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 847 records · Page 47
All sourcesNASA NTRSDOE OSTI
NASA NTRS1977

An implicit shock-fitting scheme for unsteady transonic flow computations

The alternating-direction implicit scheme developed by NASA Ames for unsteady transonic flows has been modified to include a shock-fitting algorithm as well as an analytically stretched coordinate system. The shock-fitting procedure treats shock waves as discontinuities normal to the free stream. Improvements in shock position and the unsteady pressure distributions are obtained by this modification. The various types of shock motion observed experimentally by Tijdeman are well simulated in calculations using the modified computational scheme. The method of detecting shock wave formation and the procedure for fitting a moving shock wave are illustrated. Results for a pulsating parabolic arc airfoil and for an NACA 64A006 airfoil with oscillating quarter-chord flap are presented and discussed.

Yu, N. J.↗
NASA NTRS1977

Description of path-in-the-sky contact analog piloting display

A contact analog display called Path-In-The-Sky (PITS) integrates information on airplane attitude, airplane kinematic performance, navigation situation, and path prediction into one instrument. The pictorial format utilized in the PITS display concept was designed to reduce the required instrument scan and to simplify interpretation of informtion with the objective of reducing pilot work load. Described are the symbology of the PITS display, the coordinate systems used to generate the display, and the magnitudes of pertinent geometric characteristics selected during the display development. Also included are examples of the PITS display generated on a stand-alone graphics computer.

Knox, C. E.↗
NASA NTRS1977

A two-scale scattering model with application to the JONSWAP '75 aircraft microwave scatterometer experiment

The general problem of bistatic scattering from a two scale surface was evaluated. The treatment was entirely two-dimensional and in a vector formulation independent of any particular coordinate system. The two scale scattering model was then applied to backscattering from the sea surface. In particular, the model was used in conjunction with the JONSWAP 1975 aircraft scatterometer measurements to determine the sea surface's two scale roughness distributions, namely the probability density of the large scale surface slope and the capillary wavenumber spectrum. Best fits yield, on the average, a 0.7 dB rms difference between the model computations and the vertical polarization measurements of the normalized radar cross section. Correlations between the distribution parameters and the wind speed were established from linear, least squares regressions.

Wentz, F. J.↗
NASA NTRS1978

Numerical solution of the Navier-Stokes equations for super-sonic flows with strong shocks

The numerical solution of the full Navier-Stokes Equations for viscous flows with high Mach numbers and a strong detached bow shock was obtained. Two dimensional flows around a circular cylinder, and a circular cylinder with an aft-body in the form of a fairing, were considered. The solution of the compressible N.S. equations was accomplished by the method of finite differences. An implicit scheme of solution, the S.O.R., was used with the optimum acceleration parameters determined by trial and error. The tensor notation was used in writing the N-S Equations transformed into general curvilinear coordinates. The equations for the generation of the coordinate system were solved, followed by the solution of the N.S. equations, at the end of a set of given number of time steps. "Wiggles", constituted the one major problem that needed to be overcome. These oscillations give rise to quantities such as negative temperatures, which ultimately caused the computational program to break down. Certain dissipative finite-difference schemes damped these oscillations.

Devarayalu, K.↗
NASA NTRS1970

The far field diffraction pattern for corner reflectors with complex reflection coefficients

The far field diffraction pattern of a geometrically perfect corner reflector is examined analytically for normally incident monochromatic light. The states of polarization and the complex amplitudes of the emerging light are expressed through transformation matrices in terms of those of the original incident light for each sextant of the face in a single coordinate system. The analytic expression of the total diffraction pattern is obtained for a circular face. This expression consists of three component functions in addition to the basic Airy function. The coefficient of each function is expressed in terms of complex coefficients of reflectance of the reflecting surface. Some numerical results for different reflecting surfaces, including total internal reflection, are presented. The iso-intensity contours of the diffraction pattern evaluated from the analytical expressions for an uncoated solid corner reflector are also presented along with the photographs of the pattern.

