Large Radius Ratio Research Articles

Effect of the number of vortices on the torque scaling in Taylor–Couette flow

AbstractTorque measurements in Taylor–Couette flow, with large radius ratio and large aspect ratio, over a range of velocities up to a Reynolds number of 24 000 are presented. Following a specific procedure, nine states with distinct numbers of vortices along the axis were found and the aspect ratios of the vortices were measured. The relationship between the speed and the torque for a given number of vortices is reported. In the turbulent Taylor vortex flow regime, at relatively high Reynolds number, a change in behaviour is observed corresponding to intersections of the torque–speed curves for different states. Before each intersection, the torque for a state with a larger number of vortices is higher. After each intersection, the torque for a state with a larger number of vortices is lower. The exponent, from the scaling laws of the torque, always depends on the aspect ratio of the vortices. When the Reynolds number is rescaled using the mean aspect ratio of the vortices, only a partial collapse of the exponent data is found.

Capillary Bridges between Soft Substrates

A wetting droplet trapped in the thin gap between two elastic bodies will deflect the bodies towards one another. The deformation increases the total capillary adhesion force by increasing the contact radius and narrowing the gap height. For flat droplets, with a large ratio of radius to gap height, the Laplace pressure causes surface deformations that are orders of magnitude larger than those induced by a sessile droplet of the same radius. We present experiments, scalings, and closed-form solutions that describe the deformation. Using variational techniques, we also show that the problem exhibits a bifurcation, where the gap spontaneously closes due to an incremental increase in drop volume.

Electromagnetophoresis of a Colloidal Sphere in a Spherical Cavity

The quasi-steady electromagnetophoretic motion of a spherical colloidal particle positioned at the center of a spherical cavity filled with a conducting fluid is analyzed at low Reynolds number. Under uniformly applied electric and magnetic fields, the electric current and magnetic flux density distributions are solved for the particle and fluid phases of arbitrary electric conductivities and magnetic permeabilities. Applying a generalized reciprocal theorem to the Stokes equations modified with the resulted Lorentz force density and considering the contribution of the magnetic Maxwell stress to the force exerted on the particle, which turns out to be important, we obtain a closed-form formula for the migration velocity of the particle valid for an arbitrary value of the particle-to-cavity radius ratio. The particle velocity in general decreases monotonically with an increase in this radius ratio, with an exception for the case of a particle with high electric conductivity and low magnetic permeability relative to the suspending fluid. The asymptotic behaviors of the boundary effect on the electromagnetophoretic force and mobility of the confined particle at small and large radius ratios are discussed.

Breakup of cavitation bubbles within the diesel droplet

Supercavitation in the diesel nozzle increases the instability of droplets in part due to the two-phase mixture, while the effect of cavitation bubbles on the instability of drops is still unclear. In order to investigate the breakup of cavitation bubbles within the diesel droplet, a new mathematical model describing the disturbance growth rate of the diesel bubble instability is developed. The new mathematical model is applied to predict the effects of fluids viscosity on the stability of cavitation bubbles. The predicted values reveal that the comprehensive effect of fluids viscosity makes cavitation bubbles more stable. Compared with the viscosities of air and cavitation bubble, the diesel droplet’s viscosity plays a dominant role on the stability of cavitation bubbles. Furthermore, based on the modified bubble breakup criterion, the effects of bubble growth speed, sound speed, droplet viscosity, droplet density, and bubble-droplet radius ratio on the breakup time and the breakup radius of cavitation bubbles are studied respectively. It is found that a bubble with large bubble-droplet radius ratio has the initial condition for breaking easily. For a given bubble-droplet radius ratio (0.2), as the bubble growth speed increases (from 2 m/s to 60 m/s), the bubble breakup time decreases(from 3.59 μs to 0.17 μs) rapidly. Both the greater diesel droplet viscosity and the greater diesel droplet density result in the increase of the breakup time. With increasing initial bubble-droplet radius ratio (from 0.2 to 0.8), the bubble breakup radius decreases (from 8.86 μm to 6.23 μm). There is a limited breakup radius for a bubble with a certain initial bubble-droplet radius ratio. The mathematical model and the modified bubble breakup criterion are helpful to improve the study on the breakup mechanism of the secondary diesel droplet under the condition of supercavitation.

