Rozprawy doktorskie na temat „Heat transfer problems”

The aim of this thesis is to find the numerical solution for various coefficient identification problems in heat transfer and extend the possibility of simultaneous determination of several physical properties. In particular, the problems of coefficient identification in a fixed or moving domain for one and multiple unknowns are investigated. These inverse problems are solved subject to various types of overdetermination conditions such as non-local, heat flux, Cauchy data, mass/energy specification, general integral type overdetermination, time-average condition, time-average of heat flux, Stefan condition and heat momentum of the first and second order. The difficulty associated with these problems is that they are ill-posed, as their solutions are unstable to inclusion of random noise in input data, therefore traditional techniques fail to provide accurate and stable solutions. Throughout this thesis, the Crank-Nicolson finite-difference method (FDM) is mainly used as a direct solver except in Chapter 7 where a three-level scheme is employed in order to deal with the nonlinear heat equation. An explicit FDM scheme is also employed in Chapter 10 for the two-dimensional case. The inverse problems investigated are discretised using the FDM and recast as nonlinear least-squares minimization problems with simple bounds on the unknown coefficients. The resulting problem is efficiently solved using the \emph{fmincon} or \emph{lsqnonlin} routines from MATLAB optimization toolbox. The Tikhonov regularization method is included where necessary. The choice of the regularization parameter(s) is thoroughly discussed. The stability of the numerical solution is investigated by introducing Gaussian random noise into the input data. The numerical solutions are compared with their known analytical solution, where available, and with the corresponding direct problem numerical solution where no analytical solution is available.

In the presented thesis work, meshfree method with distance fields was extended to obtain solution of nonlinear transient heat transfer problems. The thesis work involved development and implementation of numerical algorithms, data structure, and software. Numerical and computational properties of the meshfree method with distance fields were investigated. Convergence and accuracy of the methodology was validated by analytical solutions, and solutions produced by commercial FEM software (ANSYS 12.1). The research was focused on nonlinearities caused by temperature-dependent thermal conductivity. The behavior of the developed numerical algorithms was observed for both weak and strong temperature-dependency of thermal conductivity. Oseen and Newton-Kantorovich linearization techniques were applied to linearized the governing equation and boundary conditions. Results of the numerical experiments showed that the meshfree method with distance fields has the potential to produced fast accurate solutions. The method enables all prescribed boundary conditions to be satisfied exactly.

In the present work, the multi-objective optimization by genetic algorithms is investigated and applied to heat transfer problems. Firstly, the work aims to compare different reproduction processes employed by genetic algorithms and two new promising processes are suggested. Secondly, in this work two heat transfer problems are studied under the multi-objective point of view. Specifically, the two cases studied are the wavy fins and the corrugated wall channel. Both these cases have already been studied by a single objective optimizer. Therefore, this work aims to extend the previous works in a more comprehensive study.

In the present work, the multi-objective optimization by genetic algorithms is investigated and applied to heat transfer problems. Firstly, the work aims to compare different reproduction processes employed by genetic algorithms and two new promising processes are suggested. Secondly, in this work two heat transfer problems are studied under the multi-objective point of view. Specifically, the two cases studied are the wavy fins and the corrugated wall channel. Both these cases have already been studied by a single objective optimizer. Therefore, this work aims to extend the previous works in a more comprehensive study.

This thesis describes detailed investigations of two different problems in gas-liquid two-phase flow, namely, a study of interfacial stability in a partially filled cylinder subjected to vertical oscillations and a study of heat and mass transfer from hot spray droplets injected into an closed vessel. The interfacial instability study considers experimental data taken from the author's previous work. Cylinders of various diameters, partially filled with water, ethanol or glycerol were subjected to a sinusoidal vertical motion. The critical acceleration, causing the interfacial wave to grow unstable, was found to be approximately constant for a given cylinder diameter, independent on the amplitude of the forcing oscillations. The experiments also indicate that the critical Acceleration always decreases with increasing cylinder diameter. A mathematical analysis of the interfacial instability is based on a stability investigation of a Mathieu equation. It is shown that the experimental data fall into unstable regions for a single, first mode of oscillations. This finding is supported by the experimental analysis given by Cilliberto and Gollub. The analysis shows the effects of the liquid column height on the interfacial instability to be dependent on tanh (k..l.). This multiplier is equal to 1 for the column heights of 250mm, 500 mm and 750 mm, investigated, and a given cylinder diameter, thus having no effect on the results. Computational analysis of the interfacial problem is developed which is based on the simplified MAC method incorporating the Continuum Surface Force (CSF) model for simulating the effects of surface tension. Computational experiments were run for water and glycerol, the two liquids of significantly different properties. The results are presented in the form of time sequenced plots showing the interfacial positions and graphs relating the interfacial wave amplitude and time. Stability of the interface is found to be dependent on the initial surface disturbance. Growth of the interfacial wave is observed in some cases. In the range of situations investigated, surface tension effects are found to have only a small influence both on the stability and frequency of the interfacial oscillations. The period of interfacial oscillations with no forcing vibrations is found to be in good agreement with the period predicted by mathematical analysis. Influence of the initial disturbance profile was also investigated. The results indicate that the interfacial wave adopts oscillatory behaviour similar to the other cases. The oscillation frequency of the interfacial wave undergoing forcing vibrations is found to match the findings of the mathematical analysis. The wave oscillates with an angular velocity equal to the multiples of the half the forcing vibration angular velocity, co/2. In the second investigation a testing rig was constructed to investigate the heat and mass transfer processes in dense hot sprays injected into an enclosed cylindrical vessel. Heat and mass transfer rates were investigated indirectly from the measurements of the gas - vapour mixture pressure rise in the cylinder. The experiments covered different combinations of the parameters influencing the processes. The number and size of spray nozzles, the vessel volume, the type of gas and the initial pressure level in the cylinder were investigated. The experimental results indicate that, for the range of solid cone nozzles tested, the heat and mass transfer characteristics are, to a first approximation independent of the size of the nozzles. The results also show that the rise of spray chamber internal pressure is directly proportional to liquid temperature and flowrate. An analysis, based on energy balances for the whole cylinder, has yielded a new dimensionless group incorporating the important parameters of droplet heat transfer namely the droplet velocity and radius, spray chamber dimensions, gravity, conductivity and convectivity. A good match has been found between the analytical results and experimental findings. An improved analysis, incorporating the effect of evaporation from drops, is also presented. It is based on simultaneous solution of energy and mass balance equations for a single droplet. Again, good agreement with the experimental results is found. Both analyses indicate that, for this particular case of dense, evaporative spray, the Nusselt number tends to have a value equal to I.

In this thesis study, a least-squares finite element method (LSFEM) based conjugate heat transfer solver was developed. In the mentioned solver, fluid flow and heat transfer computations were performed separately. This means that the calculated velocity values in the flow calculation part were exported to the heat transfer part to be used in the convective part of the energy equation. Incompressible Navier-Stokes equations were used in the flow simulations. In conjugate heat transfer computations, it is required to calculate the heat transfer in both flow field and solid region. In this study, conjugate behavior was accomplished in a fully coupled manner, i.e., energy equation for fluid and solid regions was solved simultaneously and no boundary conditions were defined on the fluid-solid interface. To assure that the developed solver works properly, lid driven cavity flow, backward facing step flow and thermally driven cavity flow problems were simulated in three dimensions and the findings compared well with the available data from the literature. Couette flow and thermally driven cavity flow with conjugate heat transfer in two dimensions were modeled to further validate the solver. Finally, a microchannel conjugate heat transfer problem was simulated. In the flow solution part of the microchannel problem, conservation of mass was not achieved. This problem was expected since the LSFEM has problems related to mass conservation especially in high aspect ratio channels. In order to overcome the mentioned problem, weight of continuity equation was increased by multiplying it with a constant. Weighting worked for the microchannel problem and the mass conservation issue was resolved. Obtained results for microchannel heat transfer problem were in good agreement in general with the previous experimental and numerical works. In the first computations with the solver
quadrilateral and triangular elements for two dimensional problems, hexagonal and tetrahedron elements for three dimensional problems were tried. However, since only the quadrilateral and hexagonal elements gave satisfactory results, they were used in all the above mentioned simulations.

