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NASA NTRS2017

Scale Dependence of Multiplier Distributions for Particle Concentration, Enstrophy, and Dissipation in the Inertial Range of Homogeneous Turbulence

Turbulent flows preferentially concentrate inertial particles depending on their stopping time or Stokes number, which can lead to significant spatial variations in the particle concentration. Cascade models are one way to describe this process in statistical terms. Here, we use a direct numerical simulation (DNS) dataset of homogeneous, isotropic turbulence to determine probability distribution functions (PDFs) for cascade multipliers, which determine the ratio by which a property is partitioned into subvolumes as an eddy is envisioned to decay into smaller eddies. We present a technique for correcting effects of small particle numbers in the statistics. We determine multiplier PDFs for particle number, flow dissipation, and enstrophy, all of which are shown to be scale dependent. However, the particle multiplier PDFs collapse when scaled with an appropriately defined local Stokes number. As anticipated from earlier works, dissipation and enstrophy multiplier PDFs reach an asymptote for sufficiently small spatial scales. From the DNS measurements, we derive a cascade model that is used it to make predictions for the radial distribution function (RDF) for arbitrarily high Reynolds numbers, Re, finding good agreement with the asymptotic, infinite Re inertial range theory of Zaichik and Alipchenkov [New J. Phys. 11, 103018 (2009)]. We discuss implications of these results for the statistical modeling of the turbulent clustering process in the inertial range for high Reynolds numbers inaccessible to numerical simulations.

turbulent flows↗

NASA NTRS1986

Physical and numerical sources of computational inefficiency in integration of chemical kinetic rate equations: Etiology, treatment and prognosis

The design of a very fast, automatic black-box code for homogeneous, gas-phase chemical kinetics problems requires an understanding of the physical and numerical sources of computational inefficiency. Some major sources reviewed in this report are stiffness of the governing ordinary differential equations (ODE's) and its detection, choice of appropriate method (i.e., integration algorithm plus step-size control strategy), nonphysical initial conditions, and too frequent evaluation of thermochemical and kinetic properties. Specific techniques are recommended (and some advised against) for improving or overcoming the identified problem areas. It is argued that, because reactive species increase exponentially with time during induction, and all species exhibit asymptotic, exponential decay with time during equilibration, exponential-fitted integration algorithms are inherently more accurate for kinetics modeling than classical, polynomial-interpolant methods for the same computational work. But current codes using the exponential-fitted method lack the sophisticated stepsize-control logic of existing black-box ODE solver codes, such as EPISODE and LSODE. The ultimate chemical kinetics code does not exist yet, but the general characteristics of such a code are becoming apparent.

Pratt, D. T.↗

NASA NTRS1987

Evolution of a localized thermal explosion in a reactive gas

Experimental observations of ignition in premixed gaseous reactants indicate that perfectly homogeneous initiation is practically unrealizable. Instead, combustion first sets in, as a rule, at small, discrete sites where inherent inhomogeneities cause chemical activity to proceed preferentially and lead to localized explosions. Combustion waves propagating away from these hot spots or reaction centers eventually envelop the remaining bulk. This study examines the spatial structure and temporal evolution of a hot spot for a model involving Arrhenius kinetics. The hot spot, characterized by peaks in pressure and temperature with little diminution in local density, is shown to have one of two possible self-similar structures. The analysis employs a combination of asymptotics and numerics, and terminates when pressure and temperature in the explosion have peaked.

Jackson, T. L.↗

NASA NTRS1990

Structure of turbulence at high shear rate

The structure of homogeneous turbulence subject to high shear rate has been investigated by using three-dimensional, time-dependent numerical simulations of the Navier-Stokes equations. This study indicates that high shear rate alone is sufficient for generation of the streaky structures, and that the presence of a solid boundary is not necessary. Evolution of the statistical correlations is examined to determine the effect of high shear rate on the development of anisotropy in turbulence. It is shown that the streamwise fluctuating motions are enhanced so profoundly that a highly anisotropic turbulence state with a 'one-component' velocity field and 'two-component' vorticity field develops asymptotically as total shear increases. Because of high-shear rate, rapid distortion theory predicts remarkably well the anisotropic behavior of the structural quantities.