Numerical Analysis of Thermal Development of Laminar Flow in a Concentric Multilayer Annulus

AbstractThe thermal behavior of laminar flow in a concentric multilayer annulus is investigated numerically for varying dimensionless inner radii and a defined number of fluid layers. Under a hydrodynamically developed flow assumption within the fluid layers, the development of temperature profiles and heat transfer along the annulus are analyzed for two different boundary conditions. The mean temperature distribution, local Nusselt number, and mean Nusselt number are discussed in detail with an emphasis on the effects of the inner radius and number of fluid layers. The obtained results indicate that the change in heat transfer coefficient in a layered annulus is more pronounced at a small inner radius or larger radius ratio. A further insertion of more than ten layers has insignificant influence on the convective heat transfer in a layered annulus.

Geodesic acoustic mode in tokamaks: local consideration and eigenvalue analysis

A set of magnetohydrodynamic equations describing the geodesic acoustic mode (GAM) in tokamak plasmas is derived. The obtained equations take into account the presence of the energetic ions and allow to study energetic-ion-driven GAM instability perturbatively or non-perturbatively (EGAM mode). They are applicable to plasmas with , where , , cs is the sound velocity, vA is the Alfvén velocity, q is the tokamak safety factor. Using these equations, GAM/EGAM instability is studied in a local approach and by means of the eigenvalue analysis. It is shown that β-coupling (the coupling of Fourier harmonics of the perturbation due to finite β—ratio of the plasma pressure to the magnetic field pressure—and the curvature of the field lines) can be responsible for the radial structure of the GAM-mode. A conclusion is drawn that conditions for the GAM/EGAM instability to arise are mildest in the case of counter-injection of energetic ions with pitch angles χ2 < 0.6 and large ratio of Larmor radius of the energetic ions to a characteristic length of inhomogeneity of these ions. A numerical code solving the derived equations is developed. Specific calculations are carried out for tokamaks with a non-monotonic safety factor. On the other hand, it is found that due to the presence of the energetic ions the GAM/EGAM continuum can have an extremum even when the safety factor q(r) is monotonic, which indicates that global modes can exist also in this case.

Disordered strictly jammed binary sphere packings attain an anomalously large range of densities

Previous attempts to simulate disordered binary sphere packings have been limited in producing mechanically stable, isostatic packings across a broad spectrum of packing fractions. Here we report that disordered strictly jammed binary packings (packings that remain mechanically stable under general shear deformations and compressions) can be produced with an anomalously large range of average packing fractions 0.634≤φ≤0.829 for small to large sphere radius ratios α restricted to α≥0.100. Surprisingly, this range of average packing fractions is obtained for packings containing a subset of spheres (called the backbone) that are exactly strictly jammed, exactly isostatic, and also generated from random initial conditions. Additionally, the average packing fractions of these packings at certain α and small sphere relative number concentrations x approach those of the corresponding densest known ordered packings. These findings suggest for entropic reasons that these high-density disordered packings should be good glass formers and that they may be easy to prepare experimentally. We also identify an unusual feature of the packing fraction of jammed backbones (packings with rattlers excluded). The backbone packing fraction is about 0.624 over the majority of the α-x plane, even when large numbers of small spheres are present in the backbone. Over the (relatively small) area of the α-x plane where the backbone is not roughly constant, we find that backbone packing fractions range from about 0.606 to 0.829, with the volume of rattler spheres comprising between 1.6% and 26.9% of total sphere volume. To generate isostatic strictly jammed packings, we use an implementation of the Torquato-Jiao sequential linear programming algorithm [Phys. Rev. E 82, 061302 (2010)], which is an efficient producer of inherent structures (mechanically stable configurations at the local maxima in the density landscape). The identification and explicit construction of binary packings with such high packing fractions could have important practical implications for granular composites where density is critical both to material properties and fabrication cost, including for solid propellants, concrete, and ceramics. The densities and structures of jammed binary packings at various α and x are also relevant to the formation of a glass phase in multicomponent metallic systems.

