Three-Dimensional Unsteady Hydrodynamics of Tidal Turbines
Tidal power is an emerging industry in the renewable energy sector; a development which is uniquely beneficial to the United Kingdom, which has a significant tidal resource and a mature knowledge base for turbine technology. One of the challenges facing the tidal industry is the harsh nature of the operating environment, due to the presence of waves and ocean turbulence. The turbines sustain damage due to the fluctuating loads that result from the unsteady flow, either from high-cycle fatigue or from extreme loading events exceeding the ultimate tensile strength of components.
In this thesis, the problem of unsteady loading is addressed by identifying the shortcomings of the models currently used to estimate unsteady forces on turbines due to gusts, and by providing new low-order modelling tools for more accurate calculations of these forces. The focus of this thesis is on the assumption of locally two-dimensional (2D) flow used in the majority of turbine loading models. Tidal turbines are strongly three-dimensional (3D) in shape, with low aspect ratio and strongly tapered blades. As such, the assumption of locally 2D flow is unlikely to apply. In this thesis the consequences of this assumption are explored, dividing 3D effects into two categories: 3D geometry effects, and the effects of 3D features in the incoming unsteady flow. The effect of these 3D features is shown by studying generic aerofoil geometries and a model tidal turbine, using a combination of first-order inviscid modelling with a vortex lattice model (VLM) and higher-order viscous modelling with URANS CFD.
The VLM is used in the frequency-domain to perform a parametric study of a range of aerofoil geometries. The unsteady response of aerofoils with finite span, rotation or varying planform is shown to deviate strongly from 2D predictions by linear analytic theory (such as the Theodorsen or Sears functions). At low reduced frequencies and low aspect ratios, 3D effects are strongly visible. In the vicinity of the aerofoil tips, 3D effects are significant at any reduced frequency. An exception is found in swept wings, where the unsteady response does not approach the 2D response in any conditions. The primary driver of the 3D load response is found to be the unsteady wake downwash, which is divided into contributions from the spanwise and streamwise components of wake vorticity. The former is modelled as extending infinitely in 2D models, while the latter is neglected altogether. URANS modelling and a time-domain vortex lattice model is used to estimate second order effects on the unsteady load response, due to viscous separation events and wake deformation, respectively. These second order effects on the unsteady loads are shown to be minor, and the URANS simulations also successfully validate the inviscid vortex lattice model.
For the analysis of 3D features in the incoming flow, this thesis uses eigenmode decomposition of the vortex lattice model, which finds the spatial shapes of the gusts that will cause the largest forces on a given aerofoil geometry. This is shown through the concept of "mode resonance": if a gust is similar in shape to a particular aerofoil eigenmode, that mode will contribute more to the total load response of the aerofoil. This analysis allows the definition of a "cut-off" spatial length scale for turbine load response; if the oncoming unsteady gust has a spanwise wavelength shorter than the cut-off value, the load response of the aerofoil to that gust will be negligible. This finding is used at the end of this thesis to show the impact of 3D flow features when evaluating the load response of a turbine in a realistic flow environment.
This thesis concludes that accounting for the effects of both 3D geometry and 3D flow is vital for accurate prediction of turbine load response to unsteady gusts.