# Comparative Study of Deflector Configurations under Variable Vertical Angle of Incidence and Wind Speed through Transient 3D CFD Modeling of Savonius Turbine

Hady Aboujaoude, Guillaume Polidori, Fabien Beaumont, Sébastien Murer, Yessine Toumi, Fabien Bogard

► To cite this version:

Hady Aboujaoude, Guillaume Polidori, Fabien Beaumont, Sébastien Murer, Yessine Toumi, et al. Comparative Study of Deflector Configurations under Variable Vertical Angle of Incidence and Wind Speed through Transient 3D CFD Modeling of Savonius Turbine. Computation, 2024, 12 (10), pp.204. 10.3390/computation12100204. [https://doi.org/10.3390/computation12100204](https://doi.org/10.3390/computation12100204)

HAL Id: hal-04737035

https://hal.science/hal-04737035v1

Submitted on 4 Mar 2025

HAL is a multi-disciplinary open access
archive for the deposit and dissemination of sci-
entific research documents, whether they are pub-
lished or not. The documents may come from
teaching and research institutions in France or
abroad, or from public or private research centers.

L'archive ouverte pluridisciplinaire HAL, est
destinée au dépôt et à la diffusion de documents
scientifiques de niveau recherche, publiés ou non,
émanant des établissements d'enseignement et de
recherche français ou étrangers, des laboratoires
publics ou privés.

<figure><img src="image_1.png" /></figure>

Distributed under a Creative Commons Attribution 4.0 International License
Article

# Comparative Study of Deflector Configurations under Variable Vertical Angle of Incidence and Wind Speed through Transient 3D CFD Modeling of Savonius Turbine

Hady Aboujaoude <fnref n="1" />,* ID, Guillaume Polidori <fnref n="1" /> ID, Fabien Beaumont <fnref n="1" /> ID, Sébastien Murer <fnref n="1" /> ID, Yessine Toumi <fnref n="1" />,<fnref n="2" />
and Fabien Bogard <fnref n="1" />,<fnref n="2" /> ID

**Abstract:** The demand for clean and sustainable energy has led to the exploration of innovative technologies for renewable energy generation. The Savonius turbine has emerged as a promising solution for harnessing wind energy in urban environments due to its unique design, simplicity, structural stability, and ability to capture wind energy from any direction. However, the efficiency of Savonius turbines poses a challenge that affects their overall performance. Extensive research efforts have been dedicated to enhancing their efficiency and optimizing their performance in urban settings. For instance, an axisymmetric omnidirectional deflector (AOD) was introduced to improve performance in all wind directions. Despite these advancements, the effect of wind incident angles on Savonius turbine performance has not been thoroughly investigated. This study aims to fill this knowledge gap by examining the performance of standard Savonius configurations (STD) compared to the basic configuration of the deflector (AOD1) and to the optimized one (AOD2) under different wind incident angles and wind speeds. One key finding was the consistent superior performance of this AOD2 configuration across all incident angles and wind speeds. It consistently outperformed the other configurations, demonstrating its potential as an optimized configuration for wind turbine applications. For instance, at an incident angle of 0°, the power coefficient of the configuration of AOD2 was 61% more than the STD configuration. This ratio rose to 88% at an incident angle of 20° and 125% at an incident angle of 40°.

**Keywords:** vertical axis wind turbine; transient three-dimensional simulation; CFD simulation; power coefficient; Savonius rotor; aerodynamics; wind deflector

## 1. Introduction

With the increasing demand for clean and sustainable energy, the exploration of innovative technologies for renewable energy production has become crucial. Among the various available options, the Savonius wind turbine stands out as a promising solution for harnessing wind energy in urban environments. Its distinctive design, simplicity, structural stability, and ability to capture wind energy from all directions make it an ideal choice for areas characterized by complex wind patterns. However, the efficiency of Savonius turbines still needs improvement, which prevents their widespread use. Indeed, the superior power coefficient of the horizontal axis wind speed turbines (HAWT) and the Darrieus-type vertical axis wind turbine (VAWT) contribute significantly to their prevalence in various applications. To overcome this limitation, considerable research efforts have been dedicated to improving their efficiency and optimizing their performance in urban environments. By implementing new techniques, researchers are addressing these limitations with the aim of achieving wider adoption and thus making a significant contribution to a sustainable future. Several articles [1–6] have extensively examined the results of experimental and

<figure><img src="image_2.png" /></figure>

check for
updates

**Citation:** Aboujaoude, H.; Polidori, G.; Beaumont, F.; Murer, S.; Toumi, Y.; Bogard, F. Comparative Study of Deflector Configurations under Variable Vertical Angle of Incidence and Wind Speed through Transient 3D CFD Modeling of Savonius Turbine.

Computation **2024**, *12*, 204.

https://doi.org/10.3390/computation12100204

Academic Editors: Ali Cemal Benim, Abdulmajeed A. Mohamad, Sang-Ho Suh, Rachid Bennacer, Pawel Oclon and Jan Taler

Received: 7 September 2024

Revised: 9 October 2024

Accepted: 10 October 2024

Published: 14 October 2024

<figure><img src="image_3.png" /></figure>

**Copyright:** © 2024 by the authors.
Licensee MDPI, Basel, Switzerland.
This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).

<footnote n="1">1 ITHEMM, University de Reims Champagne-Ardenne, 51100 Reims, France</footnote>

<footnote n="2">2 Pôle de Recherche Châlonnais, Université de Reims Champagne-Ardenne, 51000 Châlons en Champagne, France</footnote>

<footnote>* Correspondence: hady.aboujaoude@univ-reims.fr</footnote>
numerical research on wind turbines. These numerous studies have focused on enhancing performance by adjusting parameters such as the number of blades [7], the presence of an end plate, the Overlap Ratio (OR), the ratio between the height and diameter of the turbine, the aspect ratio (AR = H/D) [8,9]. The calculated performance criterion is the Cp (the ratio of power provided by the turbine to the wind existing power) (Equation (4)).