The new trace fossil Gyrolithes lorcaensis isp. n. from the Miocene of SE Spain and a critical review of the Gyrolithes ichnospecies

The 18 ichnospecies of the vertically oriented, helical marine to marginal marine trace fossil Gyrolithes Saporta, 1884 known so far are revised. A new ichnospecies, G. lorcaensis isp. n. (Miocene, SE Spain), is introduced, and Conispiron Vialov, 1969 and Spirocircus Mikulas and Pek, 1994 are included in Gyrolithes. The ichnotaxobases of the Gyrolithes ichnospecies are based on the character of the burrow margin (presence or absence of a wall or ornamentation) and/or on morphometric parameters (burrow width versus radius of the whorls). As a result of synonymization, 13 ichnospecies are recommended. The morphometric parameters of Gyrolithes show two distinct lineages (large ratio of whorl radius to burrow width and medium ratio of whorl radius to burrow width; 10–12 and 1–1.6, respectively). The third lineage (small ratio of whorl radius to burrow width; up to 1) is less distinct.

Investigation on heat transfer between two coaxial cylinders for measurement of thermal accommodation coefficient

The heat flux between two coaxial cylinders was measured in the range from the free molecular to the early transitional flow regimes for extraction of the thermal accommodation coefficient using an approximate relation on the pressure dependence of the heat flux. The experimental coaxial cylinders' geometry has been traditionally implemented for the measurement of the thermal accommodation coefficient using the low-pressure method; however, the actual experimental setup was characterized by large temperature difference and large cylinders' radius ratio. Compared to the original low-pressure method, much higher pressure range was applied. In order to verify assumptions in the accommodation coefficient extraction, the heat flux under measurement conditions was simulated numerically by the nonlinear S-model kinetic equation. Very good agreement was found between the measured and the simulated heat flux. The proposed procedure of the thermal accommodation coefficient extraction was discussed in detail and verified. The temperature dependence of the thermal accommodation coefficient was also found.

Densest binary sphere packings

The densest binary sphere packings in the α-x plane of small to large sphere radius ratio α and small sphere relative concentration x have historically been very difficult to determine. Previous research had led to the prediction that these packings were composed of a few known "alloy" phases including, for example, the AlB(2) (hexagonal ω), HgBr(2), and AuTe(2) structures, and to XY(n) structures composed of close-packed large spheres with small spheres (in a number ratio of n to 1) in the interstices, e.g., the NaCl packing for n=1. However, utilizing an implementation of the Torquato-Jiao sphere-packing algorithm [Torquato and Jiao, Phys. Rev. E 82, 061302 (2010)], we have discovered that many more structures appear in the densest packings. For example, while all previously known densest structures were composed of spheres in small to large number ratios of one to one, two to one, and very recently three to one, we have identified densest structures with number ratios of seven to three and five to two. In a recent work [Hopkins et al., Phys. Rev. Lett. 107, 125501 (2011)], we summarized these findings. In this work, we present the structures of the densest-known packings and provide details about their characteristics. Our findings demonstrate that a broad array of different densest mechanically stable structures consisting of only two types of components can form without any consideration of attractive or anisotropic interactions. In addition, the structures that we have identified may correspond to currently unidentified stable phases of certain binary atomic and molecular systems, particularly at high temperatures and pressures.

Structure Design and Research on a Spiral Pipe Type Reactor

As the core part of a reactor, a spiral pipe structure working under loads of high temperature and high pressure was designed and researched by using CAE method. The properties of high temperature resistance, high-pressure resistance and corrosion resistance play a crucial role for the reactor whether working well or not. Spiral structure was designed for a core component of this reactor in order to increase the staying time that the medium stays in the pipe. The performances of this spiral structure under its working conditions were calculated and analyzed. The changes of performance of the spiral structure caused by changing of elastic modulus of material under high temperature was studied; because the structure has very large length radius ratio, operation of elements meshing is difficult when using FEM method, in order to solving this problem, the methods of establishing elements modal for this kind of structure was proposed in this paper.

Ion Beam Irradiation-induced Amorphization in Nano-sized KxLnyTa2O7-v Tantalate Pyrochlore

