Story of the Week  
The Flow Induced Vibrations
 

Beyond a certain critical flow velocity, flow past a stationary object can become unsteady. It may also lead to a phenomenon called 'vortex shedding'. The unsteady 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 is studied.

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
Aerospace Engineering
Indian Institute of Technology Kanpur
    eMail: smittal@iitk.ac.in
    Web: http://home.iitk.ac.in/~smittal


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