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All sourcesNASA NTRSDOE OSTI
NASA NTRS1997

Dibromine Monoxide, Br2O: The Rotational Spectrum and Molecular Properties

The rotational spectra of (79)Br2O, (79)BrO(81)Br, and Br2O in their ground vibrational states as well as (79)BrO(81)Br in its v (sub 2) = 1 state have been studied in selected regions between 90 and 523 GHz. Transitions involving a large range of quantum numbers, 6 less than or equal to J less than or equal to 123 and 0 less than or equal to K (sub a) less than or equal to 12, have been observed permitting precise rotational and a large set of centrifugal distortion constants to be determined. All isotopic species as well as the excited state data were fit simultaneously. Ground-state effective and average structural parameters as well as an estimate of the equilibrium structure have been derived. The quartic distortion constants were used for a calculation of the harmonic force field. The complete quadrupole tensor has been determined. Its diagonalization reveals a largely covalent BrO bond with little pi-bonding. The derived properties of Br2O are compared with those of related compounds such as Cl2O, HOBR, and HOCl.

Mueller, Holger S. P.↗
NASA NTRS2000

Time Filtering in Large Eddy Simulations

An explicit time filter is applied to the Navier-Stokes equation prior to a space filter. The time filter is supposed to be smooth, and an exact expansion depending on the time derivatives of the velocity is derived for the associated stress tensor. On the contrary, the effect of the space filter is treated as usual and an eddy viscosity model is introduced in the LES equation. The total stress is thus represented using a new class of mixed models combining time and space derivatives of the LES field.

Carati, Daniele↗
NASA NTRS2000

Inertial Effects in Suspension Dynamics

The present work analyses the dynamics of a suspension of heavy particles in shear flow. The magnitude of the particle inertia is given by the Stokes number St = m(gamma/6(pi)a, which is the ratio of the viscous relaxation time of a particle tau(sub p) = m=6pi(eta)a to the flow time gamma(sup -1). Here, m is the mass of the particle, a is its size, eta is the viscosity of the suspending fluid and gamma is the shear rate. The ratio of the Stokes number to the Reynolds number, Re = (rho)f(gamma)a(exp 2)/eta, is the density ratio rho(sub p)/rho(sub f). Of interest is to understand the separate roles of particle (St) and fluid (Re) inertia in the dynamics of suspensions. In this study we focus on heavy particles, rho(sub p)/rho(sub f) much greater than 1, for which the Stokes number is finite, but the Reynolds number is sufficiently small for inertial forces in the fluid to be neglected; thus, the fluid motion is governed by the Stokes equations. On the other hand, the probability density governing the statistics of the suspended particles satisfies a Fokker-Planck equation that accounts for both configuration and momentum coordinates, the latter being essential for finite St. The solution of the Fokker-Planck equation is obtained to O(St) via a Chapman-Enskog type-procedure, and the conditional velocity distribution so obtained is used to derive a configuration-space Smoluchowski equation with inertial corrections. The inertial effects are responsible for asymmetry in the relative trajectories of two spheres in shear flow, in contrast to the well known symmetric structure in the absence of inertia. Finite St open trajectories in the plane of shear suffer a downward lateral displacement resulting from the inability of a particle of finite mass to follow the curvature of the zero-Stokes-number pathlines. In addition to the induced asymmetry, the O(St) inertial perturbation dramatically alters the nature of the near-field trajectories. The stable closed orbits (for St = 0) in the plane of shear now spiral in, approaching particle-particle contact in the limit. All trajectories starting from an initial offset of O(St(sup 1/2) or less (which remain open for St = 0) also spiral in. The asymmetry of the trajectories leads to a non-Newtonian rheology and diffusive behavior. The latter because a given particle (moving along a finite St open trajectory) suffers a net displacement in the transverse direction after a single interaction. A sequence of such uncorrelated displacements leads to the particle executing a random walk. The inertial diffusivity tensor is anisotropic on account of differing strengths of interaction in the gradient and vorticity directions. Since the entire region (constituting an in finite area) of closed orbits in the plane of shear spirals onto contact for #finite St, the latter represents a singular surface for the pair-distribution function. The exact form of the pair-distribution function at contact is still, however, indeterminate in the absence of non-hydrodynamic effects. It should also be noted that finite St non-rectilinear flows do not support a spatially uniform number density owing to the cross-streamline inertial migration of particles.

