On the re-connexion of magnetic field lines in conducting fluids
Magnetic field lines reconnection in steady incompressible hydromagnetic two dimensional flow, formulating governing equations with cylindrical polar coordinates
Axford, W. I.↗
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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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Analytic studies of local-severe-storm observables by satellites
Attention is concentrated on the exceptionally violet whirlwind, often characterized by a fairly vertical axis of rotation. For a cylindrical polar coordinate system with axis coincident with the axis of rotation, the secondary flow involves the radial and axial velocity components. The thesis advanced is, first, that a violent whirlwind is characterized by swirl speeds relative to the axis of rotation on the order of 90 m/s, with 100 m/s being close to an upper bound. This estimate is based on interpretation of funnel-cloud shape (which also suggests properties of the radial profile of swirl, as well as the maximum magnitude); an error assessment of the funnel-cloud interpretation procedure is developed. Second, computation of ground-level pressure deficits achievable from typical tornado-spawning ambients by idealized thermohydrostatic processes suggests that a two-cell structure is required to sustain such large speeds.
Dergarabedian, P.↗
A comparative study of the parabolized Navier-Stokes code using various grid-generation techniques
The parabolized Navier-Stokes (PNS) equations are used to calculate the flow-field characteristics about the hypersonic research aircraft X-24C. A comparison of the results obtained using elliptic, hyperbolic, and algebraic grid generators is presented. The outer bow shock is treated as a sharp discontinuity, and the discontinuities within the shock layer are captured. Surface pressures and heat-transfer results at angles of attack of 6 deg and 20 deg, obtained using the three grid generators, are compared. The PNS equations are marched downstream over the body in both Cartesian and cylindrical base coordinate systems, and the results are compared. A robust marching procedure is demonstrated by successfully using large marching step sizes with the implicit shock fitting procedure. A correlation is found between the marching step size, Reynolds number, and the angle of attack at fixed values of smoothing and stability coefficients for the marching scheme.
Kaul, U. K.↗
A comparative study of the parabolized Navier-Stokes code using various grid-generation techniques
The parabolized Navier-Stokes (PNS) equations are used to calculate the flow-field characteristics about the hypersonic research aircraft X-24C. A comparison of the results obtained using elliptic, hyperbolic and algebraic grid generators is presented. The outer bow shock is treated as a sharp discontinuity, and the discontinuities within the shock layer are captured. Surface pressures and heat-transfer results at angles of attack of 6 deg and 20 deg, obtained using the three grid generators, are compared. The PNS equations are marched downstream over the body in both Cartesian and cylindrical base coordinate systems, and the results are compared. A robust marching procedure is demonstrated by successfully using large marching-step sizes with the implicit shock fitting procedure. A correlation is found between the marching-step size, Reynolds number and the angle of attack at fixed values of smoothing and stability coefficients for the marching scheme.
Kaul, U. K.↗
Navier-Stokes analysis of two- and three-dimensional flow field in solid rocket motors with segment joints
A multidimensional implicit Navier-Stokes analysis which uses numerical solution of ensemble-averaged Navier-Stokes equations in a nonorthogonal bodyfitted cylindrical-polar coordinate system has been applied to simulation of the internal flow field in solid-propellant rocket motor chambers with segment joints. The calculation procedure incorporates a two-equation (k-epsilon) turbulence model and utilizes a consistently split, linearized block-implicit algorithm for numerical solution of the governing equations. Computations performed to simulate the axisymmetric flow field in the vicinity of the aft field joint in the Space Shuttle SRB using 14,725 grid points show the presence of a region of reversed axial flow near the downstream edge of the slot. Calculations were also performed for two cases involving asymmetric three-dimensional flow in the vicinity of the aft field joint in the SRB using 721,525 grid points to estimate circumferential velocities and pressure gradients at the joint.
Sabnis, J. S.↗
On a class of unsteady three-dimensional Navier Stokes solutions relevant to rotating disc flows: Threshold amplitudes and finite time singularities
A class of exact steady and unsteady solutions of the Navier Stokes equations in cylindrical polar coordinates is given. The flows correspond to the motion induced by an infinite disc rotating with constant angular velocity about the z-axis in a fluid occupying a semi-infinite region which, at large distances from the disc, has velocity field proportional to (x,-y,O) with respect to a Cartesian coordinate system. It is shown that when the rate of rotation is large, Karman's exact solution for a disc rotating in an otherwise motionless fluid is recovered. In the limit of zero rotation rate a particular form of Howarth's exact solution for three-dimensional stagnation point flow is obtained. The unsteady form of the partial differential system describing this class of flow may be generalized to time-periodic equilibrium flows. In addition the unsteady equations are shown to describe a strongly nonlinear instability of Karman's rotating disc flow. It is shown that sufficiently large perturbations lead to a finite time breakdown of that flow whilst smaller disturbances decay to zero. If the stagnation point flow at infinity is sufficiently strong, the steady basic states become linearly unstable. In fact there is then a continuous spectrum of unstable eigenvalues of the stability equations but, if the initial value problem is considered, it is found that, at large values of time, the continuous spectrum leads to a velocity field growing exponentially in time with an amplitude decaying algebraically in time.
