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NASA NTRS1995

Dynamic properties of helium ions in the solar wind

We characterize the dynamic properties of He ions of the solar wind. Because of the non-negligible abundance and the significant fraction of momentum flux inherent in helium ions, this species has an influence on the state of turbulence. Especially, we analyze the helium dynamic properties of different solar wind types. After a discussion of the influence of measurement errors on the statistical analysis of He bulk velocities, we investigate the structure function dependency on the solar wind state. We find a self-similar sealing in the range of minutes to days with characteristic structure function slopes deviating from the canonical Kolmogorov values. For comparison with previous studies, we also analyze H structure functions of the same time periods and discuss differences of coinciding He and H structure functions in the framework of the concept of intermittency.

Zurbuchen, Th.↗

NASA NTRS1996

Study of the velocity gradient tensor in turbulent flow

The behavior of the velocity gradient tensor, A(ij)=delta u(i)/delta x(j), was studied using three turbulent flows obtained from direct numerical simulation The flows studies were: an inviscid calculation of the interaction between two vortex tubes, a homogeneous isotropic flow, and a temporally evolving planar wake. Self-similar behavior for each flow was obtained when A(ij) was normalized with the mean strain rate. The case of the interaction between two vortex tubes revealed a finite sized coherent structure with topological characteristics predictable by a restricted Euler model. This structure was found to evolve with the peak vorticity as the flow approached singularity. Invariants of A(ij) within this structure followed a straight line relationship of the form: gamma(sup 3)+gammaQ+R=0, where Q and R are the second and third invariants of A(ij), and the eigenvalue gamma is nearly constant over the volume of this structure. Data within this structure have local strain topology of unstable-node/saddle/saddle. The characteristics of the velocity gradient tensor and the anisotropic part of a related acceleration gradient tensor H(ij) were also studied for a homogeneous isotropic flow and a temporally evolving planar wake. It was found that the intermediate principal eigenvalue of the rate-of-strain tensor of H(ij) tended to be negative, with local strain topology of the type stable-node/saddle/saddle. There was also a preferential eigenvalue direction. The magnitude of H(ij) in the wake flow was found to be very small when data were conditioned at high local dissipation regions. This result was not observed in the relatively low Reynolds number simulation of homogeneous isotropic flow. A restricted Euler model of the evolution of A(ij) was found to reproduce many of the topological features identified in the simulations.

Cheng, Wei-Ping↗

NASA NTRS1995

The 11 Micron Emissions of Carbon Stars

A new classification scheme of the IRAS LRS carbon stars is presented. It comprises the separation of 718 probable carbon stars into 12 distinct self-similar spectral groupings. Continuum temperatures are assigned and range from 470 to 5000 K. Three distinct dust species are identifiable: SiC, alpha:C-H, and MgS. In addition to the narrow 11 + micron emission feature that is commonly attributed to SiC, a broad 11 + micron emission feature, that is correlated with the 8.5 and 7.7 micron features, is found and attributed to alpha:C-H. SiC and alpha:C-H band strengths are found to correlate with the temperature progression among the Classes. We find a spectral sequence of Classes that reflects the carbon star evolutionary sequence of spectral types, or alternatively developmental sequences of grain condensation in carbon-rich circumstellar shells. If decreasing temperature corresponds to increasing evolution, then decreasing temperature corresponds to increasing C/O resulting in increasing amounts of carbon rich dust, namely alpha:C-H. If decreasing the temperature corresponds to a grain condensation sequence, then heterogeneous, or induced nucleation scenarios are supported. SiC grains precede alpha:C-H and form the nuclei for the condensation of the latter material. At still lower temperatures, MgS appears to be quite prevalent. No 11.3 micron PAH features are identified in any of the 718 carbon stars. However, one of the coldest objects, IRAS 15048-5702, and a few others, displays an 11.9 micron emission feature characteristic of laboratory samples of coronene. That feature corresponds to the C-H out of plane deformation mode of aromatic hydrocarbon. This band indicates the presence of unsaturated, sp(sup 3), hydrocarbon bonds that may subsequently evolve into saturated bonds, sp(sup 2), if, and when, the star enters the planetary nebulae phase of stellar evolution. The effusion of hydrogen from the hydrocarbon grain results in the evolution in wavelength of this 11.9 micron emission feature to the 11.3 micron feature.

