Two-dimensional Test Research Articles

Fatigue evaluation of surface coated railway rails using shakedown theory, finite element calculations, and lab and field trials

One solution to prevent surface fatigue of rails, investigated by the European project INFRA-STAR, is to coat the surfaces with a material which reduces or eliminates ratchetting. In this investigation, a systematic approach for fatigue design of surface coated rails (called two-material rails) against rolling contact fatigue is presented. It incorporates dynamic train–track interaction simulations, three-dimensional finite element (FE) calculations, shakedown theory, and lab and field trials. The approach was validated against two-dimensional twin-disc tests in laboratory, where surface coated disc specimens were used. Next, heavy haul traffic field trials were performed using two-material rails. Dynamic train–track interaction simulations, for train traffic situations at the test site, were performed. The results from these simulations were contact load data, which were used in the fatigue design approach to calculate railhead stresses with a three-dimensional FE model of a piece of rail; 26 load cases were identified as critical with respect to rolling contact fatigue. The stresses from the FE calculations were used to calculate shakedown diagrams for various wheel–rail contact situations at the test site. The shakedown diagrams and calculations are used to illustrate how the improvement in shakedown performance of coated rails varies with the coating thickness, traction coefficient, contact load position, the strength of the coating and substrate materials, and strain hardening of the materials. It is shown that the two-material rails with the correct rail profile can be used to prevent rolling contact fatigue and reduce wear for the current train traffic situation. The results are discussed in the light of observations at the test site.

Analysis of benzene transport in a two-dimensional aquifer model

In this study, the fate and transport of aqueous benzene was investigated in a laboratory-scale homogeneous aquifer by conducting a two-dimensional plume test. Benzene solution was introduced as a pulse type along the width of the aquifer model through a recharge zone situated at the upper-left part of the model and followed by a steady state flow. Solution samples were collected at various locations on the front side of the model to capture two-dimensional plumes at discrete time intervals. The benzene plumes showed a moderate retardation relative to chloride plumes observed from the previous study conducted for the same aquifer model. The retardation factor was obtained from the ratio of travel distances of benzene peaks to chloride peaks from the injection point, computed using a line integral method. Mass recovery of aqueous benzene revealed that there was a significant reduction of benzene mass, indicating the occurrence of volatilization and/or irreversible sorption during transport. Thus, retardation along with volatilization and/or irreversible sorption may be important processes affecting the fate and transport of aqueous benzene in the aquifer model. Copyright © 2005 John Wiley & Sons, Ltd.

STUDY ON FORMATION AND BEHAVIOR OF THE ICE COVER ON COLD REGION RESERVOIR

In the cold region Hokkaido, ice problems have occurred in the hydropower station. While we have investigated the river ice frazil and developed the river ice control structure, research on ice formation and behavior on a reservoir where the water level has fluctuated in, have never been performed.In this paper, thickness of the ice cover in a reservoir is discussed from heat balance and ice behavior. From a view point of heat balance, the transition of snow ice thickness on the reservoir during winter period was simulated by a numerical model, considering heat transfer between ice and air, and flow of water, etc. From a view point of ice behavior, by performing a two-dimensional hydraulic model test with simulating reservoir slope, fluctuation of water level, and ice jam condition, ice behavior around slope of this model was observed, and hydrological behavior to study on ice thickness distribution in a reservoir was confirmed.

Adaptive Multiscale Finite-Volume Method for Multiphase Flow and Transport in Porous Media

We present a multiscale finite-volume (MSFV) method for multiphase flow and transport in heterogeneous porous media. The approach extends our recently developed MSFV method for single-phase flow. We use a sequential scheme that deals with flow (i.e., pressure and total velocity) and transport (i.e., saturation) separately and differently. For the flow problem, we employ two different sets of basis functions for the reconstruction of a conservative fine-scale total velocity field. Our basis functions are designed to have local support, and that allows for adaptive computation of the flow field. We use a criterion based on the time change of the total mobility field to decide when and where to recompute our basis functions. We show that at a given time step, only a small fraction of the basis functions needs to be recomputed. Numerical experiments of difficult two-dimensional and three-dimensional test cases demonstrate the accuracy, computational efficiency, and overall scalability of the method.

