Modelling the Flow of Carbon Dioxide Through Beds of Cereal Grains

The insect population in grain stores can be kept under control by maintaining a high concentration of CO₂ gas (greater than 35%) throughout the grain bed. In this paper the initial phase of this process is considered, where the gas is introduced into the bed. The flow of CO₂ through the grain bulk is modelled as fluid flow in a porous medium and the effect of advection, dispersion, sorption and curvilinear isobars and streamlines are considered. An analytic solution to this problem is developed using perturbation expansions and the analysis is restricted to the dominant term in each expansion. In curvilinear flow, a useful variable is the traverse time; the time taken for the gas to travel from the inlet duct. It is shown that lines of constant traverse time are also lines of constant CO₂ concentration throughout the grain bed except in the narrow region called the front, where the concentration gradient is large. For most grain stores the isobars have a negative curvature and in these situations the front moves more slowly than in uniform flow and the width of the front increases more rapidly as it travels through the grain bed. It is shown that sorption has an effect on the CO₂ concentration in the air for some grains such as canola but not for others such as wheat.     

Implementation of CLEAR algorithm on non‐orthogonal curvilinear co‐ordinates for solution of incompressible flow and heat transfer

In this paper, the CLEAR (coupled and linked equations algorithm revised) algorithm is extended to non‐orthogonal curvilinear collocated grids. The CLEAR algorithm does not introduce pressure correction in order to obtain an incompressible flow field which satisfies the mass conservation law. Rather, it improves the intermediate velocity by solving an improved pressure equation to make the algorithm fully implicit since there is no term omitted in the derivation process. In the extension of CLEAR algorithm from a staggered grid system in Cartesian coordinates to collocated grids in non‐orthogonal curvilinear coordinates, three important issues are appropriately treated so that the extended CLEAR can lead to a unique solution without oscillation of pressure field and with high robustness. These three issues are (1) solution independency on the under‐relaxation factor; (2) strong coupling between velocity and pressure; and (3) treatment of the cross pressure gradient terms. The flow and heat transfer problems in a rectangular enclosure with an internal eccentric circle and the flow in a lid‐driven inclined cavity are computed by using the extended CLEAR. The results show that the extended CLEAR can guarantee the solution independency on the under‐relaxation factor, the smoothness of pressure profile even at very small under‐relaxation factor and good robustness which leads to a converged solution for the small inclined angle of 5^° only with 5‐point computational molecule while the extended SIMPLE‐series algorithm usually can get a converged solution for the inclined angle larger than 30^° under the same condition. Copyright © 2006 John Wiley & Sons, Ltd.     

Prediction of velocity distribution in straight open-channel flow with partial vegetation by singular perturbation method

A numerical analysis model based on two-dimensional shallow water differential equations is presented for straight open-channel flow with partial vegetation across the channel. Both the drag force acting on vegetation and the momentum exchange between the vegetation and non-vegetation zones are considered. The depth-averaged streamwise velocity is solved by the singular perturbation method, while the Reynolds stress is calculated based on the results of the streamwise velocity. Comparisons with the experimental data indicate that the accuracy of prediction is significantly improved by introducing a term for the secondary current in the model. A sensitivity analysis shows that a sound choice of the secondary current intensity coefficient is important for an accurate prediction of the depth-averaged streamwise velocity near the vegetation and non-vegetation interfaces, and the drag force coefficient is crucial for predictions in the vegetation zone.     

Characteristics of air and water velocity fields during natural convection

Air and water velocity fields have been simulated during natural convection, using a two-dimensional volume of fluid (VOF) model. The results have shown that during unstable thermal stratification, the root-mean-square (RMS) airside velocities are an order of magnitude higher than the RMS waterside velocities, whereas, during the stable thermal stratification, the velocity magnitudes are comparable for air and water sides. Furthermore, the magnitude of the air velocity changed more rapidly with the change in the bulk air–water temperature difference than the water velocity, indicating that the air velocities are more sensitive to the bulk air and water temperature difference than the water velocities. A physical model of the heat and mass transfer across the air–water interface is defined. According to this model, the vortices on the air and water sides play an important role in enhancing the heat and mass transfer. Due to the significance of the flow velocities in the transport process, it has been proposed that the correlations for the heat and mass transfer during natural convection should be improved by incorporating the flow velocity as a parameter.     