Lee, Moon Joo↗

DOE OSTI2024

On hydromagnetic wave interactions in collisionless, high- β plasmas

We describe the interaction of parallel-propagating Alfvén waves with ion-acoustic waves and other Alfvén waves, in magnetized, high- β collisionless plasmas. This is accomplished through a combination of analytical theory and numerical fluid simulations of the Chew–Goldberger–Low (CGL) magnetohydrodynamic (MHD) equations closed by Landau-fluid heat fluxes. An asymptotic ordering is employed to simplify the CGL-MHD equations and derive solutions for the deformation of an Alfvén wave that results from its interaction with the pressure anisotropy generated either by an ion-acoustic wave or another, larger-amplitude Alfvén wave. The difference in time scales of acoustic and Alfvénic fluctuations at high- β means that interactions that are local in wavenumber space yield little modification to either mode within the time it takes the acoustic wave to Landau damp away. Instead, order-unity changes in the amplitude of Alfvénic fluctuations can result after interacting with frequency-matched acoustic waves. Additionally, we show that the propagation speed of an Alfvén-wave packet in an otherwise homogeneous background is a function of its self-generated pressure anisotropy. This allows for the eventual interaction of separate co-propagating Alfvén-wave packets of differing amplitudes. The results of the CGL-MHD simulations agree well with these predictions, suggesting that theoretical models relying on the interaction of these modes should be reconsidered in certain astrophysical environments. Applications of these results to weak Alfvénic turbulence and to the interaction between the compressive and Alfvénic cascades in strong, collisionless turbulence are also discussed.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

NASA NTRS1994

The decay of axisymmetric homogeneous turbulence

The decay of a homogeneous turbulence generated by an axisymmetric distribution of random impulsive forces acting at the initial instant is considered. The impulsive forces may be either parallel or perpendicular to the symmetry axis. For impulsive forces which result in a kappa(exp 4) low wavenumber energy spectrum of the turbulence, it is determined that the flow approaches isotropy on all scales of motion at long-times provided the Reynolds number is large. However, for the type of impulsive forces originally proposed by Saffman in which a sq kappa low wavenumber energy spectrum is produced, the turbulence approaches isotropy only at the smallest scales and remains significantly anisotropic at the largest and energy-containing scales. Nevertheless, a similarity state of the flow field establishes itself asymptotically, in which the kinetic energy per unit mass of the turbulence decays as t(exp -6/5).

Chasnov, J. R.↗

DOE OSTI2022

Implications of inertial subrange scaling for stably stratified mixing

In this work, we investigate the effects of the turbulent dynamic range on active scalar mixing in stably stratified turbulence by adapting the theoretical passive scalar modelling and demonstrating their usefulness through consideration of the results of direct numerical simulations of statistically stationary homogeneous stratified and sheared turbulence. By analysis of inertial and inertial–convective subrange scalings, we show that the relationship between the active scalar and turbulence time scales is predicted by the ratio of the Kolmogorov and Obukhov–Corrsin constants, provided mean flow parameters permit the two subrange scalings to be appropriate approximations. We use the resulting relationship between time scales to parameterise an appropriate turbulent mixing coefficient $\varGamma \equiv \chi /\epsilon$, defined here as the ratio of available potential energy ($E_p$) and turbulent kinetic energy ($E_k$) dissipation rates. With the analysis presented here, we show that $\varGamma$ can be estimated by $E_p,E_k$ and a universal constant provided an appropriate Reynolds number is sufficiently high. This large Reynolds number regime appears here to occur at $ {{Re_b}} \equiv \epsilon / \nu N^{2} \gtrapprox 300$ where $\nu$ is the kinematic viscosity and $N$ is the characteristic buoyancy frequency. We propose a model framework for irreversible diapycnal mixing with robust theoretical parametrisation and asymptotic behaviour in this high-$ {{Re_b}}$ limit.

42 ENGINEERING↗

NASA NTRS1992

The structure of intense vorticity in homogeneous isotropic turbulence

The structure of the intense vorticity regions is studied in numerically simulated homogeneous, isotropic, equilibrium turbulent flow fields at four different Reynolds numbers in the range Re(sub lambda) = 36-171. In accordance with previous investigators, this vorticity is found to be organized in coherent, cylindrical or ribbon-like, vortices ('worms'). A statistical study suggests that they are just especially intense features of the background, O(omega'), vorticity. Their radii scale with the Kolmogorov microscale and their lengths with the integral scale of the flow. An interesting observation is that the Reynolds number based on the circulation of the intense vortices, gamma/nu, increases monotonically with Re(sub lambda), raising the question of the stability of the structures in the limit of Re(sub lambda) approaching infinity. One and two-dimensional statistics of vorticity and strain are presented; they are non-gaussian, and the behavior of their tails depends strongly on the Reynolds number. There is no evidence of convergence to a limiting distribution in our range of Re(sub lambda), even though the energy spectra and the energy dissipation rate show good asymptotic properties in the higher Reynolds number cases. Evidence is presented to show that worms are natural features of the flow and that they do not depend on the particular forcing scheme.

