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At least 109 records · Page 6

The electromagnetic structure of interplanetary space

A method to calculate the three-dimensional structure of the interplanetary magnetic field is presented. The integrations are based on magnetograph recordings of longitudinal magnetic fields in the solar photosphere. The program by Altschuler and Newkirk is used to calculate the radial component of the magnetic field on the source surface, situated at r = 2.6r. This determines the inner boundary conditions for the integration outwards of the interplanetary field equations by means of the method that is described. Computer-drawn plots of the interplanetary field lines out to the earth's orbit are presented for the periods around the total solar eclipses of November 12, 1966, and March 7, 1970. During the former period the interplanetary field exhibited a clean, dipole-type structure, while during the latter period the field was more complicated and had four sectors in the equatorial plane. A movie was presented, showing how the interplanetary field structure rotates as seen by a magnetometer in the sun's equatorial plane.

Stenflo, J. O.↗

Computation of oscillating airfoil flows with one- and two-equation turbulence models

The ability of one- and two-equation turbulence models to predict unsteady separated flows over airfoils is evaluated. An implicit, factorized, upwind-biased numerical scheme is used for the integration of the compressible, Reynolds-averaged Navier-Stokes equations. The turbulent eddy viscosity is obtained from the computed mean flowfield by integration of the turbulent field equations. One- and two-equation turbulence models are first tested for a separated airfoil flow at fixed angle of incidence. The same models are then applied to compute the unsteady flowfields about airfoils undergoing oscillatory motion at low subsonic Mach numbers. Experimental cases where the flow has been tripped at the leading-edge and where natural transition was allowed to occur naturally are considered. The more recently developed turbulence models capture the physics of unsteady separated flow significantly better than the standard kappa-epsilon and kappa-omega models. However, certain differences in the hysteresis effects are observed. For an untripped high-Reynolds-number flow, it was found necessary to take into account the leading-edge transitional flow region to capture the correct physical mechanism that leads to dynamic stall.

Ekaterinaris, J. A.↗

Modeling Progressive Failure of Bonded Joints Using a Single Joint Finite Element

Enhanced finite elements are elements with an embedded analytical solution which can capture detailed local fields, enabling more efficient, mesh-independent finite element analysis. In the present study, an enhanced finite element is applied to generate a general framework capable of modeling an array of joint types. The joint field equations are derived using the principle of minimum potential energy, and the resulting solutions for the displacement fields are used to generate shape functions and a stiffness matrix for a single joint finite element. This single finite element thus captures the detailed stress and strain fields within the bonded joint, but it can function within a broader structural finite element model. The costs associated with a fine mesh of the joint can thus be avoided while still obtaining a detailed solution for the joint. Additionally, the capability to model non-linear adhesive constitutive behavior has been included within the method, and progressive failure of the adhesive can be modeled by using a strain-based failure criteria and re-sizing the joint as the adhesive fails. Results of the model compare favorably with experimental and finite element results.

Stapleton, Scott E.↗

Axion Perturbations: A General Analytical Treatment

Cosmological data provides us two key constraints on dark matter (DM): it must have a particular abundance, and it must have an adiabatic spectrum of density perturbations in the early universe. Many different cosmological scenarios have been proposed that establish the abundance of axion DM in qualitatively different ways. In this paper we emphasize that, despite this variety of backgrounds, the perturbations in axion DM can be understood from universal principles. How does a feebly interacting axion field acquire perturbations proportional to those of photons? How do the isocurvature power spectrum and non-Gaussianity depend on the background evolution of the universe? We answer these questions for a completely general choice of cosmological background and temperature-dependent axion potential. We show that the most general solution to the axion field equation on super-horizon scales is entirely determined by the family of background solutions for different initial field values . This holds for both the component in the field perturbation solution contributing to the DM isocurvature perturbation (enhanced at late times by the sensitivity of the DM abundance to the initial condition, , which can be large for initial conditions near the hilltop), and the other component that contributes to the DM curvature perturbation. In particular, we explain that an unperturbed axion field in the early universe evolving into one with nontrivial adiabatic perturbations is guaranteed by Weinberg's theorem on adiabatic modes. These results have been derived before with various assumptions, such as a radiation dominated background or a quadratic potential. Our aim is to give a clear, simple derivation that is manifestly independent of those assumptions, and thus can be applied to any cosmological axion scenario.

