Increasing energy production of a ducted wind turbine system

Abstract

This article focuses on evaluating the performance of a relatively new system of a ducted wind turbine with an omnidirectional capture system, the INVELOX system. In the present study, the improvement of such patented system has been developed by performing a detailed numerical analysis varying several geometrical parameters and analysing the effect of changing wind velocity and wind direction. At first, the model validation was performed and the performance of the original system against the wind direction changes was analysed observing that the highest speed ratios are obtained for two specific directions. Based on the previous results, the most critical features of the system have been identified, and then it has been approached a geometric improvement of the system aiming at increasing the system productivity. The results show there is a possibility to largely improve the overall design and extract more energy from the wind respect with the original design.

Keywords

Ducted wind turbine wind energy wind power CFD Venturi effect INVELOX

Introduction

Wind energy exploitation started about 3000 years ago in Persia with windmills, but the critical point in terms of conversion into electricity dates back to the 19th century, thus officialising the birth of the wind energy industry (Sørensen, 2011).

In the last 30 years, wind turbine generators (WTGs) have seen an ever-increasing expansion, and wind is now one of the leader renewable energy source (RES) in terms of installed capacity (Carvalho et al., 2017). In 2017, it has been evaluated with a global capacity of 18.81 GW, out of which 15.73 GW have been installed between 2011 and 2017 (Nie and Li, 2018). That trend does not seem to be slowing down, indeed, it still has great development ambitions with scenarios that foresee future wind energy capacities ranging from 251 to 392 GW by 2030 (Davy et al., 2018). It is also foreseen that wind energy will meet one quarter of the overall European electricity consumption (Mahulja et al., 2018).

Despite that fast deployment around the world, WTGs’ levelised cost of electricity (LCOE) has not been competitive with traditional, fossil-fuelled technologies for a long time. In the last years, the fast deployment of numerous generators all over the world accelerated the LCOE reduction as demonstrated by several researches, for instance, Rusu and Onea (2019), U.S. Energy Information Administration (EIA; 2019) and International Renewable Energy Agency (IRENA; 2018), making WTGs competitive with fossil-fuelled generators. Such improvements are due to the enhancement of various aspects of a WTG and/or of a wind farm. In order to improve WTGs’ cost-effectiveness, the blade size and the turbine height have been increased as well as the wind farm size thus increasing the investment cost, but reducing the overall LCOE. On the other hand, this approach generated new issues to deal with such the ones linked to aeroelasticity and flutter (Ochieng et al., 2018) and the high loads and fatigue on blades due to the increased turbulence generated by wind farms as reported by Argyle et al. (2018). However, Ghane et al. (2018) demonstrated that low-efficiency factors, excessive downtime, and running costs are still a great problem to deal with in order to make the wind profitable and reliable. In fact, conventional wind turbines are often subject to excessive downtime with high failure and repair costs (Olauson et al., 2017; Su and Hu, 2018). Moreover, many researchers and scientists have proposed new projects for WTGs, some focused on increasing the efficiency of wind energy conversion by optimising the blade shape (Chan et al., 2018) and pitch (Li et al., 2018), and the wind farms layout (Antonini et al., 2018), others on designing systems that could be integrated in buildings for smart cities application (Aquino et al., 2017; Lee et al., 2018). Furthermore, an important branch of research focused on the development and optimisation of ducted wind turbines (DWTs; De Santoli et al., 2014; Dighe et al., 2018; Jadallah et al., 2018; Ragul et al., 2017).

DWTs are one of the most developed approaches to increase wind speed. The benefits of having a DWT that captures the wind at high altitudes from every direction and then canalise the wind energy to the ground through a wind turbine are multiple. They can be mounted in logistically demanding sites (Nardecchia et al., 2016) with weak winds on the ground. Moreover, with such systems, the high installation costs of wind turbines on top of tall towers and the resulting maintenance costs are avoided. An active yaw control system is not required to orient the turbine in the direction of the impending wind. Allaei (2010a, 2010b) found that the speed of the captured wind is then increased in a Venturi section, where also the wind turbines are placed. Furthermore, DWTs show a significant reduction in peak losses and relative noises.