For instance, the effect of incorporating upper and lower end plates has led to a 36% increase in the power coefficient Cp with the presence of these plates [10]. Furthermore, the incorporation of an overlap region (OR) between the blades, allowing the wind to circulate backward and generate positive torque, has also been analyzed through comparisons of energy production between turbines with and without the overlap section [11]. Similarly, Sobczak et al. (2018) [12] noted that an AR between 1.0 and 2.0 is a good compromise between performance and compactness. Researchers have also analyzed the pressure distribution on the rotor blades to better understand the areas of low and high pressure that contribute to the overall torque of Savonius turbines [13]. Experimental results highlight the potential for improving the power coefficient by strategically modifying the rotor blade geometry of Savonius turbines [14,15].

Furthermore, another proposed research direction involves innovative external systems to increase airflow towards the turbine and these are reported in Table 1. Researchers initially studied unidirectional wind deflectors to enhance the performance of Savonius turbines in the direction of the dominant wind. They simulated a combination of flat and circular shields, which resulted in achieving a Cpmax of 0.243 [1]. A flat deflector facing the turbine yielded a Cpmax of 0.34 [16]. Introducing a V-shaped wind concentrator increased power by 19.7% compared to a standard rotor without a deflector [17]. Circular deflectors were also investigated to reduce wind pressure on the convex blade [18]. Concentration deflectors placed upstream of the rotor effectively reduced flow on the return blade, thus minimizing negative torque [19]. Additionally, it was found that guide vanes enhanced rotor performance [3].

<table><caption>**Table 1.** Research on Savonius deflectors.</caption><thead><tr><td>Authors</td><td>Design</td><td>Reported Cpmax</td><td>Study</td><td>Wind Concentrator</td></tr></thead><tbody><tr><td>El-Askary et al., 2015 [3]</td><td>Curtain design</td><td>&gt;0.5</td><td>Numerical—2D CFD</td><td>Unidirectional</td></tr><tr><td>Burçin et al., 2010 [20]</td><td>Curtain design</td><td>0.38</td><td>Experimental—Wind tunnel</td><td>Unidirectional</td></tr><tr><td>Morcos et al., 1981 [17]</td><td>Flat plate shield</td><td>0.34</td><td>Experimental—Wind tunnel</td><td>Unidirectional</td></tr><tr><td>Aboujaoude et al., 2022 [21]</td><td>Axisymmetric deflector</td><td>0.31</td><td>Numerical—3D CFD</td><td>Axisymmetric multidirectional</td></tr><tr><td>Tartuferi et al., 2015 [22]</td><td>Curtain design</td><td>0.3</td><td>Numerical—2D CFD</td><td>Self-rotating</td></tr><tr><td>Yonghai et al., 2009 [19]</td><td>Deflector plate</td><td>0.28 *</td><td>Numerical—2D CFD</td><td>Unidirectional</td></tr><tr><td>Alexander et Holownia, 1978 [1]</td><td>Flat plate shield</td><td>0.24</td><td>Experimental—Wind tunnel</td><td>Unidirectional</td></tr><tr><td>Shaughnessy et Probert, 1992 [18]</td><td>V-shaped deflector</td><td>&lt;0.12 *</td><td>Experimental—Wind tunnel</td><td>Unidirectional</td></tr></tbody></table>

The values of Cpmax in studies marked with an asterisk * were extrapolated.

Finally, the incorporation of a conveyor-deflector curtain into a conventional Savonius rotor increased the Cp by 0.30 [20]. However, it is important to understand that these improvements are primarily theoretical, given the significant fluctuations in wind direction in urban environments where Savonius wind turbines are intended to be installed. In fact, the proposed deflectors enhanced turbine performance in the predominant wind direction, but conversely, they result in a substantial decrease in performance in all other wind directions. The authors introduced an axisymmetric omnidirectional deflector (AOD) to consider the high turbulence and fluctuating wind direction and speed in urban environments [22]. The initial deflection model (AOD1), a simple truncated cone, showed an average increase in Savonius turbine performance of 25% over the studied peak velocity ratio range and a 30% increase in starting torque in all directions. An optimized model (AOD2) was subsequently developed by the authors to reduce structural fatigue and further increase performance by 20% across the entire range of peak velocities considered [21]. However, the effect of wind incidence angles has not been thoroughly studied in these articles.
The current study aims to fill this gap by examining the performance of a standard Savonius (STD) compared to a Savonius wind turbine with a basic axisymmetric omnidirectional conical deflector (AOD1) and a Savonius wind turbine with an optimized axisymmetric omnidirectional deflector (AOD2) under different wind incidence angles and wind speeds. By accounting for the variability of wind incidence angles in urban environments, this research will contribute to a more comprehensive understanding of Savonius turbine performance and thus to a broader application of their applicability in real-world scenarios.

## 2. Methodology

### 2.1. Flow Parameters

In the computational fluid dynamics (CFD) study conducted on the Savonius turbine, various crucial flow parameters were systematically evaluated to analyze and understand its performance characteristics. For this study, three distinct inlet velocities were used, namely 4 m·s⁻¹, 7 m·s⁻¹, and 14 m·s⁻¹. Additionally, six tip speed ratios λ were imposed to comprehensively investigate the turbine's performance across the entire tip speed ratio range, as outlined in Table 2. The tip speed ratio is defined as follows:

$$ \lambda = \frac{R\omega}{V_{\infty}} \qquad (1) $$

where R is the radius of the turbine, ω the rotational speed and V∞ is freestream air speed.