Cosmology and Nongalactic Astrophysics (astro-ph.C↗

A predictive strain-gradient model with no undetermined constants or length scales

A general meso–scale (GM) crystal plasticity (CP) model was developed that accounts for lower-order (strain hardening) and higher-order (internal stress) effects of geometrically necessary dislocations (GNDs). It is predictive: no arbitrary parameters or length scales were invoked and no ad hoc numerical techniques were employed. It uses general stress field equations for GND content and a novel harmonization technique to enforce consistency of elastic long-range singular defect fields with applied elastic-plastic fields. The model facilitates implementation in commercial finite element programs without requiring special elements, special boundary conditions, or access to element shape functions. GM simulations confirmed, with improved accuracy, previously published predictions of the Hall-Petch effect, Bauschinger effect, and anelasticity. Previously unpredicted phenomena were also predicted: anelasticity and hysteresis for single Ta crystals and strain-hardening stagnation. The internal stresses (higher-order effect) dominate at large length scales, while at small length scales, the GND density hardening (lower-order effect) dominates. As a result, GM predicts that strain heterogeneity and consequent GND internal stresses are important factors in anelasticity.

36 MATERIALS SCIENCE↗

Nonlinear force-free magnetic fields

The nonlinear properties of force-free magnetic fields are reviewed with particular reference to the mechanisms for the sudden release of stored energy in flares during the quasi-steady evolution of solar fields. It is shown that in the solar atmosphere, force-free fields with a nonconstant scalar function in the field equations are more likely to occur than those with a constant scalar function, and the nonlinear properties of these fields may give rise to many interesting physical effects. Consideration is then given to two possible mechanisms of field evolution: a model in which a force-free field in a medium of infinite electrical conductivity evolves in response to slowly changing boundary conditions brought about by photospheric motions in the solar active region, and a model in which a field in a medium of small finite electrical conductivity evolves in response to the slow Ohmic dissipation of the electric current.

Low, B. C.↗

The approximation of radiative effects in relativistic gravity - Gravitational radiation reaction and energy loss in nearly Newtonian systems

An argument is presented to determine the accuracy with which a solution of Einstein's field equations of gravitation must be approximated in order to describe the dominant effects of gravitational radiation emission from weak-field systems. Several previous calculations are compared in the light of this argument, and some apparent discrepancies among them are resolved. The majority of these calculations support the 'quadrupole formulae' for gravitational radiation energy loss and radiation reaction.

Walker, M.↗

Numerical modeling of a vortex stabilized arcjet thruster

A numerical method to solve the equations governing a vortex stabilized arcjet thruster is being developed. The model will allow the effects of swirling flow and geometry on arcjet thruster performance to be determined. The propellant flow equations, i.e., the axisymmetric, thin layer, Navier-Stokes equations, are solved using a Gauss-Siedel line-relaxation procedure. An implicit FTCS method is used to solve the electromagnetic field equations. A grid generation scheme was developed for an arbitrary arcjet geometry. The model will allow the radial and axial components of velocity and current distributions to be determined from a region upstream of the cathode, through the constrictor, to the exit plane of the nozzle.

Keith, Theo G., Jr.↗

Bulk-Flow Analysis of Hybrid Thrust Bearings for Advanced Cryogenic Turbopumps

A bulk-flow analysis and computer program for prediction of the static load performance and dynamic force coefficients of angled injection, orifice-compensated hydrostatic/hydrodynamic thrust bearings have been completed. The product of the research is an efficient computational tool for the design of high-speed thrust bearings for cryogenic fluid turbopumps. The study addresses the needs of a growing technology that requires of reliable fluid film bearings to provide the maximum operating life with optimum controllable rotordynamic characteristics at the lowest cost. The motion of a cryogenic fluid on the thin film lands of a thrust bearing is governed by a set of bulk-flow mass and momentum conservation and energy transport equations. Mass flow conservation and a simple model for momentum transport within the hydrostatic bearing recesses are also accounted for. The bulk-flow model includes flow turbulence with fluid inertia advection, Coriolis and centrifugal acceleration effects on the bearing recesses and film lands. The cryogenic fluid properties are obtained from realistic thermophysical equations of state. Turbulent bulk-flow shear parameters are based on Hirs' model with Moody's friction factor equations allowing a simple simulation for machined bearing surface roughness. A perturbation analysis leads to zeroth-order nonlinear equations governing the fluid flow for the thrust bearing operating at a static equilibrium position, and first-order linear equations describing the perturbed fluid flow for small amplitude shaft motions in the axial direction. Numerical solution to the zeroth-order flow field equations renders the bearing flow rate, thrust load, drag torque and power dissipation. Solution to the first-order equations determines the axial stiffness, damping and inertia force coefficients. The computational method uses well established algorithms and generic subprograms available from prior developments. The Fortran9O computer program hydrothrust runs on a Windows 95/NT personal computer. The program, help files and examples are licensed by Texas A&M University Technology License Office. The study of the static and dynamic performance of two hydrostatic/hydrodynamic bearings demonstrates the importance of centrifugal and advection fluid inertia effects for operation at high rotational speeds. The first example considers a conceptual hydrostatic thrust bearing for an advanced liquid hydrogen turbopump operating at 170,000 rpm. The large axial stiffness and damping coefficients of the bearing should provide accurate control and axial positioning of the turbopump and also allow for unshrouded impellers, therefore increasing the overall pump efficiency. The second bearing uses a refrigerant R134a, and its application in oil-free air conditioning compressors is of great technological importance and commercial value. The computed predictions reveal that the LH2 bearing load capacity and flow rate increase with the recess pressure (i.e. increasing orifice diameters). The bearing axial stiffness has a maximum for a recess pressure rati of approx. 0.55. while the axial damping coefficient decreases as the recess pressure ratio increases. The computer results from three flow models are compared. These models are a) inertialess, b) fluid inertia at recess edges only, and c) full fluid inertia at both recess edges and film lands. The full inertia model shows the lowest flow rates, axial load capacity and stiffness coefficient but on the other hand renders the largest damping coefficients and inertia coefficients. The most important findings are related to the reduction of the outflow through the inner radius and the appearance of subambient pressures. The performance of the refrigerant hybrid thrust bearing is evaluated at two operating speeds and pressure drops. The computed results are presented in dimensionless form to evidence consistent trends in the bearing performance characteristics. As the applied axial load increases, the bearing film thickness and flow rate decrease while the recess pressure increases. The axial stiffness coefficient shows a maximum for a certain intermediate load while the damping coefficient steadily increases. The computed results evidence the paramount of centrifugal fluid inertia at low recess pressures (i.e. low loads), and where there is actually an inflow through the bearing inner diameter, accompanied by subambient pressures just downstream of the bearing recess edge. These results are solely due to centrifugal fluid inertia and advection transport effects. Recommendations include the extension of the computer program to handle flexure pivot tilting pad hybrid bearings and the ability to calculate moment coefficients for shaft angular misalignments.