19.4: Generalization of Parameters Representing Magnitudes of Motion Artifacts

Several motion blur parameters of flat panel displays are introduced. One of them is an integrated edge profile distortion (IEPD) used for gray level two block test patterns. An integrated pattern profile distortion (IPPD) is newly proposed for two-dimensional test patterns, and may be a generalized parameter representing strengths of motion blur and also those of other motion artifacts.

A Least-Squares Mixed Finite Element Method for Biot's Consolidation Problem in Porous Media

A least-squares mixed finite element method for the coupled problem of flow and deformation is presented and analyzed in this paper. For the analysis, we restrict ourselves to fully saturated conditions for the flow process and to a linearly elastic material law for the deformation process. This is known in the literature as Biot's consolidation problem. For simplicity, the analysis is presented for the problem in two space dimensions. Our least-squares approach is motivated by the fact that all process variables, i.e., fluid pressure and flux as well as displacement field and stress tensor, are approximated directly by suitable finite element spaces. Ellipticity of the corresponding variational formulation is proven for the stationary case as well as for the subproblems arising at each step of an implicit time discretization in the general time-dependent case. Standard H1 -conforming piecewise linear and quadratic finite elements are used for the fluid pressure and for (each component of) the displacement, respectively. For the flux and stress components, the H(div)-conforming Raviart--Thomas spaces (of lowest order) are used. Computational results are presented for some two-dimensional test problems.

A Comparison of Troubled-Cell Indicators for Runge--Kutta Discontinuous Galerkin Methods Using Weighted Essentially Nonoscillatory Limiters

In [SIAM J. Sci. Comput., 26 (2005), pp. 907--929], we initiated the study of using WENO (weighted essentially nonoscillatory) methodology as limiters for the RKDG (Runge--Kutta discontinuous Galerkin) methods. The idea is to first identify cells, namely, those cells where limiting might be needed, then to abandon all moments in those cells except the cell averages and reconstruct those moments from the information of neighboring cells using a WENO methodology. This technique works quite well in our one- and two-dimensional test problems [SIAM J. Sci. Comput., 26 (2005), pp. 907--929] and in the follow-up work where more compact Hermite WENO methodology is used in the troubled cells. In these works we used the classical minmod-type TVB (total variation bounded) limiters to identify the troubled cells; that is, whenever the minmod limiter attempts to change the slope, the cell is declared to be a troubled cell. This troubled-cell indicator has a TVB parameter $M$ to tune and may identify more cells than necessary as troubled cells when $M$ is not chosen adequately, making the method costlier than necessary. In this paper we systematically investigate and compare a few different limiter strategies as troubled-cell indicators with an objective of obtaining the most efficient and reliable troubled-cell indicators to save computational cost.

Fluid–particle flow simulation by averaged continuous model

In this paper we present a numerical method for fluid–particle flow simulation. The mathematical model is based on the averaged continuum. The presence of particles is taken into account in terms of effective viscosity, which is defined by means of both Newtonian and non-Newtonian (Bingham plastic) models. The dispersed phase equation closure is based on particle buoyancy as well as on shear-induced self-diffusion effects. The proposed approach allows us to study sediment transport problems and the related evolution of bed forms, without requiring the generation of curvilinear coordinate systems and time-consuming step-by-step regridding. In fact, the present model describes the bottom shape in terms of a density contour surface, rather than a moving boundary of the fluid domain. Simple two-dimensional numerical tests have been performed: (i) Bingham flow in a driven cavity and (ii) particle settling in a pure Couette flow. Finally, preliminary results concerning (iii) two-dimensional scour below pipelines in steady flow have been presented and discussed.

A numerical approach for the simulation of ductile fracture with embedded discontinuities

AbstractIn the present study, a computational approach for the numerical simulation of ductile fracture within the framework of the finite element method is proposed. In the developed macroscopic formulation, the inelastic behavior in the bulk of the material is described by the finite elasto‐plastic material model proposed in [4]. The failure process is modeled by introducing discontinuities when a special local fracture criterion is satisfied. The discontinuities are incorporated via special triangular finite elements with embedded interfaces following the line of [2]. Finally, the numerical procedure is evaluated for a twodimensional representative test problem. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Glacier flow modelling: a comparison of the Shallow Ice Approximation and the full-Stokes solution

