Two-dimensional Test Research Articles

Industrial Computational Fluid Dynamics Tools for the Evaluation of Aerodynamic Coefficients

An automatic differentiation techniqueis applied here to anindustrial computational fluid dynamics code with the goal of efficiently evaluating aerodynamic coefficients. Basic concepts about the numerical technique to automatically differentiate a code are first discussed, and then methodologies to apply the capabilities of the Institut National de Recherche en Informatique et en Automatique derivation tool to an industrial finite volume solver are discussed. Afterward, two examples of application to representative two-dimensional and three-dimensional test cases are shown and, for each one, comparisons are carried out between the results gathered using the automatic differentiation and the classical second-order finite difference technique for the evaluation of derivatives. Such comparison highlights the capability of automatic differentiation to produce reliable results even if applied to complex configurations and in very complex numerical structures. Finally, tradeoff considerations are made as a conclusion

Solvability of a dynamic contact problem between a piezoelectric body and a conductive foundation

We consider a mathematical model which describes the dynamic process of contact between a piezoelectric body and an electrically conductive foundation. We model the material’s behavior with a nonlinear electro-viscoelastic constitutive law; the contact is frictionless and is described with the normal compliance condition and a regularized electrical conductivity condition. We derive a variational formulation for the problem and then, under a smallness assumption on the data, we prove the existence of a unique weak solution to the model. We also investigate the behavior of the solution with respect the electric data on the contact surface and prove a continuous dependence result. Then, we introduce a fully discrete scheme, based on the finite element method to approximate the spatial variable and the backward Euler scheme to discretize the time derivatives. We treat the contact by using a penalized approach and a version of Newton’s method. We implement this scheme in a numerical code and, in order to verify its accuracy, we present numerical simulations in the study of two-dimensional test problems. These simulations provide a numerical validation of our continuous dependence result and illustrate the effects of the conductivity of the foundation, as well.

Scale dependence of direct shear tests

Direct shear test has been widely used to measure the shear strength of soils and other particulate materials in industry because of its simplicity. However, the results can be dependent on the specimen size. The ASTM (American Society for Testing and Materials) publications suggest that for testing soils the shear box should be at least ten times the diameter of the largest particle and the height of the box should be no more than half of its diameter. These guidelines are empirically based. A series of two-dimensional numerical direct shear tests are performed to investigate this scaling effect. By analyzing the bulk friction, particle translation and rotation, percentage of sliding, average volume (area) and shear strain and the evolution of the shear band, we find that the traditional guidelines for direct shear tests are questionable. Scaling dependency of bulk friction on the property of granular materials is clearly present. Our current analysis points out that the scaling effects can vary significantly depending on the particle properties other than their sizes. Of all the parameters we observed, particle rotation appears to have a decisive correlation with the bulk friction. Formation of a shear band is universal. As the shearing progresses, particle rotation begins to concentrate near the shear plane. By defining the width of a shear band as the standard deviation of the distribution of translational gradient or the standard deviation of the distribution of particle rotation, quantitative evolutions of shear band are presented. Both measures of the shear band width dropped rapidly during pre-failure stage. After peak stress both measures begin to approach steady state as the bulk friction stabilizes to the residual stage. These observations suggest that structure formation inside the shear band controls the scaling effect.

Simulation of continuous casting of steel by a meshless technique

A recently developed local radial basis function collocation method is used for the solution of the transient convective–diffusive heat transport in continuous casting of steel. The solution of the thermal field with moving boundaries due to phase-change and the growing computational domain is based on the mixture continuum formulation. The growth of the domain and the movement of the starting block are described by activation of additional nodes and by the movement of the boundary nodes through the computational domain, respectively. Time-stepping is performed in an explicit way by a simple characteristic procedure. A two-dimensional transient test case solution is shown at different times and its accuracy is verified by comparison with the reference finite volume method results. The method is very attractive in the present context due to its trivial implementation of curved geometry for two and three dimensions, accuracy and stability of the results.

Distributed Target Detection in Sensor Networks Using Scan Statistics

We introduce a sequential procedure to detect a target with distributed sensors in a two dimensional region. The detection is carried out in a mobile fusion center which successively counts the number of binary decisions reported by local sensors lying inside its moving field of view. This is a two-dimensional scan statistic-an emerging tool from the statistics field that has been applied to a variety of anomaly detection problems such as of epidemics or computer intrusion, but that seems to be unfamiliar to the signal processing community. We show that an optimal size of the field of view exists. We compare the sequential two-dimensional scan statistic test and two other tests. Results for system level detection are presented.

