For modeling agglomeration processes in the frame of the Lagrangian approach, where the particles are treated as point masses, an extended structure model was developed. This model provides not only information on the number of primary particles in the agglomerate, but also on the geometrical distension of the agglomerates. These are for example the interception diameter, the radius of gyration, the fractal dimension and the porosity of the agglomerate using the convex hull. The question however arises now, which is the proper agglomerate cross-section for the calculation of the drag force. In order to find an answer, the Lattice-Boltzmann-Method (LBM) was applied for simulating the flow about fixed agglomerates of different morphology and number of primary particles involved. From these simulations the drag coefficient was determined using different possible cross-sections of the agglomerate. Numerous simulations showed that the cross-section of the convex hull yields a drag coefficient which is almost independent on the structure of the agglomerate if they have the same cross-sectional area in flow direction. Using the cross-section of the volume equivalent sphere showed a very large scatter in the simulated drag coefficient. This information was accounted for in the Lagrangian agglomeration model. The basis of modeling particle collisions and possible agglomeration was the stochastic inter-particle collision model accounting for the impact efficiency. The possibility of particle sticking was based on a critical velocity determined from an energy balance which accounts for dissipation and the van der Waals adhesion. If the instantaneous relative velocity between the particles is smaller than this critical velocity agglomeration occurs. In order to allow the determination of the agglomerate structure reference vectors are stored between a reference particle and all other primary particles collected in the agglomerate. For describing the collision of a new primary particle with an agglomerate the collision model was extended in order to determine which primary particle in the agglomerate is the collision partner. For demonstrating the capabilities of the Lagrangian agglomerate structure model the dispersion and collision of small primary particles in a homogeneous isotropic turbulence was considered. From these calculations statistics on the properties of the agglomerates were made, e.g. number of primary particles, radius of gyration, porosity, sphericity and fractal dimension. Finally, the dispersion of particles in vertical grid turbulence was calculated by the Lagrangian approach. For one selected model agglomerate, dispersion calculations were performed with different possible characteristic cross-sections of the agglomerate. These calculations gave a deviation of the mean square dispersion of up to 20% after a dispersion time of 0.4 seconds for the different cross-sections. This demonstrates that a proper selection of the cross-section is essential for calculating agglomerate motion in turbulent flows.
Polymers under Load and Heating Deformability: Modelling and Predicting
