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At least 1,171 records · Page 65

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NASA NTRS1990

A review of reduced Navier-Stokes computations for compressible viscous flows

A reduced form of the Navier-Stokes equations, defined by a single composite of the Euler, boundary layer, and triple deck approximations, is considered for the computation of viscous interacting flows. Global pressure or pseudopotential relaxation methods are integrated with coupled sparse matrix direct solvers or coupled strongly implicit ILU algorithms to efficiently capture sharp shocks and regions of recirculation. Solutions are obtained for a variety of 2D and 3D geometries and for Mach numbers (M) spanning the range from incompressible (M = 0) to supersonic (M = 6) flow.

Rubin, S. G.↗

NASA NTRS1998

Algebraic Nonoverlapping Domain Decomposition Methods for Stabilized FEM and FV Discretizations

We consider preconditioning methods for convection dominated fluid flow problems based on a nonoverlapping Schur complement domain decomposition procedure for arbitrary triangulated domains. The triangulation is first partitioned into a number of subdomains and interfaces which induce a natural 2 x 2 partitioning of the p.d.e. discretization matrix. We view the Schur complement induced by this partitioning as an algebraically derived coarse space approximation. This avoids the known difficulties associated with the direct formation of an effective coarse discretization for advection dominated equations. By considering various approximations of the block factorization of the 2 x 2 system, we have developed a family of robust preconditioning techniques. A computer code based on these ideas has been developed and tested on the IBM SP2 using MPI message passing protocol. A number of 2-D CFD calculations will be presented for both scalar advection-diffusion equations and the Euler equations discretized using stabilized finite element and finite volume methods. These results show very good scalability of the preconditioner for various discretizations as the number of processors is increased while the number of degrees of freedom per processor is fixed.

Barth, Timothy J.↗

NASA NTRS2005

Baseline Computational Fluid Dynamics Methodology for Longitudinal-Mode Liquid-Propellant Rocket Combustion Instability

A computational method for the analysis of longitudinal-mode liquid rocket combustion instability has been developed based on the unsteady, quasi-one-dimensional Euler equations where the combustion process source terms were introduced through the incorporation of a two-zone, linearized representation: (1) A two-parameter collapsed combustion zone at the injector face, and (2) a two-parameter distributed combustion zone based on a Lagrangian treatment of the propellant spray. The unsteady Euler equations in inhomogeneous form retain full hyperbolicity and are integrated implicitly in time using second-order, high-resolution, characteristic-based, flux-differencing spatial discretization with Roe-averaging of the Jacobian matrix. This method was initially validated against an analytical solution for nonreacting, isentropic duct acoustics with specified admittances at the inflow and outflow boundaries. For small amplitude perturbations, numerical predictions for the amplification coefficient and oscillation period were found to compare favorably with predictions from linearized small-disturbance theory as long as the grid exceeded a critical density (100 nodes/wavelength). The numerical methodology was then exercised on a generic combustor configuration using both collapsed and distributed combustion zone models with a short nozzle admittance approximation for the outflow boundary. In these cases, the response parameters were varied to determine stability limits defining resonant coupling onset.

Litchford, R. J.↗

NASA NTRS1976

A NASTRAN implementation of the doubly asymptotic approximation for underwater shock response

A detailed description is given of how the decoupling approximation known as the doubly asymptotic approximation is implemented with NASTRAN to solve shock problems for submerged structures. The general approach involves locating the nonsymmetric terms (which couple structural and fluid variables) on the right hand side of the equations. This approach results in coefficient matrices of acceptable bandwidth but degrades numerical stability, requiring a smaller time step size than would otherwise be used. It is also shown how the structure's added (virtual) mass matrix, is calculated with NASTRAN.

