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Stellar convection 3: Convection at large Rayleigh numbers
A three dimensional study of convection in a self gravitating sphere of Boussinesq fluid with a Rayleigh number of 10 to the 10th power and a Prandtl of 1 is presented. The velocity and temperature of the fluid are computed at the largest wavelengths using spectral methods. A confirmation that the fluid is anisotropic and that the energy spectra are not smooth functions of wavelength but have a large amount of fine structure is discussed. The parameterization of the transport properties of the unresolvable inertial subrange with eddy viscosities and diffusivities is described. The time dependent fluctuations in the energy spectra and how they cascade from large to small wavelengths is examined.
Turbofan noise generation. Volume 1: Analysis
Computer programs were developed which calculate the in-duct acoustic modes excited by a fan/stator stae operating at subsonic tip speed. Three noise source mechanisms are included: (1) sound generated by the rotor blades interacting with turbulence ingested into, or generated within, the inlet duct; (2) sound generated by the stator vanes interacting with the turbulent wakes of the rotors blades; and (3) sound generated by the stator vanes interacting with the mean velocity deficit wakes of the rotor blades. The fan/stator stage is modeled as an ensemble of blades and vanes of zero camber and thickness enclosed within an infinite hard-walled annular duct. Turbulence drawn into or generated within the inlet duct is modeled as nonhomogeneous and anisotropic random fluid motion, superimposed upon a uniform axial mean flow, and convected with that flow. Equations for the duct mode amplitudes, or expected values of the amplitudes, are derived.
Linear theory of the Kelvin-Helmholtz instability in the low-latitude boundary layer
The feasibility is examined of establishing characteristic profiles across the magnetospheric low-latitude boundary layer for the Kelvin-Helmholtz mode so that these profiles can be compared with satellite observations or a latitudinal chain of ground stations. An anisotropic collisionless fluid model is used instead of conventional MHD, and the finite thickness of the boundary layer and the thickness and position of the current layer are taken into account. The instability is found to be enhanced by a decrease in the thickness of the shear layer and of the current layer and by the proximity of the 'current layer' to the outer edge of the shear layer. The velocity threshold for the onset of instability is insensitive to the thickness. Characteristic profiles of the variation of plasma and field parameters across the boundary are obtained, and the importance of parameters specifying the current layer position and thickness is demonstrated.
Adaptive Numerical Algorithms in Space Weather Modeling
Space weather describes the various processes in the Sun-Earth system that present danger to human health and technology. The goal of space weather forecasting is to provide an opportunity to mitigate these negative effects. Physics-based space weather modeling is characterized by disparate temporal and spatial scales as well as by different physics in different domains. A multi-physics system can be modeled by a software framework comprising of several components. Each component corresponds to a physics domain, and each component is represented by one or more numerical models. The publicly available Space Weather Modeling Framework (SWMF) can execute and couple together several components distributed over a parallel machine in a flexible and efficient manner. The framework also allows resolving disparate spatial and temporal scales with independent spatial and temporal discretizations in the various models. Several of the computationally most expensive domains of the framework are modeled by the Block-Adaptive Tree Solar wind Roe Upwind Scheme (BATS-R-US) code that can solve various forms of the magnetohydrodynamics (MHD) equations, including Hall, semi-relativistic, multi-species and multi-fluid MHD, anisotropic pressure, radiative transport and heat conduction. Modeling disparate scales within BATS-R-US is achieved by a block-adaptive mesh both in Cartesian and generalized coordinates. Most recently we have created a new core for BATS-R-US: the Block-Adaptive Tree Library (BATL) that provides a general toolkit for creating, load balancing and message passing in a 1, 2 or 3 dimensional block-adaptive grid. We describe the algorithms of BATL and demonstrate its efficiency and scaling properties for various problems. BATS-R-US uses several time-integration schemes to address multiple time-scales: explicit time stepping with fixed or local time steps, partially steady-state evolution, point-implicit, semi-implicit, explicit/implicit, and fully implicit numerical schemes. Depending on the application, we find that different time stepping methods are optimal. Several of the time integration schemes exploit the block-based granularity of the grid structure. The framework and the adaptive algorithms enable physics based space weather modeling and even forecasting.
A constitutive relation for the viscous flow of an oriented fiber assembly
A constitutive relation for an equivalent, homogeneous fluid is developed for the anisotropic viscous flow of an oriented assembly of discontinuous fibers suspended in a viscous fluid. The anisotropic viscous compliance matrix can be expressed in terms of three constants by assuming the equivalent fluid to be incompressible and the microstructure to have axial symmetry (transversely isotropic). By means of a micromechanics analysis, the three terms of the constitutive relation are expressed in terms of the viscosity of the matrix fluid, the fiber aspect ratio, and the fiber volume fraction. A comparison of the viscosity terms reveals that the elongational viscosity in the fiber direction varies as the square of the fiber aspect ratio and a complex function of the fiber volume fraction. Furthermore, the ratio of the axial elongational viscosity to the transverse elongational viscosity and both axial and transverse shear viscosities was shown to be 10 exp 4 - 10 exp 6 for fiber aspect ratio of 100-1000, except at extreme values of the fiber volume fraction.
