Abstract
A complete and consistent, one-dimensional momentum theory is derived for the aero-dynamics of slotted diffuser-augmented wind turbine (sDAWT). This theory does not require empirical relations. It results in a set of three-parameter relations for aerodynamic characteristics such as power coefficient Cp , rotor resistance k, rotor axial force coefficient CT , axial induction factor α, wake-expansion factor β, duct axial force coefficient CT,duct and slot mass flux . The theory predicts that the maximum achievable power coefficient Cp of (s)DAWT’s increases monotonically with increasing β, surpassing the Betz limit of open-rotor wind turbines (ORWT’s), already for modest (>2) β’s. The slot of an sDAWT feeds outside air into the diffuser, which for given β decreases the flow through the rotor and therewith Cp . However, the flow through the slot delays the onset of flow separation in the diffuser, increasing the maximum achievable β and therewith the power coefficient of sDAWT’s beyond that of DAWT’s.Based on a vortex model of the (s)DAWT, an expression is derived for the velocity induced at the rotor plane by the diffuser and for the corresponding circulation of the diffuser.The derived three-parameter relations for sDAWT’s reduce to two-parameter relations for DAWT’s and the familiar one-parameter relations for ORWT’s.
Highlights
The one-parameter-results for open-rotor wind turbines (ORWT’s) are found by setting Ṁ duct = 0, (i.e. β = β) and CT,duct = 0. The latter implies that in the DAWT expressions in terms of (k,β), (CT,β) and (a,β) the wake-expansion factor β is to be specified as β = 4, β = 1+√1−CT and β = 1−a, (7)
The outside momentum added to the flow inside the diffuser, will have as result that the maximum value of β for which the diffuser still achieves attached flow will be higher, i.e. the maximum achievable power coefficient will be higher for slotted diffuser-augmented wind turbine (sDAWT)’s than for DAWT’s
In the limit of zero mass flow through the slot, Ṁ duct = 0, these relations reduce to two-parameter relations for the aerodynamic performance of DAWT’s
Summary
The first control volume consists of: the stream surface passing through the edge of the actuator disc and passing along the interior side of the duct, bridging the slot; an entrance and an exit cross-flow plane This control volume is intersected by five cross-flow planes: (1) Plane 1: The plane far upstream, cross-sectional area of stream tube A∞, with the pressure and the velocity equal to their free stream values p∞ and V∞, respectively. The second control volume consists of: a far-field circular-cylindrical surface, of constant cross-sectional area A0, which envelopes the actuator disc and the (slotted) diffuser; an entrance and an exit crosssectional plane. First seven equations are derived by applying the laws of conservation of mass and momentum to the two control volumes sketched in figure 2 for the sDAWT
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
