Multi-scale method for multi-component granular materials

• Autorzy: Thornton C. , Weinhart T. , Ogarko V. , Luding S.

Warianty tytułu

PL

Wieloskalowe metody dla wieloskładnikowych materiałów ziarnistych

• Języki publikacji: EN

Abstrakty

EN

In this paper we review recent progress made to understand granular chutes flow using multi-scale modeling techniques. We introduce the discrete particle method (DPM) and explain how to construct continuum fields from discrete data in a way that is consistent with the macroscopic concept of mass and momentum conservation. We present a novel advanced contact detection method that is able of dealing with multiple distinct granular components with sizes ranging over orders of magnitude. We discuss how such advanced DPM simulations can be used to obtain closure relations for continuum frameworks (the mapping between the micro-scale and macro-scale variables and functions): the micro-macro transition. This enables the development of continuum models that contain information about the micro-structure of the granular materials without the need for a priori assumptions. The micro-macro transition will be illustrated with two granular chute/avalanche flow problems. The first is a shallow granular chute flow where the main unknown in the continuum models is the macro-friction coefficient at the base. We investigate how this depends on both the properties of the flow particles and the surface over which the flow is taking place. The second problem is that of gravity-driven segregation in poly-dispersed granular chute flows. In both these problems we consider small steady-state periodic box DPM simulations to obtain the closure relations. Finally, we discuss the issue of the validity of such closure-relations for complex dynamic problems, that are a long way from the simple period box situation from which they were obtained. For simple situations the pre-computed closure relations will hold. In more complicated situations new strategies are required were macro-continuum and discrete micromodels are coupled with dynamic, two-way feedback between them.

PL

W artykule przedstawiono postęp w zrozumieniu przepływu przesypywanych materiałów ziarnistych, jaki został ostatnio osiągnięty dzięki technikom modelowania wieloskalowego. Na początku omówiono metodę dyskretnych cząstek (ang. Discrete particle method - DPM) i wyjaśniono w jaki sposób należy konstruować ciągłe pole na podstawie dyskretnych danych tak, aby model był spójny z makroskopową zasadą zachowania masy i pędu. Zaprezentowano też nową metodę wykrywania kontaktu, która może być wykorzystana do wieloskładnikowych materiałów sypkich o rozmiarze cząstek zmieniających się w zakresie rzędów wielkości. Pokazano jak zaawansowane symulacje DPM mogą być zastosowane do uzyskiwania zależności dla modelu ciągłego (mapowanie zmiennych i funkcji między skalami mikro i makro). To umożliwiło rozwój modeli kontinuum zawierających informację o mikrostrukturze materiałów sypkich bez potrzeby robienia dodatkowych założeń. Przejście mikro-makro przedstawiono dla dwóch problemów płynięcia materiału sypkiego. Pierwszym jest płynięcie w płytkim zsypie, gdzie główną niewiadomą w modelu kontinuum jest makro współczynnik tarcia. W pracy badano jak ten współczynnik zależy od własności przepływających cząstek i powierzchni, względem której cząstki przepływają. Drugim analizowanym problemem jest segregacja przy zsypie polidyspersyjnych cząstek. W obydwu analizowanych problemach rozważono krótkie okresy stacjonarne w symulacji DPM, aby otrzymać realistyczne, wzajemnie dopełniające się zależności opisujące ciągłe własności materiału. W pracy omówiono również problem dokładności i poprawności opisanych wzajemnie dopełniających się zależności dla złożonych problemów dynamicznych. Problemy te są odległe od omówionych wcześniej rozwiązań dla krótkich okresów stacjonarnych, dla których te zależności były otrzymywane. Dla prostych przypadków zastosowanie zdefiniowanych wzajemnie dopełniających się zależności dawało poprawne wyniki. W bardziej skomplikowanych sytuacjach potrzebne są nowe, bardziej zaawansowane rozwiązania, w których makrokontinuum i mikro dyskretny model są połączone w sposób dynamiczny ze sprzężeniem zwrotnym.

Słowa kluczowe

EN

coupled multiscale model; multicomponent granular materials; Navier-Stokes equation; discrete particle; simulations

• Wydawca: Wydawnictwa AGH
• Czasopismo: Computer Methods in Materials Science
• Rocznik: 2013
• Tom: Vol. 13, No. 2
• Strony: 197--212
• Opis fizyczny: Bibliogr. 64 poz., rys.

Twórcy

autor

Thornton C.

• Multi-Scale Mechanics, Department of Mechanical Engineering, University of Twente, 7500 AE Enschede, The Netherlands
• Mathematics of Computational Science, Department of Applied Mathematics, University of Twente, 7500 AE Enschede, The Netherlands

autor

Weinhart T.

• Multi-Scale Mechanics, Department of Mechanical Engineering, University of Twente, 7500 AE Enschede, The Netherlands

autor

Ogarko V.

• Multi-Scale Mechanics, Department of Mechanical Engineering, University of Twente, 7500 AE Enschede, The Netherlands

autor

Luding S.

• Multi-Scale Mechanics, Department of Mechanical Engineering, University of Twente, 7500 AE Enschede, The Netherlands

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