Development and validation of a low-cost electrical resistivity tomographer for soil process monitoring

This paper presents the development and validation of a low-cost electrical resistivity tomography (ERT) system for the monitoring of process in soils. The ERT technique is capable of evaluating the distribution of electrical properties within a cross section of soil specimens by measuring the applied electrical current and monitoring the voltage distribution along boundary electrodes. This new ERT system consists of (i) a two-dimensional (2D) acrylic testing cell with strip copper electrodes, (ii) an acquisition system and control software, and (iii) a third-party reconstruction software. The tomographer is developed to collect low-noise data at moderate acquisition speeds. To validate the quality of the proposed ERT system, noise levels were evaluated with and without the testing cell and imaging tests were conducted to calibrate the system, evaluate the sensitivity of the instrument to locate a low-resistivity inclusion, and to monitor chemical diffusion in a saturated Ottawa sand specimen. Results show that the proposed low-noise, low-cost ERT acquisition system can be successfully used, with proper interpretation, to locate inclusions and obtain images of diffusion processes in soils. These validation tests show the applicability of the developed acquisition system in monitoring time-dependent processes that do not require real-time acquisition and reconstruction.

A Pebble Bed Reactor cross section methodology

A method is presented for the evaluation of microscopic cross sections for the Pebble Bed Reactor (PBR) neutron diffusion computational models during convergence to an equilibrium (asymptotic) fuel cycle. This method considers the isotopics within a core spectral zone and the leakages from such a zone as they arise during reactor operation. The randomness of the spatial distribution of fuel grains within the fuel pebbles and that of the fuel and moderator pebbles within the core, the double heterogeneity of the fuel, and the indeterminate burnup of the spectral zones all pose a unique challenge for the computation of the local microscopic cross sections. As prior knowledge of the equilibrium composition and leakage is not available, it is necessary to repeatedly re-compute the group constants with updated zone information. A method is presented to account for local spectral zone composition and leakage effects without resorting to frequent spectrum code calls. Fine group data are pre-computed for a range of isotopic states. Microscopic cross sections and zone nuclide number densities are used to construct fine group macroscopic cross sections, which, together with fission spectra, flux modulation factors, and zone buckling, are used in the solution of the slowing down balance to generate a new or updated spectrum. The microscopic cross-sections are then re-collapsed with the new spectrum for the local spectral zone. This technique is named the Spectral History Correction (SHC) method. It is found that this method accurately recalculates local broad group microscopic cross sections. Significant improvement in the core eigenvalue, flux, and power peaking factor is observed when the local cross sections are corrected for the effects of the spectral zone composition and leakage in two-dimensional PBR test problems.

Validation of a simple, sensitive enzyme immunoassay (EIA) for the determination of caprine plasma LH

The study describes the development and validation of a simple and highly sensitive enzyme immunoassay (EIA) for the determination of goat plasma LH, utilizing the biotin–streptavidin peroxidase amplification system in a competitive-binding assay. Micro-titer plates were coated with goat anti-rabbit globulin as the second antibody and biotin was coupled to oLH and used as a bridge between streptavidin peroxidase and immobilized oLH beta antisera. A simple 4-step procedure was used at room temperature for the sample analysis: (1) overnight incubation of LH standards and plasma samples with the LH antibody in a 96-well micro-titer plate, pre-coated with a second antibody; (2) incubation in a biotinylated–LH conjugate for 30 min; (3) incubation with streptavidin peroxidase for a further 30 min and (4) lastly incubation in tetramethyl benzidine substrate for 40 min to develop colour. A two-dimensional titer determination test proved the antibody titer of 1:100,00,000 and the biotinylated–LH conjugate titer of 1:4000 to be the most suitable. As the absolute binding sensitivity of different concentrations of oLH in 80 μl plasma was similar to that observed in buffer standards, all assays were conducted using 80 μl of the unknown plasma samples. A standard curve was obtained in the range of 25–12,800 pg LH/well in 80 μl hormone-free plasma. The sensitivity of the EIA procedure was 25 pg/well LH, which corresponds to 0.31 ng/ml plasma. In a parallelism test, the relative percentage binding curve for serially diluted goat plasma samples containing high levels of endogenous LH and for the oLH standard ran parallel to each other, thereby confirming the actual LH estimation in goat plasma. The classical patterns of plasma LH during the estrous cycle and the gradual increases in LH concentrations after gonadotrophin releasing hormone (GnRH) administration provided biological validation of the assay for the determination of plasma LH in caprine species. This EIA technique provides a simple and sensitive method for routine analysis of goat plasma LH.

