Uniform Boundary Conditions Research Articles

The impact of azimuthally asymmetric carbon deposition upon pellet-clad mechanical interaction in advanced gas reactor fuel

Cracked nuclear fuel pellets were modelled in the r-θ plane with an azimuthally varying clad surface temperature boundary condition using the PELICAN set of fuel performance models for the commercial finite element software, Abaqus. The temperature boundary condition was assumed to represent heat transfer impairment due to an azimuthally asymmetric carbon deposit on advanced gas-cooled reactor pins. The model predicts the radial and azimuthal displacement of the idealised fuel fragments, together with the resulting elastic, creep and plastic strains in the cladding. These were compared to simulations assuming a uniformly hot or cold boundary condition. Apart from a short period during the return to power from reduced power (70%) operation and outages, the hoop stress in the simulation with an azimuthally varying clad surface temperature was bounded by that of models with a uniform hot or cold surface temperature. The reduced stress was proposed to be due to the greater ability of the fuel fragments to relocate in order to accommodate changes to the power level. As a result, the creep strains in the model with an azimuthally varying clad surface temperature were lower than assuming either a uniform hot or cold boundary condition.

WISHE-Moisture Mode in an Aquaplanet Simulation.

This study aims to understand the nature of the tropical intraseasonal oscillations (ISOs) in an aquaplanet simulation performed using Geophysical Fluid Dynamics Laboratory's AM2.1 with a uniform sea surface temperature within the deep tropics. The simulated ISO resembles the observed Madden‐Julian Oscillation in that the spectral peak in precipitation appears at zonal wave number 1 and a period of ~60 days. Vertically integrated moist static energy budget of the simulated ISO shows that enhanced latent heat flux to the east of anomalously active convection causes eastward propagation of the ISO mode, which is weakly opposed by horizontal moisture advection. A series of mechanism denial experiments are conducted either by homogenizing select variables—surface wind stress, longwave radiative heating, and surface evaporation—with their zonal means from the control simulation or by suppressing free‐tropospheric moisture variation. Results of the mechanism denial experiments show that the simulated ISO disappears when the interactive surface evaporation is disabled, suggesting that the wind‐induced surface heat exchange (WISHE) mechanism is essential to the simulated ISO. Longwave cloud‐radiation feedbacks and moisture‐convection feedbacks affect horizontal scale and phase speed of the simulated ISO, respectively. Our results strongly suggest that the simulated ISO is the linear WISHE‐moisture mode of Fuchs and Raymond under horizontally uniform boundary conditions.

Numerically-aided 3D printed random isotropic porous materials approaching the Hashin-Shtrikman bounds

The present study introduces a methodology that allows to combine 3D printing, experimental testing, numerical and analytical modeling to create random closed-cell porous materials with statistically controlled and isotropic overall elastic properties that are extremely close to the relevant Hashin-Shtrikman bounds. In this first study, we focus our experimental and 3D printing efforts to isotropic random microstructures consisting of single-sized (i.e. monodisperse) spherical voids embedded in a homogeneous solid matrix. The 3D printed specimens are realized by use of the random sequential adsorption method. A detailed FE numerical study allows to define a cubic representative volume element (RVE) by combined periodic and kinematically uniform (i.e. average strain or affine) boundary conditions. The resulting cubic RVE is subsequently assembled to form a standard dog-bone uniaxial tension specimen, which is 3D printed by use of a photopolymeric resin material. The specimens are then tested at relatively small strains by a proper multi-step relaxation procedure to obtain the effective elastic properties of the porous specimens.

Analysis of fully developed flow and heat transfer through n-sided polygonal ducts with round corners using the Galerkin weighted residual method

The Galerkin weighted residuals method is extended solve the laminar, fully developed flow and heat transfer of Al2O3-water nanofluid inside polygonal ducts with round corners for the constant heat flux and uniform wall temperature boundary conditions. Using the method, semi-analytical, closed-form solutions are obtained for the friction coefficient and the Nusselt number in terms of the radius of the round corners for the triangular, rectangular, hexagonal, and octagonal ducts. The effects of varying the radius of the round corners and the volume fraction of the nanoparticles on the friction coefficient and the Nusselt number are analyzed. The results show that the friction factor and the average Nusselt number increase with increasing the radius of the round corners. The study indicates that the Galerkin weighted residuals method is an accurate and efficient technique to obtain closed-form solutions for the flow and temperature fields in ducts with complex cross sectional shapes.