Jimenez, J.↗

NASA NTRS1988

Acousto-ultrasonic input-output characterization of unidirectional fiber composite plate by SV waves

A unidirectional fiberglass epoxy compostie specimen is modelled as a homogeneous transversely isotropic continuum plate medium. Acousto-ultrasonic noncontact input-output characterization is studied theoretically with a transmitting and a receiving transducer located on the same face of the plate. The single reflection problem for an incident SV wave at a plane boundary in transversely isotropic medium is analyzed. An obliquely incident SV wave results in a reflected SV wave and a reflected P wave for an angle of incidence of the incident SV wave less than the critical angle. Otherwise, there exists only an SV wave in the medium as the reflected P wave degenerates into a surface wave travelling parallel to the plane boundary. The amplitude ratio of the reflected SV wave is -1 when the angle of incidence is greater than or = the critical angle. The directional dependence of the phase velocity of the SV wave propagating in the transversely isotropic medium has a significant effect on the delay time, as opposed to the directional independence of the phase velocity of a shear wave propagating in an isotropic medium. The displacements associated with the SV wave in the plate and which may be detected by the noncontact receiving transducer are approximated by an asymptotic solution for an infinite transversely isotropic medium subjected to a harmonic point load.

Liao, Peter↗

NASA NTRS1997

A Near-Wall Reynolds-Stress Closure Without Wall Normals

Turbulent wall-bounded complex flows are commonly encountered in engineering practice and are of considerable interest in a variety of industrial applications. The presence of a wall significantly affects turbulence characteristics. In addition to the wall effects, turbulent wall-bounded flows become more complicated by the presence of additional body forces (e.g. centrifugal force and Coriolis force) and complex geometry. Most near-wall Reynolds stress models are developed from a high-Reynolds-number model which assumes turbulence is homogenous (or quasi-homogenous). Near-wall modifications are proposed to include wall effects in near-wall regions. In this process, wall normals are introduced. Good predictions could be obtained by Reynolds stress models with wall normals. However, ambiguity arises when the models are applied in flows with multiple walls. Many models have been proposed to model turbulent flows. Among them, Reynolds stress models, in which turbulent stresses are obtained by solving the Reynolds stress transport equations, have been proved to be the most successful ones. To apply the Reynolds stress models to wall-bounded flows, near-wall corrections accounting for the wall effects are needed, and the resulting models are called near-wall Reynolds stress models. In most of the existing near-wall models, the near-wall corrections invoke wall normals. These wall-dependent near-wall models are difficult to implement for turbulent flows with complex geometry and may give inaccurate predictions due to the ambiguity of wall normals at corners connecting multiple walls. The objective of this study is to develop a more general and flexible near-wall Reynolds stress model without using any wall-dependent variable for wall-bounded turbulent flows. With the aid of near-wall asymptotic analysis and results of direct numerical simulation, a new near-wall Reynolds stress model (NNWRS) is formulated based on Speziale et al.'s high-Reynolds-stress model with wall-independent near-wall corrections. Moreover, only one damping function is used for flows with a wide range of Reynolds numbers to ensure that the near-wall modifications diminish away from the walls.

Yuan, S. P.↗

NASA NTRS1990

Theory of biaxial graded-index optical fiber

A biaxial graded-index fiber with a homogeneous cladding is studied. Two methods, wave equation and matrix differential equation, of formulating the problem and their respective solutions are discussed. For the wave equation formulation of the problem it is shown that for the case of a diagonal permittivity tensor the longitudinal electric and magnetic fields satisfy a pair of coupled second-order differential equations. Also, a generalized dispersion relation is derived in terms of the solutions for the longitudinal electric and magnetic fields. For the case of a step-index fiber, either isotropic or uniaxial, these differential equations can be solved exactly in terms of Bessel functions. For the cases of an istropic graded-index and a uniaxial graded-index fiber, a solution using the Wentzel, Krammers and Brillouin (WKB) approximation technique is shown. Results for some particular permittivity profiles are presented. Also the WKB solutions is compared with the vector solution found by Kurtz and Streifer. For the matrix formulation it is shown that the tangential components of the electric and magnetic fields satisfy a system of four first-order differential equations which can be conveniently written in matrix form. For the special case of meridional modes, the system of equations splits into two systems of two equations. A general iterative technique, asymptotic partitioning of systems of equations, for solving systems of differential equations is presented. As a simple example, Bessel's differential equation is written in matrix form and is solved using this asymptotic technique. Low order solutions for particular examples of a biaxial and uniaxial graded-index fiber are presented. Finally numerical results obtained using the asymptotic technique are presented for particular examples of isotropic and uniaxial step-index fibers and isotropic, uniaxial and biaxial graded-index fibers.