Multicloud: Multigrid convergence with a meshless operator

The primary objective of this work is to develop and test a new convergence acceleration technique we call multicloud. Multicloud is well-founded in the mathematical basis of multigrid, but relies on a meshless operator on coarse levels. The meshless operator enables extremely simple and automatic coarsening procedures for arbitrary meshes using arbitrary fine level discretization schemes. The performance of multicloud is compared with established multigrid techniques for structured and unstructured meshes for the Euler equations on two-dimensional test cases. Results indicate comparable convergence rates per unit work for multicloud and multigrid. However, because of its mesh and scheme transparency, multicloud may be applied to a wide array of problems with no modification of fine level schemes as is often required with agglomeration techniques. The implication is that multicloud can be implemented in a completely modular fashion, allowing researchers to develop fine level algorithms independent of the convergence accelerator for complex three-dimensional problems.

Measured and simulated heat transfer to foundation soils

The drive towards energy-efficient, low-carbon buildings is a clear priority for many countries. Furthermore, ground heat transfer is understood to play an important role in the overall thermal performance of buildings. This paper presents the results of an in-depth investigation of heat transfer from buildings to the ground. The research involved in situ measurements of heat transfer to the ground from full-scale buildings. The results have been utilised to help develop and validate suitable predictive tools to aid thermal design. Numerical simulations have been undertaken that reveal the transient form of energy losses from typical buildings to the ground over a seasonal time frame. Comparisons are made between numerical results and measured data over an annual cycle. Overall, good correlation of results has been achieved. The thermal properties of foundation soils are known to be dependent on water content. A preliminary assessment of the significance of this aspect of the problem is also considered. In particular, it has been shown that an increase in soil moisture content may cause an increase in heat flux of over 20% for a two-dimensional test case. In summary, innovative low-energy sustainable design is receiving increasing attention. The current work will contribute to this overall objective by ensuring that adequate attention is given to subsurface heat transfer.

Calculation of unsteady flow past a cube on the wall of a narrow channel using URANS and the Spalart–Allmaras turbulence model

UDC 532.517.4 The results of numerical simulation of fully developed turbulent flow in a channel with the cube on the lower wall (for the characteristic Reynolds number Re = 40,000) within the framework of the traditional approach to the solution of unsteady Reynolds-averaged Navier-Stokes equations (URANS) in combination with the semiempirical Spalart-Allmaras turbulence model (with a correction for rotation) have been presented. A de- tailed comparative analysis of the results of numerical simulation of local and integral flow characteristics and the Martinuzzi experimental data has shown that the self-oscillating regime of flow past the cube is a su- perposition of oscillations of the arms of a horseshoe vortex and the rear arched and detached vortex struc- tures. Using fast Fourier transformation, it has been found that the oscillations are of a bimodal character in the longitudinal and vertical directions, whereas in the transverse direction, they are of a unimodal character. Introduction. The problem on unsteady flow past a cube in a narrow channel with the fully developed turbu- lent flow being formed at the inlet is of particular interest for testing today's calculation algorithms of computational hydrodynamics. In this case channel flow is of a self-oscillating character and is distinguished by a complex vortex structure (Fig. 1). Flow separation begins ahead of the cube and further develops from its frontal face side and on the lateral walls. A horseshoe vortex that interacts with the near wake of the cube results. We recognize the following basic large-scale flow elements for their subsequent analysis and comparison to experimental data: 1) a horseshoe vor- tex; 2) a vortex ensemble consisting of a vortex attached to the face side of the cube and two columnar vortices near the lateral walls; 3) a rear detached vortex; 4) an attached vortex behind the end wall of the cube, which is not iden- tified in the Martinuzzi experiment, as should be noted, but is visualized in many calculations; 5) an arched vortex with two oppositely rotating bends, which is formed in the near wake. Experimental data to which we compare results of numerical investigations were obtained by Martinuzzi (1) and have been introduced into the ERCOFTAC (European Research Community on Flow, Turbulence and Combustion) databank (2). About ten large-scale numerical investigations based on solution of steady and unsteady Reynolds-aver- aged Navier-Stokes equations (RANS ⁄ URANS) and on application of the large-eddy model (see, e.g., (3-5)) have been carried out over a period of 15 years. It is noteworthy that, except for the results obtained by Durbin with the V2F turbulence model (6), none of the works gives satisfactory agreement between the results of calculations within the framework of the RANS ⁄ URANS methodology and the experimental data. This work is primarily aimed at substantiating the applicability of the URANS approach to the prediction of turbulent separated flows. The commercial FLUENT v6.3 package (7) is used. Preliminary verification and approval of the package with a catalog of semiempirical models realized in it, which were carried out on two-dimensional test problems such as flow past a circular cylinder (8) and circulation flow in a square cavity with a moving upper bound- ary (9, 10), have shown satisfactory correlation with experimental data, when the two-parametric model of shear-stress transfer MSST and the Spalart-Allmaras (SA) vortex-viscosity model were selected. It has been shown in (8-10) that the SA model in its traditional formulation substantially overstates turbulent-viscosity values, which renders it unsuit- able for calculations of turbulent separated flows. For further testing, we have selected the SA model modified with allowance for rotation.

