General Geometrical Configurations Research Articles

Validation of transition modeling techniques for a simplified fuselage configuration

A Reynolds-averaged Navier-Stokes solver has been equipped with two different transition prediction and modeling techniques for automatic transition prediction on general three-dimensional geometrical configurations. The first technique is a streamline-based approach that applies an automated local linear stability code, the eN-method and a simplified two-N-factor strategy and is applicable with any kind of turbulence model. The second technique is a transition transport equation approach and uses the γ-Reθ,t model. The standard γ-Reθ,t model has been extended by a modeling approach that captures transition due to crossflow instabilities. The extended model can be applied to three-dimensional configuration exhibiting crossflow transition whereas the original γ-Reθ,t model only captures streamwise transition mechanisms. The paper focuses on a three-dimensional inclined 6:1 prolate spheroid which can be considered as a simplified fuselage configuration. For a number of years this configuration has become a standard basic three-dimensional test case for transition prediction approaches and has been used in a number of international workshops and research activities. The focus of the paper is the validation of the two transition modeling approaches for six different angles of attack using two different turbulence models, a standard two-equation eddy-viscosity model and a differential Reynolds-stress model. The simulation results from the two approaches have been compared against each other and to the available experimental data. The comparisons highlight as many qualitative and quantitative similarities and agreements as they reveal quantitative differences and deviations of specific details.

Gravitational wave background search by correlating multiple triangular detectors in the mHz band

With the recent strong developments of TianQin and Taiji, we now have an increasing chance to make a correlation analysis in the mHz band by operating them together with LISA. Assuming two LISA-like triangular detectors at general geometrical configurations, we develop a simple formulation to evaluate the network sensitivity to an isotropic gravitational wave background. In our formulation, we fully use the symmetry of data channels within each triangular detector and provide tractable expressions without directly employing cumbersome detector tensors. We concretely evaluate the expected network sensitivities for various potential detector combinations, including the LISA-TianQin pair.

Effect of Surface Roughness and Hardness of Continuum Materials on Interface Shear Strength of Granular Materials

Abstract The aim of this study was to provide a general conceptual understanding of the effect of hardness and roughness of a continuum surface on its interface shear behavior against granular materials. A carefully designed experimental program was conducted to investigate this issue. The results were utilized to define schematically the general geometric configurations of the constitutive interface shear surface (CISS) in the three-dimensional domain of surface roughness, surface hardness, and interface shear coefficient. The proposed CISS provides a robust mean to understand the coupling effect of continuum surface roughness and hardness on the interface shear behaviour.

Theoretical and experimental study of ice accretion due to freezing rain on an inclined cylinder

This paper reports on an investigation of ice formation on a cylinder exposed to freezing rain. Freezing rain icing is characterized by supercooled raindrop impingement, with vertical and horizontal velocity components, water flow over the surface driven by aerodynamic and gravity forces, and freezing or shedding of the surface water. In the first part of the paper, a novel, three-dimensional analytical model of ice growth on a cylinder is derived and the results are discussed. This is followed by a discussion of experimental tests in the NRC Altitude Icing Wind Tunnel. The experiments were constrained to horizontal drop impingement, and we encountered difficulties delivering large drops at low speed to the test section. Hence, the experiments were used primarily to validate the NRC morphogenetic ice accretion model. The morphogenetic model is a discrete element, random walk model that emulates the motion and freezing of individual fluid elements on the accretion surface. After validating the numerical methodology against the wind tunnel experiments, the model was used to simulate ice formation under more realistic and general geometrical configurations and environmental conditions.

ON BERNOULLI'S FREE BOUNDARY PROBLEM WITH A RANDOM BOUNDARY

This article is dedicated to the solution of Bernoulli’s exterior free boundary problem in the situation of a random interior boundary. We provide the theoretical background that ensures the well-posedness of the problem under consideration and describe two different frameworks to define the expectation and the deviation of the resulting annular domain. The first approach is based on the Vorob’ev expectation, which can be defined for arbitrary sets. The second approach is based on the particular parametrization. In order to compare these approaches, we present analytical examples for the case of a circular interior boundary. Additionally, numerical experiments are performed for more general geometric configurations. For the numerical approximation of the expectation and the deviation, we propose a sampling method like the Monte Carlo or the quasi-Monte Carlo quadrature. Each particular realization of the free boundary is then computed by the trial method, which is a fixed-point-like iteration for the solution of Bernoulli’s free boundary problem.

