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At least 829 records · Page 46

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NASA NTRS1995

Analysis of discretization errors in LES

All numerical simulations of turbulence (DNS or LES) involve some discretization errors. The integrity of such simulations therefore depend on our ability to quantify and control such errors. In the classical literature on analysis of errors in partial differential equations, one typically studies simple linear equations (such as the wave equation or Laplace's equation). The qualitative insight gained from studying such simple situations is then used to design numerical methods for more complex problems such as the Navier-Stokes equations. Though such an approach may seem reasonable as a first approximation, it should be recognized that strongly nonlinear problems, such as turbulence, have a feature that is absent in linear problems. This feature is the simultaneous presence of a continuum of space and time scales. Thus, in an analysis of errors in the one dimensional wave equation, one may, without loss of generality, rescale the equations so that the dependent variable is always of order unity. This is not possible in the turbulence problem since the amplitudes of the Fourier modes of the velocity field have a continuous distribution. The objective of the present research is to provide some quantitative measures of numerical errors in such situations. Though the focus of this work is LES, the methods introduced here can be just as easily applied to DNS. Errors due to discretization of the time-variable are neglected for the purpose of this analysis.

Ghosal, Sandip↗

DOE OSTI2025

Fast calculation of diffraction patterns from an ensemble of aligned molecules

We report an algorithm to calculate electron diffraction patterns for molecules with anisotropic angular distribution, which is significantly faster than existing methods. The algorithm uses a transform to convert the molecular orientation distribution, which is a function of three Euler angles, to the atom-pair distribution functions which depend on the polar and azimuthal angles. The diffraction signal can then be calculated from the atom-pair distributions. We demonstrate the computation method numerically by calculating electron diffraction patterns for a symmetric top molecule (trifluoroiodomethane) and an asymmetric top molecule (formaldehyde) and show that it reduces the calculation time by approximately two orders of magnitude compared to the standard brute-force method. Here, the method can also be applied to the calculation of x-ray diffraction patterns.

74 ATOMIC AND MOLECULAR PHYSICS↗

NASA NTRS1990

3D Euler analysis of ducted propfan flowfields

A numerical method is presented for predicting the steady inviscid flow through a ducted propfan based on a time-marching solution of the three-dimensional Euler equations. A four-stage multiple-block Runge-Kutta finite volume numerical technique, utilizing implicit residual smoothing and a blended second and fourth difference dissipation, is applied to predict the transonic flowfield about both single-rotation and counter-rotations ducted rotors. Counter-rotation predictions are based on an average-passage system of equations approach. Calculations are performed for both a single sheared H-type grid system and a multiple-block grid system incorporating a C-type grid about the cowl. Numerical results are compared with experimental data for two cases: a low speed ducted propeller and a 1.15 pressure ratio fan stage.

Hall, Edward J.↗

NASA NTRS2015

A Survey of the Isentropic Euler Vortex Problem Using High-Order Methods

The flux reconstruction (FR) method offers a simple, efficient, and easy to implement method, and it has been shown to equate to a differential approach to discontinuous Galerkin (DG) methods. The FR method is also accurate to an arbitrary order and the isentropic Euler vortex problem is used here to empirically verify this claim. This problem is widely used in computational fluid dynamics (CFD) to verify the accuracy of a given numerical method due to its simplicity and known exact solution at any given time. While verifying our FR solver, multiple obstacles emerged that prevented us from achieving the expected order of accuracy over short and long amounts of simulation time. It was found that these complications stemmed from a few overlooked details in the original problem definition combined with the FR and DG methods achieving high-accuracy with minimal dissipation. This paper is intended to consolidate the many versions of the vortex problem found in literature and to highlight some of the consequences if these overlooked details remain neglected.

High-Order↗

NASA NTRS1983

Design procedures for compressor blades

The conventional methods for the design of the blades in the case of axial turbomachines are considered, taking into account difficulties concerning the determination of optimal blade profiles. These difficulties have been partly overcome as a consequence of the introduction of new numerical methods during the last few years. It is pointed out that, in the case of the subsonic range, a new procedure is now available for the determination of the form of blade profile on the basis of a given velocity distribution on the profile surface. The search for a profile form with favorable characteristics is consequently transformed into a search for a favorable velocity or pressure distribution on the blade. The distribution of velocities depends to a large degree on the characteristics of the profile boundary layers. The considered concept is not new. However, its practical implementation has only recently become possible. The employment of the new design procedure is illustrated with the aid of an example involving a concrete design problem.