Everstine, G. C.↗

NASA NTRS1978

A reformulation of the Linear-Quadratic-Gaussian stochastic control problem for application to low thrust navigation analysis

The formulation of the classical Linear-Quadratic-Gaussian stochastic control problem as employed in low thrust navigation analysis is reviewed. A reformulation is then presented which eliminates a potentially unreliable matrix subtraction in the control calculations, improves the computational efficiency, and provides for a cleaner computational interface between the estimation and control processes. Lastly, the application of the U-D factorization method to the reformulated equations is examined with the objective of achieving a complete set of factored equations for the joint estimation and control problem.

Jacobson, R. A.↗

NASA NTRS1993

Preconditioned domain decomposition scheme for three-dimensional aerodynamic sensitivity analysis

A preconditioned domain decomposition scheme is introduced for the solution of the 3D aerodynamic sensitivity equation. This scheme uses the iterative GMRES procedure to solve the effective sensitivity equation of the boundary-interface cells in the sensitivity analysis domain-decomposition scheme. Excluding the dense matrices and the effect of cross terms between boundary-interfaces is found to produce an efficient preconditioning matrix.

Eleshaky, Mohammed E.↗

NASA NTRS1996

The Effect of Wake Passing on Turbine Blade Film Cooling

The effect of upstream blade row wake passing on the showerhead film cooling performance of a downstream turbine blade has been investigated through a combination of experimental and computational studies. The experiments were performed in a steady-flow annular turbine cascade facility equipped with an upstream rotating row of cylindrical rods to produce a periodic wake field similar to that found in an actual turbine. Spanwise, chordwise, and temporal resolution of the blade surface temperature were achieved through the use of an array of nickel thin-film surface gauges covering one unit cell of showerhead film hole pattern. Film effectiveness and Nusselt number values were determined for a test matrix of various injectants, injectant blowing ratios, and wake Strouhal numbers. Results indicated a demonstratable reduction in film effectiveness with increasing Strouhal number, as well as the expected increase in film effectiveness with blowing ratio. An equation was developed to correlate the span-average film effectiveness data. The primary effect of wake unsteadiness was found to be correlated well by a chordwise-constant decrement of 0.094-St. Measurable spanwise film effectiveness variations were found near the showerhead region, but meaningful unsteady variations and downstream spanwise variations were not found. Nusselt numbers were less sensitive to wake and injection changes. Computations were performed using a three-dimensional turbulent Navier-Stokes code which was modified to model wake passing and film cooling. Unsteady computations were found to agree well with steady computations provided the proper time-average blowing ratio and pressure/suction surface flow split are matched. The remaining differences were isolated to be due to the enhanced mixing in the unsteady solution caused by the wake sweeping normally on the pressure surface. Steady computations were found to be in excellent agreement with experimental Nusselt numbers, but to overpredict experimental film effectiveness values. This is likely due to the inability to match actual hole exit velocity profiles and the absence of a credible turbulence model for film cooling.

Heidmann, James David↗

NASA NTRS2004

Kalman Filter Estimation of Spinning Spacecraft Attitude using Markley Variables

There are several different ways to represent spacecraft attitude and its time rate of change. For spinning or momentum-biased spacecraft, one particular representation has been put forward as a superior parameterization for numerical integration. Markley has demonstrated that these new variables have fewer rapidly varying elements for spinning spacecraft than other commonly used representations and provide advantages when integrating the equations of motion. The current work demonstrates how a Kalman filter can be devised to estimate the attitude using these new variables. The seven Markley variables are subject to one constraint condition, making the error covariance matrix singular. The filter design presented here explicitly accounts for this constraint by using a six-component error state in the filter update step. The reduced dimension error state is unconstrained and its covariance matrix is nonsingular.

Sedlak, Joseph E.↗

NASA NTRS1989

On the parallel solution of parabolic equations

Parallel algorithms for the solution of linear parabolic problems are proposed. The first of these methods is based on using polynomial approximation to the exponential. It does not require solving any linear systems and is highly parallelizable. The two other methods proposed are based on Pade and Chebyshev approximations to the matrix exponential. The parallelization of these methods is achieved by using partial fraction decomposition techniques to solve the resulting systems and thus offers the potential for increased time parallelism in time dependent problems. Experimental results from the Alliant FX/8 and the Cray Y-MP/832 vector multiprocessors are also presented.

