A 2.5D-Fourier-BEM model for vibrations in a tunnel running through layered anisotropic soil

A boundary element model of a tunnel running through horizontally layered soil with anisotropic material properties is presented. Since there is no analytical fundamental solution for wave propagation inside a layered orthotropic medium in 3D, the fundamental displacements and stresses have to be calculated numerically. In our model this is done in the Fourier domain with respect to space and time. The assumption of a straight tunnel with infinite extension in the x direction makes it possible to decouple the system for every wave number k_x, leading to a 2.5D-problem, which is suited for parallel computation. The special form of the fundamental solution, resulting from our Fourier ansatz, and the fact, that the calculation of the boundary integral equation is performed in the Fourier domain, enhances the stability and efficiency of the numerical calculations.     

The convection heat transfer coefficient in a Circulating Fluidized Bed (CFB)

Circulating Fluidized Beds are increasingly used in gas–solid and gas–catalytic reactions. A recent development involves their use in physical gas–solid processes such as drying, VOC adsorption or solar energy capture and storage. The heat transfer from the wall of the CFB to the flowing gas–solid suspension is the major design parameter, and was studied for different powders at different operating conditions as determined by the gas velocity and solids circulation flux. Measured values of the heat transfer coefficients are discussed, and compared with empirical predictions of Molodtsof–Muzyka, and Gorliz–Grace. Whereas Gorliz–Grace predicts heat transfer coefficients correctly within a narrow range of operating conditions only, the Molodtsof–Muzyka approach can be simplified into a linear relationship.     

Boundary element method analyses of transient heat conduction in an unbounded solid layer containing inclusions

The boundary element method (BEM) is used to compute the three-dimensional transient heat conduction through an unbounded solid layer that may contain heterogeneities, when a pointwise heat source placed at some point in the media is excited. Analytical solutions for the steady-state response of this solid layer when subjected to a spatially sinusoidal harmonic heat line source are presented when the solid layer has no inclusions. These solutions are incorporated into a BEM formulation as Greens functions to avoid the discretization of flat media interfaces. The solution is obtained in the frequency domain, and time responses are computed by applying inverse (Fast) Fourier Transforms. Complex frequencies are used to prevent the aliasing phenomena. The results provided by the proposed Greens functions and BEM formulation are implemented and compared with those computed by a BEM code that uses the Greens functions for an unbounded media which requires the discretization of all solid interfaces with boundary elements. The proposed BEM model is then used to evaluate the temperature field evolution through an unbounded solid layer that contains cylindrical inclusions with different thermal properties, when illuminated by a plane heat source. In this model zero initial conditions are assumed. Different simulation analyses using this model are then performed to evaluate the importance of the thermal properties of the inclusions on transient heat conduction through the solid layer.     

Time-domain MoM for the analysis of thin-wire structures above half-space media using complex-time Green's functions and band-limited quadratic B-spline temporal basis functions

The transient response of a thin wire in the presence of a half-space is calculated with a new formulation of the Method of Moments (MoM) in time domain, based on a novel Time-Domain Mixed Potential Integral Equation (TD-MPIE), using complex-time Green's functions. The excitation is a Gaussian voltage source and the solution is obtained by using a Marching-On-in-Time (MOT) procedure. Band-Limited Quadratic B-spline (BL-QB) functions are used as Temporal Basis Functions (TBFs). They are compared with Band-Limited Linear B-spline (BL-LB) interpolation functions. Numerical results show that the solution using BL-QB TBFs is stable and accurate, without late-time instabilities, and efficient in terms of memory usage and computation time.     

Green's function formalism extended to systems of applied mechanical differential equations posed on graphs

The Green's function formalism is extended here to multi-point posed boundary-value problems of a special type occurring in some situations in applied mechanics. Problems which reduce to special systems of linear ordinary differential equations are considered. These are formulated on finite weighted graphs in such a way that every equation in the system governs a single unknown function and is defined on a single edge of the graph. The individual equations are put into a system format by means of contact and boundary conditions at the vertices and endpoints of the graph, respectively. Based on such a statement, the notion of the matrix of Green's type is introduced. Two methods are proposed for the analytic construction of such matrices. Illustrative examples from different areas of applied mechanics are presented.     

