Mass, heat and momentum transfer in natural draft wet cooling tower with flue gas discharge

The paper presents CFD simulation results of a natural draught wet-coolingtower (NDWCT) with flue gas discharge. The problem considered is mixing of the fluegases with the rising plume and possible corrosion of the tower shell due to acid condensate.A previously developed CFD model of a NDWCT has been used in the analysis. Nowind conditions have been assumed and the results have shown that under this conditionthe corrosion is unlikely to occu

An Inverse POD-RBF Network Approach to Parameter Estimation in Mechanics

An inverse approach is formulated using proper orthogonal decomposition (POD) integrated with a trained radial basis function (RBF) network to estimate various physical parameters of a specimen with little prior knowledge of the system. To generate the truncated POD-RBF network utilized in the inverse problem, a series of direct solutions based on FEM, BEM or exact analytical solutions are used to generate a data set of temperatures or deformations within the system or body, each produced for a unique set of physical parameters. The data set is then transformed via POD to generate an orthonormal basis to accurately solve for the desired material characteristics using the Levenberg-Marquardt (LM) algorithm to minimize the objective least squares functional. While the POD-RBF inverse approach outlined in this paper focuses primarily in application to conduction heat transfer, elasticity, and fracture mechanics, this technique is designed to be directly applicable to other realistic conditions and/or relevant industrial problems

Reconstruction Of Time-Dependent Boundary Heat Flux By A Bem-Based Inverse Algorithm

The objective of this study is to reconstruct an unknown time-dependent heat flux distribution at a surface whose temperature history is provided by a broad-band thermochromic liquid crystal (TLC) thermographic technique. The information given for this inverse problem is the surface temperature history. Although this is not an inverse problem, it is solved as such in order to filter the errors in input temperatures which are reflected in errors in heat fluxes. We minimize a quadratic functional which measures the sum of the squares of the deviation of estimated (computed) temperatures relative to measured temperatures provided by the TLC thermography. The objective function is minimized using the Levenberg-Marquardt method, and we develop an explicit scheme to compute the required sensitivity coefficients. The unknown flux is allowed to vary in space and time. Results are presented for a simulation in which a spatially varying and time-dependent flux is reconstructed over an airfoil. © 2006 Elsevier Ltd. All rights reserved

Solving Transient Nonlinear Heat Conduction Problems By Proper Orthogonal Decomposition And Fem

A method of reducing the number of degrees of freedom and the overall computing times, so called Proper Orthogonal Decomposition (POD) combined with Finite Element Method (FEM) has been devised. The technique POD-FEM can be applied both to linear and nonlinear problems. At the first stage of the method standard FEM time stepping procedure is invoked. The temperature fields obtained for the first few time steps undergo statistical analysis yielding an optimal set of globally defined trial and weighting functions for the Galerkin solution of the problem at hand. The resulting set of Ordinary Differential Equations (ODEs) is of greatly reduced dimensionality when compared with the original FEM formulation. For linear problems, the set can be solved either analytically, resorting to the modal analysis technique, or by time stepping. In the case of nonlinear problems, only time stepping can be applied. The stress in this paper is on time stepping approach where the generation of the FEM-POD matrices, requiring some additional matrix manipulations, can be embedded in the assembly of standard FEM matrices. The gain in execution times comes from the significantly shorter time of solution of the set of algebraic equations at each time step. Included numerical results concern both linear and nonlinear problems. In the case of linear problems, the derived time stepping technique is compared with the standard FEM and the modal analysis. For nonlinear problems the proposed POD-FEM approach is compared with standard FEM. Good accuracy of the POD-FEM solver has been observed. Controlling the error introduced by the reduction of the degrees of freedom in POD is also discussed

Solving Transient Nonlinear Heat Conduction Problems By Proper Orthogonal Decomposition And Fem