ABSTRACTThe radiation response of nano-sized tantalate pyrochlores, KxLnyTa2O7-v (Ln = Gd, Y, and Lu) with average grain sizes of ~ 10 nm was investigated using 1 MeV Kr2+ ion beam irradiations. EDS measurements and XRD refinement reveal that the Y3+ and Lu3+-doped samples consist of two pyrochlore phases as K0.8YTa2O6.9/K0.4Y0.8Ta2O6.4 and KLuTa2O7/K0.4Lu0.8Ta2O6.4 respectively; whereas a single phase of K0.8GdTa2O7 only exists in the Gd3+-doped tantalate pyrochlore. In situ TEM observation confirms ion beam-induced amorphization occurring in all of the nano-sized KxLnyTa2O7-v. At elevated temperatures, both K0.8GdTa2O7 and K0.8YTa2O6.9/K0.4Y0.8Ta2O6.4 exhibit higher radiation tolerance than KLuTa2O7/K0.4Lu0.8Ta2O6.4, and the critical temperatures of K0.8GdTa2O7 and K0.8YTa2O6.9/K0.4Y0.8Ta2O6.4 are estimated to be 1167 ± 41 K and 1165 ± 34 K, respectively, lower than that of KLuTa2O7/K0.4Lu0.8Ta2O6.4 (~ 1291 K). The K0.8GdTa2O7, K0.8YTa2O6.9 and KLuTa2O7 phases have less structural deviation from the parent fluorite structure and thus may be responsible for the overall radiation tolerance. The high K+ occupancy at pyrochlore A sites in KLuTa2O7 is believed to contribute to the decrease of radiation tolerance, consistent with the large ionic radius ratio of K+/Ta5+. These results highlight that the radiation tolerance of nanostructured materials is highly compositional dependent, and nano-sized tantalate pyrochlores are sensitive to radiation damage.

Circumferential wave in functionally graded piezoelectric cylindrical curved plates

Functionally graded piezoelectric material (FGPM), with a gradual change of the mechanical and electric properties, has large fields of application. Based on linear three-dimensional piezoelasticity, a Legendre orthogonal polynomial series expansion approach is used for determining the characteristics of circumferential waves in FGPM cylindrical curved plates. Our results from an FGPM cylindrical curved plate with a large ratio of radius to thickness are compared with an FGPM flat plate published earlier to confirm the accuracy and range of applicability of the computational program. Circumferential wave dispersion curves for FGPM and the corresponding FGM cylindrical curved plates are calculated and the effect of piezoelectricity is shown. The influence of the ratio of radius to thickness on the piezoelectric effect and electric potential distribution is discussed. The ratio has a significant influence on the electric potential distribution. Finally, the influence of the polarizing direction on the piezoelectric effect is illustrated. The phenomenon that piezoelectricity weakens the guided wave dispersion in the FGPM cylindrical plate is observed.

HEAT TRANSFER, PHASE CHANGE, AND THERMOCAPILLARY FLOW IN FILMS OF MOLTEN METAL ON A SUBSTRATE

A mathematical model has been developed for heat transfer and fluid flow in thin films of molten metal during nanosecond pulsed laser irradiation. Heat conduction in the substrate is modeled using the finite-difference approach, while description of heat transfer and viscous flow in the film is based on the assumption of the large ratio of laser beam radius to film thickness and involves numerical solution of a partial differential equation for the thickness. The model includes the highly nonlinear dependence of evaporative flux on local interfacial temperature and positive disjoining pressure due to free electrons in the metal. Thermo-capillary stresses which result from radially nonuniform heating are identified as the main mechanism of removal of liquid metal from the irradiated area. Characteristic times of the process, as well as shapes of the molten surface, agree with experimental observations.

Effects of stem structure and cell wall components on bending strength in wheat

Morphological traits, anatomical features, chemical components and bending stress in the stems of three genotypes of wheat (Triticum aestivum L.), namely Xiaoyan54, 8602 and Xiaoyan81, were examined by means of light microscopy coupled with Fourier transform infrared spectroscopy (FTIR). Noticeable changes in morphological and anatomical traits were observed, including outer radius of stem, the ratio of stem outer radius to stem wall thickness, various tissue proportions and variations among different types of vascular bundles. The results of chemical analysis revealed that Xiaoyan81 had the highest cellulose content in comparison with Xiaoyan54 and 8602, whereas lignin level in Xiaoyan81 was lower than that in 8602 but higher that that in Xiaoyan54. Bending stress analysis demonstrated that Xiaoyan81 may be the main target for identification, for it had the highest bending stress among the stems of three genotypes. Associated with bending stress, all the results presented here suggested that the ratio of stem wall thickness to its outer radius, schlerenchyma tissue proportion, the average number of big VB per unit and the cellulose content are four important factors affecting the mechanical strength of Xiaoyan81 wheat stems, which can be considered as the key parameters for selecting varieties with bending stress. Therefore, it was suggested that in the selection of lodging resistant cultivars one should consider those characterized with large ratio of outer radius of stem to stem wall thickness, greaterschlerenchyma tissue proportion, high average number of big VB per unit with high cellulose content in their stems.

