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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.

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At least 163 records · Page 9
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NASA NTRS1976

Split Space-Marching Finite-Volume Method for Chemically Reacting Supersonic Flow

A space-marching finite-volume method employing a nonorthogonal coordinate system and using a split differencing scheme for calculating steady supersonic flow over aerodynamic shapes is presented. It is a second-order-accurate mixed explicit-implicit procedure that solves the inviscid adiabatic and nondiffusive equations for chemically reacting flow in integral conservation-law form. The relationship between the finite-volume and differential forms of the equations is examined and the relative merits of each discussed. The method admits initial Cauchy data situated on any arbitrary surface and integrates them forward along a general curvilinear coordinate, distorting and deforming the surface as it advances. The chemical kinetics term is split from the convective terms which are themselves dimensionally split, thereby freeing the fluid operators from the restricted step size imposed by the chemical reactions and increasing the computational efficiency. The accuracy of this splitting technique is analyzed, a sufficient stability criterion is established, a representative flow computation is discussed, and some comparisons are made with another method.

Rizzi, Arthur W.↗
NASA NTRS1992

Development of new flux splitting schemes

Maximizing both accuracy and efficiency has been the primary objective in designing a numerical algorithm for computational fluid dynamics (CFD). This is especially important for solutions of complex three dimensional systems of Navier-Stokes equations which often include turbulence modeling and chemistry effects. Recently, upwind schemes have been well received for their capability in resolving discontinuities. With this in mind, presented are two new flux splitting techniques for upwind differencing. The first method is based on High-Order Polynomial Expansions (HOPE) of the mass flux vector. The second new flux splitting is based on the Advection Upwind Splitting Method (AUSM). The calculation of the hypersonic conical flow demonstrates the accuracy of the splitting in resolving the flow in the presence of strong gradients. A second series of tests involving the two dimensional inviscid flow over a NACA 0012 airfoil demonstrates the ability of the AUSM to resolve the shock discontinuity at transonic speed. A third case calculates a series of supersonic flows over a circular cylinder. Finally, the fourth case deals with tests of a two dimensional shock wave/boundary layer interaction.

Liou, Meng-Sing↗
NASA NTRS1985

Recent advances in computational transonic aerodynamics

The near-term prospects are discussed for calculation of viscous transonic flow fields about realistic configurations at full-scale Reynolds numbers. Three basic algorithms are considered: The central-difference, three-factor ADI method; the central-difference, explicit, multistep Runge-Kutta method with multigrid acceleration; and the relaxation method for the upwind-differenced, flux-split equations. Each method has distinct advantages and disadvantages regarding stability, convergence rate, and vectorizability. It appears that computation times can be 15 to 60 hours on the latest super computers unless 3D algorithms are improved to perform as well as current 2D algorithms.

South, J. C., Jr.↗
NASA NTRS1936

A method of estimating the aerodynamic effects of ordinary and split flaps of airfoils similar to the Clark Y

An empirical method is given for estimating the aerodynamic effect of ordinary and split flaps on airfoils similar to the Clark Y. The method is based on a series of charts that have been derived from an analysis of existing wind-tunnel data. Factors are included by which such variables as flap location, flap span, wing aspect ratio, and wing taper may be taken into account. A series of comparisons indicate that the method would be suitable for use in making preliminary performance calculations and in structural design.

Pearson, H A↗
NASA NTRS2011

Split-screen display system and standardized methods for ultrasound image acquisition and multi-frame data processing

A standardized acquisition methodology assists operators to accurately replicate high resolution B-mode ultrasound images obtained over several spaced-apart examinations utilizing a split-screen display in which the arterial ultrasound image from an earlier examination is displayed on one side of the screen while a real-time "live" ultrasound image from a current examination is displayed next to the earlier image on the opposite side of the screen. By viewing both images, whether simultaneously or alternately, while manually adjusting the ultrasound transducer, an operator is able to bring into view the real-time image that best matches a selected image from the earlier ultrasound examination. Utilizing this methodology, dynamic material properties of arterial structures, such as IMT and diameter, are measured in a standard region over successive image frames. Each frame of the sequence has its echo edge boundaries automatically determined by using the immediately prior frame's true echo edge coordinates as initial boundary conditions. Computerized echo edge recognition and tracking over multiple successive image frames enhances measurement of arterial diameter and IMT and allows for improved vascular dimension measurements, including vascular stiffness and IMT determinations.

