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NASA NTRS1974

Hydrodynamic models of a cepheid atmosphere

A method for including the solution of the transfer equation in a standard Henyey type hydrodynamic code was developed. This modified Henyey method was used in an implicit hydrodynamic code to compute deep envelope models of a classical Cepheid with a period of 12(d) including radiative transfer effects in the optically thin zones. It was found that the velocity gradients in the atmosphere are not responsible for the large microturbulent velocities observed in Cepheids but may be responsible for the occurrence of supersonic microturbulence. It was found that the splitting of the cores of the strong lines is due to shock induced temperature inversions in the line forming region. The adopted light, color, and velocity curves were used to study three methods frequently used to determine the mean radii of Cepheids. It is concluded that an accuracy of 10% is possible only if high quality observations are used.

Karp, A. H.↗

NASA NTRS1995

Implementation of a multiblock sensitivity analysis method in numerical aerodynamic shape optimization

A multiblock sensitivity analysis method is applied in a numerical aerodynamic shape optimization technique. The Sensitivity Analysis Domain Decomposition (SADD) scheme which is implemented in this study was developed to reduce the computer memory requirements resulting from the aerodynamic sensitivity analysis equations. Discrete sensitivity analysis offers the ability to compute quasi-analytical derivatives in a more efficient manner than traditional finite-difference methods, which tend to be computationally expensive and prone to inaccuracies. The direct optimization procedure couples CFD analysis based on the two-dimensional thin-layer Navier-Stokes equations with a gradient-based numerical optimization technique. The linking mechanism is the sensitivity equation derived from the CFD discretized flow equations, recast in adjoint form, and solved using direct matrix inversion techniques. This investigation is performed to demonstrate an aerodynamic shape optimization technique on a multiblock domain and its applicability to complex geometries. The objectives are accomplished by shape optimizing two aerodynamic configurations. First, the shape optimization of a transonic airfoil is performed to investigate the behavior of the method in highly nonlinear flows and the effect of different grid blocking strategies on the procedure. Secondly, shape optimization of a two-element configuration in subsonic flow is completed. Cases are presented for this configuration to demonstrate the effect of simultaneously reshaping interfering elements. The aerodynamic shape optimization is shown to produce supercritical type airfoils in the transonic flow from an initially symmetric airfoil. Multiblocking effects the path of optimization while providing similar results at the conclusion. Simultaneous reshaping of elements is shown to be more effective than individual element reshaping due to the inclusion of mutual interference effects.

Lacasse, James M.↗

NASA NTRS2023

HLPW-4: Wall-Modeled LES and Lattice-Boltzmann Technology Focus Group Workshop Summary

A summary of the nine submissions to the Wall-Modeled LES and Lattice-Boltzmann(WMLESLB) Technical Focus Group (TFG) at the 4th High lift Prediction Workshop is provided. The focus of this TFG was to assess the current capabilities of WMLES and LB methods on a complex high-lift configuration across a wide range of angles-of-attack. Analysis of the submitted data suggests that>250𝑀spatial degrees of freedom are needed to accurately predict pitching moments at high angles-of-attack due to large pressure gradients present on the outboard slat and main element for 𝛼 >17◦(corrected for free-air). While some scatter is reported in pitching moment coefficient at the low-angles of attack (𝛼 <11◦) - excellent agreement is observed between submissions near the 𝐶𝐿,max state. Objective superiority of WMLES methods over RANS can be seen in terms of lack of excess outboard separation; a majority of the WMLES and LB submissions predict wedge-shaped separation patterns consistent with the experimental oil flow. The in-tunnel simulations show excellent agreement with the experiment in terms of a) integrated loads, b) surface flow-topology, and c) mechanism for the onset of inboard stall. Further evidence is provided to demonstrate both qualitative and quantitative superiority of the WMLES submissions over RANS.

TTT↗

NASA NTRS1985

Potential productivity benefits of float-zone versus Czochralski crystal growth

Efficient mass production of single-crystal silicon is necessary for the efficient silicon solar arrays needed in the coming decade. However, it is anticipated that there will be difficulty growing such volumes of crystals using conventional Czochralski (Cz) methods. While the productivity of single crystals might increase with a crystal diameter increase, there are two obstacles to the mass production of large diameter Czochralski crystals, the long production cycle due to slow growth rate and the high heat requirements of the furnaces. Also counterproductive would be the large resistivity gradient along the growth direction of the crystals due to impurity concentration. Comparison between Float zone (FZ) and Cz crystal growth on the basis of a crystal 150 mm in diameter is on an order of two to four times in favor of the FZ method. This advantage results from high growth rates and steady-state growth while maintaining a dislocation-free condition and impurity segregation.

