Methodenentwicklung zur numerischen Strömungsanalyse von Freispiegelströmungen bei Schaufelwasserrädern

Scientific Conference (2014, March)

Der Ausbau der Wasserkraft gewinnt im Kontext der Energiewende weltweit an Bedeutung. Neben der Turbinentechnologie erweisen sich Wasserräder im Hinblick auf ihre hohe ökologische Verträglichkeit und ihr ... [more ▼]

Der Ausbau der Wasserkraft gewinnt im Kontext der Energiewende weltweit an Bedeutung. Neben der Turbinentechnologie erweisen sich Wasserräder im Hinblick auf ihre hohe ökologische Verträglichkeit und ihr hohes ganzjähriges Arbeitsvermögen als besonders geeignet. Das sich drehende Wasserrad, umgeben von Wasser und Luft, stellt mechanisch ein gekoppeltes Drei- Feld-System bestehend aus einer Struktur und zwei Fluiden dar. Hinreichend genau ist es möglich, die Wasserradstruktur als Starrkörper zu beschreiben, während Luft und Wasser mit Hilfe der inkom- pressiblen Navier-Stokes Gleichungen gut modelliert werden können. Durch Anwendung der Raum-Zeit-Finite-Elemente-Methode zur Diskretisierung der inkompressiblen Navier-Stokes Gleichungen wird die Grenzfläche zwischen dem Starrkörper und den Fluiden explizit beschrieben und stets automatisch korrekt erfasst. Die Beschreibung der freien Wasseroberfläche als Grenzfläche zwischen den beiden Fluiden erfolgt implizit mit Hilfe der Level-Set Methode. Die Netzknoten der Fluid-Struktur-Grenzfläche verändern ihre Position infolge der Wasserraddrehung mit der Zeit, so dass ein Netzbewegungsalgorithmus notwendig ist. Die shear-slip mesh update method (SSMUM) ermöglicht als diskontinuierliches Netzbewegungsverfahren eine durchgehende Berechnung des Gesamtsystems, ohne dass das gesamte Gebiet neu vernetzt werden muss. Anhand verschiedener Testbeispiele wird die Güte der entwickelten numerischen Methode im Hinblick auf Ihre Erhaltungseigenschaften untersucht. Besonderes Augenmerk wird auf die Lösungsübertragung am shear-slip layer sowie auf die Abbildung der implizit beschriebenen freien Wasseroberfläche gelegt. [less ▲]

Numerical analysis of free-surface flow through rotating machines

Presentation (2013)

In the context of the transformation process currently taking place in the energy production sector, energy gained from renewable power sources shall replace the present mixture, which mostly relies on ... [more ▼]

In the context of the transformation process currently taking place in the energy production sector, energy gained from renewable power sources shall replace the present mixture, which mostly relies on fossil burnings. Therefore, in the future most of the energy shall be gained by harvesting power from sun, wind or water, geothermal heat or biomass. In case of converting energy from wind into electrical power wind turbines are used in general, while hydropower turbines are the state-of-the-art machinery to derive energy from running water. In order to convert the potential energy from running water as well water wheels pose the method of choice. Turbines in air or water represent mechanically a two-field system, in which the structure of the turbine is surrounded by a streaming fluid. Due to the elasticity of the rotor blades the stresses of the fluid onto the structure deform the blades, which in return yield a time-dependent flow domain. Therefore turbines in a streaming fluid represent a typical example of fluid-structure interaction. Furthermore, in case of water wheels the surrounding air as third field and additional fluid phase comes into play introducing a free surface. In this contribution the governing equations of incompressible fluid flow are presented using primal variables and discretised via the space-time finite element method [3]. The discretised model equations of the fluid are stabilised using an SUPG/PSPG approach. Shape and test functions are continuous within the space-time slabs, while across the space- time slabs the shape and test functions are continuous only in space, but discontinuous in time yielding a time-discontinuous Galerkin approach. Due to the moving rotor blades a mesh moving technique needs to be incorporated into the computational set-up. Considering the occurring large but regular displacements of the flow boundary arising from the rotating rotor blades the shear-slip mesh update method (SSMUM) [1] as discontinuous mesh moving technique is applied. In case of water wheels the free surface is described implicitly via a Level-Set function [2] yielding a single fluid phase with almost discontinuous density and viscosity. The verification and validation of the developed numerical scheme is carried out with the help of computing classical benchmark problems as well as via a comparison to existing experimental data. [less ▲]

Modification of the Shear-Slip Mesh Update Method with Respect to Space-Time Finite Element Discretisation of Fluid Flows

Scientific Conference (2012, April 27)

Space-time discretisations of physical problems involving moving and deforming bodies, boundaries and interfaces have been shown to offer advantageous properties while being methodologically uniform and ... [more ▼]

Space-time discretisations of physical problems involving moving and deforming bodies, boundaries and interfaces have been shown to offer advantageous properties while being methodologically uniform and flexible. Well-known phenomena which are ideally suited to be analysed by space-time methods, are fluid-structure interaction problems in general as well as fluid flows with subdomain phase boundaries or immersed moving objects. In this contribution a short overview of existing mesh- moving techniques is given within the framework of finite element discretisations of the incompressible Navier-Stokes equations in space and time. The investigation is based on a SUPG/PSPG velocity-pressure formulation on the deforming space-time domain. A modification of the shear-slip mesh update method in the framework of space-time finite element discretisation is presented leading to a continuous space-time mesh in the shear-slip layer. The modified mesh moving technique is applied to engineering problems with rotating space-time fluid meshes. Its conservation properties and its quality regarding the approximated solutions on moving and deforming meshes are investigated. [less ▲]