Different Types Of Grids Research Articles

Effective transport properties of the porous electrodes in solid oxide fuel cells

This article presents a numerical framework for the computation of the effective transport properties of solid oxide fuel cells (SOFCs) porous electrodes from three-dimensional (3D) constructions of the microstructure. Realistic models of the 3D microstructure of porous electrodes are first constructed from measured parameters such as porosity and particle size distribution. Then each phase in the model geometries is tessellated with a computational grid. Three different types of grids are considered: Cartesian, octree, and body-fitted/cut-cell with successive levels of surface refinement. Finally, a finite volume method is used to compute the effective transport properties in the three phases (pore, electron, and ion) of the electrode. To validate the numerical approach, results obtained with the finite volume method are compared to those calculated with a random walk simulation for the case of a body-centred cubic lattice of spheres. Then, the influence of the sample size is investigated for random geometries with monosized particle distributions. Finally, effective transport properties are calculated for model geometries with polydisperse particle size distributions similar to those observed in actual SOFC electrodes.

Numerically simulating the thermal–hydraulic characteristics within the fuel rod bundle using CFD methodology

With the dramatic progress in the computer processing power, computational fluid dynamics (CFD) methodology can be applied in investigating the detailed knowledge of thermal–hydraulic characteristics in the rod bundle, especially with the spacer grid. These localized information, including flow, turbulence, and heat transfer characteristics, etc., can assist in the design and the improvement of rod bundles for nuclear power plants. In this paper, a three-dimensional (3D) CFD model with the Reynolds stresses turbulence model is proposed to simulate these characteristics within the rod bundle and subsequently to investigate the effects of different types of grid on the turbulent mixing and heat transfer enhancement. Two types of grid designs are used herein, including the standard grid and split-vane pair one, respectively. Based on the CFD simulations, the secondary flow can be reasonably captured in the rod bundle with the grid. The split-vane pair grid would enhance both the flow mixing and the heat transfer capability more than the standard grid does, as clearly shown in the simulation results. In addition, compared with the results of experiment and correlation, the present predicted result for the Nusselt (Nu) number distribution downstream the grid shows reasonable agreement for the standard grid design. However, there is discrepancy in the decay trend of Nu number between the prediction and measurement for the split-vane pair gird. This would be improved by adopting the finer mesh ( y + < 1) simulation and Low-Reynolds form turbulence model, which is our future research work.

Effect of free-stream turbulence on the flow over a sphere

In this paper, the effect of free-stream turbulence (FST) on the flow over a sphere is experimentally investigated at the Reynolds numbers of 0.5×105–2.8×105. Three levels of FST are generated in a wind tunnel by installing three different types of grids upstream of the sphere. It is found that FST triggers the boundary layer instability above the sphere surface and delays the separation. Once laminar separation occurs, the disturbances both from the boundary-layer instability and FST trigger the shear-layer instability. Then, high momentum is entrained toward the sphere surface and the separated flow is reattached, forming a separation bubble on the sphere surface. Due to high momentum near the surface, the main separation is delayed and the drag is reduced. The critical Reynolds number, at which the drag coefficient decreases rapidly, decreases as the FST intensity increases. With increasing Reynolds number, the first separation point moves downstream, but the reattachment and main separation points are nearly fixed, resulting in a constant drag coefficient. As the Reynolds number further increases, the separation bubble finally disappears but the main separation point is still nearly unchanged, resulting in a constant drag coefficient within the Reynolds number range considered. Therefore, the formation, regression, and disappearance of a separation bubble on the sphere surface are the key mechanisms of the drag change by FST.

English

This paper deals with nonlinear FVM approach based on different kinds of meshing (using grids-C,O,H ).Theory is utilized to obtain the convergence rate, CPU time, coefficient of drag, coefficient of lift, lift/drag of the airfoil(NACA0012). The airfoil considered is studied with three different types of grids viz. O-grid, C-grid and H-grid and accordingly obtain the values of pressure, velocity and temperature. Airfoil is studied with two different flow regimes (i.e., 0.8M & 1.2M). A Finite discretization is applied throughout the process in case of gridding. The computational method does not require any tuning of parameters. The solution obtained shows the good resolution of all flow phenomenon and are obtained by computational analysis.

