Length Scale Factor Research Articles

Prediction of wind properties in urban environments using artificial neural network

Artificial neural network (ANN) modeling has been performed to predict turbulent boundary layer characteristics for rough terrain based on experimental tests conducted in a boundary-layer wind tunnel to simulate atmospheric boundary layer using passive roughness devices such as spires, barriers, roughness elements on the floor, and slots in the extended test section. Different configurations of passive devices assisted to simulate urban terrains. A part of the wind tunnel test results are used as training sets for the ANN, and the other part of the test results are used to compare the prediction results of the ANN. Two ANN models have been developed in this study. The first one has been used to predict mean velocity, turbulence intensity, and model length scale factor. Results show that ANN is an efficient, accurate, and robust modeling procedure to predict turbulent characteristics of wind. In particular, it was found that the ANN-predicted wind mean velocities are within 4.7%, turbulence intensities are within 6.2%, and model length scale factors are within 3.8% of the actual measured values. In addition, another ANN model has been developed to predict instantaneous velocities that enables calculating the power spectral density of longitudinal velocity fluctuations. Results show that the predicted power spectra are in a good agreement with the power spectra obtained from measured instantaneous velocities.

Evaluation of length-scale effects for mechanical behaviour of micro- and nanocantilevers: I. Experimental determination of length-scale factors

When the thickness of micro- and nanocantilevers, which are the building blocks of micro- and nanoelectromechanical systems, are below 10 µm, the natural frequency and quasi-static deflection of the cantilevers cannot be estimated accurately using the conventional natural frequency and quasi-static-deflection models. The effect of the thickness is summed into what is known as the length-scale factor, which is incorporated into the models in order to improve the accuracy of the models. With this in mind, this paper, which is the first of two parts, reports on the experimental determination of length-scale factors for micro- and nano-sized silicon cantilevers, the micro- and nano-sized length-scale factors are estimated using experimental data collected from nanoindentation and microindentation experiments. The same experimental data are used to cross-validate the empirical length-scale factors in the literature. The experimentally estimated length-scale factors are then incorporated into the natural frequency and static-deflection models. The experimental results presented suggest that the length-scale factors have a great influence on the natural frequency and quasi-static deflection of micro- and nano-sized silicon cantilevers, compared with the natural frequency and deflection calculated using the conventional models not incorporating the length-scale factor.

Evaluation of length-scale effects for mechanical behaviour of micro- and nanocantilevers: II. Experimental verification of deflection models using atomic force microscopy

This paper is the second of two parts that reports on evaluating the length-scale effects for micro- and nano-sized silicon cantilevers using experimental data provided by atomic force microscopy. The tip deflections estimated with the conventional tip deflection model and the modified deflection model incorporating the length-scale factor are determined and compared with the experimental data. These comparative data demonstrate that the length-scale factor should be considered in accurately estimating the tip deflection of the micro- and nano-sized cantilevers. We also present the effect of the length-scale factor on the stiffness of the cantilevers, which also indicate that the classical models derived for macro-sized cantilevers cannot be used to accurately estimate the bending stiffness of the micro- and nano-sized cantilevers. The implications of accurately estimating the tip deflection and stiffness for micro- and nanocantilever sensors are discussed and it is concluded that when these sensors are used in the static mode, the modified deflection model should be used in estimating the mass of the species of interest binding (analyte) on the surface of the cantilevers.

Mechanical properties of an Al91–Mn6–Nd3 nanostructured alloy

Abstract A methodology for obtaining a nanocrystalline Al91–Mn6–Nd3 alloy and characterizing its mechanical properties is presented. The fabrication procedure, based on the melt spinning method, allowed the preparation of thin ribbons of ∼30 μm in thickness. The hardness and elastic modulus have been determined by classical and instrumented indentation tests considering the influence of the ribbon thickness on the indentation measurements. The Martens hardness has been calculated by means of instrumented indentation tests, for which the fixing support of the sample has no influence on the indentation measurement. The results have been subsequently compared with those obtained from classical Vickers hardness measurements, for which some composite hardness models have been applied in order to separate the contribution of the fixing support to the hardness measurement. It has been concluded that both methodologies lead to similar values for the mechanical properties of the alloy, i.e. ∼3.4 GPa for the macrohardness and ∼3.8 MPa m1/2 for the hardness length-scale factor of the material. The elastic modulus of the material, resulting from the analysis of the unloading indentation curves, has been found to be ∼131 GPa.

