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NASA NTRS1981

Grid evolution in time asymptotic problems

The selection of the proper coordinate system in solving any fluid flow or heat transfer problem is a very important consideration. A new technique of moving mesh points in physical space is introduced so as to reduce the error in a computed asymptotic solution relative to that obtained using a fixed mesh. The technique has been used to solve the simple viscous Burgers' equation in one and two dimensions. Substantial error reductions are demonstrated. The treatment of boundary points and the effect of using different error criteria in generating grids are discussed.

Rai, M. M.↗

NASA NTRS1982

Energetic electrons in the magnetosheath and upstream of the bow shock

Four years of data gathered by the IMP 8 electron/isotope spectrometer are used in a study of the characteristics and transport of electrons of more than 200 keV, both upstream of the earth's bow shock and in the outer magnetosheath. With the aid of a new coordinate system, it is shown that (1) the upstream electron bursts are most often seen on interplanetary field lines which trace to the inner magnetosheath, and (2) the total energy transported sunward by the electrons averages about 1.6 x 10 to the 14th ergs/sec. This figure is comparable to the tailward energy flow observed in the permanent layer of energetic electrons adjacent to the magnetopause. The net flow of energetic electrons in the magnetosheath is toward the shock, and nearly equals the net flow away from the shock in the adjacent upstream region. The energetic electrons studied appear to be closely related, and may have a common origin in either the inner magnetosheath or the magnetosphere.

Bieber, J. W.↗

NASA NTRS1981

Numerical integration of the satellites of the outer planets

The formulation of a numerical integration program, used to construct ephemerides for satellites of the outer planets, is described. The equations of motion are derived, including (1) n massive integrated satellites, (2) m massive perturbing planets, (3) J2, J4 oblateness coefficients of the primary and each satellite, and (4) a barycentric coordinate system. Variational equations are also found: (1) 6n initial states and n masses of the integrated satellites, (2) J2, J4 of the primary planet, (3) the mass of the system, and (4) right ascension and declination of the pole. The formulation was used to construct the satellite ephemerides of Saturn for the Voyager mission.

Peters, C. F.↗

NASA NTRS1982

Numerical solution of Space Shuttle Orbiter flow field

The supersonic, viscous laminar flow around the Space Shuttle Orbiter forebody has been computed with a parabolized Navier-Stokes code using a generalized coordinate transformation. The initial solution for the nose part of the Orbiter geometry was obtained with a three-dimensional time-dependent Navier-Stokes solver. It was necessary to employ a wind axis oriented coordinate system to obtain the initial solution with the time-dependent code. The generalized PNS technique used in this study allows the solution to be marched from the given initial data surface to any desired surface downstream. A grid point clustering scheme was employed to accurately describe the body shape by clustering points at the wing tip and at the wing body juncture. The computed heat transfer coefficients, pressure coefficients, and shock shapes are compared with the available experimental data for 0 degrees and 30 degrees angle of attack.

Venkatapathy, E.↗

NASA NTRS1981

Analysis and computation of three-dimensional flow in strongly curved ducts

Numerical solutions are presented for three-dimensional laminar and turbulent flow in curved ducts of rectangular cross section and significant curvature. The analysis is based on a primary-secondary velocity decomposition in a given coordinate system, and leads to approximate governing equations which correct an a priori inviscid solution for viscous effects, secondary flows, total pressure distortion, heat transfer, and internal flow blockage and losses. Solution of the correction equations is accomplished as an initial-value problem in space using an implicit forward-marching technique. The overall solution procedure requires significantly less computational effort than Navier-Stokes algorithms. The present solution procedure is effective even with the extreme local mesh resolution which is necessary to resolve near-wall sublayer regions in turbulent flow calculations. Computed solutions for both laminar and turbulent flow compare very favorably with available analytical and experimental results.

