Passive and Self-Propelled Locomotion of an Elastic Swimmer in a Perfect Fluid

Alexandre Munnier (Institut Elie Cartan, Nancy - INRIA Nancy Grand-Est)

Alexandre Munnier (Institut Elie Cartan, Nancy - INRIA Nancy Grand-Est)

On this web site, we present the numerical simulations of which the details are provided in the paper:

- Passive and Self-Propelled Locomotion of an Elastic Swimmer in a Perfect Fluid (HAL)

Abstract: In this paper we
are interested in studying the free motion of a hyperelastic body (also
called swimmer) immersed in a perfect fluid. We derive the
Euler-Lagrange equations from the Least Action Principle of Lagrangian
Mechanics and prove that they are well-posed when the number of elastic
modes is finite. The recourse to a strain energy density function in
the modeling allows many different constitutive equations for the
hyperelastic material to be considered. We perform numerical
simulations, aiming to study passive locomotion (i.e. locomotion at
zero energy cost). As a first quite surprising result, we observe that
the swimmer does not even have to be elastic to experience passive
locomotion in its idealized environment. Indeed, we provide an example
of deformable (but non elastic) swimmer, for which the fluid-body
system behaves as an oscillating mechanical system. The shape changes
caused solely by the hydrodynamical forces on the body's boundary turn
out to be periodic strokes resulting in locomotion. This phenomenon can
be seen as a generalization, to deformable bodies, of the famous
D'Alembert's paradox (1752), claiming that the
drag force is zero on a rigid solid moving with constant velocity. Many
other examples of passive locomotion, involving different kind of
hyperelastic swimmers, are studied. A special interest is devoted
to the study of energy and impulse exchanges between the fluid
and the body.

In the last section, we assume that the swimmer has the ability
to modify its shape by means of internal forces. We prove that in this
case, the equations of motion are still well-posed and we illustrate
again with numerical simulations that, starting from rest,
self-propelled locomotion can be achieved.

In section Constitutive equations, we present some models for the hyperelastic material composing the swimmer. In Passive locomotion I, we explain how a swimmer which is not even elastic can experience passive locomotion. Plenty examples of locomotion strategies for hyperelastic swimmers are provided in section Passive locomotion II. We are mainly interested in studying the distribution of energy and of impulse between the fluid and the swimmer in section Energy / impulse distribution and in section Self-propelled swimming ball, we make a soft hyperelastic ball swim by means of internal forces.

Author supported by ANRs CISIFS and GAOS. All of the simulations and pictures have been realized with MATLAB (R2007a) - CSS design by Nicolas Fafchamps