Axisymmetric Pattern Research Articles

Analyzing X-ray pulsar profiles: geometry and beam pattern of A 0535+26

We applied a decomposition method to the energy dependent pulse profiles of the accreting binary pulsar A 0535+26, in order to identify the contribution of the two magnetic poles of the neutron star and to obtain constraints on the geometry of the system and on the beam pattern. We analyzed pulse profiles obtained from RXTE observations in the X-ray regime. Basic assumptions of the method are that the asymmetry observed in the pulse profiles is caused by non-antipodal magnetic poles and that the emission regions have axisymmetric beam patterns. Constraints on the geometry of the pulsar and a possible solution of the beam pattern are given. We interpreted the reconstructed beam pattern in terms of a geometrical model of a hollow column plus a halo of scattered radiation on the neutron star surface, which includes relativistic light deflection.

Pattern formation in drying drops of blood

The drying of a drop of human blood exhibits coupled physical mechanisms, such as Marangoni flow, evaporation and wettability. The final stage of a whole blood drop evaporation reveals regular patterns with a good reproducibility for a healthy person. Other experiments on anaemic and hyperlipidaemic people were performed, and different patterns were revealed. The flow motion inside the blood drop is observed and analysed with the use of a digital camera: the influence of the red blood cells motion is revealed at the drop periphery as well as its consequences on the final stage of drying. The mechanisms which lead to the final pattern of the dried blood drops are presented and explained on the basis of fluid mechanics in conjunction with the principles of haematology. The blood drop evaporation process is evidenced to be driven only by Marangoni flow. The same axisymmetric pattern formation is observed, and can be forecast for different blood drop diameters. The evaporation mass flux can be predicted with a good agreement, assuming only the knowledge of the colloids mass concentration.

MAGNETIC FIELDS AND THE OUTER ROTATION CURVE OF M31

Recent observations of the rotation curve of M31 show a rise of the outer part that can not be understood in terms of standard dark matter models or perturbations of the galactic disc by M31's satellites. Here, we propose an explanation of this dynamical feature based on the influence of the magnetic field within the thin disc. We have considered standard mass models for the luminous mass distribution, a NFW model to describe the dark halo, and we have added up the contribution to the rotation curve of a magnetic field in the disc, which is described by an axisymmetric pattern. Our conclusion is that a significant improvement of the fit in the outer part is obtained when magnetic effects are considered. The best-fit solution requires an amplitude of ~4 microG with a weak radial dependence between 10 and 38 kpc.

CFD ANALYSIS OF TURBULENT JET BEHAVIOR INDUCED BY A STEAM JET DISCHARGED THROUGH A VERTICAL UPWARD SINGLE HOLE IN A SUBCOOLED WATER POOL

Thermal mixing by steam jets in a pool is dominantly influenced by a turbulent water jet generated by the condensing steam jets, and the proper prediction of this turbulent jet behavior is critical for the pool mixing analysis. A turbulent jet flow induced by a steam jet discharged through a vertical upward single hole into a subcooled water pool was subjected to computational fluid dynamics (CFD) analysis. Based on the small-scale test data derived under a horizontal steam discharging condition, this analysis was performed to validate a CFD method of analysis previously developed for condensing jet-induced pool mixing phenomena. In previous validation work, the CFD results and the test data for a limited range of radial and axial directions were compared in terms of profiles of the turbulent jet velocity and temperature. Furthermore, the behavior of the turbulent jet induced by the steam jet through a horizontal single hole in a subcooled water pool failed to show the exact axisymmetric flow pattern with regards to an overall pool mixing, whereas the CFD analysis was done with an axisymmetric grid model. Therefore, another new small-scale test was conducted under a vertical upward steam discharging condition. The purpose of this test was to generate the velocity and temperature profiles of the turbulent jet by expanding the measurement ranges from the jet center to a location at about 5% of <TEX>$U_m$</TEX> and 10 cm to 30 cm from the exit of the discharge nozzle. The results of the new CFD analysis show that the recommended CFD model of the high turbulent intensity of 40% for the turbulent jet and the fine mesh grid model can accurately predict the test results within an error rate of about 10%. In this work, the turbulent jet model, which is used to simply predict the temperature and velocity profiles along the axial and radial directions by means of the empirical correlations and Tollmien's theory was improved on the basis of the new test data. The results validate the CFD model of analysis. Furthermore, the turbulent jet model developed in this study can be used to analyze pool thermal mixing when an ellipsoidal steam jet is discharged under a high steam mass flux in a subcooled water pool.