J. F. Brady↗
NASA NTRS2001

High Temperature Elastic Properties of Single Crystal Mullite (Approximately 2.5Al2O3.SiO2) by Brillouin Spectroscopy

The complete elastic tensor of mullite has been determined by brillouin spectroscopy at room temperature and elevated temperatures up to 1200C. Equivalent, isotropic moduli (bulk, shear, and Young's) have been calculated. The room temperature values obtained using Voigt-Reuss-Hill averaging are: K(sub VRH) = 173.5 + 6.9 GPa, G(sub VRH) = 88.0 + 3.5 GPa, E(sub VRH) = 225.9 + 9.0 GPa. All moduli show relatively gradual decreases with temperature. The temperature derivatives obtained for the equivalent, isotropic moduli are: dK(sub VRH)/dT = - 17.5 + 2.5 MPa/deg. C, dG(sub VRH)/dT = -8.8 + 1.4 MPa/deg. C, dE(sub VRH)/dT = -22.6 + 2.8 MPa/deg C. Substantial differences between bulk properties calculated from the single crystal measurements in this study and the properties reported in the literature for polycrystalline sintered mullite are identified, indicating the importance of factors such as microstructure, intergranular phases, and composition to the elasticity of mullite ceramics.

Palko, James W.↗
NASA NTRS2001

Statistical Ensemble of Large Eddy Simulations

A statistical ensemble of large eddy simulations (LES) is run simultaneously for the same flow. The information provided by the different large scale velocity fields is used to propose an ensemble averaged version of the dynamic model. This produces local model parameters that only depend on the statistical properties of the flow. An important property of the ensemble averaged dynamic procedure is that it does not require any spatial averaging and can thus be used in fully inhomogeneous flows. Also, the ensemble of LES's provides statistics of the large scale velocity that can be used for building new models for the subgrid-scale stress tensor. The ensemble averaged dynamic procedure has been implemented with various models for three flows: decaying isotropic turbulence, forced isotropic turbulence, and the time developing plane wake. It is found that the results are almost independent of the number of LES's in the statistical ensemble provided that the ensemble contains at least 16 realizations.

Carati, Daniele↗
NASA NTRS2001

Cosmic Rays in Interplanetary Space

The science problem I have tackled in this grant is the derivation of the diffusion tensor of energetic particles in turbulent magnetic fields, with a sensible mean field. The new approach was to use quasi-linear theory with a consistent treatment of those scattering terms leading to diffusion perpendicular to the mean magnetic field; and, to use modern data and formats for three-dimensional turbulence.

Forman, Miriam A.↗
NASA NTRS2001

Precision Measurement of Large Scale Structure

The purpose of this grant was to develop and to start to apply new precision methods for measuring the power spectrum and redshift distortions from the anticipated new generation of large redshift surveys. A highlight of work completed during the award period was the application of the new methods developed by the PI to measure the real space power spectrum and redshift distortions of the IRAS PSCz survey, published in January 2000. New features of the measurement include: (1) measurement of power over an unprecedentedly broad range of scales, 4.5 decades in wavenumber, from 0.01 to 300 h/Mpc; (2) at linear scales, not one but three power spectra are measured, the galaxy-galaxy, galaxy-velocity, and velocity-velocity power spectra; (3) at linear scales each of the three power spectra is decorrelated within itself, and disentangled from the other two power spectra (the situation is analogous to disentangling scalar and tensor modes in the Cosmic Microwave Background); and (4) at nonlinear scales the measurement extracts not only the real space power spectrum, but also the full line-of-sight pairwise velocity distribution in redshift space.

Hamilton, A. J. S.↗
NASA NTRS2002

Definition of Contravariant Velocity Components

In this paper we have reviewed the basics of tensor analysis in an attempt to clarify some misconceptions regarding contravariant and covariant vector components as used in fluid dynamics. We have indicated that contravariant components are components of a given vector expressed as a unique combination of the covariant base vector system and, vice versa, that the covariant components are components of a vector expressed with the contravariant base vector system. Mathematically, expressing a vector with a combination of base vector is a decomposition process for a specific base vector system. Hence, the contravariant velocity components are decomposed components of velocity vector along the directions of coordinate lines, with respect to the covariant base vector system. However, the contravariant (and covariant) components are not physical quantities. Their magnitudes and dimensions are controlled by their corresponding covariant (and contravariant) base vectors.