Several different approaches of various complexities have been used in glacier and ice sheet modelling studies. Amongst them, owing to its simplicity, the Shallow Ice Approximation appears to be the most widely adopted method. This approach, essentially used for ice sheets, owes its success to the shallow aspect of the modelled ice mass embodied in an aspect ratio ζ. When considering smaller ice bodies like alpine-type glaciers, the question arises as to whether the SIA is still valid, given that the method is all the more accurate as ζ is small. In order to test the domain of applicability of the method, results of a SIA finite difference model are compared to those of a finite element model in which the flow equations are fully considered. From a set of two-dimensional flow tests, it is shown that the accuracy of the method is much more deteriorated with increasing bedrock slopes than it is with increasing accumulation rates, even if higher accumulations lead to thicker glaciers with a larger ζ. This leads to the conclusion that when slopes become pronounced, it is a bedrock-related aspect ratio that becomes of relevance such that the bedrock slope should be the most important parameter to consider for assessing the validity of the SIA Method. A 3-dimensional simulation shows that longitudinal shear stresses explain a large part of the misfit between SIA and full-Stokes approaches. To cite this article: E. Le Meur et al., C. R. Physique 5 (2004).

Simulation of multicomponent flows using high order central schemes

This paper concerns with the conservative extension of the classical Euler equations to the multicomponent flows. We use high-resolution central schemes to solve these equations. The equilibrium states for each component are coupled in space and time to have a common temperature and velocity. Usually conservative Euler solvers for the gas mixtures produces nonphysical oscillations near contact discontinuities, if the temperature and the ratio of specific heats both are not constant there. However in the current schemes the oscillations near the interfaces are negligible. The schemes also guarantee the exact mass conservation for each component and the exact conservation of total momentum and energy in the whole particle system. The central schemes are robust, reliable, compact and easy to implement. Several one- and two-dimensional numerical test cases are included in this paper, which validates the application of these schemes to multicomponent flows.

On Tension Failure of 2-D Rock Specimens and Associated Acoustic Emission

To understand the failure mechanism of quasi-brittle materials like rock under tensile stress, observations on the failure process of granite and marble plate specimens under tension are summarized and presented. Micro- and macro-failure properties of rock plates under uniaxial tension have been characterized by using an acoustic emission technique. Acoustic emission signals associated with micro-fractures are captured to locate the sources. An algorithm based on arrival time difference is developed for this purpose. The results reveal clearly the failure processes of rock which include initiation, nucleation and propagation of micro-fractures when the axial stress is close to the peak strength of rock. It is believed that the difference in heterogeneity between granite and marble specimens leads to different fracture shapes and different behaviors of associated acoustic emissions. Numerical simulation of acoustic emissions for two-dimensional tensile test is also carried out. The simulated characteristics are in good agreement with the experimental results.

Two-dimensional tension tests in plant biomechanics--sweet cherry fruit skin as a model system.

Splitting of fruits is a function of two-dimensional tension caused by different growth rates of tissues and turgor, especially water uptake shortly before harvest. In order to analyse the mechanical properties of spheroid plant material close to stress-strain conditions in vivo, a new hydraulic two-dimensional testing device was set up. Sweet cherry (Prunus avium L.) fruit skin was chosen as a model system. The recorded pressure-deflection curves were non-linear, with a considerable initial "lag phase" and a distinct increasing end part. Taking into account the special geometry, these curves could be modelled with a newly developed analytical approach based on linear elastic material behaviour. The results demonstrated good correlation if a modulus of elasticity ranging from 160 to 250 MPa for the cherry fruit skin was chosen. In addition, a mean strength value of 47 MPa was calculated based on the theory of thin shells and spheres. The results are compared with mechanical data found for fruits and other plant material. In order to test the theoretical approach, two- and one-dimensional tension tests were performed on packaging PE foil, revealing a mean modulus of 171 MPa in bi-axial tension, and 193 and 242 MPa in uni-axial tension, depending on the test speed. The results demonstrate that it seems to be feasible to use this method to analyse the two-dimensional stress-strain conditions of spheroid plant materials such as cherry fruit skins. It may be applied as a tool for crop testing to elucidate the mechanical basis of cracking susceptibility of fruits.

