Thin inclusion approach for modelling of heterogeneous conducting materials

Experimental data show that heterogeneous nanostructure of solid oxide and polymer electrolyte fuel cells could be approximated as an infinite set of fiber-like or penny-shaped inclusions in a continuous medium. Inclusions can be arranged in a cluster mode and regular or random order. In the newly proposed theoretical model of nanostructured material, the most attention is paid to the small aspect ratio of structural elements as well as to some model problems of electrostatics. The proposed integral equation for electric potential caused by the charge distributed over the single circular or elliptic cylindrical conductor of finite length, as a single unit of a nanostructured material, has been asymptotically simplified for the small aspect ratio and solved numerically. The result demonstrates that surface density changes slightly in the middle part of the thin domain and has boundary layers localized near the edges. It is anticipated, that contribution of boundary layer solution to the surface density is significant and cannot be governed by classic equation for smooth linear charge. The role of the cross-section shape is also investigated. Proposed approach is sufficiently simple, robust and allows extension to either regular or irregular system of various inclusions. This approach can be used for the development of the system of conducting inclusions, which are commonly present in nanostructured materials used for solid oxide and polymer electrolyte fuel cell (PEMFC) materials.     

Eigenvalue Approach to Linear Micropolar Thermoelasticity Under Distributed Loading

The eigenvalue approach is developed for the two-dimensional problem in a micropolar thermoelastic medium for a half-space subjected to distributed loading and zero temperature change. The formulation is applied to the coupled theory as well as to two generalizations, the Lord–Shulman and the Green–Lindsay theories. The Fourier transforms are inverted analytically. The inversion of the Laplace transforms are carried out using the inversion formula of the transform together with Fourier expansion techniques. Numerical methods are used to accelerate the convergence of the resulting series and to evaluate the improper integrals involved to obtain temperature, displacement, force and couple stress in the physical domain. The results of micropolar elasticity and generalized thermoelasticity are deduced as special cases from the present formulation. Numerical results are represented graphically and discussed.     

Frequency response characteristics of the fuzzy polar power systemstabilizer

A fuzzy polar power system stabilizer (FPPSS) which was recently developed is analyzed using frequency domain methods. The frequency domain approach allows the PSS designer to compare the new FPPSS with more conventional controllers. The significance of the three FPPSS design parameters are readily seen from the frequency response data, and their relationship to the conventional lead-lag design approach can be evaluated. Furthermore, the frequency response data for the FPPSS allows an alternate design approach for this stabilizer, and can be used to develop information concerning the small signal stability of the resulting power system     

Characterisation of mechanical behaviour and coupled electrical properties of polymer electrolyte membrane fuel cell gas diffusion layers

Local compression distribution in the gas diffusion layer (GDL) of a polymer electrolyte membrane fuel cell (PEMFC) and the associated effect on electrical material resistance are examined. For this purpose a macroscopic structural material model is developed based on the assumption of orthotropic mechanical material behaviour for the fibrous paper and non-woven GDLs. The required structural material parameters are measured using depicted measurement methods. The influence of GDL compression on electrical properties and contact effects is also determined using specially developed testing tools. All material properties are used for a coupled 2D finite element simulation approach, capturing structural as well as electrical simulation in combination. The ohmic voltage losses are evaluated assuming constant current density at the catalyst layer and results are compared to cell polarisation measurements for different materials.     

A High-Order-Accurate GPU-Based Radiative Transfer Equation Solver for Combustion and Propulsion Applications

In this article we present a high-order-accurate solver for the radiative transfer equation (RTE) which uses the discontinuous Galerkin (DG) method and is designed for graphics processing units (GPUs). The compact nature of the high-order DG method enhances scalability, particularly on GPUs. High-order spatial accuracy can be used to reduce discretization errors on a given computational mesh, and can also reduce the mesh size needed to achieve a desired error tolerance. Computational efficiency is a key concern in solutions to radiative heat transfer problems, due to potentially large problem sizes created by (a) the presence of participating nongray media in a full-spectrum analysis, (b) the need to resolve a large number of angular directions and spatial extent of the domain for an accurate solution, and (c) potentially large variations in material and flow properties in the domain. We present here a simulation strategy, as well as a set of physical models, accompanied by a number of case studies, demonstrating the accuracy and superior performance in terms of computational efficiency of this approach.     

