Numerical modeling in induction heating for axisymmetric geometries
Chaboudez, C.; Glardon, R.; Mari, D.; Clain, S.; Rappaz, J.; Swierkosz, M.
1997-01-01
Induction heating is widely used in today`s industry, in operations such as metal hardening, preheating for forging operations, or brazing. It is a complex process, involving both electromagnetic and thermal phenomena. Since the design and the investigation of an induction heating system usually relies upon a series of tedious, expensive and long experiments, numerical simulation can be a valuable help in this field. This paper deals with numerical simulation of induction heating for axisymmetric geometries. A mathematical model is presented, together with a numerical scheme based on the Finite Element Method. A numerical simulation code was implemented using the model presented in this paper. A comparison between results given by the code and experimental measurements is provided.
Axisymmetric curvature-driven instability in a model divertor geometry
Farmer, W. A.; Ryutov, D. D.
2013-09-15
A model problem is presented which qualitatively describes a pressure-driven instability which can occur near the null-point in the divertor region of a tokamak where the poloidal field becomes small. The model problem is described by a horizontal slot with a vertical magnetic field which plays the role of the poloidal field. Line-tying boundary conditions are applied at the planes defining the slot. A toroidal field lying parallel to the planes is assumed to be very strong, thereby constraining the possible structure of the perturbations. Axisymmetric perturbations which leave the toroidal field unperturbed are analyzed. Ideal magnetohydrodynamics is used, and the instability threshold is determined by the energy principle. Because of the boundary conditions, the Euler equation is, in general, non-separable except at marginal stability. This problem may be useful in understanding the source of heat transport into the private flux region in a snowflake divertor which possesses a large region of small poloidal field, and for code benchmarking as it yields simple analytic results in an interesting geometry.
Canonical transformation for trapped/passing guiding-center orbits in axisymmetric tokamak geometry
Brizard, Alain J.; Duthoit, François-Xavier
2014-05-15
The generating function for the canonical transformation from the parallel canonical coordinates (s,p{sub ||}) to the action-angle coordinates (ζ, J) for trapped/passing guiding-center orbits in axisymmetric tokamak geometry is presented. Drawing on the analogy between the phase-space portraits of the librating/rotating pendulum and the trapped/passing guiding-center orbits, the generating function is expressed in terms of the Jacobi zeta function, which can then readily be used to obtain an explicit expression for the bounce-center transformation for trapped/passing-particle guiding-center orbits in axisymmetric tokamak geometry.
Compact formulas for bounce/transit averaging in axisymmetric tokamak geometry
Duthoit, F.-X.; Brizard, A. J.; Hahm, T. S.
2014-12-15
Compact formulas for bounce and transit orbit averaging of the fluctuation-amplitude eikonal factor in axisymmetric tokamak geometry, which is frequently encountered in bounce-gyrokinetic description of microturbulence, are given in terms of the Jacobi elliptic functions and elliptic integrals. These formulas are readily applicable to the calculation of the neoclassical susceptibility in the framework of modern bounce-gyrokinetic theory. In the long-wavelength limit for axisymmetric electrostatic perturbations, we recover the expression for the Rosenbluth-Hinton residual zonal flow [M. N. Rosenbluth and F. L. Hinton, Phys. Rev. Lett. 80, 724 (1998)] accurately.
On the prediction of swirling flowfields found in axisymmetric combustor geometries
NASA Technical Reports Server (NTRS)
Rhode, D. L.; Lilley, D. G.; Mclaughlin, D. K.
1981-01-01
The paper reports research restricted to steady turbulence flow in axisymmetric geometries under low speed and nonreacting conditions. Numerical computations are performed for a basic two-dimensional axisymmetrical flow field similar to that found in a conventional gas turbine combustor. Calculations include a stairstep boundary representation of the expansion flow, a conventional k-epsilon turbulence model and realistic accomodation of swirl effects. A preliminary evaluation of the accuracy of computed flowfields is accomplished by comparisons with flow visualizations using neutrally-buoyant helium-filled soap bubbles as tracer particles. Comparisons of calculated results show good agreement, and it is found that a problem in swirling flows is the accuracy with which the sizes and shapes of the recirculation zones may be predicted, which may be attributed to the quality of the turbulence model.
NASA Technical Reports Server (NTRS)
Rhodes, D. L.; Lilley, D. G.
1985-01-01
Numerical predictions, flow visualization experiments and time-mean velocity measurements were obtained for six basic nonreacting flowfields (with inlet swirl vane angles of 0 (swirler removed), 45 and 70 degrees and sidewall expansion angles of 90 and 45 degrees) in an idealized axisymmetric combustor geometry. A flowfield prediction computer program was developed which solves appropriate finite difference equations including a conventional two equation k-epsilon eddy viscosity turbulence model. The wall functions employed were derived from previous swirling flow measurements, and the stairstep approximation was employed to represent the sloping wall at the inlet to the test chamber. Recirculation region boundaries have been sketched from the entire flow visualization photograph collection. Tufts, smoke, and neutrally buoyant helium filled soap bubbles were employed as flow tracers. A five hole pitot probe was utilized to measure the axial, radial, and swirl time mean velocity components.
NASA Astrophysics Data System (ADS)
Cai, Jian; Roy, Somesh; Modest, Michael F.
2016-10-01
In simulations of periodic or symmetric geometries, computational domains are reduced by imaginary boundaries that exploit the symmetry conditions. Two boundary conditions are proposed for Discrete Ordinate Methods to solve axisymmetric radiation problems. Firstly, a specularly reflective boundary condition similar to that is used in Photon Monte Carlo methods is developed for Discrete Ordinate Methods. Secondly, the rotational invariant formulation is revisited for axisymmetric wedge geometries. Correspondingly, a new rotationally invariant boundary condition specially designed for axisymmetric problems on wedge shape is proposed to enforce the rotational invariance properties possessed by the radiative transfer equation (RTE) but violated by three-dimensional conventional Discrete Ordinate Methods. Both boundary conditions have the advantage that the discretization and linear equation solution procedures of conventional three-dimensional DOM are not affected by changing to a reduced geometry. Consistency, accuracy and efficiency of the new boundary conditions are demonstrated by multiple numerical examples involving periodic symmetry and axisymmetry. A comparison between specularly reflective boundary conditions and the rotationally invariant formulation shows that the latter offers several advantages for wedge geometries. In other symmetry conditions, when the rotational invariant formulation is not applicable, specular reflective boundary conditions are still effective.
Royston, T. J.; Spohnholtz, T.; Ellingson, W. A.; Energy Technology; Univ. of Illinois at Chicago
2000-03-01
A novel technique is proposed for the detection of localized flaws in otherwise axisymmetric structures. The technique is based on the split-mode phenomena that occurs when the degenerate vibratory modes of the axisymmetric structure become non-degenerate due to the flaw with altered mode shapes and shifted natural frequencies. A basic theoretical motivation is offered and computational and experimental studies on cylindrical structures are reported that verify the premises of the proposed methodology and provide an assessment of its specificity and sensitivity under confounding conditions, such as out-of-roundness.
NASA Astrophysics Data System (ADS)
Parker, Jeffrey B.; Catto, Peter J.
2012-08-01
We present a numerical solution of the drift-kinetic equation retaining the linearized Fokker-Planck collision operator which is valid for general axisymmetric magnetic geometry in the low collisionality limit. We use the well-known variational principle based on entropy production and expand in basis functions. Uniquely, we expand in pitch-angle basis functions which are eigenfunctions of the transit-averaged test particle collision operator. These eigenfunctions, which depend on the geometry, are extremely well suited to this problem, with only one or two basis functions required to obtain an accurate solution. As a simple example of the technique, the neoclassical ion heat flux and poloidal flow are calculated for circular flux surfaces and compared with analytic approximations for arbitrary aspect ratio.
Shapiro, A.B.
1983-08-01
The computer code FACET calculates the radiation geometric view factor (alternatively called shape factor, angle factor, or configuration factor) between surfaces for axisymmetric, two-dimensional planar and three-dimensional geometries with interposed third surface obstructions. FACET was developed to calculate view factors for input to finite-element heat-transfer analysis codes. The first section of this report is a brief review of previous radiation-view-factor computer codes. The second section presents the defining integral equation for the geometric view factor between two surfaces and the assumptions made in its derivation. Also in this section are the numerical algorithms used to integrate this equation for the various geometries. The third section presents the algorithms used to detect self-shadowing and third-surface shadowing between the two surfaces for which a view factor is being calculated. The fourth section provides a user's input guide followed by several example problems.
NASA Technical Reports Server (NTRS)
Lilley, D. G.; Rhode, D. L.
1982-01-01
A primitive pressure-velocity variable finite difference computer code was developed to predict swirling recirculating inert turbulent flows in axisymmetric combustors in general, and for application to a specific idealized combustion chamber with sudden or gradual expansion. The technique involves a staggered grid system for axial and radial velocities, a line relaxation procedure for efficient solution of the equations, a two-equation k-epsilon turbulence model, a stairstep boundary representation of the expansion flow, and realistic accommodation of swirl effects. A user's manual, dealing with the computational problem, showing how the mathematical basis and computational scheme may be translated into a computer program is presented. A flow chart, FORTRAN IV listing, notes about various subroutines and a user's guide are supplied as an aid to prospective users of the code.
Perturbation analysis of trapped-particle dynamics in axisymmetric dipole geometry
Duthoit, F.-X.; Brizard, A. J.; Peysson, Y.; Decker, J.
2010-10-15
The bounce-action-angle coordinates (J,{zeta}) for charged particles trapped in an axisymmetric dipole magnetic field are constructed by perturbation analysis. First, the lowest-order bounce-action-angle coordinates (J{sub 0},{zeta}{sub 0}) are derived for deeply trapped particles in the harmonic-oscillator approximation. Next, the Lie-transform perturbation method is used to derive higher-order anharmonic action-angle corrections (J=J{sub 0}+{epsilon}{sub t}J{sub 1}, {zeta}={zeta}{sub 0}+{epsilon}{sub t{zeta}1}), where the dimensionless parameter {epsilon}{sub t{identical_to}}(s{sub b}/r{sub e}){sup 2}<<1 is defined as the ratio of the turning-point distance |s{sub b}| (measured from the equator) along a magnetic field line labeled by the equatorial distance r{sub e}. Explicit expressions (with anharmonic corrections) for the canonical parallel coordinates s(J,{zeta}) and p{sub ||}(J,{zeta}) are presented, which satisfy the canonical identity {l_brace}s,p{sub ||{r_brace}{identical_to}}1. Lastly, analytical expressions for the bounce and drift frequencies (which include anharmonic corrections) yield excellent agreement with exact numerical results.
Global axisymmetric simulations of two-fluid reconnection in an experimentally relevant geometry
Murphy, N. A.; Sovinec, C. R.
2008-04-15
To address the interplay between local and global effects in magnetic reconnection, axisymmetric numerical simulations for the Magnetic Reconnection Experiment [M. Yamada et al., Phys. Plasmas 4, 1936 (1997)] are performed using the NIMROD code [C. R. Sovinec et al., J. Comput. Phys. 195, 355 (2004)]. The 'pull' and 'push' modes of the device are simulated both with and without two-fluid effects in the generalized Ohm's law. As in experiment, the pull reconnection rate is slowed due to the presence of downstream pressure associated with the outflow. Effects induced by toroidicity include a radially inward drift of the current sheet during pull reconnection and a radially outward displacement of the X-point during push reconnection. These effects result from the inboard side of the current sheet having less volume than the outboard side, facilitating the formation of large scale pressure gradients since the inboard side is more susceptible to a buildup or depletion of density. Toroidicity also leads to asymmetry of the quadrupole field during two-fluid simulations. During pull reconnection, the outboard lobes of the quadrupole typically peak close to the X-point, whereas the inboard quadrupole lobes peak near the flux core surfaces. At experimentally relevant parameters, the reconnection rate is found to depend more on the mode of operation than on the inclusion of two-fluid effects. The current sheet in two-fluid co-helicity simulations tilts due to a Lorentz force associated with the guide field and the outflowing electrons, resulting in asymmetric flow patterns for both ions and electrons. In two-fluid counter-helicity simulations, the Hall effect leads to a radial shift in position of the X-point and an asymmetric outflow pattern, which is examined in terms of separate force-density contributions. In general, asymmetry due to toroidicity or the Hall effect often leads to uneven outflow, which then feeds back on the reconnection process through large scale
Kelleher, W.P.
1987-01-01
In the assessment of Magnetohydrodynamic (MHD) equilibrium and Poloidal Field Coil (PFC) arrangement for toroidal axisymmetric geometry, the Grad-Shafranov equation must be solved, either analytically or numerically. Existing numerical tools have been developed primarily for mainframe usage and can prove cumbersome for screening assessments and parametric evaluations. The objective of this thesis was to develop a personal computer (PC)-based calculational tool for assessing MHD/PFC problems in a highly interactive mode, well suited for scoping studies. The approach adopted involves a two-step process: first the MHD equilibrium is calculated and then the PFC arrangement, consistent with the equilibrium, is determined in an interactive design environment. The PC-based system developed consists of two programs: (1) PCEQ, which solve the MHD equilibrium problem and (2) PFDE-SIGN, which is employed to arrive at a PFC arrangement. PCEQ provides an output file including, but not limited to, the following: poloidal beta, total beta, safety factors, q, on axis and on edge. PCEQ plots the following contours and/or profiles: flux, pressure and toroidal current density, safety factor, and ratio of plasma toroidal field to vacuum field.
NASA Astrophysics Data System (ADS)
Sambasivan, Shiv Kumar; Shashkov, Mikhail J.; Burton, Donald E.
2013-03-01
A finite volume cell-centered Lagrangian formulation is presented for solving large deformation problems in cylindrical axisymmetric geometries. Since solid materials can sustain significant shear deformation, evolution equations for stress and strain fields are solved in addition to mass, momentum and energy conservation laws. The total strain-rate realized in the material is split into an elastic and plastic response. The elastic and plastic components in turn are modeled using hypo-elastic theory. In accordance with the hypo-elastic model, a predictor-corrector algorithm is employed for evolving the deviatoric component of the stress tensor. A trial elastic deviatoric stress state is obtained by integrating a rate equation, cast in the form of an objective (Jaumann) derivative, based on Hooke's law. The dilatational response of the material is modeled using an equation of state of the Mie-Grüneisen form. The plastic deformation is accounted for via an iterative radial return algorithm constructed from the J2 von Mises yield condition. Several benchmark example problems with non-linear strain hardening and thermal softening yield models are presented. Extensive comparisons with representative Eulerian and Lagrangian hydrocodes in addition to analytical and experimental results are made to validate the current approach.
Geometry, Student's Text, Part II, Unit 14.
ERIC Educational Resources Information Center
Allen, Frank B.; And Others
Unit 14 in the SMSG secondary school mathematics series is a student text covering the following topics in geometry: areas of polygonal regions, similarity, circles and spheres, characterization of sets, constructions, areas of circles and sectors, volumes of solids, and plane coordinate geometry. Appendices cover Eratosthenes' measurement of the…
NASA Technical Reports Server (NTRS)
Sugioka, I.; Widnall, S. E.
1985-01-01
The self induced evolution of a vortex sheet was simulated by modeling the sheet using an integration of discrete elements of vorticity. Replacing small sections of a vortex sheet by flat panels of constant vorticity is found to reproduce more accurately the initial conditions for the Lagrangian simulation technique than replacement by point vortices. The flat panel method for the vortex sheet was then extended to model axisymmetric vortex sheets. The local and far field velocities induced by the axisymmetric panels were obtained using matched asymptotic analysis, and some of the uncertainties involved in other models of the axisymmetric vortex sheet have been eliminated. One important result of this analysis is the determination of the proper choice of core size for a circular vortex filament which may replace a section of an axisymmetric vortex sheet. Roll-up of both two dimensional and axisymmetric vortex sheets was computed using the panel methods developed in the report.
NASA Technical Reports Server (NTRS)
Carson, G. T., Jr.; Lee, E. E., Jr.
1981-01-01
Quantitative pressure and force data for five axisymmetric boattail nozzle configurations were examined. These configurations simulate the variable-geometry feature of a single nozzle design operating over a range of engine operating conditions. Five nozzles were tested in the Langley 16-Foot Transonic Tunnel at Mach numbers from 0.60 to 1.30. The experimental data were also compared with theoretical predictions.
Madasu, Srinath; Borhan, Ali; Ultman, James
2007-03-01
Mass transfer coefficients were predicted and compared for uptake of a formaldehyde-air gas system using an axisymmetric single path model (ASPM) and a three-dimensional computational fluid dynamics model (CFDM) in three-generation model geometry at steady expiratory flow. The flow and concentration fields in the ASPM were solved using Galerkin's finite-element method and in the CFDM using a commercial finite-element software, FIDAP. Numerical results were compared for two different inlet flow rates, wall mass transfer coefficients, and bifurcation angles. The mass transfer coefficients variation with bifurcation unit from the ASPM and CFDM compared qualitatively and quantitatively closely at all flows and lower wall mass transfer coefficients for both 40 degrees and 70 degrees bifurcation angles. However, at higher wall mass transfer coefficients, quantitatively they were within 40% for both the bifurcation angles. Also, at higher flow and wall mass transfer coefficients, they were off qualitatively for a 70 degrees bifurcation angle although the uptake compared qualitatively. This is due to the normalization of uptake within a bifurcation unit with the average of inlet and outlet average concentrations. Both CFDM and ASPM predict the same trends of increase in mass transfer coefficients with inlet flow and wall mass transfer coefficients. Also, the local values of the mass transfer coefficients compared closely at all conditions. These results validate the simplified ASPM and the complex CFDM. Mass transfer coefficients increase with bifurcation angles and with a flat inlet velocity profile compared to a parabolic velocity profile since the flow is non-fully developed and hence, the uptake increases.
NASA Technical Reports Server (NTRS)
Chick, Kenneth M.; Gombosi, Tamas I.
1993-01-01
A numerical solution for the multiple light scattering in spherical axisymmetric geometry is applied to the simulation of images of a coma as it would appear to a near-flying satellite such as Giotto. The appearance of symmetric comas and dust jets is examined in detail; the nucleus visibility is studied; the effect of forward scattering is considered; and single and multiple scattering effects are quantified. Attention is given to simulated images of a coma with a hollow cone of dust, as predicted by dust-gas hydrodynamic modeling. The cone's appearance is very similar to the northern area of activity on Comet Halley, observed by the Giotto HMC.
Axisymmetric capillary waves on thin annular liquid sheets. II. Spatial development
NASA Astrophysics Data System (ADS)
Mehring, C.; Sirignano, W. A.
2000-06-01
The forced motion of semi-infinite axisymmetric thin inviscid annular liquid sheets, exiting from a nozzle or atomizer into a surrounding void under zero gravity but with constant gas-core pressure is analyzed by means of the reduced-dimension approach described in C. Mehring and W. A. Sirignano [Phys. Fluids 12, 1417 (2000)]. Linear analytical time-dependent ("limit-cycle") solutions to the pure boundary-value problem are presented as well as linear and nonlinear numerical (transient) solutions to the mixed boundary- and initial-value problem of initially undisturbed sheets harmonically forced at the orifice or nozzle exit. Group velocities for the six independent solutions to the linear boundary-value problem are used to determine the location of boundary conditions. Numerical simulations of the linear transient problem are employed to validate these predictions. Parameter studies on sheet breakup and collapse lengths as well as on breakup and collapse times are reported. The dependence on modulation frequency, modulated disturbance amplitude, Weber number, and annular radius is presented for various cases of the mixed problem, i.e., for linearly or nonlinearly stable and unstable, dilationally or sinusoidally forced sheets. Nonlinear effects often have significant effects on breakup times and lengths or on collapse times and lengths. Nonlinear wave forms can deviate substantially from linear predictions resulting in major impacts on the size of the rings and shells that will remain after breakup.
Madasu, Srinath; Borhan, Ali; Ultman, James
2007-05-01
Mass transfer coefficients were predicted and compared for uptake of reactive gas system using an axisymmetric single-path model (ASPM) with experimentally predicted values in a two-generation geometry and with a three-dimensional computational fluid dynamics model (CFDM) in a three-generation model geometry at steady inspiratory flow with a flat inlet velocity profile. The flow and concentration fields in the ASPM were solved using Galerkin's finite element method and in the CFDM using a commercial finite element software FIDAP. ASPM predicted average gas phase mass transfer coefficients within 25% of the experimental values. Numerical results in terms of overall mass transfer coefficients from the two models within each bifurcation unit were compared for two different inlet flow rates, wall mass transfer coefficients, and bifurcation angles. The overall mass transfer coefficients variation with bifurcation unit from the ASPM and CFDM compared qualitatively and quantitatively closely at lower wall mass transfer coefficients for both 40 degree and 70 degree bifurcation angles. But at higher wall mass transfer coefficients, quantitatively they were off in the range of 2-10% for 40 degree bifurcation angle and in the range of 4-15% for 70 degree bifurcation angle. Both CFDM and ASPM predict the same trends of increase in mass transfer coefficients with inlet flow, wall mass transfer coefficients, and during inspiration compared to expiration. Higher mass transfer coefficients were obtained with a flat velocity profile compared to a parabolic velocity profile using ASPM. These results validate the simplified ASPM and the complex CFDM.
Dependence of Helium II Turbulence on Nonlocality and System Geometry
NASA Astrophysics Data System (ADS)
Dix, Owen M.
We have investigated two aspects of open-orbit vortices in He II turbulence simulations. These vortices form when using the local induction approximation in a system with full periodic boundaries. Using the fully nonlocal Biot-Savart law prevents this state from forming, but also increases computation time. We found that including the nonlocal calculation up to some truncated distance, on order of the average intervortex spacing, prevents this open-orbit state from forming. It is capable of significantly reducing computation time, while still accurately modeling homogeneous turbulence, as compared to the fully-nonlocal calculation. We also sought a geometric approach to this phenomenon. Open-orbit vortices are in a state that is topologically distinct from ordinary turbulence. Vortex reconnections change the topology of the superfluid and are immediately responsible for vortices entering the open-orbit state. They are also required to free vortices from it. The periodic cube, equivalent to a flat 3-torus, is multiply-connected. This property allows the open-orbit vortex state to persist. We use the 3-sphere geometry, which is simply-connected, while keeping as many other properties of Euclidean turbulence as possible. However, the simplest driving velocity on the 3-sphere, the Hopf vector field, is not irrotational. It results in a state of highly-polarized turbulence, dissimilar to ordinary homogeneous turbulence found in experiment.
Modeling axisymmetric flow and transport.
Langevin, Christian D
2008-01-01
Unmodified versions of common computer programs such as MODFLOW, MT3DMS, and SEAWAT that use Cartesian geometry can accurately simulate axially symmetric ground water flow and solute transport. Axisymmetric flow and transport are simulated by adjusting several input parameters to account for the increase in flow area with radial distance from the injection or extraction well. Logarithmic weighting of interblock transmissivity, a standard option in MODFLOW, can be used for axisymmetric models to represent the linear change in hydraulic conductance within a single finite-difference cell. Results from three test problems (ground water extraction, an aquifer push-pull test, and upconing of saline water into an extraction well) show good agreement with analytical solutions or with results from other numerical models designed specifically to simulate the axisymmetric geometry. Axisymmetric models are not commonly used but can offer an efficient alternative to full three-dimensional models, provided the assumption of axial symmetry can be justified. For the upconing problem, the axisymmetric model was more than 1000 times faster than an equivalent three-dimensional model. Computational gains with the axisymmetric models may be useful for quickly determining appropriate levels of grid resolution for three-dimensional models and for estimating aquifer parameters from field tests. PMID:18384599
Modeling axisymmetric flow and transport
Langevin, C.D.
2008-01-01
Unmodified versions of common computer programs such as MODFLOW, MT3DMS, and SEAWAT that use Cartesian geometry can accurately simulate axially symmetric ground water flow and solute transport. Axisymmetric flow and transport are simulated by adjusting several input parameters to account for the increase in flow area with radial distance from the injection or extraction well. Logarithmic weighting of interblock transmissivity, a standard option in MODFLOW, can be used for axisymmetric models to represent the linear change in hydraulic conductance within a single finite-difference cell. Results from three test problems (ground water extraction, an aquifer push-pull test, and upconing of saline water into an extraction well) show good agreement with analytical solutions or with results from other numerical models designed specifically to simulate the axisymmetric geometry. Axisymmetric models are not commonly used but can offer an efficient alternative to full three-dimensional models, provided the assumption of axial symmetry can be justified. For the upconing problem, the axisymmetric model was more than 1000 times faster than an equivalent three-dimensional model. Computational gains with the axisymmetric models may be useful for quickly determining appropriate levels of grid resolution for three-dimensional models and for estimating aquifer parameters from field tests.
Mathematical aspects of molecular replacement. II. Geometry of motion spaces.
Chirikjian, Gregory S; Yan, Yan
2012-03-01
Molecular replacement (MR) is a well established computational method for phasing in macromolecular crystallography. In MR searches, spaces of motions are explored for determining the appropriate placement of rigid models of macromolecules in crystallographic asymmetric units. In the first paper of this series, it was shown that this space of motions, when endowed with an appropriate composition operator, forms an algebraic structure called a quasigroup. In this second paper, the geometric properties of these MR search spaces are explored and analyzed. This analysis includes the local differential geometry, global geometry and symmetry properties of these spaces.
Multiplane gravitational lensing. II. Global geometry of caustics.
NASA Astrophysics Data System (ADS)
Petters, A. O.
1995-08-01
The global geometry of caustics due to a general multiplane gravitational lens system is investigated. Cusp-counting formulas and total curvatures are determined for individual caustics as well as whole caustic networks. The notion of light path obstruction points is fundamental in these studies. Lower bounds are found for such points and are used to get upper bounds for the total curvature. Curvature functions of caustics are also treated. All theorems obtained do not rely on the detailed nature of any specific potential assumed as a gravitational lens model, but on the overall differential-topological properties of general potentials.
Li, Yang; Lehmann, Teresa
2012-06-01
The solution structure of Fe(II)-peplomycin was determined from NMR data collected for this molecule. As found previously for Fe(II)- and Co(II)-bound bleomycin; the coordination sphere of the metal is composed of the primary and secondary amines in β-aminoalanine, the pyrimidine and imidazole rings in the pyrimidinylpropionamide, and β-hydroxyhistidine moieties, respectively, the amine nitrogen in β-hydroxyhistidine, and either the carbamoyl group in mannose or a solvent molecule. The two most discussed coordination geometries for the aforementioned ligands in metallo-bleomycins have been tested against the NMR data generated for Fe(II)-peplomycin. The interpretation of the experimental evidence obtained through molecular dynamics indicates that both geometries are equally likely in solution for this compound in the absence of DNA, but arguments are offered to explain why one of these geometries is preferred in the presence of DNA.
Differential geometry based solvation model II: Lagrangian formulation.
Chen, Zhan; Baker, Nathan A; Wei, G W
2011-12-01
Solvation is an elementary process in nature and is of paramount importance to more sophisticated chemical, biological and biomolecular processes. The understanding of solvation is an essential prerequisite for the quantitative description and analysis of biomolecular systems. This work presents a Lagrangian formulation of our differential geometry based solvation models. The Lagrangian representation of biomolecular surfaces has a few utilities/advantages. First, it provides an essential basis for biomolecular visualization, surface electrostatic potential map and visual perception of biomolecules. Additionally, it is consistent with the conventional setting of implicit solvent theories and thus, many existing theoretical algorithms and computational software packages can be directly employed. Finally, the Lagrangian representation does not need to resort to artificially enlarged van der Waals radii as often required by the Eulerian representation in solvation analysis. The main goal of the present work is to analyze the connection, similarity and difference between the Eulerian and Lagrangian formalisms of the solvation model. Such analysis is important to the understanding of the differential geometry based solvation model. The present model extends the scaled particle theory of nonpolar solvation model with a solvent-solute interaction potential. The nonpolar solvation model is completed with a Poisson-Boltzmann (PB) theory based polar solvation model. The differential geometry theory of surfaces is employed to provide a natural description of solvent-solute interfaces. The optimization of the total free energy functional, which encompasses the polar and nonpolar contributions, leads to coupled potential driven geometric flow and PB equations. Due to the development of singularities and nonsmooth manifolds in the Lagrangian representation, the resulting potential-driven geometric flow equation is embedded into the Eulerian representation for the purpose of
Differential geometry based solvation model II: Lagrangian formulation
Chen, Zhan; Baker, Nathan A.; Wei, G. W.
2010-01-01
Solvation is an elementary process in nature and is of paramount importance to more sophisticated chemical, biological and biomolecular processes. The understanding of solvation is an essential prerequisite for the quantitative description and analysis of biomolecular systems. This work presents a Lagrangian formulation of our differential geometry based solvation model. The Lagrangian representation of biomolecular surfaces has a few utilities/advantages. First, it provides an essential basis for biomolecular visualization, surface electrostatic potential map and visual perception of biomolecules. Additionally, it is consistent with the conventional setting of implicit solvent theories and thus, many existing theoretical algorithms and computational software packages can be directly employed. Finally, the Lagrangian representation does not need to resort to artificially enlarged van der Waals radii as often required by the Eulerian representation in solvation analysis. The main goal of the present work is to analyze the connection, similarity and difference between the Eulerian and Lagrangian formalisms of the solvation model. Such analysis is important to the understanding of the differential geometry based solvation model. The present model extends the scaled particle theory (SPT) of nonpolar solvation model with a solvent-solute interaction potential. The nonpolar solvation model is completed with a Poisson-Boltzmann (PB) theory based polar solvation model. The differential geometry theory of surfaces is employed to provide a natural description of solvent-solute interfaces. The minimization of the total free energy functional, which encompasses the polar and nonpolar contributions, leads to coupled potential driven geometric flow and Poisson-Boltzmann equations. Due to the development of singularities and nonsmooth manifolds in the Lagrangian representation, the resulting potential-driven geometric flow equation is embedded into the Eulerian representation for
NASA Astrophysics Data System (ADS)
Centeno, Felipe Roman; Brittes, Rogério; França, Francis. H. R.; Ezekoye, Ofodike A.
2015-05-01
The weighted-sum-of-gray-gases (WSGG) model is widely used in engineering computations of radiative heat transfer due to its relative simplicity, robustness and flexibility. This paper presents the computation of radiative heat transfer in a 2D axisymmetric chamber using two WSGG models to compute radiation in H2O and CO2 mixtures. The first model considers a fixed ratio between the molar concentrations of H2O and CO2, while the second allows the solution for arbitrary ratios. The correlations for both models are based on the HITEMP2010 database. The test case considers typical conditions found in turbulent methane flames, with steep variations in the temperature field as well as in the molar concentrations of the participating species. To assess the accuracy of the WSGG model, the results are compared with a solution obtained by line-by-line integration (LBL) of the spectrum.
NASA Technical Reports Server (NTRS)
Tam, C. K. W.; Burton, D. E.
1984-01-01
An investigation is conducted of the phenomenon of sound generation by spatially growing instability waves in high-speed flows. It is pointed out that this process of noise generation is most effective when the flow is supersonic relative to the ambient speed of sound. The inner and outer asymptotic expansions corresponding to an excited instability wave in a two-dimensional mixing layer and its associated acoustic fields are constructed in terms of the inner and outer spatial variables. In matching the solutions, the intermediate matching principle of Van Dyke and Cole is followed. The validity of the theory is tested by applying it to an axisymmetric supersonic jet and comparing the calculated results with experimental measurements. Very favorable agreements are found both in the calculated instability-wave amplitude distribution (the inner solution) and the near pressure field level contours (the outer solution) in each case.
ERIC Educational Resources Information Center
Stanford Univ., CA. School Mathematics Study Group.
The first chapter, Perpendiculars and Parallels (II), of the ninth unit in this SMSG series includes a discussion of the properties of triangles, circles and perpendiculars, parallels in space, perpendicular lines and planes, and parallel planes. The next chapter, on coordinate geometry, covers distance; midpoints; algebraic descriptions of…
NASA Astrophysics Data System (ADS)
Pfefferlé, D.; Graves, J. P.; Cooper, W. A.
2015-05-01
To identify under what conditions guiding-centre or full-orbit tracing should be used, an estimation of the spatial variation of the magnetic field is proposed, not only taking into account gradient and curvature terms but also parallel currents and the local shearing of field-lines. The criterion is derived for general three-dimensional magnetic equilibria including stellarator plasmas. Details are provided on how to implement it in cylindrical coordinates and in flux coordinates that rely on the geometric toroidal angle. A means of switching between guiding-centre and full-orbit equations at first order in Larmor radius with minimal discrepancy is shown. Techniques are applied to a MAST (mega amp spherical tokamak) helical core equilibrium in which the inner kinked flux-surfaces are tightly compressed against the outer axisymmetric mantle and where the parallel current peaks at the nearly rational surface. This is put in relation with the simpler situation B(x, y, z) = B0[sin(kx)ey + cos(kx)ez], for which full orbits and lowest order drifts are obtained analytically. In the kinked equilibrium, the full orbits of NBI fast ions are solved numerically and shown to follow helical drift surfaces. This result partially explains the off-axis redistribution of neutral beam injection fast particles in the presence of MAST long-lived modes (LLM).
Cobalt(II) complex with new terpyridine ligand: An ab initio geometry optimization investigation
NASA Astrophysics Data System (ADS)
Ciesielski, Artur; Gorczyński, Adam; Jankowski, Piotr; Kubicki, Maciej; Patroniak, Violetta
2010-06-01
Structural parameters of a complex formed between Co(II), and a terpyridine ligand were investigated using the unrestricted Becke three-parameter hybrid exchange functional combined with the Lee-Yang-Parr correlation functional (B3LYP) with the LANL2DZ, 6-31G(d,p), and 6-31G++(d,p) basis sets applied for geometry optimizations. The computations reveal that frequently used methods, which take into consideration primary and secondary interactions, can often be efficient in optimizing structural geometries of systems based on organic molecules and transition-metal ions.
THREE-DIMENSIONAL GEOMETRIES AND THE ANALYSIS OF H II REGIONS
Wood, Kenneth; Barnes, J. E.; Ercolano, Barbara; Haffner, L. M.; Reynolds, R. J.; Dale, J.
2013-06-20
We compare emission line intensities from photoionization models of smooth and fractal shell geometries for low density H II regions, with particular focus on the low-ionization diagnostic diagram [N II]/H{alpha} versus H{alpha}. Building on previously published models and observations of Barnard's Loop, we show that the observed range of intensities and variations in the line intensity ratios may be reproduced with a three-dimensional shell geometry. Our models adopt solar abundances throughout the model nebula, in contrast with previous one-dimensional modeling which suggested the variations in line intensity ratios could only be reproduced if the heavy element abundances were increased by a factor of {approx}1.4. For spatially resolved H II regions, the multiple sightlines that pierce and sample different ionization and temperature conditions within smooth and fractal shells produce a range of line intensities that are easily overlooked if only the total integrated intensities from the entire nebula model are computed. Our conclusion is that inference of H II region properties, such as elemental abundances, via photoionization models of one-dimensional geometries must be treated with caution and further tested through three-dimensional modeling.
Zn(II) and Hg(II) binding to a designed peptide that accommodates different coordination geometries.
Szunyogh, Dániel; Gyurcsik, Béla; Larsen, Flemming H; Stachura, Monika; Thulstrup, Peter W; Hemmingsen, Lars; Jancsó, Attila
2015-07-28
Designed metal ion binding peptides offer a variety of applications in both basic science as model systems of more complex metalloproteins, and in biotechnology, e.g. in bioremediation of toxic metal ions, biomining or as artificial enzymes. In this work a peptide (HS: Ac-SCHGDQGSDCSI-NH2) has been specifically designed for binding of both Zn(II) and Hg(II), i.e. metal ions with different preferences in terms of coordination number, coordination geometry, and to some extent ligand composition. It is demonstrated that HS accommodates both metal ions, and the first coordination sphere, metal ion exchange between peptides, and speciation are characterized as a function of pH using UV-absorption-, synchrotron radiation CD-, (1)H-NMR-, and PAC-spectroscopy as well as potentiometry. Hg(II) binds to the peptide with very high affinity in a {HgS2} coordination geometry, bringing together the two cysteinates close to each end of the peptide in a loop structure. Despite the high affinity, Hg(II) is kinetically labile, exchanging between peptides on the subsecond timescale, as indicated by line broadening in (1)H-NMR. The Zn(II)-HS system displays more complex speciation, involving monomeric species with coordinating cysteinates, histidine, and a solvent water molecule, as well as HS-Zn(II)-HS complexes. In summary, the HS peptide displays conformational flexibility, contains many typical metal ion binding groups, and is able to accommodate metal ions with different structural and ligand preferences with high affinity. As such, the HS peptide may be a scaffold offering binding of a variety of metal ions, and potentially serve for metal ion sequestration in biotechnological applications.
Type II InAs/GaAsSb quantum dots: Highly tunable exciton geometry and topology
Llorens, J. M.; Wewior, L.; Cardozo de Oliveira, E. R.; Alén, B.; Ulloa, J. M.; Utrilla, A. D.; Guzmán, A.; Hierro, A.
2015-11-02
External control over the electron and hole wavefunctions geometry and topology is investigated in a p-i-n diode embedding a dot-in-a-well InAs/GaAsSb quantum structure with type II band alignment. We find highly tunable exciton dipole moments and largely decoupled exciton recombination and ionization dynamics. We also predicted a bias regime where the hole wavefunction topology changes continuously from quantum dot-like to quantum ring-like as a function of the external bias. All these properties have great potential in advanced electro-optical applications and in the investigation of fundamental spin-orbit phenomena.
XAFS study of copper(II) complexes with square planar and square pyramidal coordination geometries
NASA Astrophysics Data System (ADS)
Gaur, A.; Klysubun, W.; Nitin Nair, N.; Shrivastava, B. D.; Prasad, J.; Srivastava, K.
2016-08-01
X-ray absorption fine structure of six Cu(II) complexes, Cu2(Clna)4 2H2O (1), Cu2(ac)4 2H2O (2), Cu2(phac)4 (pyz) (3), Cu2(bpy)2(na)2 H2O (ClO4) (4), Cu2(teen)4(OH)2(ClO4)2 (5) and Cu2(tmen)4(OH)2(ClO4)2 (6) (where ac, phac, pyz, bpy, na, teen, tmen = acetate, phenyl acetate, pyrazole, bipyridine, nicotinic acid, tetraethyethylenediamine, tetramethylethylenediamine, respectively), which were supposed to have square pyramidal and square planar coordination geometries have been investigated. The differences observed in the X-ray absorption near edge structure (XANES) features of the standard compounds having four, five and six coordination geometry points towards presence of square planar and square pyramidal geometry around Cu centre in the studied complexes. The presence of intense pre-edge feature in the spectra of four complexes, 1-4, indicates square pyramidal coordination. Another important XANES feature, present in complexes 5 and 6, is prominent shoulder in the rising part of edge whose intensity decreases in the presence of axial ligands and thus indicates four coordination in these complexes. Ab initio calculations were carried out for square planar and square pyramidal Cu centres to observe the variation of 4p density of states in the presence and absence of axial ligands. To determine the number and distance of scattering atoms around Cu centre in the complexes, EXAFS analysis has been done using the paths obtained from Cu(II) oxide model and an axial Cu-O path from model of a square pyramidal complex. The results obtained from EXAFS analysis have been reported which confirmed the inference drawn from XANES features. Thus, it has been shown that these paths from model of a standard compound can be used to determine the structural parameters for complexes having unknown structure.
NASA Astrophysics Data System (ADS)
Kramer, S. L.; Ghosh, V. J.; Breitfeller, M.; Wahl, W.
2016-11-01
Third generation high brightness light sources are designed to have low emittance and high current beams, which contribute to higher beam loss rates that will be compensated by Top-Off injection. Shielding for these higher loss rates will be critical to protect the projected higher occupancy factors for the users. Top-Off injection requires a full energy injector, which will demand greater consideration of the potential abnormal beam miss-steering and localized losses that could occur. The high energy electron injection beam produces significantly higher neutron component dose to the experimental floor than a lower energy beam injection and ramped operations. Minimizing this dose will require adequate knowledge of where the miss-steered beam can occur and sufficient EM shielding close to the loss point, in order to attenuate the energy of the particles in the EM shower below the neutron production threshold (<10 MeV), which will spread the incident energy on the bulk shield walls and thereby the dose penetrating the shield walls. Designing supplemental shielding near the loss point using the analytic shielding model is shown to be inadequate because of its lack of geometry specification for the EM shower process. To predict the dose rates outside the tunnel requires detailed description of the geometry and materials that the beam losses will encounter inside the tunnel. Modern radiation shielding Monte-Carlo codes, like FLUKA, can handle this geometric description of the radiation transport process in sufficient detail, allowing accurate predictions of the dose rates expected and the ability to show weaknesses in the design before a high radiation incident occurs. The effort required to adequately define the accelerator geometry for these codes has been greatly reduced with the implementation of the graphical interface of FLAIR to FLUKA. This made the effective shielding process for NSLS-II quite accurate and reliable. The principles used to provide supplemental
NASA Astrophysics Data System (ADS)
Gaur, A.; Klysubun, W.; Soni, Balram; Shrivastava, B. D.; Prasad, J.; Srivastava, K.
2016-10-01
X-ray absorption spectroscopy (XAS) is very useful in revealing the information about geometric and electronic structure of a transition-metal absorber and thus commonly used for determination of metal-ligand coordination. But XAFS analysis becomes difficult if differently coordinated metal centers are present in a system. In the present investigation, existence of distinct coordination geometries around metal centres have been studied by XAFS in a series of trimesic acid Cu(II) complexes. The complexes studied are: Cu3(tma)2(im)6 8H2O (1), Cu3(tma)2(mim)6 17H2O (2), Cu3(tma)2(tmen)3 8.5H2O (3), Cu3(tma) (pmd)3 6H2O (ClO4)3 (4) and Cu3(tma)2 3H2O (5). These complexes have not only Cu metal centres with different coordination but in complexes 1-3, there are multiple coordination geometries present around Cu centres. Using XANES spectra, different coordination geometries present in these complexes have been identified. The variation observed in the pre-edge features and edge features have been correlated with the distortion of the specific coordination environment around Cu centres in the complexes. XANES spectra have been calculated for the distinct metal centres present in the complexes by employing ab-initio calculations. These individual spectra have been used to resolve the spectral contribution of the Cu centres to the particular XANES features exhibited by the experimental spectra of the multinuclear complexes. Also, the variation in the 4p density of states have been calculated for the different Cu centres and then correlated with the features originated from corresponding coordination of Cu. Thus, these spectral features have been successfully utilized to detect the presence of the discrete metal centres in a system. The inferences about the coordination geometry have been supported by EXAFS analysis which has been used to determine the structural parameters for these complexes.
The axisymmetric stellar wind of AG Carinae
NASA Technical Reports Server (NTRS)
Schulte-Ladbeck, Regina E.; Clayton, Geoffrey C.; Hillier, D. John; Harries, Tim J.; Howarth, Ian D.
1994-01-01
We present optical linear spectropolarimetry of the Luminous Blue Variable AG Carinae obtained after a recent visual brightness increase. The absence of He II lambda 4686 emission, together with the weakening of the He I spectrum and the appearance of Fe lines in the region around 5300 A, confirm that AG Car has started a new excursion across the HR diagram. The H alpha line profile exhibits very extended line wings that are polarized differently in both amount and position angle from either the continuum or the line core. The polarization changes across H alpha, together with variable continuum polarization, indicate the presence of intrinsic polarization. Coexistence of the line-wing polarization with extended flux-line wings evidences that both are formed by electron scattering in a dense wind. The position angle rotates across the line profiles, in a way that presently available models suggest is due to rotation and expansion of the scattering material. AG Car displays very large variations of its linear polarization with time, Delta P approximately 1.2%, indicating significant variations in envelope opacity. We find that the polarization varies along a preferred position angle of approximately 145 deg (with a scatter of +/- 10 deg) which we interpret as a symmetry axis of the stellar wind (with an ambiguity of 90 deg). This position angle is co-aligned with the major axis of the AG Car ring nebula and perpendicular to the AG Car jet. Our observations thus suggest that the axisymmetric geometry seen in the resolved circumstellar environment at various distances already exists within a few stellar radii of AG Car. From the H alpha polarization profile we deduce an interstellar polarization of Q = 0.31%, U = -1.15% at H alpha. The inferred interstellar polarization implies that the intrinsic polarization is not always of the same sign. This indicates either significant temporal changes in the envelope geometry, or it may arise from effects of multiple scattering
Axisymmetric single shear element combustion instability experiment
NASA Technical Reports Server (NTRS)
Breisacher, Kevin J.
1993-01-01
The combustion stability characteristics of a combustor consisting of a single shear element and a cylindrical chamber utilizing LOX and gaseous hydrogen as propellants are presented. The combustor geometry and the resulting longitudinal mode instability are axisymmetric. Hydrogen injection temperature and pyrotechnic pulsing were used to determine stability boundaries. Mixture ratio, fuel annulus gap, and LOX post configuration were varied. Performance and stability data are presented for chamber pressures of 300 and 1000 psia.
Axisymmetric single shear element combustion instability experiment
NASA Technical Reports Server (NTRS)
Breisacher, Kevin J.
1993-01-01
The combustion stability characteristics of a combustor consisting of a single shear element and a cylindrical chamber utilizing LOX and gaseous hydrogen as propellants are presented. The combustor geometry and the resulting longitudinal mode instability are axisymmetric. Hydrogen injection temperature and pyrotechnic pulsing were used to determine stability boundaries. Mixture ratio, fuel annulus gap, and LOX post configuration were varied. Performance and stability data were obtained for chamber pressures of 300 and 1000 psia.
Black holes in the Einstein-Gauss-Bonnet theory and the geometry of their thermodynamics—II
NASA Astrophysics Data System (ADS)
Biswas, Ritabrata; Chakraborty, Subenoy
2010-03-01
In the present work we study (i) the charged black hole in Einstein-Gauss-Bonnet (EGB) theory, known as the Einstein-Maxwell-Gauss-Bonnet (EMGB) black hole and (ii) the black hole in EGB gravity with a Yang-Mills field. The thermodynamic geometry of these two black hole solutions has been investigated, using the modified entropy in Gauss-Bonnet theory.
Galaxies, Axisymmetric Systems and Relativity
NASA Astrophysics Data System (ADS)
MacCallum, M. A. H.
2011-06-01
List of contributors; Preface; Prof. W. B. Bonnor: a biological sketch; Part I. Galaxies and Cosmology: 1. The origin of large scale cosmic structure B. J. T. Jones and P. L. Palmer; 2. The problem of origin of the primordial pertubations and the modern cosmology V. N. Lukash and I. D. Novikov; 3. The automorphism group and field equations for Bianchi universes W. L. Rogue and G. F. R. Ellis; 4. New perspectives on galaxy formation J. Silk; Part II. Axisymmetric Systems: 5. On exact radiative solutions representing finite sources J. Bicak; 6. Proof of a generalized Geroch conjecture I. Hauser and F. J. Ernst; 7. Limits of the double Kerr solution C. Hoenselaers; 8. Non-inheritance of static symmetry by Maxwell fields M. A. H. MacCallum and N. Van den Bergh; 9. Stationary axisymmetric electrovacuum fields in general relativity G. Neugebauer and D. Kramer; 10. An almost conformal approach to axial symmetry Z. Perjes; 11. Conformally stationary axisymmetric space-times J. Winicour; Part III. Relativity: 12. A family of conformally flat space-times having the same curvature tensor in a given co-ordinate frame C. D. Collinson; 13. On the Bell-Szekeres solution for colliding electromagnetic waves J. B. Griffiths; 14. A remark on the Hauser metric A. Held; 15. Numerical relativity by power series R. Penrose; 16. Projective relativity and the equation of motion E. Schmutzer; 17. On generalized equations of goedesic deviation B. F. Schutz; 18. Lobatchevski plane gravitational waves S. T. C. Siklos; 19. Perfect fluid and vacuum solutions of Einstein's field equations with flat 3-dimensional slices H. Stephani and Th. Wolf; 20. Self-similar solutions of Einstein's equations J. Wainwright.
Axisymmetric instabilities between coaxial rotating disks
NASA Astrophysics Data System (ADS)
Pécheux, Jean; Foucault, E.
2006-09-01
This paper concerns the stability of the von Kármán swirling flow between coaxial disks. A linear stability analysis shows that for moderate Reynolds numbers (Re≤50) and for any rotation ratio sin[-1,1[ there is a radial location r_{pc} from which the self-similar von Kármán solutions become unstable to axisymmetric disturbances. When the disks are moderately counter-rotating (sin[-0.56,0[), two different disturbances (types I and II) appear at the same critical radius. A spatio-temporal analysis shows that, at a very short distance from this critical radius, the first disturbance (type I) becomes absolutely unstable whereas the second (type II) remains convectively unstable. Outside this range of aspect ratios, all the disturbances examined are found to be absolutely unstable. The flow between two coaxial rotating disks enclosed in a stationary sidewall is then numerically investigated. For sufficently large aspect ratios, the cavity flow is found to be globally unstable for axisymmetric disturbances similar to that calculated with the self-similar solutions. The flow in cavities with aspect ratios smaller than R {≈} 10.3 (and Re {≤} 50) is not destabilized by these axisymmetric disturbances. An experimental investigation conducted for a cavity with aspect ratio R {=} 15 confirms the numerical results. Axisymmetric disturbances similar to those calculated for the same cavity are detected and three-dimensional modes can also be observed near the sidewall.
Geometry with Coordinates, Student's Text, Part II, Unit 48. Revised Edition.
ERIC Educational Resources Information Center
Allen, Frank B.; And Others
This is part two of a two-part SMSG geometry text for high school students. One of the goals of the text is the development of analytic geometry hand-in-hand with synthetic geometry. The authors emphasize that both are deductive systems and that it is useful to have more than one mode of attack in solving problems. The text begins the development…
Axisymmetric flows from fluid injection into a confined porous medium
NASA Astrophysics Data System (ADS)
Guo, Bo; Zheng, Zhong; Celia, Michael A.; Stone, Howard A.
2016-02-01
We study the axisymmetric flows generated from fluid injection into a horizontal confined porous medium that is originally saturated with another fluid of different density and viscosity. Neglecting the effects of surface tension and fluid mixing, we use the lubrication approximation to obtain a nonlinear advection-diffusion equation that describes the time evolution of the sharp fluid-fluid interface. The flow behaviors are controlled by two dimensionless groups: M, the viscosity ratio of displaced fluid relative to injected fluid, and Γ, which measures the relative importance of buoyancy and fluid injection. For this axisymmetric geometry, the similarity solution involving R2/T (where R is the dimensionless radial coordinate and T is the dimensionless time) is an exact solution to the nonlinear governing equation for all times. Four analytical expressions are identified as asymptotic approximations (two of which are new solutions): (i) injection-driven flow with the injected fluid being more viscous than the displaced fluid (Γ ≪ 1 and M < 1) where we identify a self-similar solution that indicates a parabolic interface shape; (ii) injection-driven flow with injected and displaced fluids of equal viscosity (Γ ≪ 1 and M = 1), where we find a self-similar solution that predicts a distinct parabolic interface shape; (iii) injection-driven flow with a less viscous injected fluid (Γ ≪ 1 and M > 1) for which there is a rarefaction wave solution, assuming that the Saffman-Taylor instability does not occur at the reservoir scale; and (iv) buoyancy-driven flow (Γ ≫ 1) for which there is a well-known self-similar solution corresponding to gravity currents in an unconfined porous medium [S. Lyle et al. "Axisymmetric gravity currents in a porous medium," J. Fluid Mech. 543, 293-302 (2005)]. The various axisymmetric flows are summarized in a Γ-M regime diagram with five distinct dynamic behaviors including the four asymptotic regimes and an intermediate regime
Locomotive consequences of non-axisymmetric flagellar configurations
NASA Astrophysics Data System (ADS)
Fu, Henry; Marcos, Marcos; Hyon, Yunkyong; Powers, Thomas; Stocker, Roman
2011-11-01
Although peritrichous bacteria can form flagellar bundles at many attachment points and directions relative to the cell body, locomotion of these bacteria is often modeled as arising from a polar bundle oriented along the cell body axis. We discuss the consequences of non-axisymmetric flagellar configurations for bacterial locomotion and implications for bacterial behavior using a boundary element method (BEM) based on the method of regularized Stokeslets. We validate our BEM by comparing to analytic results for spheres and ellipsoids, as well as results in the literature for axisymmetric flagella with spherical and ellipsoidal heads obtained from other boundary element methods and slender body theory. Non-axisymmetric flagellar configurations generically lead to wobbling cell bodies and wiggling helical cell trajectories, both of which have been observed experimentally. We compare experimental and numerically calculated wiggling trajectories to deduce information about flagellar geometries of swimming B. subtilis. We discuss the implications of off-axis flagellar geometries for bacterial rheotaxis and chemotaxis.
Nonassociative geometry in quasi-Hopf representation categories II: Connections and curvature
NASA Astrophysics Data System (ADS)
Barnes, Gwendolyn E.; Schenkel, Alexander; Szabo, Richard J.
2016-08-01
We continue our systematic development of noncommutative and nonassociative differential geometry internal to the representation category of a quasitriangular quasi-Hopf algebra. We describe derivations, differential operators, differential calculi and connections using universal categorical constructions to capture algebraic properties such as Leibniz rules. Our main result is the construction of morphisms which provide prescriptions for lifting connections to tensor products and to internal homomorphisms. We describe the curvatures of connections within our formalism, and also the formulation of Einstein-Cartan geometry as a putative framework for a nonassociative theory of gravity.
Axisymmetric multiwormholes revisited
NASA Astrophysics Data System (ADS)
Clément, Gérard
2016-06-01
The construction of stationary axisymmetric multiwormhole solutions to gravitating field theories admitting toroidal reductions to three-dimensional gravitating sigma models is reviewed. We show that, as in the multi-black hole case, strut singularities always appear in this construction, except for very special configurations with an odd number of centers. We also review the analytical continuation of the multicenter solution across the n cuts associated with the wormhole mouths. The resulting Riemann manifold has 2^n sheets interconnected by 2^{n-1}n wormholes. We find that the maximally extended multicenter solution can never be asymptotically locally flat in all the Riemann sheets.
Axisymmetric Coanda-assisted vectoring
NASA Astrophysics Data System (ADS)
Allen, Dustin; Smith, Barton L.
2009-01-01
An experimental demonstration of a jet vectoring technique used in our novel spray method called Coanda-assisted Spray Manipulation (CSM) is presented. CSM makes use of the Coanda effect on axisymmetric geometries through the interaction of two jets: a primary jet and a control jet. The primary jet has larger volume flow rate but generally a smaller momentum flux than the control jet. The primary jet flows through the center of a rounded collar. The control jet is parallel to the primary and is adjacent to the convex collar. The Reynolds number range for the primary jet at the exit plane was between 20,000 and 80,000. The flow was in the incompressible Mach number range (Mach < 0.3). The control jet attaches to the convex wall and vectors according to known Coanda effect principles, entraining and vectoring the primary jet, resulting in controllable r - θ directional spraying. Several annular control slots and collar radii were tested over a range of momentum flux ratios to determine the effects of these variables on the vectored jet angle and spreading. Two and Three-component Particle Image Velocimetry systems were used to determine the vectoring angle and the profile of the combined jet in each experiment. The experiments show that the control slot and expansion radius, along with the momentum ratios of the two jets predominantly affected the vectoring angle and profile of the combined jets.
ERIC Educational Resources Information Center
Curtis, Charles W.; And Others
These materials were developed to help high school teachers to become familiar with the approach to tenth-grade Euclidean geometry which was adopted by the School Mathematics Study Group (SMSG). It is emphasized that the materials are unsuitable as a high school textbook. Each document contains material too difficult for most high school students.…
Waychunas, G.A.; Fuller, C.C.; Davis, J.A.; Rehr, J.J.
2003-01-01
X-ray absorption near-edge spectroscopy (XANES) analysis of sorption complexes has the advantages of high sensitivity (10- to 20-fold greater than extended X-ray absorption fine structure [EXAFS] analysis) and relative ease and speed of data collection (because of the short k-space range). It is thus a potentially powerful tool for characterization of environmentally significant surface complexes and precipitates at very low surface coverages. However, quantitative analysis has been limited largely to "fingerprint" comparison with model spectra because of the difficulty of obtaining accurate multiple-scattering amplitudes for small clusters with high confidence. In the present work, calculations of the XANES for 50- to 200-atom clusters of structure from Zn model compounds using the full multiple-scattering code Feff 8.0 accurately replicate experimental spectra and display features characteristic of specific first-neighbor anion coordination geometry and second-neighbor cation geometry and number. Analogous calculations of the XANES for small molecular clusters indicative of precipitation and sorption geometries for aqueous Zn on ferrihydrite, and suggested by EXAFS analysis, are in good agreement with observed spectral trends with sample composition, with Zn-oxygen coordination and with changes in second-neighbor cation coordination as a function of sorption coverage. Empirical analysis of experimental XANES features further verifies the validity of the calculations. The findings agree well with a complete EXAFS analysis previously reported for the same sample set, namely, that octahedrally coordinated aqueous Zn2+ species sorb as a tetrahedral complex on ferrihydrite with varying local geometry depending on sorption density. At significantly higher densities but below those at which Zn hydroxide is expected to precipitate, a mainly octahedral coordinated Zn2+ precipitate is observed. An analysis of the multiple scattering paths contributing to the XANES
The Influence of Environment Geometry on Injury Outcome: II. Lumbosacral Spine
NASA Astrophysics Data System (ADS)
Shaibani, Saami J.
2006-03-01
It is widely agreed that the type of motor vehicle in which an occupant is situated can sometimes make a noticeable difference in injury potential even when the insult suffered is the same. A simple example might be the same occupant being in a sports car as opposed to a minivan, but such anecdotal experience does not usually help to distinguish the effect of particular features within the same category of vehicle. Other research has addressed the role of environment geometry in neck injury,[1] and this paper adopts the same methodology for the low back. The heights, lengths and angles of the seat cushion and seat back (including head rest) are all examined as descriptors of passenger compartment geometry, and any changes caused by these are determined. Useful results are feasible with the large patient population available even if clear patterns in these are not always present. As in earlier work, there is still the option of finding individual outcomes on a case-by-case basis. [1] The influence of environment geometry on injury outcome: I. Cervical spine, Bull Am Phys Soc, in press (2006).
Ion temperature gradient turbulence in helical and axisymmetric RFP plasmas
Predebon, I.; Xanthopoulos, P.
2015-05-15
Turbulence induced by the ion temperature gradient (ITG) is investigated in the helical and axisymmetric plasma states of a reversed field pinch device by means of gyrokinetic calculations. The two magnetic configurations are systematically compared, both linearly and nonlinearly, in order to evaluate the impact of the geometry on the instability and its ensuing transport, as well as on the production of zonal flows. Despite its enhanced confinement, the high-current helical state demonstrates a lower ITG stability threshold compared to the axisymmetric state, and ITG turbulence is expected to become an important contributor to the total heat transport.
Structure of axisymmetric mantle plumes
NASA Technical Reports Server (NTRS)
Olson, Peter; Schubert, Gerald; Anderson, Charles
1993-01-01
The structure of axisymmetric subsolidus thermal plumes in the earth's lower mantle is inferred from calculations of axisymmetric thermal plumes in an infinite Prandtl number fluid with thermally activated viscosity. The velocity and temperature distribution is determined for axisymmetric convection above a heated disk in an incompressible fluid cylinder 2,400 km in height and 1,200 km in diameter. Several calculations of plumes with heat transport in the range 100-400 GW, similar to the advective heat transport at the Hawaiian hotspot, are presented. Hotspot formation by plumes originating at the base of the mantle requires both large viscosity variations and a minimum heat transport.
Wright, B.L.; Alrick, K.R.; Fritz, J.N.
1994-05-01
Axisymmetric magnetic (ASM) gauges are useful diagnostic tools in the study of the conversion of energy from underground explosions to distant seismic signals. Requiring no external power, they measure the strength (particle velocity) of the emerging shock wave under conditions that would destroy most instrumentation. Shock pins are included with each gauge to determine the angle of the shock front. For the Non-Proliferation Experiment, two ASM gauges were installed in the ANFO mixture to monitor the detonation wave and 10 were grouted into boreholes at various ranges in the surrounding rock (10 to 64 m from the center of explosion). These gauges were of a standard 3.8-inch-diameter design. In addition, two unique Jumbo ASM gauges (3-ft by 3-ft in cross section) were grouted to the wall of a drift at a range of 65 m. We discuss issues encountered in data analysis, present the results of our measurements, and compare these results with those of model simulations of the experiment.
Geometry of river networks. II. Distributions of component size and number
Dodds, Peter Sheridan; Rothman, Daniel H.
2001-01-01
The structure of a river network may be seen as a discrete set of nested subnetworks built out of individual stream segments. These network components are assigned an integral stream order via a hierarchical and discrete ordering method. Exponential relationships, known as Horton's laws, between stream order and ensemble-averaged quantities pertaining to network components are observed. We extend these observations to incorporate fluctuations and all higher moments by developing functional relationships between distributions. The relationships determined are drawn from a combination of theoretical analysis, analysis of real river networks including the Mississippi, Amazon, and Nile, and numerical simulations on a model of directed, random networks. Underlying distributions of stream segment lengths are identified as exponential. Combinations of these distributions form single-humped distributions with exponential tails, the sums of which are in turn shown to give power-law distributions of stream lengths. Distributions of basin area and stream segment frequency are also addressed. The calculations identify a single length scale as a measure of size fluctuations in network components. This article is the second in a series of three addressing the geometry of river networks.
Geometry of deformed black holes. II. Schwarzschild hole surrounded by a Bach-Weyl ring
NASA Astrophysics Data System (ADS)
Basovník, M.; Semerák, O.
