Radial Boundary Research Articles

J051064 回転円板周り流れの数値解析([J05106]流体機械の研究開発におけるEFD/CFD(6))

Flow between rotating disk and stationary wall with different rotating speed and gap scale is analyzed numerically. The result with very fine grid with SST turbulent model agrees very well with experimental result, when the local rotating Reynolds number is high. The velocity distributions show some similarity law, and the thickness of boundary layer is different between rotational and radial boundary layers. The interference of boundary layers is also detected by the velocity distribution, and in the area of R>0.8, some linear relation exists on the interference conditions.

Method of radial sounding and elemental analysis of formations during well logging using neutron inelastic scattering gamma time-of-flight spectrometry

This paper describes a well logging method and device designed to determine radial inhomogeneities in the elemental content of the borehole environment with high spatial resolution. The sounding factor that determines the spatial resolution is the time elapsed from the moment of neutron emission from the device to the moment the device records the gamma rays from neutron inelastic scattering (inelastic gamma rays, IGRs) in the formation. The time interval characterizes the distance to the point of origin of a gamma ray, and the energy of a gamma ray passing through the formation without interaction determines the chemical element involved in inelastic scattering. Simulations have shown that at each time, the density of inelastic scattering is very well localized in space owing to the small number of fast-neutron scatterings: on average, one to two events. It is the compact localization of inelastic scattering events that provides high radial resolution (and, if necessary, high azimuth resolution) during fast-neutron sounding of formations and measurement of unsteady IGR fluxes. Recording of IGR distributions over time also provides increasing sounding depth because powerful IGR fluxes from nearby regions reach the detector at short times and do not overlap the weaker IGR fluxes from distant regions because the latter reach the detector later. To evaluate the radial resolution of the method, we calculated the response of the sonde for typical models of a borehole environment which include a borehole, an iron casing, cement, an invaded zone, and an uninvaded rock. The boundaries of spatial inhomogeneities and the elemental content in the regions between these boundaries were determined from time dependences of unscattered spectral lines in IGR spectra for the elements Ca, Si, C, O, and Fe. The results of the numerical simulation indicate a high sensitivity of the measurements to the radial boundaries and an adequate spatial resolution: about 1 cm at a 0.1 ns time sampling of logs. The interfaces between the radial zones are clearly marked in the time distributions by steep fronts with a length of 0.1 ns (at a collimation angle of the source of about 30°) to 0.15–0.4 ns (at an angle of 90°). A method of solution was formulated for the inverse problem consisting of determining the boundaries of the radial zones and the elemental content in these zones. The problem is solved using a qualitative model of the borehole environment, for example, a “borehole–casing–cement–invaded zone–uninvaded rock” model. The method is based on searching for approximating model curves to measured time distributions of unscattered IGR fluxes jointly for all components of the model. The search is conducted by spatial optimization of the sought parameters—the distances { rS} from the neutron source to the boundaries of the zones and the concentrations { C} of specified chemical compounds in these zones. The initial approximations for the sought parameters { rS} and { C} are calculated by linear inversion of logs, which proves to be very accurate because the contribution of singly scattered neutrons to the inelastic scattering density at small times (10 ns) is, on average, 50–90%. Model curves are calculated by numerical simulation of the transport of neutrons and gamma rays. An appropriate calculation method is the Monte Carlo technique. Since the multiplicity of neutron scattering is low and, for gamma rays, only the unscattered component is of interest, the numerical simulation is a fast process. The practical implementation of the method requires the use of advanced developments in the design of neutron generators, spectral gamma-ray detectors, and fast analyzers for recording subnanosecond processes. Use of associated-particle neutron generators, Ge semiconductor detectors with electron cooling or LaBr3 (Ce) and BaF2 based fast scintillator blocks of high energy resolution will allow the application of the proposed method to logging measurements.

Two-dimensional quantum rings with oscillating spin-orbit interaction strength: A wave function picture

We determine the relevant spinor valued wave functions for a two-dimensional quantum ring in the presence of Rashba-type spin-orbit interaction (SOI). The case of constant SOI strength is considered first, then we investigate the physical consequences of time-dependent (oscillating) SOI strength. Floquet's method is applied to find time-dependent eigenspinors, and it is shown that the Floquet quasienergies and thus their differences (the generalized Rabi frequencies) are determined by the radial boundary conditions. Time evolution of various initial states is calculated.