Hung, Ching-moa↗
NASA NTRS2002

Definition of Contravariant Velocity Components

This is an old issue in computational fluid dynamics (CFD). What is the so-called contravariant velocity or contravariant velocity component? In the article, we review the basics of tensor analysis and give the contravariant velocity component a rigorous explanation. For a given coordinate system, there exist two uniquely determined sets of base vector systems - one is the covariant and another is the contravariant base vector system. The two base vector systems are reciprocal. The so-called contravariant velocity component is really the contravariant component of a velocity vector for a time-independent coordinate system, or the contravariant component of a relative velocity between fluid and coordinates, for a time-dependent coordinate system. The contravariant velocity components are not physical quantities of the velocity vector. Their magnitudes, dimensions, and associated directions are controlled by their corresponding covariant base vectors. Several 2-D (two-dimensional) linear examples and 2-D mass-conservation equation are used to illustrate the details of expressing a vector with respect to the covariant and contravariant base vector systems, respectively.

Hung, Ching-Mao↗
NASA NTRS2002

Large-Eddy Simulations with Explicit Equations for Subgrid-Scale Quantities

Various alternative formulations of the LES equations have been explored in which additional evolution equations for variables such as the acceleration, the subgrid-scale stress tensor, or the subgrid-scale force are explicitly carried. Statistics of the velocity field obtained from the equation for the acceleration are shown to depend strongly on the initial conditions. This feature, which is independent of LES modeling issues, seems to prove that the velocity-acceleration formulation of the Navier-Stokes is not useful for numerical simulation. Equations for the subgrid-scale quantities appear to be much more stable. However, models required by this formulation of the LES problem still require additional study.

Carati, Daniele↗
NASA NTRS2002

Entrainment-Zone Restratification and Flow Structures in Stratified Shear Turbulence

Late-time dynamics and morphology of a stratified turbulent shear layer are examined using 1) Reynolds-stress and heat-flux budgets, 2) the single-point structure tensors introduced by Kassinos et al. (2001), and 3) flow visualization via 3D volume rendering. Flux reversal is observed during restratification in the edges of the turbulent layer. We present a first attempt to quantify the turbulence-mean-flow interaction and to characterize the predominant flow structures. Future work will extend this analysis to earlier times and different values of the Reynolds and Richardson numbers.

Reif, B. Anders Pettersson↗
NASA NTRS2003

Implementation of an Associative Flow Rule Including Hydrostatic Stress Effects Into the High Strain Rate Deformation Analysis of Polymer Matrix Composites

A previously developed analytical formulation has been modified in order to more accurately account for the effects of hydrostatic stresses on the nonlinear, strain rate dependent deformation of polymer matrix composites. State variable constitutive equations originally developed for metals have been modified in order to model the nonlinear, strain rate dependent deformation of polymeric materials. To account for the effects of hydrostatic stresses, which are significant in polymers, the classical J2 plasticity theory definitions of effective stress and effective inelastic strain, along with the equations used to compute the components of the inelastic strain rate tensor, are appropriately modified. To verify the revised formulation, the shear and tensile deformation of two representative polymers are computed across a wide range of strain rates. Results computed using the developed constitutive equations correlate well with experimental data. The polymer constitutive equations are implemented within a strength of materials based micromechanics method to predict the nonlinear, strain rate dependent deformation of polymer matrix composites. The composite mechanics are verified by analyzing the deformation of a representative polymer matrix composite for several fiber orientation angles across a variety of strain rates. The computed values compare well to experimentally obtained results.