Abe, T.↗

NASA NTRSDate not supplied

Towards a Third-Order Accurate, Second-Derivative-Free, Shock-Capturing Finite-Volume Method for Hypersonic Flows on Tetrahedral Grids

In this paper, we report progress in the development of a third-order accurate, second-derivative-free, shock-capturing finite-volume solver for three-dimensional unstructured grids. The method is economical in the sense that the computation and storage of second derivatives are not required for third-order accuracy. It is based on point-valued numerical solutions stored at cells, gradients computed and stored at nodes, and an efficient projected-derivative formula that eliminates the need for second derivatives in a quadratic solution interpolation. The projected-derivative formula is also used to eliminate second derivatives from a high-order flux quadrature formula, so that it can be implemented conveniently in the form of a numerical flux at a face center plus a correction term. Similarly, a high-order source quadrature formula can also be implemented in the form of a cell-center point evaluation plus a similar correction term. These features make it relatively straightforward to extend an existing second-order finite-volume code to third-order. This paper reports progress of implementing the method in the NASA VULCAN-CFD code and discusses the implementation of a high-order accurate limiter for shock capturing.

Weighted Least-Squares↗

NASA NTRS1972

A method for calculating aerodynamic heating on sounding rocket tangent ogive noses

A method is presented for calculating the aerodynamic heating and shear stresses at the wall for tangent ogive noses that are slender enough to maintain an attached nose shock through that portion of flight during which heat transfer from the boundary layer to the wall is significant. The lower entropy of the attached nose shock combined with the inclusion of the streamwise pressure gradient yields a reasonable estimate of the actual flow conditions. Both laminar and turbulent boundary layers are examined and an approximation of the effects of (up to) moderate angles-of-attack is included in the analysis. The analytical method has been programmed in FORTRAN 4 for an IBM 360/91 computer.

Wing, L. D.↗

NASA NTRS1973

A method for calculating aerodynamic heating on sounding rocket tangent ogive noses.

Wing, L. D.↗

NASA NTRS1971

Prediction of flow profiles in arteries from local measurements.

This paper develops an approximate numerical method for calculating flow profiles in arteries. The theory takes into account the nonlinear terms of the Navier-Stokes equations as well as the large deformations of the arterial wall. The method, assuming axially symmetric flow, determines velocity distribution and wall shear at a given location from the locally measured values of the pressure, pressure gradient, and pressure-radius relation. The computed results agree well with the corresponding experimental data.

Ling, S. C.↗

NASA NTRS1980

Surface tension-driven convections

The study of time-dependent flows generated by surface-tension gradients in thin liquid layers is reported. Numerical techniques for dealing with the complete float-zone process were investigated. In particular, finite element methods with fast iterative procedures, using multipoint constraints and nonlinear optimization were examined.

Ostrach, S.↗

NASA NTRS1981

Quantitative simulation of a magnetospheric substorm. I - Model logic and overview

Results of a comprehensive computer simulation of the behavior of the earth's inner magnetosphere during a substorm-type event are reported. It is pointed out that the computer model self-consistently computes electric fields, currents, and plasma distributions and velocities in the inner-magnetosphere/ionosphere system; parallel electric fields and ionospheric neutral winds, however, are not included. The basic equations of the model are derived, and the inputs are described. An overview of the results is also given. The first appendix contains derivations of general, useful laws of bounce-averaged gradient, curvature, and E x B drifts in a plasma with isotropic pitch angle distribution. The second appendix gives a description of the numerical method used in the simulation.

Harel, M.↗

NASA NTRS1982

Direct observation of interface instability during crystal growth

The general aim of this investigation was to study interface stability and solute segregation phenomena during crystallization of a model system. Emphasis was to be placed on direct observational studies partly because this offered the possibility at a later stage of performing related experiments under substantially convection-free conditions in the space shuttle. The major achievements described in this report are: (1) the development of a new model system for fundamental studies of crystal growth from the melt and the measurement of a range of material parameters necessary for comparison of experiment with theory. (2) The introduction of a new method of measuring segregation coefficient using absorption of a laser beam by the liquid phase. (3) The comparison of segregation in crystals grown by gradient freezing and by pulling from the melt. (4) The introduction into the theory of solute segregation of an interface field term and comparison with experiment. (5) The introduction of the interface field term into the theories of constitutional supercooling and morphological stability and assessment of its importance.

