A low-order model for the circulation budget within a leading-edge vortex (LEV) is proposed, based on one-dimensional species advection. The model is composed of two parts: first, a shear-layer model predicts the circulation feeding rate into the LEV; and second, a spanwise transport model initializes vorticity-containing mass with a finite circulation, allowing circulation to advect along the span with spanwise flow. No empirical data are necessary to inform the results of the model. As a proof of concept, both components of the proposed model are evaluated against a flat-plate delta wing. Using particle image velocimetry, the proposed shear-layer model is found to predict circulation flux into the LEV. Particle-tracking velocimetry is used to validate the spanwise transport of circulation. By allowing a vorticity-containing mass to advect with the spanwise flow, the model automatically satisfies the vorticity transport equation when vortex tilting and viscous diffusion are neglected. Neglecting the vortex tilting and viscous diffusion terms results in an error of approximately 10% of the spanwise advection, such that these terms are within the acceptable tolerance of a low-cost model. Thus, the proposed model is a computationally inexpensive tool for predicting circulation redistribution in flows with specific three-dimensional effects, providing a framework for broader parameter studies going forward.
Circulation Redistribution in Leading-Edge Vortices with Spanwise Flow
AIAA Journal ; 56 , 10 ; 3857-3862
2018-10-01
Article (Journal)
Electronic Resource
English
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