2016-08-01
We continue to study the response of black-hole space-times on the presence of additional strong sources of gravity. Restricting ourselves to static and axially symmetric (electro)vacuum exact solutions of Einstein's equations, we first considered the Majumdar-Papapetrou solution for a binary of extreme black holes in a previous paper, while here we deal with a Schwarzschild black hole surrounded by a concentric thin ring described by the Bach-Weyl solution. The geometry is again revealed on the simplest invariants determined by the metric (lapse function) and its gradient (gravitational acceleration), and by curvature (Kretschmann scalar). Extending the metric inside the black hole along null geodesics tangent to the horizon, we mainly focus on the black-hole interior (specifically, on its sections at constant Killing time) where the quantities behave in a way indicating a surprisingly strong influence of the external source. Being already distinct on the level of potential and acceleration, this is still more pronounced on the level of curvature: for a sufficiently massive and/or nearby (small) ring, the Kretschmann scalar even becomes negative in certain toroidal regions mostly touching the horizon from inside. Such regions have been interpreted as those where magnetic-type curvature dominates, but here we deal with space-times which do not involve rotation and the negative value is achieved due to the electric-type components of the Riemann/Weyl tensor. The Kretschmann scalar also shapes rather nontrivial landscapes outside the horizon.
Supergravity as generalised geometry II: E d( d) × ℝ+ and M theory
NASA Astrophysics Data System (ADS)
Coimbra, André; Strickland-Constable, Charles; Waldram, Daniel
2014-03-01
We reformulate eleven-dimensional supergravity, including fermions, in terms of generalised geometry, for spacetimes that are warped products of Minkowski space with a d-dimensional manifold M with d ≤ 7. The reformulation has an E d( d) × ℝ+ structure group and it has a local symmetry, where is the double cover of the maximally compact subgroup of E d( d). The bosonic degrees for freedom unify into a generalised metric, and, defining the generalisked analogue D of the Levi-Civita connection, one finds that the corresponding equations of motion are the vanishing of the generalised Ricci tensor. To leading order, we show that the fermionic equations of motion, action and supersymmetry variations can all be written in terms of D. Although we will not give the detailed decompositions, this reformulation is equally applicable to type IIA or IIB supergravity restricted to a ( d - 1)-dimensional manifold. For completeness we give explicit expressions in terms of = Spin(5) and = SU(8) representations for d = 4 and d = 7.
Axisymmetric Liquid Hanging Drops
ERIC Educational Resources Information Center
Meister, Erich C.; Latychevskaia, Tatiana Yu
2006-01-01
The geometry of drops hanging on a circular capillary can be determined by numerically solving a dimensionless differential equation that is independent on any material properties, which enables one to follow the change of the height, surface area, and contact angle of drops hanging on a particular capillary. The results show that the application…
Twisted versus braided magnetic flux ropes in coronal geometry. II. Comparative behaviour
NASA Astrophysics Data System (ADS)
Prior, C.; Yeates, A. R.
2016-06-01
Aims: Sigmoidal structures in the solar corona are commonly associated with magnetic flux ropes whose magnetic field lines are twisted about a mutual axis. Their dynamical evolution is well studied, with sufficient twisting leading to large-scale rotation (writhing) and vertical expansion, possibly leading to ejection. Here, we investigate the behaviour of flux ropes whose field lines have more complex entangled/braided configurations. Our hypothesis is that this internal structure will inhibit the large-scale morphological changes. Additionally, we investigate the influence of the background field within which the rope is embedded. Methods: A technique for generating tubular magnetic fields with arbitrary axial geometry and internal structure, introduced in part I of this study, provides the initial conditions for resistive-MHD simulations. The tubular fields are embedded in a linear force-free background, and we consider various internal structures for the tubular field, including both twisted and braided topologies. These embedded flux ropes are then evolved using a 3D MHD code. Results: Firstly, in a background where twisted flux ropes evolve through the expected non-linear writhing and vertical expansion, we find that flux ropes with sufficiently braided/entangled interiors show no such large-scale changes. Secondly, embedding a twisted flux rope in a background field with a sigmoidal inversion line leads to eventual reversal of the large-scale rotation. Thirdly, in some cases a braided flux rope splits due to reconnection into two twisted flux ropes of opposing chirality - a phenomenon previously observed in cylindrical configurations. Conclusions: Sufficiently complex entanglement of the magnetic field lines within a flux rope can suppress large-scale morphological changes of its axis, with magnetic energy reduced instead through reconnection and expansion. The structure of the background magnetic field can significantly affect the changing morphology of a
Axisymmetric annular curtain stability
NASA Astrophysics Data System (ADS)
Ahmed, Zahir U.; Khayat, Roger E.; Maissa, Philippe; Mathis, Christian
2012-06-01
A temporal stability analysis was carried out to investigate the stability of an axially moving viscous annular liquid jet subject to axisymmetric disturbances in surrounding co-flowing viscous gas media. We investigated in this study the effects of inertia, surface tension, the gas-to-liquid density ratio, the inner-to-outer radius ratio and the gas-to-liquid viscosity ratio on the stability of the jet. With an increase in inertia, the growth rate of the unstable disturbances is found to increase. The dominant (or most unstable) wavenumber decreases with increasing Reynolds number for larger values of the gas-to-liquid viscosity ratio. However, an opposite tendency for the most unstable wavenumber is predicted for small viscosity ratio in the same inertia range. The surrounding gas density, in the presence of viscosity, always reduces the growth rate, hence stabilizing the flow. There exists a critical value of the density ratio above which the flow becomes stable for very small viscosity ratio, whereas for large viscosity ratio, no stable flow appears in the same range of the density ratio. The curvature has a significant destabilizing effect on the thin annular jet, whereas for a relatively thick jet, the maximum growth rate decreases as the inner radius increases, irrespective of the surrounding gas viscosity. The degree of instability increases with Weber number for a relatively large viscosity ratio. In contrast, for small viscosity ratio, the growth rate exhibits a dramatic dependence on the surface tension. There is a small Weber number range, which depends on the viscosity ratio, where the flow is stable. The viscosity ratio always stabilizes the flow. However, the dominant wavenumber increases with increasing viscosity ratio. The range of unstable wavenumbers is affected only by the curvature effect.
Periodic forcing of a Turbulent Axisymmetric Wake
NASA Astrophysics Data System (ADS)
Morrison, Jonathan; Qubain, Ala
2008-11-01
The near wake of a blunt, axisymmetric body subject to periodic forcing is investigated. A high-fidelity speaker located inside the cylinder is used to generate a pulsed jet from a small circumferential gap located on the underside of the separating boundary layer, with its axis aligned in the streamwise direction. A detailed investigation of the growth of the disturbances is performed using hot wires, PIV and base-pressure transducers. It is shown that, with azimuthal symmetric forcing (m =0), the base pressure may be reduced by 30% at ``low'' frequencies or increased by 10%, at ``high'' frequencies with consistent changes to the velocity field. As in previous, similar investigations, it is shown that the important scaling parameter is the boundary-layer momentum thickness at separation - in contrast to other geometries such as a 2D bluff body for example, where the von Kármán vortex shedding is universal, or control of separating-reattaching flows, where a range of actuation frequencies is often effective. Moreover, caution is required when comparing to other axisymmetric bodies because the wake is quite sensitive to boundary conditions and the nature of separation from the body. Many previous studies have demonstrated successful alterations of the wake of a 3D bluff body, all using passive geometric modifications.
CLASSIFICATION OF STELLAR ORBITS IN AXISYMMETRIC GALAXIES
Li, Baile; Holley-Bockelmann, Kelly; Khan, Fazeel Mahmood E-mail: k.holley@vanderbilt.edu
2015-09-20
It is known that two supermassive black holes (SMBHs) cannot merge in a spherical galaxy within a Hubble time; an emerging picture is that galaxy geometry, rotation, and large potential perturbations may usher the SMBH binary through the critical three-body scattering phase and ultimately drive the SMBH to coalesce. We explore the orbital content within an N-body model of a mildly flattened, non-rotating, SMBH-embedded elliptical galaxy. When used as the foundation for a study on the SMBH binary coalescence, the black holes bypassed the binary stalling often seen within spherical galaxies and merged on gigayear timescales. Using both frequency-mapping and angular momentum criteria, we identify a wealth of resonant orbits in the axisymmetric model, including saucers, that are absent from an otherwise identical spherical system and that can potentially interact with the binary. We quantified the set of orbits that could be scattered by the SMBH binary, and found that the axisymmetric model contained nearly six times the number of these potential loss cone orbits compared to our equivalent spherical model. In this flattened model, the mass of these orbits is more than three times that of the SMBH, which is consistent with what the SMBH binary needs to scatter to transition into the gravitational wave regime.
Rotating string in doubled geometry with generalized isometries
NASA Astrophysics Data System (ADS)
Kikuchi, Toru; Okada, Takashi; Sakatani, Yuho
2012-08-01
In this paper, we first construct a globally well-defined nongeometric background which contains several branes in type II string theory compactified on a 7-torus. One of these branes is called 522, which is a codimension-2 object and has a nontrivial monodromy given by a T-duality transformation. The geometry near the 522-brane is shown to approach the nongeometric background constructed in J. de Boer and M. Shigemori, Phys. Rev. Lett. 104, 251603 (2010)PRLTAO0031-900710.1103/PhysRevLett.104.251603. We then construct the solution of a fundamental string rotating along a nontrivial cycle in the 522 background. Although the background is not axisymmetric in the usual sense, we show that it is actually axisymmetric as a doubled geometry by explicitly finding a generalized Killing vector. We also show that a vector on the doubled geometry associated with the winding and momentum charges of the rotating string solution is Lie-transported in the generalized sense along the generalized Killing vector.
EXTINCTION AND DUST GEOMETRY IN M83 H II REGIONS: AN HUBBLE SPACE TELESCOPE/WFC3 STUDY
Liu, Guilin; Calzetti, Daniela; Hong, Sungryong; Whitmore, Bradley; Chandar, Rupali; O'Connell, Robert W.; Blair, William P.; Cohen, Seth H.; Kim, Hwihyun; Frogel, Jay A.
2013-12-01
We present Hubble Space Telescope/WFC3 narrow-band imaging of the starburst galaxy M83 targeting the hydrogen recombination lines (Hβ, Hα, and Paβ), which we use to investigate the dust extinction in the H II regions. We derive extinction maps with 6 pc spatial resolution from two combinations of hydrogen lines (Hα/Hβ and Hα/Paβ), and show that the longer wavelengths probe larger optical depths, with A{sub V} values larger by ≳1 mag than those derived from the shorter wavelengths. This difference leads to a factor ≳2 discrepancy in the extinction-corrected Hα luminosity, a significant effect when studying extragalactic H II regions. By comparing these observations to a series of simple models, we conclude that a large diversity of absorber/emitter geometric configurations can account for the data, implying a more complex physical structure than the classical foreground ''dust screen'' assumption. However, most data points are bracketed by the foreground screen and a model where dust and emitters are uniformly mixed. When averaged over large (≳100-200 pc) scales, the extinction becomes consistent with a ''dust screen'', suggesting that other geometries tend to be restricted to more local scales. Moreover, the extinction in any region can be described by a combination of the foreground screen and the uniform mixture model with weights of 1/3 and 2/3 in the center (≲2 kpc), respectively, and 2/3 and 1/3 for the rest of the disk. This simple prescription significantly improves the accuracy of the dust extinction corrections and can be especially useful for pixel-based analyses of galaxies similar to M83.
Axi-symmetric patterns of active polar filaments on spherical and composite surfaces
NASA Astrophysics Data System (ADS)
Srivastava, Pragya; Rao, Madan
2014-03-01
Experiments performed on Fission Yeast cells of cylindrical and spherical shapes, rod-shaped bacteria and reconstituted cylindrical liposomes suggest the influence of cell geometry on patterning of cortical actin. A theoretical model based on active hydrodynamic description of cortical actin that includes curvature-orientation coupling predicts spontaneous formation of acto-myosin rings, cables and nodes on cylindrical and spherical geometries [P. Srivastava et al, PRL 110, 168104(2013)]. Stability and dynamics of these patterns is also affected by the cellular shape and has been observed in experiments performed on Fission Yeast cells of spherical shape. Motivated by this, we study the stability and dynamics of axi-symmetric patterns of active polar filaments on the surfaces of spherical, saddle shaped and conical geometry and classify the stable steady state patterns on these surfaces. Based on the analysis of the fluorescence images of Myosin-II during ring slippage we propose a simple mechanical model for ring-sliding based on force balance and make quantitative comparison with the experiments performed on Fission Yeast cells. NSF Grant DMR-1004789 and Syracuse Soft Matter Program.
Numerical computation of gravitational field for general axisymmetric objects
NASA Astrophysics Data System (ADS)
Fukushima, Toshio
2016-10-01
We developed a numerical method to compute the gravitational field of a general axisymmetric object. The method (i) numerically evaluates a double integral of the ring potential by the split quadrature method using the double exponential rules, and (ii) derives the acceleration vector by numerically differentiating the numerically integrated potential by Ridder's algorithm. Numerical comparison with the analytical solutions for a finite uniform spheroid and an infinitely extended object of the Miyamoto-Nagai density distribution confirmed the 13- and 11-digit accuracy of the potential and the acceleration vector computed by the method, respectively. By using the method, we present the gravitational potential contour map and/or the rotation curve of various axisymmetric objects: (i) finite uniform objects covering rhombic spindles and circular toroids, (ii) infinitely extended spheroids including Sérsic and Navarro-Frenk-White spheroids, and (iii) other axisymmetric objects such as an X/peanut-shaped object like NGC 128, a power-law disc with a central hole like the protoplanetary disc of TW Hya, and a tear-drop-shaped toroid like an axisymmetric equilibrium solution of plasma charge distribution in an International Thermonuclear Experimental Reactor-like tokamak. The method is directly applicable to the electrostatic field and will be easily extended for the magnetostatic field. The FORTRAN 90 programs of the new method and some test results are electronically available.
Axisymmetric inlet minimum weight design method
NASA Technical Reports Server (NTRS)
Nadell, Shari-Beth
1995-01-01
An analytical method for determining the minimum weight design of an axisymmetric supersonic inlet has been developed. The goal of this method development project was to improve the ability to predict the weight of high-speed inlets in conceptual and preliminary design. The initial model was developed using information that was available from inlet conceptual design tools (e.g., the inlet internal and external geometries and pressure distributions). Stiffened shell construction was assumed. Mass properties were computed by analyzing a parametric cubic curve representation of the inlet geometry. Design loads and stresses were developed at analysis stations along the length of the inlet. The equivalent minimum structural thicknesses for both shell and frame structures required to support the maximum loads produced by various load conditions were then determined. Preliminary results indicated that inlet hammershock pressures produced the critical design load condition for a significant portion of the inlet. By improving the accuracy of inlet weight predictions, the method will improve the fidelity of propulsion and vehicle design studies and increase the accuracy of weight versus cost studies.
Mean flowfields in axisymmetric combustor geometries with swirl
Rhode, D.L.; Lilley, D.G.
1982-01-01
Six flowfield configurations are investigated with sidewall angles of 90 and 45/sup 0/, and swirl vane angles of 0, 45, and 70/sup 0/. It is found that central recirculation zones occur for the swirling flow cases investigated, which extend from the inlet to x/D 1.7, where x is the axial polar coordinate, and D is the test section diameter. Five-hole pitot probe pressure measurements are used to determine time-mean velocities, and corresponding flow situations are predicted and compared to results of experimental data. Excellent agreement is found for the nonswirling flow, although poor agreement is found for swirling flow cases, especially near the inlet. The discrepancy is attributed to the lack of realism in the turbulence model, and/or to inaccurate specification of time-mean velocity and turbulence energy distributions at the inlet.
Stability of axisymmetric liquid bridges
NASA Astrophysics Data System (ADS)
Fel, Leonid G.; Rubinstein, Boris Y.
2015-12-01
Based on the Weierstrass representation of second variation, we develop a non-spectral theory of stability for isoperimetric problem with minimized and constrained two-dimensional functionals of general type and free endpoints allowed to move along two given planar curves. We establish the stability criterion and apply this theory to the axisymmetric liquid bridge between two axisymmetric solid bodies without gravity to determine the stability of menisci with free contact lines. For catenoid and cylinder menisci and different solid shapes, we determine the stability domain. The other menisci (unduloid, nodoid and sphere) are considered in a simple setup between two plates. We find the existence conditions of stable unduloid menisci with and without inflection points.
Solar proton exposure of an ICRU sphere within a complex structure part II: Ray-trace geometry.
Slaba, Tony C; Wilson, John W; Badavi, Francis F; Reddell, Brandon D; Bahadori, Amir A
2016-06-01
A computationally efficient 3DHZETRN code with enhanced neutron and light ion (Z ≤ 2) propagation was recently developed for complex, inhomogeneous shield geometry described by combinatorial objects. Comparisons were made between 3DHZETRN results and Monte Carlo (MC) simulations at locations within the combinatorial geometry, and it was shown that 3DHZETRN agrees with the MC codes to the extent they agree with each other. In the present report, the 3DHZETRN code is extended to enable analysis in ray-trace geometry. This latest extension enables the code to be used within current engineering design practices utilizing fully detailed vehicle and habitat geometries. Through convergence testing, it is shown that fidelity in an actual shield geometry can be maintained in the discrete ray-trace description by systematically increasing the number of discrete rays used. It is also shown that this fidelity is carried into transport procedures and resulting exposure quantities without sacrificing computational efficiency. PMID:27345204
Solar proton exposure of an ICRU sphere within a complex structure part II: Ray-trace geometry
NASA Astrophysics Data System (ADS)
Slaba, Tony C.; Wilson, John W.; Badavi, Francis F.; Reddell, Brandon D.; Bahadori, Amir A.
2016-06-01
A computationally efficient 3DHZETRN code with enhanced neutron and light ion (Z ≤ 2) propagation was recently developed for complex, inhomogeneous shield geometry described by combinatorial objects. Comparisons were made between 3DHZETRN results and Monte Carlo (MC) simulations at locations within the combinatorial geometry, and it was shown that 3DHZETRN agrees with the MC codes to the extent they agree with each other. In the present report, the 3DHZETRN code is extended to enable analysis in ray-trace geometry. This latest extension enables the code to be used within current engineering design practices utilizing fully detailed vehicle and habitat geometries. Through convergence testing, it is shown that fidelity in an actual shield geometry can be maintained in the discrete ray-trace description by systematically increasing the number of discrete rays used. It is also shown that this fidelity is carried into transport procedures and resulting exposure quantities without sacrificing computational efficiency.
2016-01-01
2-Alkenylphenols react with allenes, upon treatment with catalytic amounts of Pd(II) and Cu(II), to give benzoxepine products in high yields and with very good regio- and diastereoselectivities. This contrasts with the results obtained with Rh catalysts, which provided chromene-like products through a pathway involving a β-hydrogen elimination step. Computational studies suggest that the square planar geometry of the palladium is critical to favor the reductive elimination process required for the formation of the oxepine products. PMID:27807509
Inversions for axisymmetric galactic disks
NASA Astrophysics Data System (ADS)
Hiotelis, N.; Patsis, P. A.
1993-08-01
We use two models for the distribution function to solve an inverse problem for axisymmetric disks. These systems may be considered - under certain assumptions - as galactic disks. In some cases the solutions of the resulting integral equations are simple, which allows the determination of the kinematic properties of self-consistent models for these systems. These properties for then = 1 Toomre disk are presented in this study.
NASA Astrophysics Data System (ADS)
Gao, Zhongmei; Shao, Xinyu; Jiang, Ping; Wang, Chunming; Zhou, Qi; Cao, Longchao; Wang, Yilin
2016-06-01
An integrated multi-objective optimization approach combining Kriging model and non-dominated sorting genetic algorithm-II (NSGA-II) is proposed to predict and optimize weld geometry in hybrid fiber laser-arc welding on 316L stainless steel in this paper. A four-factor, five-level experiment using Taguchi L25 orthogonal array is conducted considering laser power ( P), welding current ( I), distance between laser and arc ( D) and traveling speed ( V). Kriging models are adopted to approximate the relationship between process parameters and weld geometry, namely depth of penetration (DP), bead width (BW) and bead reinforcement (BR). NSGA-II is used for multi-objective optimization taking the constructed Kriging models as objective functions and generates a set of optimal solutions with pareto-optimal front for outputs. Meanwhile, the main effects and the first-order interactions between process parameters are analyzed. Microstructure is also discussed. Verification experiments demonstrate that the optimum values obtained by the proposed integrated Kriging model and NSGA-II approach are in good agreement with experimental results.
Non-axisymmetric annular curtain stability
NASA Astrophysics Data System (ADS)
Ahmed, Zahir U.; Khayat, Roger E.; Maissa, Philippe; Mathis, Christian
2013-08-01
A stability analysis of non-axisymmetric annular curtain is carried out for an axially moving viscous jet subject in surrounding viscous gas media. The effect of inertia, surface tension, gas-to-liquid density ratio, inner-to-outer radius ratio, and gas-to-liquid viscosity ratio on the stability of the jet is studied. In general, the axisymmetric disturbance is found to be the dominant mode. However, for small wavenumber, the non-axisymmetric mode is the most unstable mode and the one likely observed in reality. Inertia and the viscosity ratio for non-axisymmetric disturbances show a similar stability influence as observed for axisymmetric disturbances. The maximum growth rate in non-axisymmetric flow, interestingly, appears at very small wavenumber for all inertia levels. The dominant wavenumber increases (decreases) with inertia for non-axisymmetric (axisymmetric) flow. Gas-to-liquid density ratio, curvature effect, and surface tension, however, exhibit an opposite influence on growth rate compared to axisymmetric disturbances. Surface tension tends to stabilize the flow with reductions of the unstable wavenumber range and the maximum growth rate as well as the dominant wavenumber. The dominant wavenumber remains independent of viscosity ratio indicating the viscosity ratio increases the breakup length of the sheet with very little influence on the size of the drops. The range of unstable wavenumbers is affected only by curvature in axisymmetric flow, whereas all the stability parameters control the range of unstable wavenumbers in non-axisymmetric flow. Inertia and gas density increase the unstable wavenumber range, whereas the radius ratio, surface tension, and the viscosity ratio decrease the unstable wavenumber range. Neutral curves are plotted to separate the stable and unstable domains. Critical radius ratio decreases linearly and nonlinearly with the wavenumber for axisymmetric and non-axisymmetric disturbances, respectively. At smaller Weber numbers, a
Ideal MHD stability calculations in axisymmetric toroidal coordinate systems
Grimm, R.C.; Dewar, R.L.; Manickam, J.
1982-03-01
A scalar form of the ideal MHD energy principle is shown to provide a more accurate and efficient numerical method for determining the stability of an axisymmetric toroidal equilibrium than the usual vector form. Additional improvement is obtained by employing a class of straight magnetic field line flux coordinates which allow for an optimal choice of the poloidal angle in the minor cross section of the torus. The usefulness of these techniques is illustrated by a study (using a new code, PEST 2) of the convergence properties of the finite element Galerkin representation in tokamak and spheromak geometries, and by the accurate determination of critical ..beta.. values for ballooning modes.
Transition and mixing in axisymmetric jets and vortex rings
NASA Technical Reports Server (NTRS)
Allen, G. A., Jr.; Cantwell, B. J.
1986-01-01
A class of impulsively started, axisymmetric, laminar jets produced by a time dependent joint source of momentum are considered. These jets are different flows, each initially at rest in an unbounded fluid. The study is conducted at three levels of detail. First, a generalized set of analytic creeping flow solutions are derived with a method of flow classification. Second, from this set, three specific creeping flow solutions are studied in detail: the vortex ring, the round jet, and the ramp jet. This study involves derivation of vorticity, stream function, entrainment diagrams, and evolution of time lines through computer animation. From entrainment diagrams, critical points are derived and analyzed. The flow geometry is dictated by the properties and location of critical points which undergo bifurcation and topological transformation (a form of transition) with changing Reynolds number. Transition Reynolds numbers were calculated. A state space trajectory was derived describing the topological behavior of these critical points. This state space derivation yielded three states of motion which are universal for all axisymmetric jets. Third, the axisymmetric round jet is solved numerically using the unsteady laminar Navier Stokes equations. These equations were shown to be self similar for the round jet. Numerical calculations were performed up to a Reynolds number of 30 for a 60x60 point mesh. Animations generated from numerical solution showed each of the three states of motion for the round jet, including the Re = 30 case.
Two-dimensional axisymmetric Child-Langmuir scaling law
Ragan-Kelley, Benjamin; Verboncoeur, John; Feng Yang
2009-10-15
The classical one-dimensional (1D) Child-Langmuir law was previously extended to two dimensions by numerical calculation in planar geometries. By considering an axisymmetric cylindrical system with axial emission from a circular cathode of radius r, outer drift tube radius R>r, and gap length L, we further examine the space charge limit in two dimensions. Simulations were done with no applied magnetic field as well as with a large (100 T) longitudinal magnetic field to restrict motion of particles to 1D. The ratio of the observed current density limit J{sub CL2} to the theoretical 1D value J{sub CL1} is found to be a monotonically decreasing function of the ratio of emission radius to gap separation r/L. This result is in agreement with the planar results, where the emission area is proportional to the cathode width W. The drift tube in axisymmetric systems is shown to have a small but measurable effect on the space charge limit. Strong beam edge effects are observed with J(r)/J(0) approaching 3.5. Two-dimensional axisymmetric electrostatic particle-in-cell simulations were used to produce these results.
Zhu, Xiaolei
2008-03-01
The DFT(B3LYP)/6-31G(d)//CCSD(T)/6-31G(d) method is used to investigate the low-lying electronic states of C(10)N(2)(II) and its ions. Mulliken populations, leading configurations, bond orders, and compositions of molecular orbitals are employed to explore the nature of bonding in the electronic states of C(10)N(2)(II) and its ions. Electron affinity, ionization energy, binding energy of C(10)N(2)(II), and anion photoelectron spectra of C(10)N(2)(II)(-) are also estimated at the CCSD(T)/6-31G(d) level. On the other hand, the similarities and differences between C(10)N(2)(I) and C(10)N(2)(II) are compared and discussed.
Li, Yajun
2011-06-01
The theory developed in Part I of this study [Y. Li, "Differential geometry of the ruled surfaces optically generated by mirror-scanning devices. I. Intrinsic and extrinsic properties of the scan field," J. Opt. Soc. Am. A28, 667 (2011)] for the ruled surfaces optically generated by single-mirror scanning devices is extended to multimirror scanning systems for an investigation of optical generation of the well-known ruled surfaces, such as helicoid, Plücker's conoid, and hyperbolic paraboloid.
MHD Simulations of Plasma Dynamics with Non-Axisymmetric Boundaries
NASA Astrophysics Data System (ADS)
Hansen, Chris; Levesque, Jeffrey; Morgan, Kyle; Jarboe, Thomas
2015-11-01
The arbitrary geometry, 3D extended MHD code PSI-TET is applied to linear and non-linear simulations of MCF plasmas with non-axisymmetric boundaries. Progress and results from simulations on two experiments will be presented: 1) Detailed validation studies of the HIT-SI experiment with self-consistent modeling of plasma dynamics in the helicity injectors. Results will be compared to experimental data and NIMROD simulations that model the effect of the helicity injectors through boundary conditions on an axisymmetric domain. 2) Linear studies of HBT-EP with different wall configurations focusing on toroidal asymmetries in the adjustable conducting wall. HBT-EP studies the effect of active/passive stabilization with an adjustable ferritic wall. Results from linear verification and benchmark studies of ideal mode growth with and without toroidal asymmetries will be presented and compared to DCON predictions. Simulations of detailed experimental geometries are enabled by use of the PSI-TET code, which employs a high order finite element method on unstructured tetrahedral grids that are generated directly from CAD models. Further development of PSI-TET will also be presented including work to support resistive wall regions within extended MHD simulations. Work supported by DoE.
Guided waves by axisymmetric and non-axisymmetric surface loading on hollow cylinders
Shin; Rose
1999-06-01
Guided waves generated by axisymmetric and non-axisymmetric surface loading on a hollow cylinder are studied. For the theoretical analysis of the superposed guided waves, a normal mode concept is employed. The amplitude factors of individual guided wave modes are studied with respect to varying surface pressure loading profiles. Both theoretical and experimental focus is given to the guided waves generated by both axisymmetric and non-axisymmetric excitation. For the experiments, a comb transducer and high power tone burst function generator system are used on a sample Inconel tube. Surface loading conditions, such as circumferential loading angles and axial loading lengths, are used with the frequency and phase velocity to control the axisymmetric and non-axisymmetric mode excitations. The experimental study demonstrates the use of a practical non-axisymmetric partial loading technique in generating axisymmetric modes, particularly useful in the inspection of tubing and piping with limited circumferential access. From both theoretical and experimental studies, it also could be said that the amount of flexural modes reflected from a defect contains information on the reflector's circumferential angle, as well as potentially other classification and sizing feature information. The axisymmetric and non-axisymmetric guided wave modes should both be carefully considered for improvement of the overall analysis of guided waves generated in hollow cylinders.
A Two-dimensional Cartesian and Axisymmetric Study of Combustion-acoustic Interaction
NASA Technical Reports Server (NTRS)
Hood, Caroline; Frendi, Abdelkader
2006-01-01
This paper describes a study of a lean premixed (LP) methane-air combustion wave in a two-dimensional Cartesian and axisymmetric coordinate system. Lean premixed combustors provide low emission and high efficiency; however, they are susceptible to combustion instabilities. The present study focuses on the behavior of the flame as it interacts with an external acoustic disturbance. It was found that the flame oscillations increase as the disturbance amplitude is increased. Furthermore, when the frequency of the disturbance is at resonance with a chamber frequency, the instabilities increase. For the axisymmetric geometry, the flame is found to be more unstable compared to the Cartesian case. In some cases, these instabilities were severe and led to flame extinction. In the axisymmetric case, several passive control devices were tested to assess their effectiveness. It is found that an acoustic cavity is better able at controlling the pressure fluctuations in the chamber.
NASA Astrophysics Data System (ADS)
Jana, Subrata; Santra, Ramesh Chandra; Das, Saurabh; Chattopadhyay, Shouvik
2014-09-01
Two new copper(II) complexes, [Cu(L)(OCN)] (1) and [CuL(dca)]n (2), where HL = 2-(-(2-(diethylamino)ethylimino)methyl)naphthalen-1-ol, dca = N(CN)2-, have been synthesized and characterized by elemental analysis, IR, UV-VIS spectroscopy and single crystal X-ray diffraction studies. Complex 1 has square planar and complex 2 square pyramidal geometries in solid state around metal centre. Interactions of the complexes with calf thymus DNA (CT DNA) were studied by UV-VIS spectroscopy. Binding constant and site size of interaction were determined. Binding site size and intrinsic binding constant K revealed complex 1 interacted with calf thymus DNA better than complex 2.
Stability of perturbed geodesics in nD axisymmetric spacetimes
NASA Astrophysics Data System (ADS)
Coimbra-Araújo, C. H.; Anjos, R. C.
2016-09-01
The effect of self-gravity of a disk matter is evaluated by the simplest modes of oscillation frequencies for perturbed circular geodesics. We plotted the radial profiles of free oscillations of an equatorial circular geodesic perturbed within the orbital plane or in the vertical direction. The calculation is carried out to geodesics of an axisymmetric n-dimensional spacetime. The profiles are computed by examples of disks embeded in five-dimensional or six-dimensional spacetime, where we studied the motion of free test particles for three axisymmetric cases: (i) the Newtonian limit of a general proposed 5D and 6D axisymmetric spacetime; (ii) a simple Randall–Sundrum (RS) 5D spacetime; (iii) general 5D and 6D RS spacetime. The equation of motion of such particles is derived and the stability study is computed for both horizontal and vertical directions, to see how extra dimensions could affect the system. In particular, we investigate a disk constructed from Miyamoto–Nagai and Chazy–Curzon with a cut parameter to generate a disk potential. Those solutions have a simple extension for extra dimensions in case (i), and by solving vacuum Einstein field equations for a kind of RS–Weyl metric in cases (ii) and (iii). We find that it is possible to compute a range of possible solutions where such perturbed geodesics are stable. Basically, the stable solutions appear, for the radial direction, in special cases when the system has 5D and in all cases when the system has 6D and, for the axial direction, in all cases when the system has both 5D or 6D.
Stability of perturbed geodesics in nD axisymmetric spacetimes
NASA Astrophysics Data System (ADS)
Coimbra-Araújo, C. H.; Anjos, R. C.
2016-09-01
The effect of self-gravity of a disk matter is evaluated by the simplest modes of oscillation frequencies for perturbed circular geodesics. We plotted the radial profiles of free oscillations of an equatorial circular geodesic perturbed within the orbital plane or in the vertical direction. The calculation is carried out to geodesics of an axisymmetric n-dimensional spacetime. The profiles are computed by examples of disks embeded in five-dimensional or six-dimensional spacetime, where we studied the motion of free test particles for three axisymmetric cases: (i) the Newtonian limit of a general proposed 5D and 6D axisymmetric spacetime; (ii) a simple Randall-Sundrum (RS) 5D spacetime; (iii) general 5D and 6D RS spacetime. The equation of motion of such particles is derived and the stability study is computed for both horizontal and vertical directions, to see how extra dimensions could affect the system. In particular, we investigate a disk constructed from Miyamoto-Nagai and Chazy-Curzon with a cut parameter to generate a disk potential. Those solutions have a simple extension for extra dimensions in case (i), and by solving vacuum Einstein field equations for a kind of RS-Weyl metric in cases (ii) and (iii). We find that it is possible to compute a range of possible solutions where such perturbed geodesics are stable. Basically, the stable solutions appear, for the radial direction, in special cases when the system has 5D and in all cases when the system has 6D and, for the axial direction, in all cases when the system has both 5D or 6D.
Franzone, P C; Guerri, L; Pennacchio, M; Taccardi, B
1998-01-15
We investigate a three-dimensional macroscopic model of wave-front propagation related to the excitation process in the left ventricular wall represented by an anisotropic bidomain. The whole left ventricle is modeled, whereas, in a previous paper, only a flat slab of myocardial tissue was considered. The direction of cardiac fibers, which affects the anisotropic conductivity of the myocardium, rotates from the epi- to the endocardium. If the ventricular wall is conceived as a set of packed surfaces, the fibers may be tangent to them or more generally may cross them obliquely; the latter case is described by an "imbrication angle." The effect of a simplified Purkinje network also is investigated. The cardiac excitation process, more particularly the depolarization phase, is modeled by a nonlinear elliptic equation, called an eikonal equation, in the activation time. The numerical solution of this equation is obtained by means of the finite element method, which includes an upwind treatment of the Hamiltonian part of the equation. By means of numerical simulations in an idealized model of the left ventricle, we try to establish whether the eikonal approach contains the essential basic elements for predicting the features of the activation patterns experimentally observed. We discuss and compare these results with those obtained in our previous papers for a flat part of myocardium. The general rules governing the spread of excitation after local stimulations, previously delineated for the flat geometry, are extended to the present, more realistic monoventricular model.
NASA Astrophysics Data System (ADS)
Ruiz, H. S.; Badía-Majós, A.; López, C.
2011-11-01
Relying on our theoretical approach for the superconducting critical state problem in 3D magnetic field configurations, we present an exhaustive analysis of the electrodynamic response for the so-called longitudinal transport problem in the slab geometry. A wide set of experimental conditions have been considered, including modulation of the applied magnetic field either perpendicular or parallel (longitudinal) to the transport current density. The main objective of our work was to characterize the role of the macroscopic material law that should properly account for the underlying mechanisms of flux cutting and depinning. The intriguing occurrence of negative current patterns and the enhancement of the transport current flow along the center of the superconducting sample are reproduced as a straightforward consequence of the magnetically induced internal anisotropy. Moreover, we show that, related to a maximal projection of the current density vector onto the local magnetic field, a maximal transport current density occurs somewhere within the sample. The elusive measurement of the flux cutting threshold (critical value of such parallel component J_{ {c} \\parallel } ) is suggested on the basis of local measurements of the transport current density. Finally, we show that a high correlation exists between the evolution of the transport current density and the appearance of paramagnetic peak structures in terms of the applied longitudinal magnetic field.
NASA Astrophysics Data System (ADS)
Romero-Salazar, C.
2016-04-01
A critical-state model is postulated that incorporates, for the first time, the structural anisotropy and flux-line cutting effect in a type-II superconductor. The model is constructed starting from the theoretical scheme of Romero-Salazar and Pérez-Rodríguez to study the anisotropy induced by flux cutting. Here, numerical calculations of the magnetic induction and static magnetization are presented for samples under an alternating magnetic field, orthogonal to a static dc-bias one. The interplay of the two anisotropies is analysed by comparing the numerical results with available experimental data for an yttrium barium copper oxide (YBCO) plate, and a vanadium-titanium (VTi) strip, subjected to a slowly oscillating field {H}y({H}z) in the presence of a static field {H}z({H}y).
NASA Astrophysics Data System (ADS)
Nakonieczna, Anna; Yeom, Dong-han
2016-05-01
Investigating the dynamics of gravitational systems, especially in the regime of quantum gravity, poses a problem of measuring time during the evolution. One of the approaches to this issue is using one of the internal degrees of freedom as a time variable. The objective of our research was to check whether a scalar field or any other dynamical quantity being a part of a coupled multi-component matter-geometry system can be treated as a `clock' during its evolution. We investigated a collapse of a self-gravitating electrically charged scalar field in the Einstein and Brans-Dicke theories using the 2+2 formalism. Our findings concentrated on the spacetime region of high curvature existing in the vicinity of the emerging singularity, which is essential for the quantum gravity applications. We investigated several values of the Brans-Dicke coupling constant and the coupling between the Brans-Dicke and the electrically charged scalar fields. It turned out that both evolving scalar fields and a function which measures the amount of electric charge within a sphere of a given radius can be used to quantify time nearby the singularity in the dynamical spacetime part, in which the apparent horizon surrounding the singularity is spacelike. Using them in this respect in the asymptotic spacetime region is possible only when both fields are present in the system and, moreover, they are coupled to each other. The only nonzero component of the Maxwell field four-potential cannot be used to quantify time during the considered process in the neighborhood of the whole central singularity. None of the investigated dynamical quantities is a good candidate for measuring time nearby the Cauchy horizon, which is also singular due to the mass inflation phenomenon.
SEAWAT-based simulation of axisymmetric heat transport.
Vandenbohede, Alexander; Louwyck, Andy; Vlamynck, Nele
2014-01-01
Simulation of heat transport has its applications in geothermal exploitation of aquifers and the analysis of temperature dependent chemical reactions. Under homogeneous conditions and in the absence of a regional hydraulic gradient, groundwater flow and heat transport from or to a well exhibit radial symmetry, and governing equations are reduced by one dimension (1D) which increases computational efficiency importantly. Solute transport codes can simulate heat transport and input parameters may be modified such that the Cartesian geometry can handle radial flow. In this article, SEAWAT is evaluated as simulator for heat transport under radial flow conditions. The 1971, 1D analytical solution of Gelhar and Collins is used to compare axisymmetric transport with retardation (i.e., as a result of thermal equilibrium between fluid and solid) and a large diffusion (conduction). It is shown that an axisymmetric simulation compares well with a fully three dimensional (3D) simulation of an aquifer thermal energy storage systems. The influence of grid discretization, solver parameters, and advection solution is illustrated. Because of the high diffusion to simulate conduction, convergence criterion for heat transport must be set much smaller (10(-10) ) than for solute transport (10(-6) ). Grid discretization should be considered carefully, in particular the subdivision of the screen interval. On the other hand, different methods to calculate the pumping or injection rate distribution over different nodes of a multilayer well lead to small differences only.
Radiative transfer in arbitrarily-shaped axisymmetric bodies
NASA Astrophysics Data System (ADS)
Nunes, Edmundo Miguel
2001-08-01
A mathematical model for evaluating thermal radiative transport in axisymmetric enclosures is presented. Based on the Discrete Exchange Factor (DEF) method, exchange factors between arbitrarily-oriented differential surface/volume ring elements are systematically calculated. The formulation is capable of treating geometrically complex systems including enclosures with shadowing effects ensuing from inner and/or outer obstructing bodies. The model is developed for isotropically scattering participating media. The solutions to several cylindrical media benchmark problems are found to be in excellent agreement with existing solutions in the literature. The solutions to several rocket-nozzle and plug-chamber geometries are presented for a host of geometric conditions and optical thicknesses. In addition, two variants of the DEF method are presented for anisotropically scattering media. The N-bounce method approximates total exchange factors by summing direct and user-designated higher order terms representative of multiple reflections/scattering. The source function approach is an intensity-based method relating the source function (gas leaving intensity) to the surface leaving intensity. The results obtained via these methods are found to be in good agreement with the existing solutions to several axisymmetric benchmark problems. A mathematical formulation is additionally proposed for addressing the effects of nonhomogeneous property distributions. Several nonhomogeneous benchmark problems are solved in an effort to validate the model.
SEAWAT-based simulation of axisymmetric heat transport.
Vandenbohede, Alexander; Louwyck, Andy; Vlamynck, Nele
2014-01-01
Simulation of heat transport has its applications in geothermal exploitation of aquifers and the analysis of temperature dependent chemical reactions. Under homogeneous conditions and in the absence of a regional hydraulic gradient, groundwater flow and heat transport from or to a well exhibit radial symmetry, and governing equations are reduced by one dimension (1D) which increases computational efficiency importantly. Solute transport codes can simulate heat transport and input parameters may be modified such that the Cartesian geometry can handle radial flow. In this article, SEAWAT is evaluated as simulator for heat transport under radial flow conditions. The 1971, 1D analytical solution of Gelhar and Collins is used to compare axisymmetric transport with retardation (i.e., as a result of thermal equilibrium between fluid and solid) and a large diffusion (conduction). It is shown that an axisymmetric simulation compares well with a fully three dimensional (3D) simulation of an aquifer thermal energy storage systems. The influence of grid discretization, solver parameters, and advection solution is illustrated. Because of the high diffusion to simulate conduction, convergence criterion for heat transport must be set much smaller (10(-10) ) than for solute transport (10(-6) ). Grid discretization should be considered carefully, in particular the subdivision of the screen interval. On the other hand, different methods to calculate the pumping or injection rate distribution over different nodes of a multilayer well lead to small differences only. PMID:24571415
Induced stresses due to fluid extraction from axisymmetric reservoirs
Segall, P.
1992-01-01
Earthquakes can be induced by fluid extraction, as well as by fluid injection. Segall (1989) proposed that poroelastic stresses are responsible for inducing earthquakes associated with fluid extraction. Here, I present methods for computing poroelastic stress changes due to fluid extraction for general axisymmetric reservoir geometries. The results of Geertsma (1973) for a thin disk reservoir with uniform pressure drop are recovered as a special case. Predicted surface subsidence agrees very well with measured leveling changes over the deep Lacq gas field in southwestern France. The induced stresses are finite if the reservoir pressure changes are continuous. Computed stress changes are on the order of several bars, suggesting that the preexisting stress states in regions of extraction induced seismicity are very close to frictional instability prior to production. ?? 1992 Birkha??user Verlag.
Two-dimensional and axisymmetric bifurcated channel flow
NASA Astrophysics Data System (ADS)
Goldman, A.
1981-10-01
Flow characteristics within the turbofan engine passageway for arbitrary geometries over a range of Reynolds numbers (1350 to 750,000) are determined by constructing a numerical model capable of handling irregularly shaped flow regions with laminar or turbulent flow. This is accomplished by using a vorticity-stream function formulation of the governing equations for two-dimensional and axisymmetrical flows with a two-equation eddy viscosity model for turbulence closure. A body-fitted coordinate system (Chu, 1971; Amsden and Hirt, 1973; Thompson et al., 1974) is used to treat the arbitrary geomtry. All equations are solved using finite-difference techniques (Goldman, 1980). Conclusions are presented, including: first-order terms must be separately upwind differenced to form stable solutions, regardless of whether the term is a true velocity term of a geometrically generated term created by the transformation.
Numerical solutions of ICRF fields in axisymmetric mirrors
Phillips, M.W.
1985-07-01
The results of a new numerical code called GARFIELD (Grumman Aerospace Rf Field code) that calculates ICRF Fields in axisymmetric mirror geometry (such as the central cell of a tandem mirror or an RF test stand) are presented. The code solves the electromagnetic wave equation using a cold plasma dispersion relation with a small collision frequency to simulate absorption. The purpose of the calculation is to examine how ICRF wave structure and propagation is effected by the axial variation of the magnetic field in a mirror for various antenna designs. In the code the wave equation is solved in flux coordinates using a finite element method. This should allow more complex dielectric tensors to be modeled in the future. The resulting matrix is solved iteratively, to maximize the allowable size of the spatial grid. Results for a typical antenna array in a simple mirror will be shown.
Fast optimization of static axisymmetric shell structures
NASA Astrophysics Data System (ADS)
Jacoby, Jeffrey
An axisymmetric shell optimization procedure is developed which is a fast, user-friendly and practical tool for design use in disciplines including aerospace, mechanical and civil engineering. The shape and thickness of a shell can be optimized to minimize shell mass, mass/volume ratio or stress with constraints imposed on von Mises stress and local buckling. The procedure was created with the aid of the GENOPT optimization development system (Dr. D. Bushnell, Lockheed Missiles and Space Co) and uses the FAST1 shell analysis program (Prof. C. R. Steele, Stanford University) to perform the constraint analysis. The optimization method used is the modified method of feasible directions. The procedure is fast because exact analysis methods allow complex shells to be modelled with only a few large shell elements and still retain a sufficiently accurate solution. This is of particular advantage near shell boundaries and intersections which can have small regions of very detailed variation in the solution. Finite element methods would require many small elements to capture accurately this detail with a resulting increase in computation time and model complexity. Reducing the complexity of the model also reduces the size of the required input and contributes to the simplicity of the procedure. Optimization design variables are the radial and axial coordinates of nodes and the shape parameters and thicknesses of the elements. Thickness distribution within an element can be optimized by specifying the thickness at evenly spaced control points. Spline interpolation is used to provide a smooth thickness variation between the control points. An effective method is developed for reducing the number of required stress constraint equations. Various shells have been optimized and include models for comparison with published results. Shape, thickness and shape/thickness optimization has been performed on examples including a simple aerobrake, sphere-nozzle intersections, ring
Static internal performance characteristics of two thrust reverser concepts for axisymmetric nozzles
NASA Technical Reports Server (NTRS)
Leavitt, L. D.; Re, R. J.
1982-01-01
The statis performance of two axisymmetric nozzle thrust reverser concepts was investigated. A rotating vane thrust reverser represented a concept in which reversing is accomplished upstream of the nozzle throat, and a three door reverser concept provided reversing downstream of the nozzle throat. Nozzle pressure ratio was varied from 2.0 to approximately 6.0. The results of this investigation indicate that both the rotating vane and three door reverser concepts were effective static thrust spoilers with the landing approach nozzle geometry and were capable of providing at least a 50 percent reversal of static thrust when fully deployed with the ground roll nozzle geometry.
Kinetically Stabilized Axisymmetric Tandem Mirrors: Summary of Studies
Post, R F
2005-02-08
The path to practical fusion power through plasma confinement in magnetic fields, if it is solely based on the present front-runner, the tokamak, is clearly long, expensive, and arduous. The root causes for this situation lie in the effects of endemic plasma turbulence and in the complexity the tokamak's ''closed'' field geometry. The studies carried out in the investigations described in the attached reports are aimed at finding an approach that does not suffer from these problems. This goal is to be achieved by employing an axisymmetric ''open'' magnetic field geometry, i.e. one generated by a linear array of circular magnet coils, and employing the magnetic mirror effect in accomplishing the plugging of end leakage. More specifically, the studies were aimed at utilizing the tandem-mirror concept in an axisymmetric configuration to achieve performance superior to the tokamak, and in a far simpler system, one for which the cost and development time could be much lower than that for the tokamak, as exemplified by ITER and its follow-ons. An important stimulus for investigating axisymmetric versions of the tandem mirror is the fact that, beginning from early days in fusion research there have been examples of axisymmetric mirror experiments where the plasma exhibited crossfield transport far below the turbulence-enhanced rates characteristic of tokamaks, in specific cases approaching the ''classical'' rate. From the standpoint of theory, axisymmetric mirror-based systems have special characteristics that help explain the low levels of turbulence that have been observed. Among these are the facts that there are no parallel currents in the equilibrium state, and that the drift surfaces of all of the trapped particles are closed surfaces, as shown early on by Teller and Northrop. In addition, in such systems it is possible to arrange that the radial boundary of the confined plasma terminates without contact with the chamber wall. This possibility reduces the
Magneto-hydrodynamically stable axisymmetric mirrors
Ryutov, D. D.; Cohen, B. I.; Molvik, A. W.; Berk, H. L.; Simonen, T. C.
2011-09-15
Making axisymmetric mirrors magnetohydrodynamically (MHD) stable opens up exciting opportunities for using mirror devices as neutron sources, fusion-fission hybrids, and pure-fusion reactors. This is also of interest from a general physics standpoint (as it seemingly contradicts well-established criteria of curvature-driven instabilities). The axial symmetry allows for much simpler and more reliable designs of mirror-based fusion facilities than the well-known quadrupole mirror configurations. In this tutorial, after a summary of classical results, several techniques for achieving MHD stabilization of the axisymmetric mirrors are considered, in particular: (1) employing the favorable field-line curvature in the end tanks; (2) using the line-tying effect; (3) controlling the radial potential distribution; (4) imposing a divertor configuration on the solenoidal magnetic field; and (5) affecting the plasma dynamics by the ponderomotive force. Some illuminative theoretical approaches for understanding axisymmetric mirror stability are described. The applicability of the various stabilization techniques to axisymmetric mirrors as neutron sources, hybrids, and pure-fusion reactors are discussed; and the constraints on the plasma parameters are formulated.
Axisymmetric ideal MHD stellar wind flow
NASA Technical Reports Server (NTRS)
Heinemann, M.; Olbert, S.
1978-01-01
The ideal MHD equations are reduced to a single equation under the assumption of axisymmetric flow. A variational principle from which the equation is derivable is given. The characteristics of the equation are briefly discussed. The equation is used to rederive the theorem of Gussenhoven and Carovillano.
NASA Astrophysics Data System (ADS)
Rasmussen, N. G.; Simeoni, G. G.; Lefmann, K.
2016-04-01
A dedicated beam-focusing device has been designed for the direct geometry thermal-cold neutron time-of-flight spectrometer TOFTOF at the neutron facility FRM II (Garching, Germany). The prototype, based on the compressed Archimedes' mirror concept, benefits from the adaptive-optics technology (adjustable supermirror curvature) and the compact size (only 0.5 m long). We have simulated the neutron transport across the entire guide system. We present a detailed computer characterization of the existing device, along with the study of the factors mostly influencing the future improvement. We have optimized the simulated prototype as a function of the neutron wavelength, accounting also for all relevant features of a real instrument like the non-reflecting side edges. The results confirm the "chromatic" displacement of the focal point (flux density maximum) at fixed supermirror curvature, and the ability of a variable curvature to keep the focal point at the sample position. Our simulations are in excellent agreement with theoretical predictions and the experimentally measured beam profile. With respect to the possibility of a further upgrade, we find that supermirror coatings with m-values higher than 3.5 would have only marginal influence on the optimal behaviour, whereas comparable spectrometers could take advantage of longer focusing segments, with particular impact for the thermal region of the neutron spectrum.
Stacey, W. M.; Bae, C.
2015-06-15
A systematic formalism for the calculation of rotation in non-axisymmetric tokamaks with 3D magnetic fields is described. The Braginskii Ωτ-ordered viscous stress tensor formalism, generalized to accommodate non-axisymmetric 3D magnetic fields in general toroidal flux surface geometry, and the resulting fluid moment equations provide a systematic formalism for the calculation of toroidal and poloidal rotation and radial ion flow in tokamaks in the presence of various non-axisymmetric “neoclassical toroidal viscosity” mechanisms. The relation among rotation velocities, radial ion particle flux, ion orbit loss, and radial electric field is discussed, and the possibility of controlling these quantities by producing externally controllable toroidal and/or poloidal currents in the edge plasma for this purpose is suggested for future investigation.
Solves Poisson's Equation in Axizymmetric Geometry on a Rectangular Mesh
1996-09-10
DATHETA4.0 computes the magnetostatic field produced by multiple point current sources in the presence of perfect conductors in axisymmetric geometry. DATHETA4.0 has an interactive user interface and solves Poisson''s equation using the ADI method on a rectangular finite-difference mesh. DATHETA4.0 uncludes models specific to applied-B ion diodes.
Buettner, G R; Coffman, R E
1977-02-01
The physical significance of the observed structure of the EPR signal, commonly known as the "doublet" spectrum, is that it contains information not only about the exchange coupling but also about the geometry of the magnetic dipole-dipole spin-spin coupling. We can show this because we have developed a general method of analysis applicable to this type of system and because we demand a quantitative fit of theory to experiment at two microwave frequencies. We have chosen the "doublet" free radical signal, which arises in the ribonucleotide reductase-5'-deoxyadenosylcobalamin system (from Lactobacillus leichmannii, see Hamilton et al., Biochemistry 11, 4696--4705 (1972)), for study, for the particular reason that the 35 GHz "doublet" spectrum has three components (in this case) rather than two, which provides an important test of the recently proposed model of isotropic exchange coupling by Schepler et al. ((1975) Biochim. Biophys. Acta 397, 510--518). We find that a quantitative fit to the EPR "doublet" lineshape can be obtained with a model of isotropic exchange, and a "point" magnetic dipole-dipole interaction acting over a distance of 9.9 A with the radical located approx. 34 degrees off the principal gzz axis and less than 1 degree off the principal gxx axis of the Co(II) in the corrin ring. Quantitative fits of the doublet portion of the observed lineshape at both 9 and 35 GHz were achieved with this model, assuming an axially symmetric free radical signal and a Gaussian spin-packet lineshape with isotropic linewidth.
A Fourier-spectral element algorithm for thermal convection in rotating axisymmetric containers
NASA Astrophysics Data System (ADS)
Fournier, Alexandre; Bunge, Hans-Peter; Hollerbach, Rainer; Vilotte, Jean-Pierre
2005-04-01
We present a Fourier-spectral element approach for modeling thermal convection in a rotating axisymmetric container. Following the theory detailed in Bernardi et al. [C. Bernardi, M. Dauge, Y. Maday, Spectral Methods for Axisymmetric Domains, Gauthier-Villars, Paris, 1999], a Fourier expansion of the field variables is performed in the periodic direction, and the resulting collection of meridional problems is discretized by means of a parallel spectral element method. A Gauss-Lobatto-Jacobi (0,1) quadrature, which incorporates the cylindrical radius in its weight, is introduced to avoid a potential degeneracy of the discrete set of equations, due to those nodes located on the axis of symmetry. A second-order timestepping scheme is presented, which treats the Coriolis and viscous forces implicitly. Numerical comparisons with analytical and published numerical solutions in spherical and cylindrical geometries are presented which highlight the accuracy of the model and demonstrate its spectral convergence properties.
AXISYMMETRIC, NONSTATIONARY BLACK HOLE MAGNETOSPHERES: REVISITED
Song, Yoo Geun; Park, Seok Jae E-mail: sjpark@kasi.re.kr
2015-10-10
An axisymmetric, stationary, general-relativistic, electrodynamic engine model of an active galactic nucleus was formulated by Macdonald and Thorne that consisted of a supermassive black hole surrounded by a plasma magnetosphere and a magnetized accretion disk. Based on this initial formulation, a nonstationary, force-free version of their model was constructed by Park and Vishniac (PV), with the simplifying assumption that the poloidal component of the magnetic field line velocity be confined along the radial direction in cylindrical polar coordinates. In this paper, we derive the new, nonstationary “Transfield Equation,” which was not specified in PV. If we can solve this “Transfield Equation” numerically, then we will understand the axisymmetric, nonstationary black hole magnetosphere in more rigorous ways.
Axisymmetric, Nonstationary Black Hole Magnetospheres: Revisited
NASA Astrophysics Data System (ADS)
Song, Yoo Geun; Park, Seok Jae
2015-10-01
An axisymmetric, stationary, general-relativistic, electrodynamic engine model of an active galactic nucleus was formulated by Macdonald and Thorne that consisted of a supermassive black hole surrounded by a plasma magnetosphere and a magnetized accretion disk. Based on this initial formulation, a nonstationary, force-free version of their model was constructed by Park & Vishniac (PV), with the simplifying assumption that the poloidal component of the magnetic field line velocity be confined along the radial direction in cylindrical polar coordinates. In this paper, we derive the new, nonstationary “Transfield Equation,” which was not specified in PV. If we can solve this “Transfield Equation” numerically, then we will understand the axisymmetric, nonstationary black hole magnetosphere in more rigorous ways.
Axisymmetric vibrations of layered tapered plates
NASA Astrophysics Data System (ADS)
Navaneethakrishnan, P. V.; Chandrasekaran, K.; Ravisrinivas, N.
1992-12-01
The study of Navaneethakrishnan and Chandrasekaran (1989) on axisymmetric free vibrations of layered annular plates is extended to the vibrations of layered annular plates whose thickness can vary as the radial distance from the arbitrary concentric circle. Numerical results are presented, showing the relationship between the circular frequency of the plate vibration and the ratio between the inner and the outer radii of the plate.
Magneto-hydrodynamically stable axisymmetric mirrors
NASA Astrophysics Data System (ADS)
Ryutov, Dmitri
2010-11-01
The achievement of high beta (60%) plasma with near classical confinement in a linear axisymmetric magnetic configuration has sparked interest in the Gas Dynamic Trap concept. The significance of these results is that they can be projected directly to a neutron source for materials testing. The possibility of axisymmetric mirrors (AM) being magneto-hydrodynamically (MHD) stable is also of interest from a general physics standpoint (as it seemingly contradicts to well-established criteria of curvature-driven instabilities). The axial symmetry allows for much simpler and more reliable designs of mirror-based fusion facilities than the well-known quadrupole mirror configurations. In this tutorial, after a brief summary of classical results (in particular of the Rosenbluth-Longmire theory and of the energy principle as applied to AM) several approaches towards achieving MHD stabilization of the AM will be considered: 1) Employing the favorable field-line curvature in the end tanks; 2) Using the line-tying effect; 3) Setting the plasma in a slow or fast differential rotation; 4) Imposing a divertor configuration on the solenoidal magnetic field; 5) Controlling the plasma dynamics by the ponderomotive force; 6) Other techniques. Several of these approaches go beyond pure MHD and require accounting for finite Larmor radius effects and trapped particle modes. Some illuminative theoretical approaches for understanding axisymmetric mirror stability will be described. Wherever possible comparison of theoretical and experimental results on AM will be provided. The applicability of the various stabilization techniques to axisymmetric mirrors as neutron sources, hybrids, and pure-fusion reactors will be discussed and the constraints on the plasma parameters will be formulated. Prepared by LLNL under Contract DE-AC52-07NA27344.
Numerical description of cavitation on axisymmetric bodies
Hickox, C.E.; Hailey, C.E.; Wolfe, W.P.; Watts, H.A.; Gross, R.J.; Ingber, M.S.
1988-01-01
This paper reports on ongoing studies which are directed toward the development of predictive techniques for the modeling of steady cavitation on axisymmetric bodies. The primary goal of the modeling effort is the prediction of cavity shape and pressure distribution from which forces and moments can be calculated. Here we present an overview of the modeling techniques developed and compare predictions with experimental data obtained from water tunnel tests for both limited and supercavitation. 14 refs., 4 figs.
Stabilization of the vertical instability by non-axisymmetric coils
NASA Astrophysics Data System (ADS)
Turnbull, A. D.; Reiman, A. H.; Lao, L. L.; Cooper, W. A.; Ferraro, N. M.; Buttery, R. J.
2016-08-01
In a published Physical Review Letter (Reiman 2007 Phys. Rev. Lett. 99 135007), it was shown that axisymmetric (or vertical) stability can be improved by placing a set of parallelogram coils above and below the plasma oriented at an angle to the constant toroidal planes. The physics of this stabilization can be understood as providing an effective additional positive stability index. The original work was based on a simplified model of a straight tokamak and is not straightforwardly applicable to a finite aspect ratio, strongly shaped plasma such as in DIII-D. Numerical calculations were performed in a real DIII-D -like configuration to provide a proof of principal that 3-D fields can, in fact raise the elongation limits as predicted. A four field period trapezioid-shaped coil set was developed in toroidal geometry and 3D equilibria were computed using trapezium coil currents of 10 kA , 100 kA , and 500 kA . The ideal magnetohydrodynamics growth rates were computed as a function of the conformal wall position for the n = 0 symmetry-preserving family. The results show an insignificant relative improvement in the stabilizing wall location for the two lower coil current cases, of the order of 10‑3 and less. In contrast, the marginal wall position is increased by 7% as the coil current is increased to 500 kA , confirming the main prediction from the original study in a real geometry case. In DIII-D the shift in marginal wall position of 7% would correspond to being able to move the existing wall outward by 5 to 10 cm. While the predicted effect on the axisymmetric stability is real, it appears to require higher coil currents than could be provided in an upgrade to existing facilities. Additional optimization over the pitch of the coils, the number of field periods and the coil positions, as well as plasma parameters, such as the internal inductivity {{\\ell}\\text{i}} , β , and {{q}95} would mitigate this but seem unlikely to change the conclusion.
Stabilization of the vertical instability by non-axisymmetric coils
NASA Astrophysics Data System (ADS)
Turnbull, A. D.; Reiman, A. H.; Lao, L. L.; Cooper, W. A.; Ferraro, N. M.; Buttery, R. J.