SanAndres, Luis↗

Three-dimensional continuum point cloud method for large deformation and its verification

This study presents a strong form based meshfree collocation method, which is named Continuum Point Cloud Method, to solve nonlinear field equations derived from classical mechanics for deformed bodies in three-dimensional Euclidean space. The method and its implementation are benchmarked against a nonlinear vector field using manufactured solutions. The analysis of mechanical fields firstly focuses on the study of St. Venant Kirchhoff and compressible neo-Hookean materials. Results for various initial boundary value problems are presented, including benchmark cases involving unidirectional tension and simple shear. Subsequently, the study concludes with an analysis of a displacement-controlled simulation of a compressible neo-Hookean material, specifically a bar that is pulled to 50% of its original length and rotated 90°. The pure tension case yields a 1.5% error in displacement between computed and expected values and a combined tension and torsion loading case provides further insight into material behavior under complex loading conditions. The resulting normal axial and transverse stress-strain curves are also presented. Lastly, the consistency and robustness of the proposed nonlinear numerical schemes are successfully demonstrated through various numerical experiments.

Compressible neo-Hookean materials↗

Acoustic forcing of a liquid drop

The development of systems such as acoustic levitation chambers will allow for the positioning and manipulation of material samples (drops) in a microgravity environment. This provides the capability for fundamental studies in droplet dynamics as well as containerless processing work. Such systems use acoustic radiation pressure forces to position or to further manipulate (e.g., oscillate) the sample. The primary objective was to determine the effect of a viscous acoustic field/tangential radiation pressure forcing on drop oscillations. To this end, the viscous acoustic field is determined. Modified (forced) hydrodynamic field equations which result from a consistent perturbation expansion scheme are solved. This is done in the separate cases of an unmodulated and a modulated acoustic field. The effect of the tangential radiation stress on the hydrodynamic field (drop oscillations) is found to manifest as a correction to the velocity field in a sublayer region near the drop/host interface. Moreover, the forcing due to the radiation pressure vector at the interface is modified by inclusion of tangential stresses.

Lyell, M. J.↗

The method of lines in analyzing solids containing cracks

A semi-numerical method is reviewed for solving a set of coupled partial differential equations subject to mixed and possibly coupled boundary conditions. The line method of analysis is applied to the Navier-Cauchy equations of elastic and elastoplastic equilibrium to calculate the displacement distributions in various, simple geometry bodies containing cracks. The application of this method to the appropriate field equations leads to coupled sets of simultaneous ordinary differential equations whose solutions are obtained along sets of lines in a discretized region. When decoupling of the equations and their boundary conditions is not possible, the use of a successive approximation procedure permits the analytical solution of the resulting ordinary differential equations. The use of this method is illustrated by reviewing and presenting selected solutions of mixed boundary value problems in three dimensional fracture mechanics. These solutions are of great importance in fracture toughness testing, where accurate stress and displacement distributions are required for the calculation of certain fracture parameters. Computations obtained for typical flawed specimens include that for elastic as well as elastoplastic response. Problems in both Cartesian and cylindrical coordinate systems are included. Results are summarized for a finite geometry rectangular bar with a central through-the-thickness or rectangular surface crack under remote uniaxial tension. In addition, stress and displacement distributions are reviewed for finite circular bars with embedded penny-shaped cracks, and rods with external annular or ring cracks under opening mode tension. The results obtained show that the method of lines presents a systematic approach to the solution of some three-dimensional mechanics problems with arbitrary boundary conditions. The advantage of this method over other numerical solutions is that good results are obtained even from the use of a relatively coarse grid.

