Numerical Analysis of a Steam Turbine Rotor subjected to Thermo-Mechanical Cyclic Loads

The contribution at hand discusses the thermo-mechanical analysis of a steam turbine rotor, made of a heat-resistant steel. Thereby, the analysis accounts for the complicated geometry of a real steam turbine rotor, subjected to practical and complex thermo-mechanical boundary conditions. Various thermo-mechanical loading cycles are taken into account, including different starting procedures (cold and warm starts). Within the thermal analysis using the FE code ABAQUS, instationary steam temperatures as well as heat transfer coefficients are prescribed, and the resulting temperature field serves as input for the subsequent structural analysis. In order to describe the mechanical behavior of the heat-resistant steel, which exhibits significant rate-dependent inelasticity combined with hardening and softening phenomena, a robust nonlinear constitutive approach, the binary mixture model, is employed and implemented in ABAQUS in two different ways, i.e. using explicit as well as implicit  methods for the time integration of the governing evolution equations. The numerical performance, the required computational effort, and the obtained accuracy of both integration methods are examined with reference to the thermo-mechanical analysis of a steam turbine rotor, as a typical practical example for the numerical analysis of a complex component. In addition, the obtained temperature, stress, and strain fields in the steam turbine rotor are discussed in detail, and the influence of the different starting procedures is examined closely

Partitioned Coupling vs. Monolithic Block-Preconditioning Approaches for Solving Stokes-Darcy Systems

We consider the time-dependent Stokes-Darcy problem as a model case for the challenges involved in solving coupled systems. Keeping the model, its discretization, and the underlying numerics for the subproblems in the free-flow domain and the porous medium constant, we focus on different solver approaches for the coupled problem. We compare a partitioned coupling approach using the coupling library preCICE with a monolithic block-preconditioned one that is tailored to different formulations of the problem. Both approaches enable the reuse of already available iterative solvers and preconditioners, in our case, from theDuMuxframework. Our results indicate that the approaches can yield performance and scalability improvements compared to using direct solvers: Partitioned coupling is able to solve large problems faster if iterative solvers with suitable preconditioners are applied for the subproblems. The monolithic approach shows even stronger requirements on preconditioning, as standard simple solvers fail to converge. Our monolithic block preconditioning yields the fastest runtimes for large systems, but they vary strongly with the preconditioner configuration. Interestingly, using a specialized Uzawa preconditioner for the Stokes subsystem leads to overall increased runtimes compared to block preconditioners utilizing a more general algebraic multigrid. This highlights that optimizing for the non-coupled cases does not always pay off

Numerical solution of optimal control problems with implicitly defined discontinuities with applications in engineering

In the thesis on hand we treat optimal control problems for implicitly discontinuous dynamical processes. We give a general model formulation which includes implicitly given state dependent discontinuities in the right hand sides of the DAE system. The formulation is adapted to real-world applications from chemical and biotechnological engineering. The resulting problems are large scale constrained problems of optimal control with implicitly given discontinuities of a priori unknown chronology and number. Our solution approach builds on the direct multiple shooting approach which allows the combination of appropriate DAE solvers with modern simultaneous optimization strategies. To solve the underlying optimization problem we apply SQP methods. We explain our strategy to provide sensitivity information at the presence of implicitly given discontinuities for large scale models. Efficient techniques for the derivative generation of the right hand sides particularly adapted to structural sparsity pattern changes of the adjacent Jacobians are presented. We formulate an algorithm to treat the optimization problem which depends on the chronology and number of discontinuities occuring in a digraph given by the successive trajectories of the SQP steps. We explain our modeling of a complex rack-in process of a distillation column and present the models of two biotechnological processes. Each of the models is equipped with characteristical implicit state dependent discontinuities of a priori unknown chronology. In numerical experiments we show the efficient applicability of our algorithms to the presented chemical process and to the two biotechnological applications. We apply our approach to optimal feedback control of a biotechnological application with implicit discontinuities

Discrete Adjoints: Theoretical Analysis, Efficient Computation, and Applications

The technique of automatic differentiation provides directional derivatives and discrete adjoints with working accuracy. A complete complexity analysis of the basic modes of automatic differentiation is available. Therefore, the research activities are focused now on different aspects of the derivative calculation, as for example the efficient implementation by exploitation of structural information, studies of the theoretical properties of the provided derivatives in the context of optimization problems, and the development and analysis of new mathematical algorithms based on discrete adjoint information. According to this motivation, this habilitation presents an analysis of different checkpointing strategies to reduce the memory requirement of the discrete adjoint computation. Additionally, a new algorithm for computing sparse Hessian matrices is presented including a complexity analysis and a report on practical experiments. Hence, the first two contributions of this thesis are dedicated to an efficient computation of discrete adjoints. The analysis of discrete adjoints with respect to their theoretical properties is another important research topic. The third and fourth contribution of this thesis focus on the relation of discrete adjoint information and continuous adjoint information for optimal control problems. Here, differences resulting from different discretization strategies as well as convergence properties of the discrete adjoints are analyzed comprehensively. In the fifth contribution, checkpointing approaches that are successfully applied for the computation of discrete adjoints, are adapted such that they can be used also for the computation of continuous adjoints. Additionally, the fifth contributions presents a new proof of optimality for the binomial checkpointing that is based on new theoretical results. Discrete adjoint information can be applied for example for the approximation of dense Jacobian matrices. The development and analysis of new mathematical algorithms based on these approximate Jacobians is the topic of the sixth contribution. Is was possible to show global convergence to first-order critical points for a whole class of trust-region methods. Here, the usage of inexact Jacobian matrices allows a considerable reduction of the computational complexity

Aeronautical Engineering: A continuing bibliography with indexes, supplement 128, November 1980

This bibliography lists 419 reports, articles, and other documents introduced into the NASA scientific and technical information system in October 1980