This thesis proposes equations extending the Free Surface Actuator Disc Theory to yield drag forces and interference factors from a series of two porous discs in open channel flows. The new model includes blockage ratio and Froude number as independent variables, which are inferred in advance to yield a single solution in the prescribed domain. The theoretical extension is integrated with the Blade Element Theory in a Double Multiple Streamtube model (DMS) to predict axial loads and the performance of confined Darrieus turbines. The turbine thrust force influences the flow approaching the rotor. Hence, a momentum method is applied to solve the hydraulic transition in the channel, achieving the unknown inflow factor from the undisturbed flow imposed downstream. The upstream blockage ratio and Froude number are thus updated iteratively to adapt the DMS to subcritical applications. The DMS is corrected further to account for the energy losses due to mechanical struts and turbine shaft, flow curvature, turbine depth, and streamtube expansion. Sub-models from the literature are partly corrected to comply with the extended actuator disc model. The turbine model is validated with experimental data of a high-solidity cross-flow hydrokinetic turbine that was previously tested at increasing rotor speeds. Turbine arrays are investigated by integrating the previous turbine model with wake sub-models to predict the plant layout maximizing the array power. An assessment of multi-row plants shows that the array power improves with closely spaced turbines. In addition, highly spaced arrays allow a partial recovery of the available power to be exploited upstream by a new turbine array. The highest array power is predicted by simulations on different array layouts considering constant array blockage ratio and rotor solidity. Finally, assuming a long ideal channel, the deviation in the inflow depth is speculated to become asymptotic after many arrays, implying almost identical power conversion upstream.

This thesis combines measurements with the development of simulation tools for vertical axis wind turbines (VAWT). Numerical models of aerodynamic blade forces are developed and validated against experiments. The studies were made on VAWTs which were operated at open sites. Significant progress within the modeling of aerodynamics of VAWTs has been achieved by the development of new simulation tools and by conducting experimental studies.         An existing dynamic stall model was investigated and further modified for the conditions of the VAWT operation. This model was coupled with a streamtube model and assessed against blade force measurements from a VAWT with curved blades, operated by Sandia National Laboratories. The comparison has shown that the accuracy of the streamtube model has been improved compared to its previous versions. The dynamic stall model was further modified by coupling it with a free vortex model. The new model has become less dependent on empirical constants and has shown an improved accuracy.     Unique blade force measurements on a 12 kW VAWT were conducted. The turbine was operated north of Uppsala. Load cells were used to measure the forces on the turbine. A comprehensive analysis of the measurement accuracy has been performed and the major error sources have been identified. The measured aerodynamic normal force has been presented and analyzed for a wide range of operational conditions including dynamic stall, nominal operation and the region of high flow expansion. The improved vortex model has been validated against the data from the new measurements. The model agrees quite well with the experiments for the regions of nominal operation and high flow expansion. Although it does not reproduce all measurements in great detail, it is suggested that the presented vortex model can be used for preliminary estimations of blade forces due to its high computational speed and reasonable accuracy.

Globally the amount of electricity produced each year is increasing significantly. Between 1980 and 2010 the average increase was 407 billion kWh per year. To be able to meet this increasing electricity demand, without burdening the environment in a too large extent, the research and development of renewable energy production techniques is of great importance. In the light of this we wanted to dedicate our master thesis to help SubseaTechnology Scandinavia AB with the development of a vertical axis tidal current turbine. The project set out to do the initial design proposal of a 2 x 4 meter H-shaped Darrieus turbine by applying the Double Multiple Streamtube model. The optimization process was performed with the aid of MATLAB for four different foils. The study included two symmetrical foils; NACA 0012 and S-1046 together with two asymmetrical foils; S-1210 and E216. The parameters studied were the number of blades, chord length, tip speed ratio, fixed pitch and the operational range. In the project, effects such as blade to wake interaction, torque fluctuations etc. were also considered. From the simulations the two bladed turbine fitted with the S-1046 hydrofoil showed the highest performance but was struggling with an unfavorable oscillating torque. In the light of this the three bladed turbine fitted with the S-1046 hydrofoil with a chord of 0.13 m and an optimal tip speed ratio of 3.2 was determined. From the simulations the power coefficient reached 53.47 % for this case. This configuration also showed good performance in a relatively wide range of both tip speed ratios and free stream velocities. The model does not include several effects causing losses and the power coefficients calculated in this model are to be used as a comparison between the different turbine configurations and not as absolute values of performance. The simulations showed good potential for the use of asymmetrical foils in vertical axis turbines. The performance was evaluated for the upstream half of the turbine where the E216 foil exceeded the symmetrical foils in the range of ten percentage points.

Two computationally fast fluid mechanical models for vertical axis turbines are the streamtube and the vortex model. The streamtube model is the fastest, allowing three-dimensional modeling of the turbine, but lacks a proper time-dependent description of the flow through the turbine. The vortex model used is two-dimensional, but gives a more complete time-dependent description of the flow. Effects of a velocity profile and the inclusion of struts have been investigated with the streamtube model. Simulations with an inhomogeneous velocity profile predict that the power coefficient of a vertical axis turbine is relatively insensitive to the velocity profile. For the struts, structural mechanic loads have been computed and the calculations show that if turbines are designed for high flow velocities, additional struts are required, reducing the efficiency for lower flow velocities.Turbines in channels and turbine arrays have been studied with the vortex model. The channel study shows that smaller channels give higher power coefficients and convergence is obtained in fewer time steps. Simulations on a turbine array were performed on five turbines in a row and in a zigzag configuration, where better performance is predicted for the row configuration. The row configuration was extended to ten turbines and it has been shown that the turbine spacing needs to be increased if the misalignment in flow direction is large.A control system for the turbine with only the rotational velocity as input has been studied using the vortex model coupled with an electrical model. According to simulations, this system can obtain power coefficients close to the theoretical peak values. This control system study has been extended to a turbine farm. Individual control of each turbine has been compared to a less costly control system where all turbines are connected to a mutual DC bus through passive rectifiers. The individual control performs best for aerodynamically independent turbines, but for aerodynamically coupled turbines, the results show that a mutual DC bus can be a viable option.Finally, an implementation of the fast multipole method has been made on a graphics processing unit (GPU) and the performance gain from this platform is demonstrated.

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