Selzer, Robert H.↗
NASA NTRS1991

Automated cloud screening of AVHRR imagery using split-and-merge clustering

Previous methods to segment clouds from ocean in AVHRR imagery have shown varying degrees of success, with nighttime approaches being the most limited. An improved method of automatic image segmentation, the principal component transformation split-and-merge clustering (PCTSMC) algorithm, is presented and applied to cloud screening of both nighttime and daytime AVHRR data. The method combines spectral differencing, the principal component transformation, and split-and-merge clustering to sample objectively the natural classes in the data. This segmentation method is then augmented by supervised classification techniques to screen clouds from the imagery. Comparisons with other nighttime methods demonstrate its improved capability in this application. The sensitivity of the method to clustering parameters is presented; the results show that the method is insensitive to the split-and-merge thresholds.

Gallaudet, Timothy C.↗
NASA NTRS1984

Universal single level implicit algorithm for gasdynamics

A single level effectively explicit implicit algorithm for gasdynamics is presented. The method meets all the requirements for unconditionally stable global iteration over flows with mixed supersonic and supersonic zones including blunt body flow and boundary layer flows with strong interaction and streamwise separation. For hyperbolic (supersonic flow) regions the method is automatically equivalent to contemporary space marching methods. For elliptic (subsonic flow) regions, rapid convergence is facilitated by alternating direction solution sweeps which bring both sets of eigenvectors and the influence of both boundaries of a coordinate line equally into play. Point by point updating of the data with local iteration on the solution procedure at each spatial step as the sweeps progress not only renders the method single level in storage but, also, improves nonlinear accuracy to accelerate convergence by an order of magnitude over related two level linearized implicit methods. The method derives robust stability from the combination of an eigenvector split upwind difference method (CSCM) with diagonally dominant ADI(DDADI) approximate factorization and computed characteristic boundary approximations.

Lombard, C. K.↗
NASA NTRS2019

Entropy Stable Method for the Euler Equations Revisited: Central Differencing via Entropy Splitting and SBP

The two decades old high order central differencing via entropy splitting and summation-by-parts (SBP) difference boundary closure of Olsson & Oliger, Gerritsen & Olsson, and Yee et al. (15, 7, 37) is revisited. The objective of this paper is to prove for the first time that the entropy split scheme is an entropy stable method for central differencing with SBP operators for both periodic and non-periodic boundary conditions for nonlinear Euler equations. Standard high order spatial central differencing as well as high order central spatial DRP (dispersion relation preserving) spatial differencing is part of the entropy stable methodology framework. The proof is to replace the spatial derivatives by summation-by-parts (SBP) difference operators in the entropy split form of the equations using the physical entropy of the Euler equations. The numerical boundary closure follows directly from the SBP operator. No additional numerical boundary procedure is required. In contrast, Tadmor-type entropy conserving schemes (31) using mathematical entropies and more recently in (35], do not naturally come with a numerical boundary closure and a generalized SBP operator has to be developed (18). Long time integration of 2D and 3D test cases is included to show the comparison of this efficient entropy stable method with the Tadmor-type of entropy conservative methods. Studies also include the comparison among the three skew-symmetric splittings on their nonlinear stability and accuracy performance without added numerical dissipations for smooth flows. These are, namely, entropy splitting, Ducros et al. splitting and the Kennedy & Grubber splitting.

Sjogreen, Bjorn↗
NASA NTRS1989

Flux-vector splitting for unsteady calculations on dynamic meshes

The method of flux vector splitting used is that of Van Leer. The fluxes split in this manner have the advantage of being continuously differentiable at eigenvalue sign changes and this allows normal shocks to be captured with at most two interior zones, although in practice only one zone is usually observed. The fluxes as originally derived, however did not include the necessary terms appropriate for calculations on a dynamic mesh. The extension of the splitting to include these terms while retaining the advantages of the original splitting is the main purpose of this investigation. In addition, the use of multiple grids to reduce the computer time is investigated. A subiterative procedure to eliminate factorization and linearization error so that larger time steps can be used is also investigated.

