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A wake model for free-streamline flow theory Part 1. Fully and partially developed wake flows past an oblique flat plate

Published online by Cambridge University Press:  28 March 2006

T. Yao-Tsu Wu
T. Yao-Tsu Wu
Affiliation:
California Institute of Technology, Pasadena, California
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Abstract

A wake model for the free-streamline theory is proposed to treat the two-dimensional flow past an obstacle with a wake or cavity formation. In this model the wake flow is approximately described in the large by an equivalent potential flow such that along the wake boundary the pressure first assumes a prescribed constant under-pressure in a region downstream of the separation points (called the near-wake) and then increases continuously from this under-pressure to the given free-stream value in an infinite wake strip of finite width (the far-wake). Application of this wake model provides a rather smooth continuous transition of the hydrodynamic forces from the fully developed wake flow to the fully wetted flow as the wake disappears. When applied to the wake flow past an inclined flat plate, this model yields the exact solution in a closed form for the whole range of the wake under-pressure coefficient.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 13 , Issue 2 , June 1962 , pp. 161 - 181
Copyright
© 1962 Cambridge University Press

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References

Acosta, A. J. 1955 A note on partial cavitation of flat-plate hydrofoils. Calif. Inst. Tech. Hydrodynamics Lab. Rep. no. E-19. 9.Google Scholar
Dawson, T. E. 1959 An Experimental investigation of a fully cavitating two-dimensional flat plate hydrofoil near a free surface. A. E. thesis, Calif. Inst. Tech.
Eppler, R. 1954 Beiträge zu Theorie und Anwendung der ünstetingen Strömungen. J. Rat. Mech. Anal. 3, 591.Google Scholar
Fabula, A. G. 1958 A note on the linear theory of cavity flows. (Unpublished.) Mechanics Branch, Office of Naval Research, Washington, D. C.
Fage, A. & Johansen, F. C. 1927 On the flow of air behind an inclined flat plate of infinite span. Proc. Roy. Soc. A, 116, 170–97.Google Scholar
Geurst, J. A. 1960 Linearized theory for partially cavitated hydrofoils. Intern. Shipb. Progr., 6, 369–84.Google Scholar
Geurst, J. A. & Timman, R. 1956 Linearized theory of two-dimensional cavitational flow around a wing section. IX Int. Congr. Appl. Mech., Brussels.Google Scholar
Gilbarg, D. & Serrin, J. 1950 Free boundaries and jets in the theory of cavitation. J. Math. Phys. 29, 1–12.Google Scholar
Joukowsky, N. E. 1890 I. A modification of Kirchhoff's method of determining a two dimensional motion of a fluid given a constant velocity along an unknown streamline. II. Determination of the motion of a fluid for any condition given on a streamline. Rec. Math. 25. (Also Collected works of N. E. Joukowsky, vol. III: Issue 3, Trans. CAHI, 1930.)Google Scholar
Kreisel, G. 1946 Cavitation with finite cavitation numbers. Admiralty Res. Lab. Rep. no. R 1/H/36.Google Scholar
Mimura, Y. 1958 The flow with wake past an oblique plate. J. Phys. Soc. Japan, 13, 1048–55.Google Scholar
Parkin, B. R. 1956 Experiments on circular-arc and flat-plate hydrofoils in non-cavitating and full cavity flows. Calif. Inst. Tech. Hydrodynamics Lab. Rep. no. 47-7. (See also: Experiments on circular-arc and flat-plate hydrofoils. 1958 J. Ship Res., 1, 34–56).Google Scholar
Parkin, B. R. 1959 Linearized theory of cavity flow in two-dimensions. The RAND Corporation, Santa Monica, Calif. Rep. no. P-1745.Google Scholar
Parkin, B. R. 1961 Munk integrals for fully cavitated hydrofoils. The RAND Corporation Rep. no. P-2350. (To appear in J. Aerospace Sci.)Google Scholar
Riabouchinsky, D. 1920 On steady flow motions with free surfaces. Proc. London Math. Soc., 19, 206–15.Google Scholar
Roshko, A. 1954 A new hodograph for free-streamline theory. NACA TN no. 3168.Google Scholar
Roshko, A. 1955 On the wake and drag of bluff bodies. J. Aero. Sci., 22, 124–32.Google Scholar
Silberman, E. 1959 Experimental studies of supercavitating flow about simple two-dimensional bodies in a jet. J. Fluid Mech., 5, 337–54.Google Scholar
Tulin, M. P. 1955 Supercavitating flow past foils and struts. Proc. Symp. on Cavitation in Hydrodynamics, N.P.L. Teddington. London: Her Majesty's Stationery Office.
Wu, T. Y. 1956a A free streamline theory for two-dimensional fully cavitated hydrofoils. J. Math. Phys., 35, 236–65.Google Scholar
Wu, T. Y. 1956b A note on the linear and nonlinear theories for fully cavitated hydrofoils. Calif. Inst. Tech. Hydrodynamics Lab. Rep. no. 21-22.Google Scholar