Hall, Philip↗
Noise Radiation by Instability Waves in Coaxial Jets
In this paper predictions are made for the noise radiation from supersonic coaxial jets. The noise in the downstream arc of a supersonic jet is dominated by highly directional radiation from the supersonically convecting large scale structures in the jet mixing layer. Since the mean flow is not described easily in terms of simple analytic functions, a numerical prediction is made for its development. The compressible Reynolds-averaged boundary layer equations in cylindrical polar coordinates are solved. A mixing length turbulence model is used. Empirical correlations are developed the effects of velocity and temperature ratio and Mach number. Both normal and inverted velocity profiles are considered. Comparisons with measurements for both single and coaxial jets show good agreement. The large scale structures are modeled as instability waves. The noise radiation generated by the instability waves is determined by a matching between the inner instability wave solution and the outer acoustic solution. Predictions are made for the differences between the noise radiated by coaxial jets with different operating conditions and a single equivalent jet with the same exit area, thrust, and mass-flow.
Dahl, Milo D.↗
Non-force-free solar magnetic fields in magnetohydrostatic equilibrium
The objective of the paper is to examine a class of non-force-free fields analytically. Specifically, magnetic fields in magnetohydrostatic equilibrium with a plasma in a gravitational field are treated in an approximation of two independent variables but three vector components. Spherical coordinates are emphasized, although the formal results for cylindrical and Cartesian coordinates are presented in the appendices. Formal solutions for the magnetic-field components are obtained in terms of the plasma variables, and field line equations are derived. A final equation governing the plasma variables is then obtained. Procedures are developed for analyzing this equation and obtaining sets of self-consistent particular solutions to the governing equations; a number of such sets of solutions are presented. As an example, one solution set is examined, illustrating the application of the results to the analysis of solar observational data.
Comfort, R. H.↗
Development of Modified Perturbation Solutions to the One-Phase Stefan Problems With a Convective Boundary
The classical Stefan problem is used to track the moving solid-liquid interface during the freezing process. Perturbation theory has often been applied to find an approximate analytical solution due to the nonlinearity of the moving interface. However, the Stefan number (i.e., the sensible over latent heat) must be small and usually less than 0.01 to assume the perturbation expansion, which in turn limits the thermal engineering applications. In this study, a modified perturbation solution is developed by adding a correction term after the leading-order solution to be valid for a much wider range of Stefan numbers (i.e., 0.01 less than or equal to Ste less than or equal to 1). Specifically, a one-phase Stefan problem is first formulated subjected to a convective boundary in the Cartesian, cylindrical, and spherical coordinate systems for inward solidification. The leading-order solution is calculated based on the regular perturbation theory, while the correction term is obtained using the Monte-Carlo method and a multi-variant regression. Results show that the correction term has a linear relationship with the Stefan number and is not significantly influenced by the Biot number. The proposed modified perturbation solution can accurately and rapidly predict the nonlinear moving interface motion for the freezing process.
