Heat flux evaluation in high temperature ring-on-ring contacts

A comprehensive methodology to investigate heat flux in a ring-on-ring tribometer is presented. Thermal fluxes under high contact pressures and temperature differences were evaluated through an experimental campaign and by a numerical procedure of inverse analysis applied to surface temperature measurements. An approximation of a two-dimensional time-dependent analytical solution for the temperature distribution was first developed and subsequently adapted to mimic the specific testing configuration characteristics; the problem was finally simplified to enable further inverse analysis. Experiments were performed using an innovative high temperature ring-on-ring tribometer. The evaluated contact heat transfer rates were reported as a function of normal load and temperature difference between the discs under steady-state conditions; the results reported here show that, in the present test configuration, the temperature difference has stronger influence than the applied load in terms of heat transfer induced by contact

Calibration and Rescaling Principles for Nonlinear Inverse Heat Conduction and Parameter Estimation Problems

This dissertation provides a systematic method for resolving nonlinear inverse heat conduction problems based on a calibration formulation and its accompanying principles. It is well-known that inverse heat conduction problems are ill-posed and hence subject to stability and uniqueness issues. Regularization methods are required to extract the best prediction based on a family of solutions. To date, most studies require sophisticated and combined numerical methods and regularization schemes for producing predictions. All thermophysical and geometrical properties must be provided in the simulations. The successful application of the numerical methods relies on the accuracy of the related system parameters as previously described. Due to the existence of uncertainties in the system parameters, these numerical methods possess bias of varying magnitudes. The calibration based approaches are proposed to minimize the systematic errors since system parameters are implicitly included in the mathematical formulation based on several calibration tests. To date, most calibration inverse studies have been based on the assumption of constant thermophysical properties. In contrast, this dissertation focuses on accounting for temperature-dependent thermophysical properties that produces a nonlinear heat equation. A novel rescaling principle is introduced for linearzing the system. This concept generates a mathematical framework similar to that of the linear formulation. Unlike the linear formulation, the present approach does require knowledge of thermophysical properties. However, all geometrical properties and sensor characterization are completely removed from the system. In this dissertation, a linear one-probe calibration method is first introduced as background. After that, the calibration method is generalized to the one-probe and two-probe, one-dimensional thermal system based on the assumption of temperature-dependent thermophysical properties. All previously proposed calibration equations are expressed in terms of a Volterra integral equation of the first kind for the unknown surface (net) heat flux and hence requires regularization owning to the ill-posed nature of first kind equations. A new strategy is proposed for determining the optimal regularization parameter that is independent of the applied regularization approach. As a final application, the described calibration principle is used for estimating unknown thermophysical properties above room temperature

Thermal Property Estimation of Fibrous Insulation: Heat Transfer Modeling and the Continuous Genetic Algorithm

Thermal properties of high-temperature fibrous insulation materials were estimated from transient thermal tests using an inverse heat transfer technique. Transient temperature data from an experimental set up was collected and a simple, one-dimensional numerical model was constructed to replicate the temperatures within the test assembly. The Continuous Genetic Algorithm optimization technique in conjunction with a numerical thermal model and transient test data was used to estimate coefficients of a functional representation of the thermal property. The thermal properties, i.e., thermal conductivity and specific heat, of an alumina insulation felt were estimated over the temperature range of 300 K to 1700 K at various constant static pressures in nitrogen gas and compared with published data. The resulting thermal property estimates were within 10% of published values over the entire temperature range at various pressures. The methodology, application, and results are presented

A Method for Geometry Optimization in a Simple Model of Two-Dimensional Heat Transfer

This investigation is motivated by the problem of optimal design of cooling elements in modern battery systems. We consider a simple model of two-dimensional steady-state heat conduction described by elliptic partial differential equations and involving a one-dimensional cooling element represented by a contour on which interface boundary conditions are specified. The problem consists in finding an optimal shape of the cooling element which will ensure that the solution in a given region is close (in the least squares sense) to some prescribed target distribution. We formulate this problem as PDE-constrained optimization and the locally optimal contour shapes are found using a gradient-based descent algorithm in which the Sobolev shape gradients are obtained using methods of the shape-differential calculus. The main novelty of this work is an accurate and efficient approach to the evaluation of the shape gradients based on a boundary-integral formulation which exploits certain analytical properties of the solution and does not require grids adapted to the contour. This approach is thoroughly validated and optimization results obtained in different test problems exhibit nontrivial shapes of the computed optimal contours.Comment: Accepted for publication in "SIAM Journal on Scientific Computing" (31 pages, 9 figures

Novel optimisation methods for numerical inverse problems

Inverse problems involve the determination of one or more unknown quantities usually appearing in the mathematical formulation of a physical problem. These unknown quantities may be boundary heat flux, various source terms, thermal and material properties, boundary shape and size. Solving inverse problems requires additional information through in-situ data measurements of the field variables of the physical problems. These problems are also ill-posed because the solution itself is sensitive to random errors in the measured input data. Regularisation techniques are usually used in order to deal with the instability of the solution. In the past decades, many methods based on the nonlinear least squares model, both deterministic (CGM) and stochastic (GA, PSO), have been investigated for numerical inverse problems. The goal of this thesis is to examine and explore new techniques for numerical inverse problems. The background theory of population-based heuristic algorithm known as quantum-behaved particle swarm optimisation (QPSO) is re-visited and examined. To enhance the global search ability of QPSO for complex multi-modal problems, several modifications to QPSO are proposed. These include perturbation operation, Gaussian mutation and ring topology model. Several parameter selection methods for these algorithms are proposed. Benchmark functions were used to test the performance of the modified algorithms. To address the high computational cost of complex engineering optimisation problems, two parallel models of the QPSO (master-slave, static subpopulation) were developed for different distributed systems. A hybrid method, which makes use of deterministic (CGM) and stochastic (QPSO) methods, is proposed to improve the estimated solution and the performance of the algorithms for solving the inverse problems. Finally, the proposed methods are used to solve typical problems as appeared in many research papers. The numerical results demonstrate the feasibility and efficiency of QPSO and the global search ability and stability of the modified versions of QPSO. Two novel methods of providing initial guess to CGM with approximated data from QPSO are also proposed for use in the hybrid method and were applied to estimate heat fluxes and boundary shapes. The simultaneous estimation of temperature dependent thermal conductivity and heat capacity was addressed by using QPSO with Gaussian mutation. This combination provides a stable algorithm even with noisy measurements. Comparison of the performance between different methods for solving inverse problems is also presented in this thesis