Algis Džiugys

An approach to simulate the motion of spherical and non-spherical fuel particles in combustion chambers

Abstract The objective of this paper is to identify a numerical method to simulate motion of a packed or fluidized bed of fuel particles in combustion chambers, such as a grate furnace and a rotary kiln. Therefore, the various numerical methods applied in the areas of granular matter and molecular dynamics were reviewed extensively. As a result, a time driven approach was found to be suited for the numerical simulation of particle motion in combustion chambers. Furthermore, this method can also be employed to moving boundaries which are required for the present application e.g. travelling grate. The method works in a Lagrangian frame of reference, which uses the position and orientation of particles as independent variables. These are obtained by time integration of the three-dimensional dynamics equations derived from the classical Newtonian approach for each particle. This includes the keeping track of all forces and momentums acting on each particle at every time step. Viscoelastic contact forces include normal and tangential components with viscoelastic models for energy dissipation and friction. The particle shapes are approximated by spheres and ellipsoids with a varying size and ratio of the semi-axis accounting for the variety of particle geometries in a combustion chamber. For these shapes the overlap of particles during contact is expressed by a polynomial of 4th order in the two-dimensional case and a polynomial of 6th order in the three-dimensional case. A new algorithm to detect two-dimensional elliptical particle contact with sufficient accuracy was developed. It is based on a sequence of coordinate transformations and has demonstrated its reliability in numerous applications. Finally, the method was applied to simulate the motion of spherical and elliptical particles in a rectangular enclosure, on a travelling grate, and in a rotary kiln.

Discrete element method and its application to the analysis of penetration into granular media

Abstract Application of discrete element method (DEM) to keel penetration in granular media is investigated. The basic relations for visco‐elastic granular media composed of spherical particles are presented, together with 5th order Gear predictor‐corrector scheme for time‐integration. The background version of DEM and numerical time integration algorithm are developed and implemented into DEMMAT code. The implementation of time‐integration algorithm is verified by simple tests concerning particle‐particle, particle‐wall interactions, for which analytical expressions exist. By limiting the size of the media domain, the three‐dimensional problem is reduced to particular case presented as two‐dimensional domain of spherical particles. The variation of keel reaction and distribution of the particle forces due to different material properties are investigated.

Investigation of performance of programming approaches and languages used for numerical simulation of granular material by the discrete element method

Abstract Performance of programming approaches and languages used for the development of software codes for numerical simulation of granular material dynamics by the discrete element method (DEM) is investigated. The granular material considered represents a space filled with discrete spherical visco-elastic particles, and the behaviour of material under imposed conditions is simulated using the DEM. The object-oriented programming approach (implemented via C++) was compared with the procedural approach (using FORTRAN 90 and OBJECT PASCAL) in order to test their efficiency. The identical neighbour-searching algorithm, contact forces model and time integration method were implemented in all versions of codes. Two identical representative examples of the dynamic behaviour of granular material on a personal computer (compatible with IBM PC) were solved. The results show that software based on procedural approach runs faster in compare with software based on OOP, and software developed by FORTRAN 90 runs faster in compare with software developed by OBJECT PASCAL.

Numerical simulation of the motion of granular material using object-oriented techniques

Abstract The objective of this contribution is to present a numerical simulation method to model the motion of a packed bed on a moving grate or in a rotary kiln using object-oriented techniques. The packed bed can be described as granular material consisting of a large number of particles. The method chosen is the Lagrangian time-driven method and it uses the position, the orientation, the velocity and the angular velocity of particles as independent variables. These are obtained by time integration of the three-dimensional dynamics equations which were derived from the classical Newtonian mechanics approach based on the second law of Newton for the translation and rotation of each particle in the granular material. This includes keeping track of all forces and moments acting on each particle at every time-step. Particles are treated as contacting visco-elastic bodies which can overlap each other. Contact forces depend on the overlap geometry, material properties and dynamics of particles and include normal and tangential components of repulsion force with visco-elastic models for energy dissipation through internal and surface friction. The resulting equations of particle motion are solved by the Gear predictor–corrector scheme of fifth-order accuracy. The simulation method is based on object-oriented methodologies and programmed in the programming language C++. This approach supports objects which can be used for three-dimensional particles of various shapes and sizes and for walls as boundaries. The programming modules are implemented in the TOSCA (tools of object-oriented software for continuum mechanic applications) software package which allows for a high degree of flexibility and for shortening the duration of the software development process. As methods for particle motion may deal with particles of different sizes and materials, the approach allows to describe transport processes in technical applications.

Comparison of the Heat-up of a Moving Bed on Forward and Backward Acting Grates

Within this contribution, heat-up of a moving bed on a forward and backward acting grate is compared through results obtained by numerical predictions. The dynamics of the grate bars determine motion of packed beds and their temperature distribution during heat-up to a large extent. Therefore, both bar amplitude and periodicity were subject to change, and its effect on individual particle temperatures was predicted. The heat-up process of the entire packed bed was characterized by maximum, minimum, and mean temperatures in conjunction with its standard deviation.

Community structure of force chains in granular hopper discharge

We analyse the force chain structure in granular matter during discharge from a hopper using discrete element modeling (DEM). Having obtained the particle configurations and the mechanical forces acting between the particles from DEM simulations, we build interaction graphs for the particle configurations at the respective time moments. The particles are represented as the graph vertices, the vertices are connected by edges if the respective particles are in contact, and the edge weights are proportional to the force moduli between the particle pairs. The community structures of the resulting graphs are then identified using a “walktrap” community detection algorithm. Evolution of the community structures is analysed during the hopper discharge and its dependence on the static friction coefficient between the particles.We analyse the force chain structure in granular matter during discharge from a hopper using discrete element modeling (DEM). Having obtained the particle configurations and the mechanical forces acting between the particles from DEM simulations, we build interaction graphs for the particle configurations at the respective time moments. The particles are represented as the graph vertices, the vertices are connected by edges if the respective particles are in contact, and the edge weights are proportional to the force moduli between the particle pairs. The community structures of the resulting graphs are then identified using a “walktrap” community detection algorithm. Evolution of the community structures is analysed during the hopper discharge and its dependence on the static friction coefficient between the particles.