Starken, H.↗

NASA NTRS1996

The Effect of Strain Rate on the Evolution of Plane Wakes Subjected to Irrotational Strains

Direct numerical simulations of time-evolving turbulent plane wakes developing in the presence of irrotational plane strain applied at three different strain rates have been generated. The strain geometry is such that the flow is compressed in the streamwise direction and expanded in the cross-stream direction with the spanwise direction being unstrained. This geometry is the temporally evolving analogue of a spatially evolving wake in an adverse pressure gradient. A pseudospectral numerical method with up to 16 million modes is used to solve the equations in a reference frame moving with the irrotational strain. The initial condition for each simulation is taken from a previous turbulent self-similar plane wake direct numerical simulation at a velocity deficit Reynolds number, Re, of about 2,000. Although the evolutions of many statistics are nearly collapsed when plotted against total strain, there are some differences owing to the different strain rate histories. The impact of strain-rate on the wake spreading rate, the peak velocity deficit, the Reynolds stress profiles, and the flow structure is examined.

Rogers, Michael M.↗

NASA NTRS1995

The Evolution of Plane Wakes Subjected to Irrotational Strains

Three direct numerical simulations of time-evolving turbulent plane wakes developing in the presence of various irrotational plane strains have been generated. A pseudospectral numerical method with up to 26 million modes is used to solve the equations in a reference frame moving with the irrotational strain. The initial condition for each simulation is taken from a previous turbulent self-similar plane wake direct numerical simulation at a velocity deficit Reynolds number, Re, of about 2000. Three different plane strains (of the same magnitude) are imposed. In the first two simulations the strain is in a plane normal to the streamwise wake direction (the two cases having strain of opposite sign); in the third the wake is compressed in the streamwise direction and stretched in the inhomogeneous cross-stream direction. The two flows that are stretched in the cross-stream direction experience an exponential increase of Re; flow visualization indicates many small-scale vortices with little or no organized large-scale structure. In the flow that is compressed in the cross-stream direction Re decays exponentially and the layer appears to be relaminarizing. The evolution of several turbulence statistics in each of these flows is examined.

Rogers, M. R.↗

NASA NTRS1997

Reynolds Stress Balance in Plane Wakes Subjected to Irrotational Strains

Direct numerical simulations of time-evolving turbulent plane wakes developing in the presence of various irrotational plane strains have been generated. A pseudospectral numerical method with up to 25 million modes is used to solve the equations in a reference frame moving with the irrotational strain. The initial condition for each simulation is taken from a previous turbulent self-similar plane wake direct numerical simulation at a velocity deficit Reynolds number, R(sub e), of about 2,000. All the terms in the equations governing the evolution of the Reynolds stresses have been calculated. The relative importance of the various terms is examined for the different strain geometries and the behavior of the individual terms is used to better assess whether the strained wakes are evolving self-similarly.

Rogers, Miichael M.↗

NASA NTRS1999

Reactions and Surface Transformations of a Bone-Bioactive Material in a Simulated Microgravity Environment

A comprehensive program to investigate the expeditious in vitro formation of three-dimensional bone-like tissue is currently underway at the University of Pennsylvania. The study reported here forms a part of that program. Three-dimensional bone-like tissue structures may be grown under the simulated microgravity conditions of NASA designed Rotating Wall Bioreactor Vessels (RWV's). Such tissue growth will have wide clinical applications. In addition, an understanding of the fundamental changes that occur to bone cells under simulated microgravity would yield important information that will help in preventing or minimizing astronaut bone loss, a major health issue with travel or stay in space over long periods of time. The growth of three-dimensional bone-like tissue structures in RWV's is facilitated by the use of microcarriers which provide structural support. If the microcarrier material additionally promotes bone cell growth, then it is particularly advantageous to employ such microcarriers. We have found that reactive, bone-bioactive glass (BBG) is an attractive candidate for use as microcarrier material. Specifically, it has been found that BBG containing Ca- and P- oxides upregulates osteoprogenitor cells to osteoblasts. This effect on cells is preceded by BBG reactions in solution which result in the formation of a Ca-P surface layer. This surface further transforms to a bone-like mineral (i.e., carbonated crystalline hydroxyapatite (c-HA)). At normal gravity, time-dependent, immersion-induced BBG reactions and transformations are greatly affected both by variations in the composition of the milieu in which the glass is immersed and on the immersion conditions. However, the nature of BBG reactions and phase transformations under the simulated microgravity conditions of RWV's are unknown, and must be understood in order to successfully use BBG as microcarrier material in RWV'S. In this paper, we report some of our recent findings in this regard using experimental and numerical methods. BBG composition 45S5, the most reactive among known bone-bioactive glasses, was chosen for the study. BBG 45S5 behavior in physiological solutions was tested in simulated microgravity and compared with that at normal gravity. On the basis of our numerical study, we have chosen the BBG granule size to be in the range 40-70 microns, and a RWV rotational speed of 10 rpm. Our numerical study has shown that these parameters enable the microcarrier to remain suspended in the medium without experiencing collisions with the wall of the vessel. Immersion-induced changes in the solution composition and the material surface were analyzed after immersion.

