Instabilities in tidal turbine wakes

Abstract

We report on the observation of vortex instabilities in the wake of a tidal turbine undergoing harmonic unsteady axial inflow (e.g. due to surface waves). The work was carried out using unsteady RANS (URANS) modelling using the open-source CFD software OpenFOAM, using the `pimpleDyMFoam' solver. The PIMPLE algorithm used in the URANS solver is a combination of the PISO (Pressure Implicit with Splitting of Operator) and SIMPLE (Semi-Implicit Method for Pressure-Linked Equations) algorithms. URANS simulations usually have a limitation on the time step set by the Courant number (C = u (delta t)/(delta x), where delta x is the minimum cell length and u the local velocity. In the PISO algorithm, C<1 is usually required. However, the PIMPLE algorithm allows stable transient simulations at C>>1 by applying under-relaxation to each time-step until a convergence criterion is met, before allowing the time-step to complete with no applied relaxation factors. The turbulence model used was komega-SST, which has been used extensively in tidal turbine modelling.

As with a wind turbine, the response of a tidal turbine to unsteady flow is heavily influenced by the behaviour of the helical wake that returns in close proximity to the turbine blades  times per revolution ( – number of blades). Unsteady inflow causes the blades to shed vorticity into the wake, which in turn leads to a spatial variation in wake vortex strength, such that the vorticity of adjacent returning wake segments can differ, and thus there is a spatially varying velocity deficit in the wake. This spatial variation in velocity deficit triggers instability in the blade tip vortices, the emergence of which we demonstrate is governed by the non-dimensional group  relating the blade passing frequency to the gust frequency. If the ratio between these two frequencies is an integer, the wake is stable. If not, the tip vortices exhibit various forms of instability. If the wake is unstable, adjacent wake segments will eventually coalesce as they move downstream, such that the wake consists of larger regions of vorticity with lower spatial frequency, compared to the wake immediately behind the turbine. There is also some indication that these unstable, coalesced wakes persist further downstream, compared with stable wakes. This has implications for wind and tidal farm design, where interaction of a row of turbines with the wakes of upstream turbines is an important consideration.