Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “Vector Potential”

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.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 109 records · Page 6
All sourcesNASA NTRSDOE OSTI
NASA NTRS1977

Dissipative, forced turbulence in two-dimensional magnetohydrodynamics

The equations of motion of a turbulent two-dimensional MHD flow are solved in the presence of finite viscosity and resistivity for the case when external mechanical and/or magnetic forces act on the fluid, the goal of the study being to verify the existence of a MHD dynamo effect which is represented by a substantial back-transfer of mean square vector potential to the longest allowed Fourier wavelengths. The regime explored is that for which the mechanical and magnetic Reynolds numbers are in the range 100 to 1000. It is concluded that mechanical forcing terms alone cannot lead to dynamo action, but that dynamo action can result from either magnetic forcing terms or from both mechanical and magnetic forcing terms simultaneously.

Fyfe, D.↗
NASA NTRS1977

Analysis of magnetic fields using variational principles and CELAS2 elements

Prospective techniques for analyzing magnetic fields using NASTRAN are reviewed. A variational principle utilizing a vector potential function is presented which has as its Euler equations, the required field equations and boundary conditions for static magnetic fields including current sources. The need for an addition to this variational principle of a constraint condition is discussed. Some results using the Lagrange multiplier method to apply the constraint and CELAS2 elements to simulate the matrices are given. Practical considerations of using large numbers of CELAS2 elements are discussed.

Frye, J. W.↗
NASA NTRS1978

Solving magnetostatic field problems with NASTRAN

Determining the three-dimensional magnetostatic field in current-induced situations has usually involved vector potentials, which can lead to excessive computational times. How such magnetic fields may be determined using scalar potentials is reviewed. It is shown how the heat transfer capability of NASTRAN level 17 was modified to take advantage of the new method.

Hurwitz, M. M.↗
NASA NTRS1977

Finite-element solutions for geothermal systems

Vector potential and scalar potential are used to formulate the governing equations for a single-component and single-phase geothermal system. By assuming an initial temperature field, the fluid velocity can be determined which, in turn, is used to calculate the convective heat transfer. The energy equation is then solved by considering convected heat as a distributed source. Using the resulting temperature to compute new source terms, the final results are obtained by iterations of the procedure. Finite-element methods are proposed for modeling of realistic geothermal systems; the advantages of such methods are discussed. The developed methodology is then applied to a sample problem. Favorable agreement is obtained by comparisons with a previous study.

Chen, J. C.↗
NASA NTRS1979

Two-dimensional magnetohydrodynamic turbulence - Cylindrical, non-dissipative model

Incompressible magnetohydrodynamic turbulence is treated in the presence of cylindrical boundaries which are perfectly conducting and rigidly smooth. The model treated is non-dissipative and two-dimensional, the variation of all quantities in the axial direction being ignored. Equilibrium Gibbs ensemble predictions are explored assuming the constraint of constant axial current (appropriate to tokamak operation). No small-amplitude approximations are made. The expectation value of the turbulent kinetic energy is found to approach zero for the state of maximum mean-square vector potential to energy ratio. These are the only states for which large velocity fluctuations are not expected.

Montgomery, D.↗
NASA NTRS1980

Determination of efficiencies, loss mechanisms, and performance degradation factors in chopper controlled dc vehical motors. Section 2: The time dependent finite element modeling of the electromagnetic field in electrical machines: Methods and applications

The time dependent solution of the magnetic field is introduced as a method for accounting for the variation, in time, of the machine parameters in predicting and analyzing the performance of the electrical machines. The method of time dependent finite element was used in combination with an also time dependent construction of a grid for the air gap region. The Maxwell stress tensor was used to calculate the airgap torque from the magnetic vector potential distribution. Incremental inductances were defined and calculated as functions of time, depending on eddy currents and saturation. The currents in all the machine circuits were calculated in the time domain based on these inductances, which were continuously updated. The method was applied to a chopper controlled DC series motor used for electric vehicle drive, and to a salient pole sychronous motor with damper bars. Simulation results were compared to experimentally obtained ones.