A Pressurized Vitiated Co-Flow Burner and Its Preliminary Application for a Methane Lifted Flame

A new pressurized vitiated co-flow burner (PVCB) was designed and built for the investigation of lifted flame properties and was supported by a vitiated co-flow of hot combustion products from a lean H2/air flame at a controllable pressure; its preliminary application for a methane lifted flame was tested. The distribution of the co-flow temperature, oxygen mole fraction, flow rate, and pressure of the PVCB was measured and calculated. The research results show that the co-flow temperature range is from 300 to 1300 K, the background pressure range is from 1 to 1.5 bar, the stable temperature field of the PVCB is wider, and the background pressure of the PVCB can be controlled. The simulation results show that the PVCB provides a controllable, pressurized co-flow of hot and vitiated gases, which makes it possible to investigate flame stabilization mechanisms. The PVCB has the advantages of controllable background pressure and a stable temperature field. The well-defined uniform boundary conditions and simplified flow of the PVCB simplify the establishment of a numerical model and decouple the turbulent chemical kinetics from the complex recirculating flow. It can be widely used in the research on lifted flames. A lifted flame of methane was recorded under conditions of a co-flow temperature of 1133 K and pressure from 1 to 1.043 bar. The lift-off height decreased and stabilized with the increase in the background pressure. The laminar flame speed and the autoignition delay time were tested and simulated at the same time by Chemkin; the influence of background pressure on the lift-off height, laminar flame speed, and autoignition delay were analyzed. The results show that the autoignition, as well as the flame propagation, dominated the stabilization mechanism of the lifted flame in the PVCB.

Finite-rate chemistry modelling of non-conventional combustion regimes using a Partially-Stirred Reactor closure: Combustion model formulation and implementation details

The present work focuses on the numerical simulation of Moderate or Intense Low oxygen Dilution combustion condition, using the Partially-Stirred Reactor model for turbulence-chemistry interactions. The Partially-Stirred Reactor model assumes that reactions are confined in a specific region of the computational cell, whose mass fraction depends both on the mixing and the chemical time scales. Therefore, the appropriate choice of mixing and chemical time scales becomes crucial to ensure the accuracy of the numerical simulation prediction. Results show that the most appropriate choice for mixing time scale in Moderate or Intense Low oxygen Dilution combustion regime is to use a dynamic evaluation, in which the ratio between the variance of mixture fraction and its dissipation rate is adopted, rather than global estimations based on Kolmogorov or integral mixing scales. This is supported by the validation of the numerical results against experimental profiles of temperature and species mass fractions, available from measurements on the Adelaide Jet in Hot Co-flow burner. Different approaches for chemical time scale evaluation are also compared, using the species formation rates, the reaction rates and the eigenvalues of the formation rate Jacobian matrix. Different co-flow oxygen dilution levels and Reynolds numbers are considered in the validation work, to evaluate the applicability of Partially-Stirred Reactor approach over a wide range of operating conditions. Moreover, the influence of specifying uniform and non-uniform boundary conditions for the chemical scalars is assessed. The present work sheds light on the key mechanisms of turbulence-chemistry interactions in advanced combustion regimes. At the same time, it provides essential information to advance the predictive nature of computational tools used by scientists and engineers, to support the development of new technologies.

Analytical thermal analysis of advanced disk brake in high speed vehicles

ABSTRACTTemperature is one of the most important parameters in designing brake systems, in high speed vehicles. In this research, the thermal conduction model of advanced disk brake of high speed vehicles such as trains with velocity 350 km/h is produced under two kinds of frictional heat loads of uniform pressure and uniform friction and time-dependent convective boundary conditions. The governing heat conduction equation is solved in cylindrical coordinate by using the method of separation of variables combined with Duhamel integral. Results show the good ability of analytical solution to estimate exact temperature profile in brake disk.

Effect of interphase region on the elastic behavior of unidirectional glass-fiber/epoxy composites

Using a FEA homogenization technique, this study presents the influence of interphase region on composites. Numerical models using Abaqus™ are developed in order to predict the mechanical behavior of a unidirectional composite (E-glass fibers/epoxy) under monotonic transverse traction. A Representative Volume Element description with a random distribution of the fibers is used. Linear elastic constitutive materials and Kinematic Uniform Boundary Conditions are considered.A numerical/experimental comparison is made in order to validate the model. The thickness and the modulus of the interphase have been determined by experimental measurements based on Atomic Force Microscopy and introduced in the numerical simulation, the effect of these properties as well as the effect of the interphase Poisson’s ratio, on the effective elastic properties of the composite is discussed. The obtained results are in good agreement with the experimental values previously measured by tensile test on macroscopic samples. The fact of considering the interphase improves the accuracy of the prediction of the composite's mechanical elastic behavior.