Goebel, J. H.↗

NASA NTRS1995

The 11 Micron Emissions of Cabon Stars

A new classification scheme of the IRAS LRS carbon stars is presented. It comprises the separation of 718 probable carbon stars into 12 distinct self-similar spectral groupings. Continuum temperatures are assigned and range from 470 to 5000 K. Three distinct dust species are identifiable: SiC, alpha:C-H, and MgS. In addition to the narrow 11 + micron emission feature that is commonly attributed to SiC, a broad 11 + micron emission feature, that is correlated with the 8.5 and 7.7 micron features, is found and attributed to alpha:C-H. SiC and alpha:C-H band strengths are found to correlate with the temperature progression among the Classes. We find a spectral sequence of Classes that reflects the carbon star evolutionary sequence of spectral types, or alternatively developmental sequences of grain condensation in carbon-rich circumstellar shells. If decreasing temperature corresponds to increasing evolution, then decreasing temperature corresponds to increasing CIO resulting in increasing amounts of carbon rich dust, namely alpha:C-H. If decreasing the temperature corresponds to a grain condensation sequence, then heterogeneous, or induced nucleation scenarios are supported. SiC grains precede alpha:C-H and form the nuclei for the condensation of the latter material. At still lower temperatures, MgS appears to be quite prevalent. No 11.3 micron PAH features are identified in any of the 718 carbon stars. However, one of the coldest objects, IRAS 15048-5702, and a few others, displays an 11.9 micron emission feature characteristic of laboratory samples of coronene. That feature corresponds to the C-H out of plane deformation mode of aromatic hydrocarbon. This band indicates the presence of unsaturated, sp(sup 3), hydrocarbon bonds that may subsequently evolve into saturated bonds, sp(sup 2), if, and when, the star enters the planetary nebulae phase of stellar evolution. The effusion of hydrogen from the hydrocarbon grain results in the evolution in wavelength of this 11.9 micron emission feature to the 11.3 micron feature.

Goebel, J. H.↗

NASA NTRS1996

Nonlinear Response and Residual Strength of Damaged Stiffened Shells Subjected to Combined Loads

The results of an analytical study of the nonlinear response of stiffened fuselage shells with long cracks are presented. The shells are modeled with a hierarchical modeling strategy and analyzed with a nonlinear shell analysis code that maintains the shell in a nonlinear equilibrium state while the crack is grown. The analysis accurately accounts for global and local structural response phenomena. Fuselage skins, frames stringers and failsafe straps are included in the models. Results are presented for various combinations of internal pressure and mechanical bending, vertical shear and torsion loads, and the effects of crack orientation and location on the shell response are described. These results indicate that the nonlinear interaction between the in-plane stress resultants and the out-of-plane displacements near a crack can significantly affect the structural response of the shell, and the stress-intensity factors associated with a crack that are used to predict residual strength. The effects of representative combined loading conditions on the stress-intensity factors associated with a crack are presented. The effects of varying structural parameters on the stress-intensity factors associated with a crack, and on self-similar and non-self-similar crack-growth are also presented.

Starnes, James H., Jr.↗

NASA NTRS1995

Protostellar Collapse with a Shock

We reexamine both numerically and analytically the collapse of the singular isothermal sphere in the context of low-mass star formation. We consider the case where the onset of collapse is initiated by some arbitrary process which is accompanied by a central output of either heat or kinetic energy. We find two classes of numerical solutions describing this manner of collapse. The first approaches in time the expansion wave solution of Shu, while the second class is characterized by an ever-decreasing central accretion rate and the presence of an outwardly propagating weak shock. The collapse solution which represents the dividing case between these two classes is determined analytically by a similarity analysis. This solution shares with the expansion wave solution the properties that the gas remains stationary with an r(exp -2) density profile at large radius and that, at small radius, the gas free-falls onto a nascent core at a constant rate which depends only on the isothermal sound speed. This accretion rate is a factor of approx. 0.1 that predicted by the expansion wave solution. This reduction is due in part to the presence of a weak shock which propagates outward at 1.26 times the sound speed. Gas in the postshock region first moves out subsonically but is then decelerated and begins to collapse. The existence of two classes of numerical collapse solutions is explained in terms of the instability to radial perturbations of the analytic solution. Collapse occurring in the manner described by some of our solutions would eventually unbind a finite-sized core. However, this does not constitute a violation of the instability properties of the singular isothermal sphere which is unstable both to collapse and to expansion. To emphasize this, we consider a purely expanding solution for isothermal spheres. This solution is found to be self-similar and results in a uniform density core in the central regions of the gas. Our solutions may be relevant to the 'luminosity' problem of protostellar cores since the predicted central accretion rates are significantly reduced relative to that of the expansion wave solution. Furthermore, our calculations indicate that star-forming cloud cores are not very tightly bound and that modest disturbances can easily result in both termination of infall and dispersal of unaccreted material.