<table><caption>**Table 2.** Simulation parameters.</caption><thead><tr><td>Parameters</td><td>Description</td><td>Unit</td><td>Values</td></tr></thead><tbody><tr><td>λ</td><td>Tip speed ratio</td><td>Dimensionless</td><td>0.2; 0.4; 0.6; 0.8; 1.0</td></tr><tr><td>θ</td><td>Vertical wind incident angle</td><td>Degree</td><td>0°; 10°; 20°; 30°; 40°</td></tr><tr><td>V<sub>∞</sub></td><td>Freestream air speed</td><td>m/s</td><td>3.5; 7.0; 14.0</td></tr></tbody></table>

This inclusive approach enabled a comprehensive examination of the turbine's efficiency and effectiveness under varying flow conditions and operational parameters. To address the primary focus of this study, which is the impact of wind incident angle (θ), five specific angles were chosen for each simulation, ranging from 0° to 40° with an increment of 10°, as depicted in Figure 1. By carefully considering and manipulating these flow parameters, a detailed analysis of the Savonius turbine's behavior and performance under diverse operating conditions was achieved.

<figure><img src="image_4.png" /><figcaption>**Figure 1.** Geometric parameters of the Savonius rotor and the different wind incident angle θ.</figcaption></figure>
## 2.2. Geometric Details of the Standard Savonius Turbine (STD)

The Savonius rotor studied, devoid of deflectors, comprises a two-blade configuration in line with the suggestions set out in [23], which advocate the use of a two-blade design to improve performance. The aspect ratio AR is set to 1.66 as per the available experimental results conveyed by Blackwell et al. (1977) in order to validate the model. The turbine is chosen to have end plates. As per the literature recommendations [24], the ratio chosen between the diameter of the end plate and the diameter of the turbine is set to 1.1 to benefit from the best performance. The dimensionless gap width is defined by the ratio e/d, see Figure 1. According to [6], the turbine efficiency is optimal for a dimensionless gap width of 0.15. The main geometric parameters impacting the performance of the Savonius rotor are shown in Figure 1 and are defined as follows (Table 3):

<table><caption>**Table 3.** Turbine dimensions.</caption><thead><tr><td>Number of Blades</td><td>Blade Diameter</td><td>Turbine Height</td><td>Endplate Diameter</td><td>Endplate Height</td><td>Dimensionless Gap Width e/d</td></tr></thead><tbody><tr><td>2</td><td>0.5 m</td><td>1.5 m</td><td>1.0 m</td><td>0.01 m</td><td>0.15</td></tr></tbody></table>

## 2.3. Geometric Details of Axisymmetric Omnidirectional Deflector (AOD1) and (AOD2)

Wind deflectors applied to Savonius turbines can improve their power coefficient by enhancing the aerodynamic characteristics of the rotor blades. The primary function of the deflector is to redirect and increase the incoming wind flow towards the turbine blades, resulting in improved torque and rotational speed. Additionally, wind deflectors are used to redirect the airflow to the rotor in a way to increase the efficiency of the turbine. The first deflector used as a benchmark in this study is the one developed in [21], specified as axisymmetric omnidirectional deflector 1 (AOD1), as shown in Figure 2. The profile consists of a fixed, non-rotating, three-dimensional truncated cone installed above and below the rotating Savonius turbine. The height of the deflector is 75 cm while the small diameter and the big diameter are, respectively, 105 cm and 150 cm. The mounting system of the deflectors is not represented, but it is thought to be completely dissociated and independent from the turbine structure. The second deflector used is an aerodynamically enhanced geometrical shape of AOD1 presented by Aboujaoude et al. [23] based on a convex spline shape deflector with the dimensions presented in Figure 2 and will be referred to as AOD2. This AOD2 spline is defined as a quadratic Bezier curve with three control points represented as black dots in Figure 2a with their relative coordinate dimensions. It showed an improved performance compared with AOD1 [23] along with reduced fatigue and stress on the turbine axis on a wind incident angle θ of 0°.

<figure><img src="image_5.png" /><figcaption>**Figure 2.** (a) AOD2 (optimized cone), (b) AOD1 (truncated cone), (c) STD (without deflector).</figcaption></figure>
## 2.4. Computational Domain and Mesh

The computational domain containing a rotor should be sufficiently large to minimize its effect on the performance parameters of the rotor [25]. To analyze the impact of the wind incident angle $θ$, the inlet boundary was positioned close to the turbine, with an upstream distance of 1 m equivalent to 1 diameter of the rotor. Additionally, considering a maximum wind tested incident angle of 40°, the height of the computational domain was increased to 12 times the rotor diameter (12D) to accurately capture the characteristics of the wake region and, consequently, calculate precisely the torque developed around the turbine axis. The ratio of the frontal cross-sectional area of the rotor and that of the computational domain is known as the blockage ratio. The blockage ratio, which relates the frontal cross-sectional area of the rotor to that of the computational domain, could overestimate the power coefficient (Cp) of a turbine [26]. In our study, we aimed to minimize computational domain boundary effects on the rotor’s performance, so a blockage ratio of 0.003125 was chosen to ensure negligible influence. As shown in Figure 3, the downstream distance of the outlet boundary from the rotor domain is set to be 18.5D. The distance between the walls of the computational and the rotor domain is 10D on the left and right side and 12D on the top and bottom side. Considering the blockage ratio requirements, the dimensions of the computational domain were set to 20D × 20D × 24D. The inlet boundary was defined with constant velocity speeds (3.5 m·s⁻¹, 7 m·s⁻¹, and 14 m·s⁻¹) and variable wind incident angles $θ$ ranging from 0° to 40° with an increment angle of 10°. A pressure outlet boundary condition was applied on the right side of the computational domain to enforce the dissipation of airflow at atmospheric pressure outside the computational domain. The remaining sides of the computational domain were set as non-slip wall boundaries. Simulating a system involving a rotating part, such as the turbine rotor in our study, required the use of the sliding meshing method [26]. This method enables separate regions with different meshing requirements for the rotating and stationary subdomains. The stationary subdomain was obtained by extracting the rotating part and the designed deflector from the initial computational domain. The rotating subdomain was then modeled and added as a separate cylinder, as shown in Figure 3. The sliding mesh technique in ANSYS Fluent was utilized to impose the turbine rotation speed for each simulation and monitor the torque developed around the turbine axis. An unstructured mesh consisting of 4 million tetrahedral elements was generated using ANSYS Meshing software (2024 R2 version) (Figure 3). Downstream of the rotor, the mesh was refined to capture wake vortices. Additionally, an inflation mesh with 18 layers of prismatic elements was created around the blades to achieve appropriate (y+) values. The growth ratio used was 1.1 near the walls and 1.2 in the free airstream to reduce the cell number. The dimensionless height of the first mesh node adjacent to the wall (y+) has a significant impact on the simulation results. To ensure accurate resolution of the viscous sublayer and the torque produced around the turbine axis, a (y+) value below 5 on the blades was targeted. This optimized mesh allowed for an average (y+) value of 1.8 on the turbine surface. The STD model was validated previously by comparing the simulated values of Cp with Blackwell et al. (1977) [2] wind tunnel experiments in the authors’ previous published paper [21].

