Dynamic response of clamped sandwich beams: analytical modeling

An improved analytical model is developed to predict the dynamic response of clamped lightweight sandwich beams with cellular cores subjected to shock loading over the entire span.The clamped face sheets are simplified as a single-degree-of-freedom(SDOF) system, and the core is idealized using the rigid-perfectly-plastic-locking(RPPL) model. Reflection of incident shock wave is considered by incorporating the bending/stretching resistance of the front face sheet and compaction of the core. The model is validated with existing analytical predictions and FE simulation results, with good agreement achieved. Compared with existing analytical models, the proposed model exhibits superiority in two aspects: the deformation resistance of front face sheet during shock wave reflection is taken into account; the effect of pulse shape is considered. The practical application range of the proposed model is therefore wider.     

Mathematical modeling of near-wall flows of two-phase mixture with evaporating droplets

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An analytical procedure to determine constitutive coefficients of a mixture of two linear elastic solids

In this paper, we study the coefficients of constitutive equations of a binary mixture of elastic solids and give an analytical approach to determine them. Assuming a material of two-phase elastic composite with randomly distributed elastic spheres is equivalent to a mixture of two elastic solids, we find the values of unknown coefficients by making use of Boussinesq problem. Furthermore, a mean displacement vector definition is also given.     

Laminar flow of a reacting gaseous mixture through a vertical duct with catalytic walls

Numerical analysis has been performed for predicting the onset and establishment of a steady state flow of a reactive hydrogen/air/vapour mixture through a two-dimensional vertical duct of finite length with its side walls coated by catalytic material. The flow is initiated by the exothermic reaction of hydrogen with air oxygen on the catalytic wall, that causes the hot gases to flow upwards through the vertical duct and by continuity sucks fresh mixture through the lower end of the duct. The flow is always laminar and the two-dimensional governing transport differential equations are solved by means of the numerical finite volume method, using a collocated variable arrangement. Comparisons between calculated and experimental data are presented, showing good agreement between them. The method is employed for various initial mixture compositions and duct geometries.     

modeling of multicomponent multiphase mixture flows on the basis of the density-functional method

Examples of numerical calculations of isothermal flows of two-phase two-component mixtures based on the density-functional method are presented. Using this method, the following problems are calculated in the two-dimensional formulation: drop impact on a liquid layer, drop rupture in a Couette flowfield, wetting-angle formation for a drop on a solid surface, development of Rayleigh-Taylor and Kelvin-Helmholtz instability on a gas-liquid interface.Translated from Izvestiya Rossiiskoi Academii Nauk, Mekhanika Zhidkosti i Gaza, No. 6, 2004, pp. 101–114.Original Russian Text Copyright © 2004 by Demyanov and Dinariev.     

Turbulence modeling for the axially rotating pipe from the viewpoint of analytical closures

A single-point model eddy viscosity model of rotation effects on the turbulent flow in an axially rotating pipe is developed based on two-point closure theories. Rotation is known to impede energy transfer in turbulence; this fact is reflected in the present model through a reduced eddy viscosity, leading to laminarization of the mean velocity profile and return to a laminar friction law in the rapid rotation limit. This model is compared with other proposals including linear redistribution effects through the rapid pressure-strain correlation, Richardson number modification of the eddy viscosity in a model of non-rotating turbulence, and the reduction of turbulence through the suppression of near-wall production mechanisms. PACS 47.27.Eq, 47.32.-y     

ISPH modeling of natural convection heat transfer with an analytical kernel renormalization factor

The objective of this study is to extend the attention of the incompressible smoothed particle hydrodynamics method (ISPH) in the heat transfer field. The ISPH method for the natural convection heat transfer under the Boussinesq approximation in various environments: pure-fluid, nanofluid, and non-Darcy porous medium is introduced. We adopted the improved analytical method for calculating the kernel renormalization factor and its gradient based on a quintic kernel function for the wall boundary treatment in the ISPH method. The proposed method requires no dummy particle layer to meet the impermeability condition and makes the heat flux over the wall boundary easy to implement. We performed four different numerical simulations of natural convection in cavities with increasing complexity in modeling and implementation: the natural convection in a square cavity with constant differentially heated wall temperature, natural convection with the heat flux from the bottom wall for a wide range of Rayleigh numbers, natural convection in a non-Darcy porous cavity fully filled with nanofluid in different flow regimes, and natural convection in a partially layered porous cavity. The results showed excellent agreement with results from literatures and the in-house P1–P1 finite element method code.     

Flowing simulation of injection molded parts with micro-channel简

In the micro-molding of component with a micro-sized channel, the ability for polymer melt to flowing into the micro-channel in a macro-sized part is a big challenge. The multidimensional flow behaviors are included in the injection molding the macro-component with a micro-channel. In this case, a simplified model is used to analyze the flow behaviors of the macro-sized part within a micro-channel. The flow behaviors in the macro-cavity are estimated by using the finite element and finite difference methods. The influence of the injection rate, micro-channel size, heat transfer coefficient, and mold temperature on the flowing distance is investigated based on the non-isothermal analytic method. The results show that an increase in the radius of the micro-channel and mold temperature can improve effectively the flowing distance in the micro-channel.     