Bontempo and Manna (2016) investigated the performance of DWTs through the axial momentum theory (AMT). They showed the opportunity to significantly increase the turbine power output by enclosing it in a conduit and demonstrating that the growth of thrust in the conduit has a beneficial effect on the device performance. A simple numerical model of a DWT was proposed by Grant and Kelly (2003), proposing and analysing a case study application. In this work, the output power is studied, in particular when this type of turbine is installed on a building roof. This concept was then developed by the same author in 2008 (Grant et al., 2008), where they presented a study of a DWT installed on the roof of a building, which uses the pressure differences created by the wind flow. Many authors have carried out studies on the pipe geometry and the associated diffuser (Abe et al., 2005; Liu and Yoshida, 2015; Ohya et al., 2008; Wang et al., 2015). Hu and Cheng (2008) proposed an algorithm for optimising the geometry of the duct for a DWT, finding a shape for the diffuser to accelerate the wind speed by 60%. Also, Matsushima et al. (2006) focused their studies on the aerodynamic performance of a diffuser demonstrating that wind speed can be increased by 1.7 times by a suitable shape of the diffuser itself. However, those design concepts were economically unreasonable to be used on an urban scale. In this regard, a recently introduced DWT with an omnidirectional capture system (Allaei and Andreopoulos, 2014), called INVELOX (named for INcreased VELocity), promises to obtain very good results.

The INVELOX concept has all the benefits that are typical for DWTs, but it also introduces an important advantage that is the omnidirectional capture system. Allaei and Andreopoulos (2014) have been the first to present on-field measurements thus demonstrating that INVELOX can enhance the daily energy production ratio. In their following works (Allaei, 2012; Allaei and Andreopoulos, 2014; Allaei et al., 2015), they have also studied the flux within and outside of the prototype by performing numerical simulations, also varying the number of turbines within the Venturi section. Nevertheless, in literature, there are few evidences of analysis of the INVELOX geometry (Anbarsooz et al., 2017). In particular, a detailed analysis aiming at improving the system geometry is currently lacking. Such an analysis could significantly affect the system aerodynamic performance.

In the present work, an optimised DWT model has been developed by analysing the variation of several geometrical parameters of the INVELOX system that has been used as baseline geometry. Moreover, the optimised DWT system performance in response to changes in the wind characteristics (i.e. wind speed and direction) has been numerically simulated in order to study their effect on the whole system performance. The numerical simulations have been performed by means of the commercial software Ansys Fluent. After the validation of the baseline model and a parametric analysis, several improvements of the system geometry have been analysed seeking for the highest wind velocity in the Venturi section. Specifically, variation in the inlet funnel, in the duct section before and after the Venturi, has been analysed. In the following chapters, at first, the validation process and then the parametric analysis on the original model have been explained. Then, all the proposed improvements are presented and deeply studied singularly and to conclude the overall improved omnidirectional DWT model is analysed.

Materials and methods

In the present section, the tools and methods used for the system analysis are explained. At first, the DWT basic geometry is explained. Afterwards, the numerical model features are detailly shown as well as their implementation in the Ansys Fluent software. Then, the numerical model is validated against the original work simulation values (Allaei and Andreopoulos, 2014). Once the model has been validated, a thorough parametric analysis to study the response of the original system to wind speed and direction changes is provided. To conclude the present section, the proposed geometric improvements are explained singularly. Furthermore, all the improvements whose results benefit the system performance have been merged to create a new model.

The developed DWT model builds up over the INVELOX system model that is used as a baseline geometry. The original INVELOX system is presented in Figure 1 and explained in detail in the original research paper (Allaei and Andreopoulos, 2014). As shown in Figure 1, the five basic parts are as follows:

An intake composed of two cones (S1 and S3) whose positions generate the capture section, delimited by fins (S2);

A conduit where the wind is flowing (S4 and S5);

A section where the wind speed is accelerated by a Venturi duct (S6);

A diffuser (S7).