## 2.5. Governing Equations and Turbulence Models

In CFD studies of Savonius wind turbines, three available techniques for turbulence modelling are used: (a) unsteady Reynolds-averaged Navier-Stokes (URANS), (b) large eddy simulation (LES), and (c) direct numerical simulation (DNS). In the URANS approach, the governing equations are computationally solved for the time-averaged flow behavior along with a suitable turbulence model for the closure of the governing equations. Unlike LES and DNS, the URANS method models all the turbulence scales. While it is less accurate, it is cost effective and less time consuming and provides the accuracy needed in the engineering applications like design optimization and therefore is widely used in wind turbine applications. URANS showed accurate predictions of torque calculation in rotating machinery which is the main parameter used to determine the performance of
turbines [27]. In this approach, the flow properties averaged over time are examined. The URANS momentum and continuity equations are written as follows:

$$ \frac{\partial (\bar{\rho}u_i)}{\partial t} + \frac{\partial}{\partial x_j} (\bar{\rho}u_i u_j) = -\frac{\partial \bar{p}}{\partial x_i} + \frac{\partial}{\partial x_j} \left[ \mu \left( \frac{\partial \bar{u}_i}{\partial x_j} + \frac{\partial \bar{u}_j}{\partial x_i} - \frac{2}{3} \delta_{ij} \frac{\partial \bar{u}_k}{\partial u_k} \right) \right] + \frac{\partial}{\partial x_j} \left( -\bar{\rho} \overline{u'_i u'_j} \right) \quad (2) $$

$$ \frac{\partial \bar{\rho}}{\partial t} + \frac{\partial}{\partial x_i} (\bar{\rho}u_i) = 0 \quad (3) $$

where $\bar{u}_i$ and $u'_i$ are the mean and fluctuating velocity components ($i = 1, 2, 3$), $\rho$ is the fluid density, $\mu$ the molecular viscosity, $p$ is the pressure, and the function $\delta_{ij}$ is defined as $\delta_{ij} = \begin{cases} 1, & i = j \\ 0, & i \neq j \end{cases}$. The Reynolds stress term $-\bar{\rho}u'_i u'_j$ is modeled by the k-ω SST two equation turbulence model which was found to be the most appropriate for wind turbine applications. The flow is considered as incompressible where the density is constant, and the molecular viscosity is also considered as constant.

<figure><img src="image_6.png" /><figcaption>Figure 3. Computational domain and mesh cross sections used.</figcaption></figure>

The typical k-ω model works well for wall-bounded flows, but not for free-shear flows. The SST k-ω model is an extensively used model that combines the features of k-ω and k-ε models. It showed accurate prediction for rotating applications such as the vertical axis wind turbine compared to experimental values [28,29].

It has been used and validated by many researchers for modelling the Reynolds stress in the vertical axis wind turbine simulations.
## 2.6. Solver Settings

Numerical simulations were carried out using the commercial CFD software ANSYS Fluent (2024 R2 version), employing the finite volume method. Given the computationally intensive nature of the transient 3D CFD simulations, steps were taken to reduce simulation time. This involved reducing the mesh count and employing larger time steps. To achieve these computational time reductions, a hybrid algorithm scheme was implemented, as recommended by [23]. This hybrid approach combined a segregated algorithm with a pressure-based coupling. The pressure-based coupled algorithm, while providing greater accuracy and fewer divergences compared to the segregated algorithm, is computationally demanding. However, it enables the use of a coarser mesh and prevents divergence at the beginning of the simulation. To leverage the benefits of both schemes, the hybrid algorithm initially employs a coarser mesh along with the pressure-based coupled algorithm for the first three iterations, see Figure 4. Afterward, it switches to the segregated algorithm to further optimize computational time. Additionally, a second-order upwind scheme was employed to enhance solution stability and accuracy, particularly for the convective terms. Table 4 sums up the CFD parameters.

<figure><img src="image_7.png" /><figcaption>**Figure 4.** Solver's algorithm. (a) Coupled solver algorithm. (b) Segregated solver algorithm. (c) Hybrid solver scheme [23].</figcaption></figure>
<table><caption>**Table 4.** CFD parameters and settings.</caption><thead><tr><td>Parameters</td><td>Method or Specification</td></tr></thead><tbody><tr><td>Solver Type</td><td>Transient</td></tr><tr><td>Turbulence Model</td><td>kw-SST</td></tr><tr><td>Solution Method</td><td>Hybrid solver using Pressure Coupled and Simple Algorithms</td></tr><tr><td>Timestep</td><td>1°</td></tr><tr><td>Residual Criteria</td><td>10–4 for the continuity and 10–6 for all the other parameters</td></tr><tr><td>Rotational Model</td><td>Sliding mesh technique</td></tr><tr><td>Spatial discretization: Gradient</td><td>Least square cell based</td></tr><tr><td>Spatial discretization: Pressure</td><td>Second order</td></tr><tr><td>Momentum, Turbulence Kinetic Energy & Specific Dissipation Rate</td><td>Second order upwind</td></tr><tr><td>Transient Formulation</td><td>Second order implicit</td></tr></tbody></table>

