Red. serii : Wodziński, PiotrModelowanie 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