缓变主流中三维气泡的非线性振动

空化现象和水下噪声机制与液体中气泡的动力学行为密切相关．在无粘势流的假定下，采用多参数摄动分析，研究了缓变主流中三维气泡的非线性体积模态振动．推导了关于缓变泡形展开的各阶扰动方程，获得了一阶振动的演化方程和一些特殊情况下的解析解；并采用高阶有限元离散的边界积分方程方法，对平面固壁和自由面附近三维气泡的固有频率进行了数值计算     

Aerosol aspiration into a cylindrical sampler from a low-velocity downward flow and from calm air

The problem of aerosol aspiration into a two-dimensional cylindrical sampler from a low-velocity downward flow and from calm air is solved. A simple analytical model for the velocity field of the carrier medium in the vicinity of the sampler with allowance for the finite size of the input orifice is proposed. Parametric studies of the aspiration factor as a function of the Stokes number for different ratios of the free-stream and aspiration velocities and different gravity-induced sedimentation velocities for two positions of the sampler are performed. Sedimentation of particles on the lower side of the cylinder for the sampler with a downward-oriented orifice is discussed.Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 46, No. 2, pp. 122–129, March–April, 2005.     

Stochastic analysis of two-phase flow in porous media: I. Spectral/perturbation approach

Stochastic analysis of steady-state two-phase (water and oil) flow in heterogeneous porous media is performed using the perturbation theory and spectral representation techniques. The governing equations describing the flow are coupled and nonlinear. The key stochastic input variables are intrinsic permeability,k, and the soil and fluid dependent retention parameter, . Three different stochastic combinations of these two imput parameters were considered. The perturbation/spectral analysis was used to develop closed-form expressions that describe stochastic variability of key output processes, such as capillary and individual phase pressures and specific discharges. The analysis also included the estimation of the effective flow properties. The impact of the spatial variability ofk and on the variances of pressures, effective conductivities, and specific discharges was examined.     

Electrokinetic flow and energy conversion in a curved microtube

Curved channels are ubiquitous in microfluidic systems. The pressuredriven electrokinetic flow and energy conversion in a curved microtube are investigated analytically by using a perturbation analysis method under the assumptions of the small curvature ratio and the Reynolds number. The results indicate that the curvature of the microtube leads to a skewed pattern in the distribution of the electrical double layer (EDL) potential. The EDL potential at the outer side of the bend is larger than that at the inner side of the bend. The curvature shows an inhibitory effect on the magnitude of the streaming potential field induced by the pressure-driven flow. Since the spanwise pressure gradient is dominant over the inertial force, the resulting axial velocity profile is skewed into the inner region of the curved channel. Furthermore, the flow rate in a curved microtube could be larger than that in a straight one with the same pressure gradient and shape of cross section. The asymptotic solutions of the axial velocity and flow rate in the absence of the electrokinetic effect are in agreement with the classical results for low Reynolds number flows. Remarkably, the curved geometry could be beneficial to improving the electrokinetic energy conversion (EKEC) efficiency.     

Stochastic analysis of two-phase flow in porous media: II. Comparison between perturbation and Monte-Carlo results

The first paper (Changet al., 1995) described stochastic analysis of two-phase flow in a fully liquid-saturated system. In this paper, the results of Monte-Carlo simulations are compared with the closed-form expressions obtained using the perturbation approach. We present analytical solutions to the one-dimensional, steady-state oil-and-water flow equations. These solutions are subsequently used in the Monte-Carlo analysis to estimate the statistical properties of the key output processes. The comparison between the results of perturbation and Monte-Carlo approaches shows a good agreement between the two methods over a wide range lnk (k is the intrinsic permeability) variability with three different combinations of input stochastic processes of lnk and soil parameter . In particular, a good agreement was obtained for capillary and individual pressure variances and effective phase conductivities. The results showed that as the mean capillary pressure in the profile increased, the variance of capillary pressure increased while the variances of individual pressures decreased. Overall comparison between the two methods showed that the first-order perturbation theory can be successfully used to describe the effective behavior of large-scale, two-phase systems.     