Estimation of spray cooling characteristics on a hot surface using the hybrid inverse scheme

A hybrid technique of the Laplace transform and finite-difference methods in conjunction with the least-squares method and experimental temperature data inside the test material is applied to investigate the spray cooling of a hot surface. In this study, the unknown surface temperature and heat flux will be predicted. Their functional forms are unknown a priori in the present study and are assumed to be the functions of time before performing the inverse calculation. The whole time domain is divided into several analysis sub-time intervals and then these unknown estimates on each analysis interval can be predicted. In order to validate the accuracy of the present inverse method, comparisons between the present estimates and previous estimated results are made. The results show that the present estimates of the unknown temperature at various measurement locations agree with the previous estimated results and experimental temperature data. However, the present estimates of the unknown surface heat flux deviate from the previous estimated results for larger times.     

TRANSIENT LINEAR AND NONLINEAR HEAT CONDUCTION IN WEAKLY MODULATED DOMAINS

Heat conduction in two-dimensional domains with spatially periodic boundary is addressed in this study. The periodic modulation is assumed to be weak, but is of arbitrary shape. A regular perturbation approach is implemented to determine the temperature and heat flux throughout the domain. It is observed that the validity of the perturbation approach extends to include geometries of practical importance. Transient linear as well as steady nonlinear heat conduction problems are examined. The periodic domain is mapped onto the rectangular domain. For both steady and transient linear heat conduction, a fully analytical spectral solution becomes possible. The nonlinear problem is shown to reduce to a set of ordinary differential equations of the two-point-boundary-value type, which is solved using a variable-step-size finite-difference scheme. The perturbation approach is validated upon comparison with conventional methods; excellent agreement is obtained against the boundary- and finite-element methods.     

Risk assessment through probabilistic structural analysis

The increase in computer power over the last twenty to thirty years has resulted in the availability of a wide range of programs for structural analysis. Best-known among these are finite element programs which can solve many problems involving static and dynamic loading, heat transfer and fluid dynamics.

Most of these programs are deterministic in that users specify “constant” values for the model parameters. In many instances this is sufficient: in the design or analysis of non-critical components, or ones for which all parameters are well-known, a deterministic analysis can provide adequate solutions. In the design of critical components the conventional approach is to perform a deterministic analysis and to build in reliability through suitably chosen safety factors.

In problems where the risk associated with a component needs to be assessed conventional deterministic analysis methods are insufficient and methods which incorporate the probabilistic aspects of loads and material properties need to be used, especially if material degradation with time is a factor. Although the randomness of the problem parameters can be simulated through, for instance, Monte Carlo methods, these methods are computationally expensive. This paper discusses computationally efficient, fast probability integration methods where conventional deterministic programs can be adapted to calculate the reliability of a component using mean value-based perturbation methods. This adaptation has been performed for the general purpose finite element program ABAQUS and the general purpose fracture mechanics program NASCRAC.

The methods are illustrated in a case study involving the fracture mechanics analysis of a turbine shaft: it is suspected that cracks have been present since commissioning at a shoulder in the shaft. The likely failure time and the probability of catastrophic failure prior to the first scheduled shutdown is calculated.     

Imposing resolved turbulence in CFD simulations

In large‐eddy simulations, the inflow velocity field should contain resolved turbulence. This paper describes and analyzes two methods for imposing resolved turbulence in the interior of the domain in Computational Fluid Dynamics simulations. The intended application of the methods is to impose resolved turbulence immediately upstream of the region or structure of interest. Comparing to the alternative of imposing the turbulence at the inlet, there is a large potential to reduce the computational cost of the simulation by reducing the total number of cells. The reduction comes from a lower demand for mesh resolution in the upstream part of the domain. The first method uses a modification of the source terms in the discrete Navier‐Stokes equations. In the second method, an actuator is used to impose the turbulence. The methods are tested, and the most accurate is shown to be the approach of modifying the source terms. None of the two methods can impose synthetic turbulence with good results, but it is shown that by running the turbulence field through a short precursor simulation, very good results are obtained. Copyright © 2011 John Wiley & Sons, Ltd.     

