Dense gas-solid flows are encountered in many different processes in the chemical industry, electricity industry or the steel and iron producing industry. A major challenge in modelling these flows are the wide range of length scales involved: the characteristic size of process equipment, such as a fluidized bed reactor, is typically of the order 1 - 10 meters. Yet,the large scale flow phenomena are directly influenced by particle-particle and particle-gas interaction, which happens on the scale of the size of the particles, which is in the range of 1 - 0.1 mm. This thesis is concerned with the modelling of dense gas-particle flow at the most detailed level, which is usually termed Direct Numerical Simulation (DNS). By this we mean simulations with models that resolve the flow on a scale smaller than the particles immersed in the fluid, and where the fluid-solid interactions are dictated by the no-slip boundary condition on the particles surface. Note that DNS does not imply particles. Although this number will increase in the coming years due to the expected advancements in computer resources, fully resolved simulation of even laboratory scale equipment will remain impossible for the foreseeable future. For this reason, one has to adopt a multi-scale modelling approach, were the insights on the detailed scale are used to develop and test "coarse-grained" models appropriate for larger-scale simulations. A key input in those larger-scale models is the averaged gas-solid interaction or drag force, which will be a recurring theme in this thesis. In the DNS simulation model, a finite difference discretisation of the Navier-Stokes equation is used to compute the fluid flow. In order to satisfy the constraint of stick boundary conditions at the surface of the particle, two different immersed-boundary (IB) methods have been developed and implemented in this work. The concept of an effective hydrodynamic diameter is introduced by comparing the simulation results for the drag force in a dilute simple cubic arrays of particles with the exact solution by Hasimoto. This is different from other works which introduce the effective diameter in an ad-hoc manner. With the use of such an effective diameter, the IB simulation results are found to be in good agreement with available theoretical and simulation data for dense regular and random arrays. A artificial test of the newly developed method is whether it can adequately model the hydrodynamic interaction force between two spheres. The results are compared with exact solutions that were obtained by a multipole-expansion solution to the Stokes equation and simulation results obtained with the well-established lattice-Boltzmann (LB) code Susp3D by Anthony Ladd. It is found that error in both IB- and LB-method are comparable for the same spatial resolution. Also it is established that even with a relatively that the smallest turbulent length scales are resolved by the spatial discretisation, as is common in the studies of turbulent flows. With the current computer resources it is possible to perform DNS simulation of systems that contain nor more than say 20000 low spatial resolution of the individual particles, a reasonably accurate prediction of the hydrodynamic force can be obtained. After these basic tests, the IB method is applied to model the slow flow past spherocylindrical particles, which are the first of these kind. The flow around single particles and static random arrays of particles is analysed and the results are found to be consistent with experimental data and theoretical results from literature. In chapter 5 the drag force on particle in random arrays of spheres is analysed in detail,this time by the use of the lattice-Boltzmann method. The data of extensive simulations have been analysed to study the fluctuations of the gas-solid force in homogeneous arrays of particles. This is of particular interest since in the larger-scale (DPM) models these fluctuations are not accounted for, since only the mean drag is parameterised. The rootmean-square deviation of these fluctuations is found to be about 10% of the mean force, and the maximum deviation is found to be up to 40%. The fluctuations do not only depend on the local microstructure (characterized by a local porosity), but also strongly depend on the local flow field and changes in the microstructure of the particle assembly within a distance of 2 to 3 particle diameters. Finally a comparison of fully-resolved simulations of small gasfluidized beds with O(1000) particles, using the IB method, with unresolved simulations, using the discrete particle model with the standard drag and a modified drag model based on chapter 5, is done. Since the focus is on the influence of the gas-solid interaction, only fully-elastic, frictionless particles are considered. Pressure drop, granular temperature and mean bed height are found to be larger in the IB simulations compared to the larger scale (DPM) simulation results obtained with the standard drag model, and lower compared to the DPM simulation results obtained with the modified drag model. Also, for each particle a drag force is computed that would follow from a correlation, i.e. the drag force that it would feel in a DPM simulation. On average this force is found to be about 30% smaller than the "true" DNS value. Apparently the drag force in beds with moving particles (in other words with a granular temperature) is higher than in static arrays, from which the commonly used closure relation for the drag force are derived.
|Qualification||Doctor of Philosophy|
|Award date||7 Dec 2011|
|Place of Publication||Eindhoven|
|Publication status||Published - 2011|