A mechanical coordinate converter
Mechanical converter for spherical coordinates used in polariscope balloon programs
Gehrels, T.↗
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Results for “spherical coordinates”
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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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.↗
The Adaptively-Refined MHD Solver (ARMS)
ARMS is a robust code for solving the single-fluid, fully compressible equations of magnetohydrodynamics. In this presentation I will describe how to access and run ARMS and how to use HelioSpace to analyze the results. The main features of the code are the following: 1. Equations are solved in either Cartesian or Spherical coordinates. For the latter, either a linear or a Log(r) coordinate can be used. 2. The latest flux-corrected-transport schemes developed at NRZ, are used to advance the convective equations. All waves and shocks are accurately captured. 3. A fully adaptive grid can be used. The code incorporates the PARAMESH technology for block-adaptation. Arbitrary adaptation criteria can be specified. 4. The code maintains a divergence-free magnetic field to machine accuracy throughout all refinement and de-refinement. 5. A uniform resistivity and thermal conduction can be included. Solution is either explicit or implicit. 6. Arbitrary boundary and initial conditions can be used in either Cartesian or spherical coordinates. 7. An accompanying visualization package, HelioSpace, is available for viewing and analyzing the native ARMS output, (without need for interpolating onto a structured grid).
Antichos, S. K.↗
A comparative study of dynamically expanding force-free, constant-alpha magnetic configurations with applications to magnetic clouds
We contrast two different solutions of the constant alpha, force-free MHD equation, both of which have been suggested as models for magnetic clouds: a solution in cylindrical coordinates and one in spherical coordinates. In line with the observation that magnetic clouds expand, we generalize these static models and construct their expanding counterparts. We find that expansion introduces in both cases a large asymmetry in the field strength signature which is in the same sense as that seen the the data, i.e. towards the leading edge of the cloud. We then do a least squares fit of the respective models to one-spacecraft data on a magnetic cloud. We find that the fitting routine converges in both cases. However, while purely formally we cannot distinguish between the two models using data from one spacecraft, the field components in the 'spherical' model have features not compatible with data on magnetic clouds.
Farrugia, C. J.↗
Observer time as a coordinate in relativistic spherical hydrodynamics.
Retarded observer time as coordinate in relativistic spherical hydrodynamic equations prevents Schwarzschild surface formation
SPACE-TIME METRIC↗
Improved State Estimation in Distorted Magnetic Fields
The magnetic field of the Earth – besides varying naturally – may be disturbed locally by the (man-made) environment. State estimation and corresponding navigation frameworks that use magnetometers on-board of mobile platforms suffer from severe performance loss or failure upon local magnetic distortions if these are not detected and mitigated adequately. Advanced estimators include the magnetic variation in the state vector. However, Cartesian coordinates, although widely used in the literature, suffer from observability issues when it comes to disturbance detection. This paper shows the importance of representing the magnetic variation in a spherical coordinate system and subsequent improvements with respect to the common representation in Cartesian coordinates. The spherical representation improves estimator consistency and allows for accurate and fast mitigation of magnetic disturbances through consistent statistical tests which leads to better system state estimates in magnetically distorted areas. The approach is validated by performing tests with simulated and real-world data on embedded hardware.
Brommer, Christian↗
Uncertainty Analysis of Coaxial Thermocouple Calorimeters Used in Arc Jets
Recent introduction of Coaxial Thermocouple type calorimeters into the NASA Ames arc jet facilities has inspired an analysis of 2D conduction effects internal to this type of calorimeter. Lateral conduction effects violate the 1D finite slab inverse analysis which is typically used to deduce the heat transfer to such calorimeters. The spherical shaped nose associated with most calorimeters (rather than flat) leads to a bias error that over-estimates the stagnation heating. Non-uniform heating on the face of spherically shaped calorimeters leads to conduction losses to the colder rim of the calorimeter which causes an underestimate of the stagnation heating. These two effects come into play at different times of the calorimeter's exposure to the arc jet, so they do not cancel. The spherical body effects come into play in the early stages of exposure, while the non-uniform heating effect becomes most severe at the later stages of exposure. The bias associated with spherical effects can be avoided by rewriting the 1D finite slab inverse analysis code to solve for 1D conduction in spherical coordinates. However, reducing the bias error associated non-uniform heating requires a somewhat ad hoc modification to the 1D finite element inverse analysis.
