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At least 1,387 records · Page 77

Adding computationally efficient realism to Monte Carlo turbulence simulation

Frequently in aerospace vehicle flight simulation, random turbulence is generated using the assumption that the craft is small compared to the length scales of turbulence. The turbulence is presumed to vary only along the flight path of the vehicle but not across the vehicle span. The addition of the realism of three-dimensionality is a worthy goal, but any such attempt will not gain acceptance in the simulator community unless it is computationally efficient. A concept for adding three-dimensional realism with a minimum of computational complexity is presented. The concept involves the use of close rational approximations to irrational spectra and cross-spectra so that systems of stable, explicit difference equations can be used to generate the turbulence.

Campbell, C. W.↗

On the attitude motion of a self-excited rigid body

Leimanis (1965) has published a monograph, which contains Boedewadt's solution of Euler's equations of motion for a symmetric rigid body subject to a time-independent, self-excitement in a body-fixed direction. In addition, the monograph provided also Boedewadt's solution for the corresponding angles of rotation. It is pointed out that the solution of Euler's equations of motion provides a poor approximation to the problem of nearly symmetric rigid bodies in cases in which a high degree of accuracy (less than 1 percent error) is required. A much more accurate approximate solution has been provided by Longuski (1980). The result given by Leimanis in the case of the Eulerian angles is incorrect for arbitrary constant torques. The approximate solution given by Longuski, however, is extremely accurate and suitable for computer design work and error analysis of spacecraft performance. The present investigation is concerned with a review of the solutions and the specific regions of validity of the solution for the Eulerian angles.

Longuski, J. M.↗

Applications products of aviation forecast models

A service called the Optimum Path Aircraft Routing System (OPARS) supplies products based on output data from the Naval Oceanographic Global Atmospheric Prediction System (NOGAPS), a model run on a Cyber-205 computer. Temperatures and winds are extracted from the surface to 100 mb, approximately 55,000 ft. Forecast winds are available in six-hour time steps.

Garthner, John P.↗

A solution method for the unsteady incompressible Navier-Stokes equations in generalized coordinate systems

A solution method based on a fractional step approach is developed for obtaining time-dependent solutions of the three-dimensional, incompressible Navier-Stokes equations in generalized coordinate systems. The governing equations are discretized conservatively by finite volumes using a staggered mesh system. The primitive variable formulation uses the volume fluxes across the faces of each computational cell as dependent variables. This procedure, combined with accurate and consistent approximations of geometric parameters, is done to satisfy the discretized mass conservation equation to machine accuracy as well as to gain favorable convergence properties of the Poisson solver. The discretized equations are second-order-accurate in time and space and no smoothing terms are added. An approximate-factorization scheme is implemented in solving the momentum equations. A novel ZEBRA scheme with four-color ordering is devised for the efficient solution of the Poisson equation. Several two and three-dimensional solutions are compared with other numerical and experimental results to validate the present method.

Rosenfeld, Moshe↗

A transonic wind tunnel wall interference prediction code

A small disturbance transonic wall interference prediction code has been developed that is capable of modeling solid, open, perforated, and slotted walls as well as slotted and solid walls with viscous effects. This code was developed by modifying the outer boundary conditions of an existing aerodynamic wing-body-pod-pylon-winglet analysis code. The boundary conditions are presented in the form of equations which simulate the flow at the wall, as well as finite difference approximations to the equations. Comparisons are presented at transonic flow conditions between computational results and experimental data for a wing alone in a solid wall wind tunnel and wing-body configurations in both slotted and solid wind tunnels.

Phillips, Pamela S.↗

The photodissociation and chemistry of interstellar CO

Recent work on the vacuum UV absorption spectrum of CO to the description of the photodissociation of interstellar CO and its principal isotopic varieties is discussed. The effects of line broadening, self-shielding, shielding by H and H2, and isotope-selective shielding are examined as functions of depth into interstellar clouds. The photodissociation rates of the isotopic species are larger than that of (C-12)O inside the clouds by up to one to two orders of magnitude. A simple approximation to the attenuation by line absorption is given in tabular form. Computed abundances of CO and related species C and C+ are presented for a variety of interstellar clouds ranging from diffuse clouds to dense photodissociation regions. Several series of models of translucent clouds are presented which illustrate how the CO abundance increases rapidly with total cloud thickness. The variations of the isotopic abundances with depth and their sensitivity to temperature and total cloud thickness are explored in detail.