The thesis describes a computer program (FASTP), written for the DOS environment and based on finite difference algorithms, which can be used to solve both transient heat and mass transfer problems. Relatively simple geometries can be used as building blocks to model problems in cartesian, cylindrical, and spherical coordinate systems. The user can model diffusion behavior through any material provided the relevant material properties are known. A completely menu driven system allows for the specification of a number of boundary conditions including convection, constant or zero flux, and radiation. Heat generation or mass accumulation, as well as interboundary resistance or partition coefficient terms can also be assigned. The program can also be used to model phase transformations and the effects of mixing in liquid systems. The results of several problems run on FASTP have been documented in this report and are shown to compare favourably with results generated from mathematically exact solutions.

The objective of this work is to apply the method of variation of parameters to various direct and inverse nonlinear, multimode heat transfer problems. An overview of the general method of variation of parameters is presented and applied to a simple example problem. The method is then used to obtain solutions to three specific extended surface heat transfer problems: 1. a radiating annular fin, 2. convective and radiative exchange between the surface of a continuously moving strip and its surroundings, and 3. convection from a fin with temperature-dependent thermal conductivity and variable cross-sectional area. The results for each of these examples are compared to those obtained using other analytical and numerical methods. The method of variation of parameters is also applied to the more complex problem of combined conduction-radiation in a one-dimensional, planar, absorbing, emitting, non-gray medium with non-gray opaque boundaries. Unlike previous solutions to this problem, the solution presented here is exact. The model is verified by comparing the temperature profiles calculated from this work to those found using numerical methods for both gray and non-gray cases. The combined conduction-radiation model is then applied to determine the temperature profile in a ceramic thermal barrier coating designed to protect super alloy turbine blades from large and extended heat loads. Inverse methods are implemented in the development of a non-contact method of measuring the properties and temperatures within the thermal barrier coating. Numerical experiments are performed to assess the effectiveness of this measurement technique. The combined conduction-radiation model is also applied to determine the temperature profile along the fiber of an optical fiber thermometer. An optical fiber thermometer consists of an optical fiber whose sensing tip is coated with an opaque material which emits radiative energy along the fiber to a detector. Inverse methods are used to infer the tip temperature from spectral measurements made by the detector. Numerical experiments are conducted to assess the effectiveness of these methods. Experimental processes are presented in which a coating is applied to the end of an optical fiber and connected to an FTIR spectrometer. The system is calibrated and the inverse analysis is used to infer the tip temperature in various heat sources.

A theoretical study of convective heat transfer is presented for a laminar flow subjected to an axial variation in the external heat transfer coefficient (or dimensionless Biot number). Since conventional techniques fail for a variable boundary condition parameter, a variable eigenfunction approach is developed. An analysis is carried out for a periodic heat transfer coefficient, which serves as a model for heat transfer from a duct fitted with an array of evenly spaced fins. Three solution methods for the variable eigenfunction technique are examined: an Nth order approximation method, an iterative method and a stepwise periodic method. The stepwise periodic method provides the most convenient and accurate solution for a stepwise periodic Biot number. Graphical results match exactly to ones obtained by Charmchi and Sparrow from a finite-difference scheme. A connected region technique is also developed to provide limited exact results to test the validity of the three solution methods. The study of a finned duct by a stepwise periodic Biot number is carried out via a parametric study, an average (constant) Biot number approximation and an assumed velocity profile analysis. Results for the parametric study show that external finning yields substantial heat transfer enhancement over an unfinned duct, especially when the Biot number of the unfinned regions is low. A decrease in the interfin spacing causes increased enhancement. Variations of the period of the Biot number causes relatively small changes in enhancement as long as the ratio of finned to unfinned surface remains unchanged. An average (constant) Biot number approximation for a specified finned tube is compared to the stepwise periodic Biot number solution. The results show that the constant Biot number approximation provides accurate results. Finally, the results for the influence of the assumed velocity profile demonstrate that a constant velocity flow provides increased heat transfer and more effective enhancement by external finning than a laminar fully developed flow, especially at high Biot numbers. This study provides insight into heat transfer enhancement due to finning and also develops a solution methodology for problems involving variable boundary condition parameters.
M.S.

The solutions of nonlinear ordinary or partial differential equations are important in the study of fluid flow and heat transfer. In this thesis we apply the Homotopy Analysis Method (HAM) and obtain solutions for several fluid flow and heat transfer problems. In chapter 1, a brief introduction to the history of homotopies and embeddings, along with some examples, are given. The application of homotopies and an introduction to the solutions procedure of differential equations (used in the thesis) are provided. In the chapters that follow, we apply HAM to a variety of problems to highlight its use and versatility in solving a range of nonlinear problems arising in fluid flow. In chapter 2, a viscous fluid flow problem is considered to illustrate the application of HAM. In chapter 3, we explore the solution of a non-Newtonian fluid flow and provide a proof for the existence of solutions. In addition, chapter 3 sheds light on the versatility and the ease of the application of the Homotopy Analysis Method, and its capability in handling non-linearity (of rational powers). In chapter 4, we apply HAM to the case in which the fluid is flowing along stretching surfaces by taking into the effects of "slip" and suction or injection at the surface. In chapter 5 we apply HAM to a Magneto-hydrodynamic fluid (MHD) flow in two dimensions. Here we allow for the fluid to flow between two plates which are allowed to move together or apart. Also, by considering the effects of suction or injection at the surface, we investigate the effects of changes in the fluid density on the velocity field. Furthermore, the effect of the magnetic field is considered. Chapter 6 deals with MHD fluid flow over a sphere. This problem gave us the first opportunity to apply HAM to a coupled system of nonlinear differential equations. In chapter 7, we study the fluid flow between two infinite stretching disks. Here we solve a fourth order nonlinear ordinary differential equation. In chapter 8, we apply HAM to a nonlinear system of coupled partial differential equations known as the Drinfeld Sokolov equations and bring out the effects of the physical parameters on the traveling wave solutions. Finally, in chapter 9, we present prospects for future work.
Ph.D.
Department of Mathematics
Sciences
Mathematics PhD

The performance of regenerative miniature refrigerators is governed by heat transfer and pressure drop losses, particularly in the regenerator. Steady flow experiments have been performed on various regenerator matrices at cryogenic temperatures and heat transfer from helium gas to the matrix, and pressure drop across the matrix have been determined. These data have been found to be in reasonable agreement with data obtained by other workers using transient flow techniques. In order to determine the applicability of such data to the performance of a cooling engine, experimental methods have been developed to measure the performance and losses in a working Stirling-cycle miniature refrigerator. These techniques have led to the analysis of pressure drop and shuttle heat transfer losses, regenerator efficiency, and to the measurement of other losses in the refrigerator. An energy balance is performed on the machine. These novel techniques, which allow the factors determining poor performance of a working refrigerator to be measured in situ, may be applied profitably to other cyclic machines.

Thesis: S.M., Massachusetts Institute of Technology, Department of Aeronautics and Astronautics, 2014.
Cataloged from PDF version of thesis.
Includes bibliographical references (pages 143-151).
Heat transfer between a conductive solid and an adjacent convective fluid is prevalent in many aerospace systems. The ability to achieve accurate predictions of the coupled heat interaction is critical in advancing thermodynamic designs. Despite their growing use, coupled fluid-solid analyses known as conjugate heat transfer (CHT) are hindered by the lack of automation and robustness. The mesh generation process is still highly dependent on user experience and resources, requiring time-consuming involvement in the analysis cycle. This thesis presents work toward developing a robust PDE solution framework for CHT simulations that autonomously provides reliable output predictions. More specifically, the framework is comprised of the following components: a simplex cut-cell technique that generates multi-regioned meshes decoupled from the design geometry, a high-order discontinuous Galerkin (DG) discretization, and an anisotropic output-based adaptation method that autonomously adapts the mesh to minimize the error in an output of interest. An existing cut-cell technique is first extended to generate fully-embedded meshes with multiple sub-domains. Then, a coupled framework that combines separate disciplines is developed, while ensuring compatibility between the cut-cell and mesh adaptation algorithms. Next, the framework is applied to high-order discretizations of the heat, Navier-Stokes, and Reynolds-Averaged Navier-Stokes (RANS) equations to analyze the heat flux interaction. Through a series of numerical studies, high-order accurate outputs solved on autonomously controlled cut-cell meshes are demonstrated. Finally, the conjugate solutions are analyzed to gain physical insight to the coupled interaction.
by Steven Matthew Ojeda.
S.M.