Tsai, John C.↗

NASA NTRS1996

Annual Research Briefs - 1996, Center for Turbulence Research

Partial contents include: (1) Simulation of jet impingement heat transfer with the k-e-V2 model; (2) A new methodology for turbulence modelers using Direct Numerical Simulation (DNS) database analysis; (3) A particle representation model for the deformation of homogeneous turbulence; (4) Modeling of inhomogeneous compressible turbulence using a two-scale statistical theory; (5) Lewis number effects on partially premixed flames; (6) Conditional moment closure of mixing and reaction in turbulent non-premixed combustion; (7) Dynamic models for LES of turbulent front propagation with a spectral method; (8) Jet noise using large eddy simulation; (9) Towards numerical simulations of trailing-edge aeroacoustics; (10) A model for the onset of vortex breakdown; (11) Compressing an elliptic vortex: transition to turbulence by tumble breakdown; (12) A new method for the adaptive control of vortex-wall interactions; (13) Symmetries in turbulent boundary layer flows; (14) Near-wall models in large eddy simulations of flow behind a backward-facing step; (15) Assessment of the subgrid-scale models at low and high Reynolds numbers; (16) Large-eddy simulations of flow around a NACA 4412 airfoil using unstructured grids; (17) Progress on LES of flow past a circular cylinder; (18) Experimental investigation of flow through an asymmetric plane diffuser; (19) Progress in the large-eddy simulation of an asymmetric plane diffuser; (20) A numerical study of self-similarity in a turbulent plane wake using large-eddy simulation; (21) On the generation of turbulent inflow conditions for boundary layer simulations, and (22) A new class of finite difference schemes.

COMPUTATIONAL FLUID DYNAMICS↗

NASA NTRS1995

The Distance to the Heliospheric VLF Emission Region

Two major episodes of heliospheric VLF emissions near 3 kHz have been observed by the Voyager spacecraft in 1983-1984 and 1992-1993. This higher-frequency component is apparently triggered by solar wind transients with sufficiently large spatial extents and energies to continue to propagate as shocks in the heliosheath. Entrainment of previously unshocked material and changed flow conditions in the heliosheath both tend to slow the shock propagation. The shock evolution is not self-similar. Rather, it is intermediate to two blast-wave similarity solutions in the moving solar wind frame. In one solution the shock moves as time to the 2/3 power and in the other as time to the 4/5 power. Using these models, the shock/Forbush decrease observed at Voyager 2 in September, 1991 and the turn-on of the 1992 emission is consistent with an emission region distance of approx. 130 AU (assuming no additional slowing of the shock in the heliosheath). If the termination shock was at approx. 70 AU when the transient shock collided with it, the true distance to the source region was probably closer to approx. 115 AU.

McNutt, R. L., Jr.↗

NASA NTRS1995

Radiation Pressure-Driven Magnetic Disk Winds in Broad Absorption Line Quasi-Stellar Objects

We explore a model in which QSO broad absorption lines (BALS) are formed in a radiation pressure-driven wind emerging from a magnetized accretion disk. The magnetic field threading the disk material is dragged by the flow and is compressed by the radiation pressure until it is dynamically important and strong enough to contribute to the confinement of the BAL clouds. We construct a simple self-similar model for such radiatively driven magnetized disk winds, in order to explore their properties. It is found that solutions exist for which the entire magnetized flow is confined to a thin wedge over the surface of the disk. For reasonable values of the mass-loss rate, a typical magnetic field strength such that the magnetic pressure is comparable to the inferred gas pressure in BAL clouds, and a moderate amount of internal soft X-ray absorption, we find that the opening angle of the flow is approximately 0.1 rad, in good agreement with the observed covering factor of the broad absorption line region.