Application of low-order potential solutions to higher-order vertical traction boundary problems in an elastic half-space.

New solutions of potential functions for the bilinear vertical traction boundary condition are derived and presented. The discretization and interpolation of higher-order tractions and the superposition of the bilinear solutions provide a method of forming approximate and continuous solutions for the equilibrium state of a homogeneous and isotropic elastic half-space subjected to arbitrary normal surface tractions. Past experimental measurements of contact pressure distributions in granular media are reviewed in conjunction with the application of the proposed solution method to analysis of elastic settlement in shallow foundations. A numerical example is presented for an empirical ‘saddle-shaped’ traction distribution at the contact interface between a rigid square footing and a supporting soil medium. Non-dimensional soil resistance is computed as the reciprocal of normalized surface displacements under this empirical traction boundary condition, and the resulting internal stresses are compared to classical solutions to uniform traction boundary conditions.

Appropriate utilization of the unit cell method in thermal calculation of composites

The unit cell method is widely used in thermal calculations of composite. The formulation of a unit cell involves construction of geometric configuration and derivation of boundary conditions. The process is closely related to the structure symmetries of composites and the macro heat flux. In this work, two issues are studied to further appropriate utilization of such method. First, unit cells that formulated based on different paths with different structure symmetries could have the same configuration while different boundary conditions, and leads to some confusions; second, the uniform temperature boundary condition is frequently used without rigorous mathematical derivation and physical consideration, and leaves some uncertainty of its reliability. In this work, three typical composites, unidirectional fiber reinforced, plain woven and three-dimensional four-directional braided composites are studied. For each composite, one unit cell is formulated and two types of boundary conditions are derived. The influence of formulation path on unit cell formulation and the application scope of uniform temperature boundary conditions are then clarified based on corresponding calculations and analysis.

Analytical Solution for 2D Inter-Well Porous Flow in a Rectangular Reservoir

Inter-well fluid flows through porous media are commonly encountered in the production of groundwater, oil, and geothermal energy. In this paper, inter-well porous flow inside a rectangular reservoir is solved based on the complex variable function theory combined with the method of mirror images. In order to derive the solution analytically, the inter-well flow is modeled as a 2D flow in a homogenous and isotropic porous medium. The resulted exact analytical solution takes the form of an infinite series, but it can be truncated to give high accuracy approximation. In terms of nine cases of inter-well porous flow associated with enhanced geothermal systems, the applications of the obtained analytical solution are demonstrated, and the convergence properties of the truncated series are investigated. It is shown that the convergent rate of the truncated series increases with the symmetric level of well distribution inside the reservoir, and the adoption of Euler transform significantly accelerates the convergence of alternating series cases associated with asymmetric well distribution. In principle, the analytical solution proposed in this paper can be applied to other scientific and engineering fields, as long as the involved problem is governed by 2D Laplace equation in a rectangular domain and subject to similar source/sink and boundary conditions, i.e., isolated point sources/sinks and uniform Dirichlet or homogeneous Neumann boundary conditions.

Parameterization study on the moderately thick laminated rectangular plate-cavity coupling system with uniform or non-uniform boundary conditions

This paper investigates the vibro-acoustic characteristics of the moderately thick laminated rectangular plate-cavity coupling system by using a modified Fourier series method. In the established model, two boundary conditions of moderately thick laminated rectangular plate are set as uniform elastic supports and non-uniform elastic supports including multi-points elastic supports or partial elastic supports. Besides, the three-dimensional rectangular cavity with rigid walls or impedance walls is discussed in the studied model. The admissible function of the displacements and sound pressure of the coupling system is set as the superposition function combined with Fourier cosine series and Fourier sin series. The Lagrangian energy principle is used to express the coupling system. The vibro-acoustic coupling characteristics can be obtained based on Rayleigh-Ritz technique. It shows good convergence and agreement of the present method by being compared with the finite element method (FEM) and the related literatures. This paper focuses on the study of free and forced vibro-acoustic analysis for the moderately thick laminated rectangular plate-cavity coupling system. Moreover, some results are achieved by discussing the effects of various plate thicknesses, different types of elastic supports, lamination schemes and various impedance boundary conditions on the natural characteristics and responses of the coupling system.

