SEARCH · Engineering Papers

Results for “rectangular 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.

SourceResearch connectionFrom yearThrough year

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

At least 145 records · Page 8

All sources NASA NTRS DOE OSTI

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 NTRS1996

Solwnd: A 3D Compressible MHD Code for Solar Wind Studies. Version 1.0: Cartesian Coordinates

Solwnd 1.0 is a three-dimensional compressible MHD code written in Fortran for studying the solar wind. Time-dependent boundary conditions are available. The computational algorithm is based on Flux Corrected Transport and the code is based on the existing code of Zalesak and Spicer. The flow considered is that of shear flow with incoming flow that perturbs this base flow. Several test cases corresponding to pressure balanced magnetic structures with velocity shear flow and various inflows including Alfven waves are presented. Version 1.0 of solwnd considers a rectangular Cartesian geometry. Future versions of solwnd will consider a spherical geometry. Some discussions of this issue is presented.

Deane, Anil E.↗

NASA NTRS1990

Three-dimensional solutions for antisymmetrically laminated anisotropic plates

Analytic three-dimensional elasticity solutions are presented for the stress and free vibration problems of multilayered anisotropic plates. The plates are assumed to have rectangular geometry and antisymmetric lamination with respect to the middle plane. A mixed formulation is used with the fundamental unknowns consisting of the six stress components and the three displacement components of the plate. Each of the plate variables is decomposed into symmetric and antisymmetric components in the thickness direction, and is expressed in terms of a double Fourier series in the Cartesian surface coordinates. Extensive numerical results are presented showing the effects of variation in the lamination and geometric parameters of composite plates on the importance of the transverse stress and strain components.

Noor, Ahmed K.↗

NASA NTRS1983

Numerical simulation of electrothermal de-icing systems

Transient simulations of de-icing of composite aircraft components by electrothermal heating have been computed for both one and two-dimensional rectangular geometries. The implicit Crank-Nicolson formulation is used to insure stability of the finite-differenced heat conduction equations and the phase change in the ice layer is simulated using the Enthalpy method. Numerical solutions illustrating de-icer performance for various composite aircraft blades and environmental conditions are presented. Comparisons are made with previous studies and with available experimental data. Initial results using a coordinate mapping technique to describe the actual blade geometry are discussed.

De Witt, K. J.↗

NASA NTRS1977

Numerical solution of three-dimensional free turbulent shear flows

Numerical results are presented for three-dimensional compressible turbulent jet and wake flows. An alternating direction implicit numerical procedure is used to solve the finite-difference form of the parabolic elliptic Navier-Stokes equations. A coordinate transformation maps the boundaries at infinity into a finite computational domain in order to properly specify infinity boundary conditions as well as contain the downstream growth of the viscous flow field in a fixed computational grid. Turbulence closure is achieved through an algebraic mixing length eddy viscosity model. Numerical results for supersonic flow are presented for an axisymmetric jet, an elliptical jet, an elliptical wake, and two interacting rectangular jets. Experimental data were not available for comparison with the numerical results. However, the results compare well with empirical results for free shear flows.

Oh, Y. H.↗

NASA NTRS1981

Solutions of the Helmholtz equation with boundary conditions for force-free magnetic fields

It is shown that the solution, with one ignorable coordinate, for the Taylor minimum energy state (resulting in a force-free magnetic field) in either a straight cylindrical or a toroidal geometry with arbitrary cross section can be reduced to the solution of either an inhomogeneous Helmholtz equation or a Grad-Shafranov equation with simple boundary conditions. Standard Green's function theory is, therefore, applicable. Detailed solutions are presented for the Taylor state in toroidal and cylindrical domains having a rectangular cross section. The focus is on solutions corresponding to the continuous eigenvalue spectra. Singular behavior at 90 deg corners is explored in detail.

Rasband, S. N.↗

NASA NTRS1993

Streamwise computation of three-dimensional flows using two stream functions

An approach to compute 3D flows using two stream functions is presented. The independent variables used are chi, a spatial coordinate, and xi and eta, values of stream functions along two sets of suitably chosen intersecting stream surfaces. The dependent variables used are the streamwise velocity, and two functions that describe the stream surfaces. Since the value of a stream function is constant along the solid boundaries, this choice of variables makes it easy to satisfy the boundary conditions. To illustrate the approach, computations of incompressible potential flow through a circular-to-rectangular transition duct are also presented.

Greywall, M. S.↗

NASA NTRS1996

The Multigrid-Mask Numerical Method for Solution of Incompressible Navier-Stokes Equations

A multigrid-mask method for solution of incompressible Navier-Stokes equations in primitive variable form has been developed. The main objective is to apply this method in conjunction with the pseudospectral element method solving flow past multiple objects. There are two key steps involved in calculating flow past multiple objects. The first step utilizes only Cartesian grid points. This homogeneous or mask method step permits flow into the interior rectangular elements contained in objects, but with the restriction that the velocity for those Cartesian elements within and on the surface of an object should be small or zero. This step easily produces an approximate flow field on Cartesian grid points covering the entire flow field. The second or heterogeneous step corrects the approximate flow field to account for the actual shape of the objects by solving the flow field based on the local coordinates surrounding each object and adapted to it. The noise occurring in data communication between the global (low frequency) coordinates and the local (high frequency) coordinates is eliminated by the multigrid method when the Schwarz Alternating Procedure (SAP) is implemented. Two dimensional flow past circular and elliptic cylinders will be presented to demonstrate the versatility of the proposed method. An interesting phenomenon is found that when the second elliptic cylinder is placed in the wake of the first elliptic cylinder a traction force results in a negative drag coefficient.