Extreme multiplicity in cylindrical Rayleigh-Bénard convection. II. Bifurcation diagram and symmetry classification

A large number of flows with distinctive patterns have been observed in experiments and simulations of Rayleigh-Bénard convection in a water-filled cylinder whose radius is twice the height. We have adapted a time-dependent pseudospectral code, first, to carry out Newton's method and branch continuation and, second, to carry out the exponential power method and Arnoldi iteration to calculate leading eigenpairs and determine the stability of the steady states. The resulting bifurcation diagram represents a compromise between the tendency in the bulk toward parallel rolls and the requirement imposed by the boundary conditions that primary bifurcations be toward states whose azimuthal dependence is trigonometric. The diagram contains 17 branches of stable and unstable steady states. These can be classified geometrically as roll states containing two, three, and four rolls; axisymmetric patterns with one or two tori; threefold-symmetric patterns called Mercedes, Mitsubishi, marigold, and cloverleaf; trigonometric patterns called dipole and pizza; and less symmetric patterns called CO and asymmetric three rolls. The convective branches are connected to the conductive state and to each other by 16 primary and secondary pitchfork bifurcations and turning points. In order to better understand this complicated bifurcation diagram, we have partitioned it according to azimuthal symmetry. We have been able to determine the bifurcation-theoretic origin from the conductive state of all the branches observed at high Rayleigh number.

Measurement of liquid film thickness in micro square channel

In micro channels, slug flow becomes one of the main flow regimes due to strong surface tension. In micro channel slug flow, elongated bubble flows with the thin liquid film confined between the bubble and the channel wall. Liquid film thickness is an important parameter in many applications, e.g., micro heat exchanger, micro reactor, coating process etc. In the present study, liquid film thickness in micro square channels is measured locally and instantaneously with the confocal method. Square channels with hydraulic diameter of D h = 0.3, 0.5 and 1.0 mm are used. In order to investigate the effect of inertial force on the liquid film thickness, three working fluids, ethanol, water and FC-40 are used. At small capillary numbers, liquid film at the channel center becomes very thin and the bubble interface is not axisymmetric. However, as capillary number increases, bubble interface becomes axisymmetric. Transition from non-axisymmetric to axisymmetric flow pattern starts from lower capillary number as Reynolds number increases. An empirical correlation for predicting axisymmetric bubble radius based on capillary number and Weber number is proposed from the present experimental data.

Axial buckling of an orthotropic circular cylinder: Application to orthogrid concept

A novel re-defining of the orthotropic material properties in terms of a so-called associated geometric mean isotropic (GMI) material is used to develop a thorough buckling analysis of an axially-loaded orthotropic circular cylinder. A membrane prebuckling condition is assumed and an expression for the buckling stress is derived in terms of cylinder geometry, orthotropic material properties, and the number of waves in the buckling deformation pattern in the axial and circumferential directions. By assuming the number of waves in each direction are real-valued variables, as opposed to integers, conditions which result in stationary values of the buckling stress are sought, and once found, examined for their character as regards representing minima, maxima, or saddle points. Three quite different buckling characteristics are predicted, the particulars depending on the shear modulus of the orthotropic material relative to that of the associated GMI material. It is shown that if the shear modulus of the orthotropic material is greater than the shear modulus of the associated GMI material, the cylinder buckles into a unique axisymmetric deformation pattern. If the shear modulus of the orthotropic material is less than the shear modulus of the associated GMI material, the cylinder buckles into a unique nonaxisymmetric deformation pattern. If the shear modulus of the orthotropic material is exactly equal to the shear modulus of the associated GMI material (this is the situation for an isotropic cylinder), the cylinder can buckle into either axisymmetric or nonaxisymmetric deformation patterns. Moreover it is shown that, in this case, there exists a number of deformation patterns, all at essentially the same stress level. Closed-form lower-bound expressions for the buckling stress are developed using the adopted notation, the value of the shear modulus relative to the shear modulus of the GMI material determining which expression is applicable. The results of this analysis are applied to a circular cylinder constructed of a lattice structure consisting of helical and circumferential ribs, a so-called orthogrid lattice cylinder, where it is assumed that the ribs of the lattice structure are dense enough to be able to represent the elastic properties of the lattice with an equivalent homogenized orthotropic material. An isogrid cylinder, where the helical rib angle is 30° relative to the axial direction, is a special case. The orthotropic cylinder analysis is reformulated in terms of the material properties of the ribs and the angle of the helical ribs. For this situation the isogrid case is the GMI material, and the rib angle determines whether the shear modulus of the equivalent orthotropic material is greater than or less than the GMI material. This translates into the character of the buckling deformations depending directly on the rib angle.