Fine-tuning Nonlinear Finite Element Analysis Methodology for Aircraft Seat Certification using Component Level Testing and Validation

Finite element analysis (FEA) has become a part of new development in automotive as well as in aircraft seating industries. The goal of the FEA in product development is not only to design but to substantiate the certification tests or possibly replace the certification tests. The case of a certification by substantiation tests increases the necessity of validation of the Finite Element (FE) model. In the aircraft industry, the seating Advisory Circular (AC) 20-146 specifies a methodology for the dynamic seat, Certification By Analysis, for use in the Parts 23, 25, 27 and 29 airplanes and rotorcraft. In FE modeling of typically nonlinear environments such as the aircraft dynamic seat simulations, input parameters such as material model, element type, time step scale factor, element length, material model etc. play a vital role in the accuracy of the results. Selecting appropriate material models and other parameters leads to improved accuracy in the FE model and hence to validation with the experimental test results. The purpose of this study is to fine-tune non-linear FEA methodology for aircraft seat certification using component level testing and validation. For this purpose, the effects of input parameters such as the material model, element length, and time step scale factor are evaluated using component test-FE simulation on static tension test on aluminum, high speed load-deflection test on seat cushion and belt pull test. Verification of FE input parameters is determined in each case. Appropriate input variables are selected and provided to an aircraft seat FEA case study and validated against sled test results to demonstrate the validity of the finite element models.

Measurement Slub Yarn Parameter by Parallel-Plate Capacitor

Process Parameter of slub yarn determine style of its fabric. A new method of measuring process parameter of slub yarn was put forward to improve precision and efficient . The basic principal of parallel-plate capacitor was introduced in this paper. And sample yarns were tested with test system of slubby yarn developed by ourselves. Time sequence for slub length and slub space of slubby yarn can be gotten. And distribution of slub length , slub space and slub scaling factor can also be obtained. The agreement can be attained compared with those original setting. Some error was analyzed also. Consequently this testing system is effectively, and can be adopted in practice.

Experiments on integral length scale control in atmospheric boundary layer wind tunnel

Accurate predictions of turbulent characteristics in the atmospheric boundary layer (ABL) depends on understanding the effects of surface roughness on the spatial distribution of velocity, turbulence intensity, and turbulence length scales. Simulation of the ABL characteristics have been performed in a short test section length wind tunnel to determine the appropriate length scale factor for modeling, which ensures correct aeroelastic behavior of structural models for non-aerodynamic applications. The ABL characteristics have been simulated by using various configurations of passive devices such as vortex generators, air barriers, and slot in the test section floor which was extended into the contraction cone. Mean velocity and velocity fluctuations have been measured using a hot-wire anemometry system. Mean velocity, turbulence intensity, turbulence scale, and power spectral density of velocity fluctuations have been obtained from the experiments for various configuration of the passive devices. It is shown that the integral length scale factor can be controlled using various combinations of the passive devices.

Wind-tunnel simulations of the suburban ABL and comparison with international standards

Three wind-tunnel simulations of the atmospheric boundary layer (ABL) flow in suburban country exposure were generated for length scale factors 1:400, 1:250 and 1:220 to investigate scale effects in wind-tunnel simulations of the suburban ABL, to address recommended wind characteristics for suburban exposures reported in international standards, and to test redesigned experimental hardware. Investigated parameters are mean velocity, turbulence intensity, turbulent Reynolds shear stress, integral length scale of turbulence and power spectral density of velocity fluctuations. Experimental results indicate it is possible to reproduce suburban natural winds in the wind tunnel at different length scales without significant influence of the simulation length scale on airflow characteristics. However, in the wind tunnel it was not possible to reproduce two characteristic phenomena observed in full-scale: dependence of integral length scales on reference wind velocity and a linear increase in integral length scales with height. Furthermore, in international standards there is a considerable scatter of recommended values for suburban wind characteristics. In particular, recommended integral length scales in ESDU 85020 (1985) are significantly larger than in other international standards. Truncated vortex generators applied in this study proved to be successful in part-depth suburban ABL wind-tunnel simulation that yield a novel methodology in studies on wind effects on structures and air pollution dispersion.