Numerical simulation of Electron Energy Loss Spectroscopy using a Generalized Multipole Technique

We numerically simulate low-loss Electron Energy Loss Spectroscopy (EELS) of isolated spheroidal nanoparticles, using an electromagnetic model based on a Generalized Multipole Technique (GMT). The GMT is fast and accurate, and, in principle, flexible regarding nanoparticle shape and the incident electron beam. The implemented method is validated against reference analytical and numerical methods for plane-wave scattering by spherical and spheroidal nanoparticles. Also, simulated electron energy loss (EEL) spectra of spherical and spheroidal nanoparticles are compared to available analytical and numerical solutions. An EEL spectrum is predicted numerically for a prolate spheroidal aluminum nanoparticle. The presented method is the basis for a powerful tool for the computation, analysis and interpretation of EEL spectra of general geometric configurations.

MAPPING EARTH ANALOGS FROM PHOTOMETRIC VARIABILITY: SPIN-ORBIT TOMOGRAPHY FOR PLANETS IN INCLINED ORBITS

Aiming at obtaining detailed information of surface environment of Earth analogs, Kawahara & Fujii (2011) proposed an inversion technique of annual scattered light curves named the spin-orbit tomography (SOT), which enables one to sketch a two-dimensional albedo map from annual variation of the disk-integrated scattered light, and demonstrated the method with a planet in a face-on orbit. We extend it to be applicable to general geometric configurations, including low-obliquity planets like the Earth in inclined orbits. We simulate light curves of the Earth in an inclined orbit in three photometric bands (0.4-0.5um, 0.6-0.7um, and 0.8-0.9um) and show that the distribution of clouds, snow, and continents is retrieved with the aid of the SOT. We also demonstrate the SOT by applying it to an upright Earth, a tidally locked Earth, and Earth analogs with ancient continental configurations. The inversion is model independent in the sense that we do not assume specific albedo models when mapping the surface, and hence applicable in principle to any kind of inhomogeneity. This method can potentially serve as a unique tool to investigate the exohabitats/exoclimes of Earth analogs.

Simultaneous inversion of surface deformation and gravity changes by means of extended bodies with a free geometry: Application to deforming calderas

[1] Changes in gravity and/or surface deformation are often associated with volcanic activity. Usually, bodies with simple geometry (e.g., point sources, prolate or oblate spheroids) are used to model these signals considering anomalous mass and/or pressure variations. We present a new method for the simultaneous, nonlinear inversion of gravity changes and surface deformation using bodies with a free geometry. Assuming simple homogenous elastic conditions, the method determines a general geometrical configuration of pressure and density sources. These sources are described as an aggregate of pressure and density point sources, fitting the whole data set (given some regularity conditions). The approach works in a growth step-by-step process that allows us to build very general geometrical configurations. The methodology is validated against an ellipsoidal body with anomalous pressure and a parallelepiped body with anomalous density, buried in an elastic medium. The simultaneous inversion of deformation and gravity values permits a good reconstruction of the assumed bodies. Finally, the inversion method is applied to the interpretation of gravity, leveling, and interferometric synthetic aperture radar (InSAR) data from the volcanic area of Campi Flegrei (Italy) for the period 1992–2000. For this period, a model with no significant mass change and an extended decreasing pressure region satisfactorily fits the data. The pressure source is located at about ∼1500 m depth, and it is interpreted as corresponding to the dynamics of the shallow (depth 1–2 km) hydrothermal system confined to the caldera fill materials.