2016-08-01
In a published Physical Review Letter (Reiman 2007 Phys. Rev. Lett. 99 135007), it was shown that axisymmetric (or vertical) stability can be improved by placing a set of parallelogram coils above and below the plasma oriented at an angle to the constant toroidal planes. The physics of this stabilization can be understood as providing an effective additional positive stability index. The original work was based on a simplified model of a straight tokamak and is not straightforwardly applicable to a finite aspect ratio, strongly shaped plasma such as in DIII-D. Numerical calculations were performed in a real DIII-D -like configuration to provide a proof of principal that 3-D fields can, in fact raise the elongation limits as predicted. A four field period trapezioid-shaped coil set was developed in toroidal geometry and 3D equilibria were computed using trapezium coil currents of 10 kA , 100 kA , and 500 kA . The ideal magnetohydrodynamics growth rates were computed as a function of the conformal wall position for the n = 0 symmetry-preserving family. The results show an insignificant relative improvement in the stabilizing wall location for the two lower coil current cases, of the order of 10-3 and less. In contrast, the marginal wall position is increased by 7% as the coil current is increased to 500 kA , confirming the main prediction from the original study in a real geometry case. In DIII-D the shift in marginal wall position of 7% would correspond to being able to move the existing wall outward by 5 to 10 cm. While the predicted effect on the axisymmetric stability is real, it appears to require higher coil currents than could be provided in an upgrade to existing facilities. Additional optimization over the pitch of the coils, the number of field periods and the coil positions, as well as plasma parameters, such as the internal inductivity {{\\ell}\\text{i}} , β , and {{q}95} would mitigate this but seem unlikely to change the conclusion.
NASA Astrophysics Data System (ADS)
Lutter, W. J.; Ryberg, T.; Fuis, G. S.; Murphy, J. M.; Okaya, D. A.
2001-12-01
We acquired combined refraction and low-fold reflection data along a north-south-trending profile through the epicentral regions of the 1994 M 6.7 Northridge and 1971 M 6.7 San Fernando earthquakes as part of the Los Angeles Region Seismic Experiment, Phase II (LARSE II). The chief goal of LARSE is to image sedimentary basins and faults in the Los Angeles region to better understand and mitigate earthquake hazards associated with sedimentary basins and hidden faults. The LARSE II profile crossed the San Fernando and Santa Clarita Valleys, locations of the Northridge and San Fernando earthquakes, respectively. Refraction and reflection data show asymmetric basins beneath both valleys. Stacked wide-angle basin-bottom reflections and iso-velocity lines dip gently northward from the Santa Monica Mts, on the south margin of the San Fernando Valley, to 5-6 km below sea level in the northern part of the San Fernando Valley. Similar reflections and iso-velocity lines dip southward from the Sierra Pelona, on the north margin of the Santa Clarita Valley, to 3.5-4.5 km below sea level at the San Gabriel fault, in the central part of the Santa Clarita Valley. In both valleys, the basin-bottom reflections are generally slightly below the 5 km/s iso-velocity line, indicating that ``basement'' beneath these two valleys has velocities generally upwards of 5 km/s. In the San Fernando Valley, the basin-bottom reflections are truncated on the north by what we interpret to be the Northridge Hills blind thrust fault. In the Santa Clarita Valley, these reflections are truncated on the south at the steeply north-dipping San Gabriel fault. The region between these two faults, including the Santa Susana Mts and the southern part of the Santa Clarita Valley is characterized by complexity in both the velocity model and reflectivity. Below ~10-km depth, reflectivity is higher in the hanging walls of the Northridge and San Fernando faults than in the footwalls. The Northridge fault dips ~30o
Adaptation of TRIPND Field Line Tracing Code to a Shaped, Poloidal Divertor Geometry
NASA Astrophysics Data System (ADS)
Monat, P.; Moyer, R. A.; Evans, T. E.
2001-10-01
The magnetic field line tracing code TRIPND(T.E. Evans, Proc. 18th Conf. on Control. Fusion and Plasma Phys., Berlin, Germany, Vol. 15C, Part II (European Physical Society, 1991) p. 65.) has been modified to use the axisymmetric equilibrium magnetic fields from an EFIT reconstruction in place of circular equilibria with multi-filament current profile expansions. This adaptation provides realistic plasma current profiles in shaped geometries. A major advantage of this modification is that it allows investigation of magnetic field line trajectories in any device for which an EFIT reconstruction is available. The TRIPND code has been used to study the structure of the magnetic field line topology in circular, limiter tokamaks, including Tore Supra and TFTR and has been benchmarked against the GOURDON code used in Europe for magnetic field line tracing. The new version of the code, called TRIP3D, is used to investigate the sensitivity of various shaped equilibria to non-axisymmetric perturbations such as a shifted F coil or error field correction coils.
ERIC Educational Resources Information Center
Desseyn, H. O.; And Others
1985-01-01
Compares linear-nonlinear and planar-nonplanar geometry through the valence-shell electron pairs repulsion (V.S.E.P.R.), Mulliken-Walsh, and electrostatic force theories. Indicates that although the V.S.E.P.R. theory has more advantages for elementary courses, an explanation of the best features of the different theories offers students a better…
Axisymmetric instability in a thinning electrified jet.
Dharmansh; Chokshi, Paresh
2016-04-01
The axisymmetric stability of an electrified jet is analyzed under electrospinning conditions using the linear stability theory. The fluid is considered Newtonian with a finite electrical conductivity, modeled as a leaky dielectric medium. While the previous studies impose axisymmetric disturbances on a cylindrical jet of uniform radius, referred to as the base state, in the present study the actual thinning jet profile, obtained as the steady-state solution of the one-dimensional slender filament model, is treated as the base state. The analysis takes into account the role of variation in the jet variables like radius, velocity, electric field, and surface charge density along the thinning jet in the stability behavior. The eigenspectrum of the axisymmetric disturbance growth rate is constructed from the linearized disturbance equations discretized using the Chebyshev collocation method. The most unstable growth rate for the thinning jet is significantly different from that for the uniform radius jet. For the same electrospinning conditions, while the uniform radius jet is predicted to be highly unstable, the thinning jet profile is found to be unstable but with a relatively very low growth rate. The stabilizing role of the thinning jet is attributed to the variation in the surface charge density as well as the extensional deformation rate in the fluid ignored in the uniform radius jet analysis. The dominant mode for the thinning jet is an oscillatory conducting mode driven by the field-charge coupling. The disturbance energy balance finds the electric force to be the dominant force responsible for the disturbance growth, potentially leading to bead formation along the fiber. The role of various material and process parameters in the stability behavior is also investigated.
Numerical investigation of transitional supersonic axisymmetric wakes
NASA Astrophysics Data System (ADS)
Sandberg, Richard D.; Fasel, Hermann F.
2006-09-01
Transitional supersonic axisymmetric wakes are investigated by conducting various numerical experiments. The main objective is to identify hydrodynamic instability mechanisms in the flow at M {=} 2.46 for several Reynolds numbers, and to relate these to coherent structures that are found from various visualization techniques. The premise for this approach is the assumption that flow instabilities lead to the formation of coherent structures. Three high-order accurate compressible codes were developed in cylindrical coordinates for this work: a spatial Navier Stokes (N-S) code to conduct direct numerical simulations (DNS), a linearized N-S code for linear stability investigations using axisymmetric basic states, and a temporal N-S code for performing local stability analyses. The ability of numerical simulations to exclude physical effects deliberately is exploited. This includes intentionally eliminating certain azimuthal/helical modes by employing DNS for various circumferential domain sizes. With this approach, the impact of structures associated with certain modes on the global wake-behaviour can be scrutinized. Complementary spatial and temporal calculations are carried out to investigate whether instabilities are of local or global nature. Circumstantial evidence is presented that absolutely unstable global modes within the recirculation region co-exist with convectively unstable shear-layer modes. The flow is found to be absolutely unstable with respect to modes k {>} 0 for Re_D {>} 5000 and with respect to the axisymmetric mode k {=} 0 for Re_D {>} 100 000. It is concluded that azimuthal modes k {=} 2 and k {=} 4 are the dominant modes in the trailing wake, producing a ‘four-lobe’ wake pattern. Two possible mechanisms responsible for the generation of longitudinal structures within the recirculation region are suggested.
Axisymmetric instability in a thinning electrified jet.
Dharmansh; Chokshi, Paresh
2016-04-01
The axisymmetric stability of an electrified jet is analyzed under electrospinning conditions using the linear stability theory. The fluid is considered Newtonian with a finite electrical conductivity, modeled as a leaky dielectric medium. While the previous studies impose axisymmetric disturbances on a cylindrical jet of uniform radius, referred to as the base state, in the present study the actual thinning jet profile, obtained as the steady-state solution of the one-dimensional slender filament model, is treated as the base state. The analysis takes into account the role of variation in the jet variables like radius, velocity, electric field, and surface charge density along the thinning jet in the stability behavior. The eigenspectrum of the axisymmetric disturbance growth rate is constructed from the linearized disturbance equations discretized using the Chebyshev collocation method. The most unstable growth rate for the thinning jet is significantly different from that for the uniform radius jet. For the same electrospinning conditions, while the uniform radius jet is predicted to be highly unstable, the thinning jet profile is found to be unstable but with a relatively very low growth rate. The stabilizing role of the thinning jet is attributed to the variation in the surface charge density as well as the extensional deformation rate in the fluid ignored in the uniform radius jet analysis. The dominant mode for the thinning jet is an oscillatory conducting mode driven by the field-charge coupling. The disturbance energy balance finds the electric force to be the dominant force responsible for the disturbance growth, potentially leading to bead formation along the fiber. The role of various material and process parameters in the stability behavior is also investigated. PMID:27176407
Axisymmetric instability in a thinning electrified jet
NASA Astrophysics Data System (ADS)
Dharmansh; Chokshi, Paresh
2016-04-01
The axisymmetric stability of an electrified jet is analyzed under electrospinning conditions using the linear stability theory. The fluid is considered Newtonian with a finite electrical conductivity, modeled as a leaky dielectric medium. While the previous studies impose axisymmetric disturbances on a cylindrical jet of uniform radius, referred to as the base state, in the present study the actual thinning jet profile, obtained as the steady-state solution of the one-dimensional slender filament model, is treated as the base state. The analysis takes into account the role of variation in the jet variables like radius, velocity, electric field, and surface charge density along the thinning jet in the stability behavior. The eigenspectrum of the axisymmetric disturbance growth rate is constructed from the linearized disturbance equations discretized using the Chebyshev collocation method. The most unstable growth rate for the thinning jet is significantly different from that for the uniform radius jet. For the same electrospinning conditions, while the uniform radius jet is predicted to be highly unstable, the thinning jet profile is found to be unstable but with a relatively very low growth rate. The stabilizing role of the thinning jet is attributed to the variation in the surface charge density as well as the extensional deformation rate in the fluid ignored in the uniform radius jet analysis. The dominant mode for the thinning jet is an oscillatory conducting mode driven by the field-charge coupling. The disturbance energy balance finds the electric force to be the dominant force responsible for the disturbance growth, potentially leading to bead formation along the fiber. The role of various material and process parameters in the stability behavior is also investigated.
Axisymmetric oscillations of magnetic neutron stars
NASA Astrophysics Data System (ADS)
Lee, Umin
2007-01-01
We calculate axisymmetric oscillations of rotating neutron stars composed of the surface fluid ocean, solid crust and fluid core, taking account of a dipole magnetic field as strong as BS ~ 1015 G at the surface. The adiabatic oscillation equations for the solid crust threaded by a dipole magnetic field are derived in Newtonian dynamics, on the assumption that the axis of rotation is aligned with the magnetic axis so that perturbations on the equilibrium can be represented by series expansions in terms of spherical harmonic functions Yml(θ, φ) with different degrees l for a given azimuthal wave number m around the magnetic axis. Although the three component models can support a rich variety of oscillation modes, axisymmetric (m = 0) toroidal ltn and spheroidal lsn shear waves propagating in the solid crust are our main concerns, where l and n denote the harmonic degree and the radial order of the modes, respectively. In the absence of rotation, axisymmetric spheroidal and toroidal modes are completely decoupled, and we consider the effects of rotation on the oscillation modes only in the limit of slow rotation. We find that the oscillation frequencies of the fundamental toroidal torsional modes ltn in the crust are hardly affected by the magnetic field as strong as BS ~ 1015 G at the surface. As the radial order n of the shear modes in the crust becomes higher, however, both spheroidal and toroidal modes become susceptible to the magnetic field, and their frequencies in general get higher with increasing BS. We also find that the surface g modes and the crust/ocean interfacial modes are suppressed by a strong magnetic field, and that there appear magnetic modes in the presence of a strong magnetic field.
Quantitative shearography in axisymmetric gas temperature measurements
NASA Astrophysics Data System (ADS)
VanDerWege, Brad A.; O'Brien, Christopher J.; Hochgreb, Simone
1999-06-01
This paper describes the use of shearing interferometry (shearography) for the quantitative measurement of gas temperatures in axisymmetric systems in which vibration and shock are substantial, and measurement time is limited. The setup and principle of operation of the interferometer are described, as well as Fourier-transform-based fringe pattern analysis, Abel transform, and sensitivity of the phase lead to temperature calculation. A helium jet and a Bunsen burner flame are shown as verification of the diagnostic. The accuracy of the measured temperature profile is shown to be limited by the Abel transform and is critically dependent on the reference temperature used.
Super-collimation by axisymmetric photonic crystals
Purlys, V.; Gailevičius, D.; Peckus, M.; Gadonas, R.; Maigyte, L.; Staliunas, K.
2014-06-02
We propose and experimentally show the mechanism of beam super-collimation by axisymmetric photonic crystals, specifically by periodic (in propagation direction) structure of layers of concentric rings. The physical mechanism behind the effect is an inverse scattering cascade of diffracted wave components back into on- and near-axis angular field components, resulting in substantial enhancement of intensity of these components. We explore the super-collimation by numerical calculations and prove it experimentally. We demonstrate experimentally the axial field enhancement up to 7 times in terms of field intensity.
Mach disk from underexpanded axisymmetric nozzle flow
NASA Technical Reports Server (NTRS)
Chang, I.-S.; Chow, W. L.
1974-01-01
The flowfield associated with the underexpanded axisymmetric nozzle freejet flow including the appearance of a Mach disk has been studied. It is shown that the location and size of the Mach disk are governed by the appearance of a triple-point shock configuration and the condition that the central core flow will reach a state of 'choking at a throat'. It is recognized that coalescence of waves requires special attention and the reflected wave, as well as the vorticity generated from these wave interactions, have to be taken accurately into account. The theoretical results obtained agreed well with the experimental data.
Axisymmetric scrape-off plasma transport
Singer, C.E.; Langer, W.D.
1983-05-01
The two-dimensional flow of a collision dominated hydrogen scrape-off plasma in an axisymmetric tokamak is examined. This flow is described by a set of equations which contain the dominant terms in a maximal ordering appropriate to high density experimental divertors and reactor scrape-off plasmas. Comparison of the theory to estimates of scrape-off parameters in the Doublet III expanded boundary plasmas suggests that analysis of classical and neoclassical processes alone may be sufficient to predict plasma transport in high density scrape-off plasmas of practical importance.
Isodynamic axisymmetric equilibrium near the magnetic axis
Arsenin, V. V.
2013-08-15
Plasma equilibrium near the magnetic axis of an axisymmetric toroidal magnetic confinement system is described in orthogonal flux coordinates. For the case of a constant current density in the vicinity of the axis and magnetic surfaces with nearly circular cross sections, expressions for the poloidal and toroidal magnetic field components are obtained in these coordinates by using expansion in the reciprocal of the aspect ratio. These expressions allow one to easily derive relationships between quantities in an isodynamic equilibrium, in which the absolute value of the magnetic field is constant along the magnetic surface (Palumbo’s configuration)
NASA Astrophysics Data System (ADS)
Prástaro, Agostino
2008-02-01
Following our previous results on this subject [R.P. Agarwal, A. Prástaro, Geometry of PDE's. III(I): Webs on PDE's and integral bordism groups. The general theory, Adv. Math. Sci. Appl. 17 (2007) 239-266; R.P. Agarwal, A. Prástaro, Geometry of PDE's. III(II): Webs on PDE's and integral bordism groups. Applications to Riemannian geometry PDE's, Adv. Math. Sci. Appl. 17 (2007) 267-285; A. Prástaro, Geometry of PDE's and Mechanics, World Scientific, Singapore, 1996; A. Prástaro, Quantum and integral (co)bordism in partial differential equations, Acta Appl. Math. (5) (3) (1998) 243-302; A. Prástaro, (Co)bordism groups in PDE's, Acta Appl. Math. 59 (2) (1999) 111-201; A. Prástaro, Quantized Partial Differential Equations, World Scientific Publishing Co, Singapore, 2004, 500 pp.; A. Prástaro, Geometry of PDE's. I: Integral bordism groups in PDE's, J. Math. Anal. Appl. 319 (2006) 547-566; A. Prástaro, Geometry of PDE's. II: Variational PDE's and integral bordism groups, J. Math. Anal. Appl. 321 (2006) 930-948; A. Prástaro, Th.M. Rassias, Ulam stability in geometry of PDE's, Nonlinear Funct. Anal. Appl. 8 (2) (2003) 259-278; I. Stakgold, Boundary Value Problems of Mathematical Physics, I, The MacMillan Company, New York, 1967; I. Stakgold, Boundary Value Problems of Mathematical Physics, II, Collier-MacMillan, Canada, Ltd, Toronto, Ontario, 1968], integral bordism groups of the Navier-Stokes equation are calculated for smooth, singular and weak solutions, respectively. Then a characterization of global solutions is made on this ground. Enough conditions to assure existence of global smooth solutions are given and related to nullity of integral characteristic numbers of the boundaries. Stability of global solutions are related to some characteristic numbers of the space-like Cauchy dataE Global solutions of variational problems constrained by (NS) are classified by means of suitable integral bordism groups too.
Kinetic theory model predictions compared with low-thrust axisymmetric nozzle plume data
NASA Technical Reports Server (NTRS)
Riley, B. R.; Fuhrman, S. J.; Penko, P. F.
1993-01-01
A system of nonlinear integral equations equivalent to the steady-state Krook kinetic equation was used to model the flow from a low-thrust axisymmetric nozzle. The mathematical model was used to numerically calculate the number density, temperature, and velocity of a simple gas as it expands into a near vacuum. With these quantities the gas pressure and flow directions of the gas near the exit plane were calculated and compared with experimental values for a low-thrust nozzle of the same geometry and mass flow rate.
Using curvature extrema to track the evolution of axisymmetric interfaces
NASA Astrophysics Data System (ADS)
Vogel, M. J.; Nitsche, M.; Steen, P. H.
2003-11-01
The temporal evolution of the shape of an interface can exhibit phenomena such as break-up or pinch-off, which are fundamental events that must be controlled in many capillary systems of technological importance. For an axisymmetric surface, lemmas rooted in differential geometry dictate that curvature extrema coincide with curvature crossings or profile extrema. These features provide a convenient means to characterize the profiles of interfaces and to track their evolution even up to singularities, such as occurs at pinch-off. Being solely geometric in nature, this characterization is not limited by the physical properties of the system, e.g., Newtonian versus non-Newtonian behavior, viscous versus inviscid etc. We illustrate by tracking images from evolving soap-films (passive) and polymeric films (non-Newtonian), both observed in experiment, and a deforming mathematical surface predicted by the inviscid vortex-sheet model in simulation. We will discuss extensions of this approach that bring in some model of the flow (e.g. inviscid) and thereby lead to a dynamical system for the motion of the extrema.
Computing Axisymmetric Jet Screech Tones Using Unstructured Grids
NASA Technical Reports Server (NTRS)
Jorgenson, Philip C. E.; Loh, Ching Y.
2002-01-01
The space-time conservation element and solution element (CE/SE) method is used to solve the conservation law form of the compressible axisymmetric Navier-Stokes equations. The equations are time marched to predict the unsteady flow and the near-field screech tone noise issuing from an underexpanded circular jet. The CE/SE method uses an unstructured grid based data structure. The unstructured grids for these calculations are generated based on the method of Delaunay triangulation. The purpose of this paper is to show that an acoustics solution with a feedback loop can be obtained using truly unstructured grid technology. Numerical results are presented for two different nozzle geometries. The first is considered to have a thin nozzle lip and the second has a thick nozzle lip. Comparisons with available experimental data are shown for flows corresponding to several different jet Mach numbers. Generally good agreement is obtained in terms of flow physics, screech tone frequency, and sound pressure level.
Refraction and Shielding of Noise in Non-Axisymmetric Jets
NASA Technical Reports Server (NTRS)
Khavaran, Abbas
1996-01-01
This paper examines the shielding effect of the mean flow and refraction of sound in non-axisymmetric jets. A general three-dimensional ray-acoustic approach is applied. The methodology is independent of the exit geometry and may account for jet spreading and transverse as well as streamwise flow gradients. We assume that noise is dominated by small-scale turbulence. The source correlation terms, as described by the acoustic analogy approach, are simplified and a model is proposed that relates the source strength to 7/2 power of turbulence kinetic energy. Local characteristics of the source such as its strength, time- or length-scale, convection velocity and characteristic frequency are inferred from the mean flow considerations. Compressible Navier Stokes equations are solved with a k-e turbulence model. Numerical predictions are presented for a Mach 1.5, aspect ratio 2:1 elliptic jet. The predicted sound pressure level directivity demonstrates favorable agreement with reported data, indicating a relative quiet zone on the side of the major axis of the elliptic jet.
Understanding axisymmetric Bernstein modes in a nonneutral plasma
NASA Astrophysics Data System (ADS)
Hart, Grant W.; Spencer, Ross L.
2012-10-01
We have been studying axisymmetric Bernstein modes in a nonneutral plasma using both kinetic theory and simulation. Because of the large electric fields in these unneutralized plasmas, the oscillations are shifted down from the cyclotron frequency. Most of the modes occur near the Doppler-shifted upper-hybrid frequency, called the vortex frequency. In cylindrical geometry for a constant-density initial plasma, the perturbed velocity goes as J1(kr). For any given k there are two modes, one upshifted from the vortex frequency and one downshifted. The boundary condition which determines the allowed values of k is that the perturbed pressure must go to zero at the boundary. There is also another mode that does not follow this rule, however. This mode is very near the vortex frequency (0.1% - 1% frequency difference) and the pressure does not contribute significantly to the dynamics of the mode. This mode is most fruitfully treated as a small pressure perturbation of the upper-hybrid oscillation. The pressure causes a small upward frequency shift, which creates a small deviation from a self-similar velocity profile and therefore a non-zero k. The simultaneous solution of the perturbed dynamics and the dispersion relation allows the frequency and k to be calculated.
Lund, S M
2007-03-28
The transverse Vlasov equilibrium distribution function of an unbunched ion beam propagating in a continuous focusing channel is specified by a function f{perpendicular} (H{perpendicular}), where H{perpendicular} is the single-particle Hamiltonian. In standard treatments of continuous focusing equilibria in Vlasov-Poisson electrostatic models, it is assumed that a stable beam equilibrium specified by monotonic f{perpendicular}(H{perpendicular}) with {partial_derivative}f{perpendicular}(H{perpendicular})/{partial_derivative}H{perpendicular} {le} 0 is axisymmetric (no variation in azimuthal angle, i.e., with {partial_derivative}/{partial_derivative}{theta} = 0). In this paper a simple, but rigorous, proof is presented that only axisymmetric equilibrium solutions are possible in Vlasov-Poisson models for any physical choice of f{perpendicular}(H{perpendicular}) with {partial_derivative}f{perpendicular}(H{perpendicular})/{partial_derivative}H{perpendicular} {le} 0 if the confining boundary of the system (the beam pipe) is axisymmetric or if the geometry is radially unbounded.
Stress Analysis of Laminated Composite Cylinders Under Non-Axisymmetric Loading
Starbuck, J.M.
1999-10-26
The use of thick-walled composite cylinders in structural applications has seen tremendous growth over the last decade. Applications include pressure vessels, flywheels, drive shafts, spoolable tubing, and production risers. In these applications, the geometry of a composite cylinder is axisymmetric but in many cases the applied loads are non-axisymmetric and more rigorous analytical tools are required for an accurate stress analysis. A closed-form solution is presented for determining the layer-by-layer stresses, strains, and displacements and first-ply failure in laminated composite cylinders subjected to non-axisymmetric loads. The applied loads include internal and external pressure, axial force, torque, axial bending moment, uniform temperature change, rotational velocity, and interference fits. The formulation is based on the theory of anisotropic elasticity and a state of generalized plane deformation along the axis of the composite cylinder. Parametric design trade studies can be easily and quickly computed using this closed-form solution. A computer program that was developed for performing the numerical calculations is described and results from specific case studies are presented.
Vortexons in axisymmetric Poiseuille pipe flows
NASA Astrophysics Data System (ADS)
Fedele, F.; Dutykh, D.
2013-02-01
We present a study on the nonlinear dynamics of small long-wave disturbances to the laminar state in non-rotating axisymmetric Poiseuille pipe flows. At high Reynolds numbers, the associated Navier-Stokes equations can be reduced to a set of coupled Korteweg-de Vries-type (KdV) equations that support inviscid and smooth travelling waves numerically computed using the Petviashvili method. In physical space they correspond to localized toroidal vortices concentrated near the pipe boundaries (wall vortexons) or that wrap around the pipe axis (centre vortexons), in agreement with the analytical soliton solutions derived by Fedele (Fluid Dyn. Res., 44 (2012) 45509). The KdV dynamics of a perturbation is also investigated by means of a high accurate Fourier-based numerical scheme. We observe that an initial vortical patch splits into a centre vortexon radiating patches of vorticity near the wall. These can undergo further splitting leading to a proliferation of centre vortexons that eventually decay due to viscous effects. The splitting process originates from a radial flux of azimuthal vorticity from the wall to the pipe axis in agreement with the inverse cascade of cross-stream vorticity identified in channel flows by Eyink (Plysica D, 237 (2008) 1956). The inviscid vortexon most likely is unstable to non-axisymmetric disturbances and may be a precursor to puffs and slug flow formation.
Linear lateral vibration of axisymmetric liquid briges
NASA Astrophysics Data System (ADS)
Ferrera, C.; Montanero, J. M.; Cabezas, M. G.
A liquid bridge is a mass of liquid sustained by the action of the surface tension force between two parallel supporting disks Apart from their basic scientific interest a liquid bridge can be considered as the simplest idealization of the configuration appearing in the floating zone technique used for crystal growth and purification of high melting point materials footnote Messeguer et al emph Crystal Growth Res bf 5 27 1999 This has conferred considerable interest on the study of liquid bridges not only in fluid mechanics but also in the field of material engineering The axisymmetric dynamics of an isothermal liquid bridge has been frequently analysed over the past years The studies have considered different phenomena such as free oscillations footnote Montanero emph E J Mech B Fluids bf 22 169 2003 footnote Acero and Montanero emph Phys Fluids bf 17 078105 2005 forced vibrations footnote Perales and Messeguer emph Phys Fluids A bf 4 1110 1992 g-jitter effects footnote Messeguer and Perales emph Phys Fluids A bf 3 2332 1991 extensional deformation footnote Zhang et al emph J Fluid Mech bf 329 207 1996 and breakup process footnote Espino et al emph Phys Fluids bf 14 3710 2002 among others Works considering the nonaxisymmetric dynamical behaviour of a liquid bridge has been far less common footnote Sanz and Diez emph J Fluid Mech bf 205 503 1989 In the present study the linear vibration of an axisymmetric liquid
NASA Astrophysics Data System (ADS)
Malobabic, M.; Buttschardt, W.; Rautenberg, M.
The paper presents a theoretical derivation of the relationship between a variable geometry turbocharger and the combustion engine, using simplified boundary conditions and model restraints and taking into account the combustion process itself as well as the nonadiabatic operating conditions for the turbine and the compressor. The simulation algorithm is described, and the results computed using this algorithm are compared with measurements performed on a test engine in combination with a controllable turbocharger with adjustable turbine inlet guide vanes. In addition, the results of theoretical parameter studies are presented, which include the simulation of a given turbocharger with variable geometry in combination with different sized combustion engines and the simulation of different sized variable-geometry turbochargers in combination with a given combustion engine.
Experimental study of turbulent axisymmetric cavity flow
NASA Astrophysics Data System (ADS)
Lee, D. H.; Sung, H. J.
1994-08-01
An experimental study is made of turbulent axisymmetric cavity flow. The flow configuration consists of a sudden expansion and contraction pipe joint. In using the LDV system, in an effort to minimize refraction of laser beams at the curved interface, a refraction correction formula for the Reynolds shear stress is devised. Three values of the cavity length ( L = 300, 600 and 900 mm) are chosen, and the cavity height ( H) is fixed at 55 mm. Both open and closed cavities are considered. Special attention is given to the critical case L = 600 mm, where the cavity length L is nearly equal to the reattachment length of the flow. The Reynolds number, based on the inlet diameter ( D = 110 mm) is 73,000. Measurement data are presented for the static wall pressure, mean velocity profiles, vorticity thickness distributions, and turbulence quantities.
Nonlinear axisymmetric liquid currents in spherical annuli
NASA Technical Reports Server (NTRS)
Astafyeva, N. M.; Vvedenskaya, N. D.; Yavorskaya, I. M.
1978-01-01
A numerical analysis of non-linear axisymmetric viscous flows in spherical annuli of different gap sizes is presented. Only inner sphere was supposed to rotate at a constant angular velocity. The streamlines, lines of constant angular velocity, kinetic energy spectra, and spectra of velocity components are obtained. A total kinetic energy and torque needed to rotate the inner sphere are calculated as functions of Re for different gap sizes. In small-gap annulus nonuniqueness of steady solutions of Navier-Stokes equations is established and regions of different flow regime existences are found. Numerical solutions in a wide-gap annulus and experimental results are used in conclusions about flow stability in the considered range of Re. The comparison of experimental and numerical results shows close qualitative and quantitative agreement.
A Compact Quasi-axisymmetric Stellarator Reactor
L.P. Ku; the ARIES-CS Team
2003-10-20
We report the progress made in assessing the potential of compact, quasi-axisymmetric stellarators as power-producing reactors. Using an aspect ratio A=4.5 configuration derived from NCSX and optimized with respect to the quasi-axisymmetry and MHD stability in the linear regime as an example, we show that a reactor of 1 GW(e) maybe realizable with a major radius *8 m. This is significantly smaller than the designs of stellarator reactors attempted before. We further show the design of modular coils and discuss the optimization of coil aspect ratios in order to accommodate the blanket for tritium breeding and radiation shielding for coil protection. In addition, we discuss the effects of coil aspect ratio on the peak magnetic field in the coils.
Axisymmetric supersonic flow in rotating impellers
NASA Technical Reports Server (NTRS)
Goldstein, Arthur W
1952-01-01
General equations are developed for isentropic, frictionless, axisymmetric flow in rotating impellers with blade thickness taken into account and with blade forces eliminated in favor of the blade-surface function. It is shown that the total energy of the gas relative to the rotating coordinate system is dependent on the stream function only, and that if the flow upstream of the impeller is vortex-free, a velocity potential exists which is a function of only the radial and axial distances in the impeller. The characteristic equations for supersonic flow are developed and used to investigate flows in several configurations in order to ascertain the effect of variations of the boundary conditions on the internal flow and the work input. Conditions varied are prerotation of the gas, blade turning rate, gas velocity at the blade tips, blade thickness, and sweep of the leading edge.
Compact neutron imaging system using axisymmetric mirrors
Khaykovich, Boris; Moncton, David E; Gubarev, Mikhail V; Ramsey, Brian D; Engelhaupt, Darell E
2014-05-27
A dispersed release of neutrons is generated from a source. A portion of this dispersed neutron release is reflected by surfaces of a plurality of nested, axisymmetric mirrors in at least an inner mirror layer and an outer mirror layer, wherein the neutrons reflected by the inner mirror layer are incident on at least one mirror surface of the inner mirror layer N times, wherein N is an integer, and wherein neutrons reflected by the outer mirror are incident on a plurality of mirror surfaces of the outer layer N+i times, where i is a positive integer, to redirect the neutrons toward a target. The mirrors can be formed by a periodically reversed pulsed-plating process.
Multispecies transport theory for axisymmetric rotating plasmas
Tessarotto, M.; White, R.B.
1992-01-01
A reduced gyrokinetic equation is derived for a multi-species toroidal axisymmetric plasma with arbitrary toroidal differential rotation speeds and in the presence of a finite induced electric field. The kinetic equation obtained, extending previous results obtained by Hinton and Wong and by Catto, Bernstein and Tessarotto, has a form suited for transport applications, via variational techniques; in particular it exhibits the feature that all source terms, including the Spitzer source term, carrying the contribution due to the inductive electric field, appear to be acted upon by the collision operator. Moreover, the equation displays a new contribution due to ``explicit`` velocity perturbations, here proven to be consistent with transport ordering, whose evaluation appears relevant for transport calculations. In addition, general expressions are obtained for the neoclassical fluxes in terms of a variational principle, as well as for the classical ones, retaining, in both cases, the contributions due to the Spitzer`s inductive terms.
Multispecies transport theory for axisymmetric rotating plasmas
Tessarotto, M. . Dipt. di Scienze Matematiche); White, R.B. . Plasma Physics Lab.)
1992-01-01
A reduced gyrokinetic equation is derived for a multi-species toroidal axisymmetric plasma with arbitrary toroidal differential rotation speeds and in the presence of a finite induced electric field. The kinetic equation obtained, extending previous results obtained by Hinton and Wong and by Catto, Bernstein and Tessarotto, has a form suited for transport applications, via variational techniques; in particular it exhibits the feature that all source terms, including the Spitzer source term, carrying the contribution due to the inductive electric field, appear to be acted upon by the collision operator. Moreover, the equation displays a new contribution due to explicit'' velocity perturbations, here proven to be consistent with transport ordering, whose evaluation appears relevant for transport calculations. In addition, general expressions are obtained for the neoclassical fluxes in terms of a variational principle, as well as for the classical ones, retaining, in both cases, the contributions due to the Spitzer's inductive terms.
Nebeck, H.E.
1986-08-01
The MAZE mesh generator represents an arbitrary two dimensional region of space as an ordered collection of quadrilateral elements. Each element is defined by its four corner points (nodes) and an integer material number. Models are created by subdividing the region(s) of interest into one or more PARTS and specifying the element distribution in each part. Then, parts can be merged together to form the meshed representation of the entire region. Applying boundary conditions and describing material properties completes the model construction process. This activity takes place in three distinct phases: phase I-define geometry, subdivide regions into elements; phase II-refine geometry, establish interface and boundary conditions; phase III-describe material properties. This work presents explanations and examples of the phase I commands, along with an overview of the MAZE mesh generation process.
Axisymmetric Shearing Box Models of Magnetized Disks
NASA Astrophysics Data System (ADS)
Guan, Xiaoyue; Gammie, Charles F.
2008-01-01
The local model, or shearing box, has proven a useful model for studying the dynamics of astrophysical disks. Here we consider the evolution of magnetohydrodynamic (MHD) turbulence in an axisymmetric local model in order to evaluate the limitations of global axisymmetric models. An exploration of the model parameter space shows the following: (1) The magnetic energy and α-decay approximately exponentially after an initial burst of turbulence. For our code, HAM, the decay time τ propto Res , where Res/2 is the number of zones per scale height. (2) In the initial burst of turbulence the magnetic energy is amplified by a factor proportional to Res3/4λR, where λR is the radial scale of the initial field. This scaling applies only if the most unstable wavelength of the magnetorotational instability is resolved and the final field is subthermal. (3) The shearing box is a resonant cavity and in linear theory exhibits a discrete set of compressive modes. These modes are excited by the MHD turbulence and are visible as quasi-periodic oscillations (QPOs) in temporal power spectra of fluid variables at low spatial resolution. At high resolution the QPOs are hidden by a noise continuum. (4) In axisymmetry disk turbulence is local. The correlation function of the turbulence is limited in radial extent, and the peak magnetic energy density is independent of the radial extent of the box LR for LR > 2H. (5) Similar results are obtained for the HAM, ZEUS, and ATHENA codes; ATHENA has an effective resolution that is nearly double that of HAM and ZEUS. (6) Similar results are obtained for 2D and 3D runs at similar resolution, but only for particular choices of the initial field strength and radial scale of the initial magnetic field.
The evolution of swirling axisymmetric vortex rings
NASA Astrophysics Data System (ADS)
Gargan-Shingles, C.; Rudman, M.; Ryan, K.
2015-08-01
Swirling vortex rings form in any turbulent flow where a swirling component is present, such as in combustion chambers or the downwash of helicopter blades. Instabilities on initially non-swirling vortex rings result in a localized swirl velocity being generated within the core. The presence of a swirl component of velocity in a vortex ring modifies the relaxation and evolution of numerical Gaussian cores in a manner that is currently unknown. The evolution of Gaussian axisymmetric vortex rings of size 0.2 < Λ < 0.5, with Gaussian swirls of magnitude 0.0 < W < 0.5, is analyzed with reference to the governing equations. A relaxation time, at which the initial Gaussian approximation has minimal influence on the subsequent evolution, has been estimated for each case. An axial vortex forms along the axis of the ring and is responsible for the growth of a shear layer that is found to form at the leading edge. The circulation based Reynolds number is set at 10 000 to encourage the growth of shear layer instabilities from within this region. Secondary vortex rings are subsequently shown to evolve from the Kelvin-Helmholtz instability for shear layers of sufficient strength and are convected around the original ring and shed from the system. It is shown that complete settling of the strain rate within the core does not occur until all sheddings have ceased. Increasing the swirl magnitude past that considered in this paper is expected to result in the original ring losing its structure before the instability can occur. The evolution is found to be qualitatively similar to that of a piston generated axisymmetric vortex ring with swirl, with both cases eventually reaching a similar quasi-steady state.
The field lines of an axisymmetric magnetic field
NASA Technical Reports Server (NTRS)
Backus, George E.
1988-01-01
The equations of Willis and Young (1987) for the field lines of an arbitrary axisymmetric multipole are generalized to an arbitrary linear combination of multipoles, i.e., to an arbitrary axisymmetric magnetic field B outside a sphere of radius a, S(a), centered on the origin, and containing all the sources of B. For this field, axisymmetric Stokes stream function is expressed in terms of the Gauss coefficients. It is shown that if only one Gauss coefficient is nonzero, the field line equations are identical to those obtained by Willis and Young.
Axisymmetric Numerical Modeling of Pulse Detonation Rocket Engines
NASA Technical Reports Server (NTRS)
Morris, Christopher I.
2005-01-01
Pulse detonation rocket engines (PDREs) have generated research interest in recent years as a chemical propulsion system potentially offering improved performance and reduced complexity compared to conventional rocket engines. The detonative mode of combustion employed by these devices offers a thermodynamic advantage over the constant-pressure deflagrative combustion mode used in conventional rocket engines and gas turbines. However, while this theoretical advantage has spurred considerable interest in building PDRE devices, the unsteady blowdown process intrinsic to the PDRE has made realistic estimates of the actual propulsive performance problematic. The recent review article by Kailasanath highlights some of the progress that has been made in comparing the available experimental measurements with analytical and numerical models. In recent work by the author, a quasi-one-dimensional, finite rate chemistry CFD model was utilized to study the gasdynamics and performance characteristics of PDREs over a range of blowdown pressure ratios from 1-1000. Models of this type are computationally inexpensive, and enable first-order parametric studies of the effect of several nozzle and extension geometries on PDRE performance over a wide range of conditions. However, the quasi-one-dimensional approach is limited in that it cannot properly capture the multidimensional blast wave and flow expansion downstream of the PDRE, nor can it resolve nozzle flow separation if present. Moreover, the previous work was limited to single-pulse calculations. In this paper, an axisymmetric finite rate chemistry model is described and utilized to study these issues in greater detail. Example Mach number contour plots showing the multidimensional blast wave and nozzle exhaust plume are shown. The performance results are compared with the quasi-one-dimensional results from the previous paper. Both Euler and Navier-Stokes solutions are calculated in order to determine the effect of viscous
Coupled neoclassical-magnetohydrodynamic simulations of axisymmetric plasmas
NASA Astrophysics Data System (ADS)
Lyons, Brendan C.
2014-10-01
Neoclassical effects (e.g., the bootstrap current and neoclassical toroidal viscosity [NTV]) have a profound impact on many magnetohydrodynamic (MHD) instabilities, including tearing modes, edge-localized modes (ELMs), and resistive wall modes. High-fidelity simulations of such phenomena require a multiphysics code that self-consistently couples the kinetic and fluid models. We present the first results of the DK4D code, a dynamic drift-kinetic equation (DKE) solver being developed for this application. In this study, DK4D solves a set of time-dependent, axisymmetric DKEs for the non-Maxwellian part of the electron and ion distribution functions (fNM) with linearized Fokker-Planck-Landau collision operators. The plasma is formally assumed to be in the low- to finite-collisionality regimes. The form of the DKEs used were derived in a Chapman-Enskog-like fashion, ensuring that fNM carries no density, momentum, or temperature. Rather, these quantities are contained within the background Maxwellian and are evolved by an appropriate set of extended MHD equations. We will discuss computational methods used and benchmarks to other neoclassical models and codes. Furthermore, DK4D has been coupled to a reduced, transport-timescale MHD code, allowing for self-consistent simulations of the dynamic formation of the ohmic and bootstrap currents. Several applications of this hybrid code will be presented, including an ELM-like pressure collapse. We will also discuss plans for coupling to the spatially three-dimensional, extended MHD code M3D-C1 and generalizing to nonaxisymmetric geometries, with the goal of performing self-consistent hybrid simulations of tokamak instabilities and calculations of NTV torque. This work supported by the U.S. Department of Energy (DOE) under Grant Numbers DE-FC02-08ER54969 and DE-AC02-09CH11466.
NASA Astrophysics Data System (ADS)
Potter, William J.; Cotter, Garret
2013-02-01
In this paper we develop the jet model of Potter & Cotter to include a magnetically dominated accelerating parabolic base transitioning to a slowly decelerating conical jet with a geometry set by recent radio observations of M87. We conserve relativistic energy-momentum and particle number along the jet and calculate the observed synchrotron emission from the jet by calculating the integrated line-of-sight synchrotron opacity through the jet in the rest frame of each section of plasma. We calculate the inverse-Compton emission from synchrotron, cosmic microwave background (CMB), accretion disc, starlight, broad-line region (BLR), dusty torus and narrow-line region photons by transforming into the rest frame of the plasma along the jet. We fit our model to simultaneous multi-wavelength observations of the Compton-dominant FSRQ type blazar PKS 0227-369, with a jet geometry set by M87 and an accelerating bulk Lorentz factor consistent with simulations and theory. We investigate models in which the jet comes into equipartition at different distances along the jet and equipartition is maintained via the conversion of jet bulk kinetic energy into particle acceleration. We find that the jet must still be magnetically dominated within the BLR and cannot be in equipartition due to the severe radiative energy losses. The model fits the observations, including radio data, very well if the jet comes into equipartition outside the BLR within the dusty torus (1.5 pc) or at further distances (34 pc). The fits require a high-power jet with a large bulk Lorentz factor observed close to the line of sight, consistent with our expectations for a Compton-dominant blazar. We find that our fit in which the jet comes into equipartition furthest along the jet, which has a jet with the geometry of M87 scaled linearly with black hole mass, has an inferred black hole mass close to previous estimates. This implies that the jet of PKS 0227 might be well described by the same jet geometry as M87.
Asymmetric and axisymmetric dynamics of tropical cyclones
NASA Astrophysics Data System (ADS)
Persing, J.; Montgomery, M. T.; McWilliams, J. C.; Smith, R. K.
2013-05-01
We present the results of idealized numerical experiments to examine the difference between tropical cyclone evolution in three-dimensional (3-D) and axisymmetric (AX) model configurations. We focus on the prototype problem for intensification, which considers the evolution of an initially unsaturated AX vortex in gradient-wind balance on an f-plane. Consistent with findings of previous work, the mature intensity in the 3-D model is reduced relative to that in the AX model. In contrast with previous interpretations invoking barotropic instability and related horizontal mixing processes as a mechanism detrimental to the spin-up process, the results indicate that 3-D eddy processes associated with vortical plume structures can assist the intensification process by contributing to a radial contraction of the maximum tangential velocity and to a vertical extension of tangential winds through the depth of the troposphere. These plumes contribute significantly also to the azimuthally-averaged heating rate and the corresponding azimuthal-mean overturning circulation. The comparisons show that the resolved 3-D eddy momentum fluxes above the boundary layer exhibit counter-gradient characteristics and are generally not represented properly by the subgrid-scale parameterizations in the AX configuration. The resolved eddy fluxes act to support the contraction and intensification of the maximum tangential winds. The comparisons indicate fundamental differences between convective organization in the 3-D and AX configurations for meteorologically relevant forecast time scales. While the radial and vertical gradients of the system-scale angular rotation provide a hostile environment for deep convection in the 3-D model, with a corresponding tendency to strain the convective elements in the tangential direction, deep convection in the AX model does not suffer this tendency. Also, since during the 3-D intensification process the convection has not yet organized into annular rings
Modeling and simulation of axisymmetric stagnation flames
NASA Astrophysics Data System (ADS)
Sone, Kazuo
Laminar flame modeling is an important element in turbulent combustion research. The accuracy of a turbulent combustion model is highly dependent upon our understanding of laminar flames and their behavior in many situations. How much we understand combustion can only be measured by how well the model describes and predicts combustion phenomena. One of the most commonly used methane combustion models is GRI-Mech 3.0. However, how well the model describes the reacting flow phenomena is still uncertain even after many attempts to validate the model or quantify uncertainties. In the present study, the behavior of laminar flames under different aerodynamic and thermodynamic conditions is studied numerically in a stagnation-flow configuration. In order to make such a numerical study possible, the spectral element method is reformulated to accommodate the large density variations in methane reacting flows. In addition, a new axisymmetric basis function set for the spectral element method that satisfies the correct behavior near the axis is developed, and efficient integration techniques are developed to accurately model axisymmetric reacting flow within a reasonable amount of computational time. The numerical method is implemented using an object-oriented programming technique, and the resulting computer program is verified with several different verification methods. The present study then shows variances with the commonly used GRI-Mech 3.0 chemical kinetics model through a direct simulation of laboratory flames that allows direct comparison to experimental data. It is shown that the methane combustion model based on GRI-Mech 3.0 works well for methane-air mixtures near stoichiometry. However, GRI-Mech 3.0 leads to an overprediction of laminar flame speed for lean mixtures and an underprediction for rich mixtures. This result is slightly different from conclusion drawn in previous work, in which experimental data are compared with a one-dimensional numerical solutions
NASA Astrophysics Data System (ADS)
Eichwald, O.; Bayle, P.; Yousfi, Y.; Jugroot, M.
1998-11-01
This article is devoted to the analysis of the confinement effects of the neutral dynamics generated by a short-gap (0.5 mm) discharge inside three different microcavity geometries (cylinder, cube, and bricklike) filled with air at atmospheric pressure (760 Torr) and ambient temperature (293 K). The discharge is modelled by two mathematical functions representing the Joule heating and the momentum transfer between charged and neutral particles. Their spatio-temporal evolution are taken from experimental results with 470 ns for the duration and 13.5 W for the maximum injected power. The neutral gas evolution is described by the classical transport equations and solved by a powerful numerical monotonic upstream-centered scheme for conversion laws. Because of the microcavity dimensions considered, particular care has been used in the analysis of the thermal and hydrodynamics boundary layers which condition the gas-solid interaction in terms of viscous slip effects and thermal exchanges. The results presented show the microcavity geometry effects on the distribution of the initial cylindrical pressure wave as soon as it reaches the lateral walls. They show the specificity of the cube and bricklike microcavities due to the delayed reflections on the corners leading to a more heterogeneous gas behavior than in the case of the cylindrical microcavity. We also discuss the specific gas behaviors near the wall resulting from heat exchange and viscous stress.
Four motional invariants in axisymmetric tori equilibria
A ring gren, O.; Moiseenko, V.E.
2006-05-15
In addition to the standard set ({epsilon},{mu},p{sub {phi}}) of three invariants in axisymmetric tori, there exists a fourth independent radial drift invariant I{sub r}. For confined particles, the net radial drift has to be zero, whereby the drift orbit average I{sub r}=
EXACT VECTORIAL LAW FOR AXISYMMETRIC MAGNETOHYDRODYNAMICS TURBULENCE
Galtier, S.
2009-10-20
Three-dimensional incompressible magnetohydrodynamics turbulence is investigated under the assumptions of homogeneity and axisymmetry. We demonstrate that previous works of Chandrasekhar may be improved significantly by using a different formalism for the representation of two-point correlation tensors. From this axisymmetric kinematics, the equations a la von Karman-Howarth are derived from which an exact relation is found in terms of measurable correlations. The relation is then analyzed in the particular case of a medium permeated by an imposed magnetic field B{sub 0} . We make the ansatz that the development of anisotropy implies an algebraic relation between the axial and the radial components of the separation vector r and we derive an exact vectorial law which is parameterized by the intensity of anisotropy. The critical balance proposed by Goldreich and Sridhar is used to fix this parameter and to obtain a unique exact expression; the particular limits of correlations transverse and parallel to B{sub 0} are given for which simple expressions are found. Predictions for the energy spectra are also proposed by a straightforward dimensional analysis of the exact law; it gives a stronger theoretical background to the heuristic spectra previously proposed in the context of the critical balance. We also discuss the wave turbulence limit of an asymptotically large external magnetic field which appears as a natural limit of the vectorial relation. A new interpretation of the anisotropic solar wind observations is eventually discussed.
Transient, hypervelocity flow in an axisymmetric nozzle
NASA Technical Reports Server (NTRS)
Jacobs, P. A.
1991-01-01
The performance of an axisymmetric nozzle was examined which was designed to produce uniform, parallel flow with a nominal Mach number of 8. A free-piston driven shock tube was used to supply the nozzle with high-temperature, high-pressure test gas. Performance was assessed by measuring Pitot pressures across the exit plane of the nozzle and, over the range of operating conditions examined, the nozzle produced satisfactory test flows. However, there were flow disturbances that persisted for significant times after flow initiation. The detailed starting process of the nozzle was also investigated by performing numerical simulations at several nominal test conditions. The classical description of the starting process, based on a quasi-one-dimensional model, provided a reasonable approximation and was used to demonstrate that the starting process could consume a significant fraction of the otherwise usable test gas. This was especially important at high operating enthalpies where nozzle supply conditions were maintained for shorter times. Multidimensional simulations illustrated a mechanism by which the starting process in the actual nozzle could take longer than that predicted by the quasi-one-dimensional analysis. However, the cause of the persistent disturbances observed in the experimental calibration was not identified.
Exact vectorial law for axisymmetric MHD turbulence
NASA Astrophysics Data System (ADS)
Galtier, S.
2009-12-01
3D incompressible MHD turbulence is investigated under the assumptions of homogeneity and axisymmetry. We demonstrate that previous works of Chandrasekhar (1950) may be improved significantly by using a different formalism for the representation of two-point correlation tensors. From this axisymmetric kinematics, the equations a la von Karman-Howarth are derived from which an exact relation is found in terms of measurable correlations. The relation is then analyzed in the particular case of a medium permeated by an imposed magnetic field. We make the ansatz that the development of anisotropy implies an algebraic relation between the axial and the radial components of the separation vector and we derive an exact vectorial law which is parametrized by the intensity of anisotropy. The critical balance proposed by Goldreich & Sridhar (1995) is used to fix this parameter and to obtain a unique exact expression; the particular limits of correlations transverse and parallel to the mean field are given for which simple expressions are found. Predictions for the energy spectra are also proposed by a straightforward dimensional analysis of the exact law; it gives a stronger theoretical background to the heuristic spectra previously proposed in the context of the critical balance. We also discuss the wave turbulence limit of an asymptotically large external magnetic field which appears as a natural limit of the vectorial relation. A new interpretation of the anisotropic solar wind observations is eventually discussed.
Exact Vectorial Law for Axisymmetric Magnetohydrodynamics Turbulence
NASA Astrophysics Data System (ADS)
Galtier, S.
2009-10-01
Three-dimensional incompressible magnetohydrodynamics turbulence is investigated under the assumptions of homogeneity and axisymmetry. We demonstrate that previous works of Chandrasekhar may be improved significantly by using a different formalism for the representation of two-point correlation tensors. From this axisymmetric kinematics, the equations à la von Kármán-Howarth are derived from which an exact relation is found in terms of measurable correlations. The relation is then analyzed in the particular case of a medium permeated by an imposed magnetic field B0 . We make the ansatz that the development of anisotropy implies an algebraic relation between the axial and the radial components of the separation vector r and we derive an exact vectorial law which is parameterized by the intensity of anisotropy. The critical balance proposed by Goldreich & Sridhar is used to fix this parameter and to obtain a unique exact expression; the particular limits of correlations transverse and parallel to B0 are given for which simple expressions are found. Predictions for the energy spectra are also proposed by a straightforward dimensional analysis of the exact law; it gives a stronger theoretical background to the heuristic spectra previously proposed in the context of the critical balance. We also discuss the wave turbulence limit of an asymptotically large external magnetic field which appears as a natural limit of the vectorial relation. A new interpretation of the anisotropic solar wind observations is eventually discussed.
Magnetic surfaces in an axisymmetric torus
Skovoroda, A. A.
2013-04-15
A method is developed for specifying the boundary equilibrium magnetic surface in an axially symmetric torus by using the absolute values of the magnetic field B = B{sub s}({theta}) and the gradient of the poloidal flux vertical bar vertical bar {nabla}{Psi} vertical bar = vertical bar {nabla}{Psi} vertical bar {sub s}({theta}) in a special flux coordinate system. By setting two surface constants (e.g., the safety factor q and dp/d{Psi}) and matching the absolute values of the magnetic field and the flux gradient on a closed magnetic surface, it is possible to find all equilibrium magnetic functions (including n {center_dot} {nabla} ln B and the local shear s) and all constants (including the toroidal current J and the shear d{mu}/d{Psi}) on this surface. Such a non-traditional formulation of the boundary conditions in solving the stability problem in an axisymmetric torus allows one to impose intentional conditions on plasma confinement and MHD stability at the periphery of the system.
Vélez-Cordero, J Rodrigo; Yáñez Soto, Bernardo; Arauz-Lara, José L
2016-08-16
Nonhomogeneous evaporation fluxes have been shown to promote the formation of internal currents in sessile droplets, explaining the patterns that suspended particles leave after the droplet has dried out. Although most evaporation experiments have been conducted using spherical-cap-shaped drops, which are essentially in an axisymmetric geometry, here we show an example of nonhomogeneous evaporation in asymmetric geometries, which is visualized by following the motion of colloidal particles along liquid fingers forming a meniscus at square corners. It is found that the particle's velocity increases with the diffusive evaporation factor [Formula: see text] for the three tested fluids: water, isopropyl alcohol (IPA), and ethanol (EtOH). Here, [Formula: see text] is the vapor diffusivity in air, RH is the relative amount of vapor in the atmosphere, and cs is the saturated vapor concentration. We observed that in IPA and EtOH the internal currents promote a 3D spiral motion, whereas in water the particle's trajectory is basically unidirectional. By adding 0.25 critical micelle concentration (CMC) of sodium dodecyl sulfate (SDS) surfactant in water, a velocity blast was observed in the whole circulation flow pattern, going from [Formula: see text] to nearly [Formula: see text] in the longitudinal velocity component. To assess the effect of breaking the axisymmetric condition on the evaporation flux profile, we numerically solved the diffusive equation in model geometries that preserve the value of the contact angle θ but introduce an additional angle ϕ that characterizes the solid substrate. By testing different combinations of θ and ϕ, we corroborated that the evaporation flux increases when the substrate and the gas-liquid curves meet at corners with increasing sharpness. PMID:27437865
Vélez-Cordero, J Rodrigo; Yáñez Soto, Bernardo; Arauz-Lara, José L
2016-08-16
Nonhomogeneous evaporation fluxes have been shown to promote the formation of internal currents in sessile droplets, explaining the patterns that suspended particles leave after the droplet has dried out. Although most evaporation experiments have been conducted using spherical-cap-shaped drops, which are essentially in an axisymmetric geometry, here we show an example of nonhomogeneous evaporation in asymmetric geometries, which is visualized by following the motion of colloidal particles along liquid fingers forming a meniscus at square corners. It is found that the particle's velocity increases with the diffusive evaporation factor [Formula: see text] for the three tested fluids: water, isopropyl alcohol (IPA), and ethanol (EtOH). Here, [Formula: see text] is the vapor diffusivity in air, RH is the relative amount of vapor in the atmosphere, and cs is the saturated vapor concentration. We observed that in IPA and EtOH the internal currents promote a 3D spiral motion, whereas in water the particle's trajectory is basically unidirectional. By adding 0.25 critical micelle concentration (CMC) of sodium dodecyl sulfate (SDS) surfactant in water, a velocity blast was observed in the whole circulation flow pattern, going from [Formula: see text] to nearly [Formula: see text] in the longitudinal velocity component. To assess the effect of breaking the axisymmetric condition on the evaporation flux profile, we numerically solved the diffusive equation in model geometries that preserve the value of the contact angle θ but introduce an additional angle ϕ that characterizes the solid substrate. By testing different combinations of θ and ϕ, we corroborated that the evaporation flux increases when the substrate and the gas-liquid curves meet at corners with increasing sharpness.
NASA Astrophysics Data System (ADS)
Jiao, Cui-huan; Geng, Jian-chen; He, Cui-hong; Cui, Guang-hua
2012-08-01
Based on three structurally related flexible bis(5,6-dimethylbenzimidazole) ligand, five novel metal-organic CdII coordination architectures: from 0D to 3D structures CdII complexes have been hydrothermally synthesized and structurally characterized, namely, Cd2I4(L1)2 (1), [CdCl2(L1)]n (2), [CdCl2(L2)]n (3), {[Cd(chdc)(L2)0.5]·H2O}n (4), {[Cd(pydca)(L3)0.5(H2O)2]·H2O}n (5) (where L1 = 1,2-bis(5,6-dimethylbenzimidazole)ethane, L2 = 1,3-bis(5,6-dimethylbenzimidazole)propane, L3 = 1,4-bis(5,6-dimethylbenzimidazole)butane, H2chdc = 1,4-cyclohexanedicarboxylic acid, H2pydca = pyridine-2,6-dicarboxylic acid). A discrete binuclear [2 + 2] metallomacrocycles cadmium(II) complex of 1 is 0D, 3 and 5 exhibit one-dimensional helical and zigzag chain structures, respectively. 4 Forms a 2D layer with sql net topology bridged by carboxylate anion and L2, while 2 is an overall 3D array with the diamond topology (dia). In these complexes, the influences of anions coordination on the framework formation were observed and discussed. These results indicate the spacer length of the ligands and anions play important roles in controlling the diversity structural topologies of such metal-organic coordination architectures. The thermogravimetric analyses, X-ray powder diffraction and solid-state luminescent properties of the complexes have also been investigated.
Asymmetric and axisymmetric dynamics of tropical cyclones
NASA Astrophysics Data System (ADS)
Persing, J.; Montgomery, M. T.; McWilliams, J. C.; Smith, R. K.
2013-12-01
We present the results of idealized numerical experiments to examine the difference between tropical cyclone evolution in three-dimensional (3-D) and axisymmetric (AX) model configurations. We focus on the prototype problem for intensification, which considers the evolution of an initially unsaturated AX vortex in gradient-wind balance on an f plane. Consistent with findings of previous work, the mature intensity in the 3-D model is reduced relative to that in the AX model. In contrast with previous interpretations invoking barotropic instability and related horizontal mixing processes as a mechanism detrimental to the spin-up process, the results indicate that 3-D eddy processes associated with vortical plume structures can assist the intensification process by contributing to a radial contraction of the maximum tangential velocity and to a vertical extension of tangential winds through the depth of the troposphere. These plumes contribute significantly also to the azimuthally averaged heating rate and the corresponding azimuthal-mean overturning circulation. The comparisons show that the resolved 3-D eddy momentum fluxes above the boundary layer exhibit counter-gradient characteristics during a key spin-up period, and more generally are not solely diffusive. The effects of these eddies are thus not properly represented by the subgrid-scale parameterizations in the AX configuration. The resolved eddy fluxes act to support the contraction and intensification of the maximum tangential winds. The comparisons indicate fundamental differences between convective organization in the 3-D and AX configurations for meteorologically relevant forecast timescales. While the radial and vertical gradients of the system-scale angular rotation provide a hostile environment for deep convection in the 3-D model, with a corresponding tendency to strain the convective elements in the tangential direction, deep convection in the AX model does not suffer this tendency. Also, since
The water entry of slender axisymmetric bodies
NASA Astrophysics Data System (ADS)
Bodily, Kyle G.; Carlson, Stephen J.; Truscott, Tadd T.
2014-07-01
We present a study of the forces, velocities, and trajectories of slender (length/diameter = 10) axisymmetric projectiles using an embedded inertial measurement unit (IMU). Three nose shapes (cone, ogive, and flat) were used. Projectiles were tested at vertical and oblique impact angles with different surface treatments. The trajectory of a half-hydrophobic and half-hydrophilc case impacting vertically was compared to the trajectory of symmetrically coated projectiles impacting the free surface at oblique angles. The oblique impact cases showed significantly more final lateral displacement than the half-and-half case over the same depth. The amount of lateral displacement was also affected by the nose shape, with the cone nose shape achieving the largest lateral displacement for the oblique entry case. Instantaneous lift and drag coefficients were calculated using data from the IMU for the vertical, half-and-half, and oblique entry cases. Impact forces were calculated for each nose shape and the flat nose shape experienced the largest impulsive forces up to 37 N when impacting vertically. The impact force of the flat nose decreased for the oblique entry case. The location of the center of pressure was determined at discrete time steps using a theoretical torque model and values from the IMU. Acoustic spectrograms showed that the sound produced during the water entry event predominately arises from the pinch-off for the cone and ogive nose shapes, with additional sound production from impact for the flat nose shape. Each test run was imaged using two Photron SA3 cameras.
NASA Astrophysics Data System (ADS)
Yoo, S.; Zeng, X. C.
2006-05-01
We performed a constrained search for the geometries of low-lying neutral germanium clusters GeN in the size range of 21⩽N⩽29. The basin-hopping global optimization method is employed for the search. The potential-energy surface is computed based on the plane-wave pseudopotential density functional theory. A new series of low-lying clusters is found on the basis of several generic structural motifs identified previously for silicon clusters [S. Yoo and X. C. Zeng, J. Chem. Phys. 124, 054304 (2006)] as well as for smaller-sized germanium clusters [S. Bulusu et al., J. Chem. Phys. 122, 164305 (2005)]. Among the generic motifs examined, we found that two motifs stand out in producing most low-lying clusters, namely, the six/nine motif, a puckered-hexagonal-ring Ge6 unit attached to a tricapped trigonal prism Ge9, and the six/ten motif, a puckered-hexagonal-ring Ge6 unit attached to a bicapped antiprism Ge10. The low-lying clusters obtained are all prolate in shape and their energies are appreciably lower than the near-spherical low-energy clusters. This result is consistent with the ion-mobility measurement in that medium-sized germanium clusters detected are all prolate in shape until the size N ˜65.
