A vorticity-based model relating herringbone riblet geometric parameters to induced vorticity

Previous numerical and experimental parametric studies of the yaw angle and wavelength of the herringbone riblets have been carried out to understand the evolution of a pair of induced counter-rotating vortices. There is still a lack of theoretical models to quantitatively describe the mathematical relationship between the geometrical parameters of the riblet and the vorticity of the induced vortex pairs, which is even more important in the control of the downstream flow field from the point of view of guiding the forward design of the herringbone riblet and the organization of the flow structure in the boundary layer. Therefore, this paper describes the evolution process of the pair of counter rotating induce vortices based on the boundary vortex dynamics theory according to the flow field demonstrated in previous experiment. A theoretical model describing the mathematical relationship between the geometric parameters of the herringbone riblets and the vorticity of induce vortices is constructed, and then, verified by numerical simulation. The results demonstrate that the model accurately predicts the optimal wavelength, the optimal yaw angle, and the optimal immersion height for inducing the maximum vorticity. Based on the model, the customized design of herringbone riblets can be realized under flow deterioration conditions (e.g., separation of airfoils) based on local Reynolds number.