Array Of Cubes Research Articles

角锥棱镜阵列后腔镜钕玻璃激光器

角锥棱镜阵列后腔镜钕玻璃激光器

Turbulent flow similarity over an array of cubes in near-neutrally stratified atmospheric flow

The main objective of this study is to examine the robustness of the inner-layer scaling similarity of near-wall turbulence. The turbulent boundary layer of interest is over a very rough surface with a very high Reynolds number and significant outer-layer disturbances. This is not consistent with the canonical turbulent flows studied in laboratories, but it is common in urban areas. The investigation was conducted using the comprehensive outdoor scale model (COSMO) facility. COSMO is composed of a regular array of 1.5 m concrete cubes on a 50×100 m2flat concrete base. This unique facility allows us to obtain the turbulent dataset within the vertical constant stress region under near-neutral stratification at high Reynolds numbers. The turbulent spectra and the standard deviation of velocity fluctuations from COSMO were compared with the values obtained over rural and urban surfaces, and in wind-tunnel experiments.The results confirmed that the inner-layer scaling similarity was robust for the wall-normal fluctuations and the Reynolds stress, independent of the roughness types and the outer-layer conditions. The inner-layer scaling similarity failed for the horizontal velocity fluctuations owing to the influence of the outer-layer disturbance. The relative importance of outer-layer turbulence to inner-layer-scale eddies in the horizontal velocity fluctuations was successfully quantified in terms of the roughness scale normalized by the outer-layer scale.

Large-Eddy Simulation of Flows over Random Urban-like Obstacles

Further to our previous large-eddy simulation (LES) of flow over a staggered array of uniform cubes, a simulation of flow over random urban-like obstacles is presented. To gain a deeper insight into the effects of randomness in the obstacle topology, the current results, e.g. spatially-averaged mean velocity, Reynolds stresses, turbulence kinetic energy and dispersive stresses, are compared with our previous LES data and direct numerical simulation data of flow over uniform cubes. Significantly different features in the turbulence statistics are observed within and immediately above the canopy, although there are some similarities in the spatially-averaged statistics. It is also found that the relatively high pressures on the tallest buildings generate contributions to the total surface drag that are far in excess of their proportionate frontal area within the array. Details of the turbulence characteristics (like the stress anisotropy) are compared with those in regular roughness arrays and attempts to find some generality in the turbulence statistics within the canopy region are discussed.

Evaluation of the QUIC-URB fast response urban wind model for a cubical building array and wide building street canyon

This paper describes the QUIC-URB fast response urban wind modeling tool and evaluates it against wind tunnel data for a 7 × 11 cubical building array and wide building street canyon. QUIC-URB is based on the Rockle diagnostic wind modeling strategy that rapidly produces spatially resolved wind fields in urban areas and can be used to drive urban dispersion models. Rockle-type models do not solve transport equations for momentum or energy; rather, they rely heavily on empirical parameterizations and mass conservation. In the model-experiment comparisons, we test two empirical building flow parameterizations within the QUIC-URB model: our implementation of the standard Rockle (SR) algorithms and a set of modified Rockle (MR) algorithms. The MR model attempts to build on the strengths of the SR model and introduces additional physically based, but simple parameterizations that significantly improve the results in most regions of the flow for both test cases. The MR model produces vortices in front of buildings, on rooftops and within street canyons that have velocities that compare much more favorably to the experimental results. We expect that these improvements in the wind field will result in improved dispersion calculations in built environments.

Experimental Demonstration of Isotropic Negative Permeability in a Three-Dimensional Dielectric Composite

Isotropic negative permeability resulting from Mie resonance is demonstrated in a three-dimensional (3D) dielectric composite consisting of an array of dielectric cubes. A strong subwavelength magnetic resonance, corresponding to the first Mie resonance, was excited in dielectric cubes by electromagnetic wave. Negative permeability is verified in the magnetic resonance area via microwave measurement and the dispersion properties. The resonance relies on the size and permittivity of the cubes. It is promising for construction of novel isotropic 3D left-handed materials with a simple structure.