A method of reduc ing the number of degrees of freedom and the overall computing times, so called Proper Orthogonal Decomposition (POD) combined with Finite Element Method (FEM) has been devised. The technique POD-FEM can be applied both to linear and nonlinear problems. At the first stage of the method standard FEM time stepping procedure is invoked. The temperature fields obtained for the first few time steps undergo statistical analysis yielding an optimal set of globally defined trial and weighting functions for the Galerkin solution of the problem at hand. The resulting set of Ordinary Differential Equations (ODEs) is of greatly reduced dimensionality when compared with the original FEM formulation. For linear problems, the set can be solved either analytically, resorting to the modal analysis technique, or by time stepping. In the case of nonlinear problems, only time stepping can be applied. The stress in this paper is on time stepping approach where the generation of the FEM-POD matrices, requiring some additional matrix manipulations, can be embedded in the assembly of standard FEM matrices. The gain in execution times comes from the significantly shorter time of solution of the set of algebraic equations at each time step. Included numerical results concern both linear and nonlinear problems. In the case of linear problems, the derived time stepping technique is compared with the standard FEM and the modal analysis. For nonlinear problems the proposed POD-FEM approach is compared with standard FEM. Good accuracy of the POD-FEM solver has been observed. Controlling the error introduced by the reduction of the degrees of freedom in POD is also discussed

Application Of The Proper Orthogonal Decomposition In Steady State Inverse Problems

This chapter provides an overview of an inverse analysis technique for retrieving unknown boundary conditions. The first step of this approach is to solve a sequence of forward problems made unique, by defining the missing boundary condition as a function of some unknown parameters. Several combinations of values of these parameters that produce a sequence of solutions are considered. These combinations are then sampled at a predefined set of points. Proper Orthogonal Decomposition (POD) is used to produce a truncated sequence of orthogonal basis function. The solution of the forward problem is written as a linear combination of the basis vectors. The unknown coefficients of this combination are evaluated by minimizing the discrepancy between the measurements and the POD approximation of the field. The chapter also discusses numerical examples to show the robustness and numerical stability of the proposed scheme. © 2003 Elsevier B.V. All rights reserved

An Inverse POD-RBF Network Approach to Parameter Estimation in Mechanics

An inverse approach is formulated using proper orthogonal decomposition (POD) integrated with a trained radial basis function (RBF) network to estimate various physical parameters of a specimen with little prior knowledge of the system. To generate the truncated POD-RBF network utilized in the inverse problem, a series of direct solutions based on FEM, BEM or exact analytical solutions are used to generate a data set of temperatures or deformations within the system or body, each produced for a unique set of physical parameters. The data set is then transformed via POD to generate an orthonormal basis to accurately solve for the desired material characteristics using the Levenberg-Marquardt (LM) algorithm to minimize the objective least squares functional. While the POD-RBF inverse approach outlined in this paper focuses primarily in application to conduction heat transfer, elasticity, and fracture mechanics, this technique is designed to be directly applicable to other realistic conditions and/or relevant industrial problems

An Inverse Pod-Rbf Network Approach To Parameter Estimation In Mechanics

An inverse approach is formulated using proper orthogonal decomposition (POD) integrated with a trained radial basis function (RBF) network to estimate various physical parameters of a specimen with little prior knowledge of the system. To generate the truncated POD-RBF network utilized in the inverse problem, a series of direct solutions based on the finite element method, the boundary element method or exact analytical solutions are used to generate a data set of temperatures or deformations within the system or body, each produced for a unique set of physical parameters. The data set is then transformed via POD to generate an orthonormal basis to accurately solve for the desired material characteristics using the Levenberg-Marquardt algorithm to minimize the objective least-squares functional. While the POD-RBF inverse approach outlined in this article focuses primarily in application to conduction heat transfer, elasticity and fracture mechanics, this technique is designed to be directly applicable to other realistic conditions and/or relevant industrial problems. © 2012 Copyright Taylor and Francis Group, LLC