Anderson, W. Kyle↗
NASA NTRS2020

Shape Estimation for Elongated Deformable Object using B-spline Chained Multiple Random Matrices Model

In this paper, a B-spline chained multiple random matrix models (RMMs) representation is proposed to model geometric characteristics of an elongated deformable object. The hyper degrees of freedom structure of the elongated deformable object make its shape estimation challenging. Based on the likelihood function of the proposed B-spline chained multiple RMMs, an expectation-maximization (EM) method is derived to estimate the shape of the elongated deformable object. A split and merge method based on the Euclidean minimum spanning tree (EMST) is proposed to provide initialization for the EM algorithm. The proposed algorithm is evaluated for the shape estimation of the elongated deformable objects in scenarios, such as the static rope with various configurations (including configurations with intersection), the continuous manipulation of a rope and a plastic tube, and the assembly of two plastic tubes. The execution time is computed and the accuracy of the shape estimation results is evaluated based on the comparisons between the estimated width values and its ground-truth, and the intersection over union (IoU) metric.

Gang Yao↗
NASA NTRS1981

A preliminary study of relaxation methods for the inviscid conservative gasdynamics equations using flux splitting

Plus minus flux vector split schemes are combined with the multigrid relaxation method to obtain fast rates of iterative (or steady state) convergence. On model nonlifting biconvex airfoil flow, steady state convergence is obtained using multigrid in 40 iteractions for subsonic cases and in 120 iterations for transonic cases. A 65 x 33 stretched grid is used. However, the multigrid scheme used here (and there are numerous variations) sometimes could not be made to work for transonic cases with a large number of supersonic points. Moreover, the multigrid method is only several times faster than the conventional algorithm which itself could perhaps be accelerated by other means. Nethertheless, with proper adjustment the multigrid method will ultimately lead to very fast rates of iterative convergence.

Steger, J. L.↗
NASA NTRS1989

Free-vibration characteristics and correlation of a space station split-blanket solar array

Two methods for studying the free-vibration characteristics of a large split-blanket solar array in a zero-g cantilevered configuration are presented. The zero-g configuration corrresponds to an on-orbit configuration of the Space Station solar array. The first method applies the equations of continuum mechanics to determine the natural frequencies of the array; the second uses the finite element method program, MSC/NASTRAN. The stiffness matrix from the NASTRAN solution was found to be erroneously grounded. The results from the two methods are compared. It is concluded that the grounding does not seriously compromise the solution to the elastic modes of the solar array. However, the correct rigid body modes need to be included to obtain the correct dynamic model.

Carney, Kelly S.↗
NASA NTRS1989

Free-vibration characteristics and correlation of a Space Station split-blanket solar array

Two methods for studying the free-vibration characteristics of a large split-blanket solar array in a zero-g cantilevered configuration are presented. The zero-g configuration corresponds to an on-orbit configuration of the Space Station solar array. The first method applies the equations of continuum mechanics to determine the natural frequencies of the array; the second uses the finite element method program, MSC/NASTRAN. The stiffness matrix from the NASTRAN solution was found to be erroneously grounded. The results from the two methods are compared. It is concluded that the grounding does not seriously compromise the solution to the elastic modes of the solar array. However, the correct rigid body modes need to be icluded to obtain the correct dynamic model.

Carney, Kelly S.↗
NASA NTRS1994

On Bi-Grid Local Mode Analysis of Solution Techniques for 3-D Euler and Navier-Stokes Equations

A procedure is presented for utilizing a bi-grid stability analysis as a practical tool for predicting multigrid performance in a range of numerical methods for solving Euler and Navier-Stokes equations. Model problems based on the convection, diffusion and Burger's equation are used to illustrate the superiority of the bi-grid analysis as a predictive tool for multigrid performance in comparison to the smoothing factor derived from conventional von Neumann analysis. For the Euler equations, bi-grid analysis is presented for three upwind difference based factorizations, namely Spatial, Eigenvalue and Combination splits, and two central difference based factorizations, namely LU and ADI methods. In the former, both the Steger-Warming and van Leer flux-vector splitting methods are considered. For the Navier-Stokes equations, only the Beam-Warming (ADI) central difference scheme is considered. In each case, estimates of multigrid convergence rates from the bi-grid analysis are compared to smoothing factors obtained from single-grid stability analysis. Effects of grid aspect ratio and flow skewness are examined. Both predictions are compared with practical multigrid convergence rates for 2-D Euler and Navier-Stokes solutions based on the Beam-Warming central scheme.

