Research On The Two-Dimensional Analytical Models For Wind-Turbine Wakes

As a hot topic and difficulty in the field of wind power,the wind-turbine wakes would lead to a decreased wind speed and an increased turbulence level in the downstream region,which results in the reduction of power generation and the accumulation of fatigue damage.The analytical wake models can quantitatively predict the turbine wake and are widely used in both theoretical study and engineering applications,due to their simplicity,quick compute,high accuracy and low cost.However,there are still some defects in the commonly-used analytical wake models.To address these issues,this paper first deeply researches the evolution of single wake using large-eddy simulation(LES),and then proposes two wake models with high accuracy based on the momentum theory and mass conservation,respectively.The comparison with high-fidelity data shows that the newly-derived models are in reasonable agreement with simulations and experiments.The main research contents and achievements of this dissertation are summarized as follows:(i)LES is adopted to study the flow structure and evolution of single wind-turbine wake under three surface roughness lengths.Some typical turbulence characteristics are analyzed in detail,such as the wake velocity deficit,turbulence intensity and Reynolds shear stress.The numerical results show that the turbulence mixing and momentum transport in the wake would become more violent over the rough surface and thus lead to a faster wake recovery.And the surface roughness directly affects the wake expansion coefficient.(ii)Based on the momentum theory,a two-dimensional analytical wake model is proposed.First,taking the difference between the actual profile of wake deficit and the standard Gaussian function into account,the physical wake boundary rw is determined as 2a of Gaussian curve,where a is the standard deviation of Gaussian function.Second,a more physically wake expansion rate k is introduced to represent the linear expansion of wake boundary.Third,a two-dimensional analytical wake model with high accuracy is proposed on the basis of momentum theory,Gaussian distribution and wake expansion model.The model predictions are in good agreement with simulations,wind-tunnel experiments and field measurements.As a useful result for real applications,for a wind turbine operating under the general conditions,k=0.075 recommended for onshore wind farms works very well in the new model over moderate ground roughness.(iii)Based on the mass conservation,a two-dimensional analytical wake model is proposed.First,mass conservation,momentum theory and Bernoulli equation are applied to an infinitesimal stream tube to figure out the velocity deficit from the upstream to the pressure recovery region.Second,a direct extension of the Jensen model is developed by applying the mass conservation to the far wake region.Third,taking the effect of pressure recovery region into account,a correction is made to propose a two-dimensional analytical wake model with high accuracy.The validation parts indicate that the present model outperforms the ID wake models and other 2D Jensen models with simplicity and low computational cost,thus it is easy to use for the real-world engineering applications.Both two-dimensional analytical wake models proposed in this work have the advantage of simple structure,quick calculation,low cost and high precision,thus have a good potential for practical engineering cases.