two dimensional experimental results and other theoretical work for intermediate values of momentum coefficient, but the regions of agreement vary with jet exit angle. At small values of momentum coefficient, the trajectory for the jet, as computed by this method, has more penetration than that of other available data, while at high values of moment coefficient this solution results in less penetration of the jet into the main flow.

Herold, A. C.↗

NASA NTRS1972

Finite element solution for energy conservation using a highly stable explicit integration algorithm

Theoretical derivation of a finite element solution algorithm for the transient energy conservation equation in multidimensional, stationary multi-media continua with irregular solution domain closure is considered. The complete finite element matrix forms for arbitrarily irregular discretizations are established, using natural coordinate function representations. The algorithm is embodied into a user-oriented computer program (COMOC) which obtains transient temperature distributions at the node points of the finite element discretization using a highly stable explicit integration procedure with automatic error control features. The finite element algorithm is shown to posses convergence with discretization for a transient sample problem. The condensed form for the specific heat element matrix is shown to be preferable to the consistent form. Computed results for diverse problems illustrate the versatility of COMOC, and easily prepared output subroutines are shown to allow quick engineering assessment of solution behavior.

Baker, A. J.↗

NASA NTRS1973

Interior radiances in optically deep absorbing media. 1: Exact solutions for one-dimensional model

The exact solutions are obtained for a one dimensional model of a scattering and absorbing medium. The results are given for both the reflected and transmitted radiance for any arbitrary surface albedo as well as for the interior radiance. These same quantities are calculated by the matrix operator method. The relative error of the solutions is obtained by comparison with the exact solutions as well as by an error analysis of the equations. The importance of an accurate starting value for the reflection and transmission operators is shown. A fourth order Runge-Kutta method can be used to solve the differential equations satisfied by these operators in order to obtain such accurate starting values.

Kattawar, G. W.↗

NASA NTRS1973

A solution of the geodetic boundary value problem to order e3

A solution is obtained for the geodetic boundary value problem which defines height anomalies to + or - 5 cm, if the earth were rigid. The solution takes into account the existence of the earth's topography, together with its ellipsoidal shape and atmosphere. A relation is also established between the commonly used solution of Stokes and a development correct to order e cubed. The data requirements call for a complete definition of gravity anomalies at the surface of the earth and a knowledge of elevation characteristics at all points exterior to the geoid. In addition, spherical harmonic representations must be based on geocentric rather than geodetic latitudes.

Mather, R. S.↗

NASA NTRS1973

Coincidence degree and periodic solutions of neutral equations

The problem of existence of periodic solutions for some nonautonomous neutral functional differential equations is examined. It is an application of a basic theorem on the Fredholm alternative for periodic solutions of some linear neutral equations and of a generalized Leray-Schauder theory. Although proofs are simple, the results are nontrivial extensions to the neutral case of existence theorems for periodic solutions of functional differential equations.

Hale, J. K.↗

NASA NTRS1972

Solution of non-isoenergetic supersonic flows by method of characteristics, volume 3

The calculation of supersonic flow fields by the method of characteristics. The theoretical approach to the solution of these flow fields and a computer program to implement the numerical solution of the flow equations are discussed. This versatile program has a flexible set of boundary conditions enabling the calculation of nozzles, plumes and many other complex flow fields. A complete derivation of the equations of motion for reacting gas systems is presented. An important consequence of this derivation is that, for the reaction assumptions which were made, the thermochemistry was shown to be uncoupled from the flow solution and as such could be solved separately. The methods of characteristics equations are shown to be formally the same for ideal, frozen, and equilibrium reacting gas mixtures.

Prozan, R. J.↗

NASA NTRS1973

Research on the sonic boom problem. Part 1: Second-order solutions for the flow field around slender bodies in supersonic flow for sonic boom analysis

A second-order theory for supersonic flow past slender bodies is presented. Through the introduction of characteristic coordinates as independent variables and the expansion procedure proposed by Lin and Oswatitsch, a uniformly valid solution is obtained for the whole flow field in the axisymmetric case and for far field in the general three-dimensional case. For distances far from the body the theory is an extension of Whitham's first-order solution and for the domain close to the body it is a modification of Van Dyke's second-order solution in the axisymmetric case. From the theory useful formulas relating flow deflections to the Whitham F-function are derived, which permits one to determine the sonic boom strength from wind tunnel measurements fairly close to the body.

Landahl, M.↗

NASA NTRS1973

Solute diffusion in liquid metals

A gas model of diffusion in liquid metals is presented. In this model, ions of liquid metals are assumed to behave like the molecules in a dense gas. Diffusion coefficient of solute is discussed with reference to its mass, ionic size, and pair potential. The model is applied to the case of solute diffusion in liquid silver. An attempt was made to predict diffusion coefficients of solutes with reasonable accuracy.

Bhat, B. N.↗