Figure 1.

INVELOX model.

The upper part where the wind is captured consists of a double cone with 360° wind suction capacity. The upper cone acts as a guide to the air, which is then directed into the lower cone. The upper cone has a diameter of 12.192 m and a height of 12.203 m. The lower cone has an upper diameter of 12.192 m and a lower diameter of 3.048 m. The distance between the two cones is 6.096 m. The elbow section has a constant diameter (3.048 m) and a curvature radius of 4.572 m. The Venturi section has a diameter of 1.829 m, while the total height of the tower is 18.288 m. The entrance contains four partitions (i.e. fins) symmetrically positioned at 90°, 180°, 270° and 360° with respect to the vertical axis of the axisymmetric diffuser.

Numerical model

The considered computational domain is the same used by Allaei and Andreopoulos (2014), which is a rectangular cube with dimensions of 120 m × 67.2 m × 72 m, as shown in Figure 2. The computational domain has been extended in the streamwise direction by a factor 3 compared to the system height (3H) between the inflow boundary and the considered object and by 3H between the considered object and the outflow boundary. Its height has been set equal to 3H too. The domain size has been selected based on the characteristics that had been previously used in the original research in order to enable the model validation. Furthermore, additional analyses have been performed in order to check the domain size validity. The distances that have been adopted for the domain size have been chosen to prevent an artificial acceleration of the flow over the object. The distances given above have been checked to prevent an artificial acceleration of the flow over the object.

Figure 2.

Domain and mesh.

The wind enters the intake with a speed of 6.7 m/s. For the inflow, a constant uniform velocity is imposed with a turbulent intensity of 5% and a turbulence scale of 1.0 m. The temperature is set constant and equal to 300 K. All solid faces have a no slip boundary condition, while the outlet condition is pressure outlet, with a uniform relative pressure equal to zero.

Since the problem considered has a non-simple geometry, the computational domain has been discretised using an unstructured grid (Figure 2). The mesh is refined near the solid surfaces: this technique allowed a better control of the relationship between the fine grid very close to the considered object, which is necessary due to the presence of walls, and the coarsest grid on the external domain. The cell stretching ratio was kept under a value of 1.15 near the object. Furthermore, since the Venturi section is of particular interest for the study, a further mesh refinement was carried out in that area (Figure 3).

Figure 3.

Venturi section mesh.

Defining the correct mesh spacing is not a trivial task because when a mesh is too coarse, erroneous results can be obtained; while if the mesh is excessively fine, there is a long calculation time. Based on this, any CFD simulation should be preceded by a mesh sensitivity analysis.

In the present work, four meshes of different density were analysed, refining only the internal sections of the system (Table 1). The probe point, in each of these models, was positioned at the centre of the Venturi section, where the mean velocity was extrapolated; the mean velocity was thus compared between the four grids, assuming the Mesh A (about 900,000 cells) as a reference mesh. In Table 1, it can be seen that the percentage difference Δ(%) between Mesh A and the best (Mesh D) is only 2%. This shows that with Mesh A the simulation is robust, and, at the same time, the calculation time is acceptable. Therefore, in this article, Mesh A is used for all the CFD analyses.

Table 1.

Characteristics of the four meshes used for the sensitivity test and the corresponding percentage difference.

	Mesh A	Mesh B	Mesh C	Mesh D
Total number of cells	~ 900,000	~ 700,000	~ 500,000	~ 1,100,000
Mesh interval size (m)	0.1	0.2	0.4	0.025
Δ(%)	–	15.76	25.50	2.08

The commercial software Ansys Fluent v.14.5 (Ansys Fluent, 2013) was used for performing the CFD simulations. Pressure-based solver, steady-state analysis and RANS (Reynolds-averaged Navier–Stokes) steady equations in combination with the standard k-ε model are the main characteristics of the simulations. Furthermore, pressure–velocity coupling was developed using the PISO algorithm (Issa, 1986) and the pressure interpolation scheme was used as second order.

