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NASA NTRS1978

Effect of concentration dependence of the diffusion coefficient on homogenization kinetics in multiphase binary alloy systems

Diffusion calculations were performed to establish the conditions under which concentration dependence of the diffusion coefficient was important in single, two, and three phase binary alloy systems. Finite-difference solutions were obtained for each type of system using diffusion coefficient variations typical of those observed in real alloy systems. Solutions were also obtained using average diffusion coefficients determined by taking a logarithmic average of each diffusion coefficient variation considered. The constant diffusion coefficient solutions were used as reference in assessing diffusion coefficient variation effects. Calculations were performed for planar, cylindrical, and spherical geometries in order to compare the effect of diffusion coefficient variations with the effect of interface geometries. In most of the cases considered, the diffusion coefficient of the major-alloy phase was the key parameter that controlled the kinetics of interdiffusion.

Tenney, D. R.↗

NASA NTRS1978

Characteristics of Mach 10 transitional and turbulent boundary layers

Measurements of the mean flow properties of transitional and turbulent boundary layers in helium on 4 deg and 5 deg wedges were made for flows with edge Mach numbers from 9.5 to 11.3, ratios of wall temperature to total temperature of 0.4 to 0.95, and maximum length Reynolds numbers of one hundred million. The data include pitot and total temperature surveys and measurements of heat transfer and surface shear. In addition, with the assumption of local similarity, turbulence quantities such as the mixing length were derived from the mean flow profiles. Low Reynolds number and precursor transition effects were significant factors at these test conditions and were included in finite difference boundary layer predictions.

Watson, R. D.↗

NASA NTRS1970

Calculation of the planar supercritical flow over a NASA supercritical profile

An unsteady finite difference procedure was used to calculate the steady inviscid flow over an 11% thickness ratio NASA supercritical profile of LWP 505 at M sub infinity = 0.80 and alpha = 0. An attempt is made to include the viscous effects using a modified form of Head's entrainment method to calculate the turbulent boundary layer. The attempt to predict the viscous effects using the compressible form of Head's integral method with a modified auxiliary equation for the form factors was unsatisfactory. Though a reasonably separation bubble was established on the lower surface, a grossly exaggerated displacement effect resulted downstream of the shock on the upper surface. There clearly is substantial further effort required to evolve a satisfactory boundary layer procedure, which must then be coupled in a still unproven manner with the inviscid procedure.

Yoshihara, H.↗

NASA NTRS1979

Generation of linear dynamic models from a digital nonlinear simulation

The results and methodology used to derive linear models from a nonlinear simulation are presented. It is shown that averaged positive and negative perturbations in the state variables can reduce numerical errors in finite difference, partial derivative approximations and, in the control inputs, can better approximate the system response in both directions about the operating point. Both explicit and implicit formulations are addressed. Linear models are derived for the F 100 engine, and comparisons of transients are made with the nonlinear simulation. The problem of startup transients in the nonlinear simulation in making these comparisons is addressed. Also, reduction of the linear models is investigated using the modal and normal techniques. Reduced-order models of the F 100 are derived and compared with the full-state models.

Daniele, C. J.↗

NASA NTRS1979

An improved supersonic, three-dimensional, external, inviscid flow field code

A numerical procedure was developed to compute the inviscid super/hypersonic flow fields about complex vehicle geometries accurately and efficiently. A second-order accurate finite difference scheme is used to integrate the three-dimensional Euler equations in regions of continuous flow, while all shock waves are computed as discontinuities via the Rankine-Hugoniot jump conditions. Conformal mappings are used to develop a computational grid. The effects for equilibrium air are included using curve fits of Mollier charts. This report deals only with modifications to these procedures in four specific areas: inlet mass ingestion, subsonic axial Mach number, improved conformal mappings, and vehicles flying at yaw. In each area both the modifications to the computational procedures and computer code are discussed.

Marconi, F.↗

NASA NTRS1979

Mathematical model investigation of long-term transport of ocean-dumped sewage sludge related to remote sensing

An existing, three-dimensional, Eulerian-Lagrangian finite-difference model was modified and used to examine the transport processes of dumped sewage sludge in the New York Bight. Both in situ and laboratory data were utilized in an attempt to approximate model inputs such as mean current speed, horizontal diffusion coefficients, particle size distributions, and specific gravities. The results presented are a quantitative description of the fate of a negatively buoyant sewage sludge plume resulting from continuous and instantaneous barge releases. Concentrations of the sludge near the surface were compared qualitatively with those remotely sensed. Laboratory study was performed to investigate the behavior of sewage sludge dumping in various ambient density conditions.

