# 第15回 計算工学講演会

主 催：日本計算工学会
日 時： 2010年5月26日(水)〜5月28日(金)

会 場： 九州大学医学部百年講堂（福岡市東区馬出3-1-1）

## 特別講演

講師：David Roger Jones Owen教授（Swansea University, UK）

話題：Multi-Field Coupling Strategies for Large Scale Problems Involving Multi-Fracturing Solids and Particulate Media

日時：5月27日（木）14:35〜15:35

場所：Ａ・Ｂ室（1F中ホール1・2）

参加費：無料

### MULTI-FIELD COUPLING STRATEGIES FOR LARGE SCALE PROBLEMS INVOLVING MULTI-FRACTURING SOLIDS AND PARTICULATE MEDIA

D. R. J. Owen, Y. T. Feng, K. Han and C. R. Leonardi

Civil and Computational Engineering Centre Swansea University, Singleton Park, Swansea, SA2 8PP, UK

In several applications of industrial relevance involving multi-fracturing solids and/or particulate media, the system response is governed by the presence of an additional phase, either gaseous, liquid or both, or by the need to consider other physical phenomena, such as thermal effects. Alternatively, the problem may involve the combined flow of particles interspersed with fine grained material, necessitating a multi-scale approach to solution. The presentation considers the essential issues necessary for an effective computational treatment of such coupled systems, with the most appropriate route to solution being highly problem dependent. Specific problems that are addressed include the following:

** Rock blasting**. In this application coupling takes place through interaction between the gas pressure due to explosive detonation and the progressively fracturing rock. The most appropriate route to solution is provided by superposing a background Eulerian grid over the Lagrangian mesh used for fracture modelling [Owen et al. 1]. Within this regular grid the gas pressure modelling is based on the mass conservation and momentum equations for gas flow employing directional porosities derived from the rock fracture simulation. The coupling takes place through interdependence between the evolving gas pressure driving the fracturing process which, in turn, provides the porosity distribution which controls the gas pressure. Computationally, solution can be effectively provided through use of a staggered solution scheme based upon time integration of the two fields with partitioned time stepping.

** Particle transport**. The treatment of particle transport problems crucially depends of the size of the particles in relation to the domain size. For small particle sizes, as occur in fluidised beds for example, effective methods have been developed based on background fluid grids in which fluid forces can be computed and applied to particles residing within a particular grid cell. However, for problems in which the particle sizes are large and extend over more than one (or several) grid sizes, alternative solution strategies must be adopted. One option, which is considered here, is to employ a Lattice-Boltzmann (LB) procedure to model the fluid flow. This has the advantage that large particle sizes can be accommodated and moving boundaries of the fluid domain can also be incorporated. Furthermore, employing the Discrete Element Method (DEM) to account for the particle interaction in the problem leads naturally to a combined LB-DEM solution procedure. Key modelling issues involved in this coupled solution strategy [Feng et al. 2] include the standard LB formulation for fluid flow, the interaction between fluid flow and boundaries/moving particles, incorporation of a turbulence model for high Reynolds number cases, and the interaction between solid particles in the DEM.

Other application areas in which Lattice-Boltzmann approaches can also be used include the modelling of heat transfer between a moving particle system at elevated temperatures and a surrounding pressure driven gas environment, using a double population LB formulation to describe the gas velocity distribution and thermal energy balance. A further source of heat transfer is direct conduction between the particles which can be modelled through a quasi-finite element procedure developed specifically for particle systems [Feng et al. 3]. Additionally, an important issue in block cave mining operations is fines migration in which fine particles that are several orders of magnitude smaller than the main rock fragments flow through the moving particle system [Owen et al. 4]. In this multi-scale problem the fines can be modelled within a LB setting using a power law fluid or Bingham plastic formulation to describe the quasi-continuum flow involved, which is then coupled to the DEM modelling of the larger rock fragments.

Applicability of the methodology developed is illustrated through several practical examples related to mineral mining/processing operations and other industrial problems.

**References**

1. D. R. J. Owen, Y. T. Feng, E. DeSouza Neto, F. Wang, M. G. Cottrell, F. A. Pires and J. Yu: The modelling of multi-fracturing solids and particulate media. *Int. J. Numer. Meth Engng,* 60(1): 317-340, 2004.

2. Y. T. Feng, K. Han and D. R. J. Owen, Coupled lattice Boltzmann method and discrete element modeling of particle transport in turbulent fluid flows: Computational issues, Int. J. Num. Meth. In Engng., Vol72, pp 1111-1134, 2007.

3. Y. T. Feng, K. Han, C. F. Li and D. R. J. Owen, Discrete thermal element modeling of heat conduction in particle systems: Basic formulations, J Computational Physics, Vol. 227, pp 5072-5089, 2008.

4. D. R. J. Owen, Y. T. Feng, K. Han and C. R. Leonardi Computational modelling of multi-field problems involving particulate media, WCCM’08, 8th World Congress for Computational Mechanics, Venice, Italy, 30th June - 4th July, 2008.