Scaling the propulsive performance of heaving and pitching foils

Scaling laws for the propulsive performance of rigid foils undergoing oscillatory heaving and pitching motions are presented. Water tunnel experiments on a nominally two-dimensional flow validate the scaling laws, with the scaled data for thrust, power and efficiency all showing excellent collapse. The analysis indicates that the behaviour of the foils depends on both Strouhal number and reduced frequency, but for motions where the viscous drag is small the thrust closely follows a linear dependence on reduced frequency. The scaling laws are also shown to be consistent with biological data on swimming aquatic animals.

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Unsteady Force Measurements on Fully Wetted Hydrofoils in Heaving Motion

Journal of Ship Research ◽

10.5957/jsr.1968.12.1.69 ◽

1968 ◽

Vol 12 (01) ◽

pp. 69-80

Author(s):

G. J. Klose ◽

A. J. Acosta

Keyword(s):

Theoretical Calculations ◽

Oscillation Amplitude ◽

Angle Of Attack ◽

Two Dimensional ◽

Force Measurements ◽

Unsteady Forces ◽

Reduced Frequency ◽

Unsteady Force ◽

Two Dimensional Flow ◽

Submergence Depth

An experimental investigation is reported of the unsteady forces due to heaving motion of fully wetted hydrofoils of unity aspect ratio and also in two-dimensional flow. The tests covered a broad range of reduced frequency and determined the effects of variation in submergence depth, angle of attack, oscillation amplitude, and flow velocity. In general, the findings agree well with available theoretical calculations, but some unexpected variations were found for the case of a wedge-shaped foil and for changes in angle of attack.

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A study of two-dimensional flow past regular polygons via conformal mapping

Journal of Fluid Mechanics ◽

10.1017/s0022112009006168 ◽

2009 ◽

Vol 628 ◽

pp. 121-154 ◽

Cited By ~ 9

Author(s):

ZHONG WEI TIAN ◽

ZI NIU WU

Keyword(s):

Reynolds Number ◽

Circular Cylinder ◽

Viscous Flow ◽

Strouhal Number ◽

Bifurcation Point ◽

Critical Reynolds Number ◽

Inviscid Flow ◽

Two Dimensional ◽

Regular Polygons ◽

Two Dimensional Flow

In this paper we study two-dimensional flow around regular polygons with an arbitrary but even number of edges N and one apex pointing to the free stream, with comparison to circular-cylinder flow. Both inviscid flow and low-Reynolds-number viscous flow are addressed. For inviscid flow, we obtained the exact solution for pure potential flow through Schwarz–Christoffel transformation, with the emphasis on the role of edge number, N, on the flow details. We also studied the behaviour, stationary lines and stability of vortex pair and found new stationary lines compared to circular cylinder. For viscous flow we derived the equation of stream function in the mapped (circle) domain, based on which approximate expressions for the critical Reynolds numbers and Strouhal number, as functions of the edge number, are obtained. The Reynolds number is based on the diameter of the circumscribed circle. For the steady flow, the first critical Reynolds number is a monotonically decreasing function of N, while N → ∞ corresponds to that for circular cylinder. The bifurcation point is ahead of the bifurcation point for circular cylinder. For unsteady flow, the critical Reynolds number for vortex shedding and the Strouhal number are both monotonically decreasing functions of N.

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Two-Dimensional Flow at Right Angles to a Flexible Membrane

Aeronautical Quarterly ◽

10.1017/s0001925900009173 ◽

1981 ◽

Vol 32 (3) ◽

pp. 243-269 ◽

Cited By ~ 3

Author(s):

B.G. Newman ◽

H.T. Low

Keyword(s):

Strouhal Number ◽

Incompressible Flow ◽

Separated Flow ◽

Experimental Results ◽

Two Dimensional ◽

Flexible Membrane ◽

Dimensional Flow ◽

Two Dimensional Flow ◽

Universal Correlation ◽

Membrane Density

SummaryIncompressible flow perpendicular to a flexible, impervious membrane has been studied for two-dimensional conditions. The membrane was mounted on relatively thin supports spaced c apart. Measurements of drag, base pressure and the frequency of membrane oscillation are presented for various lengths ℓ, and for two densities, of membrane. These parameters are related to one another theoretically and in particular Bearman′s universal correlation for Strouhal number agrees with the experimental results. It is found that for values of< 0.50 the drag is independent of membrane density. The drag decreases at larger values ofand this is related to a periodic reattachment of the separated flow to the back of the membrane. For a given ℓ the drag is greatest whenis very small and the membrane is almost flat.

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Numerical Water Tunnel in Two and Three Dimensions

Journal of Ship Research ◽

10.5957/jsr.1998.42.2.86 ◽

1998 ◽

Vol 42 (02) ◽

pp. 86-98

Author(s):

Jin Keun Choi ◽

Spyros A. Kinnas

Keyword(s):

Iterative Method ◽

Flow Velocity ◽

The Other ◽

Three Dimensions ◽

Water Tunnel ◽

Two Dimensional ◽

Tunnel Length ◽

Potential Formulation ◽

Perturbation Potential ◽

Two Dimensional Flow

The flow of a propeller inside of a tunnel is addressed. A numerical method is developed in which the flow inside the tunnel is treated via a potential based panel method. First, the method is applied to the two-dimensional flow of a hydrofoil inside of a tunnel. The total and the perturbation potential formulations are developed, and solved via a direct and an iterative method. The results from both formulations and solution schemes are found to converge very fast with the number of panels and truncated tunnel length. Then, the perturbation potential formulation is applied to the analysis of the flow of a propeller inside a tunnel. The propeller problem and the tunnel problem are solved separately, with the effects of one on the other being accounted for in an iterative manner. The equivalent unbounded flow velocity is calculated and compared with that predicted by Glauert.

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