For turbulent flows, RANS steady equations for solving the balance of mass momentum, and energy have been used. These two equations can be expressed as

\frac{\partial {\bar{u}}_{i}}{\partial x_{i}} = 0 i = 1, 2, 3

(1)

{\bar{u}}_{j} \frac{\partial {\bar{u}}_{i}}{\partial x_{j}} = - g_{i} - \frac{1}{ρ} \frac{\partial \bar{p}}{\partial x_{i}} + \frac{\partial}{\partial x_{j}} [ν \frac{\partial {\bar{u}}_{i}}{\partial x_{j}} - \bar{u_{i}^{'} u_{j}^{'}}] i = 1, 2, 3

(2)

where ${\bar{u}}_{i}$ are the components of the mean velocity, $\bar{p}$ the mean pressure, $g_{i}$ the gravitational acceleration and $\bar{u_{i}^{'} u_{j}^{'}}$ the Reynolds stress tensors.

The k-ε model solves the RANS equations coupled with transport equations for the turbulent kinetic energy, k, and its dissipation rate, ε. In this model, only the mean flow is solved, while turbulence is parameterised at all scales by means of suitable laws.

The choice of the turbulence model k-ε is mandatory since the original studies (Allaei and Andreopoulos, 2014), on which the authors of this article base their numerical validation, were executed by modelling turbulence through k-ε.

The standard k-ε is a two-equation model in which two transport equations are added to the system (1–3). This model, originally proposed by Launder and Spalding in 1972, has become one of the most widely used turbulence models, since it provides robustness, computer time saving and reasonable accuracy for a wide range of turbulent flows.

The convergence of the simulations was determined once all the scaled residuals levelled off and reached a minimum of 10^–6 for x, y and z momentum, k, ε and 10^–4 for continuity. Variables of interest, like velocity, were controlled at several chosen steps during the solving process to ensure they were monitored before the convergence occurred.

In order to solve and simplify the problem, the following assumptions were made: no unsteady motion and analysis is involved, but only steady-state formulations are assumed; uniform and incompressible fluid flow is assumed; effect of heat and heating is neglected; model thickness is neglected; all the simulations are made by assuming constant-free stream velocity throughout the domain.

Model validation

In the present section, the validation of the developed INVELOX model is shown. The validation has been performed by comparison with the results obtained by the first developer in Allaei and Andreopoulos (2014). Subsequently, a parametric study to assess wind speed and direction effect on the system performance has been performed.

Numerical model validation

The first step consisted of simulating the original geometry in order to validate the developed model. In that simulation, the wind speed and direction are fixed at 6.7 m/s and parallel to the turbine axis. Considering that the system performance strongly depends on the wind speed in the Venturi section, the parameters that have been considered for the validation process are the average wind speed and the mass flow rate in that section.

The obtained wind speed profile over the symmetry plane from the original paper (Allaei and Andreopoulos, 2014) and the present work are shown in Figure 4(a) and (b).

Figure 4.

Results (a) obtained in Allaei and Andreopoulos (2014) and results (b) obtained in the present article.

As it is shown in Figure 4, velocity fields are similar. That similarity is also confirmed by the numerical results in terms of average wind speed (V_m) and mass flow rate ( $\dot{m}$ ) within the Venturi section that are summarised in Table 2. The percentage error (Δ%) has been evaluated to be equal to 4% and 3% for average wind speed and mass flow rate, respectively.

Table 2.

Comparison of validation results.

	V_m [m/s]	Δ%	$\dot{m}$ (kg/s)	Δ%
Alleai (0)	10.60	–	34.50	–
Present work	11.04	4.15	35.51	2.93

Hence, the obtained results are comparable with the one presented in Allaei and Andreopoulos (2014) and thus the model is validated and can be adopted for further analysis.