Nested maximin Latin hypercube designs

In the field of design of computer experiments (DoCE), Latin hypercube designs are frequently used for the approximation and optimization of black-boxes. In certain situations, we need a special type of designs consisting of two separate designs, one being a subset of the other. These nested designs can be used to deal with training and test sets, models with different levels of accuracy, linking parameters, and sequential evaluations. In this paper, we construct nested maximin Latin hypercube designs for up to ten dimensions. We show that different types of grids should be considered when constructing nested designs and discuss how to determine which grid to use for a specific application. To determine nested maximin designs for dimensions higher than two, four variants of the ESE algorithm of Jin et al. (J Stat Plan Inference 134(1):268–287, 2005) are introduced and compared. Our main focus is on GROUPRAND, the most successful of these four variants. In the numerical comparison, we consider the calculation times, space-fillingness of the obtained designs and the performance of different grids. Maximin distances for different numbers of points are provided; the corresponding nested maximin designs can be found on the website http://www.spacefillingdesigns.nl.

Nested Maximin Latin Hypercube Designs

In the field of design of computer experiments (DoCE), Latin hypercube designs are frequently used for the approximation and optimization of black-boxes. In certain situations, we need a special type of designs consisting of two separate designs, one being a subset of the other. These nested designs can be used to deal with training and test sets, models with different levels of accuracy, linking parameters, and sequential evaluations. In this paper, we construct nested maximin Latin hypercube designs for up to ten dimensions. We show that different types of grids should be considered when constructing nested designs and discuss how to determine which grid to use for a specific application. To determine nested maximin designs for dimensions higher than two, four different variants of the ESE-algorithm of Jin et al. (2005) are introduced and compared. In the appendix, maximin distances for different numbers of points are provided.

Problems and Techniques

The paper featured in this issue is “Logically Rectangular Grids and Finite Volume Methods for PDEs in Circular and Spherical Domains” by Donna Calhoun, Christiane Helzel, and Randy LeVeque. The topic is the numerical solution of partial differential equations (PDEs) whose domains are circles, balls, spheres, and related geometries. The main idea is to solve the PDE on a “logically rectangular” grid. This means, for instance, if the physical space is a circle, then the computational space is a square. The authors focus on hyperbolic PDEs, including Euler, acoustics, and shallow water equations, and also give an example for solving reaction-diffusion equations. This paper is a pleasure to read. One finds lucid explanations of what can go wrong with different types of grids for circular and spherical domains, such as grid cells of widely differing sizes and extreme shapes. In contrast, the algorithms in this paper map a single rectangular block into a spherical shape; and the resulting cell sizes differ by a factor of at most two. The different mappings from computational space to physical space are presented as short, intuitive MATLAB algorithms. Many crisp pictures illustrate the uniform appearance and effectiveness of the grids. Even those who are not PDE experts will appreciate the simplicity, elegance, and generality of the logically rectangular grids when they are combined with a discretization of the PDE by finite volume methods.

Testing of the Fluent Package in Calculation of Supersonic Flow in a Step Channel

Nonstationary supersonic flow of a nonviscous gas in a step channel with Mach number M = 3 is calculated using the FLUENT package. The accuracy of predictions is analyzed on different types of grids, including those with dynamic local adaptation, and on numerical schemes of different approximation orders.

G STL: the geostatistical template library in C++

The development of geostatistics has been mostly accomplished by application-oriented engineers in the past 20 years. The focus on concrete applications gave birth to many algorithms and computer programs designed to address different issues, such as estimating or simulating a variable while possibly accounting for secondary information such as seismic data, or integrating geological and geometrical data. At the core of any geostatistical data integration methodology is a well-designed algorithm. Yet, despite their obvious differences, all these algorithms share many commonalities on which to build a geostatistics programming library, lest the resulting library is poorly reusable and difficult to expand. Building on this observation, we design a comprehensive, yet flexible and easily reusable library of geostatistics algorithms in C++. The recent advent of the generic programming paradigm allows us elegantly to express the commonalities of the geostatistical algorithms into computer code. Generic programming, also referred to as “programming with concepts”, provides a high level of abstraction without loss of efficiency. This last point is a major gain over object-oriented programming which often trades efficiency for abstraction. It is not enough for a numerical library to be reusable, it also has to be fast. Because generic programming is “programming with concepts”, the essential step in the library design is the careful identification and thorough definition of these concepts shared by most geostatistical algorithms. Building on these definitions, a generic and expandable code can be developed. To show the advantages of such a generic library, we use G STL to build two sequential simulation programs working on two different types of grids—a surface with faults and an unstructured grid—without requiring any change to the G STL code.