Structural-acoustic interaction of a three-dimensional panel–cavity–duct system with non-uniform boundary restraints

Plate drum-silencer has received a lot of research attention due to its excellent low frequency noise attenuation and flow-through characteristics. The majority of existing studies are limited to the classical or uniform elastic boundary conditions, while there is little effort devoted to the study of boundary restraint non-uniformity effect on the vibro-acoustic behavior of such silencing system. Motivated by the current limitation, the structural-acoustic coupling model of a three-dimensional panel–cavity–duct silencer is established, in which the elastic boundary restraint can be set as arbitrary distribution function. Energy principle is formulated to describe the vibro-acoustic dynamics of such 3-D panel–cavity–duct silencing system, with the admissible field functions constructed as the superposition of standard Fourier series and the auxiliary edge/interface smoothed terms. All the coupled system response information can be derived in conjunction with Rayleigh–Ritz procedure. Numerical examples are presented to validate the proposed model through the comparison with those from other approaches. The coupling effects of boundary restraining coefficient and plate bending stiffness on sound attenuation performance of such cavity–backed plate–duct silencer are then discussed and analyzed. The results show that the relationship of translational restraints at the duct entrance and exit, kx0 and kxLx, can be obtained through property inverse proportional functions to achieve the optimal sound attenuation. There will be significant improvement in some special frequency band compared with the uniform restraints distribution, especially for the plate with lower bending stiffness The experimental study is also performed to verify the theoretical prediction from current model. In reality, the arbitrary non-uniform elastic edge restraints represent the most general class of boundary conditions, and can provide more optimal space for such drum silencer design.

Magnetohydrodynamic squeezing flow analysis of nanofluid under the effect of slip boundary conditions using variation of parameter method

In this paper, two-dimensional squeezing flow of nanofluid under the effects of a uniform transverse magnetic field and slip boundary conditions is analyzed using variation of parameter method. The approximate analytical solutions of the variation of parameter method show excellent agreement and accuracy with the solutions of numerical method using shooting method coupled with Runge–Kutta coupled. Therefore, the developed analytical solutions are used to investigate the effects of fluid properties, magnetic field and slip parameters on the squeezing flow of nanofluid. From the results, it is observed that the velocity of the fluid increases with increase in the magnetic field parameter under the influence of slip condition while under no-slip condition, the velocity of the fluid decreases with increase in the magnetic field parameter. Also, the fluid velocity increases as the slip parameter increases but it decreases with increase in the magnetic field parameter and Reynolds number under the no-slip condition. It is hoped that this study will enhance the understanding of squeezing flow process such as found in various biological and industrial applications.

Experimental study of natural convection heat transfer from a nonuniformly heated flat plate simulating PV panel

In view of the characteristic of Photovoltaic (PV) conversion, an experimental study has been conducted to investigate the natural convection heat transfer from a flat plate. In order to simulate the real PV cells, three electrical heating circuits were employed to achieve a linear nonuniform heat flux boundary condition. The major parameters, such as the gradient parameter of heat flux k, tilt angle θ and heat flux qw were introduced to analyze their influence on heat transfer ability. Both the local temperature distribution and the overall trend of Nusselt number have been presented. Comparing with the uniform thermal boundary condition, the results show that the local convection heat transfer coefficient is fluctuated at the positions where heat flux has changed. When gradient parameter of heat flux increases, the difference of local convection heat transfer coefficient at the top of the plate between tilt angle θ = 0° and 90° becomes smaller. Moreover, it is observed that the gradient parameter of heat flux has a promotion effect on average convection Nusselt number at larger tilt angle, but the effect becomes complex as tilt angle is smaller. Finally, a correlation combining all significant factors has been put forward to estimate the natural convection heat transfer.

An Influence of the Wall Acoustic Impedance on the Room Acoustics. The Exact Solution

Abstract The Fourier method is applied to the description of the room acoustics field with the combination of uniform impedance boundary conditions imposed on some walls. These acoustic boundary conditions are expressed by absorption coefficient values In this problem, the Fourier method is derived as the combination of three one-dimensional Sturm-Liouville (S-L) problems with Robin-Robin boundary conditions at the first and second dimension and Robin-Neumann ones at the third dimension. The Fourier method requires an evaluation of eigenvalues and eigenfunctions of the Helmholtz equation, via the solution of the eigenvalue equation, in all directions. The graphic-analytical method is adopted to solve it It is assumed that the acoustic force constitutes a monopole source and finally the forced acoustic field is calculated. As a novelty, it is demonstrated that the Fourier method provides a useful and efficient approach for a room acoustics with different values of wall impedances. Theoretical considerations are illustrated for rectangular cross-section of the room with particular ratio. Results obtained in the paper will be a point of reference to the numerical calculations.

