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Blockage correction with a free surface

Published online by Cambridge University Press:  19 April 2006

Kwang June Bai
Kwang June Bai
Affiliation:
David W. Taylor Naval Ship Research and Development Center, Bethesda, Maryland 20084
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Abstract

A simple analysis shows that with a disturbance present the potential jump in a steady flow in a canal is expressed in terms of (1) the effective volume (displaced volume and added mass/density of fluid) and (2) the depth Froude number for either a submerged body or a body with thin waterplane area. For a ship moving in a canal, the expression for potential jump contains a contribution from the line integral term along the intersection between the ship hull and the free surface. When a pressure distribution is given on the free surface, the potential jump can be expressed explicitly in terms of the depth Froude number and the total pressure force, regardless of the shape of the pressure distribution. From the present relations, the added mass of a ship in steady motion in a canal is computed from the potential jump computed previously by the author for various Froude numbers. This added mass plays an essential role in the equation of motion initially when a sudden external force is applied to a steady moving ship. The present analysis is complimentary to that of Newman (1976) and the extension of that to the three-dimensional case. As practical applications of the potential jump, which has had a limited interest, we proposed approximate formulas for speed correction and sinkage of a ship in a towing tank experiment. Also proposed is an approximate formula for the speed correction in a wind tunnel experiment. The present approximate formula is compared with ‘exact’ numerical results obtained by the localized finite element method for both towing tank and wind tunnel experiments. The present speed correction formula is also compared with existing approximate formulas for a wind tunnel experiment. The present formulas compare favourably with the exact numerical results.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 94 , Issue 3 , 16 October 1979 , pp. 433 - 452
Copyright
© 1979 Cambridge University Press

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References

Bai, K. J. 1975 A localized finite-element method for steady, two-dimensional free-surface flow problems. Proc. 1st Int. Conf. on Numerical Ship Hydrodyn. (ed. Schot and Salvesen), pp. 209–229. Gaithersburg, Maryland.
Eai, K. J. 1977 A localized finite-element method for steady three-dimensional free-surface flow problems. Proc. 2nd Int. Conf. on Numerical Ship Hydrodyn., Berkley, California.
Bai, K. J. 1978a A localized finite-element method for two-dimensional steady potential flows with a free surface. J. Ship Res. 22, 4.Google Scholar
Bai, K. J. 1978b A note on blockage correction. David W. Taylor Naval Ship R & D Center Ship Performance Dept. (DTNSRDC) Rep. 78/081.Google Scholar
Birkhoff, G. 1950 Hydrodynamics. Princeton.
Calisal, S. 1977 Effect of initial acceleration on ship wave pattern and wake survey method. J. Ship Res. 21, 239.Google Scholar
Chen, H. S. & Mei, C. C. 1975 Calculations of two-dimensional ship waves by a hybrid element method based on variational principles. Proc. 1st Int. Conf. on Numerical Ship Hydrodyn. (ed. Schot and Salvesen). Gaithersburg, Maryland.
Cummins, W. E. 1953 The forces and moments acting on a body moving in an arbitrary potential stream. DTMB Rep. no. 780.
Gross, A. & Watanabe, K. 1972 On blockage correction. Rep. Performance Committee, 13th Int. Towing Tank Conf., appendix 3.
Hughes, G. 1961 Tank boundary effects on model resistance. Trans. Roy. Inst. Naval Architects, 103, 421.Google Scholar
Kim, H. C. 1963 Blockage correction in a ship model towing tank. Univ. Michigan, College of Engng, Dept Naval Architecture, ORA Project no. 04542.
Kreitner, J. 1934 Über den Schiffswiderstand auf beschränktem Wasser. Zeitschrift Werft, Reederei, Hafen.
Landweber, L. 1956 On a generalization of Taylor's virtual mass relation for Rankine bodies. Quart. Appl. Math. 14, 51.Google Scholar
Landweber, L. 1974 Axisymmetric potential flow in a circular tube. J. Hydronaut. 8 (4), 137.Google Scholar
Landweber, L. & Nakayama, A. 1975 Effect of tank walls on ship model resistance. 14th Int. Towing Tank Conf. Canada, vol. 3, pp. 62–91.
Landweber, L. & Yih, C. S. 1956 Forces, moments and masses for rankine bodies. J. Fluid Mech. 1, 319.Google Scholar
Lamb, H. 1932 Hydrodynamics. 6th edn, p. 738. Cambridge University Press.
Newman, J. N. 1969 Lateral motions of a slender body between two parallel walls. J. Fluid Mech. 39, 97.Google Scholar
Newman, J. N. 1976 Blockage with a free-surface. J. Ship Res. 20, 199.Google Scholar
Newman, J. N. 1977 Marine Hydrodynamics. Cambridge, Mass.: MIT Press.
Ogiwara, S. 1975 Calculations of blockage effects. 14th Int. Towing Tank Conf., Ottawa, Canada, vol. 3, pp. 163–172.
Pope, A. 1947 Wind Tunnel Testing, p. 319. Wiley.
Tamura, K. 1972 Study on the blockage correction. J. Soc. nav. Archit. Japan 131.Google Scholar
Tamura, K. 1975 Blockage correction. 17th Int. Towing Tank Conf. Canada, vol. 3, pp. 173–182.
Taylor, G. I. 1928 The energy of a body moving in an infinite fluid, with an application to airships. Proc. Roy. Soc. A 120, 13.Google Scholar
Tuck, E. O. 1967 Sinkage and trim in shallow water of finite width. Schiffstechnik 4 (73), 92.Google Scholar
Wehausen, J. V. 1964 Effect of the initial acceleration upon the wave resistance of ship model. J. Ship Res. 7, 38.Google Scholar
Yeung, R. W. 1977 Hybrid integral-equation method for the steady ship-wave problem. Proc. 2nd Int. Conf. on Numerical Ship Hydrodynamics, Berkeley, California.