Ku, Hwar-Ching↗

NASA NTRS2013

Experimental Validation of Numerical Simulations for an Acoustic Liner in Grazing Flow

A coordinated experimental and numerical simulation effort is carried out to improve our understanding of the physics of acoustic liners in a grazing flow as well our computational aeroacoustics (CAA) method prediction capability. A numerical simulation code based on advanced CAA methods is developed. In a parallel effort, experiments are performed using the Grazing Flow Impedance Tube at the NASA Langley Research Center. In the experiment, a liner is installed in the upper wall of a rectangular flow duct with a 2 inch by 2.5 inch cross section. Spatial distribution of sound pressure levels and relative phases are measured on the wall opposite the liner in the presence of a Mach 0.3 grazing flow. The computer code is validated by comparing computed results with experimental measurements. Good agreements are found. The numerical simulation code is then used to investigate the physical properties of the acoustic liner. It is shown that an acoustic liner can produce self-noise in the presence of a grazing flow and that a feedback acoustic resonance mechanism is responsible for the generation of this liner self-noise. In addition, the same mechanism also creates additional liner drag. An estimate, based on numerical simulation data, indicates that for a resonant liner with a 10% open area ratio, the drag increase would be about 4% of the turbulent boundary layer drag over a flat wall.

Tam, Christopher K. W.↗

NASA NTRS1989

Development and application of a program to calculate transonic flow around an oscillating three-dimensional wing using finite difference procedures

A finite difference method for solving the unsteady transonic flow about harmonically oscillating wings is investigated. The procedure is based on separating the velocity potential into steady and unsteady parts and linearizing the resulting unsteady differential equation for small disturbances. The differential equation for the unsteady potential is linear with spatially varying coefficients and with the time variable eliminated by assuming harmonic motion. Difference equations are derived for harmonic transonic flow to include a coordinate transformation for swept and tapered planforms. A pilot program is developed for three-dimensional planar lifting surface configurations (including thickness) for the CRAY-XMP at Boeing Commercial Airplanes and for the CYBER VPS-32 at the NASA Langley Research Center. An investigation is made of the effect of the location of the outer boundaries on accuracy for very small reduced frequencies. Finally, the pilot program is applied to the flutter analysis of a rectangular wing.

Weatherill, Warren H.↗

NASA NTRS1984

Vibration and buckling of general periodic lattice structures

A method is presented for vibration and buckling analysis of arbitrary lattice structures having repetitive geometry in any combination of coordinate directions. The approach is based on exact member theory for representing the stiffness of an individual member subject to axial load, and in the case of vibration, undergoing harmonic oscillation. The method is an extension of previous work that was limited to specific geometries. The resulting eigenvalue problem is of the size associated with the repeating element of the structure. A computer program has been developed incorporating the theory and results are given for vibration of rectangular platforms and a large antenna structure having rotational symmetry. Buckling and vibration results for cable-stiffened rings are also given.

Anderson, M. S.↗

NASA NTRS1989

EAC: A program for the error analysis of STAGS results for plates

A computer code is now available for estimating the error in results from the STAGS finite element code for a shell unit consisting of a rectangular orthotropic plate. This memorandum contains basic information about the computer code EAC (Error Analysis and Correction) and describes the connection between the input data for the STAGS shell units and the input data necessary to run the error analysis code. The STAGS code returns a set of nodal displacements and a discrete set of stress resultants; the EAC code returns a continuous solution for displacements and stress resultants. The continuous solution is defined by a set of generalized coordinates computed in EAC. The theory and the assumptions that determine the continuous solution are also outlined in this memorandum. An example of application of the code is presented and instructions on its usage on the Cyber and the VAX machines have been provided.

Sistla, Rajaram↗

NASA NTRS1989

A numerically exact full wave packet approach to molecule-surface scattering

A numerically exact spectral method for solving the time-dependent Schroedinger equation in spherical coordinates is described. The angular dependence of the wave function is represented on a two-dimensional grid of evenly spaced points. The fast Fourier transform algorithm is used to transform between the angle space representation of the wave function and its conjugate representation in momentum space. The time propagation of the wave function is evaluated using an expansion of the time evolution operator as a series of Chebyshev polynomials. Calculations performed for a model system representing H2 scattering from a rectangular corrugated surface yield transition probabilities that are in excellent agreement with those obtained using the close-coupling wave packet (CCWP) method. However, the new method is found to require substantially more computation time than the CCWP method because of the large number of grid points needed to represent the angular dependence of the wave function and the variation in the number of terms required in the Chebyshev representation of the time evolution operator.

