On the Recurrence Signatures of Flapping Wings Exposed to Gusty Simple Shear Flow

  • Manabendra M. DeEmail author
  • J. S. Mathur
  • S. Vengadesan
Conference paper
Part of the Lecture Notes in Mechanical Engineering book series (LNME)


The primary aim of the research reported in this paper was to understand the effect of change of gusty simple shear inflow’s gradient on the force and moment patterns of a flapping wing in the 3D reference frame. A wing undergoing one degree of freedom asymmetric flapping and rectangular planform shape was considered. The gradient of the gusty simple shear inflow profile, Vgrad, was varied from –10 to +10 in steps of 5 and corresponding vertical and horizontal forces and moment about the flapping axis were computed. Time series of these forces and moment were used to plot the global recurrence plots and were compared. Quantitative analysis of the findings was carried out by the windowed recurrence quantification analysis of the force and moment patterns. Eight recurrence parameters, viz. recurrence rate, determinism, laminarity, trapping time, ratio, entropy, maximum line and trend were calculated and compared. Numerical investigations revealed that negative gusty shear gradient induced a considerable increase in vertical force and moment and marginally decreased the horizontal forces. Positive gusty shear gradient induced a marginal increase in horizontal forces but caused a substantial decrement in vertical force and moment.


1 DoF asymmetric flapping Gusty shear flow Pico aerial vehicle Global recurrence plots Windowed recurrence quantification analysis 


  1. 1.
    Lian Y, Shyy (2007) Aerodynamics of low Reynolds number plunging airfoil under gusty environment. In: 45th AIAA aerospace sciences meeting and exhibit, AIAA paper 2007-70.
  2. 2.
    Viswanath K, Tafti DK (2010) Effect of frontal gusts on forward flapping flight. AIAA J 48(9):2049–2062. Scholar
  3. 3.
    Prater R, Lian Y (2012) Aerodynamic response of stationary and flapping wings in oscillatory low Reynolds number flows. In: 50th AIAA aerospace science meeting including the new horizons forum and aerospace exposition, AIAA paper 2012-0418.
  4. 4.
    Sarkar S, Chajjed S, Krishnan A (2013) Study of asymmetric hovering in flapping flight. Eur J Mech B Fluids 37:72–89. Scholar
  5. 5.
    Zhu J, Jiang L, Zhao H, Tao B, Lei B (2015) Numerical study of a variable camber plunge airfoil under wind gust condition. J Mech Sci Technol 29(11):4681–4690. Scholar
  6. 6.
    Jones M, Yamaleev NK (2016) Effect of lateral, downward and frontal gusts on flapping-wing performance. Comput Fluids 140:175–190. Scholar
  7. 7.
    De MM, Mathur JS, Vengadesan S (2016) Numerical investigation of insect-sized flapping wings in inclined-stroke plane under the influence of spatio-temporally varying frontal gust, 61-istam-fm-fp-386. In: 61st Congress of the Indian society of theoretical and applied mechanics (an international conference), 11th–14th Dec 2016. VIT, VelloreGoogle Scholar
  8. 8.
    De MM, Mathur JS, Vengadesan S (2018) Recurrence perspective of forces generated by flapping wing under different frontal inflow conditions. In: NAFEMS Indian regional conference on engineering modelling, analysis, simulation and 3D printing (NIRC-2018), 20th–21st July 2018, BengaluruGoogle Scholar
  9. 9.
    Hong YS, Altman A (2008) Lift from spanwise flow in simple flapping wings. J Aircr 45:1206–1216. Scholar
  10. 10.
    Webber Jr CL, Marwan N (2015) Recurrence quantification analysis: theory and best practices. Springer, SwitzerlandGoogle Scholar

Copyright information

© Springer Nature Singapore Pte Ltd. 2020

Authors and Affiliations

  1. 1.CSIR-National Aerospace LaboratoriesBengaluruIndia
  2. 2.Indian Institute of Technology MadrasChennaiIndia

Personalised recommendations