The Proceedings Fifth International Conference on Numerical Ship Hydrodynamics (1990) / Chapter Skim
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Theoretical Prediction of Midchord and Face Unsteady Propeller Sheet Cavitation
Theoretical Prediction of Midchord and Face Unsteady Propeller Sheet Cavitation
Pages 685-700
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From page 685... ...
Then, the cavitating hydrofoil problem is solved numerically bar cliscretizing Else problem into point source and vortex distributions and lay applying the boundary conditions at appropriately selected collocation points. I;`inally, the disrete vortex and source method is extendecl to predict unsteady propeller sleet cavitation with arbitrary miclchord a,ncl/or face deta,cl~ment.
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From page 686... ...
The leading edge correction has also been implemented in the formulation of the cav itating hydrofoil problem to account for the non-linear foil thickness effects t2.34. In the present work, the technique used in t214 for supercavitating hydrofoils is extended to treat superca`- and ities with arbitrary detachment on either Else suction side and/or the pressure side of the l~drofoil.
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From page 687... ...
The point of separation, s, may be found by considering the following two conditions: v Figure 2: Face detachment on a supercavitating hydrofoil 1. the pressure on the wetted foil surface must be greater than the cavity pressure 2.
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From page 688... ...
This can be seen in Figures 3 to 5, where the cavity shapes and the vorticity distributions as predicted by the presented analytical method, are shown for different detachment points. In Figure 3, the circulation distribution is negative at the trailing edge ~ A(s,l)
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From page 689... ...
The predicted cavity shapes and pressure distributions on the suction side are shown in Figures ~ to 11. The cavities in Figures 8 and 9 are unacceptable, because they intersect the foil surface.
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From page 690... ...
2.5 The Leading Edge Correction The linearized partial cavity theory is known to predict that, for given flow conditions, increasing the foil thicl:ness results in an increase in the cavity extent and volume. This is contrary to experimental evidence, the nonlinear theory [3.5]
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From page 691... ...
The cavity shapes O ax, as predicted by the linear theory, with or without th leading edge correction, are added normal to the foil and the produced foil geometry is analyzed with a potentia.l based panel method t17i, where the exact l;inema.tic boundary condition is applied on the exact foil or c< ity surface. The pressure clistril~ut.ions produced from the panel method are shown in Figures 1:3 arid 14, together with the linearized pressure dist~il~.~tio~.~.s from linear theory with or without tl-~e leading edge correction.
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From page 692... ...
The points Vs and X'p coincide with any of the source panel boundaries ,X'psi on the foil. By separating the total source q into the thickness source qC and the calcite source I, the corresponding boundary integral equations become: The kinematic boundary conditions 2 + 27r j; ~ - ~ ~ ~ do ~ = 0+ 0 < x < His c = vortex pOSitions I
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From page 693... ...
M - NP + N - NS - 1 dynamic boundary conditions · 1 cavity closure condition · 1 equation relating F~ to Qua The last equation, which relates the discrete singula.rities Qua and Hi, replaces the Fist d~nan~ic boundary condition [1Si. However, in the case of midchord detachment, there is no dynamic l~ounda.ry condition to be satisfied on the first source panel and this relation is not applied.
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From page 694... ...
The time.history of the cavity shapes is determined for each blade strip by applying the three-dimensional linearized unsteady cavity boundary conditions t25~. The extent of the cavity on each strip is detern~ined iteratively until the pressure on the cavity becomes equal to the vapor pressure Pa The effect of the other strips on tl~e same blade as shell as on the other I'lades is accounted for in an iterative sense.
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From page 695... ...
Detachment on the suction side, at 3.2% of the local chord; Blade angle = 12° from the top, An = 1.5, J = VSHIP/n/D = 0.8 f;7 Figure 21: Cavity shapes for propeller N4497 at blade sections No. 3, 5 and 7 as predicted by the modified PUF-3.
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From page 696... ...
· A numerical discrete vortex and source method hats been developed to predict the cavitation on h~drofoils with a.rbit~a.ry~ cavity detachment points. The numerical method has been extended to predict unsteady propeller sheet cavitation with arbitrary midchord and/or face cavity detachment.
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From page 697... ...
Leading edge corrections to the linear theory of partially cavitating hydrofoils. Submitted for publication, March 19S9.
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From page 698... ...
To determine the unknown UC+w for O ~ ~ ~ lo, the kinematic boundary condition 22 must be applied on the upper wetted part of the hydrofoil. Combining equations 22 with 21 it can be proven that `45' the condition 22 is equivalent to: qfx)
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From page 699... ...
The cavitation number, a, is obtained by applying the cavity closure condition 7. It can be shown that t9~: 31 = a0— with the following definitions: (65)
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From page 700... ...
We agree, however, that more physical model, is an open cavity model with the "openness" supplied from further knowledge of the cavity viscous wake. This "openness" does not affect much the predicted cavity shape and the cavitation number, in the case of supercavitating flows.
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