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At least 127 records · Page 7

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NASA NTRS1990

Analysis and design of optimized truncated scarfed nozzles subject to external flow effects

Rao's method for computing optimum thrust nozzles is modified to study the effects of external flow on the performance of a class of exhaust nozzles. Members of this class are termed scarfed nozzles. These are two-dimensional, nonsymmetric nozzles with a flat lower wall. The lower wall (the cowl) is truncated in order to save weight. Results from a parametric investigation are presented to show the effects of the external flowfield on performance.

Shyne, Rickey J.↗

NASA NTRS1989

Compressible flow calculations employing the Galerkin/least-squares method

A multielement group, domain decomposition algorithm is presented for solving linear nonsymmetric systems arising in the finite-element analysis of compressible flows employing the Galerkin/least-squares method. The iterative strategy employed is based on the generalized minimum residual (GMRES) procedure originally proposed by Saad and Shultz. Two levels of preconditioning are investigated. Applications to problems of high-speed compressible flow illustrate the effectiveness of the scheme.

Shakib, F.↗

NASA NTRS1990

Stationary and nonstationary random vibrations of laminated composite plates via a higher order theory

Higher order shear deformation theory is utilized to study he weakly stationary and nonstationary random vibrations of cross-ply laminated plates. Normal mode method, in conjunction with the biorthogonality condition, for the nonsymmetric differential equations is applied. Detailed derivation is given for the governing equations, biorthogonality condition, the generalized mass and the generalized forces. Results are listed for a plate which is simply supported at all the edges, and subjected to a point load which is either timewise stationary or nonstationary random process.

Elishakoff, Isaac↗

NASA NTRS1990

Analysis and design of optimized truncated scarfed nozzles subject to external flow effects

Shyne, Rickey J.↗

NASA NTRS1990

Development of a two-dimensional zonally averaged statistical-dynamical model. III - The parameterization of the eddy fluxes of heat and moisture

A number of perpetual January simulations are carried out with a two-dimensional zonally averaged model employing various parameterizations of the eddy fluxes of heat (potential temperature) and moisture. The parameterizations are evaluated by comparing these results with the eddy fluxes calculated in a parallel simulation using a three-dimensional general circulation model with zonally symmetric forcing. The three-dimensional model's performance in turn is evaluated by comparing its results using realistic (nonsymmetric) boundary conditions with observations. Branscome's parameterization of the meridional eddy flux of heat and Leovy's parameterization of the meridional eddy flux of moisture simulate the seasonal and latitudinal variations of these fluxes reasonably well, while somewhat underestimating their magnitudes. New parameterizations of the vertical eddy fluxes are developed that take into account the enhancement of the eddy mixing slope in a growing baroclinic wave due to condensation, and also the effect of eddy fluctuations in relative humidity. The new parameterizations, when tested in the two-dimensional model, simulate the seasonal, latitudinal, and vertical variations of the vertical eddy fluxes quite well, when compared with the three-dimensional model, and only underestimate the magnitude of the fluxes by 10 to 20 percent.

Stone, Peter H.↗

NASA NTRS1990

Viscous three-dimensional analyses for nozzles for hypersonic propulsion

A Navier-Stokes computer code was validated using a number of two- and three-dimensional configurations for both laminar and turbulent flows. The validation data covers a range of freestream Mach numbers from 3 to 14, including wall pressures, velocity pressure, and skin friction. Nozzle flow fields computed for a generic scramjet nozzle from Mach 3 to 20, wall pressures, wall skin friction values, heat transfer values, and overall performance are presented. In addition, three-dimensional solutions obtained for two asymmetric, single expansion ramp nozzles at a pressure ratio of 10 consists of the internal expansion region in the converging/diverging sections and the external superonic exhaust in a quiescent ambient environment. The fundamental characteristics that were captured successfully include expansion fans; Mach wave reflections; mixing layers; and nonsymmetrical, multiple inviscid cell, supersonic exhausts. Comparison with experimental data for wall pressure distributions at the center planes shows good agreement.

Harloff, G. J.↗

NASA NTRS1991

Theoretical evaluation of engine auxiliary inlet design for supersonic V/STOL aircraft

A higher order panel method is used to evaluate the potential flow of a 2-D supersonic V/STOL inlet. A nonsymmetric analytical inlet model is developed to closely match a wind tunnel model tested at NASA-Lewis. The analytical inlet used is analyzed for flow characteristics around the lower cowl lip and auxiliary inlets. The results for this analysis are obtained for the output of a computer program produced by the McDonnell Douglas Corp. This program is based on the Hess Panel Method which determines source strengths of panel distributed over a 3-D body. The analytical model was designed for the implementation of a drooped/translated cowl lip and auxiliary inlets as flow improvement concepts. A 40 or 70 deg droop lip can be incorporated on the inlet to determine if these geometry changes result in flow improvements which may reduce the propensity for flow separation on the interior portion of the lip. Auxiliary inlets are used to decrease the mass flow over the inlet lip; thus, the peak flow velocity is reduced at the lip which also lessens the likelihood of flow separation on the interior portion of the lip. A 2, 4, and 6 in. translated lip can be used to also decrease mass flow over the inlet lower lip in the same manner.

