Uniform Boundary Conditions Research Articles

Uniform approximations and effective boundary conditions for a high-contrast elastic interface

A difficulty in the theory of a thin elastic interface is that series expansions in its thickness become disordered in the high-contrast limit, i.e. when the interface is much softer or much stiffer than the media on either side. We provide a mathematical analysis of such series for an annular coating around a cylindrical fibre embedded in an elastic matrix subject to biaxial forcing. We determine the order of magnitude of successive terms in the series, and hence the terms that need to be retained in order to ensure that every neglected term is smaller in order of magnitude than at least one retained term. In this way, we obtain uniform approximations for quantities such as the jump in the displacement and stress across the coating, and explain some peculiarities that have been observed in numerical work. A key finding is that it is essential to distinguish three types of boundary-value problem, corresponding to ‘distant forcing’, ‘localized forcing’ and ‘the homogeneous problem’, since they give different patterns of disorder in the corresponding series expansions. This provides a meaningful correspondence between physical principles and our mathematical results.

Entropy and exergy analysis of coupled radiative heat transfer and heat conduction: A new thermodynamics approach

This study presents a new approach for evaluating the thermodynamic efficiency of a coupled radiative and conductive heat transfer process with an internal heat source. In this approach, the exergy balance equation is derived, and the exergy augmentation rate due to the internal heat source is found to be the sum of the exergy of the system output to the environment surroundings, the exergy stored in the system, and the exergy consumption rate due to the irreversibility of heat transfer in the system. The exergetic efficiency of the coupled heat transfer process is then obtained according to the radiative exergy balance equation. Based on the above theoretical derivation, we carry out a thermodynamic analysis of an example including five coupled heat conduction-radiation transfer systems with a uniform internal heat source and different boundary conditions. The variations in the numerical results are discussed according to the exergy balance principle, and the behaviours of the exergy components over time under transient conditions are analysed. Our numerical results show that increasing the area of the adiabatic boundary and reducing the heat loss of the system should be considered when designing heat-transfer systems (as the exergetic efficiency increases from 0.515 to 0.617). The larger the area of the adiabatic boundary of the system, the stronger the effect of increasing this area on the overall optimisation. When a system has two adiabatic boundaries, a symmetrical arrangement of the adiabatic boundaries is suggested, although this is much less effective than increasing the number of adiabatic boundaries.

Effect of inlet gas and liquid velocity profiles on one-group interfacial area transport equation in a vertical large rectangular channel

Bubbly flows appear in many heat and mass transfer equipment. The interfacial area concentration is a critical parameter in determining the performance of the heat and mass transfer systems. The one-dimensional one-group interfacial area transport equation (IATE) was developed based on area-averaged bubbly flow data collected under uniform inlet flow boundary conditions. The applicability of the IATE to the flow systems with non-uniform inlet flow boundary conditions was not comprehensively examined. This study investigated the effect of inlet liquid and gas velocity profiles on measured interfacial area concentration changes along the flow direction. The data used in this study were collected for vertical upward air-water two-phase flow in a rectangular channel with a gap length of 10 mm and width of 200 mm. The test conditions were the superficial gas velocity ranging from 0.0870 to 0.288 m/s and the superficial liquid velocity ranging from 0.515 to 2.53 m/s. The interfacial area concentrations with uniform and non-uniform inlet flow boundary conditions measured in a large vertical rectangular channel were compared under the same area-averaged flow rate conditions. Then, the predictive capability of the IATE to the bubbly flow test data with uniform and non-uniform inlet flow boundary conditions was assessed. Some non-uniform inlet flow boundary conditions, including channel-center peaking of liquid flow (CPF), channel-center peaking of gas flow (CPG), single-side-wall peaking of liquid flow (SPF), and single-side-wall peaking of gas flow (SPG), significantly affected the interfacial area concentration changes along the axial location at relatively high superficial gas or liquid velocity conditions. The IATE's predictive capability deteriorated for several non-uniform inlet flow boundary conditions, including double-side-wall peaking of gas flow (DPG) and single-side-wall peaking of liquid flow (SPF), specifically at relatively high superficial liquid velocity conditions. The maximum percentage error of the interfacial area concentration prediction by the IATE for these non-uniform inlet flow boundary conditions reached 75%.