Gallopoulos, E.↗

NASA NTRS1976

Recursive partitioned inversion of large (1500 x 1500) symmetric matrices

A recursive algorithm was designed to invert large, dense, symmetric, positive definite matrices using small amounts of computer core, i.e., a small fraction of the core needed to store the complete matrix. The described algorithm is a generalized Gaussian elimination technique. Other algorithms are also discussed for the Cholesky decomposition and step inversion techniques. The purpose of the inversion algorithm is to solve large linear systems of normal equations generated by working geodetic problems. The algorithm was incorporated into a computer program called SOLVE. In the past the SOLVE program has been used in obtaining solutions published as the Goddard earth models.

Putney, B. H.↗

NASA NTRS1978

An implicit algorithm for the conservative transonic full potential equation using an arbitrary mesh

A new, implicit approximate factorization (AF) algorithm designed to solve the conservative full-potential equation for the transonic flow past arbitrary airfoils has been developed. The new algorithm uses an upwind bias of the density coefficient to provide stability in supersonic regions. This allows the simple two- and three-banded matrix form of the AF scheme to be retained over the entire flow field, even in regions of supersonic flow. A numerical transformation is used to establish an arbitrary body-fitted finite-difference mesh. Airfoil pressure distributions have been computed and are in good agreement with independent results.

Holst, T. L.↗

NASA NTRS1994

A linear method for analyzing lightning field changes

A constrained, least-squares method for analyzing multiple-station measurements of lightning field changes (delta Es) is introduced. Previous methods have attempted to fit the spatial pattern of lightning delta Es using nonlinear models, such as a point charge (Q) or a point dipole (P) model. With the linear method, the delta Es are described not by models but by a general volume charge distribution that is deposited on a large (40 x 40 x 20 cu km) Cartesian grid above the measuring network. A linear system of equations is used to relate the measured delta Es to the charges that are deposited at each grid point. With this approach, the information content of the measurements can be quantified by an eigenanalysis of the covariance matrix of the linear system. Constraints can be used to reduce the infinity of possible solutions to the linear system and also to reduce systematic biases that can be introduced by the method of solution. It is shown that a Landweber iterative method, derived from the general method of steepest descent, can be used to solve the linear system and that the resulting volume charge distributions are generally consistent with computer-simulated charge sources, when these sources are over the measuring network. The Landweber iteration has also provided solutions for natural lightning events that are consistent with Q- and P-model results.

Koshak, William J.↗

NASA NTRS1996

Micromechanics for particulate reinforced composites

A set of micromechanics equations for the analysis of particulate reinforced composites is developed using the mechanics of materials approach. Simplified equations are used to compute homogenized or equivalent thermal and mechanical properties of particulate reinforced composites in terms of the properties of the constituent materials. The microstress equations are also presented here to decompose the applied stresses on the overall composite to the microstresses in the constituent materials. The properties of a 'generic' particulate composite as well as those of a particle reinforced metal matrix composite are predicted and compared with other theories as well as some experimental data. The micromechanics predictions are in excellent agreement with the measured values.

Murthy, Pappu L. N.↗

NASA NTRS2009

Relation of Cloud Occurrence Frequency, Overlap, and Effective Thickness Derived from CALIPSO and CloudSat Merged Cloud Vertical Profiles

A cloud frequency of occurrence matrix is generated using merged cloud vertical profile derived from Cloud-Aerosol Lidar with Orthogonal Polarization (CALIOP) and Cloud Profiling Radar (CPR). The matrix contains vertical profiles of cloud occurrence frequency as a function of the uppermost cloud top. It is shown that the cloud fraction and uppermost cloud top vertical pro les can be related by a set of equations when the correlation distance of cloud occurrence, which is interpreted as an effective cloud thickness, is introduced. The underlying assumption in establishing the above relation is that cloud overlap approaches the random overlap with increasing distance separating cloud layers and that the probability of deviating from the random overlap decreases exponentially with distance. One month of CALIPSO and CloudSat data support these assumptions. However, the correlation distance sometimes becomes large, which might be an indication of precipitation. The cloud correlation distance is equivalent to the de-correlation distance introduced by Hogan and Illingworth [2000] when cloud fractions of both layers in a two-cloud layer system are the same.