Kuo, C. Y.↗

NASA NTRS1977

An efficient numerical technique for calculating thermal spreading resistance

An efficient numerical technique for solving the equations resulting from finite difference analyses of fields governed by Poisson's equation is presented. The method is direct (noniterative)and the computer work required varies with the square of the order of the coefficient matrix. The computational work required varies with the cube of this order for standard inversion techniques, e.g., Gaussian elimination, Jordan, Doolittle, etc.

Gale, E. H., Jr.↗

NASA NTRS1979

Significance of shock and body slip conditions on Jovian entry heating

The influence of the body and shock slip conditions on the heating of a Jovian entry body is investigated. The flow in the shock layer is considered to be axisymmetric, steady, laminar, viscous, and in chemical equilibrium. Realistic thermophysical and step-function spectral models are employed and results are obtained by implicit finite-difference and iteractive procedures. The freestream conditions correspond to a typical Jovian entry trajectory point. The results indicate that the effect of the slip conditions is significant when the altitudes are higher than 225 km and that the contribution of a radiative heat-flux term in the energy equation should not be neglected at any altitude.

Tiwari, S. N.↗

NASA NTRS1978

Some calculations of transonic potential flow for the NACA 64A006 airfoil with oscillating flap

A method for calculating the transonic flow over steady and oscillating airfoils was developed by Isogai. It solves the full potential equation with a semi-implicit, time-marching, finite difference technique. Steady flow solutions are obtained from time asymptotic solutions for a steady airfoil. Corresponding oscillatory solutions are obtained by initiating an oscillation and marching in time for several cycles until a converged periodic solution is achieved. In this paper the method is described in general terms, and results are compared with experimental data for both steady flow and for oscillations at several values of reduced frequency. Good agreement for static pressures is shown for subcritical speeds, with increasing deviation as Mach number is increased into the supercritical speed range. Fair agreement with experiment was obtained at high reduced frequencies with larger deviations at low reduced frequencies.

Bennett, R. M.↗

NASA NTRS1978

Transonic flow over the NACA 64A006 with an oscillating flap-calculations based on the Euler equations

Exploratory calculations of transonic flows over the airfoil with a quarter-chord oscillating flap were made using a program which obtains approximate solutions to the Euler equations with an explicit, shock-capturing, finite-difference scheme. The calculations, essentially inviscid and for the airfoil at zero angle-of-attack in a free-stream, are at Mach numbers and reduced frequencies which were tested in experiments by Tijdeman. The oscillatory lifts from analogus calculations by various investigators generally agree with one another better than they agree with Tijdeman's data. Inclusion in the calculations of an approximate modelling of boundary conditions expected at slotted wind tunnel walls tends to shift some of the results closer to the experimental values.

Magnus, R. J.↗

NASA NTRS1979

Laminar and turbulent flows over spherically blunted cone and hyperboloid with massive surface blowing

Numerical solutions are presented for the flow over a spherically blunted cone and hyperboloid with massive surface blowing. Time-dependent viscous shock-layer equations are used to describe the flow field. The boundary conditions on the body surface include a prescribed blowing-rate distribution. The governing equations are solved by a time-asymptotic finite-difference method. Results presented here are only for a perfect gas-type flow at zero angle of attack. Both laminar and turbulent flow solutions are obtained. It is found that the effect of the surface blowing on the laminar flow field is to smooth out the curvature discontinuity at the sphere-cone juncture point, which results in a positive pressure gradient over the body. The shock slope increases on the downstream portion of the body as the surface blowing rate is increased. The turbulent flow with surface blowing is found to redevelop a boundary-layer-like region near the surface. The effects of this boundary-layer region on the flow field and heating rates are discussed.

Kumar, A.↗

NASA NTRS1979

Generalization of analytical tools for helicopter-rotor airfoils

A state-of-the-art finite difference boundary-layer program incorporated into the NYU Transonic Analysis Program is described. Some possible treatments for the trailing edge region were investigated. Findings indicate the trailing edge region, still within the scope of an iterative potential flow, boundary layer program, appears feasible.