Modulated rotating convection: radially travelling concentric rolls

Recent experiments in rotating convection have shown that the spatio-temporal bulk convective state with Küppers–Lortz dynamics can be suppressed by small-amplitude modulations of the rotation rate. The resultant axisymmetric pulsed target patterns were observed to develop into axisymmetric travelling target patterns as the modulation amplitude and Rayleigh number were increased. Using the Navier–Stokes–Boussinesq equations with physical boundary conditions, we are able to numerically reproduce the experimental results and gain physical insight into the responsible mechanism, relating the onset of the travelling target patterns to a symmetry-restoring saddle-node on an invariant circle bifurcation. Movies are available with the online version of the paper.

Pearl and mushroom instability patterns in two miscible fluids' core annular flows

We report on experiments with two miscible fluids of equal density but different viscosities. The fluids were injected co-currently and concentrically into a cylindrical pipe. The resulting base state is an axisymmetric parallel flow. The ratio of the two fluid flow rates determines the relative amount of the fluids, thus the radius of the inner core fluid. Depending on this radius and the total flow rate, two different and unstable axisymmetric patterns, denoted by mushrooms and pearls, were observed. We delineate the diagram of occurrence of the two patterns as a function of the various parameters.

Visualization of convection patterns near an evaporating meniscus using μPIV

Experimental visualizations of the three dimensional (3D) convection patterns generated near an evaporating meniscus in horizontally oriented capillary tubes are presented. These patterns are caused due to the differential evaporation along the meniscus. In this study, transparent capillary tubes with refractive index close to that of the evaporating liquid were used to minimize refraction effects and obtain velocity vectors near the walls. Polystyrene fluorescent particles of 0.5 μm diameter suspended in methanol were used to make the measurements in tubes of 75, 200 and 400 μm diameter. For the 75 μm tube, gravity was observed to have no effect on the flow patterns and an axisymmetric counter-rotating vortex pair was present along the horizontal and vertical center planes, suggesting the presence of a toroidal vortex near the meniscus. With an increase in tube size, buoyancy effects became apparent as the axisymmetric pattern broke down. A counter-rotating symmetric vortex pair was observed in the horizontal center plane, whereas in the vertical center plane, a single vortex dominated the flow and pushed the secondary vortex to a corner. Particle streak and μPIV images were obtained in multiple horizontal planes and a vertical center plane to understand this 3D flow behavior.

Competition between axisymmetric and three-dimensional patterns between exactly counter-rotating disks

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&amp;gt;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.

Experimental study on the transition process to the oscillatory thermocapillary convections in a floating half zone

The transition process of the thermocapillary convection from a steady and axisymmetric mode to the oscillatory mode in a liquid bridge with a fixed aspect ratio and varied volume ratio was studied experimentally. To ensure the surface tension to play an important role in the ground-based experiment, the geometrical configuration of the liquid bridge was so designed that the associated dynamic Bond number Bd ≈ 1. The velocity fields were measured by Particle Image Velocimetry (PIV) technique to effectively distinguish the different flow modes during the transition period in the experiments. Our experiments showed that as the temperature difference increased the slender and fat bridges presented quite different features on the evolution in their flow feature: for the former the thermocapillary convection transformed from a steady and axisymmetric pattern directly into an oscillatory one; but for the latter a transition flow status, characterized by an axial asymmetric steady convection, appeared before reaching the oscillatory mode. Experimental observations agree with the results of numerical simulations and it is obvious that the volume of liquid bridge is a sensitive geometric parameter. In addition, at the initial stage of the oscillation, for the former a rotating oscillatory convection with azimuthal wave number m = 1 was observed while for the latter a pulsating oscillatory pattern with azimuthal wave number m = 2 emerged, and then with further increase of the temperature difference, the pulsating oscillatory convection with azimuthal wave number m = 2 evolved into a rotating oscillatory pattern with azimuthal wave number m = 2.