Meshless method of dual reciprocity hybrid radial boundary node method for elasticity

Combining the radial point interpolation method (RPIM), the dual reciprocity method (DRM) and the hybrid boundary node method (HBNM), a dual reciprocity hybrid radial boundary node method (DHRBNM) is proposed for linear elasticity. Compared to DHBNM, RPIM is exploited to replace the moving least square (MLS) in DHRBNM, and it gets rid of the deficiency of MLS approximation, in which shape functions lack the delta function property, the boundary condition can not be applied easily and directly and it's computational expense is high. Besides, different approximate functions are discussed in DRM to get the interpolation property, in which the accuracy and efficiency for different basis functions are compared. Then RPIM is also applied in DRM to replace the conical function interpolation, which can greatly improve the accuracy of the present method. To demonstrate the effectiveness of the present method, DHBNM is applied for comparison, and some numerical examples of 2-D elasticity problems show that the present method is much more effective than DHBNM.

Characterization of Flowerlike Silicon Particles Obtained from Chemical Etching: Visible Fluorescence and Superhydrophobicity

Flowerlike silicon particles are obtained by chemical etching of polycrystalline silicon polyhedrons using a mixture of hydrofluoric acid and nitric acid. The etched flowerlike particles show stable bright red photoluminescence under UV irradiation. The formation of pores with diameters of 3, 5.5, and 20 nm is revealed during etching. The etched particles exhibit superhydrophobic behavior with a contact angle of 158 degrees because of the sharp tips of their "petals". The source silicon polyhedrons are shown to possess radial grain boundaries. Preferential etching along the radial grain boundaries of the polyhedrons is thought to be the key reason for the formation of flowerlike porous silicon particles.

IMPLEMENTATION OF THE SHEARING BOX APPROXIMATION IN ATHENA

We describe the implementation of the shearing box approximation for the study of the dynamics of accretion disks in the Athena magnetohydrodynamics (MHD) code. Second-order Crank-Nicholson time differencing is used for the Coriolis and tidal gravity source terms that appear in the momentum equation for accuracy and stability. We show this approach conserves energy for epicyclic oscillations in hydrodynamic flows to round-off error. In the energy equation, the tidal gravity source terms are differenced as the gradient of an effective potential in a way which guarantees that total energy (including the gravitational potential energy) is also conserved to round-off error. We introduce an orbital advection algorithm for MHD based on constrained transport to preserve the divergence-free constraint on the magnetic field. This algorithm removes the orbital velocity from the time step constraint, and makes the truncation error more uniform in radial position. Modifications to the shearing box boundary conditions applied at the radial boundaries are necessary to conserve the total vertical magnetic flux. In principle similar corrections are also required to conserve mass, momentum and energy, however in practice we find the orbital advection method conserves these quantities to better than 0.03% over hundreds of orbits. The algorithms have been applied to studies of the nonlinear regime of the MRI in very wide (up to 32 scale heights) horizontal domains.

Tornado-type stationary vortex with nonlinear term due to moisture transport

Abstract. Tornado vortex is believed to be essentially nonlinear phenomenon; and the puzzle to choose the nonlinear term(s) responsible for its formation is still unresolved. In the present work we consider the nonlinear term associated with atmosphere humidity, by introducing variable temperature gradient depending on the vertical velocity of the fluid. Such term is able to yield energy to the system and is very suitable for such a problem. Other nonlinear terms are neglected, assuming slow rotation, or in other words a "weak" tornado approximation. We consider one-dimensional radial boundary problem, and use a modificaiton of shooting method to satisfy boundary conditions at large radii. Obtained numerical solutions of the nonlinear differential equation qualitatively agree with the observed atmosphere vortices (tornados, tropical cyclones). The obtained results show general possibility of existence of unstable motion even in convectively stable atmosphere stratification.

ELECTROMAGNETIC CASIMIR EFFECT IN WEDGE GEOMETRY AND THE ENERGY-MOMENTUM TENSOR IN MEDIA

The wedge geometry closed by a circular-cylindrical arc is a nontrivial generalization of the cylinder, which may have various applications. If the radial boundaries are not perfect conductors, the angular eigenvalues are only implicitly determined. When the speed of light is the same on both sides of the wedge, the Casimir energy is finite, unlike the case of a perfect conductor, where there is a divergence associated with the corners where the radial planes meet the circular arc. We advance the study of this system by reporting results on the temperature dependence for the conducting situation. We also discuss the appropriate choice of the electromagnetic energy-momentum tensor.