Comparative Study of the Accuracy of the Fundamental Mesh Structures for the Numerical Solution of Incompressible Navier-Stokes Equations in the Two-Dimensional Cavity Problem

The accuracies of the staggered, semistaggered, vertex collocated, and cell-center collocated meshes are compared for the incompressible Navier-Stokes equations in primitive variables using the two-dimensional lid-driven cavity test problem in both the traditional form with uniform lid velocity and in the regularized form without corner discontinuities. Central differencing is used in all discretizations. The momentum equations are integrated explicitly after the solution of a Poisson pressure equation that enforces mass conservation. Richardson extrapolation is employed to estimate the correct solutions in cases without precise reference solutions. For both forms of the problem, the staggered and the cell-center collocated meshes are shown to produce comparably accurate results, while the vertex collocated mesh shows poorer accuracy. The almost unknown semistaggered mesh, which is too sensitive to the velocity discontinuity in the traditional cavity problem, appears as the most accurate mesh in the regularized cavity problem.

Comparative Study of UNIFAES and other Finite-Volume Schemes for the Discretization of Advective and Viscous Fluxes in Incompressible Navier-Stokes Equations, Using Various Mesh Structures

The performance of the unified finite approaches exponential-type scheme (UNIFAES) for advective and diffusive transport equations, for the incompressible Navier-Stokes equations in primitive variables, is evaluated by comparison with the central differencing and the exponential scheme. Staggered, semistaggered, vertex collocated, and cell-center collocated meshes are considered. The Cartesian two-dimensional lid-driven cavity test problem is employed both in its traditional form with uniform lid velocity and in the regularized form without corner discontinuities. Richardson extrapolation is employed to produce reference results in the cases without prior precise reference solutions. The UNIFAES shows accuracy generally superior to the other schemes and stability even at the highest Reynolds numbers employed. This article also completes a previous comparative study of the performance of the mesh structures, generalizing the results there observed for higher Reynolds numbers and for schemes other than central differencing.

Modeling and analysis of the unilateral contact of a piezoelectric body with a conductive support

We consider a mathematical model which describes the quasistatic process of contact between a piezoelectric body and an electrically conductive support, the so-called foundation. We model the material's behavior with a nonlinear electro-viscoelastic constitutive law; the contact is frictionless and is described with the Signorini condition and a regularized electrical conductivity condition. We derive a variational formulation for the problem and then we prove the existence of a unique weak solution to the model. The proof is based on arguments of nonlinear equations with multivalued maximal monotone operators and fixed point. Then we introduce a fully discrete scheme, based on the finite element method to approximate the spatial variable and the backward Euler scheme to discretize the time derivatives. We treat the unilateral contact conditions by using an augmented Lagrangian approach. We implement this scheme in a numerical code then we present numerical simulations in the study of two-dimensional test problems, together with various comments and interpretations.

Discrete element modelling of a granular platform supported by piles in soft soil – Validation on a small scale model test and comparison to a numerical analysis in a continuum

This paper focuses on the mechanisms taking place in a granular platform supported by piles in soft soil. Several modelling approaches were explored. A two-dimensional small scale model test using the Taylor–Schneebeli soil analogue was first developed and the experimental results were compared to a discrete element model using the particle code PFC. The validation of this numerical approach allowed the parametric study to be extended numerically. Parametric studies were also performed on continuum model using the finite-difference code FLAC. Comparison of the parametric studies performed on each modelling approach underlined some differences and lead to a consideration on the macro- and micromechanical parameters.