Doctor of Philosophy
Department of Mathematics
Alexander G. Ramm
In this dissertation, the author presents two independent researches on inverse problems: (1) creating materials in which heat propagates a long a line and (2) 3D inverse scattering problem with non-over-determined data. The theories of these methods were developed by Professor Alexander Ramm and are presented in Chapters 1 and 3. The algorithms and numerical results are taken from the papers of Professor Alexander Ramm and the author and are presented in Chapters 2 and 4.

Bon nombre de problèmes d’ingénierie requièrent l’estimation de l’état de systèmes dynamiques. La modélisation de l’espace des états du système est faite à travers un vecteur d’état qui contient toutes informations utiles pour la description du système. Les problèmes d’estimation d’état sont aussi connus comme problèmes inverses non stationnaires. Ils sont d'un grand intérêt dans de nombreuses applications pratiques, afin de produire une estimation séquentielle des variables souhaitées, à partir de modèles stochastiques et de mesures expérimentales. Ceci dans le but d’optimiser statistiquement l’erreur. Ce travail a pour objectif d’appliquer des méthodes de Filtres à Particules à des thermiques et de combustion. Ces algorithmes sont appliqués successivement à un problème de conduction de chaleur, à un problème de solidification et finalement à un problème de propagation d’incendies.

The present study considers the numerical simulation of the different flow characteristics involved in the conjugate heat transfer analysis of an internally cooled gas turbine blade. Conjugate simulations require full coupling of convective heat transfer in fluid regions to the heat diffusion in solid regions. Therefore, accurate prediction of heat transfer quantities on both external and internal surfaces has the uppermost importance and highly connected with the performance of the employed turbulence models. The complex flow on both surfaces of the internally cooled turbine blades is caused from the boundary layer laminar-to-turbulence transition, shock wave interaction with boundary layer, high streamline curvature and sequential flow separation. In order to discover the performances of different turbulence models on these flow types, analyses have been conducted on five different experimental studies each concerned with different flow and heat transfer characteristics. Each experimental study has been examined with four different turbulence models available in the commercial software (ANSYS FLUENT13.0) to decide most suitable RANS-based turbulence model. The Realizable k-&epsilon
model, Shear Stress Transport k-&omega
model, Reynolds Stress Model and V2-f model, which became increasingly popular during the last few years, have been used at the numerical simulations. According to conducted analyses, despite a few unreasonable predictions, in the majority of the numerical simulations, V2-f model outperforms other first-order turbulence models (Realizable k-&epsilon
and Shear Stress Transport k-&omega
) in terms of accuracy and Reynolds Stress Model in terms of convergence.

Research is performed to assess the viability of applying the least squares model to one-dimensional heat transfer and Euler-Bernoulli Beam Theory problems. Least squares models were developed for both the full and mixed forms of the governing one-dimensional heat transfer equation along weak form Galerkin models. Both least squares and weak form Galerkin models were developed for the first order and second order versions of the Euler-Bernoulli beams. Several numerical examples were presented for the heat transfer and Euler- Bernoulli beam theory. The examples for heat transfer included: a differential equation having the same form as the governing equation, heat transfer in a fin, heat transfer in a bar and axisymmetric heat transfer in a long cylinder. These problems were solved using both least squares models, and the full form weak form Galerkin model. With all four examples the weak form Galerkin model and the full form least squares model produced accurate results for the primary variables. To obtain accurate results with the mixed form least squares model it is necessary to use at least a quadratic polynominal. The least squares models with the appropriate approximation functions yielde more accurate results for the secondary variables than the weak form Galerkin. The examples presented for the beam problem include: a cantilever beam with linearly varying distributed load along the beam and a point load at the end, a simply supported beam with a point load in the middle, and a beam fixed on both ends with a distributed load varying cubically. The first two examples were solved using the least squares model based on the second order equation and a weak form Galerkin model based on the full form of the equation. The third problem was solved with the least squares model based on the second order equation. Both the least squares model and the Galerkin model calculated accurate results for the primary variables, while the least squares model was more accurate on the secondary variables. In general, the least-squares finite element models yield more acurate results for gradients of the solution than the traditional weak form Galkerkin finite element models. Extension of the present assessment to multi-dimensional problems and nonlinear provelms is awaiting attention.

In this work, three novel, locally conservative Galerkin methods in their semi-implicit form are developed for one dimensional blood flow and heat transfer modelling in a human arterial network. The study is also extended for predicting aging effects on the circulation function with an associated thermoregulatory mechanism. These semi-implicit discretizations are the second order Taylor expansion (SILCG-TE) method, the streamline upwind Petrov-Galerkin (SILCG-SUPG) procedure and the backward in time and central in space (SILCG-BTCS) method. In the well established fully explicit locally conservative Galerkin method (LCG), enforcement of the flux continuity condition at the element interfaces allows solving the discretized system of equations at the element level. For problems with a large number of degrees of freedoms, this offers a significant advantage over the standard continuous Galerkin (CG) procedure. The original explicit LCG method is used for assessing the accuracy of the proposed new methods. First, mass and momentum equations are solved in the whole system of 91 arterial segments by using the proposed techniques. Results demonstrate that the proposed SILCG methods are stable and as accurate as the explicit LCG method. Among the three methods proposed, the SILCG-BTCS method requires considerably lower number of iterations per element, and thus requires the lowest amount of CPU time. On the other hand, the SILCG-TE and SILCG-SUPG methods are stable and accurate for larger time step sizes due to the presence of the stabilization terms from Taylor expansion based approach and streamline upwind Petrov-Galerkin method. Second, the three approaches are extended to the heat problem by solving the energy equation and combining with blood flow. Here, the interaction between temperature and flexible vessels is tackled. Again, the outcomes show that the new techniques provide desirable accuracy and stability similar to the flow. As SILCG-BTCS is the simplest and fastest one for flow and the same conclusions are derived for heat transfer. Similarly, SLICG-TE and SILCG-SUPG methods still admit higher time steps. Finally, ageing effect is considered on both flow and heat in a human body. The methods presented previously are adapted by changing the necessary parameters related to ageing. The results obtained confirm the ability of the proposed methods for predicting the changes that occur with age such as the changes in blood pressure, flow and heat transfer. Significant consequences of ageing are highlighted.

A weakly ionized hypersonic flow solver for the simulation of reentry flow is firstly developed at the University of Kentucky. This code is the fluid dynamics module of known as Kentucky Aerothermodynamics and Thermal Response System (KATS). The solver uses a second-order finite volume approach to solve the laminar Navier– Stokes equations, species mass conservation and energy balance equations for flow in chemical and thermal non-equilibrium state, and a fully implicit first-order backward Euler method for the time integration. The hypersonic flow solver is then extended to account for very low Mach number flow using the preconditioning and switch of the convective flux scheme to AUSM family. Additionally, a multi-species preconditioner is developed. The following part of this work involves the coupling of a free flow and a porous medium flow. A new set of equation system for both free flows and porous media flows is constructed, which includes a Darcy–Brinkmann equation for momentum, mass conservation, and energy balance equation. The volume-average technique is used to evaluate the physical properties in the governing equations. Instead of imposing interface boundary conditions, this work aims to couple the free/porous problem through flux balance, therefore, flow behaviors at the interface are satisfied implicitly.