Effect of ferromagnetic particles on the elastic and magnetostriction parameters of bulk superconductors

Based on the magnetic dipole theory and the Eshelby's equivalent inclusion theory, a theoretical model of ferromagnetic particle inclusion-superconducting matrix is established in this paper, intrinsic strain is introduced and uniform stress boundary conditions are used to calculate the mechanical properties of the composite material. The effects of changes in parameters such as the elastic modulus, volume fraction ratio, and magnetic field of ferromagnetic particle inclusions on the effective mechanical properties of bulk superconductors such as the effective elastic modulus, effective Poisson's ratio, and effective magnetostriction were compared in detail, providing a theoretical reference for the preparation of superconducting materials containing ferromagnetic particle inclusions.

Isotropic yield surfaces for porous ductile materials: complete geometric representation by a computational homogenisation procedure

PurposeThe present paper aims to explore a computational homogenisation procedure to investigate the full geometric representation of yield surfaces for isotropic porous ductile media. The effects of cell morphology and imposed boundary conditions are assessed. The sensitivity of the yield surfaces to the Lode angle is also investigated in detail.Design/methodology/approachThe microscale of the material is modelled by the concept of Representative Volume Element (RVE) or unit cell, which is numerically simulated through three-dimensional finite element analyses. Numerous loading conditions are considered to create complete yield surfaces encompassing high, intermediate and low triaxialities. The influence of cell morphology on the yield surfaces is assessed considering a spherical cell with spherical void and a cubic RVE with spherical void, both under uniform strain boundary condition. The use of spherical cell is interesting as preferential directions in the effective behaviour are avoided. The periodic boundary condition, which favours strain localization, is imposed on the cubic RVE to compare the results. Small strains are assumed and the cell matrix is considered as a perfect elasto-plastic material following the von Mises yield criterion.FindingsDifferent morphologies for the cell imply in different yield conditions for the same load situations. The yield surfaces in correspondence to periodic boundary condition show significant differences compared to those obtained by imposing uniform strain boundary condition. The stress Lode angle has a strong influence on the geometry of the yield surfaces considering low and intermediate triaxialities.Originality/valueThe exhaustive computational study of the effects of cell morphologies and imposed boundary conditions fills a gap in the full representation of the flow surfaces. The homogenisation-based strategy allows us to further investigate the influence of the Lode angle on the yield surfaces.

Reduced order modelling using parameterized non-uniform boundary conditions in room acoustic simulations.

Quick simulations for iterative evaluations of multi-design variables and boundary conditions are essential to find the optimal acoustic conditions in building design. We propose to use the reduced basis method (RBM) for realistic room acoustic scenarios where the surfaces have inhomogeneous acoustic properties, which enables quick evaluations of changing absorption materials for different surfaces in room acoustic simulations. The RBM has shown its benefit to speed up room acoustic simulations by 3 orders of magnitude for uniform boundary conditions. This study investigates the RBM with two main focuses: (1) various source positions in diverse geometries, e.g., square, rectangular, L-shaped, and disproportionate room, (2) two-dimensional and three-dimensional (3D) inhomogeneous surface absorption by parameterizing numerous acoustic parameters of surfaces, e.g., the thickness of a porous material, cavity depth, switching between a frequency independent (e.g., hard surface) and frequency dependent boundary condition. Results of numerical experiments show speedups of more than 2 orders of magnitude compared to a high fidelity numerical solver in a 3D case where reverberation time varies within one just noticeable difference in all the frequency octave bands.

