Skin-Friction Formula for Tapered and Delta Wings

ARNE BARKHEM

doi:10.2514/3.59424

Skin friction fields on delta wings

Experiments in Fluids ◽

10.1007/s00348-009-0686-6 ◽

2009 ◽

Vol 47 (6) ◽

pp. 897-911 ◽

Cited By ~ 20

Author(s):

S. A. Woodiga ◽

Tianshu Liu

Keyword(s):

Skin Friction ◽

Delta Wings

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On the High-Speed Porpoising Instability of a Prismatic Hull

Journal of Ship Research ◽

10.5957/jsr.1984.28.2.77 ◽

1984 ◽

Vol 28 (02) ◽

pp. 77-89 ◽

Cited By ~ 1

Author(s):

Peter R. Payne

Keyword(s):

Skin Friction ◽

High Speed ◽

Degrees Of Freedom ◽

Transient Solution ◽

Delta Wings ◽

Closed Form Solutions ◽

Wetted Area ◽

The Stability ◽

Transient Forces ◽

Vertical Impact

Simple closed-form solutions are obtained for the steady-state and transient forces and moments on a prismatic hull at speeds high enough for hydrostatic forces to be negligible and the chines to be above the undisturbed water surface ("chines dry"). We first show that this solution can be transformed to get the correct results for other hydrodynamic problems, such as the vertical impact of a wedge, a slender foil, or the two-dimensional planing of a flat plate. We then show that the full transient solution is essentially identical with Ribner's [1]2 equations for delta wings, except for terms which depend on the reduction in wetted width with heave. These results are employed to study the stability of such a hull on the assumption that only heave and pitch degrees of freedom are important, following the reasoning of Per̂ing [2]. In contradistinction to all four previous studies [2–5], the effect of skin friction is included and is found to be very powerful. If the center of gravity is above the centroid of the wetted area (which it generally is), then the effect of skin friction is stabilizing.

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Skin Friction Fields and Surface Dye Patterns on Delta Wings in Water Flows

Journal of Fluids Engineering ◽

10.1115/1.4030041 ◽

2015 ◽

Vol 137 (7) ◽

Cited By ~ 6

Author(s):

Tianshu Liu ◽

M. H. M. Makhmalbaf ◽

RS Vewen Ramasamy ◽

S. Kode ◽

P. Merati

Keyword(s):

Optical Flow ◽

Skin Friction ◽

Delta Wing ◽

Flow Equation ◽

Delta Wings ◽

Error Sources ◽

Water Flows ◽

Image Velocimetry ◽

Intensity Images ◽

The Relationship

This paper discusses the relationship between skin friction fields and surface dye patterns in surface luminescent dye visualizations in water flows, providing a theoretical foundation for extraction of high-resolution skin friction fields. The limiting form of the mass diffusion equation at a wall is recast as an optical flow equation connecting skin friction with the luminescent dye intensity. Snapshot solutions are obtained from a time sequence of luminescent intensity images by solving the optical flow equation via the variational method, and then a normalized skin friction field is reconstructed by averaging the snapshot solutions. An error analysis is given to identify the major error sources and the limitations of the technique. To evaluate the feasibility of this technique, surface luminescent dye visualizations on a 65 deg delta wing and a 76/40 deg double-delta wing are conducted in a water tunnel. The extracted skin friction topology on the delta wings and the velocity fields obtained by using particle image velocimetry (PIV) are discussed.

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