3‐D Modeling of Irregular Volcanic Sources Using Sparsity‐Promoting Inversions of Geodetic Data and Boundary Element Method

AbstractGeodetic observations of surface deformation associated with volcanic activities can be used to constrain volcanic source parameters and their kinematics. Simple analytical models, such as point and spherical sources, are widely used to model deformation data. The inherent nature of oversimplified model geometries makes them unable to explain fine details of surface deformation. Current nonparametric, geometry‐free inversion approaches resolve the distributed volume change, assuming it varies smoothly in space, which may detect artificial volume change outside magmatic source regions. To obtain a physically meaningful representation of an irregular volcanic source, we devise a new sparsity‐promoting modeling scheme assuming active magma bodies are well‐localized melt accumulations, namely, outliers in the background crust. First, surface deformation data are inverted using a hybridL1‐ andL2‐norm regularization scheme to solve for sparse volume change distributions. Next, a boundary element method is implemented to solve for the displacement discontinuity distribution of the reservoir, which satisfies a uniform pressure boundary condition. The inversion approach is thoroughly validated using benchmark and synthetic tests, of which the results show that source dimension, depth, and shape can be recovered appropriately. We apply this modeling scheme to deformation observed at Kilauea summit for periods of uplift and subsidence leading to and following the 2007 Father's Day event. We find that the magmatic source geometries for these periods are statistically distinct, which may be an indicator that magma is released from isolated compartments due to large differential pressure leading to the rift intrusion.

Statistics informed boundary conditions for statistically equivalent representative volume elements of clustered composite microstructures

ABSTRACTHomogenized effective constitutive response of arbitrarily dispersed multiphase composites systems are computed using property-based statistically equivalent representative volume elements or P-SERVEs. P-SERVEs are subjected to affine transformation-based displacement boundary conditions, uniform traction boundary conditions or periodic boundary conditions. Predicted P-SERVE sizes are larger as the above boundary conditions ignore the influence of the inclusions exterior to the P-SERVE. Exterior statistics-based boundary conditions (ESBCs) accounting for the presence of fibers and their interactions in the domain exterior to the P-SERVE have been derived in Ghosh and Kubair (2016, J. Mech. Phys. Solids, vol. 96, pp. 1–24). In the present study, ESBCs are derived for statistically inhomogeneous microstructures using the two-point correlation functions used in the statistically informed Greens functions. Comparisons are also made with the statistical volume element approach. It is concluded that the simulations with ESBCs prescribed on the P-SERVEs have a definite advantage over other methods in defining optimal sized P-SERVEs for clustered and matrix-rich microstructures.

Effects of the Random Distributions on the Laminar Flow and Heat Transfer in a Quasi-Counter Flow Parallel-Plate Membrane Channel

ABSTRACTAn internally cooled parallel-plate membrane contactor has been employed for liquid desiccant air dehumidification. The contactor is comprised of a series of quasi-counter flow parallel-plate membrane channels (QCPMC). The processing air and the liquid desiccant (solution) streams are separated by the membranes. Cooling tubes are installed in the solution channel to take away the absorption heat. The laminar flow and heat transfer in the QCPMC with the cooling tubes in the solution side (QCPMCC) are studied based on a unit cell containing the sandwiched domain outside the cooling tubes between two neighboring membranes. This paper is focused on the effects of the random distributions in the height direction on the transport phenomena in the QCPMCC. The governing equations of the momentum and thermal transports are built up together with a uniform wall temperature boundary condition. The product of the mean friction factor and Reynolds number and the mean Nusselt number are then calculated. Effects of the various random distributions in the height direction on the product of the mean friction factor and Reynolds number and the mean Nusselt number are analyzed. Compared to the regular arrangement, the mean Nusselt number for the random distribution is larger than that for the regular one when the Reynolds number is less than 68.5. However when the Reynolds number is larger than 68.5, the mean Nusselt number for the random distribution is smaller than that for the regular one.

Size dependent thermal buckling and postbuckling of functionally graded circular microplates based on modified couple stress theory

ABSTRACTIn this article, size-dependent thermal buckling and postbuckling behavior of a functionally graded circular microplate under uniform temperature rise field and clamped boundary conditions is investigated. Material properties are assumed to gradually vary through the thickness according to a simple power law. Equilibrium equations and associated boundary conditions are derived using variational method and based on modified couple stress theory, classical plate theory and von Kármán geometric nonlinearity. The differential quadrature method is used to discretize the governing equations. This technique is accompanied by an iterative method to determine the thermal postbuckling behavior of microplate. Finally, effects of length scale parameter, power law index and ratio of thickness to radius on the thermal buckling and postbuckling behavior of FG circular microplate are investigated.