DIRECT ENERGY CONVERSION,MATHEMATICS AND COMPUTING↗
REYNO: A Reactive Hydrodynamics Modeling Suite
REYNO is a Python library that is primarily designed as a platform for the agile development and testing of novel reactive flow models. Equations of state and multi-step rate laws can be implemented using the provided class hierarchy with different thermodynamic closure conditions. The library includes a one-dimensional Lagrangian hydrodynamic solver to simulate multi-material reactive or inert problems in planar, cylindrical, or spherical coordinates. Custom time-dependent boundary conditions are also available for problems such as ramp compression. This document describes the different numerical methods and algorithms that are included in REYNO.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Linear Velocity Problems Part 2: Thermodynamic Considerations
A compressible polytropic gas, in one dimensional planar, cylindrical, or spherical coordinate systems, is examined through four thermodynamic properties: mass density, pressure, specific internal energy (SIE), and entropy, under the assumptions that the fluid velocity is linearly proportional to the radial coordinate and that the Euler gas dynamics equations assert a self similar solution class. The behavior of the thermodynamics is almost entirely determined by an arbitrary function that results from the derivation of the density distribution. Through physical and other arguments, the arbitrary function can be plotted spatially with time profiles, providing a deeper understanding of the system and how the arbitrary function affects the behavior of the compressible gas.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
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.↗
Interactive modeling using the PATRAN-G program
PATRAN-G is an interactive finite element generating and graphics display program. The program is currently executable on the VAX or PRIME computers and is compatible with 19 commercially available graphics terminals. The PATRAN program can be used in two modes: generation of a finite element model, or postprocessing of output data from a finite element analysis program. The finite element generating mode is divided into two phases. Phase I is the geometry construction. During this phase, the geometric boundaries of the model are defined and the material properties are input. Mirror imaging, translation and scaling of lines, surfaces, and volumes, and rotation of regions permit the geometry to be described efficiently. Points may be defined in alternate rectangular, cylindrical, or spherical coordinate systems. Also, PATRAN-G can calculate the intersection of lines or surfaces. This capability allows a user to easily model, for example, the intersection of a cylinder which cuts through a sphere at an angle. Once the geometry of the model has been described in terms of points, lines, surfaces, and volumes. Phase II is used to generate the computer finite element model.
Stalnaker, W. A.↗
Three-dimensional transonic potential flow about complex 3-dimensional configurations
An analysis has been developed and a computer code written to predict three-dimensional subsonic or transonic potential flow fields about lifting or nonlifting configurations. Possible condfigurations include inlets, nacelles, nacelles with ground planes, S-ducts, turboprop nacelles, wings, and wing-pylon-nacelle combinations. The solution of the full partial differential equation for compressible potential flow written in terms of a velocity potential is obtained using finite differences, line relaxation, and multigrid. The analysis uses either a cylindrical or Cartesian coordinate system. The computational mesh is not body fitted. The analysis has been programmed in FORTRAN for both the CDC CYBER 203 and the CRAY-1 computers. Comparisons of computed results with experimental measurement are presented. Descriptions of the program input and output formats are included.
Reyhner, T. A.↗
Munsell color analysis of Landsat color-ratio-composite images of limonitic areas in southwest New Mexico
The causes of color variations in the green areas on Landsat 4/5-4/6-6/7 (red-blue-green) color-ratio-composite (CRC) images, defined as limonitic areas, were investigated by analyzing the CRC images of the Lordsburg, New Mexico area. The red-blue-green additive color system was mathematically transformed into the cylindrical Munsell color coordinates (hue, saturation, and value), and selected areas were digitally analyzed for color variation. The obtained precise color characteristics were then correlated with properties of surface material. The amount of limonite (L) visible to the sensor was found to be the primary cause of the observed color differences. The visible L is, is turn, affected by the amount of L on the material's surface and by within-pixel mixing of limonitic and nonlimonitic materials. The secondary cause of variation was vegetation density, which shifted CRC hues towards yellow-green, decreased saturation, and increased value.
Kruse, F. A.↗
Tail modeling in a stretched magnetosphere. I - Methods and transformations
A new method is developed for representing the magnetospheric field B as a distorted dipole field. Because Delta-B = 0 must be maintained, such a distortion may be viewed as a transformation of the vector potential A. The simplest form is a one-dimensional 'stretch transformation' along the x axis, concisely represented by the 'stretch function' f(x), which is also a convenient tool for representing features of the substorm cycle. One-dimensional stretch transformations are extended to spherical, cylindrical, and parabolic coordinates and then to arbitrary coordinates. It is shown that distortion transformations can be viewed as mappings of field lines from one pattern to another; the final result only requires knowledge of the field and not of the potentials. General transformations in Cartesian and arbitrary coordinates are derived, and applications to field modeling, field line motion, MHD modeling, and incompressible fluid dynamics are considered.
Stern, David P.↗
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.↗
A Combined Scanning Configuration for Near-Field Antenna Measurements
Scanning configuration for near-field antenna measurements uses cylindrical and plane-polar coordinate surfaces to guide motions of electromagnetic-field probes. Near-field measurements needed especially to enable determination of far fields of large, low-sidelobe, multiplebeam antennas, for which application of far-field measurements often not suitable. New cylindrical/plane-polar scanning configuration requires less space, yet expected to give complete measurements with fewer mechanical complications.
Rahmat-Samii, Y.↗