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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 253 records · Page 14
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NASA NTRS1977

A solution to the Navier-Stokes equations based upon the Newton Kantorovich method

An implicit finite difference scheme based on the Newton-Kantorovich technique was developed for the numerical solution of the nonsteady, incompressible, two-dimensional Navier-Stokes equations in conservation-law form. The algorithm was second-order-time accurate, noniterative with regard to the nonlinear terms in the vorticity transport equation except at the earliest few time steps, and spatially factored. Numerical results were obtained with the technique for a circular cylinder at Reynolds number 15. Results indicate that the technique is in excellent agreement with other numerical techniques for all geometries and Reynolds numbers investigated, and indicates a potential for significant reduction in computation time over current iterative techniques.

Davis, J. E.↗
NASA NTRS1978

Solution of transonic flows by an integro-differential equation method

Solutions of steady transonic flow past a two-dimensional airfoil are obtained from a singular integro-differential equation which involves a tangential derivative of the perturbation velocity potential. Subcritical flows are solved by taking central differences everywhere. For supercritical flows with shocks, central differences are taken in subsonic flow regions and backward differences in supersonic flow regions. The method is applied to a nonlifting parabolic-arc airfoil and to a lifting NACA 0012 airfoil. Results compare favorably with those of finite-difference schemes.

Ogana, W.↗
NASA NTRS1977

Computational design of the basic dynamical processes of the UCLA general circulation model

The 12-layer UCLA general circulation model encompassing troposphere and stratosphere (and superjacent 'sponge layer') is described. Prognostic variables are: surface pressure, horizontal velocity, temperature, water vapor and ozone in each layer, planetary boundary layer (PBL) depth, temperature, moisture and momentum discontinuities at PBL top, ground temperature and water storage, and mass of snow on ground. Selection of space finite-difference schemes for homogeneous incompressible flow, with/without a free surface, nonlinear two-dimensional nondivergent flow, enstrophy conserving schemes, momentum advection schemes, vertical and horizontal difference schemes, and time differencing schemes are discussed.

Arakawa, A.↗
NASA NTRS1978

Computational transonic flow about realistic aircraft configurations

A numerical method has been developed to compute transonic flows about realistic wing-fuselage configurations. The finite difference scheme employs an improved small disturbance flow equation. A unique grid embedding technique, which was heretofore applied to airfoils and wings, has been extended to include the treatment of both body and wing-body shapes. The resulting high-density mesh is shown to be a valuable asset in resolving details of the three-dimensional flow. A mathematical modeling system is used to process arbitrary fuselage geometries for body boundary conditions. Correlations with experimental data for simple isolated bodies, an isolated fuselage, and wing-fuselage combinations are included.

Boppe, C. W.↗
NASA NTRS1978

Extrapolation methods for dynamic partial differential equations

Several extrapolation procedures are presented for increasing the order of accuracy in time for evolutionary partial differential equations. These formulas are based on finite difference schemes in both the spatial and temporal directions. On practical grounds the methods are restricted to schemes that are fourth order in time and either second, fourth or sixth order in space. For hyperbolic problems the second order in space methods are not useful while the fourth order methods offer no advantage over the Kreiss-Oliger method unless very fine meshes are used. Advantages are first achieved using sixth order methods in space coupled with fourth order accuracy in time. Computational results are presented confirming the analytic discussions.

Turkel, E.↗
NASA NTRS1977

Navier-Stokes solution for the laminar and turbulent supersonic flow near the trailing edge of a flat plate

The present paper deals with problems of two-dimensional laminar and turbulent flow of a viscous incompressible fluid near the trailing edge of a thin flat plate. The complete system of Navier-Stokes equations is solved by means of MacCormack's finite-difference scheme. In the laminar case, the results are compared with the triple deck solution of Daniels (1973). The comparisons indicate that the asymptotic triple deck theory for supersonic trailing-edge flow is accurate within five percent for Reynolds numbers greater than 1000. In the turbulent case, the Prandtl-Van Driest-Clausner algebraic eddy viscosity model is used, showing that the region of upstream influence is roughly of the order of the boundary layer thickness.

Hussaini, M. Y.↗
NASA NTRS1978

Non-linear effects on sound propagation in a variable area duct carrying high subsonic Mach number flows

The general one-dimensional non-linear equation for the acoustic velocity potential in a variable area duct carrying high subsonic Mach number flows is presented and solved numerically using an implicit finite difference scheme. For the linearized equation with no flow, the present scheme is compared with the exact solution and the fourth-order Runge-Kutta method with excellent agreement for dimensionless time periods. Non-linear solutions are more sensitive to Mach numbers and exciting amplitudes and less sensitive to exciting frequencies. In general, non-linear effects can be safely neglected for low Mach number flows but must be accounted for when high Mach number flows are encountered.

Lumsdaine, E.↗
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 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

Flux vector splitting of the inviscid equations with application to finite difference methods

The conservation-law form of the inviscid gasdynamic equations has the remarkable property that the nonlinear flux vectors are homogeneous functions of degree one. This property readily permits the splitting of flux vectors into subvectors by similarity transformations so that each subvector has associated with it a specified eigenvalue spectrum. As a consequence of flux vector splitting, new explicit and implicit dissipative finite-difference schemes are developed for first-order hyperbolic systems of equations. Appropriate one-sided spatial differences for each split flux vector are used throughout the computational field even if the flow is locally subsonic. The results of some preliminary numerical computations are included.