Translation dual of a semifield

In this paper we obtain a new description of the translation dual of a semifield introduced in [G. Lunardon, Translation ovoids, J. Geom. 76 (2003) 200–215]. Using such a description we are able to prove that a semifield and its translation dual have nuclei of the same order. Combining the Knuth cubical array and the translation dual, we give an alternate description of the chain of twelve semifields in the table of [S. Ball, G.L. Ebert, M. Lavrauw, A geometric construction of finite semifields, J. Algebra 311 (2007) 117–129].

Measurements in an urban-type boundary layer

Wind tunnel measurements of the boundary layer flow over a very rough surface comprising a staggered array of cubes are presented and discussed. Attention is concentrated on the near-wall region, including the canopy region below the tops of the roughness elements. Particle image velocimetry (PIV) and laser Doppler anemometry were used to identify the dominant features of the mean and turbulent flow and these are compared with the better-known features of the flow above the roughness. Spatial correlation data, extracted from the PIV images, are used to provide information about eddy structures and it is shown that these differ in some crucial respects from those typical of more classical boundary layers. The implications of the results are discussed in terms of their relevance to flows within the urban environment.

Tunable negative permeability in an isotropic dielectric composite

A tunable isotropic negative effective permeability is experimentally demonstrated in a three-dimensional (3D) dielectric composite consisting of dielectric ceramic cube arrays by temperature changing. It shows that a strong subwavelength magnetic resonance can be excited in dielectric cubes corresponding to the first Mie resonance mode and can be continuously and reversibly adjusted from 13.65to19.28GHz with the temperature changing from −15to35°C. Accordingly, negative permeability can be performed in the frequency range of about 6GHz by adjusting the temperature. It provides a convenient route to design adaptive metamaterials and 3D invisible cloak.

A Simple Model for Spatially-averaged Wind Profiles Within and Above an Urban Canopy

This paper deals with the modelling of the flow in the urban canopy layer. It critically reviews a well-known formula for the spatially-averaged wind profile, originally proposed by Cionco in 1965, and provides a new interpretation for it. This opens up a number of new applications for modelling mean wind flow over the neighbourhood scale. The model is based on a balance equation between the obstacle drag force and the local shear stress as proposed by Cionco for a vegetative canopy. The buildings within the canopy are represented as a canopy element drag formulated in terms of morphological parameters such as λ f and λ p (the ratios of plan area and frontal area of buildings to the lot area). These parameters can be obtained from the analysis of urban digital elevation models. The shear stress is parameterised using a mixing length approach. Spatially-averaged velocity profiles for different values of building packing density corresponding to different flow regimes are obtained and analysed. The computed solutions are compared with published data from wind-tunnel and water-tunnel experiments over arrays of cubes. The model is used to estimate the spatially-averaged velocity profile within and above neighbourhood areas of real cities by using vertical profiles of λ f .

Numerical Simulation of Droplet Impact on Patterned Surfaces

This work presents numerical simulation results for molten nickel and zirconia (YZS) droplets impacting on different microscale-patterned surfaces of silicon. The numerical simulation clearly showed the effect of surface roughness and solidification on the shape of the final splat, as well as the pore creation beneath the sprayed material. Simulations were performed using computational fluid dynamic software, SimDrop. The code uses a three-dimensional finite-difference algorithm solving the full Navier-Stokes equation, including heat transfer and phase change. A volume of fluid (VOF) tracking algorithm is used to track the droplet-free surface. Thermal contact resistance at the droplet-substrate interface is also included in the model. Specific attention is paid to the simulation of droplet impact under plasma spraying conditions. Droplet sizes ranged from 15 to 60 microns with initial velocities of 70-250 m/s. Substrate surfaces were patterned with regular arrays of cubes 1-3 μm high, spaced either 1 μm or 5 μm from each other. Different splat morphologies produced by simulations are compared with those obtained from the experiment conducted under the same impact and surface conditions.