An analytic method for vibration analysis of non-uniformly coupled L-shaped plates with arbitrary boundary conditions

L-shaped plates are extensively utilized in practical engineering and plates are uniformly coupled in most previous studies. However, spot welding, riveting or bolting is also employed to link two plates and these connection types lead to non-uniform coupling conditions. In this regard, an analytic model is developed for vibration analysis of L-shaped plates with non-uniform coupling conditions. The system is decomposed into two independent rectangular plates, and both bending and in-plane vibrations are analyzed via the classic plate theory and superposition method. The artificial spring technique is adopted to deal with non-uniform continuity conditions and arbitrary uniform boundary conditions, and these conditions are assembled into the governing equation. Comparisons of natural frequencies of L-shaped plates with different boundary and coupling conditions are firstly made, and high accuracy and wide application of the developed model are demonstrated. Furthermore, influences of boundary conditions, coupling conditions, coupling angle and length of plates are investigated. Results reveal that out-of-plane and in-plane displacements are coupled in every plate of L-shaped plate systems. Uniform distribution of coupling nodes can efficiently increase natural frequencies and a few coupling nodes play the role of uniform rigid coupling conditions. Natural frequencies of L-shaped plates at a right angle are the maximum or very close to maximum one. Besides, present results can be used as benchmarks for future researchers.

Accuracy of osseointegrated screw-bone construct stiffness and peri-implant loading predicted by homogenized FE models relative to micro-FE models

Computational predictions of stiffness and peri-implant loading of screw-bone constructs are highly relevant to investigate and improve bone fracture fixations. Homogenized finite element (hFE) models have been used for this purpose in the past, but their accuracy has been questioned given the numerous simplifications, such as neglecting screw threads and modelling the trabecular bone structure as a continuum. This study aimed to investigate the accuracy of hFE models of an osseointegrated screw-bone construct when compared to micro-FE models considering the simplified screw geometry and different trabecular bone material models.Micro-FE and hFE models were created from 15 cylindrical bone samples with a virtually inserted, osseointegrated screw (fully bonded interface). Micro-FE models were created including the screw with threads (=reference models) and without threads to quantify the error due to screw geometry simplification. In the hFE models, the screws were modelled without threads and four different trabecular bone material models were used, including orthotropic and isotropic material derived from homogenization with kinematic uniform boundary conditions (KUBC), as well as from periodicity-compatible mixed uniform boundary conditions (PMUBC). Three load cases were simulated (pullout, shear in two directions) and errors in the construct stiffness and the volume average strain energy density (SED) in the peri-implant region were evaluated relative to the micro-FE model with a threaded screw.The pooled error caused by only omitting screw threads was low (max: 8.0%) compared to the pooled error additionally including homogenized trabecular bone material (max: 92.2%). Stiffness was predicted most accurately using PMUBC-derived orthotropic material (error: -0.7 ± 8.0%) and least accurately using KUBC-derived isotropic material (error: +23.1 ± 24.4%). Peri-implant SED averages were generally well correlated (R2 ≥ 0.76), but slightly over- or underestimated by the hFE models and SED distributions were qualitatively different between hFE and micro-FE models.This study suggests that osseointegrated screw-bone construct stiffness can be predicted accurately using hFE models when compared to micro-FE models and that volume average peri-implant SEDs are well correlated. However, the hFE models are highly sensitive to the choice of trabecular bone material properties. PMUBC-derived isotropic material properties represented the best trade-off between model accuracy and complexity in this study.

Study of Influence of Boundary Condition of Diffuser with Non-Uniform Velocity on the Jet Characteristics and Indoor Flow Field

In practice, the outflow from a diffuser is highly non-uniform due to many reasons. However, the air outflow velocity from a diffuser is uniform in most current studies. Little research has been conducted to determine under what conditions uniform velocity can be used. Therefore, based on the non-uniformity of velocity, airflow characteristics of grille and ceiling diffusers were investigated experimentally and numerically. Two generic CFD cases (non-uniform and uniform velocity) are presented. The velocity field near the diffuser is investigated with measurements in order to determine velocity-inlet boundary conditions. The study shows that the uniform velocity-inlet boundary condition can be considered accurate only under certain conditions. For the grille diffuser, the aspect ratio affects the distribution of the outflow velocity. Using uniform velocity as the velocity-inlet boundary condition for the grille diffuser would result in at least a 14.2% error in the jet region, except when the outflow aspect ratio is 1 and the average velocity is greater than 1.83 m/s. However, when the average velocity of the ceiling diffuser is 3.64 m/s, the error of using uniform velocity as the velocity-inlet boundary condition reaches 58.3%. This study provides the basis for determining the velocity-inlet boundary conditions during numerical simulations.

