Dalibor Cavar, Dan N. Sørensen, Jens N. Sørensen, Technical University of Denmark

Danish invention, The Waveplane, harnesses the energy of ocean waves by catching water in a reservoir and using gravity to inject it tangentially into a straight pipe. A highly swirling flow inside the pipe is established and a hydraulic axial turbine extracts energy (Figure 1 above). A scale model of the sections affecting the flow to the turbine was built at ‘The Technical University of Denmark’, and extensive experimental investigations, aimed at optimizing the inflow to the axial turbine, were conducted.

It was soon seen that the swirling flow inside the turbine pipe flow was highly asymmetric, reducing the efficiency of the turbine. It was decided to investigate this further by CFD. The numerical study focused mainly on the flow upstream of the turbine. The turbine itself was omitted from the calculations. Fig. 2, shows the set-up and the outline of the computational grid.

Most RANS models cannot accurately model internal turbulent flows with large swirl-angles, and preliminary tests on published measurements of axisymmetrical swirling flows showed that none of the wide choice of turbulence models available in STAR-CD were quite suitable. A correction to the equation for the dissipation of turbulent kinetic energy, e, was required. This was implemented by user-programming, based on the Richardson-number. The axisymmetrical results were significantly improved, mainly because of a lowered turbulent viscosity at the center of
the duct.

The correction for swirl requires knowledge of the rotational centre, which is not known a priori for the non-axisymmetrical flow in the turbine pipe of the present study. To circumvent this, the radial distribution of turbulent viscosity within the duct was prescribed to characterize the distribution in the axisymmetrical case In the supply funnel, the k-w SST-model was used, and a suitable transition zone between the two models was applied.

Fig. 3 shows the axial and tangential velocity profiles measured near the position of the turbine. The results demonstrate that the corrected calculations are superior to results obtained by the k-e model. Figure 4a shows the swirl-center along the pipe and the highly asymmetrical flow is clearly seen. Various modifications were tested numerically to make the flow more symmetrical. Fig. 4b is a result of changing the funnel angle to 90° and also incorporating a thin plate inside the funnel extending 270° into the pipe.

These modifications clearly make the flow much more symmetrical at the expense of only a small loss in swirl. As a result of The Technical University of Denmark’s’ studies using STAR-CD, modifications to the Waveplane were suggested that, ultimately, have the potential of increasing energy conversion efficiency of the Waveplane.

For further information, contact: dns@mek.dtu.dk or visit www.waveplane.com