Subject: Isogeometric fluid analysis with applications in turbine design
Author: Dipl.-Ing. Ulrike Schwarzmair
Supervision: A.Univ.-Prof. Dr. Walter Zulehner
Referee: Prof. Dr. Bert Jüttler

In the frame of the European project EXCITING, we work on the design and optimization process of hydroelectric turbine blades. The main issue is to improve the current process of designing and developing blades of turbines by using isogeometric analysis. In the hydraulic design of turbines, CFD simulations are an important part of the development process. In order to avoid time consuming conversion processes between different geometric models, the turbine blades are modeled by NURBS throughout the whole design process, which gives rise to an isogeometric approach in this context.

We assume a volumetric NURBS representation of the surrounding medium of the blades to be given. We use the incompressible Euler equations transformed to a rotating coordinate system as the underlying mathematical model. Furthermore we adopt the concept of artificial compressibility. The resulting system of hyperbolic balance equations is analyzed with respect to its behavior as time goes to infinity. This is crucial because the used numerical methods rely on the convergence towards a steady-state solution.

The discretization in space is based on the volumetric NURBS representation of the computational domain. For stabilization we use an SUPG-method. The resulting semi-discretized system is solved with different time iteration schemes. We compare these schemes and examine the influence of the involved numerical parameters for an appropriate test example. Furthermore we give numerical results for a Kaplan turbine.

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