Validation of a Monte Carlo based depletion methodology via High Flux Isotope Reactor HEU post-irradiation examination measurements

The purpose of this study is to validate a Monte Carlo based depletion methodology by comparing calculated post-irradiation uranium isotopic compositions in the fuel elements of the High Flux Isotope Reactor (HFIR) core to values measured using uranium mass-spectrographic analysis. Three fuel plates were analyzed: two from the outer fuel element (OFE) and one from the inner fuel element (IFE). Fuel plates O-111-8, O-350-I, and I-417-24 from outer fuel elements 5-O and 21-O and inner fuel element 49-I, respectively, were selected for examination. Fuel elements 5-O, 21-O, and 49-I were loaded into HFIR during cycles 4, 16, and 35, respectively (mid to late 1960s). Approximately one year after each of these elements were irradiated, they were transferred to the High Radiation Level Examination Laboratory (HRLEL) where samples from these fuel plates were sectioned and examined via uranium mass-spectrographic analysis. The isotopic composition of each of the samples was used to determine the atomic percent of the uranium isotopes. A Monte Carlo based depletion computer program, ALEPH, which couples the MCNP and ORIGEN codes, was utilized to calculate the nuclide inventory at the end-of-cycle (EOC). A current ALEPH/MCNP input for HFIR fuel cycle 400 was modified to replicate cycles 4, 16, and 35. The control element withdrawal curves and flux trap loadings were revised, as well as the radial zone boundaries and nuclide concentrations in the MCNP model. The calculated EOC uranium isotopic compositions for the analyzed plates were found to be in good agreement with measurements, which reveals that ALEPH/MCNP can accurately calculate burn-up dependent uranium isotopic concentrations for the HFIR core. The spatial power distribution in HFIR changes significantly as irradiation time increases due to control element movement. Accurate calculation of the end-of-life uranium isotopic inventory is a good indicator that the power distribution variation as a function of space and time is accurately calculated, i.e. an integral check. Hence, the time dependent heat generation source terms needed for reactor core thermal hydraulic analysis, if derived from this methodology, have been shown to be accurate for highly enriched uranium (HEU) fuel.

A dual reciprocity hybrid radial boundary node method based on radial point interpolation method

A novel truly meshless method called dual reciprocity hybrid radial boundary node method (DHRBNM) is developed in present, which combines dual reciprocity method (DRM), hybrid boundary node method (HBNM) and radial point interpolation method (RPIM). Compared to the dual reciprocity hybrid boundary node method (DHBNM), RPIM is exploited to replace the moving least square in DHRBNM, unlike HBNM, the shape function obtained by present method has the delta function property, so the boundary conditions can be applied directly and easily, and computational expense is greatly reduced. In order to get the interpolation property of different basis function in DRM, different approximate functions are applied in DRM for comparison, and the accuracy and efficiency of them are discussed. Besides, RPIM is also exploited in DRM, which can greatly improve the accuracy of present method. Moreover, the accuracy of DRM is greatly influenced by the nodes number and their location, hence, some examples are investigated to show that the internal node number is equal to boundary node number and they are arranged parallel to the high gradient direction of the problem are the best choice. Finally, DHBNM is applied for comparison and some selected numerical examples are given to illustrate that the present method is efficient and less computational expense than that of DHBNM.

An exact analytical solution for two-dimensional, unsteady, multilayer heat conduction in spherical coordinates

Analytical series solution is proposed for the transient boundary-value problem of multilayer heat conduction in r– θ spherical coordinates. Spatially non-uniform, but time-independent, volumetric heat sources may exist in the concentric layers. Proposed solution is valid for any combination of homogenous boundary conditions of the first or second kind in the θ -direction. However, inhomogeneous boundary conditions of the first, second or third kind may be applied at the inner and outer radial boundaries of the concentric layers. It is noted that the proposed solution is “free” from imaginary eigenvalues. Real eigenvalues are obtained by virtue of precluded explicit dependence of radial eigenvalues on those in the θ-direction. Solution is shown to be relatively simple for the most common spherical geometries−(multilayer) hemisphere and full sphere. An illustrative problem of heat conduction in a three-layer hemisphere is solved. Results along with the isotherms are shown graphically and discussed.