Optimization of distribution patterns of link beams in a double‐column tall pier bent subjected to earthquake excitations

AbstractSeismic performance of double‐column tall pier bents has to date scarcely been investigated. The deployment of link beams between columns, including numbers and locations, is generally designed according to the experience of engineers, without any sophisticated procedure. This paper proposes a response surface‐based optimization procedure that searches for optimal configurations of link beams of double‐column tall pier bents, considering multiple performance objectives. The response surface model is well‐developed by considering training samples from uniform design methods, boundary conditions, and iteration procedures. With a typical double‐column tall pier bent in southwest China as an example, the correctness of the proposed procedure is validated by comparing seismic responses with those from conventional optimization methods. Furthermore, this response surface‐based procedure possesses a substantially higher time efficiency than is the case with conventional methods, due to less nonlinear time history analyses as required. The Pareto optimal front is employed to trade off competing objectives in this example and to provide potential optimal design options for engineers.

Temperature of energy boreholes accounting for climate change and the built environment – A new model for its estimation

Changes in the ground surface temperature, as it can occur in built-up areas or due to climate change, affect the temperatures of geothermal boreholes. Analytical models for the thermal simulation of boreholes and considering this factor have been proposed. However, they all impose a uniform heat extraction boundary condition along the borehole walls. This boundary condition overestimates the temperature change in the underground caused by the borehole heat extraction and underestimates it in case of rejection. More accurate results are most often obtained by imposing a uniform temperature boundary condition.In this paper, we propose a new model to calculate the boreholes wall temperature taking into account both the heat extractions/rejections from all the boreholes in the area and the change in ground surface temperature. The model is tailored for areas with independent ground source heat pumps and imposes a uniform temperature boundary condition along the borehole walls, overcoming the limitation of the existing models.We apply the new model to a real Swedish neighbourhood and show that existing systems may already be significantly affected by the increased ground surface temperature due to urbanization.We also compare our new model with an existing similar model and show that while the two models provide similar results for smaller areas, their difference tends to be relevant for bigger areas – including the real Swedish neighbourhood analysed - thus making the application of our model important for neighbourhood- and city-scale studies.

Heat Transfer Effects on Carbon Nanotubes Along a Moving Flat Plate Subjected to Uniform Heat Flux

In the present paper, a theoretical analysis is made to investigate fluid flow and heat energy transformation features of single and multi-walled water functionalized carbon nanotubes (CNTs) with uniform heat inconstancy boundary conditions onward a flat plate. The liquid motion and momentum transfer of carbon nanotubes (CNTs) have been analyzed using a homogeneous flow model. Both single-wall CNTs (SWCNTs) and multi-wall CNTs (MWCNTs) used base fluids, namely, water. The thermophysical characteristics of CNTs regarding the solid volume fraction of CNTs are studied by applying empirical correlations. Similarity transformations have been used to the governing partial differential equations turning them into ordinary differential equations. The outcome of similarity transformations which are nonlinear ordinary differential equations subjected to reconstructed boundary conditions, are subsequently solved numerically using bvp4c. The effects of the governing parameters on the dimensionless velocity, temperature, and skin friction are investigated numerically and graphically. An increase in the volume fraction and the velocity ratio parameter increase the flow, the velocity, and the temperature profile. Regardless of any physical parameter, SWCNTs give better heat transfer than MWCNTs.

Influence of jumping-droplet condensation on the properties of separated flow in an air-cooled condenser tube: An Euler-Lagrange approach

An Air-cooled condenser (ACC), which finds popularity in a steam power plant in arid areas, is usually less efficient as film condensation occurs inside the condenser tube. Recent research is directed towards eliminating the thermally insulating liquid film with the application of novel superhydrophobic surfaces. The self-cleaning property of such surfaces facilitates easy condensate drainage in the form of jumping droplets exposing favourable nucleation sites, thereby significantly promoting dropwise condensation. The present study explores the characteristics of jumping droplet condensation in finite condenser tubes using computational fluid dynamics (CFD). The wall-heat-flux for condensation is modelled here by a uniform suction boundary condition. The strength of suction is quantified by a suction Reynolds number Re s. We mainly focus on the zone corresponding to 2.3 < Re s < 10, where no previous solution exists. In a long horizontal tube, the progressive realization of a self-similar region starting from the developing regions is demonstrated. We examine the characteristics of the developing region based on the sign of the pressure gradient. The results of three-dimensional CFD simulations illustrate the variations of droplet trajectories with the inception size and coordinates of jumping droplets determined locally by the relative contributions of various force components, viz. gravity, axial drag in the vapour core, suction induced radial drag and Saffman lift. The present study also predicts the effect of pipeline inclination on condensate drainage. Ultimately, considering multiple jumps, we found that the maximum condensate emission can be obtained for small droplets (5−15 μm), while medium-sized droplets (20−50 μm) are most advantageous for isolated jumps.