DeKool, Martin↗

NASA NTRS1995

Protostellar Collapse with a Shock

We reexamine both numerically and analytically the collapse of the singular isothermal sphere in the context of low-mass star formation. We consider the case where the onset of collapse is initiated by some arbitrary process which is accompanied by a central output of either heat or kinetic energy. We find two classes of numerical solutions describing this manner of collapse. The first approaches in time the expansion wave solution of Shu, while the second class is characterized by an ever-decreasing central accretion rate and the presence of an outwardly propagating weak shock. The collapse solution which represents the dividing case between these two classes is determined analytically by a similarity analysis. This solution shares with the expansion wave solution the properties that the gas remains stationary with an r(sup -2) density profile at large radius and that, at small radius, the gas free-falls onto a nascent core at a constant rate which depends only on the isothermal sound speed. This accretion rate is a factor of approx. 0.1 that predicted by the expansion wave solution. This reduction is due in part to the presence of a weak shock which propagates outward at 1.26 times the sound speed. Gas in the postshock region first moves out subsonically but is then decelerated and begins to collapse. The existence of two classes of numerical collapse solutions is explained in terms of the instability to radial perturbations of the analytic solution. Collapse occurring in the manner described by some of our solutions would eventually unbind a finite-sized core. However, this does not constitute a violation of the instability properties of the singular isothermal sphere which is unstable both to collapse and to expansion. To emphasize this, we consider a purely expanding solution for isothermal spheres. This solution is found to be self-similar and results in a uniform density core in the central regions of the gas. Our solutions may be relevant to the 'luminosity' problem of protostellar cores since the predicted central accretion rates are significantly reduced relative to that of the expansion wave solution. Furthermore, our calculations indicate that star-forming cloud cores are not very tightly bound and that modest disturbances can easily result in both termination of infall and dispersal of unaccreted material.

Tsai, John C.↗

NASA NTRS1996

Ion Viscosity Mediated by Tangled Magnetic Fields: An Application to Black Hole Accretion Disks

We examine the viscosity associated with the shear stress exerted by ions in the presence of a tangled magnetic field. As an application, we consider the effect of this mechanism on the structure of black hole accretion disks. We do not attempt to include a self-consistent description of the magnetic field. Instead, we assume the existence of a tangled field with coherence length lambda(sub coh), which is the average distance between the magnetic 'kinks' that scatter the particles. For simplicity, we assume that the field is self-similar, and take lambda(sub coh) to be a fixed fraction zeta of the local disk height H. Ion viscosity in the presence of magnetic fields is generally taken to be the cross-field viscosity, wherein the effective mean free path is the ion Larmor radius lambda(sub L), which is much less than the ion-ion Coulomb mean free path A(sub ii) in hot accretion disks. However, we arrive at a formulation for a 'hybrid' viscosity in which the tangled magnetic field acts as an intermediary in the transfer of momentum between different layers in the shear flow. The hybrid viscosity greatly exceeds the standard cross-field viscosity when (lambda/lambda(sub L)) much greater than (lambda(sub L)/lambda(sub ii)), where lambda = ((lambda(sub ii)(sup -1) + lambda(sub (coh)(sup -1))(sup -1) is the effective mean free path for the ions. This inequality is well satisfied in hot accretion disks, which suggests that the ions may play a much larger role in the momentum transfer process in the presence of magnetic fields than was previously thought. The effect of the hybrid viscosity on the structure of a steady-state, two-temperature, quasi-Keplerian accretion disk is analyzed. The hybrid viscosity is influenced by the degree to which the magnetic field is tangled (represented by zeta = lambda(sub coh)), and also by the relative accretion rate M/M(sub E), where M(sub E) = L(sub E)/c(sup 2) and L(sub E) is the Eddington luminosity. We find that ion viscosity in the presence of magnetic fields (hybrid viscosity) can dominate over conventional magnetic viscosity for fields that are tangled on sufficiently small scales.

Subramanian, Prasad↗

NASA NTRS1983

Stability and Interaction of Coherent Structure in Supersonic Reactive Wakes

A theoretical formulation and analysis is presented for a study of the stability and interaction of coherent structure in reacting free shear layers. The physical problem under investigation is a premixed hydrogen-oxygen reacting shear layer in the wake of a thin flat plate. The coherent structure is modeled as a periodic disturbance and its stability is determined by the application of linearized hydrodynamic stability theory which results in a generalized eigenvalue problem for reactive flows. Detailed stability analysis of the reactive wake for neutral, symmetrical and antisymmetrical disturbance is presented. Reactive stability criteria is shown to be quite different from classical non-reactive stability. The interaction between the mean flow, coherent structure and fine-scale turbulence is theoretically formulated using the von-Kaman integral technique. Both time-averaging and conditional phase averaging are necessary to separate the three types of motion. The resulting integro-differential equations can then be solved subject to initial conditions with appropriate shape functions. In the laminar flow transition region of interest, the spatial interaction between the mean motion and coherent structure is calculated for both non-reactive and reactive conditions and compared with experimental data wherever available. The fine-scale turbulent motion determined by the application of integral analysis to the fluctuation equations. Since at present this turbulence model is still untested, turbulence is modeled in the interaction problem by a simple algebraic eddy viscosity model. The applicability of the integral turbulence model formulated here is studied parametrically by integrating these equations for the simple case of self-similar mean motion with assumed shape functions. The effect of the motion of the coherent structure is studied and very good agreement is obtained with previous experimental and theoretical works for non-reactive flow. For the reactive case, lack of experimental data made direct comparison difficult. It was determined that the growth rate of the disturbance amplitude is lower for reactive case. The results indicate that the reactive flow stability is in qualitative agreement with experimental observation.