Boeuf, J. P.; Claustre, J.; Chaudhury, B.; Fubiani, G.
2012-11-15
The physics of a magnetic filter under conditions similar to those of the negative ion source for the ITER neutral beam injector is analyzed with the help of a two-dimensional particle-in-cell Monte Carlo Collisions model. A detailed analysis of the different terms of the electron momentum equations shows how diamagnetic and drift currents can be dominant in different regions of the filter. Electron transport through the filter is due to an E Multiplication-Sign B drift current on one side of the chamber induced by the presence of the chamber walls perpendicular to the electron diamagnetic current. The filter design of the ITER negative ion source, which does not allow a closed electron diamagnetic current, induces an asymmetry of the plasma that is analyzed with the particle model. It is shown that electron transport through the filter in this geometry is very different from the transport in an ideal, one-dimensional magnetic filter often considered in the literature and described in detail in the companion paper [Boeuf et al., Phys. Plasmas 19, 113509 (2012)].
NASA Technical Reports Server (NTRS)
Power, G. D.; Anderson, O. L.
1986-01-01
The flow paths in gas turbine passages encompass a wide range of flow properties such as Reynolds number and Mach number as well as many other variable flow conditions such as swirl, free-stream turbulence, and laminar/turbulent transition. An existing computer program, the Axisymmetric Diffuser Duct (ADD) code, which calculates compressible, turbulent, swirling flow through axisymmetric ducts has been modified to include the effects of free-stream turbulence and laminar/turbulent transition. The program has been evaluated on a matrix of test cases to determine its accuracy, robustness, and limits of applicability. This improved version of the ADD code calculates solutions which compare well with available data and can now be applied to a wider range of problems than previously possible. In addition a concept called local enhancement was developed and tested on a simple two-dimensional geometry in order to demonstrate a method to reduce computer time. In this concept the pressure distribution is calculated on a coarse grid using the ADD code and the viscous layer is locally enhanced using a boundary layer analysis. By applying this concept, an order of magnitude reduction in computer time was possible without any loss in accuracy.
Revisiting Turbulence Model Validation for High-Mach Number Axisymmetric Compression Corner Flows
NASA Technical Reports Server (NTRS)
Georgiadis, Nicholas J.; Rumsey, Christopher L.; Huang, George P.
2015-01-01
Two axisymmetric shock-wave/boundary-layer interaction (SWBLI) cases are used to benchmark one- and two-equation Reynolds-averaged Navier-Stokes (RANS) turbulence models. This validation exercise was executed in the philosophy of the NASA Turbulence Modeling Resource and the AIAA Turbulence Model Benchmarking Working Group. Both SWBLI cases are from the experiments of Kussoy and Horstman for axisymmetric compression corner geometries with SWBLI inducing flares of 20 and 30 degrees, respectively. The freestream Mach number was approximately 7. The RANS closures examined are the Spalart-Allmaras one-equation model and the Menter family of kappa - omega two equation models including the Baseline and Shear Stress Transport formulations. The Wind-US and CFL3D RANS solvers are employed to simulate the SWBLI cases. Comparisons of RANS solutions to experimental data are made for a boundary layer survey plane just upstream of the SWBLI region. In the SWBLI region, comparisons of surface pressure and heat transfer are made. The effects of inflow modeling strategy, grid resolution, grid orthogonality, turbulent Prandtl number, and code-to-code variations are also addressed.
Computation of supersonic jet mixing noise for an axisymmetric convergent-divergent nozzle
NASA Astrophysics Data System (ADS)
Khavaran, Abbas; Krejsa, Eugene A.; Kim, Chan M.
1994-05-01
The turbulent mixing noise of a supersonic jet is calculated for an axisymmetric convergent-divergent nozzle at the design pressure ratio. Aerodynamic computations are performed using the PARC code with a k-epsilon turbulence model. Lighthill's acoustic analogy is adopted. The acoustics solution is based upon the methodology followed in the MGB code. The source correlation function is expressed as a linear combination of second-order tensors (Ribner's assumption). Assuming separable second-order correlations and incorporating Batchelor's isotropic turbulence model, the source term was calculated from the kinetic energy of turbulence. A Gaussian distribution for the time-delay of correlation was introduced. The CFD solution was used to obtain the source strength as well as the characteristic time-delay of correlation. The effect of sound/flow interaction was incorporated using the high frequency asymptotic solution to Lilley's equation for axisymmetric geometries. Acoustic results include sound pressure level directivity and spectra at different polar angles. The aerodynamic and acoustic results demonstrate favorable agreement with experimental data.
Stability of the laminar wake behind spinning axisymmetric bluff bodies: sensitivity and control
NASA Astrophysics Data System (ADS)
Jimenez-Gonzalez, Jose Ignacio; Martinez-Bazan, Carlos; Coenen, Wilfried; Manglano, Carlos; Sevilla, Alejandro
2014-11-01
We carry out direct and adjoint global stability analyses of the laminar wake behind several spinning axisymmetric bluff bodies, i.e. sphere, hemisphere, bullet-shaped bodies of ellipsoidal nose and spherical nose respectively; for moderate Reynolds numbers (Re <= 450) and values of the spin parameter (Ω <= 1), defined as the ratio between the azimuthal velocity at the outer body surface and the free-stream velocity. Both the axisymmetric base flow computations and the assembling of the eigenvalue problems are tackled by means of the finite element solver FreeFEM + + , computing finally the eigenmodes with an Arnoldi algorithm in Matlab. We show that spin acts as a stabilization mechanism for the wake behind bodies with a cylindrical trailing part, while it destabilizes the wake of the other geometries. The computation of the adjoint modes and the identification of the wavemaker allow us to discuss the nature of the different unstable modes found and understand the differences in the stabilizing or destabilizing effect of rotation due to the base flow modifications. The controllability of the unstable regimes by means of base bleed is also addressed. Supported by the Spanish MINECO, Junta de Andalucía and EU Funds under Projects DPI2011-28356-C03-03 and P11-TEP7495.
Waychunas, G.A.; Fuller, C.C.; Davis, J.A.
2002-01-01
"Two-line" ferrihydrite samples precipitated and then exposed to a range of aqueous Zn solutions (10-5 to 10-3 M), and also coprecipitated in similar Zn solutions (pH 6.5), have been examined by Zn and Fe K-edge X-ray absorption spectroscopy. Typical Zn complexes on the surface have Zn-O distances of 1.97(0.2) A?? and coordination numbers of about 4.0(0.5), consistent with tetrahedral oxygen coordination. This contrasts with Zn-O distances of 2.11(.02) A?? and coordination numbers of 6 to 7 in the aqueous Zn solutions used in sample preparation. X-ray absorption extended fine structure spectroscopy (EXAFS) fits to the second shell of cation neighbors indicate as many as 4 Zn-Fe neighbors at 3.44(.04) A?? in coprecipitated samples, and about two Zn-Fe neighbors at the same distance in adsorption samples. In both sets of samples, the fitted coordination number of second shell cations decreases as sorption density increases, indicating changes in the number and type of available complexing sites or the onset of competitive precipitation processes. Comparison of our results with the possible geometries for surface complexes and precipitates suggests that the Zn sorption complexes are inner sphere and at lowest adsorption densities are bidentate, sharing apical oxygens with adjacent edge-sharing Fe(O,OH)6 octahedra. Coprecipitation samples have complexes with similar geometry, but these are polydentate, sharing apices with more than two adjacent edge-sharing Fe(O,OH)6 polyhedra. The results are inconsistent with Zn entering the ferrihydrite structure (i.e., solid solution formation) or formation of other Zn-Fe precipitates. The fitted Zn-Fe coordination numbers drop with increasing Zn density with a minimum of about 0.8(.2) at Zn/(Zn + Fe) of 0.08 or more. This change appears to be attributable to the onset of precipitation of zinc hydroxide polymers with mainly tetrahedral Zn coordination. At the highest loadings studied, the nature of the complexes changes further
Ju, Dehao; Shrimpton, John; Bowdrey, Moira; Hearn, Alex
2012-08-01
A breath activated, pressurized metered dose inhaler (pMDI) device (Oxette(®)) has been developed to replace the traditional cigarette. In this paper, internal and external spray characters are measured by high speed imaging along with sizing the residual droplets at the distance from the discharge orifice where the human oropharynx locates. Two different formulations with 95% and 98% mass fraction of HFA 134a and two prototype cigarette alternatives with different expansion chamber volumes have been analyzed. The internal and external flows issuing from early stage prototype Oxette(®) are discussed along with boiling and evaporation phenomena. The expansion and entrainment regions of the jet are observed and discussed with comparison to the turbulent round jet of a single phase. From the visualizations of internal flows in the earlier design, a small expansion chamber can hardly generate small bubbles, which is difficult to produce fine sprays. The larger the expansion chamber volume, the more room for the propellant evaporation, recirculation, bubble generation and growth, all of which produces finer sprays. Therefore the later prototype of Oxette(®) 2 made a significant improvement to produce fine sprays and facilitated development of the cigarette alternative. Furthermore, the characters of the spray generated by Oxette(®) are compared to that issuing from a pMDI by previous researchers, where the residual MMD is larger than that of a pMDI, because the Oxette(®) has a smaller expansion chamber and the geometry provides less opportunity for the recirculation due to restrictions of the design space. Although the formulation with higher mass fraction of HFA 134a can generate smaller droplets, it cannot produce steady puffs with relatively low mass flow rate.
Parametric Study of Axisymmetric Fusion Devices.
NASA Astrophysics Data System (ADS)
Ducar, William Scott
1987-09-01
Three different axisymmetric magnetic mirror fusion machines are examined in order to optimize the ratio the fusion power produced by them to the power injected into them to maintain the plasma. These three devices were chosen to study the continuum between a simple mirror and a tandem mirror. This allowed the evolutionary process leading from the simple to the tandem mirror to be examined in detail. The Kelley mirror, which corresponds to the middle step, was examined in depth for the first time. A computer code that models the plasma in these machines was written to investigate the steady state operation of these machines. The balance equations are solved by using an ordinary differential equation solver, LSODE ^{11}, to numerically solve the system of differential equations. Unlike previous methods, this technique allowed for a quick, inexpensive, and exhaustive examination of parameter space and has the added advantage that the steady state solutions obtained are numerically stable, which is not always the case with fixed point iteration. Furthermore, this computer model also permitted investigation of the use of polarized fuels, which has not been done before in mirror machines. The computer model was used to examine parameter space to optimize Q for each of the three machines. When feasible, a comparison with a Fokker-Planck code was made for the optimal Q case for each machine. It was found that the computer model compared favorably with the Fokker -Planck code, HYBRIDII^{22}. HYBRIDII used 54 minutes of Cray-1 computing time for a tandem mirror case to reach steady state, while the computer model obtained a steady state solution in one and a half minutes. Finally, the possible roles these devices might fill was discussed. It was found that none of the devices appeared suited for the role of a pure fussion electrical power plant. However, the Kelley machine and tandem machine appeared to be strong candidates for the role of a hybrid fusion-fission reactor
Axisymmetric Tandem Mirrors: Stabilization and Confinement Studies
Post, R F; Fowler, T K; Bulmer, R; Byers, J; Hua, D; Tung, L
2004-07-15
The 'Kinetic Stabilizer' has been proposed as a means of MHD stabilizing an axisymmetric tandem mirror system. The K-S concept is based on theoretical studies by Ryutov, confirmed experimentally in the Gas Dynamic Trap experiment in Novosibirsk. In the K-S beams of ions are directed into the end of an 'expander' region outside the outer mirror of a tandem mirror. These ions, slowed, stagnated, and reflected as they move up the magnetic gradient, produce a low-density stabilizing plasma. At the Lawrence Livermore National Laboratory we have been conducting theoretical and computational studies of the K-S Tandem Mirror. These studies have employed a low-beta code written especially to analyze the beam injection/stabilization process, and a new code SYMTRAN (by Hua and Fowler) that solves the coupled radial and axial particle and energy transport in a K-S TM. Also, a 'legacy' MHD stability code, FLORA, has been upgraded and employed to benchmark the injection/stabilization code and to extend its results to high beta values. The FLORA code studies so far have confirmed the effectiveness of the K-S in stabilizing high-beta (40%) plasmas with stabilizer plasmas the peak pressures of which are several orders of magnitude smaller than those of the confined plasma. Also the SYMTRAN code has shown D-T plasma ignition from alpha particle energy deposition in T-M regimes with strong end plugging. Our studies have confirmed the viability of the K-S-T-M concept with respect to MHD stability and radial and axial confinement. We are continuing these studies in order to optimize the parameters and to examine means for the stabilization of possible residual instability modes, such as drift modes and 'trapped-particle' modes. These modes may in principle be controlled by tailoring the stabilizer plasma distribution and/or the radial potential distribution. In the paper the results to date of our studies are summarized and projected to scope out possible fusion-power versions of the K
NASA Technical Reports Server (NTRS)
Shvets, A. L.; Gilinsky, M.; Blankson, I. M.
2004-01-01
Experimental test results of air flow inside and at the cylindrical cavity located on axisymmetric body are presented. These tests were conducted in the wind tunnel A-7 of Institute of Mechanics at Moscow State University. Pressure distribution along the cavities and optical measurements were obtained. Dependence of these characteristics of length of a cavity in the range: L/D = 0.5 - 14 and free stream Mach in the range: M(sub infinity) = 0.6 - 3.0 was determined. Flow structure inside the cavity, cause of flow regime change, separation zones geometry and others were studied. In particular, the flow modes of with open and closed separation zones are determined.
Low-speed test of translating lip axisymmetric inlets for subsonic transports
NASA Technical Reports Server (NTRS)
Henne, P. A.
1974-01-01
Translating lip, axisymmetric inlets have been tested at freestream Mach numbers between 0.0 and 0.30 and at angles of attack between 0 and 90 degrees. Three isolated inlet models were tested. One model represented the inlet geometry at cruise, that is, with no lip translation. The other two models had forward translating lips with different contours. The low forward speed inlet angle-of-attack capability with the translating lip was increased more than twenty degrees over the basic untranslated lip configuration at the higher inlet airflows. The static inlet performance with the translating lip was also greatly improved. The design translation distance, defined by potential flow analysis, was near optimum.
Impedance Calculations of Non-Axisymmetric Transitions Using the Optical Approximation
Bane, K.L.F.; Stupakov, G.; Zagorodov, I.; /DESY
2007-03-06
In a companion report, we have derived a method for finding the impedance at high frequencies of vacuum chamber transitions that are short compared to the catch-up distance, in a frequency regime that--in analogy to geometric optics for light--we call the optical regime. In this report we apply the method to various non-axisymmetric geometries such as irises/short collimators in a beam pipe, step-in transitions, step-out transitions, and more complicated transitions of practical importance. Most of our results are analytical, with a few given in terms of a simple one dimensional integral. Our results are compared to wakefield simulations with the time-domain, finite-difference program ECHO, and excellent agreement is found.
Non-axisymmetric viscous lower-branch modes in axisymmetric supersonic flows
NASA Technical Reports Server (NTRS)
Duck, Peter W.; Hall, Philip
1990-01-01
A previous paper by Duck and Hall (1989) considered the weakly nonlinear interaction of a pair of axisymmetric lower-branch Tollmien-Schlichting instabilities in cylindrical supersonic flows. Here, the possibility that nonaxisymmetric modes might also exist is investigated. In fact, it is found that such modes do exist and, on the basis of linear theory, it appears that these modes are the most important. The nonaxisymmetric modes are found to exist for flows around cylinders with nondimensional radius a less than some critical value a(c). This critical value a(c) is found to increase monotonically with the azimuthal wavenumber n of the disturbance, and it is found that unstable modes always occur in pairs. It is shown that, in general, instability in the form of lower-branch Tollmien-Schlichting waves will occur first for nonaxisymmetric modes and that, in the unstable regime, the largest growth rates correspond to the latter modes.
Transient axial solution for plane and axisymmetric waves focused by a paraboloidal reflector.
Tsai, Yi-Te; Zhu, Jinying; Haberman, Michael R
2013-04-01
A time domain analytical solution is presented to calculate the pressure response along the axis of a paraboloidal reflector for a normally incident plane wave. This work is inspired by Hamilton's axial solution for an ellipsoidal mirror and the same methodology is employed in this paper. Behavior of the reflected waves along reflector axis is studied, and special interest is placed on focusing gain obtained at the focal point. This analytical solution indicates that the focusing gain is affected by reflector geometry and the time derivative of the input signal. In addition, focused pressure response in the focal zone given by various reflector geometries and input frequencies are also investigated. This information is useful for selecting appropriate reflector geometry in a specific working environment to achieve the best signal enhancement. Numerical simulation employing the finite element method is used to validate the analytical solution, and visualize the wave field to provide a better understanding of the propagation of reflected waves. This analytical solution can be modified to apply to non-planar incident waves with axisymmetric wavefront and non-uniform pressure distribution. An example of incident waves with conical-shaped wavefront is presented.
Stationary axisymmetric fields in a teleparallel theory of gravitation
NASA Astrophysics Data System (ADS)
Saez, D.
1984-12-01
The stationary axisymmetric field in the tetrad theory of gravitation of Moller (1978) and hence (as shown by Meyre, 1982) in the teleparallel limit of the gauge theory of Hehl et al. (1978) is investigated analytically. A set of tetrads satisfying the Moller equations and giving a Kerr metric is defined, and its existence is proved. It is suggested that the introduction of suitable conditions could reduce the number of tetrads in the Kerr case to one or a small number, and that the present analytical techniques could be applied to other stationary axisymmetric metrics of general relativity.
ERIC Educational Resources Information Center
Cukier, Mimi; Asdourian, Tony; Thakker, Anand
2012-01-01
Geometry provides a natural window into what it is like to do mathematics. In the world of geometry, playful experimentation is often more fruitful than following a procedure, and logic plus a few axioms can open new worlds. Nonetheless, teaching a geometry course in a way that combines both rigor and play can be difficult. Many geometry courses…
ERIC Educational Resources Information Center
Yilmaz, Gül Kaleli
2015-01-01
This study aims to investigate the effects of using Dynamic Geometry Software (DGS) Cabri II Plus and physical manipulatives on the transformational geometry achievement of candidate teachers. In this study, the semi-experimental method was used, consisting of two experimental and one control groups. The samples of this study were 117 students. A…
Fluid dynamics analysis of a rotating axisymmetric part using FIDAP
NASA Astrophysics Data System (ADS)
Giles, G. E.; Kirkpatrick, J. R.; Wendel, M. W.; Bullock, J. S., IV
1990-03-01
The effect of fluid flow on electrochemical plating on a rotating axisymmetric part was investigated by using a finite element computer code, FIDAP. The results from these investigations compare well with analytical results for laminar flow conditions. The addition of a nonrotating shield was also investigated for laminar flow conditions. An attempt to extend these analyses to turbulent conditions was unsuccessful.
Consistent lattice Boltzmann methods for incompressible axisymmetric flows.
Zhang, Liangqi; Yang, Shiliang; Zeng, Zhong; Yin, Linmao; Zhao, Ya; Chew, Jia Wei
2016-08-01
In this work, consistent lattice Boltzmann (LB) methods for incompressible axisymmetric flows are developed based on two efficient axisymmetric LB models available in the literature. In accord with their respective original models, the proposed axisymmetric models evolve within the framework of the standard LB method and the source terms contain no gradient calculations. Moreover, the incompressibility conditions are realized with the Hermite expansion, thus the compressibility errors arising in the existing models are expected to be reduced by the proposed incompressible models. In addition, an extra relaxation parameter is added to the Bhatnagar-Gross-Krook collision operator to suppress the effect of the ghost variable and thus the numerical stability of the present models is significantly improved. Theoretical analyses, based on the Chapman-Enskog expansion and the equivalent moment system, are performed to derive the macroscopic equations from the LB models and the resulting truncation terms (i.e., the compressibility errors) are investigated. In addition, numerical validations are carried out based on four well-acknowledged benchmark tests and the accuracy and applicability of the proposed incompressible axisymmetric LB models are verified. PMID:27627407
Non-axisymmetric instabilities in discs with imposed zonal flows
NASA Astrophysics Data System (ADS)
Vanon, R.; Ogilvie, G. I.
2016-09-01
We conduct a linear stability calculation of an ideal Keplerian flow on which a sinusoidal zonal flow is imposed. The analysis uses the shearing sheet model and is carried out both in isothermal and adiabatic conditions, with and without self-gravity (SG). In the non-SG regime a structure in the potential vorticity (PV) leads to a non-axisymmetric Kelvin-Helmholtz (KH) instability; in the short-wavelength limit its growth rate agrees with the incompressible calculation by Lithwick (2007), which only considers perturbations elongated in the streamwise direction. The instability's strength is analysed as a function of the structure's properties, and zonal flows are found to be stable if their wavelength is ≳ 8H, where H is the disc's scale height, regardless of the value of the adiabatic index γ. The non-axisymmetric KH instability can operate in Rayleigh-stable conditions, and it therefore represents the limiting factor to the structure's properties. Introducing SG triggers a second non-axisymmetric instability, which is found to be located around a PV maximum, while the KH instability is linked to a PV minimum, as expected. In the adiabatic regime, the same gravitational instability is detected even when the structure is present only in the entropy (not in the PV) and the instability spreads to weaker SG conditions as the entropy structure's amplitude is increased. This eventually yields a non-axisymmetric instability in the non-SG regime, albeit of weak strength, localised around an entropy maximum.
Similarity Theory for an Axisymmetric Turbulent Wake with Rotation
NASA Astrophysics Data System (ADS)
Wosnik, Martin
2011-11-01
Axisymmetric wakes are special cases of turbulent shear flows in the sense that the local Reynolds number based on velocity deficit and wake width decreases with downstream position. Recently, Johansson et al. (Physics of Fluids, 15, no.3, 603-617, 2003) showed that two distinct similarity solutions for the non-swirling axisymmetric turbulent wake exist - one for infinite and one for low local Reynolds number. Every axisymmetric wake, no matter how high the initial Reynolds number, will eventually transition to the low Reynolds number similarity state in the far wake. Here equilibrium similarity considerations are applied to axisymmetric turbulent wakes with rotation (swirl), as can be found downstream of wind or hydrokinetic turbines. By examining under which conditions the reduced momentum and Reynolds stress transport equations for swirling wakes as well as the momentum integrals admit to similarity solutions, asymptotic scaling relations for the decay of velocity deficit and swirl are found. Swirl is introduced as an initial condition, and additional constraints on the similarity solution are introduced from the turbine (wake generator) operating parameters, e.g., tip speed ratio, angular induction, etc. The consequences of having a non-point source of thrust (drag) and angular momentum are investigated. Implications of the findings on the operation of wind and hydrokinetic turbines and turbine arrays are discussed.
Consistent lattice Boltzmann methods for incompressible axisymmetric flows
NASA Astrophysics Data System (ADS)
Zhang, Liangqi; Yang, Shiliang; Zeng, Zhong; Yin, Linmao; Zhao, Ya; Chew, Jia Wei
2016-08-01
In this work, consistent lattice Boltzmann (LB) methods for incompressible axisymmetric flows are developed based on two efficient axisymmetric LB models available in the literature. In accord with their respective original models, the proposed axisymmetric models evolve within the framework of the standard LB method and the source terms contain no gradient calculations. Moreover, the incompressibility conditions are realized with the Hermite expansion, thus the compressibility errors arising in the existing models are expected to be reduced by the proposed incompressible models. In addition, an extra relaxation parameter is added to the Bhatnagar-Gross-Krook collision operator to suppress the effect of the ghost variable and thus the numerical stability of the present models is significantly improved. Theoretical analyses, based on the Chapman-Enskog expansion and the equivalent moment system, are performed to derive the macroscopic equations from the LB models and the resulting truncation terms (i.e., the compressibility errors) are investigated. In addition, numerical validations are carried out based on four well-acknowledged benchmark tests and the accuracy and applicability of the proposed incompressible axisymmetric LB models are verified.
Thermal deformation of concentrators in an axisymmetric temperature field
NASA Technical Reports Server (NTRS)
Bairamov, R.; Machuev, Y. I.; Nazarov, A.; Sokolov, Y. V.; Solodovnikova, L. A.; Fokin, V. G.
1985-01-01
Axisymmetric thermal deformations of paraboloid mirrors, due to heating, are examined for a mirror with a optical axis oriented toward the Sun. A governing differential equation is derived using Mushtari-Donnel-Vlasov simplifications, and a solution is presented which makes it possible to determine the principal deformation characteristics.
Geometric integrator for charged particle orbits in axisymmetric fusion devices
NASA Astrophysics Data System (ADS)
Kasilov, S. V.; Runov, A. M.; Kernbichler, W.
2016-10-01
A semi-analytical geometric integrator of guiding centre orbits in an axisymmetric tokamak is described. The integrator preserves all three invariants of motion up to computer accuracy at the expense of reduced orbit accuracy and it is roughly an order of magnitude more efficient than a direct solution of the equations of guiding centre motion with a standard high order adaptive ODE integrator.
MHD-stable plasma confinement in an axisymmetric mirror system
Stupakov, G.V.
1988-02-01
If the magnetic field of a nonparaxial mirror system is chosen appropriately, it is possible to maintain a sharp plasma boundary in an open axisymmetric confinement system in a manner which is stable against flute modes (both global and small-scale). Stability prevails in the ideal MHD approximation without finite-ion-Larmor radius effects.
Angular-momentum--mass inequality for axisymmetric black holes.
Dain, Sergio
2006-03-17
The inequality square root J
An elementary discussion of propellant flame geometry
Buckmaster, J.; Jackson, T.L.; Yao, J.
1999-05-01
The authors examine the geometry of diffusion flames generated by the burning of a heterogeneous solid propellant, using a simple model designed to provide qualitative insights. In the fast chemistry limit a strategy is used which has its roots in Burke and Schumann`s 1928 study of diffusion flames, albeit with different boundary conditions. This shows that the stoichiometric level surface (SLS) intersects the propellant surface at a point displaced from the fuel/oxidizer interface, and the variations of this displacement with Peclet number are discussed. The authors show that for model sandwich propellants, or their axisymmetric counterpart, the geometry of the SLS when the core is oxidizer is quite different from the geometry of the SLS when the core is fuel. Also, it is much easier to quench the flame on an oxidizer core, by reducing the Peclet number, than it is to quench the flame on a fuel core. When finite chemistry effects are accounted for, the flame only occupies a portion of the SLS, and there is a leading edge structure in which premixing plays a role. Enhancement of the burning rate due to premixing is identified, but a well-defined tribrachial structure is not observed. The authors show how a sharp reduction in pressure can lead to a detachment of the flame from the SLS, with subsequent quenching as it is swept downstream.
Computations of Internal and External Axisymmetric Nozzle Aerodynamics at Transonic Speeds
NASA Technical Reports Server (NTRS)
Dalbello, Teryn; Georgiadis, Nicholas; Yoder, Dennis; Keith, Theo
2003-01-01
Computational Fluid Dynamics (CFD) analyses of axisymmetric circular-arc boattail nozzles have been completed in support of NASA's Next Generation Launch Technology Program to investigate the effects of high-speed nozzle geometries on the nozzle internal flow and the surrounding boattail regions. These computations span the very difficult transonic flight regime, with shock-induced separations and strong adverse pressure gradients. External afterbody and internal nozzle pressure distributions computed with the Wind code are compared with experimental data. A range of turbulence models were examined in Wind, including an Explicit Algebraic Stress model (EASM). Computations on two nozzle geometries have been completed at freestream Mach numbers ranging from 0.6 to 0.9, driven by nozzle pressure ratios (NPR) ranging from 2.9 to 5. Results obtained on converging-only geometry indicate reasonable agreement to experimental data, with the EASM and Shear Stress Transport (SST) turbulence models providing the best agreement. Calculations completed on a converging-diverging geometry involving large-scale internal flow separation did not converge to a true steady-state solution when run with variable timestepping (steady-state). Calculations obtained using constant timestepping (time-accurate) indicate less variations in flow properties compared with steady-state solutions. This failure to converge to a steady-state solution was found to be the result of difficulties in using variable time-stepping with large-scale separations present in the flow. Nevertheless, time-averaged boattail surface pressure coefficient and internal nozzle pressures show fairly good agreement with experimental data. The SST turbulence model demonstrates the best over-all agreement with experimental data.
NASA Technical Reports Server (NTRS)
Flamm, Jeffrey D.; Deere, Karen A.; Mason, Mary L.; Berrier, Bobby L.; Johnson, Stuart K.
2007-01-01
An axisymmetric version of the Dual Throat Nozzle concept with a variable expansion ratio has been studied to determine the impacts on thrust vectoring and nozzle performance. The nozzle design, applicable to a supersonic aircraft, was guided using the unsteady Reynolds-averaged Navier-Stokes computational fluid dynamics code, PAB3D. The axisymmetric Dual Throat Nozzle concept was tested statically in the Jet Exit Test Facility at the NASA Langley Research Center. The nozzle geometric design variables included circumferential span of injection, cavity length, cavity convergence angle, and nozzle expansion ratio for conditions corresponding to take-off and landing, mid climb and cruise. Internal nozzle performance and thrust vectoring performance was determined for nozzle pressure ratios up to 10 with secondary injection rates up to 10 percent of the primary flow rate. The 60 degree span of injection generally performed better than the 90 degree span of injection using an equivalent injection area and number of holes, in agreement with computational results. For injection rates less than 7 percent, thrust vector angle for the 60 degree span of injection was 1.5 to 2 degrees higher than the 90 degree span of injection. Decreasing cavity length improved thrust ratio and discharge coefficient, but decreased thrust vector angle and thrust vectoring efficiency. Increasing cavity convergence angle from 20 to 30 degrees increased thrust vector angle by 1 degree over the range of injection rates tested, but adversely affected system thrust ratio and discharge coefficient. The dual throat nozzle concept generated the best thrust vectoring performance with an expansion ratio of 1.0 (a cavity in between two equal minimum areas). The variable expansion ratio geometry did not provide the expected improvements in discharge coefficient and system thrust ratio throughout the flight envelope of typical a supersonic aircraft. At mid-climb and cruise conditions, the variable geometry
Combinatorial Geometry Printer Plotting.
1987-01-05
Picture generates plots of two-dimensional slices through the three-dimensional geometry described by the combinatorial geometry (CG) package used in such codes as MORSE and QAD-CG. These plots are printed on a standard line printer.
Cutanda-Henríquez, Vicente; Juhl, Peter Møller
2013-11-01
The formulation presented in this paper is based on the boundary element method (BEM) and implements Kirchhoff's decomposition into viscous, thermal, and acoustic components, which can be treated independently everywhere in the domain except on the boundaries. The acoustic variables with losses are solved using extended boundary conditions that assume (i) negligible temperature fluctuations at the boundary and (ii) normal and tangential matching of the boundary's particle velocity. The proposed model does not require constructing a special mesh for the viscous and thermal boundary layers as is the case with the existing finite element method (FEM) implementations with losses. The suitability of this approach is demonstrated using an axisymmetrical BEM and two test cases where the numerical results are compared with analytical solutions.
Distributed forcing of the flow past a blunt-based axisymmetric bluff body
NASA Astrophysics Data System (ADS)
Jardin, Thierry; Bury, Yannick; DAEP Team
2012-11-01
The topology of bluff body wakes may be highly sensitive to forcing at frequencies close to intrinsic flow instabilities. In a similar way, a steady but spatially varying forcing at wavelengths close to specific flow instabilities can lead to analogous outcomes. Such forcing is commonly referred to as distributed forcing. However, although distributed forcing has proven to be a relevant control strategy for three-dimensional flows past nominally two-dimensional geometries (e.g. extruded circular cylinder at Re > 180), its impact on the flow past nominally three-dimensional geometries is still unknown. Here we assess the receptivity of the flow past a blunt-based axisymmetric bluff body to an azimuthally distributed forcing applied at the periphery of the bluff-body base. We show that the impact of RSPa, RSPb and RSPc instabilities on the drag fluctuations experienced by the bluff body can be suppressed, depending on the forcing wavelengths. The authors acknowledge the French Ministry of Defence and DGA for funding this work.
Collection-efficient, axisymmetric vacuum sublimation module for the purification of solid materials
NASA Astrophysics Data System (ADS)
May, Michael; Paul, Elizabeth; Katovic, Vladimir
2015-11-01
A vacuum sublimation module of axisymmetric geometry was developed and employed to purify solid-phase materials. The module provides certain practical advantages and it comprises: a metering valve, glass collector, glass lower body, main seal, threaded bushing, and glass internal cartridge (the latter to contain starting material). A complementary process was developed to de-solvate, sublime, weigh, and collect solid chemical materials exemplified by oxalic acid, ferrocene, pentachlorobenzene, chrysene, and urea. The oxalic acid sublimate was analyzed by titration, melting range, Fourier Transform Infrared (FT-IR) Spectroscopy, cyclic voltammetry, and its (aqueous phase) electrolytically generated gas. The analytical data were consistent with a high-purity, anhydrous oxalic acid sublimate. Cyclic voltammograms of 0.11 mol. % oxalic acid in water displayed a 2.1 V window on glassy carbon electrode beyond which electrolytic decomposition occurs. During module testing, fifteen relatively pure materials were sublimed with (energy efficient) passive cooling and the solid-phase recovery averaged 95 mass %. Key module design features include: compact vertical geometry, low-angle conical collector, uniformly compressed main seal, modest power consumption, transparency, glovebox compatibility, cooling options, and preferential conductive heat transfer. To help evaluate the structural (module) heat transfer, vertical temperature profiles along the dynamically evacuated lower body were measured versus electric heater power: for example, an input of 18.6 W generated a temperature 443-K at the bottom. Experimental results and engineering calculations indicate that during sublimation, solid conduction is the primary mode of heat transfer to the starting material.
Axisymmetric trawl cod-ends made from netting of a generalized mesh shape
NASA Astrophysics Data System (ADS)
O'Neill, F. G.
1999-06-01
The equations governing the geometry of axisymmetric trawl cod-ends made from netting of meshes of a particular generalized structure are derived. 6rom this, by suitable setting of the initial mesh bar lengths, the equations governing the geometry of cod-ends that are of importance to the fishing industry can be readily deduced. It is assumed that arbitrary membrane forces act normal to the edges of the mesh elements, that there is no shear force acting on the edge of a mesh element and that the twine that makes up the netting is extensible. The case where there is slackness in the mesh bars in the circumferential direction is dealt with and it is demonstrated how the finite structure of a knot can be taken into account. The case where the membrane forces arise solely as a result of and can be expressed by the appropriate components of the tensions in the mesh bars is also examined and numerical solutions are found for a range of examples.
ERIC Educational Resources Information Center
McDonald, Nathaniel J.
2001-01-01
Chronicles a teacher's first year teaching geometry at the Hershey Montessori Farm School in Huntsburg, Ohio. Instructional methods relied on Euclid primary readings and combined pure abstract logic with practical applications of geometry on the land. The course included geometry background imparted by Montessori elementary materials as well as…
DEP thermal convection in annular geometry under microgravity conditions
NASA Astrophysics Data System (ADS)
Yoshikawa, Harunori; Crumeyrolle, Olivier; Mutabazi, Innocent
2012-11-01
Thermal convection driven by the dielectrophoretic force is investigated in annular geometry in microgravity environments. A radial heating and a radial alternating electric field are imposed on a dielectric fluid layer filling the gap of two concentric infinite-length cylinders. The resulting dielectric force field is regarded as spatially varying radial gravity that can develop thermal convection. The linear stability problem of a purely conductive basic state is solved by a spectral-collocation method for both axisymmetric and non-axisymmetric disturbances. A stationary non-axisymmetric mode becomes first unstable at a critical Rayleigh number to develop convection. The stability boundary shows asymmetry with respect to heating direction. For an outward heating the critical value approaches that of the Rayleigh-Bénard problem (1708) as the gap size decreases, while it converges to larger values in the narrow gap limit. For an inward heating the instability occurs only when the gap is narrower than a certain value. The critical number diverges with increasing the gap size. Instability mechanism is examined from energetic viewpoints. The feedback of electric field to temperature disturbances is found to stabilize the conductive state for narrow gaps. This work has been partly supported by the CNES, the CNRS and the FEDER.
Stable photon orbits in stationary axisymmetric electrovacuum spacetimes
NASA Astrophysics Data System (ADS)
Dolan, Sam R.; Shipley, Jake O.
2016-08-01
We investigate the existence and phenomenology of stable photon orbits (SPOs) in stationary axisymmetric electrovacuum spacetimes in four dimensions. First, we review the classification of equatorial circular photon orbits on Kerr-Newman spacetimes in the charge-spin plane. Second, using a Hamiltonian formulation, we show that Reissner-Nordström diholes (a family encompassing the Majumdar-Papapetrou and Weyl-Bach special cases) admit SPOs, in a certain parameter regime that we investigate. Third, we explore the transition from order to chaos for typical SPOs bounded within a toroidal region around a dihole, via a selection of Poincaré sections. Finally, for general axisymmetric stationary spacetimes, we show that the Einstein-Maxwell field equations allow for the existence of SPOs in electro vacuum, but not in pure vacuum.
Application of the PTT model to axisymmetric free surface flows
NASA Astrophysics Data System (ADS)
Merejolli, R.; Paulo, G. S.; Tomé, M. F.
2013-10-01
This work is concerned with numerical simulation of axisymmetric viscoelastic free surface flows using the Phan-Thien-Tanner (PTT) constitutive equation. A finite difference technique for solving the governing equations for unsteady incompressible flows written in Cylindrical coordinates on a staggered grid is described. The fluid is modelled by a Marker-and-Cell type method and an accurate representation of the fluid surface is employed. The full free surface stress conditions are applied. The numerical method is verified by comparing numerical predictions of fully developed flow in a pipe with the corresponding analytic solutions. To demonstrate that the numerical method can simulate axisymmetric free surface flows governed by the PTT model, numerical results of the flow evolution of a drop impacting on a rigid dry plate are presented. In these simulations, the rheological effects of the parameters ɛ and ξ are investigated.
On the stability of compressible flow past axisymmetric bodies
NASA Technical Reports Server (NTRS)
Malik, M. R.; Spall, R. E.
1991-01-01
Compressible linear stability theory for axisymmetric flows is presented. The theory is applied to flow past a cylinder and a sharp cone at a Mach number of 5 with adiabatic wall conditions. The effect of transverse curvature and body divergence is studied. It is found that transverse curvature has a stabilizing influence on axisymmetric (first and second mode) disturbances while it has a destabilizing influence on the asymmetric (oblique first mode) disturbances. The body divergence effects are stabilizing for both symmetric and asymmetric disturbances. Comparisons made with the results of planar stability theory show that, for a cylinder, curvature effects become more pronounced with increasing distance along the cylinder. For a sharp cone, these effects become less significant further away from the cone tip since the body radius increases faster than the growth of the boundary layer. The effect of cone angle on stability is also studied.
Stability of flow over axisymmetric bodies with porous suction strips
NASA Technical Reports Server (NTRS)
Nayfeh, A. H.; Reed, H. L.
1982-01-01
Linear triple deck, closed form solutions for mean-flow quantities are developed for axisymmetric incompressible flow past a body with porous strips. The solutions account for upstream influence and are linear superpositions of the flow past the body without suction plus the perturbations due to the suction strips. Flow past the suctionless body is calculated using the Transition Analysis Program System, and a simple linear optimization scheme to determine number, spacing, and mass flow rate through the strips on an axisymmetric body is developed using the linear, triple-deck, closed-form solutions. The theory is demonstrated by predicting optimal strip distributions, and the effect of various adverse pressure-gradient situations on stability is studied.
Chen, P.J.
1981-04-01
The CHEMFLUB code was designed to provide predictions of the transient, two-phase, reactive flow fields occurring in a fluidized bed coal gasification reactor. CHEMFLUB can be operated in either two-dimensional Cartesian (planar) or axisymmetric geometry. The solid particle phase is treated in a Lagrangian manner in order to maintain sharp interfaces around bubbles and at the freeboard while the gas phase is treated using an Eulerian approach. A detailed chemistry model, encompassing both heterogeneous and homogeneous reactions of both combustion and gasification, is included in the model. Thus, the computer model CHEMFLUB incorporates the coupled dynamic effects of the hydrodynamic, thermodynamic and chemical phenomena which dominate flow in most fluidized bed coal gasifiers. Datailed discussions of the governing equations are given in Volume II of this report. This volume contains a summary of the governing differential and constitutive equations; a brief descritpion of the code, including a flow chart, subroutine structure and dimension parameters; as well as a detailed input sequence are presented. A sample of input and output is provided in the Appendix.
Resonant Absorption of Axisymmetric Modes in Twisted Magnetic Flux Tubes
NASA Astrophysics Data System (ADS)
Giagkiozis, I.; Goossens, M.; Verth, G.; Fedun, V.; Van Doorsselaere, T.
2016-06-01
It has been shown recently that magnetic twist and axisymmetric MHD modes are ubiquitous in the solar atmosphere, and therefore the study of resonant absorption for these modes has become a pressing issue because it can have important consequences for heating magnetic flux tubes in the solar atmosphere and the observed damping. In this investigation, for the first time, we calculate the damping rate for axisymmetric MHD waves in weakly twisted magnetic flux tubes. Our aim is to investigate the impact of resonant damping of these modes for solar atmospheric conditions. This analytical study is based on an idealized configuration of a straight magnetic flux tube with a weak magnetic twist inside as well as outside the tube. By implementing the conservation laws derived by Sakurai et al. and the analytic solutions for weakly twisted flux tubes obtained recently by Giagkiozis et al. we derive a dispersion relation for resonantly damped axisymmetric modes in the spectrum of the Alfvén continuum. We also obtain an insightful analytical expression for the damping rate in the long wavelength limit. Furthermore, it is shown that both the longitudinal magnetic field and the density, which are allowed to vary continuously in the inhomogeneous layer, have a significant impact on the damping time. Given the conditions in the solar atmosphere, resonantly damped axisymmetric modes are highly likely to be ubiquitous and play an important role in energy dissipation. We also suggest that, given the character of these waves, it is likely that they have already been observed in the guise of Alfvén waves.
Small Engine Technology (SET) - Task 14 Axisymmetric Engine Simulation Environment
NASA Technical Reports Server (NTRS)
Miller, Max J.
1999-01-01
As part of the NPSS (Numerical Propulsion Simulation System) project, NASA Lewis has a goal of developing an U.S. industry standard for an axisymmetric engine simulation environment. In this program, AlliedSignal Engines (AE) contributed to this goal by evaluating the ENG20 software and developing support tools. ENG20 is a NASA developed axisymmetric engine simulation tool. The project was divided into six subtasks which are summarized below: Evaluate the capabilities of the ENG20 code using an existing test case to see how this procedure can capture the component interactions for a full engine. Link AE's compressor and turbine axisymmetric streamline curvature codes (UD0300M and TAPS) with ENG20, which will provide the necessary boundary conditions for an ENG20 engine simulation. Evaluate GE's Global Data System (GDS), attempt to use GDS to do the linking of codes described in Subtask 2 above. Use a turbofan engine test case to evaluate various aspects of the system, including the linkage of UD0300M and TAPS with ENG20 and the GE data storage system. Also, compare the solution results with cycle deck results, axisymmetric solutions (UD0300M and TAPS), and test data to determine the accuracy of the solution. Evaluate the order of accuracy and the convergence time for the solution. Provide a monthly status report and a final formal report documenting AE's evaluation of ENG20. Provide the developed interfaces that link UD0300M and TAPS with ENG20, to NASA. The interface that links UD0300M with ENG20 will be compatible with the industr,, version of UD0300M.
Axisymmetric MHD Instabilities in Solar/Stellar Tachoclines
NASA Astrophysics Data System (ADS)
Dikpati, Mausumi; Gilman, Peter A.; Cally, Paul S.; Miesch, Mark S.
2009-02-01
Extensive studies over the past decade showed that HD and MHD nonaxisymmetric instabilities exist in the solar tachocline for a wide range of toroidal field profiles, amplitudes, and latitude locations. Axisymmetric instabilities (m = 0) do not exist in two dimensions, and are excited in quasi-three-dimensional shallow-water systems only for very high field strengths (2 mG). We investigate here MHD axisymmetric instabilities in a three-dimensional thin-shell model of the solar/stellar tachocline, employing a hydrostatic, non-Boussinesq system of equations. We deduce a number of general properties of the instability by use of an integral theorem, as well as finding detailed numerical solutions for unstable modes. Toroidal bands become unstable to axisymmetric perturbations for solar-like field strengths (100 kG). The e-folding time can be months down to a few hours if the field strength is 1 mG or higher, which might occur in the solar core, white dwarfs, or neutron stars. These instabilities exist without rotation, with rotation, and with differential rotation, although both rotation and differential rotation have stabilizing effects. Broad toroidal fields are stable. The instability for modes with m = 0 is driven from the poleward shoulder of banded profiles by a perturbation magnetic curvature stress that overcomes the stabilizing Coriolis force. The nonaxisymmetric instability tips or deforms a band; with axisymmetric instability, the fluid can roll in latitude and radius, and can convert bands into tubes stacked in radius. The velocity produced by this instability in the case of low-latitude bands crosses the equator, and hence can provide a mechanism for interhemispheric coupling.
Axisymmetric Simulations of the ITER Vertical Stability Coil
Titus, Peter H.
2013-07-09
The ITER in-vessel coil system includes Vertical Stability (VS) coils and Edge Localized Mode (ELM) coils. There are two large VS ring coils, one upper and one lower. Each has four turns which are independently connected. The VS coils are needed for successful operation of ITER for most all of its operating modes. The VS coils must be highly reliable and fault tolerant. The operating environment includes normal and disruption Lorentz forces. To parametrically address all these design conditions in a tractable analysis requires a simplified model. The VS coils are predominately axisymmetric, and this suggests that an axisymmetric model can be meaningfully used to address the variations in mechanical design, loading, material properties, and time dependency. The axisymmetric finite element analysis described in this paper includes simulations of the bolted frictional connections used for the mounting details. Radiation and elastic-plastic response are modeled particularly for the extreme faulted conditions. Thermal connectivity is varied to study the effects of partial thermal connection of the actively cooled conductor to the remaining structure.
Control of an axisymmetric turbulent wake by a pulsed jet
NASA Astrophysics Data System (ADS)
Morrison, J. F.; Qubain, A.
It has been shown [1] that the axisymmetric wake is dominated by three types of instability mechanism: an axisymmetric "pumping" of the recirculation bubble at very low frequencies, antisymmetric fluctuations induced by a helical vortex structure that forms just downstream of the rear stagnation point and several higher-frequency, axisymmetric instability modes of the separated shear layer. The environmental requirement for drag reduction has placed a greater emphasis on base-pressure recovery of bluff bodies. The active control of separating flow around bluff bodies has tended to focus on 2D bodies [2, 3] demonstrating that large drag reductions are possible, usually by controlled blowing, at frequencies close to the von Kármán shedding frequency. However, in terms of control, 3D bluff bodies have received considerably less attention even though this configuration appears in many practical problems. Even then, active control has tended to focus on the delay of separation [4]. In the present work, we show that the base pressure of a blunt trailing edge may be increased by a high-frequency jet from a zero-net-mass-flux (ZNMF) device.
Options for axisymmetric operation of MFTF-B
Fenstermacher, M.E.; Devoto, R.S.; Thomassen, K.I.
1986-03-30
The flexibility of MFTF-B for axisymmetric experiments has been investigated. Interhcanging the axicell coils and increasing their separation results in an axisymmetric plug cell with 12:1 and 6:1 inner and outer mirror ratios, respectively. For axisymmetric operation, the sloshing-ion neutral beams, ECRH gyrotrons, and the pumping system would be moved to the axicell. Stabilization by E-rings could be explored in this configuration. With the addition of octopole magnets, off-axis multipole stabilization could also be tested. Operating points for octopole and E-ring-stabilized configurations with properties similar to those of the quadrupole MFTF-B, namely T/sub ic/ = 10 - 15 keV and n/sub c/ approx. = 3 x 10/sup 13/ cm/sup -3/, have been obtained. Because of the negligible radial transport of central-cell ions, the required neutral-beam power in the central cell has been dramatically reduced. In addition, because MHD stabilization is achieved by off-axis hot electrons in both cases, much lower barrier beta is possible, which aids in reducing the barrier ECRH power. Total ECRH power in the end cell is projected to be approx. =1 MW. Possible operating points for both octopole and E-ring configurations are described along with the stability considerations involved.
Energy and energy flux in axisymmetric slow and fast waves
NASA Astrophysics Data System (ADS)
Moreels, M. G.; Van Doorsselaere, T.; Grant, S. D. T.; Jess, D. B.; Goossens, M.
2015-06-01
Aims: We aim to calculate the kinetic, magnetic, thermal, and total energy densities and the flux of energy in axisymmetric sausage modes. The resulting equations should contain as few parameters as possible to facilitate applicability for different observations. Methods: The background equilibrium is a one-dimensional cylindrical flux tube model with a piecewise constant radial density profile. This enables us to use linearised magnetohydrodynamic equations to calculate the energy densities and the flux of energy for axisymmetric sausage modes. Results: The equations used to calculate the energy densities and the flux of energy in axisymmetric sausage modes depend on the radius of the flux tube, the equilibrium sound and Alfvén speeds, the density of the plasma, the period and phase speed of the wave, and the radial or longitudinal components of the Lagrangian displacement at the flux tube boundary. Approximate relations for limiting cases of propagating slow and fast sausage modes are also obtained. We also obtained the dispersive first-order correction term to the phase speed for both the fundamental slow body mode under coronal conditions and the slow surface mode under photospheric conditions. Appendix A is available in electronic form at http://www.aanda.org
Holographic measurement of wave propagation in axi-symmetric shells
NASA Technical Reports Server (NTRS)
Evensen, D. A.; Aprahamian, R.; Jacoby, J. L.
1972-01-01
The report deals with the use of pulsed, double-exposure holographic interferometry to record the propagation of transverse waves in thin-walled axi-symmetric shells. The report is subdivided into sections dealing with: (1) wave propagation in circular cylindrical shells, (2) wave propagation past cut-outs and stiffeners, and (3) wave propagation in conical shells. Several interferograms are presented herein which show the waves reflecting from the shell boundaries, from cut-outs, and from stiffening rings. The initial response of the shell was nearly axi-symmetric in all cases, but nonsymmetric modes soon appeared in the radial response. This result suggests that the axi-symmetric response of the shell may be dynamically unstable, and thus may preferentially excite certain circumferential harmonics through parametric excitation. Attempts were made throughout to correlate the experimental data with analysis. For the most part, good agreement between theory and experiment was obtained. Occasional differences were attributed primarily to simplifying assumptions used in the analysis. From the standpoint of engineering applications, it is clear that pulsed laser holography can be used to obtain quantitative engineering data. Areas of dynamic stress concentration, stress concentration factors, local anomalies, etc., can be readily determined by holography.
Theoretical and numerical study of axisymmetric lattice Boltzmann models
NASA Astrophysics Data System (ADS)
Huang, Haibo; Lu, Xi-Yun
2009-07-01
The forcing term in the lattice Boltzmann equation (LBE) is usually used to mimic Navier-Stokes equations with a body force. To derive axisymmetric model, forcing terms are incorporated into the two-dimensional (2D) LBE to mimic the additional axisymmetric contributions in 2D Navier-Stokes equations in cylindrical coordinates. Many axisymmetric lattice Boltzmann D2Q9 models were obtained through the Chapman-Enskog expansion to recover the 2D Navier-Stokes equations in cylindrical coordinates [I. Halliday , Phys. Rev. E 64, 011208 (2001); K. N. Premnath and J. Abraham, Phys. Rev. E 71, 056706 (2005); T. S. Lee, H. Huang, and C. Shu, Int. J. Mod. Phys. C 17, 645 (2006); T. Reis and T. N. Phillips, Phys. Rev. E 75, 056703 (2007); J. G. Zhou, Phys. Rev. E 78, 036701 (2008)]. The theoretical differences between them are discussed in detail. Numerical studies were also carried out by simulating two different flows to make a comparison on these models’ accuracy and τ sensitivity. It is found all these models are able to obtain accurate results and have the second-order spatial accuracy. However, the model C [J. G. Zhou, Phys. Rev. E 78, 036701 (2008)] is the most stable one in terms of τ sensitivity. It is also found that if density of fluid is defined in its usual way and not directly relevant to source terms, the lattice Boltzmann model seems more stable.
Three-Dimensional Electromagnetic High Frequency Axisymmetric Cavity Scars.
Warne, Larry Kevin; Jorgenson, Roy Eberhardt
2014-10-01
This report examines the localization of high frequency electromagnetic fi elds in three-dimensional axisymmetric cavities along periodic paths between opposing sides of the cavity. The cases where these orbits lead to unstable localized modes are known as scars. This report treats both the case where the opposing sides, or mirrors, are convex, where there are no interior foci, and the case where they are concave, leading to interior foci. The scalar problem is treated fi rst but the approximations required to treat the vector fi eld components are also examined. Particular att ention is focused on the normalization through the electromagnetic energy theorem. Both projections of the fi eld along the scarred orbit as well as point statistics are examined. Statistical comparisons are m ade with a numerical calculation of the scars run with an axisymmetric simulation. This axisymmetric cas eformstheoppositeextreme(wherethetwomirror radii at each end of the ray orbit are equal) from the two -dimensional solution examined previously (where one mirror radius is vastly di ff erent from the other). The enhancement of the fi eldontheorbitaxiscanbe larger here than in the two-dimensional case. Intentionally Left Blank
Goswami, A.; Sing Babu, P.; Pandit, V. S.
2012-12-15
This paper describes the dynamics of space charge dominated beam through a Glaser magnet which is often used to focus charged particle beams in the low energy section of accelerators and in many other devices. Various beam optical properties of the magnet and emittance evolution that results from the coupling between the two transverse planes are studied. We have derived ten independent first order differential equations for the beam sigma matrix elements assuming the linear space-charge force consistent with the assumption of the canonically transformed KV like distribution. In addition, the feasibility of using a Glaser magnet doublet in a low energy beam injection line to match an initial non-axisymmetric high intensity beam with net angular momentum to an axisymmetric system to suppress effective emittance growth after transition back to an uncoupled system, has also been studied.
Simonen, T; Cohen, R; Correll, D; Fowler, K; Post, D; Berk, H; Horton, W; Hooper, E B; Fisch, N; Hassam, A; Baldwin, D; Pearlstein, D; Logan, G; Turner, B; Moir, R; Molvik, A; Ryutov, D; Ivanov, A A; Kesner, J; Cohen, B; McLean, H; Tamano, T; Tang, X Z; Imai, T
2008-10-24
Experimental results, theory and innovative ideas now point with increased confidence to the possibility of a Gas Dynamic Trap (GDT) neutron source which would be on the path to an attractively simple Axisymmetric Tandem Mirror (ATM) power plant. Although magnetic mirror research was terminated in the US 20 years ago, experiments continued in Japan (Gamma 10) and Russia (GDT), with a very small US effort. This research has now yielded data, increased understanding, and generated ideas resulting in the new concepts described here. Early mirror research was carried out with circular axisymmetric magnets. These plasmas were MHD unstable due to the unfavorable magnetic curvature near the mid-plane. Then the minimum-B concept emerged in which the field line curvature was everywhere favorable and the plasma was situated in a MHD stable magnetic well (70% average beta in 2XII-B). The Ioffe-bar or baseball-coil became the standard for over 40 years. In the 1980's, driven by success with minimum-B stabilization and the control of ion cyclotron instabilities in PR6 and 2XII-B, mirrors were viewed as a potentially attractive concept with near-term advantages as a lower Q neutron source for applications such as a hybrid fission fuel factory or toxic waste burner. However there are down sides to the minimum-B geometry: coil construction is complex; restraining magnetic forces limit field strength and mirror ratios. Furthermore, the magnetic field lines have geodesic curvature which introduces resonant and neoclassical radial transport as observed in early tandem mirror experiments. So what now leads us to think that simple axisymmetric mirror plasmas can be stable? The Russian GDT experiment achieves on-axis 60% beta by peaking of the kinetic plasma pressure near the mirror throat (where the curvature is favorable) to counter-balance the average unfavorable mid-plane curvature. Then a modest augmentation of plasma pressure in the expander results in stability. The GDT
NASA Technical Reports Server (NTRS)
Gyekenyesi, J. P.; Mendelson, A.; Kring, J.
1973-01-01
A seminumerical method is presented for solving a set of coupled partial differential equations subject to mixed and coupled boundary conditions. The use of this method is illustrated by obtaining solutions for two circular geometry and mixed boundary value problems in three-dimensional elasticity. Stress and displacement distributions are calculated in an axisymmetric, circular bar of finite dimensions containing a penny-shaped crack. Approximate results for an annular plate containing internal surface cracks are also presented.
Browning, R.V.; Anderson, C.A.
1982-02-01
The finite element method is used to determine the temperatures, displacements, stresses, and strains in axisymmetric solids with orthotropic, temperature-dependent material properties under axisymmetric thermal and mechanical loads. The mechanical loads can be surface pressures, surface shears, and nodal point forces as well as an axial or centripetal acceleration. The continuous solid is replaced by a system of ring elements with triangular or quadrilateral cross sections. Accordingly, the method is valid for solids that are composed of many different materials and that have complex geometry. Nonlinear mechanical behavior as typified by plastic, locking, or creeping materials can be approximated. Two dimensional mesh generation, plotting, and editing features allow the computer program to be readily used. In addition to a stress analysis program that is based on a modified version of the SAAS code, TSAAS can carry out a transient thermal analysis with the finite element mesh used in stress analysis. An implicit time differencing scheme allows the use of arbitrary time steps with consequent fast running times. At specified times, the program will return to SAAS for thermal stress analysis. Nonlinear thermal properties and Arrhenius reaction kinetics are also incorporated into TSAAS. Several versions of TSAAS are in use at Los Alamos, running on CDC-7600, CRAY-1 and VAX 11/780 computers. This report describes the nominal TSAAS; other versions may have some unique features.
ERIC Educational Resources Information Center
Lyublinskaya, Irina; Funsch, Dan
2012-01-01
Several interactive geometry software packages are available today to secondary school teachers. An example is The Geometer's Sketchpad[R] (GSP), also known as Dynamic Geometry[R] software, developed by Key Curriculum Press. This numeric based technology has been widely adopted in the last twenty years, and a vast amount of creativity has been…
Euclidean Geometry via Programming.
ERIC Educational Resources Information Center
Filimonov, Rossen; Kreith, Kurt
1992-01-01
Describes the Plane Geometry System computer software developed at the Educational Computer Systems laboratory in Sofia, Bulgaria. The system enables students to use the concept of "algorithm" to correspond to the process of "deductive proof" in the development of plane geometry. Provides an example of the software's capability and compares it to…
NASA Astrophysics Data System (ADS)
Aiken, Brenda L.
The Commonwealth of Virginia requires high school students to receive a passing grade in core courses and a passing score on End-of-Course Standards of Learning (EOC SOL) tests to receive verified credits that lead to a Virginia high school diploma. These tests are believed to accurately reflect what students should know and be able to do in order to experience success in their endeavors beyond high school. For some students remediation is required to experience success on EOC SOL tests. This study sought to determine the effect of a County's public high school summer remediation program on student gains on EOC SOL tests in Algebra I, Biology, Chemistry, Geometry, and World History and Geography II. Specifically, the purpose of the study sought to determine the following: (a) If significant gains were made by students who attended the summer remediation program; (b) If significant gains were made by students who did not attend the summer remediation program; (c) If there were differences in gain scores of students who attended and those who did not attend the summer remediation program; and (d) If there were differences in gain scores among students who attended the summer remediation program related to school site, gender, ethnicity, learning ability group, socioeconomic status, and level of English proficiency. The results of the study indicate that students who attended and those who did not attend the summer remediation program made significant gains. However, the gains for students who attended the summer remediation program were significantly greater than the gains made by students who did not attend. The study also found that there were no significant differences in gain scores among students who attended the summer remediation program related to gender, ethnicity, learning ability group, socioeconomic status, and level of English proficiency. There were significant differences in Algebra I gain scores related to school site. Recommendations for
Frolov, Vadim A; Escalada, Artur; Akimov, Sergey A; Shnyrova, Anna V
2015-01-01
Cellular membranes define the functional geometry of intracellular space. Formation of new membrane compartments and maintenance of complex organelles require division and disconnection of cellular membranes, a process termed membrane fission. Peripheral membrane proteins generally control membrane remodeling during fission. Local membrane stresses, reflecting molecular geometry of membrane-interacting parts of these proteins, sum up to produce the key membrane geometries of fission: the saddle-shaped neck and hour-glass hemifission intermediate. Here, we review the fundamental principles behind the translation of molecular geometry into membrane shape and topology during fission. We emphasize the central role the membrane insertion of specialized protein domains plays in orchestrating fission in vitro and in cells. We further compare individual to synergistic action of the membrane insertion during fission mediated by individual protein species, proteins complexes or membrane domains. Finally, we describe how local geometry of fission intermediates defines the functional design of the protein complexes catalyzing fission of cellular membranes. PMID:25062896
Particle trajectory computer program for icing analysis of axisymmetric bodies
NASA Technical Reports Server (NTRS)
Frost, Walter; Chang, Ho-Pen; Kimble, Kenneth R.