Chang, R. F.↗
NASA NTRS1978

Equations of motion and two-equation turbulence model for plane or axisymmetric turbulent flows in body-oriented orthogonal curvilinear coordinates and mass-averaged dependent variables

The full Navier-Stokes time-dependent, compressible, turbulent, mean-flow equations in mass-averaged variables for plane or axisymmetric flow are presented. The equations are derived in a body-oriented, orthogonal, curvilinear coordinate system. Turbulence is modelled by a system of two equations for mass-averaged turbulent kinetic energy and dissipation rate proposed. These equations are rederived and some new features are discussed. A system of second order boundary layer equations is then derived which includes the effects of longitudinal curvature and the normal pressure gradient. The Wilcox and Chambers approach is used in considering effects of streamline curvature on turbulence phenomena in turbulent boundary layer type flows. Their two-equation turbulence model with curvature terms are rederived for the cases considered in the present report. The derived system equations serves as a basis for an investigation of problems where streamline curvature is of the order of the characteristic length in the longitudinal direction.

Sislian, J. P.↗
NASA NTRS1978

Earth orientation from lunar laser range-differencing

For the optimal use of high precision lunar laser ranging (LLR), an investigation regarding a clear definition of the underlying coordinate systems, identification of estimable quantities, favorable station geometry and optimal observation schedule is given.

Leick, A.↗
NASA NTRS1977

Computational models for the analysis of three-dimensional internal and exhaust plume flowfields

This paper describes computational procedures developed for the analysis of three-dimensional supersonic ducted flows and multinozzle exhaust plume flowfields. The models/codes embodying these procedures cater to a broad spectrum of geometric situations via the use of multiple reference plane grid networks in several coordinate systems. Shock capturing techniques are employed to trace the propagation and interaction of multiple shock surfaces while the plume interface, separating the exhaust and external flows, and the plume external shock are discretely analyzed. The computational grid within the reference planes follows the trace of streamlines to facilitate the incorporation of finite-rate chemistry and viscous computational capabilities. Exhaust gas properties consist of combustion products in chemical equilibrium. The computational accuracy of the models/codes is assessed via comparisons with exact solutions, results of other codes and experimental data. Results are presented for the flows in two-dimensional convergent and divergent ducts, expansive and compressive corner flows, flow in a rectangular nozzle and the plume flowfields for exhausts issuing out of single and multiple rectangular nozzles.

Dash, S. M.↗
NASA NTRS1977

Data handling for the geometric correction of large images

Several geometric distortions are present in remotely sensed images depending on the type of sensors and the object being observed. It is often desirable to compensate for these distortions and store the images in reference to a standard coordinate system. Digital techniques for correction are versatile and introduce a minimum of radiometric errors. The main problems to be considered in this area are the determination of the corrective transformation, resampling, and the management of the large quantities of data. It is shown that, by a judicious rearrangement of the input data, considerable reductions in the required memory capacity can be achieved. The rearrangement can be accomplished in several stages. The method presented here is amenable to pipeline implementation for processing a continuous stream of images.

Ramapriyan, H. K.↗
NASA NTRS1978

Calculation of unsteady transonic flows using the integral equation method

The basic integral equations for a harmonically oscillating airfoil in a transonic flow with shock waves are derived; the reduced frequency is assumed to be small. The problems associated with shock wave motion are treated using a strained coordinate system. The integral equation is linear and consists of both line integrals and surface integrals over the flow field which are evaluated by quadrature. This leads to a set of linear algebraic equations that can be solved directly. The shock motion is obtained explicitly by enforcing the condition that the flow is continuous except at a shock wave. Results obtained for both lifting and nonlifting oscillatory flows agree satisfactorily with other accurate results.

Nixon, D.↗
NASA NTRS1978

Longitudinal control of Jovian magnetopause motion

The magnetopause crossings of the Pioneer 10 and 11 spacecraft in Jovian magnetic coordinates (system III) are largely restricted in longitude to one hemisphere of Jupiter. This hemisphere is the one that has been identified by Vasyliunas (1975) as the 'active hemisphere'. This finding is interpreted as indicating that the magnetopause of the active hemisphere moves inward and outward with a radial speed that is typically faster than that of the inactive hemisphere.

