Numerical simulating and analytical modelling the wake behind vertical axis wind turbines: a verification analysis

Vertical axis wind turbines VAWTs have been demonstrated to possibly be more efficient than traditional turbines, especially in wind farms, where the wake-turbine interaction is intensive. Tools to analyse VAWTs are still studied and improved, especially analytical wake models which are widely used by companies when studying wind farm layouts thanks to the low computational cost. Nevertheless, they are often based on neglecting relevant aspects and incorrect assumptions and derivation, being most of the times horizontal axis wind turbines HAWTs wake models simply transposed to VAWTs. Therefore they are considered inaccurate. The purpose of this thesis is to investigate such methods, defining their validity range and their limitations, shedding light on possible improvements and corrections. Two existing analytical wake models are implemented and investigated: one based on a top-hat and the other on a Gaussian distribution for the velocity deficit. The models were supported by two different equations for the wake decay constant for HAWTs: the Niayifar and Abkar laws. Several tests were run and models were compared against high fidelity simulation data in the literature, covering different conditions by changing the aspect ratio AR from 0.25 to 2 as well as thrust coefficient CT from 0.3 up to 0.8. The range of validity of these analytical tools was then analysed. Numerical simulations based on the actuator line theory coupled with URANS equations were introduced as a higher fidelity data source for comparison, to better understand the effects of Reynolds number Re and turbulence intensity TI. Such model was validated against experimental and literature data that covered conditions ranging from low ≈105 to high ≈107 Re. Effect of environmental TI on wake recovery was qualitatively analysed with values ranging from extremely low 1% to high 8% TI. Results obtained from the numerical simulations were then compared with analytical wake models for the different scales and Re. Existing analytical wake models for VAWTs were found being accurate especially when dealing with the far wake region and in high TI environment. Gaussian model supported by Abkar's law showed the best accuracy with a deviation from high fidelity data for the maximum velocity deficit ranging from less than 1 % up to 8%. When the near wake or low TI conditions were considered, the error for the Gaussian models increased up to 55-60%. Top-hat models showed better agreement in extreme conditions, when high aspect ratios and low TIs are experienced, showing 40% deviation less than Gaussian models in the near. Additional analysis of the numerical results showed that wake's structures at different Re were similar. Similarly the TI effect on the wake was investigated and found to be strictly related to the Re, leading to different shape and deficit values. The detailed analysis of wake models for VAWTs leads to significant considerations about their validity and their limitations. When considering far wake regions and high TIs, wake models are capable of providing accurate results. In contrast, the models perform poorly in the near wake, as well as in low TIs mainly because existing formulation of wake decay/expansion are for HAWTs. The second main limitation is related to the inability to replicate wake deflection. It is important to improve the models in future by introducing expressions for the wake decay based on VAWT aerodynamics and modelling wake's centre displacement.