Hamilton, H. B.↗
NASA NTRS1981

Determination of magnetic helicity in the solar wind and implications for cosmic ray propagation

The mean value of the correlation between local magnetic field and vector potential, known as the magnetic helicity, is a measure of the lack of mirror reflection symmetry of magnetic covariances in a turbulent medium. A method is presented for extraction of helicity spectra from magnetometer data, and applied to an evaluation of the magnetic helicity of interplanetary magnetic fluctuations.

Matthaeus, W. H.↗
NASA NTRS1981

Determination of magnetic helicity in the solar wind and implications for cosmic ray propagation

Magnetic helicity (Hm) is the mean value of the correlation between a turbulent magnetic field and the magnetic vector potential. A technique is described for determining Hm and its 'reduced' spectrum from the two point magnetic correlation matrix. The application of the derived formalism to solar wind magnetic fluctuations is discussed, taking into account cases for which only single point measurements are available. The application procedure employs the usual 'frozen in approximation' approach. The considered method is applied to an analysis of several periods of Voyager 2 interplanetary magnetometer data near 2.8 AU. During these periods the correlation length, or energy containing length, was found to be approximately 3 x 10 to the 11th cm

Matthaeus, W. M.↗
NASA NTRS1982

Two-and-a-half-dimensional magnetohydrodynamic turbulence

The homogeneous turbulence for which fluctuating magnetic fields and velocity fields are independent of one spatial coordinate but still possess all three components are studied to form a generalized two-and-half dimensional geometry. The integral of the z-vector potential and the magnetic helicity are shown to be ideal invariants, and the basic dynamical variables and the equations of uniform-density incompressible magnetohydrodynamics are defined. The possibility of simultaneous inverse cascades is considered, and Kolmogoroff dimensional analysis is employed to infer omnidirectional inverse cascade spectra. Implications of a selective decay hypothesis, where a tendency exists in the initial value problem for the ideal invariants directly cascaded to higher wavenumbers to be selectively dissipated, and the possibility of a dynamo action in the considered geometry, are examined.

Montgomery, D.↗
NASA NTRS1985

Forced MHD turbulence in a uniform external magnetic field

Two-dimensional dissipative MHD turbulence is randomly driven at small spatial scales and is studied by numerical simulation in the presence of a strong uniform external magnetic field. A behavior is observed which is apparently distinct from the inverse cascade which prevails in the absence of an external magnetic field. The magnetic spectrum becomes dominated by the three longest wavelength Alfven waves in the system allowed by the boundary conditions: those which, in a box size of edge 2 pi, have wave numbers (kx' ky) = (1, 1), and (1, -1), where the external magnetic field is in the x direction. At any given instant, one of these three modes dominates the vector potential spectrum, but they do not constitute a resonantly coupled triad. Rather, they are apparently coupled by the smaller-scale turbulence.

Hossain, M.↗
NASA NTRS1985

Rapid magnetic reconnection caused by finite amplitude fluctuations

The nonlinear dynamics of the magnetohydrodynamic sheet pinch have been investigated as an unforced initial value problem for large scale Reynolds numbers up to 1000. Reconnection is triggered by adding to the sheet pinch a small but finite level of broadband random perturbations. Effects of turbulence in the solutions include the production of reconnected magnetic islands at rates that are insensitive to resistivity at early times. This is explained by noting that electric field fluctuations near the X point produce irregularities in the vector potential, sometimes taking the form of 'magnetic bubbles', which allow rapid change of field topology.

Matthaeus, W. H.↗
NASA NTRS1983

The sensitivity of a general circulation model to Saharan dust heating

Evidence is accumulating that tropospheric aerosols, such as Saharan dust, can significantly influence weather and climate. The Climate Model of the Goddard Laboratory for Atmospheric Sciences is presently used to assess the possible effects of Saharan dust on the weather and climate of North Africa and the tropical Atlantic Ocean. The three-dimensional model solves the conservation equations for the horizontal wind vector, potential temperature, water vapor mixing ratio, and surface pressure. Parameterizations are included for turbulent exchange at the earth surface, cumulus convection, large scale saturation, diurnally varying solar radiation, and terrestrial radiation. Realistic simulations are thereby produced for many aspects of the observed climate.

