Twenty-First Symposium on Naval Hydrodynamics (1997) / Chapter Skim
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Asymptotic Solution of the Flow Problem and Estimate of Delay of Cavitation Inception for a Hydrofoil with a Jet Flap
Asymptotic Solution of the Flow Problem and Estimate of Delay of Cavitation Inception for a Hydrofoil with a Jet Flap
Pages 772-782
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From page 772... ...
e7ntng Free local pow, as solvea oy means of oarleman inversion formulae and Mellin transforms. It is shown that for practical case of small jet mo- 1 Introduction Plenty coefficients the farfield asympto ties of the local solution contains a square root singularity of The jet flap, formed by ~ high-speed jet of air or hydrodynamic loading at the trailing edge, which water injected from the trailing edge of the lifting is compatible tenth the "saddle-backed" character of surface, represents one of the effective devices of the loading for a jet flapped using observed in eloper- lift control accompanied by a drag reduction due intents The matching principle not only prompts to longitudinal component of the jet momentum, the increase of loading near the jet Rapped trailing 1.
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From page 773... ...
Comparing loading distributions for a wing with and without jet flap, one can easily conclude that for the Bane magnitude of the lift coefficient the ~naxi~num s,~ction at the leading edge is lower for the jet flapped wing. With use of Fourier method Spence had calculated 9 terms of the series decsribing the strength of the vortex layer with a square root singularity at he leading edge and logarithmic singularity at the trailing edge.
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From page 774... ...
In particular, part of the solution due to the angle of attack is represented by Prandtl-Birnbaum double series with a square root singularity at the leading edge arid square root zeros at the trailing edge and side edges. Representation of contribution of the jet flap into the loading differs due to the fact in compliance with the outer asymptotics of the local solution, there should be introduced in the outer solution a square root singularity at the trailing edge with the strength determined in terms of the jet deflection angle and momentum coeffi~Note, that an early 1956 in his investigation of the twos dimensional Bow problem for the case c)
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From page 775... ...
Additionally there should be satisfied upon the jet sheet a dynamic condition, according to which the pressure jump across the jet is proportional to the jet momentum coefficient Cub) and its longitudinal curvature at any cross section z =const.
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From page 776... ...
we can evaluate asymptotic dimension a = ~(z) of characteristic flow region e-ear the jet-flapped trailing edge from the order equation £~2 den ,'—Of do ~ (8)
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From page 777... ...
, Lighthill derived the following equation for W(S) and Press < 1/2 M' (S)
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From page 778... ...
, we derive from (53) deflection angle and jet momentum coefficients at the root chord cross section, yio(~' z)
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From page 779... ...
shows that for small magnitudes of the jet momentum coefficient Cj the pressure difference across the jet in the outer downstream region has the order of 0~0~. This means that for small Cj the contribution of the outer part of the jet sheetinto the lifting capacity of the jet flapped wing can be neglected.
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From page 780... ...
Fig. 2 illustrates the lift coefficient of a rectangular jet flapped wing versus the angle of attack cat for wing's aspect ratio ~ = 6.8, jet deflection angle r° = 31.3° and the jet momentum coefficient Cj = 0.42.
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From page 781... ...
where, as earlier, ~ is relative thickness of the foil, Ple = Pie/62, Ple is radius of curvature of the leading edge. In the case of small jet momentum coefficients.
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From page 782... ...
"Unsteady Plows Near Leading Edges of Lifting Surfaces: Pressures, Flow Separation, Cavities", Proc. Symposium "Bubble Noise and Cavitation Erosion in Fluid Systems" FED Vol.
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