Direct Numerical Simulation of Concentric Annular Turbulent Flows with Very Thin Inner Rods

Turbulent concentric annular pipe flows with several thin inner rods were invistigated by means of the direct numerical simulation (DNS). In the inner region, the mean velocity shifts downward from the logarithmic law and the Reynolds stresses normalized by the inner-wall friction velocity decrease monotonously as the radius ratio decreases. In the budget of the Reynolds stress for the very small radius ratios, the pressure-strain term is restrained near the inner wall. We found that the skewness, flatness, two-point correlation and instantaneous field for very small radius ratios are much different from those for large radius ratios.

Double-domain spectral method for black hole excision data

In this paper a new double-domain spectral method to compute binary black hole excision initial data is presented. The method solves a system of elliptic partial differential equations in the exterior of two excised spheres. At the surface of these spheres, boundary conditions need to be imposed. As such, the method can be used to construct arbitrary initial data corresponding to binary black holes with specific boundary conditions at their apparent horizons. We give representative examples corresponding to initial data that fulfill the requirements of the quasi-stationary framework, which combines the thin sandwich formulation of the constraint equations with the isolated horizon conditions for black holes in quasi-equilibrium. For all examples considered, numerical solutions with extremely high accuracy were obtained with moderate computational effort. Moreover, the method proves to be applicable even when tending toward limiting cases such as large radius ratios for the black holes.

Turbulent Taylor-Couette vortex flow between large radius ratio concentric cylinders

Turbulent Taylor vortices between two concentric cylinders have been studied at a very high radius ratio of 0.985, equivalent to that found in relatively small underwater thruster units (typically with gaps of 2 mm). In order to study the flow at this radius ratio, a 1.42-m diameter experimental apparatus (with a rotating inner cylinder and a stationary outer cylinder) was constructed possessing a gap of 10 mm. Consequently, air bubbles could be visualised translating in water. A method was developed for identifying Taylor vortex properties from filtered digital images of the air bubbles and summing intensities to produce bubble density distributions. Whereas individual instantaneous images can be misleading, averaged bubble density distributions make it possible to identify vortex separation sizes and the positions of vortex outflow boundaries.

Thermocapillary flow and rupture in films of molten metal on a substrate

We consider fluid flow in thin films of molten metal resulting from irradiation by a Gaussian laser beam. Surface tension gradients due to nonuniform heating induce a flow of the molten liquid away from the center of the irradiated area, leading to formation of dry areas on the substrate. We develop a mathematical model of the flow under the assumption of the large ratio of laser beam radius to film thickness. The model extends the standard lubrication-type analysis to include the highly nonlinear dependence of evaporative flux on local interfacial temperature, unsteady heat conduction in the substrate, and positive disjoining pressure due to unbalanced contributions from the kinetic energy of free electrons in the metal. The latter is proportional to the inverse square of the film thickness. We identify thermocapillary stresses as the main mechanism of rapid removal of liquid metal from the irradiated area. Characteristic times of the process, as well as shapes of the molten region surface, agree with experimental observations. We investigate rupture of the molten film and find two different rupture scenarios. The melt surface can either touch the substrate at a point (point rupture) or along a line at a certain radial distance away from the center of the irradiated area (ring rupture). Nondimensional criteria for these two mechanisms are identified. In particular, we show that positive disjoining pressure promotes ring rupture.

Near-Wall Space-Charge Sheaths in a Positive Dust-Electron Plasma

A space-charge sheath near a negative surface in a plasma composed of dust grains of a variable positive charge, electrons, and neutral particles, is considered. The limiting case of large ratio of the electron Debye radius to the length scale of variation of the charge of a dust grain is treated. The charging of dust grains in the sheath is quasi-equilibrium in such a case, i.e. the current of the electrons emitted by a dust grain is approximately equal to the current of the plasma electrons collected by the grain. An analytical solution decribing the sheath is found for this limiting case. A further simplification may be achieved in cases when the mean energy of electrons emitted by the dust grain is much smaller than the surface potential of the grain.