## 3. Results

### 3.1. *Mesh and Timestep Sensitivity Analysis*

A mesh sensitivity analysis was carried out on the STD type turbine configuration to ensure grid independency using four meshes with different y+ values and cell sizes. The number of cells varied from 0.5 million to 8.0 million across the four different grids. Figure 5 sums up the variations in Cp values with tip speed ratio for the four grids. It can be observed that the 8-million-cell grid has quite similar results as the 4-million-cell grid for all the values of $\lambda$. For this study, the 4-million-cell grid is selected for the subsequent study to reduce the computational cost and provide good accuracy. The maximum courant number in this study is fixed at 0.8. The averaging of torque and power coefficients is performed for three values of rotations of 0.5°, 1.0°, and 2.0° per time step. Table 5 shows the averaged torque coefficient for three values of the time step considered. The variation between 2.0° per time step and 1.0° per time step rotation is 2.4%. However, the variation between 1.0° per time step and 0.5° per time step is 0.8%. Therefore, a time step of 1.0° is selected for simulations.

<figure><img src="image_8.png" /><figcaption>**Figure 5.** Power coefficient for different meshes.</figcaption></figure>
<table><caption>**Table 5.** Power coefficient using different timesteps.</caption><thead><tr><td>Rotation Angle per Time Step</td><td>Cp at λ = 1.0</td></tr></thead><tbody><tr><td>0.5°</td><td>0.2307</td></tr><tr><td>1°</td><td>0.2305</td></tr><tr><td>2°</td><td>0.225</td></tr></tbody></table>

## 3.2. Incidence Angle Effect on Power Coefficient on Various Configurations at a Wind Speed of 7 m·s⁻¹

### 3.2.1. Power Coefficient

The variation of wind speed and direction in urban environments and on high-rise buildings is significant due to turbulence. Savonius turbines, commonly installed in these locations, often operate under conditions where both the wind speed and direction are changing. Although VAWT turbines have the advantage of being able to harvest wind energy from any direction, the vertical wind incidence angle θ still significantly affects their performance. The numerical and experimental investigations provided in the literature consider θ = 0°. This simplified assumption, while helpful for initial understanding, does not represent real-world urban conditions. To fill this knowledge gap, 75 cases of 3D unsteady numerical simulation were launched to monitor the performance variations of these Savonius turbine configurations under various θ.

The power coefficient defined by (Equation (4)), is a key indicator of the wind turbine performance and is widely used in the literature as a basis for comparison between novel turbine designs and standard configurations or between numerical and experimental results. Similarly, in this study, Cp is used to compare the different configuration performances.

$$C_P = \frac{T\omega}{0.5\rho V_{\infty}^3 DH} \quad (4)$$

where T is the torque developed around the axis of the wind turbine, ω is the rotational speed of the wind turbine, ρ is the air density, V∞ is the air velocity, D is the diameter of the wind turbine and H is its height.

Figure 6 retraces the Cp values of each of the configuration STD, AOD1, and AOD2 versus the tip speed ratio λ. In addition, and to monitor the impact of the vertical incidence angle on the performance, separate curves were plotted for each θ.

<figure><img src="image_9.png" /><figcaption>**Figure 6.** Power coefficient of different turbine configurations (STD, AOD1, and AOD2) under varying incidence angle and tip speed ranges. (a) Wind speed of 3.5 m·s⁻¹, (b) wind speed of 7 m·s⁻¹, (c) wind speed of 14 m·s⁻¹.</figcaption></figure>

Analysis of the simulation Cp values revealed a distinct overall pattern.

A negative correlation exists between turbine performance (Cp) and vertical wind incidence angle θ for all the configurations. This phenomenon is attributable to the fact that the Savonius turbine's rotational energy is derived from the drag forces exerted on
its blades. As θ increases, the resulting drag force exerted on the turbine blade decrease,s while the lift force exerted on the deflector and the end plate increases. Obviously, at θ = 0° the conversion of the wind kinetic energy to drag force is at its maximum.

As shown in Figure 6, this is true for all configurations and for all inlet wind speeds (3.5 m/s, 7 m/s, and 14 m/s).

Another key finding was the consistent superior performance of the AOD2 configuration across all incidence angles. The simulation results show that AOD2 significantly surpasses AOD1 and STD. Notably, even at a wind incidence angle of 30°, AOD2's power coefficient remains higher than the best-case power coefficient of STD at 0°.

To delve deeper into the deflectors' impact, we introduced a parameter called PIR (performance increase ratio) defined by Equation (5) below:

$$PIR_{\theta}^{AOD2|STD} = \left[ \frac{C_{p}^{\theta}(AOD2)}{C_{p}^{\theta}(STD)} - 1 \right] \quad (5)$$

where $C_p^θ(AOD2)$ and $C_p^θ(STD)$ are the power coefficient of the respective configurations at specific vertical wind incident θ.

It was observed that $PIR_{\theta}^{AOD2|STD}$ is directly correlated with θ. For instance, while $PIR_{\theta=0°}^{AOD2|STD} = 62\%$, $PIR_{\theta=10°}^{AOD2|STD} = 78\%$, $PIR_{\theta=20°}^{AOD2|STD} = 89\%$, $PIR_{\theta=30°}^{AOD2|STD} = 102\%$ and $PIR_{\theta=40°}^{AOD2|STD} = 187\%$.

As depicted in Figure 7, a direct correlation exists between the increase in θ and the PIR. Notably, this increase becomes progressively more pronounced at higher values of θ. In simpler terms, the anticipated energy gain from using the AOD2 deflector compared to the standard turbine is even more significant in turbulent settings like urban areas. As a result, the seasonal energy harvested by the AOD2 configuration cannot be reflected solely by the power coefficient at 0 = 0° as per the state of the art. A more precise methodology would be to estimate the wind incidence angle yearly profile and to integrate the energy as per the angle-specific power coefficient. This would account for the additional gain in performance at higher θ and could eventually impact the decision of installing the AOD2 deflector.