Kreskovsky, J. P.↗

NASA NTRS1981

Detection and damage assessment of citrus tree losses with aerial color infrared photography /ACIR/

Detection and disease damage assessment of citrus tree losses in a Florida citrus grove were made by establishing a registration (grove site location) coordinate system, developing a damage assessment system, and testing sequential aerial color infrared (ACIR) photography at the scale of 1 in. = 333 ft (2.5 cm = 100 m) during the winter, spring, and summer seasons of 1978 and spring of 1979. Spring photography was the easiest to photo interpret, showed the greatest differences between healthy and diseased trees, and had the least shadow and background interference for photo interpretation. Trees showing slight disease damage were detected in ACIR before they were found in ground surveys.

Blazquez, C. H.↗

NASA NTRS1982

Evaluation of temporal registration of Landsat scenes

The registration of Landsat images is important for multitemporal classification and for detecting change. Landsat data are now rectified to a ground coordinate system during preprocessing, hence scenes obtained over the same area are registered. The machine responsible for preprocessing the Landsat multispectral scanner data is the master data processor (MDP). This paper describes the rectification approach taken by the MDP, reviews the accuracy standards of the resultant product, and provides an assessment of the accuracy of the scene to scene registration of two Landsat images.

Nelson, R.↗

NASA NTRS1982

A study of viscous flow in stator and rotor passages

A numerical technique to predict the viscous behavior in the three-dimensional domain of rotating and stationary blade passages is presented. The analysis is based upon the numerical integration of the incompressible Navier-Stokes equations. An approach is taken to combine the three momentum equations and the continuity equation into two sets of vorticity transport-stream function equations. These equations are expressed along families of arbitrarily defined orthogonally intersecting surfaces placed within the blade passage. Unlike the stream surfaces, the arbitrary surfaces allow fluid to flow across. The numerical code employs a nonorthogonal body fitted coordinate system on each of the intersecting surfaces. The solution process involves the iterative combination of the solutions on the two families of intersecting surfaces for a complete solution. The results of flow in thin blade stationary and rotating polar ducts is presented.

Sheoran, Y.↗

NASA NTRS1982

A conservative finite difference algorithm for the unsteady transonic potential equation in generalized coordinates

An implicit, approximate-factorization, finite-difference algorithm has been developed for the computation of unsteady, inviscid transonic flows in two and three dimensions. The computer program solves the full-potential equation in generalized coordinates in conservation-law form in order to properly capture shock-wave position and speed. A body-fitted coordinate system is employed for the simple and accurate treatment of boundary conditions on the body surface. The time-accurate algorithm is modified to a conventional ADI relaxation scheme for steady-state computations. Results from two- and three-dimensional steady and two-dimensional unsteady calculations are compared with existing methods.

Bridgeman, J. O.↗

NASA NTRS1982

Nonlinear and tangent stiffness of imperfect beam columns

A curved member under axial load is analyzed using beam column theory to determine nonlinear response and the tangent stiffness associated with small displacements from the nonlinear state. Such a result is suitable for incorporation into a general nonlinear analysis using a corotational coordinate system to describe the rigid body type motion of individual members. The method is applied to buckling problems. Several examples are given to show the accuracy of the method.

Anderson, M. S.↗

NASA NTRS1982

The reduction, verification and interpretation of MAGSAT magnetic data over Canada

Consideration is being given to representing the magnetic field in the area 40 deg N to 83 deg N by means of functions in spherical coordinates. A solution to Laplace's equation for the magnetic potential over a restricted area was found, and programming and testing are currently being carried out. Magnetic anomaly modelling is proceeding. The program SPHERE, which was adapted to function correctly on the Cyber computer, is now operational, for deriving gravity and magnetic models in a spherical coordinate system.

Coles, R. L.↗

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

Theoretical investigations of high lift aerodynamics

A program which generates a coordinate system for a two element airfoil with the mesh points concentrated in areas of significant vorticity, i.e., boundary layer and wake is operational. The 'imbedded' grid method developed allows a transition from the scale of the main airfoil to the scale of the flap. This requirement is essential for the modeling of viscous flows over the flap and slat of a multielement airfoil. An airfoil mounted in a 2-D wind tunnel was formulated. The program is ready for a fine grid and a large number of planes to explore the characteristics of a Navier-Stokes solver in a quasi-3D case. The program was converted to a form suitable for the STAR computer. Runs were made to map a three dimensional flow field for a wall airfoil intersection with and without lift.