Heat Transfer Modeling of a Charring Material Using Isoconversional Kinetics

An isoconversional modeling approach has been considered in the modeling of heat transfer and pyrolysis in a charring material. The isoconversional approach is appealing due to the use of only a single reacting component as opposed to the multi-component model typically used. This reduces the number of required field variables which reduces numerical demands in large multi-dimensional models. In this study, isoconversional parameters have been reduced from available test data for a generic ablative material. The results were evaluated by implementing the approach into a 1-D ablation heat transfer program and modeling the thermal and decomposition response of a charring material subjected to an elevated surface temperature. The results were compared to the same modeling using a traditional multi-component Arrhenius approach. Modeling outputs showed that the two methods produced very similar results when proper care was taken in the tabulated parameters of the isoconversional model which is susceptible to variations in supporting test data and is sensitive to table resolution. The results of this study indicate that the isoconversional model provides a viable alternative to the widely used multi-component approach.     

The prediction of creep damage in type 347 weld metal. Part I: the determination of material properties from creep and tensile tests

Calculations of creep damage under conditions of strain control are often carried out using either a time fraction approach or a ductility exhaustion approach. In the case of the time fraction approach the rupture strength is used to calculate creep damage, whereas creep ductility is used in the ductility exhaustion approach. In part I of this paper the methods that are used to determine these material properties are applied to some creep and constant strain rate tests on a Type 347 weld metal. In addition, new developments to the ductility exhaustion approach are described which give improved predictions of creep damage at failure in these tests. These developments use reverse modelling to determine the most appropriate creep damage model as a function of strain rate, stress and temperature. Hence, the new approach is no longer a ductility exhaustion approach but is a true creep damage model.     

Feasibility study on a full-scale wind turbine blade monitoring campaign: Comparing performance and robustness of features extracted from medium-frequency active vibrations

The present work investigates the performance of different features, extracted from vibration-based data, for structural health monitoring of a 52-meter wind turbine blade during fatigue testing. An active vibration monitoring system was used during the test campaign, providing periodic excitation of single frequencies in the medium-frequency range, and using accelerometers to measure the vibration output on different parts of the blade. Based on previous work from the authors, data is available for the wind turbine blade in healthy state, with a manually induced damage, and with progressively increasing damage severity. Using the vibration data, different signal processing methods are used to extract damage-sensitive features. Time series methods and time-frequency domain methods are used to quantify the applied active vibration signal. Using outlier analysis, the health state of the blade is classified, and the classification accuracy through use of the different features is compared. Highest performance is generally obtained by auto-regressive modeling of the vibration outputs, using the auto-regressive parameters as features. Finally, suggestions for future improvements of the present method toward practical implementation are given.     

A SEMIANALYTIC APPROACH TO GENERAL TRANSIENT PROBLEMS AND ITS APPLICATIONS TO HEAT TRANSFER

Abstract

In this article a new method of solving the transient problems is developed that is based on convolution-type variational principles, where finite-element discretization in the space domain and series representation in the time domain are considered. This approach can overcome the shortcomings of existing methods and combine the advantages of those methods for solving transient problems. The examples show that the new method is a most effective method of obtaining solutions for transient problems.     

Non-iterative estimation of temperature-dependent thermal conductivity without internal measurements

In this work a direct integration method is proposed to estimate temperature-dependent thermal conductivity in a one-dimensional heat conduction domain without internal measurements. By approximating the spatial temperature distribution in the domain as a third-order polynomial of position and by integrating the heat conduction equation over the spatial and temporal domain, the present method estimates the thermal conductivity directly. Also, this method does not require any prior information on the functional form of the thermal conductivity. Some illustrative examples are examined to verify the proposed approach. The proposed approach may also be useful to make sufficiently accurate initial guesses for sophisticated algorithms usually based on iterative refinement scheme.     

AN APPROACH COMBINING BODY-FITTED GRID GENERATION AND CONJUGATE GRADIENT METHODS FOR SHAPE DESIGN IN HEAT CONDUCTION PROBLEMS

The present study is focused on the development of a computational method for shape design of heat conduction problems by using a combination of the body-fitted grid-generation scheme and the conjugate gradient optimization method. The body-fitted coordinate transformation technique is used to generate a curvilinear grid for each iteration automatically, by sensing the change of the shape of the solution domain during the optimization process. The conjugate gradient method is incorporated with direct sensitivity analysis for seeking the optimal shape which minimizes the objective function. The temperature distribution in the solution domain is solved by means of the finite volume method. A practical problem is used for demonstration, and the results show that the proposed method provides a simple and efficient approach for determining the shape profile.     