Simplectic spreads and finite semifields

It is well known that associated with a translation plane ? there is a family of equivalent spreads. In this paper, we prove that if one of these spreads is symplectic and ? is finite, then all the associated spreads are symplectic. Also, using the geometric intepretation of the Knuth's cubical array, we prove that a symplectic semifield spread of dimension n over its left nucleus is associated via a Knuth operation to a commutative semifield of dimension n over its middle nucleus.

Flow over cube arrays of different packing densities

Measurements by 120° x-wire anemometry over uniform urban-type surfaces of two different area densities were performed in a wind tunnel, together with direct measurements of the surface drag. The aerodynamic characteristics of each surface were determined and compared, the influence of area density and array geometry on these parameters was examined. Various approaches were discussed for the determination of the roughness length ( z 0) for a given surface. The surface shear stress (determined from form drag measurements by pressure tapping a roughness element or from the total surface drag determined by a floating drag balance) and the shear stress (determined from spatially averaged vertical profiles of Reynolds shear stress) were compared. The surface shear stress was found to be about 25% greater than the measured Reynolds shear stress in the inertial sub-layer over the surfaces. There was, however, no constant stress region and extrapolation of the shear stress profiles in the inertial sub-layer to the zero-plane displacement provided a much better estimate of the surface shear stress. The results did not support the argument put forward in the literature that the zero-plane displacement could be reliably predicted from the height of the centre of drag force. Finally, the accuracy of existing geometrical methods of determining the aerodynamic properties of rough surfaces was shown to be limited by the use of inappropriate wind tunnel data in their formulation.

Estimating the potential yield of small building‐mounted wind turbines

AbstractThe wind profile in the urban boundary layer is described as following a logarithmic curve above the mean building height and an exponential curve below it. By considering the urban landscape to be an array of cubes, a method is described for calculating the surface roughness length and displacement height of this profile. Firstly, a computational fluid dynamics (CFD) model employing a k‐ϵ turbulence model is used to simulate the flow around a cube. The results of this simulation are compared with wind tunnel measurements in order to validate the code. Then, the CFD model is used to simulate the wind flow around a simple pitched‐roof building, using a semi‐logarithmic inflow profile. An array of similar pitched‐roof houses is modelled using CFD to determine the flow characteristics within an urban area. Mean wind speeds at potential turbine mounting points are studied, and optimum mounting points are identified for different prevailing wind directions. A methodology is proposed for estimating the energy yield of a building‐mounted turbine from simple information such as wind atlas wind speed and building density. The energy yield of a small turbine on a hypothetical house in west London is estimated. The energy yield is shown to be very low, particularly if the turbine is mounted below rooftop height. It should be stressed that the complexity of modelling such urban environments using such a computational model has limitations and results can only be considered approximate, but nonetheless, gives an indication of expected yields within the built environment. Copyright © 2007 John Wiley & Sons, Ltd.

CFD simulation of airflow over a regular array of cubes. Part II: analysis of spatial average properties

In the first part of this study, results of a computational fluid dynamics simulation over an array of cubes have been validated against a set of wind-tunnel measurements. In Part II, such numerical results are used to investigate spatially-averaged properties of the flow and passive tracer dispersion that are of interest for high resolution urban mesoscale modelling (e.g. non resolved obstacle approaches). The results show that vertical profiles of mean horizontal wind are linear within the canopy and logarithmic above. The drag coefficient, derived from the numerical results using the classical formula for the drag force, is height dependent (it decreases with height). However, a modification of the formula is proposed (accounting for subgrid velocity scales) that makes the drag coefficient constant with height. Results also show that the dispersive fluxes are similar in magnitude to the turbulent fluxes, and that they play a very important role within the canopy. Vertical profiles of turbulent length scales (to be used in k–l closure schemes, where k is the turbulent kinetic energy and l a turbulent length scale) are also derived. Finally the distribution of the values around the mean over the reference volumes are analysed for wind and tracer concentrations.