Deep CNNs as universal predictors of elasticity tensors in homogenization

In the present work, 3D convolutional neural networks (CNNs) are trained to link random heterogeneous, multiphase materials to their elastic macroscale stiffness thus replacing explicit homogenization simulations. The proposed CNN model is universal in that it accounts for various types of microstructures, for arbitrary phase fractions, non-constant and thereby very large ranges of Young’s moduli of the constituent phases (from 1 to 1000 GPa) and of their Poisson’s ratios (from 0 to 0.4). Moreover, the CNN predicts the stiffness for periodic boundary conditions (BCs) along with its upper bound through kinematically uniform BCs and its lower bound through stress uniform BCs. The triple of BCs reduces the stiffness uncertainty due to the embedding of the material volume into arbitrary adjacent host materials. Beyond, the stiffness bounds provide an indicator for the proper size of a representative volume element. The proposed universal CNN model achieves high accuracy in its predictions. The reasons for the rare outliers with larger errors are rigorously analyzed. For a real, two-phase diamond–SiC coating material the universal CNN is almost as accurate as a CNN exclusively trained for fixed elastic phase properties of that material. The speedup compared to finite element computations for homogenization is above factor 20500. The proposed CNN model hence enables fast and accurate stiffness predictions in universal analyses of heterogeneous materials in their linear elastic regime.

Magnetohydrodynamic instability of fluid flow in a porous channel with slip boundary conditions

We investigate the linear instability of a fully developed pressure-driven flow of an electrically conducting fluid in a porous channel using the Brinkman-Darcy model and the additional effects of a uniform magnetic field and slip boundary conditions. Two Chebyshev collocation techniques are used to solve the ordinary eigenvalue system governing the onset of convection. The critical Reynolds number, Rec, wavenumber, ac, and wave speed cc are found in terms of the porous parameter M, the dimensionless slip length, N0, and the Hartmann number Ha.

Heat Transfer under Magnetohydrodynamics Flow of Nanofluids Past an Inclined Plate with Non Uniform Boundary Conditions

This paper deals with natural thermal convection combined with the mass transfer of nanoparticles occurring in the boundary layers of a nanofluid subjected to magnetohydrodynamics. The wall consists of an inclined plate is considered according to a temperature as well as the volume fraction of the nanoparticles varying as the power of the axial coordinate. In addition, internal heat generation/absorption is taken into account in the mathematical formulation. The governing partial differential equations based on Buongiorno's approach are transformed into a set of ordinary differential equations. The two-level method of no-similarity equations is used to achieve higher accuracy. The whole calculation procedure is implemented using a limit value problem program written according to the Matlab computer language that applies the Lobbato IIIa finite difference method. The obtained results have revealed that small variations of the boundary conditions with the axial coordinate become very significant on the local Nusselt number and the local Sherwood number for nanoparticles. Moreover, a better heat transfer has been obtained with a larger S. However, a trade-off between desired heat transfer rate and level of reduced skin friction should be scheduled.

A Uniform Model for Stray Current of Long-Line DC Metro Systems

With the rapid development of the metro, a series of problems caused by the stray current is becoming increasingly serious. Evaluation of stray current is the primary but difficult step for dealing with the problems. In fact, since metros are usually constructed by cut-an-cover tunnel, shield tunnel, and viaduct, the metro structure is one of the most important factors of stray current. It is significant to evaluate stray current in the long line with the variable metro structures. Based on this, a uniform model is built in this article. The return current system is equivalent to multiple differential units considering the variability of the metro structure, and differential units at each location can be set according to the actual metro structure. Furthermore, uniform equations for solving stray currents are deuced based on the electrical relationships of differential units. For variable metro structures, uniform boundary conditions are discussed to solve the equations. The model is verified by comparing the test data and simulation data of Shenzhen Metro. Finally, stray current along the long line is evaluated in this article. It is shown that the stray current is smaller along the long line, which is formed by the viaduct.

