Beyond a certain critical flow velocity, flow past
a stationary object can become unsteady.
It may also lead to a phenomenon called 'vortex shedding'.
flow leads to time-varying forces on the object.
Under certain conditions, such as when the natural
frequency of the structure is sufficiently close to
the frequency of time-varying forces, the structure
might be induced into vibrating. This phenomenon is
encountered in various engineering applications
such as aeroelasticity, singing of electrical cables in high speed winds,
response of tall towers and chimneys to breeze.
The collapse of the ill fated Tacoma Narrows suspension bridge
on November 7, 1940 due to wind-induced
vibrations points to the relevance of proper accounting of wind loads in the
design of civil structures (more details on this bridge collapse
can be found at http://www.enm.bris.ac.uk/research/nonlinear/tacoma/tacoma.html).
At IIT Kanpur, Prof. Sanjay Mittal and his students are working
on understanding some basic aspects of Vortex-Induced Vibrations (VIV).
To reduce the complexity of the problem arising due to the geometries involved, flow
past a circular cylinder is considered. Despite its simple geometry,
flow past a circular cylinder exhibits all the rich fluid phenomena that
one encounters in flows around objects of much more complex shapes.
The cylinder is mounted on elastic supports; the stiffness, damping, inflow
velocity of the fluid and mass of the cylinder are parameters whose effect
The investigation is based on numerical modeling of the
fluid structure system. The fluid flow is governed by the Navier-Stokes
equations. The motion of the cylinder is modeled via a simple harmonic
oscillator which can vibrate in, both, in-line and cross-flow directions.
Stabilized finite element methods are employed to solve the governing
equations. A Deforming Spatial Domain/Stabilized Space Time (DSD/SST)
method is utilized to account for the deformation of the grid as the
cylinder moves around, in time. The large non-linear equation systems are solved
via an iterative procedure. For very large scale problems, the computations
are carried out on the 64 processor Linux Cluster that was funded by
Department of Science and Technology (DST).
The interaction between the fluid and structure is non-linear and
leads to very interesting phenomena. Compared to the flow past a
stationary object, its motion alters the flow significantly.
For example, the vortex shedding frequency and the strength of
vortices that are shed changes. Even the mode of shedding can
change as a result of the structural oscillations. As is typical
of non-linear systems, 'hysteresis' and 'intermittency' are
observed for certain range of parameters. In a very recent study
Dr. Mittal and his students have found that the lateral dimensions
of the domain of study (blockage) has a very significant impact
on the flow and structural vibrations. This seems to have been
largely ignored in the past investigations. In another study
they found that compared to a body on rigid supports the
critical inflow speed, at which the flow becomes unstable, is
much lower when the structure is mounted to elastic supports.
Shown below is an animation from a finite element simulation
of vortex-induced vibrations of a cylinder that is mounted
on elastic supports. The Reynolds number based on the free-stream
speed and diameter of the cylinder is 100. At this low Reynolds
number the flow is laminar. As a result of vortex shedding
the cylinder executes oscillations of amplitude that are
approximately 70% of its diameter.
Professor Sanjay Mittal
Indian Institute of Technology Kanpur