Dessler, A. J.↗
NASA NTRS1978

Viking Orbiter stereophotogrammetry

Orbit characteristics of the two Viking Orbiter spacecraft made possible the acquisition of high-resolution imagery of the Martian surface, resulting in many excellent convergent stereopairs. Evaluation of these stereopairs presented a few unconventional problems because the routine relative orientation was not feasible, mainly due to a lack of good passpoints and to the technical peculiarities of TV vidicon imaging techniques. One of the ways to circumvent these problems is to use the orbital and navigational parameters of the spacecraft for an external 'forced' relative orientation. This approach requires a number of rotations and counter-rotations between various coordinate systems, which may make the involved mathematics look rather complicated, but its computational applications become very simple, fast, accurate, and inexpensive.

Benesh, M.↗
NASA NTRS1978

Typhoon June /1975/ viewed by a scanning microwave spectrometer

Data were collected by the scanning microwave spectrometer onboard Nimbus 6 during the June 1975 typhoon in the Philippine Sea. The spectrometer was equipped with channels centered on 22.23 GHz (a water vapor band), 31.65 GHz (a transmittance window), and 52.85, 53.85, and 55.45 GHz (an oxygen band). Temperature maps, derived from oxygen band measurements, showed that the typhoon eye had a single peak varying in amplitude with time. Water line and window measurements were used to develop a coordinate system having mutually orthogonal atmospheric variables of column water-vapor content and cloud liquid-water content. Vapor measurements showed a maximum around the intensifying typhoon with a more developed structure during typhoon development. Values were extrapolated for surface wind speed and cloud liquid water vapor content by assuming the troposphere to be saturated with respect to the water vapor in the typhoon. Comparisons with infrared cloud imagery and aircraft flight data show different time variations, attributed to poor typhoon-eye resolution in the microwave images.

Rosenkranz, P. W.↗
NASA NTRS1978

Perturbations in two- and three-dimensional transonic flows

The difficulty of treating the perturbation of transonic flow, during which shock waves change position, can be overcome by using a distorted coordinate system in which the locations of all shock waves do not change; the distortion is found as part of the solution. This device leads to a relation that allows a range of flows, with differing shock locations, to be related algebraically to two known 'calibration' flows. Results for flows around finite wings, including those with multiple, intersecting shock waves, are presented. A typical computing time for such examples is 0.3 sec on a CDC 7600 computer.

Nixon, D.↗
NASA NTRS1978

Analysis of three-dimensional ducted and exhaust plume flowfields

Computational procedures are described for analyzing three-dimensional supersonic internal flows and multinozzle exhaust plume flowfields. The computer codes (BIGMAC and CHAR3D) embodying these procedures cater to a broad spectrum of geometric situations via the use of multiple reference plane grid networks in several coordinate systems. Shock capturing techniques are employed to trace the propagation and interaction of multiple shock surfaces. Gas properties consist of combustion products in chemical equilibrium. The computational accuracy of the codes is assessed via comparisons with the results of other codes and experimental data. Results are presented for the flows in two-dimensional ducts, corner flows, flow in a rectangular nozzle, and the plume flowfields for exhausts issuing out of single and multiple rectangular nozzles.

Dash, S. M.↗
NASA NTRS1978

Direct numerical solution of the transonic perturbation integral equation for lifting and nonlifting airfoils

The linear transonic perturbation integral equation previously derived for nonlifting airfoils is formulated for lifting cases. In order to treat shock wave motions, a strained coordinate system is used in which the shock location is invariant. The tangency boundary conditions are either formulated using the thin airfoil approximation or by using the analytic continuation concept. A direct numerical solution to this equation is derived in contrast to the iterative scheme initially used, and results of both lifting and nonlifting examples indicate that the method is satisfactory.

Nixon, D.↗
NASA NTRS1976

Transonic flow calculations

The development of relaxation methods to calculate transonic flows is discussed. Rather accurate predictions can be made for a number of flows of interest using the transonic potential flow equation, which may be derived from the Euler equations for inviscid compressible flow by introducing the assumption that the flow is irrotational. Once the choice of a mathematical model has been settled, the numerical procedure for actually computing a solution contains two main elements: the construction of a discrete approximation which converges to the solution of the continuous problem in the limit as the mesh width is reduced to zero, and the solution of the resulting set of nonlinear difference equations by a convergent iterative scheme. The choice of an appropriate coordinate system and its influence on the accuracy of the discrete approximation is discussed. Several applications of the general method are described.

Jameson, A.↗