Menon, Suresh↗

NASA NTRS1997

Fitting a 3-D analytic model of the coronal mass ejection to observations

The application of an analytic magnetohydrodynamic model is presented to observations of the time-dependent explusion of 3D coronal mass ejections (CMEs) out of the solar corona. This model relates the white-light appearance of the CME to its internal magnetic field, which takes the form of a closed bubble, filled with a partly anchored, twisted magnetic flux rope and embedded in an otherwise open background field. The density distribution frozen into the expanding CME expanding field is fully 3D, and can be integrated along the line of sight to reproduce observations of scattered white light. The model is able to reproduce the three conspicuous features often associated with CMEs as observed with white-light coronagraphs: a surrounding high-density region, an internal low-density cavity, and a high-density core. The model also describes the self-similar radial expansion of these structures. By varying the model parameters, the model can be fitted directly to observations of CMEs. It is shown how the model can quantitatively match the polarized brightness contrast of a dark cavity emerging through the lower corona as observed by the HAO Mauna Loa K-coronameter to within the noise level of the data.

Gibson, S. E.↗

NASA NTRS1994

Sonic and Supersonic Jet Plumes

Study of sonic and supersonic jet plumes are relevant to understanding such phenomenon as jet-noise, plume signatures, and rocket base-heating and radiation. Jet plumes are simple to simulate and yet, have complex flow structures such as Mach disks, triple points, shear-layers, barrel shocks, shock- shear- layer interaction, etc. Experimental and computational simulation of sonic and supersonic jet plumes have been performed for under- and over-expanded, axisymmetric plume conditions. The computational simulation compare very well with the experimental observations of schlieren pictures. Experimental data such as temperature measurements with hot-wire probes are yet to be measured and will be compared with computed values. Extensive analysis of the computational simulations presents a clear picture of how the complex flow structure develops and the conditions under which self-similar flow structures evolve. From the computations, the plume structure can be further classified into many sub-groups. In the proposed paper, detail results from the experimental and computational simulations for single, axisymmetric, under- and over-expanded, sonic and supersonic plumes will be compared and the fluid dynamic aspects of flow structures will be discussed.

Venkatapathy, E.↗

NASA NTRS1994

Experimental and Computational Study of Sonic and Supersonic Jet Plumes

Study of sonic and supersonic jet plumes are relevant to understanding such phenomenon as jet-noise, plume signatures, and rocket base-heating and radiation. Jet plumes are simple to simulate and yet, have complex flow structures such as Mach disks, triple points, shear-layers, barrel shocks, shock-shear-layer interaction, etc. Experimental and computational simulation of sonic and supersonic jet plumes have been performed for under- and over-expanded, axisymmetric plume conditions. The computational simulation compare very well with the experimental observations of schlieren pictures. Experimental data such as temperature measurements with hot-wire probes are yet to be measured and will be compared with computed values. Extensive analysis of the computational simulations presents a clear picture of how the complex flow structure develops and the conditions under which self-similar flow structures evolve. From the computations, the plume structure can be further classified into many sub-groups. In the proposed paper, detail results from the experimental and computational simulations for single, axisymmetric, under- and over-expanded, sonic and supersonic plumes will be compared and the fluid dynamic aspects of flow structures will be discussed.

Venkatapathy, E.↗

NASA NTRS1995

Linear Stability Regime Analysis of the Compressible Reacting Mixing Layer

Previous investigations have shown that a compressible reacting mixing layer can develop two peaks in the mean density weighted vorticity profile. Linear stability analyses show that at these peaks two distinct 'outer' instability modes appear in addition to the more common central mode, which exists unaccompanied in incompressible nonreacting flows. The present study parametrically analyzes the effects of compressibility, heat release, stoichiometry, and density ratio on the amplification rate and obliquity of each stability mode. The mean profiles used in the spatial stability calculation are generated by self-similar solutions of the compressible boundary layer equations combined with the assumption of infinitely fast chemistry. It is shown that the influence of stoichiometry and density ratio on the peaks of the density weighted vorticity profile determines which modes will dominate. Of particular interest are the conditions where two modes are equally amplified, causing the mixing layer to develop into a 'colayer' structure.

Day, M. J.↗

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.↗