Hostname: page-component-5c6d5d7d68-wpx84 Total loading time: 0 Render date: 2024-08-09T15:05:34.415Z Has data issue: false hasContentIssue false

A numerical solution of axisymmetric cavity flows

Published online by Cambridge University Press:  29 March 2006

Christopher Brennen
Affiliation:
Ship Division, National Physical Laboratory Present address: California Institute of Technology, Pasadena.

Abstract

In the first part of the paper a method is developed for the relaxation or numerical solution of axisymmetric fully cavitating flows. Employing the technique suggested in a paper by Woods (1951 a) of working in a transformed (ϕ ϕ)-plane, solutions are obtained for cavities behind a disk and a sphere in different sizes of solid wall tunnel. Under certain conditions flow ‘choking’ occurs.

The results of a series of experiments carried out with such headforms are then reported. The apparent viscous effect on the position of separation from the sphere and thus on the drag proves to be of particular interest.

Type
Research Article
Copyright
© 1969 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

Armstrong, A. H. 1953 Abrupt and smooth separation in plane and asixymmetric flow. Memor. Arm. Res. Est. G.B. no. 22/63.Google Scholar
Armstrong, A. H. & Dunham, J. H. 1953 Axisymmetric cavity flow. Rep. Arm. Res. Est. G.B. no. 12/53.Google Scholar
Armstrong, A. H. & Tadman, K. G. 1954 Axisymmetric cavity flow about ellipsoids. Proc. of the Joint Admiralty-U.S. Navy Meeting on Hydroballistics.Google Scholar
Brennen, C. 1966 D.Phil. Thesis, University of Oxford.Google Scholar
Brennen, C. 1969 The dynamic balances of dissolved air and heat in natural cavity flows. J. Fluid Mech. 37, 115.Google Scholar
Birkhoff, G., Plesset, M. & Simmons, N. 1952 Wall effects in cavity flows, I. Q. appl. Math. 8, 151. Wall effects in cavity flows, II. Q. appl. Math. 9, 413.Google Scholar
Birkhoff, G. & Zarantonello, E. H. 1957 Jets, Wakes and Cavities. New York: Academic Press.Google Scholar
Eisenberg, P. & Pond, H. L. 1948 Water tunnel investigations of steady state cavities. David Taylor Model Basin Report, no. 668.Google Scholar
Fisher, J. W. 1944 The drag on a circular plate generating a cavity in water. Underwater Ballistics Commun. no. 17.Google Scholar
Gadd, G. E. & Grant, S. 1965 Some experiments on cavities behind disks. J. Fluid Mech. 23, 645.Google Scholar
Garabedian, P. R. 1955 The calculation of axially symmetric cavities and jets. Pacif. J. Math. 6.CrossRefGoogle Scholar
Hsu, E-Y. & Perry, B. 1954 Water tunnel experiments on spheres in cavity flow. Calif. Inst. of Tech. Report, no. E-24.9.Google Scholar
Konstantinov, V. A. 1950 Influence of Reynolds number on the separation (cavitation) flow. David Taylor Model Basin Translation, no. 233.Google Scholar
Lamb, H. 1932 Hydrodynamics. Cambridge University Press.Google Scholar
Plesset, M. S. & Shaffer, P. A. 1948 Cavity drag in two and three dimensions. J. appl. Phys. 19, 10.Google Scholar
Reichardt, H. 1945 The physical laws governing the cavitation bubbles produced behind solids of revolution in a fluid flow. The Kaiser Wilhelm Institute for Hyd. Res., Göttingen, Rep. UM 6628.Google Scholar
Riabouchinsky, D. 1920 On steady fluid motion with free surfaces. Proc. Lond. Math. Soc. 19, 202.Google Scholar
Rouse, H. & Mcnown, J. M. 1948 Cavitation and pressure distribution: headforms at zero angles of yaw. Bull. St. Univ. Iowa, Studies Engineering, no. 32.Google Scholar
Russell, D. B. 1963 The numerical solution of problems in fluid flow. Thesis, University of Oxford.Google Scholar
Silverleaf, A. 1960 Basic design of the N.P.L. no. 2 water tunnel. N.P.L. Ship Division, Rep. no. 15.Google Scholar
Southwell, R. V. & Vaisey, G. 1946 Fluid motions characterized by free streamlines. Phil. Trans. Roy. Soc. 240, 117.Google Scholar
Waid, R. L. 1957 Water tunnel investigations of two-dimensional cavities. Calif. Inst. Tech. Rep. no. E-73.6.Google Scholar
Woods, L. C. 1951a A new relaxation treatment of flow with axial symmetry. Quart. J. Mech. appl. Math. 4, 358.Google Scholar
Woods, L. C. 1951b The relaxation treatment of singular points in Poisson's equation. Quart. J. Mech. appl. Math. 6, 163.Google Scholar
Woods, L. C. 1961 The Theory of Subsonic Plane Flow. Cambridge University Press.Google Scholar