Radin, S.↗

NASA NTRS2001

Designing Adaptive Low-Dissipative High Order Schemes for Long-Time Integrations

A general framework for the design of adaptive low-dissipative high order schemes is presented. It encompasses a rather complete treatment of the numerical approach based on four integrated design criteria: (1) For stability considerations, condition the governing equations before the application of the appropriate numerical scheme whenever it is possible; (2) For consistency, compatible schemes that possess stability properties, including physical and numerical boundary condition treatments, similar to those of the discrete analogue of the continuum are preferred; (3) For the minimization of numerical dissipation contamination, efficient and adaptive numerical dissipation control to further improve nonlinear stability and accuracy should be used; and (4) For practical considerations, the numerical approach should be efficient and applicable to general geometries, and an efficient and reliable dynamic grid adaptation should be used if necessary. These design criteria are, in general, very useful to a wide spectrum of flow simulations. However, the demand on the overall numerical approach for nonlinear stability and accuracy is much more stringent for long-time integration of complex multiscale viscous shock/shear/turbulence/acoustics interactions and numerical combustion. Robust classical numerical methods for less complex flow physics are not suitable or practical for such applications. The present approach is designed expressly to address such flow problems, especially unsteady flows. The minimization of employing very fine grids to overcome the production of spurious numerical solutions and/or instability due to under-resolved grids is also sought. The incremental studies to illustrate the performance of the approach are summarized. Extensive testing and full implementation of the approach is forthcoming. The results shown so far are very encouraging.

Yee, Helen C.↗

NASA NTRS1975

Calculation of arbitrary-order diffraction efficiencies of thick gratings with arbitrary grating shape

A method for calculating arbitrary-order diffraction efficiencies of thick, lossless transmission gratings with arbitrary periodic grating shapes has been developed. A Fourier-series representation of the grating is employed, along with a coupled-mode theory of diffraction. For illustration, numerical values of the diffraction efficiencies at the first three Bragg angles are calculated for sinusoidal, square-wave, triangular, and saw-tooth gratings. Numerical results for the same grating shapes with the same parameters are also calculated for comparison, by extending Burckhardt's numerical method for analyzing thick sinusoidal gratings. The comparison shows that the coupled-mode theory provides results with relative computational ease and results that are in agreement with calculations obtained by extending the more-rigorous Burckhardt theory to nonsinusoidal grating shapes and to higher-order Bragg angles.

Su, S. F.↗

NASA NTRS1981

Analysis of starvation effects on hydrodynamic lubrication in nonconforming contacts

The effects of lubricant starvation on minimum film thickness, under conditions of a hydrodynamic point contact, are determined by numerical methods where: (1) starvation is effected by varying the fluid inlet level; (2) the Reynolds boundary conditions are applied at the cavitation boundary; and (3) zero pressure is stipulated at the meniscus or inlet boundary. Seventy-four cases were used to numerically determine a minimum-film-thickness equation, as a function of the ratio of dimensionless load to dimensionless speed for varying degrees of starvation. A film reduction factor was in turn determined as a function of the fluid inlet level, and a starved, fully-flooded boundary was defined along with an expression determining the onset of starvation. It is found that as the degree of starvation increases, the minimum film thickness decreases gradually until the fluid inlet becomes critical. The changes in the inlet pressure buildup due to changing the available lubricant supply are presented in the form of three-dimensional isometric plots.

Brewe, D. E.↗

NASA NTRS1989

The role of topography in geodetic gravity field modelling

Masses associated with the topography, bathymetry, and its isostatic compensation are a dominant source of gravity field variations, especially at shorter wavelengths. On global scales the topographic/isostatic effects are also significant, except for the lowest harmonics. In practice, though, global effects need not be taken into account as such effects are included in the coefficients of the geopotential reference fields. On local scales, the short-wavelength gravity variations due to the topography may, in rugged terrain, be an order of magnitude larger than other effects. In such cases, explicit or implicit terrain reduction procedures are mandatory in order to obtain good prediction results. Such effects may be computed by space-domain integration or by fast Fourier transformation (FFT) methods. Numerical examples are given for areas of the Canadian Rockies. In principle, good knowledge of the topographic densities is required to produce the smoothest residual field. Densities may be determined from sample measurements or by gravimetric means, but both are somewhat troublesome methods in practice. The use of a standard density, e.g., 2.67 g/cu cm, may often yield satisfactory results and may be put within a consistent theoretical framework. The independence of density assumptions is the key point of the classical Molodensky approach to the geodetic boundary value problem. The Molodensky solutions take into account that land gravity field observations are done on a non-level surface. Molodensky's problem may be solved by integral expansions or more effective FFT methods, but the solution should not be intermixed with the use of terrain reductions. The methods are actually complimentary and may both be required in order to obtain the smoothest possible signal, least prone to aliasing and other effects coming from sparse data coverage, typical of rugged topography.