Van Dishoeck, Ewine F.↗

Cognitive performance deficits in a simulated climb of Mount Everest - Operation Everest II

Cognitive function at simulated altitude was investigated in a repeated-measures within-subject study of performance by seven volunteers in a hypobaric chamber, in which atmospheric pressure was systematically lowered over a period of 40 d to finally reach a pressure equivalent to 8845 m, the approximate height of Mount Everest. The automated performance test system employed compact computer design; automated test administrations, data storage, and retrieval; psychometric properties of stability and reliability; and factorial richness. Significant impairments of cognitive function were seen for three of the five tests in the battery; on two tests, grammatical reasoning and pattern comparison, every subject showed a substantial decrement.

Kennedy, R. S.↗

The Helmholtz-Kirchhoff integral relation as a framework for developing algorithms for sound propagation through inhomogeneous moving media

Transient sound propagation in an inhomogeneous moving medium is considered. For circumstances in which the medium is slowly varying over distances of a wavelength but possibly varying substantially over the propagation distance, a derivation is given of a new wave equation, which implicitly allows for diffraction and scattering and which also is consistent with earlier geometrical acoustics formulations. This wave equation is used as a starting point to derive a version of the Helmholtz-Kirchhoff integral relation that applies to inhomogeneous moving medium. It is suggested that a good approximation to the Green's function that appears in this relation is that derived from geometrical acoustics, the approximation becoming progressively better the shorter the distance between surfaces in the computation. It should also be at least as good as conventional ray acoustics, but can account for diffraction effects, such as at caustics.

Pierce, Allan D.↗

Shifts of the spectral lines of He(+) produced by electron collisions

The shifts of the Ly-alpha, Ly-beta, and H-alpha lines of He(+) in a plasma, produced by electron scattering from radiating ions are calculated. Electron densities in the neighborhood of 10 to the 17th/cu cm and plasma temperatures from 1 to 6 eV are considered. The calculation is made in the impact approximation, and is based on a six-state close-coupling computation of the scattering matrices, into which an optical potential has been inserted. Small red shifts of the lines are obtained. The contribution of electron scattering to the linewidths is also considered.

Unnikrishnan, K.↗

A fractional step solution method for the unsteady incompressible Navier-Stokes equations in generalized coordinate systems

The time-dependent, three-dimensional incompressible Navier-Stokes equations are presently solved in generalized coordinate systems by means of a fractional-step method whose primitive variable formulation uses as dependent variables, in place of the Cartesian components of the velocity: (1) pressure (defined at the center of the computational cell), and (2) volume fluxes across the faces of the cells. The momentum equations are solved by means of an approximate factorization method. A novel 'ZEBRA' scheme incorporating four-color ordering efficiently solves the Poisson equation. Illustrative two- and three-dimensional laminar flow test cases are computed and evaluated relative to extant numerical and experimental results, and good agreement is obtained.

Rosenfeld, Moshe↗

Viscous simulation method for unsteady flows past multicomponent configurations

The present algorithm for the numerical simulation of flows about complex configurations (whose multiple and nonsimilar components have arbitraty geometries) employs a hybridization of the domain decomposition techniques for grid generation as well as to reduce computer-memory requirements. A fully vectorized, finite-volume, upwind-biased, approximately factored multigrid method is used to solve 3D Reynolds-averaged unsteady and compressible Navier-Stokes equations simulating supersonic flows past an ogive-nose-cylinder near or within a cavity. The time-averaged surface pressures obtained compare favorably with the wind tunnel data.

Fouladi, Kamran↗

On laminar and turbulent friction

Report deals, first with the theory of the laminar friction flow, where the basic concepts of Prandtl's boundary layer theory are represented from mathematical and physical points of view, and a method is indicated by means of which even more complicated cases can be treated with simple mathematical means, at least approximately. An attempt is also made to secure a basis for the computation of the turbulent friction by means of formulas through which the empirical laws of the turbulent pipe resistance can be applied to other problems on friction drag. (author)

Von Karman, TH↗

Chordwise load distribution of a simple rectangular wing

The chordwise distribution theory was taken over from the theory of the infinite wing. Since in this work a series expansion in b/t was used, the computation converges only for large aspect ratios. In this paper a useful approximate solution will be found also for wings with large chord - i.e., small aspect ratio.

