Wind turbine wakes: exploring the underexplored

In this thesis, we aim to contribute to the research on two topics, namely, vertical-axis wind turbines (VAWTs) and wind turbines on topography.

In the VAWT part, first, we implement two actuator-type VAWT parameterization models (i.e. the actuator swept-surface model and the actuator line model) for use in numerical flow simulations with the purpose of studying the wake of VAWTs and their performance in the atmospheric boundary layer (ABL). These models are implemented in a large-eddy simulation (LES) framework, and the results are validated with experimental data. After validating the model, we investigate the energetic performance and wake structure of a megawatt-VAWT which is placed in the ABL. We characterize, in particular, the energetic performance of such a turbine by calculating the power coefficient of the turbine for more than 100 different combinations of tip-speed ratios and solidities. The optimum combination of solidity (defined as $Nc/R$, where $N$ is the number of blades, $c$ is the chord length and $R$ is the rotor radius) and tip-speed ratio is found to be 0.18 and 4.5, respectively. This combination results in a power coefficient of 0.47.

In the topography part, we implement the combined actuator disk model and the coordinate transformation method in our LES framework to simulate a wind farm sited on topography and also to validate our LES framework for turbine-topography systems with wind-tunnel measurements. Next, we consider the effect of pressure gradient on turbulent planar and axisymmetric wakes. For both cases, we develop analytical models to predict the wake evolution in pressure gradient conditions. The models are validated with both experimental and LES data.

Furthermore, in the last study of the topography part, we build on all of the previous accomplishments of this part to give a better picture on what happens to a turbine wake when it interacts with a hill. We present an analytical framework to model turbine wakes over two-dimensional hills. The model consists of two steps. In the first step, we deal with the effect of pressure gradient on the wake evolution; and in the second step, we consider the effect of the hill-induced streamline distortion on the wake. This model enables us to obtain the wake recovery rate, the mean velocity and velocity deficit profiles and the wake trajectory in the presence of the hill. Moreover, we perform LES to test our model and also to obtain new complementary insight about such flows. Especially, we take advantage of the LES data to carry out a special treatment for the behaviour of the wake on the leeward side of the hill. It is found that the mainly favourable pressure gradient on the windward side of the hill accelerates the wake recovery and the adverse pressure gradient on the leeward side decelerates it. The wake trajectory for a hill of the same height as the turbine's hub-height is found to be almost following the hill profile in the windward side but it maintains an almost constant elevation (a horizontal line) downstream of the hilltop. The trajectory of the wake on the leeward side is also studied for the limiting case of an escarpment, and it is shown that an internal boundary layer forms on the plateau which leads to an upward displacement of the wake center. Finally, a parametric study of the position of the turbine with respect to the hill is performed to more elucidate the effect of the hill-induced pressure gradient on the wind turbine wake recovery.