1982-01-01
General aviation aircraft and helicopters exposed to an icing environment can accumulate ice resulting in a sharp increase in drag and reduction of maximum lift causing hazardous flight conditions. NASA Lewis Research Center (LeRC) is conducting a program to examine, with the aid of high-speed computer facilities, how the trajectories of particles contribute to the ice accumulation on airfoils and engine inlets. This study, as part of the NASA/LeRC research program, develops a computer program for the calculation of icing particle trajectories and impingement limits relative to axisymmetric bodies in the leeward-windward symmetry plane. The methodology employed in the current particle trajectory calculation is to integrate the governing equations of particle motion in a flow field computed by the Douglas axisymmetric potential flow program. The three-degrees-of-freedom (horizontal, vertical, and pitch) motion of the particle is considered. The particle is assumed to be acted upon by aerodynamic lift and drag forces, gravitational forces, and for nonspherical particles, aerodynamic moments. The particle momentum equation is integrated to determine the particle trajectory. Derivation of the governing equations and the method of their solution are described in Section 2.0. General features, as well as input/output instructions for the particle trajectory computer program, are described in Section 3.0. The details of the computer program are described in Section 4.0. Examples of the calculation of particle trajectories demonstrating application of the trajectory program to given axisymmetric inlet test cases are presented in Section 5.0. For the examples presented, the particles are treated as spherical water droplets. In Section 6.0, limitations of the program relative to excessive computer time and recommendations in this regard are discussed.
Constants of motion in stationary axisymmetric gravitational fields
NASA Astrophysics Data System (ADS)
Markakis, C.
2014-07-01
The motion of test particles in stationary axisymmetric gravitational fields is generally non-integrable unless a non-trivial constant of motion, in addition to energy and angular momentum along the symmetry axis, exists. The Carter constant in Kerr-de Sitter space-time is the only example known to date. Proposed astrophysical tests of the black hole no-hair theorem have often involved integrable gravitational fields more general than the Kerr family, but the existence of such fields has been a matter of debate. To elucidate this problem, we treat its Newtonian analogue by systematically searching for non-trivial constants of motion polynomial in the momenta and obtain two theorems. First, solving a set of quadratic integrability conditions, we establish the existence and uniqueness of the family of stationary axisymmetric potentials admitting a quadratic constant. As in Kerr-de Sitter space-time, the mass moments of this class satisfy a `no-hair' recursion relation M2l +2 = a2M2l, and the constant is Noether related to a second-order Killing-Stäckel tensor. Second, solving a new set of quartic integrability conditions, we establish non-existence of quartic constants. Remarkably, a subset of these conditions is satisfied when the mass moments obey a generalized `no-hair' recursion relation M2l +4 = (a2 + b2)M2l +2 - a2b2M2l. The full set of quartic integrability conditions, however, cannot be satisfied non-trivially by any stationary axisymmetric vacuum potential.
Marginally stable circular orbits in stationary axisymmetric spacetimes
NASA Astrophysics Data System (ADS)
Beheshti, Shabnam; Gasperín, Edgar
2016-07-01
We derive necessary and sufficient conditions for the existence of marginally stable circular orbits (MSCOs) of test particles in a stationary axisymmetric (SAS) spacetime which possesses a reflection symmetry with respect to the equatorial plane; photon orbits and marginally bound orbits (MBOs) are also addressed. Energy and angular momentum are shown to decouple from metric quantities, rendering a purely geometric characterization of circular orbits for this general class of metrics. The subsequent system is analyzed using resultants, providing an algorithmic approach for finding MSCO conditions. MSCOs, photon orbits and MBOs are explicitly calculated for concrete examples of physical interest.
Vortex motion in axisymmetric piston-cylinder configurations
NASA Technical Reports Server (NTRS)
Shih, T. I. P.; Smith, G. E.; Springer, G. S.
1982-01-01
By using the Beam and Warming implicit-factored method of solution of the Navier-Stokes equations, velocities were calculated inside axisymmetric piston cylinder configurations during the intake and compression strokes. Results are presented in graphical form which show the formation, growth and breakup of those vortices which form during the intake stroke by the jet issuing from the valve. It is shown that at bore-to-stroke ratio of less than unity, the vortices may breakup during the intake stroke. It is also shown that vortices which do not breakup during the intake stroke coalesce during the compression stroke.
Area-angular-momentum inequality for axisymmetric black holes.
Dain, Sergio; Reiris, Martin
2011-07-29
We prove the local inequality A≥8π|J|, where A and J are the area and angular momentum of any axially symmetric closed stable minimal surface in an axially symmetric maximal initial data. From this theorem it is proved that the inequality is satisfied for any surface on complete asymptotically flat maximal axisymmetric data. In particular it holds for marginal or event horizons of black holes. Hence, we prove the validity of this inequality for all dynamical (not necessarily near equilibrium) axially symmetric black holes.
A New Axi-Symmetric Element for Thin Walled Structures
NASA Astrophysics Data System (ADS)
Cardoso, Rui P. R.; Yoon, Jeong Whan; Dick, Robert E.
2010-06-01
A new axi-symmetric finite element for sheet metal forming applications is presented in this work. It uses the solid-shell element's concept with only a single element layer and multiple integration points along the thickness direction. The cross section of the element is composed of four nodes with two degrees of freedom each. The proposed formulation overcomes major locking pathologies including transverse shear locking, Poisson's locking and volumetric locking. Some examples are shown to demonstrate the performance and accuracy of the proposed element with special focus on the numerical simulations for the beverage can industry.
Axisymmetric vibrations of laminated composite conical shells with varying thickness
Shikanai, G.; Suzuki, K.; Kojima, M.
1995-11-01
An exact solution procedure is presented for solving axisymmetric free vibrations of laminated composite conical shells with varying thickness. Based on the classical lamination theory neglecting shear deformation and rotary inertia, equations of motion and boundary conditions are obtained from the stationary conditions of the Lagrangian. The equations of motion are solved exactly by using a power series expansion for symmetrically laminated, cross-ply conical shells. Numerical studies are made for conical shells having both ends clamped to show the effects of the number of laminae, stacking sequences and other parameters upon the frequencies.
Fusion-product transport in axisymmetric tokamaks: losses and thermalization
Hively, L.M.
1980-01-01
High-energy fusion-product losses from an axisymmetric tokamak plasma are studied. Prompt-escape loss fluxes (i.e. prior to slowing down) are calculated including the non-separable dependence of flux as a function of poloidal angle and local angle-of-incidence at the first wall. Fusion-product (fp) thermalization and heating are calculated assuming classical slowing down. The present analytical model describes fast ion orbits and their distribution function in realistic, high-..beta.., non-circular tokamak equilibria. First-orbit losses, trapping effects, and slowing-down drifts are also treated.
Preserving spherical symmetry in axisymmetric coordinates for diffusion problems
Brunner, T. A.; Kolev, T. V.; Bailey, T. S.; Till, A. T.
2013-07-01
Persevering symmetric solutions, even in the under-converged limit, is important to the robustness of production simulation codes. We explore the symmetry preservation in both a continuous nodal and a mixed finite element method. In their standard formulation, neither method preserves spherical solution symmetry in axisymmetric (RZ) coordinates. We propose two methods, one for each family of finite elements, that recover spherical symmetry for low-order finite elements on linear or curvilinear meshes. This is a first step toward understanding achieving symmetry for higher-order elements. (authors)
Quasi-static axisymmetric eversion hemispherical domes made of elastomers
NASA Astrophysics Data System (ADS)
Kabrits, Sergey A.; Kolpak, Eugeny P.
2016-06-01
The paper considers numerical solution for the problem of quasi-static axisymmetric eversion of a spherical shell (hemisphere) under action of external pressure. Results based on the general nonlinear theory of shells made of elastomers, proposed by K. F. Chernykh. It is used two models of shells based on the hypotheses of the Kirchhoff and Timoshenko, modified K.F. Chernykh for the case of hyperelastic rubber-like material. The article presents diagrams of equilibrium states of eversion hemispheres for both models as well as the shape of the shell at different points in the diagram.
Vortex motion in axisymmetric piston-cylinder configurations
Shih, T.I.P.; Smith, G.E.; Springer, G.S.
1982-09-01
By using the Beam and Warming implicit-factored method of solution of the Navier-Stokes equations, velocities were calculated inside axisymmetric piston cylinder configurations during the intake and compression strokes. Results are presented in graphical form which show the formation, growth and breakup of those vortices which form during the intake stroke by the jet issuing from the valve. It is shown that at bore-to-stroke ratio of less than unity, the vortices may breakup during the intake stroke. It is also shown that vortices which do not breakup during the intake stroke coalesce during the compression stroke.
Exact vectorial model for nonparaxial focusing by arbitrary axisymmetric surfaces.
Panneton, Denis; St-Onge, Guillaume; Piché, Michel; Thibault, Simon
2016-05-01
We present a new approach, based on Richards-Wolf formalism, to rigorously model nonparaxial focusing of radially and azimuthally polarized electromagnetic beams by axisymmetric systems without a single-point focus. Our approach is based on a combined method that uses ray tracing and diffraction integrals. Our method is validated by comparing known results obtained with a parabolic mirror. Our integral representation of the focused beams, compliant with diffraction theory, is thoroughly discussed and solved for various conics that, so far, have not been treated analytically. The extension of the method to other polarization states is straightforward. PMID:27140877
Axisymmetric inviscid swirling flows produced by bellmouth and centerbody
NASA Technical Reports Server (NTRS)
Nakamura, Y.; Yasuhara, M.; Hama, T.
1982-01-01
The effect of large deformation in the flow between the bellmouth and centerbody is considered analytically for application to studies of vortex breakdown in a pipe. Basic equations are defined for axisymmetric inviscid swirling flows at the inflow and outflow sections. Axial and circumferential velocity component profiles are presented, and comparisons are made with trials involving vane angles of 42 deg and Re of 2300. Axial components of the prediction matched well in the inner half of the pipe radius and not well with the outer, while circumferential predictions were good only at the axis. A lack of viscosity was concluded to result in the inaccuracies near the wall.
Axisymmetric inviscid swirling flows produced by bellmouth and centerbody
NASA Astrophysics Data System (ADS)
Nakamura, Y.; Yasuhara, M.; Hama, T.
1982-04-01
The effect of large deformation in the flow between the bellmouth and centerbody is considered analytically for application to studies of vortex breakdown in a pipe. Basic equations are defined for axisymmetric inviscid swirling flows at the inflow and outflow sections. Axial and circumferential velocity component profiles are presented, and comparisons are made with trials involving vane angles of 42 deg and Re of 2300. Axial components of the prediction matched well in the inner half of the pipe radius and not well with the outer, while circumferential predictions were good only at the axis. A lack of viscosity was concluded to result in the inaccuracies near the wall.
Accuracy Improvement in Magnetic Field Modeling for an Axisymmetric Electromagnet
NASA Technical Reports Server (NTRS)
Ilin, Andrew V.; Chang-Diaz, Franklin R.; Gurieva, Yana L.; Il,in, Valery P.
2000-01-01
This paper examines the accuracy and calculation speed for the magnetic field computation in an axisymmetric electromagnet. Different numerical techniques, based on an adaptive nonuniform grid, high order finite difference approximations, and semi-analitical calculation of boundary conditions are considered. These techniques are being applied to the modeling of the Variable Specific Impulse Magnetoplasma Rocket. For high-accuracy calculations, a fourth-order scheme offers dramatic advantages over a second order scheme. For complex physical configurations of interest in plasma propulsion, a second-order scheme with nonuniform mesh gives the best results. Also, the relative advantages of various methods are described when the speed of computation is an important consideration.
Constant Density Approximations for the Flow Behind Axisymmetric Shock Waves
NASA Technical Reports Server (NTRS)
Munson, Albert G.
1961-01-01
The incompressible rotational flow equations are used to obtain solutions for the flow behind axisymmetric shock waves with conic longitudinal sections. The nonlinear part of the term due to rotation is retained in the analysis. Numerical results for standoff distance and stagnation point velocity gradient are presented for the case in which the shock wave is a paraboloid, a sphere, or an oblate or prolate ellipsoid. A similarity parameter is proposed which correlates approximately the flow behind geometrically similar shock waves at different free-stream conditions.
The inviscid stability of supersonic flow past axisymmetric bodies
NASA Technical Reports Server (NTRS)
Duck, Peter W.
1990-01-01
The supersonic flow past a sharp cone is studied. The associated boundary layer flow (i.e., the velocity and temperature field) is computed. The inviscid linear temporal stability of axisymmetric boundary layers in general is considered, and in particular, a so-called 'triply generalized' inflection condition for 'subsonic' nonaxisymmetric neutral modes is presented. Preliminary numerical results for the stability of the cone boundary layer are presented for a freestream Mach number of 3.8. In particular, a new inviscid mode of instability is seen to occur in certain regimes, and this is shown to be related to a viscous mode found by Duck and Hall (1988).
Stability and Halo Formation in Axisymmetric Intense Beams.
NASA Astrophysics Data System (ADS)
Gluckstern, Robert L.; Kurennoy, Sergey S.
1996-05-01
Beam stability and halo formation in high-intensity axisymmetric 2D beams in a uniform focusing channel are analyzed using particle-in-cell simulations. The tune depression - mismatch space is explored for the uniform distribution of the particle transverse phase space density (K-V), as well as for more realistic ones (in particular, the water-bag distribution), to determine the stability limits and halo parameters. The numerical results obtained are compared and show an agreement with the predictions of the analytical model for halo formation developed earlier.(R.L. Gluckstern, Phys. Rev. Lett., 73), 1247 (1994).
Stability and Halo Formation in Axisymmetric Intense Beams.
NASA Astrophysics Data System (ADS)
Gluckstern, Robert L.; Kurennoy, Sergey S.
1997-05-01
Beam stability and halo formation in high-intensity axisymmetric 2D beams in a uniform focusing channel are analyzed using particle-in-cell simulations. The tune depression - mismatch space is explored for the uniform distribution of the particle transverse phase space density (Kapchinsky-Vladimirsky), as well as for more realistic ones (in particular, the water-bag distribution), to determine the stability limits and halo parameters. The numerical results obtained are compared and show an agreement with the predictions of the analytical model for halo formation developed earlier (R.L. Gluckstern, Phys. Rev. Lett., 73), 1247 (1994)..
Macroscopic analysis of axisymmetric functionally gradient material under thermal loading
Kwon, P.; Dharan, C.K.H.; Ferrari, M. )
1994-06-01
The axisymmetric functionally gradient materials (FGMs) subject to nonuniform temperature variations were studied with the combined use of homogenization and inhomogeneous eigenstrained media analysis. The material properties and the temperature variations were assumed to depend on the radial coordinate only. The inhomogeneous material properties of the FGM cylinder can be obtained by modulating the concentration level of spherical alumina particles in an aluminum matrix. The resulting stresses due to the temperature variation are presented for numerous distribution functions of alumina particles. It is shown that the particle distribution extensively influences the intensity and profile of the thermal stresses.
Numerical boundary condition procedure for the transonic axisymmetric inverse problem
NASA Technical Reports Server (NTRS)
Shankar, V.
1981-01-01
Two types of boundary condition procedures for the axisymmetric inverse problem are described. One is a Neumann type boundary condition (analogous to the analysis problem) and the other is a Dirichlet type boundary conditon, both requiring special treatments to make the inverse scheme numerically stable. The dummy point concept is utilized in implementing both. Results indicate the Dirichlet type inverse boundary condition is more robust and conceptually simpler to implement than the Neumann type procedure. A few results demonstrating the powerful capability of the newly developed inverse method that can handle both shocked as well as shockless body design are included.
Planetoid string solutions in 3+1 axisymmetric spacetimes
de Vega, H.J.; Egusquiza, I.L.
1996-12-01
The string propagation equations in axisymmetric spacetimes are exactly solved by quadratures for a planetoid ansatz. This is a straight nonoscillating string, radially disposed which rotates uniformly around the symmetry axis of the spacetime. In Schwarzschild black holes, the string stays outside the horizon pointing towards the origin. In de Sitter spacetime the planetoid rotates around its center. We quantize semiclassically these solutions and analyze the spin/(mass{sup 2}) (Regge) relation for the planetoids, which turns out to be nonlinear. {copyright} {ital 1996 The American Physical Society.}
Non-axisymmetric flows on hot Jupiters with oblique magnetic fields
Batygin, Konstantin; Stanley, Sabine
2014-10-10
Giant planets that reside in close proximity to their host stars are subject to extreme irradiation, which gives rise to thermal ionization of trace alkali metals in their atmospheres. On objects where the atmospheric electrical conductivity is substantial, the global circulation couples to the background magnetic field, inducing supplementary fields and altering the nature of the flow. To date, a number of authors have considered the influence of a spin-pole aligned dipole magnetic field on the dynamical state of a weakly ionized atmosphere and found that magnetic breaking may lead to significantly slower winds than predicted within a purely hydrodynamical framework. Here, we consider the effect of a tilted dipole magnetic field on the circulation and demonstrate that in addition to regulating wind velocities, an oblique field generates stationary non-axisymmetric structures that adhere to the geometry of the magnetic pole. Using a kinematic perturbative approach, we derive a closed-form solution for the perturbed circulation and show that the fractional distortion of zonal jets scales as the product of the field obliquity and the Elsässer number. The results obtained herein suggest that on planets with oblique magnetic fields, advective shifts of dayside hotspots may have substantial latitudinal components. This prediction may be tested observationally using the eclipse mapping technique.
NASA Technical Reports Server (NTRS)
St. John, Clinton W.; Frederick, Michael Alan
2013-01-01
Flight-testing of a channeled center-body axisymmetric supersonic inlet design concept was conducted at the National Aeronautics and Space Administration (NASA) Dryden Flight Research Center in collaboration with the NASA Glenn Research Center (Cleveland, Ohio) and TechLand Research, Inc. (North Olmsted, Ohio). This testing utilized the Propulsion Flight Test Fixture, flown on the NASA F-15B research test bed airplane (NASA tail number 836) at local experiment Mach numbers up to 1.50. The translating channeled center-body inlet was designed by TechLand Research, Inc. (U.S. Patent No. 6,276,632 B1) to allow for a novel method of off-design flow matching, with original test planning conducted under a NASA Small Business Innovative Research study. Data were collected in flight at various off-design Mach numbers for fixed-geometry representations of both the channeled center-body design and an equivalent area smooth center-body design for direct comparison of total pressure recovery and limited distortion measurements.
Non-axisymmetric Flows on Hot Jupiters with Oblique Magnetic Fields
NASA Astrophysics Data System (ADS)
Batygin, Konstantin; Stanley, Sabine
2014-10-01
Giant planets that reside in close proximity to their host stars are subject to extreme irradiation, which gives rise to thermal ionization of trace alkali metals in their atmospheres. On objects where the atmospheric electrical conductivity is substantial, the global circulation couples to the background magnetic field, inducing supplementary fields and altering the nature of the flow. To date, a number of authors have considered the influence of a spin-pole aligned dipole magnetic field on the dynamical state of a weakly ionized atmosphere and found that magnetic breaking may lead to significantly slower winds than predicted within a purely hydrodynamical framework. Here, we consider the effect of a tilted dipole magnetic field on the circulation and demonstrate that in addition to regulating wind velocities, an oblique field generates stationary non-axisymmetric structures that adhere to the geometry of the magnetic pole. Using a kinematic perturbative approach, we derive a closed-form solution for the perturbed circulation and show that the fractional distortion of zonal jets scales as the product of the field obliquity and the Elsässer number. The results obtained herein suggest that on planets with oblique magnetic fields, advective shifts of dayside hotspots may have substantial latitudinal components. This prediction may be tested observationally using the eclipse mapping technique.
Space reconstruction of the morphology and kinematics of axisymmetric radio sources
NASA Astrophysics Data System (ADS)
Diep, P. N.; Phuong, N. T.; Hoai, D. T.; Nhung, P. T.; Thao, N. T.; Tuan-Anh, P.; Darriulat, P.
2016-10-01
The unprecedented quality of the observations available from the Atacama Large Millimetre/sub-millimetre Array (ALMA) calls for analysis methods making the best of them. Reconstructing in space the morphology and kinematics of radio sources is an underdetermined problem that requires imposing additional constraints for its solution. The hypothesis of rotational invariance, which is a good approximation to, or at least a good reference for the description of the gas envelopes of many evolved stars and protostars, is particularly efficient in this role. In the first part of the article, a systematic use of simulated observations allows us for identifying the main problems and for constructing quantities aimed at solving them. In particular the evaluation of the orientation of the star axis in space and the differentiation between expansion along the star axis and rotation about it are given special attention. The use of polar rather than Cartesian sky coordinates to display the results of the analysis is shown to often better match the morphology and kinematics of actual stars. The radial dependence of the gas density and temperature and the possible presence of velocity gradients are briefly considered. In the second part, these results are applied to a few stars taken as examples with the aim of evaluating their usefulness when applied to concrete cases. A third part takes stock of what precedes and formulates some guidelines for modelling the radio emission of axisymmetric radio sources, limited however to the mathematics and geometry of the problem, physics considerations being generally ignored.
May, Michael; Paul, Elizabeth; Katovic, Vladimir
2015-11-01
A vacuum sublimation module of axisymmetric geometry was developed and employed to purify solid-phase materials. The module provides certain practical advantages and it comprises: a metering valve, glass collector, glass lower body, main seal, threaded bushing, and glass internal cartridge (the latter to contain starting material). A complementary process was developed to de-solvate, sublime, weigh, and collect solid chemical materials exemplified by oxalic acid, ferrocene, pentachlorobenzene, chrysene, and urea. The oxalic acid sublimate was analyzed by titration, melting range, Fourier Transform Infrared (FT-IR) Spectroscopy, cyclic voltammetry, and its (aqueous phase) electrolytically generated gas. The analytical data were consistent with a high-purity, anhydrous oxalic acid sublimate. Cyclic voltammograms of 0.11 mol. % oxalic acid in water displayed a 2.1 V window on glassy carbon electrode beyond which electrolytic decomposition occurs. During module testing, fifteen relatively pure materials were sublimed with (energy efficient) passive cooling and the solid-phase recovery averaged 95 mass %. Key module design features include: compact vertical geometry, low-angle conical collector, uniformly compressed main seal, modest power consumption, transparency, glovebox compatibility, cooling options, and preferential conductive heat transfer. To help evaluate the structural (module) heat transfer, vertical temperature profiles along the dynamically evacuated lower body were measured versus electric heater power: for example, an input of 18.6 W generated a temperature 443-K at the bottom. Experimental results and engineering calculations indicate that during sublimation, solid conduction is the primary mode of heat transfer to the starting material. PMID:26628150
NASA Astrophysics Data System (ADS)
Kiefer, W. S.
1993-02-01
For a fixed heat flow, the surface flow velocity of a convecting layer is not strongly sensitive to the variation of viscosity as a function of depth. Thus, the inferred absence of a low viscosity asthenosphere on Venus can not account for the limited surface motions there. The surface velocity is dependent on the convective geometry. Cartesian geometry convection can produce large surface velocities if the high viscosity surface layer is broken in places by weak zones. On the other hand, a high viscosity surface layer may inhibit the development of large surface velocities in axisymmetric convection.
Nozzle design study for a quasi-axisymmetric scramjet-powered vehicle at Mach 7.9 flight conditions
NASA Astrophysics Data System (ADS)
Tanimizu, Katsuyoshi; Mee, David J.; Stalker, Raymond J.; Jacobs, Peter A.
2013-09-01
A nozzle shape optimization study for a quasi-axisymmetric scramjet has been performed for a Mach 7.9 operating condition with hydrogen fuel, aiming at the application of a hypersonic airbreathing vehicle. In this study, the nozzle geometry which is parameterized by a set of design variables, is optimized for the single objective of maximum net thrust using an in-house CFD solver for inviscid flowfields with a simple force prediction methodology. The combustion is modelled using a simple chemical reaction code. The effects of the nozzle design on the overall vehicle performance are discussed. For the present geometry, net thrust is achieved for the optimized vehicle design. The results of the nozzle-optimization study show that performance is limited by the nozzle area ratio that can be incorporated into the vehicle without leading to too large a base diameter of the vehicle and increasing the external drag of the vehicle. This study indicates that it is very difficult to achieve positive thrust at Mach 7.9 using the basic geometry investigated.
NASA Technical Reports Server (NTRS)
Schnell, W. C.
1982-01-01
The jet induced effects of several exhaust nozzle configurations (axisymmetric, and vectoring/modulating varients) on the aeropropulsive performance of a twin engine V/STOL fighter design was determined. A 1/8 scale model was tested in an 11 ft transonic tunnel at static conditions and over a range of Mach Numbers from 0.4 to 1.4. The experimental aspects of the static and wind-on programs are discussed. Jet effects test techniques in general, fow through balance calibrations and tare force corrections, ASME nozzle thrust and mass flow calibrations, test problems and solutions are emphasized.
Spatio-Temporal Reconstruction of Vortex Dynamics in Axisymmetric Wakes
NASA Astrophysics Data System (ADS)
Brücker, C.
2001-04-01
With time recording Digital-Particle-Image Velocimetry and spatio-temporal reconstruction technique, we obtained detailed quantitative results of the evolution of the velocity and vorticity field in the wake of axisymmetric bluff bodies-a sphere and an axially oriented cylinder with an elliptic nose and a blunt base. Experiments were carried out for Reynolds numbers of Re=500, 700 and 1000 in the transition range from ``regular'' to ``irregular'' shedding. DPIV-recordings in radial cross-sections at several distances downstream of the bodies allowed us to reconstruct the dynamics of the streamwise vorticity over a large number of shedding cycles. Our results prove that the wake in this regime consists of a double-sided chain of oppositely oriented hairpin vortices. In addition, the results show a well-defined low-frequency modulation of the vortex shedding, with a distinct peak in the frequency spectrum at a Strouhal number of about Sr~0.05 (in case of the sphere). The wake pattern in this ``irregular'' shedding regime typically exhibits periodic packets of 3-4 ``regular'' shedding cycles which are interrupted by phases with less action. The results indicate the coexistence of a long-wave instability of axisymmetric wakes against helical waves in addition to the primary instability causing the vortex shedding process.
Large-Eddy Simulation of Supersonic Axisymmetric Bluff Body Wakes
NASA Astrophysics Data System (ADS)
Tourbier, D.; Fasel, H. F.
1997-11-01
The time-dependent behavior of the turbulent wake of an axisymmetric bluff body is investigated using Large-Eddy Simulation (LES). The axisymmetric body is aligned with a supersonic free stream at a Mach number of M_∞ = 2.46 . It has been shown previously that this flow field is subject to an absolute instability for global Reynolds numbers higher than ReD = 30,000 . As a result of this instability large structures are present in the near wake and render the flow field highly unsteady. These structures have a strong influence on the global behavior of the flow field and thus on the overall drag of the body. Commonly used turbulence models (e.g. in RANS) fail to accurately describe the flow field and are inadequate for drag prediction. Preliminary LES calculations for global Reynolds numbers up to ReD = 400,000 using a Smagorinsky type subgrid-scale model with a fixed constant have shown qualitative agreement with experimental observations in terms of pressure distribution along the blunt base and magnitude of rms values in the wake. However, the model is too dissipative for most parts of the free shear layer emanating from the corner of the base and the evolution of structures in the close vicinity of the corner is suppressed. Therefore, a dynamic subgrid-scale model was implemented into the code and tested to evaluate the performance of the model for this flow configuration.
Non-intrusive characterization of a dispersed, bubbly, axisymmetric jet
NASA Astrophysics Data System (ADS)
Stanley, Kevin Nathaniel
2000-12-01
This study investigated the effects of bubble size and phase distribution on the liquid and bubble flow fields in a dispersed, bubbly axisymmetric jet. Of primary interest was the interaction of the bubbles with large-scale structures in the developing region of the jet. Measurements were made non-intrusively via Laser Doppler Velocimetry (LDV), Phase-Doppler Analysis (PDA) and video imaging techniques. Liquid Reynolds' numbers were varied from approximately 6,000 to 18,000 while gas volume fraction ranged from 0 to 3%. Bubble sizes varied from approximately 600 mum to 1500 mum. Axial mean velocities and RMS fluctuations have been reported for the liquid phase. Axial and radial mean velocities and RMS fluctuations have been reported for the bubbles. Measurements have been made along the centerline and radially at downstream locations of x/Djet = 0.08, 4, 8, and 16. The effects of bubble size and phase distribution on the development of the axisymmetric shear layer as well as liquid phase and bubble velocity properties in general have been examined. These data have been put into perspective with respect to traditional two-phase flow parameters as well as previous experimental, analytical and computational works. Bubble/turbulence interaction was examined in the context of the turbulent kinetic energy spectrum and a critical wave number corresponding to bubble diameter was found above which turbulence was enhanced, and below which it was attenuated.
THE ADVECTION OF SUPERGRANULES BY THE SUN'S AXISYMMETRIC FLOWS
Hathaway, David H.; Williams, Peter E.; Rosa, Kevin Dela; Cuntz, Manfred E-mail: peter.williams@nasa.go
2010-12-10
We show that the motions of supergranules are consistent with a model in which they are simply advected by the axisymmetric flows in the Sun's surface shear layer. We produce a 10 day series of simulated Doppler images at a 15 minute cadence that reproduces most spatial and temporal characteristics seen in the SOHO/MDI Doppler data. Our simulated data have a spectrum of cellular flows with just two components-a granule component that peaks at spherical wavenumbers of about 4000 and a supergranule component that peaks at wavenumbers of about 110. We include the advection of these cellular components by the axisymmetric flows-differential rotation and meridional flow-whose variations with latitude and depth (wavenumber) are consistent with observations. We mimic the evolution of the cellular pattern by introducing random variations to the phases of the spectral components at rates that reproduce the levels of cross-correlation as functions of time and latitude. Our simulated data do not include any wave-like characteristics for the supergranules yet can reproduce the rotation characteristics previously attributed to wave-like behavior. We find rotation rates which appear faster than the actual rotation rates and attribute this to projection effects. We find that the measured meridional flow does accurately represent the actual flow and that the observations indicate poleward flow to 65{sup 0}-70{sup 0} latitude with equatorward countercells in the polar regions.
Resolving the uncertainties of non-axisymmetric fields in tokamaks
NASA Astrophysics Data System (ADS)
in, Yongkyoon; Seol, J.; Ko, W. H.; Lee, S. G.; Yoon, S. W.; Lee, H. H.; Jeon, Y. M.; Kim, J.; Bak, J. G.; Park, H.; Park, J. K.; Yun, G. S.; 3D Physics Task Force Team
2015-11-01
Recent study suggests that KSTAR could be a benefactor of the extremely low level of intrinsic error field in n =1 resonant magnetic perturbation (RMP) driven edge localized modes (ELM) control. Specifically, when the n = 1 RMP currents increases in order to suppress/mitigate ELMs, a kink-resonant mode-locking is not usually invoked in KSTAR, unlike in other devices. Besides we have discovered that the mid-plane RMP appeared much more effective than the off-midplane RMPs in affecting the ELMs with strong density pump-outs and enhanced ELM frequency. Presently, the enhanced understanding of non-axisymmetric field in tokamaks has been in great need, in particular, for the ITER RMP requirements. As the prevailing design of in-vessel RMP coils in ITER is similar to that in KSTAR, we are keen to resolve the uncertainties of the non-axisymmetric fields on transport and stability, and their limits, contributing directly to ITER and beyond.
Acoustic intensity calculations for axisymmetrically modeled fluid regions
NASA Technical Reports Server (NTRS)
Hambric, Stephen A.; Everstine, Gordon C.
1992-01-01
An algorithm for calculating acoustic intensities from a time harmonic pressure field in an axisymmetric fluid region is presented. Acoustic pressures are computed in a mesh of NASTRAN triangular finite elements of revolution (TRIAAX) using an analogy between the scalar wave equation and elasticity equations. Acoustic intensities are then calculated from pressures and pressure derivatives taken over the mesh of TRIAAX elements. Intensities are displayed as vectors indicating the directions and magnitudes of energy flow at all mesh points in the acoustic field. A prolate spheroidal shell is modeled with axisymmetric shell elements (CONEAX) and submerged in a fluid region of TRIAAX elements. The model is analyzed to illustrate the acoustic intensity method and the usefulness of energy flow paths in the understanding of the response of fluid-structure interaction problems. The structural-acoustic analogy used is summarized for completeness. This study uncovered a NASTRAN limitation involving numerical precision issues in the CONEAX stiffness calculation causing large errors in the system matrices for nearly cylindrical cones.
Two-integral distribution functions for axisymmetric galaxies
NASA Technical Reports Server (NTRS)
Hunter, C.; Qian, Edward
1993-01-01
The new method presented for finding distribution functions, which depend only on the classical integrals of energy and angular momentum for stellar systems with known axisymmetric densities, is the analog for the axisymmetric case of Eddington's classical solution for the isotropic distribution function, depending only on energy, of a known spherical density. It is required that density be expressed as a function of the potential and of a radial coordinate. Our solution is also an integral which is derived directly from the density, and hence can be used with complicated densities. A numerical quadrature is generally required to evaluate this solution, but contour integrals can be computed accurately by numerical quadrature; this is preferable to an explicit evaluation if the latter is an infinite series, such as is obtained using Fricke's method. We give several examples, including some for which our distribution functions are new. Our method can be extended simply to the related problems of finding anisotropic distribution functions for spherical or disk systems.
Non-axisymmetric Plasma Response to External Magnetic Perturbations
NASA Astrophysics Data System (ADS)
Chu, M. S.; Lao, L. L.; Evans, T. E.; Schaffer, M. J.; Strait, E. J.; Liu, Y. Q.; Lanctot, M. J.; Reimerdes, H.
2009-11-01
Very low frequency non-axisymmetric magnetic response in tokamaks excited by external magnetic perturbations is studied with the MARS-F code [1] using different assumptions on the plasma dynamics. In the limit of vacuum plasma response, the fields are benchmarked against the SURFMN [2] code and an analytic model. In other plasma models, the response is affected by plasma pressure, resistivity, toroidal flow, and the kinetic effects associated with the particle drifts. Depending on the coil arrangement, the plasma response could be dominated by the resonant or non-resonant components of the external field. The responses can be tested by employing different combinations of currents in appropriately designed external coils as those in DIII-D. The combined magnetic field of the axisymmetric plasma equilibrium and its non-axisymmetic responses corresponds to a perturbed 3D plasma equilibrium. 8pt [1] Y.Q. Liu, et al., Phys. Plasmas 7 (2000) 3681. [2] M.J. Schaffer, et al., Nucl. Fusion 48 (2008) 024004.
Generalized energy principle for flute perturbations in axisymmetric mirror machines
Lansky, I.M.; Ryutov, D.D.
1993-01-20
Axial symmetry is a very desirable property of the mirror devices both for fusion and neutron source applications. The main obstacle to be circumvented in the development of such systems, is the flute instability of axisymmetric mirrors. In recent years there appeared a number of proposals, devoted to the stabilization of the flute perturbations in the framework of axisymmetric magnetic configurations, which are based on the combining of the MHD unstable central cell with various types of end-cell stabilizers. In the present paper we concentrate ourselves just on this scheme, including long solenoid with a uniform field, conjugated with the end stabilizing anchor, intended to provide MHD stability of the system as a whole. The attractive feature of such a configuration is that it allows to exploit finite larmor radius (FLR) effects for the stabilization of the flute perturbations. As is well known, FLR effects, being strong, stabilize all flute modes, except the one with azimuthal number m = 1, corresponding to the ``rigid`` displacement of the plasma column (the ``global`` mode). Consequently, in the conditions when FLR effects dominate, the anchor has to stabilize the ``global` mode only. Bearing in mind a favorable influence of FLR effects we, however, don`t restrict our paper by discussion of only ``global`` mode stability and consider a general case of an arbitrary azimuthal mode.
Dynamic modeling of a turbulent axisymmetric bluff-body wake
NASA Astrophysics Data System (ADS)
Rigas, Georgios; Morgans, Aimee; Morrison, Jonathan
2013-11-01
En route to chaos the stable laminar wake past axisymmetric bluff bodies undergoes two well-documented transitions by increasing the Reynolds number: a steady bifurcation of the m = 1 azimuthal mode followed by an unsteady bifurcation with m = +/- 1 , the latter giving rise to periodic shedding of vortices with opposite signs, known as vortex shedding. In this study we present experimental evidence that these structures persist far from the critical points at high Reynolds numbers (Re = 2 ×105). We show that a low-order model based on the normal form describing the codimension-two bifurcation captures accurately the dynamic behavior of the large-scale coherent structures associated with the destabilized modes, if noise is appropriately accounted for in the model. The model is validated based on simultaneous aerodynamic force measurements on the base of an axisymmetric bullet-shaped body and Time-Resolved Stereo PIV in the near wake. Finally, we extend the model to include external forcing when periodic blowing and suction is applied at the base below the point of separation.
Noncommutative Geometry and Physics
Connes, Alain
2006-11-03
In this very short essay we shall describe a 'spectral' point of view on geometry which allows to start taking into account the lessons from both renormalization and of general relativity. We shall first do that for renormalization and explain in rough outline the content of our recent collaborations with Dirk Kreimer and Matilde Marcolli leading to the universal Galois symmetry of renormalizable quantum field theories provided by the renormalization group in its cosmic Galois group incarnation. As far as general relativity is concerned, since the functional integral cannot be treated in the traditional perturbative manner, it relies heavily as a 'sum over geometries' on the chosen paradigm of geometric space. This will give us the occasion to discuss, in the light of noncommutative geometry, the issue of 'observables' in gravity and our joint work with Ali Chamseddine on the spectral action, with a first attempt to write down a functional integral on the space of noncommutative geometries.
ERIC Educational Resources Information Center
Chern, Shiing-Shen
1990-01-01
Discussed are the major historical developments of geometry. Euclid, Descartes, Klein's Erlanger Program, Gaus and Riemann, globalization, topology, Elie Cartan, and an application to molecular biology are included as topics. (KR)
Proof in Transformation Geometry
ERIC Educational Resources Information Center
Bell, A. W.
1971-01-01
The first of three articles showing how inductively-obtained results in transformation geometry may be organized into a deductive system. This article discusses two approaches to enlargement (dilatation), one using coordinates and the other using synthetic methods. (MM)
ERIC Educational Resources Information Center
Emenaker, Charles E.
1999-01-01
Describes a sixth-grade interdisciplinary geometry unit based on Charles Dickens's "A Christmas Carol". Focuses on finding area, volume, and perimeter, and working with estimation, decimals, and fractions in the context of making gingerbread houses. (ASK)
Induced geometry from disformal transformation
NASA Astrophysics Data System (ADS)
Yuan, Fang-Fang; Huang, Peng
2015-05-01
In this note, we use the disformal transformation to induce a geometry from the manifold which is originally Riemannian. The new geometry obtained here can be considered as a generalization of Weyl integrable geometry. Based on these results, we further propose a geometry which is naturally a generalization of Weyl geometry.
Neoclassical Flows, Transport, and Non-Axisymmetric Effects in the Tokamak Plasma Edge
NASA Astrophysics Data System (ADS)
Belli, E. A.
2013-10-01
The drift-kinetic code NEO is used to explore the neoclassical transport and flows for parameters relevant in the plasma edge. NEO includes multiple ion species, general geometry, strong rotation effects, and full-linearized Fokker-Planck collisions. Comparisons are made with measurements of the deuterium and carbon flows for DIII-D L-mode discharges. An assessment of the accuracy of analytic models for the bootstrap current finds that NEO provides a 15% correction to the Sauter model for experimental plasmas. Analysis of the recent XGC0-based modification by Koh et al., finds that while the Koh modification is negligible for typical DIII-D plasmas, there is a large discrepancy from the NEO results in the pedestal for NSTX plasmas due to a failure in the formula at large inverse aspect ratio for large collision frequency (ν*e ~ 1), and thus the Koh formula is not accurate in regions where it differs from the Sauter model. Overall, the resulting implication that NEO could significantly improve the accuracy of peeling ballooning and kinetic ballooning mode stability calculations in the edge barrier region is explored through coupling with the EPED model. Finally, NEO is extended to include toroidal non-axisymmetric effects for studies of magnetic field ripple and resonant magnetic perturbations. The equilibrium is generated using a new 3D local analytic equilibrium solver, analogous to a 3D extension of the Miller formalism for shaped axisymmetric equilibria, based on the formalism by Hegna. Unlike a global solver, the method allows for systematic studies of the effects of 3D flux-surface shaping parameters. With the solver, the onset of stochasticity for general 3D flux surface configurations is studied. Combined with NEO, the effects of enhanced neoclassical transport due to the formation of superbanana orbits and the development of a more accurate kinetic-based NTV are explored. Supported by the US Department of Energy under DE-FG02-95ER54309 and DE-FC02-06ER
Wave Propagation in Axi-Symmetrical Magmatic Conduits Due to an Internal Source
NASA Astrophysics Data System (ADS)
De Negri, R. S.; Sanchez-Sesma, F. J.; Arciniega-Ceballos, A.
2014-12-01
The classical Trefftz's method is implemented to simulate wave propagation in and around axi-symmetrical magmatic conduits. In this fluid-solid system the fluid (magma) is confined by an elastic unbounded medium that represents the surrounding rock. Our aim is to associate wave behavior with mechanical and geometrical conduit characteristics. The source is assumed to be at a point along the conduit centered axis medium are constructed in both cases as linear combinations of particular solutions.Within the fluid such solutions are spherical standing waves that are smooth at the origins. In the elastic solid region the field is constructed with monopoles and dipoles for the P waves and spheroidal dipoles for SV waves. The particular solutions satisfy the elastodynamic equations that govern the wave motion at those media and are associated to origins (selected points) distributed along the conduit axis. For the surrounding rock the solutions are sources that satisfy Sommerfeld's radiation condition. These sets of solutions are assumed to be complete. This conjecture is exact in 2D acoustic problems. The conduit can be closed or open at the ends and the surrounding elastic domain is unbounded. In order to find the coefficients of Trefftz's wave expansions, boundary conditions at the fluid-solid interface (null shear and continuity of pressures and normal velocities) are satisfied in the least squares sense. The solution is obtained in the frequency domain and the source time function can be introduced using Fourier analysis.Regardless the low order of the formulation our results display a rich variety of behaviors. For a uniform infinite cylinder we reproduced the exact analytical solution. In addition, this approach allows identifying some important effects of the conduit geometry, including changes of sections. Lateral and longitudinal resonances of irregular axi-symmetric conduits are well resolved. The stiffness of the solid domain with respect to the fluid
Software Geometry in Simulations
NASA Astrophysics Data System (ADS)
Alion, Tyler; Viren, Brett; Junk, Tom
2015-04-01
The Long Baseline Neutrino Experiment (LBNE) involves many detectors. The experiment's near detector (ND) facility, may ultimately involve several detectors. The far detector (FD) will be significantly larger than any other Liquid Argon (LAr) detector yet constructed; many prototype detectors are being constructed and studied to motivate a plethora of proposed FD designs. Whether it be a constructed prototype or a proposed ND/FD design, every design must be simulated and analyzed. This presents a considerable challenge to LBNE software experts; each detector geometry must be described to the simulation software in an efficient way which allows for multiple authors to easily collaborate. Furthermore, different geometry versions must be tracked throughout their use. We present a framework called General Geometry Description (GGD), written and developed by LBNE software collaborators for managing software to generate geometries. Though GGD is flexible enough to be used by any experiment working with detectors, we present it's first use in generating Geometry Description Markup Language (GDML) files to interface with LArSoft, a framework of detector simulations, event reconstruction, and data analyses written for all LAr technology users at Fermilab. Brett is the other of the framework discussed here, the General Geometry Description (GGD).
2005-01-01
The Common Geometry Module (CGM) is a code library which provides geometry functionality used for mesh generation and other applications. This functionality includes that commonly found in solid modeling engines, like geometry creation, query and modification; CGM also includes capabilities not commonly found in solid modeling engines, like geometry decomposition tools and support for shared material interfaces. CGM is built upon the ACIS solid modeling engine, but also includes geometry capability developed beside and onmore » top of ACIS. CGM can be used as-is to provide geometry functionality for codes needing this capability. However, CGM can also be extended using derived classes in C++, allowing the geometric model to serve as the basis for other applications, for example mesh generation. CGM is supported on Sun Solaris, SGI, HP, IBM, DEC, Linux and Windows NT platforms. CGM also indudes support for loading ACIS models on parallel computers, using MPI-based communication. Future plans for CGM are to port it to different solid modeling engines, including Pro/Engineer or SolidWorks. CGM is being released into the public domain under an LGPL license; the ACIS-based engine is available to ACIS licensees on request.« less
Tokamak Magnetohydrodynamic Equilibrium States with Axisymmetric Boundary and a 3D Helical Core
Cooper, W. A.; Graves, J. P.; Pochelon, A.; Sauter, O.; Villard, L.
2010-07-16
Magnetohydrodynamic (MHD) equilibrium states with imposed axisymmetric boundary are computed in which a spontaneous bifurcation develops to produce an internal three-dimensional (3D) configuration with a helical structure in addition to the standard axisymmetric system. Equilibrium states with similar MHD energy levels are shown to develop very different geometric structures. The helical equilibrium states resemble saturated internal kink mode structures.
Tokamak magnetohydrodynamic equilibrium states with axisymmetric boundary and a 3D helical core.
Cooper, W A; Graves, J P; Pochelon, A; Sauter, O; Villard, L
2010-07-16
Magnetohydrodynamic (MHD) equilibrium states with imposed axisymmetric boundary are computed in which a spontaneous bifurcation develops to produce an internal three-dimensional (3D) configuration with a helical structure in addition to the standard axisymmetric system. Equilibrium states with similar MHD energy levels are shown to develop very different geometric structures. The helical equilibrium states resemble saturated internal kink mode structures.
NASA Astrophysics Data System (ADS)
Louwyck, Andy; Vandenbohede, Alexander; Bakker, Mark; Lebbe, Luc
2014-08-01
A procedure is outlined to simulate axisymmetric groundwater flow in radially heterogeneous and layered aquifer systems using the unmodified version of MODFLOW. The procedure is straightforward, as it only requires correction of some of the input parameters. In contrast to other MODFLOW procedures to simulate axisymmetric flow, no restrictions are imposed on the type of flow, the discretization of radial distance, or the parameter values. Hence, the method can deal with both confined and unconfined flow, wellbore storage, and axisymmetric aquifer inhomogeneities including effects of finite-thickness skin and gravel pack. Several test cases are presented, which compare the calculated results with existing analytical solutions, the analytic element solver TTim, and the axisymmetric, finite-difference model MAxSym. It is concluded that the MODFLOW procedure is capable of simulating accurately axisymmetric flow in radially heterogeneous multi-aquifer systems.
Magnetohydrodynamics in stationary and axisymmetric spacetimes: A fully covariant approach
Gourgoulhon, Eric; Markakis, Charalampos; Uryu, Koji; Eriguchi, Yoshiharu
2011-05-15
A fully geometrical treatment of general relativistic magnetohydrodynamics is developed under the hypotheses of perfect conductivity, stationarity, and axisymmetry. The spacetime is not assumed to be circular, which allows for greater generality than the Kerr-type spacetimes usually considered in general relativistic magnetohydrodynamics. Expressing the electromagnetic field tensor solely in terms of three scalar fields related to the spacetime symmetries, we generalize previously obtained results in various directions. In particular, we present the first relativistic version of the Soloviev transfield equation, subcases of which lead to fully covariant versions of the Grad-Shafranov equation and of the Stokes equation in the hydrodynamical limit. We have also derived, as another subcase of the relativistic Soloviev equation, the equation governing magnetohydrodynamical equilibria with purely toroidal magnetic fields in stationary and axisymmetric spacetimes.
Fluidic Control of Aerodynamic Forces on an Axisymmetric Body
NASA Astrophysics Data System (ADS)
Abramson, Philip; Vukasinovic, Bojan; Glezer, Ari
2007-11-01
The aerodynamic forces and moments on a wind tunnel model of an axisymmetric bluff body are modified by induced local vectoring of the separated base flow. Control is effected by an array of four integrated aft-facing synthetic jets that emanate from narrow, azimuthally-segmented slots, equally distributed around the perimeter of the circular tail end within a small backward facing step that extends into a Coanda surface. The model is suspended in the wind tunnel by eight thin wires for minimal support interference with the wake. Fluidic actuation results in a localized, segmented vectoring of the separated base flow along the rear Coanda surface and induces asymmetric aerodynamic forces and moments to effect maneuvering during flight. The aerodynamic effects associated with quasi-steady and transitory differential, asymmetric activation of the Coanda effect are characterized using direct force and PIV measurements.
Ideal, steady-state, axisymmetric magnetohydrodynamic equations with flow
Baransky, Y.A.
1987-01-01
The motivation of this study is to gain additional understanding of the effect of rotation on the equilibrium of a plasma. The axisymmetric equilibria of ideal magnetohydrodynamics (MHD) with flow have been studied numerically and analytically. A general discussion is provided of previous work on plasmas with flow and comparisons are made to the static model. A variational principle has been derived for the two dimensional problem with comments as to appropriate boundary conditions. An inverse aspect ratio expansion has been used for a study of the toroidal flow equation for both low- and high-..beta... The inverse aspect ratio expansion has also been used for a study of equations with both poloidal and toroidal flow. An overview is provided of the adaptive finite-difference code which was developed to solve the full equations. (FI)
Three-dimensional axisymmetric flow-focusing device using stereolithography.
Morimoto, Yuya; Tan, Wei-Heong; Takeuchi, Shoji
2009-04-01
This paper describes a three-dimensional microfluidic axisymmetric flow-focusing device (AFFD) fabricated using stereolithography. Using this method, we can fabricate AFFDs rapidly and automatically without cumbersome alignment needed in conventional methods. The AFFDs are able to be fabricated reproducibly with a micro-sized orifice of diameter around 250 mum. Using this device, we are able to produce monodisperse water-in-oil (W/O) droplets with a coefficient of variation (CV) of less than 4.5%, W/O droplets with encapsulated microbes (CV < 4.9%) and oil-in-water (O/W) droplets (CV < 3.2%) without any surface modifications. The diameter of these droplets range from 54 to 244 mum with respect to the flow rate ratio of the fluids used; these results are in good agreement with theoretical behavior. For applications of the AFFD, we demonstrate that these devices can be used to produce double emulsions and monodisperse hydrogel beads.
Experimental investigation of a confined developing axisymmetric wall jet
NASA Astrophysics Data System (ADS)
Guo, Tianqi; Rau, Matthew; Vlachos, Pavlos; Garimella, Suresh
2014-11-01
The present work reports an experimental study of an axisymmetric, confined wall jet using planar particle image velocimetry (PIV) and the dielectric liquid HFE-7100. The wall jet is formed downstream from a confined and submerged impinging round jet, 3.75 mm in diameter. Both the developing region and self-similar region of the wall jet are investigated. The experiments are conducted for Reynolds numbers (Re = Ud/ υ) ranging from 1500 to 38000 and at a nozzle-to-plate spacing of four jet diameters. Image-preprocessing techniques are used to eliminate background noise and an ensemble correlation scheme is applied to improve the resolution of the measurement of the mean velocity field near the wall. A maximum measurement resolution of 36 μm is achieved. Profiles of the mean velocity, turbulent intensities, decay rate, spread rate and wall shear stress are used to characterize the influence of confinement on the wall jet development and inner layer scaling.
Axisymmetric nonlinear waves and structures in Hall plasmas
Islam, Tanim
2012-06-15
In this paper, a general equation for the evolution of an axisymmetric magnetic field in a Hall plasma is derived, with an integral similar to the Grad-Shafranov equation. Special solutions arising from curvature-whistler drift modes that propagate along the electron drift as a Burger's shock and nonlinear periodic and soliton-like solutions to the generalized Grad-Shafranov integral-are analyzed. We derive analytical and numerical solutions in a classical electron-ion Hall plasma, in which electrons and ions are the only species in the plasmas. Results may then be applied to the following low-ionized astrophysical plasmas: in protostellar disks, in which the ions may be coupled to the motion of gases; and in molecular clouds and protostellar jets, in which the much heavier charged dust in a dusty Hall plasma may be collisionally coupled to the gas.
Buoyancy Driven Flow in an Axisymmetric Spherical Annular Sector
NASA Astrophysics Data System (ADS)
Thamire, Chandrasekhar; Wright, Neil T.; von Kerczek, Christian H.
1996-11-01
Results from analysis of axisymmetric, laminar buoyancy driven flows in a spherical annular sector with its outer radius equal to 1.5 times the inner radius and a sector angle of .75π are presented. The spherical surfaces of the enclosure are assumed to be heated and cooled isothermally, the radial surface being insulated. A time marching finite differencing scheme is used to solve the governing equations. The effects of Grashof number Gr and Prandtl number Pr on convective motion and heat transfer are examined. Flow patterns, changing from unicellular to multicellular flows with increasing Gr, and heat transfer results are graphically illustrated. Interesting recirculation zones develop at the insulated boundary for Gr = 10^5. The heat transfer calculations indicate that the Nusselt number depends strongly on Gr, and weakly on Pr in the range of parameters studied.
Development of Compact Quasi-Axisymmetric Stellarator Reactor Configurations
L.P. Ku; M. Zarnstorff; R.B. White; W.A. Cooper; R. Sanchez; H. Neilson; J.A. Schmidt
2003-09-19
We have started to examine the reactor potential of quasi-axisymmetric (QA) stellarators with an integrated approach that includes systems evaluation, engineering considerations, and plasma and coil optimizations. In this paper, we summarize the progress made so far in developing QA configurations with reduced alpha losses while retaining good MHD stability properties. The minimization of alpha losses is achieved by directly targeting the collisionless orbits to prolong the average resident times. Configurations with an overall energy loss rate of {approx}10% or less, including collisional contributions, have been found. To allow remotely maintaining coils and machine components in a reactor environment, there is a desire to simplify to the extent possible the coil design. To this end, finding a configuration that is optimized not only for the alpha confinement and MHD stability but also for the good coil and reactor performance, remains to be a challenging task.
Viscous effects on the instability of an axisymmetric jet
NASA Technical Reports Server (NTRS)
Zaman, K. B. M. Q.; Seiner, J. M.
1990-01-01
The stability characteristics of a laminar, axisymmetric jet, issuing from fully developed Poiseuille flow, are investigated. The jet preferred frequency, as inferred from surveys of u'-spectra, is found to yield a Strouhal number (St) that depends on the Reynolds number (R); St and R are based on the jet diameter (D) and the average velocity (U sub av) at the jet origin. The value of St increases with increasing R in the range 400 less than approximately R less than approximately 4000, attaining an asymptotic value of about 0.45. Flow visualization confirms that the instability is primarily in a helical mode, as predicted by stability analyses. Analyses do predict a similar St versus R variation in approximately the correct St-range. However, the R-range where this is predicted is lower than that found experimentally.
Effect of tabs on the evolution of an axisymmetric jet
NASA Technical Reports Server (NTRS)
Zaman, K. B. M. Q.; Samimy, M.; Reeder, M. F.
1991-01-01
The effect of vortex generators, in the form of small tabs at the nozzle exit, on the evolution of an axisymmetric jet was investigated experimentally over a jet Mach number range of 0.34 to 1.81. The effects of one, two, and four tabs were studied in comparison with the corresponding case without a tab. Each tab introduced an indentation in the shear layer, apparently through the action of streamwise vortices which appeared to be of the trailing vortex type originating from the tips of the tab rather that of the necklace vortex type originating from the base of the tab. The resultant effect of two tabs, placed at diametrically opposite locations, was to essentially bifurcate the jet. The influence of the tabs was essentially the same at subsonic and supersonic conditions indicating that compressibility has little to do with the effect.
Three component velocity measurements in an axisymmetric jet using LDA
NASA Technical Reports Server (NTRS)
Kuhlman, John M.; Gross, Robert W.
1990-01-01
A commercial three-component laser Doppler anemometer (LDA) has been used to acquire a detailed set of three-dimensional mean and fluctuating velocity measurements in a low-speed air jet entering a stagnant ambient, over the first 15 jet exit diameters along the jet trajectory. These data are consistent with previous measurements in axisymmetric, turbulent jets. Mean velocity and Reynolds stress data approach a self-preserving behavior by x/D equal to about 15. However, the RMS turbulence fluctuations were not self-preserving at this axial location, as expected based upon previous experimental studies. These data confirm the ability to obtain reliable three-dimensional velocity data using the present three-dimensional LDA system.
Natural gas production from hydrate dissociation: An axisymmetric model
Ahmadi, G.; Ji, Chuang; Smith, D.H.
2007-08-01
This paper describes an axisymmetric model for natural gas production from the dissociation of methane hydrate in a confined reservoir by a depressurizing well. During the hydrate dissociation, heat and mass transfer in the reservoir are analyzed. The system of governing equations is solved by a finite difference scheme. For different well pressures and reservoir temperatures, distributions of temperature and pressure in the reservoir, as well as the natural gas production from the well are evaluated. The numerical results are compared with those obtained by a linearization method. It is shown that the gas production rate is a sensitive function of well pressure. The simulation results are compared with the linearization approach and the shortcomings of the earlier approach are discussed.
Spectral approach to axisymmetric evolution of Einstein's equations
NASA Astrophysics Data System (ADS)
Schell, Christian; Rinne, Oliver
2015-04-01
We present a new formulation of Einstein's equations for an axisymmetric spacetime with vanishing twist in vacuum. We propose a fully constrained scheme and use spherical polar coordinates. A general problem for this choice is the occurrence of coordinate singularities on the axis of symmetry and at the origin. Spherical harmonics are manifestly regular on the axis and hence take care of that issue automatically. In addition a spectral approach has computational advantages when the equations are implemented. Therefore we spectrally decompose all the variables in the appropriate harmonics. A central point in the formulation is the gauge choice. One of our results is that the commonly used maximal- isothermal gauge turns out to be incompatible with tensor harmonic expansions, and we introduce a new gauge that is better suited. We also address the regularisation of the coordinate singularity at the origin.
Nonaxisymmetric viscous lower branch modes in axisymmetric supersonic flows
NASA Technical Reports Server (NTRS)
Duck, Peter W.; Hall, Philip
1988-01-01
In a previous paper, the weakly nonlinear interaction of a pair of axisymmetric lower branch Tollmien-Schlichting instabilities in cylindrical supersonic flows was considered. Here the possibility that nonaxisymmetric modes might also exist is investigated. In fact, it is found that such modes do exist and, on the basis of linear theory, it appears that these modes are the most important. The nonaxisymmetric modes are found to exist for flows around cylinders with nondimensional radius alpha less than some critical value alpha sub c. This critical value alpha sub c is found to increase monotonically with the azimuthal wavenumber nu of the disturbance and it is found that unstable modes always occur in pairs. It is also shown that, in general, instability in the form of lower branch Tollmien-Schlichting waves will occur first for nonaxisymmetric modes and that in the unstable regime the largest growth rates correspond to the latter modes.
Modular Coils and Plasma Configurations for Quasi-axisymmetric Stellarators
L.P. Ku and A.H. Boozer
2010-09-10
Characteristics of modular coils for quasi-axisymmetric stellarators that are related to the plasma aspect ratio, number of field periods and rotational transform have been examined systematically. It is observed that, for a given plasma aspect ratio, the coil complexity tends to increase with the increased number of field periods. For a given number of field periods, the toroidal excursion of coil winding is reduced as the plasma aspect ratio is increased. It is also clear that the larger the coil-plasma separation is, the more complex the coils become. It is further demonstrated that it is possible to use other types of coils to complement modular coils to improve both the physics and the modular coil characteristics.
Minimum weight design of a generic axisymmetric inlet
NASA Technical Reports Server (NTRS)
Nadell, Shari-Beth
1996-01-01
A new minimum weight design method for high-speed axisymmetric inlets was demonstrated on a generic inlet. The method uses Classical Beam Theory and shell buckling to determine the minimum required equivalent isotropic thickness for a stiffened shell based on prescribed structural design requirements and load conditions. The optimum spacing and equivalent isotropic thickness of ring frame supports are computed to prevent buckling. The method thus develops a preliminary structural design for the inlet and computes the structural weight. Finite element analyses were performed on the resulting inlet design to evaluate the analytical results. Comparisons between the analytical and finite element stresses and deflections identified areas needing improvement in the analytical method. The addition of the deflection due to shear and a torsional buckling failure mode to the new method brought its results in line with those from the finite element analyses. Final validation of the new method will be made using data from actual inlets.
Nonlinear electromagnetic gyrokinetic equations for rotating axisymmetric plasmas
Artun, M.; Tang, W.M.
1994-03-01
The influence of sheared equilibrium flows on the confinement properties of tokamak plasmas is a topic of much current interest. A proper theoretical foundation for the systematic kinetic analysis of this important problem has been provided here by presented the derivation of a set of nonlinear electromagnetic gyrokinetic equations applicable to low frequency microinstabilities in a rotating axisymmetric plasma. The subsonic rotation velocity considered is in the direction of symmetry with the angular rotation frequency being a function of the equilibrium magnetic flux surface. In accordance with experimental observations, the rotation profile is chosen to scale with the ion temperature. The results obtained represent the shear flow generalization of the earlier analysis by Frieman and Chen where such flows were not taken into account. In order to make it readily applicable to gyrokinetic particle simulations, this set of equations is cast in a phase-space-conserving continuity equation form.
Steady axisymmetric vortex flows with swirl and shear
NASA Astrophysics Data System (ADS)
Elcrat, Alan R.; Fornberg, Bengt; Miller, Kenneth G.
A general procedure is presented for computing axisymmetric swirling vortices which are steady with respect to an inviscid flow that is either uniform at infinity or includes shear. We consider cases both with and without a spherical obstacle. Choices of numerical parameters are given which yield vortex rings with swirl, attached vortices with swirl analogous to spherical vortices found by Moffatt, tubes of vorticity extending to infinity and Beltrami flows. When there is a spherical obstacle we have found multiple solutions for each set of parameters. Flows are found by numerically solving the Bragg-Hawthorne equation using a non-Newton-based iterative procedure which is robust in its dependence on an initial guess.
Prediction of pressurant mass requirements for axisymmetric liquid hydrogen tanks
NASA Technical Reports Server (NTRS)
Vandresar, N. T.
1995-01-01
Experimental data from several test series are compared to an existing correlation that predicts the amount of pressurant gas mass required to expel liquid hydrogen from axisymmetric tanks. It was necessary to use an alternate definition of the tank equivalent diameter to accommodate thermal mass in the tank wall that is initially warm and to accommodate liquid residuals in the tank after expulsion is stopped. With this modification, the existing correlation predicted mass requirements to within 14 percent of experimental results. Revision of the correlation constants using a nonlinear least-squares fit of the current experimental data has a minor effect, thus supporting the validity of the original correlation's form, its fitted constants, and the alternate definition of the tank equivalent diameter.
