Computational Fluid Dynamics Analysis of Multi-Bladed Horizontal Axis Wind Turbine Rotor

The principal objective of this work was to investigate the 3D flow field around a multi-bladed horizontal axis wind turbine (HAWT) rotor and to investigate its performance characteristics. The aerodynamic performance of this novel rotor design was evaluated by means of a Computational Fluid Dynamics commercial package. The Reynolds Averaged Navier-Stokes (RANS) equations were selected to model the physics of the incompressible Newtonian fluid around the blades. The Shear Stress Transport (SST) k-ω turbulence model was chosen for the assessment of the 3D flow behavior as it had widely used in other HAWT studies. The pressure-based simulation was done on a model representing one-ninth of the rotor using a 40-degree periodicity in a single moving reference frame system. Analyzing the wake flow behavior over a wide range of wind speeds provided a clear vision of this novel rotor confi-guration. From the analysis, it was determined that the flow becomes accelerated in outer wake region downstream of the rotor and by placing a mul-ti-bladed rotor with a larger diameter behind the forward rotor resulted in an acceleration of this wake flow which resulted in an increase the overall power output of the wind machine.


Introduction
The escalation of the global energy demand has led countries to consider renewable energy sources more seriously. In the 2019 released version of the International Energy Outlook, the U.S. Energy Information Administration projects that the world energy consumption will grow by nearly 50% between 2018 and 2050 [1]. The 2019 report of the International Renewable Energy Agency claims that the cost of renewable energy technologies will continue to decline throughout the decade [2], and that solar and wind power are the two most affordable energy solutions for markets worldwide. Following the decline of the weighted-average cost of on-shore wind power during the past years, the report also anticipates the on-shore wind power technologies will be considerably less expensive than the existing conventional coal-fueled plants. The Annual Energy Outlook 2020 predicts that wind and solar energy would increase to 80 percent of the total renewable energy produced by 2050 and the growth of renewable energy would take place in all parts of the U.S. with the West and Mid-Continent areas experiencing the biggest increase in energy production from wind [3]. The steady advancements in wind energy technologies, such as rotor designs and manufacturing processes, have caused a reduction of the levelized cost of wind produced electricity which has resulted in its growth in the global energy market [2].
Over the past two decades, the traditional experimental methods of studying wind turbine fluid dynamics have decreased [4] due to lack of prototypes for the designs [5] and the increase in the large scale of the modern wind rotors. The experimental studies are labor-intensive, whereas the computational fluid dynamics and semi-empirical methods are cost-and time-effective and spatial friendly.
These methods enable designers to apply geometrical modifications to their existing models and these methods are used in the wind turbine industry.
The work presented in this paper is a numerical study of the flow characteristics around a multi-bladed rotor wind turbine, a novel concept patented by the Thunderbird Power Corp [6]. The invention introduces a horizontal wind machine comprised of multiple sails that are supported by several arms which span outward from the hub. Also, a shroud is attached around the rear side of rotor, enabling the machine to capture energy of the incoming wind. The patent also discloses the addition of a second rotor placed in series with the first one. Each rotor is coupled with an individual shaft, where both shafts are coupled through a clutch mechanism. The patent claims that the multi-rotor concept was capable of delivering more power compared to a single stand-alone rotor of the same diameter. This turbine can be used for electric power generation and water pumping [6]. Figure 1 and Figure 2 illustrate the multi-bladed and multi-rotor design configurations.
A high-solidity windmill generates more torque at low-tip speeds compared to a modern horizontal axis wind turbine [7]. This means that a wind machine with a higher solidity can operate in wider range of wind speeds, leading to an increase in overall power output of the turbine. The model which was studied throughout this paper was a simplified version of the above-described patented wind machine design and consists of a single multi-bladed rotor. The work conducted analyzed the effects of the high-solidity rotor on the wake flow and studied   the torque and power outputs of the wind turbine with different rotational speeds and varying wind velocities. In order to evaluate the proper location of the subsequent rotors, velocity profiles of the rotor wake were thoroughly investigated.

