Modelling pellet flow in single extrusion with DEM

Plasticating single-screw extrusion involves the continuous conversion of loose solid pellets into a pressurized homogeneous melt that is pumped through a shaping tool. Traditional analyses of the solids conveying stage assume the movement of an elastic solid plug at a fixed speed. However, not only the corresponding predictions fail considerably, but it is also well known that, at least in the initial screw turns, the flow of loose individual pellets takes place. This study follows previous efforts to predict the characteristics of such a flow using the discrete element method. The model considers the development of normal and tangential forces resulting from the inelastic collisions between the pellets and between them and the neighbouring metallic surfaces. The algorithm proposed here is shown to be capable of capturing detailed features of the granular flow. The predictions of velocities in the cross- and down-channel directions and of the coordination number are in good agreement with equivalent reported results. The effect of pellet size on the flow features is also discussed

Melting of polymer blends in single-screw extrusion : an experimental study

Melting is a major step in plasticating single screw extrusion, but most of the existing phenomenological know how was gathered by performing Maddock-type experiments with homopolymers. Given the current widespread industrial use of polymer blends, it is worth determining whether the same mechanisms and mathematical models apply, or whether different sequences develop. This work reports the results of Maddock-type experiments using a PA6/PP blend, both in its immiscible and compatibilized varieties. A melting mechanism combining the features of the classical Tadmor mechanism and of the dispersed melting mechanism, also previously reported in the literature, was observed.The authors are grateful to Portuguese Fundacao para a Ciencia e Tecnologia for supporting this work under grant SFRH/BD/19997/2004 and to DSM, the Netherlands, for supplying PA6

Singular Cucker-Smale Dynamics

The existing state of the art for singular models of flocking is overviewed, starting from microscopic model of Cucker and Smale with singular communication weight, through its mesoscopic mean-filed limit, up to the corresponding macroscopic regime. For the microscopic Cucker-Smale (CS) model, the collision-avoidance phenomenon is discussed, also in the presence of bonding forces and the decentralized control. For the kinetic mean-field model, the existence of global-in-time measure-valued solutions, with a special emphasis on a weak atomic uniqueness of solutions is sketched. Ultimately, for the macroscopic singular model, the summary of the existence results for the Euler-type alignment system is provided, including existence of strong solutions on one-dimensional torus, and the extension of this result to higher dimensions upon restriction on the smallness of initial data. Additionally, the pressureless Navier-Stokes-type system corresponding to particular choice of alignment kernel is presented, and compared - analytically and numerically - to the porous medium equation

Construction of Modern Robust Nodal Discontinuous Galerkin Spectral Element Methods for the Compressible Navier-Stokes Equations

Discontinuous Galerkin (DG) methods have a long history in computational physics and engineering to approximate solutions of partial differential equations due to their high-order accuracy and geometric flexibility. However, DG is not perfect and there remain some issues. Concerning robustness, DG has undergone an extensive transformation over the past seven years into its modern form that provides statements on solution boundedness for linear and nonlinear problems. This chapter takes a constructive approach to introduce a modern incarnation of the DG spectral element method for the compressible Navier-Stokes equations in a three-dimensional curvilinear context. The groundwork of the numerical scheme comes from classic principles of spectral methods including polynomial approximations and Gauss-type quadratures. We identify aliasing as one underlying cause of the robustness issues for classical DG spectral methods. Removing said aliasing errors requires a particular differentiation matrix and careful discretization of the advective flux terms in the governing equations.Comment: 85 pages, 2 figures, book chapte

Multidimensional Conservation Laws: Overview, Problems, and Perspective

Some of recent important developments are overviewed, several longstanding open problems are discussed, and a perspective is presented for the mathematical theory of multidimensional conservation laws. Some basic features and phenomena of multidimensional hyperbolic conservation laws are revealed, and some samples of multidimensional systems/models and related important problems are presented and analyzed with emphasis on the prototypes that have been solved or may be expected to be solved rigorously at least for some cases. In particular, multidimensional steady supersonic problems and transonic problems, shock reflection-diffraction problems, and related effective nonlinear approaches are analyzed. A theory of divergence-measure vector fields and related analytical frameworks for the analysis of entropy solutions are discussed.Comment: 43 pages, 3 figure

The effect of materials' rheology on process energy consumption and melt thermal quality in polymer extrusion

YesPolymer extrusion is an important but an energy intensive method of processing polymeric materials. The rapid increase in demand of polymeric products has forced manufactures to rethink their processing efficiencies to manufacture good quality products with low-unit-cost. Here, analyzing the operational conditions has become a key strategy to achieve both energy and thermal efficiencies simultaneously. This study aims to explore the effects of polymers' rheology on the energy consumption and melt thermal quality (ie, a thermally homogeneous melt flow in both radial and axil directions) of extruders. Six commodity grades of polymers (LDPE, LLDPE, PP, PET, PS, and PMMA) were processed at different conditions in two types of continuous screw extruders. Total power, motor power, and melt temperature profiles were analyzed in an industrial scale single-screw extruder. Moreover, the active power (AP), mass throughput, torque, and power factor were measured in a laboratory scale twin-screw extruder. The results confirmed that the specific energy consumption for both single and twin screw extruders tends to decrease with the processing speed. However, this action deteriorates the thermal stability of the melt regardless the nature of the polymer. Rheological characterization results showed that the viscosity of LDPE and PS exhibited a normal shear thinning behavior. However, PMMA presented a shear thickening behavior at moderate-to-high shear rates, indicating the possible formation of entanglements. Overall, the findings of this work confirm that the materials' rheology has an appreciable correlation with the energy consumption in polymer extrusion and also most of the findings are in agreement with the previously reported investigations. Therefore, further research should be useful for identifying possible correlations between key process parameters and hence to further understand the processing behavior for wide range of machines, polymers, and operating conditions