J.A. Sparenberg - Böcker

This work is an extended version of "Elements of Hydrodynamic Propulsion" (Martinus Nijhoff 1984), and treats many subjects in a more general way or with more far-reaching results. The theories discussed are mainly linear although, where appropriate, nonlinearity is considered. The subjects treated have four different aspects: (1) basic hydrodynamics, in which topics such as non-divergent dipole flow, a general lifting surface theory, the orthogonality property of the flow far behind a screw propeller and the roll-up of free vortex sheets; (2) optimization theory of lifting surface systems which leave behind as little kinetic energy as possible under the constraint of prescribed force actions; (3) application of optimization theory to screw propellers with or without end plates at the tips of their blades and to sculling propulsion by means of wings; and (4) fundamental problems concerning the existence or non-existence of optimum propellers, especially in the case of unsteady propulsion. It is suitable for naval architects and marine engineers whose work involves applying mathematics to propulsion problems, and applied mathematicians interested in hydrodynamics.

This work is an extended version of Elements of Hydrodynamic Propulsion (Martinus Nijhoff 1984), and treats many subjects in a more general way or with more far-reaching results. The theories discussed are mainly linear although, where appropriate, nonlinearity is considered. The subjects treated have four different aspects: (1) basic hydrodynamics, in which topics such as non-divergent dipole flow, a general lifting surface theory, the orthogonality property of the flow far behind a screw propeller and the roll-up of free vortex sheets; (2) optimization theory of lifting surface systems which leave behind as little kinetic energy as possible under the constraint of prescribed force actions; (3) application of optimization theory to screw propellers with or without end plates at the tips of their blades and to sculling propulsion by means of wings; and (4) fundamental problems concerning the existence or non-existence of optimum propellers, especially in the case of unsteady propulsion. For naval architects and marine engineers whose work involves applying mathematics to propulsion problems, and applied mathematicians interested in hydrodynamics.

This is a treatment of a number of aspects of the theory of hydrody­ namic propulsion. It has been written with in mind technical propulsion systems generally based on lift producing profiles. We assume the fluid, which is admitted in conventional hydrody­ namics, to be incompressible. Further we assume the occurring Reynolds numbers to be sufficiently high such that the inertia forces dominate by far the viscous forces, therefore we take the fluid to be inviscid. Of course it must be realized that viscosity plays an important part in a number of phenomena displayed in real flows, such as flow separation at the nose of a profile and the entrainment of fluid by a ship's hull. Another ap­ proximation which will be used in general is that the problems are linearized. In other words it is assumed that the induced disturbance velocities are sufficiently small, such that their squares can be neglected with respect to these velocities themselves. Hence it is necessary to evaluate the domain of validity of the results with respect to these two a priori assumptions. Anyhow it seems advisable to have first a good understanding of the linearized non-viscous theory before embarking on complicated theories which describe more or less realistic situations. For elaborations of the theory to realistic situations we will refer to current literature. In low Reynolds number flow, singular external forces and moments are very useful.