An Investigation of a Mathematical Model for the Internal Velocity Profile of Conical Diffusers Applied to DAWTs.

Disterfano L.M Barbosa,Sávio W.O Figueiredo,Jerson R.P Vaz,Marcelo De Oliveira E Silva,Erb F Lins,André L.A Mesquita

doi:10.1590/0001-3765201520140114

Disterfano L.M Barbosa, Sávio W.O Figueiredo + Show 4 more

Open Access

https://doi.org/10.1590/0001-3765201520140114

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Abstract

The Diffuser Augmented Wind Turbines (DAWTs) have been widely studied, since the diffusers improve the power coefficient of the wind turbine, particularly of small systems. The diffuser is a device which has the function of causing an increase on the flow velocity through the wind rotor plane due to pressure drop downstream, therefore resulting in an increase of the rotor power coefficient. This technology aids the turbine to exceed the Betz limit, which states that the maximum kinetic energy extracted from the flow is 59.26%. Thus, the present study proposes a mathematical model describing the behavior of the internal velocity for three conical diffusers, taking into account the characteristics of flow around them. The proposed model is based on the Biot-Savart's Law, in which the vortex filament induces a velocity field at an arbitrary point on the axis of symmetry of the diffusers. The results are compared with experimental data obtained for the three diffusers, and present good agreement.

Highlights

The use of the diffusers on the horizontal-axis wind turbines aims at increasing the mass flow through the wind rotor
The present study shows a mathematical model which describes the internal velocity profile of a conical diffuser, using the Biot-Savart's Law (Kart and Plotkin 2001, Van Beveren 2008) to calculate the velocity induced by a vortex ring
A long and heavy structure is not preferable in the practical sense. This velocity increasing effect has enabled the development of new technologies, which benefit from the modification of the diffusers geometries that have been widely studied in the last years (Ohya and Karasudani 2010, Abe and Ohya 2004), in order to improve the wind turbine design, in more economic manner

Summary

INTRODUCTION

The use of the diffusers on the horizontal-axis wind turbines aims at increasing the mass flow through the wind rotor. Hansen et al (2000) conducted a study on diffuser augmented turbines using Computational Fluid Dynamic (CFD), where the increase of the velocity in the rotor plane was 1.83 for a case in which the cross section of the diffuser was the deformed NACA 0015 airfoil These aspects highlight the importance of the development of models capable of accurately designing DAWTs. The main limitation of the diffuser augmented horizontal-axis wind turbines design, is that there is no formulation able to satisfactorily describe the diffuser geometry influence on the internal velocity profile. The velocity distributions at the positions 150, 300 and 450mm are shown below: These results, in Figure 7, indicate that the speeds measured at positions equidistant from the wind tunnel are very close; this means profile remains almost constant 450mm far from the wind tunnel exit. An example of the velocity measurements with Diffuser 3 is shown in Figure 8 with the Pitot probe installed on the positioner

EXPERIMENTAL RESULTS

RESULTS

CONCLUSIONS