Fourier-Bessel Expansions with Arbitrary Radial Boundaries

Series expansion of single variable functions is represented in Fourier-Bessel form with unknown coefficients. The proposed series expansions are derived for arbitrary radial boundaries in problems of circular domain. Zeros of the generated transcendental equation and the relationship of orthogonality are employed to find the unknown coefficients. Several numerical and graphical examples are explained and discussed.

Cluster sets and quasiconformal mappings

Certain classical results on cluster sets and boundary cluster sets of analytic functions, due to Iversen, Lindelöf, Noshiro, Tsuji, Ohtsuka, Pommerenke, Carmona, Cufi and others, are extended to n-dimensional quasiconformal mappings. Unlike what is usually the case in the context of analytic functions, our considerations are not restricted to mappings of a disk or ball only. It is shown, for instance, that quasiconformal cluster sets and boundary cluster sets, taken at a non-isolated boundary point of an arbitrary domain, coincide. More refined versions are established in the special case where the domain is the open unit ball. These include cluster set considerations of the induced radial boundary extension and results where certain exceptional sets on the boundary are allowed for.

Enhancing radial temperature uniformity and boundary layer development in viscous Newtonian and non-Newtonian flow by transverse oscillations: A CFD study

Radial heat transfer in laminar pipe flow is limited to slow thermal conduction which results in a wide temperature distribution over the pipe cross-section. This is undesirable in many industrial processes as it leads to an uneven distribution of fluid heat treatment. Often the fluids involved are relatively viscous and processing them under turbulent conditions is impractical and/or uneconomical. On the other hand, the use of static in-line mixers to promote radial mixing may be prohibited in hygienic processes because they are difficult to keep clean. In this paper, we use a validated Computational Fluid Dynamics (CFD) model to show that the imposition of a transverse vibration motion on a steady laminar flow generates sufficient chaotic fluid motion which leads to considerable radial mixing. This results in a large enhancement in wall heat transfer as well as a near-uniform radial temperature field accompanied by a substantial heating of the inner region of the flow. Vibration also causes the temperature profile to develop very rapidly in the axial direction reducing the thermal entrance length by a large factor, so that much shorter pipes could in principle be used to achieve a desired temperature at the outlet. The effects are quantitatively demonstrated for Newtonian and non-Newtonian pseudoplastic fluids of different viscosities, for a wide range of vibration amplitudes and frequencies. For processes where vibrational motion can be implemented the benefits can be very significant.

Anchoring transition and influence of director fluctuations in liquid crystal droplets

Micro-droplets of nematic liquid crystals have been investigated under radial boundary conditions, based on a lattice model which incorporates explicitly the elastic properties of the medium as variable parameters in the Hamiltonian. Equilibrium director configurations have been simulated, employing the Monte Carlo technique, as a function of anchoring strength ϵ S at the spherical boundary surface. A very sharp transition from a uniaxial nematic structure to a radially ordered state results in ϵ S being increased beyond a threshold. The flexibility offered by this Hamiltonian is utilised to investigate this structural transition as a function of the splay elastic coefficient K 1. The results indicate several features: (1) the transition is as expected influenced by K 1; (2) the transition seems to be mediated by a process of complete wetting by the outer spherical surface, except for the small uniaxial core region sustained by the elastic energy penalty otherwise incurred; (3) the degree of splay contribution has multiple effects on the transition including changes in the critical anchoring strength at the transition, and the nature of the transition itself; (4) profiles of the director fluctuations across the (concentric) spherical layers indicate evidence of frustration caused by the competing interactions generated in the system due to the boundary conditions imposed.

Radial structure of low pressure rf capacitive discharges

This paper studies the glow intensity distribution of the discharge plasma against the tube radius and reports the radial profiles of electron temperature and plasma concentration in the rf capacitive discharge registered with a Langmuir probe. An abrupt increase of electron temperature and glow intensity near the tube wall in the weak-current α-mode of the rf capacitive discharge is revealed, the radial distribution of plasma concentration and ion flow to the electrodes possessing a maximum near the radial sheath boundary. In the γ-mode of the rf capacitive discharge the electron temperature decrease in the total plasma volume leads to an electric field weakening and the peak of the glow intensity near the tube wall vanishes. The radial sheath thickness in the α-mode of the rf capacitive discharge obtained with 2D simulation experiences pulsations during the rf field period, the changing radial electric field heating electrons and increasing the plasma concentration near the boundary of the radial sheath.

