Modelowanie przepływu materiału sypkiego metodą punktów materialnych

Abstract

Modelowanie komputerowe procesu przepływu materiału sypkiego ma duże znaczenie praktyczne, ponieważ pozwala wyznaczyć profil i prędkość przepływu oraz oddziaływania materiału na ściany zbiornika znacznie mniejszym kosztem niż badania eksperymentalne. Modelowanie numeryczne może również w znacznym stopniu zredukować koszt eksperymentu, jeśli zostanie on poprzedzony odpowiednio przygotowaną analizą numeryczną. Niniejsze opracowanie poświęcone jest temu zagadnieniu, przy czym analizowano procesy zarówno opróżniania, jak i napełniania zbiornika. Opis mechaniczny przepływu materiału sypkiego charakteryzuje się silnymi nieliniowościami związanymi z dużymi odkształceniami, nieliniowymi związkami fizycznymi oraz zjawiskiem kontaktu z tarciem. Jako narzędzie analizy zastosowano metodę punktów materialnych - wykorzystaną w analizie zagadnień mechaniki ciała stałego implementację metody cząstki w komórce ( ang. particle-in-cell method). Metodę punktów materialnych można także interpretować jako metodę elementów skończonych, sformułowaną w mieszanym, materialno- przestrzennym opisie ruchu. W opracowaniu porównano kilka modeli konstytutywnych materiału sypkiego. Metodę analizy zastosowano do zbiorników o złożonych kształtach - analizowano przepływ płaski i osiowosymetryczny.[...]Dynamie processes of granular flow have been analysed using the materiał point method. Piane strain and axi-symmetric flows have been investigated. Dynamie, strongly non-linear problems including large strains, materiał non-linearity and frictional contact have been solved. The materiał point method (MPM) has been proved to be a reliable numerical tool in the analysis of highly complex problems as discharging and filling containers (silos). The materiał point method is a variant of the finite element method formulated in an arbitrary Lagrangian-Eulerian description of motion. Although MPM uses the computational element mesh, it can also be regarded as a pointbased (meshless) method as the history of state variables is traced at the materiał points that are defined independently of the computational mesh used in the method. The point-based methods including MPM are more efficient in an analysis of large strain problems than the finite element method (FEM) formulated in the purely Lagrangian format as the latter method suffers from the excessive distortions of the element mesh used in calculations. The dynamie problem of granular flow has been formulated variationally and solved in the incrementa! way. The dynamie equations of MPM have been integrated in time by an explicit procedure. The mechanical behaviour of the granular materiał has been described by the use of several constitutive models: elastic-ideal plastic model, elastic-viscoplastic one, and several hypoplastic models. The Drucker-Prager yield condition and the non-associative (plastic incompressible) flow rule have been utilised in the case of the first two models. The constitutive relations have been integrated with respect to time by implicit algorithms. Problems of granular flow in silos of different shapes have been analysed. The silos with flat bottoms and trapezoidal or conical outlets have been considered. Two basie kinds of flow pattem (in the siło discharge process) have been modelled: the mass and funnel ones. The problem of granular flow around inserts has also been investigated including the flow in a container of the "silo-in-silo" type. In the case of the analysis of siło filling problem, an additional algorithm of mass density field calculation has been added to the MPM procedure. The density field has been determined on the base of the masses and current position of the materiał points. This approach is more accurate than the calculation of the density field by time integration of the constitutive relations, and also allows to determine the density in the stress-free state when the materiał grains are separated. A combination of viscous and non-linear elastic terms has been used to relate the volumetric strain and pressure in the constitutive equations. To avoid the mesh dependency of the numerical solution, the viscoplastic regularisation in the constitutive model has been used. This approach allows to obtain the thickness of shear bands - occurring in granular flow problems - related to the materiał model parameter, not to the size of element mesh. The mesh independence of the materiał point solution has been shown in the work. The phenomenon of dome which can be created over an outlet of a siło has also been investigated in the book. The phenomenon can appear when the granular materiał reveals some cohesion which can be an effect of materiał moistness. The small materiał cohesion can lead to an unreliable flow or flow suspension. MPM allows to analyse this problem. The minimum values of cohesion have been found for which the flow is stopped in the cases of siło discharge and stock-pile reclaim problems. To reduce the real time of computations, the parallel programming has been used by means of OpenMP. The loop-level parallelism has been applied for the main loops of the computer program. Although the approach is rather straightforward, the significant value of 2.6 has been achieved for the speed-up factor when 4 threads are used in the calculations. Some numerical results have been compared with those obtained from empirical formulae; good agreement has been noticed. The materiał point modelling of the granular flow seems to have the practical significance as it allows to find the flow profile, flow rate and the interaction between the flowing materiał and siło walls by means of smaller cost than an experiment. This does not mean that the modelling can entirely replace the experiment. However, the cost of the experimental research can be remarkably reduced when the computer modelling is utilised in preparing the experiment.