CFD simulation of airflow over a regular array of cubes. Part I: Three-dimensional simulation of the flow and validation with wind-tunnel measurements

Air flow inside an array of cubes is simulated. Cubes (edge length 0.15 m) are arranged in a regular array, separated by 0.15 m in the streamwise and spanwise directions. Numerical simulations are performed based on Reynolds-averaged Navier–Stokes equations (RANS), solved in a computational fluid dynamics model (CFD), with standard k–e turbulent closure (two prognostic equations are solved for the turbulent kinetic energy k and its dissipation e, respectively). Simulations are validated against wind-tunnel data using a technique based on hit-rate calculations, and calculated statistical parameters. The results show that the horizontal velocity is very well modelled, and despite some discrepancies, the model that fulfils the hit-rate test criteria gives useful results that are used to investigate three-dimensional (3-D) flow structures. The 3-D analysis of the flow shows interesting patterns: the centre of the canyon vortex is at 3/4 of the canyon height, and stronger downward than upward motions are present within the canyon. Such behaviour is explained by the presence of a compensation flow through the side of the canyon, which enters the canyon from the upper part and exits from the lower part. This complex 3-D structure affects the tracer dispersion, and is responsible for pollutant transport and diffusion.

Large-eddy simulation for urban micro-meteorology

Abstract Validation of large-eddy simulation (LES) computations of flows over an array of cubes with imposed periodic inflow-outflow condition is described. Then, a method of generation of appropriate inflow data for such flows is proposed and the results are compared with those using periodic boundary conditions in the streamwise direction and wind tunnel measurements [3]. Finally, some results obtained using the inflow method for an oscillatory through- flow combined with a steady current are discussed.

Analysis of three-dimensional grids: Alternative polynomial equations for the nine-point prismatic array

Equations representing data in prismatic array are useful for interpreting experiments involving three independent parameters. This paper illustrates two sets of four polynomial equations for the nine-point cubical array. The equations are exact on trilinear numbers and their second and third powers. The equations are potentially useful alternatives to the trilinear equation when they do not generate complex-number coefficients.

Analysis of three-dimensional grids: The cube and the octahedron

The analysis of three-dimensional data is customarily performed by arranging eight measurements in a cubical array and representing them by the trilinear equation. The octahedral design offers the prospect of reduced laboratory costs because it requires only six measurements. Operational interpolating equations for six data in octahedral array can be more accurate than the trilinear equation for eight data in cubical array. The operational equations apply to the six- or seven-point octahedron.

Turbulence Over Urban-type Roughness: Deductions from Wind-tunnel Measurements

Turbulence data from experiments conducted over a staggered cube array, modelling a neutrally stable atmospheric boundary layer in an urban environment, are presented. The results support the contention that organised eddy structures in the near-wall region differ significantly from those in regular smooth-wall flows or in rough-wall boundary layers with much smaller h/δ ratios (where δ and h are the boundary-layer thickness and the height of the roughness elements, respectively). Attention is concentrated on spatial correlations, spectra (and thus the dominant length and time scales), maps of anisotropy invariants and quadrant analyses of the stress tensor. Results are obtained within both the roughness sublayer (i.e. the region above the roughness but within which the flow is spatially inhomogeneous) and the canopy region (i.e. below the height of the roughness elements) and discussion includes consideration of the turbulence kinetic energy balance at various heights.

Effect of surface roughness on splat shapes in the plasma spray coating process

We used a three-dimensional model of droplet impact and solidification to simulate the effect of surface roughness on the impact dynamics and the splat shape of an alumina droplet impinging onto a substrate. The substrate surface was patterned by a regular array of cubes spaced at an interval twice their size. Three different cube sizes were considered, and the results were compared to the case of droplet impact onto a smooth substrate. To understand the effect of solidification on the droplet impact dynamics and splat morphology, the simulations were run with and without considering solidification. Comparing the results, we have concluded that solidification plays a major role in determining splat shape on a rough surface. We also present results of the distribution of voids between the splat and the substrate.