Schnelle Löser für Partielle Differentialgleichungen

The workshop Schnelle Löser für partielle Differentialgleichungen, organised by Randolph E. Bank (La Jolla), Wolfgang Hackbusch (Leipzig), and Gabriel Wittum (Frankfurt am Main), was held May 22nd–May 28th, 2011. This meeting was well attended by 54 participants with broad geographic representation from 7 countries and 3 continents. This workshop was a nice blend of researchers with various backgrounds

Measurements and finite element modelling of transformer flux with dc and power frequency current

Geomagnetically induced currents (GIC’s) caused by solar storms or other sources of dc excitation in the presence of ac energization can disturb the normal operation of power transformers. If large enough, they cause half-cycle saturation of a power transformer’s core which could lead to overheating due to excessive stray flux. Finite element matrix (FEM) modelling software is of considerable use in transformer engineering as it is able to solve electromagnetic fields in transformers. For many problems, typically involving only specific parts of a transformer, fairly accurate solutions can be reached quickly. Modelling the effects of GIC or leakage currents from dc systems, however, is more complex because dc components are superimposed on ac in transformers with nonlinear electrical core steel parameters. At the beginning of the investigation, FEM models of different bench-scale laboratory transformers and a 40 MVA three-phase three limb power transformer were investigated, but the results did not sufficiently represent the measurement data due to the application of widely used modelling assumptions regarding the transformer joints. Following the preliminary analyses, practical measurements and FEM simulations were carried out using three industrially made model single-phase four limb transformers (1p4L) without tanks. These test transformers resemble a real power transformer because they have high-quality grain oriented electrical core steel and parallel winding assemblies. Practical laboratory measurements recorded during ac testing were used to calibrate 2D FEM models by adding “equivalent air gaps” at the joints. The implementation of this joint detail helped to overcome the shortcomings of the preliminary FEM simulation. Analyses of the electrical and magnetic responses of the FEM models using simultaneous ac and dc then followed. A refined 3D FEM simulation with more detailed modelling of the core joints of 1p4L model transformers agreed more closely with the practical measurements of ac only no-load conditions. Further, the depiction of stray flux leaving the transformer’s saturated core under simultaneous ac and dc excitation showed an improvement in the approach as measured in the physical model. Saturation inductance (Lsat) is an important parameter for input into mid- to low-frequency lumped parameter transformer models that are used in electromagnetic transients software such as PSCAD/EMTDC, but it is not easily measured and is seldom provided by manufacturers. Some Lsat measurements on the 1p4L test transformers are presented in this thesis, along with some 3D FEM analyses. The measurements and FEM analyses investigated “air core inductance” which represents a transformer without a core, and “terminal saturation inductance” which represents deep saturation due to dc excitation. An important finding in this thesis is that “terminal saturation inductance” is the more useful of the two for topological transformer models investigating realistic GIC excitation. Further to this, a new composite depiction of half-cycle saturation with a multi-parametric relationships supported by measurement and simulation is presented. The main contribution of this thesis is that it gives more accurately the electrical response and distribution of the leakage flux under conditions such as those caused by GIC or other sources of leakage dc excitation, as well as including of joint details in the FEM models through calibration with physical models. This calibration can aid transformer modelling and design in industry for mitigation of the effects of GICs, contributing to improved transformer survival during significant geomagnetic disturbances

SOLID-SHELL FINITE ELEMENT MODELS FOR EXPLICIT SIMULATIONS OF CRACK PROPAGATION IN THIN STRUCTURES

Crack propagation in thin shell structures due to cutting is conveniently simulated using explicit finite element approaches, in view of the high nonlinearity of the problem. Solidshell elements are usually preferred for the discretization in the presence of complex material behavior and degradation phenomena such as delamination, since they allow for a correct representation of the thickness geometry. However, in solid-shell elements the small thickness leads to a very high maximum eigenfrequency, which imply very small stable time-steps. A new selective mass scaling technique is proposed to increase the time-step size without affecting accuracy. New ”directional” cohesive interface elements are used in conjunction with selective mass scaling to account for the interaction with a sharp blade in cutting processes of thin ductile shells

Fast Magnetic Flux Line Allocation Algorithm for Interactive Visualization Using Magnetic Flux Line Existence Probability

The visualization of magnetic flux lines is one of the most effective ways to intuitively grasp a magnetic field. The depiction of continuous and smooth magnetic flux lines according to the magnetic field is of paramount importance. Thus, it is important to adequately allocate the distribution of magnetic flux lines in the analyzed space. The authors have already proposed two methods of determining the allocation of magnetic flux lines in 3-D space. However, both methods exhibited a long computation time to determine the allocation of magnetic flux lines. For solving this problem, in this paper, we propose a new improved method for correct allocation of magnetic flux lines in 3-D space with modest computational cost. The main advantages of this method are shorter computation time, correct allocation of the magnetic flux lines, and especially short computation time for visualization of magnetic flux lines when changes in the number of depicted flux lines is requested

Modal Analysis of the Wake Shed Behind a Horizontal Axis Wind Turbine with Flexible Blades

The proper orthogonal decomposition (POD) has been applied on a full-scale horizontal-axis wind turbine (HAWT) to shed light on the wake characteristics behind the wind turbine. In reality, the blade tip experiences high deflections even at the rated conditions which definitely alter the wake flow field, and in the case of a wind farm, may complicate the inlet conditions of the downstream wind turbine. The turbine under consideration is the full-scale model of the NREL 5MW onshore wind turbine which is accompanied by several simulation complexities including turbulence, mesh motion and fluid-structure interaction (FSI). Results indicated an almost similar modal behaviour for the rigid and flexible turbines at the wake region. In addition, more flow structures in terms of local vortices and fluctuating velocity fields take place at the far wake region. The flow structures due to the wake shed from the tower tend to move towards the center and merge with that of the nacelle leading to an integral vortical structure 2.5D away from the rotor. Also, it is concluded that the exclusion of the tower leads to missing a major part of the wake structures, especially at far-wake positions

SCEE 2008 book of abstracts : the 7th International Conference on Scientific Computing in Electrical Engineering (SCEE 2008), September 28 – October 3, 2008, Helsinki University of Technology, Espoo, Finland

This report contains abstracts of presentations given at the SCEE 2008 conference.reviewe

Adaptive Algorithms

Overwhelming empirical evidence in computational science and engineering proved that self-adaptive mesh-generation is a must-do in real-life problem computational partial differential equations. The mathematical understanding of corresponding algorithms concerns the overlap of two traditional mathematical disciplines, numerical analysis and approximation theory, with computational sciences. The half workshop was devoted to the mathematics of optimal convergence rates and instance optimality of the Dörfler marking or the maximum strategy in various versions of space discretisations and time-evolution problems with all kind of applications in the efficient numerical treatment of partial differential equations