Three-dimensional computation of convection of water at the center of a superconducting magnet

Magnetothermal convection of water (diamagnetic) contained in a shallow, cylindrical vessel heated from below and cooled from above at the center of a superconducting magnet was numerically studied. Various flow patterns appeared under the influence of the magnetic body force. The flows induced by the magnetic force whose radial component at the vessel side wall was 5.0 times gravity became axisymmetric, and the direction of the flow was opposite to that of the buoyancy-driven thermal convection. When the radial component was as large as gravity, the breaking and recovery of the axisymmetric flow pattern were aperiodically repeated. When it was 0.1 or 0.5 times gravity, the flow showed a three-spoke pattern, breaking axisymmetry. It is discussed that the conditions to obtain such a spoke pattern experimentally are application of a relatively small magnetic field, use of a shallow vessel, and observation for sufficiently long time.

Sound Generated by a Pair of Axisymmetric viscous Coaxial Vortex Rings.

The time-dependent acoustic field generated by the mutual interaction of a pair of coaxial viscous vortex rings advecting along a common axis of symmetry is simulated using a two-step numerical procedure. In the first step, the flowfield is predicted by solving the incompressible Navier‐Stokes equations. In the second step, Powell’s vortex sound theory is used to predict the far-field acoustic field associated with the flow unsteadiness. This study considers the effect of the initial toroidal ring radii on the sound radiation. The acoustic predictions are compared with those obtained using the method of matched asymptotic expansions. Our results indicate that the acoustic signature for the Mach-number range simulated shows an axisymmetric lateral quadrupole pattern. In addition, the time variation of the far-field acoustic signal displays significant effects caused by vortex dynamics associated with the finite-sized cores and viscous diffusion. These effects are more pronounced for rings with a smaller initial toroidal radius. The influence of Mach number on the far-field directivity (e.g., location of polar extinction angles) and the multipole content of the acoustic signal is examined through a multipole decomposition of the predicted acoustic fields.

Asymptotic theory for disc-like crystal growth (II): interfacial instability and pattern formation at early stage of growth

This paper is a continuation of the paper ([1] ), which is called paper (I) afterward. In the present paper, which we shall call paper (II), we study the interfacial instability property of the side interface of a growing disc-like crystal at the early stage of growth by using the approach developed in the interfacial wave (IFW) theory of dendritic growth. Our analysis show that the system allows two types of unstable modes over the side-interface: (1). The axi-symmetric $(m=0)$ modes. The most dangerous axi-symmetric mode is the base mode $A_0$, which is responsible for formation of the axi-symmetric pattern over the side-interface, anti-symmetric about the central plane of the disc; (2). The non-axi-symmetric modes, which are responsible for non-axi-symmetric pattern formation around the edge of the disc. The growth rates of these non-axi-symmetric modes are much smaller than the growth rate of the base mode $A_0$. During the course of disc growth, the unstable $A_0$-mode merges first. It leads to the formation of anti-symmetric pattern about the central plane over the side-interface. Following the onset of unstable base mode $A_0$, a set of non-axi-symmetric growing modes also appear. However, due to the smallness of growth rate of these unstable modes, the non-axi-symmetric pattern around the edge of the disc becomes observable, only after a sufficiently long time. Our theoretical predictions are in good agreement with the available experimental data.

Nanoparticle transport and deposition in bifurcating tubes with different inlet conditions

Transport and deposition of ultrafine particles in straight, bent and bifurcating tubes are considered for different inlet Reynolds numbers, velocity profiles, and particle sizes, i.e., 1 nm⩽dp⩽150 nm. A commercial finite-volume code with user-supplied programs was validated with analytical correlations and experimental data sets for nanoparticle depositions, considering a straight tube, a tubular 90° bend, and a G3-G5 double bifurcation with both planar and nonplanar configurations. The focus is on the airflow structures as well as nanoparticle deposition patterns and deposition efficiencies, which were analyzed for planar and nonplanar bifurcating lung airway models representing part of the upper bronchial tree. Deposition takes place primarily by Brownian diffusion, and thus deposition efficiencies increase with decreasing nanoparticle size and lower inlet Reynolds numbers. Deposition in the nonplanar configuration differs only slightly from that in the planar configuration. When compared with axisymmetric inlet conditions, the more realistic, skewed inlet velocity and particle profiles generate nearly axisymmetric deposition patterns as well. This work may elucidate basic physical insight of ultrafine particle transport and deposition relevant to environmental, industrial and biomedical studies.