Steger, J. L.↗
NASA NTRS1979

Numerical solution of the azimuthal-invariant thin-layer Navier-Stokes equations

The paper reports a numerical procedure developed for a two-dimensional azimuthal (or planar) invariant form of the thin-layer Navier-Stokes equations. Generalization of the governing equations is described, and the equations are solved with an implicit approximate factorization finite-difference scheme. Inviscid and viscous results are presented for both external and internal flows and for spinning and nonspinning bodies.

Nietubicz, C. J.↗
NASA NTRS1979

A computational fluid dynamic technique valid at the centerline for non-axisymmetric problems in cylindrical coordinates

A technique is described for the numerical solution of non-axisymmetric flow problems posed in cylindrical coordinates when the z-axis is included in the flowfield. The highlight of the technique is the manner in which the singularities at the centerline are handled. Specifically, the governing flowfield equations at r = 0 are put in a special form by applying L'Hospital's Rule. The required radial derivatives are evaluated using a one-sided, second-order accurate, first-difference. This leads to a smooth, convergent calculation of the flowfield at the centerline. This appears to be the first generally applicable numerical method for avoiding coordinate system singularities in the context of a finite-difference scheme, and could have application to many nonaxisymmetric flows. The technique is illustrated by specific results for the time-dependent flowfield inside an internal combustion engine.

Griffin, M. D.↗
NASA NTRS1980

Transonic Flow Field Analysis for Wing-Fuselage Configurations

A computational method for simulating the aerodynamics of wing-fuselage configurations at transonic speeds is developed. The finite difference scheme is characterized by a multiple embedded mesh system coupled with a modified or extended small disturbance flow equation. This approach permits a high degree of computational resolution in addition to coordinate system flexibility for treating complex realistic aircraft shapes. To augment the analysis method and permit applications to a wide range of practical engineering design problems, an arbitrary fuselage geometry modeling system is incorporated as well as methodology for computing wing viscous effects. Configuration drag is broken down into its friction, wave, and lift induced components. Typical computed results for isolated bodies, isolated wings, and wing-body combinations are presented. The results are correlated with experimental data. A computer code which employs this methodology is described.

Boppe, C. W.↗
NASA NTRS1980

A rapid implicit-explicit solution to the two-dimensional time dependent incompressible Navier-Stokes equations

A second-order time-accurate and spatially factored algorithm was used in a finite difference scheme for the numerical solution of the time-dependent, incompressible, two dimensional Navier-Stokes equations in conservation-law form using vorticity and stream function variables. The systems of equations are solved at each time step by an iterative technique. Numerical results were obtained for a circular cylinder at a Reynolds number of 15, and an NACA 0012 airfoil at zero angle of attack at Reynolds numbers of 10 to the third and 10 to the fourth powers. The results are in agreement with another numerical technique, and the computing time required to obtain the steady state solution at the Reynolds number of 10 to the 4th power was 49.7 sec on CDC 7600 computer using a 65 x 84 computational grind.

Davis, J. E.↗
NASA NTRS1980

Propeller slipstream/wing interaction in the transonic regime

An inviscid model for the interaction between a thin wing and a nearly uniform propeller slipstream is presented. The model allows the perturbation velocities due to the interaction to be potential although the undisturbed slipstream velocity is rotational. A finite difference scheme is used to solve the governing equation. Numerical examples indicate that the slipstream has a strong effect on the aerodynamic properties of the wing section within the slipstream and lesser effects elsewhere. The slipstream swirling motion strongly affects the wing load distribution, however, its effect on the wing's total lift and wave drag is small. The axial velocity increment in the slipstream has a small effect on the wing lift, however, it causes a large increase in wave drag.

Rizk, M. H.↗
NASA NTRS1982

Algorithm for Unsteady Potential Flow About Airfoils

Implicit finite-difference scheme efficiently computes unsteady potential flow about airfoils. Formulation uses density and velocity potential as dependent variables. Conservation form is retained to assure that shock wave location and speed are computed correctly. Scheme fills need for method to calculate efficiently unsteady potential flow about airfoils and to predict flutter and other unsteady aeroelastic phenomena in transonic flow regimes.

Chipman, R.↗
NASA NTRS1980

An alternating-direction-implicit algorithm for the unsteady potential equation in conservation form

An implicit finite difference scheme for an efficient computation of unsteady potential flow about airfoils is presented. The formulation uses density and velocity potential as dependent variables, and is cast in conservation form to assure the theoretically correct determination of shockwave location and speed. To enable boundary conditions to be imposed directly on the airfoil surface, a time varying sheared rectilinear coordinate transformation is employed. Calculated time history solutions on a pulsating airfoil are compared with the results of another unsteady transonic code. It is concluded that the method has excellent numerical stability and gives accurate solutions with sharply resolved shocks.

Chipman, R. R.↗
NASA NTRS1981

Geophysical study of the structure and processes of the continental convergence zones: Alpine-Himalayan Belt

The seismic wave velocity structure in the crust and upper mantle region beneath the Tibetan plateau was studied in detail. Also, a preliminary study of the uppermost mantle P wave velocity beneath Iran and Turkey was carried out, and the results are compared with those for the Tibetan plateau. These two studies compose the bulk of the efforts on the observational aspects of continental collision zones in addition to satellite derived data. On the theoretical aspects the thermal evolution of converging plate boundaries was explored using a finite difference scheme.

Toksoez, M. N.↗