Chemical Engineering, Department of
http://hdl.handle.net/1974/769
2017-01-21T03:01:01ZMacromolecular Origins of Fifth Shear-Stress Harmonic in Large-Amplitude Oscillatory Shear Flow
http://hdl.handle.net/1974/15331
Macromolecular Origins of Fifth Shear-Stress Harmonic in Large-Amplitude Oscillatory Shear Flow
Jbara, Layal M.; Gilbert, Peter H.; Giacomin, A. Jeffrey
This study examines the simplest relevant molecular model of a polymeric liquid in large-amplitude oscillatory shear (LAOS) flow: the suspension of rigid dumbbells in a Newtonian solvent. For such suspensions, the viscoelastic response of the polymeric liquid depends exclusively on the dynamics of dumbbell orientation. We have previously derived explicit analytical expressions for the shear rate amplitude and frequency dependences of the first and third harmonics of the alternating shear stress response in LAOS. Higher harmonics sculpt the shear stress, distorting it from its sinusoidal shape. In this work, we derive the polymer contribution to the shear stress response up to and including the next higher, fifth harmonic. For this, we use the fourth order term in the expansion of the orientation distribution to calculate the shear stress response. Our analysis employs the general method of Bird and Armstrong [J Chem Phys, 56, 3680 (1972)]. Our expression is the only one to have been derived from a molecular theory for a fifth harmonic. Our paper thus provides the first glimpse of the molecular origins of a shear stress harmonic higher than the third.
2016-08-01T00:00:00ZNew Rigorous Decomposition Methods for Mixed-integer Linear and Nonlinear Programming
http://hdl.handle.net/1974/15265
New Rigorous Decomposition Methods for Mixed-integer Linear and Nonlinear Programming
Ogbe, Emmanuel
Process systems design, operation and synthesis problems under uncertainty can readily be formulated as two-stage stochastic mixed-integer linear and nonlinear (nonconvex) programming (MILP and MINLP) problems. These problems, with a scenario based formulation, lead to large-scale MILPs/MINLPs that are well structured.
The first part of the thesis proposes a new finitely convergent cross decomposition method (CD), where Benders decomposition (BD) and Dantzig-Wolfe decomposition (DWD) are combined in a unified framework to improve the solution of scenario based two-stage stochastic MILPs. This method alternates between DWD iterations and BD iterations, where DWD restricted master problems and BD primal problems yield a sequence of upper bounds, and BD relaxed master problems yield a sequence of lower bounds. A variant of CD, which includes multiple columns per iteration of DW restricted master problem and multiple cuts per iteration of BD relaxed master problem, called multicolumn-multicut CD is then developed to improve solution time. Finally, an extended cross decomposition method (ECD) for solving two-stage stochastic programs with risk constraints is proposed. In this approach, a CD approach at the first level and DWD at a second level is used to solve the original problem to optimality. ECD has a computational advantage over a bilevel decomposition strategy or solving the monolith problem using an MILP solver.
The second part of the thesis develops a joint decomposition approach combining Lagrangian decomposition (LD) and generalized Benders decomposition (GBD), to efficiently solve stochastic mixed-integer nonlinear nonconvex programming problems to global optimality, without the need for explicit branch and bound search. In this approach,
LD subproblems and GBD subproblems are systematically solved in a single framework. The relaxed master problem obtained from the reformulation of the original problem, is solved only when necessary. A convexification of the relaxed master problem and a domain reduction procedure are integrated into the decomposition framework to improve solution efficiency. Using case studies taken from renewable resource and fossil-fuel based application in process systems engineering, it can be seen that these novel decomposition approaches have significant benefit over classical decomposition methods and state-of-the-art MILP/MINLP global optimization solvers.
Molecular Origins of Higher Harmonics in Large-Amplitude Oscillatory Shear Flow: Shear Stress Response
http://hdl.handle.net/1974/15237
Molecular Origins of Higher Harmonics in Large-Amplitude Oscillatory Shear Flow: Shear Stress Response
Gilbert, Peter H.; Giacomin, A. Jeffrey
Recent work has focused on deepening our understanding of the molecular origins of the higher harmonics that arise in the shear stress response of polymeric liquids in large-amplitude oscillatory shear flow. For instance, these higher harmonics have been explained by just considering the orientation distribution of rigid dumbbells suspended in a Newtonian solvent. These dumbbells, when in dilute suspension, form the simplest relevant molecular model of polymer viscoelasticity, and this model specifically neglects interactions between the polymer molecules [R.B. Bird et al., J Chem Phys, 140, 074904 (2014)]. In this paper, we explore these interactions by examining the Curtiss-Bird model, a kinetic molecular theory designed specifically to account for the restricted motions that arise when polymer chains are concentrated, thus interacting and specifically, entangled. We begin our comparison using a heretofore ignored
explicit analytical solution [Fan and Bird, JNNFM, 15, 341 (1984)]. For concentrated systems, the chain motion transverse to the chain axis is more restricted than along the axis. This anisotropy is described by the link tension coefficient, ε, for which several special cases arise: ε = 0 corresponds to reptation, ε > 1/8 to rod-climbing, 1/2 ≥ ε ≥ 3/4 to reasonable predictions for shear-thinning in steady simple shear flow, and ε = 1 to the dilute solution without hydrodynamic interaction. In this paper, we examine the shapes of the shear stress versus shear rate loops for the special cases ε = (0,1/8, 3/8,1) , and we compare these with those of rigid dumbbell and reptation model predictions.
2016-11-01T00:00:00ZDistributed Generation Reformer and Fuel Cell System Modeling and Reformer Catalyst Layer Optimization
http://hdl.handle.net/1974/15219
Distributed Generation Reformer and Fuel Cell System Modeling and Reformer Catalyst Layer Optimization
DePippo, Kurtis
This research presents a diesel-fed steam reformer and solid oxide fuel cell stack system Honeywell UniSim® Design Suites model and a two-dimensional diesel-fed steam reformer ANSYS Fluent model. The performance of the reformer and fuel cell system was compared to the performance of diesel generators in Canadian remote communities to illustrate the environmental and economic advantages that reformer and fuel cell systems have over typical diesel generation setups. The results show that, despite current solid oxide fuel cell technology being economically unfeasible, technology that is nearing commercialization could present substantial environmental and economic savings opportunities for diesel-based distributed generation projects.
The UniSim® model relied on several assumptions, one of which was the full conversion of the fuel feed within the steam reformer. A two-dimensional steam reformer model was therefore created in ANSYS Fluent to more accurately model the reforming process. Parameter studies on the reformer catalyst layer showed that reducing catalyst layer porosity along the length of the reformer results in improved reformer performance because of increased catalyst mass and higher reaction rates downstream that help push the reforming reaction towards equilibrium.
Thesis (Master, Chemical Engineering) -- Queen's University, 2016-11-01 15:09:14.063
2016-11-01T00:00:00Z