Bennett, G.↗

NASA NTRS1983

Prediction of high speed propeller flow fields using a three-dimensional Euler analysis

To overcome the limitations of classical propeller theory, a computer program, NASPROP-E, was developed which solves for the flow field surrounding a multibladed propeller and axisymmetric nacelle combination using a finite difference method. The governing equations are the three dimensional unsteady Euler equations written in a cylindrical coordinate system. They are marched in time until a steady state solution is obtained. The Euler equations require no special treatment to model the blade work vorticity. The equations are solved using an implicit approximate factorization method. Numerical results are presented which have greatly increased the understanding of high speed propeller flow fields. Numerical results for swirl angle downstream of the propeller and propeller power coefficient are higher than experimental results. The radial variation of coefficient are higher than experimental results. The radial variation of swirl angle, however, is in reasonable agreement with the experimental results. The predicted variation of power coefficient with blade angle agrees very well with data.

Bober, L. J.↗

NASA NTRS1982

The indirect effects on the computation of geoid undulations

The indirect effects on the geoid computation due to the second method of Helmert's condensation were studied. when Helmert's anomalies are used in Stokes's equation, there are three types of corrections to the free air geoid. The first correction, the indirect effect on geoid undulation due to the potential change in Helmert's reduction, had a maximum value of 0.51 meters in the test area covering the United States. The second correction, the attraction change effect on geoid undulation, had a maximum value of 9.50 meters when the 10 deg cap was used in Stokes' equation. The last correction, the secondary indirect effect on geoid undulatin, was found negligible in the test area. The corrections were applied to uncorrected free air geoid undulations at 65 Doppler stations in the test area and compared with the Doppler undulations. Based on the assumption that the Doppler coordinate system has a z shift of 4 meters with respect to the geocenter, these comparisons showed that the corrections presented in this study yielded improved values of gravimetric undulations.

Wichiencharoen, C.↗

NASA NTRS1983

A viscous shock-layer flowfield analysis by an explicit-implicit method

An implicit analogue of a widely used explicit method to external axisymmetric laminar flows with strong entropy gradients is extended. The details of the "numerics" of the implicit part are provided in a body oriented coordinate system with a moving outer (shock) boundary during the transient part of the solutions. The limiting values of the Courant number are obtained when the shock boundary is treated explicitly. The solution algorithm outlined includes the treatment of the source term associated with the equations in weak conservation form. From the results obtained for two sample problems, it becomes clear that accuracy of predictions is, indeed, very good at higher values of the Courant number. There is a significant saving in overall computing time, depending on the Courant number used and the flow Reynolds number. These properties combined with the simplicity of programming the implicit analog may appeal to researchers for using it in the analysis of 3-D flow problems.

Gupta, R. M.↗

NASA NTRS1982

User's manual for Axisymmetric Diffuser Duct (ADD) code. Volume 1: General ADD code description

This User's Manual contains a complete description of the computer codes known as the AXISYMMETRIC DIFFUSER DUCT code or ADD code. It includes a list of references which describe the formulation of the ADD code and comparisons of calculation with experimental flows. The input/output and general use of the code is described in the first volume. The second volume contains a detailed description of the code including the global structure of the code, list of FORTRAN variables, and descriptions of the subroutines. The third volume contains a detailed description of the CODUCT code which generates coordinate systems for arbitrary axisymmetric ducts.

Anderson, O. L.↗

NASA NTRS1982

User's manual for Axisymmetric Diffuser Duct (ADD) code. Volume 3: ADD code coordinate generator

This User's Manual contains a complete description of the computer codes known as the Axisymmetric Diffuser Duct (ADD) code. It includes a list of references which describe the formulation of the ADD code and comparisons of calculation with experimental flows. The input/output and general use of the code is described in the first volume. The second volume contains a detailed description of the code including the global structure of the code, list of FORTRAN variables, and descriptions of the subroutines. The third volume contains a detailed description of the CODUCT code which generates coordinate systems for arbitrary axisymmetric ducts.

Anderson, O. L.↗