Methodology
Fluid motion can be described by a set of differential equations, namely the mass and momentum conservation equations, known widely as Navier-Stokes Equa- where i x denotes the position vector, ρ stands for the fluid density, P is the pressure, U is the fluid velocity and ν is the kinematic viscosity. External body forces, denoted by F, act on a section of the fluid and were evaluated from the fluid rotational forces, such as the Coriolis and centrifugal forces. Osborne Reynolds developed a proposal for eliminating the turbulence unsteady fluctuations by averaging the flow quantities which lead to the so-called Reynolds Averaged Navier-Stokes (RANS) equations for the mean flow, Equations (3) and (4).
The stress tensor term in the momentum equation (Equation (4)), u u ′ ′ , corresponds to the effects of turbulence on the mean flow and results in a closure problem in the RANS equations. The semi-empirical standard k-ε model introduces two equations (Equations (5) and (6)), involving turbulent kinetic energy, k, and turbulent dissipation, ε, to RANS which closes the system.
P is the production of k, t µ is the eddy-viscosity and are defined respectively as in Equations (7) and (8), The k-ε model assumes the flow to be fully turbulent and is reliable for high Reynolds regions only. The k-ω model, on the other hand, utilizes the transport equations for k (Equation (9)) and turbulence frequency, ω (Equation (10)), to solve the turbulent viscosity.
where G is for the production terms, Y the dissipation and S represents the user-defined source expressions. The k-ω model showed better agreements with the real flow behavior for the viscous sublayer regions and hence was chosen over the k-ε model. Coupling the k-ε and k-ω models with a blending function introduces the k-ω Shear Stress Transport (SST) model [8]. This model shifts between the k-ω model for the near wall regions and the k-ε for the far field regions through the domain depending on cell distance from the closest wall boundary. The k-ω SST can also predict the flow separation in regions close to the walls by using its embedded viscosity limiter expression which damps out the shear stress in the vicinity of walls.

Physical Model and Boundary Conditions
In the present study, a simplified version of the original patented multi-bladed rotor was modeled by a SOILDWORKS CAD package. Since the blades were evenly placed around the rotor at 40 degree intervals, one-ninth of the whole rotor was chosen to be studied and the effects of the remaining blades were taken into account through applying a periodic boundary condition where it was      Table 1 and Table 2, respectively.

Results and Discussion
For this analysis, the incoming free flow was parallel to the ground in the nega-       By studying the pressure contours on the blade surface it showed that the surfaces which face the wind have higher pressure magnitudes compared to the rear surfaces, as expected. This pressure difference between both sides of the rotor sails caused lift in the direction of the rotor rotation. A closer look at the pressure-side of the blade showed the front edges, which are facing in the direction of rotation, have a higher pressure with respect to rest of the sail surface. However, the opposite holds true for the suction side of sails where the edges that faced the rotation direction are the regions with lower pressure. In Figure 16 the regions of high pressure on each face are denoted with an oval. It should be noted that regions of high pressure move into the whole sail surface as the wind velocity increases, as expected.
As mentioned earlier, the tip speed ratio throughout this analysis was kept at a fixed value of 0.7 and, therefore, the rotational speed increases linearly as the oncoming wind velocity increases. This behavior is shown in Figure 17. Figure  18 shows the increase of rotor torque at increasing values of the wind speed. Figure 19 shows that the power coefficient of the rotor improved at higher wind velocities. Finally, the increase of power extracted from the wind is shown in Figure 20.
Considering the limitations in maximum cell number of the fluid solver's Academic Teaching license, the grid independency analysis was carried out to study the stability of the main output of the flow solution for the chosen number of mesh elements. It was showed that the fluctuations of the sectional torque were very minor for cell number of around 400,000 ( Figure 21).
Considering the novelty of the evaluated rotor design, there was no available experimental data to be compared with the calculated result. However, the reported values for power coefficient in Figure 19 displayed a good consistency with the published statistical diagram of rotor power coefficient as a function of tip-speed ratio. According to Figure 22, for tip-speed ratio of 0.7 one can expect values of about 0.13 to 0.14 for the power coefficient for a multi-bladed American style HAWT. This behavior was well observed for the rotor of interest (Figure 19).

Conclusions
A high-solidity windmill generates more torque at low-tip speeds compared to modern horizontal axis wind turbines [7]. This means that wind machine with higher solidity can operate in a wider range of wind speeds, leading to an increase in the overall power output of the turbine. The model that was evaluated was a simplified version of a recently patented wind machine [6], consisting of a single multi-bladed rotor. This evaluation analyzed the flow behavior around the rotor and evaluated the torque and power output of the wind turbine with different rotational speeds for varying wind velocities. The axial velocity trend of the rotor wake was thoroughly investigated in order to properly place the added rotors. It was evident that the flow becomes accelerated in the outer wake region downstream of the rotor and, as a result, placing a multi-bladed rotor with a larger diameter behind the front rotor would make use of the accelerated wake flow and therefore would improve the overall power output of the wind machine.
For a specified rpm, the increase of solidity increased the torque production and, hence, leads to a higher wind turbine power output [11]. However, higher values of solidity cause undesirable blockage of incoming wind and impact the power extraction of rotor in a negative manner. Therefore, finding the optimum solidity degree which balances the high torque and flow blockage was of a high priority.
A more comprehensive study analyzing the effects of varying the number of blades, varying the sail geometries and evaluating the addition of rotors should be conducted. Considering the deficiencies of applying the steady-state modeling World Journal of Mechanics approach for flows with an unsteady nature, a study to apply an unsteady simulation algorithm in order to better evaluate different performance behaviors should be considered.