<figure><img src="image_10.png" /><figcaption>Figure 7. Performance increase ratio $PIR_{\theta}^{AOD2|STD}$ curve versus θ.</figcaption></figure>

On another note, it was observed that the AOD1 configuration exhibited improved performance as the angle of incidence increased, while the STD configuration showcased superior performance over AOD1 at higher turbine speeds. These observations provide
valuable insights into the performance characteristics of the different turbine configurations under varying incidence angle and tip speed ranges.

The simulations also revealed interesting trends regarding the optimal tip speed ratio $\lambda$ for each setup. Both the STD and AOD2 configurations achieved their maximum Cp at $\theta = 0°$ for a wind incident speed of $7 \text{ m} \cdot \text{s}^{-1}$, and at a turbine tip speed ratio of $\lambda = 1.0$. On the other hand, the AOD1 configuration exhibited its best performance at a lower turbine speed, $\lambda = 0.8$, indicating its suitability for specific operational conditions. Furthermore, and for all configurations, as $\theta$ increased, the maximum power coefficient Cp was achieved at lower turbine tip speed ratio $\lambda$ and hence turbine rotational velocities. This effect was more pronounced in the AOD1 configuration. At $\theta = 40°$, the Cpmax of the AOD1 configuration occurred within the $\lambda = 0.6$ range. In contrast, the Cpmax of the STD and AOD2 configurations fell within the $\lambda = 0.8$ range at the same incidence angle.

### 3.2.2. Pressure Contours and Streamlines

Pressure contours, a well-established technique in computational fluid dynamics (CFD), are instrumental in elucidating the aerodynamic forces acting upon a body. By meticulously analyzing these contours, we can glean valuable insights into the deflector's influence on the Savonius turbine's performance. As delineated in Equation (4), the power coefficient is primarily defined by the product of the torque exerted around the turbine axis and its rotational speed. The torque calculation is intrinsically linked to the differential pressure exerted on both the concave and convex facets of the turbine blades.

Figure 8 illustrates the total pressure contour results within both the horizontal plane ($z = 0$) and the vertical plane ($y = 0$), in conjunction with the velocity streamlines ($y = 0$) as derived from our CFD simulations. These simulations were conducted at a tip speed ratio of $\lambda = 1.0$ and an inlet wind speed of $7 \text{ m/s}$.

A comparative analysis of the pressure contours within the horizontal plane at $\theta = 0°$ for the STD (Figure 8a) and AOD2 (Figure 8d) configurations reveals distinct patterns. The AOD2 configuration exhibits a significantly more pronounced pressure gradient, as evidenced by the contrasting color distribution on both sides of the driving blade. This heightened pressure differential translates into a substantial enhancement of torque development and, consequently, a notable increase in power coefficients, as previously observed in Section 3.2.

It is imperative to note that when scrutinizing the color contrast, the regions farthest from the turbine's axis exert the most significant influence. This aligns with the torque definition, which is the product of force and distance from the center, thereby emphasizing the pivotal role of the peripheral regions in torque generation. On the other hand, while comparing the wake region in the velocity streamlines (Figure 8c,f), the recirculation region in the AOD2 configuration seems way more developed. This translates into lower wake pressure zone as seen in the vertical plane Figure 8e compared to Figure 8b.

The observed performance enhancement is attributable to the deflector mechanism. The deflector effectively redirects the airflow towards the rotor, resulting in an augmented mass flow rate of air traversing the turbine, as evidenced by the velocity streamlines depicted in Figure 8f.

When $\theta = 40°$, the pressure contours and velocity streamlines of the AOD2 configuration exhibit patterns comparable to those observed at $\theta = 0°$ within the wake region. Nevertheless, the diminished pressure values at the turbine inlet are a consequence of the mass flow rate bypassing the turbine through the upper deflector at elevated velocities, resulting in a reduction of the power coefficient from 0.37 to 0.17. This phenomenon gives rise to minor recirculation vortices atop the deflector. Moreover, a visual inspection of the velocity streamlines in Figure 8l unequivocally demonstrates the deflector's continued efficacy in redirecting a portion of the flow towards the turbine.
<figure><img src="image_11.png" /><figcaption>**Figure 8.** Pressure contour and velocity streamlines for STD and AOD2 at 7 m·s⁻¹ wind speed for λ = 1.0. (a) STD horizontal plane pressure contour at z = 0 at θ = 0°, (b) STD vertical plane pressure contour at y = 0 at θ = 0°, (c) STD vertical plane velocity streamlines at y = 0 at θ = 0°, (d) AOD2 horizontal plane pressure contour at z = 0 at θ = 0°, (e) AOD2 vertical plane pressure contour at y = 0 at θ = 0°, (f) AOD2 vertical plane velocity streamlines at y = 0 at θ = 0°, (g) STD horizontal plane pressure contour at z = 0 at θ = 40°, (h) STD vertical plane pressure contour at y = 0 at θ = 40°, (i) STD vertical plane velocity streamlines at y = 0 at θ = 40°, (j) AOD2 horizontal plane pressure contour at z = 0 at θ = 40°, (k) AOD2 vertical plane pressure contour at y = 0 at θ = 40°, (l) AOD2 vertical plane velocity streamlines at y = 0 at θ = 40°.</figcaption></figure>

Conversely, for the STD configuration, a substantial alteration in pressure contour
behavior is observed when θ is adjusted to 40°. The turbine operates at an elevated inlet
pressure while generating a diminished torque around its axis. These pronounced pressure
gradients, induced by the modification of θ, are also implicated in the heightened structural
stresses encountered by turbines deployed in urban environments. Figure 8i illustrates a
disrupted wake region characterized by the formation of large-scale recirculating eddies
atop the end plate at $\theta = 40°$. These eddies function as obstacles to the perpendicular wind flow, resulting in a reduction of its velocity around the turbine. The end plate, while not significantly redirecting the wind flow, contributes to the generation of flow separation at the turbine's apex.