Boles, Michael A.↗

NASA NTRS1991

Airborne observations of electric fields around growing and decaying cumulus clouds

Airborne electric field data were gathered in an atmospheric electrification study near Cape Canaveral, FL. A Learjet 36A was instrumented with eight electric field meters (mills) and five different particle probes. The local electric field enhancements at each field mill site were determined under lab conditions and verified using in-flight data. The overdetermined system of eight equations (one for each field mill) was solved using a weighted least squares algorithm to compute the magnitude and direction of the ambient electric field. The signal processing system allowed the measured data to be expressed in terms of earth coordinates, regardless of the attitude of the aircraft. Thus, it was possible to take maximum advantage of the Learjet's speed and maneuverability in studying the electric field structure in the vicinity of the clouds. Data gathered while circling just outside the boundary of a growing cumulus cloud show a nonsymmetric pattern of electric field strength. Field intensity grew rapidly over a period of less than 10 minutes. The observed direction of the ambient electric field vector can be explained by an ascending motion of the charge centers of a classic tripole model of a thunderstorm.

Giori, K. L.↗

NASA NTRS1990

QMR: A Quasi-Minimal Residual method for non-Hermitian linear systems

The biconjugate gradient (BCG) method is the natural generalization of the classical conjugate gradient algorithm for Hermitian positive definite matrices to general non-Hermitian linear systems. Unfortunately, the original BCG algorithm is susceptible to possible breakdowns and numerical instabilities. A novel BCG like approach is presented called the quasi-minimal residual (QMR) method, which overcomes the problems of BCG. An implementation of QMR based on a look-ahead version of the nonsymmetric Lanczos algorithm is proposed. It is shown how BCG iterates can be recovered stably from the QMR process. Some further properties of the QMR approach are given and an error bound is presented. Finally, numerical experiments are reported.

Freund, Roland W.↗

NASA NTRS1991

An implementation of the look-ahead Lanczos algorithm for non-Hermitian matrices

The nonsymmetric Lanczos method can be used to compute eigenvalues of large sparse non-Hermitian matrices or to solve large sparse non-Hermitian linear systems. However, the original Lanczos algorithm is susceptible to possible breakdowns and potential instabilities. An implementation is presented of a look-ahead version of the Lanczos algorithm that, except for the very special situation of an incurable breakdown, overcomes these problems by skipping over those steps in which a breakdown or near-breakdown would occur in the standard process. The proposed algorithm can handle look-ahead steps of any length and requires the same number of matrix-vector products and inner products as the standard Lanczos process without look-ahead.

Freund, Roland W.↗

NASA NTRS1991

A biconjugate gradient type algorithm on massively parallel architectures

The biconjugate gradient (BCG) method is the natural generalization of the classical conjugate gradient algorithm for Hermitian positive definite matrices to general non-Hermitian linear systems. Unfortunately, the original BCG algorithm is susceptible to possible breakdowns and numerical instabilities. Recently, Freund and Nachtigal have proposed a novel BCG type approach, the quasi-minimal residual method (QMR), which overcomes the problems of BCG. Here, an implementation is presented of QMR based on an s-step version of the nonsymmetric look-ahead Lanczos algorithm. The main feature of the s-step Lanczos algorithm is that, in general, all inner products, except for one, can be computed in parallel at the end of each block; this is unlike the other standard Lanczos process where inner products are generated sequentially. The resulting implementation of QMR is particularly attractive on massively parallel SIMD architectures, such as the Connection Machine.

Freund, Roland W.↗

NASA NTRS1990

Computational challenge - Euler solution for ellipses

The present treatment of the inviscid flow past an ellipse via the numerical solution of the Euler equations yields a lifting solution for any combination of grid and/or angle of attack which is nonsymmetric, in order to illustrate the CFD challenge posed by this unusual flow behavior. The results obtained call into question the general capability and validity of numerical Euler results in the realm of conventional difference methods; specifically, the mechanism generating lifting results is not understood, and the problem's resolution is not yet in sight.