Multi‐grid domain decomposition approach for solution of Navier–Stokes equations in primitive variable form

AbstractA new multi‐grid (two‐grid) pseudospectral element method has been carried out for solution of incompressible flow in terms of primitive variable formulation. The main objective of the proposed method is to apply the multi‐grid technique solving the incompressible flow problems associated with three commonly encountered multi‐grid environments. In domain decomposition terminology, it includes (I) partially overlapped subdomains, each of which has same types of grids; (II) partially overlapped subdomains, each of which has different types of grids; (III) local adaptive subdomains fully overlapped with the original computational domain (composite grids).The approach for flow problems, complex geometry or not, is to first divide the computational domain into a number of subdomains with the inter‐overlapping area (partially or fully overlapped). In categories I and II, the fine‐grid or coarse‐grid subdomains can be defined by their representation, while in category III the fine‐grid or coarse‐grid subdomains are defined as usual. Next, implement the Schwarz Alternating Procedure (SAP) to exchange the data among subdomains, where the coarse‐grid correction is used to remove the high frequency error that occurs when the data interpolation from the fine‐grid subdomain to the coarse‐grid subdomain is conducted. The strategy behind the coarse‐grid correction is to adopt the operator of the divergence of velocity field, which intrinsically links the pressure equation, into this process. The solution of each subdomain can be efficiently solved by the direct (or iterative) eigenfunction expansion technique or preconditioned method with the least storage requirement, i.e. O(N2) in 2‐D.Numerical results of (i) driven cavity flow (Re = 100,400) with Cartesian grids (category I) in each subdomain, (ii) driven cavity flow (Re = 3200) with local adaptive grids (category III) in each subdomain, and (iii) flow over a cylinder (Re = 250) with ‘O’ grids in one subdomain and Cartesian grids in another (category II) will be presented in the paper to account for the versatility of the proposed multi‐grid method.

Spline collocation methods for calculating orbital energies

The accuracy of the spline collocation method for solving molecular orbital equations is tested for the hydrogen atom. Two different types of grids are used that concentrate points near the nucleus. A 40 point grid defined by a polynomial transformation, which is suitable for molecular calculations, is found to produce an accuracy within a mHartree of the exact value. For many electron systems, the authors have previously employed an algorithm for solving Poisson's equation which uses the eigenvectors of the kinetic energy matrices as a basis. In order to ensure the accuracy of the eigenvalues and eigenvectors of the kinetic energy, a method is implemented using scaled splines that leads to kinetic energy matrices having a simple block structure. The eigenvalues of the kinetic energy matrices in this scheme are quite accurate.

The characteristics of the radiated noise from open grid and bascule bridges

When vehicles travel across the grid section of an open grid or bascule bridge, noise is generated which for most type of grid configurations has a very strong tonal characteristic in the frequency range between 150 and 250 Hz. To investigate the mechanism by which this noise is generated, and identify possible noise mitigation procedures, a series of measurements of both sound and vibration levels have been performed on 12 bascule bridges with different types of grid. The grid types can generally be classified into three configurations, two of which are of a rectangular or square shape, while the third configuration has diagonal members and is generally referred to as four‐way grid. For the rectangular‐shaped grids, both the vibration and the sound spectra exhibited a dominant peak at a frequency that scaled with the speed of the vehicle and a typical length of the grid spacing. For the four‐way grid, the spectrum did not show a very strong peak, but was more broadly distributed in frequency. The general overall sound level was not much different from one bridge grid type to another. The grid is an open structure and its radiation efficiency in the 200‐Hz region is very low. This makes the tire a potentially significant source of noise. [Work sponsored by FDOT.]