Rheological Properties of Quasi-2D Fluids in Microgravity
In recent years, research on complex fluids and fluids in restricted geometries has attracted much attention in the scientific community. This can be attributed not only to the development of novel materials based on complex fluids but also to a variety of important physical phenomena which have barely been explored. One example is the behavior of membranes and thin fluid films, which can be described by two-dimensional (2D) rheology behavior that is quite different from 3D fluids. In this study, we have investigated the rheological properties of freely suspended films of a thermotropic liquid crystal in microgravity experiments. This model system mimics isotropic and anisotropic quasi 2D fluids [46]. We use inkjet printing technology to dispense small droplets (inclusions) onto the film surface. The motion of these inclusions provides information on the rheological properties of the films and allows the study of a variety of flow instabilities. Flat films have been investigated on a sub-orbital rocket flight and curved films (bubbles) have been studied in the ISS project OASIS. Microgravity is essential when the films are curved in order to avoid sedimentation. The experiments yield the mobility of the droplets in the films as well as the mutual mobility of pairs of particles. Experimental results will be presented for 2D-isotropic (smectic-A) and 2D-nematic (smectic-C) phases.
Density fluctuations in the interstellar medium: Evidence for anisotropic magnetogasdynamic turbulence. II - Stationary structures
A model of anisotropic, plasma-fluid variations was used to investigate the unknown origin of the power spectra of interstellar electron fluctuations inferred by Armstrong, Cordes, and Rickett (1981). The modeled electron variations are interpreted as density components of an anisotropic stationary mode of nonlinear magnetogasdynamics-tangential pressure balances. It is suggested that the wavenumber spectra of electron variations are identical to the spectra of the convecting velocity fields over a wide range of wavenumbers.
Matter in general relativity
Two theories of matter in general relativity, the fluid theory and the kinetic theory, were studied. Results include: (1) a discussion of various methods of completing the fluid equations; (2) a method of constructing charged general relativistic solutions in kinetic theory; and (3) a proof and discussion of the incompatibility of perfect fluid solutions in anisotropic cosmologies. Interpretations of NASA gravitational experiments using the above mentioned results were started. Two papers were prepared for publications based on this work.
Reciprocal relations for transmission coefficients - Theory and application
The authors present a rigorous proof of certain intuitively plausible reciprocal relations for time harmonic plane-wave transmission and reflection at the interface between a fluid and an anisotropic elastic solid. Precise forms of the reciprocity relations for the transmission coefficients and for the transmitted energy fluxes are derived, based on the reciprocity theorem of elastodynamics. It is shown that the reciprocity relations can be used in conjunction with measured values of peak amplitudes for transmission through a slab of the solid (water-solid-water) to obtain the water-solid coefficients. Experiments were performed for a slab of a unidirectional fiber-reinforced composite. Good agreement of the experimentally measured transmission coefficients with theoretical values was obtained.
The proton cyclotron instability and the anisotropy/B inverse correlation
Spacecraft observations in the strongly compressed subsolar magnetosheath show an inverse correlation between the proton temperature anistrophy (T(sub perpendicular to p)/T(sub parallel to p) greater than 1 where perpendicular to and parallel to denote directions perpendicular and parallel to the background magnetic field) and the parallel proton beta (beta(sub parallel to p). This manuscript uses one-dimensional hybrid simulations of the proton cyclotron anisotropy instability in homogeneous electron-proton plasmas to study this correlation which may represent a limited closure relation for fluid theories of anisotropic space plasmas. The emphasis is on driven simulation which increase the temperature anisotropy by periodically reducing the magnetic-field-aligned velocities of the protons. The late-time states from ensembles of both initial value and driven simulations yield very similar expressions for the proton anisotropy/beta(sub parallel to P) inverse correlation, and provide a basis for explaining differences between sheath observations from different spacecraft. The driven simulations also yield expressions for the maximum instability growth rate and the fluctuating field energy as functions of beta (sub parallel to p) and a parameter characterizing the anisotropy driver.
Additive Manufactured Ultra-Fine Lattice Structures for Propulsion Catalysts
Traditional mono-propulsion catalysts consist of coated ceramic or graphite foams that possess anisotropic mechanical and fluid properties limiting design, cost, availability, and operational use. Ultra-fine lattice structures are repeating unit cells with ligament thickness as small as 100 μm produced via Additive manufacture (AM). These lattice structures have the potential to replace coated foams used in a mono-propellant system catalysts. AM ultra-fine lattice structures are designed to mimic the operational intent of coated foams but with improved design flexibility, compressive strength, and flow behavior printed from into a single part directly from the preferred platinum metal alloy. The investigation objective was to conduct feasibility studies of AM ultra-fine lattice structures capable of replacing coated foams with superior functionality. NASA MSFC identified desired lattice characteristics and created designs while EOS developed optimized laser powder bed fusion AM parameters to manufacture Ti6Al4V and tungsten specimens. Optimized designs, computational tools, AM parameters, and post-process methods were developed. Specimens underwent x-ray micro-focus CT, metallographic inspection, compression testing, and flow testing. Results demonstrate that AM ultra-fine lattices improved geometric and performance repeatability with the potential for significantly increased availability while decreasing cost and lead time.
