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Effects of stroke deviation on the aerodynamics of the smallest flying insects

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Abstract

In this study, mathematical modeling of fluid flow and numerical simulations were used to determine the effects of adding small amplitude stroke deviation to the typical normal-hovering mode on the aerodynamics of small insect flight at Reynolds numbers (Re) in the range 4–20. Here, “small” implies that the ratio of surging to plunging amplitude is much less than unity. The immersed boundary method was used to solve the fully coupled fluid–structure interaction problem of a wing immersed in a two-dimensional viscous fluid. Different types of surging motion with a small amplitude were added to the typical normal-hovering mode that has no stroke deviation to generate two oval-shaped and two figure-eight trajectories. The results of this study suggest that for Re in the range 4–20, adding small amplitude stroke deviation to the typical normal-hovering mode has a modest influence on the time-averaged vertical force and aerodynamic efficiency. The impact on the instantaneous aerodynamic forces (pressure, viscous, and vertical forces), however, is considerable. This, in turn, is very likely to considerably alter the noise characteristics of the wing. The small impact on the time-averaged vertical force results from the trajectories with stroke deviation consisting of sub-intervals with large gains and sub-intervals with large losses in the instantaneous vertical force relative to the typical normal-hovering mode nearly offsetting each other. Adding small amplitude stroke deviation to the typical normal-hovering mode that is considered to be incapable of enabling flight at the scale of tiny insects does not seem to offer any significant benefit in terms of weight-supporting capability. Nevertheless, this study may inform the development of miniature drones that utilize the typical normal-hovering mode for staying aloft.

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Acknowledgements

High-Performance computing resources for this work were provided by the University of Arizona’s Research Data Center (RDC). The author thanks the anonymous reviewers for their constructive comments that greatly improved the manuscript.

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  1. Department of Aerospace and Mechanical Engineering, The University of Arizona, 1130 N Mountain Ave, Tucson, AZ, 85721, USA

    Hrithik Aghav

  2. Department of Mathematics, The University of Arizona, 617 N Santa Rita Ave, Tucson, AZ, 85721, USA

    Hrithik Aghav

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Appendix A: Variation of non-dimensional forces with dimensionless time for all the stroke patterns

Appendix A: Variation of non-dimensional forces with dimensionless time for all the stroke patterns

The following figures (Figures 33, 34, 35, 36, and 37) present the variation of \(C_\mathrm{{H}}\) and \(C_\mathrm{{V}}\) with non-dimensional time during the third and fourth stroke cycles for all the stroke patterns considered in this study.

Fig. 33
figure 33

a \(C_\mathrm{{H}}\) and b \(C_\mathrm{{V}}\) as a function of dimensionless time during the third and fourth stroke cycles for pattern A

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Fig. 34
figure 34

a \(C_\mathrm{{H}}\) and b \(C_\mathrm{{V}}\) as a function of dimensionless time during the third and fourth stroke cycles for pattern OU

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Fig. 35
figure 35

a \(C_\mathrm{{H}}\) and b \(C_\mathrm{{V}}\) as a function of dimensionless time during the third and fourth stroke cycles for pattern OD

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Fig. 36
figure 36

a \(C_\mathrm{{H}}\) and b \(C_\mathrm{{V}}\) as a function of dimensionless time during the third and fourth stroke cycles for pattern EU

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Fig. 37
figure 37

a \(C_\mathrm{{H}}\) and b \(C_\mathrm{{V}}\) as a function of dimensionless time during the third and fourth stroke cycles for pattern ED

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Aghav, H. Effects of stroke deviation on the aerodynamics of the smallest flying insects. J Eng Math 137, 4 (2022). https://doi.org/10.1007/s10665-022-10242-7

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