Computational Elastic Analysis of AA7075-O using 3D-Microstructrure-Based-RVE with Really-distributed Particles

AA7075 is of special interest amongst aluminum alloys for structural applications in automotive and aerospace industries because of its higher strength. Due to advances in experimental and numerical analysis tools, there is much interest amongst researchers in developing analytical and computational methods to calculate the effective material properties of AA7075 alloy based of its complex microstructure. This paper presents a novel computationally-efficient reconstruction of three-dimensional microstructure of representative volume element model with real distribution of particles using focused ion beam equipped with scanning electron microscopy techniques and specialized computer software to investigate the mechanical properties of AA7075-O sheet. As part of material microstructure characterization for computational analysis, particle identification and chemical characterization of the AA7075-O sheet are also investigated by scanning electron microscopy-based energy dispersive X-ray spectroscopy and electron back-scatter diffraction analysis. The results show that there are three main types of particles that exist in AA7075-O sheet, i.e., irregularly-shaped iron-rich particle Al3Fe, elliptically-shaped particle MgZn2, and needle-like particle CuAl2. The spatial distribution of these particles in AA7075-O sheet from a set of scanning electron microscopy images are utilized to reconstruct RVE models in a finite element analysis environment and analyzed with periodic boundary condition and kinematically uniform boundary condition. Also, a comparison of RVE results with that of modified rule of mixtures is presented. It is shown that the particular boundary conditions have almost no influence over the effective elastic properties when the RVE size is 10 um × 10 um × 10 um and volume fraction of particle is large. Also, the modified rule of mixtures predictions of elastic properties generally well match with the trends of RVE-based computational results, which implies the validity of simpler modified rule of mixtures approach.

Mass transfer from a sheared spherical rigid capsule

Solute mass transfer from a spherical fluid-filled rigid capsule subjected to shear flow is studied numerically, while considering unsteady, continuous, and nonuniform boundary conditions on its surface. Here, the capsule acts as a reservoir with its initially encapsulated solute concentration decaying over time. This scenario differs from the classical case study of either constant concentration or constant mass flux at the surface of the particle. The flow and the concentration field are computed using fully three-dimensional lattice Boltzmann simulations, where the fluid-structure two-way coupling is achieved by the immersed boundary method. The effects of the flow and the boundary conditions on mass transfer efficacy are quantified by the Sherwood number (the dimensionless mass transfer coefficient), which is found to increase due to the combined effects of forced convection and the rotation of the capsule. Having continuity of both the concentration and the mass flux on the capsule significantly decreases the Sherwood number as compared to the case with constant and uniform boundary condition. All the obtained results can be applied to heat transfer in the case of cooling an initially hot spherical particle, for which the concentration must be replaced by the temperature and the Sherwood number by the Nusselt number.

On the intermittent nature of forest fire spread – Part 2

Based on analysis of the interaction between a spreading fire and its surrounding environment, in nominally constant and uniform boundary conditions, it is observed that the evolution of the fire front is characterised by fluctuations of its properties, including (in particular) its rate of spread (ROS). Using a database with a wide range of fires with different time–space scales, it is shown that the amplitude of the fluctuation in ROS is proportional to the average value of the ROS and that the frequency of oscillation varies with the type of fire, and for a given fuel, increases with the average ROS. In fast-spreading fires, the large amplitude of ROS increase and sudden decrease promote the intermittent behaviour of the fire. In general, the amplitude and period required for the ROS increase are larger than for its decrease. However, the acceleration and deceleration phases in junction fires do not follow this rule, suggesting the existence of different convective processes of interaction between the flow and fire. This oscillation explains the variability in many fires at all scales and challenges the current interpretation based on the three factors affecting fire spread and the classification of wind or topography-driven fires.