### 3.3. Effect of Different Incoming Wind Speed on the Turbine Performance for Different Incidence Angles

To comprehensively investigate the impact of wind speed on turbine performance across various incidence angles ($\theta$), three-dimensional CFD URANS simulations were conducted for wind speeds of 3.5 m/s$^{-1}$, 7 m/s$^{-1}$, and 14 m/s$^{-1}$. The power coefficient (Cp) results are summarized in Figure 6a-c. At $\theta = 0°$, the primary objective was to corroborate the findings of prior research [2] on the Savonius STD configuration, which established a correlation between Cp and the tip speed ratio ($\lambda$) rather than the incident wind speed or Reynolds number. As evident in Figure 6, this conclusion was validated, with the Cp of the STD turbine exhibiting comparable values across different wind speeds. Minor deviations can be attributed to inherent CFD simulation errors. Notably, the implementation of the external wind deflector in the AOD1 and AOD2 configurations did not alter these observations, as their Cp values also demonstrate comparable trends. However, a noteworthy observation is the enhanced Cpmax of the STD configuration at $\theta = 40°$ for the 14 m/s$^{-1}$ wind speed scenario. Here, the calculated Cpmax is 0.12 compared to 0.08 at 7 m/s$^{-1}$, exceeding the margin of potential CFD errors. This anomaly necessitates further investigation to elucidate the underlying mechanism

## 4. Conclusions and Perspectives

Overall, the simulations conducted in this study provide enlightening information on the impact of the incidence angle on the power coefficient of Savonius turbines through the STD, AOD1, and AOD2 configurations. This study fills the knowledge gap by examining the turbine performance under different wind incidence angles and wind speeds. The urban turbines are usually installed in urban areas and on the roof of the buildings where $\theta$ is never constant and is rarely $0°$. The AOD2 outperformed the STD and AOD1 configurations due to its aerodynamical optimized shape by avoiding the creation of eddies and redirecting the air into the center of the turbine rotor. The performance increase was correlated with the increase in the incidence angle showing a 61% Cpmax increase for $\theta = 0°$ and 125% increase at $\theta = 40°$ compared to the standard STD model. In addition, the pressure gradients exhibited by the AOD2 model were significantly lower compared to the STD configuration. This reduction in pressure gradients translates to less structural fatigue, ultimately extending the turbine operational lifespan. These findings contribute to a more comprehensive understanding of turbine performance in urban environments with high turbulence and varying wind incidence angle. The high gain in performance encourages the installation of an AOD2-type deflector on new and existing Savonius turbine installations. On the other hand, the paper highlights that the state of art in the methodology of the deflector design is not relevant in urban areas for VAWT turbines. The main key performance indicator in the assessment of the turbine performance Cp and thus the benefit from installing the deflectors is only assessed at $\theta = 0°$. As shown in this study, the benefit from AOD2 configuration is double at $\theta = 40°$. In view of the predominant vertical wind incidence angle $\theta$ at the specific site installation location, this valuable information could lead to a change in the decision regarding the installation or not of the configuration.

Despite the valuable conclusions of this study, there are important limitations related to the CFD simulations. Unlike the 2D simulations, 3D transient URANS CFD studies have shown good correlation with experiments as they can capture the effects of the fluid flow on the total height of the turbine; however, results were not validated experimentally through wind tunnel experiments. The deflector-mounting system is not considered in the model, which could impact the airflow depending on its final design. On another note,
the study is specific to AOD1 and AOD2 designs and the Savonius turbine and the results could not be generalized to other deflectors or the Darrieus turbine.

**Author Contributions:** Conceptualization, H.A.; methodology, H.A.; validation, F.B. (Fabien Bogard), G.P., F.B. (Fabien Beaumont), Y.T. and S.M.; formal analysis, H.A.; investigation, H.A.; writing—original draft preparation, H.A.; writing—review and editing, F.B. (Fabien Bogard); supervision, G.P.; project administration, H.A. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research received no external funding.

**Data Availability Statement:** Data available upon request.

**Acknowledgments:** The authors wish to thank the Communauté d'Agglomération de Châlons en Champagne (France) and the Pôle de Recherche Châlonnais for their material support.

**Conflicts of Interest:** The authors declare no conflict of interest.

## References

1. Alexander, A.; Holownia, B. Wind tunnel tests on a savonius rotor. *J. Ind. Aerodyn.* **1978**, *3*, 343–351. [CrossRef]

2. Blackwell, B.F.; Sheldahl, R.E.; Feltz, L.V. *Wind Tunnel Performance Data for Two and Three Bucket Savonius Rotor*; Sandia National Laboratories Report, SAND76-0130; Sandia Laboratories: Springfield, VA, USA, 1977.

3. El-Askary, W.A.; Nasef, M.H.; Abdelhamid, A.A.; Gad, H.E. Harvesting wind energy for improving performance of Savonius rotor. *J. Wind Eng. Ind. Aerodyn.* **2015**, *139*, 8–15. [CrossRef]

4. Ferrari, G.; Federici, D.; Schito, P.; Inzoli, F.; Mereu, R. CFD study of Savonius wind turbine: 3D model validation and parametric analysis. *Renew. Energy* **2017**, *105*, 722–734. [CrossRef]

5. Renato, R.; Roberto, R.; Sergio, M.; Daniele, V. Experimental study on a Savonius wind rotor for street lighting systems. *Appl. Energy* **2016**, *161*, 143–152. [CrossRef]

6. Fujisawa, N. On the torque mechanism of Savonius rotors. *J. Wind. Eng. Ind. Aerodyn.* **1991**, *40*, 277–292. [CrossRef]