A methodology is formulated for the solution of the inverse problem concerned with the reconstruction of multi-dimensional heat fluxes for film cooling applications. The motivation for this study is the characterization of complex thermal conditions in industrial applications such as those encountered in film cooled turbomachinery components. The heat conduction problem in the metal endwall/shroud is solved using the boundary element method (bem), and the inverse problem is solved using a genetic algorithm (ga). Thermal conditions are overspecified at exposed surfaces amenable to measurement, while the temperature and surface heat flux distributions are unknown at the film cooling hole/slot walls. The latter are determined in an iterative process by developing two approaches. The first approach, developed for 2d applications, solves an inverse problem whose objective is to adjust the film cooling hole/slot wall temperatures and heat fluxes until the temperature and heat flux at the measurement surfaces are matched in an overall heat conduction solution. The second approach, developed for 2d and 3d applications, is to distribute a set of singularities (sinks) at the vicinity of the cooling slots/holes surface inside a fictitious extension of the physical domain or along cooling hole centerline with a given initial strength distribution. The inverse problem iteratively alters the strength distribution of the singularities (sinks) until the measuring surfaces heat fluxes are matched. The heat flux distributions are determined in a post-processing stage after the inverse problem is solved. The second approach provides a tremendous advantage in solving the inverse problem, particularly in 3d applications, and it is recommended as the method of choice for this class of problems. It can be noted that the ga reconstructed heat flux distributions are robust, yielding accurate results to both exact and error-laden inputs. In all cases in this study, results from experiments are simulated using a full conjugate heat transfer (cht) finite volume models which incorporate the interactions of the external convection in the hot turbulent gas, internal convection within the cooling plena, and the heat conduction in the metal endwall/shroud region. Extensive numerical investigations are undertaken to demonstrate the significant importance of conjugate heat transfer in film cooling applications and to identify the implications of various turbulence models in the prediction of accurate and more realistic surface temperatures and heat fluxes in the cht simulations. These, in turn, are used to provide numerical inputs to the inverse problem. Single and multiple cooling slots, cylindrical cooling holes, and fan-shaped cooling holes are considered in this study. The turbulence closure is modeled using several two-equation approach, the four-equation turbulence model, as well as five and seven moment reynolds stress models. The predicted results, by the different turbulence models, for the cases of adiabatic and conjugate models, are compared to experimental data reported in the open literature. Results show the significant effects of conjugate heat transfer on the temperature field in the film cooling hole region, and the additional heating up of the cooling jet itself. Moreover, results from the detailed numerical studies presented in this study validate the inverse problem approaches and reveal good agreement between the bem/ga reconstructed heat fluxes and the cht simulated heat fluxes along the inaccessible cooling slot/hole walls
Ph.D.
Department of Mechanical, Materials and Aerospace Engineering;
Engineering and Computer Science
Mechanical Engineering

The optimal design of energy systems is a challenge due to the large design space and the complexity of the tightly-coupled multi-physics phenomena involved. Standard design methods consider a reduced design space, which heavily constrains the final geometry, suppressing the emergence of design trends. On the other hand, advanced design methods are often applied to academic examples with reduced physics complexity that seldom provide guidelines for real-world applications. This dissertation offers a systematic framework for the optimal design of energy systems by coupling detailed physical analysis and topology optimization. Contributions entail both method-related and application-oriented innovations. The method-related advances stem from the modification of topology optimization approaches in order to make practical improvements to selected energy systems. We develop optimization models that respond to realistic design needs, analysis models that consider full physics complexity and design models that allow dramatic design changes, avoiding convergence to unsatisfactory local minima and retaining analysis stability. The application-oriented advances comprise the identification of novel optimized geometries that largely outperform industrial solutions. A thorough analysis of these configurations gives insights into the relationship between design and physics, revealing unexplored design trends and suggesting useful guidelines for practitioners. Three different problems along the energy chain are tackled. The first one concerns thermal storage with latent heat units. The topology of mono-scale and multi-scale conducting structures is optimized using both density-based and level-set descriptions. The system response is predicted through a transient conjugate heat transfer model that accounts for phase change and natural convection. The optimization results yield a large acceleration of charge and discharge dynamics through three-dimensional geometries, specific convective features and optimized assemblies of periodic cellular materials. The second problem regards energy distribution with district heating networks. A fully deterministic robust design model and an adjoint-based control model are proposed, both coupled to a thermal and fluid-dynamic analysis framework constructed using a graph representation of the network. The numerical results demonstrate an increased resilience of the infrastructure thanks to particular connectivity layouts and its rapidity in handling mechanical failures. Finally, energy conversion with proton exchange membrane fuel cells is considered. An analysis model is developed that considers fluid flow, chemical species transport and electrochemistry and accounts for geometry modifications through a density-based description. The optimization results consist of intricate flow field layouts that promote both the efficiency and durability of the cell.