X-ray sources overdensity around the 3C 295 galaxy cluster

Abstract We present a statistical analysis of the Chandra observation of the source field around the 3C 295 galaxy cluster ( z =0.46). The logN-logS of this field is in good agreement with that computed for the Chandra Deep Field South in this work and in previous ones. Nevertheless, the logN-logS computed separately for the four ACIS-I chips reveals that there is a significant excess of sources to the North-North East and a void to the South of the central cluster. Such an asymmetric distribution is confirmed by the two-dimensional Kolmogorov-Smirnov test, which excludes ( P ∼3%) a uniform distribution. In addition, a strong spatial correlation emerges from the study of the angular correlation function of the field: the angular correlation function is above that expected for X-ray sources on a few arcmin scales. In synthesis, the present analysis may indicate a filament of the large scale structure of the Universe toward 3C 295. This kind of study may open-up a new way to map (with high efficiency) high-density peaks of large scale structures at high redshift.

Testing density-dependent groundwater models: two-dimensional steady state unstable convection in infinite, finite and inclined porous layers

This study proposes the use of several problems of unstable steady state convection with variable fluid density in a porous layer of infinite horizontal extent as two-dimensional (2-D) test cases for density-dependent groundwater flow and solute transport simulators. Unlike existing density-dependent model benchmarks, these problems have well-defined stability criteria that are determined analytically. These analytical stability indicators can be compared with numerical model results to test the ability of a code to accurately simulate buoyancy driven flow and diffusion. The basic analytical solution is for a horizontally infinite fluid-filled porous layer in which fluid density decreases with depth. The proposed test problems include unstable convection in an infinite horizontal box, in a finite horizontal box, and in an infinite inclined box. A dimensionless Rayleigh number incorporating properties of the fluid and the porous media determines the stability of the layer in each case. Testing the ability of numerical codes to match both the critical Rayleigh number at which convection occurs and the wavelength of convection cells is an addition to the benchmark problems currently in use. The proposed test problems are modelled in 2-D using the SUTRA [SUTRA––A model for saturated–unsaturated variable-density ground-water flow with solute or energy transport. US Geological Survey Water-Resources Investigations Report, 02-4231, 2002. 250 p] density-dependent groundwater flow and solute transport code. For the case of an infinite horizontal box, SUTRA results show a distinct change from stable to unstable behaviour around the theoretical critical Rayleigh number of 4 π 2 and the simulated wavelength of unstable convection agrees with that predicted by the analytical solution. The effects of finite layer aspect ratio and inclination on stability indicators are also tested and numerical results are in excellent agreement with theoretical stability criteria and with numerical results previously reported in traditional fluid mechanics literature.

Influence of Surface Loads and Construction Sequence on Ground Response Due to Tunnelling

ABSTRACT Two-dimensional model tests of tunnel excavation and the corresponding numerical analyses were carried out. Numerical analyses were performed with the finite element method using the elastoplastic subloading tij model, which can simulate typical soil behavior. Model tests and numerical analyses were performed for three series of tunnel excavations. To investigate the influence of tunnel excavation on surface settlement and earth pressure surrounding a tunnel, both the model tests and numerical simulations were conducted considering the ground as green field. It is found that earth pressure decreases at the place of excavation, while increasing adjacent to the excavation due to an arching effect. The results confirm the validity of the constitutive model including the initial condition of the ground. To investigate the effects of building loads in tunnel excavation, model tests and numerical analyses were carried out as well. In this series, the initial dead load was applied adjacent to the tunnel. It is demonstrated that the building loads control surface settlements such that the maximum surface settlement does not always occur above the centerline of the tunnel, but at the position of the existing building. The deformation mechanism and the earth pressure during the tunnel excavation for the ground disturbed by the building loads are different from those for the greenfield situation. The results of this series validate the model regarding the boundary condition and initial state of the ground. In a third series of tests, two different excavation sequences were considered for a tunnel with a large cross-section. In the first case, the middle section was initially excavated and later two side-sections were excavated. In the other case, two side-sections were excavated before excavation of the middle section. The results of this series show that final surface settlements vary slightly with excavation sequences, whereas final earth pressures differ considerably for different excavation sequences. The results of this series prove that the model can consider construction sequences perfectly in finite element analyses. Numerical simulations agree not only qualitatively but also quantitatively with the model tests results for both deformations and earth pressures.

