Vertical axis wind turbines (VAWTs) are popular design solutions for omnidirectional wind and limited installation area, particularly in urban areas, due to their advantages of low noise, low energy cost, and lower sensitivity to turbulence. They are often found in either of two distinct designs: the lift-driven Darrieus, with high aerodynamic power, and the drag-lift-driven Savonius, which excels in its start-up performance. The Darrieus- Savonius combined vertical axis wind turbine (hybrid VAWT) emerges from combining the advantages of Darrieus and Savonius. However, the hybrid VAWT has complex fluid dynamics, with multiple scales and interactions. Therefore, a comprehensive analysis and modeling of hybrid VAWTs can benefit from a multi-fidelity approach.
The choice of numerical methods, in either Eulerian or Lagrangian reference frames, holds paramount importance in simulating VAWTs, each method offering distinct ad- vantages and limitations. Through high-fidelity Eulerian unsteady Reynolds averaged Navier Stokes (URANS) simulations, insights into airflow patterns, and turbulence phe- nomena across varied operating conditions are gained. Conversely, Lagrangian models such as the vortex particle method (VPM) can enable efficient analyses of vortical struc- tures and wake interactions. While URANS simulation offers high-fidelity representa- tions of complex flow phenomena and allows for precise optimization of turbine design parameters, it demands significant computational resources and expertise. In contrast, VPM excels in capturing flow features efficiently but may struggle to accurately repre- sent boundary layer effects and near-wall flows. Consequently, the integration of both the Eulerian URANS and the Lagrangian VPM (hybrid method) is crucial for achieving comprehensive, reliable, and cost-effective simulations of VAWT performance. In this thesis, the hybrid VAWT is investigated using multi-fidelity numerical tools to estimate rotor/blade aerodynamics, computational efficiency and accuracy. Eulerian (U)RANS simulations in OpenFOAM and Lagrangian VPM are first applied to different types of VAWTs, followed by the application of the hybrid method in the hybrid VAWT case.
The goal of this thesis is also to investigate the flow features and power performance of the hybrid VAWT with multi-fidelity methods. In the context of the Eulerian reference frame, this thesis advances the knowledge of hybrid VAWT aerodynamics in several as- pects. The Darrieus and Savonius parts in a hybrid VAWT are modeled as uniform force fields to exclude the effects of structural and operational parameters on the power losses of the wind turbines. The results show that the hybrid configuration cannot show a sig- nificant power increase, and it is only beneficial for the startup performance. The vor- tex dynamics behind the hybrid VAWT are analyzed in different attachment angles and tip speed ratios. The blade-vortex interaction is characterized and correlated with the torque generation of the Darrieus blade. Results show that the Darrieus blade torque in- crease is dependent on the interaction with the shed vortex from the advanced Savonius blade.
In the context of Lagrangian reference frame, both Savonius and hybrid VAWT con- ix
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figurations are employed to assess the computational efficiency and accuracy of the vor- tex particle method. In the case of Savonius rotor simulations using the vortex method, the Savonius is defined as a rotor with two trailing edges because it has no clear lead- ing/trailing edge like an airfoil, named double-trailing-edge-wake-modeling vortex par- ticle method (DTVPM). Results show that a maximum power coefficient is achieved at a tip speed ratio of approximately 0.8, consistent with experimental findings. Further- more, the process of trailing-edge vortex generation and detachment is effectively cap- tured. A comparative analysis between Eulerian URANS simulations and Lagrangian DTVPM reveals that DTVPM offers a more efficient simulation of Savonius rotors with- out the need for empirical parameters. Notably, DTVPM demonstrates remarkable com- putational speed, with simulations being approximately 20 to 104 times faster than par- allel URANS simulations over five revolutions. This significant reduction in computa- tional time underscores the potential of DTVPM to enhance existing engineering mod- els for wind energy applications. In the case of hybrid VAWT simulations, this thesis extends the application of VPM to hybrid VAWTs and introduces a viscous correction to improve simulation accuracy. By incorporating the airfoil polar, the proposed La- grangian DTVPM effectively predicts comparable force variations to Eulerian URANS simulations. Importantly, the computational efficiency of URANS and DTVPM for hy- brid VAWTs is compared, revealing that serial DTVPM simulations are approximately 20 times faster than parallel URANS simulations over ten revolutions. This notable increase in computational speed highlights the potential of DTVPM to provide efficient and ac- curate simulations for hybrid VAWTs, facilitating further advancements in wind energy technology.
In the context of the hybrid Eulerian-Lagrangian reference frame, this study aims to enhance accuracy and efficiency in analyzing complex flow phenomena. Through con- ducting various scenarios of hybrid VAWT using the hybrid method, this study concludes with the demonstration of the hybrid solver’s capability in simulating hybrid VAWT aero- dynamics. The final goal of this thesis is to ascertain an efficient model for hybrid VAWT and determine the limits of individual Eulerian and Lagrangian methods while consid- ering specific flow features of VAWTs. Overall, this study contributes to comprehensive insights into the correlation of blade-vortex interaction and torque variation. The mod- eling challenge in the hybrid VAWT simulation is studied and a hybrid model is suggested to understand the performance and flow features of hybrid VAWTs.@en