This thesis proposes a coupled continuous and hybridizable discontinuous Galerkin formulation to solve conjugate heat transfer problems. This model is then used to find the thermal response of Glass Fiber Reinforced Polymer (GFRP) tubular cross-section under fire. The first step of this thesis is to compare the computational efficiency of high-order Continuous Galerkin (CG) and Hybridizable Discontinuous Galerkin (HDG) methods for incompressible fluid flow problems in low Reynolds number regimes. Only 2-D examples and direct solvers are considered in the present work. A thoroughly comparison in terms of CPU time and accuracy for both discretization methods is made under the same platform. Various results presented suggests that HDG can be more efficient than CG when the CPU time, for a given degree, is considered. The stability of HDG and CG is studied using a manufactured solution that produces a sharp boundary layer, confirming that HDG provides smooth converged solutions in the presence of sharp fronts whereas, CG failed to converge due to the presence of numerical oscillations. Following, the solution of the coupled Navier-Stokes/convection-diffusion problem, using Boussinesq approximation, is formulated within the HDG framework and analysed using numerical experiments and benchmark problems. A coupling strategy between HDG and CG methods is proposed in the framework of second-order elliptic operators. The coupled formulation is implemented and its convergence properties are established numerically by using manufactured solutions. Finally, the proposed coupled formulation between HDG and CG for heat equation is combined with the coupled Navier--Stokes/convection diffusion equations to formulate a new CG-HDG model for solving conjugate heat transfer problems. Benchmark examples are solved using the proposed model and validated with literature values. The final part of the thesis applies the proposed CG-HDG coupled formulation to predict the thermal response of the GFRP tubular cross-section. The radiosity equation that governs the internal radiation is added to the CG-HDG coupled model. Estimates of the discretization errors are computed in order to establish the confidence intervals for quantities of interest. Results with the geometry having curved corners in the cavity are presented and shown to be within the estimated uncertainty intervals. CPU times for the linear solver suggests that the proposed CG-HDG model is more efficient than CG-CG model in all the cases considered.
Neste trabalho é proposta uma formulação para acoplar os modelos continuous e hybridizable discontinuous Galerkin a fim de analisar problemas conjugados de transferência de calor. Este modelo é então usado para estudar a resposta térmica de perfis pultrudidos de secção tubular em polímero reforçado com fibras de vidro (GFRP) sob a acção do fogo. O primeiro passo desta tese é comparar a eficiência computacional dos métodos Continuous Galerkin (CG) e Hybridizable Discontinuous Galerkin (HDG) de elevada ordem para problemas de escoamento de fluidos incompressíveis para valores reduzidos do número Reynolds. Apenas exemplos bidimensionais e métodos directos são considerados no presente trabalho. Uma comparação exaustiva em termos de tempo de CPU e precisão para ambos os métodos de discretização é efectuada sob uma plataforma comum. Os resultados apresentados sugerem que, em termos do tempo de CPU requerido, o HDG pode ser mais eficiente que o CG, para um determinado grau. A estabilidade do HDG e CG é estudada usando uma solução fabricada que produz uma abrupta descontinuidade, confirmando que o HDG fornece soluções convergentes e suaves na presença de descontinuidades, enquanto o CG não conseguiu convergir devido à presença de oscilações numéricas. Em seguida, a solução do problema acoplado Navier-Stokes/convecção-difusão, utilizando a aproximação de Boussinesq, é formulada no contexto HDG e analisada usando soluções de referência. Uma estratégia de acoplamento entre os métodos HDG e CG é proposta no âmbito de operadores elípticos de segunda ordem. A formulação acoplada é implementada e suas propriedades de convergência são estabelecidas numericamente usando soluções fabricadas. Finalmente, a formulação acoplada proposta entre HDG e CG para a equação do calor é combinada com as equações acopladas de Navier-Stokes/convecção-difusão para formular um novo modelo de CG-HDG para resolver problemas de transferência de calor conjugado. Exemplos de referência são resolvidos usando o modelo proposto e validados com valores de literatura. A parte final da tese aplica a formulação proposta CG-HDG acoplada para prever a resposta térmica de uma secção transversal tubular de GFRP. A equação de radiosidade que governa a radiação interna é adicionada ao modelo acoplado CG-HDG. Os erros de discretização são calculados para estabelecer os intervalos de confiança para quantidades de interesse. Resultados considerando a geometria circular dos cantos da cavidade são apresentados. Estes estão dentro do intervalo de incerteza estimado. Os tempos de CPU requeridos para resolver os sistemas de equações lineares sugerem que o modelo proposto CG-HDG é mais eficiente do que o modelo CG-CG em todos os casos considerados.
En esta tesis se propone una formulación acoplada del método de los elementos finitos clásico (CG) y el método Hybridizable Discontinuous Galerkin (HDG) para la a solución de problemas térmicos conjugados. El modelo se utiliza para determinar la respuesta al fuego de Polímeros Reforzados con Fibras de Vidrio (GFRP) con sección tubular. El primer paso de la tesis es la comparación de la eficiencia computacional de CG y HDG de alto orden para problemas de flujo incompresible para número de Reynolds (Re) bajo. Se consideran sólo ejemplos 2D y métodos de resolución de sistemas lineales directos. Se presenta una comparación en términos de tiempo de CPU y precisión en la solución para ambas discretizaciones, bajo la misma plataforma de implementación. Los resultados sugieren que HDG puede ser más eficiente computacionalmente que CG en tiempo de CPU, para un grado fijado. La estabilidad de HDG y CG para Re alto se estudia con una solución manufacturada que produce un frente pronunciado, confirmando que HDG proporciona soluciones convergidas suaves en presencia de frentes verticales, en casos en que las oscilaciones numéricas de CG no permiten llegar a convergencia. A continuación, se plantea la solución del problema acoplado Navier-Stokes/convección-difusión, con la aproximación de Boussinesq, en el contexto del método HDG, y se analiza con experimentos numéricos. Se propone una formulación acoplada HDG-CG para la ecuación del calor. Se comprueban numéricamente las propiedades de convergencia del método propuesto. Finalmente, se combina la formulación acoplada propuesta para la ecuación del calor con el acoplamiento con la ecuaciones de Navier-Stokes en el dominio del fluido, creando una nueva formulación CG-HDG para problemas térmicos conjugados. Se consideran tests clásicos para validar los resultados comparando con la literatura existente. La parte final de la tesis aplica la formulación acoplada CG-HDG propuesta a la predicción de la respuesta térmica de secciones tubulares de GFRP, incluyendo radiosidad interna en el modelo. Se calculan estimas de los errores de discretización para determinar intervalos de confianza para las cantidades de interés. Se presentan resultados con geometría con esquinas curvas en la cavidad mostrando resultados dentro de los intervalos de incertidumbre estimados. El tiempo de CPU para la resolución de sistemas sugiere que el modelo CG-HDG propuesto es más eficiente que el clásico método CG-CG en todos los casos considerados.
This thesis proposes a coupled continuous and hybridizable discontinuous Galerkin formulation to solve conjugate heat transfer problems. This model is then used to find the thermal response of Glass Fiber Reinforced Polymer (GFRP) tubular cross-section under fire. The first step of this thesis is to compare the computational efficiency of high-order Continuous Galerkin (CG) and Hybridizable Discontinuous Galerkin (HDG) methods for incompressible fluid flow problems in low Reynolds number regimes. Only 2-D examples and direct solvers are considered in the present work. A thoroughly comparison in terms of CPU time and accuracy for both discretization methods is made under the same platform. Various results presented suggests that HDG can be more efficient than CG when the CPU time, for a given degree, is considered. The stability of HDG and CG is studied using a manufactured solution that produces a sharp boundary layer, confirming that HDG provides smooth converged solutions in the presence of sharp fronts whereas, CG failed to converge due to the presence of numerical oscillations. Following, the solution of the coupled Navier–Stokes/convection-diffusion problem, using Boussinesq approximation, is formulated within the HDG framework and analysed using numerical experiments and benchmark problems. A coupling strategy between HDG and CG methods is proposed in the framework of second-order elliptic operators. The coupled formulation is implemented and its convergence properties are established numerically by using manufactured solutions. Finally, the proposed coupled formulation between HDG and CG for heat equation is combined with the coupled Navier–Stokes/convection diffusion equations to formulate a new CG-HDG model for solving conjugate heat transfer problems. Benchmark examples are solved using the proposed model and validated with literature values. The final part of the thesis applies the proposed CG-HDG coupled formulation to predict the thermal response of the GFRP tubular cross-section. The radiosity equation that governs the internal radiation is added to the CG-HDG coupled model. Estimates of the discretization errors are computed in order to establish the confidence intervals for quantities of interest. Results with the geometry having curved corners in the cavity are presented and shown to be within the estimated uncertainty intervals. CPU times for the linear solver suggests that the proposed CG-HDG model is more efficient than CG-CG model in all the cases considered
Neste trabalho é proposta uma formulação para acoplar os modelos continuous e hybridizable discontinuous Galerkin a fim de analisar problemas conjugados de transferência de calor. Este modelo é então usado para estudar a resposta térmica de perfis pultrudidos de secção tubular em polímero reforçado com fibras de vidro (GFRP) sob a acção do fogo. O primeiro passo desta tese é comparar a eficiência computacional dos métodos continuous Galerkin (CG) e Hybridizable Discontinuous Galerkin (HDG) de elevada ordem para problemas de escoamento de fluidos incompressíveis para valores reduzidos do número Reynolds. Apenas exemplos bidimensionais e métodos directos são considerados no presente trabalho. Uma comparação exaustiva em termos de tempo de CPU e precisão para ambos os métodos de discretização é efectuada sob uma plataforma comum. Os resultados apresentados sugerem que, em termos do tempo de CPU requerido, o HDG pode ser mais eficiente que o CG, para um determinado grau. A estabilidade do HDG e CG é estudada usando uma solução fabricada que produz uma abrupta descontinuidade, confirmando que o HDG fornece soluções convergentes e suaves na presença de descontinuidades, enquanto o CG não conseguiu convergir devido à presença de oscilações numéricas. Em seguida, a solução do problema acoplado Navier-Stokes/convecção-difusão, utilizando a aproximação de Boussinesq, é formulada no contexto HDG e analisada usando soluções de referência. Uma estratégia de acoplamento entre os métodos HDG e CG é proposta no âmbito de operadores elípticos de segunda ordem. A formulação acoplada é implementada e suas propriedades de convergência são estabelecidas numericamente usando soluções fabricadas. Finalmente, a formulação acoplada proposta entre HDG e CG para a equação do calor é combinada com as equações acopladas de Navier-Stokes/convecção-difusão para formular um novo modelo de CG-HDG para resolver problemas de transferência de calor conjugado. Exemplos de referência são resolvidos usando o modelo proposto e validados com valores de literatura. A parte final da tese aplica a formulação proposta CG-HDG acoplada para prever a resposta térmica de uma secção transversal tubular de GFRP. A equação de radiosidade que governa a radiação interna é adicionada ao modelo acoplado CG-HDG. Os erros de discretização são calculados para estabelecer os intervalos de confiança para quantidades de interesse. Resultados considerando a geometria circular dos cantos da cavidade são apresentados. Estes estão dentro do intervalo de incerteza estimado. Os tempos de CPU requeridos para resolver os sistemas de equações lineares sugerem que o modelo proposto CG-HDG é mais eficiente do que o modelo CG-CG em todos os casos considerados.
En esta tesis se propone una formulación acoplada del método de los elementos finitos clásico (CG) y el método Hybridizable Discontinuous Galerkin (HDG) para la a solución de problemas térmicos conjugados. El modelo se utiliza para determinar la respuesta al fuego de Polímeros Reforzados con Fibras de Vidrio (GFRP) con sección tubular. El primer paso de la tesis es la comparación de la eficiencia computacional de CG y HDG de alto orden para problemas de flujo incompresible para número de Reynolds (Re) bajo. Se consideran sólo ejemplos 2D y métodos de resolución de sistemas lineales directos. Se presenta una comparación en términos de tiempo de CPU y precisión en la solución para ambas discretizaciones, bajo la misma plataforma de implementación. Los resultados sugieren que HDG puede ser más eficiente computacionalmente que CG en tiempo de CPU, para un grado fijado. La estabilidad de HDG y CG para Re alto se estudia con una solución manufacturada que produce un frente pronunciado, confirmando que HDG proporciona soluciones convergidas suaves en presencia de frentes verticales, en casos en que las oscilaciones numéricas de CG no permiten llegar a convergencia. A continuación, se plantea la solución del problema acoplado Navier-Stokes/conveccióndifusión, con la aproximación de Boussinesq, en el contexto del método HDG, y se analiza con experimentos numéricos. Se propone una formulación acoplada HDG-CG para la ecuación del calor. Se comprueban numéricamente las propiedades de convergencia del método propuesto. Finalmente, se combina la formulación acoplada propuesta para la ecuación del calor con el acoplamiento con la ecuaciones de Navier-Stokes en el dominio del fluido, creando una nueva formulación CG-HDG para problemas térmicos conjugados. Se consideran ejemplos clásicos para validar los resultados comparando con la literatura existente. La parte final de la tesis aplica la formulación acoplada CG-HDG propuesta a la predicción de la respuesta térmica de secciones tubulares de GFRP, incluyendo radiosidad interna en el modelo. Se calculan estimas de los errores de discretización para determinar intervalos de confianza para las cantidades de interés. Se presentan resultados con geometría con esquinas curvas en la cavidad mostrando resultados dentro de los intervalos de incertidumbre estimados. El tiempo de CPU para la resolución de sistemas sugiere que el modelo CG-HDG propuesto es más eficiente que el clásico método CG-CG en todos los casos considerados.