Kinetic flux-vector splitting schemes for the hyperbolic heat conduction

A kinetic solver is developed for the initial and boundary value problems of the symmetric hyperbolic moment system. This nonlinear system of equations is related to the heat conduction in solids at low temperatures. The system consists of a conservation equation for the energy density e and a balance equation for the heat flux Q i , where e and Q i are the four basic fields of the theory. We use kinetic flux vector splitting (KFVS) scheme to solve these equations in one and two space dimensions. The flux vectors of the equations are splitted on the basis of the local equilibrium distribution of phonons. The resulting computational procedure is efficient and straightforward to implement. The second-order accuracy of the scheme is achieved by using MUSCL-type reconstruction and min-mod nonlinear limiters. The solutions exhibit second-order accuracy and satisfactory resolution of gradients with no spurious oscillations. The scheme is extended to the two-dimensional case in a usual dimensionally split manner. In order to prescribe the boundary data, we need the knowledge of the e and Q i . However, in experiments only one of the quantities can be controlled at the boundary. This problem is removed by using a continuity condition. It turned out that after some short time energy and heat flux are related to each other according to Rankine–Hugoniot jump relations. To illustrate the performance of the KFVS scheme, we perform several one- and two-dimensional test computations. For the comparison of our results, we use high order central schemes. The present study demonstrates that this kinetic method is effective in handling such problems.

Simulation of multicomponent flows using high order central schemes

This paper is concerned with numerical methods for the conservative extension of the classical Euler equations to multicomponent flows. We use high-resolution central schemes to solve these equations. The equilibrium states for each component are coupled in space and time to have a common temperature and velocity. Usually conservative Euler solvers for the gas mixtures produces nonphysical oscillations near contact discontinuities, if the temperature and the ratio of specific heats both are not constant there. However in the schemes considered here the oscillations near the interfaces are negligible. The schemes also guarantee the exact mass conservation for each component and the exact conservation of total momentum and energy in the whole particle system. The central schemes are robust, reliable, compact and easy to implement. Several one- and two-dimensional numerical test cases are included in this paper, which validates the application of these schemes to multicomponent flows.

A surface marker algorithm coupled to an area-preserving marker redistribution method for three-dimensional interface tracking

In this work we present a new interface tracking algorithm based on surface markers to reconstruct and advect interfaces in three-dimensional space. The algorithm is coupled to a marker redistribution method, which is area-preserving along the interface. The interface is described by a set of closed lines which define a coarse Lagrangian quadrangular mesh in the fixed computational grid. Fixed markers are located where the lines cross and are maintained during the whole simulation. At each time step the interface is first reconstructed and then all markers are advected by following streamlines. In the reconstruction step, new markers are determined by computing the intersections of the interface lines with the grid cell faces and by adding area conservation markers between fixed and grid intersection markers. Intersection and conservation markers defined at the previous time step are discarded. The method maintains a smooth geometrical description of the interface for both two-dimensional and three-dimensional tests with accurate volume conservation even in very challenging situations where the fluid bodies progressively deform and stretch developing localized regions with very high curvature and thin fluid filaments. The method compares favorably with front capturing methods, such as volume-of-fluid and level set, and other hybrid techniques, such as the particle level set method.

New quantitative measuring technique for microleakage of the restored tooth through 3D reconstruction

Established microleakage tests have their own disadvantages. In this study, 3D reconstruction method was tried to overcome these disadvantages. Four types of microleakage tests were used and relationships among them were estimated: penetrated dye volume: marginal adaptability: degree of dye penetration and relative penetrated length to cavity wall. Twenty-four Class V cavities were bulk filled with composite (Esthet X) following surface treatments: N group (no treatment): E group (etching only): T group (etching + Prime & Bond NT). 50% silver nitrate was used as a dye solution after thermocycling (, 1.000 times). Teeth were serially ground with a thickness of 0.2 mm. Volume of dye penetration was estimated from a three-dimensionally reconstructed image with a software (3D-DOCTOR). Percentage of margin without gap was estimated from SEM and degree of dye penetration and the relative length of dye penetration to overall cavity wall were also estimated. ANOVA and Scheffe test for dye volume, Kruskal-Wallis and Mann-Whitney test for marginal quality, Spearman's rho test for checking of relationships among methods were used. The results were as follows: 1. Dye penetration could be seen from several directions, furthermore, its volumetric estimation was possible. 2. Reverse relationship was found between dye volume and marginal quality (r = -0.881/ p = 0.004). 3. Very low relationship was seen between dye volume and two-dimensional tests (degree of dye penetration and relative length). However, 2D evaluation methods showed high relationship (p = 0.002-0.054) each other. 4. Three times vertical section could be recommended as a 2D test.