Parametric Modelling of Vortex-Vortex Interactions in 2-DOF Flapping Wings using Empirical Methods

In our previous work, we performed numerical simulation using a dynamic mesh to analyze the wake structure over a pair of tandem dragonfly wings and further optimized their aerodynamic performance (energy-wise) with novel flapping kinematics. The input kinematics are selected as the mix of pure sinusoidal and periodic Eldredge functions. Our study found that both wings' combined vertical lift coefficient is 1.56 times more than their individual lift coefficients when summed up. Moreover, the hindwing experiences most of the enhancement in lift resulting from the vortex synergy interaction. We found the downwash-upwash wake interactions are insignificant in in-phase flapping, which agrees with previous studies.In our current work, we empirically model the Vortex-vortex interaction forces in a bid to improve the aerodynamic model of flapping wings. The results from our previous work suggested that the force enhancement experienced as a result of the vortex interactions can be modelled using a parameter k which is a function of the phase spacing (vertical alignment) and wing spacing (horizontal alignment), and the effect of k over a time period can be controlled using a piece-wise sigmoid function. A comparative study was performed over three different phase spacings of 0, 90 and 180 degrees, and four wing spacings of 0.1, 0.25, 0.5, and 1 c. It was found that though phase spacing and wing spacing are intertwined variables which inversely cancel each other, the magnitude of variation in each of the variables is considerably different and has significant ramifications on propulsive efficiency. It was found that the case with 90 degrees phase spacing and 0.1c wing spacing provided us with the best results for hovering and forward flight conditions with minor tradeoffs on power requirements and propulsive efficiency. Furthermore, 3D simulation was conducted on the 0 degrees phase spacing and 0.5c wing spacing (second closest contender case to optimal kinematics) to understand the effect of tip vortices on the hindwing. It was observed that the tip vortices from the forewing destructively interfere with the outer midspan vortices on the hindwing which are critical to generating lift. Hence, suggesting that the forewings must be longer in length to avoid its tip vortices interacting with the midspan vortices of the hindwings.