A comparison is made between numerical and experimental results for spin-up from rest in a rectangular container. The numerical results were obtained by using a three-dimensional finite volume method on a supercomputer. The experiments were performed with water, using tracer particles floating at the free surface in order to visualize the flow field. The numerical and experimental results are in good agreement. They show the formation of a stable three-cell pattern. In contrast to similar experiments performed at higher angular velocities, the center cell of this pattern appears to be anticyclonic. Initially, the relation between vorticity ω and streamfunction ψ of this organized flow is linear, but it is seen to evolve slowly into a relation with ∂2ω/∂ψ2<0.

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The importance to correctly predict the natural frequency of a turbine runner have been demonstrated several times. It is now common practice to include the added mass effect of the surrounding water when calculating the natural frequencies. In this paper the added mass effect of water on a simplified low specific speed francis turbine runner is experimentally investigated. Three cases are investigated. 1: The runner hanging in air. 2: The runner hanging in a tank of water. 3: The runner installed into the turbine housing. The measurements reveal a frequency reduction of about 40% when the runner is hanging in water. Installing the runner into the turbine housing does not significantly change the natural frequency of the main blade modes. Modes which vibrate heavily on the outside of the runner are visible in the water tank but becomes dampened when installed into the turbine housing.

This paper addresses the spin-up from rest of a free-surface fluid confined in a cylindrical container with a semicircular cross-section. The flow in the various stages of the spin-up process has been calculated numerically by using the finite-volume technique on a three-dimensional grid. Local grid refinement was applied in order to capture the effects of the boundary layer at the lateral boundaries and of the Ekman layer at the bottom. The numerical results agree very well with laboratory observations. KEY WORDS

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