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CFD-DEM Simulation of Superquadric Cylindrical Particles in a Spouted Bed and a Rotor Granulator
(2023)
The fluidization behavior of cylindrical particles in a spouted bed was first investigated experimentally using a camera setup. The obtained average spouted bed height was used to evaluate the accuracy of different drag models in CFD-DEM simulations with the superquadric approach to model the particle shape. The drag model according to Sanjeevi et al. showed the best agreement. With this model, cylindrical particles were simulated in a rotor granulator and the particle dynamics were compared with the fluidization of volume equivalent spherical particles.
Microcrystalline cellulose pellets for oral drug delivery are often produced by a combined wet extrusion-spheronization process. During the entire process, the cylindrical as well as the spherical pellets are exposed to various stresses resulting in a change of their shape and size due to plastic deformation and breakage. In this work, the effect of moisture content of pellets on their mechanical behavior is studied. In static compression tests, the strong influence of water content on deformation behavior of pellets is confirmed. Moreover, impact tests are performed using a setup consisting of three high-speed cameras to record pellet-wall collisions. Material properties, such as stiffness, restitution coefficient, breakage force, and displacement, were analyzed depending on the water content.
Coating of particles is a widely used technique in order to obtain the desired surface modification of the final product, e.g., specific color or taste. Especially in the pharmaceutical industry, rotor granulators are used to produce round, coated pellets. In this work, the coating process in a rotor granulator is investigated numerically using computational fluid dynamics (CFD) coupled with the discrete element method (DEM). The droplets are generated as a second particulate phase in DEM. A liquid bridge model is implemented in the DEM model to take the capillary and viscous forces during the wet contact of the particles into account. A coating model is developed, where the drying of the liquid layer on the particles, as well as the particle growth, is considered. The simulation results of the dry process compared to the simulations with liquid injection show an important influence of the liquid on the particle dynamics. The formation of liquid bridges and the viscous forces in the liquid layer lead to an increase of the average particle velocity and contact time. Changing the injection rate of water has an influence on the contact duration but no significant effect on the particle dynamics. In contrast, the aqueous binder solution has an important influence on the particle movement.
We study high dimensional integration in the quantum model of computation. We develop quantum algorithms for integration of functions from Sobolev classes \(W^r_p [0,1]^d\) and analyze their convergence rates. We also prove lower bounds which show that the proposed algorithms are, in many cases, optimal within the setting of quantum computing. This extends recent results of Novak on integration of functions from Hölder classes.
In this paper, the complexity of full solution of Fredholm integral equations of the second kind with data from the Sobolev class \(W^r_2\) is studied. The exact order of information complexity is derived. The lower bound is proved using a Gelfand number technique. The upper bound is shown by providing a concrete algorithm of optimal order, based on a specific hyperbolic cross approximation of the kernel function. Numerical experiments are included, comparing the optimal algorithm with the standard Galerkin method.
We survey old and new results about optimal algorithms for summation of finite sequences and for integration of functions from Hölder or Sobolev spaces. First we discuss optimal deterministic and randornized algorithms. Then we add a new aspect, which has not been covered before on conferences
about (quasi-) Monte Carlo methods: quantum computation. We give a short introduction into this setting and present recent results of the authors on optimal quantum algorithms for summation and integration. We discuss comparisons between the three settings. The most interesting case for Monte
Carlo and quantum integration is that of moderate smoothness \(k\) and large dimension \(d\) which, in fact, occurs in a number of important applied problems. In that case the deterministic exponent is negligible, so the \(n^{-1/2}\) Monte Carlo and the \(n^{-1}\) quantum speedup essentially constitute the entire convergence rate.
We study the global solution of Fredholm integral equations of the second kind by the help of Monte Carlo methods. Global solution means that we seek to approximate the full solution function. This is opposed to the usual applications of Monte Carlo, were one only wants to approximate a functional of the solution. In recent years several researchers developed Monte Carlo methods also for the global problem. In this paper we present a new Monte Carlo algorithm for the global solution of integral equations. We use multiwavelet expansions to approximate the solution. We study the behaviour of variance on increasing levels, and based on this, develop a new variance reduction technique. For classes of smooth kernels and right hand sides we determine the convergence rate of this algorithm and show that it is higher
than those of previously developed algorithms for the global problem. Moreover, an information-based complexity analysis shows that our algorithm is optimal among all stochastic algorithms of the same computational
cost and that no deterministic algorithm of the same cost can reach its convergence rate.
A new variance reduction technique for the Monte Carlo solution of integral
equations is introduced. It is based on separation of the main part. A neighboring equation with exactly known solution is constructed by the help of a deterministic Galerkin scheme. The variance of the method is analyzed, and an application to the radiosity equation of computer graphics, together with numerical test results is given.