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Fibre orientation distribution of a turbulent fibre suspension flowing in a planar contraction is considered. The fibre orientation is modelled using a diffusion–convection-type equation while the average flow velocity of the suspension is modelled using a simple one-dimensional model. Our aim is to control the fibre orientation distribution at the end of the contraction by changing its shape. The shape is discretized with Bezier function and the diffusion–convection equation with streamline upwind Petrov–Galerkin (SUPG) finite element method. Algebraic sensitivity analysis for the discretized optimization problem is done with the aid of automatic differentiation techniques. Numerical examples are given. Copyright © 2005 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

Numerical simulation of local atmospheric flows around a complex topography is important for many wind energy applications, as it can help in locating and optimizing wind farms. The aim of this paper is to simulate the atmospheric flows over the challenging and complex site of Bolund Hill (in Denmark) using Large-Eddy Simulations (LES) and to validate the simulation methodology against full-scale measurements. Wind prediction over a potential inland wind park is the main application of the validated LES methodology. For the first time, LES-based results from more than one wind direction of the Bolund case are reported and analyzed in detail herein. The LES results from each direction are compared with the Bolund field data in a quantitative way, for example, by using simulation error. According to the results comparison, it is found that the LES model provides by far the most accurate prediction for turbulent kinetic energy. The simulation error of this LES model for predicting turbulent kinetic energy is 19% smaller than that of all other models, whether experimental or numerical, employed previously over Bolund Hill. [ABSTRACT FROM AUTHOR]

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]

The presented research demonstrates the results of a series of numerical simulations of gas flow through a single-stage centrifugal compressor with a vaneless diffuser. Numerical results were validated with experiments consisting of eight regimes with different mass flow rates. The steady-state and unsteady simulations were done in ANSYS FLUENT 13.0 and NUMECA FINE/TURBO 8.9.1 for one-period geometry due to periodicity of the problem. First-order discretization is insufficient due to strong dissipation effects. Results obtained with second-order discretization agree with the experiments for the steady-state case in the region of high mass flow rates. In the area of low mass flow rates, nonstationary effects significantly influence the flow leading stationary model to poor prediction. Therefore, the unsteady simulations were performed in the region of low mass flow rates. Results of calculation were compared with experimental data. The numerical simulation method in this paper can be used to predict compressor performance. [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]

The effect of separation distance between turbines on overall cluster performance were simulated using computational fluid dynamics software and we found that at a distance equivalent to two rotors, there was an improvement of +8.06% in the average performance of the cluster compared to a single, isolated turbine. A very small improvement in performance was noted at the equivalent distance of 12 rotor diameters. The performances of three individual turbines in pyramid- and inverted pyramid-shaped vertical axis wind turbine clustered farm configurations with varying oblique angles at a fixed spacing of two equivalent rotor diameters were also investigated. The design experiment involves the simulation of test cases with oblique angles from 15° to 165° at an interval of 15° and the turbines were allowed to rotate through 18 full rotations. The results show that the left and right turbines increase in performance as the angle with respect to the streamline axis increases, with the exception of the 165° angle. The center turbine, meanwhile, attained its maximum performance at a 45° oblique angle. The maximum cluster performance was found to be in the configuration where the turbines were oriented in a line (i.e., side by side) and perpendicular to the free-stream wind velocity, exhibiting an overall performance improvement of 9.78% compared to the isolated turbine. Other array configurations show improvements ranging from 6.58% to 9.57% compared to the isolated turbine, except in the extreme cases of 15° and 165°, where a decrease in the cluster performance was noted due to blockage induced by the left and right turbines, and the center turbines, respectively. [ABSTRACT FROM AUTHOR]

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]

Designing the jet ejector optimally is a challenging task and has a great impact on industrial applications. Three different sets of nozzles (namely, 1, 3, and 5) inside the jet ejector are compared in this study by using numerical simulations. More precisely, dynamics of bubble coalescence and breakup in the multinozzle jet ejectors are studied by means of Computational Fluid Dynamics (CFD). The population balance approach is used for the gas phase such that different bubble size groups are included in CFD and the number densities of each of them are predicted in CFD simulations. Here, commercial CFD software ANSYS Fluent 14.0 is used. The realizable k-ε turbulence model is used in CFD code in three-dimensional computational domains. It is clear that Reynolds-Averaged Navier-Stokes (RANS) models have their limitations, but on the other hand, turbulence modeling is not the key issue in this study and we can assume that the RANS models can predict turbulence of the carrying phase accurately enough. In order to validate our numerical predictions, results of one, three, and five nozzles are compared to laboratory experiments data for Cl2-NaOH system. Predicted gas volume fractions, bubble size distributions, and resulting number densities of the different bubble size groups as well as the interfacial area concentrations are in good agreement with experimental results. [ABSTRACT FROM AUTHOR]

In the wind-energy sector, wind-power forecasting, turbine siting, and turbine-design selection are all highly dependent on a precise evaluation of atmospheric wind conditions. On-site measurements provide reliable data; however, in complex terrain and at the scale of a wind farm, local measurements may be insufficient for a detailed site description. On highly variable terrain, numerical models are commonly used but still constitute a challenge regarding simulation and interpretation. We propose a joint state-of-the-art study of two approaches to modelling atmospheric flow over the Bolund hill: a wind-tunnel test and a large-eddy simulation (LES). The approach has the particularity of describing both methods in parallel in order to highlight their similarities and differences. The work provides a first detailed comparison between field measurements, wind-tunnel experiments and numerical simulations. The systematic and quantitative approach used for the comparison contributes to a better understanding of the strengths and weaknesses of each model and, therefore, to their enhancement. Despite fundamental modelling differences, both techniques result in only a 5 % difference in the mean wind speed and 15 % in the turbulent kinetic energy (TKE). The joint comparison makes it possible to identify the most difficult features to model: the near-ground flow and the wake of the hill. When compared to field data, both models reach 11 % error for the mean wind speed, which is close to the best performance reported in the literature. For the TKE, a great improvement is found using the LES model compared to previous studies (20 % error). Wind-tunnel results are in the low range of error when compared to experiments reported previously (40 % error). This comparison highlights the potential of such approaches and gives directions for the improvement of complex flow modelling. [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]

In this article, a bi-level optimization problem covering upper (design) and lower (operation) levels is defined and a solution procedure for bi-level optimization problems is presented. This is devised as a dynamic multiobjective optimization problem, i.e. the values of the control and state variables change over a predefined time horizon and several competing criteria are optimized simultaneously. Moreover, the interaction between the upper and lower levels is analysed. The benefits of bi-level dynamic multiobjective optimization are illustrated in detail by examining an industrial case in which the design of a paper mill (upper level) and the mill operation (lower level) are optimized at the same time. However, the problem definition and the solution procedure are not limited to any specific application but can be exploited in many different industrial areas. [ABSTRACT FROM PUBLISHER]

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]