Goldberg, Robert K.↗
NASA NTRS2003

Automated Coronal Loop Identification Using Digital Image Processing Techniques

The results of a master thesis project on a study of computer algorithms for automatic identification of optical-thin, 3-dimensional solar coronal loop centers from extreme ultraviolet and X-ray 2-dimensional images will be presented. These center splines are proxies of associated magnetic field lines. The project is pattern recognition problems in which there are no unique shapes or edges and in which photon and detector noise heavily influence the images. The study explores extraction techniques using: (1) linear feature recognition of local patterns (related to the inertia-tensor concept), (2) parametric space via the Hough transform, and (3) topological adaptive contours (snakes) that constrains curvature and continuity as possible candidates for digital loop detection schemes. We have developed synthesized images for the coronal loops to test the various loop identification algorithms. Since the topology of these solar features is dominated by the magnetic field structure, a first-order magnetic field approximation using multiple dipoles provides a priori information in the identification process. Results from both synthesized and solar images will be presented.

Lee, Jong K.↗
NASA NTRS2003

Magnetohydrodynamic Jump Conditions for Oblique Relativistic Shocks with Gyrotropic Pressure

Shock jump conditions, i.e., the specification of the downstream parameters of the gas in terms of the upstream parameters, are obtained for steady-state, plane shocks with oblique magnetic fields and arbitrary flow speeds. This is done by combining the continuity of particle number flux and the electromagnetic boundary conditions at the shock with the magnetohydrodynamic conservation laws derived from the stress-energy tensor. For ultrarelativistic and nonrelativistic shocks, the jump conditions may be solved analytically. For mildly relativistic shocks, analytic solutions are obtained for isotropic pressure using an approximation for the adiabatic index that is valid in high sonic Mach number cases. Examples assuming isotropic pressure illustrate how the shock compression ratio depends on the shock speed and obliquity. In the more general case of gyrotropic pressure, the jump conditions cannot be solved analytically with- out additional assumptions, and the effects of gyrotropic pressure are investigated by parameterizing the distribution of pressure parallel and perpendicular to the magnetic field. Our numerical solutions reveal that relatively small departures from isotropy (e.g., approximately 20%) produce significant changes in the shock compression ratio, r , at all shock Lorentz factors, including ultrarelativistic ones, where an analytic solution with gyrotropic pressure is obtained. In particular, either dynamically important fields or significant pressure anisotropies can incur marked departures from the canonical gas dynamic value of r = 3 for a shocked ultrarelativistic flow and this may impact models of particle acceleration in gamma-ray bursts and other environments where relativistic shocks are inferred. The jump conditions presented apply directly to test-particle acceleration, and will facilitate future self-consistent numerical modeling of particle acceleration at oblique, relativistic shocks; such models include the modification of the fluid velocity profile due to the contribution of energetic particles to the momentum and energy fluxes.

Double, Glen P.↗
NASA NTRS2003

Spectral Characteristics of Wake Vortex Sound During Roll-Up

This report presents an analysis of the sound spectra generated by a trailing aircraft vortex during its rolling-up process. The study demonstrates that a rolling-up vortex could produce low frequency (less than 100 Hz) sound with very high intensity (60 dB above threshold of human hearing) at a distance of 200 ft from the vortex core. The spectrum then drops o rapidly thereafter. A rigorous analytical approach has been adopted in this report to derive the spectrum of vortex sound. First, the sound pressure was solved from an alternative treatment of the Lighthill s acoustic analogy approach [1]. After the application of Green s function for free space, a tensor analysis was applied to permit the removal of the source term singularity of the wave equation in the far field. Consequently, the sound pressure is expressed in terms of the retarded time that indicates the time history and spacial distribution of the sound source. The Fourier transformation is then applied to the sound pressure to compute its spectrum. As a result, the Fourier transformation greatly simplifies the expression of the vortex sound pressure involving the retarded time, so that the numerical computation is applicable with ease for axisymmetric line vortices during the rolling-up process. The vortex model assumes that the vortex circulation is proportional to the time and the core radius is a constant. In addition, the velocity profile is assumed to be self-similar along the aircraft flight path, so that a benchmark vortex velocity profile can be devised to obtain a closed form solution, which is then used to validate the numerical calculations for other more realistic vortex profiles for which no closed form solutions are available. The study suggests that acoustic sensors operating at low frequency band could be profitably deployed for detecting the vortex sound during the rolling-up process.