Correlation of elastic wave attenuation and scattering with volumetric grain size distribution for polycrystals of statistically equiaxed grains

This study establishes an explicit relation between spatial two-point correlation function (TPCF) and volumetric (or three-dimensional) grain size distribution for aggregates of statistically equiaxed grains by extending a prior study (Sha, JASA, 2018). This relation is further validated by applying it to available TPCF and volumetric grain size distribution in the literature. Based on this relation, analytical attenuation coefficients for longitudinal and transverse waves, accounting for volumetric grain size distribution, are derived under Born approximation for macroscopically isotropic polycrystals of equiaxed triclinic grains. These attenuation models are applicable for whole frequency range except geometric region. Moreover, scattering coefficients for a polycrystal of equiaxed triclinic grains with a volumetric grain size distribution are obtained. Finally, the analytical attenuation model for the longitudinal wave is verified by comparison with existing 3D finite element simulation results in the literature. This theoretic study has practical applications to the inverse determination of volumetric grain size distribution from ultrasonic measurements.     

Pressure effects on viscosity and flow stability of polyethylene melts during extrusion

In the present work, the effects of pressure on the viscosity and flow stability of four commercial grade polyethylenes (PEs) have been studied: linear-low-density polyethylene copolymer, high-density polyethylene, metallocene polyethylenes with short-chain branches (mPE-SCB), and metallocene polyethylenes with long chain branching (mPE-LCB). The range of shear rates considered covers both stable and unstable flow regimes. “Enhanced exit-pressure” experiments have been performed attaining pressures of the order of 500×10⁵ Pa at the die exit. The necessary experimental conditions have been clearly defined so that dissipative heating can be neglected and pressure effects isolated. The results obtained show an exponential increase in both shear and entrance-flow pressure drop with mean pressure when shear rate is fixed and as long as flow is stable. These pressure effects are described by two pressure coefficients, β_S under shear and, β_E under elongation, that are calculated using time–pressure superposition and that are independent of mean pressure and flow rate. For three out of four PE, pressure coefficient values can be considered equal under shear and under elongation. However, for the mPE-LCB, the pressure coefficient under elongation is found to be about 30% lower than under shear. Flow instabilities in the form of oscillating flows or of upstream instabilities appear at lower shear rates as mean pressure increases. Nevertheless, the critical shear stress at which they are triggered remains independent of mean pressure. Moreover, it is found that the β_S values obtained for stable flows do not differ much from the values obtained during upstream instability regimes, and differ really from pressure effects observed under oscillating flow and slip conditions.     

A numerical model for the flooding and drying of irregular domains

A numerical technique for the modelling of shallow water flow in one and two dimensions is presented in this work along with the results obtained in different applications involving unsteady flows in complex geometries. A cell‐centred finite volume method based on Roe's approximate Riemann solver across the edges of both structured and unstructured cells is presented. The discretization of the bed slope source terms is done following an upwind approach. In some applications a problem arises when the flow propagates over adverse dry bed slopes, so a special procedure has been introduced to model the advancing front. It is shown that this modification reproduces exactly steady state of still water in configurations with strong variations in bed slope and contour. The applications presented are mainly related with unsteady flow problems. The scheme is capable of handling complex flow domains as will be shown in the simulations corresponding to the test cases that are going to be presented. Comparisons of experimental and numerical results are shown for some of the tests. Copyright © 2002 John Wiley & Sons, Ltd.     

Electrical fluctuations and entry flow instabilities during capillary flow of aqueous poly (ethylene oxide) solutions

Capillary flow of poly (ethylene oxide) solutions generates voltage fluctuations (noise) between electrodes placed on both sides of the capillary. The noise has a 1/f type spectral distribution, the value of increasing with (shear rate) to a limiting level. Within certain ranges, two sets of harmonic peaks appear in the spectra. It is demonstrated that these peaks are related to the frequency components of the instabilities in the entry flow region. The lower frequency set of harmonics corresponds to axial oscillations (pulsations) of the flow, while the higher frequency peaks are associated with the transverse oscillation of the stream lines in the vicinity of the entry. The corresponding frequencies were measured by visual counting and by spectral analysis of laser light transmitted through the entry region during injection of a coloured solution.The noise measurements were carried out using both platinum and reversible Ag/AgCl electrodes. In the latter case the streaming potential was also measured; its variation due to pressure fluctuations in the instable flow region appears to provide a plausible explanation of flow-induced noise phenomena as observed in elastic solutions.Dedicated to Prof. Dr. J. Schurz on the occasion of his sixtieth birthday.     