Parametric analysis on original INVELOX model

All simulations have been performed without the turbine in the Venturi section. In the first set of simulations that are presented in this section, wind speed has been changed in the range of 1–10 m/s with a step of 1 m/s. Table 3 summarises the average wind speeds in the Venturi section (V_Venturi) that have been obtained in relation to the input wind velocity (V_in). In Table 3, the ratio between the V_Venturi and V_in, the mass flow rate in the Venturi section ( ${\dot{m}}_{Venturi}$ ) and the maximum exploitable power, evaluated according to the Betz theory (Betz, 1966), are shown versus V_in.

Table 3.

System performance analysis due to the inlet wind velocity variation.

V_in (m/s)	V_Venturi (m/s)	V_Venturi/V_in	${\dot{m}}_{Venturi}$ (kg/s)	P_max (W)
1	1.67	1.67	5.36	4.39
2	3.27	1.64	10.53	33.30
3	4.92	1.64	15.82	112.92
4	6.57	1.64	21.12	268.68
5	8.40	1.68	27.02	562.60
6	10.09	1.68	32.45	974.52
7	11.78	1.68	37.89	1551.38
8	13.48	1.68	43.34	2321.73
9	15.33	1.70	49.29	3415.25
10	16.83	1.68	54.12	4520.84

It is noteworthy that, with the varying of V_in and the consequent V_Venturi variation, the ratio between the two remains almost stable and ranges between 1.64 and 1.7. This is translated in the V_Venturi and ${\dot{m}}_{Venturi}$ linearly increase with V_in. By comparing the maximum exploitable power with and without the INVELOX system, it has been evaluated that with the same turbine, thus the same swept area, the increased power production due to INVELOX ranges between 339% and 394%.

It can be observed that INVELOX can produce up to 4 to 5 times more power than a traditional wind turbine under the same climatic condition. Moreover, results show that INVELOX has better performance than a traditional turbine under every wind condition. Thus, a further analysis has been performed.

The DWT under study is supposed to be an omnidirectional capture system. Thus, the system response to wind direction changes has been investigated. In order to run the simulations, INVELOX has been rotated so as to change the wind direction relative to the wind turbine axis. The simulated scenario considered angles between the wind direction and the turbine shaft equal to 0°, 45°, 90°, 135°, 180°, 225°, 270°, and 315° with a stable wind speed equal to 6.7 m/s. Table 4 summarises the obtained results in terms of V_Venturi, ${\dot{m}}_{Venturi}$ and P_max.

Table 4.

System performance with wind direction.

Degree	V_Venturi (m/s)	${\dot{m}}_{Venturi}$ (kg/s)	P_max (W)
0°	11.27	36.26	1359.66
45°	14.11	45.37	2663.50
90°	11.79	37.91	1553.84
135°	2.30	7.41	11.60
180°	–8.07	–25.97	0
225°	2.40	7.72	13.12
270°	9.42	30.31	794.15
315°	12.15	39.09	1703.50

Analysing the system response to wind direction, it is immediately noticeable that it is not perfectly omnidirectional. In fact, for wind direction equal to 135° and 225°, obtained V_Venturi is less than the external wind speed. Moreover, for wind direction of 180°, the system cannot exploit wind energy due to a flux inversion. The optimal performance is obtained for wind direction equal to 45° and 315°. That result is due to the fact that the wind flow directly enters the funnel; thus, losses on the fins are strongly reduced. In the other scenarios, when the wind is perpendicular to any fin direction, a fraction of the wind flux tends to bypass the structure thus reducing the amount of wind flow able to enter the system. That can be considered the first interesting conclusion of the present work.

