Numerical Simulation of Self-Propelled Steady Jet Propulsion at Intermediate Reynolds Numbers: Effects of Orifice Size on Animal Jet Propulsion

Most marine jet-propelled animals have low swimming efficiencies and relatively small jet orifices. Motivated by this, the present computational fluid dynamics study simulates the flow for a jet-propelled axisymmetric body swimming steadily at intermediate Reynolds numbers of order 1–1000. Results show that swimming-imposed flow field, drag coefficients, swimming efficiencies, and performance index (a metric comparing swimming speeds sustained by differently sized orifices ejecting the same volume flow rate) all depend strongly on orifice size, and orifice size affects the configuration of oppositely signed body vorticity and jet vorticity, thereby affecting wake and efficiency. As orifice size decreases, efficiencies decrease considerably, while performance index increases substantially, suggesting that, for a given jet volume flow rate, a smaller orifice supports faster swimming than a larger one does, albeit at reduced efficiency. These results support the notion that most jet-propelled animals having relatively small jet orifices may be an adaptation to deal with the physical constraint of limited total volume of water available for jetting, while needing to compete for fast swimming. Finally, jet orifice size is discussed regarding the role of jet propulsion in jet-propelled animal ecology, particularly for salps that use two relatively large siphons to respectively draw in and expel water.

TRANSLATIONAL-ROTATIONAL MOTION OF A NONSTATIONARY AXISYMMETRIC BODY

A nonstationary two-body problem is considered such that one of the bodies has a spherically symmetric density distribution and is central, while the other one is a satellite with axisymmetric dynamical structure, shape, and variable oblateness. Newton’s interaction force is characterized by an approximate expression of the force function up to the second harmonic. The masses of the central body and the satellite vary isotropically at different rates and do not occur reactive forces and additional rotational moments. The nonstationary axisymmetric body have an equatorial plane of symmetry. Thus, it has three mutually perpendicular planes of symmetry. The axes of its intrinsic coordinate system coincide with the principal axes of inertia and they are directed along the intersection lines of these three mutually perpendicular planes. This position remains unchangeable during the evolution. Equations of motion of the satellite in a relative system of coordinates are considered. The translational- rotational motion of the nonstationary axisymmetric body in the gravitational field of the nonstationary ball is studied by perturbation theory methods. The equations of secular perturbations reduces to the fourth order system with one first integral. This first integral is considered and three-dimensional graphs of this first integral are plotted using the Wolfram Mathematica system.