Isotherms↗
Carbon combustion supernovae - Numerical studies of the final evolution of degenerate carbon-oxygen cores
The evolution of polytropic 1.46-solar-mass 3-Gg/cu cm (4 x 10 to the 8th)-K pure C cores is investigated theoretically by means of model computations starting from the runaway stage. The temperature in central zones is raised to the runaway temperature, and the evolution is followed in a spherical coordinate system. In models of burning without detonation, it is found that the initially spherical burning front is Rayleigh-Taylor unstable, without bipolar jets or equatorial rings; that some C is not burned to Ni; and that the Ni in the 0.8-1.0 solar mass of burned fuel produced can account for observed properties of type I supernovae.
Mueller, E.↗
Geopotential Field Anomaly Continuation with Multi-Altitude Observations
Conventional gravity and magnetic anomaly continuation invokes the standard Poisson boundary condition of a zero anomaly at an infinite vertical distance from the observation surface. This simple continuation is limited, however, where multiple altitude slices of the anomaly field have been observed. Increasingly, areas are becoming available constrained by multiple boundary conditions from surface, airborne, and satellite surveys. This paper describes the implementation of continuation with multi-altitude boundary conditions in Cartesian and spherical coordinates and investigates the advantages and limitations of these applications. Continuations by EPS (Equivalent Point Source) inversion and the FT (Fourier Transform), as well as by SCHA (Spherical Cap Harmonic Analysis) are considered. These methods were selected because they are especially well suited for analyzing multi-altitude data over finite patches of the earth such as covered by the ADMAP database. In general, continuations constrained by multi-altitude data surfaces are invariably superior to those constrained by a single altitude data surface due to anomaly measurement errors and the non-uniqueness of continuation.
Kim, Jeong Woo↗
Geopotential Field Anomaly Continuation with Multi-Altitude Observations
Conventional gravity and magnetic anomaly continuation invokes the standard Poisson boundary condition of a zero anomaly at an infinite vertical distance from the observation surface. This simple continuation is limited, however, where multiple altitude slices of the anomaly field have been observed. Increasingly, areas are becoming available constrained by multiple boundary conditions from surface, airborne, and satellite surveys. This paper describes the implementation of continuation with multi-altitude boundary conditions in Cartesian and spherical coordinates and investigates the advantages and limitations of these applications. Continuations by EPS (Equivalent Point Source) inversion and the FT (Fourier Transform), as well as by SCHA (Spherical Cap Harmonic Analysis) are considered. These methods were selected because they are especially well suited for analyzing multi-altitude data over finite patches of the earth such as covered by the ADMAP database. In general, continuations constrained by multi-altitude data surfaces are invariably superior to those constrained by a single altitude data surface due to anomaly measurement errors and the non-uniqueness of continuation.
Kim, Jeong Woo↗
GEOSIM: A numerical model for geophysical fluid flow simulation
A numerical model which simulates geophysical fluid flow in a wide range of problems is described in detail, and comparisons of some of the model's results are made with previous experimental and numerical studies. The model is based upon the Boussinesq Navier-Stokes equations in spherical coordinates, which can be reduced to a cylindrical system when latitudinal walls are used near the pole and the ratio of latitudinal length to the radius of the sphere is small. The equations are approximated by finite differences in the meridional plane and spectral decomposition in the azimuthal direction. The user can specify a variety of boundary and initial conditions, and there are five different spectral truncation options. The results of five validation cases are presented: (1) the transition between axisymmetric flow and baroclinic wave flow in the side heated annulus; (2) the steady baroclinic wave of the side heated annulus; (3) the wave amplitude vacillation of the side heated annulus; (4) transition to baroclinic wave flow in a bottom heated annulus; and (5) the Spacelab Geophysical Fluid Flow Cell (spherical) experiment.