Phase-field modeling of dry snow metamorphism

Snow on the ground is a complex three-dimensional porous medium consisting of an ice matrix formed by sintered snow crystals and a pore space filled with air and water vapor. If a temperature gradient is imposed on the snow, a water vapor gradient in the pore space is induced and the snow microstructure changes due to diffusion, sublimation, and resublimation: the snow metamorphoses. The snow microstructure, in turn, determines macroscopic snow properties such as the thermal conductivity of a snowpack. We develop a phase-field model for snow metamorphism that operates on natural snow microstructures as observed by computed x-ray microtomography. The model takes into account heat and mass diffusion within the ice matrix and pore space, as well as phase changes at the ice-air interfaces. Its construction is inspired by phase-field models for alloy solidification, which allows us to relate the phase-field to a sharp-interface formulation of the problem without performing formal matched asymptotics. To overcome the computational difficulties created by the large difference between diffusional and interface-migration time scales, we introduce a method for accelerating the numerical simulations that formally amounts to reducing the heat- and mass-diffusion coefficients while maintaining the correct interface velocities. The model is validated by simulations for simple one- and two-dimensional test cases. Furthermore, we perform qualitative metamorphism simulations on natural snow structures to demonstrate the potential of the approach.

A hybrid FVM–LBM method for single and multi‐fluid compressible flow problems

AbstractThe lattice Boltzmann method (LBM) has established itself as an alternative approach to solve the fluid flow equations. In this work we combine LBM with the conventional finite volume method (FVM), and propose a non‐iterative hybrid method for the simulation of compressible flows. LBM is used to calculate the inter‐cell face fluxes and FVM is used to calculate the node parameters. The hybrid method is benchmarked for several one‐dimensional and two‐dimensional test cases. The results obtained by the hybrid method show a steeper and more accurate shock profile as compared with the results obtained by the widely used Godunov scheme or by a representative flux vector splitting scheme. Additional features of the proposed scheme are that it can be implemented on a non‐uniform grid, study of multi‐fluid problems is possible, and it is easily extendable to multi‐dimensions. These features have been demonstrated in this work. The proposed method is therefore robust and can possibly be applied to a variety of compressible flow situations. Copyright © 2009 John Wiley & Sons, Ltd.

Second-order time evolution of PN equations for radiation transport

Using polynomials to represent the angular variation of the radiation intensity is usually referred to as the P N or spherical harmonics method. For infinite order, the representation is an exact solution of the radiation transport solution. For finite N, in some physical situations there are oscillations in the solution that can make the radiation energy density be negative. For small N, the oscillations may be large enough to force the material temperature to numerically have non-physical negative values. The second-order time evolution algorithm presented here allows for more accurate solutions with larger time steps; however, it also can resolve the negativities that first-order time solutions smear out. Therefore, artificial scattering is studied to see how it can be used to decrease the oscillations in low-order solutions and prevent negativities. Small amounts of arbitrary, non-physical scattering can significantly improve the accuracy of the solution to test problems. Flux-limited diffusion solutions can also be improved by including artificial scattering. One- and two-dimensional test results are presented.

The LIQSEDFLOW: Role of two-phase physics in subaqueous sediment gravity flows

The paper describes an extension of the computational code LIQSEDFLOW proposed by the authors. The salient features of the code lie in the capabilities to describe the multi-phased physics of subaqueous sediment gravity flows. Specifically, it combines Navier-Stokes/continuity equations and equations for advection and hindered settling of grains for a liquefied soil domain, with a consolidation equation for the underlying, progressively solidifying soil domain, via a transition layer that is characterized by zero effective stress and a small yet discernable stiffness. Evolutions of the flow and solidification surfaces are traced as part of solution by using a volume-of-fluid (VOF) technique. The predicted features of gravity flows of initially fluidized sediments with different concentrations conform to the observed performances in two-dimensional flume tests. The present results demonstrate the crucial role of two-phase physics, particularly solidification, in reproducing the concurrent processes of flow stratification, deceleration, and redeposition in subaqueous sediment gravity flows.

Beach Erosion around Shoreline and Effect of Land Subsidence

Characteristic beach profile change has been observed at the beach with integrated shore protection system by large scale submerged breakwater, jetties and nourishment. In this study the cause of characteristic beach profile change was presumed. Two-dimensional hydraulic model test with movable bed was carried out to verify the presumed result. Through the model test, it was found that the cause of constant shoreline erosion is land subsidence, the beach erosion by storm surges in winter is accumulated because sand transport onshore is not occurred in calm, the flat profile is formed at the depth equal to transferred wave height by submerged breakwater.