Transient heat conduction under nonzero initial conditions: A solution using the boundary element method in the frequency domain

A boundary element method formulation is proposed to solve the diffusion equation under nonzero initial conditions. The problem is solved in the frequency domain, considering only the conduction phenomenon. Complex frequencies are used to avoid aliasing and to allow the computation of the static response. Two numerical examples are given to illustrate the effectiveness of this approach for solving 2-D diffusion equations.     

Dynamics of a 3-D panel of isotropic and orthotropic elastic layers

Presented are exact and approximate models of frequency and transient response of a rectangular 3-D panel of isotropic and orthotropic layers with general ordering across the thickness, and simply supported along its four edges. The models adopt transfer matrices to relate state variables over the two faces of a layer. Transient response utilizes a modal expansion while the forcing function utilizes the static–dynamic superposition method. The approximate model assumes that transverse displacement is constant across the thickness. Except for its inability to predict stress normal to the panel’s plane and inaccuracy in flexural stresses over the footprint, results from the approximate model compare favorably to those from the exact.     

Fundamental study of thermal conduction in dry soils

The thermal conductivity of the different soil components—mineral, liquids and air—varies across two orders of magnitude. Two studies are implemented to explore the role of contacts in heat conduction in dry granular materials. The first set of experiments is designed to elucidate heat transfer at contacts, and it is complemented with a numerically based inversion analysis for different local and boundary conditions to extract proper material parameters. Then, the thermal conductivity of dry soils is measured at different packing densities to address the relevance of coordination number and particle shape effects. Together, both studies confirm the prevailing effect of contact quality and number of contacts per unite volume on heat conduction in granular materials. Interparticle contacts and the presence of liquids in pores play a critical role in heat transfer, and determine the ordered sequence of typical thermal conductivity values: k _air < k _dry-soil < k _water < k _{saturated-soil} < k _mineral.     

Green's functions and three-dimensional steady-state heat-conduction problems in a two-layered composite

A boundary-value problem for steady-state heat conduction in a three-dimensional, two-layered composite is studied. The method of Green's function is used in the study. Green's functions are constructed as double sums in terms of eigenfunctions in two of the three directions. The eigenfunctions in the direction orthogonal to the layers are unconventional and must be defined appropriately. The use of different forms of the Green's functions leads to different representations of the solutions as double sums with different convergence characteristics and it is shown that the method of Green's functions is superior to the classical method of separation of variables.     

置换通风对地板供冷的影响

本文介绍了地板供冷置换通风复合式空调系统试验台,并以试验方式验证了置换通风可增强地板供冷对流换热效果.     

Development of a theoretical process map for laser cladding using two-dimensional conduction heat transfer model

In blown powder laser cladding process, the powder travels across the laser path, gets heated up by absorbing laser energy, and finally melts on the substrate under the intense laser beam; as the substrate moves away this melt pool solidifies to form a continuous built-up layer. In the present study a two-dimensional conduction heat transfer equation has been solved using finite volume method to develop a theoretical process map for laser cladding. The developed process map indicates a range of scanning speed and powder feed rate for the feasibility of the process; the lower limit is dictated by the maximum melt pool temperature, and the higher limit by poor bonding due to lack of melting of the substrate (i.e. low dilution). Parametric regions for thick and thin cladding with low dilution can be decided from the process map. It is found that the process range expands with the increase in total absorbed power as well as power directly absorbed by the powder. Correlations for maximum melt pool temperature and dilution are presented. A process map for identifying the form and scale of the microstructure in the solidified layer is also presented.     

Influence functions of a point source for perforated compound plates with facial convection

Steady-state heat conduction is considered for perforated thin plates with non-insulated facial surfaces. The heat conductivities of the materials and the convection coefficients are assumed piecewise constant. Influence functions of point sources are analytically obtained for some such plates of standard shape. Their singular components are derived in a closed form, ensuring accurate straightforward computer implementations. Special integral representations are then used for obtaining influence functions of a point source for perforated plates. Computability of those representations is tested with a number of illustrative examples.     

