Considerations on similarity condition of wing deformation in flapping for model and mosquito wings

Abstract

In our previous paper, to simulate mosquito flapping flight, experiments were performed using a wing model, which had n-times (n=10) enlarged shape of the mosquito wing and was made of deformable elastic material. The similarity conditions of the flows around the model and mosquito wings were satisfied by means of the Reynolds number and Strouhal number. In order to satisfy the similarity condition of wing deformation, it was considered that the Cauchy number of the model and the real case are identical. As a result, the relationship 2 m m EI n E I  was obtained, where EI is the bending rigidity of the wing, and no-subscript and subscript m denote the model and mosquito wings, respectively. However, according to the experimental results, the deformation similarity was satisfied when m m EI E I  . This phenomenon was analyzed by means of vectorial dimensional analysis and discriminated dimensional analysis. On the similarity of flapping wings with bending deformation, two independent dimensionless parameters majorly influence the results: Cauchy number and mass ratio. If a relationship between these quantities could be derived, it would be possible to understand the similarity condition by means of a unique dimensionless parameter. Based on this consideration, a combined dimensionless parameter  was derived considering the experimental results. It was shown that, by matching the parameter  between the model and mosquito wings, deformation similarity was possible and the conflicting results on bending rigidity were resolved.