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Performance Analysis of a Self-Propelling Flat Plate Fin with Joint Compliance

  • N. Srinivasa ReddyEmail author
  • Soumen Sen
  • Sumit Pal
  • Sankar Nath Shome
Original Contribution
  • 96 Downloads

Abstract

Fish fin muscles are compliant and they regulate the stiffness to suit different swimming conditions. This article attempts to understand the significance of presence of compliance in fin muscle with help of a flexible joint flat plate fin model. Blade element method is employed to model hydrodynamics and to compute the forces of interaction during motion of the plate within fluid. The dynamic model of self-propelling fin is developed through multi-body dynamics approach considering the hydrodynamic forces as external forces acting on the fin. The derived hydrodynamic model is validated with experiments on rigid flat plate fin. The effect of the joint stiffness and flapping frequency on the propulsion speed and efficiency is investigated through simulations using the derived and validated model. The propulsion efficiency is found to be highly influenced by the joint stiffness at a given flapping frequency. The fin attained maximum propulsion efficiency when the joint stiffness is tuned to a value at which flapping frequency matches near natural frequency of the fin. At this tuned joint stiffness and flapping frequency, the resulted Strouhal numbers are observed to fall within the optimum range (0.2 to 0.4) for maximized propulsion efficiency of flying birds and swimming aquatic animals reported in literature.

Keywords

Fish propulsion Caudal fin Propulsion efficiency Joint compliance Hydrodynamic force 

Notations

Ab

Projected area of the fin-carrying-body

Af

Plane area of the flapping fin

Ai

Area of the blade element i (i = 1, 2, 3,…, n)

Cd

Unsteady drag coefficient

CP

Input power coefficient

CT

Thrust coefficient

fd

Damped natural frequency

\({\text{F}}_{{{\text{AM}}_{\text{i}} }}\)

Added mass force acting on the blade element i

Fb

Total hydrodynamic force acting on the fin-carrying-body due to its motion

\({\text{F}}_{{{\text{d}}_{\text{i}} }}\)

Drag force acting on the blade element i

Fj

Hydrodynamic force acting along j-direction in global frame (j = X, Y, Z)

\({\bar{\text{F}}}_{\text{x}}\)

Average thrust force. Bar indicates averaging

Kθ

Joint stiffness

mb

Total mass of the fin-carrying-body including added mass

Pin

Motor input power

\({\bar{\text{P}}}_{\text{in}}\)

Average input power

ri

Distance of the blade element i from the axis of rotation

St

Strouhal number

\({\bar{\text{U}}}\)

Average propulsion speed

Uw

Oncoming water velocity

vi

Instantaneous velocity of the blade element i along its normal

Wmid

Wake width at the mid of the fin

θf

Fin angle

θm

Motor angle

τh

Hydrodynamic torque acting on the fin

τm

Motor torque

2hi

Height of the blade element i

a

Motor amplitude

b

Fin amplitude

dx

Width of each blade element

f

Frequency of oscillation/flapping

n

Total number of blade elements

t

Time

T

Time period of flapping cycle

U

Propulsion speed

αi

Instantaneous acceleration of the blade element i along its normal

β

Added mass factor

η

Propulsion efficiency or Froude efficiency

ρ

Density of the fluid media (water)

ϕ

Phase difference between the motor and fin angles

Notes

Acknowledgments

This work is carried out at CSIR-CMERI, Durgapur under the activities of the project (GAP-152812) funded by Department of Science and Technology, Government of India and the project UnWaR (ESC-0113) funded by Council of Scientific and Industrial Research (CSIR), Govt. of India.

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Copyright information

© The Institution of Engineers (India) 2017

Authors and Affiliations

  1. 1.CSIR-Central Mechanical Engineering Research InstituteDurgapurIndia

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