This dissertation is a summary of my works in the field of aerodynamics and wind turbine simulations. My main focus has been on analyzing and suggesting novel ideas to get more power from a wind turbine and/or wind farms. Based on the problems I have solved throughout my research, I have classified my works in three major chapters.

First, I analyzed the aerodynamic performance of the dual rotor wind turbines (DRWTs) and compared it to the traditional single rotor wind turbines (SRWTs). DRWTs were suggested as a new concept to get more power from wind farms and wind turbines in isolation. Prior investigatoins on DRWTs showed that they have potential in reducing blade root loss and wake loss. In my research, we used a higher-fidelity model (large eddy simulation, LES) to analyze the aerodynamics and loads on DRWTs under different stability conditions of the turbulent atmospheric boundary layer (ABL). Actuator line method (ALM) was selected to model the rotating turbine blades. Moeng wall model was applied to obviate a high resolution mesh in the high gradient regions near the ground. The mixing length model by Smagorinsky was used to model eddy viscosity. Aerodynamic analysis was quantified by measuring the mean velocity and turbulent intensity on different sections in the wake of wind turbine. In addition, the effect of using a secondary rotor on wake loss mitigation was checked by measuring the momentum entrainment behind the turbines. Moreover, the changes in loadings (specifically, out-of-plane blade moment) and power of wind turbines were measured both in time and spectral domains. Our findings show that the DRWT operating in isolation improves the aerodynamic performance ($C_P$) by 5-6\% for all inflow conditions compared to SRWT. The DRWT enhanced wake mixing and entrainment of higher momentum fluid from outside the wake layer for moderately high atmospheric turbulence (such as in the neutral stability ABL). Unsteady fluctuations in rotor power were observed at blade passing frequency. However, fluctuations in blade root moments are at the rotor passing frequency and its harmonics. These fluctuations occur

because of the azimuthal variation (due to the ABL) in the incoming mean wind as well as turbulence in the wind.

Results of the first investigation led us to the second part of this thesis: there was a room for improvement in energy capturing by using DRWT instead of SRWT. However, neither SRWTs or DRWTs were particularly designed to give the best aerodynamic performance. On the other hand, the aerodynamic performance is strongly dependent on the blade geometry (chord and twist distribution) among other factors, such as atmospheric stability and wind strength. Therefore, we developed an approach to find the blade geometry that leads to the best aerodynamic behavior of wind turbines. Various parameters related to wind turbines can be assessed to quantify its aerodynamic behavior. In our work, we measure the angle of attack and axial induction factor for that purpose. Then the problem is defined as follows: what should the blade geometry be to have certain values of angle of attack and axial induction factor along the blade. This is an inverse problem. We used the trust region reflective (TRF), which is an iterative method, to find the optimal point to have the desired aerodynamic behavior along the blades. For iterative design processes, high-fidelity aerodynamic solvers (such as LES) are usually not suitable as the computational costs become prohibitive. Therefore, we used the medium-fidelity Reynolds Averaged Navier-Stokes (RANS) as the aerodynamic solver. The rotating blades were represented by actuator disk model (ADM). Prandtl's tip loss correction was applied to account for the finite length of blades. Based on our choices for direct (i.e. aerodynamic) and inverse solvers, a design algorithm was proposed to find the blade geometry. The goals were 1) to make sure that the algorithm was capable of providing the desired aerodynamic features and 2) to extend the design process to DRWTs. The design algorithm was tested on different single- and dual-rotor turbines. In each case the desired aerodynamic behavior and the airfoils consitituting the blade were different to ensure the robustness of the algorithm. It was found that the proposed algorithm could reach to blade geometries that resulted in the desired aerodynamic behavior. Moreover, the TRF was compared to the multi-dimensional Newton method that is a common inverse solver.

It was found that while both methods were capable of handling the inverse problem and

converging to the same blade geometry, they had different

convergence rates in differenet test cases. The TRF was more stable in constrained problems due to its gradual increase of the trust region. Also, the extension of the design algorithm to DRWT was successful. Differences in SRWT and DRWT Jacobian matrices were discussed.

Jacobian matrix quantifies the sensitivity of the output to the input parameters.

For DRWT cases, it also demonstrated the interplay between the two rotors.

While our results demonstrated improvements in performance and design of isolated wind turbines, the ultimate goal of our research is to get maximum power from wind farms where arrays of turbines are placed to capture wind energy. One of the main reasons that the design of a wind farm is different than the design of an isolated turbine is that downstream turbines do not work in undisturbed inflow. They work in the wake of upstream turbines. Historically, researchers use aerodynamic methods that are computationally relatively cheap (such as BEM) alongside an iterative inverse scheme (such as TRF or Newton's method) to design wind turbine blades. However, methods like BEM fail in proper modelling of wake flow and are not suitable for wind farm purposes. Employing RANS and ADM enabled us to simulate the wake flow and extend the blade design to wind farms. Therefore, we tried to find an answer to this question: what should the blade geometry (defined as radial distribution of chord and twist) be to get maximum total power from a wind farm with $n$ in-line wind turbines (defined as $C_{P,tot}= \sum\limits_{i=1}^n C_{P,i}$)? In addition, from our experience in blade design we knew that calculation of Jacobian matrix with a finite difference formula takes most (i.e. more than 80\%) of total computational time. Therefore we added the Broyden's method (which is a quasi-Newton method to recursively update the Jacobian matrix) to our proposed algorithm. First, isolated SRWTs and DRWTs wind turbines were tried out. Difference between the blades that were specifically designed for maximum power and those who were not (such as Betz' optimal turbine) were remarkable. Interesting results were obtained for wind farm cases, too. It was shown that for the case of three in-line turbines, if hypothetically one can have a different blade design for each turbine, they can achieve a higher total power. However, we proposed a unique design for all turbine blades that resulted in almost the same total power without the difficulties of manufacturing three different blades. For the case of ten in-line turbines it was shown that the total power was improved by $50\%$ if the design of all turbines is considered instead of just the ones in undisturbed inflow. In addition, it was demonstrated that output power from turbines in deep wake can reach to up to 50\% of the first row if they are taken into account when designing the wind farm.