Booth, Earl R., Jr.↗
NASA NTRS2003

On the Computation of Space-Time Correlations by Large-Eddy Simulation

Numerical comparisons in decaying isotropic turbulence suggest that there exist discrepancies in time correlations evaluated by DNS and LES using eddy-viscosity-type SGS models. This is consistent with the previous observations in forced isotropic turbulence. Therefore, forcing is not the main cause of the discrepancies. Comparisons among different SGS models in the LES also indicate that the model choice affects the time correlations in the LES. The multi-scale LES method using the dynamic Smagorinsky model on the small scale equation is the most accurate of the all models, the classic Smagorinsky model is the least accurate and the dynamic Smagorinsky model and spectral eddy viscosity model give intermediate results with small differences. The generalized sweeping hypothesis implies that time correlations in decaying isotropic turbulence are mainly determined by the instantaneous energy spectra and sweeping velocities. The analysis based on the sweeping hypothesis explains the discrepancies in our numerical simulations: the LES overpredicts the decorrelation time scales because the sweeping velocities are smaller than the DNS values, and underpredicts the magnitudes of time correlations because the energy spectrum levels are lower than the DNS ones. Since the sweeping velocity is determined by the energy spectra, one concludes that an accurate prediction of the instantaneous energy spectra guarantees the accuracy of time correlations. An analytical expression of sound power spectra based on Lighthill's theory and the quasi-normal closure assumption suggests that the sound power spectra are sensitive to errors in time correlations. Small errors in time correlations can cause significant errors in the sound power spectra, which exhibit a sizable drop at moderate to high frequencies accompanied by a shift of the peaks to lower frequencies. Based on the above analysis, two possible ways to improve the acoustic power spectrum predictions can be considered. The first is to construct better SGS models to improve the LES accuracy for time correlations. The second is to remedy the temporal statistics of the Lighthill stress tensor in order to "recover" the contribution from the unresolved scales in LES to time correlations.

He, Guo-Wei↗
NASA NTRS2003

Some Analytic Results for the Study of Broadband Noise Radiation from Wings, Propellers and Jets in Uniform Motion

Alan Powell has made significant contributions to the understanding of many aeroacoustic problems, in particular, the problems of broadband noise from jets and boundary layers. In this paper, some analytic results are presented for the calculation of the correlation function of the broadband noise radiated from a wing, a propeller, and a jet in uniform forward motion. It is shown that, when the observer (or microphone) motion is suitably chosen, the geometric terms of the radiation formula become time independent. The time independence of these terms leads to a significant simplification of the statistical analysis of the radiated noise, even when the near field terms are included. For a wing in forward motion, if the observer is in the moving reference frame, then the correlation function of the near and far field noise can be related to a space-time cross-correlation function of the pressure on the wing surface. A similar result holds for a propeller in forward flight if the observer is in a reference frame that is attached to the propeller and rotates at the shaft speed. For a jet in motion, it is shown that the correlation function of the radiated noise can be related to the space-time crosscorrelation of the Lighthill stress tensor in the jet. Exact analytical results are derived for all three cases. For the cases under present consideration, the inclusion of the near field terms does not introduce additional complexity, as compared to existing formulations that are limited to the far field.

Farassat, F.↗
NASA NTRS2004

The Acoustic Analogy: A Powerful Tool in Aeroacoustics with Emphasis on Jet Noise Prediction

The acoustic analogy introduced by Lighthill to study jet noise is now over 50 years old. In the present paper, Lighthill s Acoustic Analogy is revisited together with a brief evaluation of the state-of-the-art of the subject and an exploration of the possibility of further improvements in jet noise prediction from analytical methods, computational fluid dynamics (CFD) predictions, and measurement techniques. Experimental Particle Image Velocimetry (PIV) data is used both to evaluate turbulent statistics from Reynolds-averaged Navier-Stokes (RANS) CFD and to propose correlation models for the Lighthill stress tensor. The NASA Langley Jet3D code is used to study the effect of these models on jet noise prediction. From the analytical investigation, a retarded time correction is shown that improves, by approximately 8 dB, the over-prediction of aft-arc jet noise by Jet3D. In experimental investigation, the PIV data agree well with the CFD mean flow predictions, with room for improvement in Reynolds stress predictions. Initial modifications, suggested by the PIV data, to the form of the Jet3D correlation model showed no noticeable improvements in jet noise prediction.

Farassat, F.↗