Randall, D.↗
NASA NTRS1985

Forced magnetohydrodynamic turbulence in a uniform external magnetic field

Two-dimensional dissipative MHD turbulence is randomly driven at small spatial scales and is studied by numerical simulation in the presence of a strong uniform external magnetic field. A behavior is observed which is apparently distinct from the inverse cascade which prevails in the absence of an external magnetic field. The magnetic spectrum becomes dominated by the three longest wavelength Alfven waves in the system allowed by the boundary conditions: those which, in a box size of edge 2 pi, have wave numbers (kx, ky) = (1, 1), and (1, -1), where the external magnetic field is in the x direction. At any given instant, one of these three modes dominates the vector potential spectrum, but they do not constitute a resonantly coupled triad. Rather, they are apparently coupled by the smaller-scale turbulence.

Hossain, M.↗
NASA NTRS1986

Turbulent relaxation processes in magnetohydrodynamics

Competing processes previously called 'selective decay' and 'dynamic alignment' are studied numerically for two-dimensional magnetohydrodynamic turbulence. In selective decay, the energy decays relatively to mean-square vector potential, and in dynamic alignment, the energy decays relatively to cross helicity. In the former case, the kinetic (fluid) energy decays to zero and the magnetic energy occupies the largest scales allowed by the boundary conditions. In the latter case, the velocity field and magnetic field become aligned and energetically equipartitioned. An extensive study of the initial value problem, with viscous and resistive dissipation, indicates that four distinct regimes of behavior are possible: a magnetically dominated regime, a velocity dominated regime, a dynamic alignment dominated regime, and a transition regime separating the others in parameter space. An analytical variational problem predicts several features seen in the computations, including geometrical alignment of velocity and magnetic fields, constraints on global quantities in the long-time limit, and in some cases, condensation to long wavelength modes.

Ting, Antonio C.↗
NASA NTRS1987

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.↗
NASA NTRS1987

Magnetohydrodynamic cellular automata

A generalization of the hexagonal lattice gas model of Frisch, Hasslacher and Pomeau is shown to lead to two-dimensional magnetohydrodynamics. The method relies on the ideal point-wise conservation law for vector potential.

Montgomery, David↗
NASA NTRS1988

Design of magnets inside cylindrical superconducting shields

The design of magnets inside closed, cylindrical, superconducting shields is discussed. The Green function is given for the magnetic vector potential for cylindrically symmetric currents inside such a shield. The magnetic field everywhere inside the shield can be obtained from this function, which includes the effects of the induced shield currents exactly. The field is given for a thin solenoid as an example and the convergence of the series solution for this case is discussed. The shield can significantly reduce the strength and improve the homogeneity of a magnet. The improvement in homogeneity is of particular importance in the design of correction coils. These effects, and the maximum field on the shield, are examined for a typical solenoid. The results given are also useful, although not exact, for long shields with one or two open ends.

Rigby, K. W.↗
NASA NTRS1989

Parallel processing of a rotating shaft simulation

A FORTRAN program describing the vibration modes of a rotor-bearing system is analyzed for parellelism in this simulation using a Pascal-like structured language. Potential vector operations are also identified. A critical path through the simulation is identified and used in conjunction with somewhat fictitious processor characteristics to determine the time to calculate the problem on a parallel processing system having those characteristics. A parallel processing overhead time is included as a parameter for proper evaluation of the gain over serial calculation. The serial calculation time is determined for the same fictitious system. An improvement of up to 640 percent is possible depending on the value of the overhead time. Based on the analysis, certain conclusions are drawn pertaining to the development needs of parallel processing technology, and to the specification of parallel processing systems to meet computational needs.

Arpasi, Dale J.↗