Hybrid Eulerian–Lagrangian solvers have gained increasing attention in the field of external aerodynamics, particularly when dealing with strong body–vortex interactions. This approach effectively combines the strengths of the Eulerian component, which accurately resolves boundary layer phenomena, and the Lagrangian component, which efficiently evolves the wake downstream. This study builds on our team's previous work by enhancing the capabilities of a two-dimensional hybrid Eulerian–Lagrangian solver. We aim to upgrade our solver which was initially designed for static cases, to now also simulate cases involving moving objects. To ensure the reliability and applicability of a new solver, it is essential to validate its performance in complex cases. Here, the solver is validated across the case of a traveling cylinder and the case of a rotating cylinder in two different rotational speeds at low Reynolds numbers. In the realm of Eulerian solvers, such as OpenFOAM (utilized for the Eulerian component of this hybrid approach), traditional techniques include the use of morphing meshes, overset meshes, and Arbitrary Mesh Interfaces (AMI) to model body motion. The proposed methodology involves extending the Eulerian mesh up to a short distance from the solid boundary and moving it entirely as a solid entity. Then the Lagrangian solver is responsible for calculating the updated boundary conditions, thereby completing the hybrid solver's functionality. This approach is very similar to the overset mesh technique. However, unlike the traditional method where an Eulerian mesh moves on top of a static one, our method involves the motion of an Eulerian mesh over a Lagrangian grid. We compared the results from our hybrid solver with those from a purely Eulerian solver, specifically OpenFOAM. The comparison demonstrates that our solver can replicate OpenFOAM's results with high accuracy. Another interesting point highlighted in this study is the presence of high-frequency oscillations in the body forces in hybrid solvers that incorporate the redistribution of Lagrangian particles and do not utilize surface elements such as vortex panels, specifically when dealing with dynamic mesh simulations. When the Eulerian mesh travels on top of the Lagrangian grid of particles, the positions of the particles with respect to the Eulerian mesh continuously change. This results in a constant shift of particles near the solid body, where the highest vorticity is observed. Particles that are close to the solid boundary at one time step may find themselves inside the boundary at the next time step, leading to their removal. This pattern continuously changes during the simulation, causing fluctuations in the boundary conditions of the Eulerian solver and manifesting as oscillations in the forces acting on the body. It is shown that this issue can be alleviated either by increasing the spatial resolution of the Lagrangian solver or by synchronizing the movement of the Lagrangian grid with the motion of the Eulerian mesh. The results of the study make the solver trustworthy and pave the way for more demanding external aerodynamic simulations.