Gibbs, E. H.↗

NASA NTRS1979

Numerical simulation of supersonic cone flow at high angle of attack

A conical symmetry assumption is applied to the full Navier-Stokes equations resulting in an equation set containing time and two coordinate directions as independent variables. The set is integrated by use of a finite difference technique for the particular case of sharp cones at incidence. Solutions are obtained and compared with experiment for auxiliary conditions corresponding to both laminar and turbulent flows. Closure for the turbulent flow case is provided by use of a scalor eddy viscosity model based on the mixing length hypothesis. Modifications to the eddy viscosity model were found which led to excellent surface pressure and surface flow direction agreement for turbulent flow at low supersonic Mach numbers. It is apparent that further work on the turbulence model is necessary for agreement at higher supersonic Mach numbers.

Mcrae, D. S.↗

NASA NTRS1979

Computer program to calculate three-dimensional boundary layer flows over wings with wall mass transfer

A system of computer programs for calculating three dimensional transonic flow over wings, including details of the three dimensional viscous boundary layer flow, was developed. The flow is calculated in two overlapping regions: an outer potential flow region, and a boundary layer region in which the first order, three dimensional boundary layer equations are numerically solved. A consistent matching of the two solutions is achieved iteratively, thus taking into account viscous-inviscid interaction. For the inviscid outer flow calculations, the Jameson-Caughey transonic wing program FLO 27 is used, and the boundary layer calculations are performed by a finite difference boundary layer prediction program. Interface programs provide communication between the two basic flow analysis programs. Computed results are presented for the NASA F8 research wing, both with and without distributed surface suction.

Mclean, J. D.↗

NASA NTRS1979

Skynet satellite electron precharging experiments

Large surface areas (approximately 1 sq m) of the Skynet I qualification model satellite were exposed to the environments of a flux of monoenergetic electrons and pulsed high-intensity X-ray photons from an exploding-wire-radiator source, separately and simultaneously. Experiments were performed with both the cylindrical solar cell panels and the end thermal blanket exposed to these environments. The satellite was instrumented with fiber-optics isolated fast-response sensors capable of sensing and recording the time-varying electric fields and surface currents on the satellite. Spontaneous discharges of the two surfaces were characterized prior to measurements of the interaction of the system-generated electromagnetic pulse from the X-ray photon burst with the electron precharged surfaces. A two-dimensional self-consistent finite difference computer code was used to predict the currents on the Skynet both with and without precharging of the thermal-blanket. These calculations, which used an thermal-blanket voltage profile, predicted a factor of 2 increase in satellite exterior axial currents.

Vanlint, V. A. J.↗

NASA NTRS1979

A vector-continuous loading concept for aerodynamic panel methods

An approach to the reduction of discretization errors in aerodynamic panel methods is presented. The approach is based on preventing the occurence of induced velocity singularities at panel slope discontinuities by maintaining continuity of the velocity jump vector across the panels. The approach was implemented in a two-dimensional incompressible panel method formulation and evaluated by application to several external and internal flow problems. The method is shown to exhibit a second order accuracy trend and to produce smaller errors with velocity component boundary conditions imposed on the real flow than with equipotential boundary conditions imposed on the imaginary flow behind the panels. For flows around airfoil sections with either sharp or blunt trailing edges, the method gives excellent agreement with results from a well developed finite difference method. The method is well behaved and is insensitive to irregularities in panel size distribution.

Kemp, W. B., Jr.↗

NASA NTRS1979

Studies of radiative transfer in the earth's atmosphere with emphasis on the influence of the radiation budget in the joint institute for advancement of flight sciences at the NASA-Langley Research Center

Earth and solar radiation budget measurements were examined. Sensor calibration and measurement accuracy were emphasized. Past works on the earth's radiation field that must be used in reducing observations of the radiation field were reviewed. Using a finite difference radiative transfer algorithm, models of the angular and spectral dependence of the earth's radiation field were developed.

Source record↗

NASA NTRS1979

A split finite element algorithm for the compressible Navier-Stokes equations

An accurate and efficient numerical solution algorithm is established for solution of the high Reynolds number limit of the Navier-Stokes equations governing the multidimensional flow of a compressible essentially inviscid fluid. Finite element interpolation theory is used within a dissipative formulation established using Galerkin criteria within the Method of Weighted Residuals. An implicit iterative solution algorithm is developed, employing tensor product bases within a fractional steps integration procedure, that significantly enhances solution economy concurrent with sharply reduced computer hardware demands. The algorithm is evaluated for resolution of steep field gradients and coarse grid accuracy using both linear and quadratic tensor product interpolation bases. Numerical solutions for linear and nonlinear, one, two and three dimensional examples confirm and extend the linearized theoretical analyses, and results are compared to competitive finite difference derived algorithms.

Baker, A. J.↗

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