Ibraheem, S. O.↗
NASA NTRS1996

A Method to Analyze and Optimize the Load Sharing of Split Path Transmissions

Split-path transmissions are promising alternatives to the common planetary transmissions for rotorcraft. Heretofore, split-path designs proposed for or used in rotorcraft have featured load-sharing devices that add undesirable weight and complexity to the designs. A method was developed to analyze and optimize the load sharing in split-path transmissions without load-sharing devices. The method uses the clocking angle as a design parameter to optimize for equal load sharing. In addition, the clocking angle tolerance necessary to maintain acceptable load sharing can be calculated. The method evaluates the effects of gear-shaft twisting and bending, tooth bending, Hertzian deformations within bearings, and movement of bearing supports on load sharing. It was used to study the NASA split-path test gearbox and the U.S. Army's Comanche helicopter main rotor gearbox. Acceptable load sharing was found to be achievable and maintainable by using proven manufacturing processes. The analytical results compare favorably to available experimental data.

Krantz, Timothy L.↗
NASA NTRS2019

Entropy Stable Method for the Euler Equations Revisited: Central Differencing via Entropy Splitting and SBP

The two decades old high order central differencing via entropy splitting and summation-by-parts (SBP) difference boundary closure of Ols- son & Oliger (1994), Gerritsen & Olsson (1996), and Yee et al. (2000) is revisited. The entropy splitting is a form of skew-symmetric splitting of the nonlinear Euler flux derivatives. Central differencing applied to the entropy splitting form of the Euler flux derivatives together with SBP difference operators will, hereafter, be referred to as entropy split schemes. This study is prompted by the recent growing interest in numerical methods for which a discrete entropy conservation law holds, a discrete global entropy conservation can be proved and/or the numerical method possesses a stable entropy in the framework of SBP difference operators and L2-energy norm estimate. The objective of this paper is to recast the entropy split scheme as the re- cent definition of an entropy stable method for central differencing with SBP operators for both periodic and non-periodic boundary conditions for non- linear Euler equations. Standard high order spatial central differencing as well as high order central spatial DRP (dispersion relation preserving) spatial differencing is part of the entropy stable methodology framework. Long time integration of 2D and 3D test cases is included to show the comparison of this efficient entropy stable method with the Tadmor-type of entropy conservative methods. Studies also include the comparison among the three skew-symmetric splittings on their nonlinear stability and accuracy performance without added numerical dissipations for smooth flows. These are, namely, entropy splitting, Ducros et al. splitting and the Kennedy & Grub- ber splitting.

Sjogreen, Bjorn↗
NASA NTRS1981

Eliminating gaps in split rings

Simple installation method allows thinner, lighter tether rings than conventional procedures, saving expensive materials. Installer inverts ring with pliers before it is slid over cable, then returns it to its original position after installation. Ring is in correct orientation, and coils are tightly compressed for high reliability fastening.

Gould, R. W.↗
NASA NTRS1988

Accurate solutions, parameter studies and comparisons for the Euler and potential flow equations

Parameter studies are conducted using the Euler and potential flow equation models for steady and unsteady flows in both two and three dimensions. The Euler code is an implicit, upwind, finite volume code which uses the Van Leer method of flux vector splitting which has been recently extended for use on dynamic meshes and maintain all the properties of the original splitting. The potential flow code is an implicit, finite difference method for solving the transonic small disturbance equations and incorporates both entropy and vorticity corrections into the solution procedures thereby extending its applicability into regimes where shock strength normally precludes its use. Parameter studies resulting in benchmark type calculations include the effects of spatial and temporal refinement, spatial order of accuracy, far field boundary conditions for steady flow, frequency of oscillation, and the use of subiterations at each time step to reduce linearization and factorization errors. Comparisons between Euler and potential flow results are made, as well as with experimental data where available.

Anderson, W. Kyle↗