Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “coordinate system”

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 1,207 records · Page 67
All sourcesNASA NTRSDOE OSTI
NASA NTRS1992

Some Aspects of Bifurcation Structure of Laminar Flow in Curved Ducts

A bifurcation study is made of laminar flow in curved ducts. The problem is formulated in a curvilinear coordinate system, and the governing equations, after orthogonal mapping is applied, are solved numerically by an iterative finite-difference method. Many computer runs were made with various duct cross-sections ranging from a circle to a square, to learn the transition of bifurcation structure with this change in cross-section and to reconcile the differences between them. In addition, a simpler technique is proposed to generate symmetric four-cell solutions in a circular pipe and a means is put forward to stabilize four-vortex structures in a complete cross-section.

Kao, Hsiao C.↗
NASA NTRS1992

Radiated noise of ducted fans

The differences in the radiated acoustic fields of ducted and unducted propellers of the same thrust operating under similar conditions are investigated. An FEM model is created for the generation, propagation, and radiation of steady, rotor alone noise and exit guide vane interaction noise of a ducted fan. For a specified number of blades, angular mode harmonic, and rotor angular velocity, the acoustic field is described in a cylindrical coordinate system reduced to only the axial and radial directions. It is found that, contrary to the usual understanding of the Tyler and Sofrin (1962) result, supersonic tip speed rotor noise can be cut off if the tip Mach number is only slightly in excess of unity and if the number of blades is relatively small. If there are many blades, the fundamental angular mode number is large, and the Tyler and Sofrin result for thin annuli becomes more relevant. Shrouding of subsonic tip speed propellers is a very effective means of controlling rotor alone noise.

Eversman, Walter↗
NASA NTRS1993

Inference of the angular velocity of plasma in the Jovian magnetosphere from the sweepback of magnetic field

The averaged angular velocity of plasma from magnetic observations is evaluated using plasma outflow rate as a parameter. New techniques are developed to calculate the normal and azimuthal components of the magnetic field in and near to the plasma sheet in a plasma sheet coordinate system. The revised field components differ substantially from the quantities used in previous analyses. With the revised field values, it appears that during the Voyager 2 flyby for an outflow rate of 2.5 x 10 exp 29 amu/s, the observed magnetic torque may be sufficient to keep the plasma in corotation to radial distances of 50 Rj in the postmidnight quadrant.

Khurana, Krishan K.↗
NASA NTRS1993

Propagation of high frequency jet noise using geometric acoustics

Spherical directivity of noise radiated from a convecting quadrupole source embedded in an arbitrary spreading jet is obtained by ray-tracing methods of geometrical acoustics. The six propagation equations are solved in their general form in a rectangular coordinate system. The noise directivity in the far field is calculated by applying an iteration scheme that finds the required radiation angles at the source resulting in propagation through a given observer point. Factors influencing the zone of silence are investigated. The caustics of geometrical acoustics and the exact locations where it forms is demonstrated by studying the variation in ray tube area obtained from transport equation. For a ring source convecting along the center-axis of an axisymmetric jet, the polar directivity of the radiated noise is obtained by an integration with respect to azimuthal directivity of compact quadrupole sources distributed on the ring. The Doppler factor is shown to vary slightly from point to point on the ring. Finally the scaling of the directivity pattern with power -3 of Doppler factor is investigated and compared with experimental data.

Khavaran, A.↗
NASA NTRS1993

An evaluation of three spatial differencing schemes for the discrete ordinates method in participating media

Three popular spatial differencing schemes for the discrete ordinates method are examined for two-dimensional Cartesian coordinates system. These are a positive, the step, and the diamond schemes. Contrary to the common belief that negative intensities will not occur when fine spatial discretization is used with the diamond scheme, under certain conditions, the diamond scheme will produce negative intensities irrespective of the number of control volums employed. The positive scheme can produce physically unrealistic trends. The diamond and positive schemes are also capable of producing physically unrealistic overshoots. In absorbing-emitting or absorbing-emitting-scattering media, grid refinement can result in negative intensities when the diamond or positive scheme is used.

Chai, John C.↗
NASA NTRS1993

On the generation of secondary motion in circular to rectangular transition ducts

A computer code has been developed for the calculation of three-dimensional turbulent flow in circular to rectangular transition ducts. The governing equations are written in a general curvilinear coordinate system so that all singly-connected geometrical configurations can be accommodated. Turbulence closure is through the standard k-epsilon model or a Reynolds stress closure model. Computed results show qualitative agreement with experimental data. Pressure-induced secondary flow is the dominant mode through the transition, but turbulence-induced secondary flow becomes prominent some distance downstream of the transition.

Demuren, A. O.↗
NASA NTRS1993

Waverider design for generalized shock geometries

A new design method for waverider configurations with generalized shock geometries is presented. A cross-stream Euler marching procedure is used to define the post-shock flow field, and an arbitrary 3D shock shape is specified as an input. This approach makes it possible to use nonaxisymmetric shock topologies with nonconstant shock strengths. The problem is reformulated in the proper curvilinear coordinate system to suppress its fundamental ill-posedness.

