# Numerical Investigations of Turbulent Flow in Water Turbines

[Doktorsavhandling]

This thesis investigates turbulent flow in water turbines, focusing on the flow in the vicinity of reaction water turbine runners such as the Kaplan runner and the Francis runner. The method of investigation is principally numerical although some experimental observations and measurements made in the present work and elsewhere are included. A major part of the present work was to implement an efficient and general CFD (Computational Fluid Dynamics) code that could resolve the complicated geometry of a water turbine. A parallel multiblock finite volume CFD code, CALC-PMB (Parallel MultiBlock), was developed. The main features of the code are the use of conformal block structured boundary fitted coordinates, a pressure correction scheme (SIMPLEC), Cartesian velocity components as the principal unknowns and a collocated grid arrangement together with Rhie and Chow interpolation. The turbulence is modeled using a low-Reynolds k-omega turbulence model. The parallel multiblock algorithm employs two ghost cell planes at the block interfaces. The message passing at the interfaces is done using either PVM (Parallel Virtual Machine) or MPI (Message Passing Interface). Three water turbine runners are used for the investigations, two Kaplan runners and one Francis runner. One of the Kaplan runners was used during the development of the CFD code. This runner could not be used to validate the CFD code but the work on this runner still gave valuable insights on CFD in water turbines. The other Kaplan runner is a model of the runners installed in the H¨olleforsen power plant in Indals¨alven in Sweden. The computational results of the H¨olleforsen wicket gate and runner flow are validated against the thorough experimental investigations from the Turbine 99 workshops and additional LDV (Laser Doppler Velocimetry) measurements made in the present work. The Francis runner model investigated here was used as a test case at a GAMM workshop in 1989. The present computational results of the GAMM Francis runner are validated against measurements at both the best efficiency operating condition and four off-design operating conditions. Several important flow features are visualized to make comparisons with experimental observations and to better understand the flow in water turbine runners. The validations against both detailed measurements and experimental observations show that the flow is captured qualitatively correctly. A method for numerical verification of the computational results has been derived and applied to the computational results of the present work. The method is based on the conservation of a sub-set of the angular momentum equations that is particularly important to swirling flow in water turbines. The method is based on the fact that the discretized angular momentum equations are not necessarily conserved when the discretized linear momentum equations are solved. The method shows that the first-order hybrid discretization scheme cannot be used and that the second-order Van Leer discretization scheme needs improvement to give quantitatively correct results in these kinds of applications.

**Nyckelord: **CFD, Numerical, Parallel, Multiblock, Kaplan, Francis,
Turbine, Validation, Verification, Visualization

Denna post skapades 2006-08-25. Senast ändrad 2014-09-29.

CPL Pubid: 9884