Compte tenu de l'importance de maintenir une qualité optimale des cordons de soudure et l'impossibilité d'assurer tout risque de manque de pénétration et de fusion par des contrôles non-destructifs, cette thèse permettra de développer une expertise et des outils numériques pour la simulation numérique tridimensionnelle des procédés de soudage par fusion afin de prédire la géométrie finale du cordon. Pour ce faire, on implémente une méthode de suivi d'interface afin d'améliorer la prise en compte des phénomènes thermophysiques au niveau des surfaces libres déformables. Cela permettra en outre de prendre en compte les forces agissant à la surface du bain métallique telles que la tension de surface, la gravité et la pression d'arc. Puis, il est envisagé d'améliorer l'estimation du transfert thermique entre l'arc et les pièces à assembler via un couplage instationnaire des modèles de plasma et de bain de fusion pour ainsi simuler de façon optimale la forme finale du cordon de soudure. Cette thèse permettra de traiter certaines applications industrielles spécifiques à EDF, en particulier les soudures d'étanchéité de faible épaisseur, permettant des études approfondies sur les opérations de réparations par soudage en corniche
In order to ensure total safety during maintenance operations within nuclear power plants, it is mandatory to preserve the optimal quality of the internal weld beads. To this end, we use Computational Magnetohydrodynamics to simulate adjacent phenomena within the plasma and the weld pool in order to improve the knowledge of welding operating process. One of the difficulties is to take into account the effects induced by the thermal gradient and the variations of surfactant element concentrations on the weld pool surface known as the Marangoni effect. In order to take into account all the physical phenomena at the plasma / weld pool interface, we use an interface tracking method (Arbitrary Lagrangian-Eulerian) to improve the simulation of weld pool with free surfaces. Subsequently, it enables to capture more precisely the interfacial forces such as the Marangoni effect, the arc pressure and the gravity, and improve vertical welding simulation. Thus, this work is part of the development of a tridimensional unsteady two-way coupling in order to overcome the Gaussian boundary condition used to model the heat transfer from plasma torch towards the work piece surface. Ultimately, we could obtain an unified model for an optimal welding process simulation

Este trabalho apresenta o desenvolvimento e implementação computacional de técnicas de otimização de topologia para problemas governados pela equação de Poisson. O método numérico utilizado para solução numérica das equações foi o método dos elementos de contorno (MEC). Para tanto, três metodologias foram desenvolvidas. A primeira é direcionada à aplicação de algoritmos genéticos (AG) para investigar como um domínio inicialmente preenchido com cavidades aleatórias evolui durante um processo de otimização e verificar a possibilidade de se extrair topologias ótimas a partir da interpretação da solução encontrada. Os contornos externos permanecem fixos enquanto as posições e as dimensões das cavidades são otimizadas com o objetivo extremizar uma função custo especificada. O desempenho do algoritmo proposto é ilustrada com uma série de exemplos e os resultados são discutidos. A segunda metodologia apresenta um algoritmo numérico para otimização topológica baseado na avaliação da derivada topológica (DT), adotando a energia potencial total como função custo. Este procedimento é uma alternativa às tradicionais técnicas de otimização, evitando assim soluções de projeto com densidade de material intermediária. Sólidos com comportamento anisotrópico são estudados sob condições de contorno de Robin, Neumann e Dirichlet. Uma transformação linear de coordenadas é utilizada para mapear o problema original e suas condições de contorno para um novo domínio equivalente isotrópico, onde o procedimento de otimização é aplicado. A solução otimizada é então transformada de volta ao domínio original. A metodologia proposta mostrou-se particularmente atrativa para resolver esta classe de problemas já que o MEC dispensa o uso de malha no domínio, reduzindo significantemente o custo computacional. Na última parte deste trabalho foi implementada uma formulação de sensibilidade topológica para problemas de otimização de transferência de calor e massa simultâneos. Como as sensibilidades para cada equação diferencial são diferentes, utiliza-se um coeficiente de ponderação para compor a sensibilidade do problema acoplado. Isto permite a imposição de distintos fatores para cada problema, de acordo com uma prioridade especificada. Diversos exemplos são apresentados e seus resultados comparados com os da literatura, quando disponíveis, a fim de validar as formulações propostas.
This work presents the computational development and implementation of topology optimization techniques for problems governed by the Poisson equation. The boundary element method was the numerical technique chosen to solve the equations. Three different methodologies were developed aiming this objective. The first methodology is directed to the application of genetic algorithms to investigate how a domain previously populated with randomly placed cavities evolves during the optimization process, and to verify the resemblance of the final solution with a optimal design. The external boundaries remain fixed during the process, while the location and dimension of the cavities are optimized in order to extremize a given cost function. The performance of the proposed algorithm is verified with a number of examples and the results are discussed. The second methodology presents a numerical algorithm for topology optimization based on the evaluation of topological derivatives, using the total potential energy as the cost function. This procedure is an alternative to the traditional optimization techniques, avoiding design solutions containing intermediary material densities. Solids with anisotropic constitutive behavior are studied under Robin, Neumann and Dirichlet boundary conditions. A linear coordinate transformation approach is used to map the original problem into an isotropic one, where the optimization is carried out. The final solution is then mapped back to the original coordinate system. The proposed method was found to be an attractive way to solve this class of problems, since no interior mesh is necessary, which reduces significantly the computational cost of the analysis. In the last part of the present work the topological derivative approach was further developed to deal with the optimization of problems under simultaneous heat and mass transfer. Since the sensitivities for each differential equation are different, a weighting factor was used to evaluate the final sensitivities of the coupled problem. This allows the imposition of different priorities for each problem Several examples are presented and their results are compared with the literature, when available, in order to validate the proposed formulations.

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The simultaneous heat and mass transfer phenomenon presents on the absorbers of the absorption refrigeration machine was studied by Generalized Integral Transform Technique GITT, for three practical interest cases with growing degree of difficulty in your mathematical formulation. The two first occur over an inclined flat plane with laminar flow regime. It is considered the fully developed flow and obtained the explicit velocity profile with constant thickness film. The adiabatic and isothermal wall is analyzed. The third case, that represent a real condition of operation occur over external surface of a single tube. It models the falling film on a tube where the thickness of the film varies along the perimeter. The phenomenon studied, classified like diffusion problem coupled, presents a strong couplement on the liquid-vapor interface and so, the energy and concentration equations are simultaneously solved. The solutions are obtained from two auxiliary eigenvalues problems for concentration and energy problems. Following the GITT formalism, a hybrid analyticnumerical solution to the potentials is described. Results of practical interest are found such as Sherwood and Nusselt numbers, mass flux in the interface and average potentials.
O fenômeno da transferência simultânea de calor e massa presente nos absorvedores das máquinas de refrigeração por absorção foi estudado pela Técnica da Transformada Integral Generalizada, do inglês Generalized Integral Transform Technique GITT, para três casos de interesse prático com crescente grau de dificuldade em sua formulação matemática. Os dois primeiros se referem a uma placa plana inclinada com escoamento em regime laminar, com perfil de velocidades conhecido e com a espessura da película constante ao longo do escoamento. Esta situação é examinada para as condições limites: parede adiabática e parede isotérmica. O terceiro caso, mais próximo da condição real de operação, modela o escoamento sobre um tubo onde a espessura da película varia ao longo do perímetro. O fenômeno, classificado como problema de difusão acoplado, apresenta um forte acoplamento na interface líquido-vapor e com isso as equações que representam as distribuições de energia e concentração da película líquida durante o escoamento, não podem ser solucionadas separadamente. A solução é construída com base em dois problemas auxiliares: um para a energia e outro para a concentração. Seguindo o formalismo da GITT, os potenciais são obtidos de forma híbrida analítico-numérico. Resultados de interesse práticos são obtidos como números de Sherwood e de Nusselt, bem como o fluxo de massa na interface e os potenciais médios.

