A comparative study of a direct discretization and an operator-splitting solver for population balance systems

A direct discretization approach and an operator-splitting scheme are applied for the numerical simulation of a population balance system which models the synthesis of urea with a uni-variate population. The problem is formulated in axisymmetric form and the setup is chosen such that a steady state is reached. Both solvers are assessed with respect to the accuracy of the results, where experimental data are used for comparison, and the efficiency of the simulations. Depending on the goal of simulations, to track the evolution of the process accurately or to reach the steady state fast, recommendations for the choice of the solver are given

Detailed population balance modelling of industrial titania synthesis

This thesis presents an efficient and robust detailed population balance framework for simulating aerosol synthesis of structured particles using a stochastic method. This is developed in the context of the industrial titania (TiO2) process to enable extensive numerical characterisation of the pigmentary product. A reactor network model is used to provide a modular treatment of the reactor and account for key features, including multiple reactant injections, and tubular reaction and cooling zones. This approach simplifies the flow field in order to focus computational effort on resolving particle structure using a high-dimensional particle model and its modularity offers flexibility to investigate different configurations. Initial results are presented using a pre-defined temperature profile in the network, and the particulate product is characterised by its property distributions. Numerical performance is studied, highlighting the high computational cost of simulating strong phase-coupling, fast process rates, and broad particle size distributions. A novel hybrid particle model is developed to address these challenges. The hybrid particle model employs a univariate description of small particles and switches to a detailed particle model to resolve morphology of more complicated, aggregate particles. New simulation algorithms are presented to manage interactions between particles of each type. The hybrid model is shown to improve efficiency (resolution versus computational cost) and robustness (sensitivity to numerical parameters), while generating the same solutions and convergence behaviour as earlier models. The reactor model is extended, utilizing the superior numerical performance of the new hybrid particle model to enable inclusion of a system energy balance for more accurate study of a broad range of process conditions, and a more sophisticated particle model to resolve particle geometry. These contributions facilitate the study of particle structure and its sensitivity to reactor design and operational choices, providing insight into how operation affects characteristics of the particles and allowing direct comparison with experimental images of the pigmentary product.This research was supported by the National Research Foundation, Prime Minister's Office, Singapore under its Campus for Research Excellence and Technological Enterprise (CREATE) programme, and by Venator

Active Control of Shocks and Sonic Boom Ground Signal

The manipulation of a flow field to obtain a desired change is a much heightened subject. Active flow control has been the subject of the major research areas in fluid mechanics for the past two decades. It offers new solutions for mitigation of shock strength, sonic boom alleviation, drag minimization, reducing blade-vortex interaction noise in helicopters, stall control and the performance maximization of existing designs to meet the increasing requirements of the aircraft industries. Despite the wide variety of the potential applications of active flow control, the majority of studies have been performed at subsonic speeds. The active flow control cases were investigated in transonic speed in this study. Although the active flow control provides significant improvements, the sensibility of aerodynamic performance to design parameters makes it a nontrivial and expensive problem, so the designer has to optimize a number of different parameters. For the purpose of gaining understanding of the active flow control concepts, an automated optimization cycle process was generated. Also, the optimization cycle reduces cost and turnaround time. The mass flow coefficient, location, width and angle were chosen as design parameters to maximize the aerodynamic performance of an aircraft. As the main contribution of this study, a detailed parametric study and optimization process were presented. The second step is to appraise the practicability of weakening the shock wave and thereby reducing the wave drag in transonic flight regime using flow control devices such as two dimensional contour bump, individual jet actuator, and also the hybrid control which includes both control devices together, thereby gaining the desired improvements in aerodynamic performance of the air-vehicle. After this study, to improve the aerodynamic performance, the flow control and shape parameters are optimized separately, combined, and in a serial combination. The remarkable part of all these studies is both gradient and non-gradient optimization techniques were used to find the global optimum point. The second part of this study includes investigation of the possibility of weakening the shock strength and the reduction of far field signature by using off-body energy addition. The main obstacle for flying supersonically over land is the detrimental effects of sonic boom on general public and structures. The shock waves generated from various parts of an aircraft flying at supersonic speed, coalesce to form a classic sonic boom acoustic signature, \u27N\u27 wave associated with the sonic boom on the ground. High pressure was imposed on certain parts of the computational domain to simulate the pulsed laser effects, and then the propagation and interaction of this pulsed shock with shock waves generated from the diamond shaped model were investigated. Optimization of the location and the power of the pulsed shock were achieved using the non-gradient optimization technique. The main contribution of this study is the optimization of the parameters of pulsed shock