Wieghardt, Karl↗

Performance assessment of low pressure nuclear thermal propulsion

A low pressure nuclear thermal propulsion (LPNTP) system, which takes advantage of hydrogen dissociation/recombination, was proposed as a means of increasing engine specific impulse (Isp). The effect of hydrogen dissociation/recombination on LPNTP Isp is examined. A two-dimensional computer model was used to show that the optimum chamber pressure is approximately 100 psia (at a chamber temperature of 3,000 K), with an Isp approximately 15 s higher than at 1,000 psia. At high chamber temperatures and low chamber pressures, the increase in Isp is due to both lower average molecular weights caused by dissociation and added kinetic energy from monatomic hydrogen recombination. Monatomic hydrogen recombination increases the Isp more then hydrogen dissociation. Variations in the mole fraction of monatomic hydrogen are similar to variations in static pressure along the axial nozzle position. Most recombination occurs close to the nozzle throat. Practical variations in nozzle geometry have minimal impact on recombination. Other models which can simulate a wider range of nozzle designs should be used in the future. The uncertainty of the hydrogen kinetic reaction rates at high temperatures (approximately 3,000 K) affects the accuracy of the analysis and should be verified with simple bench tests.

Gerrish, H. P., Jr.↗

Theoretical light curve of a Type 2p supernova

The light curve and other observable diagnostics are presented for what should be a typical Type II 'plateau' supernova, the explosion of a 15 solar mass red supergiant. The calculations are carried out using a multi-frequency radiation transport code that includes opacity from all important mechanisms-bound-bound, bound-free, free-free, and electron scattering. It is found that the inclusion of opacity sources besides electron scattering increases the computed lenght of the plateau in the 15 solar mass model by approximately 30 days. Especially important is the ultraviolet cutoff caused by a thick forest of lines. Deposition and escape of gamma-rays from radioactive decay are also accurately simulated. We find that the presence of 0.06 solar mass of ejected Ni-56 extends the length of the plateau from approximately 100 days to approximately 140 dys. Because of the large hydrogen envleope and radius in this model, mixing does not appreciably alter the bolometric light curve, although it does change the gamma-ray light curve significantly. With 0.06 solar mass of ejected Ni-56, the unmixed (mixed) model peaks in escaping gamma-rays at 576 (466) days with gamma-ray luminosity of 3 x 10(exp 38) ergs/s. Except for the local group, the gamma-rays from an extragalactic 15 solar mass SNe IIp will be too faint to detect with any exsiting detectors. However, a Galactic SNe IIp would be quite bright and easily detectable.

Eastman, Ronald G.↗

A PDE Sensitivity Equation Method for Optimal Aerodynamic Design

The use of gradient based optimization algorithms in inverse design is well established as a practical approach to aerodynamic design. A typical procedure uses a simulation scheme to evaluate the objective function (from the approximate states) and its gradient, then passes this information to an optimization algorithm. Once the simulation scheme (CFD flow solver) has been selected and used to provide approximate function evaluations, there are several possible approaches to the problem of computing gradients. One popular method is to differentiate the simulation scheme and compute design sensitivities that are then used to obtain gradients. Although this black-box approach has many advantages in shape optimization problems, one must compute mesh sensitivities in order to compute the design sensitivity. In this paper, we present an alternative approach using the PDE sensitivity equation to develop algorithms for computing gradients. This approach has the advantage that mesh sensitivities need not be computed. Moreover, when it is possible to use the CFD scheme for both the forward problem and the sensitivity equation, then there are computational advantages. An apparent disadvantage of this approach is that it does not always produce consistent derivatives. However, for a proper combination of discretization schemes, one can show asymptotic consistency under mesh refinement, which is often sufficient to guarantee convergence of the optimal design algorithm. In particular, we show that when asymptotically consistent schemes are combined with a trust-region optimization algorithm, the resulting optimal design method converges. We denote this approach as the sensitivity equation method. The sensitivity equation method is presented, convergence results are given and the approach is illustrated on two optimal design problems involving shocks.