Three-dimensional asymptotic antiplane shear stress fields at the front of interfacial crack/anticrack type discontinuities in trimaterial bonded plates

An eigenfuntion expansion method is employed for obtaining three-dimensional asymptotic displacement and stress fields in the vicinity of the front of a crack/anticrack type discontinuity weakening/reinforcing an infinite pie-shaped trimaterial plate, of finite thickness, formed as a result of bimaterial (matrix/semiconductor/ARC plus reaction product/scatterer) deposit over a substrate (fiber/ARC/semiconductor). The wedge is of general (unsymmetric) geometrical configuration, and is subjected to antiplane shear (mode III) far field loading. Each material is isotropic and elastic, but with different material properties. The material 2 or the substrate is always taken to be a half-space, while the wedge aperture angle of the material 1 is varied to represent varying composition of the bimaterial deposit. Numerical results pertaining to the variation of the mode III eigenvalues (or stress singularities) with various wedge aperture angles of the material 1 (reaction product/scatterer), are also presented. Hitherto generally unavailable results, pertaining to the through-thickness variations of stress intensity factors for symmetric parabolic load and its skew-symmetric counterpart that also satisfy the boundary conditions on the top and bottom surfaces of the trimaterial plates under investigation, form also an important part of the present investigation.

Three-dimensional asymptotic stress field at the front of an unsymmetric bimaterial wedge associated with matrix cracking or fiber break

A combined approach for prediction of the singular stress fields at the interfacial fronts of fiber breaks and matrix cracks is presented. A recently developed eigenfunction expansion method is employed for obtaining three-dimensional asymptotic displacement and stress fields in the vicinity of a point located at the front of a bimaterial wedge of general (unsymmetric) geometrical configuration (with respect to bimaterial interface), and subjected to extension/bending (mode I) and in-plane shear/twisting (mode II) far field loading and free–free wedge-side boundary condition. Each material is isotropic and elastic, but with different material properties. The material 2 (fiber in the case of matrix cracking or matrix in the case of fiber break) is always taken to be a half-space, while the wedge aperture angle of the material 1 is varied to represent varying matrix cracking or fiber break incidence angles at the interfaces. Numerical results pertaining to the variation of the lowest eigenvalues (or stress singularities) for various wedge aperture angles of the material 1, subjected to the afore-mentioned wedge-side boundary condition, are also presented. Variation of the same with the shear moduli ratio of the component material phases is also an important part of the present investigation. The conclusion drawn from the present asymptotic analysis of the matrix cracking problem is in agreement with that of an earlier investigation based on the energy based criterion. Similar conclusion drawn from the present asymptotic analysis of fiber break problem is in agreement with that of an energy based criterion derived here in analogy to the corresponding matrix crack problem by another investigator.

Numerical analyses of radiative heat transfer in any arbitrarily-shaped axisymmetric enclosures

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.

An accurate spectral/discontinuous finite-element formulation of a phase-space-based level set approach to geometrical optics

In this paper, we introduce a new numerical procedure for simulations in geometrical optics that, based on the recent development of Eulerian phase-space formulations of the model, can deliver very accurate, uniformly resolved solutions which can be made to converge with arbitrarily high orders in general geometrical configurations. Following previous treatments, the scheme is based on the evolution of a wavefront in phase-space, defined as the intersection of level sets satisfying the relevant Liouville equation. In contrast with previous work, however, our numerical approximation is specifically designed: (i) to take full advantage of the smoothness of solutions; (ii) to facilitate the treatment of scattering obstacles, all while retaining high-order convergence characteristics. Indeed, to incorporate the full regularity of solutions that results from the unfolding of singularities, our method is based on their spectral representation; to enable a simple high-order treatment of scattering boundaries, on the other hand, we resort to a discontinuous Galerkin finite element method for the solution of the resulting system of equations. The procedure is complemented with the use of a recently derived strong stability preserving Runge–Kutta (SSP-RK) scheme for the time integration that, as we demonstrate, allows for overall approximations that are rapidly convergent.