The analysis of the electro-mechanical model of the cylindrical radial composite piezoelectric ceramic transducer

The cylindrical radial composite piezoelectric ceramic transducer is presented and studied. The transducer consists of an inner radially polarized piezoelectric ceramic thin-walled circular tube and an outer metal thin-walled cylindrical shell which are composed in the radial direction. The radial vibrations of a metal thin-walled cylindrical shell and a piezoelectric ceramic thin-walled circular tube are analyzed. Their radial electro-mechanical equivalent circuits are obtained. Based on the equivalent circuits and the radial boundary conditions, the composite electro-mechanical equivalent circuit of a cylindrical radial composite piezoelectric ceramic transducer is obtained, the resonance frequency and anti-resonance frequency equations of the cylindrical radial composite piezoelectric transducer are derived. Then the relationship between the resonance frequency, the anti-resonance frequency, the effective electro-mechanical coupling coefficient and the geometrical dimensions of the cylindrical radial composite piezoelectric ceramic transducer is analyzed. It is illustrated that the resonance frequencies and the anti-resonance frequencies from the frequency equations are in a good agreement with that of the experimental results.

A hybrid radial boundary node method based on radial basis point interpolation

The hybrid boundary node method (HBNM) retains the meshless attribute of the moving least squares (MLS) approximation and the reduced dimensionality advantages of the boundary element method. However, the HBNM inherits the deficiency of the MLS approximation, in which shape functions lack the delta function property. Thus in the HBNM, boundary conditions are implemented after they are transformed into their approximations on the boundary nodes with the MLS scheme. This paper combines the hybrid displacement variational formulation and the radial basis point interpolation to develop a direct boundary-type meshless method, the hybrid radial boundary node method (HRBNM) for two-dimensional potential problems. The HRBNM is truly meshless, i.e. absolutely no elements are required either for interpolation or for integration. The radial basis point interpolation is used to construct shape functions with delta function property. So unlike the HBNM, the HRBNM is a direct numerical method in which the basic unknown quantity is the real solution of nodal variables, and boundary conditions can be applied directly and easily, which leads to greater computational precision. Some selected numerical tests illustrate the efficiency of the method proposed.

Identifying dendroecological growth releases in American beech, jack pine, and white oak: Within-tree sampling strategy

The objective of this project was to identify the timing of growth release events detected from tree ring widths and compare whether two cores taken from the same tree reconstructed the same disturbance history. This research question is important because current dendroecological reconstructions of canopy disturbance rely on sampling one core per tree; however, the variation of releases from different cores from the same tree has never been evaluated. We sampled two increment cores from 20 jack pine, 17 white oak, and 19 American beech and identified release events with two commonly employed methods: radial growth averaging technique and boundary line criteria. In jack pine, 85% of the paired cores showed identical releases with the radial growth averaging technique, but 15% of the paired cores varied in reconstructed growth releases. In the jack pine, no releases were identified with the boundary line criteria for any of the paired cores. In the white oak, 65% had identical releases identified with the radial growth averaging technique and 35% of the pairs showed differences. The boundary line criteria for white oak had agreement between releases for 76% of the pairs and different release histories for 24% of the pairs. In the American beech, we were only able to use the radial growth averaging technique and this method showed identical release timing for 79% of the paired cores and differences in 21% of the paired cores. This level of within-tree growth variation is unlikely to influence identification of stand-wide disturbances; however, for reconstructions of small-scale disturbances it is likely to under-represent disturbance events. Therefore, for small-scale disturbance reconstructions, we recommend dendroecologists consider sampling two cores per tree instead of the standard sample of one core per tree.

Modelling and simulation of bulk metallic glass production process with suction casting

An integrated model, which coupled nucleation and crystalline growth with the heat transfer process, is presented in the present paper. The temperature, temperature gradient, cooling rate and the crystalline fraction of Zr65Al7·5Cu17·5Ni10 in suction casting have been calculated with this model. The results show that the metallic glass can be obtained at the bottom and the radial boundary of the rod sample, and that the crystalline phase precipitates in the centre of the sample. The crystalline fraction reaches the highest value of 0·0128 in the centre of the sample. Comparatively lower nucleation rate, as well as the higher viscosity and the cooling rate account for the formation of the bulk metallic glass.