Recovery of transverse velocities of steadily rotating patterns in flat galaxies

The transverse velocities of steadily rotating, non--axisymmetric patterns in flat galaxies may be determined by a purely kinematical method, using two dimensional maps of a tracer surface brightness and radial current density. The data--maps could be viewed as the zeroth and first velocity moments of the line--of--sight velocity distribution, which is the natural output of integral--field spectrographs. Our method is closely related to the Tremaine--Weinberg method of estimating pattern speeds of steadily rotating patterns, when the tracer surface brightness satisfies a source--free continuity equation. We prove that, under identical assumptions about the pattern, two dimensional maps may be used to recover not just one number (the pattern speed), but the full vector field of tracer flow in the disc plane. We illustrate the recovery process by applying it to simulated data, and test its robustness by including the effects of noise.

Asymptotic solutions of stationary patterns in convection-reaction-diffusion systems.

We study and map the possible stationary patterns that emerge in a convection-reaction-diffusion (CRD) system using a learning polynomial kinetics. We classify the patterns according to the kinetic model (oscillatory, bistable, or intermediate), the instability nature of the bounded system (convective or absolute), the applied boundary conditions and the system length. This analysis presents a unifying approach to various pattern-inducing mechanisms such as DIFICI (differential flow induced chemical instability), which predicts moving patterns in systems with wide difference of convective rates, and differential capacity patterns, which predicts stationary patterns in cross-flow reactors with a large heat capacity. Previous studies of CRD systems have considered only oscillatory kinetics. Nonlinear analysis, which follows the front motion by approximating its velocity, accounts for the stability of the stationary, whether spatially periodic or other, patterns. The most dominant state is the large-amplitude stationary spatially periodic pattern. With oscillatory kinetics these emerge in the convectively unstable domain above the amplification threshold. The domain of absolute instability, which is determined analytically for unbounded systems, is divided in the bounded system into two subdomains with moving DIFICI waves or stationary patterns. With bistable kinetics the large-amplitude stationary patterns can be sustained only within a narrow subdomain but other stationary patterns, that incorporate several fronts upstream and an "almost homogeneous" tail downstream, can be sustained as well. With intermediate kinetics the large-amplitude axisymmetric stationary patterns may coexist with small-amplitude stationary nonaxisymmetric patterns.

Use of Computational Fluid Dynamics to Evaluate Alternative Spray Dryer Chamber Configurations

A computational fluid dynamic simulation study was carried out to compare the gas flow and temperature patterns as well as particle trajectories for a pressure nozzle atomized liquid slurry spray dried in four different chamber geometries. The gas and liquid conditions are held the same for all four chamber geometries. The gas flow is co-current and enters and exits centrally thus maintaining a two-dimensional axi-symmetric flow pattern. It is found that as a result of variations in the gas flow and thermal patterns in the four configurations examined (viz cylinder-on-cone, conical, hour-glass shaped, and lantern-shaped axi-symmetric) the droplet trajectories, residence times, and drying times vary. It was noted that the effective chamber volume occupied by drying particles depends on the chamber design.

Analysis of EHL Circular Contact Shut Down

In this paper, an isothermal study of the shut down process of elastohydrodynamic lubrication under a constant load is performed. The surface mean velocity is decreased linearly from the initial steady state value to zero. The details of the pressure and film thickness distributions in the contact area are discussed for the two stages of shut down process, namely the deceleration stage and the subsequent pure squeeze motion stage with zero entraining velocity. The nature of the balance between the pressure, the wedge and the squeeze terms in Reynolds equation enables an analytical prediction of the film thickness change on the symmetry line of the contact in the deceleration period, provided that the steady state central film thickness relationship with velocity is known. The results indicate that for a fixed deceleration rate, if the initial steady state surface mean velocity is large enough, the transient pressure and film thickness distributions in the deceleration period solely depend on the transient velocity. The pressure and film thickness at the end of the deceleration period are then the same and do not depend on the initial steady state velocity. From the same initial steady state velocity, larger deceleration rates provide higher central pressure increase, but also preserve a higher film thickness in the contact area at the end of the deceleration period. Later in the second stage when the axisymmetric pressure and film thickness patterns typical of pure squeeze motion form, the pressure distribution in the contact area resembles a Hertzian contact pressure profile with a higher maximum Hertzian pressure and a smaller Hertzian half contact width. As a result, the film thickness is close to a parabolic distribution in the contact area. The volume of the lubricant trapped in the contact area is then estimated using this parabolic film thickness profile.