1,487 research outputs found
Drag cancellation by added-mass pumping
A submerged body subject to a sudden shape-change experiences large forces
due to the variation of added-mass energy. While this phenomenon has been
studied for single actuation events, application to sustained propulsion
requires studying \textit{periodic} shape-change. We do so in this work by
investigating a spring-mass oscillator submerged in quiescent fluid subject to
periodic changes in its volume. We develop an analytical model to investigate
the relationship between added-mass variation and viscous damping and
demonstrate its range of application with fully coupled fluid-solid
Navier-Stokes simulations at large Stokes number. Our results demonstrate that
the recovery of added-mass kinetic energy can be used to completely cancel the
viscous damping of the fluid, driving the onset of sustained oscillations with
amplitudes as large as four times the average body radius . A quasi-linear
relationship is found to link the terminal amplitude of the oscillations ,
to the extent of size change , with peaking at values from 4 to 4.75
depending on the details of the shape-change kinematics. In addition, it is
found that pumping in the frequency range of
is required for
sustained oscillations. The results of this analysis shed light on the role of
added-mass recovery in the context of shape-changing bodies and
biologically-inspired underwater vehicles.Comment: 10 pages, 6 Figures, under review in JFM Rapid
Rayleigh-B\'enard convection with a melting boundary
We study the evolution of a melting front between the solid and liquid phases
of a pure incompressible material where fluid motions are driven by unstable
temperature gradients. In a plane layer geometry, this can be seen as classical
Rayleigh-B\'enard convection where the upper solid boundary is allowed to melt
due to the heat flux brought by the fluid underneath. This free-boundary
problem is studied numerically in two dimensions using a phase-field approach,
classically used to study the melting and solidification of alloys, which we
dynamically couple with the Navier-Stokes equations in the Boussinesq
approximation. The advantage of this approach is that it requires only moderate
modifications of classical numerical methods. We focus on the case where the
solid is initially nearly isothermal, so that the evolution of the topography
is related to the inhomogeneous heat flux from thermal convection, and does not
depend on the conduction problem in the solid. From a very thin stable layer of
fluid, convection cells appears as the depth -- and therefore the effective
Rayleigh number of the layer increases. The continuous melting of the solid
leads to dynamical transitions between different convection cell sizes and
topography amplitudes. The Nusselt number can be larger than its value for a
planar upper boundary, due to the feedback of the topography on the flow, which
can stabilize large-scale laminar convection cells.Comment: 36 pages, 16 figure
Time-periodic weak solutions for the interaction of an incompressible fluid with a linear Koiter type shell under dynamic pressure boundary conditions
In many occurrences of fluid-structure interaction time-periodic motions are
observed. We consider the interaction between a fluid driven by the three
dimensional Navier-Stokes equation and a two dimensional linearized elastic
Koiter shell situated at the boundary. The fluid-domain is a part of the
solution and as such changing in time periodically. On a steady part of the
boundary we allow for the physically relevant case of dynamic pressure boundary
values, prominent to model inflow/outflow. We provide the existence of at least
one weak time-periodic solution for given periodic external forces that are not
too large. For that we introduce new approximation techniques and a-priori
estimates
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