Borggaard, Jeff↗

Solving Upwind-Biased Discretizations: Multigrid Solver Using Semicoarsening - 2

This paper studies a novel multigrid approach to the solution for a second order upwind biased discretization of the convection equation in two dimensions. This approach is based on semi-coarsening and well balanced explicit correction terms added to coarse-grid operators to maintain on coarse-grid the same cross-characteristic interaction as on the target (fine) grid. Colored relaxation schemes are used on all the levels allowing a very efficient parallel implementation. The results of the numerical tests can be summarized as follows: 1) The residual asymptotic convergence rate of the proposed V(0, 2) multigrid cycle is about 3 per cycle. This convergence rate far surpasses the theoretical limit (4/3) predicted for standard multigrid algorithms using full coarsening. The reported efficiency does not deteriorate with increasing the cycle, depth (number of levels) and/or refining the target-grid mesh spacing. 2) The full multi-grid algorithm (FMG) with two V(0, 2) cycles on the target grid and just one V(0, 2) cycle on all the coarse grids always provides an approximate solution with the algebraic error less than the discretization error. Estimates of the total work in the FMG algorithm are ranged between 18 and 30 minimal work units (depending on the target (discretizatioin). Thus, the overall efficiency of the FMG solver closely approaches (if does not achieve) the goal of the textbook multigrid efficiency. 3) A novel approach to deriving a discrete solution approximating the true continuous solution with a relative accuracy given in advance is developed. An adaptive multigrid algorithm (AMA) using comparison of the solutions on two successive target grids to estimate the accuracy of the current target-grid solution is defined. A desired relative accuracy is accepted as an input parameter. The final target grid on which this accuracy can be achieved is chosen automatically in the solution process. the actual relative accuracy of the discrete solution approximation obtained by AMA is always better than the required accuracy; the computational complexity of the AMA algorithm is (nearly) optimal (comparable with the complexity of the FMG algorithm applied to solve the problem on the optimally spaced target grid).

Diskin, Boris↗

Realistic NLTE Radiative Transfer for Modeling Stellar Winds

This NASA grant supported the development of codes to solve the non-LTE multi-level spherical radiative transfer problem in the presence of velocity fields. Much of this work was done in collaboration with Graham Harper (CASA, University of Colorado). These codes were developed for application to the cool, low-velocity winds of evolved late-type stars. Particular emphasis was placed on modeling the wind of lambda Velorum (K4 lb), the brightest K supergiant in the sky, based on extensive observations of the ultraviolet spectrum with the HST/GHRS from GO program 5307. Several solution techniques were examined, including the Eddington factor Approach described in detail by Bennett & Harper (1997). An Eddington factor variant of Harper's S-MULTI code (Harper 1994) for stationary atmospheres was developed and implemented, although full convergence was not realized. The ratio of wind terminal velocity to turbulent velocity is large (approx. 0.3-0.5) in these cool star winds so this assumption of stationarity provides reasonable starting models. Final models, incorporating specified wind laws, were converged using the comoving CRD S-MULTI code. Details of the solution procedure were published by Bennett & Harper (1997). Our analysis of the wind of lambda Vel, based on wind absorption superimposed on chromospheric emission lines in the ultraviolet, can be found in Carpenter et al. (1999). In this paper, we compare observed wind absorption features to an exact CRD calculation in the comoving frame, and also to a much quicker, but approximate, method using the SEI (Sobolev with Exact Integration) code of Lamers, Cerruti-Sola, & Perinotto (1987). Carpenter et al. (1999) provide detailed comparisons of the exact CRD and approximate SEI results and discuss when SEI is adequate to use for computing wind line profiles. Unfortunately, the observational material is insufficient to unambiguously determine the wind acceleration law for lambda Vel. Relatively few unblended Fe II lines of optical depth sensitive to the wind acceleration region are present in the existing HST/GHRS data set. Most of the Fe II lines are either too optically thick (resulting in a board, black wind absorption profile) or too optically thin (resulting in no wind absorption feature present). Also, most of the ultraviolet spectra obtained from HST GO-5307 was at medium resolution (R approx. 40,000, corresponding to a velocity resolution of 7.5 km/s). This is simply inadequate to resolve the turbulence in the outer wind; a key parameter in theoretical wind models. We can now say that an unambiguous determination of the wind velocity law in lambda Vel will require complete coverage of the ultraviolet spectrum at high dispersion (R approx. 10(exp 5), or 3 km/s). This is now feasible usin, the STIS echelle spectrograph on-board HST.

Bennett, Philip D.↗