Jones, K. D.↗
NASA NTRS1992

Geodesy and cartography

An overview of geodesy and cartography of Mars over the past century is presented. The modern exploration began with the Mariner 4, 6, and 7 flyby missions, followed by the Mariner 9 and Viking missions that mapped the entire surface of Mars. The primary modern changes to the coordinate system have led to improved measurements of the rotational period, the direction of the spin axis, and the size and shape of Mars. Planimetric mapping based on Mariner 9 pictures began with a 1:25-M-scale sheet and 30 1:5-M-scale sheets that covered the entire Martian surface. The quality of the Viking Orbiter pictures was greatly improved over Mariner 9 and led to the publication of 140 controlled photomosaic sheets at a scale of 1:2 M. Two digital data bases have been compiled for Mars - the digital image model and the digital terrain model.

Davies, Merton E.↗
NASA NTRS1992

Thermocapillary Bubble Migration - An Oseen-Like Analysis of the Energy Equation

The thermocapillary migration of a bubble in a liquid possessing a temperature gradient is analyzed in the limit of large Reynolds and Marangoni numbers. Crespo and Manuel (1983) performed an analysis in this limit wherein energy conduction is completely neglected and obtained the bubble migration velocity using energy dissipation arguments. In the present analysis, performed in a coordinate system moving with the bubble, the velocity field in the convection term in the energy equation is approximated in an Oseen-like manner by replacing it with the velocity field far away from the bubble (i.e., the migration velocity of the bubble). Conduction is retained to satisfy the zero conductive heat flux boundary condition on the bubble surface. An approximate solution has been obtained for the Oseen-like energy equation. The bubble velocity obtained using energy dissipation considerations is in agreement with the result of Crespo and Manuel. The solution shows the thermal boundary layer and wake structure in the vicinity of the bubble. The Oseen-like analysis, however, has inherent limitations, as the flow penetrates the bubble surface. These issues are discussed and the result are compared to those in the literature.

Balasubramaniam, R.↗
NASA NTRS1993

The structure of a three-dimensional turbulent boundary layer

The three-dimensional turbulent boundary layer is shown to have a self-consistent two-layer asymptotic structure in the limit of large Reynolds number. In a streamline coordinate system, the streamwise velocity distribution is similar to that in two-dimensional flows, having a defect-function form in the outer layer which is adjusted to zero at the wall through an inner wall layer. An asymptotic expansion accurate to two orders is required for the cross-stream velocity which is shown to exhibit a logarithmic form in the overlap region. The inner wall-layer flow is collateral to leading order but the influence of the pressure gradient, at large but finite Reynolds numbers, is not negligible and can cause substantial skewing of the velocity profile near the wall. Conditions under which the boundary layer achieves self-similarity and the governing set of ordinary differential equations for the outer layer are derived. The calculated solution of these equations is matched asymptotically to an inner wall-layer solution and the composite profiles so formed describe the flow throughout the entire boundary layer. The effects of Reynolds number and cross-stream pressure gradient on the crossstream velocity profile are discussed and it is shown that the location of the maximum cross-stream velocity is within the overlap region.

Degani, A. T.↗
NASA NTRS1993

Multigrid methods and high order finite difference for flow in transition - Effects of isolated and distributed roughness elements

The high order finite difference and multigrid methods have been successfully applied to direct numerical simulation (DNS) for flow transition in 3D channels and 3D boundary layers with 2D and 3D isolated and distributed roughness in a curvilinear coordinate system. A fourth-order finite difference technique on stretched and staggered grids, a fully-implicit time marching scheme, a semicoarsening multigrid method associated with line distributive relaxation scheme, and a new treatment of the outflow boundary condition, which needs only a very short buffer domain to damp all wave reflection, are developed. These approaches make the multigrid DNS code very accurate and efficient. This makes us not only able to do spatial DNS for the 3D channel and flat plate at low computational costs, but also able to do spatial DNS for transition in the 3D boundary layer with 3D single and multiple roughness elements. Numerical results show good agreement with the linear stability theory, the secondary instability theory, and a number of laboratory experiments.

Liu, C.↗
NASA NTRS1993

Burnett solutions along the stagnation line of a cooled cylinder in low-density hypersonic flows

The Burnett equations in the cylindrical coordinate system have been applied to the hypersonic flow over a cylinder in low density environments. Through a local similarity transformation, the Burnett equations are degenerated into nonlinear third-order ordinary differential equations which are only valid along the stagnation line. These equations are solved by the multi-staged Runge-Kutta integration technique. Steady state solutions are asymptotically reached by the time-marching procedure. A newly-developed computer code is used to solve both the Navier-Stokes and the Burnett equations within the shock layer. The computed heat transfer coefficients are consistent with wind-tunnel and STS flight data. Comparisons with the DSMC solutions and the Boltzmann solutions show that the Burnett equations are more appropriate as the governing equations than the Navier-Stokes equations in the transitional flow regime.

