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TECHNICAL PAPERS

Scale Effect of Cavitation Inception on a 2D Eppler Hydrofoil

[+] Author and Article Information
E. L. Amromin

Mechmath LLC, Edmond, OK 73034e-mail: amromin@aol.com

J. Fluids Eng 124(1), 186-193 (Sep 13, 2001) (8 pages) doi:10.1115/1.1427689 History: Received November 09, 2000; Revised September 13, 2001
Copyright © 2002 by ASME
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References

Eppler, R., 1990, Airfoil Design and Data, Springer-Verlag, Berlin.
Garabedian,  P. R., and Spencer,  D. C., 1952, “Extermal methods in cavitation flow,” J. Rational Mech. Analysis, 1, pp. 309–320.
Dorange, P., Astolfi, J. A., Billard, J. Y. and Fruman, D. H., 1988, “Cavitation inception and development on two-dimensional hydrofoils,” Third Int. Symp. On Cavitation, Grenoble, Vol. 1, pp. 227–232.
Astolfi,  J. A., Dorange,  P., Billard,  J. Y., and Cid Tomas,  I., 2000, “An Experimental Investigation of Cavitation Inception and Development on a Two-Dimensional Eppler Hydrofoi,” ASME J. Fluids Eng., 122, pp. 164–173.
Huang,  T. T., and Peterson,  F. B., 1976, “Influence of Viscous Effects on Model/Full Scale Cavitation Scaling,” J. Ship Res., 20, pp. 215–223.
Billet,  M. L., and Holl,  J. W., 1981, “Scale Effects on Various Types of Limited Cavitation,” ASME J. Fluids Eng., 103, pp. 405–414.
Amromin,  E. L., 1985, “On Cavitation Flow Calculation for Viscous Capillary Fluid,” Fluid Dyn., 20, pp. 891–899.
Amromin,  E. L., 2000, “Analysis of Viscous Effects on Cavitation,” Appl. Mech. Rev., 53, pp. 307–322.
Jessup, S. D., and Wang, H. C., 1997, “Propeller design and evaluation for a high speed patrol boat incorporating iterative analysis with panel method,” SNAME Propeller/shafting ’97 Symp., Virginia-Beach, pp. 1101–1125.
Cox, B. D., Kimball, R. W. and Scherer, O., 1997, “Hydrofoil section with think trailing edges,” SNAME Propeller/Shafting ’97 Symp., Virginia-Beach, pp. 1801–1818.
Ivanov, A. H., 1980, Hydrodynamic of Developed Cavitating Flow, Sydostroenie, Leningrad (in Russian).
Kinnas, S. A., 1998 “The prediction of unsteady sheet cavitation” Third Intern. Symp. on Cavitation, Grenoble, Vol. 1, pp. 19–38.
Tulin, M. P., and Hsu, C. C., 1980, “New Application of Cavity Flow Theory,” 13 Symp. Nav. Hydr., Tokyo.
Brennen,  C. E., 1969, “A numerical solution for axisymmetric cavity flows,” J. Fluid Mech., 37, pp. 671–688.
Gakhov, F. D., 1966, Boundary Value Problems, Pergamon, New York.
Pellone,  C., and Rowe,  A., 1988, “Effect of Separation on Partial Cavitation,” ASME J. Fluids Eng., 110, pp. 182–189.
Arakeri,  V. H., 1975, “Viscous effects on the position of cavitation separation from smooth bodies,” J. Fluid Mech., 68, pp. 779–799.
Dupont, P., Parkinson, E., and Avellan, F., 1993, “Cavitation development in a centrifugal pump: numerical and model tests predictions,” ASME FED, Vol. 177, pp. 63–72.
Dieval, L., Arnaud, M., and Marcer, R., 1998, “Numerical modeling of unsteady cavitating flows by a VOF method.” Third Intern. Symp. on Cavitation, Grenoble, Vol. 2, pp. 243–248.
Yamaguchi,  H., and Kato,  H., 1983, “Non-linear theory for partially cavitating hydrofoils,” J. Soc. Nav. Arch. Jap., 152, pp. 117–124.
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Figures

Grahic Jump Location
Shape of hydrofoil E817
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Cavity leading (bottom) and trailing (top) edge abscissas past axissymmetric ellipsoid (2x/C-1)2+(4y/C)2=1: ▴-observations 11; author’s computation for ideal fluid is shown by solid curves, for viscous fluid-by dashed curves
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Comparison of computed and measured 26 cavity length for ITTC-body. Solid curve shows computed L, ▴ and ▪ show minimal and maximal observed L.
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Minimal pressure on E817 (♦) and NACA0012 (▪) in ideal fluid as function of α-α00=−4 degree for E817)
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Computed cavitation number as function of cavity length past disk. Author’s result (solid curve) is compared with Brennen’s 14 results (dashed curve)
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Sketch of partial cavity on a body in viscous fluid. Thin solid curve is body surface, thick solid curve is cavity surface. Boundary layer is limited by dashed curve, ▴-its separation section, ♦-its reattachment, ▪-XL.
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Comparison of L(σ) for EN-hydrofoil (α0=0) for α=4°. Solid curve-author’s computation, dashed curve-computation 21, ▴-measurements 20.
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Comparison of L(σ) for NACA-0010 hydrofoil (H=C, α=6.5 degree). Solid curve-author’s computation, dashed curve-computation 21, ▪-measurements 15.
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Cavitation inception number for body with semispherical head. Computed results are plotted by solid curve for body diameter D=0.05 m, by thick solid curve-for D=0.05 m and stimulated laminar-turbulent transition; by dashed curve-for D=0.02 m; by thick dashes-for D=0.4 m. Experimental data are shown: by ♦-for D=0.05 m 6; by ▪-for D=0.05 m and stimulated laminar-turbulent transition 28; by ▴-for D=0.4 m 27; by ×-for D=0.02 m 27.
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Computed dependencies σ1(α) for NACA-0012 hydrofoil in infinite flow: ♦-for ideal fluid curve-for FS (C=1 m, U=27 m/s), ▴-for MT (C=0.1 m, U=6.5 m/s)
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Cavitation inception number for E817 hydrofoil as function of the angle of attack. ▴-computation for ideal fluid with measured 3CL that implicitly (and incompletely) takes into account the wall influence on hydrofoil cavitation, ▪-computation for FS with measured 3CL, solid curve-computation for MT with CL (Re) and without an account of the wall effect, x-measured 4 data.
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Computed dependencies σI(CL) for E817 hydrofoil. Dashed curve relates to FS flow, solid curve-to MT.
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Computed cavity leading edges (solid curves) and trailing edges (dashed curves) on E817 hydrofoil at MT conditions (top; C=0.1 m and U=6.5 m/s) and FS conditions (bottom; C=1 m and U=27 m/s) for σ=σI
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Computed distribution Cp (dashed curve) and D * =100δ* (solid curve) on the pressure side of E817 hydrofoil at α=−6° for C=0.1 m and U=6.5 m/s
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Computed distribution of Cp (dashed curve) and D * =100δ* (solid curve) on the suction side of E817 hydrofoil with cavity of at α=4° for C=1 m and U=27 m/s
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Distributions of Cp in ideal fluid on NACA-0012 hydrofoil at α=4° (top) and on E817 at α=6° (middle) and at α=−6° (bottom)
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Error distributions along a axis-symmetric cavity affected by centrifugal force. Triangles corresponds to iteration number 10, curve to iteration number 30, squares to 90th iteration. Cavitator is located at x=15.

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