Implementation of Geometrical Domain Decomposition Method for Solution of Axisymmetric Transient Inverse Heat Conduction Problems

The objective of this article is to study the performance of iterative parameter and function estimation techniques to solve simultaneously two unknown functions (quadratic in time, and linear in time and space) using transient inverse heat conduction method in conjunction with a geometrical domain decomposition approach, in cylindrical coordinates. For geometrical decomposition of physical domain, a multi-block method has been used. The numerical scheme for the solution of the governing partial differential equations is the finite element method. The results of the present study for a configuration composed of two joined disks with different heights are compared to those of exact heat source and temperature boundary condition using inverse analysis. Good agreement between the estimated results and exact functions has been observed for parameter estimation techniques in contrast to those of function estimation approach. In summary, the results show that the function estimation technique is sensitive to the location of measurement points, but is useful to estimate unknown functions without a priori knowledge of the functions' spatial and/or temporal distributions. However, the function estimation technique suffers from a drawback: its implementation and data extraction are less straightforward than parameter estimation method. Finally, it is shown that the use of geometrical domain decomposition offers the possibility of developing a robust inverse analysis code for general purpose heat conduction problems.     

The effect of fractional thermoelasticity on two-dimensional problems in spherical regions under axisymmetric distributions

Abstract

Two-dimensional axisymmetric problems are considered within the context of the fractional order thermoelasticity theory. The general solution is obtained in the Laplace transform domain by using a direct approach without the use of potential functions. The resulting formulation is used to solve two problems of a solid sphere and of an infinite space with a spherical cavity. The surface in each case is taken to be traction free and subjected to a given axisymmetric temperature distribution. The inversion of the Laplace transforms is carried out using the inversion formula of the transform together with Fourier expansion techniques. Numerical methods are used to accelerate the convergence of the resulting series to obtain the temperature, displacement, and stress distributions in the physical domain. Numerical results are represented graphically and discussed. Some comparisons are shown in figures to estimate the effect of the fractional order parameter on all studied fields.     

PARALLEL COMPUTATION OF FORCED CONVECTION USING DOMAIN DECOMPOSITION

Boundary-fitted coordinate transformation broadens the applicability of finite difference methods. However, for a large class of geometries, coordinate transformation introduces singularities and increases grid skewness, which results in large numerical error and slow convergence rate. In this paper, we present the results of combining a finite difference scheme with domain decomposition to obtain a parallel scheme. This scheme is used to simulate steady-state forced convection in irregular axisymmetric and two-dimensional domains. The irregular domain is first dissected into subdomains that have smooth curves as their boundaries. Curvilinear coordinate systems are then generated for each subdomain. Each subdomain is mapped onto a processor in the BBN Butterfly computer. After the tasks of inner domain computation are completed in parallel, the inner boundary values are updated (also in parallel). This sets up an iterative (block Gauss-Seidel) procedure that terminates when convergence is achieved. The structure of our scheme allows a straightforward treatment of the load balance problem and alleviates memory contention.     

Effect of anisotropy on axisymmetric dynamic response of thick-walled cylinders

Effect of anisotropy on the free and forced vibration behavior of hollow cylinders under dynamic internal pressure is investigated. The material is assumed to be cylindrically orthotropic. Laplace transform method is used and the inversion into the time domain is performed exactly using calculus of residues. Complex Laplace parameter in the free vibration equation has directly given natural frequencies and the results are listed in tabular form. On the inner surface various axisymmetric dynamic pressures are applied and hoop stresses are presented in the form of graphs for different values of an anisotropy parameter and wall thickness. The anisotropy parameter which essentially indicates the degree of anisotropy is the square root of a modulus ratio defined as the ratio of circumferential modulus to radial modulus. Increasing the anisotropy parameter provides a stress-amplification effect for thick-walled cylinders. Closed-form solutions obtained in the present paper are tractable and they allow for further parametric studies. The anisotropy constant is a useful parameter from a design point of view in that it can be tailored for specific applications to control the stress distribution. The numerical values used are chosen arbitrarily and do not necessarily represent a certain material