Hostname: page-component-78c5997874-t5tsf Total loading time: 0 Render date: 2024-11-10T07:16:51.918Z Has data issue: false hasContentIssue false
  • English
  • Français

Cavity-flow wall effects and correction rules

Published online by Cambridge University Press:  29 March 2006

T. Yao-Tsu Wu ,
Arthur K. Whitney  and
Christopher Brennen
T. Yao-Tsu Wu
Affiliation:
California Institute of Technology
Arthur K. Whitney
Affiliation:
California Institute of Technology
Christopher Brennen
Affiliation:
California Institute of Technology
Get access Rights & Permissions [Opens in a new window]

Abstract

This paper is intended to evaluate the wall effects in the pure-drag case of plane cavity flow past an arbitrary body held in a closed tunnel, and to establish an accurate correction rule. The three theoretical models in common use, namely, the open-wake, Riabouchinsky and re-entrant-jet models, are employed to provide solutions in the form of some functional equations. From these theoretical solutions several different rules for the correction of wall effects are derived for symmetric wedges. These simple correction rules are found to be accurate, as compared with their corresponding exact numerical solutions, for all wedge angles and for small to moderate ‘tunnel-spacing ratio’ (the ratio of body frontal width to tunnel spacing). According to these correction rules, conversion of a drag coefficient, measured experimentally in a closed tunnel, to the corresponding unbounded flow case requires only the data of the conventional cavitation number and the tunnel-spacing ratio if based on the open-wake model, though using the Riabouchinsky model it requires an additional measurement of the minimum pressure along the tunnel wall.

The numerical results for symmetric wedges show that the wall effects in-variably result in a lower drag coefficient than in an unbounded flow at the same cavitation number, and that this percentage drag reduction increases with decreasing wedge angle and/or with decreasing tunnel spacing relative to the body frontal width. This indicates that the wall effects axe generally more significant for thinner bodies in cavity flows, and they become exceedingly small for sufficiently blunt bodies. Physical explanations for these remarkable features of cavity-flow wall effects are sought; they are supported by the present experimental investigation of the pressure distribution on the wetted body surface as the flow parameters are varied. It is also found that the theoretical drag coefficient based on the Riabouchinsky model is smaller than that predicted by the open-wake model, all the flow parameters being equal, except when the flow approaches the choked state (with the cavity becoming infinitely long in a closed tunnel), which is the limiting case common to all theoretical models. This difference between the two flow models becomes especially pronounced for smaller wedge angles, shorter cavities, and with tunnel walls farther apart.