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This work presents a 3D computational/mathematical model to solve the heat diffusion equation with phase change, considering addition of material and complex geometry. The finite volume method was used and the computational code was implemented in C++, using Borland compiler. Experimental tests were carried out for validation of the model in question. It was used a material whose thermal properties, varying with temperature, are well known: the stainless steel AISI 304. In addition, an inverse technique based on Golden Section was implemented to estimate the heat flux supplied to the sample. Experimental temperatures were measured using thermocouples type J - in a total of 07 (seven) - all connected to the metal sheet and the Agilent 34970A datalogger. The metal had a \"V\" Groove of 45°. In this location was conducted the deposition of material on only one welding pass and the dimensions (width and height) were measured after welding. The thermal model was validated from comparisons between measured and calculated temperatures. The results were consistent and validated the computational/mathematical model proposed. An innovation presented in this work consists in the calculation and visualization of the dimensions of the welding pool during welding. The complex geometry obtained proves that more studies are needed and new models must be designed to clarify and explain the formation of welding pool during welding of metal sheet.
Desenvolve-se, neste trabalho, um modelo matemático/computacional 3D (tridimensional) de difusão de calor com mudança de fase, acréscimo de material e geometria complexa. O método de volumes finitos foi implementado em linguagem C, utilizando o compilador Borland. Foram realizados testes experimentais para a validação do modelo em questão. Usou-se um material cujas propriedades térmicas, variando com a temperatura, são bem conhecidas: o aço inox AISI 304. Além do modelo direto já citado, foi implementada uma técnica inversa para o cálculo do fluxo de calor. Utilizou-se neste caso a amplamente conhecida Seção Áurea: técnica que exige uma simplificação, fluxo de calor constante ao longo do tempo de soldagem. As temperaturas na chapa foram medidas utilizando termopares do tipo J - em um total de 07 (sete) - todos ligados ao datalogger Agilent 34970A. As medições foram feitas do lado oposto à tocha de soldagem. A chapa metálica possuía um chanfro em V de 45º. Neste local foi realizada a deposição de material (reforço) em somente um passe de soldagem. As dimensões da geometria do reforço (largura e altura) foram medidas depois da realização da soldagem. Em relação aos resultados, além da comparação entre as temperaturas medidas e calculadas, foi também determinada a eficiência térmica da soldagem. Os resultados foram consistentes e validaram o modelo matemático/computacional proposto. Uma inovação apresentada neste trabalho consiste no cálculo e visualização gráfica tridimensional da poça de fusão ao longo do tempo. A complexa geometria obtida comprova que mais estudos se fazem necessários e que novos modelos devem ser concebidos para esclarecer e explicar a formação da poça de fusão durante a soldagem de chapas metálicas.
Doutor em Engenharia Mecânica

Numerical solutions of mathematical modelizations of heat and mass transfer in cubical and cylindrical reactors of solar adsorption refrigeration systems are studied. For the resolution of the equations describing the coupling between heat and mass transfer, Bubnov-Galerkin method is used. An exact solution for time dependent heat transfer in cylindrical multilayered annulus is presented. Separation of variables method has been used to investigate the temperature behavior. An analytical double series relation is proposed as a solution for the temperature distribution, and Fourier coefficients in each layer are obtained by solving some set of equations related to thermal boundary conditions at inside and outside of the cylinder.

Ces travaux portent sur la résolution successive de deux problèmes inverses en transferts thermiques : l'estimation de la densité de flux en surface d'un matériau puis de la conductivité thermique équivalente d'une couche déposée en surface de ce matériau. Le modèle direct est bidimensionnel orthotrope (géométrie réelle d'un matériau composite), instationnaire, non-linéaire et ses équations sont résolues par éléments finis. Les matériaux étudiés sont les composants face au plasma (tuiles composite carbone-carbone) dans le Tokamak JET. La densité de flux recherchée varie avec une dimension spatiale et avec le temps. La conductivité du dépôt de surface varie spatialement et peut également varier au cours du temps pendant l'expérience (toutes les autres propriétés thermophysiques dépendent de la température). Les deux problèmes inverses sont résolus à l'aide de l'algorithme des gradients conjugués associé à la méthode de l'état adjoint pour le calcul exact du gradient. La donnée expérimentale utilisée pour la résolution du premier problème inverse (estimation de flux surfacique) est le thermogramme fourni par un thermocouple enfoui. Le second problème inverse utilise, lui, les variations spatio-temporelles de la température de surface du dépôt inconnu (thermographie infrarouge) pour identifier sa conductivité. Des calculs de confiance associée aux grandeurs identifiées sont réalisés avec la démarche Monte Carlo. Les méthodes mises au point pendant ces travaux aident à comprendre la dynamique de l'interaction plasma-paroi ainsi que la cinétique de formation des dépôts de carbone sur les composants et aideront au design des composants des machines futures (WEST, ITER)
This work deals with the successive resolution of two inverse heat transfer problems: the estimation of surface heat flux on a material and equivalent thermal conductivity of a surface layer on that material. The direct formulation is bidimensional, orthotropic (real geometry of a composite material), unsteady, non-linear and solved by finite elements. The studied materials are plasma facing components (carbon-carbon composite tiles) from Tokamak JET. The searched heat flux density varies with time and one dimension in space. The surface layers conductivity varies spatially and can vary with time during the experiment (the other thermophysical properties are temperature dependent). The two inverse problems are solved by the conjugate gradient method with the adjoint state method for the exact gradient calculation. The experimental data used for the first inverse problem resolution (surface heat flux estimation) is the thermogram provided by an embedded thermocouple. The second inverse problem uses the space and time variations of the surface temperature of the unknown surface layer (infrared thermography) for the conductivity identification. The confidence calculations associated to the estimated values are done by the Monte Carlo approach. The method developed during this thesis helps to the understanding of the plasma-wall interaction dynamic, as well as the kinetic of the surface carbon layer formation on the plasma facing components, and will be helpful to the design of the components of the future machines (WEST, ITER)

This study compares engineering expert problem-solving on a highly constrained routine problem and an ill-defined complex problem. The participants (n=7) were recruited from two large public Research I institutions. Using a think aloud methodology, the experts solved both routine and non-routine problems. The protocols were transcribed and coded in Atlas ti. The first round of coding followed a grounded theory methodology, yielding interesting findings. Unprompted, the experts revealed a strong belief that the ill-defined problems are developmentally appropriate for PhD students while routine problems are more appropriate for undergraduate students. Additional rounds of coding were informed by previous problem solving studies in math and engineering. In general, this study confirmed the 5 Step Problem Solving Method used in previous challenged based instruction studies. There were observed differences based on problem type and background knowledge. The routine problem was more automatic and took significantly less time. The experts with higher amounts of background knowledge and experience were more likely to categorize the problems. The level of background knowledge was most apparent in the steps between conducting an overall energy balance and writing more problem specific relationships between the variables. These results are discussed in terms of their implications for improving undergraduate engineering education.
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碩士
逢甲大學
航空工程所
93
First of all, the thermal wave model is used in this study. Conventional Fourier conduction was modified by a relaxation time �鄛 between heat flux and temperature gradient. Micro-scale heat conduction in both a three dimensional orthotropic body and a two dimensional anisotropic body were studied in this study. Two coordinate transformation methods were applied to transform the orthotropic body and anisotropic body into isotropic body. Then the temperature solution in the isotropic body was obtained by the Green’s function solution method. The temperature distributions in both an orthotropic body and an anisotropic body were then available by the inverse coordinate transformation. The effect of thermal conductivity ratio in x1, x2, and, x3 directions on temperature distribution in an orthotropic body was investigate for different thermal Mach number. Furthermore, the effect of thermal conductivity ratio of k1, k2, and k12 on temperature solutions was also examined for different Mach numbers The numerical results were shown that both the speed of heat source and the thermal conductivity ratio had crucial impact on temperature distributions in the above mentioned bodies. The mechanism of four type of micro-scale heat conduction model, i.e., CV, dual-phase-lag (DPL), T-wave, and �鄛2-�賏2 models were examined. Will they violate the thermodynamic laws when the boundaries of one-dimensional slab are subjected to sudden heating or sudden cooling. These models were solved by the Laplace transform method and the Riemann sum approximation. The effect of �鄛2 and ����2 on temperature distributions in slab was studied. Finally, the numerical results were shown that the CV, T-wave, and �鄛2-�賏2 models violate the thermodynamic laws in certain cases.

