Twenty-Fourth Symposium on Naval Hydrodynamics (2003) / Chapter Skim
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Numerical Study on Propulsion by Undulating Motion in Laminar-Turbulent Flow
Numerical Study on Propulsion by Undulating Motion in Laminar-Turbulent Flow
Pages 806-818
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From page 806... ...
The flow is simulated by solving three-dimensional unsteady Reynolds averaged Navier-Stokes equation in a primitive value formulation, while the eddy-viscosity is described by algebraic model and transitional zone is computed by empirical formula. The numerical scheme is based on the MAC method where the RANS equation is solved by the time marching method on a body fitted coordinate system.
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From page 807... ...
numerically studied unsteady viscous flow field around a wavy oscillating plate in highly viscous fluid. They investigated the abilities of wavy oscillating plate to produce thrust in highly viscous fluid and the dependence of the wave number and nhase velocity on the thrust and propulsive efficiency.
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From page 808... ...
They applied the updated model for unsteady flow field given by the MIT flapping foil experiment and validated the model as an effective simulation for unsteady flow. Therefore in the present method, the updated model is used to calculate eddy viscosity v, in Equation (5~.
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From page 809... ...
H-type grid system is adopted, but near the leading edge the grid is modified to be adapted for the blunt body head. The numerical scheme is based on the MAC method where the momentum equation is solved by the time marching method on the body fitted coordinate system.
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From page 810... ...
, which are x-components of force coefficient given by Equation (6~. In Figure 4, Yend indicates the position of the trailing edge in y-direction.
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From page 811... ...
Table 3 shows the calculated self-propulsion condition at Re=1000' a=0.1' n=1.1. In Table 3' A is the maximum lateral excursion of the trailing edge of the plate and St is Strouhal number, defined by St=f xAlU (9)
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From page 812... ...
The time-averaged x-component of friction stress for various b is compared in Figure 9. It can be seen that the increase comes from the aft of the plate, where the larger frictional force zone enlarges with the increase of b.
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From page 813... ...
The increase of body thickness leads to the increase of phase velocity and the decrease of propulsive efficiency, which implies some advantages for slender swimmers. Laminar and turbulent flow around an undulating NACA0010 was investigated.
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From page 814... ...
.O 0.9= a) 0.8 .> _ 0.7 Q 0 0.6 Q - c _ 0.5 Figure 16: Variations of fictional force coefficient and propulsive efficiency with Reynolds number for NACAOO 10 Table 4: Drag reduction and propulsive efficiency for NACAOO10 at a=0.05 1, b=1.0 Figure 17 shows the distributions of unsteady local friction stress coefficients on the upside body surface during one undulating period at Re=2x 106.
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From page 815... ...
Meanwhile, the profiles at x=0.7617 are close to the logarithm law, but the undulation decreases the magnitude of the friction stress. O.On3 c o 0.2 0.4 0.6 0.8 1 X 4n 30 20 10 o rigid 0 0/8T 1/8T 2/8T D 3/8T ~ 4i8T ~20 a A/RT 30 10 an Figure 17: Distributions of local friction stress coefficient for NACAOO10 at R~2X 1 o6 1n o.s 0.8 0.7 0.6 ~0.5 <0.4 0.3 1 0.2 0.1 O— 0/8 The area between two dashed lines: transitional zone of rigid body The area between two solid curves: t~anstional zone of undulating body , 1/8 2/8 3/8 4/8 5/8 6/8 7/8 0.5 T Figure 18: Transition zone variations caused by undulation at Re=2x 1 o6 for NACAOO10 Figure 20 plots the variations of pressure gradient in x-direction at the mesh points most near the upside body surface.
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From page 816... ...
Turbulent flow simulation shows smaller frictional drag increase and higher propulsive efficiency, which implies again that the undulation can suppress turbulence. From cases 10 and 9, the propulsive efficiency enhances with the increase of Reynolds 11
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From page 817... ...
_ 0 0.2 0.4 0.6 0.8 1 X ~ () 0.2 0.4 X 0.6 0.8 1 Figure 25: Time-averaged x-component of pressure distributions atRe=103 and 2XlOs for a flat fish CONCLUSIONS The MAC method with a body fitted coordinate system is applied to simulate the laminar-turbulent flow around an undulating advancing body.
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From page 818... ...
Doi, Y and Yhomatsu, M., "Numerical Investigation on Thrust and Flow Generated by Wavy Oscillating Plate in Highly Viscous Fluid", Proceedings of The Eleventh International Symposium on Unmanned Untethered Submersible Technology, pp.
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