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To investigate the effect of force distributions of each turbine component on the power performance of the Darrieus–Savonius combined vertical axis wind turbine (hybrid VAWT), the hybrid VAWT is modeled as idealized turbine under various force distributions. The goal of idealization is to simplify the intricate interactions between the Savonius and Darrieus components. The simulation actuator surfaces with uniform force distributions lead to a cost-effective way to identify the optimal force distribution of each turbine component. The numerical model was validated against momentum theory. The results demonstrated that the numerical and theoretical results yield similar predictions in the low-thrust cases but show differences in the high-thrust cases. The maximum power coefficient (Formula presented.) of an idealized hybrid VAWT with given thrust coefficient (Formula presented.) is lower than that of a single actuator. This is a consequence of the nonoptimal loading on the actuator. The results indicate that an idealized hybrid VAWT does not show a significant power increase compared with an optimal single Darrieus rotor. Therefore, the presence of a Savonius rotor inside a Darrieus rotor leads to a lower power output in any circumstance. The hybrid configuration is primarily advantageous for the start-up performance of the combined rotor, which is not explored in this study.

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To investigate power losses of a Darrieus-Savonius combined vertical axis wind turbine (hybrid VAWT) associated with the interaction between blades and wake, it is crucial to understand the flow phenomena around the turbine. This study presents a two-dimensional numerical analysis of vortex dynamics for a hybrid VAWT. The integration of a Savonius rotor in the hybrid VAWT improves self-starting capability but introduces vortices that cause transient load fluctuations on the Darrieus blades. This study attempts to characterize the flow features around the hybrid VAWT and correlate them with the Darrieus blade force variation in one revolution. Results demonstrate the capability of numerical modeling in handling a wide range of operational conditions: the relevant position of Savonius and Darrieus blades (attachment angle γ = 0 ° − 90 ° ) and Savonius' tip speed ratio λ_S (0.2-0.8, varied Savonius' rotational speed). The torque increase in the Darrieus blade in hybrid VAWT (compared to a single Darrieus rotor) due to the appearance of the vortex shedding from the advanced Savonius blade is independent of the attachment angle and tip speed ratio. Apart from start-up and power performances of the hybrid VAWT, the most rapid force fluctuation is identified when the Darrieus blade interacts with Savonius' wake at γ = 0 ° and λ S = 0.8 , which is considered undesirable. Furthermore, attachment angles of 60 ° and 90 ° exhibit better power coefficients compared to those of 0 ° and 30 ° for the hybrid VAWT. This study contributes to a comprehensive understanding of flow dynamics in hybrid VAWTs, revealing the correlation between torque variation and vortex development.

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This study investigates the implementation of the vortex particle method (VPM) with the goal of efficiently and accurately estimating the power performances and flow characteristics for a Savonius rotor. The accuracy and efficiency of simulation methods are critical for the reliable design of Savonius rotors. Among various approaches, VPM is chosen because it can be flexibly incorporated with self-correction techniques, and the distribution of bound vortex particles can effectively represent complex geometries. In this work, a double-trailing-edge-wake-modeling vortex particle method (DTVPM) is presented to extend the working range of VPM for dealing with large rotating amplitudes and high tip speed ratios (TSRs). DTVPM addresses asymmetrical torque predictions for a Savonius rotor without gap width. However, DTVPM performs poorly at high TSRs due to the absence of viscous effects near the surface. To capture complex wake structures, such as reverse flow structures, the viscous correction for tip vortices is suggested. The current research focuses on the implementation and validation of DTVPM for predicting torque coefficients and wake patterns, as well as comparisons to OpenFOAM results. Two-dimensional and incompressible flow is estimated at (Formula presented.) = 0.2–1.2. For the studied cases, a maximum power coefficient is obtained at (Formula presented.), consistent with published experimental data. In addition, the process of trailing-edge vortices generation and detachment is captured by DTVPM. The comparison results between OpenFOAM and DTVPM show that DTVPM allows to efficiently simulate a Savonius rotor without any empirical parameters. DTVPM will help to improve existing engineering models for wind energy fields.

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