Camassa-Holm equations and vortexons for axisymmetric pipe flows
NASA Astrophysics Data System (ADS)
Fedele, Francesco; Dutykh, Denys
2014-02-01
In this paper, we study the nonlinear dynamics of an axisymmetric disturbance to the laminar state in non-rotating Poiseuille pipe flows. In particular, we show that the associated Navier-Stokes equations can be reduced to a set of coupled dispersive Camassa-Holm type equations. These support inviscid and smooth localized travelling waves, which are numerically computed using the Petviashvili method. In physical space they correspond to localized toroidal vortices that concentrate near the pipe boundaries (wall vortexons) or wrap around the pipe axis (centre vortexons) in agreement with the analytical soliton solutions derived by Fedele (2012 Fluid Dyn. Res. 44 45509) for small and long-wave disturbances. Inviscid singular vortexons with discontinuous radial velocities are also numerically discovered as associated to special travelling waves with a wedge-type singularity, viz. peakons. Their existence is confirmed by an analytical solution of exponentially shaped peakons that is obtained for the particular case of the uncoupled Camassa-Holm equations. The evolution of a perturbation is also investigated using an accurate Fourier-type spectral scheme. We observe that an initial vortical patch splits into a centre vortexon radiating vorticity in the form of wall vortexons. These can under go further splitting before viscosity dissipates them, leading to a slug of centre vortexons. The splitting process originates from a radial flux of azimuthal vorticity from the wall to the pipe axis in agreement with Eyink (2008 Physica D 237 1956-68). The inviscid and smooth vortexon is similar to the nonlinear neutral structures derived by Walton (2011 J. Fluid Mech. 684 284-315) and it may be a precursor to puffs and slugs observed at transition, since most likely it is unstable to non-axisymmetric disturbances.
NASA Astrophysics Data System (ADS)
Ochiai, T.; Nacher, J. C.
2011-09-01
Recently, the application of geometry and conformal mappings to artificial materials (metamaterials) has attracted the attention in various research communities. These materials, characterized by a unique man-made structure, have unusual optical properties, which materials found in nature do not exhibit. By applying the geometry and conformal mappings theory to metamaterial science, it may be possible to realize so-called "Harry Potter cloaking device". Although such a device is still in the science fiction realm, several works have shown that by using such metamaterials it may be possible to control the direction of the electromagnetic field at will. We could then make an object hidden inside of a cloaking device. Here, we will explain how to design invisibility device using differential geometry and conformal mappings.
2011-01-01
Cells are highly complex and orderly machines, with defined shapes and a startling variety of internal organizations. Complex geometry is a feature of both free-living unicellular organisms and cells inside multicellular animals. Where does the geometry of a cell come from? Many of the same questions that arise in developmental biology can also be asked of cells, but in most cases we do not know the answers. How much of cellular organization is dictated by global cell polarity cues as opposed to local interactions between cellular components? Does cellular structure persist across cell generations? What is the relationship between cell geometry and tissue organization? What ensures that intracellular structures are scaled to the overall size of the cell? Cell biology is only now beginning to come to grips with these questions. PMID:21880160
Students Discovering Spherical Geometry Using Dynamic Geometry Software
ERIC Educational Resources Information Center
Guven, Bulent; Karatas, Ilhan
2009-01-01
Dynamic geometry software (DGS) such as Cabri and Geometers' Sketchpad has been regularly used worldwide for teaching and learning Euclidean geometry for a long time. The DGS with its inductive nature allows students to learn Euclidean geometry via explorations. However, with respect to non-Euclidean geometries, do we need to introduce them to…
Computational synthetic geometry
Sturmfels, B. )
1988-01-01
This book deals with methods for realizing abstract geometric objects in concrete vector spaces. It considers a large class of problems from convexity and discrete geometry including constructing convex polytopes from simplicial complexes, vector geometries from incidence structures and hyperplane arrangements from oriented matroids. It appears that algorithms for these constructions exist if and only if arbitrary polynomial equations are decidable with respect to the underlying field. Besides such complexity theorems, a variety of symbolic algorithms are discussed, and the methods are applied to obtain mathematical results on convex polytopes, projective configurations and the combinatories of Grassmann varieties.
NASA Astrophysics Data System (ADS)
Reedy, Todd Mitchell
decreasing pressure. Implementing an array of eight electric arcs circumferentially around the base near the corner expansion, the LAFPA actuators were shown to produce significant disturbances to the separating shear layer of the base flow and cause modest influences on the base pressure when actuated over a range of high frequencies (O(kHz)), forcing modes, duty cycles, and electrical currents. To tailor the plasma actuator toward the specific flow control application of the separated base flow, several actuator geometries and energy additions were evaluated. Displaying the ability to produce disturbances in the shear layer, an open cavity actuator design outperformed the other geometries consisting of a confined cavity with an exhaust orifice. Increases in duty cycle (between 2% and 6%) and in plasma current (1/4 to 4 amps) were shown to produce large velocity disturbances causing a decrease in average base pressure. At 4 amps and a maximum duty cycle of 6%, the largest measured change in area-weighted base pressure, near -1.5%, was observed for the axisymmetric forcing mode. Positive changes in base pressure were experienced (as much as 1% increase from the no-control) for the vertical and horizontal flapping modes.
Comment on the Exterior Solutions and Their Geometry in Scalar-Tensor Theories of Gravity
NASA Astrophysics Data System (ADS)
Tsuchida, T.; Watanabe, K.
1999-01-01
We study series of stationary solutions with asymptotic flatness properties in the Einstein-Maxwell-free scalar system because they are locally equivalent to the exterior solutions in some class of scalar-tensor theories of gravity. First, we classify spherical exterior solutions into two types of solutions, an apparently black hole type solution and an apparently worm hole type solution. The solutions contain three parameters, and we clarify their physical significance. Second, we reduce the field equations for the axisymmetric exterior solutions. We find that the reduced equations are partially the same as the Ernst equations. As simple examples, we derive new series of static, axisymmetric exterior solutions, which correspond to Voorhees's solutions. We then establish a non-trivial relation between the spherical exterior solutions and our new solutions. Finally, since null geodesics have conformally invariant properties, we study the local geometry of the exterior solutions by using the optical scalar equations and find some anomalous behavior of the null geodesics.
Advanced geometries and regimes
Bulanov, S. S.; Bulanov, S. V.; Turchetti, G.; Limpouch, J.; Klimo, O.; Psikal, J.; Margarone, D.; Korn, G.
2013-07-26
We review and discuss different schemes of laser ion acceleration as well as advanced target geometries in connection with the development of the laser-driven proton source for hadron therapy of oncological diseases, which is a part of the ELIMED project.
Spacetime and Euclidean geometry
NASA Astrophysics Data System (ADS)
Brill, Dieter; Jacobson, Ted
2006-04-01
Using only the principle of relativity and Euclidean geometry we show in this pedagogical article that the square of proper time or length in a two-dimensional spacetime diagram is proportional to the Euclidean area of the corresponding causal domain. We use this relation to derive the Minkowski line element by two geometric proofs of the spacetime Pythagoras theorem.
ERIC Educational Resources Information Center
Cooper, Brett D.; Barger, Rita
2009-01-01
The many connections between music and mathematics are well known. The length of a plucked string determines its tone, the time signature of a piece of music is a ratio, and note durations are measured in fractions. One connection commonly overlooked is that between music and geometry--specifically, geometric transformations, including…
ERIC Educational Resources Information Center
Hartz, Viggo
1981-01-01
Allowing students to use a polystyrene cutter to fashion their own three-dimensional models is suggested as a means of allowing individuals to experience problems and develop ideas related to solid geometry. A list of ideas that can lead to mathematical discovery is provided. (MP)
Teaching Geometry with Tangrams.
ERIC Educational Resources Information Center
Russell, Dorothy S.; Bologna, Elaine M.
1982-01-01
Geometry is viewed as the most neglected area of the elementary school mathematics curriculum. Tangram activities provide numerous worthwhile mathematical experiences for children. A method of constructing tangrams through paper folding is followed by suggested spatial visualization, measurement, and additional activities. (MP)
Sliding vane geometry turbines
Sun, Harold Huimin; Zhang, Jizhong; Hu, Liangjun; Hanna, Dave R
2014-12-30
Various systems and methods are described for a variable geometry turbine. In one example, a turbine nozzle comprises a central axis and a nozzle vane. The nozzle vane includes a stationary vane and a sliding vane. The sliding vane is positioned to slide in a direction substantially tangent to an inner circumference of the turbine nozzle and in contact with the stationary vane.
ERIC Educational Resources Information Center
MacKeown, P. K.
1984-01-01
Clarifies two concepts of gravity--those of a fictitious force and those of how space and time may have geometry. Reviews the position of Newton's theory of gravity in the context of special relativity and considers why gravity (as distinct from electromagnetics) lends itself to Einstein's revolutionary interpretation. (JN)
ERIC Educational Resources Information Center
Martin, John
2010-01-01
The cycloid has been called the Helen of Geometry, not only because of its beautiful properties but also because of the quarrels it provoked between famous mathematicians of the 17th century. This article surveys the history of the cycloid and its importance in the development of the calculus.
Atiyah, Michael; Dijkgraaf, Robbert; Hitchin, Nigel
2010-01-01
We review the remarkably fruitful interactions between mathematics and quantum physics in the past decades, pointing out some general trends and highlighting several examples, such as the counting of curves in algebraic geometry, invariants of knots and four-dimensional topology. PMID:20123740
ERIC Educational Resources Information Center
Case, Christine L.
1991-01-01
Presented is an activity in which students make models of viruses, which allows them to visualize the shape of these microorganisms. Included are some background on viruses, the biology and geometry of viruses, directions for building viruses, a comparison of cells and viruses, and questions for students. (KR)
ERIC Educational Resources Information Center
KLIER, KATHERINE M.
PRESENTED IS A FUSED COURSE IN PLANE, SOLID, AND COORDINATE GEOMETRY. ELEMENTARY SET THEORY, LOGIC, AND THE PRINCIPLE OF SEPARATION PROVIDE UNIFYING THREADS THROUGHOUT THE TEXT. THE TWO CURRICULUM GUIDES HAVE BEEN PREPARED FOR USE WITH TWO DIFFERENT TEXTS. EITHER CURRICULUM GUIDE MAY BE USED DEPENDING UPON THE CHOICE OF THE TEACHER AND THE NEEDS…
Axisymmetric whole pin life modelling of advanced gas-cooled reactor nuclear fuel
NASA Astrophysics Data System (ADS)
Mella, R.; Wenman, M. R.
2013-06-01
Thermo-mechanical contributions to pellet-clad interaction (PCI) in advanced gas-cooled reactors (AGRs) are modelled in the ABAQUS finite element (FE) code. User supplied sub-routines permit the modelling of the non-linear behaviour of AGR fuel through life. Through utilisation of ABAQUS's well-developed pre- and post-processing ability, the behaviour of the axially constrained steel clad fuel was modelled. The 2D axisymmetric model includes thermo-mechanical behaviour of the fuel with time and condition dependent material properties. Pellet cladding gap dynamics and thermal behaviour are also modelled. The model treats heat up as a fully coupled temperature-displacement study. Dwell time and direct power cycling was applied to model the impact of online refuelling, a key feature of the AGR. The model includes the visco-plastic behaviour of the fuel under the stress and irradiation conditions within an AGR core and a non-linear heat transfer model. A multiscale fission gas release model is applied to compute pin pressure; this model is coupled to the PCI gap model through an explicit fission gas inventory code. Whole pin, whole life, models are able to show the impact of the fuel on all segments of cladding including weld end caps and cladding pellet locking mechanisms (unique to AGR fuel). The development of this model in a commercial FE package shows that the development of a potentially verified and future-proof fuel performance code can be created and used. The usability of a FE based fuel performance code would be an enhancement over past codes. Pre- and post-processors have lowered the entry barrier for the development of a fuel performance model to permit the ability to model complicated systems. Typical runtimes for a 5 year axisymmetric model takes less than one hour on a single core workstation. The current model has implemented: Non-linear fuel thermal behaviour, including a complex description of heat flow in the fuel. Coupled with a variety of
Wave focusing using symmetry matching in axisymmetric acoustic gradient index lenses
NASA Astrophysics Data System (ADS)
Romero-García, V.; Cebrecos, A.; Picó, R.; Sánchez-Morcillo, V. J.; Garcia-Raffi, L. M.; Sánchez-Pérez, J. V.
2013-12-01
The symmetry matching between the source and the lens results in fundamental interest for lensing applications. In this work, we have modeled an axisymmetric gradient index (GRIN) lens made of rigid toroidal scatterers embedded in air considering this symmetry matching with radially symmetric sources. The sound amplification obtained in the focal spot of the reported lens (8.24 dB experimentally) shows the efficiency of the axisymmetric lenses with respect to the previous Cartesian acoustic GRIN lenses. The axisymmetric design opens new possibilities in lensing applications in different branches of science and technology.
Revisiting linear dynamics of non-axisymmetric perturbations in weakly magnetized accretion discs
NASA Astrophysics Data System (ADS)
Mamatsashvili, G. R.; Chagelishvili, G. D.; Bodo, G.; Rossi, P.
2013-11-01
We investigate the linear dynamics of non-axisymmetric perturbations in incompressible, vertically stratified Keplerian discs threaded by a weak non-zero net vertical magnetic field in the local shearing box approximation. Perturbations are decomposed into shearing waves or spatial harmonics whose temporal evolution is then followed via numerical integration of the linearized ideal magnetohydrodynamic equations of the shearing box. There are two basic modes in the system - inertia-gravity waves and magnetic mode, which displays the magnetorotational instability (MRI). Distinct from previous related studies, we introduce `eigen-variables' characterizing each (counter-propagating) component of the inertia-gravity and magnetic modes, which are governed by a set of four first-order coupled ordinary differential equations. This allows us to identify a new process of linear coupling of the two above non-axisymmetric modes due to the disc's differential rotation. We also carry out a comparative analysis of the dynamics of non-axisymmetric and axisymmetric magnetic mode perturbations. It is demonstrated that the growth of `optimal' and close-to-optimal non-axisymmetric harmonics of this mode, having transient nature, can prevail over the exponential growth of axisymmetric ones (i.e. over the axisymmetric MRI) during dynamical time. A possible implication of this result for axisymmetric channel solutions emerging in numerical simulations is discussed. In particular, the formation of the (axisymmetric) channel may be affected/impeded by non-axisymmetric modes already at the early linear stage leading to its untimely disruption - the outcome strongly depends on the amplitude and spectrum of initial perturbation. Thus, this competition may result in an uncertainty in the magnetic mode's non-linear dynamics. Even so, we consider that incompressible perturbations, in the final part, speculate on the dynamics in the compressible case. It is shown that a maximum growth of non-axisymmetric
NASA Astrophysics Data System (ADS)
Liu, Jianyong; Lu, Yajun; Li, Zhiping
2010-05-01
Non-axisymmetric wake impact experiments were carried out after the best exciting frequency for a low speed axial compressor had been found by axisymmetric wake impact experiments. When the number and circumferential distribution of inlet guide vanes (IGV) are logical the wakes of non-axisymmetric IGVs can exert beneficial unsteady exciting effect on their downstream rotor flow fields and improve the compressor’s performance. In the present paper, four non-axisymmetric wake impact plans were found working better than the axisymmetric wake impact plan. Compared with the base plan, the best non-axisymmetric plan increased the compressor’s peak efficiency, and the total pressure rise by 1.1 and 2%, and enhanced the stall margin by 4.4%. The main reason why non-axisymmetric plans worked better than the axisymmetric plan was explained as the change of the unsteady exciting signal arising from IGV wakes. Besides the high-frequency components, the non-axisymmetric plan generated a beneficial low-frequency square-wave exciting signal and other secondary frequency components. Compared with the axisymmetric plan, multi-frequency exciting wakes arising from the non-axisymmetric plans are easier to get coupling relation with complex vortices such as clearance vortices, passage vortices and shedding vortices.
An introduction to Minkowski geometries
NASA Astrophysics Data System (ADS)
Farnsworth, David L.
2016-07-01
The fundamental ideas of Minkowski geometries are presented. Learning about Minkowski geometries can sharpen our students' understanding of concepts such as distance measurement. Many of its ideas are important and accessible to undergraduate students. Following a brief overview, distance and orthogonality in Minkowski geometries are thoroughly discussed and many illustrative examples and applications are supplied. Suggestions for further study of these geometries are given. Indeed, Minkowski geometries are an excellent source of topics for undergraduate research and independent study.
NASA Astrophysics Data System (ADS)
Lyons, B. C.; Jardin, S. C.; Ramos, J. J.
2012-08-01
A new code, the Neoclassical Ion-Electron Solver (NIES), has been written to solve for stationary, axisymmetric distribution functions (f) in the conventional banana regime for both ions and electrons using a set of drift-kinetic equations (DKEs) with linearized Fokker-Planck-Landau collision operators. Solvability conditions on the DKEs determine the relevant non-adiabatic pieces of f (called h). We work in a 4D phase space in which ψ defines a flux surface, θ is the poloidal angle, v is the magnitude of the velocity referenced to the mean flow velocity, and λ is the dimensionless magnetic moment parameter. We expand h in finite elements in both v and λ. The Rosenbluth potentials, Φ and Ψ, which define the integral part of the collision operator, are expanded in Legendre series in cosχ, where χ is the pitch angle, Fourier series in cosθ, and finite elements in v. At each ψ, we solve a block tridiagonal system for hi (independent of fe), then solve another block tridiagonal system for he (dependent on fi). We demonstrate that such a formulation can be accurately and efficiently solved. NIES is coupled to the MHD equilibrium code JSOLVER [J. DeLucia et al., J. Comput. Phys. 37, 183-204 (1980)] allowing us to work with realistic magnetic geometries. The bootstrap current is calculated as a simple moment of the distribution function. Results are benchmarked against the Sauter analytic formulas and can be used as a kinetic closure for an MHD code (e.g., M3D -C1 [S. C. Jardin et al., Comput. Sci. Discovery 5, 014002 (2012)]).
B.C. Lyons, S.C. Jardin, and J.J. Ramos
2012-06-28
A new code, the Neoclassical Ion-Electron Solver (NIES), has been written to solve for stationary, axisymmetric distribution functions (f ) in the conventional banana regime for both ions and elec trons using a set of drift-kinetic equations (DKEs) with linearized Fokker-Planck-Landau collision operators. Solvability conditions on the DKEs determine the relevant non-adiabatic pieces of f (called h ). We work in a 4D phase space in which Ψ defines a flux surface, θ is the poloidal angle, v is the total velocity referenced to the mean flow velocity, and λ is the dimensionless magnetic moment parameter. We expand h in finite elements in both v and λ . The Rosenbluth potentials, φ and ψ, which define the integral part of the collision operator, are expanded in Legendre series in cos χ , where χ is the pitch angle, Fourier series in cos θ , and finite elements in v . At each ψ , we solve a block tridiagonal system for hi (independent of fe ), then solve another block tridiagonal system for he (dependent on fi ). We demonstrate that such a formulation can be accurately and efficiently solved. NIES is coupled to the MHD equilibrium code JSOLVER [J. DeLucia, et al., J. Comput. Phys. 37 , pp 183-204 (1980).] allowing us to work with realistic magnetic geometries. The bootstrap current is calculated as a simple moment of the distribution function. Results are benchmarked against the Sauter analytic formulas and can be used as a kinetic closure for an MHD code (e.g., M3D-C1 [S.C. Jardin, et al ., Computational Science & Discovery, 4 (2012).]).
Lyons, B. C.; Jardin, S. C.; Ramos, J. J.
2012-08-15
A new code, the Neoclassical Ion-Electron Solver (NIES), has been written to solve for stationary, axisymmetric distribution functions (f) in the conventional banana regime for both ions and electrons using a set of drift-kinetic equations (DKEs) with linearized Fokker-Planck-Landau collision operators. Solvability conditions on the DKEs determine the relevant non-adiabatic pieces of f (called h). We work in a 4D phase space in which {psi} defines a flux surface, {theta} is the poloidal angle, v is the magnitude of the velocity referenced to the mean flow velocity, and {lambda} is the dimensionless magnetic moment parameter. We expand h in finite elements in both v and {lambda}. The Rosenbluth potentials, {Phi} and {Psi}, which define the integral part of the collision operator, are expanded in Legendre series in cos{chi}, where {chi} is the pitch angle, Fourier series in cos{theta}, and finite elements in v. At each {psi}, we solve a block tridiagonal system for h{sub i} (independent of f{sub e}), then solve another block tridiagonal system for h{sub e} (dependent on f{sub i}). We demonstrate that such a formulation can be accurately and efficiently solved. NIES is coupled to the MHD equilibrium code JSOLVER [J. DeLucia et al., J. Comput. Phys. 37, 183-204 (1980)] allowing us to work with realistic magnetic geometries. The bootstrap current is calculated as a simple moment of the distribution function. Results are benchmarked against the Sauter analytic formulas and can be used as a kinetic closure for an MHD code (e.g., M3D-C{sup 1}[S. C. Jardin et al., Comput. Sci. Discovery 5, 014002 (2012)]).
Automation of Axisymmetric Drop Shape Analysis Using Digital Image Processing
NASA Astrophysics Data System (ADS)
Cheng, Philip Wing Ping
The Axisymmetric Drop Shape Analysis - Profile (ADSA-P) technique, as initiated by Rotenberg, is a user -oriented scheme to determine liquid-fluid interfacial tensions and contact angles from the shape of axisymmetric menisci, i.e., from sessile as well as pendant drops. The ADSA -P program requires as input several coordinate points along the drop profile, the value of the density difference between the bulk phases, and gravity. The solution yields interfacial tension and contact angle. Although the ADSA-P technique was in principle complete, it was found that it was of very limited practical use. The major difficulty with the method is the need for very precise coordinate points along the drop profile, which, up to now, could not be obtained readily. In the past, the coordinate points along the drop profile were obtained by manual digitization of photographs or negatives. From manual digitization data, the surface tension values obtained had an average error of +/-5% when compared with literature values. Another problem with the ADSA-P technique was that the computer program failed to converge for the case of very elongated pendant drops. To acquire the drop profile coordinates automatically, a technique which utilizes recent developments in digital image acquisition and analysis was developed. In order to determine the drop profile coordinates as precisely as possible, the errors due to optical distortions were eliminated. In addition, determination of drop profile coordinates to pixel and sub-pixel resolution was developed. It was found that high precision could be obtained through the use of sub-pixel resolution and a spline fitting method. The results obtained using the automatic digitization technique in conjunction with ADSA-P not only compared well with the conventional methods, but also outstripped the precision of conventional methods considerably. To solve the convergence problem of very elongated pendant drops, it was found that the reason for the
Numerical investigation of transitional and turbulent supersonic axisymmetric wakes
NASA Astrophysics Data System (ADS)
Sandberg, Richard David
Transitional and turbulent supersonic axisymmetric wakes are investigated by conducting various numerical experiments. The main objective is to identify hydrodynamic instability mechanisms in the flow at M = 2.46 for several Reynolds numbers, and relating these to coherent structures that are found from various visualization techniques. The premise for this approach is the assumption that flow instabilities lead to the formation of coherent structures. The effect of these structures on the mean flow is of particular interest, as they strongly affect the base drag. Three high-order accurate compressible codes were developed in cylindrical coordinates for this research: A spatial Navier-Stokes (N-S) code to conduct Direct Numerical Simulations (DNS), a linearized N-S code for linear stability investigations using two-dimensional basic states, and a temporal N-S code for performing local stability analyses. The ability of numerical simulations to deliberately exclude physical effects is exploited. This includes intentionally eliminating certain azimuthal/helical modes by employing DNS for various circumferential domain-sizes. With this approach, the impact of structures associated with certain modes on the global wake-behavior can be scrutinized. It is concluded that azimuthal modes with low wavenumbers are responsible for a flat mean base-pressure distribution and that k = 2 and k = 4 are the dominant modes in the trailing wake, producing a four-lobe wake pattern. Complementary spatial and temporal calculations are carried out to investigate whether instabilities are of local or global nature. Circumstantial evidence is presented that absolutely unstable global modes within the recirculation region coexist with convectively unstable shear-layer modes. The flow is found to be absolutely unstable with respect to modes k > 0 for ReD > 5,000 and with respect to the axisymmetric mode for ReD > 100,000. Furthermore, it is investigated whether flow control measures designed
Cylindrical geometry hall thruster
Raitses, Yevgeny; Fisch, Nathaniel J.
2002-01-01
An apparatus and method for thrusting plasma, utilizing a Hall thruster with a cylindrical geometry, wherein ions are accelerated in substantially the axial direction. The apparatus is suitable for operation at low power. It employs small size thruster components, including a ceramic channel, with the center pole piece of the conventional annular design thruster eliminated or greatly reduced. Efficient operation is accomplished through magnetic fields with a substantial radial component. The propellant gas is ionized at an optimal location in the thruster. A further improvement is accomplished by segmented electrodes, which produce localized voltage drops within the thruster at optimally prescribed locations. The apparatus differs from a conventional Hall thruster, which has an annular geometry, not well suited to scaling to small size, because the small size for an annular design has a great deal of surface area relative to the volume.
Micro vortex generator control of axisymmetric high-speed laminar boundary layer separation
NASA Astrophysics Data System (ADS)
Estruch-Samper, D.; Vanstone, L.; Hillier, R.; Ganapathisubramani, B.
2015-09-01
Interest in the development of micro vortex generators (MVGs) to control high-speed flow separation has grown in the last decade. In contrast to conventional vortex generators, MVGs are fully submerged in the boundary layer and have the potential of inducing surface flow mixing with marginal drag penalty when suitably designed. Also, they do not result in undesired reduced mass flow such as with suction methods. The flow mechanisms at the location of MVGs are not yet fully understood, and optimal designs are difficult to establish given that both numerical predictions and experiments are particularly challenged for short element heights, yet optimal MVGs are generally expected to be at least shorter than half the local boundary layer thickness. The present work aims at investigating experimentally the fundamental flow physics concerning an individual MVG element (of `canonical' or simplified geometry) at a range of near-wall heights. A fully laminar base flow is considered so as to isolate the effect of incoming turbulence as well as the more complex physics that may occur when specific and/or multiple elements are used. Tests were performed in a gun tunnel at a freestream Mach number of 8.9 and Reynolds number of /m, and the basic test model consisted of a blunt-nosed cylinder which produced an axisymmetric laminar boundary layer with an edge Mach number of 3.4 and Reynolds number of /m at the MVG location. A laminar shock-wave/boundary layer interaction with separation was induced by a flare located further downstream on the model. Measurements consisted of time-resolved surface heat transfer obtained in the axial direction immediately downstream of the MVG and along the interaction, together with simultaneous high-speed schlieren imaging. The height () of the MVG element used in a `diamond' configuration (square planform with one vertex facing the flow) was adjusted between tests ranging from = 0.03 to 0.58, where the local undisturbed boundary layer thickness
Self-consistent hybrid neoclassical-magnetohydrodynamic simulations of axisymmetric plasmas
NASA Astrophysics Data System (ADS)
Lyons, Brendan Carrick
Neoclassical effects (e.g., conductivity reduction and bootstrap currents) have a profound impact on many magnetohydrodynamic (MHD) instabilities in toroidally-confined plasmas, including tearing modes, edge-localized modes, and resistive wall modes. High-fidelity simulations of such phenomena require a multiphysics code that self-consistently couples the kinetic and fluid models. We review a hybrid formulation from the recent literatureAB that is appropriate for such studies. In particular, the formulation uses a set of time-dependent drift-kinetic equations (DKEs) to advance the non-Maxwellian part of the electron and ion distribution functions (fNM) with linearized Fokker-Planck-Landau collision operators. The form of the DKEs used were derived in a Chapman-Enskog-like fashion, ensuring that fNM carries no density, momentum, or temperature. Rather, these quantities are contained within the background Maxwellian and are evolved by a set of MHD equations which are closed by moments of fNM . We then present two DKE solvers based upon this formulation in axisymmetric toroidal geometries. The Neoclassical Ion-Electron Solver (NIES) solves the steady-state DKEs in the low-collisionality limit. Convergence and benchmark studies are discussed, providing a proof-of-principle that this new formulation can accurately reproduce results from the literature in the limit considered. We then present the DK4D code which evolves the finite-collisionality DKEs time-dependently. Computational methods used and successful benchmarks to other neoclassical models and codes are discussed. Furthermore, we couple DK4D to a reduced, transport-timescale MHD code. The resulting hybrid code is used to simulate the evolution of the current density in a large-aspect-ratio plasma in the presence of several different time-dependent pressure profiles. These simulations demonstrate the self-consistent, dynamic formation of the ohmic and bootstrap currents. In the slowly-evolving plasmas considered
FEATS - Finite element thermal stress analysis of plane or axisymmetric solids
NASA Technical Reports Server (NTRS)
Swanson, J. A.
1971-01-01
FEATS computer code uses finite element analysis to calculate steady state temperature and thermal stress fields for either axisymmetric or plane two-dimensional bodies with boundary conditions, including specified displacements, loads, and thermal boundary conditions.
Inflation from quantum geometry.
Bojowald, Martin
2002-12-23
Quantum geometry predicts that a universe evolves through an inflationary phase at small volume before exiting gracefully into a standard Friedmann phase. This does not require the introduction of additional matter fields with ad hoc potentials; rather, it occurs because of a quantum gravity modification of the kinetic part of ordinary matter Hamiltonians. An application of the same mechanism can explain why the present day cosmological acceleration is so tiny.
NASA Astrophysics Data System (ADS)
Bengtsson, Ingemar; Zyczkowski, Karol
2007-12-01
Preface; 1. Convexity, colours and statistics; 2. Geometry of probability distributions; 3. Much ado about spheres; 4. Complex projective spaces; 5. Outline of quantum mechanics; 6. Coherent states and group actions; 7. The stellar representation; 8. The space of density matrices; 9. Purification of mixed quantum states; 10. Quantum operations; 11. Duality: maps versus states; 12. Density matrices and entropies; 13. Distinguishability measures; 14. Monotone metrics and measures; 15. Quantum entanglement; Epilogue; Appendices; References; Index.
Freezing in confined geometries
NASA Technical Reports Server (NTRS)
Sokol, P. E.; Ma, W. J.; Herwig, K. W.; Snow, W. M.; Wang, Y.; Koplik, Joel; Banavar, Jayanth R.
1992-01-01
Results of detailed structural studies, using elastic neutron scattering, of the freezing of liquid O2 and D2 in porous vycor glass, are presented. The experimental studies have been complemented by computer simulations of the dynamics of freezing of a Lennard-Jones liquid in narrow channels bounded by molecular walls. Results point to a new simple physical interpretation of freezing in confined geometries.
Integral geometry and holography
Czech, Bartlomiej; Lamprou, Lampros; McCandlish, Samuel; Sully, James
2015-10-27
We present a mathematical framework which underlies the connection between information theory and the bulk spacetime in the AdS_{3}/CFT_{2} correspondence. A key concept is kinematic space: an auxiliary Lorentzian geometry whose metric is defined in terms of conditional mutual informations and which organizes the entanglement pattern of a CFT state. When the field theory has a holographic dual obeying the Ryu-Takayanagi proposal, kinematic space has a direct geometric meaning: it is the space of bulk geodesics studied in integral geometry. Lengths of bulk curves are computed by kinematic volumes, giving a precise entropic interpretation of the length of any bulk curve. We explain how basic geometric concepts -- points, distances and angles -- are reflected in kinematic space, allowing one to reconstruct a large class of spatial bulk geometries from boundary entanglement entropies. In this way, kinematic space translates between information theoretic and geometric descriptions of a CFT state. As an example, we discuss in detail the static slice of AdS_{3} whose kinematic space is two-dimensional de Sitter space.
Integral geometry and holography
Czech, Bartlomiej; Lamprou, Lampros; McCandlish, Samuel; Sully, James
2015-10-27
We present a mathematical framework which underlies the connection between information theory and the bulk spacetime in the AdS3/CFT2 correspondence. A key concept is kinematic space: an auxiliary Lorentzian geometry whose metric is defined in terms of conditional mutual informations and which organizes the entanglement pattern of a CFT state. When the field theory has a holographic dual obeying the Ryu-Takayanagi proposal, kinematic space has a direct geometric meaning: it is the space of bulk geodesics studied in integral geometry. Lengths of bulk curves are computed by kinematic volumes, giving a precise entropic interpretation of the length of any bulkmore » curve. We explain how basic geometric concepts -- points, distances and angles -- are reflected in kinematic space, allowing one to reconstruct a large class of spatial bulk geometries from boundary entanglement entropies. In this way, kinematic space translates between information theoretic and geometric descriptions of a CFT state. As an example, we discuss in detail the static slice of AdS3 whose kinematic space is two-dimensional de Sitter space.« less
Emergent Complex Network Geometry
NASA Astrophysics Data System (ADS)
Wu, Zhihao; Menichetti, Giulia; Rahmede, Christoph; Bianconi, Ginestra
2015-05-01
Networks are mathematical structures that are universally used to describe a large variety of complex systems such as the brain or the Internet. Characterizing the geometrical properties of these networks has become increasingly relevant for routing problems, inference and data mining. In real growing networks, topological, structural and geometrical properties emerge spontaneously from their dynamical rules. Nevertheless we still miss a model in which networks develop an emergent complex geometry. Here we show that a single two parameter network model, the growing geometrical network, can generate complex network geometries with non-trivial distribution of curvatures, combining exponential growth and small-world properties with finite spectral dimensionality. In one limit, the non-equilibrium dynamical rules of these networks can generate scale-free networks with clustering and communities, in another limit planar random geometries with non-trivial modularity. Finally we find that these properties of the geometrical growing networks are present in a large set of real networks describing biological, social and technological systems.
NASA Technical Reports Server (NTRS)
Hamilton, H. H., II
1980-01-01
A theoretical method was developed for computing approximate laminar heating rates on three dimensional configurations at angle of attack. The method is based on the axisymmetric analogue which is used to reduce the three dimensional boundary layer equations along surface streamlines to an equivalent axisymmetric form by using the metric coefficient which describes streamline divergence (or convergence). The method was coupled with a three dimensional inviscid flow field program for computing surface streamline paths, metric coefficients, and boundary layer edge conditions.
Axisymmetric and 3D calculations of melt flow during VCz growth
NASA Astrophysics Data System (ADS)
Bänsch, E.; Davis, D.; Langmach, H.; Miller, W.; Rehse, U.; Reinhardt, G.; Uhle, M.
2004-05-01
Axisymmetric and 3D calculations of melt flow have been performed for a configuration used at the vapour-pressure-controlled Czochalski growth of GaAs single crystals. Thermal boundary conditions were adapted from a global simulation of the temperature field. The axisymmetric calculations with the code NAVIER confirmed the ones previously perfomed with FIDAP TM. The 3D calculations showed that the flow exhibits an asymmetric transient behaviour beyond a certain critical Reynolds number.
EFFECTS OF LARGE-SCALE NON-AXISYMMETRIC PERTURBATIONS IN THE MEAN-FIELD SOLAR DYNAMO
Pipin, V. V.; Kosovichev, A. G.
2015-11-10
We explore the response of a nonlinear non-axisymmetric mean-field solar dynamo model to shallow non-axisymmetric perturbations. After a relaxation period, the amplitude of the non-axisymmetric field depends on the initial condition, helicity conservation, and the depth of perturbation. It is found that a perturbation that is anchored at 0.9 R{sub ⊙} has a profound effect on the dynamo process, producing a transient magnetic cycle of the axisymmetric magnetic field, if it is initiated at the growing phase of the cycle. The non-symmetric, with respect to the equator, perturbation results in a hemispheric asymmetry of the magnetic activity. The evolution of the axisymmetric and non-axisymmetric fields depends on the turbulent magnetic Reynolds number R{sub m}. In the range of R{sub m} = 10{sup 4}–10{sup 6} the evolution returns to the normal course in the next cycle, in which the non-axisymmetric field is generated due to a nonlinear α-effect and magnetic buoyancy. In the stationary state, the large-scale magnetic field demonstrates a phenomenon of “active longitudes” with cyclic 180° “flip-flop” changes of the large-scale magnetic field orientation. The flip-flop effect is known from observations of solar and stellar magnetic cycles. However, this effect disappears in the model, which includes the meridional circulation pattern determined by helioseismology. The rotation rate of the non-axisymmetric field components varies during the relaxation period and carries important information about the dynamo process.
Global mode analysis of a pipe flow through a 1:2 axisymmetric sudden expansion
NASA Astrophysics Data System (ADS)
Sanmiguel-Rojas, E.; del Pino, C.; Gutiérrez-Montes, C.
2010-07-01
We report the results of the global mode analysis to characterize the onset of unsteadiness in a circular pipe flow through an axisymmetric sudden expansion of inlet-to-outlet diameter ratio of d /D=0.5. We find that the axisymmetric state becomes linearly unstable at a significantly higher critical Reynolds number than the one reported in previous experimental works. This unstable global mode corresponds to an oscillatory bifurcation with wavenumber |m|=1 located at the end of the recirculation region.
Adhesion and detachment of a capsule in axisymmetric flow
NASA Astrophysics Data System (ADS)
Keh, M. P.; Leal, L. G.
2016-05-01
The adhesion and detachment of a capsule on a solid boundary surface is studied via a combination of scaling theory and numerical simulation and the behavior is compared and contrasted with a vesicle. It is shown that the dominant physical property for both capsules and vesicles is the area dilation modulus Ks of the membrane. The nonzero shear modulus Gs for capsules increases the resistance to deformation and thus decreases slightly the equilibrium contact radius for an adhered capsule compared to an adhered vesicle. The detachment process in this study is due to an external axisymmetric flow. Unlike a rigid body that must be pulled away without change of shape, capsules (and vesicles) almost always detach dominantly by peeling in which the contact radius decreases but the minimum separation distance does not change until the final moments of detachment. Compared to a vesicle with the same Ks, a capsule maintains a more compact shape and is harder to elongate under a given external flow. Hence, the detachment process is slower for capsules compared to vesicles with the same Ks.
Axisymmetric equilibria with pressure anisotropy and plasma flow
NASA Astrophysics Data System (ADS)
Throumoulopoulos, George; Evangelias, Achilleas
2015-11-01
A generalised Grad-Shafranov equation that governs the equilibrium of an axisymmetric toroidal plasma with anisotropic pressure and incompressible flow of arbitrary direction is derived. This equation includes six free surface functions and recovers known Grad-Shafranov-like equations in the literature as well as the usual static, isotropic one. The form of the generalised equation indicates that pressure anisotropy and flow act additively on equilibrium. In addition, two sets of analytical solutions, an extended Solovev one with a free boundary and an extended Hernegger-Maschke one for a plasma surrounded by a fixed boundary possessing an X-point, are constructed, particularly in relevance to the ITER and NSTX tokamaks. Furthermore, the impacts both of pressure anisotropy and plasma flow on these equilibria are examined. It turns out that depending on the maximum value and the shape of an anisotropy function, the anisotropy can act either paramagnetically or diamagnetically. Also, in most of the cases considered both the anisotropy and the flow have stronger effects on NSTX equilibria than on ITER ones. This work has been carried out within the framework of the EUROfusion Consortium and has received funding from (a) the National Programme for the Controlled Thermonuclear Fusion, Hellenic Republic, (b) Euratom research and training programme 2014-2018.
Experimental and Theoretical Studies of Axisymmetric Free Jets
NASA Technical Reports Server (NTRS)
Love, Eugene S.; Grigsby, Carl E.; Lee, Louise P.; Woodling, Mildred J.
1959-01-01
Some experimental and theoretical studies have been made of axisymmetric free jets exhausting from sonic and supersonic nozzles into still air and into supersonic streams with a view toward problems associated with propulsive jets and the investigation of these problems. For jets exhausting into still air, consideration is given to the effects of jet Mach number, nozzle divergence angle, and jet static pressure ratio upon jet structure, jet wavelength, and the shape and curvature of the jet boundary. Studies of the effects of the ratio of specific heats of the jets are included are observations pertaining to jet noise and jet simulation. For jets exhausting into supersonic streams, an attempt has been made to present primarily theoretical certain jet interference effects and in formulating experimental studies. The primary variables considered are jet Mach number, free stream Mach number, jet static pressure ratio, ratio of specific heats of the jet, nozzle exit angle, and boattail angle. The simulation problem and the case of a hypothetical hypersonic vehicle are examined, A few experimental observations are included.
A new axi-symmetric element for thin walled structures
NASA Astrophysics Data System (ADS)
Cardoso, Rui P. R.; Yoon, Jeong Whan; Dick, Robert E.
2010-03-01
A new axi-symmetric finite element for thin walled structures is presented in this work. It uses the solid-shell element’s concept with only a single element and multiple integration points along the thickness direction. The cross-section of the element is composed of four nodes with two degrees of freedom each. The proposed formulation overcomes many locking pathologies including transverse shear locking, Poisson’s locking and volumetric locking. For transverse shear locking, the formulation uses the selective reduced integration technique, for Poisson’s locking it uses the enhanced assumed strain (EAS) method with only one enhancing variable. The B-bar approach is used to eliminate the isochoric deformations in the hourglass field while the EAS method is used to alleviate the volumetric locking in the constant part of the deformation tensor. Several examples are shown to demonstrate the performance and accuracy of the proposed element with special focus on the numerical simulations for the beverage can industry.
Synthetic Jet Control of a Yawing Axisymmetric Body
NASA Astrophysics Data System (ADS)
Lambert, Thomas; Vukasinovic, Bojan; Glezer, Ari
2012-11-01
The global aerodynamic forces and moments on an axisymmetric yawing body are controlled in wind tunnel experiments by exploiting the interaction of an array of synthetic jet actuators with the cross flow over the tail section of the body. The model is supported by a vertical wire through its aerodynamic center and is free to move in yaw. The baseline motion of the model is a yaw oscillation with amplitude and frequency that both monotonously increase with free stream velocity, characteristic of vortex shedding. The aft-facing control jet actuators emanate from narrow, azimuthally segmented slots around the perimeter of the tail section, and activation of the control jets effects the model's path through localized flow attachment on integrated Coanda surfaces. The control jets are used to control the yaw trajectory of the model using a closed loop PID controller. The baseline and controlled model motion is monitored using a laser vibrometer, and the flow evolution near the body and in its near wake is investigated using PIV. The coupled, time dependent response of the model to the actuation is investigated with emphasis on controlling its unstable modes. Supported by ARO.
Unsteady Aerodynamic Flow Control of a Suspended Axisymmetric Moving Platform
NASA Astrophysics Data System (ADS)
Lambert, Thomas; Vukasinovic, Bojan; Glezer, Ari
2011-11-01
The aerodynamic forces on an axisymmetric wind tunnel model are altered by fluidic interaction of an azimuthal array of integrated synthetic jet actuators with the cross flow. Four-quadrant actuators are integrated into a Coanda surface on the aft section of the body, and the jets emanate from narrow, azimuthally segmented slots equally distributed around the model's perimeter. The model is suspended in the tunnel using eight wires each comprising miniature in-line force sensors and shape-memory-alloy (SMA) strands that are used to control the instantaneous forces and moments on the model and its orientation. The interaction of the actuation jets with the flow over the moving model is investigated using PIV and time-resolved force measurements to assess the transitory aerodynamic loading effected by coupling between the induced motion of the aerodynamic surface and the fluid dynamics that is driven by the actuation. It is shown that these interactions can lead to effective control of the aerodynamic forces and moments, and thereby of the model's motion. Supported by ARO.
Circulation Control on Axisymmetric Bodies using Synthetic Jets
NASA Astrophysics Data System (ADS)
Rinehart, Christopher; McMichael, James; Glezer, Ari
2001-11-01
The capability of fluidic actuation based on synthetic jets to modify the apparent aerodynamic shape of lifting surfaces and thereby modify the aerodynamic forces and moments has been demonstrated in a number of earlier investigations of stalled two-dimensional airfoils (e.g., Amitay et al., AIAA J., 39, 2001). The present work is a study of the fundamental ability of synthetic jets to favorably modify the flow over axisymmetric bodies at subsonic speeds. Aft-facing synthetic jets oriented tangentially to a circular Coanda surface at the base produce effective flow turning and lift generation, with ratios of lift to average jet momentum approaching values typical of conventional jet-based circulation control on two-dimensional airfoils. The result is interesting in that the body is not designed to be a lifting surface, and the actuation is effected over only a portion of the body’s circumference. The transient and steady global flow response to the actuation is demonstrated via phase- and time-averaged velocity measurements using particle image velocimetry (PIV).
The development of an axisymmetric curved turbulent wall jet
NASA Astrophysics Data System (ADS)
Gregory-Smith, D. G.; Hawkins, M. J.
1991-12-01
An experimental study has been carried out of the low speed Coanda wall jet with both streamwise and axisymmetric curvature. A single component laser Doppler technique was used, and by taking several orientations at a given point, values of the three mean velocities and five of the six Reynolds stresses were obtained. The lateral divergence and convex streamwise curvature both enhanced the turbulence in the outer part of the jet compared with a plane two-dimensional wall jet. The inner layer exhibited a large separation of the positions of maximum velocity and zero shear stress. It was found that the streamwise mean velocity profile became established very rapidly downstream of the slot exit. The profile appeared fairly similar at later downstream positions, but the mean radial velocity and turbulence parameters showed the expected nonself preservation of the flow. Removal of the streamwise curvature resulted in a general return of the jet conditions toward those expected of a plane wall jet. The range and accuracy of the data may be used for developing turbulence models and computational techniques for this type of flow.
Roll forming technology for manufacturing axisymmetric automotive components
Syn, C.K.; Lesuer, D.R.; Bieh, T.G.; Yang, H.s.; Brown, K.R.; Kaibyshev, R.O.; Petrov, E.N.
1997-10-28
A unique roll forming technology that permits complex axisymmetric components, such as automobile wheels and turbine disks, to be formed in a single forming operation, has been developed by two Russian Institute, the Institute of Technical Physics of the Russian Federal Nuclear Center and the Institute for Metals Superplasticity Problems. This process was used to fabricate automobile wheels from a Russian AVT alloy, a 6010 aluminum alloy equivalent. The process included steps of isothermal roll forming of preforms into wheels shapes, all at 430C for the AVT alloy. The microstructure and mechanical properties were evaluated at various locations in the finished wheels by optical metallography and tensile testing at elevated temperatures. Tensile properties were obtained by stain-rate change tests and tensile tests to failure at high strain rates. Microstructure and mechanical propertied of the preforms and blanks were also evaluated. The results indicate that dynamically recovered microstructures were developed during the processing, which showed relatively high strain rate sensitivity and rendered sufficiently plasticity at the elevated temperature for wheel fabrication process.
Axisymmetric toroidal equilibrium with flow and anisotropic pressure
NASA Astrophysics Data System (ADS)
Iacono, R.; Bondeson, A.; Troyon, F.; Gruber, R.
1990-08-01
Axisymmetric toroidal plasma equilibria with mass flows and anisotropic pressure are investigated. The equilibrium system is derived for a general functional form of the pressures, which includes both fluid models, such as the magnetohydrodynamic (MHD) and the double-adiabatic models, and Grad's guiding center model [Proceedings of the Symposium on Electromagnetics and Fluid Dynamics of Gaseous Plasmas, edited by J. Fox (Polytechnic Inst. of Brooklyn, New York, 1961), p. 37]. This allows for detailed comparisons between the models and clarifies how the ``first hyperbolic region,'' occurring in fluid theory when the poloidal flow is of the order of the poloidal sound speed, can be eliminated in guiding center theory. In the case of a pure toroidal rotation, macroscopic equations of state are derived from the guiding center model, characterized by a parallel temperature that is constant on each magnetic surface and a perpendicular temperature that varies with the magnetic field. The outward centrifugal shifts of the magnetic axis and of the mass density profile, caused by toroidal rotation, are increased by anisotropy if p∥
p⊥. In the guiding center model poloidal flow produces an inward shift of the density profile, in contrast with the MHD result.
Axisymmetric Time-Dependent Computations of Expansion Tube Flow
NASA Technical Reports Server (NTRS)
Wilson, Gregory J.; Arnold, James O. (Technical Monitor)
1994-01-01
The goal of this work is to add insight about the flow within expansion tubes by using computational fluid dynamics. This is accomplished by comparing the results of axisymmetric numerical simulations with finite-rate chemistry to data from the HYPULSE expansion tube facility which was previously the NASA Langley expansion tube. The numerical simulations begin at the opening of the primary diaphragm and compute the flow throughout the whole facility and, thus, are able to follow and assess the effect of many of the flow features created during operation of the facility. One particular issue that will be investigated is the effect of boundary layer formation in the acceleration tube on the test gas volume and test gas conditions. Both laminar and turbulent boundary layers will be implemented. The effect of momentary shock reflection off the secondary diaphragm will also be investigated. There is concern that such a reflection will stagnate the test gas and create high levels of dissociated molecules. This is particularly important in propulsion experiments where a freestream composition different from flight conditions may influence ignition and burning data. Several different models of diaphragm rupture will be implemented in order to help understand the importance of this issue.
Computing Axisymmetric Jet Screech Tones using Unstructured Grids
NASA Technical Reports Server (NTRS)
Jorgenson, Philip C. E.; Loh, Ching Y.
2003-01-01
The purpose of this paper is to show that computations with an aeroacoustic feedback loop, the jet screech noise, can be obtained using truly unstructured grid technology. Numerical results are presented for a nozzle with two different lip thicknesses which will be referred to in this paper as a thin and a thick lip nozzle respectively. The space-time conservation element and solution element (CE/SE) method is used to solve the conservation laws of the compressible axisymmetric Navier-Stokes equations. The equations are time marched to predict the unsteady flow and the near-field screech tone noise issuing from an underexpanded circular jet. The CE/SE method uses an unstructured grid based data structure. The unstructured grids for these calculations are generated based on the method of Delaunay triangulation. Comparisons of numerical results with available experimental data are shown for flows corresponding to several different jet Mach numbers. Generally good agreement is obtained in terms of flow physics, screech tone frequency, and sound pressure level.
Rapid Numerical Simulation of Viscous Axisymmetric Flow Fields
NASA Technical Reports Server (NTRS)
Tweedt, Daniel L.; Chima, Rodrick V.
1995-01-01
A two-dimensional Navier-Stokes code has been developed for rapid numerical simulation of axisymmetric flow fields, including flow fields with an azimuthal velocity component. The azimuthal-invariant Navier-Stokes equations in a cylindrical coordinate system are mapped to a general body-fitted coordinate system, with the streamwise viscous terms then neglected by applying the thin-layer approximation. Turbulence effects are modeled using an algebraic model, typically the Baldwin-Lomax turbulence model, although a modified Cebeci-Smith model can also be used. The equations are discretized using central finite differences and solved using a multistage Runge-Kutta algorithm with a spatially varying time step and implicit residual smoothing. Results are presented for calculations of supersonic flow over a waisted body-of-revolution, transonic flow through a normal shock wave in a straight circular duct of constant cross sectional area, swirling supersonic (inviscid) flow through a strong shock in a straight radial duct, and swirling subsonic flow in an annular-to-circular diffuser duct. Comparisons between computed and experimental results are in fair to good agreement, demonstrating that the viscous code can be a useful tool for practical engineering design and analysis work.
Intense Flows in Librationally Driven Non-Axisymmetric Systems
NASA Astrophysics Data System (ADS)
Grannan, A. M.; Le Bars, M.; Cebron, D.; Aurnou, J. M.
2013-12-01
We present laboratory experimental results that demonstrate that librational forcing can drive intense motions of interior, low viscosity fluid layers. Longitudinal libration refers to small periodic changes in a satellite's mean rotation rate as it orbits a primary body. These libration studies are conducted using ellipsoidal acrylic containers filled with water. Particle image velocimetry (PIV) methods are used to measure the 2D velocity field in the equatorial plane over hundreds and thousands of libration cycles. In doing so we determine the coupled modes of the triadic resonance responsible for the instability that produces both intermittent and persistent turbulent motions in the bulk fluid. Additionally, we measure the amplitude and the growth rate for the instability and compare it with previous studies [1][2]. Excitation of global turbulence by librational forcing provides a mechanism for transferring rotational energy into fluid turbulence and thus may play an important role in the thermal evolution, interior dynamics, and magneto-hydrodynamics of librating bodies. [1] Cébron, D., M. Le Bars, J. Noir, J.M. Aurnou. (2012). Libration driven elliptical instability. Physics of Fluids 24, 061703. [2] Noir J., D. Cébron, M. Le Bars, A. Sauret, J.M. Aurnou (2012). Experimental study of libration-driven flows in non-axisymmetric containers, Physics of the Earth and Planetary Interiors 204-205, 1-10.
Non-axisymmetric Field Effects on Alcator C-Mod
NASA Astrophysics Data System (ADS)
Wolfe, S.; Hutchinson, I.; Granetz, R.; Rice, J.; Hubbard, A.; Irby, J.; Vieira, R.; Cochran, W.; Gwinn, D.; Rosati, J.; Lynn, A.
2003-10-01
A set of coils capable of producing non-axisymmetric, predominantly n=1, fields with different toroidal phase and a range of poloidal mode (m) spectra has been installed on Alcator C-Mod. This coilset has been used to suppress locked modes during low density or high current operation and also to induce locked modes in normally stable configurations in order to study error field effects. Locked modes are observed to result in braking of core toroidal rotation, modification of sawtooth activity, and significant reduction in energy and particle confinement. The inferred value of the threshold perturbation for producing a locked mode is of order B_21/B_T ˜ 10-4, where B_21 is the helically resonant m/n=2/1 field evaluated at the q=2 surface. This value is comparable to extrapolations based on experiments on JET and DIII-D, but is inconsistent with stronger BT and size scaling inferred from Compass-D results(R. J. Buttery, et al., 17th Fusion Energy Conference, Oct. 1998, Yokohama (IAEA-CN-69) EX8/5). The C-Mod result therefore has favorable implications for the locked mode threshold in ITER.
Axisymmetric magnetorotational instability in ideal and viscous laboratory plasmas
Mikhailovskii, A. B.; Lominadze, J. G.; Churikov, A. P.; Erokhin, N. N.; Pustovitov, V. D.; Konovalov, S. V.
2008-10-15
The original analysis of the axisymmetric magnetorotational instability (MRI) by Velikhov (Sov. Phys. JETP 9, 995 (1959)) and Chandrasekhar (Proc. Nat. Acad. Sci. 46, 253 (1960)), applied to the ideally conducting magnetized medium in the laboratory conditions and restricted to the incompressible approximation, is extended by allowing for the compressibility. Thereby, two additional driving mechanisms of MRI are revealed in addition to the standard drive due to the negative medium rotation frequency gradient (the Velikhov effect). One is due to the squared medium pressure gradient and another is a combined effect of the pressure and density gradients. For laboratory applications, the expression for the MRI boundary with all the above driving mechanisms and the stabilizing magnetoacoustic effect is derived. The effects of parallel and perpendicular viscosities on the MRI in the laboratory plasma are investigated. It is shown that, for strong viscosity, there is a family of MRI driven for the same condition as the ideal one. It is also revealed that the presence of strong viscosity leads to additional family of instabilities called the viscosity-driven MRI. Then the parallel-viscositydriven MRI looks as an overstability (oscillatory instability) possessing both the growth rate and the real part of oscillation frequency, while the perpendicular-viscosity MRI is the aperiodical instability.
Nonstationary model of an axisymmetric mirror trap with nonequilibrium plasma
NASA Astrophysics Data System (ADS)
Yurov, D. V.; Prikhodko, V. V.; Tsidulko, Yu. A.
2016-03-01
The DOL nonstationary model intended to describe plasma processes in axisymmetric magnetic mirror traps is considered. The model uses averaging over the bounce period in order to take into account the dependence of plasma parameters on the coordinate along the facility axis. Examples of calculations of trap parameters by means of the DOL code based on this model are presented. Among the features of the DOL model, one can single out two points: first, the capability of calculating the terms of the collision integral with the use of a non-Maxwellian scattering function while evaluating the distribution function of fast ions and, second, concerning the background plasma, the capability of calculating the longitudinal particle and energy fluxes in confinement modes with the particle mean free path being on the order of the trap length. The influence of the scattering function approximation used to calculate the collision integral on the solution to the kinetic equation is analyzed. The dependences of plasma parameters on the power of heating injectors and the length of the fast-ion turning zone are presented as calculation examples. The longitudinal profile of the fusion reaction rate in the case of a trap with a long fast-ion turning zone is shown to depend strongly on the input parameters of the model.
Transonic analysis and design of axisymmetric bodies in nonuniform flow
NASA Technical Reports Server (NTRS)
Chang, Jen-Fu; Lan, C. Edward
1987-01-01
An inviscid nonuniform axisymmetric transonic code was developed for applications in analysis and design. Propfan slipstream effect on pressure distribution for a body with and without sting was investigated. Results show that nonuniformity causes pressure coefficient to be more negative and shock strength to be stronger and more rearward. Sting attached to a body reduced the pressure peak and moves the rear shock forward. Extent and Mach profile shapes of the nonuniformity region appeared to have little effect on the pressure distribution. Increasing nonuniformity magnitude made pressure coefficient more negative and moved the shock rearward. Design study was conducted with the CONMIN optimizer for an ellipsoid and a body with the NACA-0012 counter. For the ellipsoid, the general trend showed that to reduce the pressure drag, the front portion of the body should be thinner and the contour of the rear portion should be flatter than the ellipsoid. For the design of a body with a sharp trailing edge in transonic flow with an initial shape given by the NACA-0012 contour, the pressure drag was reduced by decreasing the nose radius and increasing the thickness in the aft portion. Drag reduction percentages are given.
Internal performance characteristics of thrust-vectored axisymmetric ejector nozzles
NASA Technical Reports Server (NTRS)
Lamb, Milton
1995-01-01
A series of thrust-vectored axisymmetric ejector nozzles were designed and experimentally tested for internal performance and pumping characteristics at the Langley research center. This study indicated that discontinuities in the performance occurred at low primary nozzle pressure ratios and that these discontinuities were mitigated by decreasing expansion area ratio. The addition of secondary flow increased the performance of the nozzles. The mid-to-high range of secondary flow provided the most overall improvements, and the greatest improvements were seen for the largest ejector area ratio. Thrust vectoring the ejector nozzles caused a reduction in performance and discharge coefficient. With or without secondary flow, the vectored ejector nozzles produced thrust vector angles that were equivalent to or greater than the geometric turning angle. With or without secondary flow, spacing ratio (ejector passage symmetry) had little effect on performance (gross thrust ratio), discharge coefficient, or thrust vector angle. For the unvectored ejectors, a small amount of secondary flow was sufficient to reduce the pressure levels on the shroud to provide cooling, but for the vectored ejector nozzles, a larger amount of secondary air was required to reduce the pressure levels to provide cooling.
Internal performance characteristics of vectored axisymmetric ejector nozzles
NASA Technical Reports Server (NTRS)
Lamb, Milton
1993-01-01
A series of vectoring axisymmetric ejector nozzles were designed and experimentally tested for internal performance and pumping characteristics at NASA-Langley Research Center. These ejector nozzles used convergent-divergent nozzles as the primary nozzles. The model geometric variables investigated were primary nozzle throat area, primary nozzle expansion ratio, effective ejector expansion ratio (ratio of shroud exit area to primary nozzle throat area), ratio of minimum ejector area to primary nozzle throat area, ratio of ejector upper slot height to lower slot height (measured on the vertical centerline), and thrust vector angle. The primary nozzle pressure ratio was varied from 2.0 to 10.0 depending upon primary nozzle throat area. The corrected ejector-to-primary nozzle weight-flow ratio was varied from 0 (no secondary flow) to approximately 0.21 (21 percent of primary weight-flow rate) depending on ejector nozzle configuration. In addition to the internal performance and pumping characteristics, static pressures were obtained on the shroud walls.
Computational Study of Axisymmetric Off-Design Nozzle Flows
NASA Technical Reports Server (NTRS)
DalBello, Teryn; Georgiadis, Nicholas; Yoder, Dennis; Keith, Theo
2003-01-01
Computational Fluid Dynamics (CFD) analyses of axisymmetric circular-arc boattail nozzles operating off-design at transonic Mach numbers have been completed. These computations span the very difficult transonic flight regime with shock-induced separations and strong adverse pressure gradients. External afterbody and internal nozzle pressure distributions computed with the Wind code are compared with experimental data. A range of turbulence models were examined, including the Explicit Algebraic Stress model. Computations have been completed at freestream Mach numbers of 0.9 and 1.2, and nozzle pressure ratios (NPR) of 4 and 6. Calculations completed with variable time-stepping (steady-state) did not converge to a true steady-state solution. Calculations obtained using constant timestepping (timeaccurate) indicate less variations in flow properties compared with steady-state solutions. This failure to converge to a steady-state solution was the result of using variable time-stepping with large-scale separations present in the flow. Nevertheless, time-averaged boattail surface pressure coefficient and internal nozzle pressures show reasonable agreement with experimental data. The SST turbulence model demonstrates the best overall agreement with experimental data.
Axisymmetric viscous gravity currents flowing over a deep porous medium
NASA Astrophysics Data System (ADS)
Spannuth, Melissa; Neufeld, Jerome; Wettlaufer, John S.; Grae Worster, M.
2006-11-01
When a viscous fluid flows over a porous substrate, it not only spreads but also seeps into the underlying medium. Such flows have relevance to the design of shingle beds for use as safety features around storage facilities of dense fluids and to flow through fissures in porous rocks. Whereas previous investigations have been confined to two-dimensional flows of fixed volume, we have investigated currents fed by a constant fluid flux flowing axisymmetrically over a deep porous bed. Our experimental system consisted of glycerin spreading over monodisperse glass spheres of known permeability and the data were analyzed using scaling analyses. We have also solved a mathematical model using the well-known equations for a viscous gravity current spreading due to the slope of its free surface augmented by a simple draining law. Its predictions agree well with our experimental results and quantify, in particular, the maximum distance to which the current spreads as a function of the material and input properties.