Kawalko, Stephen F.↗

DOE OSTI2025

Neutron-capture Element Abundances of 491 Stars in Milky Way Dwarf Satellite Galaxies from Medium-resolution Spectra

The chemical compositions of evolved stars in Local Group dwarf spheroidal galaxies (dSphs) provide insight into the galaxy’s past star formation and nucleosynthesis. Neutron-capture element abundances are especially interesting. In particular, s-process elements can provide a third chemical clock for resolving star formation histories in addition to core-collapse and Type Ia supernovae. Likewise, the primary sites of the r-process are still areas of extensive research. Until now, the number of stars with neutron-capture element abundances in dSphs has been limited by the need for stars bright enough for high-resolution spectroscopy. We present abundance measurements of the neutron-capture elements Sr, Y, Ba, and Eu with errors <0.4 dex—as well as new measurements of Mg—in 491 stars in Sculptor, Fornax, Draco, Sextans, and Ursa Minor. The large number of stars in our sample is possible because we used medium-resolution spectra from the DEIMOS spectrograph, assembling the largest homogeneous set of neutron-capture abundances in dSphs to date. By utilizing the abundances of both s- and r-process elements, we find evidence of an s-process contribution at early times in Sculptor from our measurements of [Ba/Fe]. This is a potential signature of s-process nucleosynthesis in fast-rotating massive stars. By comparing our measurements of [Eu/Fe] with [Mg/Fe], we show the need for an r-process source that has a short delay time to enrich stars in the dSphs. Thus, neutron star mergers are likely not the sole source of r-process material in dSphs.

79 ASTRONOMY AND ASTROPHYSICS↗

NASA NTRS1994

Asymptotic Giant Branch stars as a source of short-lived radioactive nuclei in the solar nebula

We carried out a theoretical evaluation of the contribution of Asymptotic Giant Branch (AGB) stars to some short-lived (10(exp 6) less than or equal to Tau-bar less than or equal to 2 x 10(exp 7) yr) isotopes in the Interstellar Medium (ISM) and in the early solar system using stellar model calculations for thermally pulsing evolutionary phases of low-mass stars. The yields of s-process nuclei in the convective He-shell for different neutron exposures tau(sub 0) were obtained, and AGB stars were shown to produce several radioactive nuclei (especially Pd-107, Pb-205, Fe-60, Zr-93, Tc-99, Cs-135, and Hf-182) in diferent amounts. Assuming either contamination of the solar nebula from a single AGB star or models for continuous injection and mixing from many stars into the ISM, we calculate the ratios of radioactive to stable nuclei at the epoch of the Sun's formation. The dilution factor between the AGB ejecta and the early solar system matter is obtained by matching the observed Pd-107/Pd-108 and depends on the value of tau(sub 0). It is found that small masses M(sub He) of He-shell material (10(exp -4)-10(exp -7) solar mass) enriched in s-process nuclei are sufficient to contaminate 1 solar mass of the ISM to produce the Pd-107 found in the early solar system. Predictions are made for all of the other radioactive isotopes. The optimal model to explain several observed radioactive species at different states of the proto-solar nebula involves a single AGB star with a low neutron exposure (tau(sub 0) = 0.03 mbarn(sup -1)) which contaminated the cloud with a dilution factor of M(sub He)/solar mass approximately 1.5 x 10(exp -4). This will also contribute newly synthesized stable s-process nuclei in the amount of approximately 10(exp -4) of their abundances already present in the proto-solar cloud. Variations in the degree of homogenization (approximately 30%) of the injected material may account for some of the small general isotopic anomalies found in meteorites. It is also found that Fe-60 is produced in small but significant quantities that may be sufficient to explain the observations if the time elapsed delta from the contamination of the ISM to the formation of protoplanetary bodies is not higher than delta = 5 x 10(exp 6) yr. If delta is longer, up to 10 x 10(exp 6) yr, this would require the single AGB star to experience enhanced neutron densities (n(sub n) approximately 3 x 10(exp 9)n/cu cm) in the s-processing zone in order to compensate for the branching at Fe-59. The alternative model of long-term continuous ejection of matter from many AGB stars does not appear to match the observations. We also estimate the Al-26 production from the H-shell and find that the Al-26 abundance in the early solar system may be readily explained in a self-consistent manner. Moreover, Al-26 from AGB stars may contribute substantially to the galactic Al-26 gamma-source, while no significant gamma-flux from Co-60 (deriving from Fe-60 decay) is to be expected.

Wasserburg, G. J.↗