Mowrey, R. C.↗

NASA NTRS2004

Compact Optoelectronic Compass

A compact optoelectronic sensor unit measures the apparent motion of the Sun across the sky. The data acquired by this chip are processed in an external processor to estimate the relative orientation of the axis of rotation of the Earth. Hence, the combination of this chip and the external processor finds the direction of true North relative to the chip: in other words, the combination acts as a solar compass. If the compass is further combined with a clock, then the combination can be used to establish a threeaxis inertial coordinate system. If, in addition, an auxiliary sensor measures the local vertical direction, then the resulting system can determine the geographic position. This chip and the software used in the processor are based mostly on the same design and operation as those of the unit described in Micro Sun Sensor for Spacecraft (NPO-30867) elsewhere in this issue of NASA Tech Briefs. Like the unit described in that article, this unit includes a small multiple-pinhole camera comprising a micromachined mask containing a rectangular array of microscopic pinholes mounted a short distance in front of an image detector of the active-pixel sensor (APS) type (see figure). Further as in the other unit, the digitized output of the APS in this chip is processed to compute the centroids of the pinhole Sun images on the APS. Then the direction to the Sun, relative to the compass chip, is computed from the positions of the centroids (just like a sundial). In the operation of this chip, one is interested not only in the instantaneous direction to the Sun but also in the apparent path traced out by the direction to the Sun as a result of rotation of the Earth during an observation interval (during which the Sun sensor must remain stationary with respect to the Earth). The apparent path of the Sun across the sky is projected on a sphere. The axis of rotation of the Earth lies at the center of the projected circle on the sphere surface. Hence, true North (not magnetic North), relative to the chip, can be estimated from paths of the Sun images across the APS. In a test, this solar compass has been found to yield a coarse estimate of the North (within tens of degrees) in an observation time of about ten minutes. As expected, the accuracy was found to increase with observation time: after a few hours, the estimated direction of the rotation axis becomes accurate to within a small fraction of a degree.

Christian, Carl↗

NASA NTRS2004

Micro Sun Sensor for Spacecraft

A report describes the development of a compact micro Sun sensor for use as a part of the attitude determination subsystem aboard future miniature spacecraft and planetary robotic vehicles. The prototype unit has a mass of only 9 g, a volume of only 4.2 cm(sup 3), a power consumption of only 30 mW, and a 120 degree field of view. The unit has demonstrated an accuracy of 1 arcminute. The unit consists of a multiple pinhole camera: A micromachined mask containing a rectangular array of microscopic pinholes, machined utilizing the microectromechanical systems (MEMS), is mounted in front of an active-pixel sensor (APS) image detector. The APS consists of a 512 x 512-pixel array, on-chip 10-bit analog to digital converter (ADC), on-chip bias generation, and on-chip timing control for self-sequencing and easy programmability. The digitized output of the APS is processed to compute the centroids of the pinhole Sun images on the APS. The Sun angle, relative to a coordinate system fixed to the sensor unit, is then computed from the positions of the centroids.

Mobasser, Sohrab↗

NASA NTRS1986

Tests with three-dimensional adjustments in the rectangular working section of the French T2 wind tunnel with an AS 07-type swept-back wing model

The results obtained on the AS 07 wing and the working section walls for three types of configurations are reported. The first, called non-adapted, corresponds to the divergent upper and lower rectilinear walls which compensate for limit layer thickening. It can serve as a basis for complete flow calculations. The second configuration corresponds to wall shapes determined from calculations which tend to minimize interference at the level of the fuselage. Finally, the third configuration, called two-dimensional adaptation, uses the standard method for T2 profile tests. This case was tested to determine the influence of wall shape and error magnitude. These results are not sufficient to validate the three-dimensional adaptation; they must be coordinated with calculations or with unlimited atmosphere tests.

Blanchard, A.↗

NASA NTRS1978

The practical application of a finite difference method for analyzing transonic flow over oscillating airfoils and wings

Separating the velocity potential into steady and unsteady parts and linearizing the resulting unsteady equations for small disturbances was performed. The steady velocity potential was obtained first from the well known nonlinear equation for steady transonic flow. The unsteady velocity potential was then obtained from a linear differential equation in complex form with spatially varying coefficients. Since sinusoidal motion is assumed, the unsteady equation is independent of time. The results of an investigation into the relaxation-solution-instability problem was discussed. Concepts examined include variations in outer boundary conditions, a coordinate transformation so that the boundary condition at infinity may be applied to the outer boundaries of the finite difference region, and overlapping subregions. The general conclusion was that only a full direct solution in which all unknowns are obtained at the same time will avoid the solution instabilities of relaxation. An analysis of the one-dimensional form of the unsteady transonic equation was studied to evaluate errors between exact and finite difference solutions. Pressure distributions were presented for a low-aspect-ratio clipped delta wing at Mach number of 0.9 and for a moderate-aspect-ratio rectangular wing at a Mach number of 0.875.

Weatherill, W. H.↗

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.↗