Generally speaking, INVELOX is omnidirectional and high V_Venturi are obtained for every wind direction except for 135°/225° and 180°. Moreover, the result shows that for wind direction of 45°/315°, the system has its optimal performance and the maximum V_Venturi can be obtained (e.g. 14.11 m/s are obtained with a V_in equal to 6.7 m/s). Thus, the optimal angle is the one that generates an angle of 45°/315° between the turbine axis (and the exit direction of the flux) and main wind direction in the installation site. Such results are confirmed by Georgescu et al. (2017) and Narendrabhai and Desmukh (2018) in their works.

In conclusion, the validation outcomes certify that the adopted numerical model represents, with an acceptable error, the original model. Thus, next steps consisted in the numerical simulation of an improved DWT starting from the original INVELOX model.

System improvements

In this section, the improvements for the original INVELOX model system will be introduced and explained. Specifically, variations in the inlet funnel, in the duct section before and after the Venturi have been analysed. Furthermore, all the improvements have been merged to create a new model.

Displacement of the fins

One of the proposed improvements consists on the displacement of fins in the capture section (section S2 in Figure 1) as shown in Figure 5.

Figure 5.

Geometry (a) with fins and (b) without fins.

The intake captures the flow of external air in a complex way: the flow of air coming close to the structure impacts on the fins. Subsequently, it is diverted downwards, to then continue inside the main duct towards the Venturi section. At the same time, a part of the airflow is diverted to the sides of the intake and separates by meeting the edge of the fins, then continuing its path away from the structure.

Removal of section S5

As a second test, the benefits brought by the constant pipe installed before the Venturi section (section S5 in Figure 1), as depicted in Figure 6, have been evaluated. After being captured by the intake, the air is diverted into the 90° elbow to then meet a constant section. The function of this section is to prepare the flow to properly enter into the Venturi section; the flow now is collimated and the turbulence that had arisen due to section variation in the elbow above is dissipated and so the flow enters parallel in the next section.

Figure 6.

Omnidirectional DWT (a) with S5 section (INVELOX model) and (b) without S5 section.

Variation of the lower part of S1 section

The third proposed solution consists of varying the lower part of the upper cone as shown in Figure 7. In detail, the final part of this section has been smoothed, compared to the original model, inserting a hemisphere. This change in geometry allows the newly arrived air to bypass the final part of the cone and not to find an edge, which generates turbulence, as in the original design.

Figure 7.

Omnidirectional DWT (a) INVELOX model and (b) S1 section change.

Addition of section S8 after Venturi section

The last analysis consisted of adding a duct with a constant section (S8 in Figure 1) to the original geometry exit, precisely right after the divergent duct after the Venturi section (Figure 8). The objective of adding such a constant duct is to avoid the external air to enter the divergent duct and thus affect the V_Venturi and the turbine functioning.

Figure 8.

Omnidirectional DWT (a) without S8 (INVELOX model) and (b) with S8.

Results

In the results section, the analysis of the potential improvement to be adopted to develop a better performing omnidirectional DWT system is presented. Specifically, changes for the entry section with the fins, the conical section after the air inlet, the constant section after the elbow and the outlet section after the Venturi section will be considered. All the simulations were performed respecting the original boundary conditions, that is, with the same direction and wind velocity used in Allaei and Andreopoulos (2014). At last, all the proposed improvements have been considered at the same time in order to assess the overall system performance compared to the original INVELOX model.

Displacement of the fins

In this section, the effects of the contribution due to the presence of the fins in the capture section are presented. Results of the analysis are shown in Table 5 and Figure 9(a) and (b).

Table 5.

Analysis of the fins in section S2.

Model	V_Venturi (m/s)	${\dot{m}}_{Venturi}$ (kg/s)	P_max (W)
With fin	11.27	36.36	1359.66
Without fin	8.69	27.94	622.05

Figure 9.

Velocity contours (a) with fins and (b) without fins.

As expected, the presence of the fins is indispensable. Indeed, with the installation of these devices, it is possible to reach an average velocity in the Venturi section greater by the 29.69% compared to the case without fins. Consequently, with the fins, the maximum wind extractable power, according to Betz theory, is greater than the case without fins of 118.58%.

