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Journal of Experimental Biology partnership with Dryad

Characteristics of vortex formation and thrust performance in drag-based paddling propulsion
Daegyoum Kim, Morteza Gharib

SUMMARY

Several characteristics of drag-based paddling propulsion are studied with a simple mechanical model and a measurement technique for mapping three-dimensional flow fields. In drag-based propulsion, the temporal change of the vortex strength is an important parameter in the relationship between vortex formation and thrust generation. Our results indicate that spanwise flow behind the paddling propulsor significantly affects tip vortex development and thrust generation. The distribution of spanwise flow is dependent on the propulsor shape and the Reynolds number. A delta-shaped propulsor generates strong spanwise flow compared with a rectangular propulsor. For the low Reynolds number case, spanwise flow is not as strong as that for the high Reynolds number case. Without sacrificing total impulse, the flexible propulsor can smooth out thrust peaks during sudden stroke motions, which is favorable for avoiding structural failures and stabilizing body motion. We also explored the role of stopping vortex shedding in efficient thrust generation by determining the relationship between stroke angles and total impulses generated by paddling propulsors.

  • LIST OF SYMBOLS

    A
    area on the z=0 plane
    A
    plate area
    c
    width of the plate
    Embedded Image
    mean width of the plate
    Cqn
    quasi-steady force coefficient acting normally on the plate surface
    CT
    thrust coefficient
    E
    Young's modulus
    EI
    non-dimensional flexural stiffness per unit width
    EId
    dimensional flexural stiffness per unit width
    F
    hydrodynamic force acting on the object
    Fqn
    total quasi-steady force acting normally on the plate surface
    h
    thickness of the plate
    I
    non-dimensional total impulse in the x-direction
    Ix
    non-dimensional impulse in the x-direction
    Embedded Image
    non-dimensional second moment of plate area with respect to the rotating axis
    s
    plate span length
    S
    vector of the surface spanned by the close vortex loop
    Sx
    area of S projected on the yz plane
    t
    non-dimensional time
    T
    stroke time of a plate during the power stroke
    td
    dimensional time
    u
    non-dimensional velocity
    ud
    dimensional velocity
    U
    characteristic velocity (=sΩ)
    V
    infinite flow field volume
    Vb
    body volume
    x
    non-dimensional coordinate
    xd
    dimensional coordinate
    α
    coordinate along the span of the plate from the base
    Γ
    non-dimensional circulation of a vortex
    Γd
    dimensional circulation of a vortex
    θ
    angle between the plate and the x=0 plane
    ρf
    fluid density
    ρm
    plate density
    τ
    integral variable for time
    φ
    stroke angle of the power stroke
    ω
    non-dimensional vorticity
    ωd
    dimensional vorticity
    Ω
    mean angular velocity of the motor during rotation
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