Probabilistic Modelling of Classical and Quantum Systems

While probabilistic modelling has been widely used in the last decades, the quantitative prediction in stochastic modelling of real physical problems remains a great challenge and requires sophisticated mathematical models and advanced numerical algorithms. In this study, we developed the mathematical tools for solving three long-standing problems in Polymer Science and Quantum Measurement theory. The question, “Why kinetic models cannot reproduce experimental observations in Controlled Radical Polymerization (CRP)?” has been answered by introducing in the kinetic model a delay and treating CRP as a non-Markovian process. The efficient stochastic simulation (SS) approach allowing for an accurate description of CRP has been formulated, theoretically grounded and tested using experimental data and the less advanced SS algorithms. An accurate prediction of a morphology development in multi-phase polymers is vital for synthesis of new materials but still not feasible due to its complexity. We proposed a Population Balance Equations (PBE)-based model and derived a conceptually new and computationally tractable numerical approach for its solution in order to provide a systematic tool for a morphology prediction in composite polymers. Finally, we designed a stochastic simulation framework for continuous measurements performed on quantum systems of theoretical and experimental interest, which helped us to re-examine the “fuzzy continuous measurements” theory by Audretsch and Mensky (1997) and expose some of its deficiencies, while making amendments where necessary. All developed modelling approaches are general enough to be applied to the broad range of physical applications and thus ultimately to contribute to the understanding and prediction of complex chemical and physical processes.BES-2014-06864, MTM2013-46553-C3-1-

Anderson Acceleration for Fixed-Point Iterations

This paper concerns an acceleration method for fixed-point iterations that originated in work of D. G. Anderson [J. Assoc. Comput. Mach., 12 (1965), pp. 547-560], which we accordingly call Anderson acceleration here. This method has enjoyed considerable success and wide usage in electronic structure computations, where it is known as Anderson mixing; however, it seems to have been untried or underexploited in many other important applications. Moreover, while other acceleration methods have been extensively studied by the mathematics and numerical analysis communities, this method has received relatively little attention from these communities over the years. A recent paper by H. Fang and Y. Saad [Numer. Linear Algebra Appl., 16 (2009), pp. 197-221] has clarified a remarkable relationship of Anderson acceleration to quasi-Newton (secant updating) methods and extended it to define a broader Anderson family of acceleration methods. In this paper, our goals are to shed additional light on Anderson acceleration and to draw further attention to its usefulness as a general tool. We first show that, on linear problems, Anderson acceleration without truncation is essentially equivalent in a certain sense to the generalized minimal residual (GMRES) method. We also show that the Type 1 variant in the Fang-Saad Anderson family is similarly essentially equivalent to the Arnoldi (full orthogonalization) method. We then discuss practical considerations for implementing Anderson acceleration and illustrate its performance through numerical experiments involving a variety of applications

Proceedings of the Eleventh UK Conference on Boundary Integral Methods (UKBIM 11), 10-11 July 2017, Nottingham Conference Centre, Nottingham Trent University

This book contains the abstracts and papers presented at the Eleventh UK Conference on Boundary Integral Methods (UKBIM 11), held at Nottingham Trent University in July 2017. The work presented at the conference, and published in this volume, demonstrates the wide range of work that is being carried out in the UK, as well as from further afield