The shearless turbulence mixing layer

The interaction of two energy-containing turbulence scales is studied in the absence of mean shear. The flow, a turbulence mixing layer, is formed in decaying grid turbulence in which there are two distinct scales, one on either side of the stream. This is achieved using a composite grid with a larger mesh spacing on one side of the grid than the other. The solidity of the grid, and thus the mean velocity, is kept constant across the entire flow. Since there is no mean shear there is no turbulence production and thus spreading is caused solely by the fluctuating pressure and velocity fields. Two different types of grids were used: a parallel bar grid and a perforated plate. The mesh spacing ratio was varied from 3.3:1 to 8.9:1 for the bar grid, producing a turbulence lengthscale ratio of 2.4:1 and 4.3:1 for two different experiments. For the perforated plate the mesh ratio was 3:1 producing a turbulence lengthscale ratio of 2.2:1. Cross-stream profiles of the velocity variance and spectra indicate that for the large lengthscale ratio (4.3:1) experiment, a single scale dominates the flow while for the smaller lengthscale ratio experiments, the energetics are controlled by both lengthscales on either side of the flow. In all cases the mixing layer is strongly intermittent and the transverse velocity fluctuations have large skewness. The downstream data of the second, third and fourth moments for all experiments collapse well using a single composite lengthscale. The component turbulent energy budgets show the importance of the triple moment transport and pressure terms within the layer and the dominance of advection and dissipation on the outer edge. It is also shown that the bar grids tend toward self-similarity with downstream distance. The perforated plate could not be measured to the same downstream extent and did not reach self-similarity within its measurement range. In other respects the two types of grids yielded qualitatively similar results. Finally, we emphasize the distinction between intermittent turbulent penetration and turbulent diffusion and show that both play an important role in the spreading of the mixing layer.

Large Scale Direct Shear Tests on Reinforced Soil

ABSTRACT This paper presents the results of direct shear tests on sand samples reinforced by inclusions. A large direct shear apparatus (1 m3) was used for the experiments in conjunction with Leighton Buzzard sand and different types of grid and sheet reinforcement. The results showed that the presence of the reinforcement layer inclined to the central plane of the box caused a significant reduction of shear strains developed along the central region of the sample and increased the overall strength of the sand. High normal stresses on the reinforcement plane prevented bond failure between soil and reinforcement, which limits the application of direct shear tests with inclined reinforcement as a way of measuring bond strength between soil and reinforcement. At large shear displacements the performance of polymer reinforcement was enhanced by the favourable deformed shape of the reinforcement. At peak shear load the deformed shape of the reinforcement had little effect on the test results. This suggests that the assumption of a deformed reinforcement layer at the interception with the failure surface may be unrealistic when analysing reinforced soil structures at peak conditions by limit equilibrium methods. As a consequence of the latter, it was also observed that, for the range of values tested, the influence of the reinforcement bending stiffness was negligible.

Determination of Stripe Structures for Finite Element Matrices

Stripe structures were introduced by the author [Parallel Computing, to appear] as a means for the inclusion of the nonzero elements of a sparse matrix into a regular pattern which allows for efficient parallel manipulation. In this paper the stripe structures of stiffness matrices resulting from irregular domains covered by regular grids are analyzed. It is proved that the nonzero elements in these matrices may be covered by very few stripes and that these stripes may be nonoverlapping if the nodes of the grids are numbered appropriately. The exact number of stripes, which is independent of the size of the problem, is derived for different types of grids and different numbering schemes. The stripe structures of some irregular grids are also examined.

Hot-cathode thyratrons: practical studies of characteristics

The paper surveys the main features which determine the characteristics and life of thyratrons in the light of direct experiment and of field experience. These include electron emission from the cathode, ionization and current build-up, grid control, the current-carrying capacity of the valve, the decay of ionization at the end of conduction, and the provision of suitable operating conditions.Emphasis is laid on factors which, while not immediately affecting electrical performance, may determine valve life; one example is positive-ion bombardment, which may cause damage to the cathode.The control characteristics of different types of grid are discussed; particular reference is made to the pentode design, a recent development enabling heavy currents to be controlled from high-impedance grid circuits.The arc voltage drop varies considerably with filling pressure and with current value, abrupt changes being associated with modifications in the form of the discharge. If the current-carrying capacity of the arc path is exceeded, the arc, if it cannot transfer to an alternative path, may suddenly go out, giving rise to generally undesirable high-voltage surges.A method of studying de-ionization time is described, and results are given showing this time as a function of the gas and its pressure. The characteristics of various gas and vapour fillings are discussed. A non-uniform pressure distribution in mercury-vapour valves assists rapid starting.