A simple closed‐form formula for the mutual impedance of dipoles

AbstractA simple and compact formula of dipole mutual impedance is presented. This method gives an analytical expression of mutual impedance between two real, thick center‐fed dipoles in a general geometrical configuration for small distances. The results of this new formulation show a good agreement with the numerical (NEC‐2) and experimental results. © 2002 Wiley Periodicals, Inc. Microwave Opt Technol Lett 34: 371–374, 2002; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.10465

Effect of local elastic softening on crack extension

Elastic softening materials are brittle materials such that crack extension is associated with a softening zone behind the crack tip, with the material elements within this zone exerting a restraining effect on the crack tip. Crack extension is sometimes characterised in terms of the stress intensity K F, due to the applied loadings, at the front of the softening zone, i.e. the actual crack tip. This paper is concerned with the determination of the maximum load K F value for a general positive geometrical configuration, for the case where the softening zone size is small compared with a solid's characteristic dimension. The resulting expression for K F is compared with the maximum load stress intensity value K T measured with regard to the initial crack position, i.e. the trailing edge of the softening zone.

Enhancement profile of phase conjugation in plasma by stimulated Brillouin scattering in a four-wave mixing scheme

A quantitative description of the enhancement gain profile of phase conjugation by four-wave mixing in plasma, based on stimulated Brillouin scattering, is presented. The Landau damping mechanism is taken into account, and general geometrical configurations are discussed.

Resonant optoacoustic cells for trace gas analysis*

An analysis of the ultimate detectivity of ideal optoacoustic cells, based on viscous gas equations, gives rigorous expressions for both signal and noise for a one-dimensional optoacoustic cell. Choice of boundary conditions for the noise calculations is dictated by the dissipation fluctuation theorem. Results of noise equivalent power calculations indicate superior performances near dc frequencies over those obtained at resonant conditions. A simplifying dissipative acoustic transmission line model describing optoacoustic cells of quite general geometric configurations is developed that is particularly useful for noise evaluation. In contrast to ideal cells, current optoacoustic cells’ detectivities are practically limited by interfering signals induced by windows’ absorption of infrared radiation; acoustical resonant conditions can help reduce such interference. A resonant optoacoustic cell exhibiting high immunity to windows interference is described that yields two orders of magnitude interference reduction compared with previously operated optoacoustic cells. The cell uses the longitudinal modes of a narrow open tube. Its minimum detectable concentration of ethylene in nitrogen is less than 0.3 parts in 109 for 1 Hz detection bandwidth using a 1 W, 10.5326 μm CO2 laser beam. Electronic noise limits the detectivity, and is ~15 dB higher than the expected Brownian noise of an ideal cell of the same configuration. Measurements with flowing trace gas are given.

The vibrational spectra of CF 3OF

The i.r. spectrum of gaseous CF 3OF from 4000-33 cm −1 and the Raman spectrum of the liquid are interpreted on the basis of C s symmetry and the same general geometrical configuration as CH 3OH. The twelve assigned fundamental frequencies provide explanation for forty-two of the forty-seven observed overtone and combination bands. A force constant calculation based on these assignments is performed which yields potential constants, potential energy distribution and normal coordinates. Analysis of i.r. band contours yields moments of inertia in agreement with those calculated from assumed geometry. The height of the threefold barrier to internal rotation is calculated to be 395 cm −1, whereas thermodynamic properties in the temperature range 200–600°K are tabulated.

Direct Measurement of the Nernst-Ettingshausen Dimensionless Figure of Merit

A method is given for obtaining the Nernst-Ettingshausen dimensionless figure of merit, in a direct measurement, as the ratio of two voltages. A discussion of the method is given for experiments involving rectangular sample geometries and also for more general geometrical configurations. Both isotropic and anisotropic materials are considered. The method is based on measurements of the ratio of the adiabatic electrical resistance to the isothermal electrical resistance. The superposition of the voltage of the Peltier-Seebeck effect is avoided by arranging for the completion of the experiments in a length of time which is short compared to the Peltier-Seebeck time constant for the sample. The required equipment and circuitry are simple, being similar to a four-probe resistivity measurement circuit with the voltage being determined by use of an oscilloscope.