Therefore, the fins are fundamental in channelling the air flow coming from the outside and then driving it to the lower part of the inner cone.

Removal of section S5

The second geometrical improvements analysis consisted in studying the effect of the constant pipe installed before the Venturi section. The results of the analysis are presented in Table 6 and in Figure 10.

Table 6.

Analysis of the S5 section.

Model	V_Venturi (m/s)	${\dot{m}}_{Venturi}$ (kg/s)	P_max (W)
With duct	11.27	36.36	1359.66
Without duct	11.49	36.96	1439.93

Figure 10.

Contours of velocity (a) with and (b) without S5 section.

The presence of the constant duct section between the elbow and the convergent is unjustified since, even if comparable, better results are obtained without such section. Without duct, a mean velocity greater than 1.95% is obtained in the Venturi section with respect to the case with the presence of the duct; the mass flow rate increases by 1.93% while the maximum extractable power is greater by 5.9%.

Moreover, as can be seen in Figure 11, even without a straight duct, the flow that arrives in the Venturi section is almost unidirectional and parallel to the turbine axis, therefore, perfect for optimising the extraction of energy. So, the little turbulence that has been created in the upper part with the elbow is not strong enough to be able to influence the flow in the next section and dissipates in a small space.

Figure 11.

Velocity vectors in the Venturi section.

In Figure 11, a detailed view of the velocity vectors on the Venturi section is presented.

Variation of the lower part of S1 section

In this test, the lower part of the air inlet cone has been modified (see Figure 7). Particularly, the final part of S1 section has been smoothed aiming at reducing the turbulence in the entry sections.

Table 7 shows the results related to the analysis of this geometric variation.

Table 7.

Analysis of the S1 section changes.

Model	V_Venturi (m/s)	${\dot{m}}_{Venturi}$ (kg/s)	P_max (W)
Not modified	11.27	36.36	1359.66
Modified	11.58	37.23	1471.72

The smoothing of the cone reduces the vorticity of the flow in the affected area by increasing the average velocity in the Venturi section by 2.75%, the mass flow rate by 2.68% and the maximum extractable power by 8.24%. So, it is an intervention that, if applied, would bring benefits.

As can be seen in Figure 12, the incoming air tends to be driven towards the next section, thus, decreasing the vorticity that was first created with the presence of a step. Then the flow enters the elbow section with a more stable regime, and then reaches the Venturi section more uniformly.

Figure 12.

Velocity vectors in the S1 section (a) not modified and (b) modified.

Addition of section S8 after Venturi section

The last analysis consisted of adding a constant section duct (S8 in Figure 1) after the divergent duct of the Venturi (Figure 8) aiming at avoiding the external air to enter the divergent duct and thus affect the V_Venturi. Table 8 summarises the results obtained by varying such geometric element.

Table 8.

System performance with and without the final duct.

Model	V_Venturi (m/s)	${\dot{m}}_{Venturi}$ (kg/s)	P_max (W)
Without duct	11.27	36.36	1359.66
With duct	11.68	37.57	1512.41

The addition of the duct at the DWT exit is a fruitful measure since it raises the V_Venturi by 3.64% and the maximum exploitable power by 11.23% compared to the original model. The flux exits the Venturi section and can proceed undisturbed within the added duct without suffering the external air effect and the corresponding turbulence. Hence, the air flux is free to expand through the turbine without being affected by the air that is exiting the DWT as it is shown in Figure 13.

Figure 13.

Velocity vectors with (a) and without (b) S8 constant duct.

Improved model

The last step consisted of merging all the interventions that resulted to improve the system performance. Specifically, it has been considered to remove the S5 duct, vary S1 and to add S8 duct at the end of the divergent section (see Figure 14). Table 9 summarises the obtained results.

Figure 14.

Omnidirectional DWT model (a) INVELOX and (b) optimised.

Table 9.

System performance with and without all the proposed changes.