对激光干涉测速中信号丢失现象的分析

分析了当应用任意反射面速度干涉仪(VISAR)测量强冲击波作用下样品自由面速度时丢失部分测量信号的问题。除了普遍的光电系统有限频率响应以及数字示波器采样率的影响,主要考虑了干涉仪延迟时间、多模光纤的多模色散对测量信号的影响。干涉仪延迟时间导致速度历史与一个宽度为延迟时间的矩形函数进行卷积,使速度历史的高频细节丢失;多模色散导致干涉信号与某一梳状函数进行卷积,使高频干涉条纹丢失。对丢条纹的整数性进行了分析。     

Effect of upstream velocity profile and integral flow straighteners on turbine flowmeters

One of the most important factors determining the shape of the calibration curve for a given turbine meter is the change in the upstream velocity distribution with flowrate. A theoretical model is evolved which can be used to predict the effects of velocity profile, viscosity and swirl on the calibration curve. It has also been used to explain the calibration curve of a commercial meter having a geometry very different from that for which the theory was developed. The effect of different types of integral flow straighteners on turbine meters is also investigated and found to depend on both the number of vanes and their length. A correlation is suggested for radial-vaned flow-straighteners     

Ellipsoidal Oscillations of a Gas Bubble with Periodic Variation of the Surrounding Fluid Pressure

Ellipsoidal linear and nonlinear oscillations of a gas bubble under harmonic variation of the surrounding fluid pressure are studied. The system is considered under conditions in which periodic sonoluminescence of the individual bubble in a standing acoustic wave is observable. A mathematical model of the bubble dynamics is suggested; in this model, the variation of the gas/fluid interface shape is described correct to the square of the amplitude of the deformation of the spherical shape of the bubble. The character of the air bubble oscillations in water is investigated in relation to the initial bubble radius and the fluid pressure variation amplitude. It is shown that nonspherical oscillations of limited amplitude can occur outside the range of linearly stable spherical oscillations. In this case, both oscillations with a period equal to one or two periods of the fluid pressure variation and aperiodic oscillations can be observed.     

Dynamic reliability analysis of a cantilever beam during a deterioration process

Considering deterioration process of a beam structure subjected to cyclic load, the reliability and sensitivity analysis is presented. Gamma process is introduced to describe the deterioration of properties and the accuracy of the model is verified by experiments of structures under cycle load. A set of experiments is designed to investigate the deterioration process of the beam under cycle load. For arbitrarily distributed random material and geometric variables, the stochastic perturbation method and Edgeworth series are used to approximate the statistical characteristics of vibration and failure probability. Monte Carlo simulation is employed to show the validity of the method proposed. Additionally, the effects of material and geometric parameters are discussed to provide important information for design and use of beam structures.     

Multiscale aspects of heat and mass transfer during drying

The macroscopic formulation of coupled heat and mass transfer has been widely used during the past two decades to model and simulate the drying of one single piece of product, including the case of internal vaporization. However, more often than expected, the macroscopic approach fails and several scales have to be considered at the same time. This paper is devoted to multiscale approaches to transfer in porous media, with particular attention to drying. The change of scale, namely homogenization, is presented first and used as a generic approach able to supply parameter values to the macroscopic formulation. The need for a real multiscale approach is then exemplified by some experimental observations. Such an approach is required as soon as thermodynamic equilibrium is not ensured at the microscopic scale. A stepwise presentation is proposed to formulate such situations.     

Effect of collision and velocity model of lattice Boltzmann model on three-dimensional turbulent flow simulation

Various collision and velocity models of the lattice Boltzmann model (LBM) were compared to determine their effects on the efficiency of a three-dimensional homogeneous isotropic decaying turbulent flow simulation. We determined that a decrease in the number of velocities, in particular, 13-velocities, which can be used in the quasi-equilibrium lattice Boltzmann and in the multiple-relaxation time models (MRT), could considerably decrease the computational effort. However, decreasing the number of velocities deteriorates the stability and the accuracy of the results. By comparing the collision models, we also determined that the stability of the entropic lattice Boltzmann model (ELBM), and 19- and 27- velocity MRT is much higher than in other models. However, the numerical viscosity introduced by the ELBM underestimates the enstrophy, and the computational effort increases because of the calculation overhead required to solve the additional equations if special care is not given to the calculation.