Kato, Seiji↗

NASA NTRS2011

Interpretation of Impact Features on the Surface of the WFPC-2 Radiator

An examination of the Hubble Space Telescope (HST) Wide Field Planetary Camera 2 (WFPC-2) radiator assembly was conducted at NASA Goddard Space Flight Center (GSFC) during the summer of 2009. Immediately apparent was the predominance of impact features resident only in the thermal paint layer; similar phenomenology was observed during a prior survey of the WFPC-1 radiator. As well, larger impact features displayed spallation zones, darkened areas, and other features not encountered in impacts onto bare surfaces. Whereas the characterization of impact features by depth and diameter on unpainted surfaces has been long established, the mitigation provided by the painted layer presented a challenge to further analysis of the WFPC-2 features; a literature search revealed no systematic characterization of the ballistic limit equations of painted or coated surfaces. In order to characterize the impactors responsible for the observed damage, an understanding of the cratering and spallation phenomenology of the painted surface was required. To address that challenge, NASA sponsored a series of hypervelocity calibration shots at the White Sands Test Facility (WSTF). This effort required the following activities: the production, painting, and artificial ageing of test coupons in a manner similar to the actual radiator; the determination of the test matrix parameters projectile diameter and material (mass density), impact velocity, and impact angle, so as to enable both an adequate characterization of the impact by projectile and impact geometry and support hydrocode modeling to fill in and extend the applicability of the calibration shots; the selection of suitable projectiles; logistics; and an analysis of feature characteristics upon return of the coupons. This paper reports the results of the test campaign and presents ballistic limit equations for painted surfaces. We also present initial results of our interpretation methodologies.

Anz-Meador, P. D.↗

NASA NTRS1974

Estimation and detection of signals in multiplicative noise

We define a class of detection-estimation problems on matrix Lie groups in which the observation noise is multiplicative in nature. By examining the differential versions of the hypotheses, which are bilinear, we are able to derive the relevant likelihood ratio formula and the associated optimal estimation equations for the signal given the observations and the assumption that the signal is present. These estimation equations are of interest in their own right, in that they represent a finite-dimensional optimal solution to a nonlinear estimation problem and consist of a Kalman-Bucy filter along with the on-line computation of the solution of the associated Riccati equation, which is driven by the observations. The usefulness of these results is illustrated via an example concerning the detection of an actuator failure in a rigid-body rotational control system.

Willsky, A. S.↗

NASA NTRS1975

Multirate sampled-data systems analysis via vector operators

The primary difficulties of both the time-domain switch decomposition method and the frequency-domain decomposition method are overcome by introducing certain matrix operators and performing spectral factorization of resulting matrices of polynomials in the z-transform variable. Topological operations of the switch-decomposition method are simplified. This new approach eliminates the need to solve a system of equations with rational polynomial coefficients such as arises in the frequency-decomposition method. The determination of a multirate sampled-data system's characteristic polynomial no longer requires the evaluation of a determinant of rational polynomial elements. New results on obtaining modified z-transforms from standard z-transforms at a faster rate and vice versa are presented.

Boykin, W. H.↗

NASA NTRS1988

Numerically stable algorithm for discrete-ordinate-method radiative transfer in multiple scattering and emitting layered media

The transfer of monochromatic radiation in a scattering, absorbing, and emitting plane-parallel medium with a specified bidirectional reflectivity at the lower boundary is considered. The equations and boundary conditions are summarized. The numerical implementation of the theory is discussed with attention given to the reliable and efficient computation of eigenvalues and eigenvectors. Ways of avoiding fatal overflows and ill-conditioning in the matrix inversion needed to determine the integration constants are also presented.

Stamnes, Knut↗