Model	V_Venturi (m/s)	${\dot{m}}_{Venturi}$ (kg/s)	P_max (W)
Not modified	11.27	36.36	1359.66
Totally modified	13.54	43.54	2354.02

The contemporary application of the abovementioned measures leads to a percentage velocity increase equal to 20.14%, a mass flow rate that is 20.08% higher than the original one and an increase of the maximum exploitable power of 73.13%. The intake flux behaviour remains unchanged, but it tends to vary at the end of the internal cone. Indeed, from that point on, it follows the elbow pipe and then accelerates up until the Venturi section. Then, it exits the system without suffering external air interference (see Figure 15).

Figure 15.

Velocity contours for (a) original model and (b) optimised model.

Thus, three different geometry variations have been proposed and their impact on the system performance has been shown. Furthermore, the fruitful effect of an enhanced geometry, which comprehends three out of the four proposed measures, has been modelled and simulated thus proving the enhanced system performance.

Conclusion

In the present work, an optimised omnidirectional DWT based on the INVELOX geometry has been presented through detailed numerical studies by means of the Ansys Fluent software. The variation of several geometrical parameters, which had been previously identified as critical sections of the geometry, have been presented and analysed. Furthermore, the effect of the wind characteristics (i.e. wind speed and direction) on the system performance has been widely studied.

After the validation of the model, several geometry variations have been proposed in order to increase wind velocity, the mass flow rate in the Venturi section and thus the maximum exploitable power. Specifically, the following modifications have been analysed: (1) fins displacement, (2) constant duct removal, (3) variation of the bottom part of the internal cone and (4) the addition of duct after the Venturi section. The results obtained are as follows:

i. The fins removal does not improve the system performance; specifically, the V_Venturi is decreased to a value of 8.69 m/s and a mass flow rate of 27.94 kg/s, thus a reduction equal to 29.69% and 29.78%, respectively. Thus, the presence of fins is indispensable; in fact, the maximum exploitable power is greater than the case without fins by the 118.58%;

ii. The displacement of S5 between the elbow and the Venturi section improves the system performance; in fact, the V_Venturi is 1.95% higher than the one of the original model. The mass flow rate and the maximum exploitable power are also increased by 1.93% and 5.9%, respectively;

iii. The variation of S1 lower part leads to important benefits for the system performance; it increases V_Venturi to a value equal to 11.58 m/s, corresponding to a percentage growth of 2.75%. The mass flow rate increases by 2.68% while the maximum extractable power raises to 1471.72 W, equal to a percentage variation of 8.24%. That performance improvements are due to the decreased vorticity that enters the Venturi section;

iv. The addition of a constant duct at the end of the divergent section leads to remarkable improvement of the system performance; V_Venturi is increased by the 3.64%, the mass flow rate of 3.61% and the maximum exploitable power, according to Betz theory, reaches the value of 1521.41 W (i.e. 11.23% greater than the original model).

The last step of the analysis consisted of integrating all the proposed measures with a positive effect on the system performance in order to improve its power exploitation. Thus, the considered measures are S5 displacement, S1 lower part geometry variation and the addition of a constant duct at the system exit. Applying all those interventions at the same time, the system results enhanced since the V_Venturi reaches a value of 13.574 m/s, 2.3 m/s greater than the one of the original model (i.e. 20.14 %), the mass flow rate is increased by 20.08% and the maximum extractable power by 73.13% reaching a value of 2354 W.

In conclusion, four different geometry variations have been proposed and their impact on the system performance has been shown. Three of them resulted in improving the system performance. Furthermore, an enhanced geometry that comprehends the three proposed measures has been modelled and numerically simulated thus proving the enhanced system performance.

Future researches should focus on the development of a smaller prototype with corresponding on-field measurements, and a fluid dynamic analysis to reduce the system size.

Footnotes

Declaration of conflicting interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) received no financial support for the research, authorship, and/or publication of this article.

ORCID iD

Fabio Nardecchia

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