Rotor aerodynamic power limits at low tip speed ratio using CFD

The Science of Making Torque from Wind 2014

Mikkelsen, Robert F.^1 ; Sarmast, Sasan^1,2 ; Henningson, Dan^1,2 ; Sørensen, Jens N.^1

DTU Wind Energy, Denmark Technical University, 2800 Kgs. Lyngby, Denmark^1

Swedish E-Science Research Centre (SeRC), Linné FLOW Centre, Royal Institute of Technology, SE-100 44 Stockholm, Sweden^2

关键词: General momentum theory;    Low tip speed ratios;    Power performance;    Rotor aerodynamics;    Tip speed ratio;    Viscous effect;    Vortex breakdown;    Vortex ring state;   

Others  :  https://iopscience.iop.org/article/10.1088/1742-6596/524/1/012099/pdf
DOI  :  10.1088/1742-6596/524/1/012099

来源: IOP

【 摘 要 】

When investigating limits of rotor aerodynamic models, the Betz limit serves as a solid marker of an upper limit which no model should be able to exceed. A century ago Joukowsky (1912) proposed a rotor aerodynamic model utilizing a rotating actuator disc with a constant circulation. This model has since then been the subject of much controversy as it predicts a power performance that for all tip speed ratios exceeds the Betz limit and which goes to infinity when the tip speed ratio goes to zero. Recently, it was demonstrated that the Joukowsky model is fully consistent with the inviscid Euler equations and that the apparent inconsistency partly can be explained by the lack of viscous effects (Sprensen and van Kuik [4]). However, even including a term to account for the effect of viscosity at small tip speed ratios, the model still predicts a power yield that exceeds the Betz limit. In the present work we study in detail, using a CFD actuator line model, the flow behavior for rotors at small tip speed ratios. It is shown that the excessive swirl appearing towards the rotor center at small tip speed ratios generates vortex breakdown, causing a recirculating zone in the wake that limits the power yield of the rotor. The appearance of vortex breakdown has a similar effect on the flow behavior as the vortex ring state that usually appears at higher tip speed ratios. Limits to where vortex breakdown might occur with tip speed ratio and rotor loading as parameter are investigated and presented in the paper. The limits found correspond to well-known criterion for vortex breakdown onset for swirling flows in general. By applying a criterion for vortex breakdown in combination with the general momentum theory, the power performance always stays below the Betz limit.