Unsteady propulsion

Abstract

In this chapter we discuss some aspects of unsteady propulsion. First we have to give a meaning to the expression “unsteady propeller”. The most simple one seems to be: a propeller is unsteady when no inertial reference frame exists with respect to which the induced flow is time independent. This however is not appropriate because then nearly all conceivable propulsion systems are unsteady with the only exception probably of the sails of a yacht in steady motion. Even such a reference frame does not exist for the screw propeller working in a homogeneous flow. A better description is: a propeller is unsteady when the fluid flow relative to its lifting surfaces is time dependent while this time dependency is essential for its functioning. The second part of this definition is vague to some degree, it is intended to exclude for instance the screw propeller in the wake behind a ship. Essential unsteady propulsion occurs in the case of the Voith-Schneider propeller (section 4.7), contra rotating propellers, the propulsion wheels of a paddle boat and the sculling by means of an oar. In nature almost all animal propulsion in water or in air is unsteady, the flapping motion of the tail of a fish or of the wings of a bird. Perhaps an exception is the “rotating” motion of the helicoidal tail of some species of bacteria which screw themselves through a fluid. In that case however the inertia forces of the fluid can be neglected with respect to the viscous forces (Stokes flow, Reynolds number of O(10-6)).