Geometry for the Secondary School
ERIC Educational Resources Information Center
Moalem, D.
1977-01-01
A sequential but non-axiomatic high school geometry course which includes Euclidean, transformation, and analytic geometry and vectors and matrices, and emphasizes the invariance property of transformations, is outlined. Sample problems, solutions, and comments are included. (MN)
NASA Astrophysics Data System (ADS)
Stee, Ph.; Delaa, O.; Monnier, J. D.; Meilland, A.; Perraut, K.; Mourard, D.; Che, X.; Schaefer, G. H.; Pedretti, E.; Smith, M. A.; Lopes de Oliveira, R.; Motch, C.; Henry, G. W.; Richardson, N. D.; Bjorkman, K. S.; Bücke, R.; Pollmann, E.; Zorec, J.; Gies, D. R.; ten Brummelaar, T.; McAlister, H. A.; Turner, N. H.; Sturmann, J.; Sturmann, L.; Ridgway, S. T.
2012-09-01
Context.γ Cas is thought to be the prototype of classical Be stars and is the most studied object among this group. However, as for all Be stars, the origin and the physics of its circumstellar disk responsible for the observed near IR-excess, emission lines, and peculiar X-ray emission is still being debated. Aims: We constrain the geometry and kinematics of its circumstellar disk from the highest spatial resolution ever achieved on this star. This investigation is a part of a large multi-technique observing campaign to obtain the most complete picture of γ Cas which emphasizes the relation of the circumstellar environment to the star's X-ray flux. Methods: We present new observations in the near infrared (MIRC) and in the visible (VEGA) obtained with the CHARA interferometer. The VEGA instrument allows us to not only obtain a global disk geometry but also spectrally dispersed visibility modulus and phases within the Hα emission line, which enables us to study the kinematics within γ Cas's disk. Results: We obtain a disk extension in the nearby Hα continuum of 1.72 stellar diameter and 1.86 stellar diameter in the H band at 1.65 μm assuming a Gaussian disk model but also compatible with an elliptical ring model with a minor internal diameter of 1.38 stellar diameter in H. For the first time we demonstrate that the rotation mapped by the emission in the Hα line within the disk of γ Cas and up to 10 R⋆ is Keplerian. Conclusions: These observations have pushed the size of the disk to greater proportions. γ Cas was also confirmed to be a nearly critical rotator. The disk imaging gives neither indication of a 1-arm spiral feature nor evidence of a secondary star reinforcing the interpretation that the secondary is certainly a low-mass and low-luminosity star or a degenerate companion.
Computer-Aided Geometry Modeling
NASA Technical Reports Server (NTRS)
Shoosmith, J. N. (Compiler); Fulton, R. E. (Compiler)
1984-01-01
Techniques in computer-aided geometry modeling and their application are addressed. Mathematical modeling, solid geometry models, management of geometric data, development of geometry standards, and interactive and graphic procedures are discussed. The applications include aeronautical and aerospace structures design, fluid flow modeling, and gas turbine design.
Teaching of Geometry in Bulgaria
ERIC Educational Resources Information Center
Bankov, Kiril
2013-01-01
Geometry plays an important role in the school mathematics curriculum all around the world. Teaching of geometry varies a lot (Hoyls, Foxman, & Kuchemann, 2001). Many countries revise the objectives, the content, and the approaches to the geometry in school. Studies of the processes show that there are not common trends of these changes…
NASA Astrophysics Data System (ADS)
Fiedler, Robert A.; Mouschovias, Telemachos Ch.
1993-10-01
The problem of the formation and contraction of fragments (or cores) in magnetically supported parent molecular clouds was formulated in a previous paper. Three dimensionless free parameters appear in the evolution equations: the initial ratio of the free-fall and neutral-ion collision times (in the uniform reference state), νff,0, the exponent κ in the relation between the ion and neutral densities ni ∝ nkn, and the initial ratio of the magnetic and thermal pressures, α0. The initial central mass-to-flux ratio in units of the critical value for gravitational collapse, μ0 enters through the initial conditions. We follow both the quasistatic and dynamic phases of contraction and demonstrate that ambipolar diffusion leads to self-initiated protostar formation ("quasistatic" meaning motion with negligible acceleration). A typical cloud core forms and contracts quasi- statically on the flux-loss time scale until the central mass-to-flux ratio (dM/dΦB)c exceeds the critical value. During quasistatic contraction, the magnetic field lines are essentially "held in place" as the neutrals contract through them, and the field strength increases by less than a factor of 2. Despite subsequent dynamic contraction perpendicular to magnetic field lines, thermal pressure continues to balance gravity along field lines, thereby enforcing quasistatic contraction in this direction. We follow the contraction until the central density nc increases by a factor of 106 (typically from 3 × 102 to 3 × 108 cm-3). The envelope remains magnetically supported. The results from our parameter study show that decreasing νff,0 speeds up ambipolar diffusion, shortens the quasistatic phase of contraction, and causes (dM/dΦB)c to increase by a greater amount above the critical value. The enhancement of the central magnetic field Bc, however, is not sensitive to the value of νff,0. A smaller κ leads to progressively more rapid ambipolar diffusion as nc increases. Reducing μ0 lengthens the duration of the quasistatic phase and results in a larger reduction of a core's magnetic flux, but the dynamic phase of contraction is independent of μ0. The value of (dM/dΦB)c in our models is initially 1.9-16.3 times smaller than the critical value, but increases (because of ambipolar diffusion) by a factor of 10-50 by the time nc has increased by a factor ≡106. The value of α0 mainly affects the relaxation of clouds from their initial states into the corresponding equilibrium states under flux-freezing, in which α is related to μ0 by αc,eqμ20 ≍ constant.
Kinetic extensions of magnetohydrodynamic models for axisymmetric toroidal plasmas
Cheng, C.Z.
1989-04-01
A nonvariational kinetic-MHD stability code (NOVA-K) has been developed to integrate a set of non-Hermitian integro-differential eigenmode equations due to energetic particles for axisymmetric toroidal plasmas in a general flux coordinate system with an arbitrary Jacobian. The NOVA-K code employs the Galerkin method involving Fourier expansions in the generalized poloidal angle theta and generalized toroidal angle /zeta/ directions, and cubic-B spline finite elements in the radial /Psi/ direction. Extensive comparisons with the existing variational ideal MHD codes show that the ideal MHD version of the NOVA-K code converges faster and gives more accurate results. The NOVA-K code is employed to study the effects of energetic particles on MHD-type modes: the stabilization of ideal MHD internal kink modes and the excitation of ''fishbone'' internal kink modes; and the alpha particle destabilization of toroidicity-induced Alfven eigenmodes (TAE) via transit resonances. Analytical theories are also presented to help explain the NOVA-K results. For energetic trapped particles generated by neutral beam injection (NBI) or ion cyclotron resonant heating (ICRH), a stability window for the n = 1 internal kink mode in the hot particle beta space exists even in the absence of the core ion finite Larmor radius effect. On the other hand, the trapped alpha particles are found to have negligible effects on the stability of the n = 1 internal kink mode, but the circulating alpha particles can strongly destabilize TAE modes via inverse Landau damping associated with the spatial gradient of the alpha particle pressure. 60 refs., 24 figs., 1 tab.
Theoretical issues on the spontaneous rotation of axisymmetric plasmas
NASA Astrophysics Data System (ADS)
Coppi, B.; Zhou, T.
2014-09-01
An extensive series of experiments have confirmed that the observed ‘spontaneous rotation’ phenomenon in axisymmetric plasmas is related to the confinement properties of these plasmas and connected to the excitation of collective modes associated with these properties (Coppi 2000 18th IAEA Fusion Energy Conf. (Sorrento, Italy, 2000) THP 1/17, www-pub.iaea.org/MTCD/publications/PDF/csp_008c/html/node343.htm and Coppi 2002 Nucl. Fusion 42 1). In particular, radially localized modes can extract angular momentum from the plasma column from which they grow while the background plasma has to recoil in the direction opposite to that of the mode phase velocity. In the case of the excitation of the plasma modes at the edge, the loss of their angular momentum can be connected to the directed particle ejection to the surrounding medium. The recoil angular momentum is then redistributed inside the plasma column mainly by the combination of an effective viscous diffusion and an inward angular momentum transport velocity that is connected, for instance, to ion temperature gradient (ITG) driven modes. The linear and quasi-linear theories of the collisionless trapped electron modes and of the toroidal ITG driven modes are re-examined in the context of their influence on angular momentum transport. Internal modes that produce magnetic reconnection and are electromagnetic in nature, acquire characteristic phase velocity directions in high temperature regimes and become relevant to the ‘generation’ of angular momentum. The drift-tearing mode, the ‘complex’ reconnecting mode and the m0 = 1 internal mode belong to this category, the last mode acquiring different features depending on the strength of its driving factor. Toroidal velocity profiles that reproduce the experimental observations are obtained considering a global angular momentum balance equation that includes the localized sources associated with the excited internal electrostatic and electromagnetic modes
Axisymmetric oscillation modes of a double droplet system
Ramalingam, Santhosh K.; Basaran, Osman A.
2010-11-15
A double droplet system (DDS) consists of a sessile and a pendant drop that are coupled through a liquid filled cylindrical hole in a plate of thickness d. For a small hole radius R, equilibrium shapes of both drops are sections of spheres. While DDSs have a number of applications in microfluidics, a DDS oscillating about its equilibrium state can be used as a fast focusing liquid lens. Here, a DDS consisting of an isothermal, incompressible Newtonian fluid of constant density p and constant viscosity u that is surrounded by a gas is excited by oscillating in time (a) themore » pressure in the gas surrounding either drop (pressure excitation), (b) the plate perpendicular to its plane (axial excitation), and (c) the hole radius (radial excitation). In contrast to previous works that assumed transient drop shapes are spherical, they are determined here by simulation and used to identify the natural modes of axisymmetric oscillations from resonances observed during frequency sweeps with DDSs for which the combined volume V of the two drops is less than (4/3)πR3. Pressure and axial excitations are found to have identical responses but axial and radial excitations are shown to excite different modes. These modes are compared to those exhibited by single pendant (sessile) drop systems. Specifically, while a single pendant (sessile) drop has one additional oscillation mode compared to a free drop, a DDS is found to exhibit roughly twice as many oscillation modes as a pendant (sessile) drop. The effects of dimensionless volume V/R3, dimensionless plate thickness d/R, and Ohnesorge number Oh =μ/√ρRσ , where σ is the surface tension of the DDS-gas interface, on the resonance frequencies are also investigated.« less
Axisymmetric oscillation modes of a double droplet system
Ramalingam, Santhosh K.; Basaran, Osman A.
2010-11-15
A double droplet system (DDS) consists of a sessile and a pendant drop that are coupled through a liquid filled cylindrical hole in a plate of thickness d. For a small hole radius R, equilibrium shapes of both drops are sections of spheres. While DDSs have a number of applications in microfluidics, a DDS oscillating about its equilibrium state can be used as a fast focusing liquid lens. Here, a DDS consisting of an isothermal, incompressible Newtonian fluid of constant density p and constant viscosity u that is surrounded by a gas is excited by oscillating in time (a) the pressure in the gas surrounding either drop (pressure excitation), (b) the plate perpendicular to its plane (axial excitation), and (c) the hole radius (radial excitation). In contrast to previous works that assumed transient drop shapes are spherical, they are determined here by simulation and used to identify the natural modes of axisymmetric oscillations from resonances observed during frequency sweeps with DDSs for which the combined volume V of the two drops is less than (4/3)πR^{3}. Pressure and axial excitations are found to have identical responses but axial and radial excitations are shown to excite different modes. These modes are compared to those exhibited by single pendant (sessile) drop systems. Specifically, while a single pendant (sessile) drop has one additional oscillation mode compared to a free drop, a DDS is found to exhibit roughly twice as many oscillation modes as a pendant (sessile) drop. The effects of dimensionless volume V/R^{3}, dimensionless plate thickness d/R, and Ohnesorge number Oh =μ/√ρRσ , where σ is the surface tension of the DDS-gas interface, on the resonance frequencies are also investigated.
NASA Astrophysics Data System (ADS)
Bengtsson, Ingemar; Zyczkowski, Karol
2006-05-01
Quantum information theory is at the frontiers of physics, mathematics and information science, offering a variety of solutions that are impossible using classical theory. This book provides an introduction to the key concepts used in processing quantum information and reveals that quantum mechanics is a generalisation of classical probability theory. After a gentle introduction to the necessary mathematics the authors describe the geometry of quantum state spaces. Focusing on finite dimensional Hilbert spaces, they discuss the statistical distance measures and entropies used in quantum theory. The final part of the book is devoted to quantum entanglement - a non-intuitive phenomenon discovered by Schrödinger, which has become a key resource for quantum computation. This richly-illustrated book is useful to a broad audience of graduates and researchers interested in quantum information theory. Exercises follow each chapter, with hints and answers supplied. The first book to focus on the geometry of quantum states Stresses the similarities and differences between classical and quantum theory Uses a non-technical style and numerous figures to make the book accessible to non-specialists
Computer Aided Process Planning for Non-Axisymmetric Deep Drawing Products
NASA Astrophysics Data System (ADS)
Park, Dong Hwan; Yarlagadda, Prasad K. D. V.
2004-06-01
In general, deep drawing products have various cross-section shapes such as cylindrical, rectangular and non-axisymmetric shapes. The application of the surface area calculation to non-axisymmetric deep drawing process has not been published yet. In this research, a surface area calculation for non-axisymmetric deep drawing products with elliptical shape was constructed for a design of blank shape of deep drawing products by using an AutoLISP function of AutoCAD software. A computer-aided process planning (CAPP) system for rotationally symmetric deep drawing products has been developed. However, the application of the system to non-axisymmetric components has not been reported yet. Thus, the CAPP system for non-axisymmetric deep drawing products with elliptical shape was constructed by using process sequence design. The system developed in this work consists of four modules. The first is recognition of shape module to recognize non-axisymmetric products. The second is a three-dimensional (3-D) modeling module to calculate the surface area for non-axisymmetric products. The third is a blank design module to create an oval-shaped blank with the identical surface area. The forth is a process planning module based on the production rules that play the best important role in an expert system for manufacturing. The production rules are generated and upgraded by interviewing field engineers. Especially, the drawing coefficient, the punch and die radii for elliptical shape products are considered as main design parameters. The suitability of this system was verified by applying to a real deep drawing product. This CAPP system constructed would be very useful to reduce lead-time for manufacturing and improve an accuracy of products.
NASA Technical Reports Server (NTRS)
Zoby, E. V.; Graves, R. A., Jr.
1973-01-01
A method for the rapid calculation of the inviscid shock layer about blunt axisymmetric bodies at an angle of attack of 0 deg has been developed. The procedure is of an inverse nature, that is, a shock wave is assumed and calculations proceed along rays normal to the shock. The solution is iterated until the given body is computed. The flow field solution procedure is programed at the Langley Research Center for the Control Data 6600 computer. The geometries specified in the program are sphores, ellipsoids, paraboloids, and hyperboloids which may conical afterbodies. The normal momentum equation is replaced with an approximate algebraic expression. This simplification significantly reduces machine computation time. Comparisons of the present results with shock shapes and surface pressure distributions obtained by the more exact methods indicate that the program provides reasonably accurate results for smooth bodies in axisymmetric flow. However, further research is required to establish the proper approximate form of the normal momentum equation for the two-dimensional case.
Jet mixing into a heated cross flow in a cylindrical duct: Influence of geometry and flow variations
NASA Technical Reports Server (NTRS)
Hatch, M. S.; Sowa, W. A.; Samuelsen, G. S.; Holdeman, J. D.
1992-01-01
To examine the mixing characteristics of jets in an axi-symmetric can geometry, temperature measurements were obtained downstream of a row of cold jets injected into a heated cross stream. Parametric, non-reacting experiments were conducted to determine the influence of geometry and flow variations on mixing patterns in a cylindrical configuration. Results show that jet to mainstream momentum flux ratio and orifice geometry significantly impact the mixing characteristics of jets in a can geometry. For a fixed number of orifices, the coupling between momentum flux ratio and injector determines (1) the degree of jet penetration at the injection plane, and (2) the extent of circumferential mixing downstream of the injection plane. The results also show that, at a fixed momentum flux ratio, jet penetration decreases with (1) an increase in slanted slot aspect ratio, and (2) an increase in the angle of the slots with respect to the mainstream direction.
Large Deformation and Adhesive Contact Studies of Axisymmetric Membranes
Laprade, Evan J.; Long, Rong; Pham, Jonathan; Lawrence, Jimmy; Emrick, Todd; Crosby, Alfred; Hui, Chung-Yuen; Shull, Kenneth R.
2013-01-01
A model membrane contact system consisting of an acrylic copolymer membrane and polydimethyl-siloxane substrate was utilized to evaluate a recently developed nonlinear large-deformation adhesive contact analysis. Direct measurements of the local membrane apex strain during non-contact inflation indicated that the neo-Hookean model provides an accurate measure of membrane strain and supports its use as the strain energy function for the analysis. A time dependent modulus emerges from the analysis, with principal tensions obtained from a comparison of predicted and experimental membrane profiles. A displacement controlled geometry was more easily modeled than the pressure controlled geometry, the applicability of the analysis was limited by wrinkling instabilities. The substantial viscoelastic behavior of these membranes made it difficult to describe the entire membrane with a single modulus, given the nonuniform deformation history of the membranes. Given the difficulty in determining membrane tension from the measured pressure and profile fits using the model, the peel energy was used as a simpler measure of adhesion. Using an analytical balance in the displacement controlled geometry, the membrane tension at the contact line was directly measured. Coupled with contact angle imaging, the peel energy was determined. For the model membranes studied, this peel energy described the membrane/substrate adhesive interactions quite well, giving well-defined peel energies that were independent of the detailed strain state of the membrane. PMID:23289644
Correa, Diego H.; Silva, Guillermo A.
2008-07-28
We discuss how geometrical and topological aspects of certain (1/2)-BPS type IIB geometries are captured by their dual operators in N = 4 Super Yang-Mills theory. The type IIB solutions are characterized by arbitrary droplet pictures in a plane and we consider, in particular, axially symmetric droplets. The 1-loop anomalous dimension of the dual gauge theory operators probed with single traces is described by some bosonic lattice Hamiltonians. These Hamiltonians are shown to encode the topology of the droplets. In appropriate BMN limits, the Hamiltonians spectrum reproduces the spectrum of near-BPS string excitations propagating along each of the individual edges of the droplet. We also study semiclassical regimes for the Hamiltonians. For droplets having disconnected constituents, the Hamiltonian admits different complimentary semiclassical descriptions, each one replicating the semiclassical description for closed strings extending in each of the constituents.
Critique of information geometry
Skilling, John
2014-12-05
As applied to probability, information geometry fails because probability distributions do not form a metric space. Probability theory rests on a compelling foundation of elementary symmetries, which also support information (aka minus entropy, Kullback-Leibler) H(p;q) as the unique measure of divergence from source probability distribution q to destination p. Because the only compatible connective H is from≠to asymmetric, H(p;q)≠H(q;p), there can be no compatible geometrical distance (which would necessarily be from=to symmetric). Hence there is no distance relationship compatible with the structure of probability theory. Metrics g and densities sqrt(det(g)) interpreted as prior probabilities follow from the definition of distance, and must fail likewise. Various metrics and corresponding priors have been proposed, Fisher's being the most popular, but all must behave unacceptably. This is illustrated with simple counter-examples.
Optically defined mechanical geometry
NASA Astrophysics Data System (ADS)
Barasheed, Abeer Z.; Müller, Tina; Sankey, Jack C.
2016-05-01
In the field of optomechanics, radiation forces have provided a particularly high level of control over the frequency and dissipation of mechanical elements. Here we propose a class of optomechanical systems in which light exerts a similarly profound influence over two other fundamental parameters: geometry and mass. By applying an optical trap to one lattice site of an extended phononic crystal, we show it is possible to create a tunable, localized mechanical mode. Owing to light's simultaneous and constructive coupling with the structure's continuum of modes, we estimate that a trap power at the level of a single intracavity photon should be capable of producing a significant effect within a realistic, chip-scale device.
Magnetism in curved geometries
NASA Astrophysics Data System (ADS)
Streubel, Robert; Fischer, Peter; Kronast, Florian; Kravchuk, Volodymyr P.; Sheka, Denis D.; Gaididei, Yuri; Schmidt, Oliver G.; Makarov, Denys
2016-09-01
Extending planar two-dimensional structures into the three-dimensional space has become a general trend in multiple disciplines, including electronics, photonics, plasmonics and magnetics. This approach provides means to modify conventional or to launch novel functionalities by tailoring the geometry of an object, e.g. its local curvature. In a generic electronic system, curvature results in the appearance of scalar and vector geometric potentials inducing anisotropic and chiral effects. In the specific case of magnetism, even in the simplest case of a curved anisotropic Heisenberg magnet, the curvilinear geometry manifests two exchange-driven interactions, namely effective anisotropy and antisymmetric exchange, i.e. Dzyaloshinskii–Moriya-like interaction. As a consequence, a family of novel curvature-driven effects emerges, which includes magnetochiral effects and topologically induced magnetization patterning, resulting in theoretically predicted unlimited domain wall velocities, chirality symmetry breaking and Cherenkov-like effects for magnons. The broad range of altered physical properties makes these curved architectures appealing in view of fundamental research on e.g. skyrmionic systems, magnonic crystals or exotic spin configurations. In addition to these rich physics, the application potential of three-dimensionally shaped objects is currently being explored as magnetic field sensorics for magnetofluidic applications, spin-wave filters, advanced magneto-encephalography devices for diagnosis of epilepsy or for energy-efficient racetrack memory devices. These recent developments ranging from theoretical predictions over fabrication of three-dimensionally curved magnetic thin films, hollow cylinders or wires, to their characterization using integral means as well as the development of advanced tomography approaches are in the focus of this review.
Magnetism in curved geometries
NASA Astrophysics Data System (ADS)
Streubel, Robert; Fischer, Peter; Kronast, Florian; Kravchuk, Volodymyr P.; Sheka, Denis D.; Gaididei, Yuri; Schmidt, Oliver G.; Makarov, Denys
2016-09-01
Extending planar two-dimensional structures into the three-dimensional space has become a general trend in multiple disciplines, including electronics, photonics, plasmonics and magnetics. This approach provides means to modify conventional or to launch novel functionalities by tailoring the geometry of an object, e.g. its local curvature. In a generic electronic system, curvature results in the appearance of scalar and vector geometric potentials inducing anisotropic and chiral effects. In the specific case of magnetism, even in the simplest case of a curved anisotropic Heisenberg magnet, the curvilinear geometry manifests two exchange-driven interactions, namely effective anisotropy and antisymmetric exchange, i.e. Dzyaloshinskii-Moriya-like interaction. As a consequence, a family of novel curvature-driven effects emerges, which includes magnetochiral effects and topologically induced magnetization patterning, resulting in theoretically predicted unlimited domain wall velocities, chirality symmetry breaking and Cherenkov-like effects for magnons. The broad range of altered physical properties makes these curved architectures appealing in view of fundamental research on e.g. skyrmionic systems, magnonic crystals or exotic spin configurations. In addition to these rich physics, the application potential of three-dimensionally shaped objects is currently being explored as magnetic field sensorics for magnetofluidic applications, spin-wave filters, advanced magneto-encephalography devices for diagnosis of epilepsy or for energy-efficient racetrack memory devices. These recent developments ranging from theoretical predictions over fabrication of three-dimensionally curved magnetic thin films, hollow cylinders or wires, to their characterization using integral means as well as the development of advanced tomography approaches are in the focus of this review.
A variational principle for the axisymmetric stability of rotating relativistic stars
NASA Astrophysics Data System (ADS)
Prabhu, Kartik; Schiffrin, Joshua S.; Wald, Robert M.
2016-09-01
It is well known that all rotating perfect fluid stars in general relativity are unstable to certain non-axisymmetric perturbations via the Chandrasekhar-Friedman-Schutz (CFS) instability. However, the mechanism of the CFS instability requires, in an essential way, the loss of angular momentum by gravitational radiation and, in many instances, it acts on too long a timescale to be physically/astrophysically relevant. It is therefore of interest to examine the stability of rotating, relativistic stars to axisymmetric perturbations, where the CFS instability does not occur. In this paper, we provide a Rayleigh-Ritz-type variational principle for testing the stability of perfect fluid stars to axisymmetric perturbations, which generalizes to axisymmetric perturbations of rotating stars a variational principle given by Chandrasekhar for spherical perturbations of static, spherical stars. Our variational principle provides a lower bound to the rate of exponential growth in the case of instability. The derivation closely parallels the derivation of a recently obtained variational principle for analyzing the axisymmetric stability of black holes.
Subsonic Euler Flows with Large Vorticity Through an Infinitely Long Axisymmetric Nozzle
NASA Astrophysics Data System (ADS)
Du, Lili; Duan, Ben
2016-04-01
This paper is a sequel to the earlier work Du and Duan (J Diff Equ 250:813-847, 2011) on well-posedness of steady subsonic Euler flows through infinitely long three-dimensional axisymmetric nozzles. In Du and Duan (J Diff Equ 250:813-847, 2011), the authors showed the existence and uniqueness of the global subsonic Euler flows through an infinitely long axisymmetric nozzle, when the variation of Bernoulli's function in the upstream is sufficiently small and the mass flux of the incoming flow is less than some critical value. The smallness of the variation of Bernoulli's function in the upstream prevents the attendance of the possible singularity in the nozzles, however, at the same time it also leads that the vorticity of the ideal flow is sufficiently small in the whole nozzle and the flows are indeed adjacent to axisymmetric potential flows. The purpose of this paper is to investigate the effects of the vorticity for the smooth subsonic ideal flows in infinitely long axisymmetric nozzles. We modify the formulation of the problem in the previous work Du and Duan (J Diff Equ 250:813-847, 2011) and the existence and uniqueness results on the smooth subsonic ideal polytropic flows in infinitely long axisymmetric nozzles without the restriction on the smallness of the vorticity are shown in this paper.
Subsonic Euler Flows with Large Vorticity Through an Infinitely Long Axisymmetric Nozzle
NASA Astrophysics Data System (ADS)
Du, Lili; Duan, Ben
2016-09-01
This paper is a sequel to the earlier work Du and Duan (J Diff Equ 250:813-847, 2011) on well-posedness of steady subsonic Euler flows through infinitely long three-dimensional axisymmetric nozzles. In Du and Duan (J Diff Equ 250:813-847, 2011), the authors showed the existence and uniqueness of the global subsonic Euler flows through an infinitely long axisymmetric nozzle, when the variation of Bernoulli's function in the upstream is sufficiently small and the mass flux of the incoming flow is less than some critical value. The smallness of the variation of Bernoulli's function in the upstream prevents the attendance of the possible singularity in the nozzles, however, at the same time it also leads that the vorticity of the ideal flow is sufficiently small in the whole nozzle and the flows are indeed adjacent to axisymmetric potential flows. The purpose of this paper is to investigate the effects of the vorticity for the smooth subsonic ideal flows in infinitely long axisymmetric nozzles. We modify the formulation of the problem in the previous work Du and Duan (J Diff Equ 250:813-847, 2011) and the existence and uniqueness results on the smooth subsonic ideal polytropic flows in infinitely long axisymmetric nozzles without the restriction on the smallness of the vorticity are shown in this paper.
A variational principle for the axisymmetric stability of rotating relativistic stars
NASA Astrophysics Data System (ADS)
Prabhu, Kartik; Schiffrin, Joshua S.; Wald, Robert M.
2016-09-01
It is well known that all rotating perfect fluid stars in general relativity are unstable to certain non-axisymmetric perturbations via the Chandrasekhar–Friedman–Schutz (CFS) instability. However, the mechanism of the CFS instability requires, in an essential way, the loss of angular momentum by gravitational radiation and, in many instances, it acts on too long a timescale to be physically/astrophysically relevant. It is therefore of interest to examine the stability of rotating, relativistic stars to axisymmetric perturbations, where the CFS instability does not occur. In this paper, we provide a Rayleigh–Ritz-type variational principle for testing the stability of perfect fluid stars to axisymmetric perturbations, which generalizes to axisymmetric perturbations of rotating stars a variational principle given by Chandrasekhar for spherical perturbations of static, spherical stars. Our variational principle provides a lower bound to the rate of exponential growth in the case of instability. The derivation closely parallels the derivation of a recently obtained variational principle for analyzing the axisymmetric stability of black holes.
Axisymmetric modes in vertically stratified self-gravitating discs
NASA Astrophysics Data System (ADS)
Mamatsashvili, G. R.; Rice, W. K. M.
2010-08-01
We carry out a linear analysis of the vertical normal modes of axisymmetric perturbations in stratified, compressible, self-gravitating gaseous discs in the shearing-box approximation. An unperturbed disc has a polytropic vertical structure that allows us to study specific dynamics for subadiabatic, adiabatic and superadiabatic vertical stratifications, by simply varying the polytropic index. In the absence of self-gravity, four well-known principal modes can be identified in a stratified disc: acoustic p modes, surface gravity f modes, buoyancy g modes and inertial r modes. After classifying and characterizing modes in the non-self-gravitating case, we include self-gravity in the perturbation equations and in the equilibrium and investigate how it modifies the properties of these four modes. We find that self-gravity, to a certain degree, reduces their frequencies and changes the structure of the dispersion curves and eigenfunctions at radial wavelengths comparable to the disc height. Its influence on the basic branch of the r mode, in the case of subadiabatic and adiabatic stratifications, and on the basic branch of the g mode, in the case of superadiabatic stratification (which in addition exhibits convective instability), does appear to be strongest. Reducing the 3D Toomre's parameter Q3D results in the latter modes becoming unstable due to self-gravity, so that they determine the onset criterion and nature of the gravitational instability of a vertically stratified disc. By contrast, the p, f and convectively stable g modes, although their corresponding ω2 are reduced by self-gravity, never become unstable however small the value of Q3D. This is a consequence of the three dimensionality of the disc. The eigenfunctions corresponding to the gravitationally unstable modes are intrinsically three dimensional. We also contrast the more exact instability criterion based on our 3D model with that of density waves in 2D (razor-thin) discs. Based on these findings, we
NASA Astrophysics Data System (ADS)
Khavaran, A.; Krejsa, E. A.; Kim, C. M.
1992-01-01
The turbulent mixing noise of a supersonic jet is calculated for a round convergent-divergent nozzle at the design pressure ratio. Aerodynamic computations are performed using the PARC code with a k-epsilon turbulence model. Lighthill's acoustic analogy combined with Ribner's assumption is adopted. The acoustics solution is based upon the methodology followed by GE in the MGB code. The source correlation function is expressed as a linear combination of second-order tensors. Assuming separable second-order correlations and incorporating Batchelor's isotropic turbulence model, the source term was calculated from the kinetic energy of turbulence. A Gaussian distribution for the time-delay of correlation was introduced. The computational fluid dynamics (CFD) solution was used to obtain the source strength as well as the characteristic time-delay of correlation. The effect of sound/flow interaction was incorporated using the high frequency asymptotic solution to Lilley's equation for axisymmetric geometries. Acoustic results include sound pressure level directivity and spectra at different polar angles. The aerodynamic and acoustic results demonstrate favorable agreement with experimental data.
NASA Astrophysics Data System (ADS)
Khavaran, Abbas; Krejsa, Eugene A.; Kim, Chan M.
1991-01-01
The turbulent mixing noise of a supersonic jet is calculated for a round convergent-divergent nozzle at the design pressure ratio. Aerodynamic computations are performed using the PARC code with a k-epsilon turbulence model. Lighthill's acoustic analogy combined with Ribner's assumption is adopted. The acoustics solution is based upon the methodology followed by GE in the MGB code. The source correlation function is expressed as a linear combination of second-order tensors. Assuming separable second-order correlations and incorporating Batchelor's isotropic turbulence model, the source term was calculated from the kinetic energy of turbulence. A Gaussian distribution for the time-delay of correlation was introduced. The computational fluid dynamics (CFD) solution was used to obtain the source strength as well as the characteristic time-delay of correlation. The effect of sound/flow interaction was incorporated using the high frequency asymptotic solution to Lilley's equation for axisymmetric geometries. Acoustic results include sound pressure level directivity and spectra at different polar angles. The aerodynamic and acoustic results demonstrate favorable agreement with experimental data.
RAXJET- TRANSONIC, AXISYMMETRIC FLOW OVER NOZZLE AFTERBODIES WITH SUPERSONIC JET EXHAUSTS
NASA Technical Reports Server (NTRS)
Wilmoth, R. G.
1994-01-01
The nozzle afterbody is one of the main drag-producing components of an aircraft propulsion system. Thus, considerable effort has been devoted to developing techniques for predicting the afterbody flow field and drag. The RAXJET computer program was developed to predict the transonic, axisymmetric flow over nozzle afterbodies with supersonic jet exhausts and includes the effects of boundary-layer displacement, separation, jet entrainment, and inviscid jet plume blockage. RAXJET iteratively combines the South-Jameson relaxation procedure, the Reshotko-Tucker boundary-layer solution, the Presz separation model, the Dash-Pergament mixing model, and the Dash-Thorpe inviscid plume model into a single, comprehensive model. The approach taken in the RAXJET program requires considerably less computational time than the Navier-Stokes solutions and generally yields results of comparable accuracy. In RAXJET, the viscous-inviscid interaction model is constructed by dividing the afterbody flow field into six separate computational regions: (1) The inviscid external flow solution is based on the relaxation procedure of South and Jameson for solving the exact nonlinear potential flow equation in nonconservative form. (2) The flow field in the inviscid jet exhaust is solved by explicit spatial marching of the conservative finite-difference form of the inviscid flow equations for a uniform composition gas mixture. (3) The properties in the attached boundary-layer region are solved by a modified version of the Reshotko-Tucker integral method for turbulent flows. (4) The analysis of the separated flow region consists of predicting the separation location and calculating the discriminating streamline shape. (5) The jet wake region is determined by either a simple extrapolation model or by an integral method that accounts for entrainment effects. (6) The displacement-thickness distribution arising from entrainment into the jet mixing layer is calculated by the overlaid mixing model
Vorticity dynamics of a bileaflet mechanical heart valve in an axisymmetric aorta
NASA Astrophysics Data System (ADS)
Dasi, L. P.; Ge, L.; Simon, H. A.; Sotiropoulos, F.; Yoganathan, A. P.
2007-06-01
We present comprehensive particle image velocimetry measurements and direct numerical simulation (DNS) of physiological, pulsatile flow through a clinical quality bileaflet mechanical heart valve mounted in an idealized axisymmetric aorta geometry with a sudden expansion modeling the aortic sinus region. Instantaneous and ensemble-averaged velocity measurements as well as the associated statistics of leaflet kinematics are reported and analyzed in tandem to elucidate the structure of the velocity and vorticity fields of the ensuing flow-structure interaction. The measurements reveal that during the first half of the acceleration phase, the flow is laminar and repeatable from cycle to cycle. The valve housing shear layer rolls up into the sinus and begins to extract vorticity of opposite sign from the sinus wall. A start-up vortical structure is shed from the leaflets and is advected downstream as the leaflet shear layers become wavy and oscillatory. In the second half of flow acceleration the leaflet shear layers become unstable and break down into two von Karman-like vortex streets. The onset of vortex shedding from the valve leaflets is responsible for the growth of significant cycle-to-cycle vorticity oscillations. At peak flow, the housing and leaflet shear layers undergo secondary instabilities and break down rapidly into a chaotic, turbulent-like state with multiple small-scale vortical structures emerging in the flow. During the deceleration and closing phases all large-scale coherent flow features disappear and a chaotic small-scale vorticity field emerges, which persists even after the valve has closed. Probability density functions of the leaflet position during opening and closing phases show that the leaflet position fluctuates from cycle to cycle with larger fluctuations evident during valve closure. The DNS is carried out by prescribing the leaflet kinematics from the experimental data. The computed instantaneous vorticity fields are in very good
NASA Astrophysics Data System (ADS)
Peterson, Mark A.
2009-07-01
Cilia are motile biological appendages that are driven to bend by internal shear stresses between tubulin filaments. A continuum model of ciliary material is constructed that incorporates the essential ciliary constraints: (i) one-dimensional inextensibility of filaments, (ii) three-dimensional incompressibility, and (iii) shear strain only longitudinally along filaments. It is shown that twist of filaments about each other is not an independent degree of freedom under ciliary constraints. The constraint on twist appears in the equations of motion for cilia as a term not previously recognized. As another application of the same geometrical idea, a general approach to the polymorphism of bacterial flagella is proposed.
Planetary Image Geometry Library
NASA Technical Reports Server (NTRS)
Deen, Robert C.; Pariser, Oleg
2010-01-01
The Planetary Image Geometry (PIG) library is a multi-mission library used for projecting images (EDRs, or Experiment Data Records) and managing their geometry for in-situ missions. A collection of models describes cameras and their articulation, allowing application programs such as mosaickers, terrain generators, and pointing correction tools to be written in a multi-mission manner, without any knowledge of parameters specific to the supported missions. Camera model objects allow transformation of image coordinates to and from view vectors in XYZ space. Pointing models, specific to each mission, describe how to orient the camera models based on telemetry or other information. Surface models describe the surface in general terms. Coordinate system objects manage the various coordinate systems involved in most missions. File objects manage access to metadata (labels, including telemetry information) in the input EDRs and RDRs (Reduced Data Records). Label models manage metadata information in output files. Site objects keep track of different locations where the spacecraft might be at a given time. Radiometry models allow correction of radiometry for an image. Mission objects contain basic mission parameters. Pointing adjustment ("nav") files allow pointing to be corrected. The object-oriented structure (C++) makes it easy to subclass just the pieces of the library that are truly mission-specific. Typically, this involves just the pointing model and coordinate systems, and parts of the file model. Once the library was developed (initially for Mars Polar Lander, MPL), adding new missions ranged from two days to a few months, resulting in significant cost savings as compared to rewriting all the application programs for each mission. Currently supported missions include Mars Pathfinder (MPF), MPL, Mars Exploration Rover (MER), Phoenix, and Mars Science Lab (MSL). Applications based on this library create the majority of operational image RDRs for those missions. A
NASA Technical Reports Server (NTRS)
Nemeth, Michael P.; Schultz, Marc R.
2012-01-01
A detailed exact solution is presented for laminated-composite circular cylinders with general wall construction and that undergo axisymmetric deformations. The overall solution is formulated in a general, systematic way and is based on the solution of a single fourth-order, nonhomogeneous ordinary differential equation with constant coefficients in which the radial displacement is the dependent variable. Moreover, the effects of general anisotropy are included and positive-definiteness of the strain energy is used to define uniquely the form of the basis functions spanning the solution space of the ordinary differential equation. Loading conditions are considered that include axisymmetric edge loads, surface tractions, and temperature fields. Likewise, all possible axisymmetric boundary conditions are considered. Results are presented for five examples that demonstrate a wide range of behavior for specially orthotropic and fully anisotropic cylinders.
NASA Astrophysics Data System (ADS)
Nore, C.; Martin Witkowski, L.; Foucault, E.; Pécheux, J.; Daube, O.; Le Quéré, P.
2006-05-01
The bifurcations and the nonlinear dynamics of the von Kármán swirling flow between exactly counter-rotating disks in a stationary cylinder are numerically and experimentally investigated. The dynamics are governed by two parameters, the radius-to-height ratio A =R/H and the Reynolds number, Re, based on disk rotation speed and cylinder height. The stability analysis performed for 2⩽A⩽20 shows that nonaxisymmetric and axisymmetric modes can be stationary or time dependent in this range. Three-dimensional modes are dominant for A ⩽13.25 while axisymmetric modes are critical for A >13.25. The patterns of the dominant perturbations are analyzed. In the particular case of A =15, nonlinear computations are performed at Reynolds numbers slightly above threshold and are compared to experimental results, showing the competition between axisymmetric and three-dimensional modes.
An Approximate Axisymmetric Viscous Shock Layer Aeroheating Method for Three-Dimensional Bodies
NASA Technical Reports Server (NTRS)
Brykina, Irina G.; Scott, Carl D.
1998-01-01
A technique is implemented for computing hypersonic aeroheating, shear stress, and other flow properties on the windward side of a three-dimensional (3D) blunt body. The technique uses a 2D/axisymmetric flow solver modified by scale factors for a, corresponding equivalent axisymmetric body. Examples are given in which a 2D solver is used to calculate the flow at selected meridional planes on elliptic paraboloids in reentry flight. The report describes the equations and the codes used to convert the body surface parameters into input used to scale the 2D viscous shock layer equations in the axisymmetric viscous shock layer code. Very good agreement is obtained with solutions to finite rate chemistry 3D thin viscous shock layer equations for a finite rate catalytic body.
NASA Astrophysics Data System (ADS)
Tieng, S. M.; Lai, W. Z.
Because of the importance of the temperature scalar measurements in combination diagonostics, application of phase shift holographic interferometry to temperature measurement of an axisymmetrically premixed flame was experimentally investigated. The test apparatus is an axisymmetric Bunsen burner. Propane of 99 percent purity is used as the gaseous fuel. A fast Fourier transform, a more efficient and accurate approach for Abel inversion, is used for reconstructed the axisymmetric temperature field from the interferometric data. The temperature distribution is compared with the thermocouple-measured values. The comparison shows that the proposed technique is satisfactory. The result errors are analyzed in detail. It is shown that this technique overcomes most of the earlier problems and limitations detrimental to the conventional holographic interferometry.
A Computationally Efficient Meshless Local Petrov-Galerkin Method for Axisymmetric Problems
NASA Technical Reports Server (NTRS)
Raju, I. S.; Chen, T.
2003-01-01
The Meshless Local Petrov-Galerkin (MLPG) method is one of the recently developed element-free methods. The method is convenient and can produce accurate results with continuous secondary variables, but is more computationally expensive than the finite element method. To overcome this disadvantage, a simple Heaviside test function is chosen. The computational effort is significantly reduced by eliminating the domain integral for the axisymmetric potential problems and by simplifying the domain integral for the axisymmetric elasticity problems. The method is evaluated through several patch tests for axisymmetric problems and example problems for which the exact solutions are available. The present method yielded very accurate solutions. The sensitivity of several parameters of the method is also studied.
Temperature and Energy of 4-Dimensional Axisymmetric Black Holes from Entropic Force
NASA Astrophysics Data System (ADS)
Zhao, Ren; Zhang, Li-Chun; Wu, Yue-Qin; Li, Huai-Fan
2011-01-01
We investigate the temperature and energy on holographic screens for 4-dimensional axisymmetric black holes with the entropic force idea proposed by Verlinde. According to the principle of thermal equilibrium, the location of holographic screen outside the axisymmetric black hole horizon is not a equivalent radius surface. The location of isothermal holographic screen outside the axisymmetric black hole horizon is obtained. Using the equipartition rule, we derive the correction expression of energy of isothermal holographic screen. When holographic screens are far away the black hole horizon, the entropic force of charged rotating particles can be expressed as Newton's law of gravity. When the screen crosses the event horizon, the temperature of the screen agrees with the Hawking temperature and the entropic force gives rise to the surface gravity for both of the black holes.
Modeling and Prediction of the Noise from Non-Axisymmetric Jets
NASA Technical Reports Server (NTRS)
Leib, Stewart J.
2014-01-01
mean flows which were meant to represent noise reduction concepts being considered by NASA. Testing (Ref. 5) showed that the method was feasible for the types of mean flows of interest in jet noise applications. Subsequently, this method was further developed to allow use of mean flow profiles obtained from a Reynolds-averaged Navier-Stokes (RANS) solution of the flow. Preliminary testing of the generalized code was among the last tasks completed under this contract. The stringent noise-reduction goals of NASA's Fundamental Aeronautics Program suggest that, in addition to potentially complex exhaust nozzle geometries, next generation aircraft will also involve tighter integration of the engine with the airframe. Therefore, noise generated and propagated by jet flows in the vicinity of solid surfaces is expected to be quite significant, and reduced-order noise prediction tools will be needed that can deal with such geometries. One important source of noise is that generated by the interaction of a turbulent jet with the edge of a solid surface (edge noise). Such noise is generated, for example, by the passing of the engine exhaust over a shielding surface, such as a wing. Work under this task supported an effort to develop a RANS-based prediction code for edge noise based on an extension of the classical Rapid Distortion Theory (RDT) to transversely sheared base flows (Refs. 6 and 7). The RDT-based theoretical analysis was applied to the generic problem of a turbulent jet interacting with the trailing edge of a flat plate. A code was written to evaluate the formula derived for the spectrum of the noise produced by this interaction and results were compared with data taken at NASA Glenn for a variety of jet/plate configurations and flow conditions (Ref. 8). A longer-term goal of this task was to work toward the development of a high-fidelity model of sound propagation in spatially developing non-axisymmetric jets using direct numerical methods for solving the relevant
Investigating Fractal Geometry Using LOGO.
ERIC Educational Resources Information Center
Thomas, David A.
1989-01-01
Discusses dimensionality in Euclidean geometry. Presents methods to produce fractals using LOGO. Uses the idea of self-similarity. Included are program listings and suggested extension activities. (MVL)
High-frequency electromagnetic scarring in three-dimensional axisymmetric convex cavities
Warne, Larry K.; Jorgenson, Roy E.
2016-04-13
Here, this article examines the localization of high-frequency electromagnetic fields in three-dimensional axisymmetric cavities along periodic paths between opposing sides of the cavity. When these orbits lead to unstable localized modes, they are known as scars. This article treats the case where the opposing sides, or mirrors, are convex. Particular attention is focused on the normalization through the electromagnetic energy theorem. Both projections of the field along the scarred orbit as well as field point statistics are examined. Statistical comparisons are made with a numerical calculation of the scars run with an axisymmetric simulation.
On axisymmetric and stationary solutions of the self-gravitating Vlasov system
NASA Astrophysics Data System (ADS)
Ames, Ellery; Andréasson, Håkan; Logg, Anders
2016-08-01
Axisymmetric and stationary solutions are constructed to the Einstein–Vlasov and Vlasov–Poisson systems. These solutions are constructed numerically, using finite element methods and a fixed-point iteration in which the total mass is fixed at each step. A variety of axisymmetric stationary solutions are exhibited, including solutions with toroidal, disk-like, spindle-like, and composite spatial density configurations, as are solutions with non-vanishing net angular momentum. In the case of toroidal solutions, we show for the first time, solutions of the Einstein–Vlasov system which contain ergoregions.
User's manual for Axisymmetric Diffuser Duct (ADD) code. Volume 1: General ADD code description
NASA Technical Reports Server (NTRS)
Anderson, O. L.; Hankins, G. B., Jr.; Edwards, D. E.
1982-01-01
This User's Manual contains a complete description of the computer codes known as the AXISYMMETRIC DIFFUSER DUCT code or ADD code. It includes a list of references which describe the formulation of the ADD code and comparisons of calculation with experimental flows. The input/output and general use of the code is described in the first volume. The second volume contains a detailed description of the code including the global structure of the code, list of FORTRAN variables, and descriptions of the subroutines. The third volume contains a detailed description of the CODUCT code which generates coordinate systems for arbitrary axisymmetric ducts.
On axisymmetric and stationary solutions of the self-gravitating Vlasov system
NASA Astrophysics Data System (ADS)
Ames, Ellery; Andréasson, Håkan; Logg, Anders
2016-08-01
Axisymmetric and stationary solutions are constructed to the Einstein-Vlasov and Vlasov-Poisson systems. These solutions are constructed numerically, using finite element methods and a fixed-point iteration in which the total mass is fixed at each step. A variety of axisymmetric stationary solutions are exhibited, including solutions with toroidal, disk-like, spindle-like, and composite spatial density configurations, as are solutions with non-vanishing net angular momentum. In the case of toroidal solutions, we show for the first time, solutions of the Einstein-Vlasov system which contain ergoregions.
NASA Astrophysics Data System (ADS)
Rajalingham, C.; Bhat, R. B.
1993-02-01
The axisymmetric vibration of circular plates and its analog in elliptic plates with clamped, simply supported and free boundary conditions are investigated using boundary characteristic orthogonal polynomials in the Rayleigh-Ritz method. Modified polar coordinates are employed to analyze the vibration of elliptical plates, with circular plates as a special case. Axisymmetric vibration of circular plates and its analog in elliptical plates with concentric nodal elipses require only one-dimensional shape functions in the Rayleigh-Ritz method. The first six natural frequencies and the parameters associated with nodal ellipses are tabulated.
Status of Axisymmetric CFD of an Eleven Inch Diameter Hybrid Rocket Motor
NASA Technical Reports Server (NTRS)
Ruf, Joseph; Sullivan, Matthew R.; Wang, Ten See
1993-01-01
Current status of a steady state, axisymmetric analysis of an experimental 11 inch diameter hybrid rocket motor internal flow field is given. The objective of this effort is to develop a steady state axisymmetric model of the 11 inch hybrid rocket motor which can be used as a design and/or analytical tool. A test hardware description, modeling approach, and future plans are given. The analysis was performed with FDNS implementing several finite rate chemistry sets. A converged solution for a two equation and five species set on a 'fine' grid is shown.
The Application of Mechanics to Geometry. Popular Lectures in Mathematics.
ERIC Educational Resources Information Center
Kogan, B. Yu
Presented in this translation are three chapters. Chapter I discusses the composition of forces and several theorems of geometry are proved using the fundamental concepts and certain laws of statics. Chapter II discusses the perpetual motion postulate; several geometric theorems are proved using the postulate that perpetual motion is impossible.…
GPS: Geometry, Probability, and Statistics
ERIC Educational Resources Information Center
Field, Mike
2012-01-01
It might be said that for most occupations there is now less of a need for mathematics than there was say fifty years ago. But, the author argues, geometry, probability, and statistics constitute essential knowledge for everyone. Maybe not the geometry of Euclid, but certainly geometrical ways of thinking that might enable us to describe the world…
Linguistic geometry for autonomous navigation
Stilman, B.
1995-09-01
To discover the inner properties of human expert heuristics, which were successful in a certain class of complex control systems, we develop a formal theory, the Linguistic Geometry. This paper reports two examples of application of Linguistic Geometry to autonomous navigation of aerospace vehicles that demonstrate dramatic search reduction.
Lobachevsky's Geometry and Research of Geometry of the Universe
NASA Astrophysics Data System (ADS)
Brylevskaya, L. I.
2008-10-01
For the first time N. I. Lobachevsky gave a talk on the new geometry in 1826; three years after he had published a work "On the fundamentals of geometry", containing all fundamental theorems and methods of non-Euclidean geometry. A small part of the article was devoted to the study of geometry of the Universe. The interpretation of geometrical concepts in pure empirical way was typical for mathematicians at the beginning of the XIX century; in this connection it was important for scientists to find application of his geometry. Having the purpose to determine experimentally the properties of real physical Space, Lobachevsky decided to calculate the sum of angles in a huge triangle with two vertexes in opposite points of the terrestrial orbit and the third -- on the remote star. Investigating the possibilities of solution of the set task, Lobachevsky faced the difficulties of theoretical, technical and methodological character. More detailed research of different aspects of the problem led Lobachevsky to the comprehension of impossibility to obtain the values required for the goal achievement, and he called his geometry an imaginary geometry.
Experimental and Computational Study fo CH, CH*, and OH* in an Axisymmetric Laminar Diffusion Flame
NASA Technical Reports Server (NTRS)
Walsh, K. T.
1998-01-01
In this study, we extend the results of previous combined numerical and experimental investigations of an axisymmetric laminar diffusion flame in which difference Raman spectroscopy, laser-induced fluorescence (LIF), and a multidimensional flame model were used to generate profiles of the temperature and major and minor species. A procedure is outlined by which the number densities of ground-state CH (X(sup 2)II) excited-state CH (A(sup 2)Delta, denoted CH*), and excited-state OH (A(sup 2)Sigma, denoted OH*) are measured and modeled. CH* and OH* number densities are deconvoluted from line-of-sight flame-emission measurements. Ground-state CH is measured using linear LIF. The computations are done with GRI Mech 2.11 as well as an alternate hydrocarbon mechanism. In both cases, additional reactions for the production and consumption of CH* and OH* are added from recent kinetic studies. Collisional quenching and spontaneous emission are responsible for the de-excitation of the excited-state radicals. As with our previous investigations, GRI Mech 2.11 continues to produce very good agreement with the overall flame length observed in the experiments, while significantly under predicting the flame lift-off height. The alternate kinetic scheme is much more accurate in predicting lift-off height but overpredicts the over-all flame length. Ground-state CH profiles predicted with GRI Mech 2.11 are in excellent agreement with the corresponding measurements, regarding both spatial distribution and absolute concentration (measured at 4 ppm) of the CH radical. Calculations of the excited-state species show reasonable agreement with the measurements as far as spatial distribution and overall characteristics are concerned. For OH*, the measured peak mole fraction, 1.3 x 10(exp -8), compared well with computed peaks, while the measured peak level for CH*, 2 x 10(exp -9), was severely underpredicted by both kinetic schemes, indicating that the formation and destruction kinetics
Electomagnetic field due to a non-axisymmetric current loop around Kerr blackhole
NASA Astrophysics Data System (ADS)
Pandey, U. S.; Dubey, G. S.
1983-12-01
The authors derive expressions for the electromagnetic field of a non-axisymmetric current loop around a Kerr blackhole. Complete solution for the "inside" as well as the "outside" regions of the current loop are determined using vacuum solutions of King (1977). A particular solution, the electromagnetic field of an equatorial current loop, is explicitly derived.
Velocity gradient method for calulating velocities in an axisymmetric annular duct
NASA Technical Reports Server (NTRS)
Katsanis, T.
1982-01-01
The velocity distribution along an arbitrary line between the inner and outer walls of an annular duct with axisymmetric swirling flow is calculated. The velocity gradient equation is used with an assumed variation of meridional streamline curvature. Upstream flow conditions can vary between the inner and outer walls, and an assumed total pressure distribution can be specified.
Numerical analyses of radiative heat transfer in any arbitrarily-shaped axisymmetric enclosures
NASA Astrophysics Data System (ADS)
Salah, M. Ben; Askri, F.; Jemni, A.; Nasrallah, S. Ben
2006-02-01
A numerical approach for the treatment of radiative heat transfer in any irregularly-shaped axisymmetric enclosure filled with absorbing, emitting and scattering gray media is developed. Radiative transfer equation (RTE) is formulated for a general axisymmetric geometrical configurations, and the discretized equation is conducted using an unstructured meshes, generated by an appropriate computer algorithm, and the control volume finite element method which frequently adopted in CFD problems. A computer procedure has been done to solve the discretized RTE and to examine the accuracy and the computational efficiency of the proposed numerical approach. By using this computer algorithm, five test cases, a cylindrical enclosure with absorbing and emitting medium, a diffuser shaped axisymmetric enclosure, a finite axisymmetric cylindrical enclosure with a curved wall, a furnace with axially varying medium temperature and a rocket nozzle, are treated and the obtained results agree very well with other published works. Furthermore, the developed computer procedure has an accurate CPU time and it can be coupled easily with CFD codes.
Jardin, S.C.; Schmidt, J.A.
1997-03-01
The Tokamak Simulation Code (TSC) has been used to model a new method of feedback stabilization of the axisymmetric instability in tokamaks using driven halo (or scrapeoff layer) currents. The method appears to be feasible for a wide range of plasma edge parameters. It may offer significant advantages over the more conventional method of controlling this instability when applied in a reactor environment.
Sakamoto, Moritsugu; Sasaki, Tomoyuki; Noda, Kohei; Tien, Tran Minh; Kawatsuki, Nobuhiro; Ono, Hiroshi
2016-02-01
Three-dimensional anisotropic structures were fabricated by a recording axisymmetrically polarized beam in azobenzene (azo)-dye doped liquid crystal polymer composites. Polarization and wavefront modulation properties of fabricated anisotropic structures are investigated by experimentally and theoretically analyzing the diffraction properties. Photo-induced anisotropic structures would be utilized to generate singular light waves, such as optical and polarization vortices.
Uniqueness theorem for stationary axisymmetric black holes in Einstein-Maxwell-axion-dilaton gravity
Rogatko, Marek
2010-08-15
We prove the uniqueness theorem for the stationary axisymmetric black hole solution in Einstein-Maxwell-axion-dilaton gravity being the low-energy limit of the heterotic string theory. We consider both the nonextremal and extremal Kerr-Sen black hole solutions.
The direct numerical simulations of the turbulent wakes of axisymmetric bodies
NASA Technical Reports Server (NTRS)
Riley, J. J.; Metcalfe, R. W.
1978-01-01
Results of direct numerical simulations of turbulence are compared with both laboratory data and self-similarity theory for the case of the turbulent wakes of towed, axisymmetric bodies. In general, the agreement of the simulation results with both the laboratory data and the self-similarity theory is good, although the comparisons are hampered by inadequate procedures for initializing the numerical simulations.
Rapid Inversion of Angular Deflection Data for Certain Axisymmetric Refractive Index Distributions
NASA Technical Reports Server (NTRS)
Rubinstein, R.; Greenberg, P. S.
1994-01-01
Certain functions useful for representing axisymmetric refractive-index distributions are shown to have exact solutions for Abel transformation of the resulting angular deflection data. An advantage of this procedure over direct numerical Abel inversion is that least-squares curve fitting is a smoothing process that reduces the noise sensitivity of the computation
NASA Technical Reports Server (NTRS)
Ferlemann, Paul G.; Gollan, Rowan J.
2010-01-01
Computational design and analysis of three-dimensional hypersonic inlets with shape transition has been a significant challenge due to the complex geometry and grid required for three-dimensional viscous flow calculations. Currently, the design process utilizes an inviscid design tool to produce initial inlet shapes by streamline tracing through an axisymmetric compression field. However, the shape is defined by a large number of points rather than a continuous surface and lacks important features such as blunt leading edges. Therefore, a design system has been developed to parametrically construct true CAD geometry and link the topology of a structured grid to the geometry. The Adaptive Modeling Language (AML) constitutes the underlying framework that is used to build the geometry and grid topology. Parameterization of the CAD geometry allows the inlet shapes produced by the inviscid design tool to be generated, but also allows a great deal of flexibility to modify the shape to account for three-dimensional viscous effects. By linking the grid topology to the parametric geometry, the GridPro grid generation software can be used efficiently to produce a smooth hexahedral multiblock grid. To demonstrate the new capability, a matrix of inlets were designed by varying four geometry parameters in the inviscid design tool. The goals of the initial design study were to explore inviscid design tool geometry variations with a three-dimensional analysis approach, demonstrate a solution rate which would enable the use of high-fidelity viscous three-dimensional CFD in future design efforts, process the results for important performance parameters, and perform a sample optimization.
Quantum Consequences of Parameterizing Geometry
NASA Astrophysics Data System (ADS)
Wanas, M. I.
2002-12-01
The marriage between geometrization and quantization is not successful, so far. It is well known that quantization of gravity , using known quantization schemes, is not satisfactory. It may be of interest to look for another approach to this problem. Recently, it is shown that geometries with torsion admit quantum paths. Such geometries should be parameterizied in order to preserve the quantum properties appeared in the paths. The present work explores the consequences of parameterizing such geometry. It is shown that quantum properties, appeared in the path equations, are transferred to other geometric entities.
NASA Astrophysics Data System (ADS)
Belogurov, S.; Berchun, Yu; Chernogorov, A.; Malzacher, P.; Ovcharenko, E.; Semennikov, A.
2011-12-01
Due to conceptual difference between geometry descriptions in Computer-Aided Design (CAD) systems and particle transport Monte Carlo (MC) codes direct conversion of detector geometry in either direction is not feasible. An original set of tools has been developed for building a GEANT4/ROOT compatible geometry in the CATIA CAD system and exchanging it with mentioned MC packages using GDML file format. A Special structure of a CATIA product tree, a wide range of primitives, different types of multiple volume instantiation, and supporting macros have been implemented.
NASA Astrophysics Data System (ADS)
Kollár, László E.; Lucas, Gary P.; Meng, Yiqing
2015-05-01
An analytical method that was developed formerly for the reconstruction of velocity profiles in asymmetric flows is improved to be applicable for both axisymmetric and asymmetric flows. The method is implemented in Matlab, and predicts the velocity profile from measured electrical potential distributions obtained around the boundary of a multi-electrode electromagnetic flow meter (EMFM). Potential distributions are measured in uniform and non-uniform magnetic fields, and the velocity is assumed as a sum of axisymmetric and polynomial components. The procedure requires three steps. First, the discrete Fourier transform (DFT) is applied to the potential distribution obtained in a uniform magnetic field. Since the direction of polynomial components of order greater than two in the plane of the pipe cross section is not unique multiple solutions exist, therefore all possible polynomial velocity profiles are determined. Then, the DFT is applied to the potential distribution obtained in a specific non-uniform magnetic field, and used to calculate the exponent in a power-law representation of the axisymmetric component. Finally, the potential distribution in the non-uniform magnetic field is calculated for all of the possible velocity profile solutions using weight values, and the velocity profile with the calculated potential distribution which is closest to the measured one provides the optimum solution. The method is validated by reconstructing two quartic velocity profiles, one of which includes an axisymmetric component. The potential distributions are obtained from simulations using COMSOL Multiphysics where a model of the EMFM is constructed. The reconstructed velocity profiles show satisfactory agreement with the input velocity profiles. The main benefits of the method described in this paper are that it provides a velocity distribution in the circular cross section of a pipe as an analytical function of the spatial coordinates which is suitable for both
Numerical simulation of the generation mechanism of axisymmetric supersonic jet screech tones
NASA Astrophysics Data System (ADS)
Li, X. D.; Gao, J. H.