饱和岩土介质地埋群管传热特性分析

该文利用格林函数法建立了半无限岩土介质传热计算模型,讨论了介质内过余温度场分布。结果表明:半无限热源作用下介质内温度响应在孔壁处最大,随离孔壁距离的增加呈指数衰减;随时间的增加而增大,并向周围岩土体扩散,热作用半径逐渐增大;地埋群管情形下,钻孔间距对孔壁温度影响明显,钻孔的布置形式对孔壁温度影响不明显,建议了最佳孔距的计算方法。提出了地表最大影响深度计算公式,计算表明地表仅影响其临近区域的温度分布,离地表较远处影响很小,地表的影响深度随时间增加而增大。但小于20 m,对地表下恒温层影响不大。     

Long wave motion in layered elastic media

Long wave motion in a geometrically symmetric 3-layer laminated elastic structure is investigated. The associated dispersion relation is established for three different boundary value problems. For all three cases, numerical solutions are presented and a long wave asymptotic analysis carried out, in each case the cut-off frequencies being shown to satisfy transcendental equations. Long wave approximations are employed to determine the asymptotic orders of the displacement components in the various long wave regimes. The asymptotic structures in a single layer plate associated with bending, extension, thickness stretch resonance and thickness shear resonance are well-known. It is shown that these structures are preserved within the multi-layer problem. This work provides the theoretical framework to generalise the above mentioned theories.     

Numerical studies on crack problems in three-layered elastic media using an image method

Two-dimensional crack problems in a three-layered material are analyzed numerically under the conditions of plane strain. An image method is adopted to obtain fundamental solutions for dislocation dipoles in trilayered media. The governing equations for equilibrium cracks can be constructed by distributed dislocation technique and their solutions are sought in terms of the displacement discontinuity method (DDM). Comparisons are made with available analytical or reference solutions for several examples at various contrasts of material constants, and good agreements are found. A crack within a brittle adhesive layer joining two semi-infinite blocks can propagate in a variety of ways. In particular, crack paths in the form of sigmoidal waves within the adhesive layer are revisited to reveal the sensitivities of cracking paths to initial crack locations and directions and residual stresses. In addition, Z-shape and H-shape cracks alternating from interface to interface are re-examined to highlight the transition of failure modes and the role of the interlayer thickness.     

A meshless model for transient heat conduction in functionally graded materials

A meshless numerical model is developed for analyzing transient heat conduction in non-homogeneous functionally graded materials (FGM), which has a continuously functionally graded thermal conductivity parameter. First, the analog equation method is used to transform the original non-homogeneous problem into an equivalent homogeneous one at any given time so that a simpler fundamental solution can be employed to take the place of the one related to the original problem. Next, the approximate particular and homogeneous solutions are constructed using radial basis functions and virtual boundary collocation method, respectively. Finally, by enforcing satisfaction of the governing equation and boundary conditions at collocation points of the original problem, in which the time domain is discretized using the finite difference method, a linear algebraic system is obtained from which the unknown fictitious sources and interpolation coefficients can be determined. Further, the temperature at any point can be easily computed using the results of fictitious sources and interpolation coefficients. The accuracy of the proposed method is assessed through two numerical examples.     

Convective instability in a gravity modulated anisotropic thermally stable porous medium

The effect of gravity modulation on the onset of convection in a horizontal fluid saturated porous layer in which the applied temperature gradient is opposite to that of gravity is investigated. The flow through the porous layer is governed by an extended form of Darcy’s law incorporating Brinkman’s boundary layer correction. The permeability and thermal conductivity of the medium are assumed to be transversely anisotropic. A stability analysis based on the method of small perturbations is performed using normal mode assumption. The study is focussed on low amplitude gravity modulation and the thresholds are found using Mathieu’s functions. The emergence of instability via the synchronous and subharmonic modes and the transition between them are discussed as a function of the physical parameters of interest.     

The Green's Function for the Two-Dimensional Helmholtz Equation in Periodic Domains

Analytical techniques are described for transforming the Green's function for the two-dimensional Helmholtz equation in periodic domains from the slowly convergent representation as a series of images into forms more suitable for computation. In particular methods derived from Kummer's transformation are described, and integral representations, lattice sums and the use of Ewald's method are discussed. Green's functions suitable for problems in parallel-plate acoustic waveguides are also considered and numerical results comparing the accuracy of the various methods are presented.