Additive Manufactured Ultra-Fine Lattice Structures for Propulsion Catalysts
Traditional mono-propulsion catalysts consist of coated ceramic or graphite foams that possess anisotropic mechanical and fluid properties limiting design, cost, availability, and operational use. Ultra-fine lattice structures are repeating unit cells with ligament thickness as small as 100 μm produced via Additive manufacture (AM). These lattice structures have the potential to replace coated foams used in a mono-propellant system catalysts. AM ultrafine lattice structures are designed to mimic the operational intent of coated foams but with improved design flexibility, compressive strength, and flow behavior printed from into a single part directly from the preferred platinum metal alloy. The investigation objective was to conduct feasibility studies of AM ultra-fine lattice structures capable of replacing coated foams with superior functionality. NASA MSFC identified desired lattice characteristics and created designs while EOS developed optimized laser powder bed fusion AM parameters to manufacture Ti6Al4V and tungsten specimens. Optimized designs, computational tools, AM parameters, and post-process methods were developed. Specimens underwent x-ray microfocus CT, metallographic inspection, compression testing, and flow testing. Results demonstrate that AM ultra-fine lattices improved geometric and performance repeatability with the potential for significantly increased availability while decreasing cost and lead time.
Additive Manufacture of Ultra-Fine Lattice Structures of Green Propulsion Catalysts
Traditional mono-propulsion catalysts consist of coated ceramic or graphite foams that possess anisotropic mechanical and fluid properties limiting design, cost, availability, and operational use. Ultra-fine lattice structures are repeating unit cells with ligament thickness as small as 100 μm produced via Additive manufacture (AM). These lattice structures have the potential to replace coated foams used in a mono-propellant system catalysts. AM ultrafine lattice structures are designed to mimic the operational intent of coated foams but with improved design flexibility, compressive strength, and flow behavior printed from into a single part directly from the preferred platinum metal alloy. The investigation objective was to conduct feasibility studies of AM ultra-fine lattice structures capable of replacing coated foams with superior functionality. NASA MSFC identified desired lattice characteristics and created designs while EOS developed optimized laser powder bed fusion AM parameters to manufacture Ti6Al4V and tungsten specimens. Optimized designs, computational tools, AM parameters, and post-process methods were developed. Specimens underwent x-ray microfocus CT, metallographic inspection, compression testing, and flow testing. Results demonstrate that AM ultra-fine lattices improved geometric and performance repeatability with the potential for significantly increased availability while decreasing cost and lead time.
Parallel Anisotropic Unstructured Grid Adaptation
Computational Fluid Dynamics (CFD) has become critical to the design and analysis of aerospace vehicles. Parallel grid adaptation that resolves multiple scales with anisotropy is identified as one of the challenges in the CFD Vision 2030 Study to increase the capacity and capability of CFD simulation. The Study also cautions that computer architectures are undergoing a radical change and dramatic increases in algorithm concurrency will be required to exploit full performance. This paper reviews four different methods to parallel anisotropic grid generation. They cover both ends of the spectrum: (i) using existing state-of-the-art software optimized for a single core and modifying it for parallel platforms and (ii) designing and implementing scalable software with incomplete, but rapidly maturating functionality. A brief overview for each grid adaptation system is presented in the context of a telescopic approach for multilevel concurrency. These methods employ different approaches to enable parallel execution, which provides a unique opportunity to illustrate the relative behavior of each approach. Qualitative and quantitative metric evaluations are used to draw lessons for future developments in this critical area for parallel CFD simulation.
Propagation of hydromagnetic waves in the upper F2-region
The theory of hydromagnetic-wave in the upper F2-region, in which electrons are in a transitional regime from collisional to collisionless conditions and ions are in a collisionless state, is examined. Derivation of the governing equations is based on the fact that the isotropic electrons are fluid-like, and the anisotropic ions follow kinetic equations modified by ion-electron collisions. Magneto-acoustic waves of a period of from about 0.2 to 10 sec are dissipated by ion Landau damping and electron thermal conduction and viscosity. Numerical solutions under ionospheric conditions show that the dissipation of hydromagnetic waves is insufficient to modify the large scale heating of the ionosphere.
Integrated Structural/Acoustic Modeling of Heterogeneous Panels
A model for the dynamic response of heterogeneous media is presented. A given medium is discretized into a number of subvolumes, each of which may contain an elastic anisotropic material, void, or fluid, and time-dependent boundary conditions are applied to simulate impact or incident pressure waves. The full time-dependent displacement and stress response throughout the medium is then determined via an explicit solution procedure. The model is applied to simulate the coupled structural/acoustic response of foam core sandwich panels as well as aluminum panels with foam inserts. Emphasis is placed on the acoustic absorption performance of the panels versus weight and the effects of the arrangement of the materials and incident wave frequency.
Purge dynamics of fuel cells.
Anisotropic porous media model for fluid motion in rectangular fuel cell cavities, analyzing pressure, velocity, stream functions and purge time