A quasi-steady numerical modeling of wake capture for a hovering flapping wing

In this study, models for the wake capture lift and drag force coefficients of a hovering flapping wing were presented using numerical fluid dynamics simulation to improve the blade element theory. The investigated wing is inspired by the fruit fly and has combined flapping and pitching movements. The effect of changing the wing acceleration time at the start (ΔτA) and end of the half cycle (ΔτD), as well as the Reynolds numbers in the range of 136–6800, on wake capture using the Taguchi orthogonal array test design, is investigated using the numerical fluid dynamics method, and the values of average lift and drag coefficients due to wake capture are obtained. These force coefficients were applied to linear and nonlinear regression methods to obtain the mathematical model, and a model for its changes was extracted. Finally, to obtain the instantaneous coefficients, the extracted models were placed in the normal distribution function, and the final instantaneous model was obtained. Examining the verification cases of the application of these wake capture relationships with the blade element theory, as well as the effects of translational force, rotational force and added mass force, revealed that this developed theory is capable of correctly predicting the wake capture force’s initial peak. The force coefficient trend in the final quasi-steady model with wake capture is similar to the computational fluid dynamics (CFD) results, according to a qualitative examination of the lift and drag force coefficients in a half cycle. This demonstrates a significant result: this theory, which is divided into four parts: transnational, rotational, added mass and wake capture, adequately covers the general physics of these complex movements.