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The Seventh Asian Congress o(Fluid MechanicsDec 8 - 12, 1997, Chennai (Madras)FLOW INDUCED VIBRATION OF SINGLE AND MULTIPLECYLINDERSVinod Kumar Sanjay MittalDepartmentof AerospaceEngineering,DT Kanpur, Kanpur 208 016, ndia.

ABSTRACT Flow induced vibration of single and two cylinders, in tandemarrangement, s investigated using the stabilized space-time inite element method.The cylinders,mounted on lighiy dampedsprings,are allowed to vibrate in both in-lineand cross-flow directions. The flow is governed by he incompressibleNavier-Stokesequationswhile the motion of cylinders ollows the Newtons laws of motion for rigidbodies. For the single cylinder case, lock-in is observed and the cylin,der motionresembles he figure of 8. In the case of two cylinder arrangement, he upstreamcylinder oscillates n the samemanner as a single cylinder while for the downstreamcylinder one observes he phenomenonof wake induced flutter. Compared to theupstream cylinder, the downstream one undergoes larget: amplitude oscillations,especially n the in-line direction.

1. IntroductionFlow inducedvibration of cylinders s an important phenomenonn engineering lows; forexample, t occurs n flows that involve off-shore structures, ransmissioncableswith ~nconductors, win chimneystacks,heat exchanger ubes [1,2]. A fairly comprehensive tudyof cross-flow vibrations of a single cylinder in a uniform flow is reported in [3]. Here;results are reported for flow induced vibration of single and two cylinders, mounted onlightly dampedsprings, hat are allowed to vibrate in both in-line and cross-flow directions.2. FormulationStabilized space-time inite-elementmethod [3] is employed o solve the incompressibleNavier-Stoke~ equations n the primitive variables formulation. The space-timemethodenablesone to handle lows that involve moving boundariesand interfaces. In this methodthe variational formulation of the equations s written over the space-timedomain and thefinite element nterpolation functions dependon both spaceand time. The GLS (Galerkin'sLeast Squares) stabilization technique is employed to stabilize the computations againstspurious numerical oscillations and to enableone to u~e equal-order-interpolation elocity-pressureelements. The equation systems, esulting from the finite element discre~ization,are solved teratively by using the preconditionedG:MRES echnique.3. Results DiscussionThe cylinders reside n a rectangularcomputationaldomain whose upstreamboundary slocated at 5 cylinder diameters rom the center of the upstreamcylinder. The downstreamboundary s located 25 cylinder diametersaway rom the center of the downstreamcylinder.

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Fig. 2. Re = 324 flow past an oscillating cylinder: vorticity and pressure fields at theminimum, zero and maximum vertical displacement f the cylinder during one cycle ofmotion.

Fig. 3. Re= 100 flow past two oscillating cylinders: vorticity and pressure fields.

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