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An in-plane elasto-plastic material model and a hygroexpansivity-shrinkage model for paper and board are introduced in this paper. The input parameters for both models are fiber orientation anisotropy and dry solids content. These two models, based on experimental results, could be used in an analytical approach to estimate, for example, plastic strain and shrinkage in simple one-dimensional cases, but for studies of the combined and more complicated effects of hygro-elasto-plastic behavior, a numerical finite element model was constructed. The finite element approach also offered possibilities for studying different structural variations of an orthotropic sheet as well as buckling behavior and internal stress situations under local strain differences. A few examples are presented of the effect of the anisotropy and moisture streaks under stretching and drying conditions on strain differences and buckling. The internal stresses were studied through a case in which the drying of different layers occurred at different stages. Both the anisotropy and moisture streaks were capable of rendering the buckling of the sample visible. The permanency of these defects highly depends on several process stages and tension conditions of the sheet, as demonstrated in this paper. The application possibilities of the hygro-elasto-plastic model are diverse, including investigation into several phenomena and defects appearing in drying, converting and printing process conditions. [ABSTRACT FROM AUTHOR]

Abstract: The rheological nature of paper or board is usually treated either as elasto-plastic or as viscoelastic depending on the studied paper making process or behavior in converting and end use. In this paper we study several stress–strain curve models and the determination of material parameters from an elasto-plastic point of view. Finally, a suitable approach for all stress–strain curves measured from 180 strips is constructed using a linear function for an elastic region and a nonlinear function for a strain hardening region. This model determines a proportional limit (elastic limit) and gives fairly elegant dependencies between material/fitting parameters and two important factors of mechanical properties of paper: dry solids content and anisotropy. In this paper the dependency of a plastic strain on dry solids content and anisotropy is estimated using the introduced stress–strain curve model. Correspondingly, the model can be used to estimate many other mechanical behaviors, for example, the tension differences arising from non-uniform moisture content of the paper web profile. However, the main target of this study is to produce competent parameters based on modeled stress–strain curves for further construction of a material model. This elasto-plastic material model will be utilized in out-of-plane deformation and fracture models. [Copyright &y& Elsevier]

Abstract: In this study, the depth-averaged flow and energy equations for plate heat exchangers are presented. The equations are derived by integrating the original 3D flow and energy equations over the height of the gap between the bottom and top plates. This approach reduces the equations from 3D to 2D but still takes into account the frictions on the surfaces and heat transfer through the plates. The depth-averaging reduces the elapsed time of CFD simulations from hours to minutes. Thus, it is very practicable modelling method in real time design work. 2D CFD simulations with depth-averaged equations are compared with full 3D models for five different corrugation angles and corrugation lengths. The simulation results show that the 2D model predicts with relatively good accuracy the profile of the pressure drop and the temperature change as a function of the corrugation angle and the function of the corrugation length. In order to get more extensive information about the significance of the different geometry parameters on the efficiency of the heat exchanger, we simulated 30 different geometries with the fast 2D model. The results suggest that the temperature change is not as sensitive for the geometrical modifications as the pressure drop. [Copyright &y& Elsevier]

Abstract: In this paper, a simple formula for the prediction of stress (strain) in the relaxation (creep) period is derived for a non-linear viscoelastic material model which takes into account the finite ramp time. Usually, it is assumed that the ramp time is small and, therefore, loading can be described via Heaviside step function. This assumption, when applied to the material parameters identification process, can lead to a large errors in the values of the approximated material parameters. Especially, for the materials which undergo significant stress decay in the beginning of relaxation the assumption of infinite small ramp time can induce severe errors. With the help of the derived formula more reliable material parameter identification can be accomplished. The proposed method is tested with numerical simulations and compared with analytical results, Heaviside step loading case and method described by Nordin and Varna. Simulations show good agreement with analytical results. [Copyright &y& Elsevier]

In this paper a new model to predict the wake of vertical axis wind turbines (VAWT) is proposed and analysed. The model is based on the actuator disk and the Double Multiple Stream Tube methods. Specifically, the model, denoted as Multiple Actuator Block, is based on the definition, inside the computational domain, of multiple parallelepipedic blocks distributed along the path of the blades. Volumetric momentum sinks are imposed in these blocks to model the effect of the blades on the flow. To analyse the performance of the model a VAWT with three NACA0022, for which numerical and experimental results are available in the literature, has been considered. Different types of simulations with the Multiple Actuator Block model have been carried out and have been compared with a complete finite volume simulation using the sliding mesh technique. This simulation requires about ten times more CPU time than the simulations using the Multiple Actuator Block model. It has been found that the large scale features of the far wake can be reproduced using the Multiple Actuator Block model applying in the block the forces, obtained from the complete finite volume simulation or obtained from a boundary-layer type code, when the blade is inside the block. [ABSTRACT FROM AUTHOR]

We study numerically orientation of rigid fibres in a turbulent flow. Instead of a Lagrangian approach, i.e. following fibres along trajectories and analyzing orientations after simulations, we are using a fibre orientation probability distribution (FOPD) model. The mathematical model predicting the two spherical orientation angles (in a three-dimensional computational domain) is presented and solved in a coupled manner, which is the novelty of our approach. Furthermore, numerical predictions are validated with experiments. The origin of the problem is in the papermaking industry, that is, distributing and orienting fibres optimally into a paper sheet produced. [ABSTRACT FROM AUTHOR]

An Eulerian model of a turbulent fibre suspension flowing through a planar contraction is proposed to predict the fibre orientation distribution. The model specifically applies to the flow of pulp suspensions through a papermachine headbox. The model accounts for the convection of orientation distribution of the mean fluid velocity and the dispersion caused by the turbulent velocity fluctuations and describes each by a dimensionless dispersion coefficient and a dimensionless velocity gradient characterized by the contraction ratio (ratio of duct inlet height to outlet height) of the duct. A numerical solution of the model equations was shown to compare well to two different experimental studies available in the literature. From comparison with experiment the rotational dispersion coefficient was estimated to be 2 s−1 for both studies. Using the experimental value of the rotational dispersion coefficient and assuming it remains constant, the fibre orientation distributions was calculated for a range of dimensionless dispersion coefficients and contraction ratios. It was demonstrated that increasing the contraction ratio, over the industrial range of 5–50, significantly increases the alignment of fibres exiting the headbox. It was also shown that varying the inlet fluid velocity, over a practical range, provides only small changes in the fibre orientation distribution. Both predicted effects agree with experimental observation. Furthermore, this study suggests that fibre orientation is approximately dependent on a single dimensionless Peclet number that is a function of the fluid contraction ratio, inlet velocity, contraction length and rotational dispersion coefficient and that this parameter can be used to guide the design and operation of commercial headboxes. [Copyright &y& Elsevier]