Pulliam, Thomas H.↗

NASA NTRS1991

MHD simulations of magnetic reconnection in a skewed three-dimensional tail configuration

The dynamic evolution of a nonsymmetric magnetotail configuration initiated by the sudden occurrence of (anomalous) resistivity are examined using a three-dimensional resistive MHD simulation developed by Birn (1990) that includes a net cross-tail field and thus breaks the mirror symmetry around the neutral sheet. Results show that the field evolution is similar to that of a symmetric configuration studied by Birn and Hones (1981), pointing to the formation and ejection of a plasmoid. On the other hand, the topological structure of the magnetic field, defined by the field line connections, was remarkably different from the symmetric case. The plasmoid in this case became 'open', connected initially with the earth but gradually becoming connected with the interplanetary field. The openness of the plasmoid and its magnetic connection with interplanetary field lines suggest the possibility of a heat flux out of the plasmoid on interconnected flux tubes.

Birn, J.↗

NASA NTRS1990

Implementation of two projection methods on a shared memory multiprocessor - DEC VAX 6240

The relative performance of two iterative schemes, based on projection techniques, is compared on a shared memory multiprocessor - VAX 6240. The CG accelerated Block-SSOR method and the CG accelerated Symmetric-Kaczmarz method are considered for the solution of large sparse nonsymmetric systems of linear equations. It is shown that the regular structure of many matrices can be exploited by the CG-accelerated Block-SSOR method to provide good speedup in a multiprocessing environment. However, the CG accelerated Symmetric-Kaczmarz method, while being a viable alternative on a scalar machine, is unable to benefit from multiprocessing.

Kamath, C.↗

NASA NTRS1991

Modeling the Orion nebula as an axisymmetric blister

The ionized gas in the Orion nebula is examined by means of axisymmetric modeling that is based on observational data from the ionized, neutral, and molecular regions. Nonsymmetrical features are omitted, radial dependence from the Trapezium is assumed, and azimuthal symmetry in the plane of the sky is used. Stellar properties and abundances of certain elements are described, and these data are used to compare the present axisymmetric-blister model to a previous spherical model. Strong singly-ionized emission that are visible near the Trapezium are found to originate in the ionization-bounded region in the dense Trapezium zone. The model can be more tightly constrained by adding near-IR data on noncentral zones for (Ar II), (AR III), (Ne II), and (S IV). The quadrant with the 'bar' creates an nonsymmetry that influences the observational data, and the model can therefore be improved with the additional data.

Rubin, R. H.↗

NASA NTRS1990

An implementation of the look-ahead Lanczos algorithm for non-Hermitian matrices, part 1

The nonsymmetric Lanczos method can be used to compute eigenvalues of large sparse non-Hermitian matrices or to solve large sparse non-Hermitian linear systems. However, the original Lanczos algorithm is susceptible to possible breakdowns and potential instabilities. We present an implementation of a look-ahead version of the Lanczos algorithm which overcomes these problems by skipping over those steps in which a breakdown or near-breakdown would occur in the standard process. The proposed algorithm can handle look-ahead steps of any length and is not restricted to steps of length 2, as earlier implementations are. Also, our implementation has the feature that it requires roughly the same number of inner products as the standard Lanczos process without look-ahead.

Freund, Roland W.↗

NASA NTRS1989

Numerical methods in Markov chain modeling

Several methods for computing stationary probability distributions of Markov chains are described and compared. The main linear algebra problem consists of computing an eigenvector of a sparse, usually nonsymmetric, matrix associated with a known eigenvalue. It can also be cast as a problem of solving a homogeneous singular linear system. Several methods based on combinations of Krylov subspace techniques are presented. The performance of these methods on some realistic problems are compared.

Philippe, Bernard↗

NASA NTRS1989

Conjugate gradient type methods for linear systems with complex symmetric coefficient matrices

We consider conjugate gradient type methods for the solution of large sparse linear system Ax equals b with complex symmetric coefficient matrices A equals A(T). Such linear systems arise in important applications, such as the numerical solution of the complex Helmholtz equation. Furthermore, most complex non-Hermitian linear systems which occur in practice are actually complex symmetric. We investigate conjugate gradient type iterations which are based on a variant of the nonsymmetric Lanczos algorithm for complex symmetric matrices. We propose a new approach with iterates defined by a quasi-minimal residual property. The resulting algorithm presents several advantages over the standard biconjugate gradient method. We also include some remarks on the obvious approach to general complex linear systems by solving equivalent real linear systems for the real and imaginary parts of x. Finally, numerical experiments for linear systems arising from the complex Helmholtz equation are reported.

Freund, Roland↗