Analysis of Three-Dimensional Potential Flow Around a Ship Hull

Abstract

The method of singularities is applied for the solution of three-dimensi onal potential flow around arbitrarily shaped bodies. The three-dimensional bodies are represented by systems of singular functions with singularities placed inside the body. An optimization procedure was applied to determine the optimal locations of the singular functions. A rigorous treatment of the problem is presented to establish the validity of the mathematical formulation and the optimization procedure. The method developed here can be applied for analyzing flow around obstacles for which the singularities at the boundaries could not be treated efficiently using presently used techniques. Presented are computational considerations and numerical results showing the velocity distribution around a regularly shaped obstacle and for the bow of an icebreaker. URING recent years there have been various applica- tions of numerical methods for solution of potential flow problems around arbitrarily shaped bodies.l'5 Many of these methods have been essentially based on Prager's concept6 of representing the surface of a three-dimensional body in a flow by a surface distribution of vorticity. Such a vorticity field is approximated at a series of discrete points on the body. Hess and Smith 1»2 have demonstrated the applicability of surface distributions of singularities to the calculation of potential flows around ship hulls and aircraft fuselage-wing com- binations. This method has produced interesting numerical results. The procedure given here was developed during an in- vestigation of potential flow around an icebreaker ship. A considerable portion of the resistance encountered by a moving ice-breaker is due to motion of the broken ice pieces depending on the flow characteristics in the bow region. The influence of the geometric configuration of the bow is com- plex, and produces several near singularities in the flow. In addition to the consideration of the bow shape, nowadays it is desirable to include the effects of pitching motion of the ship, and sometimes to include even the effect of a bubbler system on the flow patterns. Inclusion of such features in an analysis requires an elaborate and accurate discretized representation of the hull geometry. Difficulties of such a nature can hinder the application of previously developed methods, particularly from the standpoint of computational efficiency. In the following, details of the mathematical analysis of the potential flow are discussed. Following the method of von Karman,7 the three-dimensional body is represented by a system of singular functions with singularities placed inside the body. However, compared to previous analyses, an op- timum configuration of such functions was sought with the intent to increase the efficiency of the method. The presen- tation of the mathematical derivation of the analysis is essen- tial for understanding both the method and its advantages. Numerical results were obtained which show the velocity distributions for a regularly shaped obstacle, a sphere, and for an irregularly shaped body, the bow of the USSC Mackinaw,