2005-08-01
In this paper an axisymmetric computational aeroacoustic procedure is developed to investigate the generation mechanism of axisymmetric supersonic jet screech tones. The axisymmetric Navier-Stokes equations and the two equations standard k-ɛ turbulence model modified by Turpin and Troyes ["Validation of a two-equation turbulence model for axisymmetric reacting and non-reaction flows," AIAA Paper No. 2000-3463 (2000)] are solved in the generalized curvilinear coordinate system. A generalized wall function is applied in the nozzle exit wall region. The dispersion-relation-preserving scheme is applied for space discretization. The 2N storage low-dissipation and low-dispersion Runge-Kutta scheme is employed for time integration. Much attention is paid to far-field boundary conditions and turbulence model. The underexpanded axisymmetric supersonic jet screech tones are simulated over the Mach number from 1.05 to 1.2. Numerical results are presented and compared with the experimental data by other researchers. The simulated wavelengths of A0, A1, A2, and B modes and part of simulated amplitudes agree very well with the measurement data by Ponton and Seiner ["The effects of nozzle exit lip thickness on plume resonance," J. Sound Vib. 154, 531 (1992)]. In particular, the phenomena of modes jumping have been captured correctly although the numerical procedure has to be improved to predict the amplitudes of supersonic jet screech tones more accurately. Furthermore, the phenomena of shock motions are analyzed. The predicted splitting and combination of shock cells are similar with the experimental observations of Panda ["Shock oscillation in underexpanded screeching jets," J. Fluid. Mech. 363, 173 (1998)]. Finally, the receptivity process is numerically studied and analyzed. It is shown that the receptivity zone is associated with the initial thin shear layer, and the incoming and reflected sound waves.
Abarham, Mehdi; Zamankhan, Parsa; Hoard, John W.; Styles, Dan; Sluder, Scott; Storey, John Morse; Lance, Michael J; Assanis, Dennis
2013-01-01
In this study, we developed two frameworks to investigate the thermophoretic particulate deposition in non-isothermal tube flows conveying particles ranging from 10 to 300 nm; a one dimensional model where the variables are assumed to be uniform in each cross section perpendicular to the tube axis and an axi-symmetric model where the aforementioned assumption is relaxed. In the one dimensional model, the rate of mass deposition along the inner surface of the tube is computed based on the local thermophoretic velocity of the particulate phase at the wall. This velocity is proportional to the radial gradient of the temperature at the wall and is calculated via some empirical correlations for heat transfer in tube flows. In the axi-symmetric model, the rate of deposition is computed through the Fick s law after solving the species transport equation for the solid phase. We included the formation of the soot layer through moving the gas solid interface in both models. The tube effectiveness (the ratio of actual heat transfer to the maximum possible heat transfer) decreases due to the formation of the layer. Model outputs including deposited mass along the tube wall and the tube effectiveness drop have been compared against experiments. While the computed results through both models agree with the trend of experimental data, the axi-symmetric results are closer to the experiments in most cases. The calculated deposited mass is smaller (and closer to experiments) for the axi-symmetric model compared to the one dimensional model in all cases. This indicates that the axi-symmetric model estimates the deposited mass more accurately.
Large deformation and adhesive contact studies of axisymmetric membranes.
Laprade, Evan J; Long, Rong; Pham, Jonathan T; Lawrence, Jimmy; Emrick, Todd; Crosby, Alfred J; Hui, Chung-Yuen; Shull, Kenneth R
2013-02-01
A model membrane contact system consisting of an acrylic copolymer membrane and a PDMS substrate was utilized to evaluate a recently developed nonlinear large-deformation adhesive contact analysis. Direct measurements of the local membrane apex strain during noncontact inflation indicated that the neo-Hookean model provides an accurate measure of membrane strain and supports its use as the strain energy function for the analysis. Two membrane contact geometries, exhibiting significantly different strain distributions during withdrawal, were investigated. The first examines the wet contact of an air pressurized membrane. The second looks at the dry contact of a fluid deformed membrane in which a stepper motor controls membrane-substrate separation. A time-dependent modulus emerges from the analysis, with principal tensions obtained from a comparison of predicted and experimental membrane profiles. The applicability of this numerical analysis for determining membrane tension, however, is limited by wrinkling instabilities and viscoelasticity. For this reason, a conceptually simpler method, based on the direct measurement of the membrane tension and contact angle, was also utilized. The traditional peel energy defined with this direct measurement accurately described the membrane/substrate adhesive interactions, giving well-defined peel energies that were independent of the detailed strain state of the membrane. PMID:23289644
Axisymmetric analytical stiffness matrices with Green-Lagrange strains
NASA Astrophysics Data System (ADS)
Pedersen, P.
2005-02-01
Stiffness matrices based on the non-linear Green-Lagrange definition seem complicated, but for the case of a linear displacement ring-element with triangular cross-section, closed form final results are listed, directly suited for coding in a finite element program. These analytical secant and tangent element stiffness matrices are obtained by separating the dependence on the material constitutive parameters and on the stress/strain state from the dependence on the initial geometry and the displacement assumption. As an example of application, numerical results for a circular plate problem show the indirect severe errors that may result from a linear strain model. It is difficult to predict the indirect errors that follow from the erroneous displacement field, and the explanations behind such predictions are attempted. The nodal positions of an element and the displacement assumption give six basic matrices that do not depend on material and stress strain state, and thus are unchanged during the necessary iterations for obtaining a solution based on Green-Lagrange strain measure. The presented resulting stiffness matrices are especially useful in design optimization, because analytical sensitivity analysis can then be performed.
Instability of supersymmetric microstate geometries
NASA Astrophysics Data System (ADS)
Eperon, Felicity C.; Reall, Harvey S.; Santos, Jorge E.
2016-10-01
We investigate the classical stability of supersymmetric, asymptotically flat, microstate geometries with five non-compact dimensions. Such geometries admit an "evanescent ergosurface": a timelike hypersurface of infinite redshift. On such a surface, there are null geodesics with zero energy relative to infinity. These geodesics are stably trapped in the potential well near the ergosurface. We present a heuristic argument indicating that this feature is likely to lead to a nonlinear instability of these solutions. We argue that the precursor of such an instability can be seen in the behaviour of linear perturbations: nonlinear stability would require that all linear perturbations decay sufficiently rapidly but the stable trapping implies that some linear perturbation decay very slowly. We study this in detail for the most symmetric microstate geometries. By constructing quasinormal modes of these geometries we show that generic linear perturbations decay slower than any inverse power of time.
NASA Technical Reports Server (NTRS)
Owen, Albert K.
1987-01-01
A computer code was written which utilizes ray tracing techniques to predict the changes in position and geometry of a laser Doppler velocimeter probe volume resulting from refraction effects. The code predicts the position change, changes in beam crossing angle, and the amount of uncrossing that occur when the beams traverse a region with a changed index of refraction, such as a glass window. The code calculates the changes for flat plate, cylinder, general axisymmetric and general surface windows and is currently operational on a VAX 8600 computer system.
Madasu, Srinath; Ultman, James S; Borhan, Ali
2008-02-01
Reactive gas uptake is predicted and compared in a single bifurcation at steady expiratory flow in terms of Sherwood number using an axisymmetric single-path model (ASPM) and a three-dimensional computational fluid dynamics model (CFDM). ASPM is validated in a two-generation geometry by comparing the average gas-phase mass transfer coefficients with the experimental values. ASPM predicted mass transfer coefficients within 20% of the experimental values. The flow and concentration variables in the ASPM were solved using Galerkin finite element method and in the CFDM using commercial finite element software FIDAP. The simulations were performed for reactive gas flowing at Reynolds numbers ranging from 60 to 350 in both symmetric bifurcation for three bifurcation angles, 30 deg, 70 deg, and 90 deg, and in an asymmetric bifurcation. The numerical models compared with each other qualitatively but quantitatively they were within 0.4-8% due to nonfully developed flow in the parent branch predicted by the CFDM. The radially averaged concentration variation along the axial location matched qualitatively between the CFDM and ASPM but quantitatively they were within 32% due to differences in the flow field. ASPM predictions compared well with the CFDM predictions for an asymmetric bifurcation. These results validate the simplified ASPM and the complex CFDM. ASPM predicts higher Sherwood number with a flat velocity inlet profile compared to a parabolic inlet velocity profile. Sherwood number increases with the inlet average velocity, wall mass transfer coefficient, and bifurcation angle since the boundary layer grows slower in the parent and daughter branches.
NASA Astrophysics Data System (ADS)
Bruenn, Stephen W.; Lentz, Eric J.; Hix, W. Raphael; Mezzacappa, Anthony; Harris, J. Austin; Messer, O. E. Bronson; Endeve, Eirik; Blondin, John M.; Chertkow, Merek Austin; Lingerfelt, Eric J.; Marronetti, Pedro; Yakunin, Konstantin N.
2016-02-01
We present four ab initio axisymmetric core-collapse supernova simulations initiated from 12, 15, 20, and 25 {M}⊙ zero-age main sequence progenitors. All of the simulations yield explosions and have been evolved for at least 1.2 s after core bounce and 1 s after material first becomes unbound. These simulations were computed with our Chimera code employing RbR spectral neutrino transport, special and general relativistic transport effects, and state-of-the-art neutrino interactions. Continuing the evolution beyond 1 s after core bounce allows the explosions to develop more fully and the processes involved in powering the explosions to become more clearly evident. We compute explosion energy estimates, including the negative gravitational binding energy of the stellar envelope outside the expanding shock, of 0.34, 0.88, 0.38, and 0.70 Bethe (B ≡ {10}51 erg) and increasing at 0.03, 0.15, 0.19, and 0.52 {\\text{B s}}-1, respectively, for the 12, 15, 20, and 25 {M}⊙ models at the endpoint of this report. We examine the growth of the explosion energy in our models through detailed analyses of the energy sources and flows. We discuss how the explosion energies may be subject to stochastic variations as exemplfied by the effect of the explosion geometry of the 20 {M}⊙ model in reducing its explosion energy. We compute the proto-neutron star masses and kick velocities. We compare our results for the explosion energies and ejected {}56{Ni} masses against some observational standards despite the large error bars in both models and observations.
Bruenn, Stephen W.; Lentz, Eric J.; Hix, William Raphael; Mezzacappa, Anthony; Harris, James Austin; Messer, O. E. Bronson; Endeve, Eirik; Blondin, John M.; Chertkow, Merek Austin; Lingerfelt, Eric J.; et al
2016-02-16
We present four ab initio axisymmetric core-collapse supernova simulations initiated from 12, 15, 20, and 25 M⊙ zero-age main sequence progenitors. All of the simulations yield explosions and have been evolved for at least 1.2 s after core bounce and 1 s after material first becomes unbound. These simulations were computed with our Chimera code employing RbR spectral neutrino transport, special and general relativistic transport effects, and state-of-the-art neutrino interactions. Continuing the evolution beyond 1 s after core bounce allows the explosions to develop more fully and the processes involved in powering the explosions to become more clearly evident. Wemore » compute explosion energy estimates, including the negative gravitational binding energy of the stellar envelope outside the expanding shock, of 0.34, 0.88, 0.38, and 0.70 Bethe (B ≡ 1051 erg) and increasing at 0.03, 0.15, 0.19, and 0.52 BS–1, respectively, for the 12, 15, 20, and 25 M⊙ models at the endpoint of this report. We examine the growth of the explosion energy in our models through detailed analyses of the energy sources and flows. We discuss how the explosion energies may be subject to stochastic variations as exemplfied by the effect of the explosion geometry of the 20 M⊙ model in reducing its explosion energy. We compute the proto-neutron star masses and kick velocities. In conclusion, we compare our results for the explosion energies and ejected 56Ni masses against some observational standards despite the large error bars in both models and observations.« less
Deformable cells in confined geometries: From hemolysis to hydrodynamic interactions
NASA Astrophysics Data System (ADS)
Abkarian, Manouk; Faivre, Magalie; Stone, Howard A.
2004-11-01
Recent developments in microfluidics allow a wide range of possibilities for studying cellular-scale hydrodynamics. Here we use microfluidic technology to address several open questions in the blood flow literature where cell deformation and hydrodynamic interactions are significant. In particular, we investigate the pressure-driven flow of a dilute suspension in a channel and characterize the transition from steady axisymmetric cell shapes (for which numerical calculations exist) to asymmetric, highly extended shapes, which are precursors to hemolysis (i.e. destruction of the cell). In addition, we examine the influence of geometry on hydrodynamic interactions of deformable cells by contrasting one-dimensional motion of a train of particles in a channel with two-dimensional motions in a Hele-Shaw cell. This study can help to understand flow of cells in microcirculation from the unidirectional flow in capillaries to the two-dimensional flow in the lung alveoli and provides the basic steps to understand certain aspects of microcirculatory deseases like sickle cell anemia for example.
Investigation of flowfields found in typical combustor geometries
NASA Technical Reports Server (NTRS)
Lilley, D. G.
1985-01-01
Activities undertaken during the entire course of research are summarized. Studies were concerned with experimental and theoretical research on 2-D axisymmetric geometries under low speed nonreacting, turbulent, swirling flow conditions typical of gas turbine and ramjet combustion chambers. They included recirculation zone characterization, time-mean and turbulence simulation in swirling recirculating flow, sudden and gradual expansion flowfields, and furher complexities and parameter influences. The study included the investigation of: a complete range of swirl strengths; swirler performance; downstream contraction nozzle sizes and locations; expansion ratios; and inlet side-wall angles. Their individual and combined effects on the test section flowfield were observed, measured and characterized. Experimental methods included flow visualization (with smoke and neutrally-buoyant helium-filled soap bubbles), five-hole pitot probe time-mean velocity field measurements, and single-, double-, and triple-wire hot-wire anemometry measurements of time-mean velocities, normal and shear Reynolds sresses. Computational methods included development of the STARPIC code from the primitive-variable TEACH computer code, and its use in flowfield prediction and turbulence model development.
Aerodynamics of Sounding-Rocket Geometries
NASA Technical Reports Server (NTRS)
Barrowman, J.
1982-01-01
Theoretical aerodynamics program TAD predicts aerodynamic characteristics of vehicles with sounding-rocket configurations. These slender, Axisymmetric finned vehicles have a wide range of aeronautical applications from rockets to high-speed armament. TAD calculates characteristics of separate portions of vehicle, calculates interference between portions, and combines results to form total vehicle solution.
Realism, positivism, instrumentalism, and quantum geometry
NASA Astrophysics Data System (ADS)
Prugovečki, Eduard
1992-02-01
The roles of classical realism, logical positivism, and pragmatic instrumentalism in the shaping of fundamental ideas in quantum physics are examined in the light of some recent historical and sociological studies of the factors that influenced their development. It is shown that those studies indicate that the conventionalistic form of instrumentalism that has dominated all the major post-World War II developments in quantum physics is not an outgrowth of the Copenhagen school, and that despite the “schism” in twentieth century physics created by the Bohr-Einstein “disagreements” on foundational issues in quantum theory, both their philosophical stands were very much opposed to those of conventionalistic instrumentalism. Quotations from the writings of Dirac, Heisenberg, Popper, Russell, and other influential thinkers, are provided, illustrating the fact that, despite the various divergencies in their opinions, they all either opposed the instrumentalist concept of “truth” in general, or its conventionalistic version in post-World War II quantum physics in particular. The basic epistemic ideas of a quantum geometry approach to quantum physics are reviewed and discussed from the point of view of a quantum realism that seeks to reconcile Bohr's “positivism” with Einstein's “realism” by emphasizing the existence of an underlying quantum reality, in which they both believed. This quantum geometry framework seeks to introduce geometro-stochastic concepts that are specifically designed for the systematic description of that underlying quantum reality, by developing the conceptual and mathematical tools that are most appropriate for such a use.
On axisymmetric/diamond-like mode transitions in axially compressed core-shell cylinders
NASA Astrophysics Data System (ADS)
Xu, Fan; Potier-Ferry, Michel
2016-09-01
Recent interests in curvature- and stress-induced pattern formation and pattern selection motivate the present study. Surface morphological wrinkling of a cylindrical shell supported by a soft core subjected to axial compression is investigated based on a nonlinear 3D finite element model. The post-buckling behavior of core-shell cylinders beyond the first bifurcation often leads to complicated responses with surface mode transitions. The proposed finite element framework allows predicting and tracing these bifurcation portraits from a quantitative standpoint. The occurrence and evolution of 3D instability modes including sinusoidally deformed axisymmetric patterns and non-axisymmetric diamond-like modes will be highlighted according to critical dimensionless parameters. Besides, the phase diagram obtained from dimensional analyses and numerical results could be used to guide the design of core-shell cylindrical systems to achieve the desired instability patterns.
NASA Astrophysics Data System (ADS)
Tan, Dominic James; Edgington-Mitchell, Daniel; Honnery, Damon
2015-11-01
A novel application of the adaptive Fourier-Hankel (AFH) Abel algorithm to reconstruct the radial density distribution of axisymmetric jets is presented. The fluid is imaged using the non-intrusive path-integrated background-oriented schlieren (BOS) technique. BOS images are cross-correlated to obtain background displacements that are proportional to the first derivative of the refractive index. The critical step is deconvolving the projected displacements. The AFH method is applied to simulated displacement data to validate the use of averaged turbulent fluctuations that approximate an axisymmetric field. The influence of experimental noise and variations in the flow on the accuracy of the method is discussed. The limitations of the system are demonstrated by applying it to low- and high-Reynolds ( Re) number jets. The high- Re jets are produced from a high-pressure fuel injector operating at nozzle pressure ratios of 2, 3, and 4.
Towards Simulating Non-Axisymmetric Influences on Aircraft Plumes for Signature Prediction
NASA Technical Reports Server (NTRS)
Kenzakowski, D. C.; Shipman, J. D.; Dash, S. M.
2000-01-01
A methodology for efficiently including three-dimensional effects on aircraft plume signature is presented. First, exploratory work on the use of passive mixing enhancement devices, namely chevrons and tabs, in IR signature reduction for external turbofan plumes is demonstrated numerically and experimentally. Such small attachments, when properly designed, cause an otherwise axisymmetric plume to have significant 3D structures, affecting signature prediction. Second, an approach for including non-axisymmetric and installation effects in plume signature prediction is discussed using unstructured methodology. Unstructured flow solvers, using advanced turbulence modeling and plume thermochemistry, facilitate the modeling of aircraft effects on plume structure that previously have been neglected due to gridding complexities. The capabilities of the CRUNCH unstructured Navier-Stokes solver for plume modeling is demonstrated for a passively mixed turbofan nozzle, a generic fighter nozzle, and a complete aircraft.
On the interaction of Tollmien-Schlichting waves in axisymmetric supersonic flows
NASA Technical Reports Server (NTRS)
Duck, P. W.; Hall, P.
1988-01-01
Two-dimensional lower branch Tollmien-Schlichting waves described by triple-deck theory are always stable for planar supersonic flows. The possible occurrence of axisymmetric unstable modes in the supersonic flow around an axisymmetric body is investigated. In particular flows around bodies with typical radii comparable with the thickness of the upper deck are considered. It is shown that such unstable modes exist below a critical nondimensional radius of the body a sub 0. At values of the radius above a sub 0 all the modes are stable while if unstable modes exist they are found to occur in pairs. The interaction of these modes in the nonlinear regime is investigated using a weakly nonlinear approach and it is found that, dependent on the frequencies of the imposed Tollmien-Schlichting waves, either of the modes can be set up.
On the interaction of Tollmien-Schlichting waves in axisymmetric supersonic flows
NASA Technical Reports Server (NTRS)
Duck, P. W.; Hall, P.
1989-01-01
Two-dimensional lower branch Tollmien-Schlichting waves described by triple-deck theory are always stable for planar supersonic flows. The possible occurrence of axisymmetric unstable modes in the supersonic flow around an axisymmetric body is investigated. In particular flows around bodies with typical radii comparable with the thickness of the upper deck are considered. It is shown that such unstable modes exist below a critical nondimensional radius of the body a sub O. At values of the radius above a sub O all the modes are stable while if unstable modes exist they are found to occur in pairs. The interaction of these modes in the nonlinear regime is investigated using a weakly nonlinear approach and it is found that, dependent on the frequencies of the imposed Tollmien-Schlichting waves, either of the modes can be set up.
Turbine Engine Stability/Instability With Rub Forces Axisymmetric Rotor-Support Stiffness
NASA Technical Reports Server (NTRS)
Gallardo, Vicente; Lawrence, Charles
2004-01-01
The stability/instability condition of a turbine rotor with axisymmetric supports is determined in the presence of gyroscopic loads and rub-induced destabilizing forces. A modal representation of the turbine engine is used, with one mode in each of the vertical and horizontal planes. The use of non-spinning rotor modes permits an explicit treatment of gyroscopic effects. The two linearized modal equations of motion of a rotor with axisymmetric supports are reduced to a single equation in a complex variable. The resulting eigenvalues yield explicit expressions at the stability boundary, for the whirl frequency as well as the required damping for stability in the presence of the available rub-induced destabilization. Conversely, the allowable destabilization in the presence of the available damping is also given.
A RANS/DES Numerical Procedure for Axisymmetric Flows with and without Strong Rotation
Andrade, Andrew Jacob
2007-01-01
A RANS/DES numerical procedure with an extended Lax-Wendroff control-volume scheme and turbulence model is described for the accurate simulation of internal/external axisymmetric flow with and without strong rotation. This new procedure is an extension, from Cartesian to cylindrical coordinates, of (1) a second order accurate multi-grid, control-volume integration scheme, and (2) a k-ω turbulence model. This paper outlines both the axisymmetric corrections to the mentioned numerical schemes and the developments of techniques pertaining to numerical dissipation, multi-block connectivity, parallelization, etc. Furthermore, analytical and experimental case studies are presented to demonstrate accuracy and computational efficiency. Notes are also made toward numerical stability of highly rotational flows.
Stationary axisymmetric and slowly rotating spacetimes in Hořava-Lifshitz gravity.
Wang, Anzhong
2013-03-01
Stationary, axisymmetric, and slowly rotating vacuum spacetimes in the Hořava-Lifshitz (HL) gravity are studied, and it is shown that, for any given spherical static vacuum solution of the HL theory (of any model, including the ones with an additional U(1) symmetry), there always exists a corresponding slowly rotating, stationary, and axisymmetric vacuum solution, which reduces to the former, when the rotation is switched off. The rotation is universal and only implicitly depends on the models of the HL theory and their coupling constants through the spherical seed solution. As a result, all asymptotically flat slowly rotating vacuum solutions are asymptotically identical to the slowly rotating Kerr solution. This is in contrast to the claim of Barausse and Sotiriou [Phys. Rev. Lett. 109, 181101 (2012)], in which slowly rotating black holes were reported (incorrectly) not to exist in the infrared limit of the nonprojectable HL theory.
NASA Astrophysics Data System (ADS)
Fernández-Trincado, J. G.; Robin, A. C.; Bienaymé, O.; Reylé, C.; Valenzuela, O.; Pichardo, B.
2014-07-01
In this contributed poster we present a preliminary attempt to compute a non-axisymmetric potential together with previous axisymmetric potential of the Besançon galaxy model. The contribution by non-axisymmetric components are modeled by the superposition of inhomogeneous ellipsoids to approximate the triaxial bar and superposition of homogeneous oblate spheroids for a stellar halo, possibly triaxial. Finally, we have computed the potential and force field for these non-axisymmetric components in order to constraint the total mass of the Milky Way. We present preliminary results for the rotation curve and the contribution of the bar to it. This approach will allow future studies of dynamical constraints from comparisons of kinematical simulations with upcoming surveys such as RAVE, BRAVA, APOGEE, and GAIA in the near future. More details, are presented in https://gaia.ub.edu/Twiki/pub/GREATITNFC/ProgramFinalconference/Poster_JG.Fern%e1ndez.pdf.
Khomyakov, A.N.
1995-11-01
Numerical investigations of flow past axisymmetric conical cavitation bodies have shown that the drag coefficient of the cavitation body, calculated from the maximum cross-sectional area of the cavity (midsection), depends on the cavitation number and the cone angle.
Earthquake cycles in complex geometries
NASA Astrophysics Data System (ADS)
Romanet, Pierre; Bhat, Harsha; Madariaga, Raul
2016-04-01
Our understanding of earthquake cycles, from a modelling perspective, comes mainly from theoretical, and numerical, work on a single straight fault. However, natural fault systems are geometrically complex. Modelling complex fault geometry (bends, kinks and multiple faults) is in itself a challenge as it is computationally intensive. To overcome this difficulty, we appeal to the Fast Multipole Method which was developed in the context of modelling N-body problems. This method is then used to model the quasi-dynamic response of multiple faults, with complex geometries, that are governed by rate and state friction laws. Our preliminary findings tell us that when stress interaction between faults, due to complex geometry, is accounted then even strongly rate-weakening faults (a-b)<0 show a complex spectrum of slow slip and dynamic ruptures.
Conventionalism and integrable Weyl geometry
NASA Astrophysics Data System (ADS)
Pucheu, M. L.
2015-03-01
Since the appearance of Einstein's general relativity, gravitation has been associated to the space-time curvature. This theory introduced a geometrodynamic language which became a convenient tool to predict matter behaviour. However, the properties of space-time itself cannot be measurable by experiments. Taking Poincaré idea that the geometry of space-time is merely a convention, we show that the general theory of relativity can be completely reformulated in a more general setting, a generalization of Riemannian geometry, namely, the Weyl integrable geometry. The choice of this new mathematical language implies, among other things, that the path of particles and light rays should now correspond to Weylian geodesies. Such modification in the dynamic of bodies brings a new perception of physical phenomena that we will explore.
Frustrated Order on Extrinsic Geometries
Mbanga, Badel L.; Grason, Gregory M.; Santangelo, Christian D.
2012-01-03
We study, numerically and theoretically, defects in an anisotropic liquid that couple to the extrinsic geometry of a surface. Though the intrinsic geometry tends to confine topological defects to regions of large Gaussian curvature, extrinsic couplings tend to orient the order along the local direction of maximum or minimum bending. This additional frustration is generically unavoidable, and leads to complex ground-state thermodynamics. Using the catenoid as a prototype, we show, in contradistinction to the well-known effects of intrinsic geometry, that extrinsic curvature expels disclinations from the region of maximum curvature above a critical coupling threshold. On catenoids lacking an “inside-outside” symmetry, defects are expelled altogether above a critical neck size.
Quantum geometry and gravitational entropy
Simon, Joan; Balasubramanian, Vijay; Czech, Bart Iomiej; Larjo, Klaus; Marolf, Donald; Simon, Joan
2007-05-29
Most quantum states have wavefunctions that are widely spread over the accessible Hilbert space and hence do not have a good description in terms of a single classical geometry. In order to understand when geometric descriptions are possible, we exploit the AdS/CFT correspondence in the half-BPS sector of asymptotically AdS_5 x S5 universes. In this sector we devise a"coarse-grained metric operator" whose eigenstates are well described by a single spacetime topology and geometry. We show that such half-BPS universes have a non-vanishing entropy if and only if the metric is singular, and that the entropy arises from coarse-graining the geometry. Finally, we use our entropy formula to find the most entropic spacetimes with fixed asymptotic moments beyond the global charges.
NASA Technical Reports Server (NTRS)
Gould, Richard D.; Stevenson, Warren H.; Thompson, H. Doyle
1986-01-01
Simultaneous two-component laser velocimeter measurements were made in an axisymmetric sudden expansion flowfield. A specially designed correction lens was employed to correct optical aberrations introduced by the circular tube. This lens system allowed the accurate simultaneous measurement of axial and radial velocities in the test section. The experimental measurements were compared to predictions generated by a code which employed the k-epsilon turbulence model. Possible sources of differences observed between model predictions and the measurements are discussed.
Stationary axisymmetric four dimensional space-time endowed with Einstein metric
Hasanuddin; Azwar, A.; Gunara, B. E.
2015-04-16
In this paper, we construct Ernst equation from vacuum Einstein field equation for both zero and non-zero cosmological constant. In particular, we consider the case where the space-time admits axisymmetric using Boyer-Lindquist coordinates. This is called Kerr-Einstein solution describing a spinning black hole. Finally, we give a short discussion about the dynamics of photons on Kerr-Einstein space-time.
NASA Astrophysics Data System (ADS)
Vestyak, V. A.; Tarlakovskii, D. V.
2015-11-01
This paper considers a homogeneous isotropic elastic body bounded by concentric spheres and acted upon by axisymmetric unsteady volume forces. Displacement fields are determined using series expansions in Legendre and Gegenbauer polynomials, Laplace transforms in time, and integral representations with kernels in the form of Green's functions. Explicit formulas for the Green's functions are constructed that allow accurate determination of the originals. Examples of the calculations are presented.
CFD Validation Experiment of a Mach 2.5 Axisymmetric Shock-Wave/Boundary-Layer Interaction
NASA Technical Reports Server (NTRS)
Davis, David Owen
2015-01-01
Preliminary results of an experimental investigation of a Mach 2.5 two-dimensional axisymmetric shock-wave/ boundary-layer interaction (SWBLI) are presented. The purpose of the investigation is to create a SWBLI dataset specifically for CFD validation purposes. Presented herein are the details of the facility and preliminary measurements characterizing the facility and interaction region. These results will serve to define the region of interest where more detailed mean and turbulence measurements will be made.
NASA Technical Reports Server (NTRS)
Goldstein, M. E.; Rosenbaum, B. M.
1972-01-01
A model, based on Lighthill's theory, for predicting aerodynamic noise from a turbulent shear flow is developed. This model is a generalization of the one developed by Ribner. Unlike Ribner's model, it does not require that the turbulent correlations factor into space and time-dependent parts. It replaces his assumption of isotropic. turbulence by the more realistic one of axisymmetric turbulence. The implications of the model for jet noise are discussed.
Stable response of axisymmetric two-phase water-saturated soil.
Cai, Yuan-qiang; Meng, Kai; Xu, Chang-jie
2004-09-01
Biot's dynamic consolidation equations and Hankel transform were used to derive the integral solutions of stress and displacement for axisymmetric harmonic excitations in the two-phase saturated soil with subjacent rock-stratum. The influence of the coefficient of permeability and loading frequency on the soil displacement at the ground surface were studied. The results showed that higher loading frequency led to more dynamic characteristics; and that the effect of the soil permeability was more obvious at higher frequencies.
MAGNETIC HELICITY OF SELF-SIMILAR AXISYMMETRIC FORCE-FREE FIELDS
Zhang Mei; Flyer, Natasha; Low, Boon Chye
2012-08-10
In this paper, we continue our theoretical studies addressing the possible consequences of magnetic helicity accumulation in the solar corona. Our previous studies suggest that coronal mass ejections (CMEs) are natural products of coronal evolution as a consequence of magnetic helicity accumulation and that the triggering of CMEs by surface processes such as flux emergence also have their origin in magnetic helicity accumulation. Here, we use the same mathematical approach to study the magnetic helicity of axisymmetric power-law force-free fields but focus on a family whose surface flux distributions are defined by self-similar force-free fields. The semi-analytical solutions of the axisymmetric self-similar force-free fields enable us to discuss the properties of force-free fields possessing a huge amount of accumulated magnetic helicity. Our study suggests that there may be an absolute upper bound on the total magnetic helicity of all bipolar axisymmetric force-free fields. With the increase of accumulated magnetic helicity, the force-free field approaches being fully opened up with Parker-spiral-like structures present around a current-sheet layer as evidence of magnetic helicity in the interplanetary space. It is also found that among the axisymmetric force-free fields having the same boundary flux distribution, the one that is self-similar is the one possessing the maximum amount of total magnetic helicity. This gives a possible physical reason why self-similar fields are often found in astrophysical bodies, where magnetic helicity accumulation is presumably also taking place.
NASA Astrophysics Data System (ADS)
Savenkov, I. V.
2015-02-01
For the pressure-driven flow in an annular channel with a wall moving in the axial direction, its linear instability with respect to axisymmetric perturbations at high Reynolds numbers is investigated within the framework of the triple-deck theory. When the gap between the cylinders is sufficiently small (as compared to the radii of the cylinders), it is shown that the perturbations can split into two wave packets, the first of which grows faster and moves at a higher velocity.
NASA Astrophysics Data System (ADS)
Gariel, J.; Marcilhacy, G.; Santos, N. O.
2008-02-01
We extend the method of separation of variables, studied by Léauté and Marcilhacy [Ann. Inst. Henri Poincare, Sect. A 331, 363 (1979)], to obtain transcendent solutions of the field equations for stationary axisymmetric systems. These solutions depend on transcendent functions satisfying a third order differential equation. For some solutions this equation satisfies the necessary conditions, but not sufficient, to have fixed critical points.
Direct numerical simulations of the turbulent wake of an axisymmetric body
NASA Technical Reports Server (NTRS)
Riley, J. J.; Metcalfe, R. W.
1979-01-01
The paper presents comparisons of results of direct numerical simulations of turbulence with both laboratory data and self-similarity theory for the case of the turbulent wakes of towed, axisymmetric bodies. In general, the agreement of the simulation results with both the laboratory data and the self-similarity theory is good, although the comparisons are hampered by inadequate procedures for initializing the numerical simulations.
RSRM Propellant Grain Geometry Modification
NASA Technical Reports Server (NTRS)
Schorr, Andrew A.; Endicott, Joni B.; McCool, Alex (Technical Monitor)
2000-01-01
This document is composed of viewgraphs about the RSRM propellant grain geometry modification project, which hopes to improve personnel and system safety by modifying propellant grain geometry to improve structural factors of safety. Using techniques such as Finite Element Analysis to determine blend radii required to reduce localized stresses, and ballistic predictions to ensure that the ballistics, ignition transient and Block Model have not been adversely affected, the project hopes to build and test FSM-10 with a new design, and determine flight effectivity pending successful test evaluation.
Geometry, topology, and string theory
Varadarajan, Uday
2003-07-10
A variety of scenarios are considered which shed light upon the uses and limitations of classical geometric and topological notions in string theory. The primary focus is on situations in which D-brane or string probes of a given classical space-time see the geometry quite differently than one might naively expect. In particular, situations in which extra dimensions, non-commutative geometries as well as other non-local structures emerge are explored in detail. Further, a preliminary exploration of such issues in Lorentzian space-times with non-trivial causal structures within string theory is initiated.
Geometry of generalized depolarizing channels
Burrell, Christian K.
2009-10-15
A generalized depolarizing channel acts on an N-dimensional quantum system to compress the 'Bloch ball' in N{sup 2}-1 directions; it has a corresponding compression vector. We investigate the geometry of these compression vectors and prove a conjecture of Dixit and Sudarshan [Phys. Rev. A 78, 032308 (2008)], namely, that when N=2{sup d} (i.e., the system consists of d qubits), and we work in the Pauli basis then the set of all compression vectors forms a simplex. We extend this result by investigating the geometry in other bases; in particular we find precisely when the set of all compression vectors forms a simplex.
NASA Astrophysics Data System (ADS)
Panaras, A.; Drikakis, D.
2009-01-01
The axisymmetric concave body, i.e. a body in which the normals to its surface intersect, is a typical configuration about which shock/shock interactions appear. Various shapes of axisymmetric concave bodies are used in a variety of applications in aeronautics. For exampe: axisymmetric jet inlets with conical centerbody, ballistic missiles drag reduction by spike, plasma or hot gas injection, parachutes for pilot-ejection capsules. However, it is well known that two distinct modes of instability appear around a concave body in the high-speed flow regime, for a certain range of geometric parameters. These instabilities can cause undesirable effects such as severe vibration of the structure, heating and pressure loads. According to the experimental evidence, the unsteady flow is characterized by periodic radial inflation and collapse of the conical separation bubble formed around the forebody (pulsation). Various explanations have been given for the driving mechanism of the instabilities. They are based on interpretation of experimental results or on numerical simulation of the related flows. A merging of the leading explanations is done, and basic rules for the passive suppression of the instabilities are applied, in order to enforce the proposed driving mechanism of the instabilities. Most of the analysis is based on numerical simulations.
General parametrization of axisymmetric black holes in metric theories of gravity
NASA Astrophysics Data System (ADS)
Konoplya, Roman; Rezzolla, Luciano; Zhidenko, Alexander
2016-03-01
Following previous work of ours in spherical symmetry, we here propose a new parametric framework to describe the spacetime of axisymmetric black holes in generic metric theories of gravity. In this case, the metric components are functions of both the radial and the polar angular coordinates, forcing a double expansion to obtain a generic axisymmetric metric expression. In particular, we use a continued-fraction expansion in terms of a compactified radial coordinate to express the radial dependence, while we exploit a Taylor expansion in terms of the cosine of the polar angle for the polar dependence. These choices lead to a superior convergence in the radial direction and to an exact limit on the equatorial plane. As a validation of our approach, we build parametrized representations of Kerr, rotating dilaton, and Einstein-dilaton-Gauss-Bonnet black holes. The match is already very good at lowest order in the expansion and improves as new orders are added. We expect a similar behavior for any stationary and axisymmetric black-hole metric.
On the nonlinear stability of a high-speed, axisymmetric boundary layer
NASA Technical Reports Server (NTRS)
Pruett, C. David; Ng, Lian L.; Erlebacher, Gordon
1991-01-01
The stability of a high-speed, axisymmetric boundary layer is investigated using secondary instability theory and direct numerical simulation. Parametric studies based on the temporal secondary instability theory identify subharmonic secondary instability as a likely path to transition on a cylinder at Mach 4.5. The theoretical predictions are validated by direct numerical simulation at temporally-evolving primary and secondary disturbances in an axisymmetric boundary-layer flow. At small amplitudes of the secondary disturbance, predicted growth rates agree to several significant digits with values obtained from the spectrally-accurate solution of the compressible Navier-Stokes equations. Qualitative agreement persists to large amplitudes of the secondary disturbance. Moderate transverse curvature is shown to significantly affect the growth rate of axisymmetric second mode disturbances, the likely candidates of primary instability. The influence of curvature on secondary instability is largely indirect but most probably significant, through modulation of the primary disturbance amplitude. Subharmonic secondary instability is shown to be predominantly inviscid in nature, and to account for spikes in the Reynolds stress components at or near the critical layer.
Axisymmetrical separator for separating particulate matter from a fluid carrying medium
Linhardt, Hans D.
1984-09-04
A separator for separating particles carried in a fluid carrying medium is disclosed. The separator includes an elongated duct and associated openings incorporated in a solid body. The duct is axisymmetrical relative to its longitudinal axis, and includes a curved wall portion having a curved cross-section taken along the longitudinal axis. An axisymmetrical opening located downstream of the curved wall portion leads from the duct into an axisymmetrical channel which is substantially radially disposed relative to the longitudinal axis. Continuation of the duct downstream of the opening is a discharge portion which is substantially colinear with the longitudinal axis. In operation, a substantial majority of the fluid carrying medium leaves the duct radially through the opening and channel in a state substantially free of particles. A remaining small portion of the fluid carrying medium and a substantial majority of the particles are channelled into the discharge portion by centrifugal forces arising due to travel of the particles along the curved walls. For industrial scale separation of particles from a fluid carrying medium, such as for the clean-up of stack gases, an array of several hundred to several thousand of the separators is provided.
NASA Astrophysics Data System (ADS)
Zhao, Cheng-Gong; Wang, Cong; Wei, Ying-Jie; Zhang, Xiao-Shi
2015-12-01
An experimental study of the axisymmetric slender body underwater movement was conducted using high-speed photography technology. From the results of the experiment, the characteristics of cavitation and ballistic of the axisymmetric, including the formation, development, evolution and collapse of the cavity, are presented in the paper. The experimental results show that the axisymmetric slender body moves in a supercavity, and the slender body rotate in the supercavity on its head at the same time due to the perturbation of launching. The supercavity wall is transparent and smooth except the tail itself. The impact between the tail of slender body and supercavity wall resulted from the slender body's rotation is termed as tail- slap which is one way to keep the stabilization of the movement. Series of different flow mechanisms and the relationship between ballistic characteristics and cavity characteristics with defferent initial velocities are discussed. The slender bodies have different accelerations and ballistics with different initial velocity which means they have different drag forces.
DIII-D Magnetic Diagnostics Upgrade for Non-axisymmetric Fields
NASA Astrophysics Data System (ADS)
Strait, E. J.; King, J. D.; Paz-Soldan, C.; Hanson, J. M.; Shiraki, D.; Logan, N. C.; Boivin, R. L.; Taussig, D. A.; Watkins, M. G.
2013-10-01
A recent upgrade has expanded DIII-D's capabilities for measurement of non-axisymmetric fields such as resistive wall modes, locked tearing modes, and the stable plasma response to error fields and applied non-axisymmetric perturbations. The upgrade includes the addition of over 100 new poloidal field and radial field sensors inside the vacuum vessel. Combined with previously installed sensors, these allow simultaneous resolution of toroidal mode numbers n <= 3 on both the low field side and high field side, and provide poloidal resolution as small as 14 cm on the high field side. The large contribution of the axisymmetric field is eliminated by differential measurements of approximately 120 pairs of toroidally separated sensors, using special dual-input integrators. Initial results from the new system will be compared to predictions of 3D equilibrium and stability codes. Work supported by the US Department of Energy under DE-FC02-04ER54698, DE-AC05-06OR23100, DE-FG02-04ER54761, and DE-AC02-09CH11466.
Teaching Activity-Based Taxicab Geometry
ERIC Educational Resources Information Center
Ada, Tuba
2013-01-01
This study aimed on the process of teaching taxicab geometry, a non-Euclidean geometry that is easy to understand and similar to Euclidean geometry with its axiomatic structure. In this regard, several teaching activities were designed such as measuring taxicab distance, defining a taxicab circle, finding a geometric locus in taxicab geometry, and…
Convective-region geometry as the cause of Uranus' and Neptune's unusual magnetic fields.
Stanley, Sabine; Bloxham, Jeremy
2004-03-11
The discovery of Uranus' and Neptune's non-dipolar, non-axisymmetric magnetic fields destroyed the picture--established by Earth, Jupiter and Saturn--that planetary magnetic fields are dominated by axial dipoles. Although various explanations for these unusual fields have been proposed, the cause of such field morphologies remains unexplained. Planetary magnetic fields are generated by complex fluid motions in electrically conducting regions of the planets (a process known as dynamo action), and so are intimately linked to the structure and evolution of planetary interiors. Determining why Uranus and Neptune have different field morphologies is not only critical for studying the interiors of these planets, but also essential for understanding the dynamics of magnetic-field generation in all planets. Here we present three-dimensional numerical dynamo simulations that model the dynamo source region as a convecting thin shell surrounding a stably stratified fluid interior. We show that this convective-region geometry produces magnetic fields similar in morphology to those of Uranus and Neptune. The fields are non-dipolar and non-axisymmetric, and result from a combination of the stable fluid's response to electromagnetic stress and the small length scales imposed by the thin shell. PMID:15014493
Convective-region geometry as the cause of Uranus' and Neptune's unusual magnetic fields.
Stanley, Sabine; Bloxham, Jeremy
2004-03-11
The discovery of Uranus' and Neptune's non-dipolar, non-axisymmetric magnetic fields destroyed the picture--established by Earth, Jupiter and Saturn--that planetary magnetic fields are dominated by axial dipoles. Although various explanations for these unusual fields have been proposed, the cause of such field morphologies remains unexplained. Planetary magnetic fields are generated by complex fluid motions in electrically conducting regions of the planets (a process known as dynamo action), and so are intimately linked to the structure and evolution of planetary interiors. Determining why Uranus and Neptune have different field morphologies is not only critical for studying the interiors of these planets, but also essential for understanding the dynamics of magnetic-field generation in all planets. Here we present three-dimensional numerical dynamo simulations that model the dynamo source region as a convecting thin shell surrounding a stably stratified fluid interior. We show that this convective-region geometry produces magnetic fields similar in morphology to those of Uranus and Neptune. The fields are non-dipolar and non-axisymmetric, and result from a combination of the stable fluid's response to electromagnetic stress and the small length scales imposed by the thin shell.
LOGO Based Instruction in Geometry.
ERIC Educational Resources Information Center
Yusuf, Mian Muhammad
The objective of this pretest-posttest Quasi-Experimental Design study was to determine the effects of LOGO Based Instruction (LBI) compared to instruction by teacher lecture and pencil-and-paper activities on: (1) students' understanding of the concepts of point, ray, line, and line segment; (2) students' attitudes toward learning geometry,…
Exploring Bundling Theory with Geometry
ERIC Educational Resources Information Center
Eckalbar, John C.
2006-01-01
The author shows how instructors might successfully introduce students in principles and intermediate microeconomic theory classes to the topic of bundling (i.e., the selling of two or more goods as a package, rather than separately). It is surprising how much students can learn using only the tools of high school geometry. To be specific, one can…
General Relativity: Geometry Meets Physics
ERIC Educational Resources Information Center
Thomsen, Dietrick E.
1975-01-01
Observing the relationship of general relativity and the geometry of space-time, the author questions whether the rest of physics has geometrical explanations. As a partial answer he discusses current research on subatomic particles employing geometric transformations, and cites the existence of geometrical definitions of physical quantities such…
Teaching Geometry According to Euclid.
ERIC Educational Resources Information Center
Hartshorne, Robin
2000-01-01
This essay contains some reflections and questions arising from encounters with the text of Euclid's Elements. The reflections arise out of the teaching of a course in Euclidean and non-Euclidean geometry to undergraduates. It is concluded that teachers of such courses should read Euclid and ask questions, then teach a course on Euclid and later…
Analogical Reasoning in Geometry Education
ERIC Educational Resources Information Center
Magdas, Ioana
2015-01-01
The analogical reasoning isn't used only in mathematics but also in everyday life. In this article we approach the analogical reasoning in Geometry Education. The novelty of this article is a classification of geometrical analogies by reasoning type and their exemplification. Our classification includes: analogies for understanding and setting a…
Foucault pendulum through basic geometry
NASA Astrophysics Data System (ADS)
von Bergmann, Jens; von Bergmann, HsingChi
2007-10-01
We provide a thorough explanation of the Foucault pendulum that utilizes its underlying geometry on a level suitable for science students not necessarily familiar with calculus. We also explain how the geometrically understood Foucault pendulum can serve as a prototype for more advanced phenomena in physics known as Berry's phase or geometric phases.
Spectral geometry of symplectic spinors
NASA Astrophysics Data System (ADS)
Vassilevich, Dmitri
2015-10-01
Symplectic spinors form an infinite-rank vector bundle. Dirac operators on this bundle were constructed recently by Habermann, K. ["The Dirac operator on symplectic spinors," Ann. Global Anal. Geom. 13, 155-168 (1995)]. Here we study the spectral geometry aspects of these operators. In particular, we define the associated distance function and compute the heat trace asymptotics.
Exploring Fractal Geometry with Children.
ERIC Educational Resources Information Center
Vacc, Nancy Nesbitt
1999-01-01
Heightens the awareness of elementary school teachers, teacher educators, and teacher-education researchers of possible applications of fractal geometry with children and, subsequently, initiates discussion about the appropriateness of including this new mathematics in the elementary curriculum. Presents activities for exploring children's…
Differential geometry meets the cell.
Marshall, Wallace F
2013-07-18
A new study by Terasaki et al. highlights the role of physical forces in biological form by showing that connections between stacked endoplasmic reticulum cisternae have a shape well known in classical differential geometry, the helicoid, and that this shape is a predictable consequence of membrane physics.
Instructional Identities of Geometry Students
ERIC Educational Resources Information Center
Aaron, Wendy Rose; Herbst, Patricio
2012-01-01
We inspect the hypothesis that geometry students may be oriented toward how they expect that the teacher will evaluate them as students or otherwise oriented to how they expect that their work will give them opportunities to do mathematics. The results reported here are based on a mixed-methods analysis of twenty-two interviews with high school…
Physiological optics and physical geometry.
Hyder, D J
2001-09-01
Hermann von Helmholtz's distinction between "pure intuitive" and "physical" geometry must be counted as the most influential of his many contributions to the philosophy of science. In a series of papers from the 1860s and 70s, Helmholtz argued against Kant's claim that our knowledge of Euclidean geometry was an a priori condition for empirical knowledge. He claimed that geometrical propositions could be meaningful only if they were taken to concern the behaviors of physical bodies used in measurement, from which it followed that it was posterior to our acquaintance with this behavior. This paper argues that Helmholtz's understanding of geometry was fundamentally shaped by his work in sense-physiology, above all on the continuum of colors. For in the course of that research, Helmholtz was forced to realize that the color-space had no inherent metrical structure. The latter was a product of axiomatic definitions of color-addition and the empirical results of such additions. Helmholtz's development of these views is explained with detailed reference to the competing work of the mathematician Hermann Grassmann and that of the young James Clerk Maxwell. It is this separation between 1) essential properties of a continuum, 2) supplementary axioms concerning distance-measurement, and 3) the behaviors of the physical apparatus used to realize the axioms, which is definitive of Helmholtz's arguments concerning geometry.
Noncommutative geometry inspired entropic inflation
NASA Astrophysics Data System (ADS)
Nozari, Kourosh; Akhshabi, Siamak
2011-06-01
Recently Verlinde proposed that gravity can be described as an emergent phenomena arising from changes in the information associated with the positions of material bodies. By using noncommutative geometry as a way to describe the microscopic microstructure of quantum spacetime, we derive modified Friedmann equation in this setup and study the entropic force modifications to the inflationary dynamics of early universe.
Math Sense: Algebra and Geometry.
ERIC Educational Resources Information Center
Howett, Jerry
This book is designed to help students gain the range of math skills they need to succeed in life, work, and on standardized tests; overcome math anxiety; discover math as interesting and purposeful; and develop good number sense. Topics covered in this book include algebra and geometry. Lessons are organized around four strands: (1) skill lessons…
Signature geometry and quantum engineering
NASA Astrophysics Data System (ADS)
Samociuk, Stefan
2013-09-01
As the operating frequency of electromagnetic based devices increase, physical design geometry is playing an ever more important role. Evidence is considered in support of a relationship between the dimensionality of primitive geometric forms, such as transistors, and corresponding electromagnetic coupling efficiency. The industry of electronics is defined as the construction of devices by the patterning of primitive forms to physical materials. Examples are given to show the evolution of these primitives, down to nano scales, are requiring exacting geometry and three dimensional content. Consideration of microwave monolithic integrated circuits,(MMIC), photonics and metamaterials,(MM), support this trend and also add new requirements of strict geometric periodicity and multiplicity. Signature geometries,(SG), are characterized by distinctive attributes and examples are given. The transcendent form transcode algorithm, (TTA) is introduced as a multi dimensional SG and its use in designing photonic integrated circuits and metamaterials is discussed . A creative commons licensed research database, TRANSFORM, containing TTA geometries in OASIS file formats is described. An experimental methodology for using the database is given. Multidimensional SG and extraction of three dimensional cross sections as primitive forms is discussed as a foundation for quantum engineering and the exploitation of phenomena other than the electromagnetic.
On the Explosion Geometry of Red Supergiant Stars
NASA Astrophysics Data System (ADS)
Leonard, Douglas Christopher; Dessart, Luc; Pignata, Giuliano; Hillier, D. John; Williams, George Grant; Smith, Paul S.; Khandrika, Harish; Bilinski, Christopher; Duong, Nhieu; Flatland, Kelsi; Gonzalez, Luis; Hoffman, Jennifer L.; Horst, Chuck; Huk, Leah; Milne, Peter; Rachubo, Alisa A.; Smith, Nathan
2015-08-01
From progenitor studies, type II-Plateau supernovae (SNe II-P) have been decisively and uniquely determined to arise from isolated red supergiant (RSG) stars with initial masses ranging from 8 to 16 solar masses (Smartt 2009), establishing the most homogeneous -- and well understood -- progenitor class of any type of core-collapse supernova. However, we must admit a fundamental truth: We do not know how these stars explode. A basic discriminant among proposed explosion models is explosion geometry, since some models predict severe distortions from spherical symmetry. A primary method to gain such geometric information is through spectropolarimetry of the expanding (but, unresolved) atmosphere, with higher degrees of linear polarization generally demanding larger departures from spherical symmetry. Initially, as a class, SNe II-P were found to be only weakly polarized at the early epochs observed, suggesting a nearly spherical explosion for RSG stars. However, late-time observations of SN 2004dj captured a dramatic spike in polarization at just the moment the "inner core" of the ejecta was first revealed in this SN II-P (i.e., at the "drop" off of the photometric plateau; Leonard et al. 2006). This raised the possibility that the explosion of RSGs might be driven by a strongly non-spherical mechanism, with the evidence for the asphericity cloaked at early times by the massive, opaque, quasi-spherical hydrogen envelope. In this presentation we shall describe the continuing work on the explosion geometry of RSGs being carried out by the SuperNova SpectroPOLarimetry project (SNSPOL), with a particular focus on SN 2013ej -- an SN II-P that exhibited remarkably high polarization just days after the explosion (Leonard et al. 2013), and for which twelve epochs of spectropolarimetry trace an intriguing tale about its geometry deep into the nebular phase. We acknowledge support from NSF grants AST-1009571 and AST-1210311, under which part of this research was carried out.
NASA Astrophysics Data System (ADS)
Sharma, Amit Kumar; Chandra, Sulekh
2011-10-01
Complexes of the type [M(L)X 2], where M = Co(II), Ni(II) and Cu(II), have been synthesized with novel NO-donor Schiff's base ligand, 1,4-diformylpiperazine bis(4-imino-2,3-dimethyl-1-phenyl-3-pyrazolin-5-one) which is obtained by the acid catalyzed condensation of 1,4-diformylpiperazine with 4-aminoantipyrine. The elemental analyses, molar conductance measurements, magnetic susceptibility measurements, IR, UV, NMR, mass and EPR studies of the compounds led to the conclusion that the ligand acts as tetradentate chelate. The Schiff's base ligand forms hexacoordinated complexes having octahedral geometry for Ni(II) and tetragonal geometry for Co(II) and Cu(II) complexes. The mycological studies of the compounds were examined against the several opportunistic pathogens, i.e., Alternaria brassicae, Aspergillus niger and Fusarium oxysporum. The Cu(II) complexes were found to have most fungicidal behavior.
Experimental study of effect of stenosis geometry on pressure loss for periodic flow
NASA Astrophysics Data System (ADS)
Veselý, Ondřej; Nováková, Ludmila; Adamec, Josef
2016-03-01
A stenosis is a narrowing in a tubular organ. In medicine, vessel stenosis poses health risk for people. In the last work, experimental investigation of pressure loss coefficient for varying stenosis eccentricity and shape for steady flow were performed. In this work, experimental investigation of pressure loss for varying stenosis eccentricity and shape under periodic flow were performed. Four models of different geometry were studied, two models are axisymmetric stenoses and two models are eccentric stenoses. All models were stenosis of 75% area reduction. The periodic flow, generated by a controllable pump, has sinus shape in an inlet. The measuring range of medium Reynolds number was from 500 to 1500, range of ratio between an amplitude and medium flow rate was from 0.2 to 0.6 and range of frequency was from 0.2 to 1 Hz. The pressure loss for each conditions was quantified by mean value, amplitude and phase shift against flow rate.
Stringy differential geometry, beyond Riemann
NASA Astrophysics Data System (ADS)
Jeon, Imtak; Lee, Kanghoon; Park, Jeong-Hyuck
2011-08-01
While the fundamental object in Riemannian geometry is a metric, closed string theories call for us to put a two-form gauge field and a scalar dilaton on an equal footing with the metric. Here we propose a novel differential geometry that treats the three objects in a unified manner, manifests not only diffeomorphism and one-form gauge symmetry but also O(D,D) T-duality, and enables us to rewrite the known low energy effective action of them as a single term. Further, we develop a corresponding vielbein formalism and gauge the internal symmetry that is given by a direct product of two local Lorentz groups, SO(1,D-1)×SŌ(1,D-1). We comment that the notion of cosmological constant naturally changes.
Geometry-invariant resonant cavities
Liberal, I.; Mahmoud, A. M.; Engheta, N.
2016-01-01
Resonant cavities are one of the basic building blocks in various disciplines of science and technology, with numerous applications ranging from abstract theoretical modelling to everyday life devices. The eigenfrequencies of conventional cavities are a function of their geometry, and, thus, the size and shape of a resonant cavity is selected to operate at a specific frequency. Here we demonstrate theoretically the existence of geometry-invariant resonant cavities, that is, resonators whose eigenfrequencies are invariant with respect to geometrical deformations of their external boundaries. This effect is obtained by exploiting the unusual properties of zero-index metamaterials, such as epsilon-near-zero media, which enable decoupling of the temporal and spatial field variations in the lossless limit. This new class of resonators may inspire alternative design concepts, and it might lead to the first generation of deformable resonant devices. PMID:27010103
Geometry of area without length
NASA Astrophysics Data System (ADS)
Ho, Pei-Ming; Inami, Takeo
2016-01-01
To define a free string by the Nambu-Goto action, all we need is the notion of area, and mathematically the area can be defined directly in the absence of a metric. Motivated by the possibility that string theory admits backgrounds where the notion of length is not well defined but a definition of area is given, we study space-time geometries based on the generalization of a metric to an area metric. In analogy with Riemannian geometry, we define the analogues of connections, curvatures, and Einstein tensor. We propose a formulation generalizing Einstein's theory that will be useful if at a certain stage or a certain scale the metric is ill defined and the space-time is better characterized by the notion of area. Static spherical solutions are found for the generalized Einstein equation in vacuum, including the Schwarzschild solution as a special case.
Hyperbolic geometry for colour metrics.
Farup, Ivar
2014-05-19
It is well established from both colour difference and colour order perpectives that the colour space cannot be Euclidean. In spite of this, most colour spaces still in use today are Euclidean, and the best Euclidean colour metrics are performing comparably to state-of-the-art non-Euclidean metrics. In this paper, it is shown that a transformation from Euclidean to hyperbolic geometry (i.e., constant negative curvature) for the chromatic plane can significantly improve the performance of Euclidean colour metrics to the point where they are statistically significantly better than state-of-the-art non-Euclidean metrics on standard data sets. The resulting hyperbolic geometry nicely models both qualitatively and quantitatively the hue super-importance phenomenon observed in colour order systems.
Geometry Dependence of Stellarator Turbulence
H.E. Mynick, P. Xanthopoulos and A.H. Boozer
2009-08-10
Using the nonlinear gyrokinetic code package GENE/GIST, we study the turbulent transport in a broad family of stellarator designs, to understand the geometry-dependence of the microturbulence. By using a set of flux tubes on a given flux surface, we construct a picture of the 2D structure of the microturbulence over that surface, and relate this to relevant geometric quantities, such as the curvature, local shear, and effective potential in the Schrodinger-like equation governing linear drift modes.
Orbit propagation in Minkowskian geometry
NASA Astrophysics Data System (ADS)
Roa, Javier; Peláez, Jesús
2015-09-01
The geometry of hyperbolic orbits suggests that Minkowskian geometry, and not Euclidean, may provide the most adequate description of the motion. This idea is explored in order to derive a new regularized formulation for propagating arbitrarily perturbed hyperbolic orbits. The mathematical foundations underlying Minkowski space-time are exploited to describe hyperbolic orbits. Hypercomplex numbers are introduced to define the rotations, vectors, and metrics in the problem: the evolution of the eccentricity vector is described on the Minkowski plane in terms of hyperbolic numbers, and the orbital plane is described on the inertial reference using quaternions. A set of eight orbital elements is introduced, namely a time-element, the components of the eccentricity vector in , the semimajor axis, and the components of the quaternion defining the orbital plane. The resulting formulation provides a deep insight into the geometry of hyperbolic orbits. The performance of the formulation in long-term propagations is studied. The orbits of four hyperbolic comets are integrated and the accuracy of the solution is compared to other regularized formulations. The resulting formulation improves the stability of the integration process and it is not affected by the perihelion passage. It provides a level of accuracy that may not be reached by the compared formulations, at the cost of increasing the computational time.
Tanaka, Masaomi; Iye, Masanori; Kawabata, Koji S.; Yamanaka, Masayuki; Hattori, Takashi; Aoki, Kentaro; Sasaki, Toshiyuki; Mazzali, Paolo A.; Maeda, Keiichi; Nomoto, Ken'ichi; Pian, Elena
2012-07-20
We study the multi-dimensional geometry of supernova (SN) explosions by means of spectropolarimetric observations of stripped-envelope SNe, i.e., SNe without a hydrogen-rich layer. We perform spectropolarimetric observations of two stripped-envelope SNe, Type Ib SN 2009jf and Type Ic SN 2009mi. Both objects show non-zero polarization at the wavelength of the strong lines. They also show a loop in the Stokes Q - U diagram, which indicates a non-axisymmetric, three-dimensional ion distribution in the ejecta. We show that five out of six stripped-envelope SNe, which have been observed spectropolarimetrically so far, show such a loop. This implies that a three-dimensional geometry is common in stripped-envelope SNe. We find that stronger lines tend to show higher polarization. This effect is not related to the geometry, and must be corrected for to compare the polarization of different lines or different objects. Even after the correction, however, there remains a dispersion of polarization degree among different objects. Such a dispersion might be caused by three-dimensional clumpy ion distributions viewed from different directions.
Takeda, M; Hiratsuka, T; Ito, K; Finsterle, S
2011-04-25
Diffusion anisotropy is a critical property in predicting migration of substances in sedimentary formations with very low permeability. The diffusion anisotropy of sedimentary rocks has been evaluated mainly from laboratory diffusion experiments, in which the directional diffusivities are separately estimated by through-diffusion experiments using different rock samples, or concurrently by in-diffusion experiments in which only the tracer profile in a rock block is measured. To estimate the diffusion anisotropy from a single rock sample, this study proposes an axisymmetric diffusion test, in which tracer diffuses between a cylindrical rock sample and a surrounding solution reservoir. The tracer diffusion between the sample and reservoir can be monitored from the reservoir tracer concentrations, and the tracer profile could also be obtained after dismantling the sample. Semi-analytical solutions are derived for tracer concentrations in both the reservoir and sample, accounting for an anisotropic diffusion tensor of rank two as well as the dilution effects from sampling and replacement of reservoir solution. The transient and steady-state analyses were examined experimentally and numerically for different experimental configurations, but without the need for tracer profiling. These experimental configurations are tested for in- and out-diffusion experiments using Koetoi and Wakkanai mudstones and Shirahama sandstone, and are scrutinized by a numerical approach to identify favorable conditions for parameter estimation. The analysis reveals the difficulty in estimating diffusion anisotropy; test configurations are proposed for enhanced identifiability of diffusion anisotropy. Moreover, it is demonstrated that the axisymmetric diffusion test is efficient in obtaining the sorption parameter from both steady-state and transient data, and in determining the effective diffusion coefficient if isotropic diffusion is assumed. Moreover, measuring reservoir concentrations in an