7. Frederikus, W.; Andy, S.; Hadi, S. An Experimental Study on the Performance of Savonius Wind Turbines Related With The Number Of Blades. *Energy Procedia* **2015**, *68*, 297–304. [CrossRef]

8. Thiyagaraj, J.; Rahamathullah, I.; Anbuchezhiyan, G.; Barathiraja, R.; Ponshanmugakumar, A. Influence of blade numbers, overlap ratio and modified blades on performance characteristics of the savonius hydro-kinetic turbine. *Mater. Today Proc.* **2021**, *46*, 4047–4053. [CrossRef]

9. Payambarpour, S.A.; Amir, F.; Franco, M. Investigation of deflector geometry and turbine aspect ratio effect on 3D modified in-pipe hydro Savonius turbine: Parametric study. *Renew. Energy* **2020**, *148*, 44–59. [CrossRef]

10. Jeon, K.S.; Jeong, J.I.; Pan, J.-K.; Ryu, K.-W. Effects of end plates with various shapes and sizes on helical Savonius wind turbines. *Renew. Energy* **2015**, *79*, 167–176. [CrossRef]

11. Akwa, J.V.; Vielmo, H.A.; Petry, A.P. A review on the performance of Savonius wind turbines. *Renew. Sustai. Energy Rev.* **2012**, *16*, 3054–3064. [CrossRef]

12. Sobczak, K. Numerical investigations of an influence of the aspect ratio on the Savonius rotor performance. *J. Phys. Conf. Ser.* **2018**, *1101*, 012034. [CrossRef]

13. Tong, Z.; Dietmar, R. Numerical study of detailed flow field and performance of Savonius wind turbines. *Renew. Energy* **2013**, *51*, 373–381. [CrossRef]

14. Al Absi, S.M.; Jabbar, A.H.; Mezan, S.O.; Al-Rawi, B.A.; Al Attabi, S.T. An experimental test of the performance enhancement of a Savonius turbine by modifying the inner surface of a blade. *Mater. Today Proc.* **2021**, *42*, 2233–2240. [CrossRef]

15. Kamoji, M.A.; Kedare, S.B.; Prabhu, S.V. Experimental investigations on single stage modified Savonius rotor. *Appl. Energy* **2009**, *86*, 1064–1073. [CrossRef]

16. Morcos, S.; Khalafallah, M.; Heikel, H. The effect of sheilding on the aerodynamic performance of Savonius wind turbines. *ASME* **1981**, *2*, 2037–2040.

17. Shaughnessy, B.M.; Probert, S.D. Partially-Blocked Savonius Rotor. *Appl. Energ.* **1992**, *43*, 239–249. [CrossRef]

18. Yonghai, H.; Zhengmin, T.; Shanshan, W. A new type of VAWT and blade optimization. In Proceedings of the International Technology and Innovation Conference 2009 (ITIC 2009), Xi'an, China, 12–14 October 2009.

19. Burçin, D.A.; Mehmet, A. The use of a curtain design to increase the performance level of a Savonius wind rotors. *Renew. Energy* **2010**, *35*, 821–829. [CrossRef]

20. Tartuferi, M.; Alessandro, V.; Montelpare, S.; Ricci, R. Enhancement of Savonius wind rotor aerodynamic performance: A computational study of new blade shapes and curtain systems. *Energy* **2015**, *79*, 371–384. [CrossRef]

21. Aboujaoude, H.; Bogard, F.; Beaumont, F.; Murer, S.; Polidori, G. Aerodynamic Performance Enhancement of an Axisymmetric Deflector Applied to Savonius Wind Turbine Using Novel Transient 3D CFD Simulation Techniques. *Energies* **2023**, *16*, 909. [CrossRef]
22. Aboujaoude, H.; Beaumont, F.; Murer, S.; Polidori, G.; Bogard, F. Aerodynamic performance enhancement of a Savonius wind turbine using an axisymmetric deflector. *J. Wind. Eng. Ind. Aerodyn.* **2022**, *220*, 104882. [CrossRef]

23. Ross, I.; Altman, A. Wind tunnel blockage corrections: Review and application to Savonius vertical-axis wind turbines. *J. Wind. Eng. Ind. Aerodyn.* **2011**, *99*, 523–538. [CrossRef]

24. Saha, U.K.; Thotla, S.; Maity, D. Optimum design configuration of Savonius rotor through wind tunnel experiments. *J. Wind. Eng. Ind. Aerodyn.* **2008**, *96*, 1359–1375. [CrossRef]

25. Svetlana, M. Performance of a Savonius Wind Turbine in Urban Sites Using CFD Analysis. Thesis, University of VAASA, Vaasa, Finland, 2016.

26. Modi, V.J.; Fernando, M.S.U.K. On the performance of the Savonius wind turbine. *J. Sol. Energy Eng.* **1989**, *111*, 71–81. [CrossRef]

27. Duc, M.B.; The, H.T.; Van, K.P.; Le, A.D. Predicting aerodynamic performance of savonius wind turbine: An application of generalized k-ω turbulence model. *Ocean. Eng.* **2023**, *286*, 115690. [CrossRef]

28. Rezaeiha, A.; Montazeri, H.; Blocken, B. On the accuracy of turbulence models for CFD simulations of vertical axis wind turbines. *Energy* **2019**, *180*, 838–857. [CrossRef]

29. Alom, N.; Saha, U.K.; Dean, A. In the quest of an appropriate turbulence model for analyzing the aerodynamics of a conventional Savonius (S-type) wind rotor. *J. Renew. Sustain. Energy* **2021**, *13*, 023313. [CrossRef]

**Disclaimer/Publisher's Note:** The statements, opinions and data contained in all publications are solely those of the individual author(s) and contributor(s) and not of MDPI and/or the editor(s). MDPI and/or the editor(s) disclaim responsibility for any injury to people or property resulting from any ideas, methods, instructions or products referred to in the content.