Inverse problems in aerodynamics, heat transfer, elasticity and materials design (original) (raw)
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Computational approaches to some inverse problems from engineering practice
2015
Development of engineering structures and technologies frequently works with advanced materials, whose properties, because of their complicated microstructure, cannot be predicted from experience, unlike traditional materials. The quality of computational modelling of relevant physical processes, based mostly on the principles of classical thermomechanics, is conditioned by the reliability of constitutive relations, coming from simplified experiments. The paper demonstrates some possibilities of computational identification of such relations, namely for heat and mass transfer, coming from original experimental and numerical results obtained at the Brno University of Technology, in selected engineering applications.
A non-iterative finite element method for inverse heat conduction problems
International Journal for Numerical Methods in Engineering, 2003
A non-iterative, finite element-based inverse method for estimating surface heat flux histories on thermally conducting bodies is developed. The technique, which accommodates both linear and non-linear problems, and which sequentially minimizes the least squares error norm between corresponding sets of measured and computed temperatures, takes advantage of the linearity between computed temperatures and the instantaneous surface heat flux distribution. Explicit minimization of the instantaneous error norm thus leads to a linear system, i.e. a matrix normal equation, in the current set of nodal surface fluxes. The technique is first validated against a simple analytical quenching model. Simulated low-noise measurements, generated using the analytical model, lead to heat transfer coefficient estimates that are within 1% of actual values. Simulated high-noise measurements lead to h estimates that oscillate about the low-noise solution. Extensions of the present method, designed to smooth oscillatory solutions, and based on future time steps or regularization, are briefly described. The method's ability to resolve highly transient, early-time heat transfer is also examined; it is found that time resolution decreases linearly with distance to the nearest subsurface measurement site. Once validated, the technique is used to investigate surface heat transfer during experimental quenching of cylinders. Comparison with an earlier inverse analysis of a similar experiment shows that the present method provides solutions that are fully consistent with the earlier results. Although the technique is illustrated using a simple one-dimensional example, the method can be readily extended to multidimensional problems. Copyright © 2003 John Wiley & Sons, Ltd.
Inverse finite element formulations for transient heat conduction problems
Heat and Mass Transfer, 2008
Transient heat conduction problems are normally simulated by the conventional consistent and lumped finite element methods. The discretization error and the physical reality violation in such problems are noticeable and unwanted responses are observed in the results when using the consistent formulations. Although in utilizing the lumped formulations, the violation of physical reality becomes reduced; however, emerging the discretization error would also become obvious to the degree of being quantifiable. In using the inverse finite element method without considering the element shape functions, the element matrices will be obtained by minimizing the governing equation and its generalized discretized corresponding formula. The results obtained by using this method indicates that the reduction in both the discretization error as well as the violation of physical reality would be realized.
International Journal for Computational Methods in Engineering Science and Mechanics, 2019
This paper presents an inverse problem of determination of a space-dependent heat flux in steady-state heat conduction problems. The thermal conductivity of a heat conducting body depends on the temperature distribution over the body. In this study the simulated measured temperature distribution on part of the boundary is related to the variable heat flux imposed on a different part of the boundary through incorporating the variable thermal conductivity components into the sensitivity coefficients. To do so, a body-fitted grid generation technique is used to mesh the two-dimensional irregular body and solve the direct heat conduction problem. An efficient, accurate, robust, and easy to implement method is presented to compute the sensitivity coefficients through derived expressions. The main novelty of the study lies in the sensitivity analysis in which all sensitivities can be obtained in only one direct solution at each iteration, irrespective of the number of unknown parameters. The conjugate gradient method along with the discrepancy principle is used in the inverse analysis to minimize the objective function and achieve the desired solution.
Extended Mapping and Characteristics Techniques for Inverse Aerodynamic Design
Some ideas for using hodograph theory, mapping techniques and method of characteristics to formulate typical aerodynamic design boundary value problems are developed. Inverse method of characteristics is shown to be a fast tool for design of transonic flow elements as well as supersonic flows with given shock waves.
A viscous inverse method for aerodynamic design
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A numerical technique to solve two-dimensional inverse problems that arise in aerodynamic design is presented. The approach, which is well established for inviscid, rotational flows, is here extended to the viscous case. Two-dimensional and axisymmetric configurations are here considered. The solution of the inverse problem is given as the steady state of an ideal transient during which the flowfield assesses itself to the boundary conditions by changing the boundary contour. Comparisons with theoretical and experimental results are used to validate the numerical procedure.
An Inverse Heat Conduction Problem With Bem And Optimization Techniques
governed by the Laplace's equation. In such IHCP it is necessary to determine the position, size, and shape of a heating/cooling channel inside a conducting body. The geometric configuration of the internal channel is such that specific boundary conditions in terms of temperature or heat flux (called reference data) are satisfied at specific boundary points (called reference points). The solution procedure for this inverse problem starts with an initial guess of the internal channel configuration described by geometric variables. In the proposed formulation, the initial guess configuration reaches the final solution through the minimization of an objective function which is the difference between the reference data and the respective calculated response. The final solution corresponds to an internal heating/cooling channel configuration such that the calculated responses at the reference points match the respective reference data. Although more complex, from the mathematical point of view, the Boundary Element Method (BEM) is more appropriate for this type of inverse geometry problem because with the BEM it is easier to make continuos updates of the mesh which discretizes the internal channel. In the minimization process, the sensibility of the objective function with respect to the design variables. In this paper the sensibilities are calculated using Finite Difference and also Implicit Differentiation of the fundamental solutions. Finally, some applications of the proposed formulation is presented and discussed.