Scaling law for bubbles induced by different external sources: Theoretical and experimental study

The scaling relations for bubbles induced by different external sources are investigated based on a modified Rayleigh model and experimental observations. The equations derived from the modified Rayleigh model are presented to describe the collapse of bubbles induced by the different external sources such as electrical spark, laser, and underwater explosion. A scaling law is then formulated to establish the scaling relations between the different types of bubbles. The scaling law reveals the fact that the characteristic length scale factor differs from the characteristic time scale factor for the different types of bubbles. It is then validated by our experimental observations of the spark- and laser-generated bubbles as well as the bubbles induced by underwater explosions from previous published reports. With the present scaling law, studies on spark- or laser-generated bubbles as well as their applications (for example, in industrial or biomedical related applications) can benefit from the experiences and information built up over the years in underwater explosion bubbles. Conversely, it is possible to substitute a spark- or laser-generated bubble for an underwater explosion bubble in the study of a large-scale and complex physical problem.

Thin film hardness determination using indentation loading curve modelling

A methodology for determining the thin film hardness from a microindentation loading curve is proposed. The loading curve is modelled to compute the dynamic Martens hardness using the indentation depth reached during the test. Moreover, the indentation size effect is taken into account by applying the strain gradient plasticity theory. Then, the dynamic Martens hardness and the hardness length-scale factor are used to express the applied load as a function of the indentation depth. The proposed model involves three parameters: ( i) the dynamic Martens macro-hardness, equivalent to the hardness obtained for an infinite applied load, ( ii) the hardness length-scale factor, which represents the material resistance to plastic deformation under indentation and ( iii) a corrective load, considering the rounded tip effect of the indenter and the zero shift. The model is validated on a 316L stainless steel which subsequently is used as a substrate material for two different Diamond Like-Carbon thin films. The coated systems involved both a hydrogen-free mostly amorphous carbon–chromium (a-C) film of ∼ 2.6 μm in thickness and a hydrogenated, amorphous carbon (a-C:H) solid lubricant of ∼ 2 μm.

Scale effects in wind tunnel modeling of an urban atmospheric boundary layer

Precise urban atmospheric boundary layer (ABL) wind tunnel simulations are essential for a wide variety of atmospheric studies in built-up environments including wind loading of structures and air pollutant dispersion. One of key issues in addressing these problems is a proper choice of simulation length scale. In this study, an urban ABL was reproduced in a boundary layer wind tunnel at different scales to study possible scale effects. Two full-depth simulations and one part-depth simulation were carried out using castellated barrier wall, vortex generators, and a fetch of roughness elements. Redesigned “Counihan” vortex generators were employed in the part-depth ABL simulation. A hot-wire anemometry system was used to measure mean velocity and velocity fluctuations. Experimental results are presented as mean velocity, turbulence intensity, Reynolds stress, integral length scale of turbulence, and power spectral density of velocity fluctuations. Results suggest that variations in length-scale factor do not influence the generated ABL models when using similarity criteria applied in this study. Part-depth ABL simulation compares well with two full-depth ABL simulations indicating the truncated vortex generators developed for this study can be successfully employed in urban ABL part-depth simulations.