Gyekenyesi, John P.↗

Quaternion wave equations in curved space-time

The quaternion formulation of relativistic quantum theory is extended to include curvilinear coordinates and curved space-time in order to provide a framework for a unified quantum/gravity theory. Six basic quaternion fields are identified in curved space-time, the four-vector basis quaternions are identified, and the necessary covariant derivatives are obtained. Invariant field equations are derived, and a general invertable coordinate transformation is developed. The results yield a way of writing quaternion wave equations in curvilinear coordinates and curved space-time as well as a natural framework for solving the problem of second quantization for gravity.

Edmonds, J. D., Jr.↗

Multidimensional computer simulation of Stirling cycle engines

The computer code ALGAE (algorithms for the gas equations) treats incompressible, thermally expandable, or locally compressible flows in complicated two-dimensional flow regions. The solution method, finite differencing schemes, and basic modeling of the field equations in ALGAE are applicable to engineering design settings of the type found in Stirling cycle engines. The use of ALGAE to model multiple components of the space power research engine (SPRE) is reported. Videotape computer simulations of the transient behavior of the working gas (helium) in the heater-regenerator-cooler complex of the SPRE demonstrate the usefulness of such a program in providing information on thermal and hydraulic phenomena in multiple component sections of the SPRE.

Hall, C. A.↗

Inertia and Double Bending of Light from Equivalence

Careful examination of light paths in an accelerated reference frame, with use of Special Relativity, can account fully for the observed bending of light in a gravitational field, not just half of it as reported in 1911. This analysis also leads to a Machian formulation of inertia similar to the one proposed by Einstein in 1912 and later derived from gravitational field equations in Minkowsky Space by Sciama in 1953. There is a clear inference from equivalence that there is some type of inertial mass increase in a gravitational field. It is the purpose of the current paper to suggest that equivalence provides a more complete picture of gravitational effects than previously thought, correctly predicting full light bending, and that since the theory of inertia is derivable from equivalence, any theory based on equivalence must take account of it. Einstein himself clearly was not satisfied with the status of inertia in GRT, as our quotes have shown. Many have tried to account for inertia and met with less than success, for example Davidson s integration of Sciama s inertia into GRT but only for a steady state cosmology [10], and the Machian gravity theory of Brans and Dicke [11]. Yet Mach s idea hasn t gone away, and now it seems that it cannot go away without also disposing of equivalence.

Shuler, Robert L., Jr.↗

Scale-covariant theory of gravitation and astrophysical applications

A scale-covariant theory of gravitation is presented which is characterized by a set of equations that are complete only after a choice of the scale function is made. Special attention is given to gauge conditions and units which allow gravitational phenomena to be described in atomic units. The generalized gravitational-field equations are derived by performing a direct scale transformation, by extending Riemannian geometry to Weyl geometry through the introduction of the notion of cotensors, and from a variation principle. Modified conservation laws are provided, a set of dynamical equations is obtained, and astrophysical consequences are considered. The theory is applied to examine certain homogeneous cosmological solutions, perihelion shifts, light deflections, secular variations of planetary orbital elements, stellar structure equations for a star in quasi-static equilibrium, and the past thermal history of earth. The possible relation of the scale-covariant theory to gauge field theories and their predictions of cosmological constants is discussed.

Canuto, V.↗

Superposed metric for spinning black hole binaries approaching merger

Here, we construct an approximate metric that represents the spacetime of spinning binary black holes (BBH) approaching merger. We build the metric as an analytical superposition of two Kerr metrics in harmonic coordinates, where we transform each black hole term with time-dependent boosts describing an inspiral trajectory. The velocities and trajectories of the boost are obtained by solving the post-Newtonian (PN) equations of motion at 3.5 PN order. We analyze the spacetime scalars of the new metric and we show that it is an accurate approximation of Einstein’s field equations in vacuum for a BBH system in the inspiral regime. Furthermore, to prove the effectiveness of our approach, we test the metric in the context of a 3D general relativistic magnetohydrodynamical (GRMHD) simulation of accreting minidisks around the black holes. We compare our results with a previous well-tested spacetime construction based on the asymptotic matching method. We conclude that our new spacetime is well-suited for long-term GRMHD simulations of spinning binary black holes on their way to the merger.

79 ASTRONOMY AND ASTROPHYSICS↗