A Unified Introduction to Fluid Mechanics of Flying and Swimming at High Reynolds Number
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Modeling the flow around a deformable and moving surface is required to calculate the forces exerted by a swimming or flying animal on the surrounding fluid. Assuming that viscosity plays a minor role, linear potential models can be used. These models derived from unsteady airfoil theory are usually divided in two categories depending on the aspect ratio of the moving surface: for small aspect ratios, slender-body theory applies while for large aspect ratios two-dimensional or lifting-line theory is used. This paper aims at presenting these models with a unified approach. These potential models being analytical, they allow fast computations and can therefore be used for optimization or control.
KeywordsPotential flow Unsteady airfoil theory Slender-body theory Lifting-line theory Lifting-surface integral Asymptotic methods
This work was sponsored by the French ANR under the project ANR-06-JCJC-0087.
- 3.Lighthill J (1987) Mathematical biofluiddynamics. SIAM, PhiladelphiaGoogle Scholar
- 6.Wu TY (2002) On theoretical modeling of aquatic and aerial animal locomotion. In: van der Giessen E, Wu TY (eds) Advances in applied mechanics, vol 38. Elsevier, Amsterdam, pp 291–353Google Scholar
- 13.Hadamard J (1932) Lectures on Cauchy’s problem in linear differential equation. Dover, New YorkGoogle Scholar
- 14.Mangler KW (1951) Improprer integrals in theoretical aerodynamics. Tech. Rep. Aero 2424, British Aeronautical Research CouncilGoogle Scholar
- 17.Watkins CE, Runyan HL, Woolston DS (1955) On the kernel function of the integral equation relating the lift and downwash distributions of oscillating finite wings in subsonic flow. Tech. Rep. TR-1234, NACAGoogle Scholar
- 23.Bisplinghoff RL, Ashley H, Halfman RL (1983) Aeroelasticity. Dover, New YorkGoogle Scholar
- 24.Theodorsen T (1935) General theory of aerodynamic instability and the mechanism of flutter. Tech. Rep. TR-496, NACAGoogle Scholar