Forsberg, R.↗

DOE OSTI2024

Level 2 Milestone: Develop and Incorporate Novel Code Verification of Fundamental Equations in Gemma and Set Up Appropriate Tests

For computational physics simulations, code verification plays a major role in establishing the credibility of the results by assessing the correctness of the implementation of the underlying numerical methods. In computational electromagnetics, surface integral equations, such as the method-of-moments implementations of the electric-, magnetic-, and combinedfield integral equations, are frequently used to solve Maxwell’s equations on the surfaces of electromagnetic scatterers. These electromagnetic surface integral equations yield many code-verification challenges due to the various sources of numerical error and their possible interactions. In this report, we provide approaches to separately measure the numerical errors arising from these different error sources. We demonstrate the effectiveness of these approaches in Gemma.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

NASA NTRS1985

The anisotropic radiative transfer problem in optically thick, strongly magnetized plasma - A comparison of results

The accuracy of four different methods for solving the coherent radiative transfer problem in a strongly magnetized plasma is compared. Specific attention is given to the case of a semi-infinite homogeneous plasma with a magnetic field perpendicular to the surface. The four approaches evaluated were: diffusion approximation schemes; the generalized H-function method of Silant'ev (1982) the Feautrier method of Nagel (1981) and the integral equation approach of Meszares and Bonazzola (1981). It is found that the coupled diffusion approximation schemes of Nagel (1981) and Kaminker et al. (1982) provided satisfactory results and were more efficient in many cases than direct numerical methods.

Pavlov, G. G.↗

NASA NTRS2016

Development of a High-Order Space-Time Matrix-Free Adjoint Solver

The growth in computational power and algorithm development in the past few decades has granted the science and engineering community the ability to simulate flows over complex geometries, thus making Computational Fluid Dynamics (CFD) tools indispensable in analysis and design. Currently, one of the pacing items limiting the utility of CFD for general problems is the prediction of unsteady turbulent ows.1{3 Reynolds-averaged Navier-Stokes (RANS) methods, which predict a time-invariant mean flowfield, struggle to provide consistent predictions when encountering even mild separation, such as the side-of-body separation at a wing-body junction. NASA's Transformative Tools and Technologies project is developing both numerical methods and physical modeling approaches to improve the prediction of separated flows. A major focus of this e ort is efficient methods for resolving the unsteady fluctuations occurring in these flows to provide valuable engineering data of the time-accurate flow field for buffet analysis, vortex shedding, etc. This approach encompasses unsteady RANS (URANS), large-eddy simulations (LES), and hybrid LES-RANS approaches such as Detached Eddy Simulations (DES). These unsteady approaches are inherently more expensive than traditional engineering RANS approaches, hence every e ort to mitigate this cost must be leveraged. Arguably, the most cost-effective approach to improve the efficiency of unsteady methods is the optimal placement of the spatial and temporal degrees of freedom (DOF) using solution-adaptive methods.

Adjoint↗

NASA NTRS1974

Analysis of acoustic radiation in a jet flow environment

The analysis of sound fields from arbitrary source distributions in terms of Legendre and spherical Hankel functions is well known. The purpose of this paper is to extend this classical method of analysis to environments such as jet flows where flow and flow gradients are inherently present. The wave-equation governing the radiation of sound in such an environment is derived. The steady state flow and flow gradients in the axial and transverse directions appear as coefficients in the terms of the wave-equation. A semi-numerical method is used to solve the wave-equation in terms of modified spherical harmonics yielding the phase velocities and the directivities of an infinite set of modes. The directivity of each mode is obtained in terms of modified Legendre functions by numerical integration. Some results of these directivity and phase-velocity calculations are presented for a limited number of frequency and flow parameters. Both convective and shear refraction are shown to be important.

Mungur, P.↗

NASA NTRS1987

Reduction of the radar cross section of arbitrarily shaped cavity structures

The problem of the reduction of the radar cross section (RCS) of open-ended cavities was studied. The issues investigated were reduction through lossy coating materials on the inner cavity wall and reduction through shaping of the cavity. A method was presented to calculate the RCS of any arbitrarily shaped structure in order to study the shaping problem. The limitations of this method were also addressed. The modal attenuation was studied in a multilayered coated waveguide. It was shown that by employing two layers of coating, it was possible to achieve an increase in both the magnitude of attenuation and the frequency band of effectiveness. The numerical method used in finding the roots of the characteristic equation breaks down when the coating thickness is very lossy and large in terms of wavelength. A new method of computing the RCS of an arbitrary cavity was applied to study the effects of longitudinal bending on RCS reduction. The ray and modal descriptions for the fields in a parallel plate waveguide were compared. To extend the range of validity of the Shooting and Bouncing Ray (SBR) method, the simple ray picture must be modified to account for the beam blurring.

Chou, R.↗