微沟槽结构注塑成形的充型过程计算方法

微注塑成形制造方法适合于热塑性材料微小型器件大批量加工,对微注塑关键步骤——充型进行分析计算,有助于微注塑工艺参数和模具结构优化。目前研究表明,微尺度聚合物熔体流动与常规流动存在显著差异,采用常规尺度流动计算分析工具会带来较大偏差。本文以开源计算代码OpenFOAM为基础,综合由实验获得的熔体表面特性规律和粘度变化规律等,采用面向对象编程方法构建了熔体填充微结构型腔流动过程的计算模块,以微流体器件中的典型微结构——微沟槽注塑充型过程为例进行数值模拟,分析了表面力和粘度作用对其注塑充型填充率的影响。     

Compressible gas-liquid mixture flow at abrupt pipe enlargements

A detailed investigation was made of the flow of compressible gas-liquid mixtures through sudden enlargements in diameter of circular pipes. One-dimensional analysis shows that the dimensionless pressure rise varies with mixture void fraction and mixture momentum, while the establishment of choking conditions at the enlargement is controlled by the length of pipe downstream in which frictional pipe flow occurs. The flows were found to exhibit two characteristic modes, jet flow and submerged flow, with intermediate flows displaying unsteady oscillation between these modes. The distance to the downstream position of maximum pressure increased steadily with mixture void fraction when the upstream pipe outlet was choked, varying from 5 to 50 times the downstream pipe diameter. If the flow was not choked, this distance was much smaller and showed discrete fixed values associated with the mode of flow.

One-dimensional analysis accurately predicted maximum pressure, but when flow was choked at the enlargement the calculation was sensitive to the pressure in the region of separated flow surrounding the central jet in the enlargement. Although analysis of maximum pressure in terms of flow expansion and normal shock gave a general indication of the maximum pressure (which was thus concluded to depend on the general flow processes expected in the enlargement), accurate prediction of maximum pressures will depend on empirical knowledge of the separated flow region pressures. The maximum pressure rise was found to be in the range extending down to 0.3 of the upstream pipe outlet pressure and reduced with void fraction; it was also influenced by the enlargement area ratio. Flows in the approach and outlet pipes were found to be compressible, frictional pipe flows of the Fanno type, with somewhat reduced friction factors occurring in the outlet pipe.     

Wave propagation modeling of fluid-filled pipes using hybrid analytical/two-dimensional finite element method

In this paper, a Hybrid Analytical/Two-Dimensional Finite Element Method (2-D HAFEM) is proposed to analyze wave propagation characteristics of fluid-filled, composite pipes. In the proposed method, a fluid-filled pipe with a constant cross-section is modeled by using a 2-D finite element approximation in the cross-sectional area while an analytical wave solution is assumed in the axial direction. Thus, it makes possible to use a small number of finite elements even for high frequency analyses in a computationally efficient manner. Both solid and fluid elements as well as solid–fluid interface boundary conditions are developed to model the cross-section of the fluid-filled pipe. In addition, an acoustical transfer function (ATF) approach based on the 2-D HAFEM formulation is suggested to analyze a pipe system assembled with multiple pipe sections with different cross-sections. An ATF matrix relating two sets of acoustic wave variables at the ends of each individual pipe section with a constant cross-section is first calculated and the total ATF matrix for the multi-sectional pipe system is then obtained by multiplying all individual ATF matrices. Therefore, the HAFEM-based ATF approach requires significantly low computational resources, in particular, when there are many pipe sections with a same cross-sectional shape since a single 2-D HAFEM model is needed for these pipe sections. For the validation of the proposed method, experimental and full 3-D FE modeling results are compared to the results obtained by using the HAFEM-based ATF procedure.     

On the phase field modeling of crack growth and analytical treatment on the parameters

Continuum Mechanics and Thermodynamics - A thermodynamically consistent phase field model for crack propagation is analyzed. The thermodynamic driving force for the crack propagation is derived...     

Self-propulsion of a free hydrofoil with localized discrete vortex shedding: analytical modeling and simulation

We present a model for the self-propulsion of a free deforming hydrofoil in a planar ideal fluid. We begin with the equations of motion for a deforming foil interacting with a pre-existing system of point vortices and demonstrate that these equations possess a Hamiltonian structure. We add a mechanism by which new vortices can be shed from the trailing edge of the foil according to a time-periodic Kutta condition, imparting thrust to the foil such that the total impulse in the system is conserved. Simulation of the resulting equations reveals at least qualitative agreement with the observed dynamics of fishlike locomotion. We conclude by comparing the energetic properties of two distinct turning gaits for a free Joukowski foil with varying camber.     

