Systematic investigation of a flapping wing in inclined stroke-plane hovering

The objective of the paper is to perform a systematic investigation of a flapping wing in inclined stroke-plane hovering which is observed in insects such as dragonflies, true hoverflies and Coleopteran. Numerical simulations are performed at pitch amplitudes (15° ≤ B ≤ 75°) in conjunction with other kinematic parameters such as stroke-plane inclination (10° ≤ β ≤ 80°), stroke amplitude (0.5 ≤ Ao/c ≤ 5), heave-pitch phase difference (− 45° ≤ φ ≤ 90°) and Reynolds number (15.7 ≤ Re ≤ 10,000). Moving mesh strategy implemented in finite volume code is used to simulate the flapping motion. The aerodynamic performance and vortex structures are obtained for each parametric space. Results indicate that the maximum time-averaged vertical force coefficient Cv¯\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\overline{{C_{\text{v}} }}$$\end{document} is obtained at B ≈ 30°–40°, β ≈ 52°–60°, Ao/c ≈ 2–4 and φ ≈ + 27°–+ 60°. On the other hand, the maximum lifting efficiency ηl is obtained at B ≈ 42°–57°, β ≈ 50°–70°, Ao/c ≈ 1–2 and φ ≈ 0°–+ 15°. Vortex structures show that the strength, growth and position of LEV and TEV play a significant role in the vertical force generation. To the best of author’s knowledge, this is the first work which has discussed the significance of pitch amplitude in inclined hovering insects. In addition, the best operating conditions are determined by mapping Cv¯\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\overline{{C_{\text{v}} }}$$\end{document} and ηl over a wide parametric space. The optimal parameters are then compared with the existing experimental results that show a good match.