Tiller, W. A.↗

NASA NTRS1984

Computation of viscous flow in planar and axisymmetric ducts by an implicit marching procedure

A streamwise marching procedure, approximately 200 times faster than a full Navier-Stokes procedure with comparable accuracy, is presented for solving problems of compressible viscous subsonic flow. Results are presented and compared with experimental data for the cases of developing turbulent flow in a circular pipe; turbulent flow in a two-dimensional S-duct; and turbulent flow in a typical subsonic diffuser. Prior to each main marching step, a preliminary marching step is taken in which the integral continuity equation and an uncoupled form of the streamwise momentum equation are solved simultaneously to obtain the viscous pressure correction. During the main marching step the equations for continuity, streamwise momentum, cross-flow momentum, and energy are solved simultaneously as a coupled system using an implicit finite-difference method, with the viscous pressure correction treated as a source term. The analysis may be used for flows with both favorable and adverse pressure gradients and to predict the location of flow separation.

Towne, C. E.↗

NASA NTRS1984

Advances in electrophoretic separations

Free fluid electrophoresis is described using laboratory and space experiments combined with extensive mathematical modeling. Buoyancy driven convective flows due to thermal and concentration gradients are absent in the reduced gravity environment of space. The elimination of convection in weightlessness offers possible improvements in electrophoresis and other separation methods which occur in fluid media. The mathematical modeling suggests new ways of doing electrophoresis in space and explains various phenomena observed during past experiments. The extent to which ground based separation techniques are limited by gravity induced convection is investigated and space experiments are designed to evaluate specific characteristics of the fluid/particle environment. A series of experiments are proposed that require weightlessness and apparatus is developed that can be used to carry out these experiments in the near future.

Snyder, R. S.↗

NASA NTRS1986

Global collocation methods for approximation and the solution of partial differential equations

Polynomial interpolation methods are applied both to the approximation of functions and to the numerical solutions of hyperbolic and elliptic partial differential equations. The derivative matrix for a general sequence of the collocation points is constructed. The approximate derivative is then found by a matrix times vector multiply. The effects of several factors on the performance of these methods including the effect of different collocation points are then explored. The resolution of the schemes for both smooth functions and functions with steep gradients or discontinuities in some derivative are also studied. The accuracy when the gradients occur both near the center of the region and in the vicinity of the boundary is investigated. The importance of the aliasing limit on the resolution of the approximation is investigated in detail. Also examined is the effect of boundary treatment on the stability and accuracy of the scheme.

Solomonoff, A.↗

NASA NTRS1986

Interactive graphics and analysis accuracy

An important objective of graphical finite element postprocessing is the facility to indicate to the engineer the accuracy of analysis results. The inclusion of mesh quality sensors permits a subjective evaluation of the adequacy of a single analysis being interpreted. For graphical approaches, both strain energy density gradients and discontinuities of unsmoothed responses and their gradients have proved to be effective sensors. Graphical tools which can display discontinuity information effectively are described; these are essentially different from the ordinary methods used for the viewing of smoothed results.

Abel, J. F.↗

NASA NTRS1986

Separated flow

A brief overview of flow separation phenomena is provided. Langley has many active research programs in flow separation related areas. Three cases are presented which describe specific examples of flow separation research. In each example, a description of the fundamental fluid physics and the complexity of the flow field is presented along with a method of either reducing or controlling the extent of separation. The following examples are discussed: flow over a smooth surface with an adverse pressure gradient; flow over a surface with a geometric discontinuity; and flow with shock-boundary layer interactions. These results will show that improvements are being made in the understanding of flow separation and its control.

Sellers, W. L., III↗

NASA NTRS1990

NASA-UVA light aerospace alloy and structures technology program

The objective of the Light Aerospace Alloy and Structures Technology Program is to conduct interdisciplinary graduate student research on the performance of next generation, light weight aerospace alloys, composites, and associated thermal gradient structures. Individual technical objectives are established for each project. Efforts aim to produce basic understanding of material behavior, monolithic and composite alloys, processing methods, solid and mechanics analyses, measurement advances, and a pool of educated graduate students. Progress is reported for 11 areas of study.

Gangloff, Richard P.↗

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↗