On upscaling heat conductivity for a class of industrial problems

Calculating effective heat conductivity for a class of industrial problems is discussed. The considered composite materials are glass and metal foams, fibrous materials, and the like, used in isolation or in advanced heat exchangers. These materials are characterized by a very complex internal structure, by low volume fraction of the higher conductive material (glass or metal), and by a large volume fraction of the air. The homogenization theory (when applicable), allows to calculate the effective heat conductivity of composite media by postprocessing the solution of special cell problems for representative elementary volumes (REV). Different formulations of such cell problems are considered and compared here. Furthermore, the size of the REV is studied numerically for some typical materials. Fast algorithms for solving the cell problems for this class of problems, are presented and discussed

Structure and pressure drop of real and virtual metal wire meshes

An efficient mathematical model to virtually generate woven metal wire meshes is presented. The accuracy of this model is verified by the comparison of virtual structures with three-dimensional images of real meshes, which are produced via computer tomography. Virtual structures are generated for three types of metal wire meshes using only easy to measure parameters. For these geometries the velocity-dependent pressure drop is simulated and compared with measurements performed by the GKD - Gebr. Kufferath AG. The simulation results lie within the tolerances of the measurements. The generation of the structures and the numerical simulations were done at GKD using the Fraunhofer GeoDict software

Using the Sharp Operator for edge detection and nonlinear diffusion

In this paper we investigate the use of the sharp function known from functional analysis in image processing. The sharp function gives a measure of the variations of a function and can be used as an edge detector. We extend the classical notion of the sharp function for measuring anisotropic behaviour and give a fast anisotropic edge detection variant inspired by the sharp function. We show that these edge detection results are useful to steer isotropic and anisotropic nonlinear diffusion filters for image enhancement

A proof of convergence of a finite volume scheme for modified steady Richards’ equation describing transport processes in the pressing section of a paper machine

A number of water flow problems in porous media are modelled by Richards’ equation [1]. There exist a lot of different applications of this model. We are concerned with the simulation of the pressing section of a paper machine. This part of the industrial process provides the dewatering of the paper layer by the use of clothings, i.e. press felts, which absorb the water during pressing [2]. A system of nips are formed in the simplest case by rolls, which increase sheet dryness by pressing against each other (see Figure 1). A lot of theoretical studies were done for Richards’ equation (see [3], [4] and references therein). Most articles consider the case of x-independent coefficients. This simplifies the system considerably since, after Kirchhoff’s transformation of the problem, the elliptic operator becomes linear. In our case this condition is not satisfied and we have to consider nonlinear operator of second order. Moreover, all these articles are concerned with the nonstationary problem, while we are interested in the stationary case. Due to complexity of the physical process our problem has a specific feature. An additional convective term appears in our model because the porous media moves with the constant velocity through the pressing rolls. This term is zero in immobile porous media. We are not aware of papers, which deal with such kind of modified steady Richards’ problem. The goal of this paper is to obtain the stability results, to show the existence of a solution to the discrete problem, to prove the convergence of the approximate solution to the weak solution of the modified steady Richards’ equation, which describes the transport processes in the pressing section. In Section 2 we present the model which we consider. In Section 3 a numerical scheme obtained by the finite volume method is given. The main part of this paper is theoretical studies, which are given in Section 4. Section 5 presents a numerical experiment. The conclusion of this work is given in Section 6

FROM 3D IMAGING OF STRUCTURES TO DIFFUSIVE PROPERTIES OF ANISOTROPIC CELLULAR MATERIALS

International audienceThis paper deals with diffusive properties phenomena in metallic foams. We have developed a 3D morphological tool to extract geometrical characteristics of the media from X-ray images. The anisotropy of the geometry of each phase is observed and the relationship between microstructure and effective properties is analyzed. We emphasize on geometrical tortuosity determination and impact on con¬ductive transport tensor. The conductive heat transfers are computed on a vertex-edge network to determine directional effective conductivities by solving the energy equa¬tion on this network. We realize a systematic study carried on a wide range of different Nickel foam samples. Finally, we propose a simple model of effective diffusion prop¬erties dependence on tortuosity and porosity

Numerical upscaling of discrete network models

In this paper a numerical multiscale method for discrete networks is presented. The method gives an accurate coarse scale representation of the full network by solving sub-network problems. The method is used to solve problems with highly varying connectivity or random network structure, showing optimal order convergence rates with respect to the mesh size of the coarse representation. Moreover, a network model for paper-based materials is presented. The numerical multiscale method is applied to solve problems governed by the presented network model

Experimental validation and numerical upscaling of linear network models for simulation of paper

Paper modeling results in complex geometries that lead to enormous numerical problems. The complexity lies in the material\u27s microstructure. Individual paper fibers must be considered for useful material simulations in paper development, where wood composition and other fiber-based parameters are essential. Multiple time-dependent and nonlinear modeling techniques have been proposed in the literature. In this work, a simplified approach to paper modeling is proposed. A simple but effective model can be created by seeing the paper as a network of one-dimensional beams and using linearized one-dimensional beam theory. Working in the industrial collaboration Innovative Simulation Of Paper (ISOP), the model was constructed to be relevant for product developers in papermaking industry, which means fast evaluations and representative results. The model was validated against experimental data for tensile stiffness, tensile strength, and bending resistance in both cross and machine direction for several low-density sheets. These simulations are fast, taking no more than a couple of minutes to generate and evaluate randomly generated paper samples. For larger simulations, a multiscale approach is proposed. The multiscale method is the Localized Orthogonal Decomposition (LOD) method, a generalized finite element method. In this method, the heterogeneities (fibers) in the paper model are resolved using special local orthogonal projection operators. This work presents the theoretical foundation of using the LOD method on discrete network models, which builds up to an a priori error bound for the multiscale approximations. The theoretical a priori error results are confirmed with numerical examples. Both structural problems and scalar-valued discrete network problems are presented in these examples. This work ends with numerical results showing the successful use of the LOD method on one of the structural simulations in the validation of the paper model, showing that the LOD method can be used for practical simulations

Network design decisions in supply chain planning

Structuring global supply chain networks is a complex decision-making process. The typical inputs to such a process consist of a set of customer zones to serve, a set of products to be manufactured and distributed, demand projections for the different customer zones, and information about future conditions, costs (e.g. for production and transportation) and resources (e.g. capacities, available raw materials). Given the above inputs, companies have to decide where to locate new service facilities (e.g. plants, warehouses), how to allocate procurement and production activities to the variousmanufacturing facilities, and how to manage the transportation of products through the supply chain network in order to satisfy customer demands. We propose a mathematical modelling framework capturing many practical aspects of network design problems simultaneously. For problems of reasonable size we report on computational experience with standard mathematical programming software. The discussion is extended with other decisions required by many real-life applications in strategic supply chain planning. In particular, the multi-period nature of some decisions is addressed by a more comprehensivemodel, which is solved by a specially tailored heuristic approach. The numerical results suggest that the solution procedure can identify high quality solutions within reasonable computational time