Liaw, G. S.↗
NASA NTRS1993

Effect of curvature on stationary crossflow instability of a three-dimensional boundary layer

An incompressible three-dimensional laminar boundary-layer flow over a swept wing is used as a model to study both the wall-curvature and streamline-curvature effects on the stationary crossflow instability. The basic state is obtained by solving the full Navier-Stokes (N-S) equations numerically. The linear disturbance equations are cast on a fixed, body-intrinsic, curvilinear coordinate system. Those nonparallel terms which contribute mainly to the streamline-curvature effect are retained in the formulation of the disturbance equations and approximated by their local finite difference values. The resulting eigenvalue problem is solved by a Chebyshev collocation method. The present results indicate that the convex wall curvature has a stabilizing effect, whereas the streamline curvature has a destabilizing effect. A validation of these effects with an N-S solution for the linear disturbance flow is provided.

Lin, Ray-Sing↗
NASA NTRS1992

Sensor fusion IV: Control paradigms and data structures; Proceedings of the Meeting, Boston, MA, Nov. 12-15, 1991

Various papers on control paradigms and data structures in sensor fusion are presented. The general topics addressed include: decision models and computational methods, sensor modeling and data representation, active sensing strategies, geometric planning and visualization, task-driven sensing, motion analysis, models motivated biology and psychology, decentralized detection and distributed decision, data fusion architectures, robust estimation of shapes and features, application and implementation. Some of the individual subjects considered are: the Firefly experiment on neural networks for distributed sensor data fusion, manifold traversing as a model for learning control of autonomous robots, choice of coordinate systems for multiple sensor fusion, continuous motion using task-directed stereo vision, interactive and cooperative sensing and control for advanced teleoperation, knowledge-based imaging for terrain analysis, physical and digital simulations for IVA robotics.

Schenker, Paul S.↗
NASA NTRS1993

2D axisymmetric analysis of SRM ignition transient

To analyze ignition transient of Space Shuttle solid rocket motor, a transient two-dimensional numerical model based on turbulent compressible Navier-Stokes equations in a generalized coordinate system was developed. One-dimensional numerical models (Peretz et al., 1973; Han, 1992; Pardue and Han, 1992) with empirical correlations data obtained from steady turbulent boundary layer flows agrees reasonably well with test rocket data by adjusting a few parameters. However, a 1D model can not provide a physical insight into the complex multidimensional thermal fields and flowfields in the chamber and the converging-diverging rocket nozzle. As an interim step, a 2D model was developed and compared with test data. A modified version of SIMPLE algorithm was used for the numerical model, and the standard k-epsilon model with a wall function was used for turbulence closure. Transient flowfields and thermal fields in the combustion chamber and the attached nozzle were obtained for a selected rocket geometry and propellant. Transient behaviors of the flow and thermal fields were analyzed, and were found to be in good agreement with physical expectations.

Bai, S. D.↗
NASA NTRS1993

Diffraction analysis of frequency selective reflector antennas

In this paper, a unified computational technique is presented which allows the incorporation of the curved frequency-selective surface (FSS) geometry in the computation of the reflector antenna radiation pattern. The scattered fields from an illuminated FSS reflector are formalized using Huygens' principle in such a way that the 'reflecting' and the 'transparent' FSS subreflector cases are treated identically and the thickness of the FSS subreflector remains arbitrary. The analysis utilizes local surface coordinates to describe the reflection/transmission matrices of the FSS subreflector where it is assumed that these matrices are available. In most cases one may use the local tangent plane for approximating the plane of the FSS in the local coordinate surface of the reflector. The paper demonstrates how the local curved coordinate system can be introduced in the diffraction modeling of FSS reflectors and its importance in accurately predicting the side-lobe and crosspolarization levels. Results of numerical simulations are presented for several FSS subreflector configurations.

Rahmat-Samii, Yahya↗
NASA NTRS1993

Design of a reading test for low vision image warping

NASA and the University of Houston College of Optometry are examining the efficacy of image warping as a possible prosthesis for at least two forms of low vision - maculopathy and retinitis pigmentosa. Before incurring the expense of reducing the concept to practice, one would wish to have confidence that a worthwhile improvement in visual function would result. NASA's Programmable Remapper (PR) can warp an input image onto arbitrary geometric coordinate systems at full video rate, and it has recently been upgraded to accept computer-generated video text. We have integrated the Remapper with an SRI eye tracker to simulate visual malfunction in normal observers. A reading performance test has been developed to determine if the proposed warpings yield an increase in visual function; i.e., reading speed. We will describe the preliminary experimental results of this reading test with a simulated central field defect with and without remapped images.

Loshin, David S.↗
NASA NTRS1952

Axisymmetric supersonic flow in rotating impellers

General equations are developed for isentropic, frictionless, axisymmetric flow in rotating impellers with blade thickness taken into account and with blade forces eliminated in favor of the blade-surface function. It is shown that the total energy of the gas relative to the rotating coordinate system is dependent on the stream function only, and that if the flow upstream of the impeller is vortex-free, a velocity potential exists which is a function of only the radial and axial distances in the impeller. The characteristic equations for supersonic flow are developed and used to investigate flows in several configurations in order to ascertain the effect of variations of the boundary conditions on the internal flow and the work input. Conditions varied are prerotation of the gas, blade turning rate, gas velocity at the blade tips, blade thickness, and sweep of the leading edge.

Goldstein, Arthur W↗