Butler, Karen A.↗
LM lookangle program
Program computes the spacecraft look angles and the slant range, which define a spherical coordinate system located in the spacecraft body. The program is designed to reduce data from the Lunar Module Missions and to output desired information.
Agee, W. E.↗
An algorithm for computing spherical partials
Algorithm for computing acceleration and partial derivatives in satellite equations of motion, using recurrences in spherical coordinates
Borchers, R. V.↗
Acoustic wave propagation in an axisymmetric swirling jet.
An analysis has been developed to study the acoustic wave propagation in an axisymmetric swirling subsonic jet flow. The governing convected wave equation derived in the spherical coordinates includes mean shears, shear gradients and pressure gradients. The directivity patterns for various spinning and non-spinning modes due to the influence of the mean jet swirl were obtained by numerically integrating the governing wave equation. The mean flow field used in the computation was that obtained semiempirically for subsonic swirling turbulent jet and is completely specified once the degree of swirl is known. The dependence of sound directivity on jet Mach number, swirl ratio and frequency are discussed.
Yu, J. C.↗
A finite element solution algorithm for the Navier-Stokes equations
A finite element solution algorithm is established for the two-dimensional Navier-Stokes equations governing the steady-state kinematics and thermodynamics of a variable viscosity, compressible multiple-species fluid. For an incompressible fluid, the motion may be transient as well. The primitive dependent variables are replaced by a vorticity-streamfunction description valid in domains spanned by rectangular, cylindrical and spherical coordinate systems. Use of derived variables provides a uniformly elliptic partial differential equation description for the Navier-Stokes system, and for which the finite element algorithm is established. Explicit non-linearity is accepted by the theory, since no psuedo-variational principles are employed, and there is no requirement for either computational mesh or solution domain closure regularity. Boundary condition constraints on the normal flux and tangential distribution of all computational variables, as well as velocity, are routinely piecewise enforceable on domain closure segments arbitrarily oriented with respect to a global reference frame.
Baker, A. J.↗
The theory of the gravitational potential applied to orbit prediction
A complete derivation of the geopotential function and its gradient is presented. Also included is the transformation of Laplace's equation from Cartesian to spherical coordinates. The analytic solution to Laplace's equation is obtained from the transformed version, in the classical manner of separating the variables. A cursory introduction to the method devised by Pines, using direction cosines to express the orientation of a point in space, is presented together with sample computer program listings for computing the geopotential function and the components of its gradient. The use of the geopotential function is illustrated.
Kirkpatrick, J. C.↗
A comparison of implicit numerical methods for solving the transient spherical diffusion equation
Comparative numerical temperature results obtained by using two implicit finite difference procedures for the solution of the transient diffusion equation in spherical coordinates are presented. The validity and accuracy of these solutions are demonstrated by comparison with exact analytical solutions.
Curry, D. M.↗
Study of a fail-safe abort system for an actively cooled hypersonic aircraft: Computer program documentation
The Fail-Safe Abort System TEMPerature Analysis Program, (FASTEMP), user's manual is presented. This program was used to analyze fail-safe abort systems for an actively cooled hypersonic aircraft. FASTEMP analyzes the steady state or transient temperature response of a thermal model defined in rectangular, cylindrical, conical and/or spherical coordinate system. FASTEMP provides the user with a large selection of subroutines for heat transfer calculations. The various modes of heat transfer available from these subroutines are: heat storage, conduction, radiation, heat addition or generation, convection, and fluid flow.
Haas, L. A., Sr.↗