Strain gradient plasticity to study hardness behavior of magnetite (Fe3O4) under multicyclic indentation

The hardness of a material is generally affected by the indentation size effect. The strain gradient plasticity (SGP) theory is largely used to study this load dependence because it links the hardness to the intrinsic properties of the material. However, the characteristic scale-length is linked to the macrohardness, impeding any sound discussion. To find a relevant parameter, we suggest introducing a hardness length-scale factor that only depends on the shear modulus and the Burgers vector of the material and is easily calculable from the relation of the SGP theory. The variation of the hardness length-scale factor is thereafter used to discuss the hardness behavior of a magnetite crystal, the objective being to study the effect of the cumulative plasticity resulting from cyclic indentation. As a main result, the hardness length-scale factor is found to be constant by applying repeated cycles at a constant peak load whereas the macrohardness and the characteristic scale-length are both cycle dependent. When using incremental loads, the hardness length-scale factor monotonically decreases between two limits corresponding to those obtained at high and low loading rates, while the dwell-load duration increases. The physical meaning of such behavior is based on the modification of the dislocation network during the indentation process depending on the deformation rate.

Hardness length-scale factor to model nano- and micro-indentation size effects

In this paper, we show that nano- and micro-indentation hardness data can be represented adequately by the strain gradient plasticity (SGP) theory if the uniformity of the dislocation spacing is taken into account. To give relevant information on the plastic deformation process, we suggest to use a hardness length-scale (HLS) factor equal to Ho ⋅ h * , where Ho is the macro-hardness and h* the characteristic scale-length deduced from the hardness–depth relation of the SGP theory. Theoretically, the HLS factor is proportional to both the shear modulus and the Burgers vector, depending on the dislocation spacing. Applied to various crystalline metals, the representation of the experimental HLS factor as a function of the theoretical one shows two distinct linear behaviours related to the micrometer and nanometer depth regimes associated with a uniform dislocation organisation beneath the indenter and with dislocations located at the vicinity of the indenter tip in a largest plastic zone, respectively.

Master crossover functions for one-component fluids

By introducing three well-defined dimensionless numbers, we establish the link between the scale dilatation method able to estimate master (i.e., unique) singular behaviors of the one-component fluid subclass and the universal crossover functions recently estimated [Garrabos and Bervillier, Phys. Rev. E 74, 021113 (2006)] from the bounded results of the massive renormalization scheme applied to the Phi(d)(4)(n) model of scalar order parameter (n=1) and three dimensions (d=3), representative of the Ising-like universality class. The master (i.e., rescaled) crossover functions are then able to fit the singular behaviors of any one-component fluid without adjustable parameter, using only one critical energy scale factor, one critical length scale factor, and two dimensionless asymptotic scale factors, which characterize the fluid critical interaction cell at its liquid-gas critical point. An additional adjustable parameter accounts for quantum effects in light fluids at the critical temperature. The effective extension of the thermal field range along the critical isochore where the master crossover functions seems to be valid corresponds to a correlation length greater than three times the effective range of the microscopic short-range molecular interaction.

Solid-phase crystallization under continuous heating: Kinetic and microstructure scaling laws

The kinetics and microstructure of solid-phase crystallization under continuous heating conditions and random distribution of nuclei are analyzed. An Arrhenius temperature dependence is assumed for both nucleation and growth rates. Under these circumstances, the system has a scaling law such that the behavior of the scaled system is independent of the heating rate. Hence, the kinetics and microstructure obtained at different heating rates differ only in time and length scaling factors. Concerning the kinetics, it is shown that the extended volume evolves with time according to αex = [exp(κCt′)]m+1, where t′ is the dimensionless time. This scaled solution not only represents a significant simplification of the system description, it also provides new tools for its analysis. For instance, it has been possible to find an analytical dependence of the final average grain size on kinetic parameters. Concerning the microstructure, the existence of a length scaling factor has allowed the grain-size distribution to be numerically calculated as a function of the kinetic parameters.