In order to gauge the degree of accuracy of these theoretical models in approximating the real flows, and t o ascertain the validity of the correction rules, a series of definitive experiments was carefully designed to complement the theory, and then carried out in a high-speed water tunnel. The measurements on a series of fully cavitating wedges at zero incidence suggest that, of the theoretical models, that due to Riabouchinsky is superior throughout the range tested. The accuracy of the correction rule based on that model has also been firmly established. Although the experimental investigation has been limited to symmetric wedges only, this correction rule (equations (85), (86) of the text) is expected to possess a general validity, at least for symmetric bodies without too large curvatures, since the geometry of the body profile is only implicitly involved in the correction formula. This experimental study is perhaps one of a very few with the particular objective of scrutinizing various theoretical cavity-flow models.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 49 , Issue 2 , 29 September 1971 , pp. 223 - 256
Copyright
© 1971 Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Ackerberg, R. C. 1970 Boundary layer separation at a free streamline. Proc. 2nd Int conf. on Numerical Methods in Fluid Mechanics, Berkeley, Calif.
Ai, D.K. 1966 The wall effect in cavity flows. Trans. ASME, J. Basic Eng. 88D, 132.Google Scholar
Allen, H. J. & Vincenti, W. G. 1944 Wall interference in a two-dimensional-flow wind tunnel with consideration of the effect of compressibility. NACA TR 782.Google Scholar
Armstrong, A. H. & Tadman, K. G. 1953 Wall corrections to axially symmetric cavities in circular tunnels and jets. Ministry of Supply A.R.E. Rep. 7–52.Google Scholar
Barr, R. A. 1966 An investigation of the cavity flow behind drag discs and supercavitating propellers. M.S. Thesis, University of Maryland.
Birkhoff, G. 1950 Hydrodynamics. Princeton University Press.
Birkhoff, G., Plesset, M. & Simmons, N. 1950 Wall effects in cavity flow I. Quart. Appl. Math., 8, 161.Google Scholar
Birkhoff, G., Plesset, M. & Simmons, N. 1952 Wall effects in cavity flow II. Quart. Appl. Math., 9, 413.Google Scholar
Birkhoff, G. & Zarantonello, E. H. 1957 Jets, Wakes and Cavities. Academic.
Brennen, C. 1969a Dynamic balances of dissolved air and heat in natural cavity flows. J. Fluid Mech., 37, 115.Google Scholar
Brennen, C. 1969b A numerical solution of axisymmetric cavity flows. J. Fluid Mech., 37, 671.Google Scholar
Campbell, I. J. & Thomas, G. E. 1956 Water tunnel boundary effects on axially symmetric fully developed cavities. Admiralty Res. Lab. R1-G-HY-18-1.Google Scholar
Cisotti, U. 1922 Idromeccanica Piana. Milan.
Cohen, H. & DiPrima, R. C. 1958 Wall effects in cavitating flows. Proc. 2nd Symp. on Naval Hydrodynamics, ACR-38. Washington, D.C.: Govt. Printing Office.
Cohen, H. & Gilbert, R. 1957 Two-dimensional, steady, cavity flow about slender bodies in channels of finite breadth. J. Appl. Mech., 24, 170.Google Scholar
Cohen, H., Sutherland, C. C. & Tu, Y. 1957 Wall effects in cavitating hydrofoil flow. J. Ship Res., 3, 31.Google Scholar
Cox, A. D. & Clayden, W. A. 1958 Cavitating flow about a wedge at incidence. J. Fluid Conf. Mech., 3, 615.Google Scholar
Dobay, G. V. 1967 Experimental investigation of wall effect on simple cavity flows. Proc. Symp. Testing Techniques in Ship Cavitation Research, 1, 175.Skipsmodelltanken, Trondheim, Norway.Google Scholar
Eppler, R. 1954 Beitrage zu Theorie und Anwendung der unstetigen Stromungen. J. Rat. Mech. Anal. 3, 591.Google Scholar
Fabula, A. G. 1964 Choked flow about vented or cavitating hydrofoils. Trans. ASME, J. Basic Eng. 86D, 561.Google Scholar
Gilbarg, D. 1949 Proc. Nat. Acad. Sci. U.S.A. 35, 609.
Gilbarg, D. 1961 Jets and cavities. Handbuch der Physik, 9, 311. Springer.
Glauert, H. 1933 Wind tunnel interference on wing, bodies, and air-screws. R & M. 1566.Google Scholar
Grove, A. S., Shair, F. H., Petersen, E. E. & Acrivos, A. 1964 An experimental investigation of the steady separated flow past a circular cylinder. J. Fluid Mech., 19, 60.Google Scholar
Gurevich, M. I. 1953 Proc. A. I. Mikoyan, Moscow Tech. Inst. of Fis. Ind. Econ. 5.
Joukowsky, N. E. 1890 A modification of Kirchhoff's method of determining a two dimensional motion of a fluid given a constant velocity along an unknown streamline. Rec. Math., 25. (Also 1936 Collected Works of N. E. Joukowsky 3, 195. Moscow).Google Scholar
Kiceniuk, T. 1964 A two-dimensional working section for the high speed water tunnel at the California Institute of Technology. ASME, Cau. Ree. Fac. Tech.Google Scholar
Meijer, M. C. 1967 Pressure measurement on flapped hydrofoils in cavity flows and wake flows. J. Ship. Res, 11, 170.Google Scholar
Meijer, M. C. 1969 Discussion of the Cavitation Committee Rep., 12th Int. Towing Tank Conf., Rome.
Morgan, W. B. 1966 The testing of hydrofoils and propellers for fully-cavitating or ventilated operation. Proc. 11th Int. Towing Tank Conf., Tokyo.Google Scholar
Pope, A. 1958 Wind Tunnel Testing (2nd edn.). Wiley.
Roshko, A. 1954 A new hodograph for free streamline theory. NCAA TN 3168.Google Scholar
Simmons, N. 1948 The geometry of liquid cavities with especial reference to the effects of finite extent of the stream. Ministry of Supply, A.D.E. Rep. 17–48.Google Scholar
Valcovici, V. 1913 Über discontinuierliche Flussigkeitsbewegungen mit zwei freien Strahlen. Thesis, Göttingen University.
Villat, H. 1914 Sur la validite des solutions de certains problemes d'hydrodynamique. J. Math. (6) 10, 231.Google Scholar
Waid, R. L. 1957 Water tunnel investigation of two-dimensional cavities. Calif. Inst. Of Tech. Rep. E-73.6.Google Scholar
Wang, D. P. & Wu, T. Y. 1963 Small-time behaviour of unsteady cavity flows. Arch. Rat. Mech. Anal., 14, 127.Google Scholar
Whitney, A. K. 1969 A simple correction rule for wall effect in two-dimensional cavity flow. Cavitation: State of Knowledge. New York: ASME.
Wu, T. Y. 1962 A wake model for free streamline flow theory. Part 1. Fully and partially developed wake flows and cavity flows past an oblique flat plate. J. Fluid Mech., 13, 161.Google Scholar
Wu, T. Y. 1968 Inviscid cavity and wake flows. Basic Developments in Fluid Dynamics (ed. M. Holt). Academic.
Wu, T. Y. & Wang, D. P. 1964a A wake model for free-streamline flow theory. Part 2. Cavity flows past obstacles of arbitrary profile. J. Fluid Mech., 18, 65.Google Scholar
Wu, T. Y. & Wang, D. P. 1964b An approximate numerical scheme for the theory of cavity flows past obstacles of arbitrary profile. Trans. ASME, J. Basic Eng. 86D, 556.Google Scholar
Wu, T. Y., Whitney, A. K. & Lin, J. D. 1969 Wall effect in cavity flows. Calif. Inst. of Tech. Rep. E-111A. 5.Google Scholar