The developing heat transfer and fluid flow in micro-channel heat sink with viscous heating effect

The numerical modeling of the conjugate heat transfer and fluid flow through the micro-heat sink was presented in the paper, considering the viscous dissipation effect. Three different fluids with temperature dependent fluid viscosity are considered: water, dielectric fluid HFE-7600 and isopropanol. The square shape of the cross-section is considered with D _h  = 50 μm with a channel length L = 50 mm. As most of the reported researches dealt with fully developed fluid flow and constant fluid properties in this paper the thermal and hydro-dynamic developing laminar fluid flow is analyzed. Two different heat transfer conditions are considered: heating and cooling at various Br. The influence of the viscous heating on local Nu and Po is analyzed. It was shown that for a given geometry the local Po and Nu numbers are strongly affected by the viscous heating. Moreover the Po number attains the fully developed value as the external heating is equal with the internal viscous heating.     

Overview of cold regions mobility modeling at CRREL

Over the last several decades, the Cold Regions Research and Engineering Laboratory (CRREL) has extensively tested and analyzed issues related to vehicle performance in winter. Using this knowledge and the experimental database, models were developed to capture the important elements for cold regions mobility performance. These models span a range of resolutions and fidelities and include three-dimensional finite element models of tire–terrain interaction, vehicle dynamics models of vehicles on winter surfaces, semi-empirical cold regions algorithms for winter performance within the NATO reference mobility model (NRMM), all-season vehicle performance in force-on-force war-gaming simulations, and vehicle–surface interaction for real-time vehicle simulators. Each of these types of models is presented along with examples of their application.     

Numerical modeling of carbon monoxide neutralization by metered water injection into a high-temperature mixture of combustion products

A closed mathematical model of the flow of a two-phase mixture consisting of evaporating water droplets and a chemically reacting multicomponent gas is described. The effect of the real droplet heating and evaporationkinetics on the gas-phase chemical reactions in a mixture of combustion products is studied within the framework of this model.Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No.6, pp. 96–106, November–December, 1993.     

Molecular modeling of cracks at interfaces in nanoceramic composites

Toughness in Ceramic Matrix Composites (CMCs) is achieved if crack deflection can occur at the fiber/matrix interface, preventing crack penetration into the fiber and enabling energy-dissipating fiber pullout. To investigate toughening in nanoscale CMCs, direct atomistic models are used to study how matrix cracks behave as a function of the degree of interfacial bonding/sliding, as controlled by the density of C interstitial atoms, at the interface between carbon nanotubes (CNTs) and a diamond matrix. Under all interface conditions studied, incident matrix cracks do not penetrate into the nanotube. Under increased loading, weaker interfaces fail in shear while stronger interfaces do not fail and, instead, the CNT fails once the stress on the CNT reaches its tensile strength. An analytic shear lag model captures all of the micromechanical details as a function of loading and material parameters. Interface deflection versus fiber penetration is found to depend on the relative bond strengths of the interface and the CNT, with CNT failure occurring well below the prediction of the toughness-based continuum He–Hutchinson model. The shear lag model, in contrast, predicts the CNT failure point and shows that the nanoscale embrittlement transition occurs at an interface shear strength scaling as _τs~_εf,CNTσCNT${\tau }_s~{\epsilon }_{f,CNT}{\sigma }_{CNT}$ rather than _τs~_σCNT${\tau }_s~{\sigma }_{CNT}$ typically prevailing for micron scale composites, where _εf,CNT${\epsilon }_{f,CNT}$ and _σCNT${\sigma }_{CNT}$ are the CNT failure strain and stress, respectively. Interface bonding also lowers the effective fracture strength in SWCNTs, due to formation of defects, but does not play a role in DWCNTs having interwall coupling, which are weaker than SWCNTs but less prone to damage in the outerwall.     

Auto-ignitions of a methane/air mixture at high and intermediate temperatures

A rapid compression machine (RCM) and a shock tube (ST) have been employed to study ignition delay times of homogeneous methane/air mixtures at intermediate-to-high temperatures. Both facilities allow measurements to be made at temperatures of 900–2000 K, at pressures of 0.38–2.23 MPa, and at equivalence ratios of 0.5, 1.0, and 2.0. In ST experiments, nitrogen served as a diluent gas, whereas in RCM runs the diluent gas composition ranged from pure nitrogen to pure argon. Recording pressure, UV, and visible emissions identified the evolution of chemical reactions. Correlations of ignition delay time were generated from the data for each facility. At temperatures below 1300 K, a significant reduction of average activation energy from 53 to 15.3 kcal/mol was obtained. Moreover, the RCM data showed significant scatter that dramatically increased with decreasing temperature. An explanation for the abnormal scatter in the data was proposed based on the high-speed visualization of auto-ignition phenomena and experiments performed with oxygen-free and fuel-free mixtures. It is proposed that the main reason for such a significant reduction of average activation energy is attributable to the premature ignition of ultrafine particles in the reactive mixture.