DNA as a Metrology Standard for Length and Force Measurements with Optical Tweezers

Optical tweezers have broad applications in studies of structures and processes in molecular and cellular biophysics. Use of optical tweezers for quantitative molecular-scale measurement requires careful calibration in physical units. Here we show that DNA molecules may be used as metrology standards for force and length measurements. Analysis of DNA molecules of two specific lengths allows simultaneous determination of all essential measurement parameters. We validate this biological-calibration method experimentally and with simulated data, and show that precisions in determining length scale factor (∼0.2%), length offset (∼0.03%), force scale factor (∼2%), and compliance of the traps (∼3%) are limited only by current measurement variation, much of which arises from polydispersity of the microspheres (∼2%). We find this procedure to be simpler and more convenient than previous methods, and suggest that it provides an easily replicated standard that can insure uniformity of measurements made in different laboratories.

Viscosity Model for CO-Noble Gas Mixtures at Atmospheric Conditions

We have presented an empirical model for predicting the viscosity of binary mixtures of gases, based on our previous correlation for natural gas mixtures (Miadonye and Clyburn, 2003). New parameters were derived for binary mixtures of carbon monoxide-noble gases and for carbon monoxide-nitrogen gases, for temperatures from 0–1000°C. The model was validated with the Chapman-Enskog equation for gas mixtures, with and without length scaling factor. For five equimolar and eight non-equimolar mixtures of gases at temperatures from 0–1000°C, the model gave an excellent viscosity prediction with an overall average absolute deviation of 0.45%. The model is simple to incorporate in design and simulation packages, and more accurate than any correlation currently used for estimating the viscosities of gas mixtures.

Modelling of multi-component gas flows in capillaries and porous solids

The paper presents a derivation of the governing equations for multi-component convective-diffusive flow in capillaries and porous solids starting from a well-defined model and clear assumptions. The solution for the continuum regime is discussed in detail including a derivation of the diffusion slip boundary condition based on an improved momentum transfer theory. The Stefan–Maxwell species momentum equations are also re-examined and important distinctions made between the local and tube-averaged equations. An equation for the pressure gradient is derived and some examples of binary flows in capillaries are discussed. The theory for free-molecule flow is standard but the equations are recast into a form identical to the continuum equations which suggests an obvious method of interpolation for flow at arbitrary Knudsen number. There are no problems concerning viscous terms which have marred other derivations. The extension to flow in porous bodies is achieved by introducing a porosity–tortuosity factor but, unlike other treatments, this parameter is not absorbed into the gas diffusivities and flow permeability. It can then be eliminated from all but one of the equations and, with appropriate boundary conditions, the flux ratios can be obtained in terms of a mean pore radius only. The porosity–tortuosity parameter simply controls the absolute flux level and is best interpreted as a length scale-factor. The theory is applied with success to the prediction of some experimental data for helium–argon counter-diffusion and it is shown that, contrary to common belief, the mean pore radius is well-defined by flux ratio measurements if these are made with non-zero pressure differences.

The effect of stable thermal stratification on the onset of double-diffusive convection in electrochemical systems

The onset time of double-diffusive convection in time-dependent, nonlinear concentration fields was investigated theoretically and experimentally. The stability analysis was conducted on the basis of the propagation theory. Under the linear stability theory, the linearized perturbation equations were transformed similarly by using the concentration penetration depth as a length-scaling factor. The newly derived stability equations were solved numerically. Also the onset time was determined experimentally by employing an electrochemical technique where 0.03–0.3 M CuSO 4 + 1.5 M H 2SO 4 aqueous solutions were adopted as electrolyte. The onset time of double-diffusive convection was delayed or shortened depending on the degree of stable stratification.

Turbulence Correlation Length-Scale Relationships for the Prediction of Aeroacoustic Response

Expressions to describe the correlation length scales of turbulent inflow to an aerodynamic body are derived as functions of the classic integral length scale and anisotropy correction factors. These one-point parameters are significantly easier to determine experimentally than traditional correlation-scale measurement techniques, which involve multiple probes at multiple locations. As such correlation scales are necessary to properly estimate the aeroacoustic response of the body, such a technique could have substantial benefit in a wide variety of applications. The approach is applied to a recent experimental study examining the response of a stator downstream of a propeller that is itself ingesting broadband turbulence. Results suggest that the derived expressions not only accurately represent correlation length scales, but also enable the accurate prediction of the acoustic output of the stator.