碩士
國立成功大學
工程科學系碩博士班
100
As technology advances, the heat transfer behavior on a micro scale has graduallybeen taken seriously. There is not muchresearch about the micro-scale non-Fourier phase change heat transfer problems.The main focus of this paper is to use the hybrid Laplace transform method to investigate Fourier and non-Fourier phase change heat transfer problems. Hybrid Laplace transform method is used in the research, with one using Riemann sum approximation based on inverse Laplace transform method and the other using the same Riemann sum approximation and control volume method.The temperature recovery method is applied to solve numerical problem of latent heat in phase-change.To solve non-Fourier heat transfer laser problems, study focuses on the application of hybrid numerical method and the instability ensued from iteration. ∂θ(δ,0)/∂β and (∂^2 θ(δ,0))/(∂^2 δ)can lead to unstable numerical results.As a result, Laplace transform methodis applied alone with control volume method and the finite difference method to acquire modified differential term. Then comes the iteration that effectively resolves the oscillated problem. Without the oscillation, the more complicated laser heat source issue can be addressed. Using the proposed method of this thesis to calculate the non –Fourier heat transfer problems can obtain anaccurate result and solve more complicated non-Fourier phase change problem.Applying the hybrid Laplace transform method together with temperature recovery method can solve the Steven problemaccurately. The non-Fourier dual phase laser heat source phase change problem involves two processes: the melting and solidification.In melting, part of the laser energy is absorbed by latent heat, making a relatively higher point in temperature than the point that does not consider phase change.On the other hand, in solidification, the release of latent heat mitigates the thermal diffusion. That makes a relatively higher point in temperature than the point that does not consider phase change.

博士
國立成功大學
機械工程學系碩博士班
96
This article applies Grey Prediction Method of Grey System Theory to improve the problem of errors in inverse operation due to the error of temperature measurement when analyze Inverse Heat Transfer Problems (IHTP) with Reversed Matrix Method. For IHTP, this research adopted Revered Matrix Method with Linear Least-squares Error Method to construct a linear inverse model. With finite difference method, we discretized governing equation that is designed to solve IHTP to construct a linear matrix equation. Through the re-arrangement of matrix equation, the unknown conditions (such as initial conditions, boundary conditions, thermal property or geometrical shape) could be demonstrated clearly and independently. Then substitute a small amount of successive measuring points temperature into the linear inverse model and solve the problems by Linear Least-squares Error Method. The process of inverse operation only need to measure a small amount points temperature to estimate the solution of IHTP, but in practical measurement of temperature, the errors of measurement of temperature are inevitable. Such errors will affect the accuracy of estimation value of inverse operation or even lead to an erroneous results. One of improvement method is to increase the number of temperature measurement points. Certainly, more accurate results of inverse operation we want to obtain, the number of measurement points we should increase. Therefore, this research uses the Grey Prediction Method to improve the defect with a hope that significant reduction of the number of practical temperature measurement points could also obtain the same accurate results of inverse operation. The small amount of direct temperature measurement points can increase to more amount of temperature points by Grey Prediction Method, and the temperatures of those increased points could still keep the correlations with previous temperatures from direct measurement. The increased number of temperature points could replace the number of temperature points that is necessary to increase for inverse operation. In other words, Grey Prediction Method could significantly reduce the number of practical temperature measurement points while keep the same accuracy as the results of inverse operation using a great number of direct temperature measurement points.

碩士
國立成功大學
工程科學系碩博士班
93
There are many researches worked on solidification and heat transfer problems, such as the casting of sand mold, the fabrication of poly-Si thin films by using an excimer laser, the crystal growth of GaAs. When solving these problems with a single CPU computer, it may take a great deal of computing time or the node number is too big to solve the problems. The purpose of this paper is to use the parallel computing to solve the solidification and heat-transfer problem by dividing the computing domain. The numerical method is the finite difference method. To verify the feasibility of the parallel programs for solving the solidification and heat transfer problems set up in this work, firstly the one-dimensional and extended two-dimensional Stefan problems are applied. The linear system of difference equations for the two-dimensional problems is solved by using the sweep by line and Jacobi methods. After the computing results are analyzed, an optimum data-transfer mode between computers is proposed. Secondly, the Rathjen problem is utilized to prove that the parallel program and the data transfer mode can work for different boundary conditions. Finally, the computing method used in this paper is applied to the problem of the crystal growth of GaAs, which has a large node number and needs a great deal of computing time. From the computing results of the testing and practical problems, it can be verified that the parallel computing program with the proposed data-transfer mode is a feasible and appropriate way to solve a huge solidification and heat-transfer problem for different working conditions, such as different boundary conditions, numerical solvers, node numbers, etc. And the results of this study can be referred to in the future research.

碩士
國立成功大學
工程科學系碩博士班
100
Abstract This study is to use the software package COMSOL Multiphysics to analyze the nonlinear solidification or phase-change problems, the natural convection problems, the coupling of convection and solidification problems and the thermal problems in the designed Susceptor. The accuracy of COMSOL for solving nonlinear and discontinuous interface problems and that of the practical design problem are compared and analyzed. First, the Stefan and Rathjen solidification problems with exact solutions are investigated by using COMSOL. Furthermore, COMSOL is employed to study the natural convection problems and the convection and solidification problems in which the temperature and flow fields are coupled with each other. Finally, COMSOL is applied to the heater design of a Susceptor for obtaining the uniform temperature distribution. Inverse calculation is utilized to acquire the design parameters from the experimental data of the previously designed Susceptor. The heater design is modified by the COMSOL analysis. From the analysis results, it can be found that COMSOL works very well for the heater design of the Susceptor and for solving the coupling problems. However, the location prediction of the solid/liquid interface of a solidified problem is not very accurate.

碩士
國立成功大學
工程科學系碩博士班
101
Phase-change in a solidification process is a very important physical phenomenon, in which the latent-heat effect cannot be ignored. In the thesis, the finite element method with different numerical schemes of handling the latent-heat effect is used to analyze the temperature distributions of phase-change heat transfer problems. In the work, the one-dimensional Stefan and the two-dimensional Rathjen problems are numerically studied. The effective specific heat and the specific heat/enthalpy methods are employed to deal with the latent-heat effect and the accuracy and CPU time of these schemes are compared and analyzed. From the results, it can be found that the latter method could solve the problems more accurately and faster than the former one. With different integration methods and numbers of integration points, the rectangle and triangle elements are utilized to study the phase-change problems. The total error is used to compare the solution accuracies of these schemes. The closed-form integration formula is not a good way applied to solve the solidification problems. The rectangle element could have the more accurate result than the triangle one.

碩士
國立成功大學
機械工程學系碩博士班
95
The study applies the method of Laplace transform and the finite difference method in conjunction with the least-squares methods, the cubic spline and the measured temperature inside the test material to predict the transient heat transfer coefficient on the boundary for the two-dimensional transient inverse heat conduction problems. For the inverse algorithm of the study, the functional form of the heat transfer coefficient is unknown a priori. The whole spatial domain is first divided into p sub-intervals. A series of connected cubic polynomial functions in space and a linear function in time are then introduced to simulate the distribution of the unknown surface heat flux over space and time for the transient inverse heat conduction problem. The study investigates into the effects of p value, the initial guesses of the unknown coefficient, the measurement locations and the measurement errors on the estimated results. The results show that when there is no temperature measurement error, a good estimation on the surface heat flux and the heat transfer coefficient can be derived with the inverse algorithm. The estimated results seem to be not very sensitive to the initial guesses, the measurement locations and the p value. Nevertheless, the predictions agree with the correct results perfectly even if there exist measurement errors, except for the long time estimations. It means that the inverse algorithm of the study presents a good accuracy.